{"id": "fd75f919cbb6-0", "text": "Park et al. (2023)\uf0c1\nTitle:\nFuture sea-level projections with a coupled atmosphere-ocean-ice-sheet model\nKey Points:\nPresents sea-level projections using an Earth system model of intermediate complexity where the model interacts with both the Greenland Ice Sheet and Antarctic Ice Sheet.\nExploration of potential sea-level contribution from these regions under SSP 1-1.9, 2-4.5, 5-8.5 future emission scenarios.\nThe model predicts ice-sheet contributions to global sea-level rise by 2150 of 0.2\u2009\u00b1\u20090.01, 0.5\u2009\u00b1\u20090.01 and 1.4\u2009\u00b1\u20090.1\u2009m  under SSP 1-1.9, 2-4.5, 5-8.5, respectively.\nOnly the most substantial climate mitigation scenario SPP1-1.9 avoids a long-term sustained sea-level contribution from Greenland and Antarctica.\nKeywords:\nSea-level rise, Climate modeling, Coupled atmosphere-ocean-ice-sheet model, Ice-sheet dynamics, Greenhouse warming simulations, Shared Socioeconomic Pathways, Antarctic Ice Sheet, Greenland Ice Sheet\nCorresponding author:\nJun-Young Park\nCitation:\nPark, J.-Y., Schloesser, F., Timmermann, A., Choudhury, D., Lee, J.-Y., & Nellikkattil, A. B. (2023). Future sea-level projections with a coupled atmosphere-ocean-ice-sheet model. Nature Communications, 14(1), 636. doi:10.1038/s41467-023-36051-9\nURL:\nhttps://www.nature.com/articles/s41467-023-36051-9\nAbstract\uf0c1\nClimate-forced, offline ice-sheet model simulations have been used extensively in assessing how much ice-sheets can contribute to future global sea-level rise. Typically, these model projections do not account for the two-way interactions between ice-sheets and climate. To quantify the impact of ice-ocean-atmosphere feedbacks, here we conduct greenhouse warming simulations with a coupled global climate-ice-sheet model of intermediate complexity. Following the Shared Socioeconomic Pathway (SSP) 1-1.9, 2-4.5, 5-8.5 emission scenarios, the model simulations ice-sheet contributions to global sea-level rise by 2150 of 0.2\u2009\u00b1\u20090.01, 0.5\u2009\u00b1\u20090.01 and 1.4\u2009\u00b1\u20090.1\u2009m, respectively. Antarctic ocean-ice-sheet-ice-shelf interactions enhance future subsurface basal melting, while freshwater-induced atmospheric cooling reduces surface melting and iceberg calving. The combined effect is likely to decelerate global sea-level rise contributions from Antarctica relative to the uncoupled climate-forced ice-sheet model configuration. Our results demonstrate that estimates of future sea-level rise fundamentally depend on the complex interactions between ice-sheets, icebergs, ocean and the atmosphere.\nIntroduction\uf0c1\nGlobal mean sea-level (SL) has risen over the past century by about 20\u2009cm, in part due to the thermal expansion of seawater, glacier and ice-sheet melt and changes in groundwater storage1,2,3. This trend is likely to accelerate in response to increasing atmospheric greenhouse gas concentrations and anthropogenic warming. With a considerable fraction of the world\u2019s population living near coastlines, it is crucial to provide accurate projections of global and regional future SL trends and constrain remaining uncertainties. The largest uncertainty originates from the response of the Antarctic ice-sheet (AIS) to greenhouse warming. Recent model-based estimates of the 21st century AIS contribution to future SL rise for a Representative Concentration Pathway (RCP) 8.5 scenario range from 0 to 1.4 m3,4,5,6,7,8.\nThese estimates were obtained with offline ice-sheet models that use atmospheric and oceanic forcings from future climate model projections. Accordingly, several issues need to be considered: (i) the transient and equilibrium climate sensitivities of the current generation of earth system models still have remaining uncertainties of 1.5\u20132.2\u2009K and 2.6\u20134.1\u2009K, respectively9, (ii) several processes such as iceberg calving or basal melting are not well constrained and represented; also different ice-sheet models show varying sensitivities to warming scenarios5,10,11, and (iii) the impact of climate-ice-sheet coupling is not included in offline ice-sheet model simulations, even though it may play an important role in Southern Hemisphere climate change12,13. Here, we present a new suite of coupled future earth system model simulations, which captures important interactions between atmosphere, ocean, ice-sheets, ice-shelves, and icebergs in both hemispheres.\nObservational data shows that AIS meltwater discharge has increased over the past decades14,15. This in turn can increase Southern Ocean (SO) stratification and subsurface warming due to reduced vertical heat exchange. Subsurface Southern Ocean (SSO) warming enhances sub-shelf melting16,17,18,19 which can lead to a reduction of the buttressing effect of ice-shelf on grounded ice20,21. As a consequence the flow of ice streams can accelerate toward the ocean22, which would translate to SL rise. These processes can be further amplified by other feedbacks, including the Marine Ice-Sheet Instability (MISI) along retrograde slopes23, hydrofracturing and the Marine Ice-Cliff Instability (MICI)5\u2014all of which remain poorly constrained8,10.\nTo quantify the effect of these interactions on future SL projections, one needs to employ coupled global climate-ice-sheet models24,25, which capture the complex interactions between climate components and ice-sheet, ice-shelf and iceberg dynamics and thermodynamics. Our study focuses on the AIS and Greenland ice-sheet (GrIS) contributions to future SL projections using an ensemble of simulations conducted with the coupled three-dimensional climate-ice-sheet-iceberg modeling system26 LOVECLIP (Supplementary Fig. S1). LOVECLIP is based on the climate model of intermediate complexity LOVECLIM27 and the Penn State University Ice-Sheet model (PSUIM)5,28,29. Biases of surface air temperature, precipitation, and SSO are corrected from LOVECLIM to PSUIM26. PSUIM is forced by surface air temperature, precipitation, evaporation, solar radiation, and annual mean subsurface ocean temperature. Surface air temperature and precipitation are downscaled vertically to PSUIM grid with applied lapse rate corrections28.\nThe simulations include an 8000-years-long coupled pre-industrial spin-up run for initialization and 10\u2009member ensemble of simulations forced by increasing CO2 concentrations following the Shared Socioeconomic Pathway (SSP) 1\u20131.9, 2\u20134.5 and 5\u20138.5 scenarios30 until 2150 CE. To further elucidate the effect of AIS meltwater flux on polar climate, the stability of the ice-sheets and SL we performed an additional idealized sensitivity experiment (Supplementary Table S1) for which we scaled the amplitudes of AIS liquid runoff and iceberg calving to balance net precipitation over Antarctica (experiment SSP5-8.5_MWOFF). In addition, to quantify the impact of AIS hydrofracturing and ice-cliff failure on the ice-sheet evolution, these parameterizations are turned off (CREVLIQ\u2009=\u20090 m per (m/year)\u22122 and VCLIF\u2009=\u20090\u2009km/year) with and without meltwater flux coupling (experiments SSP5-8.5_HFCMOFF and SSP5-8.5_MWHFCMOFF). Furthermore, to estimate the sensitivity of Antarctic ice-shelf mass loss to SSO warming, we doubled the sub-shelf SSO temperature anomaly (relative to 1850 CE) in the SSP5-8.5 scenario with (Re_SSP5-8.5_2xSOTA) and without meltwater fluxes (Re_SSP5-8.5_2xSOTA_MWOFF).\nResults\uf0c1\nRecent trend and interannual variability of GrIS and AIS\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/park23.html"}
{"id": "fd75f919cbb6-1", "text": "The simulations include an 8000-years-long coupled pre-industrial spin-up run for initialization and 10\u2009member ensemble of simulations forced by increasing CO2 concentrations following the Shared Socioeconomic Pathway (SSP) 1\u20131.9, 2\u20134.5 and 5\u20138.5 scenarios30 until 2150 CE. To further elucidate the effect of AIS meltwater flux on polar climate, the stability of the ice-sheets and SL we performed an additional idealized sensitivity experiment (Supplementary Table S1) for which we scaled the amplitudes of AIS liquid runoff and iceberg calving to balance net precipitation over Antarctica (experiment SSP5-8.5_MWOFF). In addition, to quantify the impact of AIS hydrofracturing and ice-cliff failure on the ice-sheet evolution, these parameterizations are turned off (CREVLIQ\u2009=\u20090 m per (m/year)\u22122 and VCLIF\u2009=\u20090\u2009km/year) with and without meltwater flux coupling (experiments SSP5-8.5_HFCMOFF and SSP5-8.5_MWHFCMOFF). Furthermore, to estimate the sensitivity of Antarctic ice-shelf mass loss to SSO warming, we doubled the sub-shelf SSO temperature anomaly (relative to 1850 CE) in the SSP5-8.5 scenario with (Re_SSP5-8.5_2xSOTA) and without meltwater fluxes (Re_SSP5-8.5_2xSOTA_MWOFF).\nResults\uf0c1\nRecent trend and interannual variability of GrIS and AIS\uf0c1\nAccording to satellite observations, the GrIS and AIS have been losing mass at a rate of ~286 Gt/year in 2010\u20132018 CE and ~252 Gt/year in 2009\u20132017 CE, respectively31,32. Quantifying the natural and anthropogenic contributions to this trend remains difficult because of our limited understanding of naturally occurring low-frequency ice-sheet dynamics and the relatively short observational period. Here we compare the observed 19-year trend of ice mass balance from the Gravity Recovery and Climate Experiment (GRACE)33 for the period 2002\u20132020 CE to the corresponding values in forced experiments as well as a 5000-year-long pre-industrial control run (CTR) (Supplementary Fig. S2) conducted with LOVECLIP (Fig. 1). In Fig. 1, each 19-year chunk of mass balance in CTR is cut after high-pass filtering over than 80 years and then, 19-year trends of nature variability are extracted. Those trends are expressed here in terms of sea-level-equivalent (SLE, 1\u2009m SLE\u2009=\u20093.62 \u00d7 1014 m3). Consistent with the GRACE measurements, changes in the mass balance are calculated only from the grounded parts of the ice-sheets for LOVECLIP. Interannual variability of the mass balance recorded by GRACE and simulated by the forced LOVECLIP experiments during 2002\u20132020 CE fall within the range of natural variability exhibited by the CTR (Supplementary Fig. S3). This indicates that the range of interannual mass balance changes of ice-sheets are represented realistically in the model simulation on the global scale. However, the observed GrIS 19-year trend (\u22120.075\u2009cm/year SLE) lies outside the respective 95% confidence interval range of CTR (Fig. 1a), which suggests that the current observed mass loss in Greenland is inconsistent with natural variability, as estimated from LOVECLIP. Although the simulated GrIS trend (\u22120.13 to \u22120.08\u2009cm/year SLE) is slightly overestimated than the observed GRACE estimate for the same period (Fig. 1a, red range), we can still conclude that greenhouse warming contributed to GrIS melting over the past decades. On the other hand, the AIS mass balance trend recorded by GRACE (\u22120.04\u2009cm/year SLE) and the forced AIS trend (\u22120.1 to \u22120.02\u2009cm/year SLE) lie within the 95% confidence range of the LOVECLIP CTR simulation due to the fact that AIS natural variability amplitude exceeds that of the GrIS by a factor of 7.\nFigure 1: 19-year trends of observed and simulated mass balance of Greenland ice-sheet (GrIS) and Antarctic ice-sheet (AIS). a Histogram of each extracted 19-year trend of Greenland mass balance after 80-year-high-pass filtering in the 5000-year-long pre-industrial control run (CTR, gray histogram) with 95% confidence interval range of CTR (black dashed line), and observed estimates of 19-year trend for 2002\u20132020 CE from the Gravity Recovery and Climate Experiment (GRACE)33 (blue dashed line) and simulated by the forced LOVECLIP ensemble (red line) in sea-level-equivalent (SLE); b same as a, but for Antarctica. Consistent with the GRACE measurements, mass balance terms for LOVECLIM are calculated in this figure using only the grounded ice-sheet portion.\nFuture change of global surface temperature and SL\uf0c1\nThe projected ensemble average of global surface temperature rise in 2100 CE (2150 CE) relative to the pre-industrial levels (1850\u20131900 CE) amounts to 1.4\u2009\u00b1\u20090.17\u2009\u00b0C (1.2\u2009\u00b1\u20090.14\u2009\u00b0C), 2.4\u2009\u00b1\u20090.15\u2009\u00b0C (2.7\u2009\u00b1\u20090.16\u2009\u00b0C) and 4.0\u2009\u00b1\u20090.15\u2009\u00b0C (5.3\u2009\u00b1\u20090.09\u2009\u00b0C) for the SSP1-1.9, SSP2-4.5, and SSP5-8.5 scenarios, respectively (Fig. 2a). The uncertainty values are calculated at 95% confidence interval in this paper. Relative to the recent past (1995\u20132014 CE) the simulated end-of-century warming (2081\u20132100 CE) attains values of 0.3\u2009\u00b0C for SSP1-1.9 and 2.6\u2009\u00b0C for SSP5-8.5, which is at the lower end of the multi-model range in projected changes obtained from the respective Coupled Model Intercomparison 6 (CMIP6) models34,35.\nFigure 2: Global surface temperature and sea-level (SL) projections, and their tendencies. a\u2013d Annual anomalies (relative to the 1850\u20131900 CE mean) of (a) the global surface temperature, (b) SL, and (c) SL contributions from the Greenland ice-sheet (GrIS) and (d) Antarctic ice-sheet (AIS). e\u2013h are the respective time derivatives of a\u2013d (change per year). Solid lines of a\u2013d indicate the ensemble mean and shading the ensemble range. The solid line in e represents the 9-year moving average of the time derivative of global surface temperature, with the dashed line indicating 0\u2009\u00b0C/year. Different colors represent the historical (black line; period 1850\u20132014 CE), and SSP1-1.9 (blue line), SSP2-4.5 (pink line), SSP5-8.5 (red line) and SSP5-8.5_MWOFF (orange line) simulations during the period 2014\u20132150 CE.", "source": "https://sealeveldocs.readthedocs.io/en/latest/park23.html"}
{"id": "fd75f919cbb6-2", "text": "The projected ensemble average of global surface temperature rise in 2100 CE (2150 CE) relative to the pre-industrial levels (1850\u20131900 CE) amounts to 1.4\u2009\u00b1\u20090.17\u2009\u00b0C (1.2\u2009\u00b1\u20090.14\u2009\u00b0C), 2.4\u2009\u00b1\u20090.15\u2009\u00b0C (2.7\u2009\u00b1\u20090.16\u2009\u00b0C) and 4.0\u2009\u00b1\u20090.15\u2009\u00b0C (5.3\u2009\u00b1\u20090.09\u2009\u00b0C) for the SSP1-1.9, SSP2-4.5, and SSP5-8.5 scenarios, respectively (Fig. 2a). The uncertainty values are calculated at 95% confidence interval in this paper. Relative to the recent past (1995\u20132014 CE) the simulated end-of-century warming (2081\u20132100 CE) attains values of 0.3\u2009\u00b0C for SSP1-1.9 and 2.6\u2009\u00b0C for SSP5-8.5, which is at the lower end of the multi-model range in projected changes obtained from the respective Coupled Model Intercomparison 6 (CMIP6) models34,35.\nFigure 2: Global surface temperature and sea-level (SL) projections, and their tendencies. a\u2013d Annual anomalies (relative to the 1850\u20131900 CE mean) of (a) the global surface temperature, (b) SL, and (c) SL contributions from the Greenland ice-sheet (GrIS) and (d) Antarctic ice-sheet (AIS). e\u2013h are the respective time derivatives of a\u2013d (change per year). Solid lines of a\u2013d indicate the ensemble mean and shading the ensemble range. The solid line in e represents the 9-year moving average of the time derivative of global surface temperature, with the dashed line indicating 0\u2009\u00b0C/year. Different colors represent the historical (black line; period 1850\u20132014 CE), and SSP1-1.9 (blue line), SSP2-4.5 (pink line), SSP5-8.5 (red line) and SSP5-8.5_MWOFF (orange line) simulations during the period 2014\u20132150 CE.\nHigher surface temperatures increase ice-sheet surface melting and subsequent meltwater discharge, and ice-sheet calving in both hemispheres. For the SSP1-1.9, SSP2-4.5 and SSP5-8.5 scenarios the GrIS contributes about 12\u2009\u00b1\u20091, 18\u2009\u00b1\u20090.9 and 23\u2009\u00b1\u20091.6\u2009cm and the AIS adds 3\u2009\u00b1\u20090.8, 7\u2009\u00b1\u20091.4, and 15\u2009\u00b1\u20091.5\u2009cm to SL by the year 2100 relative to pre-industrial levels (Fig. 2c, d). 2100 CE (2150 CE) LOVECLIP simulates for the respective scenarios a total ice-sheet contribution to SL of 15\u2009\u00b1\u20090.9, 24\u2009\u00b1\u20091.3, 39\u2009\u00b1\u20092 (19\u2009\u00b1\u20091.4, 48\u2009\u00b1\u20091.4, 136\u2009\u00b1\u20096.2) cm (Fig. 2b). The GrIS and AIS contributions lie within the range of estimates obtained from uncoupled scenario-forced models for Greenland36,37,38 and Antarctica6,8,39,40. One factor impacting the LOVECLIP ice-sheet response is the relatively weak temperature sensitivity to greenhouse forcing compared to most CMIP6 models (Supplementary Fig. S8). With lower sensitivity, nonetheless, our LOVECLIP shows both Arctic and Antarctic amplification. On the other hand, CMIP6 models do not show the aspect of Antarctic amplification. From a climate sensitivity point of view, our model results can therefore be regarded as conservative estimates. Our simulated SL is also substantially lower than the projected 1\u2009m end-of-century AIS contribution to SL presented in a series of offline ice-sheet model simulations conducted with the PSUIM5. In our coupled model simulations, which use the same ice-sheet model, but a different climate model, different ice-sheet and coupling parameters and at lower resolution, the rate of global temperature change slows down (negative second derivative with respect to time) around 2100 CE for SSP2-4.5 and SSP5-8.5 (Fig. 2a). This strongly contrasts the continued acceleration (positive second derivative) of SL (Fig. 2b) for these scenarios. This behavior illustrates the combined effect of long response timescales of the ice-sheets, the effect of positive feedbacks and their prolonged contribution to SL, even long after CO2 emissions have started to decline. Reductions in future greenhouse gas emissions can help slowdown global warming trends for the high-end emission scenarios (Fig. 2e). However, they are unlikely to stop the ice-sheet-driven SL rise acceleration (Fig. 2f\u2013h) and the apparent run-away in SL for the next 130 years. Only the much more aggressive SSP1-1.9 scenario can lead to a gradual slow-down of SL rise acceleration (Fig. 2f), which implies that, according to our simulations, the 2\u00b0C warming (above the pre-industrial level) target emphasized by the Paris agreement41 is insufficient to prevent accelerated SL rise over the next century [42].\nIce loss from GrIS and AIS\uf0c1\nIn our model simulations, future warming leads to an increase in snow accumulation and ice thickness in the central part of GrIS (Fig. 3c\u2013e, Fig. 4a) and West Antarctica (Fig. 3f\u2013h, Fig. 4e). However, the negative mass balance terms together are considerably larger (Fig. 4b\u2013d, f\u2013h), leading to a net projected 80-year mass loss for the different scenarios of 14\u2009\u00b1\u20091.5, 20\u2009\u00b1\u20090.9 and 25\u2009\u00b1\u20091.5\u2009cm SLE for GrIS and 46\u2009\u00b1\u20096, 94\u2009\u00b1\u20098 and 152\u2009\u00b1\u20098\u2009cm for AIS, respectively (Fig. 3a, b). Although the AIS shows significantly more ice melting until 2100 CE in comparison to the GrIS, its contribution to SL is similar or even lower (Fig. 2c, d) because most of the GrIS melting occurs at the surface as ice ablation (Fig. 3d, e, Fig. 4b), whereas the AIS loses mass primarily below-SL and at the shelves through melting and calving, especially in the Ross ice-shelf and Ronne-Filchner ice-shelf regions (Fig. 3g, h, Fig. 4g, h). Ice-shelf and submarine ice-loss do not directly contribute to SL rise (except for marginal contributions from the difference in ice and seawater density). In our simulations warmer Circumpolar Deep Water (CDW) reaches the continental shelf regions which in turn increases basal melting, sub-shelf melting and potential grounding line retreat (Fig. 3g, h). Due to the larger extent of ice-shelves, basal melting is more important for the AIS than for the GrIS (Fig. 4c, g). Note that global coarse-resolution ocean models, such as the one used here with a 3\u00b0\u2009\u00d7\u20093\u00b0 degree horizontal resolution cannot fully resolve the small-scale coastal ocean circulation processes around Antarctica43 and ignore sub-cavity flows, which are important to explicitly resolve basal melting processes. In our modeling framework basal melting is parameterized using open ocean temperatures interpolated on the finer ice-sheet model grid28.\nFigure 3: Projected changes in mass balance, ice thickness and subsurface ocean temperature. a, b Time series of the annual mean (a) Greenland ice-sheet (GrIS) and (b) Antarctic ice-sheet (AIS) net mass balance in sea-level-equivalent (SLE) (including contributions from ice shelves), respectively; c GrIS 1850\u20131860 CE mean ice thickness (grayscale colormap) and 400\u2009m Arctic Ocean (AO) temperature (red-yellow colormap); d 2090\u20132100 CE change in SSP5-8.5 scenario of GrIS ice thickness with respect to 1850\u20131860 CE and change in mean AO subsurface temperature; e same as d, but for period 2140\u20132150 CE; f, g same as c\u2013e, but for AIS with 400\u2009m Southern Ocean (SO) temperature. Black contours indicate simulated grounding lines for different periods. Cyan contours indicate the edge lines of ice-shelves for different periods.", "source": "https://sealeveldocs.readthedocs.io/en/latest/park23.html"}
{"id": "fd75f919cbb6-3", "text": "Figure 3: Projected changes in mass balance, ice thickness and subsurface ocean temperature. a, b Time series of the annual mean (a) Greenland ice-sheet (GrIS) and (b) Antarctic ice-sheet (AIS) net mass balance in sea-level-equivalent (SLE) (including contributions from ice shelves), respectively; c GrIS 1850\u20131860 CE mean ice thickness (grayscale colormap) and 400\u2009m Arctic Ocean (AO) temperature (red-yellow colormap); d 2090\u20132100 CE change in SSP5-8.5 scenario of GrIS ice thickness with respect to 1850\u20131860 CE and change in mean AO subsurface temperature; e same as d, but for period 2140\u20132150 CE; f, g same as c\u2013e, but for AIS with 400\u2009m Southern Ocean (SO) temperature. Black contours indicate simulated grounding lines for different periods. Cyan contours indicate the edge lines of ice-shelves for different periods.\nFigure 4: Individual mass balance terms for Greenland ice-sheet (GrIS) and Antarctic ice-sheet (AIS). a\u2013d Represent the individual GrIS mass balance terms for (a) the accumulation, (b) surface melting, (c) basal melting and (d) ice calving expressed as sea-level-equivalent (SLE) per year; e\u2013h same as a\u2013d, but for AIS. Solid lines indicate the ensemble mean and shading the ensemble range. Different colors represent the historical (black line; period 1850\u20132014 CE), and SSP1-1.9 (blue line), SSP2-4.5 (pink line), SSP5-8.5 (red line) and SSP5-8.5_MWOFF (orange line) simulations during the period 2014\u20132150 CE.\nAccording to our numerical experiments, the Ross ice-shelf completely disappears in the SSP5-8.5 scenario after 2100 CE (Fig. 3g, h). At this time basal melting and calving rates peak (Fig. 4g, h). A secondary simulated increase in these fluxes at the beginning of the 22nd century is associated with an accelerated retreat of the Ronne-Filchner ice-shelves (Figs. 3h, 4g, h). Even though the AIS contribution to SL rise is initially smaller than that of the GrIS (before 2100 CE), the rapid loss of stabilizing ice-shelves leads to a gradual increase of ice flow across the grounding lines that will initiate positive ice-sheet feedbacks associated with the MISI23, hydrofracturing and MICI5,29. The AIS calving fluxes, which attain values of ~2\u2009cm/year SLE by 2080 CE (corresponding to a freshwater flux into the ocean of ~0.34\u2009Sv; 1\u2009Sv = 106 m3/s), dominate the negative mass balance and global SL contribution. The accelerated mass loss over the AIS is related to a combination of surface melting, basal melting and grounding line retreat which contributes to the massive ice calving fluxes (Fig. 4f\u2013h) \u2013 each component with their individual temporal contributions to the total freshwater and SL effect.\nIn contrast to the AIS, the GrIS shows a gradual decrease in basal melting and ice calving fluxes (Fig. 4c, d), interrupted only by an abrupt GrIS ice calving event around 2090 CE in SSP5-8.5, which is associated with a complete loss of small ice-shelf areas. In Greenland the dominant mass loss and the contribution to SL are due to the positive trend in surface melting, which attains values of up to 2.1\u2009\u00b1\u20090.3\u2009cm/year SLE by 2150 CE (Fig. 4b)\u2014a ~30-fold increase compared to the recent observed interannual rates of GrIS mass loss (Supplementary Fig. S3a).\nIce-sheet/climate feedbacks in Southern Hemisphere\uf0c1\nTo further quantify the effects of climate-ice-sheet coupling in the Southern Hemisphere, and test the previously hypothesized positive CDW/MISI feedback16,17,18,19,44 we performed idealized SSP5-8.5 ensemble sensitivity experiments in which the freshwater coupling from the Antarctic meltwater is decoupled (experiment SSP5-8.5_MWOFF). Increased AIS meltwater fluxes in the fully coupled model experiment (experiment SSP5-8.5) reduce surface ocean salinity in the SO relative to SSP5-8.5_MWOFF (Fig. 5a). In turn this increases ocean stratification and reduces vertical heat exchange between cold surface and warmer subsurface waters. As a result, annual mean subsurface temperatures around Antarctica increase by 1.5\u2009\u00b0C over the 21st century in SSP5-8.5 (Fig. 5b). In contrast, in SSP5-8.5_MWOFF the AIS melting does not directly impact the SO stratification, which leads to a temporary 30% reduction in subsurface ocean warming (Fig. 5b) and a 50% reduction in basal melting (Fig. 4g). At the surface, increased stratification in SSP5-8.5 and reduced vertical heat exchange lead to cooling and increased sea-ice production6,12,13,45 (Fig. 5d), relative to the SSP5-8.5_MWOFF experiment. The 21st century annual mean surface air temperatures around Antarctica are about 1.4\u2009\u00b0C colder in SSP5-8.5 as compared to SSP5-8.5_MWOFF (Fig. 5c). This cooling effect provides a negative feedback for AIS surface melting6,42. Moreover, without meltwater coupling temperatures, precipitation and snow accumulation increase over Antarctica by about 0.1\u2009cm/year SLE (Fig. 4e) around 2100 CE. At the ice-sheet margins, higher temperatures and increased precipitation in SSP5-8.5_MWOFF contribute to hydrofracturing and the simulated increased calving rates5 (Fig. 4h). Overall, in the fully coupled simulation reduced surface melting (Fig. 4f) and calving rates (Fig. 4h) outweigh reduced accumulation rates, and hence the freshwater-induced surface cooling (Fig. 5c) provides a net-negative feedback to ice-sheet melting. As a consequence of the substantial differences in AIS mass balance between SSP5-8.5 and SSP5-8.5_MWOFF, the rate of total ice volume loss and the corresponding rate of SL contribution are decelerated when accounting for the fully coupled system (Fig. 2d, Fig. 3b) and the surface temperature effects (Fig. 2a). Although it has been suggested that AIS meltwater fluxes could remotely impact the GrIS via changes in Atlantic Meridional Overturning circulation and interhemispheric heat fluxes46, we do not find any noticeable changes in the GrIS response between SSP5-8.5 and SSP5-8.5_MWOFF. A higher-resolution climate simulation may be required to explain the teleconnection at the end of 21st century shown in Supplementary Fig. S6d.\nFigure 5: Climate-ice-sheet feedbacks in Southern Hemisphere. a\u2013c Annual anomalies (relative to the 1850\u20131900 CE mean) of (a) the Southern Ocean (SO) surface salinity, (b) 400\u2009m subsurface Southern Ocean (SSO) temperature and (c) surface air temperature averaged between 60\u00b0S and 90\u00b0S. d is the SO sea-ice area averaged between 60\u00b0S and 90\u00b0S. Solid lines indicate the ensemble mean and shading the ensemble range. Different colors represent the SSP5-8.5 (red line) and SSP5-8.5_MWOFF (blue line) simulations during the period 2014\u20132150 CE.\nWhen hydrofracturing and ice-cliff failure parameterizations are turned off in the additional model experiments (Supplementary Table S1), the AIS meltwater flux still decelerates global warming (experiments SSP5-8.5_HFCMOFF and SSP5-8.5_MWHFCMOFF, Supplementary Fig. S4a orange and blue lines). However, the negative and positive coupled feedbacks on SL rise related to the meltwater flux are more in balance (Supplementary Figs. S4b, S5). Despite meltwater and calving fluxes being substantially reduced relative to SSP5-8.5, the surface cooling is nearly as strong in SSP5-8.5_HFCMOFF, due to the cooling becoming less efficient with increasing meltwater flux amplitude13. Without hydrofracturing, however, increased surface temperatures and rainfall do not directly impact the calving flux, therefore surface temperature-related feedbacks are weaker (calving is still stronger in SSP5-8.5_MWHFCMOFF than in SSP5-8.5_HFCMOFF to compensate for changes in other fluxes, in particular reduced basal melting).\nSensitivity of subsurface Southern Ocean warming\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/park23.html"}
{"id": "fd75f919cbb6-4", "text": "Figure 5: Climate-ice-sheet feedbacks in Southern Hemisphere. a\u2013c Annual anomalies (relative to the 1850\u20131900 CE mean) of (a) the Southern Ocean (SO) surface salinity, (b) 400\u2009m subsurface Southern Ocean (SSO) temperature and (c) surface air temperature averaged between 60\u00b0S and 90\u00b0S. d is the SO sea-ice area averaged between 60\u00b0S and 90\u00b0S. Solid lines indicate the ensemble mean and shading the ensemble range. Different colors represent the SSP5-8.5 (red line) and SSP5-8.5_MWOFF (blue line) simulations during the period 2014\u20132150 CE.\nWhen hydrofracturing and ice-cliff failure parameterizations are turned off in the additional model experiments (Supplementary Table S1), the AIS meltwater flux still decelerates global warming (experiments SSP5-8.5_HFCMOFF and SSP5-8.5_MWHFCMOFF, Supplementary Fig. S4a orange and blue lines). However, the negative and positive coupled feedbacks on SL rise related to the meltwater flux are more in balance (Supplementary Figs. S4b, S5). Despite meltwater and calving fluxes being substantially reduced relative to SSP5-8.5, the surface cooling is nearly as strong in SSP5-8.5_HFCMOFF, due to the cooling becoming less efficient with increasing meltwater flux amplitude13. Without hydrofracturing, however, increased surface temperatures and rainfall do not directly impact the calving flux, therefore surface temperature-related feedbacks are weaker (calving is still stronger in SSP5-8.5_MWHFCMOFF than in SSP5-8.5_HFCMOFF to compensate for changes in other fluxes, in particular reduced basal melting).\nSensitivity of subsurface Southern Ocean warming\uf0c1\nTo analyze the sensitivity of the Antarctic ice-shelves to SSO warming, first, we obtained new equilibrium conditions from the 10 member initial conditions by doubling the SSO temperature anomaly (with respect to 1850 CE) near the Antarctic ice-shelves during 650 years without greenhouse forcing. SSO temperatures in the Antarctic ice model TIM are calculated using\nT^{IM} = 2 \u00d7 (T^{LC} - T^{LC}_{1850}) + T^{LC}_{1850} (1)\nwhere T^{LC} is the 400\u2009m ocean temperature simulated in LOVECLIM and T^{LC}_{1850} is the corresponding LOVECLIM temperature in the year 1850. Subsequently, we ran a 10 member ensemble covering the historical period and the SSP5-8.5 scenario with/without Antarctic meltwater flux (experiments Re_SSP5-8.5_2xSOTA and Re_SSP5-8.5_2xSOTA_MWOFF). Warming SSO temperature (Fig. 6m) increases basal melting under the Antarctic ice-shelves, thereby accelerating grounding line retreat (Fig. 6e\u2013h) relative to SSP5-8.5 (Fig. 6a\u2013d). This is most evident in Ross ice-shelf which vanishes completely by 2100 CE, leading to an integrated freshwater input of 2\u2009\u00b1\u20090.35\u2009m SLE total AIS mass by 2100 CE (Fig. 6p) and de facto SL rise of 0.5\u2009\u00b1\u20090.04\u2009m (Fig. 6o). Ice calving is the largest term in the mass balance over AIS (Fig. 4e\u2013h). However, as the shelf retreat accelerates mainly due to the basal melting, the role of ice calving term diminishes (Supplementary Fig. S6g, h).\nFigure 6: Transections of the Antarctic Ross ice-shelf, and global temperature and SL. a\u2013l Transects of Antarctic Ross-ice-shelf simulated in (a\u2013d) SSP5-8.5, (e\u2013h) Re_SSP5-8.5_2xSOTA and (i\u2013l) Re_SSP5-8.5_2xSOTA_MWOFF experiments in 1850, 1950, 2015 and 2100 CE. Dashed lines indicate grounding lines. m\u2013p Time series of annual anomalies (relative to the 1850\u20131900 CE mean) of (m) subsurface Southern Ocean (SSO) temperature, (n) global surface temperature, (o) sea-level (SL) and (p) Antarctic ice-sheet (AIS) net mass balance in sea-level-equivalent (SLE). Different colors represent the SSP5-8.5 with historical (black line), Re_SSP5-8.5_2xSOTA (red line) and Re_SSP5-8.5_2xSOTA_MWOFF (blue line) simulations. Horizontal scales of a\u2013l are shown in Supplementary Fig. S9 as a red line.\nThe result of increased Antarctic meltwater fluxes by enhanced SSO warming concurs with our previous discussion of a global warming slowdown by 0.4\u2009\u00b0C, relative to a simulation without such coupling (Fig. 6n red and blue lines). However, this sensitivity experiment increases SL by an additional 3\u2009cm SL rise (Fig. 6o). Not unexpectedly, SSO warming does not show any significant influence on the GrIS (Supplementary Fig. S6a\u2013d).\nDiscussion\uf0c1\nHere we used the coupled three-dimensional climate-ice-sheet model LOVECLIP to better understand the impact of ice-sheet/ice-shelf/ocean/atmosphere coupling processes on the future evolution of GrIS and AIS, and to estimate their respective contributions to SL rise.\nIn our high-end emission scenario, the GrIS and AIS each contribute about 60\u201370\u2009cm to global mean SL rise over the next 130 years. Even though for SSP2-4.5 and SSP5-8.5 global surface temperatures are projected to increase at a reduced rate after 2100 CE (Fig. 2e), the ice-sheet contributions to SL continue to accelerate beyond 2100 CE (Fig. 2g, h), mostly driven by accelerated surface melting in case of the GrIS and due to a combination of effects for the AIS. According to our simulations, limiting 21st century global surface temperature rise to 2\u2009\u00b0C above the pre-industrial level41,47 would be insufficient to slowdown the rate of global SL rise over the next 130 years42. Only the more aggressive low greenhouse gas emission scenario (SSP1-1.9), with temperatures leveling off below 1.5\u2009\u00b0C (Fig. 2a), avoids SL rise acceleration (Fig. 2f). A longer-term warming and SL perspective until 2500 CE (Supplementary Table S1) illustrates that for the SSP2-4.5 scenario, SL rise due to GrIS melting accelerates for over 250 years after maximum global warming rates occur, and peaks at over 0.3\u2009cm/year shortly before 2300 CE (Supplementary Fig. S7g). The Antarctic SL contribution for SSP2-4.5 fluctuates between 0.2 and 0.3\u2009cm/year from 2200\u20132500 CE (Supplementary Fig. S7h). This indicates an even more prolonged response and larger commitment to SL rise due to 21st century warming, with the total AIS contribution reaching about 1.1\u2009m by 2500 CE. In contrast, the aggressive greenhouse gas reduction scenario SSP1-1.9 with temperatures leveling off at less than 1.5\u2009\u00b0C (Supplementary Fig. S7a, e) is sufficient to prevent substantial ice-loss in Antarctica (Supplementary Fig. S7h) over the next centuries.\nOur results are to some extent consistent with recent uncoupled single-hemisphere ice-sheet model simulations5,8,38 which also show the tendency for unabated SL acceleration over the next two centuries in response to strong greenhouse gas forcing. One of the key advantages of our coupled model setup, even though it uses lower oceanic resolution, is that it allows us to quantify the role of meltwater forcing and calving fluxes on the stability of the ice-sheet. This is particularly timely because recent observations already show a marked increase in AIS meltwater fluxes14,15, which could increase SO stratification, reduce vertical heat exchange, increase subsurface temperatures and lead to enhanced basal melting. Numerous studies have suggested that, in combination with MISI and MICI, this may set in motion a run-away effect for ice loss. We can clearly see the positive feedback between ice-sheet melting, warm CDW intrusions and basal melting in our model (Figs. 4g, 5b). According to our study, however, the impact of MICI shows a weaker influence on the future SL contributions from AIS, as compared to earlier studies5,10 (Supplementary Fig. S4).", "source": "https://sealeveldocs.readthedocs.io/en/latest/park23.html"}
{"id": "fd75f919cbb6-5", "text": "Our results are to some extent consistent with recent uncoupled single-hemisphere ice-sheet model simulations5,8,38 which also show the tendency for unabated SL acceleration over the next two centuries in response to strong greenhouse gas forcing. One of the key advantages of our coupled model setup, even though it uses lower oceanic resolution, is that it allows us to quantify the role of meltwater forcing and calving fluxes on the stability of the ice-sheet. This is particularly timely because recent observations already show a marked increase in AIS meltwater fluxes14,15, which could increase SO stratification, reduce vertical heat exchange, increase subsurface temperatures and lead to enhanced basal melting. Numerous studies have suggested that, in combination with MISI and MICI, this may set in motion a run-away effect for ice loss. We can clearly see the positive feedback between ice-sheet melting, warm CDW intrusions and basal melting in our model (Figs. 4g, 5b). According to our study, however, the impact of MICI shows a weaker influence on the future SL contributions from AIS, as compared to earlier studies5,10 (Supplementary Fig. S4).\nIn our high-emission scenario model simulations that include parameterizations for hydrofracturing, ice-cliff instabilities, and capture sea-ice and atmospheric responses, the net impact of ice-sheet/climate feedbacks on SL rise is negative. These processes strongly contribute to the fast AIS response to warming temperatures, slightly less so in the coupled model than in meltwater-decoupled sensitivity experiments due to reduced surface temperature warming, rainfall, and surface melt. Given this sensitivity, it is plausible that the net effect of including the coupling and even its sign is strongly dependent by models: negative feedbacks related to meltwater fluxes are reduced when hydrofracturing and ice-cliff failure parameterizations are turned off in the model in our sensitivity experiments, where positive and negative feedbacks nearly balance. Furthermore, the net effect of including meltwater coupling is positive in the experiments with increased SSO warming. A more dramatic fall in SL, 22\u2009mm by 2100 in the SSP5-8.5 scenario, was found in the U.K. Earth System Model coupled to BISICLES dynamic ice-sheet model25. Thereby, standalone ice-sheet simulations may create misleading projections about the GrIS and AIS contributions to global SL rise. Coupled simulations document that trajectories of future climate change and SL rise depend on the complex and delicate balance of climate-ice-sheet coupling processes, some of which are not yet well constrained observationally. The results presented here from our earth system model of intermediate complexity multi-parameter simulations may provide further guidance in designing new coupled climate-ice-sheet model simulations using the next generation of coupled general circulation models.\nWhereas the LOVECLIP model employed here captures climate-ice-sheet coupling in both hemispheres, as well as iceberg routing and thermodynamic effects of melting icebergs, it does not resolve sub-shelf ocean dynamical processes48,49, interactive changes in ocean bathymetry, as well as narrow coastal currents, which can play an important role in basal melting50. Moreover, several important ice-sheet processes are still not well constrained, and both the ice-sheet/ice-shelf model and the atmospheric model use relatively low horizontal resolutions of ~20\u2009km in Antarctica and ~5.6\u00b0, respectively. This can lead to additional biases in ice-stream dynamics and poleward moisture transport, respectively. Additionally, glacial-isostatic adjustment51 other than vertical bedrock response by elastic lithosphere is not fully implemented in LOVECLIP. Nevertheless, our simulations also illustrate that ice-sheet ocean/atmosphere coupling, which can account for individual mass balance differences of 0.5-0.8\u2009cm/year SLE over the next ~100 years (Fig. 4f\u2013h), is a first order process that needs to be included in future SL assessments.\nMethods\uf0c1\nThe coupled climate-ice-sheet-ice-shelf-iceberg model LOVECLIP26 is based on the earth-system climate model LOVECLIM27 and the Penn State University Ice-Sheet/Shelf model (PSUIM)5,28,29. Here we review its main components, the coupling algorithm, experimental setup, and highlight modeling differences to previous studies.\nLOVECLIM earth system model\uf0c1\nThe earth system model of intermediate complexity [27] used here, LOVECLIM model (version 1.3), includes ocean, atmosphere, sea-ice, iceberg components as well as a vegetation model. The atmospheric model ECBILT [52] uses a T21 spectral truncation (corresponding to ~5.6\u00b0\u2009\u00d7\u20095.6\u00b0 horizontal resolution) and the prognostic quasi-geostrophic atmospheric equations are solved on three vertical levels. The model includes parameterizations of ageostrophic terms [53] to better capture tropical dynamics. The free-surface primitive equation ocean model, CLIO [54,55,56], which is also coupled to a thermodynamic-dynamic sea-ice model, adopts a 3\u00b0\u2009\u00d7\u20093\u00b0 horizontal resolution and 20 vertical levels. The coupling between atmosphere and ocean is expressed in terms of freshwater, momentum and heat flux exchanges. An iceberg model integrates iceberg trajectories, melting and freshwater release along individual simulated iceberg trajectories [57,58]. VECODE [59], the terrestrial vegetation model of LOVECLIP calculates the temporal evolution of annual mean desert, tree and grass fractions in each land grid cell. LOVECLIM has been used extensively to study the earth system response to a variety of boundary conditions [60,61,62,63]. Here the model is configured with a present-day land mask and an open Bering Strait.\nPSUIM ice-sheet/shelf model\uf0c1\nThe ice-sheet/shelf model PSUIM [5,28,29] is used here in a bi-hemispheric configuration. By adopting shallow ice and shallow shelf approximations, the model retains the ability to simulate streaming and stretching flow and to capture ice streams and floating ice-shelves. Floating ice-shelves, grounding line migration, and basal ice fluxes are parameterized [21]. PSUIM estimates the surface energy and ice mass balance by accounting for contributions from changes in temperature and radiation [64,65]. Similar to previous versions of the model [5,29], we include parameterizations for enhanced calving caused by rainwater-driven hydrofracturing and surface melting, as well as a representation of marine ice-cliff failure. Through calculating changes of ice calving, floating-ice, grounding line migration and pinning by bathymetric bedrock perturbations, the SL is estimated. A horizontal resolution of 1\u00b0 latitude and 0.5\u00b0 longitude is used in the Northern Hemisphere and a stereographic grid is adopted for Antarctica with a resolution of 20\u2009km.\nThe model version employed here differs from the one used in a recent SL study [5] in that our spatial resolution is lower over Antarctica. Moreover, different parameters were used, namely those characterizing sub-ice-shelf ocean melting (OCFAC), the coefficient in the parameterization of hydrofracturing due to surface liquid (CREVLIQ), and the maximum rate of horizontal wastage due to ice-cliff failure (VCLIF). The default parameter values are OCFAC\u2009=\u20091.0, CREVLIQ\u2009=\u2009100\u2009m per (m/year)\u22122 and VCLIF\u2009=\u20093\u2009km/year5. Here we use a value of OCFAC\u2009=\u20091.5, which were chosen such that the AIS has a realistic extent under pre-industrial conditions and for the corresponding LOVECLIM climate forcing. Additionally, LOVECLIP realistically simulates the Antarctic ice velocity and shape of ice-shelves compared to the mean of 1996\u20132016 Antarctic ice velocity obtained from the satellite data66,67 (Supplementary Fig. S11). Although, the size of the ice-shelves and the associated outflow velocities are overestimated.\nClimate-ice-sheet model coupling (LOVECLIP)\uf0c1\nA coupling algorithm exchanges variables and boundary conditions between LOVECLIM and PSUIM in both hemispheres (Supplementary Fig. S1), in a series of alternating climate and ice-sheet model runs (\u201cchunks\u201d) [26,68,69,70]. The chunk length is set to 1 year for LOVECLIM and PSUIM. The ice model is forced by monthly LOVECLIM surface air temperature, precipitation, evaporation, solar radiation and annual mean subsurface ocean temperature. LOVECLIM has polar temperature and precipitation biases, similar to those documented for more complex CMIP5 models [71]. Present-day climatological surface air temperature and precipitation biases, as well as subsurface ocean temperature biases near Antarctica, are removed in the coupler through a bias correction [70]. Surface air temperature and precipitation are downscaled vertically to the PSUIM grid with applied lapse rate corrections26,28. Subsurface ocean temperature is interpolated under ice-shelves on the PSUIM grid.", "source": "https://sealeveldocs.readthedocs.io/en/latest/park23.html"}
{"id": "fd75f919cbb6-6", "text": "The model version employed here differs from the one used in a recent SL study [5] in that our spatial resolution is lower over Antarctica. Moreover, different parameters were used, namely those characterizing sub-ice-shelf ocean melting (OCFAC), the coefficient in the parameterization of hydrofracturing due to surface liquid (CREVLIQ), and the maximum rate of horizontal wastage due to ice-cliff failure (VCLIF). The default parameter values are OCFAC\u2009=\u20091.0, CREVLIQ\u2009=\u2009100\u2009m per (m/year)\u22122 and VCLIF\u2009=\u20093\u2009km/year5. Here we use a value of OCFAC\u2009=\u20091.5, which were chosen such that the AIS has a realistic extent under pre-industrial conditions and for the corresponding LOVECLIM climate forcing. Additionally, LOVECLIP realistically simulates the Antarctic ice velocity and shape of ice-shelves compared to the mean of 1996\u20132016 Antarctic ice velocity obtained from the satellite data66,67 (Supplementary Fig. S11). Although, the size of the ice-shelves and the associated outflow velocities are overestimated.\nClimate-ice-sheet model coupling (LOVECLIP)\uf0c1\nA coupling algorithm exchanges variables and boundary conditions between LOVECLIM and PSUIM in both hemispheres (Supplementary Fig. S1), in a series of alternating climate and ice-sheet model runs (\u201cchunks\u201d) [26,68,69,70]. The chunk length is set to 1 year for LOVECLIM and PSUIM. The ice model is forced by monthly LOVECLIM surface air temperature, precipitation, evaporation, solar radiation and annual mean subsurface ocean temperature. LOVECLIM has polar temperature and precipitation biases, similar to those documented for more complex CMIP5 models [71]. Present-day climatological surface air temperature and precipitation biases, as well as subsurface ocean temperature biases near Antarctica, are removed in the coupler through a bias correction [70]. Surface air temperature and precipitation are downscaled vertically to the PSUIM grid with applied lapse rate corrections26,28. Subsurface ocean temperature is interpolated under ice-shelves on the PSUIM grid.\nLOVECLIM\u2019s surface land-ice cover and orography are updated using the simulated ice-sheet and vertical bedrock evolution from PSUIM which is based on elastic lithosphere response with fixed bedrock response time [28]. The spatial distribution of liquid runoff into the ocean is calculated based on model topography and the calving flux is released as icebergs into the LOVECLIM iceberg model. Both liquid runoff from the surface and basal melting are released into the surface ocean. Ocean currents and wind-drag subsequently steer the icebergs and along their pathways they melt and cool the ocean. Contributions to SL changes are calculated in PSUIM in both hemispheres, and take into account the bedrock response28. The total SL evolution is calculated in the coupler based on the Northern Hemisphere and Antarctic contributions.\nSpin-up and initial conditions\uf0c1\nThe model is initialized from constant pre-industrial conditions. Because of the different equilibration timescales of the ice-sheet and climate components, asynchronous coupling is used to obtain equilibrated initial conditions. In particular, the model has been integrated for 120 chunk lengths with chunk lengths of 50 years for PSUIM and 5 years for LOVECLIM, and then 2000 chunk lengths with chunk length of 1 year for each ice model and LOVECLIM, which results in 8000 years of spin-up for the ice component and 2600 years for LOVECLIM (Supplementary Table S1), after climate trends are negligible (Supplementary Fig. S10). Ensembles of 10 members with different initial conditions have been conducted for each of the experiments, with the initial conditions taken from the last 100 chunks of the spin-up run.\nStatistics of forced and unforced ice-sheet mass balance\uf0c1\nTo compare whether the observed ice-sheet mass balance estimated from the Gravity Recovery and Climate Experiment (GRACE)33 for the period 2002\u20132020 CE is consistent with the null hypothesis of unforced ice-sheet variability, we conducted a 5000 years LOVECLIP control experiment with constant, pre-industrial CO2 concentrations (CTR) (Supplementary Table S1). There is still a remaining very weak drift in the unforced simulation, which amounts to \u22121.5\u2009cm for GrIS and \u22124 cm for AIS of mass balance in SLE over 5000 years (Supplementary Fig. S2). The drift is removed by high-pass filtering over than 80 years, the net mass balance and the resulting high-frequency components are then used as an estimate for the unforced ice-sheet variability. Each 19-year chunk is cut after high-pass filtering to get 19-year trends of natural variability (Fig. 1).\nScenario simulations\uf0c1\nTo assess the ice-sheet sensitivity to different greenhouse gas emission pathways, we conducted a suite of coupled scenario simulations (each with 10 individual ensemble members), in which CO2 concentrations in LOVECLIP follow the historical from the year 1850 to 2014, and SSP1-1.9, SSP2-4.5 and SSP5-8.5 from the year 2015 to 2150 (Supplementary Table S1). In terms of the Antarctic contribution to SL by 2100 CE the LOVECLIP model projections (Fig. 2) lie within the range simulated by offline models which were forced by RCP2.6, 4.5 and 8.5 climate scenarios6,39,40. For the Greenland ice-sheet we find a similar agreement with other modeling studies6,36,37 and the \u201clikely range\u201d of provided by the 5th assessment report, WG1 of the Intergovernmental Panel on Climate Change (Chapter 13)4. The SSP1-1.9 and SSP2-4.5 simulations were further extended until 2500 CE (Supplementary Fig. S7).\nTo further quantify the impact of climate-ice-sheet coupling in the Southern Hemisphere in global SL rise we conducted an additional SSP5-8.5 sensitivity experiment, for which the AIS liquid runoff and iceberg calving balance net precipitation over Antarctica (experiment SSP5-8.5_MWOFF) (Fig. 5 and Supplementary Table S1). To explore the impact of AIS hydrofracturing and ice-cliff failure parameterizations, we also obtained ensembles with these parameterizations turned off (CREVLIQ\u2009=\u20090\u2009m per (m/year)\u22122 and VCLIF\u2009=\u20090\u2009km/year) with and without meltwater flux coupling (experiments SSP5-8.5_HFCMOFF and SSP5-8.5_MWHFCMOFF) (Supplementary Figs. S4, S5).\nAnother sensitivity experiment of the Antarctic ice-shelves to SSO warming is conducted by doubling the SSO temperature anomaly (relative to 1850 CE) to the Antarctic ice shelves in the SSP5-8.5 scenario with/without Antarctic meltwater flux (experiments Re_SSP5-8.5_2xSOTA and Re_SSP5-8.5_2xSOTA_MWOFF). Specifically, SSO temperatures in the Antarctic ice model TIM are calculated using Eq. (1). Applying doubled SSO temperature anomaly would lead to a different climate equilibrium. Therefore, new initial conditions were created. To get the new equilibrium conditions we added the SSO temperature anomalies from the 10 member initial conditions for 650 years, with fixed pre-industrial CO2 concentration.\nSupplementary information\uf0c1\nFigure S1: Coupling algorithm. This schematic shows how the LOVECLIP is coupled and exchanges variables and boundary conditions between LOVECLIM and PSUIM.\nFigure S2: Ice-sheet volume change in control experiment with pre- industrial CO2 concentrations. (a) total ice-sheet volume change (relative to initial condition) over Greenland simulated by control experiment with constant, pre-industrial CO2 concentrations; (b) same as (a), but for Antarctica. Shading indicates ensemble range, solid line the 19-year moving average of time series result and dashed line the linear regression by the Least Squares Method.\nFigure S3: Observed and simulated interannual mass balance of Greenland ice-sheet (GrIS) and Antarctic ice-sheet (AIS). (a) the histogram of Greenland interannual mass balance in the 5,000-year-long pre-industrial control run (CTR, gray histogram) with the 95% confidence interval range (black dashed line), and observed estimates for interannual change during 2002-2020 CE from the Gravity Recovery and Climate Experiment (GRACE) (blue line) and simulated by the forced LOVECLIP ensemble (red line); (b) same as (a), but for Antarctica. Consistent with the GRACE measurements, mass balance changes for LOVECLIM are calculated in this figure using only the grounded ice-sheet portion.", "source": "https://sealeveldocs.readthedocs.io/en/latest/park23.html"}
{"id": "fd75f919cbb6-7", "text": "Another sensitivity experiment of the Antarctic ice-shelves to SSO warming is conducted by doubling the SSO temperature anomaly (relative to 1850 CE) to the Antarctic ice shelves in the SSP5-8.5 scenario with/without Antarctic meltwater flux (experiments Re_SSP5-8.5_2xSOTA and Re_SSP5-8.5_2xSOTA_MWOFF). Specifically, SSO temperatures in the Antarctic ice model TIM are calculated using Eq. (1). Applying doubled SSO temperature anomaly would lead to a different climate equilibrium. Therefore, new initial conditions were created. To get the new equilibrium conditions we added the SSO temperature anomalies from the 10 member initial conditions for 650 years, with fixed pre-industrial CO2 concentration.\nSupplementary information\uf0c1\nFigure S1: Coupling algorithm. This schematic shows how the LOVECLIP is coupled and exchanges variables and boundary conditions between LOVECLIM and PSUIM.\nFigure S2: Ice-sheet volume change in control experiment with pre- industrial CO2 concentrations. (a) total ice-sheet volume change (relative to initial condition) over Greenland simulated by control experiment with constant, pre-industrial CO2 concentrations; (b) same as (a), but for Antarctica. Shading indicates ensemble range, solid line the 19-year moving average of time series result and dashed line the linear regression by the Least Squares Method.\nFigure S3: Observed and simulated interannual mass balance of Greenland ice-sheet (GrIS) and Antarctic ice-sheet (AIS). (a) the histogram of Greenland interannual mass balance in the 5,000-year-long pre-industrial control run (CTR, gray histogram) with the 95% confidence interval range (black dashed line), and observed estimates for interannual change during 2002-2020 CE from the Gravity Recovery and Climate Experiment (GRACE) (blue line) and simulated by the forced LOVECLIP ensemble (red line); (b) same as (a), but for Antarctica. Consistent with the GRACE measurements, mass balance changes for LOVECLIM are calculated in this figure using only the grounded ice-sheet portion.\nFigure S4: Global surface temperature and sea-level (SL) projections, and their tendencies. (a-d) annual anomalies (relative to the 1850\u20131900 CE mean) of (a) the global surface temperature, (b) SL, and (c) SL contributions from the Greenland ice-sheet (GrIS) and (d) Antarctic ice-sheet (AIS). (e-h) are the respective time derivatives of (a-d) (change per year). Solid lines of (a-d) indicate the ensemble mean and shading the ensemble range. The solid line in (e) represents the 9-year moving average of the time derivative of global surface temperature, with the dashed line indicating 0 \u00b0C/year. Different colors represent the SSP5-8.5 with historical (black line; period 1850\u2013 2150 CE), and SSP5-8.5_MWOFF (cyan line), SSP5-8.5_HFOFF (red line), SSP5- 8.5_CMOFF (pink line), SSP5-8.5_HFCMOFF (orange line) and SSP5- 8.5_MWHFCMOFF (blue line) simulations during the period 2014\u20132150 CE. The sudden drops seen in (f and g) are due to the changes in parameters associated with hydrofracturing and ice-cliff failure.\nFigure S5: Individual mass balance terms for Antarctic ice-sheet (AIS). (a-d) represent the individual AIS mass balance terms for (a) the accumulation, (b) surface melting, (c) basal melting and (d) ice calving expressed as sea-level-equivalent (SLE) per year. Solid lines indicate the ensemble mean and shading the ensemble range. Different colors represent the SSP5-8.5 with historical (black line; period 1850\u20132150 CE), and SSP5-8.5_MWOFF (cyan line), SSP5-8.5_HFOFF (red line), SSP5-8.5_CMOFF (pink line), SSP5-8.5_HFCMOFF (orange line) and SSP5-8.5_MWHFCMOFF (blue line) simulations during the period 2014\u20132150 CE.\nFigure S6: Individual mass balance terms for Greenland ice-sheet (GrIS) and Antarctic ice-sheet (AIS) by subsurface Southern Ocean warming. (a-d) represent the individual GrIS mass balance terms for (a) the accumulation, (b) surface melting, (c) basal melting and (d) ice calving expressed as sea-level-equivalent (SLE) per year; (e-h), same as (a-d), but for AIS. Solid lines indicate the ensemble mean and shading the ensemble range. Different colors represent the SSP5-8.5 (black line) and Re_SSP5- 8.5_2xSOTA (red line).\nFigure S7: Long-term Global surface temperature and sea-level (SL) projections, and their tendencies. (a-d) annual anomalies (relative to the 1850\u20131900 CE mean) of (a) the global surface temperature, (b) SL, and (c) SL contributions from the Greenland ice-sheet (GrIS) and (d) Antarctic ice-sheet (AIS). (e-h) are the respective time derivatives of (a-d) (change per year). Solid lines of (a-d) indicate the ensemble mean and shading the ensemble range. The solid line in (e) represents the 19-year moving average of the time derivative of global surface temperature, with the dashed line indicating 0 \u00b0C/year. Different colors represent the historical (black line; period 1850\u20132014 CE), and SSP1-1.9 (blue line) and SSP2-4.5 (pink line) simulations during the period 2014\u20132500 CE.\nFigure S8: Arctic and Antarctic sensitivities compared to global surface temperature increase by the end of 21st century. (a) Arctic amplification of LOVECLIP and CMIP6 under the historical and SSP5-8.5 scenarios. \u2206temperature is the anomalous mean surface temperature in 2090-2100 relative to 1850-1900. (b) same as (a), but for Antarctic amplification. The Arctic region is defined as latitudes from 60oN to 90oN, and the Antarctic region from 60oS to 90oS.\nFigure S9: Transection of Ross ice-shelf. The red line in this map indicates the location of Ross ice-shelf transection shown in figure 6.\nFigure S10: Global temperature and ice height of Greenland ice- sheet (GrIS) and Antarctic ice-sheet (AIS) by the spin-up simulation. (a-c) global surface air temperature at (a) the starting point, (b) ending point and (c) difference between (b) and (a). (d-f) ice height of the GrIS at (d) the starting point, (e) ending point and (f) difference between (e) and (d); (g-i) same as (d-f), but for AIS.\nFigure S11: Ice velocity over Antarctica. (a) Annual average of the 1996-2016 ice velocity over Antarctica (a) observed NSIDC-0484 satellite data1,2 and simulated by (b) LOVECLIP.\nTable S1: List of experiments conducted with LOVECLIP. This table shows the experiments that we conducted in this study. Ensembles of 10 members with different initial conditions were simulated for historical and SSP experiments, with the initial conditions taken from the last 100 chunks of the spin-up run.", "source": "https://sealeveldocs.readthedocs.io/en/latest/park23.html"}
{"id": "83d9565fb013-0", "text": "Palmer et al. (2020)\uf0c1\nTitle:\nExploring the Drivers of Global and Local Sea-Level Change Over the 21st Century and Beyond\nKey Points:\nWe have developed a new set of global and local sea-level projections for the 21st century and extended to 2300 that are rooted in CMIP5 climate model simulations, including more comprehensive treatment of uncertainty than previously reported in IPCC AR5\nAnalysis of local sea-level projections and tide gauge data suggests that local variability will dominate the total variance in sea-level change for the coming decades at all locations considered\nThe extended sea-level projections highlight the substantial multicentury sea-level rise commitment under all RCP scenarios and the dependence of modeling uncertainty on geographic location, time horizon, and climate scenario\nCorresponding author:\nPalmer\nCitation:\nPalmer, M. D., Gregory, J. M., Bagge, M., Calvert, D., Hagedoorn, J. M., Howard, T., et al. (2020). Exploring the Drivers of Global and Local Sea\u2010Level Change Over the 21st Century and Beyond. Earth\u2019s Future, 8(9). doi:10.1029/2019ef001413\nURL:\nhttps://agupubs.onlinelibrary.wiley.com/doi/10.1029/2019EF001413\nAbstract\uf0c1\nWe present a new set of global and local sea-level projections at example tide gauge locations under the RCP2.6, RCP4.5, and RCP8.5 emissions scenarios. Compared to the CMIP5-based sea-level projections presented in IPCC AR5, we introduce a number of methodological innovations, including (i) more comprehensive treatment of uncertainties, (ii) direct traceability between global and local projections, and (iii) exploratory extended projections to 2300 based on emulation of individual CMIP5 models. Combining the projections with observed tide gauge records, we explore the contribution to total variance that arises from sea-level variability, different emissions scenarios, and model uncertainty. For the period out to 2300 we further breakdown the model uncertainty by sea-level component and consider the dependence on geographic location, time horizon, and emissions scenario. Our analysis highlights the importance of local variability for sea-level change in the coming decades and the potential value of annual-to-decadal predictions of local sea-level change. Projections to 2300 show a substantial degree of committed sea-level rise under all emissions scenarios considered and highlight the reduced future risk associated with RCP2.6 and RCP4.5 compared to RCP8.5. Tide gauge locations can show large (\u200a>\u200a50%) departures from the global average, in some cases even reversing the sign of the change. While uncertainty in projections of the future Antarctic ice dynamic response tends to dominate post-2100, we see substantial differences in the breakdown of model variance as a function of location, time scale, and emissions scenario.\nIntroduction\uf0c1\nThe IPCC Special Report on Oceans and Cryosphere in a Changing Climate (SROCC) estimates that global-mean sea level (GMSL) increased by 0.16 \u00b1 0.05 m over the period 1902\u20132015 (IPCC, 2019). Furthermore, GMSL rise is accelerating: The estimated rate for 2006\u20132015 (3.6 mm yr\u200a\u2212\u200a1) is about 2.5 times the rate for 1901\u20131990 (1.4 mm yr\u200a\u2212\u200a1) with the contribution from melting ice sheets and glaciers exceeding that of thermal expansion for the recent period. Sea-level rise exacerbates extreme sea-level events and coastal hazards and has numerous adverse impacts on marine coastal ecosystems (IPCC, 2019). Information on future sea-level rise is therefore a key component for climate change impacts studies and informing coastal decision makers, particularly for adaptation planning.\nA number of recent studies have considered potential future changes in both local mean sea-level change and drivers of extreme sea-level events (such as waves and storm surges) to explore changes in future coastal flood risk (e.g., Cannaby et al., 2016; Howard et al., 2019; Vousdoukas et al., 2018). While changes in the drivers of extreme sea levels can make a substantive contribution, the overwhelmingly dominant factor in projections of future coastal flood risk is mean sea-level rise, which results primarily from melting of land-based ice and the expansion of seawater as the oceans warm (Church et al., 2013). Therefore, the work presented here focuses on projections of mean sea-level change at global and local scales. Throughout the manuscript, we adopt the sea-level nomenclature and definitions recently put forward by Gregory et al. (2019).\nThe sea-level projections presented here have their origins in research carried out as part of UKCP18 (Lowe et al., 2018), a government-funded project to deliver state-of-the-art climate projections primarily for the United Kingdom. Detailed methods on the UKCP18 sea-level projections, including consideration of changes in surges, tides, and coastal waves, are described in Palmer, Howard, et al. (2018), with a synthesis of the results for the 21st century presented by Howard et al. (2019). The UKCP18 mean sea-level projections were rooted in the CMIP5 model simulations and Monte Carlo approach used for GMSL projections in the IPCC 5th Assessment Report of Working Group I (Church et al., 2013; hereafter, AR5), with several extensions and innovations, as described below.\nFirst, the contribution to future GMSL rise from dynamic ice input from Antarctica was updated based on the scenario-dependent projections from Levermann et al. (2014). Second, a scaling approach was adopted for local projections of sterodynamic sea-level change that better isolates the forced response from internal variability (e.g., Bilbao et al., 2015; Perrette, Landerer, Riva, Frieler, & Meinshausen, 2013). Third, the AR5 Monte Carlo approach was extended to the local sea-level projections to ensure traceability to the GMSL projections and preserve the correlations among the different terms. Fourth, a more comprehensive treatment of uncertainty was devised, by including several different estimates of (i) the sea-level change associated with glacial isostatic adjustment (GIA) and (ii) the barystatic-GRD fingerprints, that is, the spatial patterns of sea-level change associated with projections of land-based ice loss that arise from gravitational, rotational, and deformation effects. Note that the term \u201cGRD\u201d has been introduced by Gregory et al. (2019). Previously these effects have been referred to as the \u201csea-level equation\u201d or \u201c(gravitational) fingerprints,\u201d for example.\nIn addition, UKCP18 provided an additional set of projections based on an emulated ensemble of CMIP5 models that extend to 2300 (Palmer, Harris, et al., 2018). These exploratory projections have a high degree of consistency with the UKCP18 21st century projections and maintain traceability to the CMIP5 models. The methods presented here are almost identical to those used for UKCP18 and described by Palmer, Howard, et al. (2018). Here, we make use of global GIA estimates, rather than regional solutions developed specifically for the United Kingdom. Only two of the three sets of GRD \u201cfingerprints\u201d presented here were available for UKCP18, but this limitation does not make any substantive difference to the results (see section 4). Whereas UKCP18 considered only local sea-level projections for the United Kingdom, this study is global in scope, and we include new analysis of the drivers of variance for both GMSL and local projections.\nThe local sea-level projections presented here correspond to a limited number of example tide gauge locations around the world. These locations are selected based on the availability of tide gauge records long enough to estimate local sea-level variability and to span a range of future projection regimes that illustrate important geographic differences. While we also make use of satellite altimeter observations, tide gauge records are particularly useful for estimating local interannual variability owing to thelonger records available and more direct monitoring of coastal sea level. In addition, tide gauge records include vertical land motion associated with glacial isostatic adjustment\u2014a process included in our projections but absent from satellite altimeter observations. The focus on a limited set of tide gauges allows a deeper exploration of the drivers and uncertainties in future local sea-level change through computation of the covariance matrix of our large Monte Carlo simulations.", "source": "https://sealeveldocs.readthedocs.io/en/latest/palmer20.html"}
{"id": "83d9565fb013-1", "text": "In addition, UKCP18 provided an additional set of projections based on an emulated ensemble of CMIP5 models that extend to 2300 (Palmer, Harris, et al., 2018). These exploratory projections have a high degree of consistency with the UKCP18 21st century projections and maintain traceability to the CMIP5 models. The methods presented here are almost identical to those used for UKCP18 and described by Palmer, Howard, et al. (2018). Here, we make use of global GIA estimates, rather than regional solutions developed specifically for the United Kingdom. Only two of the three sets of GRD \u201cfingerprints\u201d presented here were available for UKCP18, but this limitation does not make any substantive difference to the results (see section 4). Whereas UKCP18 considered only local sea-level projections for the United Kingdom, this study is global in scope, and we include new analysis of the drivers of variance for both GMSL and local projections.\nThe local sea-level projections presented here correspond to a limited number of example tide gauge locations around the world. These locations are selected based on the availability of tide gauge records long enough to estimate local sea-level variability and to span a range of future projection regimes that illustrate important geographic differences. While we also make use of satellite altimeter observations, tide gauge records are particularly useful for estimating local interannual variability owing to thelonger records available and more direct monitoring of coastal sea level. In addition, tide gauge records include vertical land motion associated with glacial isostatic adjustment\u2014a process included in our projections but absent from satellite altimeter observations. The focus on a limited set of tide gauges allows a deeper exploration of the drivers and uncertainties in future local sea-level change through computation of the covariance matrix of our large Monte Carlo simulations.\nSince the publication of AR5 several studies have highlighted the need for more comprehensive information on potential future sea-level change \u201ctail risk\u201d to complement IPCC-like sea-level projections that characterize the central part of the probability distribution, in order to facilitate effective coastal planning (e.g., Hinkel et al., 2019; Stammer et al., 2019). This requirement has motivated the development of probabilistic projections that aim to provide more comprehensive information on the projected probability density functions (PDFs; e.g., Garner et al., 2018; Jevrejeva et al., 2019). However, probabilistic sea-level projections are sensitive to the assumptions made about the tails of the PDFs. For example, using different methods, both Kopp et al. (2014) and Jackson and Jevrejeva (2016) drew on the expert elicitation study of Bamber and Aspinall (2013) to introduce non-Gaussian uncertainty into the tails of Greenland and Antarctic ice sheet contributions. The substantial differences in their PDFs of projected global and local sea-level at 2100 (Jevrejeva et al., 2019) are indicative of the uncertainty associated with our understanding of key ice sheet processes and low scientific confidence in the extreme percentiles.\nAn alternative approach to exploring tail risk is through consideration of possible high-end scenarios of future sea-level rise (Stammer et al., 2019), such as the \u201cH\u200a+\u200a\u200a+\u200a\u201d scenario developed for UKCP09 (Lowe et al., 2018). Shepherd et al. (2018) suggested an event-orientated storyline approach with no requirement for a priori probability assessment. Ideally, these physicallybased narratives should be testable with future observations (e.g., marine ice cliff instability; DeConto & Pollard, 2016) and can be a useful framework to aid the communication and interpretation of risk. The UKCP18 Marine Report (Palmer, Howard, et al., 2018) recommended that information from high-end scenarios be used alongside climate-model-derived sea-level projections, such as those presented here, to more fully sample future possibility space (Rohmer, Le Cozannet, & Manceau, 2019).\nThe outline of the paper is as follows. In section 2 we describe the observational and model data used in this study and present the tide gauge locations used for our local sea-level projections. In section 3 we present an overview of the methods used in our global and local sea-level projections. GMSL projections are presented in section 4.1, including a breakdown of the component uncertainties and discussion of the correlations among the different components. In section 4.2 we present sea-level projections at several tide gauge locations and explore the relative importance of variability, scenario, and model uncertainty over the 21st century following Hawkins and Sutton (2009). Section 4.3 focuses on model uncertainty and how the breakdown of total variance into the different components varies by geographic location, scenario, and time scale. Finally, in section 5, we discuss our key findings and present a summary.\nData\uf0c1\nTide Gauge Data\uf0c1\nThe local sea-level projections presented in section 4.2 are premised on several example tide gauge locations around the world (Figure 1). These locations are chosen to span a range of future sea-level change regimes and to provide reasonable tide gauge time series with which to estimate the local interannual variability. Data are sourced from the Permanent Service for Mean Sea Level (Holgate et al., 2013; https://www.psmsl.org/). The latitude and longitude of each tide gauge location are summarized in Table S1. The tide gauge records used have not been corrected for vertical land motions. This is appropriate, since our local sea-level projections include an estimate of local glacial isostatic adjustment (GIA), and therefore, we do not want to remove this signal from the tide gauge record.\nFigure 1: Locations of tide gauge data used in this study. The same locations are used for extraction of satellite altimeter observations and the local sea-level projections presented in section 4.2.\nSatellite Altimeter Data\uf0c1\nThe satellite altimeter data used in this study come from v2.0 of the European Space Agency (ESA) Climate Change Initiative for observations of sea level (http://www.esa-sealevel-cci.org), as described by Legeais et al. (2018). This data product is based on reprocessed and homogenized gridded observations from nine altimeter missions over the period 1993\u20132015 and provides monthly mean values for GMSL and two-dimensional fields on a \u00bc \u00d7 \u00bc\u00b0 latitude-longitude grid. Monthly mean timeseries of GMSL anomaly are converted to annual means for comparison with our projections of GMSL. Similarly, we convert monthly mean two-dimensional fields of gridded sea-level anomaly to annual-mean values. We extract the annual-mean time series from the closest available grid box to the tide gauge locations shown in Figure 1. The only exception to this is for Palermo, where we select values from two grid boxes further east in order to avoid apparent data issues that may be associated with land-proximity effects.\nCMIP5 Data\uf0c1\nThe sea-level projections presented in this study are rooted in climate model simulations carried out as part of the Coupled Model Intercomparison Project Phase 5 project (CMIP5; Taylor et al., 2012). A full list of the CMIP5 models used and their various applications is summarized in Table S2.\nThe 21st century projections presented here are based on the same CMIP5 model ensemble as used for the GMSL projections presented in AR5. These projections make use of simulations of global-mean surface temperature (tas) and global-mean thermosteric sea-level (zostoga) rise from 21 CMIP5 models under the representative concentration pathway climate change scenarios (RCPs, Meinshausen et al., 2011). Time series of zostoga have been drift-corrected using a quadratic fit to the corresponding pre-industrial control simulation for each model. This step is performed to remove any artificial signals associated with ongoing spin-up deep ocean and/or limitations in the representation of energy conservation in the model domain, as discussed by Sen Gupta et al. (2013) and Hobbs et al. (2016). Further information is provided in the supplementary materials of AR5 (Church et al., 2013).\nOur extended sea-level projections to 2300 are based on an ensemble of two-layer energy balance model (TLM) simulations with parameter settings that have been tuned to emulate the forced response of individual CMIP5 models in idealized CO2 experiments models following Geoffroy et al. (2013). This ensemble also provides time series of tas and zostoga under the extended RCP scenarios (Meinshausen et al., 2011), and it is based on 14 CMIP5 models, with 11 models common to the AR5 CMIP5 ensemble. Full details of the methods and evaluation of the TLM simulations are described by Palmer, Harris, et al. (2018).", "source": "https://sealeveldocs.readthedocs.io/en/latest/palmer20.html"}
{"id": "83d9565fb013-2", "text": "CMIP5 Data\uf0c1\nThe sea-level projections presented in this study are rooted in climate model simulations carried out as part of the Coupled Model Intercomparison Project Phase 5 project (CMIP5; Taylor et al., 2012). A full list of the CMIP5 models used and their various applications is summarized in Table S2.\nThe 21st century projections presented here are based on the same CMIP5 model ensemble as used for the GMSL projections presented in AR5. These projections make use of simulations of global-mean surface temperature (tas) and global-mean thermosteric sea-level (zostoga) rise from 21 CMIP5 models under the representative concentration pathway climate change scenarios (RCPs, Meinshausen et al., 2011). Time series of zostoga have been drift-corrected using a quadratic fit to the corresponding pre-industrial control simulation for each model. This step is performed to remove any artificial signals associated with ongoing spin-up deep ocean and/or limitations in the representation of energy conservation in the model domain, as discussed by Sen Gupta et al. (2013) and Hobbs et al. (2016). Further information is provided in the supplementary materials of AR5 (Church et al., 2013).\nOur extended sea-level projections to 2300 are based on an ensemble of two-layer energy balance model (TLM) simulations with parameter settings that have been tuned to emulate the forced response of individual CMIP5 models in idealized CO2 experiments models following Geoffroy et al. (2013). This ensemble also provides time series of tas and zostoga under the extended RCP scenarios (Meinshausen et al., 2011), and it is based on 14 CMIP5 models, with 11 models common to the AR5 CMIP5 ensemble. Full details of the methods and evaluation of the TLM simulations are described by Palmer, Harris, et al. (2018).\nAt regional scales, changes in ocean dynamic sea level (arising from changes in ocean circulation and/or density) are important determinants of local sea-level change. To account for this, we make use of CMIP5 model simulations of global-mean thermosteric sea level (zostoga) and ocean dynamic sea level (zos) from 21 CMIP5 models under the RCP climate change scenarios. Following previous studies (Cannaby et al., 2016; Palmer, Howard, et al., 2018), both zostoga and zos are drift-corrected using a linear fit to the corresponding pre-industrial control simulations. These data are then used to establish regression relationships between the local sterodynamic sea-level change (zostoga \u200a+\u200a zos) and global-mean thermosteric sea-level change (zostoga) across the CMIP5 ensemble at each tide gauge location.\nThe spatial pattern of sterodynamic sea-level change is illustrated for RCP4.5 (Figure 2). The characteristic multimodel mean response includes an increase in sea-level gradient across the Southern Ocean and enhanced sea-level rise in the North Atlantic and Arctic Oceans. The multimodel spread is largest in the North Atlantic and Arctic Oceans. Analysis of AOGCM experiments conducted for the flux-anomaly-forced model intercomparison project (FAFMIP, Gregory et al., 2016) shows that the change in the Southern Ocean is due to a combination of increases in wind stress and heat input, in the North Atlantic due to reduced heat loss and the consequent weakening of the Atlantic meridional overturning circulation (especially along the North American coast; Bouttes et al., 2014; Yin et al., 2009), and in the Arctic due to increased freshwater input from precipitation and river inflow.\nFigure 2: Projections of sterodynamic sea level change for the period 2081\u20132100 relative to the 1986\u20132005 average from an ensemble of 21 CMIP5 models: (a) ensemble mean; (b) ensemble spread (90% confidence interval based on the ensemble standard deviation). The spatial patterns arise from the forced response of ocean dynamic sea level across the CMIP5 ensemble. Adapted from IPCC AR5 (Church et al., 2013; Figure 13.16).\nGRD Estimates\uf0c1\nChanges in the amount of ice and water stored on land give rise to spatial patterns of mean sea-level (MSL) change associated with the effects on Earth\u2019s gravity, rotation, and solid earth deformation (e.g., Tamisiea & Mitrovica, 2011). Gregory et al. (2019) refer to these effects collectively as GRD (Gravity, Rotation, Deformation), and we adopt their nomenclature here. We use three different estimates of GRD for the different ice mass terms following Slangen et al. (2014), Spada and Melini (2019), and Klemann and Groh (2013) extended to include rotational deformation following Martinec and Hagedoorn (2014). We use a single GRD estimate for changes in land water storage based on the projections of Wada et al. (2012), following Slangen et al. (2014). The geographic distributions of mass change for each component come from Slangen et al. (2014). Note that, while our results incorporate some uncertainty arising from different GRD model solutions, they do not account for uncertainties in the geographic distribution of mass change. Further details on the GRD calculations are available in the supporting information.\nThe GRD estimates are expressed as the local MSL change per unit GMSL rise from each of the following barystatic (i.e., GMSL mass addition/loss) terms: (i) Antarctic surface mass balance, (ii) Antarctic ice dynamics, (iii) Greenland surface mass balance, (iv) Greenland ice dynamics, (v) worldwide glaciers, and (vi) changes in land water storage (Figure 3). Loss of ice from the Antarctic and Greenland ice sheets are characterized by a near-field MSL fall and a greater-than-unity rise in the far-field (e.g., Figures 3a and 3g), with notable differences in the GRD estimates for surface mass balance and ice dynamics, owing to different geographic distributions of mass change. The GRD estimates associated with worldwide glaciers and land water storage are spatially more complex, owing to the more geographically widespread mass distributions (Figures 3c and 3i). The glacier GRD pattern assumes a fixed distribution of the ratios of glacier mass loss between the glacier regions based on the projected distribution in 2100 under RCP8.5 (Church et al., 2013). Previous analysis showed that this pattern does not vary much over the 21st century and the amount of mass closely related to the initial glacier mass for a given region. We acknowledge that this is a simplistic approach, and recent studies have shown that the mass loss distribution to be model and scenario dependent (Hock et al., 2019). For the local sea-level projections presented here, we expect the uncertainty in the total glacier contribution to dominate. However, future sea-level projections could be improved by more comprehensive representation of the uncertainties associated with the spatial pattern of future glacier mass loss.\nFigure 3: Estimates of the combined effect of mass changes on Earth\u2019s gravity, rotation, and solid earth deformation (GRD) on local relative sea level. Panels (a), (b), (c), (g) and (h) show the mean of three sets of estimates with corresponding standard deviations across estimates shown in (d), (e), (f), (j) and (k). only a single estimate was available for land water, and therefore, no standard deviation is shown. GRD estimates are expressed as the ratio of local MSL to GMSL per unit rise/fall with the 1:1 and zero contours indicated by the solid and dotted gray lines, respectively.\nThe spatial patterns of GRD can have an important impact on projections of local MSL change. Depending on the geographic location, components of GMSL change can be greatly attenuated (if the location is close to where the GRD pattern is zero) and even result in a change of sign of one or more components (where the GRD pattern has negative values).", "source": "https://sealeveldocs.readthedocs.io/en/latest/palmer20.html"}
{"id": "83d9565fb013-3", "text": "Figure 3: Estimates of the combined effect of mass changes on Earth\u2019s gravity, rotation, and solid earth deformation (GRD) on local relative sea level. Panels (a), (b), (c), (g) and (h) show the mean of three sets of estimates with corresponding standard deviations across estimates shown in (d), (e), (f), (j) and (k). only a single estimate was available for land water, and therefore, no standard deviation is shown. GRD estimates are expressed as the ratio of local MSL to GMSL per unit rise/fall with the 1:1 and zero contours indicated by the solid and dotted gray lines, respectively.\nThe spatial patterns of GRD can have an important impact on projections of local MSL change. Depending on the geographic location, components of GMSL change can be greatly attenuated (if the location is close to where the GRD pattern is zero) and even result in a change of sign of one or more components (where the GRD pattern has negative values).\nComputing the standard deviations across the three GRD estimates shows that differences are largest in the regions of ice/water mass loss (Figures 3d\u20133f, 3j, and 3k), corresponding to the negative value regions seen in the mean GRD patterns (Figures 3a\u20133c and 3g\u20133i). Away from these areas, the agreement among GRD estimates is high, with the standard deviation representing only a few % of the local mean signal. The circular spatial structures seen in the panels of standard deviation for the Greenland components (Figures 3j and 3k) and Antarctic ice dynamics (Figure 3e) resemble a 2-1 pattern of spherical harmonics and are indicative of slight differences in the rotational effects among the three estimates. Although all three estimates are based on the same well-understood physics, differences arise from the methods used to compute the Love numbers, as well as different grid formulations and spatial resolutions to solve the convolution integral (Table S3; see Martinec et al., 2018, for a discussion). From a practical standpoint, we find that the small differences among estimates lead to a negligible uncertainty for the tide gauge locations considered here, compared to the other factors (see section 4.3). For future studies that consider regions in closer proximity to the ice mass changes, increasing the spatial resolution would promote greater consistency among the GRD estimates.\nGlacial Isostatic Adjustment\uf0c1\nSimilar to the effects of GRD discussed in the previous section, ongoing glacial isostatic adjustment (GIA) also leaves its imprint in the spatial pattern of MSL change. GIA is associated with the adjustment of Earth\u2019s lithosphere and viscous mantle material to past changes in ice loading since the last glaciation (e.g., Tamisiea & Mitrovica, 2011). This adjustment process gives rise to areas of upward and downward vertical land motion, and the associated mass redistribution also influences Earth\u2019s rotation and gravity field with additional impacts on local MSL. It is well known that GIA leads to substantial spatial variations in the rates of MSL change observed at tide gauges and, such as the lower rate of sea-level rise seen for the north of the United Kingdom compared to the south (Howard et al., 2019; Palmer, Harris, et al., 2018). Since the adjustment time scales of GIA are thousands of years, we make the approximation that the contemporary rates of its effect on local MSL change are valid for the projections (i.e., the rates are assumed to be time constant).\nWe use three global GIA estimates in this study. The first is based on the ICE-5G (VM2 L90) model (Peltier, 2004). The second is based on ICE-6G_C (VM5a) (Argus et al., 2014; Peltier et al., 2015). ICE-6G_C is a refinement of the ICE-5G model, based on a wider range of observational constraints, including new data from Global Positioning System (GPS) receivers and as time-dependent gravity observations from both surface measurements and the satellite-based Gravity Recovery and Climate Experiment GRACE (Peltier et al., 2015). Peltier et al. (2015) state that the GIA solution from ICE-6G_C uses an improved ice loading history compared to ICE5G. Both of these data sets were sourced from http://www.atmosp.physics.utoronto.ca/~peltier/data.php. The final global GIA data product represents an independent estimate from the Australian National University based on an update of Nakada and Lambeck (1988) in 2004\u20132005. This final GIA estimate is identical to that used by Slangen et al. (2014). All three GIA data sets are provided on a 1 \u200a\u00d7\u200a 1\u00b0 latitude-longitude grid.\nThere are substantial differences among all three GIA estimates, despite ICE5G and ICE6G originating from the same modeling group. The overall spread in GIA estimates is largest for areas of North America, the Arctic, and Antarctica, that is, the regions of large ice mass changes during the last deglaciation. A detailed comparison and explanation for the differences is beyond the scope of this paper. A major limitation in GIA modeling is the lack of 3-D earth structures together with glaciation histories which in combination can be constrained locally against observational data. However, the optimized global 1-D estimates presented here represent a compromise, and therefore, our study may tend to overestimate the GIA uncertainty compared to locally optimized solutions. For example, UKCP18 used a regional, observationally constrained GIA solution with substantially smaller estimated uncertainties reported here (Howard et al., 2019; Palmer, Howard, et al., 2018).\nMethods\uf0c1\nGlobal-Mean Sea-Level Projections\uf0c1\nThe local MSL projections presented here are based on 21st century process-based projections of GMSL presented in IPCC AR5 (Church et al., 2013). The GMSL projections are composed of seven components: (i) global-mean thermosteric sea level; and barystatic sea level due to (ii) Antarctic surface mass balance; (iii) Antarctic ice dynamics; (iv) Greenland surface mass balance; (v) Greenland ice dynamics; (vi) worldwide glaciers; and (vii) net changes in land water storage. The first component is also referred to as \u201cglobal thermal expansion\u201d and is the only term that does not constitute a change in ocean mass following Gregory et al. (2019).\nFor the period out to 2100, the GMSL projections are underpinned by 21 CMIP5 climate model simulations (Taylor et al., 2012) of global thermal expansion (GTE) and global-mean surface temperature (GMST) change under the Representative Concentration Pathway (RCP) climate change scenarios (Meinshausen et al., 2011). For the extended period out to 2300 we use projections of GTE and GMST change from a physically based emulator that has been tuned to 16 CMIP5 models (Palmer, Harris, et al., 2018) under the RCP extensions (Meinshausen et al., 2011). Of the two sets of CMIP5 models, 11 are common across both the 21st century projections and the extended 2300 projections (Table S2).\nNote that the extended projections were not included in AR5 and represent one of the novel aspects of this study. We stress here that there is a much greater degree of uncertainty associated with the extended projections to 2300 than for the 21st century projections. For example, the RCP extensions make very simple assumptions about emissions trajectories, and there is deep uncertainty associated with the response of ice sheets on multicentury time scales (e.g., Edwards et al., 2019). While we present the two time horizons alongside each other for reader convenience, the extended 2300 projections should be regarded with a lower degree of confidence and treated as illustrative of the potential changes.", "source": "https://sealeveldocs.readthedocs.io/en/latest/palmer20.html"}
{"id": "83d9565fb013-4", "text": "Methods\uf0c1\nGlobal-Mean Sea-Level Projections\uf0c1\nThe local MSL projections presented here are based on 21st century process-based projections of GMSL presented in IPCC AR5 (Church et al., 2013). The GMSL projections are composed of seven components: (i) global-mean thermosteric sea level; and barystatic sea level due to (ii) Antarctic surface mass balance; (iii) Antarctic ice dynamics; (iv) Greenland surface mass balance; (v) Greenland ice dynamics; (vi) worldwide glaciers; and (vii) net changes in land water storage. The first component is also referred to as \u201cglobal thermal expansion\u201d and is the only term that does not constitute a change in ocean mass following Gregory et al. (2019).\nFor the period out to 2100, the GMSL projections are underpinned by 21 CMIP5 climate model simulations (Taylor et al., 2012) of global thermal expansion (GTE) and global-mean surface temperature (GMST) change under the Representative Concentration Pathway (RCP) climate change scenarios (Meinshausen et al., 2011). For the extended period out to 2300 we use projections of GTE and GMST change from a physically based emulator that has been tuned to 16 CMIP5 models (Palmer, Harris, et al., 2018) under the RCP extensions (Meinshausen et al., 2011). Of the two sets of CMIP5 models, 11 are common across both the 21st century projections and the extended 2300 projections (Table S2).\nNote that the extended projections were not included in AR5 and represent one of the novel aspects of this study. We stress here that there is a much greater degree of uncertainty associated with the extended projections to 2300 than for the 21st century projections. For example, the RCP extensions make very simple assumptions about emissions trajectories, and there is deep uncertainty associated with the response of ice sheets on multicentury time scales (e.g., Edwards et al., 2019). While we present the two time horizons alongside each other for reader convenience, the extended 2300 projections should be regarded with a lower degree of confidence and treated as illustrative of the potential changes.\nWhile AR5 included scenario-independent projections of Antarctic ice dynamics based on the assessed literature, we use a parameterization of scenario-dependent projections presented by Levermann et al. (2014). This procedure is based on temperature-dependent log-normal fits to the percentiles from probability distribution functions for the sea-level contribution at 2100 for each scenario (Levermann et al., 2014; Table 6, \u201cshelf models\u201d with time delay). All percentiles are reproduced to within \u00b10.01 m by our fits, except that the 95th percentile for RCP2.6 is slightly too high (0.26 m for the fit compared to 0.23 m in their table). We use the parameterized 5th to 95th percentile ranges at 2100 with the time dependence obtained as in the AR5 (Church et al., 2013; 13.SM1.6). Recent work has highlighted the potential importance of self-sustaining dynamic ice feedbacks (DeConto & Pollard, 2016), which are not explicitly accounted for in Levermann et al. (2014). However, the Levermann et al. (2014) study yields a similar projected range to other recent studies that do include these effects (Edwards et al., 2019). In addition, a recent analysis suggests that the likelihood of rapid acceleration of dynamic ice loss from West Antarctica simulated by DeConto and Pollard (2016) was overestimated (Edwards et al., 2019).\nWe follow the same approach as AR5 in constructing a 450,000-member Monte Carlo simulation for each RCP scenario that forms the basis of both the GMSL and local MSL projections. The methods used for each component and for our two different time horizons are summarized in Table 1. With the exception of changes in Greenland ice dynamics and land water storage, all GMSL components are dependent on the climate change scenario. The scenario-independent projections have ranges based on the literature assessed in AR5.\nTable 1: The Methods Used for Each Component of Global-Mean Sea Level (GMSL) Change According to Time Horizon\nSea-level component     21st century method     Extended 2300 method\nGlobal thermal expansion (GTE)      Projections are based on simulations with an ensemble of 21 CMIP5 models (Table S2) as described by Church et al. (2013) and in the text above. Any scenarios not available for a given model were estimated by the method of Good et al. (2013) from its other RCP and abrupt 4\u200a\u00d7 CO2 experiments.     Projections are based on the CMIP5-based emulator ensemble of Palmer, Harris, et al. (2018) and the corresponding CMIP5 model expansion efficiencies documented by Lorbacher et al. (2015).\nAntarctica: surface mass balance   GMSL rise is projected from global-mean surface temperature (GMST) change T(t) (as described by Church et al. (2013), as the time-integral of APR(1\u2013S) T(t), where A is the time-mean snowfall accumulation during 1985\u20132005, P \u200a= 5.1 \u00b1 1.5% \u00b0C\u200a\u22121 is the rate of increase of snowfall with Antarctic warming, R \u200a= 1.1 \u00b1 0.2 is the ratio of Antarctic to global warming, and S is a number in the range 0.00\u20130.035 that quantifies the increase in ice discharge due to increased accumulation. The Monte Carlo chooses P, R, and S independently; P and R are normally distributed and S uniformly. Projections of GMST change come from the same ensemble of 21 CMIP5 models as for GTE.   The same relationship with global surface temperature change is applied out to 2300 (Church et al., 2013). Projections of time-integral global surface temperature change come from the CMIP5-based 16-member emulator ensemble of Palmer, Harris, et al. (2018; Table S2).\nAntarctica: ice dynamics  A scenario-dependent projection based on the results of Levermann et al. (2014). GMSL rise is modeled as a quadratic function of time, beginning with the observational rate of dynamic mass loss in 2006 and reaching Lex at 2100, where x is chosen by the Monte Carlo from a normal distribution with zero mean and standard deviation \u03bb. The parameters L and \u03bb are scenario-dependent; for instance, RCP2.6 has L \u200a=\u200a 56 mm and \u03bb \u200a=\u200a 0.92, RCP8.5 91 mm and 0.86. The 2100 rate is held constant between 2100 and 2300.\nGreenland: surface mass balance    GMSL rise is projected from GMST change (Church et al., 2013) as the time integral of EFG(T(t)), where G gives the change in Greenland SMB as a cubic function of GMST change according to Equation (2) of Fettweis et al. (2013), derived from regional climate model projections. F is a factor representing systematic uncertainty in G, and E is a factor in the range 1.00\u20131.15 representing the enhancement of mass loss due to reduction of surface elevation. The Monte Carlo chooses E and F independently; E is uniformly distributed, and F \u200a=\u200a eN, where N is normally distributed with zero mean and standard deviation of 0.4. Projections of GMST change are the same as for Antarctic surface mass balance.     The 2100 rate is held constant between 2100 and 2300.\nGreenland: ice dynamics     Scenario-dependent projection based on the literature at the time of AR5 (Church et al., 2013). GMSL rise is modeled as a quadratic function of time, beginning with the observational rate of dynamic mass loss in 2006 and reaching 0.020\u20130.085 m for RCP8.5 and 0.014\u20130.063 m for the other RCPs at 2100. The Monte Carlo chooses the final amount uniformly within the ranges given.        The 2100 rate is held constant between 2100 and 2300.", "source": "https://sealeveldocs.readthedocs.io/en/latest/palmer20.html"}
{"id": "83d9565fb013-5", "text": "Antarctica: ice dynamics  A scenario-dependent projection based on the results of Levermann et al. (2014). GMSL rise is modeled as a quadratic function of time, beginning with the observational rate of dynamic mass loss in 2006 and reaching Lex at 2100, where x is chosen by the Monte Carlo from a normal distribution with zero mean and standard deviation \u03bb. The parameters L and \u03bb are scenario-dependent; for instance, RCP2.6 has L \u200a=\u200a 56 mm and \u03bb \u200a=\u200a 0.92, RCP8.5 91 mm and 0.86. The 2100 rate is held constant between 2100 and 2300.\nGreenland: surface mass balance    GMSL rise is projected from GMST change (Church et al., 2013) as the time integral of EFG(T(t)), where G gives the change in Greenland SMB as a cubic function of GMST change according to Equation (2) of Fettweis et al. (2013), derived from regional climate model projections. F is a factor representing systematic uncertainty in G, and E is a factor in the range 1.00\u20131.15 representing the enhancement of mass loss due to reduction of surface elevation. The Monte Carlo chooses E and F independently; E is uniformly distributed, and F \u200a=\u200a eN, where N is normally distributed with zero mean and standard deviation of 0.4. Projections of GMST change are the same as for Antarctic surface mass balance.     The 2100 rate is held constant between 2100 and 2300.\nGreenland: ice dynamics     Scenario-dependent projection based on the literature at the time of AR5 (Church et al., 2013). GMSL rise is modeled as a quadratic function of time, beginning with the observational rate of dynamic mass loss in 2006 and reaching 0.020\u20130.085 m for RCP8.5 and 0.014\u20130.063 m for the other RCPs at 2100. The Monte Carlo chooses the final amount uniformly within the ranges given.        The 2100 rate is held constant between 2100 and 2300.\nGlaciers   GMSL rise is projected from GMST change (Church et al., 2013) as mfI(t)p, where I(t) is the time integral of GMST change (in \u00b0C yr) since 2006. Four glacier models are represented by different f,p pairs, with f in the range 3\u20135 mm and p \u200a\u2248\u200a 0.7. The Monte Carlo gives equal probability to the four glacier models and chooses the random normally distributed factor m with a standard deviation of 20% representing systematic uncertainty. Projections of GMST change are the same as for Antarctic surface mass balance.      The same relationship with global surface temperature change is applied out to 2300 (Church et al., 2013) with a cap on the total sea level equivalent of 0.32 m to reflect current estimates of global glacier volume (Farinotti et al., 2019; Grinsted, 2013). Projections of global surface temperature change come from the CMIP5-based 16-member emulator ensemble of Palmer, Howard, et al. (2018; Table S2).\nLand water storage        Scenario-independent projection based on the literature at the time of AR5 (Church et al., 2013). GMSL rise is modeled as a quadratic function of time, beginning with the estimated rate for 2006 and having its time-mean for 2081\u20132100 uniformly distributed within the range \u200a\u2212\u200a10 to \u200a+\u200a90 mm by the Monte Carlo.  The 2100 rate is held constant between 2100 and 2300.\nFor the scenario-dependent terms, the ensemble spread arises from differences among the underlying CMIP5 (or emulator) simulations of GTE and GMST change and from any additional methodological uncertainties (Church et al., 2013). For each scenario, the climate model ensemble (CMIP5 or emulator) was treated as a normal distribution, with time-dependent ensemble mean QM(t) and standard deviation QS(t), where Q is GTE or GMST, both with respect to the time mean of 1986\u20132005, and t is time. Larger Monte Carlo ensembles were constructed with members Qi(t) \u200a=\u200a QM(t) \u200a+\u200a riQS(t), where {ri} is a set of normal random numbers (with zero mean and unit standard deviation). The {ri} are time-independent, and the same {ri} were used for GTE and GMST, so that variations within the ensemble were correlated over time and between the two quantities.\nThe glacier contribution to GMSL is based on a relationship between the global glacier contribution and GMST change (Church et al., 2013), which is also applied post-2100. The total contribution is capped at 0.32 m, based on current estimates of total glacier mass (Farinotti et al., 2019; Grinsted, 2013). However, we note that this is a simplistic assumption. It is possible that remaining glaciers might reach a new steady state under a stable future climate following preferential loss of low-altitude ablation areas, a possibility that was not accounted for in the AR5 projections, or here.\nThe different GMSL components are combined using a 450,000-member Monte Carlo simulation that samples from the underlying distributions. The procedure preserves the correlation between GTE and GMST change in the underlying CMIP5 model simulations (or the emulator ensemble for the period post-2100). As a result, many of the GMSL components are correlated, as discussed further in section 4. In addition, the effect of increased accumulation on the dynamics of the Antarctic ice sheet is represented in the same way as described in AR5 (Church et al., 2013; SM1.5), resulting in these terms also being weakly correlated. The sampled distributions are based on the 5th to 95th percentile ranges of the climate model simulations and literature-based assessed ranges for the scenario-independent terms. Each member of the Monte Carlo simulation is composed of a time series for each of the seven GMSL contributions listed in Table 1 with the correlations between terms preserved.\nLocal Sea-Level Projections\uf0c1\nAs we move to local MSL projections, a number of additional processes are taken into account. First, the spatial patterns of MSL change associated with each of the barystatic GMSL contributions (Table 1, ii\u2013vii) are incorporated using estimates of the effects on Earth\u2019s gravity, rotation, and solid earth deformation (GRD, Figure 3). Following previous studies (Bilbao et al., 2015; Palmer, Howard, et al., 2018; Perrette et al., 2013), the effects of local changes in ocean density and circulation are included by establishing regression relationships between global thermal expansion and local sterodynamic sea-level change in CMIP5 climate model simulations (see supporting information, Figures S1\u2013S4). Finally, the spatial pattern of local MSL change from ongoing glacial isostatic adjustment (GIA, Figure 4) is included in our local MSL projections.\nFigure 4: (a)\u2013(c) three estimates of the effect of glacial isostatic adjustment (GIA) on sea-level change. The zero line is indicated by the dotted contours. (d) the standard deviation of the three GIA estimates. Units for all panels are mm yr^{\u22121}.\nThe projections of local MSL change for specific tide gauge locations (Figure 1, Table S1) are derived directly from the GMSL Monte Carlo projections described in the previous section. This represents an advance over the local MSL projections presented in AR5 (Church et al., 2013), which combined the different components post hoc using statistical approximations (see supplementary materials of Cannaby et al., 2016; Church et al., 2013). These approximations break the correlation structure among sea-level components and compromise the traceability of the local projections, including our understanding of how the different variances combine for total sea-level change locally.", "source": "https://sealeveldocs.readthedocs.io/en/latest/palmer20.html"}
{"id": "83d9565fb013-6", "text": "Local Sea-Level Projections\uf0c1\nAs we move to local MSL projections, a number of additional processes are taken into account. First, the spatial patterns of MSL change associated with each of the barystatic GMSL contributions (Table 1, ii\u2013vii) are incorporated using estimates of the effects on Earth\u2019s gravity, rotation, and solid earth deformation (GRD, Figure 3). Following previous studies (Bilbao et al., 2015; Palmer, Howard, et al., 2018; Perrette et al., 2013), the effects of local changes in ocean density and circulation are included by establishing regression relationships between global thermal expansion and local sterodynamic sea-level change in CMIP5 climate model simulations (see supporting information, Figures S1\u2013S4). Finally, the spatial pattern of local MSL change from ongoing glacial isostatic adjustment (GIA, Figure 4) is included in our local MSL projections.\nFigure 4: (a)\u2013(c) three estimates of the effect of glacial isostatic adjustment (GIA) on sea-level change. The zero line is indicated by the dotted contours. (d) the standard deviation of the three GIA estimates. Units for all panels are mm yr^{\u22121}.\nThe projections of local MSL change for specific tide gauge locations (Figure 1, Table S1) are derived directly from the GMSL Monte Carlo projections described in the previous section. This represents an advance over the local MSL projections presented in AR5 (Church et al., 2013), which combined the different components post hoc using statistical approximations (see supplementary materials of Cannaby et al., 2016; Church et al., 2013). These approximations break the correlation structure among sea-level components and compromise the traceability of the local projections, including our understanding of how the different variances combine for total sea-level change locally.\nThe local MSL projection Monte Carlo simulations presented here are computed as follows. For a given RCP scenario, a single instance of the 450,000-member Monte Carlo of GMSL is randomly drawn. Each instance includes a time series for the seven GMSL components that preserves the underlying correlations among them. The barystatic timeseries (Table 1, ii\u2013vii) are combined with the corresponding GRD estimates (Figure 3) from one of the three sets at the tide gauge latitude and longitude. This selection is made at random with all GRD patterns based on the same model, in order to preserve any correlated errors. The only exception is for land water, for which only a single GRD estimate is available (Slangen et al., 2014). The timeseries of global thermal expansion is combined with a randomly drawn regression coefficient from one of the 21 CMIP5 models in order to estimate the sterodynamic sea-level change at the tide gauge location. The resulting seven timeseries of local MSL change are then combined with an estimate of the rate of MSL change associated with GIA using one of the three estimates (Figure 4) drawn at random. This procedure (shown schematically in Figure 5) is repeated 100,000 times for each tide gauge location to build up a distribution of MSL projections under each RCP scenario. Following the approach of AR5, we take the 5th and 95th percentiles of this distribution to indicate the spread of projections for individual components and the total MSL change.\nFigure 5: A schematic representation of the Monte Carlo simulation performed for the local mean sea level (MSL) projections. The above process is repeated 100,000 times to build up a distribution of sea level projections for each tide gauge location for each RCP scenario.\nResults\uf0c1\nGlobal-Mean Sea-Level Projections\uf0c1\nOur projections of GMSL change show good agreement with recent observations based on satellite altimeter measurements (Figure 6). For the overlapping period of 2007\u20132015 the 50th percentile of the RCP4.5 projection gives the same rate as the altimeter observations of 3.8 mm per year. The observed rate of GMSL for the entire 1993\u20132015 period is 3.0 mm per year, indicating an acceleration over time (Nerem et al., 2018) that is also seen in the projections. For the period out to 2030 there is little difference among the projected rates of across the three RCP scenarios.\nFigure 6: Comparison of satellite altimeter observations (black) with our projections of global-mean sea-level change for the period 1993 to 2030. The 50th percentile and 5th to 95th percentile range for RCP4.5 are shown by the solid line and shaded region, respectively. Also shown are the 5th and 95th percentile projections for RCP2.6 and RCP8.5 (dotted lines) as indicated in the figure legend. The satellite altimeter timeseries has been adjusted so that the mean value matches the 50th percentile of the RCP4.5 projections over the period 2007\u20132015.\nOur projections of GMSL change over the 21st century (Figure 7; Table 2) yield similar ranges to those presented in AR5 (Church et al., 2013) and SROCC (Oppenheimer et al., 2019). The inclusion of an updated Antarctic ice dynamics component following Levermann et al. (2014) in the present study increases the overall uncertainties and the skewness of the distribution and results in a slightly higher central estimate for RCP8.5 compared to AR5. The SROCC projections were also based on AR5, but with an updated estimate of the contribution from Antarctica based on several process-based studies (including Levermann et al., 2014). The SROCC projected ranges at 2100 are very similar to AR5, except for the RCP8.5 scenario, which is systematically higher and shows a larger uncertainty. Our extended GMSL projections show a high degree of consistency with the CMIP5-based 21st century projections evaluated at 2100 (Table 2), with all ranges agreeing to within a few centimeters.\nFigure 7: Projections of global-mean sea-level change for RCP2.6 (left), RCP4.5 (middle), and RCP8.5 (right) based on the 21st century methods (a\u2013c) and the extended 2300 methods (d\u2013f) (Table 1). Sea-level components are shown as indicated in the figure legend. The shaded regions show the 5th to 95th percentile range from the 450,000-member Monte Carlo simulation for global thermal expansion (red) and the total (gray). The dashed and dotted lines indicate the 50th percentile and 5th to 95th percentile range from the Monte Carlo simulation presented in IPCC AR5 (Church et al., 2013). The gray shaded bars on the right-hand side of each plot indicates the 5th to 95th percentile range at 2100 or 2300 from the IPCC SROCC (Oppenheimer et al., 2019). All projections are plotted relative to a baseline period of 1986\u20132005. Note the change of y-axis scale for for panel (f).\nTable 2: Comparison of Projected Ranges of Global-Mean Sea-Level Rise\nProjection      Year    RCP2.6  RCP4.5  RCP8.5\nIPCC AR5        2100    0.28\u20130.61 m     0.36\u20130.71 m     0.52\u20130.98 m\nIPCC SROCC      2100    0.28\u20130.59 m     0.38\u20130.72 m     0.61\u20131.11 m\nThis study (21st century)       2100    0.28\u20130.66 m     0.37\u20130.78 m     0.55\u20131.11 m\nThis study (extended 2300)      2100    0.28\u20130.67 m     0.35\u20130.78 m     0.52\u20131.11 m\nThis study (extended 2300)      2200a   0.5\u20131.5 m       0.7\u20131.8 m       1.3\u20132.9 m\nThis study (extended 2300)      2300a   0.6\u20132.2 m       0.9\u20132.6 m       1.7\u20134.5 m\nIPCC SROCC      2300a   0.6\u20131.1 m       \u2014       2.3\u20135.4 m\nSROCC expert elicitation        2300a   0.5\u20132.3 m       \u2014       2.0\u20135.4 m\nNauels et al. (2017)    2300a   0.8\u20131.4 m       1.3\u20132.3 m       3.4\u20136.8 m\nNote. All projections are expressed relative to a baseline period of 1986\u20132005.\n^a Due to large uncertainties associated with post-2100 projections, these values are reported to the nearest 0.1 m.", "source": "https://sealeveldocs.readthedocs.io/en/latest/palmer20.html"}
{"id": "83d9565fb013-7", "text": "Table 2: Comparison of Projected Ranges of Global-Mean Sea-Level Rise\nProjection      Year    RCP2.6  RCP4.5  RCP8.5\nIPCC AR5        2100    0.28\u20130.61 m     0.36\u20130.71 m     0.52\u20130.98 m\nIPCC SROCC      2100    0.28\u20130.59 m     0.38\u20130.72 m     0.61\u20131.11 m\nThis study (21st century)       2100    0.28\u20130.66 m     0.37\u20130.78 m     0.55\u20131.11 m\nThis study (extended 2300)      2100    0.28\u20130.67 m     0.35\u20130.78 m     0.52\u20131.11 m\nThis study (extended 2300)      2200a   0.5\u20131.5 m       0.7\u20131.8 m       1.3\u20132.9 m\nThis study (extended 2300)      2300a   0.6\u20132.2 m       0.9\u20132.6 m       1.7\u20134.5 m\nIPCC SROCC      2300a   0.6\u20131.1 m       \u2014       2.3\u20135.4 m\nSROCC expert elicitation        2300a   0.5\u20132.3 m       \u2014       2.0\u20135.4 m\nNauels et al. (2017)    2300a   0.8\u20131.4 m       1.3\u20132.3 m       3.4\u20136.8 m\nNote. All projections are expressed relative to a baseline period of 1986\u20132005.\n^a Due to large uncertainties associated with post-2100 projections, these values are reported to the nearest 0.1 m.\nThe extended 2300 projections illustrate the long-term committed sea-level rise under all RCP scenarios and the large uncertainties associated with these time horizons. At these extended time horizons, there is a greater distinction between scenarios than for the 21st century, and the benefits of reduced greenhouse gas emissions on the potential magnitude of committed future sea-level rise are clear (cf. RCP2.6 and RCP8.5 at 2300, Table 2). For the extended 2300 projections, the total glacier ice mass becomes exhausted between 2200 and 2300 under RCP4.5 and between 2100 and 2300 under RCP8.5 (Figure 7).\nGiven the different methods, and the inherently large uncertainty associated with projections on multicentury time horizons, our projected values at 2300 are broadly consistent with the estimates presented in IPCC SROCC (Oppenheimer et al., 2019) and Nauels et al. (2017) (Table 2). Our results show a substantially larger projected range for RCP2.6 (0.6\u20132.2 m) than the SROCC likely range (0.6\u20131.1 m) and Nauels et al. (2017; 0.8\u20131.4 m). This larger range arises primarily from the Antarctica ice dynamics term (Figure 8; Figure S5) and may have important implications for adaptation planning. Both SROCC (2.3\u20135.4 m) and Nauels et al. (2017; 3.4\u20136.8 m) show higher projected ranges under RCP8.5 than the present study (1.7\u20134.5 m). For SROCC, these larger values arise primarily from the Antarctic component (Figure 8). For Nauels et al. (2017) the difference seems to arise from larger contributions and greater uncertainties in both global thermal expansion and Greenland surface mass balance (Figure S5).\nFigure 8: Components of projected global-mean sea-level (GMSL) change at 2100 (a\u2013c, based on 21st century methods) and 2300 (d\u2013f, based on extended 2300 methods) for RCP2.6 (left), RCP4.5 (middle), and RCP8.5 (right). The horizontal lines and shaded regions indicate the 50th percentile and the 5th to 95th percentile range, respectively, from the 450,000-member Monte Carlo simulation. Scenario-independent projections are shown in gray. For reference, the corresponding global-mean surface temperature (GMST) change is shown in the final column of each panel, with secondary y-axis on the right-hand side. All projections are expressed relative to the 1986\u20132005 average. Corresponding projected ranges from IPCC SROCC (Oppenheimer et al., 2019) are indicated by the dashed rectangles, based on the supplementary data files (GMSL and Antarctica) and table 13.SM.1/table 13.8 (other components) of Church et al. (2013).\nIn order to gain some initial insights into the drivers of GMSL change, we present the breakdown of components at 2100 and 2300 based on the 5th to 95th percentile range (Figure 8). For all scenarios and both time horizons, the single largest component of uncertainty is that associated with the contribution from Antarctica (combined effects of changes in surface mass balance and ice dynamics). The 5th to 95th percentile range for Antarctica includes negative values, which arises from positive surface mass balance owing to a warmer atmosphere transporting more moisture. The components and their uncertainties generally increase under the higher emissions scenarios for both time horizons. At 2100, the RCP8.5 scenario induces substantial increases in the contribution ranges for Greenland and worldwide glaciers. The exhaustion of glacier mass for the extended projections under RCP4.5 and RCP8.5 results in reduced uncertainty for this term at 2300.\nSince the 21st century projections in both SROCC and the current study use AR5 methods with updates only for Antarctica, the GMSL-component projections at 2100 are identical to SROCC except for that term (Figures 8a\u20138c). For all three RCP scenarios our projections show substantially larger uncertainties in the Antarctica component with higher 95th percentiles that translate into more modest differences in GMSL. For the projections on extended time horizons, the methods differ to a greater extent. The SROCC 2300 projections are based on Table 13.8 of AR5 (Church et al., 2013), which drew upon a diverse set of model simulations that were broadly categorized as \u201cLow,\u201d \u201cMedium,\u201d and \u201cHigh\u201d scenarios. The extended 2300 projections presented here are based on the RCP scenarios, using a physical framework that is consistent with the 21st century projections and traceable to CMIP5 climate model simulations.\nFor 2300, we see substantial differences between SROCC and the present study for the available GMSL components (Figures 8d\u20138f). No estimate of post-2100 land water changes were made for AR5/SROCC, and our methods use a simple assumption of applying the 2100 rates over the period 2100\u20132300 (Table 1). The magnitude and relative importance of GMSL components at 2300 show strong scenario dependence. For RCP8.5 the dominant terms become thermal expansion, Greenland and Antarctica with the scenario-independent land water changes and mass-limited glacier contribution becoming less important compared to RCP2.6 or RCP4.5. RCP8.5 also shows the largest difference between the projected ranges for the present study and SROCC, with substantial differences for all three of the leading component terms.\nThe 5th to 95th percentile component ranges combine nonlinearly to the overall projected ranges for GMSL (Figure 8). The reason for this is illustrated in Figure 9, which shows the correlation between components evaluated across the 450,000-member Monte Carlo set at 2100. Global thermal expansion, Greenland surface mass balance, and worldwide glaciers are all positively correlated: Stronger warming promotes an increased contribution to GMSL from all of these terms.\nFigure 9: Correlation matrices of the different GMSL components for each RCP scenario based on the Monte Carlo spread at 2100. The matrices illustrate the relationships between GMSL components and explain why the total variance is not identical to the sum of the variances of the components.", "source": "https://sealeveldocs.readthedocs.io/en/latest/palmer20.html"}
{"id": "83d9565fb013-8", "text": "For 2300, we see substantial differences between SROCC and the present study for the available GMSL components (Figures 8d\u20138f). No estimate of post-2100 land water changes were made for AR5/SROCC, and our methods use a simple assumption of applying the 2100 rates over the period 2100\u20132300 (Table 1). The magnitude and relative importance of GMSL components at 2300 show strong scenario dependence. For RCP8.5 the dominant terms become thermal expansion, Greenland and Antarctica with the scenario-independent land water changes and mass-limited glacier contribution becoming less important compared to RCP2.6 or RCP4.5. RCP8.5 also shows the largest difference between the projected ranges for the present study and SROCC, with substantial differences for all three of the leading component terms.\nThe 5th to 95th percentile component ranges combine nonlinearly to the overall projected ranges for GMSL (Figure 8). The reason for this is illustrated in Figure 9, which shows the correlation between components evaluated across the 450,000-member Monte Carlo set at 2100. Global thermal expansion, Greenland surface mass balance, and worldwide glaciers are all positively correlated: Stronger warming promotes an increased contribution to GMSL from all of these terms.\nFigure 9: Correlation matrices of the different GMSL components for each RCP scenario based on the Monte Carlo spread at 2100. The matrices illustrate the relationships between GMSL components and explain why the total variance is not identical to the sum of the variances of the components.\nConversely, Antarctic surface mass balance is strongly anticorrelated with these terms because a warmer atmosphere tends to promote greater snowfall on Antarctica and reduce GMSL. As discussed in section 3.1, the AR5 methods resulted in a weak correlation between the surface mass balance and ice dynamics terms for Antarctica, which is also included here. We find similar correlations among components for all RCPs (Figure 9), although these tend to be slightly reduced for the higher emissions scenarios. Analysis of correlations at 2300 in the extended projections yields similar results (Figure S6), except for the glacier term that shows weaker correlations for RCP4.5 and RCP8.5 owing to the cap on total ice mass (illustrated in Figures 7e and 7f).\nLocal Sea-Level Projections\uf0c1\nIn this section we present our local MSL projections for 16 example tide gauge sites (Figure 1; Table S1). We focus our presentation on the highest (RCP8.5) and lowest (RCP2.6) emissions scenarios and include annual-mean tide gauge and satellite altimeter timeseries to illustrate the observed trends and local sea-level variability (Figure 10). In general, there is good agreement between the observed decadal rates of MSL change and the early part of the projections, noting that the satellite altimeter timeseries do not account for vertical land motion processes associated with, for example, GIA, local subsidence, or tectonic activity. Locations of poorer agreement between observed and projected MSL trends include Lima and Port Louis. However, the high degree of consistency between altimeter and tide gauge observations at these locations suggests the discrepancy arises from climatic variability rather than non-GIA vertical land-motion processes. There is an apparent jump in the Pago Pago tide gauge timeseries towards the end of the record that could be related to a nearby earthquake in 2009 that resulted in several tsunami waves hitting the island. This jump is not seen in the satellite altimeter timeseries, confirming the likely role of substantial vertical land motion at this location. The observed interannual sea-level variability varies considerably by location and demonstrates that the reality of future sea-level change will be a combination of the climate response and unforced variability (e.g., Roberts et al., 2016).\nFigure 10: Local sea-level projections for RCP2.6 (blue) and RCP8.5 (red). Shaded regions indicate the 5th to 95th percentile range of the 100,000-member Monte Carlo simulation. The dotted lines indicate the 5th and 95th percentile projections from the IPCC SROCC (Oppenheimer et al., 2019). Local annual-mean tide gauge data are indicated by the solid black line. Local annual-mean satellite altimeter data are indicated by the solid gray line. All timeseries are shown relative to the 1986\u20132005 average. Note the different y-axis for Barentsburg.\nAs with GMSL, local MSL projections for the 21st century are similar to those reported in the IPCC SROCC (Figure 10) with agreement varying somewhat across tide gauge sites. Differences are thought to arise primarily from (i) the methods for estimating sterodynamic sea level and/or (ii) the methods used to combine sea-level components. It is apparent that the SROCC projections include some residual variability that originates from the underlying CMIP5 climate model simulations of sterodynamic sea-level change, which may also be present in the 1986\u20132005 reference state. Our regression-based approach to local sterodynamic sea-level change is designed to better isolate the climate change signal, resulting in smoother projections that do not include this simulated variability. This regression approach makes the approximation of a linear relationship between local sterodynamic sea-level change and global thermal expansion, which may also result in some differences with SROCC projections. Statistical approximations were used to combine the different local sea-level components for AR5 outside of the GMSL Monte Carlo framework that assumed terms were either perfectly correlated or perfectly uncorrelated, as described in equation 13.SM.1 of Church et al. (2013). This breaks the correlation structure among the GMSL components (Figure 9) and likely results in differences in the SROCC projected ranges for some locations. Re-running our local projections using only the GIA estimates used for AR5/SROCC (i.e., Lambeck and ICE5G, Figure 4) makes a negligible difference to the results shown in Figure 10. Analysis of the differences among our GRD fingerprints suggests that any differences in this regard are also likely to be negligible (see section 4.3).\nMost tide gauge locations show that MSL is currently rising and that this rise will accelerate over the 21st century under the RCP8.5 scenario. The 21st century rates of sea-level change under RCP2.6 are relatively stable and most locations show the scenarios diverging from the mid-21st century. For most locations, the change in sea level over the 21st century is large compared to the tide gauge variability and implies that adaptation measures will be necessary to preserve current levels of coastal flood protection.\nBarentsburg (Svalbard) and Reykjavik (Iceland) show atypical MSL projections. In both cases, the proximity to Greenland results in negative sea-level rise from this component (see Figure 3), which largely cancels out the positive contributions from the other climatic components, resulting in small scenario dependency at these locations. Barentsburg has a substantial rate of MSL fall associated with GIA, which accounts for the more negative values seen at this location compared to Reykjavik. While Oslo retains substantive scenario dependency, the negative GIA signal results in a much-reduced rates of rise under RCP8.5 and the expectation of a sea-level fall under RCP2.6. Barentsburg, Reykjavik, and Oslo clearly illustrate that projections of GMSL cannot necessarily be taken as indicative of local MSL change.\nExcluding these atypical tide gauge locations, we still see substantive variations in future sea-level rise across the remaining tide gauge sites. The range of behavior is spanned by New York and Stanley II with ranges at 2100 under RCP2.6 (RCP8.5) of 0.27\u20130.84 m (0.57\u20131.35 m) and 0.21\u20130.51 m (0.45\u20130.91 m), respectively. New York has a large spread in sterodynamic sea-level change and also a substantial positive contribution from GIA. The relative proximity of Stanley II (the Falkland Islands) to Antarctica results in a strong attenuation of the MSL change associated with Antarctic ice dynamics, which reduces both the overall magnitude and the spread of uncertainty in future projections.", "source": "https://sealeveldocs.readthedocs.io/en/latest/palmer20.html"}
{"id": "83d9565fb013-9", "text": "Most tide gauge locations show that MSL is currently rising and that this rise will accelerate over the 21st century under the RCP8.5 scenario. The 21st century rates of sea-level change under RCP2.6 are relatively stable and most locations show the scenarios diverging from the mid-21st century. For most locations, the change in sea level over the 21st century is large compared to the tide gauge variability and implies that adaptation measures will be necessary to preserve current levels of coastal flood protection.\nBarentsburg (Svalbard) and Reykjavik (Iceland) show atypical MSL projections. In both cases, the proximity to Greenland results in negative sea-level rise from this component (see Figure 3), which largely cancels out the positive contributions from the other climatic components, resulting in small scenario dependency at these locations. Barentsburg has a substantial rate of MSL fall associated with GIA, which accounts for the more negative values seen at this location compared to Reykjavik. While Oslo retains substantive scenario dependency, the negative GIA signal results in a much-reduced rates of rise under RCP8.5 and the expectation of a sea-level fall under RCP2.6. Barentsburg, Reykjavik, and Oslo clearly illustrate that projections of GMSL cannot necessarily be taken as indicative of local MSL change.\nExcluding these atypical tide gauge locations, we still see substantive variations in future sea-level rise across the remaining tide gauge sites. The range of behavior is spanned by New York and Stanley II with ranges at 2100 under RCP2.6 (RCP8.5) of 0.27\u20130.84 m (0.57\u20131.35 m) and 0.21\u20130.51 m (0.45\u20130.91 m), respectively. New York has a large spread in sterodynamic sea-level change and also a substantial positive contribution from GIA. The relative proximity of Stanley II (the Falkland Islands) to Antarctica results in a strong attenuation of the MSL change associated with Antarctic ice dynamics, which reduces both the overall magnitude and the spread of uncertainty in future projections.\nWe combine the tide gauge data with our local MSL projections to explore the relative importance of variability, scenario, and model uncertainty over the 21st century following Hawkins and Sutton (2009). Local sea-level variability is estimated by de-trending the tide gauge records and computing the standard deviation of the residual timeseries. The scenario standard deviation is estimated using the central estimates under RCP2.6, RCP4.5, and RCP8.5. Finally, the model uncertainty is estimated by computing the average standard deviation of the Monte Carlo simulation across the three RCP scenarios. Our analysis suggests that sea-level variability is likely to be a key driver of MSL change for the coming decades at all tide gauge locations (Figure 11). Conversely, the impact of RCP scenario will only make a substantive contribution towards the end of the 21st century. At Barentsburg and Reykjavik, differences across scenarios explain 10\u201320% of the projected variance, which is related to the negative contribution from Greenland canceling out other terms (as discussed above). At all locations, model uncertainty explains a large share of the overall variance and is particularly important for Barentsburg and Reykjavik.\nFigure 11: Assessment of the fraction of total variance of sea-level change explained by model, scenario, and variability, following Hawkins and Sutton (2009) as indicated in the figure legend for Auckland.\nThe extended 2300 projections again illustrate the large levels of committed sea-level change associated with both RCP2.6 and RCP8.5 for the coming centuries (Figure 12). The projections show greater separation between these two scenarios post-2100 and the large degree of uncertainty on these time horizons. For several sites, the projected range at 2300 for RCP8.5 exceeds 5 m. Even under RCP2.6 central estimates of sea-level rise are in excess of 1 m for most locations, and the projected range exceeds 2 m at many locations. The geographical variations in projections seen over the 21st century (Figure 10) are essentially preserved (as a proportion of the signal size), resulting in differences in the projected ranges up to several meters. At these extended time horizons, the projected sea-level changes are an order of magnitude greater than the interannual tide gauge variability. At most locations, the magnitude of MSL rise and the projected range is larger than for the corresponding projection of GMSL (Figure 7). A large part of the increased spread comes from the amplification of the Antarctic ice sheet signals (the greatest source of uncertainty, Figure 8) by the GRD patterns, which have local values greater than unity for most tide gauge sites.\nFigure 12: Local sea-level projections for RCP2.6 (blue) and RCP8.5 (red). Shaded regions indicate the 5th to 95th percentile range of the 100,000-member Monte Carlo simulation. Annual tide gauge data are indicated by the black line. All timeseries are shown relative to the 1986\u20132005 average. Note the different y-axis for Barentsburg, Oslo, and Reykjavik.\nAnalysis of Model Uncertainty\uf0c1\nIn this section, we further explore the contributions to the model uncertainty that is represented by the projected ranges of sea-level change for a given scenario. In particular, we consider which MSL components are dominant in determining the total variance in projected ranges as a function of geographic location, time horizon, and RCP scenario. We compute the total variance for the GMSL timeseries and several example tide gauge locations for both RCP2.6 and RCP8.5. We also compute the covariance matrix across the Monte Carlo ensembles as a function of time. The off-diagonal elements of the matrix are combined into an additional term that we label \u201cinteractions\u201d\u2014with this contribution arising from correlations among the components. While this analysis was performed on both, the 21st century and extended 2300 projections, the results up to 2100 are similar (Figure S7). For this reason, we focus our presentation on the extended 2300 results so that we can look across all relevant time scales. In some instances, the anticorrelation between terms leads to a reduction of total variance. For simplicity of the graphical representation and to focus discussion on the relative importance of contributions to variance in general, our analysis is based on the absolute variances.\nThe total variance at 2300 under RCP8.5 is more than double that for RCP2.6, both globally and at all tide gauge locations (Figures 13 and 14; left column), indicating the inherently larger uncertainties under high emissions scenarios, related to the uncertainty in model climate sensitivity. For GMSL (Figure 13, top row) the ensemble spread is initially dominated by global thermal expansion, but uncertainty in Antarctic ice dynamics becomes the dominant term from the latter half of the 21st century. Prior to 2100, there is little difference in the breakdown of variance by RCP scenario. Post-2100 we see a much larger contribution from Greenland surface mass balance under RCP8.5, becoming the second largest source of variance after Antarctic ice dynamics.\nFigure 13: Time evolution of variance associated with model uncertainty for GMSL and three example tide gauge sites under RCP2.6 and RCP8.5 based on the extended projections to 2300. The left column shows the time evolution of total variance. The central and right columns show the time-evolution fraction of variance explained for RCP2.6 and RCP8.5, respectively, as indicated in the bottom-right panel legend. For GMSL, \u201cexp\u201d refers to global thermal expansion. For tide gauge sites, \u201cexp\u201d refers to sterodynamic sea-level change. Estimates for each variance term come from the diagonal of the covariance matrix. The off-diagonal contributions are presented as a combined term labeled \u201cinteractions.\u201d\nFigure 14: Time evolution of variance associated with model uncertainty for four example tide gauge sites under RCP2.6 and RCP8.5 based on the extended projections to 2300. The left column shows the time evolution of total variance. The central and right columns show the time-evolution fraction of variance explained for RCP2.6 and RCP8.5, respectively, as indicated in the bottom-right panel legend. Note that \u201cexp\u201d refers to sterodynamic sea-level change. Estimates for each variance term come from the diagonal of the covariance matrix. The off-diagonal contributions are presented as a combined term labeled \u201cinteractions.\u201d\nThe breakdown of variance for Barentsburg (Svalbard; Figure 13) shows a dominant contribution from glaciers over the 21st century, and this term remains important out to 2300. This feature is due to the large glacier mass on Svalbard, which leads to large negative values in the GRD estimates associated primarily with vertical land uplift. We see strong scenario dependence on the contributions to variance post-2100, with Greenland surface mass balance and sterodynamic sea-level change becoming much more important under RCP8.5 than RCP2.6. Variance arising from GIA estimates makes only a minor contribution at this location.", "source": "https://sealeveldocs.readthedocs.io/en/latest/palmer20.html"}
{"id": "83d9565fb013-10", "text": "Figure 13: Time evolution of variance associated with model uncertainty for GMSL and three example tide gauge sites under RCP2.6 and RCP8.5 based on the extended projections to 2300. The left column shows the time evolution of total variance. The central and right columns show the time-evolution fraction of variance explained for RCP2.6 and RCP8.5, respectively, as indicated in the bottom-right panel legend. For GMSL, \u201cexp\u201d refers to global thermal expansion. For tide gauge sites, \u201cexp\u201d refers to sterodynamic sea-level change. Estimates for each variance term come from the diagonal of the covariance matrix. The off-diagonal contributions are presented as a combined term labeled \u201cinteractions.\u201d\nFigure 14: Time evolution of variance associated with model uncertainty for four example tide gauge sites under RCP2.6 and RCP8.5 based on the extended projections to 2300. The left column shows the time evolution of total variance. The central and right columns show the time-evolution fraction of variance explained for RCP2.6 and RCP8.5, respectively, as indicated in the bottom-right panel legend. Note that \u201cexp\u201d refers to sterodynamic sea-level change. Estimates for each variance term come from the diagonal of the covariance matrix. The off-diagonal contributions are presented as a combined term labeled \u201cinteractions.\u201d\nThe breakdown of variance for Barentsburg (Svalbard; Figure 13) shows a dominant contribution from glaciers over the 21st century, and this term remains important out to 2300. This feature is due to the large glacier mass on Svalbard, which leads to large negative values in the GRD estimates associated primarily with vertical land uplift. We see strong scenario dependence on the contributions to variance post-2100, with Greenland surface mass balance and sterodynamic sea-level change becoming much more important under RCP8.5 than RCP2.6. Variance arising from GIA estimates makes only a minor contribution at this location.\nIn contrast, Reykjavik (Iceland; Figure 13) has a large contribution to variance from the different GIA estimates, and this is the dominant source of variance over most of the 21st century. Post-2100, Antarctic ice dynamics dominates the variance under RCP2.6, with GIA remaining an important contribution for this scenario. For RCP8.5, Greenland surface mass balance and Antarctic ice dynamics contribute similarly to total variance post-2100.\nAs discussed in the previous section, New York (USA; Figure 13) has a particularly large uncertainty associated with future changes in ocean circulation, and this is reflected in the dominance of sterodynamic sea-level change over the 21st century. GIA is also relatively important at this location, particularly under RCP2.6. Again, it is ultimately the Antarctic ice dynamics that becomes the dominant source of variance post-2100, but sterodynamic sea-level change remains a sizeable contribution under RCP8.5.\nThe breakdown of variance for Mera (Japan; Figure 14) and Diamond Harbour (India; Figure 14) is typical of many lower latitude locations with characteristics that are very similar to that of GMSL (Figure 13, top row). Mera has a substantive contribution from land water under RCP2.6 that is absent from Diamond Harbour. At both locations, the contribution from GIA is very small, indicating that future changes will be dominated by contemporary climate-driven changes. As with all tide gauge locations, we cannot rule out the potential importance of nonclimatic processes, particularly those associated with vertical motion (e.g., subsidence and tectonic activity).\nPalermo (Argentina; Figure 14) shows a marked reduction in the contribution from Antarctic ice dynamics, which is associated with its proximity to West Antarctica (Figure 3b). This is also reflected in the reduced total variance seen at this tide gauge location for both RCP scenarios compared to GMSL. This results in a larger relative importance of many of the other MSL components. Variance arising from different scenarios of land water change is the second largest post-2100 term (after Antarctic ice dynamics) under RCP2.6. For RCP8.5, post-2100 variance is dominated by Greenland surface mass balance.\nLike Palermo, Stanley II (Falkland Islands; Figure 14) also sees a reduced total variance compared to GMSL resulting from the proximity of Antarctica. In this case, Antarctic ice dynamics makes a negligible contribution to total variance because the tide gauge location is close to the zero contour of the associated GRD pattern of MSL change (Figure 3b). The relative importance of the other terms over the 21st century is similar to Palermo. Post-2100, land water dominates the variance under the RCP2.6 scenario, and Greenland surface mass balance dominates for the RCP8.5 scenario. In the absence of substantive signals from Antarctic ice dynamics, the anticorrelated contributions of Greenland and Antarctic surface mass balance lead to a particularly large \u201cinteractions\u201d term that reduces the overall variance compared to GMSL.\nThe importance of the land water contribution for both Palermo and Stanley II under RCP2.6 arises for a number of reasons. First, the land water projections are scenario-independent, so its relative importance increases under RCP2.6 compared to RCP8.5. Second, the relative importance of land water is further increased at these locations due to the strong attenuation of the Antarctica signals, in relation to GRD (Figure 3), as discussed above. Third, both Palermo and Stanley II are in a region where the global land water contribution (and its uncertainty) is amplified at regional scales by the GRD patterns (Figure 3).\nOverall, we see a strong geographic and time dependence of the contribution to total variance. There is little scenario dependence until after 2100, and this is typified by a substantially increased contribution from Greenland surface mass balance under RCP8.5. Antarctic ice dynamics tend to dominate the total variance from the latter half of the 21st century out to 2300 under both RCP2.6 and RCP8.5. However, this is not the case for locations in proximity to West Antarctica (e.g., southern South America), where the GRD pattern of MSL results in greatly attenuated signals for Antarctic ice dynamics. The contrasting results presented here make a clear case for the need for site-specific local sea-level projections. In addition, the reduction of variance (uncertainty) in future projections implies different research priorities, depending on geographic location and time horizon.\nAs part of our analysis of variance, we also investigate the contribution from uncertainty in the GRD estimates presented in section 2.4 (Figure 3). We choose the three tide gauge sites with the largest spread in one or more GRD components, that is, Barentsburg, Reykjavik, and Stanley II, and conduct the following simple analysis. We run an additional instance of the MSL Monte Carlo for each location using the average value of the GRD fingerprints at each site for RCP8.5 (i.e., the scenario with the largest signal). The projected MSL and component ranges are then compared to the full Monte Carlo simulations that include a random choice of GRD estimate. The results demonstrate that using multiple GRD estimates has an essentially negligible contribution to the total variance\u2014the differences at 2100 for RCP8.5 are just about perceptible for Barentsburg (Figure 15). It is therefore reasonable to use only a single set of GRD estimates when computing local MSL projections. However, our analysis does not account for uncertainty in the associated space-time mass distributions that is used to compute the GRD patterns. This is an area that may benefit from further research.\nFigure 15: Projected ranges of MSL change at 2100 for three example tide gauge locations under RCP8.5. The dashed lines indicate the results when the average of three GRD estimates (rather than random selection) is used in the Monte Carlo simulations. All projections are expressed relative to a baseline period of 1986\u20132005. Scenario-independent components are indicated in gray.\nSummary and Conclusions\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/palmer20.html"}
{"id": "83d9565fb013-11", "text": "As part of our analysis of variance, we also investigate the contribution from uncertainty in the GRD estimates presented in section 2.4 (Figure 3). We choose the three tide gauge sites with the largest spread in one or more GRD components, that is, Barentsburg, Reykjavik, and Stanley II, and conduct the following simple analysis. We run an additional instance of the MSL Monte Carlo for each location using the average value of the GRD fingerprints at each site for RCP8.5 (i.e., the scenario with the largest signal). The projected MSL and component ranges are then compared to the full Monte Carlo simulations that include a random choice of GRD estimate. The results demonstrate that using multiple GRD estimates has an essentially negligible contribution to the total variance\u2014the differences at 2100 for RCP8.5 are just about perceptible for Barentsburg (Figure 15). It is therefore reasonable to use only a single set of GRD estimates when computing local MSL projections. However, our analysis does not account for uncertainty in the associated space-time mass distributions that is used to compute the GRD patterns. This is an area that may benefit from further research.\nFigure 15: Projected ranges of MSL change at 2100 for three example tide gauge locations under RCP8.5. The dashed lines indicate the results when the average of three GRD estimates (rather than random selection) is used in the Monte Carlo simulations. All projections are expressed relative to a baseline period of 1986\u20132005. Scenario-independent components are indicated in gray.\nSummary and Conclusions\uf0c1\nWe have presented MSL projections under the RCP2.6, RCP4.5, and RCP8.5 climate change scenarios for both global-mean sea level and for a number of example tide gauge locations around the world. Our 21st century projections are directly traceable to the CMIP5-based sea-level projections presented in AR5 (Church et al., 2013) with updated treatment of the contribution from Antarctic ice dynamics following Levermann et al. (2014) and show similar results to projections presented in the SROCC (Oppenheimer et al., 2019). Our regression approach for sterodynamic sea-level change more cleanly isolates the forced signal and enables us to characterize the relative importance of variance arising from scenario, model spread, and observed sea-level variability over the 21st century, following Hawkins and Sutton (2009). A key aspect of the study is the use of the same Monte Carlo framework for both global and local sea-level projections. This means that global and local projections are entirely consistent, preserving the correlations among components and allowing us to quantify the contributions to total variance (uncertainty) by geographic location, time horizon, and scenario. We introduced a new set of exploratory extended projections to 2300 that are rooted in CMIP5 projections through the use of a physically based emulator to extend individual CMIP5 climate model simulations (Palmer, Harris, et al., 2018). These emulator-based projections are designed for maximum consistency with the 21st century projections and show a high level of agreement at 2100. Our main findings are summarized as follows:\nWe have developed a consistent set of local sea-level projections that are directly traceable to the GMSL projections developed for AR5 and preserve the relationships between components (an important factor in determining the fraction of variance explained).\nOur projections of GMSL at both 2100 and 2300 yield similar numbers to those recently reported in the IPCC Special Report on the Ocean and Cryosphere in a Changing Climate (IPCC, 2019), noting the large inherent uncertainties associated with multicentury time horizons. For RCP2.6, our projected ranges at 2300 are larger than some recent studies (including the SROCC likely range) and may have important implications for long-term adaptation planning.\nCombined analysis of local MSL projections and tide gauge records suggests that sea-level variability dominates the total variance in the coming decades, with climate change scenario becoming increasingly important over the 21st century. Model uncertainty tends to be the largest source of variance from the mid-21st century.\nLocal MSL projections can show large departures from the GMSL response and are typically associated with substantially larger uncertainties. A few locations will see MSL decrease in future owing to spatial patterns of GRD and the local contribution from GIA.\nOn century time scales, the projected MSL changes are large compared to observations of local sea-level variability. This indicates that many places will be exposed to greater coastal flood risk unless effective adaptation measures are taken.\nThe extended projections to 2300 illustrate the large degree of committed sea-level rise even in strong mitigation scenarios. They also illustrate the substantially increased risk for the highest emissions scenarios, which are associated with several meters of MSL rise at most tide gauge locations.\nCorrelations between component terms mean that the variance of the total MSL change is not identical to the sum of the variances of the components. Moreover, the breakdown of variance depends on both, geographic location and time horizon, with differences in scenario post-2100. Antarctic ice dynamics dominate the total variance post-2100 except at locations where GRD patterns strongly attenuate this signal.\nThis study highlights the need for development of site-specific MSL projections for effective planning (GMSL projections of cannot be reliably used to indicate the local changes). The time-space-scenario dependence in the contributions to total variance suggests that research priorities for reducing uncertainty in sea-level projections are likely to vary by geographic location and planning time horizon.", "source": "https://sealeveldocs.readthedocs.io/en/latest/palmer20.html"}
{"id": "4418cc28ef3a-0", "text": "Hay et al. (2015)\uf0c1\nTitle:\nProbabilistic reanalysis of twentieth-century sea-level rise\nKey Points:\nReconstruction of the global mean sea-level changes since 1900, from combining the probability distributions of a set of tide gauge records, refines estimates and is more consitent with estimates based on the sum of contributions\nThe global mean sea level rose by about 1.2 \u00b1 0.2 mm/year between 1901 and 1990 and by 3.0 \u00b1 0.7 mm/year between 1993 and 2010.\nThe rate of sea-level rise has been accelerating\nKeywords:\nsea level reconstruction, tide gauge, global mean sea level rise, probabilistic framework\nCorresponding author:\nCarling C. Hay.\nCitation:\nHay, C. C., Morrow, E., Kopp, R. E., & Mitrovica, J. X. (2015). Probabilistic reanalysis of twentieth-century sea-level rise. Nature, 517(7535), 481\u2013484. doi:10.1038/nature14093\nURL:\nhttps://www.nature.com/articles/nature14093\nAbstract\uf0c1\nEstimating and accounting for twentieth-century global mean sea-level (GMSL) rise is critical to characterizing current and future human-induced sea-level change. Several previous analyses of tide gauge records [1,2,3,4,5,6] \u2014 employing different methods to accommodate the spatial sparsity and temporal incompleteness of the data and to constrain the geometry of long-term sea-level change \u2014 have concluded that GMSL rose over the twentieth century at a mean rate of 1.6 to 1.9 millimetres per year. Efforts to account for this rate by summing estimates of individual contributions from glacier and ice-sheet mass loss, ocean thermal expansion, and changes in land water storage fall significantly short in the period before 1990 [7]. The failure to close the budget of GMSL during this period has led to suggestions that several contributions may have been systematically underestimated [8]. However, the extent to which the limitations of tide gauge analyses have affected estimates of the GMSL rate of change is unclear. Here we revisit estimates of twentieth-century GMSL rise using probabilistic techniques [9,10] and find a rate of GMSL rise from 1901 to 1990 of 1.2 \u00b1 0.2 millimetres per year (90% confidence interval). Based on individual contributions tabulated in the Fifth Assessment Report [7] of the Intergovernmental Panel on Climate Change, this estimate closes the twentieth-century sea-level budget. Our analysis, which combines tide gauge records with physics-based and model-derived geometries of the various contributing signals, also indicates that GMSL rose at a rate of 3.0 \u00b1 0.7 millimetres per year between 1993 and 2010, consistent with prior estimates from tide gauge records4. The increase in rate relative to the 1901\u201390 trend is accordingly larger than previously thought; this revision may affect some projections11 of future sea-level rise.\nEditorial Summary: Twentieth century sea levels revisited\uf0c1\nRates of sea-level rise calculated from tide gauge data tend to exceed bottom-up estimates derived from summing loss of ice mass, thermal expansion and changes in land storage. Carling Hay et al. provide a statistical reassessment of the tide gauge record \u2014 which is subject to bias due to sparse and non-uniform geographic coverage and other uncertainties \u2014 and conclude that sea-level rose by about 1.2 millimetres per year from 1901 to 1990. This is slightly lower than prior estimates and is consistent with the bottom-up estimates. The same analysis applied to the period 1993\u20132010, however, indicates a sea-level rise of about three millimetres per year, consistent with other work and suggesting that the recent acceleration in sea-level rise has been greater than previously thought.\nMain\uf0c1\nTide gauges provide records of local sea-level changes that, in the case of some sites, extend back to the eighteenth century [12,13,14]. However, using the database of tide gauge records [15] to estimate historical GMSL rise (defined as the increase in ocean volume normalized by ocean area) is challenging. Tide gauges sample the ocean sparsely and non-uniformly, with a bias towards coastal sites and the Northern Hemisphere, and with few sites at latitudes greater than 60\u00b0 (see, for example, refs 4, 9). In addition, tide gauge time series show significant inter-annual to decadal variability, and they are characterized by missing data (that is, intervals without observations at the start, middle or end of a time series). From the perspective of estimating GMSL changes, the data are contaminated by local and regional signals due to ongoing glacial isostatic adjustment (GIA) associated with past ice ages [16,17], the spatially non-uniform pattern of sea-level rise associated with changes in contemporary land ice sources[18,19,20,21], ocean/atmosphere dynamics [22], and other local factors including tectonics, sediment compaction, groundwater pumping and harbour development.\nDifferent approaches have been used to address these complexities in efforts to estimate twentieth-century GMSL rise [23]. These include averaging rates at sites with the longest records [1,2], averaging rates determined from regional binning of records [3], incorporating shorter records into the analysis to distinguish between secular trends and decadal-scale variability [3], and using altimetry records to determine dominant sea-level geometries and then using tide gauge records to estimate the time-varying amplitudes of these geometries [4,5]. In most cases, other criteria were applied to cull the tide gauge sites adopted in the analysis (for example, excluding sites near tectonic activity or major urban centres).\nEstimates of twentieth-century GMSL rise from these previous analyses range from 1.6 to 1.9 mm yr\u22121 (refs 1, 2, 3, 4, 5, 6) and define an important enigma. Independent model- and data-based estimates of the individual sources of GMSL, including mass flux from glaciers and ice sheets, thermal expansion of oceans, and changes in land water storage, are insufficient to account for the GMSL rise estimated from tide gauge records8, particularly before 19907. For example, a tabulation of contributions to GMSL rise from 1901 to 1990 in the Fifth Assessment Report (AR5; ref. 7) of the Intergovernmental Panel of Climate Change (IPCC) total 0.5 \u00b1 0.4 mm yr\u22121 (90% confidence interval, CI) less than a recent tide gauge derived rate of 1.5 \u00b1 0.2 mm yr\u22121 (90% CI) estimated by Church and White4 for the same period (the confidence range for this estimate is taken from AR5; refs 7 and 23). Using IPCC terminology, the latter suggests that it is \u2018extremely likely\u2019 (probability P = 95%) that GMSL rise from 1901 to 1990 was greater than 1.3 mm yr\u22121, although the bottom-up sum of contributions is \u2018likely\u2019 (P > 67%) below this level. The above discrepancy has been attributed to underestimation of almost all possible sources: thermal expansion, glacier mass balance, and Greenland or Antarctic ice sheet mass balance7,8.\nIn this Letter, we revisit the analysis of GMSL since the start of the twentieth century using Kalman smoothing9 (KS; see Methods). This statistical technique naturally accommodates spatially sparse and temporally incomplete sampling of a global sea-level field, provides a rigorous, probabilistic framework for uncertainty propagation, and can correct for a distribution of GIA and ocean models. We applied the approach to analyse annual records from 622 tide gauges included in the Permanent Service for Mean Sea Level (PSMSL) Revised Local Reference database15,24 and reconstruct the global field of sea-level change for each year from 1900 to 2010.\nTo examine the skill with which the KS reconstruction reproduces the tide gauge observations, we compute the time series of residuals at each tide gauge site and examine the distribution of the mean residual (that is, bias) for each site (Fig. 1a). The mean of the mean residuals across all 622 observations is 0.3 mm, with a standard deviation of 5.1 mm, indicating minimal systemic bias.\nFigure 1: Fit of the KS-based reconstruction of sea level to the tide gauge record. a, Histogram of mean residuals (mm) between the sea-level reconstruction and the tide gauge observations at all 622 sites. The mean of all mean residuals is 0.3 \u00b1 5.1 mm (\u00b11 s.d.). b\u2013f, Time series of reconstructed annual sea level (black lines, KS mean estimate; grey shading, 1\u03c3 uncertainty) at New York, USA (b), Fremantle, Australia (c), Zemlia Bunge, Russia (d), Vaasa, Finland (e), and Champlain, Canada (f), together with the associated annual mean tide gauge observations (red lines).", "source": "https://sealeveldocs.readthedocs.io/en/latest/hay15.html"}
{"id": "4418cc28ef3a-1", "text": "In this Letter, we revisit the analysis of GMSL since the start of the twentieth century using Kalman smoothing9 (KS; see Methods). This statistical technique naturally accommodates spatially sparse and temporally incomplete sampling of a global sea-level field, provides a rigorous, probabilistic framework for uncertainty propagation, and can correct for a distribution of GIA and ocean models. We applied the approach to analyse annual records from 622 tide gauges included in the Permanent Service for Mean Sea Level (PSMSL) Revised Local Reference database15,24 and reconstruct the global field of sea-level change for each year from 1900 to 2010.\nTo examine the skill with which the KS reconstruction reproduces the tide gauge observations, we compute the time series of residuals at each tide gauge site and examine the distribution of the mean residual (that is, bias) for each site (Fig. 1a). The mean of the mean residuals across all 622 observations is 0.3 mm, with a standard deviation of 5.1 mm, indicating minimal systemic bias.\nFigure 1: Fit of the KS-based reconstruction of sea level to the tide gauge record. a, Histogram of mean residuals (mm) between the sea-level reconstruction and the tide gauge observations at all 622 sites. The mean of all mean residuals is 0.3 \u00b1 5.1 mm (\u00b11 s.d.). b\u2013f, Time series of reconstructed annual sea level (black lines, KS mean estimate; grey shading, 1\u03c3 uncertainty) at New York, USA (b), Fremantle, Australia (c), Zemlia Bunge, Russia (d), Vaasa, Finland (e), and Champlain, Canada (f), together with the associated annual mean tide gauge observations (red lines).\nComparing reconstructions and tide gauge observations at a selection of individual sites (Fig. 1b\u2013f) shows generally excellent agreement, although there are a small number of outliers. An example outlier is the Champlain tide gauge (Fig. 1f), which has a mean residual of 52 mm. This particular misfit (also evident at other sites in the vicinity) can be attributed to the St Lawrence being a regulated water system where flow is dominated by anthropogenic control rather than global-scale climate dynamics25. The eight sites that have mean residuals greater than \u00b13\u03c3 (15 mm) from the mean exhibit an average interannual sea-level variability (estimated as the standard deviation after detrending the tide gauge observations) of \u00b1130 mm, more than triple the mean inter-annual variability of \u00b140 mm across all sites. Although these outliers have large inter-annual variability, the site-specific variability is incorporated into the covariances computed in the probabilistic reconstruction, and the uncertainties in the estimated sea-level trends at these sites reflect this.\nThe sum of the KS-estimated GMSL changes associated with the mass balance of the Greenland and Antarctic ice sheets, the mass balance of 18 mountain glacier regions, and thermal expansion (Fig. 2, blue line and shading; see Methods) is characterized by an average GMSL rate of 1.2 \u00b1 0.2 mm yr\u22121 (90% CI) for 1901\u201390. As shown in Fig. 3, this is significantly lower than the estimates of 1.5 \u00b1 0.2 mm yr\u22121 from Church and White4 (magenta line in Fig. 2) and 1.9 mm yr\u22121 from Jevrejeva et al.3 (red line in Fig. 2). The KS-estimated acceleration is 0.017 \u00b1 0.003 mm yr\u22122, larger than our estimates based on the Church and White4 (0.009 \u00b1 0.002 mm yr\u22122) and Jevrejeva et al.3 (0.011 \u00b1 0.006 mm yr\u22122) time series (see Methods).\nFigure 2: Time series of GMSL for the period 1900\u20132010. Shown are estimates of GMSL based on KS (blue line), GPR (black line), Church and White4 (magenta line) and Jevrejeva et al.3 (red line). Shaded regions show \u00b11\u03c3 pointwise uncertainty. Inset, trends for 1901\u201390 and 1993\u20132010, and accelerations, all with 90% CI. Confidence intervals for Church and White4 are from refs 7 and 23. Confidence intervals were not available for Jevrejeva et al.3; data in this reference ends in 2002, so the rate quoted here for 1993\u20132010 is actually for 1993\u20132002. Since the GPR methodology outputs decadal sea level, no trend is estimated for 1993\u20132010. Accelerations are consistently estimated from the KS, GPR, and GMSL time series in refs 3 and 4 (see Methods) from 1901 to the end of each reconstruction.\nFigure 3: Comparison of mean GMSL rates for 1901\u201390. Shown are estimates of GMSL rise for the period 1901\u201390 obtained from six different sampling methods along with previously published rates (see main text for description of each). The box covers the 1\u03c3 uncertainty range, while the bars represent the 90% CI. In the case of the Jevrejeva et al.3 estimate, uncertainties and confidence intervals were not available.\nChurch and White [4] combined stationary empirical orthogonal functions (EOFs), computed from \u223c20 years of satellite altimetry data spanning latitudes up to about \u00b160\u00b0, with amplitudes estimated from sparse tide gauge observations. Given the relatively short duration of the altimeter record, the EOFs may be dominated by patterns due to interannual variability rather than the geometry associated with long-term sea-level change26,27. Jevrejeva et al.3 used tide gauge records to compute regional sea-level means and from these computed a global average. Both methodologies involve spatially sparse, temporally incomplete sampling of the global sea-level field, which introduces a potentially significant bias into estimates of GMSL. The KS technique differs from these approaches by using the spatial information inherent in the observations to infer the weights associated with the individual, underlying contributions to the sea-level change. The method extracts global information from the sparse field by taking advantage of the physics-based and model-derived geometry of the contributing processes, thereby reducing the potential for sampling bias.\nTo understand the origin of the differences between the KS estimate and the higher values of refs 3 and 4, and in particular to quantify the impact of regional binning, spatial sparsity and missing data, we performed several tests.\nFirst, we applied to the KS global sea-level reconstruction a regional binning algorithm similar to that of Jevrejeva et al.3. In particular, we sampled the reconstruction at the locations of the 622 tide gauge sites, imposed sections of missing data consistent with the PSMSL data availability15, binned the tide gauges into 12 ocean regions, and averaged across these regions to compute a GMSL curve. The resulting estimate of the mean GMSL rate from 1901 to 1990 (Fig. 3; \u2018KS PSMSL sampling\u2019), 1.6 \u00b1 0.4 mm yr\u22121 (90% CI), is significantly closer to the estimate of Jevrejeva et al.3, indicating that combined spatial sparsity and missing data generate an upward bias in estimates of GMSL rates (Fig. 3). Second, we performed a bootstrapping test that repeated the above algorithm for tide gauge subsets ranging from 25 to 600 sites that confirmed this result (see Methods and Extended Data Fig. 3). We also implemented a test to estimate the possible bias in the estimate of GMSL rate introduced in the EOF analysis of Church and White4 (see Methods; Fig. 3; \u2018KS EOF\u2019); the result was consistent with the difference between the KS and Church and White4 results in Fig. 2.\nWe performed several other tests to explore the impact of sparsity and missing data on the estimates. Specifically, we applied the binning algorithm as described above but without imposing sections of missing data. The resulting mean GMSL rate estimate for 1901\u201390 was 1.0 \u00b1 0.4 mm yr\u22121, close to the KS result (Fig. 3; \u2018KS 622 sites, no missing data\u2019). Third, we sampled the full reconstruction at a large number of globally distributed sites\u2014that is, the sampling was not confined to the tide gauge sites and no sections of missing data were imposed on the time series\u2014and performed the same regional binning and averaging (\u2018KS global reconstruction\u2019). The resulting rate estimate, 1.2 \u00b1 0.1 mm yr\u22121, was identical to the KS result (Fig. 3). This indicates that regional binning of estimates, in the absence of sparsity and missing data, does not introduce a significant bias.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hay15.html"}
{"id": "4418cc28ef3a-2", "text": "First, we applied to the KS global sea-level reconstruction a regional binning algorithm similar to that of Jevrejeva et al.3. In particular, we sampled the reconstruction at the locations of the 622 tide gauge sites, imposed sections of missing data consistent with the PSMSL data availability15, binned the tide gauges into 12 ocean regions, and averaged across these regions to compute a GMSL curve. The resulting estimate of the mean GMSL rate from 1901 to 1990 (Fig. 3; \u2018KS PSMSL sampling\u2019), 1.6 \u00b1 0.4 mm yr\u22121 (90% CI), is significantly closer to the estimate of Jevrejeva et al.3, indicating that combined spatial sparsity and missing data generate an upward bias in estimates of GMSL rates (Fig. 3). Second, we performed a bootstrapping test that repeated the above algorithm for tide gauge subsets ranging from 25 to 600 sites that confirmed this result (see Methods and Extended Data Fig. 3). We also implemented a test to estimate the possible bias in the estimate of GMSL rate introduced in the EOF analysis of Church and White4 (see Methods; Fig. 3; \u2018KS EOF\u2019); the result was consistent with the difference between the KS and Church and White4 results in Fig. 2.\nWe performed several other tests to explore the impact of sparsity and missing data on the estimates. Specifically, we applied the binning algorithm as described above but without imposing sections of missing data. The resulting mean GMSL rate estimate for 1901\u201390 was 1.0 \u00b1 0.4 mm yr\u22121, close to the KS result (Fig. 3; \u2018KS 622 sites, no missing data\u2019). Third, we sampled the full reconstruction at a large number of globally distributed sites\u2014that is, the sampling was not confined to the tide gauge sites and no sections of missing data were imposed on the time series\u2014and performed the same regional binning and averaging (\u2018KS global reconstruction\u2019). The resulting rate estimate, 1.2 \u00b1 0.1 mm yr\u22121, was identical to the KS result (Fig. 3). This indicates that regional binning of estimates, in the absence of sparsity and missing data, does not introduce a significant bias.\nTo assess the robustness of our probabilistic reanalysis, we also performed a second, independent statistical analysis based on Gaussian process regression28 (GPR), a technique that also naturally accommodates data sparsity and gaps, and incorporates a suite of GIA and ocean models (see Methods; black line in Fig. 2). The mean GMSL rate for 1901\u201390 estimated from the GPR analysis, 1.1 \u00b1 0.4 mm yr\u22121, is consistent with the results of the KS analysis (Fig. 3).\nPrevious analyses appear to have overestimated the mean GMSL rate over the twentieth century. The KS estimate for the period 1901\u201390 indicates that it is \u2018very likely\u2019 (probability P = 90%) that the rate of GMSL rise during this period was between 1.0 and 1.4 mm yr\u22121. This estimate closes the sea-level budget for 1901\u201390 estimated in AR5 (ref. 7) without appealing to an underestimation of individual contributions from ocean thermal expansion, glacier melting, or ice sheet mass balance. Moreover, it may contribute to the ultimate resolution of Munk\u2019s sea-level enigma28 (defined by the argument that Earth rotation measurements and bounds on ocean warming are inconsistent with a rate of sea-level rise beginning in the late nineteenth century of 1.5\u20132.0 mm yr\u22121), since it may lower the signal of twentieth century ice melting in Earth rotation measurements.\nIn contrast, for the period 1993\u20132010\u2014which coincides with the era of satellite altimetry measurements of sea surface height changes29\u2014the KS estimate is consistent with previous results (Fig. 2). The KS estimate, 3.0 \u00b1 0.7 mm yr\u22121 (90% CI), is essentially identical to the tide gauge analysis of Church and White4 (2.8 \u00b1 0.5 mm yr\u22121; ref. 23). It is also consistent with the estimate based on TOPEX and Jason altimeter measurements (3.2 \u00b1 0.4 mm yr\u22121; ref. 29 as cited by ref. 23 for the period 1993\u20132010, see also ref. 7).\nTo assess the anomalous nature of recent sea-level change, we compute 15-year rates through the KS-derived GMSL time series in Fig. 2 from 1901 to 2010. Figure 4 shows both the time series and distribution of these 96 rates, where the 5 most recent time windows are shown in red. The former is in qualitative agreement with a previous inference of multi-decadal trends in acceleration during the twentieth century30. While the rates show significant variability, the rate for the 1996\u20132010 time window, 3.1 mm yr\u22121, is the largest of all computed 15-year rates.\nFigure 4: Moving 15-year averages of GMSL rate estimated using the KS reconstruction of sea level across the entire interval 1901\u20132010. The x-axis represents the mid-point of each 15-year averaging window, and the shading gives the 1\u03c3 uncertainty range. Inset, histogram of 15-year mean GMSL rate estimates (mm yr\u22121) for all time windows. The five most recent windows are shown in red.\nWe have revisited twentieth century GMSL rise using probabilistic techniques that combine sea-level records with physics-based and model-derived geometries of the contributing processes. Our estimated GMSL trend for the period 1901\u201390 (1.2 \u00b1 0.2 mm yr\u22121) is lower than previous estimates, indicating that the rate of GMSL rise during the last two decades represents a more significant increase than previously recognized. Projections of future sea-level rise based on the time series of historical GMSL, notably semi-empirical approaches11, should accordingly be revisited.\nMethods\uf0c1\nProbabilistic estimation methods\uf0c1\nKalman smoothing (KS) and Gaussian process regression (GPR), both discussed in detail below, share three advantages over the approaches taken in traditional tide gauge analyses. First, the Bayesian nature of both approaches naturally accommodates the spatiotemporal changes in the availability of the sea-level records (that is, sparsity and missing data). Second, the probabilistic approaches correct for a distribution of GIA and ocean models rather than adopting a specific model for each process, and they thus reduce a potentially important bias in previous estimates of the GMSL change17,31. Last, as both methods are fully probabilistic, they allow for the propagation of measurement and inferential uncertainties and correlations throughout the complete analysis time period. Despite these commonalities, the implementations of KS and GPR differ significantly.\nKalman smoother\uf0c1\nThe KS methodology is divided into four steps9, the first three of which are repeated by employing the spatial fields of GIA and ocean dynamic models from all possible combinations of 161 different Earth rheological models and 6 global climate model (GCM) simulations from CMIP5 (ref. 32) (see below for details of the rheological and climate models). First, a priori model estimates of both local sea level and the individual mass contributions from the Greenland, West Antarctic and East Antarctic ice sheets, as well as 18 major mountain glacier regions, are recursively corrected by tide gauge observations as the estimates are propagated forward through time. The local sea level is linked to the individual mass contributions through the unique spatial patterns, or \u2018fingerprints,\u2019 of sea-level change associated with rapid mass loss from land-based ice18,19,20,21. The forward step yields an estimate of local sea level and land ice contributions at each time slice, conditional on all earlier observations and a particular combination of GIA and GCM models. Second, the procedure is run backward in time, with the initial state estimate being the last estimate from the first step. The third, smoothing step optimally combines the results of the first two passes based upon the uncertainties of the respective estimates. The result is an estimate of local sea levels and land ice contributions conditional upon the entire set of observations and specific pairings of GIA and GCM models. Finally, the results from different GIA/GCM combinations are linearly combined, weighted by their likelihood, to yield an a posteriori probability distribution for local sea levels and land ice contributions, conditional upon the tide gauge observations.\nA comprehensive discussion of our application of the KS technique to the analysis of tide gauge measurements is given in ref. 9, which also includes synthetic tests to assess the performance of the procedure. Several subsequent refinements of this approach are summarized below.\nReference 9 defined the state vector to include estimates of sea level at every tide gauge site, the mass loss rates of three ice sheets, and the temporally correlated noise in the sea-level observations. Using only tide gauge observations limits our ability to separate estimates of sea level from estimates of the temporally correlated noise. This led us to modify the KS approach in two ways.\nFirst, the state vector includes only an estimate of total sea level at every tide gauge site in addition to the desired mass loss rates. This yields the following state vector, xk, at every time step, k:", "source": "https://sealeveldocs.readthedocs.io/en/latest/hay15.html"}
{"id": "4418cc28ef3a-3", "text": "A comprehensive discussion of our application of the KS technique to the analysis of tide gauge measurements is given in ref. 9, which also includes synthetic tests to assess the performance of the procedure. Several subsequent refinements of this approach are summarized below.\nReference 9 defined the state vector to include estimates of sea level at every tide gauge site, the mass loss rates of three ice sheets, and the temporally correlated noise in the sea-level observations. Using only tide gauge observations limits our ability to separate estimates of sea level from estimates of the temporally correlated noise. This led us to modify the KS approach in two ways.\nFirst, the state vector includes only an estimate of total sea level at every tide gauge site in addition to the desired mass loss rates. This yields the following state vector, xk, at every time step, k:\nxk = [hk Bk]^T\nwhere hk is a vector of sea level at the 622 tide gauge sites, and Bk is a vector containing the scalar weightings of 3 ice sheets and 18 mountain glacier regions (see below), as well as a uniform component that accounts for global mean thermal expansion and any additional mass contributions from smaller mountain glaciers.\nSecond, while in ref. 9 the observation model consisted of the sum of the estimated sea level, correlated noise, and white noise, here, the observation model consists only of the estimated sea level and white noise at each tide gauge site. Temporal correlations due to ocean dynamics are now modelled by the annual, spatial, CMIP5 ocean model fields (see below for a more detailed description of the CMIP5 model fields).\nSea level is modelled as the Euler integration of the contributions from melt sources, Bk-1y, (with y being the matrix of sea-level fingerprints associated with rapid land-ice mass loss), the ongoing rate of sea-level change due to GIA, G, and the rate of change of sea level due to ocean dynamics, Sdot_{k-1} , from the spatial fields in the CMIP5 model outputs:\nhk = h_{k-1} + \u2206t(B_{k-1} y + G + Sdot_{k-1}) + wh\nwhere wh represents a zero-mean, white noise term associated with sea level.\nThe scalar weightings of the fingerprints are modelled as a random walk:\nBk = B_{k-1} + wB\nwhere wB represents a zero-mean, white noise term associated with the melt contributions. The forward filtering pass of the Kalman smoother follows the steps outlined in ref. 9. A final departure from the methodology presented in ref. 9 is that we implemented a three-pass fixed-interval smoother33 in place of a Rauch-Tung-Stiebel two-pass smoother [34].\nGaussian process regression\uf0c1\nThe GPR approach, in contrast, models sea level as a multivariate Gaussian field defined by spatiotemporal mean and covariance functions that describe the underlying processes responsible for sea-level variability. Specifically, Gaussian process priors describing the contributions from land ice, GIA, and ocean models are conditioned simultaneously upon the available observations to produce the conditional, posterior distribution of sea level at decadal intervals throughout the twentieth century. In contrast to the KS, the GPR approach directly estimates the intertemporal covariance of the posterior; the associated computational demands require the use of decadal rather than annual means. Rather than being based upon discrete GIA and GCM models as in the KS approach, the GPR approach employs Gaussian process priors for the GIA and ocean dynamics contributions that are estimated, respectively, from the 161 GIA model predictions and 6 GCM outputs (see below). The distribution describing each land ice mass contribution is modelled assuming a prior spatio-temporal covariance, with the temporal component estimated from previous, non-sea level based estimates of land ice melt and the spatial component from the sea-level fingerprints associated with the melt source.\nWe model decadal-average sea level as a spatiotemporal field:\nf(x,t) = fGIA(x,t) + fM(x,t) + fLSL(x,t)\nwhere fGIA, fM, and fLSL are respectively the components of sea level due to ongoing GIA, land ice mass loss, and local effects associated with ocean dynamics, tectonics and other non-climatic factors, each as a function of location, x, and time, t. Each sea-level component is modelled as a Gaussian process with a prior mean function, \u03bci(x,t), and covariance function, Ki(x,t,x\u2032,t\u2032).\nThe total field can be partitioned into observed sites, f1, and unobserved sites, f2, and subsequently written as a joint, multivariate distribution, such that:\n[f1, f2] ~ N([\u03bc1, \u03bc2],[K11 K12, K^T12 K22])\nObservations, y, are modelled as the underlying sea-level field with additive white noise characterized by zero mean and a covariance \u03a3p, such that the joint distribution becomes:\n[y, f2] ~ N([\u03bc1, f2],[K11+\u03a3p K12, K^T12 K22])\nUsing standard statistical results (see, for example, ref. 35), the posterior mean and covariance, f2 and V2, of the unobserved field conditioned upon the observations are:\nf2 = f2 + K^T12 [K11+\u03a3p]^{-1} y\nand\nV2 = K22 - K^T12 [K11+\u03a3p]^{-1} K12\nTo estimate the underlying constituents of the total sea-level field, the prior mean and covariance of the unobserved field (that is, \u03bc2, K12, K22) are set to the distribution of the desired quantity alone. For example, setting \u03bc2, K12, and K22 equal to \u03bc2M, K12M, K22M, returns the posterior mean and covariance of sea-level change due to the melt contributions. Once all the underlying constituent sea-level fields are determined, the global mean of those components can be computed and added to estimate GMSL.\nThe elements of the prior covariance matrix of the melt contribution, KM, are defined as:\nK^Mi,j = \u03a3^n_{a=1}(A^{M,L}_{i,j,a} + A^{M,RQ}_{i,j,a})(B^M_{i,j,\u03b1})\nwhere the subscripts indicate the ith row and jth column element of the ath ice sheet or mountain glacier. The time dependence of the covariance matrix is taken to be the sum of a linear component, AM,L, which accounts for secular changes in the melt contributions, and a rational quadratic term, AM,RQ, that represents a smoothly-varying function of variability:\nA^{M,L}(tq,tp) = k1 tq tp\nand\nA^{M,RQ}(tq,tp) = k2 (1 + \u2206t^2q,p / 2 \u03b1 \u03c4s^2)^{-\u03b1}\nHere, tq and tp represent the time at the qth and pth time step, \u0394tq,p represents the time difference between these steps, and k1, k2, \u03b1, and \u03c4s are hyperparameters that define the linear amplitude, rational quadratic amplitude, roughness, and characteristic timescale of the covariance functions35. To estimate the hyperparameters we adopt an empirical Bayesian approach where we compute the parameters that maximize the likelihood of reconstructed time series of previous mountain glacier estimates36 and ice sheet estimates37.\nThe spatial weighting of the prior covariance, BM, is computed as the outer product of the unique fingerprint associated with melt from the corresponding land-based ice source.\nThe prior spatiotemporal mean and covariance for the GIA contribution to sea-level change, \u03bcGIA(x,t) and KGIA(x,t), respectively, are taken as the sample mean and covariance of the 161 predictions of sea-level change described below.\nThe distribution of the contribution to sea-level changes from thermosteric and ocean dynamic effects is partially modelled as the sample mean and covariance of the CMIP5 model outputs32. However, since a small number of models are used to compute the distribution statistics, the estimated distribution may not be representative of the parent distribution. Consequently, we augment the sample covariance with a space-time separable covariance structure consisting of the product of two Mat\u00e9rn functions [35], C: one representing the temporal distribution and the other representing the spatial, such that the total prior covariance describing local sea-level change is given by:\nKLSL(x,t) = KCMIP5(x,t) + C(t,\u03bd1,\u03c4) C(x,\u03bd2,L)", "source": "https://sealeveldocs.readthedocs.io/en/latest/hay15.html"}
{"id": "4418cc28ef3a-4", "text": "where the subscripts indicate the ith row and jth column element of the ath ice sheet or mountain glacier. The time dependence of the covariance matrix is taken to be the sum of a linear component, AM,L, which accounts for secular changes in the melt contributions, and a rational quadratic term, AM,RQ, that represents a smoothly-varying function of variability:\nA^{M,L}(tq,tp) = k1 tq tp\nand\nA^{M,RQ}(tq,tp) = k2 (1 + \u2206t^2q,p / 2 \u03b1 \u03c4s^2)^{-\u03b1}\nHere, tq and tp represent the time at the qth and pth time step, \u0394tq,p represents the time difference between these steps, and k1, k2, \u03b1, and \u03c4s are hyperparameters that define the linear amplitude, rational quadratic amplitude, roughness, and characteristic timescale of the covariance functions35. To estimate the hyperparameters we adopt an empirical Bayesian approach where we compute the parameters that maximize the likelihood of reconstructed time series of previous mountain glacier estimates36 and ice sheet estimates37.\nThe spatial weighting of the prior covariance, BM, is computed as the outer product of the unique fingerprint associated with melt from the corresponding land-based ice source.\nThe prior spatiotemporal mean and covariance for the GIA contribution to sea-level change, \u03bcGIA(x,t) and KGIA(x,t), respectively, are taken as the sample mean and covariance of the 161 predictions of sea-level change described below.\nThe distribution of the contribution to sea-level changes from thermosteric and ocean dynamic effects is partially modelled as the sample mean and covariance of the CMIP5 model outputs32. However, since a small number of models are used to compute the distribution statistics, the estimated distribution may not be representative of the parent distribution. Consequently, we augment the sample covariance with a space-time separable covariance structure consisting of the product of two Mat\u00e9rn functions [35], C: one representing the temporal distribution and the other representing the spatial, such that the total prior covariance describing local sea-level change is given by:\nKLSL(x,t) = KCMIP5(x,t) + C(t,\u03bd1,\u03c4) C(x,\u03bd2,L)\nwhere KCMIP5 is the sample covariance of the CMIP5 model outputs, \u03bd1 and \u03c4 are the smoothness parameter and characteristic timescale of the temporal Mat\u00e9rn function, respectively, and \u03bd2 and L are the smoothness parameter and characteristic length scale of the spatial Mat\u00e9rn function, respectively. For the exponents within the Mat\u00e9rn functions we follow ref. 10 and set the exponent on the spatial component to \u03bd2 = 5/2 (reflecting a relatively smooth, twice-differentiable field) and the exponent on the temporal component to \u03bd1 = 3/2 (reflecting a once-differentiable time series, in which rate is always defined but can change abruptly). As with the melt covariance hyperparameters, we use an empirical Bayesian approach to estimate the maximum-likelihood time and length scales of the Mat\u00e9rn functions to be 46 years and 90 km, respectively. Note that there is some trade-off between the Mat\u00e9rn exponent values and the hyperparameter characteristic scales: the selection of, say, a lower exponent (giving rise to a less smooth functional form) would result in a longer length scale.\nIn addition to capturing the inaccuracies of the ocean dynamics distribution, the Mat\u00e9rn functions also model local tectonic, geomorphological and other non-climatic contributions to local sea-level change. These hyperparameters, and a white-noise variance, are computed by finding the parameters that maximize the likelihood of the available tide gauge observations given the complete sea-level model.\nSea-level fingerprints\uf0c1\nExtended Data Fig. 1a and b shows global maps of sea-level change, known as sea-level fingerprints, associated with rapid, uniform mass loss across the Greenland Ice Sheet (GIS) and the West Antarctic Ice Sheet (WAIS), respectively. The sea-level changes are normalized by the equivalent GMSL change. Both fingerprints are characterized by a large amplitude sea-level fall in the region adjacent to the melting ice sheet with a gradual rise in sea level moving away from the ice sheet. The computation of the fingerprints is based upon a gravitationally self-consistent sea-level theory that takes into account shoreline migration and changes in grounded, marine-based ice cover as well as the impact on sea level of perturbations in the Earth\u2019s rotation axis38,39,40.\nIn addition to the GIS and WAIS, fingerprints were computed for the East Antarctic Ice Sheet (EAIS) and glaciers of Alaska, the Alps, Baffin Island, the Caucasus, Ellesmere Island, Franz Josef Land, High Mountain Asia, Altai, Iceland, Kamchatka, the low-latitude Andes, New Zealand, Novaya Zemlya, Patagonia, Scandinavia, Severnaya Zemlya, Svalbard, and Western Canada/US.\nWe also include a spatially uniform pattern to account for changes in GMSL due to land ice sources not included in the above set of glaciers. In the Kalman smoother, this uniform \u2018fingerprint\u2019 also captures changes in GMSL due to globally uniform thermal expansion and terrestrial water storage variations9.\nGIA models\uf0c1\nThe first step when analysing tide gauge records is to correct for sea-level contributions due to the ongoing GIA of the Earth in response to the ice age cycles. Predictions of GIA are dependent on the geometry and deglaciation history of the Late Pleistocene ice sheets and the Earth\u2019s viscoelastic structure. In this study, we computed 160 different GIA predictions distinguished on the basis of the adopted lower-mantle viscosity, upper-mantle viscosity, and thickness of a high-viscosity (effectively elastic) lithosphere. Additionally, we computed a GIA prediction using the VM2 viscosity profile41. These were combined with the ICE-5G (Ref. 41) global ice sheet reconstruction for the last glacial cycle. A detailed description of physical processes that contribute to the total GIA signal can be found in ref. 42.\nWe adopted values for the three rheological model parameters that encompass all recent estimates of the Earth\u2019s structure. The lower-mantle viscosity was varied in the range (2\u2013100) \u00d7 1021 Pa s, upper-mantle viscosity in the range (0.3\u20131) \u00d7 1021 Pa s, and lithospheric thickness in the range 72\u2013150 km. Extended Data Fig. 2a and b shows the mean and standard deviation of the model predictions. The largest variance is seen in the region within the near field of the former ice sheets, including areas of ancient ice cover and the so-called peripheral bulges.\nOcean dynamics models\uf0c1\nWe treat the thermosteric and ocean dynamic contributions to sea level using the historical experiment output from 6 global climate models of the World Climate Research Programme\u2019s (WCRP) Coupled Model Intercomparison Project phase 5 (CMIP5) data set32. Following ref. 9, the models we use are: bcc-csm1-1 from the Beijing Climate Center, CanESM2 from Environment Canada, the NOAA-GFDL model GFSL-ESM2M, the Institut Pierre Simone Laplace IPSL-CM5A-LR model, MRI-CGCM3 from the Japanese Meteorological Institute, and NorESM1-M from the Norwegian Climate Centre. For the KS methodology, we use the zero-mean spatial field \u2018zos\u2019 that is supplied by all the models. In the GPR, we add to \u2018zos\u2019 each model\u2019s estimated globally averaged sea-level change due to thermal expansion: \u2018zossga\u2019.\nWhile the CMIP5 model outputs are provided as global ocean grids, the field values at the specific locations of tide gauges are required, as input, to both the KS and GPR analyses. Where the tide gauges are coincident with model grid points, the associated value of the model output is used. Otherwise, an inverse distance weighting interpolation scheme is used to estimate the field at the desired location.\nWe examined three alternative interpolation schemes to assess the sensitivity of the KS GMSL estimate to this choice: (1) a nearest-neighbour approach, selecting the value on the CMIP5 grid that is closest to the tide gauge site; (2) a Delaunay interpolant, computing a linear interpolation between the irregularly spaced model cells along the coastlines; and (3) a Gaussian process (or simple kriging) methodology. For the Gaussian process interpolation, we employed a Gaussian process prior with a mean equal to the mean of the model grid values within a 200 km radius of the tide gauge location and a Mat\u00e9rn covariance function with smoothness parameter equal to 5/2. Since we are interested in the variability of the ocean models immediately surrounding each tide gauge site, the length scale of the Mat\u00e9rn covariance function was set to 1\u00b0 (\u223c110 km). Neither the nearest-neighbour approach nor the Delaunay interpolated altered the estimate of the GMSL rate over the time period 1901\u201390. The Gaussian process interpolation scheme changed the GMSL estimate by less than 2%, significantly smaller than the estimated \u00b10.2 mm yr\u22121 90% CI on the estimate.\nComputation of GMSL rates and accelerations\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/hay15.html"}
{"id": "4418cc28ef3a-5", "text": "While the CMIP5 model outputs are provided as global ocean grids, the field values at the specific locations of tide gauges are required, as input, to both the KS and GPR analyses. Where the tide gauges are coincident with model grid points, the associated value of the model output is used. Otherwise, an inverse distance weighting interpolation scheme is used to estimate the field at the desired location.\nWe examined three alternative interpolation schemes to assess the sensitivity of the KS GMSL estimate to this choice: (1) a nearest-neighbour approach, selecting the value on the CMIP5 grid that is closest to the tide gauge site; (2) a Delaunay interpolant, computing a linear interpolation between the irregularly spaced model cells along the coastlines; and (3) a Gaussian process (or simple kriging) methodology. For the Gaussian process interpolation, we employed a Gaussian process prior with a mean equal to the mean of the model grid values within a 200 km radius of the tide gauge location and a Mat\u00e9rn covariance function with smoothness parameter equal to 5/2. Since we are interested in the variability of the ocean models immediately surrounding each tide gauge site, the length scale of the Mat\u00e9rn covariance function was set to 1\u00b0 (\u223c110 km). Neither the nearest-neighbour approach nor the Delaunay interpolated altered the estimate of the GMSL rate over the time period 1901\u201390. The Gaussian process interpolation scheme changed the GMSL estimate by less than 2%, significantly smaller than the estimated \u00b10.2 mm yr\u22121 90% CI on the estimate.\nComputation of GMSL rates and accelerations\uf0c1\nThe mean and uncertainty of GMSL rates are estimated using a generalized least squares regression of a linear trend to the reconstructed GMSL time series. While the GPR methodology outputs a full temporal covariance matrix, the KS methodology does not. For this purpose, we adopt a temporal covariance matrix \u03a3 with elements having the form:\n\u03a3_{i,j} = \u03c3i  \u03c3j exp(-(tj - ti)/\u03c4\nwhere \u03c3i and \u03c3j are the instantaneous uncertainties in GMSL at time i and j, respectively, derived in the multi-model KS analysis. To estimate the decorrelation timescale, \u03c4, we examined the annual PSMSL tide gauge data and computed the mean temporal correlation coefficient across all tide gauges. This coefficient approaches zero after 2 years, and we set \u03c4 to 3 years. Estimates of acceleration in GMSL cited in the main text for the two probabilistic analyses are computed using a generalized least squares fit of a quadratic through the associated GMSL time series. Estimates of acceleration for the Church and White4 and Jevrejeva et al.3 time series listed in Fig. 2 are based on a weighted least squares regression through the published time series (see figure legend).\nAnalysis of bias introduced by using a subset of tide gauges\uf0c1\nWe used a bootstrapping technique to assess the potential biases introduced in estimates of GMSL rates when only a subset of tide gauge records is used. We randomly sampled our global sea-level reconstruction based on the Kalman smoother at a specific number of tide gauge sites in the database of 622 sites, computed the associated GMSL curve by binning the sites into 12 regions and averaging the result, and then used this curve to determine the rate of sea-level change over the time period 1901\u201390. The time series of the sea-level reconstruction at any given tide gauge site were sampled to match any missing data at that site in the PSMSL database. We repeated the analysis 100 times for subsets ranging in size from 25 to 600 sites. The mean sea-level rate we computed in this exercise and its associated uncertainty are shown in Extended Data Fig. 3 as a function of the number of sites. The horizontal blue line and shading is the mean rate of sea-level rise from 1901 to 1990, and its associated uncertainty, respectively, obtained from the KS-derived time series (1.2 \u00b1 0.2 mm yr\u22121; Figs 2, 3).\nThe mean sea-level rate obtained from this analysis asymptotes towards its final value and the spread in rates decreases monotonically as the number of tide gauges used in the analysis increases. The asymptote lies \u223c0.4 mm yr\u22121 above the KS estimate, which is consistent with the difference between the KS and \u2018KS PSMSL sampling\u2019 rate estimates for 1901\u201390 shown in Fig. 3. This result suggests that the combined effects of data sparsity and missing data introduce an upward bias into the estimate of GMSL. This bias is reduced in the KS (and GPR) methodologies because these techniques extract global information by using the observations, together with model-based geometries (or covariances) associated with the underlying contributions, to estimate (and sum) these contributions.\nAnalysis of bias introduced by an EOF analysis of altimetry records\uf0c1\nTo compare our results with EOF-based reconstructions of sea level4,43, we computed the GMSL time series following the approach adopted by Church and White4, but replacing altimetry and tide gauge observations with our KS reconstruction. The EOFs were computed using the KS sea-level reconstruction from 1993 to 2010, limited to the latitudinal observation range of satellite altimetry (65\u00b0 N to 65\u00b0 S). As in ref. 43, a spatially uniform EOF was added to the basis set to account for changes in mean sea level within the altimetry data (here the KS reconstruction), while the weights of the EOFs were computed using the first differences of the KS reconstruction at the tide gauge locations (sampled to reflect missing data in the PSMSL database) in order to eliminate dependence on a consistent datum. The GMSL time series was computed using an area-weighted mean of the EOF-reconstruction. To compute the uncertainty in our estimated GMSL, we sampled our distribution for each KS reconstructed tide gauge 1,000 times and computed the corresponding EOF-derived GMSL time series. We used this distribution of GMSL curves with a generalized least squares regression to compute a trend and uncertainty. This analysis yielded a linear trend of 1.4 \u00b1 0.4 mm yr\u22121, demonstrating the existence of a bias since the \u2018true\u2019 underlying reconstruction has a trend of 1.2 \u00b1 0.2 mm yr\u22121 (see Fig. 3, \u2018KS EOF\u2019).\nInverted barometer correction\uf0c1\nThe results in the manuscript were obtained using tide gauge observations that were not corrected for the inverse barometer (IB) effect. Previous studies (for example, refs 44 and 45) have shown that the sea-level response to atmospheric pressure changes can be non-negligible on regional scales.\nIn order to investigate the potential effect that atmospheric pressure changes have on our probabilistic estimate of GMSL, we repeated the KS analysis on the full tide gauge data set after we corrected these records for the IB effect. Specifically, we used the HadSLP2 global reconstructed atmospheric pressure data set46 to compute the IB correction. We next applied the correction to the observations at the 622 tide gauge sites and then re-ran the KS analysis. The 1901\u201390 GMSL rate of change associated with this analysis is 1.2 \u00b1 0.2 mm yr\u22121, consistent with the value cited in the main text. We conclude that while the IB effect can impact regional sea-level histories, it has a negligible effect on our probabilistic estimates of GMSL.\nOptimality of the Kalman smoother\uf0c1\nLocal sea levels observed by tide gauges reveal significant interannual and decadal variability. This variability can lead to temporal correlation in the sea-level time series that needs to be considered if one seeks to obtain optimal estimates of the underlying GMSL contributions. In order to test the optimality of the Kalman smoother, we investigated the properties of the innovation sequence by computing the residuals between the observations and the KS model estimate of sea level at every tide gauge site. Since every KS estimate of sea level is accompanied by its associated uncertainty, we randomly sampled from each sea-level distribution to obtain 100 time series of residuals for every site. Following the optimality test described in ref. 47, we computed the mean AR(1) coefficient across the 100 samples at each tide gauge site. An optimal Kalman smoother is characterized by a white noise innovation sequence. In practice, this means that, within uncertainty, the AR(1) coefficients of the innovation sequences will be close to zero. In the exercise above, we obtained a mean AR(1) coefficient of 0.2 \u00b1 0.3 (90% confidence). This indicates that our innovation sequence is (within uncertainty) white noise and that the smoother is, or is close to, optimal.\nSensitivity of GMSL estimates to limitations of the CMIP5 climate simulations\uf0c1\nThe presence of unmodelled ocean dynamics can also affect the smoother performance. As described above, the limitations of the CMIP5 simulations as models for the true dynamic variability of the oceans is addressed in the GPR analysis by augmenting the covariance computed from the climate runs with two additional terms: a covariance modelled with two Mat\u00e9rn functions, and a white noise variance.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hay15.html"}
{"id": "4418cc28ef3a-6", "text": "Optimality of the Kalman smoother\uf0c1\nLocal sea levels observed by tide gauges reveal significant interannual and decadal variability. This variability can lead to temporal correlation in the sea-level time series that needs to be considered if one seeks to obtain optimal estimates of the underlying GMSL contributions. In order to test the optimality of the Kalman smoother, we investigated the properties of the innovation sequence by computing the residuals between the observations and the KS model estimate of sea level at every tide gauge site. Since every KS estimate of sea level is accompanied by its associated uncertainty, we randomly sampled from each sea-level distribution to obtain 100 time series of residuals for every site. Following the optimality test described in ref. 47, we computed the mean AR(1) coefficient across the 100 samples at each tide gauge site. An optimal Kalman smoother is characterized by a white noise innovation sequence. In practice, this means that, within uncertainty, the AR(1) coefficients of the innovation sequences will be close to zero. In the exercise above, we obtained a mean AR(1) coefficient of 0.2 \u00b1 0.3 (90% confidence). This indicates that our innovation sequence is (within uncertainty) white noise and that the smoother is, or is close to, optimal.\nSensitivity of GMSL estimates to limitations of the CMIP5 climate simulations\uf0c1\nThe presence of unmodelled ocean dynamics can also affect the smoother performance. As described above, the limitations of the CMIP5 simulations as models for the true dynamic variability of the oceans is addressed in the GPR analysis by augmenting the covariance computed from the climate runs with two additional terms: a covariance modelled with two Mat\u00e9rn functions, and a white noise variance.\nTo assess the sensitivity of the KS analysis to unmodelled ocean dynamics, we examined its response to (1) a known synthetic ocean dynamic signal and (2) the inclusion of the dynamic response to freshwater hosing of the North Atlantic.\nWe used the mean KS estimates of the ice sheet melt rates and uniform sea-level contribution, as well as the multi-model estimate of the GIA contribution, to construct synthetic sea-level observations at the 622 tide gauge sites. We then added the dynamic sea-level change associated with one of the six CMIP5 climate models and ran the multi-model KS using the five remaining climate models to obtain an estimate of the GMSL rate. We repeated this analysis for each of the CMIP5 simulations. By not including the climate model used in constructing the synthetics in the multi-model component of the KS methodology, we tested the ability of the smoother to account for unmodelled dynamics. The 1901\u201390 GMSL rates determined from the complete set of 6 analyses ranged from 1.1 to 1.3 mm yr\u22121. Five of these analyses yielded a 90% CI of 0.2 mm yr\u22121, while the sixth yielded a 90% CI of 0.3 mm yr\u22121. These values are consistent with the results for the KS analysis cited in the main text (1.2 \u00b1 0.2 mm yr\u22121).\nTo assess the sensitivity of our GMSL results to ocean dynamic effects due to freshwater input (\u2018hosing\u2019) from GIS melt, we used the results of a previous study48 to investigate the dynamic sea-level signal arising from North Atlantic freshwater \u2018hosing\u2019 simulations. Specifically, we computed the difference between the results of the 0.1 Sv hosing run and the control (no-hosing) simulation described in ref. 48 and scaled this difference by 0.05 to approximate a synthetic dynamic signal for a GIS melt rate equivalent to 0.5 mm yr\u22121 GMSL rise over the twentieth century. After subtracting a uniform 0.5 mm yr\u22121 from the spatial pattern, we calculated time series of this signal at all 622 tide gauge sites, added these to the observed record, and repeated the KS analysis. The presence of these unmodelled dynamics has negligible effect on our estimate of GMSL. The 1901\u201390 rate estimated in the above test agrees with the value presented in the manuscript (1.2 \u00b1 0.2 mm yr\u22121).\nWhile the above sensitivity tests indicate that the probabilistic analyses have quantified, with reasonable accuracy, the impact of uncertainties in CMIP5 models of ocean dynamic variability, improving such models is an important requirement in any effort to further refine estimates of GMSL rates.\nKalman smoother reconstruction of sea level at sites with no observations\uf0c1\nTo investigate how well the KS is able to estimate sea level at sites without observations, we ran the Kalman smoother using data from 450 randomly chosen tide gauge sites and estimated the sea level at the remaining 172 sites. Extended Data Fig. 4 shows the GMSL time series estimated in this new analysis as well as a comparison of the estimated and observed sea level at a representative subset of 5 of these 172 sites (the remaining sites show similar fits). We calculate a 1901\u201390 GMSL rate of 1.2 \u00b1 0.2 mm yr\u22121, consistent with the results presented in the manuscript when all 622 tide gauge sites are used in the analysis. The consistency between the estimated and observed values at the 172 tide gauge sites also indicates that limitations of the CMIP5 simulations in modelling ocean dynamics are not degrading the ability to predict sea-level trends at sites without observations. More generally, the analysis demonstrates the power of the KS method in reconstructing sea level when the method is applied with physics-based and model-derived geometries of the underlying physical processes.\nExtended data figures and tables\uf0c1\nExtended Data Figure 1: Illustrative sea-level fingerprints. a, b, Normalized sea-level changes due to rapid melting of the Greenland Ice Sheet (a) and the West Antarctic Ice Sheet (b). The variable \u2018normalized sea-level change\u2019 on the colour scale is formally dimensionless, but may be interpreted as having the unit of metres of sea-level change per metre of the equivalent GMSL change associated with the melt event.\nExtended Data Figure 2: The present-day rate of change of sea level in mm yr\u22121 due to GIA for a suite of Earth models. a, b, Mean sea-level change (a) and standard deviation (b) computed from the output of 161 GIA model simulations (see text). In both frames, the colour scale saturates in the near field, which includes areas of post-glacial rebound and peripheral subsidence.\nExtended Data Figure 3: Bootstrapping analysis of GMSL rate for 1901\u201390 obtained by sampling the global reconstruction of sea level. Data points show the mean computed from a bootstrapping analysis of the 1901\u201390 GMSL rate as a function of the number of geographic sites used in the analysis (ranging from 25 to 600). Error bars, \u00b11s.d. Sites are obtained by randomly sampling the global KS reconstruction at a subset of tide gauge sites and introducing data gaps that are consistent with those that exist in the PSMSL database15. The analysis was repeated 100 times for each choice of the number of sites. Also shown (horizontal blue line and shading) is the 1901\u201390 rate and its 90% CI computed from the KS GMSL curve in Fig. 2 (1.2 \u00b1 0.2 mm yr\u22121; Figs 2 and 3).\nExtended Data Figure 4: Results of the KS analysis performed using a random subset of 450 tide gauges. a, KS-estimated GMSL curve derived using a subset of 450 of the 622 tide gauge records discussed in the main text (blue line) and the reconstruction of Church and White4 (magenta line) and Jevrejeva et al.3 (red line). The shaded regions represent the 1\u03c3 certainty range. Panels b\u2013f show the KS reconstructions (black lines) at a representative set of 5 of the 122 sites that were not used in the estimation procedure. The observations are shown in red.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hay15.html"}
{"id": "5a019e65abdb-0", "text": "Suzuki et al. (2005)\uf0c1\nTitle:\nProjection of future sea level and its variability in a high-resolution climate model: Ocean processes and Greenland and Antarctic ice-melt contributions\nCorresponding author:\nTatsuo Suzuki\nCitation:\nSuzuki, T., Hasumi, H., Sakamoto, T. T., Nishimura, T., Abe\u2010Ouchi, A., Segawa, T., et al. (2005). Projection of future sea level and its variability in a high\u2010resolution climate model: Ocean processes and Greenland and Antarctic ice\u2010melt contributions. Geophysical Research Letters, 32(19), n/a-n/a. https://doi.org/10.1029/2005gl023677\nURL:\nhttps://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2005GL023677\nAbstract\uf0c1\nUsing a high-resolution climate model, we projected future sea level and its variability based on two scenarios for 21st century greenhouse gas emission. The globally averaged sea level rise attributable to the steric contribution was 23 and 30 cm for the two scenarios. The results of the high-resolution model and a medium-resolution version of the same model for global and local sea level change agreed well. However, the high-resolution model represented more detailed ocean structure changes under global warming. The changes affected not only the spatial distribution of sea level rise, but also the changes in local sea level variability associated with ocean eddies. The enhanced eddy activity was responsible for extreme sea level events.\nIntroduction\uf0c1\nSea level change is an important aspect of future climate change for human societies and the environment. Estimates of the rate of globally averaged sea level change during the 20th century are in the range of 1 to 2 mm yr\u22121 [Church et al., 2001]. This globally averaged rise in sea level is mainly the result of the thermal expansion of seawater and land-ice melt. Future projections of sea level change have been calculated using various coupled atmosphere\u2013ocean general circulation models (CGCMs [e.g., Gregory and Lowe, 2000; Gregory et al., 2001; Meehl et al., 2005]). Gregory et al. [2001] compared the results of the projections that followed the IS92a scenario for greenhouse gas (GHG) emissions. The rates of globally averaged sea level rise predicted by the models for the 21st century were in the range of 2.0\u20133.7 mm yr\u22121, but regional sea level change was not spatially uniform and some regions experienced more than twice the global average rate of rise. However, different models, while sharing some features, predicted different distributions. The geographical distribution of sea level change is principally determined by changes in density structure and wind stress forcing, both of which affect ocean circulation [Church et al., 2001]. Reproducing ocean structures is important for estimating the distribution of future sea level changes. However, the details of ocean structures, such as western boundary currents and fronts with pronounced horizontal gradients of water properties, have not been reproduced by existing coarse-resolution CGCMs. In this study, we compared sea level projections made by CGCMs with differing resolutions, focusing particularly on detailed features of the spatial distribution of sea level changes as predicted by a high-resolution model.\nWe also present global and local changes in 21st century sea level variability. Extreme changes in sea levels could severely affect human activities, and storm surges and coastal wave height have been identified in previous studies as sources of extreme sea levels [Church et al., 2001]. Unfortunately, the resolution of CGCMs has not been adequate to resolve these events. Extreme sea levels associated with ocean eddies, however, are represented by high-resolution models. Warm eddies increase the flooding risk in coastal areas. For example, Okinawa Island flooded on 22 July 2001 without the passage of an atmospheric low; rather, a warm eddy was responsible for increasing the sea level by more than 15 cm [Tokeshi and Yanagi, 2003]. Therefore, it would be advantageous to project changes in sea level variability using a high-resolution climate model that included eddies.\nModels and Experiments\uf0c1\nThe CGCM used in this study was the Model for Interdisciplinary Research on Climate, version 3.2 (MIROC3.2), developed at the Center for Climate System Research, University of Tokyo, National Institute for Environmental Studies and Frontier Research Center for Global Change [K-1 Model Developers, 2004]. The ocean component explicitly represented sea surface elevation. The higher-resolution version of MIROC3.2 (MIROC3.2_hi) consisted of a T106 global atmospheric spectral model with 56 vertical levels, an eddy-permitting global ocean model in which horizontal resolution was zonally 0.28\u00b0 and meridionally 0.19\u00b0 with 48 vertical levels, and other components (i.e., land, river, and sea ice). In the medium-resolution version of MIROC3.2 (MIROC3.2_med), a T42 global atmospheric spectral model with 20 vertical levels was coupled with a medium-resolution OGCM in which horizontal resolution was zonally 1.4\u00b0 and meridionally 0.56\u00b0 around the equator, with 44 vertical levels. The same physical parameterizations were applied to these models, but resolution-dependent parameters were adjusted per model.\nBoth models were integrated by prescribing external conditions, including solar and volcanic forcing, GHG concentrations, aerosol emissions, and land use. MIROC3.2_hi was spun up for 109 years under the fixed external conditions of the year 1900 after coupling the atmosphere and the ocean. MIROC3.2_med was spun up for 560 years under the fixed conditions of the year 1850. For control runs, we continued the integration under the same conditions for 100 years in MIROC3.2_hi and 400 years in MIROC3.2_med. Twentieth century experiments (20C3M) were performed after the spin-up. These runs were forced by the historical external conditions from 1900 to 2000 in MIROC3.2_hi and from 1850 to 2000 in MIROC3.2_med. Future projections for the 21st century were initiated by the final states of the 20C3M runs and performed by prescribing the external conditions according to the Intergovernmental Panel on Climate Change (IPCC) special report for emission scenarios. CO2 concentrations at the end of the 21st century were 720 and 550 ppm under the A1B scenario and the B1 scenario, respectively [Intergovernmental Panel on Climate Change, 2000]. For MIROC3.2_med, three 20th century runs were performed using different initial conditions (1st, 101st, and 201st years for the control run). We used the ensemble mean of the three members in this study. The model integration was restricted by computing resource limitations, especially for the high-resolution model, and the control runs showed some trends. Therefore, we subtracted these trends from the results.\nGlobally Averaged Sea Level Rise\uf0c1\nThe steric contribution (thermal expansion and haline contraction) to sea level rise was estimated from the model ocean temperature and salinity. As the Boussinesq approximation was adopted in the ocean model, the globally averaged sea level rise attributable to steric factors was diagnosed indirectly from density changes as the equivalent volume change under mass conservation:\nurn:x-wiley:00948276:media:grl20251:grl20251-math-0001\nwhere \u0394H is the globally averaged sea level rise, S is the surface area of the ocean, Z is the ocean depth, \u03c1 is the in situ density, and \u0394\u03c1 is its difference from the reference state. Because the haline contribution was small, the globally averaged change in sea level was caused mainly by changes in ocean heat content. To validate the model, the upper ocean heat content was compared with observations [Levitus et al., 2005]. Decadal variations were not in phase, but long-term trends and the changes over the last decade for both models were similar to observations (data not shown). The 21st century steric contribution was projected to be about 30 cm for the A1B scenario and 23 cm for the B1 scenario in MIROC3.2_hi (Figure 1a). This result was similar to that for MIROC3.2_med (Figure 1b) and within the range of estimations of previous CGCMs [Gregory et al., 2001]. Both models had linear trends in the control runs: about 0.15 mm yr\u22121 in MIROC3.2_hi and about 0.14 mm yr\u22121 in MIROC3.2_med. These linear trends were subtracted from the projections.\nFigure 1: A time series of globally averaged sea level change in (a) MIROC3.2_hi and (b) MIROC3.2_med (ensemble mean). Solid lines indicate the steric contribution. Broken lines represent the Greenland ice sheet and dotted lines indicate the Antarctica ice sheet.", "source": "https://sealeveldocs.readthedocs.io/en/latest/suzuki05.html"}
{"id": "5a019e65abdb-1", "text": "Globally Averaged Sea Level Rise\uf0c1\nThe steric contribution (thermal expansion and haline contraction) to sea level rise was estimated from the model ocean temperature and salinity. As the Boussinesq approximation was adopted in the ocean model, the globally averaged sea level rise attributable to steric factors was diagnosed indirectly from density changes as the equivalent volume change under mass conservation:\nurn:x-wiley:00948276:media:grl20251:grl20251-math-0001\nwhere \u0394H is the globally averaged sea level rise, S is the surface area of the ocean, Z is the ocean depth, \u03c1 is the in situ density, and \u0394\u03c1 is its difference from the reference state. Because the haline contribution was small, the globally averaged change in sea level was caused mainly by changes in ocean heat content. To validate the model, the upper ocean heat content was compared with observations [Levitus et al., 2005]. Decadal variations were not in phase, but long-term trends and the changes over the last decade for both models were similar to observations (data not shown). The 21st century steric contribution was projected to be about 30 cm for the A1B scenario and 23 cm for the B1 scenario in MIROC3.2_hi (Figure 1a). This result was similar to that for MIROC3.2_med (Figure 1b) and within the range of estimations of previous CGCMs [Gregory et al., 2001]. Both models had linear trends in the control runs: about 0.15 mm yr\u22121 in MIROC3.2_hi and about 0.14 mm yr\u22121 in MIROC3.2_med. These linear trends were subtracted from the projections.\nFigure 1: A time series of globally averaged sea level change in (a) MIROC3.2_hi and (b) MIROC3.2_med (ensemble mean). Solid lines indicate the steric contribution. Broken lines represent the Greenland ice sheet and dotted lines indicate the Antarctica ice sheet.\nThe contributions of ice-sheet melt were estimated using the methods of Wild et al. [2003]. The contributions of the Greenland and Antarctic ice-sheet melts exhibited opposite tendencies in both models, as in previous estimations [Church et al., 2001]. However, the amplitude in MIROC3.2_hi was larger than that in MIROC3.2_med (Figure 1). The difference between the two models appeared to be a result of the differences in projected temperature rises in the Greenland and snowfall increases in the Antarctica. Both of these differences in arctic temperature and snowfalls are strongly related to the difference in the climate sensitivity of the MIROC3.2_hi and MIROC3.2_med, in which the A1B run induced global warming of about 4.0\u00b0C in MIROC3.2_hi and 3.4\u00b0C in MIROC3.2_med at the end of the 21st century, respectively. This different sensitivity may partly due to the difference in the control SST and sea ice distribution in the two models.\nThe globally averaged sea level rise in MIROC3.2_hi is similar to that in MIROC3.2_med in spite of the different sensitivity. It is because the total heat flux into the ocean for the 21st century is similar in the both models, though the net heat flux into ocean in MIROC3.2_hi is larger than that in MIROC3.2_med during the early 21st century. The upper ocean in MIROC3.2_hi also warms up more than that in MIROC3.2_med. The reasons for these differences are currently under investigation.\nRegional Sea Level Change\uf0c1\nThe sea level patterns corresponding to major ocean gyres were well represented by both models (data not shown). In particular, narrow western boundary currents, such as the Kuroshio, were reproduced realistically in MIROC3.2_hi [Sakamoto et al., 2005]. The globally averaged sea level rise estimated in the previous section was added to the local sea levels calculated by each model to obtain sea level projections. Mass balance was ensured in a globally averaged sense by this procedure [Greatbatch, 1994]. Some regions experienced substantially higher sea level rise in both models than the 21st century global average (Figure 2).\nFigure 2: The changes in mean sea level between 1980 and 2000 (20C3M) and between 2080 and 2100 (A1B) in (a) MIROC3.2_hi and (b) MIROC3.2_med (ensemble mean).\nTo distinguish sea level changes caused by global warming from background variability, such as decadal variations, we estimated area-weighted spatial standard deviations of the local sea level change with respect to the control climate. Gregory et al. [2001] assumed that sea level changes associated with global warming and background variability were not spatially correlated. Under this assumption, increased spatial standard deviation would be attributable to global warming if changes in background variability were relatively small. The spatial standard deviation increased with time for both models and reached 7\u201313 cm by the end of the 21st century (Figure 3), indicating that the projected sea level changes were sufficiently significant relative to background variability. There was a conspicuous signal from the last decade of the 20th century in MIROC3.2_hi.\nFigure 3: The spatial standard deviation of the decadal mean field of local sea level change with respect to the control climate. Solid lines indicate MIROC3.2_hi and broken lines represent MIROC3.2_med (ensemble mean).\nThe regions with large sea level changes were more restricted to specific areas and the magnitudes of change were more pronounced in MIROC3.2_hi than in MIROC3.2_med (Figure 2). These results were consistent with the fact that spatial variability in MIROC3.2_hi was larger than in MIROC3.2_med at the end of the 21st century (Figure 3). The sea level variability associated with eddies was also shown in MIROC3.2_hi (Figure 4a), and this spatial distribution was consistent with satellite obsersvations. These changes were closely related to regional sea level changes and were as large as several centimeters for some regions during the 21st century (Figure 4b).\nFigure 4: (a) The root-mean-square (rms) of the sea level anomaly from the 3-month running mean for the control run in MIROC3.2_hi. (b) Changes in the rms between 1980 and 2000 (20C3M) and between 2080 and 2100 (A1B) in MIROC3.2_hi.\nBoth models exhibited a region of large sea level rises in the North Pacific. These sea level changes were also shown in the Hadley Centre coupled atmosphere-ocean general circulation model (HadCM3), which has a horizontal resolution similar to that of MIROC3.2_med [Gregory and Lowe, 2000]. This feature has not been represented in previous coarser-resolution models [Gregory et al., 2001]. With higher resolution, as in MIROC3.2_med and HadCM3, fronts at the western boundary currents and their extensions were more sharply reproduced, so sea level changes associated with their shifting or intensification were better captured. Such features became further differentiated at higher resolution (Figure 2).\nThere was a reduced sea level rise north of the Kuroshio Current at approximately 150\u00b0E and an enhanced sea level rise to the south in MIROC3.2_hi. This sea level change was associated with the acceleration of the Kuroshio caused by changes in wind stress and the consequential spin-up of the Kuroshio recirculation [Sakamoto et al., 2005]. In contrast, the Kuroshio in MIROC3.2_med overshot to the north in comparison with that in MIROC3.2_hi. Therefore, the region of large sea level rises in MIROC3.2_med extended northward relative to that in MIROC3.2_hi. MIROC3.2_hi also exhibited a region of reduced sea level rises in the North Pacific subpolar gyre. We believe that this feature was related to the intensification of the Aleutian Low, which is also considered to be the cause of the Kuroshio acceleration [Sakamoto et al., 2005]. This acceleration was associated with the enhanced eddy activity in the Kuroshio and the Kuroshio extension under global warming (Figure 4b). These features were not represented in MIROC3.2_med, partly because the subpolar gyre was not well represented due to the overshooting of the Kuroshio. Similar acceleration of a western boundary current and enhanced eddy activity were also detected east of Australia.", "source": "https://sealeveldocs.readthedocs.io/en/latest/suzuki05.html"}
{"id": "5a019e65abdb-2", "text": "Both models exhibited a region of large sea level rises in the North Pacific. These sea level changes were also shown in the Hadley Centre coupled atmosphere-ocean general circulation model (HadCM3), which has a horizontal resolution similar to that of MIROC3.2_med [Gregory and Lowe, 2000]. This feature has not been represented in previous coarser-resolution models [Gregory et al., 2001]. With higher resolution, as in MIROC3.2_med and HadCM3, fronts at the western boundary currents and their extensions were more sharply reproduced, so sea level changes associated with their shifting or intensification were better captured. Such features became further differentiated at higher resolution (Figure 2).\nThere was a reduced sea level rise north of the Kuroshio Current at approximately 150\u00b0E and an enhanced sea level rise to the south in MIROC3.2_hi. This sea level change was associated with the acceleration of the Kuroshio caused by changes in wind stress and the consequential spin-up of the Kuroshio recirculation [Sakamoto et al., 2005]. In contrast, the Kuroshio in MIROC3.2_med overshot to the north in comparison with that in MIROC3.2_hi. Therefore, the region of large sea level rises in MIROC3.2_med extended northward relative to that in MIROC3.2_hi. MIROC3.2_hi also exhibited a region of reduced sea level rises in the North Pacific subpolar gyre. We believe that this feature was related to the intensification of the Aleutian Low, which is also considered to be the cause of the Kuroshio acceleration [Sakamoto et al., 2005]. This acceleration was associated with the enhanced eddy activity in the Kuroshio and the Kuroshio extension under global warming (Figure 4b). These features were not represented in MIROC3.2_med, partly because the subpolar gyre was not well represented due to the overshooting of the Kuroshio. Similar acceleration of a western boundary current and enhanced eddy activity were also detected east of Australia.\nAnother important difference between the two models was found in the western tropical Pacific. In MIROC3.2_hi, there was a reduced sea level rise east of Mindanao Island that spread to the eastern tropical Pacific (Figure 2a). This feature was caused by intensification of the wind-induced Ekman upwelling under global warming. This wind-induced Ekman upwelling in this region was not well resolved in MIROC3.2_med [Suzuki et al., 2005]. The reduced sea level rise was associated with the acceleration of the North Equatorial Current (NEC) and the North Equatorial Counter Current (NECC). The acceleration of these currents and the Subtropical Counter Current increased the meridional gradient of zonal velocity, which was associated with an enhanced eddy (Figure 4b). The region stretched zonally to 120\u00b0W. These responses of the zonal flows to global warming will be investigated in future studies.\nBoth models showed a narrow band of enhanced sea level rise in the Southern Ocean. Under global warming in our models, the westerlies shifted southward and strengthened. These changes in the wind field contributed to the southward shift and the intensification of the circumpolar fronts, which are linked to sea level change. These changes were also connected with a couple of narrow bands of enhanced and reduced eddy activity that stretched east from Argentina to the south of Australia in MIROC3.2_hi.\nA dipole pattern of sea level change in the North Atlantic Ocean, i.e., an enhanced rise north of the Gulf Stream extension and a reduced rise to the south, was recognized in both models. Bryan [1996] suggested that this pattern was consistent with weakening of the upper branch of the Atlantic Meridional Overturning Circulation (AMOC). The AMOC was weakened from 14 Sv (1 Sv = 106 m3 s\u22121) to 9 Sv in MIROC3.2_hi and from 19.5 Sv to 12.5 Sv in MIROC3.2_med during the 21st century.\nDiscussion and Conclusions\uf0c1\nThe dynamic effect of sea level pressure was not included in either of the ocean components. The change in spatial standard deviation estimated from model sea level pressure during the 21st century was less than 2 cm. These changes, while not negligible, were small in comparison to the spatial variability caused by ocean structure changes (Figure 3). Therefore, we did not indicate the contribution of sea level pressure in this study.\nThe strengthening of eddy activity was recognized in a globally averaged sense. The global average of the root-mean-square (rms) increased from 4.8 to 5.1 cm in the A1B scenario and from 4.8 to 5.0 cm in the B1 scenario during the 21st century. These changes were small compared to levels of globally averaged sea level rise. However, enhanced eddy activity was confined to specific areas, and those areas overlapped with the areas of enhanced sea level rise around some coastal regions and islands, suggesting that the frequency of extreme sea levels may increase in those regions during the 21st century.\nWe have described future sea level changes as projected by MIROC3.2_hi according to the 21st century scenarios for GHG emissions and compared them with the results of MIROC3.2_med. The globally averaged sea level rise during the 21st century predicted by the two models was similar. The distribution of sea level changes in MIROC3.2_hi also resembled that in MIROC3.2_med on a large scale. However, MIROC3.2_hi presented more detailed ocean structure changes under global warming. The changes in the ocean structure affected not only the spatial distribution of sea level rise, but also changes in local sea level variability. Therefore, it is critical to consider changes in sea level variability when assessing the possible effects on human activities.", "source": "https://sealeveldocs.readthedocs.io/en/latest/suzuki05.html"}
{"id": "f3e8df801819-0", "text": "Welcome to SeaLevelDocs\u2019s documentation!\uf0c1\nContents:\uf0c1\nSuzuki et al. (2005)\nHughes et al. (2010)\nChurch and White (2011)\nKuhlbrodt and Gregory (2012)\nChurch et al. (2013)\nHallberg et al. (2013)\nKopp et al. (2014)\nHay et al. (2015)\nDeConto and Pollard (2016)\nChen et al. (2017)\nChen and Tung (2018)\nHorton et al. (2018)\nLittle et al. (2019)\nBamber et al. (2019)\nGregory et al. (2019)\nHamlington et al. (JGR, 2020)\nSadai et al. (2020)\nPalmer et al. (2020)\nYin et al. (2020)\nYuan and Kopp (2021)\nCouldrey et al. (2021)\nDangendorf et al. (2021)\nZika et al. (2021)\nDeConto et al. (2021)\nLi et al. (2022)\nSlangen et al. (2022)\nvan de Wal et al. (2022)\nBamber et al. (2022)\nWickramage et al. (2023)\nLi et al. (2023)\nPark et al. (2023)\nIndices and tables\uf0c1\nIndex\nModule Index\nSearch Page", "source": "https://sealeveldocs.readthedocs.io/en/latest/index.html"}
{"id": "88add8ede049-0", "text": "Hamlington et al. (JGR, 2020)\uf0c1\nTitle:\nUnderstanding of contemporary regional sea-level change and the implications for the future\nKey Points:\nAn overview of the current state of understanding of the processes that cause regional sea-level change is provided\nAreas where the lack of understanding or gaps in knowledge inhibit the ability to assess future sea-level change are discussed\nThe role of the expanded sea-level observation network in improving our understanding of sea-level change is highlighted\nCorresponding author:\nHamlington\nCitation:\nHamlington, B. D., Gardner, A. S., Ivins, E., Lenaerts, J. T. M., Reager, J. T., Trossman, D. S., et al. (2020). Understanding of contemporary regional sea-level change and the implications for the future. Reviews of Geophysics, 58, e2019RG000672. https://doi.org/10.1029/2019RG000672\nAbstract\uf0c1\nGlobal sea level provides an important indicator of the state of the warming climate, but changes in regional sea level are most relevant for coastal communities around the world. With improvements to the sea-level observing system, the knowledge of regional sea-level change has advanced dramatically in recent years. Satellite measurements coupled with in situ observations have allowed for comprehensive study and improved understanding of the diverse set of drivers that lead to variations in sea level in space and time. Despite the advances, gaps in the understanding of contemporary sea-level change remain and inhibit the ability to predict how the relevant processes may lead to future change. These gaps arise in part due to the complexity of the linkages between the drivers of sea-level change. Here we review the individual processes which lead to sea-level change and then describe how they combine and vary regionally. The intent of the paper is to provide an overview of the current state of understanding of the processes that cause regional sea-level change and to identify and discuss limitations and uncertainty in our understanding of these processes. Areas where the lack of understanding or gaps in knowledge inhibit the ability to provide the needed information for comprehensive planning efforts are of particular focus. Finally, a goal of this paper is to highlight the role of the expanded sea-level observation network - particularly as related to satellite observations - in the improved scientific understanding of the contributors to regional sea-level change.\nPlain Language Summary\uf0c1\nThis review paper addresses three important questions: (1) What do we currently know about the processes contributing to sea level change? (2) What observations do we use to gain this knowledge? and (3) Where are these gaps in our knowledge and the need for further improvement in our understanding of the drivers of regional sea level? By answering these specific questions in a focused manner, this paper should be a useful resource for other scientists, sea-level stakeholders, and a broader audience of those interested in sea level and our changing climate.\nIntroduction\uf0c1\nGlobal mean sea level (GMSL) is an important indicator of a warming climate (Church & White, 2011; Milne et al., 2009; Stammer et al., 2013), but changes in regional sea level are most relevant to coastal communities around the world (Kopp et al., 2015; Nicholls, 2011; Woodworth et al., 2019). The regional variability of the processes driving sea-level change (SLC), along with their uncertainties and relative importance over different time scales, pose challenges to planning efforts. Available observations of sea level show clear spatial and temporal inhomogeneity. From satellite altimeter observations covering the time period from 1993 to present, regional rates of rise can be more than double the global average in some locations while near zero at other locations (Cazenave & Llovel, 2010). Furthermore, as a result of internal variability, the pattern of linear trends in regional sea level has shifted or reversed in many regions from the first half of the altimeter record to the second (e.g., Han et al., 2017; Peyser et al., 2016; Figure 1). Over longer time periods (i.e., hundreds of years), tide gauge records also show regional differences in the rates of SLC, owing in part to the vertical motion of the land upon which the gauges sit (e.g., Church et al., 2004; Church & White, 2006; Hay et al., 2015; Kleinherenbrink et al., 2018; Santamaroa-Gomez et al., 2014, 2017; Thompson et al., 2016). Understanding and accounting for these regional differences are critical first steps in providing information that is useful for planning efforts at the coast.\nFigure 1: Satellite altimeter-measured regional sea-level trend patterns from (top) 1993\u20132005, (middle) 2006\u20132018, and (bottom) 1993\u20132018. Black contours and gray shading denote areas where the estimated trend is not significant at the 95% confidence level.\uf0c1\nDue in large part to improvements in the sea.level observing system, the processes contributing to recent SLC are now well known. The uncertainty in the budget of GMSL rise over the last decade has been reduced (Cazenave et al., 2018), allowing for an assessment of the relative contributions of different processes that are important on global scales. While more challenging on regional levels, satellite observations, along with in situ measurements, have also led to a dramatically improved understanding of the processes causing regional differences in SLC. Fundamentally, the drivers that dominantly impact GMSL have a regional signature, and no process will result in a change that is uniform across the ocean (Milne et al., 2009; Stammer et al., 2013). Similarly, no contributor to SLC is constant in time, and the time scales upon which the processes vary can differ dramatically. Separating the contributors temporally and geographically can be useful when considering a particular planning horizon, although the range of variability inherent to the individual contributors can make this difficult. Additionally, it is the combined impact of several factors operating on these different scales that is of direct importance.\nThe causes of global and regional SLC have been the focus of recent review papers, with regional change most comprehensively discussed and summarized in Stammer et al. (2013), Kopp et al. (2015), and Slangen et al. (2017). The understanding of these processes has progressed in recent years, and the outstanding gaps in knowledge and remaining uncertainties have shifted accordingly. The intent of the present paper is to provide an overview and update of the current state of understanding of the processes that cause regional SLC and to identify and discuss limitations and uncertainty in our understanding of these processes. Although the focus is on contemporary SLC, we do include discussion of projections of future SLC. In particular, we are concerned with areas where lack of understanding or gaps in knowledge inhibit comprehensive planning efforts at the regional level. While we do not make explicit connections to planning efforts, we expect that a detailed discussion of uncertainties could be useful to those translating science into actionable plans (e.g., Horton et al., 2018). This paper is a resource for those interested in particular aspects of regional SLC by giving a detailed presentation of the most recent estimates of their contributions and a discussion of where improvement may be made in the coming years. Finally, a goal of this paper is to highlight the potential role of the expanded sea-level observation network - particularly as related to satellites - to understanding the contributors to regional SLC.\nThis paper is organized according to the individual processes of regional relative SLC, with each process covered in a section. In section 2, we provide a brief summary of how the contributors to regional sea level are separated and we present definitions for the terminology adopted in the remainder of the paper. Sections 3 through 8 discuss the individual processes contributing to regional SLC, with each section broken into two components: (1) a summary of the current state of knowledge, and (2) an overview of current limitations or areas of uncertainty and a discussion of where progress will likely be made in the coming years. In section 9, we summarize advances toward overcoming these limitations or reducing uncertainties that may be expected through recent and future additions to the sea-level observational network, with particular emphasis on satellite-based observations.\nProcesses Contributing to Regional SLC\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/hamlington20jgr.html"}
{"id": "88add8ede049-1", "text": "The causes of global and regional SLC have been the focus of recent review papers, with regional change most comprehensively discussed and summarized in Stammer et al. (2013), Kopp et al. (2015), and Slangen et al. (2017). The understanding of these processes has progressed in recent years, and the outstanding gaps in knowledge and remaining uncertainties have shifted accordingly. The intent of the present paper is to provide an overview and update of the current state of understanding of the processes that cause regional SLC and to identify and discuss limitations and uncertainty in our understanding of these processes. Although the focus is on contemporary SLC, we do include discussion of projections of future SLC. In particular, we are concerned with areas where lack of understanding or gaps in knowledge inhibit comprehensive planning efforts at the regional level. While we do not make explicit connections to planning efforts, we expect that a detailed discussion of uncertainties could be useful to those translating science into actionable plans (e.g., Horton et al., 2018). This paper is a resource for those interested in particular aspects of regional SLC by giving a detailed presentation of the most recent estimates of their contributions and a discussion of where improvement may be made in the coming years. Finally, a goal of this paper is to highlight the potential role of the expanded sea-level observation network - particularly as related to satellites - to understanding the contributors to regional SLC.\nThis paper is organized according to the individual processes of regional relative SLC, with each process covered in a section. In section 2, we provide a brief summary of how the contributors to regional sea level are separated and we present definitions for the terminology adopted in the remainder of the paper. Sections 3 through 8 discuss the individual processes contributing to regional SLC, with each section broken into two components: (1) a summary of the current state of knowledge, and (2) an overview of current limitations or areas of uncertainty and a discussion of where progress will likely be made in the coming years. In section 9, we summarize advances toward overcoming these limitations or reducing uncertainties that may be expected through recent and future additions to the sea-level observational network, with particular emphasis on satellite-based observations.\nProcesses Contributing to Regional SLC\uf0c1\nAs we discuss in the sections to follow, changes in sea level arise from a diverse set of physical processes. As a result, scientists from a range of disciplines are working on different questions related to sea level. The need to address the impacts of ongoing and future SLC, along with associated policy considerations, further increases the breadth of those studying or interested in SLC. This diversity and broad interest have led to inconsistency in sea-level terminology that can hinder progress in research, communication, and policy. To address this issue, Gregory et al. (2019) have provided guidelines and clearly defined terminology for discussing SLC. In Gregory et al. (2019), SLC refers to the geocentric SLC, specifically  the change in the height of sea level with respect to the terrestrial reference frame. When including the movement of the land at the coast, the phrase relative SLC is used, which is the change in the height of the mean sea surface relative to the solid surface, and thus includes the effects of vertical land motion (VLM). Given that relative SLC encompasses both geocentric SLC and VLM, and to simplify the discussion in this paper, we have chosen to use SLC to refer to changes in relative sea level for the remainder of this paper. The definition of spatial scales is separated by regional and global. The term \u201cregional\u201d is used to refer to processes that are considered properties of regions, with spatial of hundreds of kilometers and less. Unless specified, this includes local changes that occur at a specific geographic location. Processes are said to be of \u201cglobal\u201d scale if they contribute to variability in GMSL. The global mean refers specifically to the area-weighted mean of SLC for the entire connected surface of the ocean.\nThere are several ways to separate and distinguish between the different processes contributing to regional SLC. Here, we separate the contributors into six different sections. Regional and global SLC associated with ice mass changes is divided into contributions from ice sheets (section 3) and contributions from glaciers (section 4), recognizing that the observational and measurement considerations can differ between the two. Further changes arising from variability in land water storage are presented in a separate section (section 5). Each of these three contributors are discussed first in terms of their impact on GMSL, and then in terms of their regional signature through changes in Earth Gravitation, Rotation, and Deformation (GRD), caused by redistributions of land ice and water (discussed in more detail below). The primary intent of this paper is to discuss regional SLC, but the magnitude of the regional contributions of these factors is related to the size of their GMSL contribution. These three contributors are also intentionally covered first due to the similarity of the mechanism that impacts regional SLC. Regional SLC associated with steric variability and ocean dynamics (also referred to as sterodynamic SLC) is combined into a single discussion (section 6), which includes both natural and anthropogenic contributions. This section also covers dynamic SLC that may occur as a result of freshwater input into the ocean associated with the contributors in sections 3 through 5. Given its large contribution to the SLC at the coast, a section is included on VLM, covering a range of temporal and spatial scales (section 7). Finally, as the goal here is to cover a wide range of time scales that impact regional and local SLC, a section on higher-frequency variability is provided that includes variations in sea level associated with astronomic tides, storm surges, ocean swell, wave setup, and wave run-up (section 8).\nWe use the term sea level in this paper to refer to both the lower-frequency variations described in sections 3 through 6, and the higher-frequency variations in section 8. Pugh and Woodworth (2014) define sea level as the sum of four main components: mean sea level, astronomical tides, a meteorological component, and waves. Using this description, sections 3 through 6 largely discuss changes in mean sea level, while section 8 covers the other higher-frequency components. As a summary of the contributing factors covered in this paper, Table 1 provides an overview of the relevant time scales of each process in addition to the magnitude of its associated contribution on a yearly basis. One of the main takeaways from this breakdown is the wide range of time scales and subcomponents associated with each factor, and the degree to which each needs to be accounted for within any particular time frame of interest.\nTable 1: Components of Regional Sea-Level Rise Covered in This Paper, Along With Their Relevant Time Scales and Potential Magnitude\nComponent\nDominant temporal\nscales\nPotential magnitude\n(yearly)\nIce sheets\nyears to centuries\nmillimeters to\ncentimeters\nGlaciers (outside of ice sheets)\nmonths to centuries\nmillimeters to\ncentimeters\nSteric and dynamic sea-level change\nmonths to decades\nmillimeters to\nmeters\nLand water storage\nmonths to decades\nmillimeters to\ncentimeters\nHigh-frequency water level\nvariability\nminutes to years\ncentimeters to\nmeters\nSolid earth deformation/vertical\nland motion\nyears to centuries\nmillimeters to\nmeters\nContributions From Ice Sheets\uf0c1\nCurrent State of Knowledge\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/hamlington20jgr.html"}
{"id": "88add8ede049-2", "text": "We use the term sea level in this paper to refer to both the lower-frequency variations described in sections 3 through 6, and the higher-frequency variations in section 8. Pugh and Woodworth (2014) define sea level as the sum of four main components: mean sea level, astronomical tides, a meteorological component, and waves. Using this description, sections 3 through 6 largely discuss changes in mean sea level, while section 8 covers the other higher-frequency components. As a summary of the contributing factors covered in this paper, Table 1 provides an overview of the relevant time scales of each process in addition to the magnitude of its associated contribution on a yearly basis. One of the main takeaways from this breakdown is the wide range of time scales and subcomponents associated with each factor, and the degree to which each needs to be accounted for within any particular time frame of interest.\nTable 1: Components of Regional Sea-Level Rise Covered in This Paper, Along With Their Relevant Time Scales and Potential Magnitude\nComponent\nDominant temporal\nscales\nPotential magnitude\n(yearly)\nIce sheets\nyears to centuries\nmillimeters to\ncentimeters\nGlaciers (outside of ice sheets)\nmonths to centuries\nmillimeters to\ncentimeters\nSteric and dynamic sea-level change\nmonths to decades\nmillimeters to\nmeters\nLand water storage\nmonths to decades\nmillimeters to\ncentimeters\nHigh-frequency water level\nvariability\nminutes to years\ncentimeters to\nmeters\nSolid earth deformation/vertical\nland motion\nyears to centuries\nmillimeters to\nmeters\nContributions From Ice Sheets\uf0c1\nCurrent State of Knowledge\uf0c1\nUsing measurements from the joint NASA (US) /DLR (Germany) Gravity Recovery and Climate Experiment (GRACE) twin satellite mission, the Greenland and Antarctic Ice Sheets lost mass and collectively contributed around 1.17 \u00b1 0.17 mm yr^{-1} to GMSL (Figure 2) from 2002 to 2017, about one third of the total GMSL rise (Dieng et al., 2017). This rate has been steadily increasing since the 1990s (Bamber et al., 2018). The Greenland Ice Sheet holds enough water to raise GMSL by 7.4 m, while the Antarctic Ice Sheet has the potential to increase GMSL by 58 m (Fretwell et al., 2013; Morlighem et al., 2017). Although both ice sheets are currently losing mass, they do so at different rates via different mechanisms. The Antarctic Ice Sheet mass loss has increased threefold from 2002-2007 (0.2 \u00b1 0.1 mm yr^{-1} sea-level equivalent) to 2012-2017 (0.6 \u00b1 0.1 mm yr^{-1}) (Shepherd et al., 2018) and is mostly attributed to an increase in ice sheet discharge from glacier acceleration in West Antarctica (Gardner et al., 2018; Mouginot et al., 2014; Rignot et al., 2011). This increase is driven by a combination of an intrinsic geometric instability associated with marine-based ice sheets grounded on bedrock that deepens toward the center of the ice sheet and changes in the availability of warm, circumpolar deep water under floating ice shelves due to decadal atmospheric variability (Jenkins et al., 2016). Warm ocean water acts in tandem with atmospheric warming to thin and break up foating ice shelves (Khazendar et al., 2016; Liu et al., 2015; Paolo et al., 2015), leading to acceleration and retreat of the glaciers they buttress (Shepherd et al., 2018; Wouters et al., 2015). In contrast, the Greenland Ice Sheet mass loss is dominated by changes in surface mass balance (SMB, precipitation minus sublimation and meltwater runoff), with a smaller contribution caused by increased discharge from marine terminating outlet glaciers (Enderlin et al., 2014; Shepherd et al., 2018). Increase in runoff along the entire Greenland Ice Sheet margin is predominantly caused by atmospheric warming which promotes the intensification of ice sheet surface melt (Van den Broeke et al., 2016) and in turn rates of frontal (ocean) melting (Carroll et al., 2016).\nFigure 2: Time series and spatial patterns of ice sheet mass changes as measured by GRACE (2002-2017, Wise et al., 2018). In the upper plot, the solid lines show the GRACE mass balance from Antarctica (blue) and Greenland (red), with uncertainties contoured in the same color, and the three dotted lines show the lower, middle, and upper estimates of ice sheet mass loss in the business-as-usual, high-emissions RCP8.5 future scenario (IPCC, 2013). The numbers in the upper plot give the best linear \u00det for each ice sheet. The lower plots show the linear trend in units of cm water equivalent per year squared over the 2002-2017 period.\uf0c1\nThree independent observational methods are used to calculate current ice sheet mass loss rates: gravimetry, altimetry, and the input\u00d0output method (Shepherd et al., 2018). Each method has various strengths and weaknesses, with differing sensitivities to necessary corrections. Mass loss estimates from gravimetry (Velicogna & Wahr, 2006) provide the only direct measure of mass change of the ice sheets, but require a correction due to glacial isostatic adjustment (GIA) processes, which dominates the uncertainty in derived mass-loss rates. GIA uncertainties are largest for Antarctic Ice Sheet, and while estimates vary among studies, a recent study (Caron et al., 2018) estimates Antarctic Ice Sheet GIA uncertainty to be ~40 Gt (Gigaton = 10^{12} kg) per year, which is approximately 30% of the mass trend. Greenland, on the other hand, has a GIA uncertainty of ~13 Gt/yr, which is less than 5% of the Greenland Ice Sheet mass loss trend. Repeated satellite and airborne laser and radar altimetry provide detailed surface height change observations over ice sheets, but conversion from surface height to mass loss requires knowledge of spatial and temporal variability in firn density, a parameter that is poorly constrained due to sparse observations within the ice sheet interior (Pritchard et al., 2009). The input-output method (Gardner et al., 2018; Rignot et al., 2011, 2019; Shirzaei & Bgmann, 2012, 2018) - the only method that gives a longer time series of ice sheet mass balance (Kjeldsen et al., 2015; Rignot et al., 2019; Mouginot et al., 2019) - combines observations of ice flux across the grounding line from satellite remote sensing with modeled SMB estimates. In general, most observational time series are less than 20 years old, making the detection of mass loss acceleration in the presence of large natural variability challenging, especially in ice sheet SMB (Wouters et al., 2013). Radar altimetry from CryoSat-2 (launched in 2010), as well as new gravimetry (GRACE Follow-On, GRACE-FO) and laser altimeter (ICESat-2) missions launched in 2018, will extend the time series and provide continuous monitoring of ice sheet changes in the coming years.\nWe depend on a suite of numerical models to project future ice sheet changes, and these models also contribute to constraining past and present behavior. These models are traditionally used in a stand-alone framework but are increasingly \u201ccoupled\u201d to represent the full spectrum of ice sheet-climate interactions. Atmospheric (surface climate and SMB) and oceanic (e.g., temperature, salinity, circulation, sea ice) forcings to the ice sheet are supplied by a variety of climate models, which are either produced for the full globe (global circulation models and climate reanalysis) or spatially limited to one particular ice sheet and surroundings (regional climate models). While circulation models historically focused on coupled ocean-land-atmosphere processes, modern earth system models also include the carbon cycle through dynamic atmospheric chemistry, as well as forcing of the ocean and atmosphere by the ice sheets. Regional climate models have become a preferred tool in representing ice sheet surface climate and SMB because they incorporate surface energy and snow hydrology processes and have the spatial resolutions (~5 km) necessary to accurately model the Greenland Ice Sheet and individual Antarctic Ice Sheet basins (Agosta et al., 2019; Lenaerts et al., 2017; Noel et al., 2018; Van Wessem et al., 2018), often with steep topographic slopes around ice sheet margins. However, the accuracy of any regional climate model depends on the quality of the atmospheric forcing at the model domain boundaries, and observations necessary to evaluate climate and SMB over extensive areas of northern Greenland and Antarctica are lacking.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hamlington20jgr.html"}
{"id": "88add8ede049-3", "text": "We depend on a suite of numerical models to project future ice sheet changes, and these models also contribute to constraining past and present behavior. These models are traditionally used in a stand-alone framework but are increasingly \u201ccoupled\u201d to represent the full spectrum of ice sheet-climate interactions. Atmospheric (surface climate and SMB) and oceanic (e.g., temperature, salinity, circulation, sea ice) forcings to the ice sheet are supplied by a variety of climate models, which are either produced for the full globe (global circulation models and climate reanalysis) or spatially limited to one particular ice sheet and surroundings (regional climate models). While circulation models historically focused on coupled ocean-land-atmosphere processes, modern earth system models also include the carbon cycle through dynamic atmospheric chemistry, as well as forcing of the ocean and atmosphere by the ice sheets. Regional climate models have become a preferred tool in representing ice sheet surface climate and SMB because they incorporate surface energy and snow hydrology processes and have the spatial resolutions (~5 km) necessary to accurately model the Greenland Ice Sheet and individual Antarctic Ice Sheet basins (Agosta et al., 2019; Lenaerts et al., 2017; Noel et al., 2018; Van Wessem et al., 2018), often with steep topographic slopes around ice sheet margins. However, the accuracy of any regional climate model depends on the quality of the atmospheric forcing at the model domain boundaries, and observations necessary to evaluate climate and SMB over extensive areas of northern Greenland and Antarctica are lacking.\nThe relation between ice sheets and climate is defined by a two-way connection: While ice sheets respond to atmospheric and oceanic conditions, they also influence the surrounding climate, for example, via the discharge of freshwater into oceans (Bronselaer et al., 2018; Schloesser et al., 2019) and changes in topographic geometries (e.g., Fyke et al., 2018). To this end, the ice sheet modeling community has increasingly focused on simulations that are fully coupled to climate models. The ongoing intercomparison of climate models (Sixth Coupled Model Intercomparison Project; CMIP6) includes several models that couple to dynamical ice sheet models for the first time (Nowicki et al., 2016). The initial development has been associated with atmosphere/ice sheet coupling over the Greenland Ice Sheet (e.g., Lipscomb et al., 2013). Major, ongoing challenges of such models include matching the temporal and spatial scales of the ice sheet model with the global models, providing accurate initial conditions for the ice sheet model, and allowing for the variable extent of the ice-covered surface. Initial improvements have been made in the representation of SMB in earth system models guided by lessons from regional climate models (e.g., Vizcaino et al., 2013). Advances in the coupling of ocean and ice sheet models (e.g., Goldberg et al., 2018) will continue to improve our ability to model the Antarctic Ice Sheet, particularly in West Antarctica, where oceanic forcings are likely to play a pivotal role in future ice sheet mass loss. Recent studies have demonstrated the impact of ice-ocean coupling on such sub-ice-shelf melt rates and grounding line migration (Golledge et al., 2019; Jordan et al., 2017; Seroussi et al., 2017).\nThe ice-sheet mass loss to the ocean strongly influences regional sea level, as associated changes in Earth\u2019s GRD responses dictate the spatial distribution of water across the global ocean (Farrell & Clark, 1976; Milne & Mitrovica, 1998; Mitrovica et al., 2001). These so-called \u201csea-level fingerprints\u201d are crucial to determining regional SLC (Figures 3a and 3b). In general, mass loss causes a sea level fall in the near field, a reduced sea-level rise at intermediate distances, and a greater-than-global-mean sea-level rise at larger distances. Sea-level fingerprints can be computed for specific portions of ice sheets, enabling accurately quantified sensitivities of basin-scale ice mass loss to local sea-level rise at any coastal cities. The collapse of Petermann Glacier in Greenland, for example, would lead to 38% lower sea-level rise at New York and 20% higher sea-level rise at Tokyo relative to the global mean (Larour et al., 2017; Mitrovica et al., 2018). Estimating the current and projecting future contributions from the two ice sheets - including spatial variability in the contribution across each ice sheet - is thus critical to understanding regional SLC. Updated assessments of the regional impact on coastal cities will continue to be made as our understanding of mass loss from ice sheets advances and projections are improved.\nUncertainties and Future Outlook\uf0c1\nWhile significant progress has been made in recent years as described above, estimating future ice sheet contributions to sea level relies on models, which contain large uncertainties. These uncertainties exist in every stage of modeling ice sheets in future climates, from fundamental understanding of ice sheet physical processes (e.g., DeConto & Pollard, 2016), initialization (Goelzer et al., 2018), parameter, and boundary condition choices (e.g., Larour et al., 2012; Nias et al., 2016; Schlegel et al., 2015), to the quality of atmospheric and ocean forcings, which in turn rely on climate models with all their associated uncertainties (Nowicki & Seroussi, 2018; Robel et al., 2019); all of these uncertainties can limit the quality of model projections. For example, climate model-driven projections reported in the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) underestimated mass loss from 2006 to present, especially in the case of the Greenland Ice Sheet, including in the strongest warming (business-as-usual) RCP8.5 scenarios (Figure 2). This example highlights the need for extensive evaluation of present-day model performance, careful selection of model forcing, and, on the longer term, a focus on earth system model development to improve high-latitude atmospheric (e.g., clouds, radiation, precipitation) and oceanic processes, horizontal resolution and/or statistical downscaling (Lenaerts et al., 2019). Multimodel ensembles and intercomparisons (e.g., the Ice Sheet Model Intercomparison Project, ISMIP6; Nowicki et al., 2016) will also provide critical contributions to uncertainty quantifications.\nFigure 3: Contribution to relative sea.level rise (mm/year) from 2002 to 2015 from (a) Antarctica Ice Sheet mass loss, (b) Greenland Ice Sheet mass loss, (c) terrestrial water storage variability, and (d) glacier mass loss. Adapted from Adhikari and Ivins (2016).\uf0c1\nIce sheet contributions are especially important when planning for future SLC (e.g., Garner & Keller, 2018; Oppenheimer & Alley, 2016; Sriver et al., 2018; Sweet et al., 2017). The research community is increasingly employing probabilistic approaches when making projections of future sea-level contributions from ice sheets (Edwards et al., 2019; Little et al., 2013; Ritz et al., 2015; Schlegel et al., 2018), which are necessary for holistic probabilistic projections of sea-level rise (e.g., Kopp et al., 2014, 2017; Perrette et al., 2013, Slangen et al., 2014). Probabilistic projections, however, are subject to the same limitations as the models or structured expert judgements (e.g., Bamber & Aspinall, 2013; Bamber et al., 2019) used to construct them. There is some utility in turning to past analogs of high sea-level contributions from ice sheets (e.g., the last interglacial or Pliocene) to calibrate ice sheet models and improve probabilistic projections (e.g., Edwards et al., 2019), but these too are impacted by prior model uncertainties, as well as by the uncertainties in paleo-reconstructions. Furthermore, the efficacy of using modern ice sheet trends for constraining future contributions remains an active area of research (Kopp et al., 2017). As these deep uncertainties in ice sheet contributions are elucidated and probabilistic projections continue to improve, they will inform policy decisions that are based on projected probabilities that regional- and global-scale sea levels will exceed critical levels (e.g., Bakker et al., 2017; Buchanan et al., 2016; Rasmussen et al., 2018; Sweet et al., 2017).", "source": "https://sealeveldocs.readthedocs.io/en/latest/hamlington20jgr.html"}
{"id": "88add8ede049-4", "text": "Figure 3: Contribution to relative sea.level rise (mm/year) from 2002 to 2015 from (a) Antarctica Ice Sheet mass loss, (b) Greenland Ice Sheet mass loss, (c) terrestrial water storage variability, and (d) glacier mass loss. Adapted from Adhikari and Ivins (2016).\uf0c1\nIce sheet contributions are especially important when planning for future SLC (e.g., Garner & Keller, 2018; Oppenheimer & Alley, 2016; Sriver et al., 2018; Sweet et al., 2017). The research community is increasingly employing probabilistic approaches when making projections of future sea-level contributions from ice sheets (Edwards et al., 2019; Little et al., 2013; Ritz et al., 2015; Schlegel et al., 2018), which are necessary for holistic probabilistic projections of sea-level rise (e.g., Kopp et al., 2014, 2017; Perrette et al., 2013, Slangen et al., 2014). Probabilistic projections, however, are subject to the same limitations as the models or structured expert judgements (e.g., Bamber & Aspinall, 2013; Bamber et al., 2019) used to construct them. There is some utility in turning to past analogs of high sea-level contributions from ice sheets (e.g., the last interglacial or Pliocene) to calibrate ice sheet models and improve probabilistic projections (e.g., Edwards et al., 2019), but these too are impacted by prior model uncertainties, as well as by the uncertainties in paleo-reconstructions. Furthermore, the efficacy of using modern ice sheet trends for constraining future contributions remains an active area of research (Kopp et al., 2017). As these deep uncertainties in ice sheet contributions are elucidated and probabilistic projections continue to improve, they will inform policy decisions that are based on projected probabilities that regional- and global-scale sea levels will exceed critical levels (e.g., Bakker et al., 2017; Buchanan et al., 2016; Rasmussen et al., 2018; Sweet et al., 2017).\nAs ice sheet models improve in their resolution, initialization procedures, and process implementation, they become increasingly reliant on observations to both force their behavior and validate their performance. Accurate reproduction of ice sheet dynamics, especially near grounding lines, requires high-resolution surface and bed topography (Aschwanden et al., 2016, 2019; Morlighem et al., 2014; Nias et al., 2018), estimates of basal shear stress (Parizek et al., 2013), and sub-ice shelf bathymetry (Schodlok et al., 2012). Geometric constraints on outlet glacier dynamics have improved dramatically in recent years (e.g., Greenbaum et al., 2015; Morlighem et al., 2017; Vaughan et al., 2012), but technological advancements (e.g., radar tomo.graphy; Al-Ibadi et al., 2018) and geophysical methods development (toward observational validation of sub-surface model parameters such as basal shear stress (Brisbourne et al., 2017), temperature (MacGregor et al., 2015; Schroeder et al., 2016), and englacial velocity (Holschuh et al., 2017, 2019; Leysinger Vieli et al., 2007) could drive significant improvement in model projections. Importantly, new aerogeophysical campaigns and satellite missions will be required to collect data optimized for these new techniques, as well as to fill gaps in existing subsurface observations. Ice sheet model development should focus on including geophysical observations directly, and extending the data assimilation capabilities from the inclusion of snapshot surface observations to the inclusion of time series data (Goldberg & Heimbach, 2013; Larour et al., 2014) to take full advantage of the abundance of remote sensing observations now available.\nContributions From Glaciers\uf0c1\nCurrent State of Knowledge\uf0c1\n[\u2026]\nFigure 4: Time series of cumulative mass anomalies from GRACE for all primary glacier regions of the Randolph Glacier Inventory, except the Greenland and Antarctic periphery, covering the time period from 2002 to 2017. From Wouters et al. (2019).\uf0c1\n[\u2026]\nUncertainties and Future Outlook\uf0c1\n[\u2026]\nContributions From Changes in Land Water Storage\uf0c1\nCurrent State of Knowledge\uf0c1\n[\u2026]\nUncertainties and Future Outlook\uf0c1\n[\u2026]\nSteric Sea-Level and Ocean Dynamics\uf0c1\nCurrent State of Knowledge\uf0c1\n[\u2026]\nUncertainties and Future Outlook\uf0c1\n[\u2026]\nVLM/Solid Earth Deformation\uf0c1\nCurrent State of Knowledge\uf0c1\n[\u2026]\nUncertainties and Future Outlook\uf0c1\n[\u2026]\nContributions From High-Frequency Water Level Variability\uf0c1\nCurrent State of Knowledge\uf0c1\n[\u2026]\nUncertainties and Future Outlook\uf0c1\n[\u2026]\nNear-Term Outlook of Regional Relative Sea-Level Understanding\uf0c1\n[\u2026]\nSummary\uf0c1\nChanges in GMSL provide an integrative measure of the state of the climate system, encompassing both the ocean and cryosphere and may be viewed as an important indicator of what is currently happening to the climate in the present and what may happen in the future. While an increase in GMSL portends an increase in sea level of some magnitude along the world\u2019s coastlines, the response on regional levels is not uniform. Water that is added to the ocean from land will not be distributed evenly everywhere (sections 3-5) and changes in ocean dynamics add to the regional variability in sea-level rise (section 6). Using observations from tide gauges and satellite altimetry, the extent of the spatial variability in the rate of sea-level rise can be understood. With the recent improved understanding of GRD effects on sea level, and the suite of VLM effects outlined here, it has become clear that the use of a single global rate to describe sea level around the globe is problematic, and improved assessment of sea-level rise on regional levels is required from a planning perspective.\nOver the past century, coastal sea levels have risen over the majority of the globe. The effect of increasing sea level relative to land is a significant reduction in the elevation gap between typical high tides and a threshold elevation at which flooding begins (Sweet et al., 2018). Coastal communities were established with this gap in mind, recognizing flooding might occur under the most extreme of conditions. Recent reports (e.g., Sweet et al., 2017, 2018) have detailed the rapidly declining gap along the coastlines of the world, and the accelerated effect this has had on flood frequencies in many coastal locations. One important implication of these analyses is that the narrowed gap between high tide and flooding conditions can now be overcome by sea-level variability on a range of time scales. Subsequently, from a decision-making perspective, improved projections of future regional SLC are needed over a variety of time horizons, not simply the longest.\nAs discussed here, sea level varies on time scales from short-term (section 8), to seasonal-to-decadal (sections 5 and 6) or longer (sections 3-5). When considered in tandem with the movement of land relative to the ocean (section 7), contributions to sea level at each of these time scales can combine constructively, increasing sea levels and high-tide flood frequencies over both the short and long terms. The gap described above is known in many locations, and time horizons can be generated over which high-tide flood frequency will begin to increase rapidly. When considering only the long-term trend, this time horizon is usually found to be on the order of decades. However, when combined with the other contributors to sea-level variability, it is highly likely that in the short term (on the order of years) the cumulative effect of high-tide flooding will extend beyond \u201cnuisance\u201d levels and becomes too frequent for business as usual in coastal areas. As such, there is a strong need for improved information regarding future sea-level rise across a range of time scales.\nWhile understanding the long-term contributions from melting glaciers and ice-sheets is essential, so too is understanding, quantifying, and possibly predicting the variability that will occur on seasonal to decadal time scales. Recent studies suggest that these contributors are becoming distinguishable with the records available (e.g., Fasullo & Nerem, 2018; Nerem et al., 2018). With the observations that are available - or will become available soon - coupled with improved data analysis and modeling efforts, our understanding of future regional SLC will continue to advance in the coming years. Knowing that planning efforts are underway and that sea-level rise is already impacting many parts of the world\u2019s coastlines, it is worth taking inventory of the current state of understanding and clearly identifying areas of uncertainty that are impacting our ability to provide complete, accurate, and actionable information at the coast. Such assessments should be undertaken frequently to update relevant information in light of new science results, and to assist those tasked with translating current scientific understanding into plans that can be put into action at the coast.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hamlington20jgr.html"}
{"id": "bc7116e222f0-0", "text": "Wickramage et al. (2023)\uf0c1\nTitle:\nSensitivity of MPI-ESM Sea Level Projections to Its Ocean Spatial Resolution\nCorresponding author:\nChathurika Wickramage\nKeywords:\nOcean, Sea level, Climate models, Mesoscale models, Model comparison\nCitation:\nWickramage, C., K\u00f6hl, A., Jungclaus, J., & Stammer, D. (2023). Sensitivity of MPI-ESM Sea Level Projections to Its Ocean Spatial Resolution, Journal of Climate, 36(6), 1957-1980. doi:10.1175/JCLI-D-22-0418.1\nURL:\nhttps://journals.ametsoc.org/view/journals/clim/36/6/JCLI-D-22-0418.1.xml\nAbstract\uf0c1\nThe dependence of future regional sea level changes on ocean model resolution is investigated based on Max Planck Institute Earth System Model (MPI-ESM) simulations with varying spatial resolution, ranging from low resolution (LR), high resolution (HR), to eddy-rich (ER) resolution. Each run was driven by the shared socioeconomic pathway (SSP) 5-8.5 (fossil-fueled development) forcing. For each run the dynamic sea level (DSL) changes are evaluated by comparing the time mean of the SSP5-8.5 climate change scenario for the years 2080\u201399 to the time mean of the historical simulation for the years 1995\u20132014. Respective results indicate that each run reproduces previously identified large-scale DSL change patterns. However, substantial sensitivity of the projected DSL changes can be found on a regional to local scale with respect to model resolution. In comparison to models with parameterized eddies (HR and LR), enhanced sea level changes are found in the North Atlantic subtropical region, the Kuroshio region, and the Arctic Ocean in the model version capturing mesoscale processes (ER). Smaller yet still significant sea level changes can be found in the Southern Ocean and the North Atlantic subpolar region. These sea level changes are associated with changes in the regional circulation. Our study suggests that low-resolution sea level projections should be interpreted with care in regions where major differences are revealed here, particularly in eddy active regions such as the Kuroshio, Antarctic Circumpolar Current, Gulf Stream, and East Australian Current.\nSignificance Statement\uf0c1\nSea level change is expected to be more realistic when mesoscale processes are explicitly resolved in climate models. However, century-long simulations with eddy-resolving models are computationally expensive. Therefore, current sea level projections are based on climate models in which ocean eddies are parameterized. The representation of sea level by these models considerably differs from actual observations, particularly in the eddy-rich regions such as the Southern Ocean and the western boundary currents, implying erroneous ocean circulation that affects the sea level projections. Taking this into account, we review the sea level change pattern in a climate model with featuring an eddy-rich ocean model and compare the results to state-of-the-art coarser-resolution versions of the same model. We found substantial DSL differences in the global ocean between the different resolutions. Relatively small-scale ocean eddies can hence have profound large-scale effects on the projected sea level which may affect our understanding of future sea level change as well as the planning of future investments to adapt to climate change around the world.\nIntroduction\uf0c1\nRising sea levels are among the largest threats of anthropogenic global warming to society, with far-reaching consequences for many coastal and island populations around the globe (Church et al. 2011; Fox-Kemper et al. 2021). Our understanding of the global mean sea level trends has improved significantly over the past decades based on coordinated modeling efforts, such as the Coupled Model Intercomparison Project (CMIP) and the analysis of past observations (e.g., Church et al. 2011; Fox-Kemper et al. 2021). However, a quantitative understanding of processes that lead to regional to local-scale sea level changes is still pending, which affects the ability to accurately forecast future coastal changes (Church et al. 2013a). Although the quantitative budget of the global sea level rise is understood, insufficient data hampers the understanding on regional and coastal scale, which makes improving modeling efforts essential for closing the gaps.\nPhysically, regional to local-scale sea level change is a global problem as it depends on processes taking place locally as well as remotely. As such, it is directly or indirectly affected by all components of the climate system as well as contributions originating from the solid Earth such as vertical seafloor movement or changes in gravity (Stammer et al. 2013). However, the relative contribution of individual processes or forcing components to the regional or local sea level changes is strongly dependent on the spatial and temporal scales under consideration and might also change under global warming conditions.\nIn this context a caveat of previous CMIP projections is that underlying climate models are of relatively low spatial resolution, thereby intrinsically excluding the impact of resolved ocean eddies on the solution. To what extent existing sea level projections are thus biased toward large-scale climate mode responses as opposed to regional dynamical balances remains therefore to be understood, making it difficult to provide quantitative information about future sea level projections in specific regions, such as coastlines. This situation now gradually changes as climate projections from eddy-resolving models are becoming available accounting for the dynamical processes associated with boundary or coastal current dynamics, which are important for accurate small-scale sea level change information (e.g., van Westen et al. 2020; van Westen and Dijkstra 2021; Li et al. 2022). Given these new opportunities, it is now timely to test previous CMIP sea level change projections against novel eddy-rich climate projections.\nAgainst this background, the aim of this paper is to provide an understanding of the sensitivity of CMIP type sea level projections to model resolution and, thus, to define an uncertainty level in CMIP previous projections resulting from the lack of small-scale processes and eddy mechanisms. Specifically, we aim to quantify differences in the resulting sea level projections obtained under shared socioeconomic pathway (SSP) 5-8.5 forcing (O\u2019Neill et al. 2017) with respect to lower-resolution simulations using a hierarchy of spatial resolutions. The respective work will be based on the eddy-rich Max Planck Institute Earth System Model (MPI-ESM-ER) experiments (Gutjahr et al. 2019), which have been performed as part of the CMIP6-endorsed HighResMIP (Haarsma et al. 2016). At the same time, we aim to identify causes for those changes in terms of mechanisms, which can result from differences in the ocean dynamics and differences in the air\u2013sea exchange of heat, freshwater, or momentum. Geographically, our work focuses on the North Atlantic, the North Pacific, and the Southern Ocean, where large-scale effects from mesoscale eddies can be expected, given the presence of strong and eddy-rich western boundary currents.\nThe structure of the remaining paper is as follows: Section 2 describes the model and the evaluation methods used. Common characteristics of sea level change in the models are described in detail in section 3. In section 4, we compare the ocean model projection in each basin. We conclude and summarize with section 5.\nMaterials and methods\uf0c1\nClimate model simulations with MPI-ESM\uf0c1\nOur study is based on climate projections obtained with the MPI-ESM1.2 and performed under the protocol of the CMIP phase 6 (CMIP6; Eyring et al. 2016). The MPI-ESM is a fully coupled climate model, using ECHAM6 (Stevens et al. 2013) for the atmosphere and MPIOM (Jungclaus et al. 2013) for the ocean. Details on the CMIP6 version in comparison with its predecessor can be found in Mauritsen et al. (2019). Our study considers three versions of the same model configuration, including the low-resolution (LR), high-resolution (HR), and eddy-rich (ER) models, all driven by the SSP5-8.5 (fossil-fueled development) (O\u2019Neill et al. 2017) forcing. From each model simulation monthly mean fields are available. Configurations for all experiments evaluated here are summarized in Table 1.\nTable 1: Summary of MPI-ESM projections used in this study.", "source": "https://sealeveldocs.readthedocs.io/en/latest/wickramage23.html"}
{"id": "bc7116e222f0-1", "text": "The structure of the remaining paper is as follows: Section 2 describes the model and the evaluation methods used. Common characteristics of sea level change in the models are described in detail in section 3. In section 4, we compare the ocean model projection in each basin. We conclude and summarize with section 5.\nMaterials and methods\uf0c1\nClimate model simulations with MPI-ESM\uf0c1\nOur study is based on climate projections obtained with the MPI-ESM1.2 and performed under the protocol of the CMIP phase 6 (CMIP6; Eyring et al. 2016). The MPI-ESM is a fully coupled climate model, using ECHAM6 (Stevens et al. 2013) for the atmosphere and MPIOM (Jungclaus et al. 2013) for the ocean. Details on the CMIP6 version in comparison with its predecessor can be found in Mauritsen et al. (2019). Our study considers three versions of the same model configuration, including the low-resolution (LR), high-resolution (HR), and eddy-rich (ER) models, all driven by the SSP5-8.5 (fossil-fueled development) (O\u2019Neill et al. 2017) forcing. From each model simulation monthly mean fields are available. Configurations for all experiments evaluated here are summarized in Table 1.\nTable 1: Summary of MPI-ESM projections used in this study.\nThe coupled control simulations were initialized and forced following the CMIP6 protocol for HR and LR. The reference year for the preindustrial control simulation (piControl) is 1850, and it is conducted under conditions that have been selected to be typical of the time before the start of large-scale industrialization. A control simulation typically begins after an initial spinup phase, during which the climate system reaches a state close to an equilibrium (Eyring et al. 2016). For ER, the coupled control simulation was however initialized following the CMIP6-HighResMIP protocol (Haarsma et al. 2016). The ER control run was initialized after 30 years of spinup initialized from the averaged state of the Met Office Hadley Centre EN4 observational dataset from 1950 to 1954 (Good et al. 2013) for the ocean and ER atmosphere initialized from HR atmospheric state (Gutjahr et al. 2019). The length of control run is 1000 years for LR, 500 years for HR, and 200 years for ER.\nThe low-resolution version of MPI-ESM (MPI-ESM-LR) approximately has a 1.9\u00b0 horizontal resolution for the atmosphere (spectral truncation at T63; 210 km at the equator; 192 \u00d7 96 longitude/latitude) and 47 hybrid sigma pressure level extending to a 0.01 hPa top level. The ocean component has a bipolar 1.5\u00b0 horizontal resolution (GR1.5; approximately 150 km near the equator; 256 \u00d7 220 longitude/latitude) and 40 vertical levels with layer thickness ranging from 12 m near the surface to several hundred meters at depth. The horizontal grid spacing varies from 185 km in the tropical Pacific to 22 km around Greenland. The poles of the ocean model are over Greenland and Antarctica (coast of the Weddell Sea). The LR version cannot capture mesoscale ocean processes and dynamics (for more details, Mauritsen et al. 2019).\nThe high-resolution configuration, MPI-ESM-HR (M\u00fcller et al. 2018), uses a 0.9\u00b0 horizontal resolution (T127; 384 \u00d7 192 longitude/latitude) for the atmosphere, which is approximately 100 km around the equator. HR has a relatively highly resolved stratosphere extending to a 0.01 hPa top level with 95 vertical levels (L95). A tripolar grid 0.4\u00b0 horizontal resolution (TP04; 802 \u00d7 404 longitude/latitude) is used for the ocean component. Two poles are placed in the Northern Hemisphere over central Asia (Siberia) and Canada, providing quasi-homogeneous resolution of a approximately 40 km in the Arctic Ocean. In the Southern Hemisphere, grid distances decrease with increasing latitude. South of the Antarctic Circumpolar Current (ACC) at around 60\u00b0S the resolution is 20 km. HR comprises 40 unevenly spaced vertical levels, allocating 20 levels within the upper 700 m. HR is permitting eddies in the tropics but not resolving the Rossby radius in the higher latitudes. Even though HR fails to resolve the Rossby radius length scales, key for the representation of boundary currents and fronts, it still can capture reasonable eddy-like structures (see Jungclaus et al. 2013; M\u00fcller et al. 2018).\nThe Gent\u2013McWilliams (GM) parameterization (Gent and McWilliams 1990) of mesoscale eddies is used in LR and HR. The GM coefficients in HR and LR are constant and quite small. They are scaled with the grid spacing. The GM parameterization decreases linearly with increasing resolution, and a value of 250 m\u22122 s\u22121 was chosen for a grid cell that is 400 km wide (Gutjahr et al. 2019).\nThe eddy-rich MPI-ESM-ER (Gutjahr et al. 2019) has the same T127/L95 atmospheric component as HR. However, the horizontal resolution of the ocean component is on a tripolar 6-min (TP6M) horizontal grid (approximately 0.1\u00b0 or 10 km) in both latitude and longitude, and has 80 vertical levels. ER has three poles over North America, Russia, and Antarctica. In the eddy-rich-resolution model simulations, the GM parameterization for mesoscale eddies is disabled, and eddy effects are resolved according to the ratio of the first baroclinic deformation radius to the horizontal grid spacing. Eddies are not resolved at higher latitudes and over shallow/shelf regions. The grid resolution is smaller south of 50\u00b0S (Table 1; for more details, check Mauritsen et al. 2019; Putrasahan et al. 2021). The ER model has nominal horizontal resolution of \u223c10 km which means that the large-scale (order of 1000 km) and oceanic mesoscale eddies (order of 10 and larger) are resolved almost everywhere; however, the ocean submesoscale eddies are typically less than 10 km are not included in the ER simulation. In addition, the air\u2013sea interactions from processes such as mesoscale storms are not resolved by the atmospheric component of ER model.\nAs part of our analysis, we compare results from all model version described above under the SSP5-8.5 climate forcing scenario covering 2080\u201399, to their historical simulations during 1995\u20132014. In all cases we consider ensemble means using all available members, which are 10 members in LR, 2 in HR, and 3 in ER to minimize the impact of climate variability. Prior to analyzing the model output, we interpolated it onto the same grid of 1\u00b0 horizontal resolution. As the development of ER was computationally expensive, it has not been tuned and spun up according to the standard of HR and LR (Mauritsen et al. 2019). Therefore, the linear trend obtained from the only member of the control run was removed from the historical and scenario data. While we focus mostly on effects of ocean resolution, we note that LR features also considerably lower resolution in the atmosphere. Therefore, we put particular emphasis in the discussion on changes we diagnose in the ER configuration, which was run with the same atmosphere as the HR model.\nAnalyzing model output\uf0c1\nThis study considers the dynamic sea level (DSL), which is defined as the mean sea level above the geoid due to ocean dynamics (Gregory et al. 2019):\n\u03b6 = \u03b7 \u2212 \u03b7\u2032. (1)\nHere \u03b6 is the variable \u201czos\u201d according to the CMIP terminology (Griffies et al. 2016), \u03b7, which is named \u201csterodynamic sea level,\u201d is the sea surface height relative to a reference geopotential surface, and \u03b7\u2032 denotes a global mean (Gregory et al. 2019). Hence, DSL change (\u0394\u03b6) should have a zero global mean by definition. We therefore subtracted the global mean from each input field.\nAs we are interested in future sea level change, our work focuses on the dynamic sea level change (\u0394\u03b6) pattern, which is calculated from the difference between the DSL change in SSP5-8.5 forcing scenario (\u0394\u03b7s) relative to the DSL change in the historical simulation (\u0394\u03b7h):\n\u0394\u03b6 = \u0394\u03b7s \u2212 \u0394\u03b7h. (2)\nConsidering that changes in circulation and changes in wind stress in principle are the key drivers of these changes, we also calculated changes in the barotropic streamfunction \u03c8, changes in surface wind stress, and variation in the meridional overturning circulation and analyzed their differences as function of model resolution.", "source": "https://sealeveldocs.readthedocs.io/en/latest/wickramage23.html"}
{"id": "bc7116e222f0-2", "text": "Analyzing model output\uf0c1\nThis study considers the dynamic sea level (DSL), which is defined as the mean sea level above the geoid due to ocean dynamics (Gregory et al. 2019):\n\u03b6 = \u03b7 \u2212 \u03b7\u2032. (1)\nHere \u03b6 is the variable \u201czos\u201d according to the CMIP terminology (Griffies et al. 2016), \u03b7, which is named \u201csterodynamic sea level,\u201d is the sea surface height relative to a reference geopotential surface, and \u03b7\u2032 denotes a global mean (Gregory et al. 2019). Hence, DSL change (\u0394\u03b6) should have a zero global mean by definition. We therefore subtracted the global mean from each input field.\nAs we are interested in future sea level change, our work focuses on the dynamic sea level change (\u0394\u03b6) pattern, which is calculated from the difference between the DSL change in SSP5-8.5 forcing scenario (\u0394\u03b7s) relative to the DSL change in the historical simulation (\u0394\u03b7h):\n\u0394\u03b6 = \u0394\u03b7s \u2212 \u0394\u03b7h. (2)\nConsidering that changes in circulation and changes in wind stress in principle are the key drivers of these changes, we also calculated changes in the barotropic streamfunction \u03c8, changes in surface wind stress, and variation in the meridional overturning circulation and analyzed their differences as function of model resolution.\nThe Sverdrup streamfunction was estimated using wind stress data based on the Sverdrup relation (Sverdrup 1947). The Sverdrup transport was integrated zonally along a latitude (y) from the eastern boundary (xe) to each zonal location (x) of the basin as follows:\n\u03c8Sv = 1/(\u03b2\u03c1) \u222b^x_{xe} curl(\u03c4) dx\u2032, (3)\nwhere \u03b2 denotes the meridional derivative of the Coriolis parameter, \u03c1 is the mean density of the ocean, and curl(\u03c4) denotes the wind stress curl.\nTo analyze the meridional displacement of gyres, the mean latitude y of the barotropic streamfunction is calculated according to \u03b8 = \u222b\u03c8 \u00d7 y dx dy / \u222b\u03c8 dx dy. (4)\nWe consider the zero contour as the boundary of each gyre and consider positive (negative) barotropic streamfunction values for subtropical (subpolar) gyre. The contours between the minimum and maximum transport (positive contours) in the Drake Passage were considered to calculate the mean central latitude of ACC transport.\nSignificance and trend\uf0c1\nAssuming that the variance remains unchanged under climate forcing conditions, the 95% significance of the difference of changes between the resolutions ER and HR was determined according to the formula,\n\u221a(2*\u03c3^2_{ER}/N_{ER} + 2*\u03c3^2_{HR}/N_{HR}) \u00d7 t_{95%}, with t_{95%} the Student t value, N_{ER} and N_{HR} are the respective numbers of members, and \u03c3^2_{ER} and \u03c3^2_{HR} are the variances of the ER and HR control simulations, respectively. The factor 2 accounts for the fact that the changes have twice the variance of the fields they are calculated from. A similar method was applied to calculate the error bar or envelope, (1/\u221aN)\u221a2\u03c3^2_{ER} \u00d7 t_{95%} for the ensemble mean changes [see von Storch and Zwiers (2002) for more details]. The linear least squares fitting was used to calculate the yearly average time series trend. The analyses were performed using CDO and NCL software (NCL 2019).\nCommonalities of sea level changes in MPI-ESM\uf0c1\nOver the past years, the global ocean has accounted for around 91% of anthropogenically induced Earth\u2019s heat content increase, resulting in an observed thermal expansion and associated sea level rise of about 0.54 (0.40\u20130.68) mm yr\u22121 over the years from 1901 to 2018 (Fox-Kemper et al. 2021). In contrast, the simulated thermal expansion in IPCC AR6 leads to sea level rise of 30 (24\u201336) cm under SSP5-8.5 for the year 2100 relative to a baseline of 1995\u20132014. From the MPI- ESM model simulations we can infer a comparable global mean thermosteric sea level (GMTSL) rise (Fig. 1) of 30.30, 30.06, and 31.95 cm at the end of the twenty-first century relative to the 1950s for ER, HR, and LR, respectively. Over the period 1901\u20132018, changes are around 60 mm and compare well with the observed change of 63.2 mm due to thermal expansion (Fox-Kemper et al. 2021). The average simulated rate of thermosteric sea level rise due to global ocean heating for the SPP5-8.5 scenario is 3.31 mm yr\u22121 in ER, 3.34 mm yr\u22121 in HR, and 3.51 mm yr\u22121 in LR between 2030 and 2099.\nFigure 1: Global 12-month running mean (a) sea surface temperature and (b) thermosteric sea level change for MPI-ESM-ER, MPI-ESM-HR, and MPI-ESM-LR, relative to the 1950s. The purple line in (a) represents a 12-month running mean of respective global mean HadISST values.\nFigure 1 also compares the increase in thermosteric sea level rise with the respective increases in global SST. On global average, both curves suggest an equivalent increase in thermosteric sea level rise of 0.11 m per 1\u00b0C of SST increase. However, SST curves are considerable noisier and, in that sense, can only be considered a very crude proxy for thermosteric sea level rise. This holds especially for individual ensemble members and should be true also for the real world. We note that a respective correspondence cannot be expected to hold on regional scale due to the temperature dependence of the thermosteric expansion coefficient and the influence of salinity.\nThe common global pattern of LR, HR, and ER for the changes in DSL (in m), the barotropic streamfunction (BSF; Sv; 1 Sv \u2261 106 m3 s\u22121), and the wind stress (N m\u22122) are discussed in this section. These changes between the patterns over the SSP5-8.5 years 2080\u201399 relative to the historical simulation (years 1995\u20132014) are shown in Fig. 2. We will discuss how the models differ from one another on regional scale in the following section.\nFigure 2: Anomalies of (a)\u2013(c) dynamic sea level (m), (d)\u2013(f) barotropic streamfunction (Sv), (g)\u2013(i) sea surface temperature (\u00b0C), and (j)\u2013(l) wind stress (N m\u22122), for (left) MPI-ESM-LR, (center) MPI-ESM-HR, and (right) MPI-ESM-ER between the SSP5-8.5 averaged over the period 2080\u201399 and the historical period averaged over the years 1995\u20132014.\nThe DSL is a helpful tool for analyzing the ocean processes contributing to sea level changes due to the close link between the DSL and the ocean circulation through the geostrophic relation. According to Figs. 2a\u2013c, sea level changes are not homogeneous in the global ocean but show diverse regional patterns. At the end of the century, the respective sea level change leads to a dipole pattern in the North Atlantic with generally increasing sea level north of the Gulf Stream (in the southern part of the subpolar gyre) and a decrease in the subtropical gyre. An opposite dipole pattern exists in the North Pacific, where sea level is higher south of the Kuroshio (in the subtropical region) and lower farther to the north (in the subpolar region). In the Southern Ocean, the ridge-like pattern is associated with a sea level increase north of \u223c50\u00b0S and decrease south of \u223c50\u00b0S. The aforementioned sea level change patterns have also been reported previously, such as Chen et al. (2019), Church et al. (2013a,b), Couldrey et al. (2021), Fox-Kemper et al. (2021), Gregory et al. (2016), and Lyu et al. (2020), and common to all the models. As in previous studies (Prandi et al. 2012; Rose et al. 2019; Xiao et al. 2020), the highest sea level rise is also found in our models in the Arctic Ocean.", "source": "https://sealeveldocs.readthedocs.io/en/latest/wickramage23.html"}
{"id": "bc7116e222f0-3", "text": "Figure 2: Anomalies of (a)\u2013(c) dynamic sea level (m), (d)\u2013(f) barotropic streamfunction (Sv), (g)\u2013(i) sea surface temperature (\u00b0C), and (j)\u2013(l) wind stress (N m\u22122), for (left) MPI-ESM-LR, (center) MPI-ESM-HR, and (right) MPI-ESM-ER between the SSP5-8.5 averaged over the period 2080\u201399 and the historical period averaged over the years 1995\u20132014.\nThe DSL is a helpful tool for analyzing the ocean processes contributing to sea level changes due to the close link between the DSL and the ocean circulation through the geostrophic relation. According to Figs. 2a\u2013c, sea level changes are not homogeneous in the global ocean but show diverse regional patterns. At the end of the century, the respective sea level change leads to a dipole pattern in the North Atlantic with generally increasing sea level north of the Gulf Stream (in the southern part of the subpolar gyre) and a decrease in the subtropical gyre. An opposite dipole pattern exists in the North Pacific, where sea level is higher south of the Kuroshio (in the subtropical region) and lower farther to the north (in the subpolar region). In the Southern Ocean, the ridge-like pattern is associated with a sea level increase north of \u223c50\u00b0S and decrease south of \u223c50\u00b0S. The aforementioned sea level change patterns have also been reported previously, such as Chen et al. (2019), Church et al. (2013a,b), Couldrey et al. (2021), Fox-Kemper et al. (2021), Gregory et al. (2016), and Lyu et al. (2020), and common to all the models. As in previous studies (Prandi et al. 2012; Rose et al. 2019; Xiao et al. 2020), the highest sea level rise is also found in our models in the Arctic Ocean.\nMany changes in DSL displayed in Figs. 2a\u2013c can be associated with changes in the vertically integrated large-scale circulation as depicted by BSF (Figs. 2d\u2013f). In the North Atlantic, circulation in subpolar regions north of the Gulf Stream and Labrador Sea and the subtropical gyre weaken, whereas the circulation southeast of Greenland strengthens (negative BSF anomalies in high latitude). The latter is accompanied by a smaller DSL. However, the opposite happens in the North Pacific, where subpolar gyre and the Kuroshio region (northern part of subtropical gyre) strengthens, while the southern part of subtropical gyre weakens. A band of positive streamfunction north of Gulf Stream could possibly indicate the poleward shift of the North Atlantic Subtropical Gyre. Moreover, Southern Ocean circulation strengthens between 40\u00b0 and 50\u00b0S in all models (Figs. 2d\u2013f).\nWhile almost every corner in the world is heating up, a cooling temperature patch, known as warming hole (aka cold blob), is identified in the vicinity of southeast Greenland (Figs. 2g\u2013i). This warming hole feature, however, appears to be north of the warming hole stated in earlier studies in response to warming (e.g., Chemke et al. 2020; Drijfhout et al. 2012; Gervais et al. 2018; Menary and Wood 2018). Together with the warming hole, a patch of DSL decline (Figs. 2a\u2013c), and a reinforced high latitude circulation (Figs. 2d\u2013f) are identified in the same subpolar region in all configurations. Numerous previous studies have discussed the occurrence of the warming hole as a result of a weakening Atlantic meridional overturning circulation (AMOC) (such as Caesar et al. 2018; Drijfhout et al. 2012; Gervais et al. 2018; Keil et al. 2020; Menary and Wood 2018; Rahmstorf et al. 2015).\nThe variation in the BSF field is linked to the changes in the wind stress curl field by the Sverdrup relation. However, it might also reflect the changes in the interior density gradients and/or interactions with sloping bottom bathymetry (e.g., Yeager 2015). We examine the Sverdrup relation in the North Atlantic and North Pacific Oceans later in section 4. A distinct feature of wind stress changes in the models is the strengthening of the westerly wind in the Southern Ocean at the end of the twenty-first century (Figs. 2j\u2013l). Over most of the Pacific Ocean except the tropical North Pacific wind stress strengthens. Changes over the Atlantic are less clear, leading mostly to weakened wind stress, except for the eastern subtropical North Atlantic.\nDiscrepancies of regional sea level change in MPI-ESM\uf0c1\nIn the following we will discuss the detailed resolution dependence of the time mean changes from historical to SSP5-8.5 on the model resolution separately for the North Atlantic, the North Pacific, and the Southern Ocean.\nNorth Atlantic\uf0c1\nDSL change in the subpolar gyre region is characterized by two distinct features: a decrease in the basins southeast of Greenland and an increase in the rest of the subpolar gyre (Figs. 3a\u2013c). Statistically significant differences at 95% are marked by dots in the spatial pattern difference and by nonoverlapping error bars in the zonal averages. This DSL decrease over the basins southeast of Greenland (the Irminger Sea and Icelandic Basin) is smallest in ER and largest in LR (by the magnitude of \u223c0.2 m see in Figs. 3a,c,d,e). The increase in the Labrador Sea and farther south until north of the Gulf Stream is also smaller in ER than HR and LR (by the magnitude of \u223c0.16 m see in Figs. 3d,e). The changes southeast of Greenland dominate the zonal mean (north of 50\u00b0N) of DSL, indicating a prominent decrease in LR and almost no change in HR (Fig. 4a). In contrast, ER shows an overall sea level increase in the northern part of the subpolar gyre, pointing to a smaller decline in the basins southeast of Greenland (Figs. 3c,d, 4a). In the southern part of the subpolar gyre (between 40\u00b0 and 50\u00b0N), the MPI-ESM models show a DSL increase with the largest rise in HR (Fig. 4a). The increase in HR can be noticed in the spatial pattern by a negative and positive sign of the difference north of the Gulf Stream (north of 40\u00b0N) in Figs. 3e and 3f, respectively.\nFigure 3: North Atlantic differences of (a)\u2013(f) dynamic sea level (m) and (g)\u2013(l) wind stress (N m\u22122); panels (a)\u2013(c) and (g)\u2013(i) illustrate the anomalies of the SSP5-8.5 (2080\u201399) average relative to the historical simulation, averaged over 1995\u20132014 for MPI-ESM-LR in (a) and (g), MPI-ESM-HR in (b) and (h), and MPI-ESM-ER in (c) and (i); panels (d)\u2013(f) and (j)\u2013(l) illustrate the differences of the anomalies between the models [ER minus LR in (d) and (j), ER minus HR in (e) and (k), and HR minus LR in (f) and (l)]. The contours represent the historical mean (1995\u20132014; contour interval is 0.1 m). The contour colors denote solid red for the positive values, green line for the zero contour, and dash blue for the negative values. In all panels stippling indicates statistically significant differences (95% confidence level). All projections were interpolated onto the same grid prior to computing differences of the anomalies.\nFigure 4: North Atlantic (a) zonal mean sea surface height (m); (b) zonal mean barotropic streamfunction (Sv); (c) zonal mean zonal wind stress (N m\u22122) anomalies, each for the time mean differences over historical simulation and SSP5-8.5 for ER, HR, and LR, respectively. Error bar envelopes represent two standard deviations.", "source": "https://sealeveldocs.readthedocs.io/en/latest/wickramage23.html"}
{"id": "bc7116e222f0-4", "text": "Figure 3: North Atlantic differences of (a)\u2013(f) dynamic sea level (m) and (g)\u2013(l) wind stress (N m\u22122); panels (a)\u2013(c) and (g)\u2013(i) illustrate the anomalies of the SSP5-8.5 (2080\u201399) average relative to the historical simulation, averaged over 1995\u20132014 for MPI-ESM-LR in (a) and (g), MPI-ESM-HR in (b) and (h), and MPI-ESM-ER in (c) and (i); panels (d)\u2013(f) and (j)\u2013(l) illustrate the differences of the anomalies between the models [ER minus LR in (d) and (j), ER minus HR in (e) and (k), and HR minus LR in (f) and (l)]. The contours represent the historical mean (1995\u20132014; contour interval is 0.1 m). The contour colors denote solid red for the positive values, green line for the zero contour, and dash blue for the negative values. In all panels stippling indicates statistically significant differences (95% confidence level). All projections were interpolated onto the same grid prior to computing differences of the anomalies.\nFigure 4: North Atlantic (a) zonal mean sea surface height (m); (b) zonal mean barotropic streamfunction (Sv); (c) zonal mean zonal wind stress (N m\u22122) anomalies, each for the time mean differences over historical simulation and SSP5-8.5 for ER, HR, and LR, respectively. Error bar envelopes represent two standard deviations.\nThese changes in sea level also reflect changes in circulation indicated by the vertically integrated flow (displayed in Figs. 6a\u2013c). The cyclonic circulation in southeast of Greenland strengthens in LR and somewhat less so in HR. It is even lesser in ER (Figs. 6a\u2013c), as does decline in sea level. Subpolar gyre circulation weakens in the Labrador Sea and the southern part of the gyre. In contrast, the weakening is considerably larger in the ER model. A weakening subpolar gyre as seen in ER was also reported for the circulation changes from the 1990s to the 2000s observed by altimetry data (Lee et al. 2010; H\u00e4kkinen and Rhines 2004, 2009), with inconclusive attribution to whether these changes remain part of natural climate variability or are already a sign of a long-term trend. Nevertheless, the circulation changes can have important consequences for the distribution of water masses as a weakening subpolar gyre can lead to an increasing transport of warm and salty Atlantic water into the Nordic seas during the historical period (H\u00e1t\u00fan et al. 2005) and significant reduction in Labrador Sea deep convection.\nMany previous studies have also highlighted the relation between weakening AMOC and DSL changes in the North Atlantic (Bouttes et al. 2014; Chen et al. 2019; Fox-Kemper et al. 2021; Hu et al. 2011; Levermann et al. 2005; Lyu et al. 2020; Pardaens et al. 2011; Yin et al. 2009, 2010). The projected change of the AMOC is likely to depend on the model resolution and therefore impact DSL differently. The pattern of the AMOC change is nearly identical to its mean AMOC (Figs. 5a\u2013c), indicating a consistent weakening of all branches from historical to SSP5-8.5 by about one-third of its strength. The overlaid contours of historical mean in Figs. 5a\u2013c provide a comparison with its anomalies. Similar to the DSL change, the warming hole feature becomes smaller in size with improved horizontal resolution, especially in ER compared to HR (Figs. 2h,i and 3b,c), whereas the AMOC slowing (Fig. 5g) does not differ much in the final years despite the smaller trend in LR at 26\u00b0N. Although, the AMOC weakening is larger in LR than in HR and ER between 30\u00b0 and 60\u00b0N centered around 1500-m depth (Figs. 5a,d,f). This puts a question mark to studies linking the strength of the warming hole directly to a slowing down of the AMOC (Caesar et al. 2018, using observations; Menary and Wood 2018; Rahmstorf et al. 2015). In this sense, Keil et al. (2020) have argued for multiple drives of the warming hole feature. During the historical period, the anthropogenically forced changes of both the gyre and overturning circulation induce heat transport increase out of the subpolar region to the Greenland\u2013Iceland\u2013Norwegian (GIN) Seas and then farther to the Arctic, contributing to the warming hole feature in the North Atlantic (Keil et al. 2020).\nFigure 5: Anomalies of the Atlantic meridional overturning circulation streamfunction (Sv) for (a) MPI-ESM-LR, (b) MPI-ESM-HR, and (c) MPI-ESM-LR, each for the time mean differences over historical simulation and SSP5-8.5. Differences of the anomalies between the models: (d) ER minus LR, (e) ER minus HR, and (f) HR minus LR. The contours represent the historical mean (1995\u20132014; contour interval is 3 Sv). The contour colors denote solid red for the positive values, green line for the zero contour, and dash blue for the negative values. In all panels stippling indicates statistically significant differences (95% confidence level). (g) Time series of 3-yr running mean AMOC streamfunction (Sv) relative to 1950s at 1000 m and 26\u00b0N. Dashed lines represent a linear trend over the period 2030\u201399 for LR, HR, and ER, plotted in green, red, and blue, respectively.\nIn the subpolar gyre, heat transport is driven by both gyre and overturning circulation. The strengthened barotropic circulation in high latitudes, where the northern part of the subpolar region and GIN Seas (Figs. 6a\u2013c) can similarly contribute to the development of the warming hole and the associated sea level decline. Conversely, the AMOC effect is mitigated by a weaker strengthening of the circulation in vicinity of Greenland in ER (Figs. 6c,e) leading to a smaller DSL decrease and a smaller-scale warming hole in comparison to HR. The DSL decline and strengthening subpolar circulation are larger in LR than in HR and ER (Figs. 6d,f), despite the warming hole in LR being smaller (Fig. 2g and Fig. S1 in the online supplemental material). This could be because LR has a weaker GIN Seas circulation (Figs. 6a,d,f), which could indicate smaller heat transport out of the subpolar region. Future DSL change in the subpolar North Atlantic and the formation of the warming hole are hence resolution dependent.\nFigure 6: Anomalies of (a)\u2013(c) barotropic streamfunction and (g)\u2013(h) Sverdrup streamfunctions for the SSP5-8.5 (2080\u201399) average relative to the historical simulation, averaged over 1995\u20132014 in North Atlantic for MPI-ESM-LR in (a) and (g), MPI-ESM-HR in (b) and (h), and MPI-ESM-ER in (c) and (i); the differences of the anomalies between the models: (d) ER minus LR, (e) ER minus HR, and (f) HR minus LR. The contours represent the historical mean [1995\u20132014; contour intervals are 2 Sv in (a)\u2013(c) and 5 Sv in (g)\u2013(h)]. The contour colors denote solid red for the positive values, green line for the zero contour, and blue dashed for the negative values. The stippling indicates the statistically significant regions at the 95% confidence level.\nCurry et al. (1998), B\u00f6ning et al. (2006), and H\u00e4kkinen et al. (2011) show the impact of the surface wind stress on both subpolar gyre variability and the strength. The decline of the surface wind stress over the subpolar gyre region could result in the spindown of the subpolar gyre circulation, leading to sea level increase (Chafik et al. 2019; Putrasahan et al. 2019). A noticeable difference between eddy-rich and lower resolutions is that wind stress reduces in ER over the subpolar North Atlantic (50\u00b0\u201365\u00b0N) in contrast to LR and HR (Figs. 3j,k), for which wind stress intensify (Fig. 4c). These changes agree with the noted spindown of the subpolar gyre in ER and the strengthened gyre circulation in LR and HR (Figs. 6a\u2013c). However, the extensive spread in zonal mean zonal wind stress anomalies implies a minor resolution dependency in subpolar gyre region (Fig. 4c) at the 95% significant level.", "source": "https://sealeveldocs.readthedocs.io/en/latest/wickramage23.html"}
{"id": "bc7116e222f0-5", "text": "Figure 6: Anomalies of (a)\u2013(c) barotropic streamfunction and (g)\u2013(h) Sverdrup streamfunctions for the SSP5-8.5 (2080\u201399) average relative to the historical simulation, averaged over 1995\u20132014 in North Atlantic for MPI-ESM-LR in (a) and (g), MPI-ESM-HR in (b) and (h), and MPI-ESM-ER in (c) and (i); the differences of the anomalies between the models: (d) ER minus LR, (e) ER minus HR, and (f) HR minus LR. The contours represent the historical mean [1995\u20132014; contour intervals are 2 Sv in (a)\u2013(c) and 5 Sv in (g)\u2013(h)]. The contour colors denote solid red for the positive values, green line for the zero contour, and blue dashed for the negative values. The stippling indicates the statistically significant regions at the 95% confidence level.\nCurry et al. (1998), B\u00f6ning et al. (2006), and H\u00e4kkinen et al. (2011) show the impact of the surface wind stress on both subpolar gyre variability and the strength. The decline of the surface wind stress over the subpolar gyre region could result in the spindown of the subpolar gyre circulation, leading to sea level increase (Chafik et al. 2019; Putrasahan et al. 2019). A noticeable difference between eddy-rich and lower resolutions is that wind stress reduces in ER over the subpolar North Atlantic (50\u00b0\u201365\u00b0N) in contrast to LR and HR (Figs. 3j,k), for which wind stress intensify (Fig. 4c). These changes agree with the noted spindown of the subpolar gyre in ER and the strengthened gyre circulation in LR and HR (Figs. 6a\u2013c). However, the extensive spread in zonal mean zonal wind stress anomalies implies a minor resolution dependency in subpolar gyre region (Fig. 4c) at the 95% significant level.\nDynamically, the simplest concept for the barotropic circulation is the balance between wind stress curl and the advection of vorticity which is described by the Sverdrup streamfunction. For the time-mean circulation the validity of the concept has been approved for interior of the subtropical circulation (e.g., Sonnewald et al. 2019; Wunsch and Roemmich 1985; Wunsch 2011). The degree of the Sverdrup concept\u2019s validity to describe temporal changing circulation changes was previously demonstrated (e.g., Willebrand et al. 1980; Hautala et al. 1994; Stammer 1997; Morris et al. 1996, Thomas et al. 2014) and an agreement was found even outside of the subtropics. The Sverdrup streamfunction was calculated in the North Atlantic and North Pacific (Figs. 6, 9) to quantify the impact of the wind stress curl. The weakening of the North Atlantic Subpolar Gyre between 50\u00b0 and 60\u00b0N can be explained by the weakening of surface wind stress curl in ER (Fig. 6i). Despite the strengthened circulation (Figs. 6a,b, 4b) and slightly intensified surface wind stress (Fig. 4c) in LR and HR, their curl weakens in both models (Figs. 6g,h). The changes in subpolar gyre circulation do not entirely concur with the Sverdrup dynamics in HR, although HR and ER have the same T127/L95 atmospheric component.\nAll three resolutions show a weakening subtropical gyre (Figs. 6a\u2013c), associated with a negative DSL, and just north of the Gulf Stream a band of positive DSL (Figs. 3a\u2013c) that signifies the reduction of Gulf Stream transport associated with the weakening subtropical gyre and the declining AMOC (Fig. 5g). The weakening of the Gulf Stream under warming conditions during the twenty-first century (Yang et al. 2016) could be related to the sea level changes in the North Atlantic associated with higher sea level rise north of the Gulf Stream (Bouttes et al. 2014; Chen et al. 2019; Levermann et al. 2005; Yin et al. 2009). The argument requires that the DSL is lower than the global mean such that a relaxation locally leads to a DSL rise; the same applies to the barotropic streamfunction.\nER shows the largest DSL reduction in the subtropical gyre (Figs. 3d,e), although a weakening of wind stress is smaller south of 40\u00b0N (Figs. 3j,k, 4c). However, the spindown of the subtropical gyre is larger in the ER compared to HR and LR (Figs. 6d,e, 4b). There is no considerable difference in the AMOC slowdown (Figs. 5e,g) between HR and ER. The AMOC deceleration is larger by 0.25 Sv in ER than in HR and 1.25 Sv than in LR (Fig. 5g) by 2100 at 26\u00b0N. The AMOC linear trend, calculated over 1995\u20132099, amounts to \u22120.061 Sv yr\u22121 for ER, \u22120.059 Sv yr\u22121 for HR, and \u22120.052 Sv yr\u22121 for LR. Despite the similar magnitude of AMOC decline at 26\u00b0N in HR and ER, spindown of the subtropical gyre and the DSL reduction is larger in ER than in HR.\nIn addition to the effect of AMOC slowdown, changes in wind stress could also be responsible for the sea level reduction in the subtropical gyre south of the Gulf Stream (40\u00b0N), as suggested by Bouttes et al. (2012). The Sverdrup circulation of the North Atlantic Subtropical Gyre weakens dramatically in all three models. Moreover, the wind stress weakens south of 40\u00b0N in the zonal mean, with a stronger decline in HR and LR relative to the ER (Fig. 4c). The associated Sverdrup circulation is illustrated in Figs. 6g\u2013i for comparison with the gyre changes as illustrated by the barotropic streamfunction (Figs. 6a\u2013c, 4b). Additionally, the contours representing the present-day state are superimposed over the streamfunction anomalies to better visualize the shifting and changing of gyres. The wind stress curl changes tend to weaken the gyre circulation in the southern part of the North Atlantic Subtropical Gyre, whereas the northern part experiences a strengthening in all model versions (Figs. 6g\u2013i). This suggests a poleward shift of the weakening subtropical gyre and Gulf Stream (Figs. 6a\u2013c).\nNorth Pacific\uf0c1\nIn contrast to the North Atlantic, in ER the DSL increases south of the Kuroshio Extension (over the subtropical gyre) and decreases farther to the north (in the subpolar gyre, Fig. 7a). This characteristic North Pacific dipole pattern is opposite to that in the North Atlantic and its axis is located along the steep DSL gradient associated with the Kuroshio causing further steepening of the frontal zone. In the southern part of the subpolar gyre, the DSL reduction is much greater in ER and HR than in LR (Figs. 7d,f), though there is no substantial difference between HR and ER (Fig. 7e). The DSL decreases in the lower resolutions along the eastern boundary of the North Pacific (Figs. 7a,b), while ER shows an increase in the Gulf of Alaska (Figs. 7c). The discrepancies between the models are negligible in the northern part of the subpolar gyre (Figs. 7d\u2013f). In the subtropical gyre, the DSL increase is larger in ER compared to the LR and HR (Figs. 7d,e), and in HR than in LR (Fig. 7f), along with a significant increase east of Japan in the eddy-rich model (Fig. 8a).\nFigure 7: As in Fig. 3, but for the North Pacific.\nFigure 8: As in Fig. 4, but for the North Pacific.", "source": "https://sealeveldocs.readthedocs.io/en/latest/wickramage23.html"}
{"id": "bc7116e222f0-6", "text": "North Pacific\uf0c1\nIn contrast to the North Atlantic, in ER the DSL increases south of the Kuroshio Extension (over the subtropical gyre) and decreases farther to the north (in the subpolar gyre, Fig. 7a). This characteristic North Pacific dipole pattern is opposite to that in the North Atlantic and its axis is located along the steep DSL gradient associated with the Kuroshio causing further steepening of the frontal zone. In the southern part of the subpolar gyre, the DSL reduction is much greater in ER and HR than in LR (Figs. 7d,f), though there is no substantial difference between HR and ER (Fig. 7e). The DSL decreases in the lower resolutions along the eastern boundary of the North Pacific (Figs. 7a,b), while ER shows an increase in the Gulf of Alaska (Figs. 7c). The discrepancies between the models are negligible in the northern part of the subpolar gyre (Figs. 7d\u2013f). In the subtropical gyre, the DSL increase is larger in ER compared to the LR and HR (Figs. 7d,e), and in HR than in LR (Fig. 7f), along with a significant increase east of Japan in the eddy-rich model (Fig. 8a).\nFigure 7: As in Fig. 3, but for the North Pacific.\nFigure 8: As in Fig. 4, but for the North Pacific.\nIn HR and ER, the subpolar gyre strengthens (Figs. 9a,b), but in LR, the barotropic streamfunction field exhibits only minor change (Fig. 9c). Although the subpolar gyre is stronger in ER than in LR, the differences in subpolar gyre circulation between the models are relatively insignificant (Figs. 9d\u2013f). The changes in the subtropical gyre indicate a pattern with a positive north and negative south parts of the gyre (Figs. 9a\u2013c). The northern part of subtropical gyre (the Kuroshio region) strengthens; here ER displays a considerable amplification (30\u00b0\u201335\u00b0N; Fig. 8b). In the same region, we also noticed the high rate of DSL changes (Fig. 8a). Although the streamfunction differences are significant between the eddy-rich and eddy parameterized models in the northern part of the subtropical gyre (Figs. 9d,e), weakening southern part shows minor changes (Figs. 9d,e). The differences between LR and HR are significant (insignificant) in the southern (northern) part of the subtropical gyre circulation (Fig. 9f).\nFigure 9: As in Fig. 6, but for the North Pacific.\nIn comparison to the DSL change, changes of the barotropic circulation (Figs. 9a\u2013c) show some distinctively different patterns in the tropical regions. Although, the DSL changes across the Kuroshio Extension front are still reflected by similar albeit much weaker streamfunction changes, the strengthening of the subtropical gyre encompasses only the region 30\u00b0\u201340\u00b0N, while for DSL it reaches down to 20\u00b0N. The negative DSL change south of 20\u00b0N covers the entire tropical region, while for the streamfunction it reaches down to only 15\u00b0N, where the pattern continues southward by a positive signal. Streamfunction and DSL are therefore inconsistent in the region north of the equator until 30\u00b0N, a region where the Pacific and the Indian Ocean are connected by the Indonesian Throughflow passages (Zhang et al. 2014).\nBecause of the absence of deep-water formation and deep convection in the North Pacific, similar changes seen in CMIP5 models were mainly attributed to changes in the wind field (Sakamoto et al. 2005; Yin et al. 2010). Merrifield (2011) has shown the relevance of off-equatorial wind changes for explaining the features of the large observed sea level trend in the western tropical Pacific during the 1990s and early 2000s. Figure 8c depicts the zonally averaged zonal wind stress changes for three models, showing an increase north of about 38\u00b0\u201345\u00b0N and a decrease to the south. Although differences in wind stress change between the models are not significant at the 95% confidence interval of the multimember mean, ER shows less weakening in the subtropical and more strengthening in the subpolar in comparison to HR and LR (Figs. 7j,k, 8c).\nChanges in wind stress curl were found to explain the intensification of the subtropical gyre in the South Pacific since the early 1990s (Roemmich et al. 2007, 2016), which were also shown by K\u00f6hl and Stammer (2008) to explain the sea level trends during the longer time scale 1960\u20132001 over much of the Pacific Ocean. We will therefore again examine the wind-driven component of the circulation by the Sverdrup streamfunction (Figs. 9g\u2013i).\nConsistent with the barotropic streamfunction, the Sverdrup circulation changes show that the southern part of the North Pacific Subtropical Gyre weakens in all models, while the northern part of the gyre (north of 30\u00b0N) indicates a strengthening (Figs. 9g\u2013i). Cheon et al. (2012) argue that this pattern (positive north part and negative south part) observed in the subtropical gyre indicates a poleward shift rather than a strengthening of the gyre under a warming future. Yin et al. (2010) further corroborate this hypothesis of the subtropical gyre poleward shift, resulting from the poleward shift of subtropical high in the western Pacific and the associated wind system. These characteristic patterns of DSL change in the western North Pacific because of the poleward shift and intensification of the Kuroshio have also been studied earlier in earlier CMIP models (e.g., Church et al. 2013a,b; Fox-Kemper et al. 2021; Sueyoshi and Yasuda 2012; Suzuki and Tatebe 2020; Terada and Minobe 2018; Yin 2012; Zhang et al. 2014). However, whether this pattern in the Sverdrup and barotropic streamfunction indicates a poleward shift of the subtropical gyre or a strengthening of the Kuroshio is debatable (see section 4d). Different from the other resolutions, in LR, Sverdrup circulation weakens in the southern part of the North Pacific Subpolar Gyre, while the northern part shows a strengthening (Fig. 9g). It significantly strengthens in ER, and crosses the present-day zero contour (Fig. 9i), while HR shows no considerable change (Fig. 9h).\nPrevious studies have emphasized that increased model resolution is necessary for the representation of accurate western boundary currents such as Gulf Stream, Kuroshio, and East Australian Currents (e.g., Chassignet and Xu 2017; Chassignet et al. 2020; Griffies et al. 2015; Hewitt et al. 2017, 2020; Roberts et al. 2018; Small et al. 2014). Similarly, Hurlburt et al. (1996) and Nishikawa et al. (2020) demonstrate that eddy-rich horizontal resolution can realistically represent the Oyashio\u2013Kuroshio fronts. Therefore, the strong, narrow current, noted in the DSL and barotropic streamfunction fields (Figs. 7, 9) east of Japan, denotes the more accurately represented Kuroshio in the eddy-rich model, which alters the characteristics of the Kuroshio\u2013Oyashio front by representing a significant number of mesoscale activities in comparison to eddy parameterized models. The Kuroshio, between 30\u00b0 and 35\u00b0N, is significantly intensified in the ER model but slightly strengthens in the high-resolution and the low-resolution climate models.\nThe Southern Ocean\uf0c1\nLike in the North Atlantic and North Pacific, a north\u2013south gradient of DSL change is found in the Southern Ocean for all resolutions (Figs. 10a\u2013c), with increasing sea level north to \u223c50\u00b0S and decreasing south of \u223c50\u00b0S, which has been described as a belt-like pattern (Yin et al. 2010). The increase (decrease) of DSL north (south) of the ACC is smaller in ER than in HR and LR at the end of the twenty-first century (Figs. 11a,b, 12a). In earlier studies, the strengthening and poleward shift of Southern Hemisphere westerlies have been shown to induce such a pattern of DSL changes, although it was also noted that it is not sufficient to explain all of the projected changes (Thompson and Solomon 2002; Bouttes et al. 2012; Frankcombe et al. 2013).", "source": "https://sealeveldocs.readthedocs.io/en/latest/wickramage23.html"}
{"id": "bc7116e222f0-7", "text": "Previous studies have emphasized that increased model resolution is necessary for the representation of accurate western boundary currents such as Gulf Stream, Kuroshio, and East Australian Currents (e.g., Chassignet and Xu 2017; Chassignet et al. 2020; Griffies et al. 2015; Hewitt et al. 2017, 2020; Roberts et al. 2018; Small et al. 2014). Similarly, Hurlburt et al. (1996) and Nishikawa et al. (2020) demonstrate that eddy-rich horizontal resolution can realistically represent the Oyashio\u2013Kuroshio fronts. Therefore, the strong, narrow current, noted in the DSL and barotropic streamfunction fields (Figs. 7, 9) east of Japan, denotes the more accurately represented Kuroshio in the eddy-rich model, which alters the characteristics of the Kuroshio\u2013Oyashio front by representing a significant number of mesoscale activities in comparison to eddy parameterized models. The Kuroshio, between 30\u00b0 and 35\u00b0N, is significantly intensified in the ER model but slightly strengthens in the high-resolution and the low-resolution climate models.\nThe Southern Ocean\uf0c1\nLike in the North Atlantic and North Pacific, a north\u2013south gradient of DSL change is found in the Southern Ocean for all resolutions (Figs. 10a\u2013c), with increasing sea level north to \u223c50\u00b0S and decreasing south of \u223c50\u00b0S, which has been described as a belt-like pattern (Yin et al. 2010). The increase (decrease) of DSL north (south) of the ACC is smaller in ER than in HR and LR at the end of the twenty-first century (Figs. 11a,b, 12a). In earlier studies, the strengthening and poleward shift of Southern Hemisphere westerlies have been shown to induce such a pattern of DSL changes, although it was also noted that it is not sufficient to explain all of the projected changes (Thompson and Solomon 2002; Bouttes et al. 2012; Frankcombe et al. 2013).\nFigure 10: Anomalies of (a)\u2013(c) dynamic sea level, (d)\u2013(f) barotropic streamfunction, and (g)\u2013(i) wind stress for the SSP5-8.5 (2080\u201399) average relative to the historical simulation, averaged over 1995\u20132014 in Southern Ocean for (left) MPI-ESM-LR, (center) MPI-ESM-HR, and (right) MPI-ESM-ER. The contours represent the historical mean [1995\u20132014; contour intervals are 0.1 m in (a)\u2013(c) and 2 Sv in (d)\u2013(f)]. The contour colors denote solid red for the positive values, green line for the zero contour, and blue dashed for the negative values. The stippling indicates the statistically significant regions at the 95% confidence level. In (a), W stands for Weddell Sea and R stands for Ross Sea.\nFigure 11: Differences of the anomalies between the models [(left) ER minus LR, (center) ER minus HR, and (right) HR minus LR] for (a)\u2013(c) dynamic sea level, (d)\u2013(f) barotropic streamfunction, and (g)\u2013(i) wind stress in Southern Ocean. The stippling indicates the statistically significant regions at the 95% confidence level.\nFigure 12: As in Fig. 4, but for the Southern Ocean.\nThe projected wind stress change shows a decrease north of the ACC, with a peak around 38\u00b0S, and an increase to the south centered around 58\u00b0S (Figs. 10g\u2013i, 12c). This dipole-type pattern in the zonal component of the wind stress is interpreted by Fyfe and Saenko (2006) as the strengthening and poleward shift. The differences in wind stress between ER and HR are minor (Figs. 11h, 12c). The changes in LR are considerably larger than both ER and HR (Figs. 11g,i, 12c).\nThe pattern of DSL reflects circulation changes characterized by similar patterns of barotropic streamfunction change (Figs. 10d\u2013f). The intriguing feature of the projected circulation change is an intensifying region centered around 45\u00b0S (Fig. 12b). This strengthening could be caused by a potential southerly shift of subtropical gyres, and as horizontal resolution improves, the magnitude of the strengthening decreases. The poleward shift in sea surface height contours is consistent with regional sea level rise patterns (Gille 2014). Therefore, understanding gyre shift is crucial for sea level change studies. The historical mean contours overlaid over the anomalies can further explain this poleward movement (Figs. 10a\u2013e). Positive dynamic sea level anomalies and negative anomalies in the barotropic streamfunction field both cross the present-day zero contour, which indicates a poleward shift. This poleward shift of subtropical gyres, interpreted as the belt-like pattern, is less pronounced in ER than in HR and LR (Figs. 10d,e). Similarly, ER reflects a thinner belt of DSL increase compared to HR and LR (Figs. 10a,b).\nA dipole-like pattern of changes in the southern Indian Ocean and South Atlantic Ocean is revealed by changes in streamfunction for the Southern Ocean (Figs. 10d\u2013f). The southern (northern) part of the Indian Ocean Gyre is shown to be strengthening (weakening) by around 18 Sv (10 Sv) in the ER. The southern part of the South Atlantic Gyre is also strengthening by about 13 Sv (Fig. 10f). However, the South Pacific Gyre weakens in all the projections by about 6 Sv. When the changes in subpolar gyres are taken into account, we found that all projections show a weakening Weddell Gyre (Fig. 10d\u2013f), which is more pronounced in HR than in LR and ER (Figs. 11e,f). With a larger acceleration in ER (Fig. 11d), the Ross Gyre strengthens in LR and ER (Figs. 10d,f), whereas it weakens in HR (Fig. 10e).\nEddies are omnipresent in the Southern Ocean, especially along the ACC (e.g., Constantinou and Hogg 2019; Frenger et al. 2015). These eddies are crucial for establishing the stratification in the presence of wind and buoyancy forcing (Karsten et al. 2002). The intensified Southern Hemisphere westerlies enhance the Southern Ocean eddy activity, leading to the phenomenon known as eddy saturation (Straub 1993) and eddy compensation. As a result, the strength of the ACC, the isopycnal slope, and the meridional circulation of the Southern Ocean become less sensitive to the enhanced wind forcing. Studies using higher-resolution ocean models (e.g., Farneti et al. 2010; Hallberg and Gnanadesikan 2006; Meredith and Hogg 2006) or observations (B\u00f6ning et al. 2008; Chidichimo et al. 2014; Firing et al. 2011) have shown the insensitivity of ACC or the Southern Ocean meridional overturning circulation to the enhanced westerlies. They stated that the non-eddy-resolving models respond with an accelerated ACC, steeper isopycnals, and robust meridional overturning circulation to wind intensification forcing changes.\nTo evaluate the response of ACC to the intensified westerly wind stress, we investigated the Drake Passage transport independently for the two time periods (Fig. 13a). Even though the studies cited above oppose the ACC\u2019s sensitivity to changing westerly winds, we discovered an accelerating ACC particularly in our eddy-rich model (Fig. 13b). With a substantial increase in ER, the strength of the ACC increases in ER and LR (Fig. 13a). The LR reveals increased transport between 60\u00b0 and 68\u00b0S, with no changes north of 60\u00b0S. The transport in HR remains unchanged until 64\u00b0S, south of which it begins to weaken (Fig. 13a), reflecting its insensitivities to accelerated southern westerlies. Furthermore, Shi et al. (2021) and Swart et al. (2018) show that factors other than wind influence the Southern Ocean circulation. Warming in the upper ocean generates a density change, accelerating the ACC. Heat and freshwater fluxes at the surface could also cause changes observed in ER.\nFigure 13: (a) Time mean transport through Drake Passage; the dashed line for the time mean future (2080\u201399) transport and the solid line indicates the historical (1995\u20132014) transport (Sv). (b) Time series of ACC transport through Drake Passage relative to 1950s mean at 65\u00b0W. The green, red, and blue lines represent MPI-ESM-LR, MPI-ESM-HR, and MPI-ESM-ER, respectively. The positive barotropic streamfunction values were considered for the calculation.", "source": "https://sealeveldocs.readthedocs.io/en/latest/wickramage23.html"}
{"id": "bc7116e222f0-8", "text": "To evaluate the response of ACC to the intensified westerly wind stress, we investigated the Drake Passage transport independently for the two time periods (Fig. 13a). Even though the studies cited above oppose the ACC\u2019s sensitivity to changing westerly winds, we discovered an accelerating ACC particularly in our eddy-rich model (Fig. 13b). With a substantial increase in ER, the strength of the ACC increases in ER and LR (Fig. 13a). The LR reveals increased transport between 60\u00b0 and 68\u00b0S, with no changes north of 60\u00b0S. The transport in HR remains unchanged until 64\u00b0S, south of which it begins to weaken (Fig. 13a), reflecting its insensitivities to accelerated southern westerlies. Furthermore, Shi et al. (2021) and Swart et al. (2018) show that factors other than wind influence the Southern Ocean circulation. Warming in the upper ocean generates a density change, accelerating the ACC. Heat and freshwater fluxes at the surface could also cause changes observed in ER.\nFigure 13: (a) Time mean transport through Drake Passage; the dashed line for the time mean future (2080\u201399) transport and the solid line indicates the historical (1995\u20132014) transport (Sv). (b) Time series of ACC transport through Drake Passage relative to 1950s mean at 65\u00b0W. The green, red, and blue lines represent MPI-ESM-LR, MPI-ESM-HR, and MPI-ESM-ER, respectively. The positive barotropic streamfunction values were considered for the calculation.\nThe stronger DSL increase relative to HR and LR is significant in ER in the South Pacific (25\u00b0\u201360\u00b0S), especially east of Australia (Figs. 11a,b). The East Australian Current system strengthens as DSL rises in the ER model (Figs. 11d,e). This intensified circulation represented by the barotropic streamfunction field is more significant in ER than in HR and LR. Lower-resolution models poorly simulate the western boundary current system due to unresolved mesoscale processes, whereas the East Australian Current is adequately simulated in ER. Increasing southward transport of the East Australia Current in a warming climate was shown to be a response to the intensified South Pacific wind stress curl (Goyal et al. 2021; Roemmich et al. 2007), which can be seen in ER. We also found the enormously increased sea surface temperature in southeastern Australia in ER as indicated in previous studies (Wu et al. 2012; Hobday and Pecl 2014), which causes this region to be a global warming hotspot.\nThe DSL decreases in southern Indian Ocean and the Pacific (north of 30\u00b0S), though it increases in the Atlantic (Figs. 10a\u2013c). The increase in the South Atlantic is larger in LR than in HR as well as ER (Figs. 11a,c). In the south Indian Ocean, the DSL decreases, in order of decreasing the reduction, in HR, LR, and ER (Figs. 11a\u2013c), similarly in the South Pacific.\nDisplacement of major ocean gyres\uf0c1\nThe poleward shift of major ocean gyres, which secondarily drives sea level change, was previously discussed by Yang et al. (2020). To comprehend how differences in poleward shift affect different DSL responses, we have calculated the change in position of major ocean gyres in the three versions of MPI-ESM and quantified the linear trend from 2030 to 2100 in Fig. 14. Most gyres shift toward the poles (except for the North Pacific), indicating a statistically significant poleward gyre displacement as a response to a warmer climate.\nFigure 14: Time series of 3 yr running mean latitudinal variations of the ocean gyres relative to the 1950s mean (\u00b0). The position is calculated based on the barotropic streamfunction weighted center of each gyre, and the contours between the minimum and maximum eastward transport in the Drake passage were considered to calculate the mean central latitude of ACC transport. Abbreviations in each panel are North Atlantic Subpolar Gyre (NASPG), North Atlantic Subtropical Gyre (NASTG), North Pacific Subpolar Gyre (NPSPG), North Pacific Subtropical Gyre (NPSTG), and Antarctic Circumpolar Current (ACC). The linear trend is indicated by the dashed lines between 2030 and 2099 for LR, HR, and ER in green, red, and blue, respectively. The related linear trends are presented in the box (\u00b0 yr\u22121).\nThe poleward shift of the North Atlantic Subtropical Gyre is almost identical in all projections, showing a magnitude of 0.0138\u00b0, 0.0112\u00b0, and 0.0161\u00b0 per year in ER, HR, and LR, respectively (Fig. 14b). The North Atlantic Subpolar Gyre, on the other hand, responds differently in each projection, with the highest displacement in ER and trends of 0.0129\u00b0, 0.0125\u00b0, and 0.0085\u00b0 per year in ER, HR, and LR, respectively (Fig. 14a), from 2030 to 2099.\nPeriods over which trends occur are also not very consistent. While HR shows no trend until the last few decades, poleward trends start in the early to mid-twenty-first century for LR and ER, respectively, but it seems to cease after 2070 for ER pointing to considerable influence of climate variability. The North Pacific Subpolar Gyre behaves contrarily to the North Atlantic in ER, which shows a southward shift, indicated by a negative trend of 0.0088\u00b0 per year, while northward shifts are small with 0.0067 per year in HR and 0.0011\u00b0 per year in LR (Fig. 14c). Similarly, North Pacific Subtropical Gyre displacements are also relatively small in HR and LR, with linear trends of 0.0028\u00b0 and 0.0010\u00b0 yr\u22121, respectively (Fig. 14d). Both poleward shifts of the ocean gyres in the North Pacific are not statistically significant in LR, and in ER, the subtropical gyre is experiencing a statistically insignificant downward trend of 0.0026\u00b0 year\u22121.\nThe displacements of the North Pacific Subpolar and Subtropical Gyres are negligible when compared to interannual variability in all configurations (Figs. 14c,d). Consistent with the changes of the barotropic streamfunction (Figs. 9c), the boundary of the negative circulation anomaly crossing the zero contour of present day (solid green line) in the Sverdrup circulation implies that the North Pacific Subpolar Gyre strengthens and moves southward in ER (Fig. 9i). Thus, ER shows a strengthening Kuroshio due to the stronger wind rather than a poleward displacement (Fig. 14d), despite the interpretation of earlier CMIP5 model investigations that the changes in the Sverdrup streamfunction indicates a northward movement of the subtropical gyre (Cheon et al. 2012). It is worth mentioning that the latitudinal variations observed in the North Atlantic Subtropical Gyre are consistent with a pattern of positive north and negative south parts of the gyre in the Sverdrup streamfunction field (Figs. 6g\u2013i) and barotropic circulation (Figs. 6a\u2013c).\nOur results indicate a distinct poleward shift of the ACC (Fig. 14e), which has been linked to climate change in many earlier studies (e.g., Morrow et al. 2008; Yang et al. 2020). Interestingly, the eddy-rich model shows less poleward migration of the ACC with induced transport increase in comparison to the high- and low-resolution models. Between 2030 and 2100, the HR has the highest trend of 0.0044\u00b0 yr\u22121, whereas the LR has the lowest trend of 0.0024\u00b0 yr\u22121, while ER\u2019s linear trend lies with 0.0028\u00b0 yr\u22121 in between. In ER, the latitudinal displacement of the ACC is less than in HR and LR (Fig. 14e), and we also observed the smallest poleward shift of the ACC in the barotropic streamfunction (Figs. 11c,d) and sea surface height field (Figs. 11a,b).", "source": "https://sealeveldocs.readthedocs.io/en/latest/wickramage23.html"}
{"id": "bc7116e222f0-9", "text": "The displacements of the North Pacific Subpolar and Subtropical Gyres are negligible when compared to interannual variability in all configurations (Figs. 14c,d). Consistent with the changes of the barotropic streamfunction (Figs. 9c), the boundary of the negative circulation anomaly crossing the zero contour of present day (solid green line) in the Sverdrup circulation implies that the North Pacific Subpolar Gyre strengthens and moves southward in ER (Fig. 9i). Thus, ER shows a strengthening Kuroshio due to the stronger wind rather than a poleward displacement (Fig. 14d), despite the interpretation of earlier CMIP5 model investigations that the changes in the Sverdrup streamfunction indicates a northward movement of the subtropical gyre (Cheon et al. 2012). It is worth mentioning that the latitudinal variations observed in the North Atlantic Subtropical Gyre are consistent with a pattern of positive north and negative south parts of the gyre in the Sverdrup streamfunction field (Figs. 6g\u2013i) and barotropic circulation (Figs. 6a\u2013c).\nOur results indicate a distinct poleward shift of the ACC (Fig. 14e), which has been linked to climate change in many earlier studies (e.g., Morrow et al. 2008; Yang et al. 2020). Interestingly, the eddy-rich model shows less poleward migration of the ACC with induced transport increase in comparison to the high- and low-resolution models. Between 2030 and 2100, the HR has the highest trend of 0.0044\u00b0 yr\u22121, whereas the LR has the lowest trend of 0.0024\u00b0 yr\u22121, while ER\u2019s linear trend lies with 0.0028\u00b0 yr\u22121 in between. In ER, the latitudinal displacement of the ACC is less than in HR and LR (Fig. 14e), and we also observed the smallest poleward shift of the ACC in the barotropic streamfunction (Figs. 11c,d) and sea surface height field (Figs. 11a,b).\nThe differences between the anomalies seen in the Arctic Ocean are not thoroughly covered in a separate section. Thus, the discrepancies found are outlined here at the end of the section 4. We noted a dipole pattern of the difference in the DSL changes between ER and the lower-resolution models in the Arctic Ocean (Fig. S5). The ER reveals no changes to the north of Greenland, where we diagnose strong sea level increase in HR and LR (Fig. 2c and Fig. S2i). As expected, the model differences of the freshwater content change show a similar behavior to the differences of sea level change (Fig. S6). Although the Beaufort Gyre weakens (Figs. 2d,e and Figs. S3d,e) at the end of the twenty-first century, our models, HR and LR, show a DSL increase in the Canada Basin (Figs. 2a,b) associated with freshwater accumulation (Fig. S7). Furthermore, we do not find any considerable changes in the wind stress field, except for its increase in the Chukchi Sea in ER (Fig. 2j and Fig. S4). The induced anticyclonic circulation in ER (Fig. 2f) causes the increase in DSL (Fig. 2c) and freshwater content (Fig. S7i) in the Canada Basin.\nSummary and concluding remarks\uf0c1\nBy analyzing model simulations from eddy-rich (ER), high-resolution (HR), and low-resolution (LR) versions of MPI-ESM run under the SSP5-8.5 scenario forcing, we found substantial DSL change differences in the global ocean among the different resolutions. We note that HR and ER have the same atmospheric component, whereas LR also has a lower-resolution atmosphere. However, when comparing LR and HR, we cannot fully discriminate between the effects of resolution changes versus intrinsic changes of surface forcing in either simulation. This is because the response to changes in external forcing is a complex coupled phenomenon that depends on details of the surface boundary condition formulation. Because of this, even ocean models coupled to the same atmosphere (Semmler et al. 2021) show different regional or global expressions of such change as soon as ocean surface fields are different. Nevertheless, in many cases we can link the responses in sea level change to the different ocean resolution, in particular comparing the HR and ER versions of the model.\nAll models simulate a meridional dipole pattern of sea level change in the North Atlantic. This dipole pattern is identified by a larger sea level rise relative to the global mean in the subpolar region and sea level decrease in the subtropical region. However, southeast of Greenland, we identify a patch of sea level decline, which shrinks with the enhanced horizontal resolution. The warming hole feature is also located in the same area as the sea level decline, indicating a similar pattern of behavior, particularly in HR and ER. We have mainly focused on the changes in the circulation to examine the causes of these differences, since the long-term changes in sea level are linked to the changes in the circulation.\nIn HR and LR, the subpolar gyre strengthens in the barotropic streamfunction field, although its component driven by the wind stress curl weakens. The strengthening circulation in the subpolar region, on the one hand, can induce the heat transport out of the region into the GIN Seas and then farther north to the Arctic, forming NA warming hole. However, in this region the changes in wind stress curl in the subpolar region do not agree with the change in circulation in the eddy permitting models.\nIn the ER model, the subpolar gyre weakens in both barotropic and Sverdrup fields, as well as the region of the sea level decline becomes small. Furthermore, the magnitude of the sea level decline is also smaller in ER compared to HR and LR. The sea level increase over the rest of the subpolar gyre has been simulated by all the models. This increase becomes smaller in the eddy-rich model, indicating lower sea level in the Labrador Sea and north of Gulf Stream. This lower increase is caused by lower freshwater content in ER than in HR and LR. Previous studies have widely reported the relation between the uncertainty in twenty-first century sea level change in the North Atlantic and the variability in projected weakening of AMOC (Yin et al. 2009; Bouttes et al. 2014). We observed a significant AMOC decline in all the versions. This decrease is very similar in HR and ER at 26\u00b0N. However, the DSL changes in the North Atlantic are considerably different between these models. These results indicate that the North Atlantic DSL change is not responding as we anticipated to the weakening AMOC. The sea level decline in the subtropical region is larger in ER compared to HR and LR, caused by the larger weakening of the circulation in ER.\nThe poleward shift of North Atlantic Subtropical Gyre, which is also observed in the Sverdrup field as a pattern of positive north and negative south parts of the gyre, is considerable in all the models. However, the differences between models are not significant.\nInterestingly, a pattern of positive north and negative south parts of the gyre identified in the Sverdrup streamfunction most likely indicates the strengthening of Kuroshio rather than the poleward shift of the subtropical gyre in the ER simulation, because the gyres in the North Pacific show a negligible poleward displacement. It is further explained by identifying a significant DSL change, robust circulation, and less reduction of wind stress in the Kuroshio region (30\u00b0\u201335\u00b0N). These robust changes are identified only in the eddy-rich model, because of the realistically represented western boundary currents.\nIt is well known that in the Southern Ocean changes in sea level correspond to changes in ACC and barotropic circulation (e.g., van Westen and Dijkstra 2021). Southern Ocean sea level change is smaller in ER, indicating a minor poleward shift of the ACC in comparison to HR and LR. The ACC, as in earlier studies, is known to be insensitive to the strengthening westerlies in the higher-resolution models that explicitly resolve eddies. One interesting result is that ACC strengthens in ER, but remains unchanged or slightly weakened in HR. The findings indicate that ER, as opposed to HR, appears to be more sensitive to strong westerlies.\nThe general understanding is that many low-lying coastal areas experience substantial threats from sea level rise due to their relatively low elevation above sea level. Figure 1 by Magnan et al. (2022) provides a detailed overview of the low-lying islands and coasts of the world. However, we have not included in-depth discussion about low lying coastal areas that are located in the Indian Ocean and southwest Pacific due to small model differences of DSL anomalies (maximum around \u00b140 mm; see supplemental Figs. S8\u2013S13). Interesting to note is that the differences of DSL change between HR and ER is significant in these regions and larger than the difference between LR and ER.", "source": "https://sealeveldocs.readthedocs.io/en/latest/wickramage23.html"}
{"id": "bc7116e222f0-10", "text": "The poleward shift of North Atlantic Subtropical Gyre, which is also observed in the Sverdrup field as a pattern of positive north and negative south parts of the gyre, is considerable in all the models. However, the differences between models are not significant.\nInterestingly, a pattern of positive north and negative south parts of the gyre identified in the Sverdrup streamfunction most likely indicates the strengthening of Kuroshio rather than the poleward shift of the subtropical gyre in the ER simulation, because the gyres in the North Pacific show a negligible poleward displacement. It is further explained by identifying a significant DSL change, robust circulation, and less reduction of wind stress in the Kuroshio region (30\u00b0\u201335\u00b0N). These robust changes are identified only in the eddy-rich model, because of the realistically represented western boundary currents.\nIt is well known that in the Southern Ocean changes in sea level correspond to changes in ACC and barotropic circulation (e.g., van Westen and Dijkstra 2021). Southern Ocean sea level change is smaller in ER, indicating a minor poleward shift of the ACC in comparison to HR and LR. The ACC, as in earlier studies, is known to be insensitive to the strengthening westerlies in the higher-resolution models that explicitly resolve eddies. One interesting result is that ACC strengthens in ER, but remains unchanged or slightly weakened in HR. The findings indicate that ER, as opposed to HR, appears to be more sensitive to strong westerlies.\nThe general understanding is that many low-lying coastal areas experience substantial threats from sea level rise due to their relatively low elevation above sea level. Figure 1 by Magnan et al. (2022) provides a detailed overview of the low-lying islands and coasts of the world. However, we have not included in-depth discussion about low lying coastal areas that are located in the Indian Ocean and southwest Pacific due to small model differences of DSL anomalies (maximum around \u00b140 mm; see supplemental Figs. S8\u2013S13). Interesting to note is that the differences of DSL change between HR and ER is significant in these regions and larger than the difference between LR and ER.\nIt is expected that the eddy-rich models improve the representation of the eddy activities, providing more accurate and informative sea level change patterns over the following decades. In general, the DSL change pattern and dynamics are similar in eddy-rich compared to the coarser-resolution climate models in each ocean basin, suggesting that the coarser-resolution models will remain valid in understanding the sea level change patterns. On the other hand, the detailed, quantitative responses depend on the resolution. The robust changes found in MPI-ESM-ER suggest that improved resolution will have an impact on the interpretation of regional sea level change in the following decades. Therefore, the sea level projections of coarse-resolution models should be interpreted with caution, predominantly in the eddy active regions such as Kuroshio, ACC, Gulf Stream, and East Australian Current, and one should consider restrictions associated with limited climate model horizontal resolutions, when planning future adaptation and mitigation investments.", "source": "https://sealeveldocs.readthedocs.io/en/latest/wickramage23.html"}
{"id": "a9cea5dae349-0", "text": "DeConto et al. (2021)\uf0c1\nTitle:\nThe Paris Climate Agreement and future sea-level rise from Antarctica\nCorresponding author:\nRobert M. DeConto\nCitation:\nDeConto, R. M., Pollard, D., Alley, R. B., Velicogna, I., Gasson, E., Gomez, N., et al. (2021). The Paris Climate Agreement and future sea-level rise from Antarctica. Nature, 593(7857), 83\u201389. doi: 10.1038/s41586-021-03427-0\nURL:\nhttps://www.nature.com/articles/s41586-021-03427-0\nAbstract\uf0c1\nThe Paris Agreement aims to limit global mean warming in the twenty-first century to less than 2 degrees Celsius above preindustrial levels, and to promote further efforts to limit warming to 1.5 degrees Celsius [1]. The amount of greenhouse gas emissions in coming decades will be consequential for global mean sea level (GMSL) on century and longer timescales through a combination of ocean thermal expansion and loss of land ice [2]. The Antarctic Ice Sheet (AIS) is Earth\u2019s largest land ice reservoir (equivalent to 57.9 metres of GMSL) [3], and its ice loss is accelerating [4]. Extensive regions of the AIS are grounded below sea level and susceptible to dynamical instabilities [5,6,7,8] that are capable of producing very rapid retreat [8]. Yet the potential for the implementation of the Paris Agreement temperature targets to slow or stop the onset of these instabilities has not been directly tested with physics-based models. Here we use an observationally calibrated ice sheet\u2013shelf model to show that with global warming limited to 2 degrees Celsius or less, Antarctic ice loss will continue at a pace similar to today\u2019s throughout the twenty-first century. However, scenarios more consistent with current policies (allowing 3 degrees Celsius of warming) give an abrupt jump in the pace of Antarctic ice loss after around 2060, contributing about 0.5 centimetres GMSL rise per year by 2100\u2014an order of magnitude faster than today [4]. More fossil-fuel-intensive scenarios [9] result in even greater acceleration. Ice-sheet retreat initiated by the thinning and loss of buttressing ice shelves continues for centuries, regardless of bedrock and sea-level feedback mechanisms [10,11,12] or geoengineered carbon dioxide reduction. These results demonstrate the possibility that rapid and unstoppable sea-level rise from Antarctica will be triggered if Paris Agreement targets are exceeded.\nIntroduction\uf0c1\nMost of the AIS terminates in the ocean, with massive ice shelves (floating extensions of glacial ice) providing resistance (buttressing) to the seaward flow of the grounded ice upstream [13]. About a third of the AIS rests on bedrock hundreds to thousands of metres below sea level [3], and in places where subglacial bedrock slopes downwards away from the ocean (reverse-sloped), the ice margin is susceptible to a marine ice-sheet instability (MISI) [5,6] and possibly a marine ice-cliff instability (MICI) [7,8]. The West Antarctic Ice Sheet (WAIS), which has the potential to cause about 5\u00a0m of GMSL rise, is particularly vulnerable. The WAIS is losing ice faster than other Antarctic sectors [4] and it sits in a deep basin >2.5\u00a0km below sea level in places [3].\nMarine ice instabilities\uf0c1\nMISI and MICI can be triggered by the thinning or loss of buttressing ice shelves in response to a warming ocean, atmosphere or both [14]. MISI is related to a self-sustaining positive feedback between seaward ice flux across the grounding line (the boundary between grounded and floating ice) and ice thickness [5,6]. If buttressing is lost and retreat is initiated on a reverse-sloped bed, the retreating grounding line will encounter thicker ice, strongly increasing ice flow. Retreat will continue until the grounding line reaches forward-sloping bedrock, or sufficient resistive stress is restored by the regrowth of a buttressing ice shelf that is confined within coastal embayments or is thick enough to \u2018pin\u2019 on shallow bedrock features. Grounding lines on reverse-sloped bedrock are conditionally unstable15 and retreat at a rate determined by the complex interplay between ice flow and stress fields, bedrock conditions, surface mass balance and other factors that make model-ling these dynamics difficult.\nMICI is also theorized to be triggered where buttressing ice shelves disappear or become too small to provide substantial back stress [7,8]. At unsupported grounding lines where ice thickness exceeds a critical value, the weight of ice above sea level can produce deviatoric stresses that exceed the material yield strength of the ice. This causes structural failure [16,17], possibly manifest as repeated slumping and calving events17. Once initiated, failure can continue until the collapsing ice front backs into shallow water, where subaerial cliff heights and the associated stresses drop below their critical values, viscous deformation lowers the cliff, or sufficient buttressing is restored by an ice shelf.\nIn undamaged ice, with small grain sizes and without large bubbles or pre-existing weaknesses, slowly emerging subaerial ice cliffs could exceed 500 m in height before failing [18]. However, natural glacial ice is typically damaged, especially near crevassed calving fronts and in fast-flowing ice upstream [19]. Assuming ice properties representative of glaciers, stress-balance calculations [16] point to maximum sustainable cliff heights of around 200 m. This value is reduced to about 100 m or less [8,16] where deep surface and basal crevasses effectively thin the supportive ice column (increasing the stress), possibly explaining why the tallest ice cliffs observed today are about 100 m tall. Recent modelling [18] using values of fracture toughness and pre-existing flaw size appropriate for damaged ice fronts [17] and consistent with field observations [19] indicates that tensile fracturing can occur at cliffs as low as 60 m. This reinforces the argument for including ice-cliff calving in ice-sheet models [20], despite current uncertainties in ice properties and the lack of observations which make ice-cliff calving laws difficult to formulate.\nThick, marine-terminating glaciers such as Jakobshavn Isbr\u00e6 in Greenland demonstrate how efficient calving can deliver ice to the ocean. The terminus of Jakobshavn is about 10 km wide, 1,000 m thick and flows seawards at about 12 km yr\u22121 (ref. 21). Since the glacier lost its ice shelf in the late 1990s, the ice front (with an intermittent ~100-m ice cliff) has retreated >12 km into the thicker ice upstream, albeit with a recent re-advance coincident with regional ocean cooling [22]. The average effective calving rate (flow speed + retreat) between 2002 and 2015 is estimated at 13.2 \u00b1 0.9 km yr\u22121 (1\u03c3; ref. 21).\nCalving in narrow fjord settings such as Jakobshavn is controlled by a complex combination of ductile and brittle processes, as well as buoyancy. After calving, subsequent fracture-driven failure is delayed until accelerated flow thins the terminus to near-flotation, allowing tidal flexure, basal crevassing, slumping or other processes to initiate the next event17,23. Resistive stresses from lateral shear along fjord walls, as well as thick m\u00e9lange strengthened by sea ice, slow calving in winter, but annual ice loss remains high.\nJakobshavn-style calving is not widespread in Antarctica today, because most marine-terminating grounding lines with comparable ice thickness are supported by the resistive back stress of ice shelves. Crane Glacier, previously buttressed by the Larsen B ice shelf on the Antarctic Peninsula, is an exception. When the ice shelf suddenly collapsed in 2002 after becoming covered in meltwater, the glacier sped up by a factor of three24. A persistent 100-m ice cliff formed at the terminus25 and the calving front retreated into its narrow fjord. The drainage of Crane Glacier was too small to contribute substantially to sea level, but similar events could become widespread in Antarctica if temperatures continue to rise.\nImportantly, some Antarctic glaciers are vastly larger than their Greenland counterparts. For example, Thwaites Glacier in West Antarctica terminates in the open Amundsen Sea rather than in a narrow fjord. The main trunk of Thwaites Glacier is about 120 km wide, widening upstream into the heart of the WAIS. Today, the heavily crevassed grounding zone of Thwaites Glacier is minimally buttressed and retreating on reverse-sloped bedrock at >1 km yr\u22121 in places26, possibly owing to MISI. The terminus currently sits in water too shallow (about 600 m deep) to produce an unstable cliff face, but if retreat continues into deeper bedrock and thicker ice, a calving face taller than that of Jakobshavn could appear, with stresses and strain rates exceeding thresholds for brittle failure16,17,18. Similar vulnerabilities exist at other Antarctic glaciers, particularly where buttressing ice shelves are already thinning from contact with warm sub-surface waters14.", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "a9cea5dae349-1", "text": "Calving in narrow fjord settings such as Jakobshavn is controlled by a complex combination of ductile and brittle processes, as well as buoyancy. After calving, subsequent fracture-driven failure is delayed until accelerated flow thins the terminus to near-flotation, allowing tidal flexure, basal crevassing, slumping or other processes to initiate the next event17,23. Resistive stresses from lateral shear along fjord walls, as well as thick m\u00e9lange strengthened by sea ice, slow calving in winter, but annual ice loss remains high.\nJakobshavn-style calving is not widespread in Antarctica today, because most marine-terminating grounding lines with comparable ice thickness are supported by the resistive back stress of ice shelves. Crane Glacier, previously buttressed by the Larsen B ice shelf on the Antarctic Peninsula, is an exception. When the ice shelf suddenly collapsed in 2002 after becoming covered in meltwater, the glacier sped up by a factor of three24. A persistent 100-m ice cliff formed at the terminus25 and the calving front retreated into its narrow fjord. The drainage of Crane Glacier was too small to contribute substantially to sea level, but similar events could become widespread in Antarctica if temperatures continue to rise.\nImportantly, some Antarctic glaciers are vastly larger than their Greenland counterparts. For example, Thwaites Glacier in West Antarctica terminates in the open Amundsen Sea rather than in a narrow fjord. The main trunk of Thwaites Glacier is about 120 km wide, widening upstream into the heart of the WAIS. Today, the heavily crevassed grounding zone of Thwaites Glacier is minimally buttressed and retreating on reverse-sloped bedrock at >1 km yr\u22121 in places26, possibly owing to MISI. The terminus currently sits in water too shallow (about 600 m deep) to produce an unstable cliff face, but if retreat continues into deeper bedrock and thicker ice, a calving face taller than that of Jakobshavn could appear, with stresses and strain rates exceeding thresholds for brittle failure16,17,18. Similar vulnerabilities exist at other Antarctic glaciers, particularly where buttressing ice shelves are already thinning from contact with warm sub-surface waters14.\nBecause of the very strong dependency of crack growth with increasing stress17,27, a previously unseen style of calving and ice failure might emerge at unbuttressed Antarctic ice fronts with higher freeboard than glaciers on Greenland7,8. The potential pace of fracturing in such settings remains uncertain20, but once a calving front backs into thicker ice upstream, brittle failure could outpace viscous flow, inhibiting the growth of a new shelf. Complete, sustained loss of an ice shelf is not required for structural failure16. If a small floating shelf survives or reforms without providing substantial buttressing, the grounding zone would remain under sufficient stress for collapse. Re-emerging ice shelves would remain vulnerable to warm ocean waters and surface meltwater, as evidenced at Jakobshavn and Crane glaciers; despite fast flow and m\u00e9lange buttressing, persistent ice tongues have not reformed and calving continues.\nExtensive loss of buttressing ice shelves (prerequisite for both MISI and MICI) represents a possible tipping point in Antarctica\u2019s future. This is concerning, because ice shelves are vulnerable to both oceanic melt from below14 and surface warming above28. Rain and meltwater can deepen crevasses28 and cause flexural stresses29, leading to hydrofracturing and ice-shelf collapse. Vulnerability to surface meltwater is enhanced where firn (the transitional layer between surface snow and underlying ice) becomes saturated and where ocean-driven thinning is already underway28. Air temperatures above Antarctica\u2019s largest ice shelves remain too cold to produce sustained meltwater rates associated with collapse30,31; however, given sufficient future warming, this could change.\nModelling the AIS response to warming\uf0c1\nWe build on previous work [8] by improving a hybrid ice sheet\u2013shelf model that includes viscous ice processes related to MISI and brittle processes related to MICI. The model allows conditionally unstable grounding lines (MISI) on reverse-sloped bedrock in response to flow and stress fields, bed conditions and surface mass balance. The model accounts for oceanic sub-ice melt and meltwater-driven hydrofracturing of ice shelves, leading to ice-cliff calving at thick, marine-terminating ice fronts where stresses exceed ice strength (MICI). Model improvements and extensions described in Methods and Supplementary Information include new formulations of ice-shelf buttressing, hydrofracturing and coupling with a comprehensive Earth\u2013sea-level model, as well as ice\u2013climate (meltwater) feedback mechanisms using the NCAR Community Earth System Model. Parametric uncertainty is assessed using modern and geological observations and statistical emulation. Regional climate model (RCM) forcing used in future ice-sheet ensembles is substantially improved relative to ref. 8, with the trajectory of warming being comparable to that of other studies30 (Supplementary Information).\nWe test the future response of the AIS to scenarios representing +1.5\u2009\u00b0C and +2\u2009\u00b0C global warming limits, a +3\u2009\u00b0C scenario representing current policies [32] and extended RCP emissions scenarios9. We consider recently proposed negative feedback mechanisms that could slow the pace of future ice loss, and emissions scenarios allowing a temporary overshoot of Paris Agreement temperature targets followed by rapid carbon dioxide reduction (CDR), assuming that such geoengineering is possible. The results identify emissions-forced climatic thresholds capable of triggering rapid retreat of the AIS.\nCalibrated model ensembles\uf0c1\nTo account for the current uncertainty in key parameters controlling (1) the sensitivity of crevasse penetration to surface melt and rainwater (hydrofracturing) and (2) the ice-cliff calving rate, we run 196 ice-sheet simulations for each climate scenario described below. Each ensemble member uses a unique combination of parameter values (Extended Data Table 1), scored using a binary history-matching approach [8,33]. Scoring is based on the model\u2019s ability to simulate the observed ice loss, d\ud835\udc40\u00af/d\ud835\udc61, between 1992 and 2017 (IMBIE) [4], and Antarctica\u2019s contribution to sea level in the last interglacial period (LIG) [34] and the mid-Pliocene epoch [35,36] (Methods). Ensemble members falling outside the likely range of observations are discarded, and only parameter combinations within the bounds of all three constraints are included in future projections. Both modern and geological constraints contain considerable uncertainty with poorly known sample distributions, so weighting of individual model outcomes is avoided. In Supplementary Information we compare our ensemble scoring to a more rigorous Gaussian process emulation approach [33,37] to verify that the central estimates of our calibrated ensembles are robust.\nComparing simulated and IMBIE estimates of d\ud835\udc40\u00af/d\ud835\udc61 (Extended Data Fig. 1a) eliminates 33 ensemble members (n = 163). The effect of replacing IMBIE with alternative (narrower) ranges of d\ud835\udc40\u00af/d\ud835\udc61 on the basis of solely GRACE data from 2002\u20132017 [38] (Methods) is shown in Extended Data Fig. 2. The model performs well over the IMBIE interval with and without hydrofracturing and ice-cliff calving enabled. Although IMBIE provides guidance on processes that cause contemporary mass change (surface mass balance, oceanic-shelf thinning and grounding-line dynamics), it does not sufficiently test the brittle-ice processes theorized to become important in a warmer climate [7,8]. Furthermore, the 25-year IMBIE record is very short relative to the dynamical response time of an ice sheet, and interdecadal and longer variability is not captured. Collectively, these issues motivate our use of geological records from past warm periods as additional training constraints.\nAdding the LIG constraint (3.1\u20136.1 m; 129\u2013128 kyr ago) to IMBIE eliminates 44 additional parameter combinations (n = 119), but only at the lower bound of the parameter range. Without MICI, the model is incapable of simulating realistic LIG ice loss. Even at the top of the parameter range, simulated rates of GMSL rise remain below 1 cm yr\u22121, slower than indicated by some LIG proxy records39 (Extended Data Fig. 1b, c). Adding a warm mid-Pliocene test (11\u201321 m; 3.26\u20133.03 Ma) further reduces the ensemble to n = 109 by eliminating some of the highest-valued parameter combinations. Similar to the LIG, hydrofracturing and ice-cliff calving must be included to satisfy Pliocene geological observations, including regional retreat into East Antarctic basins40 (Extended Data Figs. 1d, 3). The model\u2019s ability to simulate current rates of ice loss without ice-cliff calving, while failing to simulate past retreat under warmer climate conditions (Extended Data Figs. 1, 3), is at odds with the findings of ref. 33, which assumed a lower range of Pliocene sea-level constraints than the more recent data35,36 used here.", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "a9cea5dae349-2", "text": "Adding the LIG constraint (3.1\u20136.1 m; 129\u2013128 kyr ago) to IMBIE eliminates 44 additional parameter combinations (n = 119), but only at the lower bound of the parameter range. Without MICI, the model is incapable of simulating realistic LIG ice loss. Even at the top of the parameter range, simulated rates of GMSL rise remain below 1 cm yr\u22121, slower than indicated by some LIG proxy records39 (Extended Data Fig. 1b, c). Adding a warm mid-Pliocene test (11\u201321 m; 3.26\u20133.03 Ma) further reduces the ensemble to n = 109 by eliminating some of the highest-valued parameter combinations. Similar to the LIG, hydrofracturing and ice-cliff calving must be included to satisfy Pliocene geological observations, including regional retreat into East Antarctic basins40 (Extended Data Figs. 1d, 3). The model\u2019s ability to simulate current rates of ice loss without ice-cliff calving, while failing to simulate past retreat under warmer climate conditions (Extended Data Figs. 1, 3), is at odds with the findings of ref. 33, which assumed a lower range of Pliocene sea-level constraints than the more recent data35,36 used here.\nProcesses other than ice-cliff calving could be invoked to improve geological model\u2013data comparisons. For example, Pliocene retreat in East Antarctica has been simulated in a model without MICI, using a sub-ice melt scheme allowing the presence of melt beneath grounded ice upstream of the grounding line41. Tidally driven seawater intrusion and non-zero melt beneath discontinuous sectors of grounding zones has been observed26; however, model treatments used so far41 have been questioned on physical grounds42. Alternative (Coulomb) sub-glacial sliding laws have been proposed43 that can substantially increase the rate of ice loss in models with ice shelves removed44, but they have not been tested with realistic palaeoclimate forcing. We stress that hydrofracturing and ice-cliff calving processes incorporated here are observed phenomena, tested under both modern and geological settings.\nIce loss in both LIG and Pliocene ensembles saturates at the upper range of parameter values (Extended Data Fig. 1). The LIG is sufficiently warm to cause complete WAIS retreat, but not warm enough to trigger retreat into East Antarctic basins, even if our nominal ice-cliff calving limit (13,000 m yr\u22121) is doubled. Similarly, maximum ice loss in the Pliocene ensemble reflects the loss of most marine-based ice, as supported by observations35, but not more. As such, the geological constraints do not rule out the possibility of faster Antarctic ice-cliff calving rates than those observed on Greenland today, which would substantially increase our future projections while remaining consistent with geological observations.\nImplications of the Paris Agreement\uf0c1\nWe run ensembles of the transient response of the AIS to future greenhouse gas emissions scenarios (Methods) representing global mean warming limits of +1.5\u2009\u00b0C, +2\u2009\u00b0C and +3\u2009\u00b0C (similar to current policies and Nationally Determined Contributions, NDCs32), as well as RCP2.6, RCP4.5 and RCP8.59. Only simulations with validated parameter combinations (Extended Data Fig. 4d) are included in the analysis. The +1.5\u2009\u00b0C, +2\u2009\u00b0C and +3\u2009\u00b0C scenarios assume that there is no overshoot in temperature; once these global mean temperatures are reached in 2040, 2060 and 2070, respectively, atmosphere and ocean forcings are held constant.\nIn the +1.5\u2009\u00b0C and +2\u2009\u00b0C ensembles, Antarctic ice loss continues at a pace similar to today\u2019s throughout the 21st century (Fig. 1, Table 1). The median contribution to sea level in 2100 is 8 cm with +1.5\u2009\u00b0C warming and 9 cm with +2\u2009\u00b0C. By contrast, about 10% of the ensemble members in the +3\u2009\u00b0C scenario produce onset of major WAIS retreat before 2100. This skews the upper bound of the +3\u2009\u00b0C distribution (33 cm at the 90th percentile), substantially increasing the ensemble median (15 cm in 2100) relative to the +1.5\u2009\u00b0C and +2\u2009\u00b0C scenarios. The jump in late 21st century ice loss at +3\u2009\u00b0C is mainly caused by retreat of Thwaites Glacier (Fig. 2; Extended Data Fig. 5), which destabilizes the entire WAIS in some ensemble members.\nFigure 1: Antarctic contribution to future GMSL rise. a\u2013h, The fan charts show the time-evolving uncertainty and range around the median ensemble value (black line) in 10% increments. a, c, e, g, Ensemble results from 2000\u20132100, including median rates of GMSL rise (red line). b, d, f, h The same as a, c, e, g, extended to 2300. a, b, Emissions consistent with a +1.5.\u00b0C global mean warming scenario. c, d, Emissions consistent with +2.0.\u00b0C. e, f, Emissions consistent with +3.0.\u00b0C. g, h, RCP8.5. In h, two additional RCP8.5 simulations are shown with average calibrated parameter values (Methods) but with atmosphere and ocean forcing provided by the\u00a0NCAR CESM1.2.2 GCM with (blue line) and without (red line) Antarctic meltwater feedback46. Note the expanded vertical axes in g and h.\uf0c1\nTable 1: Antarctic sea-level contributions. Ensemble medians (top six rows) using IMBIE, LIG and Pliocene observational constraints, reported in metres, relative to 2000. Values in parentheses are the 17th\u201383rd percentiles (likely range). Scenarios refer to the maximum global mean temperature reached relative to pre-industrial (1850) or following RCPs. Alternative ensemble outcomes using more restrictive ranges of ice-cliff calving parameters are provided in Extended Data Table 2. Model simulations corresponding to Fig. 3 (bottom 12 rows) use average calibrated parameter values (Extended Data Table 1). NDC simulations follow the standard +3\u2009\u00b0C emissions scenario or consider CDR beginning in 2200, 2150, 2100, 2090, 2080, 2070, 2060, 2050, 2040 or 2030. An alternative scenario maintains the atmosphere and ocean climate forcing at 2020 (with no additional future warming). Note that the +3.0\u2009\u00b0C ensemble median (third row) differs from the corresponding +3.0\u2009\u00b0C (NDCs) simulation using average model parameter values (seventh row) owing to the skewness of the ensembles (Fig. 1).\nFigure 2: Ice-sheet evolution following the +3\u2009\u00b0C global warming emissions trajectory. A single +3\u2009\u00b0C ensemble member with average hydrofracturing and ice-cliff calving parameters. Transient atmosphere and ocean forcing follows the +3\u2009\u00b0C scenario, roughly consistent with current policies (NDCs). Floating and grounded ice thickness is shown in blue. The grounding line position is shown with a black line. The red square over the Thwaites Glacier (TG) and Pine Island Glacier (PIG) sector of West Antarctica corresponds to the high-resolution (1,000 m) nested model domain in Extended Data Fig. 5. a, Initial ice-sheet conditions. b, Model ice sheet in 2100, showing the onset of major retreat of Thwaites Glacier. c, Change in ice thickness in 2100. d, The ice sheet in 2300, with Thwaites Glacier retreat leading to the loss of the WAIS. e, Change in ice thickness in 2300.\nWith more extreme RCP8.5 warming, thinning and hydrofracturing of buttressing ice shelves becomes widespread, triggering marine ice instabilities in both West and East Antarctica. The RCP8.5 median contribution to GMSL is 34 cm by 2100. This is substantially less than reported by ref. 8 (64\u2013105 cm), owing to a combination of improved model physics and revised atmospheric forcing (Methods) that delays the onset of surface melt by about 25 years. Nonetheless, the median contribution to GMSL reaches 1 m by 2125 and rates exceed 6 cm yr\u22121 by 2150 (Extended Data Figs. 6, 7). By 2300, Antarctica contributes 9.6 m of GMSL rise under RCP8.5, almost 10 times more than simulations limiting warming to +1.5\u2009\u00b0C.", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "a9cea5dae349-3", "text": "Figure 2: Ice-sheet evolution following the +3\u2009\u00b0C global warming emissions trajectory. A single +3\u2009\u00b0C ensemble member with average hydrofracturing and ice-cliff calving parameters. Transient atmosphere and ocean forcing follows the +3\u2009\u00b0C scenario, roughly consistent with current policies (NDCs). Floating and grounded ice thickness is shown in blue. The grounding line position is shown with a black line. The red square over the Thwaites Glacier (TG) and Pine Island Glacier (PIG) sector of West Antarctica corresponds to the high-resolution (1,000 m) nested model domain in Extended Data Fig. 5. a, Initial ice-sheet conditions. b, Model ice sheet in 2100, showing the onset of major retreat of Thwaites Glacier. c, Change in ice thickness in 2100. d, The ice sheet in 2300, with Thwaites Glacier retreat leading to the loss of the WAIS. e, Change in ice thickness in 2300.\nWith more extreme RCP8.5 warming, thinning and hydrofracturing of buttressing ice shelves becomes widespread, triggering marine ice instabilities in both West and East Antarctica. The RCP8.5 median contribution to GMSL is 34 cm by 2100. This is substantially less than reported by ref. 8 (64\u2013105 cm), owing to a combination of improved model physics and revised atmospheric forcing (Methods) that delays the onset of surface melt by about 25 years. Nonetheless, the median contribution to GMSL reaches 1 m by 2125 and rates exceed 6 cm yr\u22121 by 2150 (Extended Data Figs. 6, 7). By 2300, Antarctica contributes 9.6 m of GMSL rise under RCP8.5, almost 10 times more than simulations limiting warming to +1.5\u2009\u00b0C.\nIn alternative ensembles, the upper bound of the maximum calving rate (VCLIFF) is reduced from 13 km yr\u22121 to 11 km yr\u22121 or 8 km yr\u22121 to reflect Jakobshavn\u2019s recent slowdown22, but the effect on the calibrated ensemble medians is small (Extended Data Table 2). The main ensembles (Fig. 1, Table 1) use 13 km yr\u22121 as the upper bound because LIG and Pliocene responses saturate above these values and observations at Jakobshavn demonstrate that such rates are indeed possible. Future simulations excluding hydrofracturing and ice-cliff calving produce less GMSL rise than our ensemble medians (Extended Data Fig. 6). Similar to other models without ice-cliff calving45, enhanced precipitation in East Antarctica partially compensates for MISI-driven retreat in West Antarctica, but these simulations are excluded from the future projections because they fail to reproduce the LIG and Pliocene.\nNegative feedback mechanisms slowing ice loss\uf0c1\nBecause our model includes hydrofracturing, the onset of major retreat is sensitive to the pace of future atmospheric warming. We compare our RCM/CCSM4-driven RCP8.5 ensemble to two alternative simulations, with atmosphere and ocean forcing supplied by the NCAR CESM1.2.2 GCM. Both CESM-forced simulations follow RCP8.5, but one includes Antarctic meltwater feedback (Methods) by adding time-evolving liquid-water and solid-ice discharge at the appropriate ocean grid cells in the GCM46.\nIncluding meltwater discharge in CESM expands Southern Ocean sea ice, stratifies the upper ocean, and warms the subsurface (400 m water depth) by 2\u20134\u2009\u00b0C around most of the Antarctic margin in the early 22nd century46. Conversely, expanded sea ice suppresses surface atmospheric warming by more than 5\u2009\u00b0C, slowing the onset of surface melt and hydrofracturing in the ice-sheet model. The net result of competing sub-surface ocean warming (enhanced sub-shelf melt) and atmospheric cooling (reduced surface melt) produces a substantial negative feedback on the pace of ice-sheet retreat (Fig. 1h). This contrasts ref. 41, which found a net positive (ocean-driven) meltwater feedback using an ice-sheet model without hydrofracturing. The CESM-driven simulations bracket our RCM/CCSM4-driven ensembles, supporting the timing of retreat in our main ensembles. Our RCM and CESM1.2.2 climate forcings are evaluated relative to independent CMIP5 and CMIP6 GCMs in Supplementary Information.\nWe test two additional negative-feedback mechanisms proposed to provide a stabilizing influence on marine ice-sheet retreat. First, the potential for channelized supraglacial runoff to delay or stop ice-shelf hydrofracturing47 is examined by reducing meltwater-enhanced surface crevassing in regions of compressional ice-shelf flow (Supplementary Information). Despite a reduced influence of meltwater, we find that hydrofracturing in a warming climate still occurs near ice-shelf calving fronts, where the ice is thinnest, convergence and buttressing are minimal13 and air temperatures (melt rates) are highest. Once initiated, meltwater-enhanced calving near the shelf edge reduces compressional flow in ice upstream and calving propagates. As a result, reduced wet crevassing in compressional flow does little to protect buttressing ice shelves48 and the impact on our simulations is minimal (Supplementary Fig. 3).\nSecond, we examine the potential for rapid bedrock uplift and ice\u2013ocean gravitational effects to lower relative sea level and reduce ice loss at retreating grounding lines12. Exceptionally fast uplift rates due to low mantle viscosities in the Amundsen Sea sector of West Antarctica have been invoked to slow future retreat of the WAIS10. This is tested by replacing the model\u2019s standard Elastic Lithosphere/Relaxed Asthenosphere representation of deforming bedrock with a more complete viscoelastic (Maxwell) Earth model combining a radially varying, depth-dependent lithosphere and viscosity structure with gravitationally self-consistent sea-level calculations (Methods)12. Simulations assuming the lowest upper mantle viscosity10 with rapid bedrock uplift under all of West Antarctica show limited potential for ice\u2013Earth feedback mechanisms to slow retreat over the next approximately two centuries (Extended Data Fig. 8). This finding is consistent with other recent studies11,12,49, although future work should explore these effects at higher resolution and with a three-dimensional Earth structure50 including lateral heterogeneity of viscoelastic properties under West and East Antarctica.\nImplications of delayed mitigation\uf0c1\nAn additional set of simulations was run using a single combination of ice-model parameters representing calibrated ensemble averages (Extended Data Table 1). The simulations either maintain current (2020) atmosphere and ocean conditions without any future warming, or begin to follow the +3\u2009\u00b0C emissions pathway, except assuming that CDR mitigation is initiated at different times in the future, beginning in 2030, 2040, 2050, 2060, 2070, 2080, 2090, 2100, 2150 or 2200. We optimistically assume that CDR technologies will be capable of reducing CO2 atmospheric mixing ratios with an e-folding time of one century (Fig. 3a).\nFigure 3: AIS thresholds and commitments to GMSL rise with delayed mitigation. a, Greenhouse gas (GHG) emissions scenarios that initially follow the +3\u2009\u00b0C (NDCs) scenario, followed by CDR (carbon dioxide reduction/negative emissions), assuming relaxation towards preindustrial levels with an e-folding time of 100 years. The timing when CDR commences is shown in b. The solid black line is the same +3\u2009\u00b0C simulation shown in Fig. 2 and Extended Data Fig. 5. The dashed black line assumes there is no additional GHG increase or warming after 2020. GHG concentrations are shown in CO2 equivalent, in units of preindustrial atmospheric level (PAL; 280 ppm). b, GMSL contributions from Antarctica, corresponding to the scenarios in a, over the 21st century. All simulations use identical model physics and average hydrofracturing and ice-cliff calving parameters. Note the sharp increase in late-21st-century ice loss when CDR is delayed until 2070. c, The same as b, but extended to 2500 (see Table 1). Note the long-term dependence of GMSL rise on the timing when mitigation begins. All scenarios exceed 1 m by 2500, and no scenario shows recovery of the ice sheet, including those returning to near-preindustrial levels of GHGs by about 2300.", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "a9cea5dae349-4", "text": "Implications of delayed mitigation\uf0c1\nAn additional set of simulations was run using a single combination of ice-model parameters representing calibrated ensemble averages (Extended Data Table 1). The simulations either maintain current (2020) atmosphere and ocean conditions without any future warming, or begin to follow the +3\u2009\u00b0C emissions pathway, except assuming that CDR mitigation is initiated at different times in the future, beginning in 2030, 2040, 2050, 2060, 2070, 2080, 2090, 2100, 2150 or 2200. We optimistically assume that CDR technologies will be capable of reducing CO2 atmospheric mixing ratios with an e-folding time of one century (Fig. 3a).\nFigure 3: AIS thresholds and commitments to GMSL rise with delayed mitigation. a, Greenhouse gas (GHG) emissions scenarios that initially follow the +3\u2009\u00b0C (NDCs) scenario, followed by CDR (carbon dioxide reduction/negative emissions), assuming relaxation towards preindustrial levels with an e-folding time of 100 years. The timing when CDR commences is shown in b. The solid black line is the same +3\u2009\u00b0C simulation shown in Fig. 2 and Extended Data Fig. 5. The dashed black line assumes there is no additional GHG increase or warming after 2020. GHG concentrations are shown in CO2 equivalent, in units of preindustrial atmospheric level (PAL; 280 ppm). b, GMSL contributions from Antarctica, corresponding to the scenarios in a, over the 21st century. All simulations use identical model physics and average hydrofracturing and ice-cliff calving parameters. Note the sharp increase in late-21st-century ice loss when CDR is delayed until 2070. c, The same as b, but extended to 2500 (see Table 1). Note the long-term dependence of GMSL rise on the timing when mitigation begins. All scenarios exceed 1 m by 2500, and no scenario shows recovery of the ice sheet, including those returning to near-preindustrial levels of GHGs by about 2300.\nWe find that without future warming beyond 2020, Antarctica continues to contribute to 21st-century sea-level rise at a rate roughly comparable to today\u2019s, producing 5 cm of GMSL rise by 2100 and 1.34 m by 2500 (Fig. 3, Table 1). Simulations initially following the +3\u2009\u00b0C pathway, but with subsequent CDR delayed until after 2060, show a sharp jump in the pace of 21st-century sea-level rise (Fig. 3b). Every decade that CDR mitigation is delayed has a substantial long-term consequence on sea level, despite the fast decline in CO2 and return to cooler temperatures (Fig. 3c). Once initiated, marine-based ice loss is found to be unstoppable on these timescales in all mitigation scenarios (Fig. 3). The commitment to sustained ice loss is caused mainly by the onset of marine ice instabilities triggered by the loss of ice shelves that cannot recover in a warmer ocean with long thermal memory (Fig. 3c).\nIn summary, these results demonstrate that current policies allowing +3\u2009\u00b0C or more of future warming could exceed a threshold, triggering extensive thinning and loss of vulnerable Antarctic ice shelves and ensuing marine ice instabilities starting within this century. Resulting ice loss would be irreversible on multi-century timescales, even if atmospheric temperatures return to preindustrial-like values (Fig. 3). Relative to the +3\u2009\u00b0C scenario, sea-level rise resulting from the +1.5\u2009\u00b0C and +2\u2009\u00b0C aspirations of the Paris Agreement (Fig. 1) would have much less impact on low-lying coastlines, islands and population centres, pointing to the importance of ambitious mitigation.\nStrong circum-Antarctic atmospheric cooling feedback caused by meltwater discharge [46] slows the pace of retreat under RCP8.5 (Fig. 1h). However, other proposed negative feedback mechanisms associated with ice\u2013Earth\u2013sea level interactions and reduced hydrofracturing through surface runoff do little to slow ice loss on 21st- to 22nd-century timescales.\nAlthough we attempt to constrain parametric uncertainty, this study uses a single ice-sheet model, and structural uncertainty is accounted for only in the model improvements described herein. Similarly, our main ensembles use a single method of climate forcing, although with future warming comparable to other state-of-the-art climate models (Supplementary Figs. 1, 2), and alternative simulations driven by CESM1.2.2 produce similar results (Fig. 1). More work is clearly needed to further explore this uncertainty, using multiple ice-sheet models accounting for processes associated with MISI and MICI, and with future climate forcing that includes interactive climate\u2013ice sheet coupling.\nIce-cliff calving remains a key wild card. Although founded on basic physical principles and observations, its potential to produce even faster rates of ice loss than those simulated here remains largely untested with process-based models of mechanical ice failure. Here we find that limiting rates of ice-cliff calving to those observed on Greenland can still drive multi-metre-per-century rates of sea-level rise from Antarctica (Extended Data Fig. 7). Given the bedrock geography of the much larger and thicker AIS, the possibility of even faster mechanical ice loss should be a top priority for further investigation.\nMethods\uf0c1\nIce-sheet modelling framework\uf0c1\nThe ice sheet\u2013shelf model uses hybrid ice dynamics [51] with an internal boundary condition on ice velocity at the grounding line [6]. Grounding lines can migrate freely, and the model accounts for the buttressing effects of ice shelves with pinning points and side shear (see Supplementary Information). In our solution of the dynamical shallow shelf (SSA) equations, ice velocities across grounding lines are imposed as a function of local sub-grid ice thickness, with the sub-grid interpolation accurate to the limit of the resolved bathymetry. This is also true for diagnosed stresses and ice-cliff failure rates, which makes the model largely independent of grid resolution (Extended Data Fig. 5). A resolution of 10 km is used for continental simulations used in our main ensembles (Figs. 1\u20133). A nested 1-km grid is used for a select simulation over West Antarctica (Extended Data Fig. 5). The model uses a standard Weertman-type basal sliding law51, with basal sliding coefficients determined by an inverse method that iteratively matches model ice-surface elevations to observations under modern climate conditions52. We use Bedmap253 bathymetric boundary conditions. Using alternative BedMachine3 bathymetry is found to have only a small effect on continental-scale sea-level projections (<1.5% difference under RCP8.5 in 2300). Several advances relative to previous versions of the model7,8,51 are described below and in Supplementary Information.\nSub-ice melt rates\uf0c1\nThe model used here includes an updated treatment of sub-ice oceanic melting. Oceanic melt rates are calculated at each floating ice grid cell as a quadratic function of the difference between nearest sub-surface ocean temperatures at 400-m water depth and the pressure melting point of ice51,54. The model accounts for evolving connectivity between a given ice model grid cell and the open ocean, and elevated plume melt on subsurface vertical ice faces51. All melt calculations are performed with spatially uniform physics, including a single, uniform coefficient in the ocean melt relation based on a 625-member ensemble of simulations of WAIS retreat through the last deglaciation55. Although it would be possible to perform inverse calculations for a distribution of coefficients within each basin based on modern ice-shelf melt observations41, their patterns are likely to change substantially within the timescales of our simulations as ocean circulation, grounding-line extents and cavity geometries evolve. A 1.5\u2009\u00b0C sub-surface ocean temperature adjustment is used in the Amundsen Sea sector to bring ocean melt rates closer to observations56 when using CCSM4 ocean model temperatures that underestimate observed shelf-bottom water temperatures57. This is a substantial improvement relative to the 3\u2009\u00b0C temperature adjustment required previously8.\nIce-shelf hydrofracturing\uf0c1\nIn the model, surface crevasses deepen as a function of the stress field and local meltwater and rainfall availability [7,8,58], leading to hydrofracturing when surface and basal crevasses penetrate 75% or more of the total ice thickness. With greatly increased surface melt, model ice shelves can be completely lost. In the standard wet crevassing scheme, we assume a quadratic relationship between surface crevasse penetration depth dw (in metres) and total meltwater production R (rain plus surface melt minus refreezing; in m yr\u22121). A tunable prefactor, CALVLIQ, is varied between zero (no meltwater influence on crevassing) and 195 m\u22121 yr2 in the ensembles presented in the main text.\ndw = CALVLIQ  R^2.\nCalving occurs in places where the sum of the surface and basal crevasse penetration caused by extensional stresses, accumulated strain (damage), thinning and meltwater (dw), exceeds the critical fraction (0.75) of total ice thickness (see appendix B of ref. 7).", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "a9cea5dae349-5", "text": "The model used here includes an updated treatment of sub-ice oceanic melting. Oceanic melt rates are calculated at each floating ice grid cell as a quadratic function of the difference between nearest sub-surface ocean temperatures at 400-m water depth and the pressure melting point of ice51,54. The model accounts for evolving connectivity between a given ice model grid cell and the open ocean, and elevated plume melt on subsurface vertical ice faces51. All melt calculations are performed with spatially uniform physics, including a single, uniform coefficient in the ocean melt relation based on a 625-member ensemble of simulations of WAIS retreat through the last deglaciation55. Although it would be possible to perform inverse calculations for a distribution of coefficients within each basin based on modern ice-shelf melt observations41, their patterns are likely to change substantially within the timescales of our simulations as ocean circulation, grounding-line extents and cavity geometries evolve. A 1.5\u2009\u00b0C sub-surface ocean temperature adjustment is used in the Amundsen Sea sector to bring ocean melt rates closer to observations56 when using CCSM4 ocean model temperatures that underestimate observed shelf-bottom water temperatures57. This is a substantial improvement relative to the 3\u2009\u00b0C temperature adjustment required previously8.\nIce-shelf hydrofracturing\uf0c1\nIn the model, surface crevasses deepen as a function of the stress field and local meltwater and rainfall availability [7,8,58], leading to hydrofracturing when surface and basal crevasses penetrate 75% or more of the total ice thickness. With greatly increased surface melt, model ice shelves can be completely lost. In the standard wet crevassing scheme, we assume a quadratic relationship between surface crevasse penetration depth dw (in metres) and total meltwater production R (rain plus surface melt minus refreezing; in m yr\u22121). A tunable prefactor, CALVLIQ, is varied between zero (no meltwater influence on crevassing) and 195 m\u22121 yr2 in the ensembles presented in the main text.\ndw = CALVLIQ  R^2.\nCalving occurs in places where the sum of the surface and basal crevasse penetration caused by extensional stresses, accumulated strain (damage), thinning and meltwater (dw), exceeds the critical fraction (0.75) of total ice thickness (see appendix B of ref. 7).\nThe crevassing scheme is modified here relative to previous model versions7,8,51, by reducing wet crevassing in areas of low-to-moderate meltwater production (<1,500 mm yr\u22121), ramping linearly from zero, where no meltwater is present, to dw, where R = 1,500 mm yr\u22121. This small modification improves performance by maintaining more realistic ice-shelf calving fronts under present climate conditions, although it conservatively precludes the loss of ice shelves with thicknesses comparable to the Larsen B until R approaches ~1,400 mm yr\u22121, which is more than that observed before the actual collapse (~750 mm yr\u22121)30. Whereas liquid water embedded in firn and partial refreezing of meltwater are accounted for8,59, the detailed evolution of firn density and development of internal ice lenses are not, which could affect the timing at which hydrodrofacturing is simulated to begin. A modification to hydrofracturing described in Supplementary Information tests the possible influence of channelized meltwater flow and supraglacial runoff in compressional ice-shelf regimes.\nCalving and ice-cliff failure\uf0c1\nTwo modes of brittle fracturing causing ice loss are represented in the model: (1) \u2018standard\u2019 calving of ice bergs from floating ice, and (2) structural failure of tall ice cliffs at the grounding line. Similar to other models, standard calving depends mainly on the grid-scale divergence of ice flow, producing crevasses to depths at which the extensional stress is equal to the hydrostatic imbalance58. Crevasse penetration is further increased as a function of surface meltwater and rain availability (see above).\nUnlike most continental-scale models, we also account for ice-cliff calving at thick, marine-terminating grounding lines. Such calving is a complex product of forces related to glacier speed, thickness, longitudinal stress gradients, bed conditions, side shear, pre-existing crevasses, m\u00e9lange and other factors60. Determining the precise mode and rate of failure is the focus of ongoing work17,18,20,61; at present, a suitable physically based calving model has yet to be developed. In our model7,8, ice-cliff calving occurs where static stresses at the calving front (assumed to be exactly at floatation) begin to exceed the depth-averaged yield strength of glacial ice, assumed here to be 0.5 MPa (ref. 16). We account for crevassing near the cliff face (influenced by the stress regime and the presence of meltwater7), which thins the supportive ice column and increases the stress at the ice front. Where the critical stress threshold is exceeded, ice-cliff calving is applied as a horizontal wastage rate, ramping linearly from zero up to a maximum rate as effective cliff heights (adjusted for buttressing and crevassing) increase from ~80 to 100 m and above. This maximum calving rate is treated as a tunable model parameter (VCLIFF), replacing the arbitrary default value of 3 km yr\u22121 in equation A.4 of ref. 7. In this formulation, ice-cliff calving rates in places diagnosed to be undergoing structural failure are generally much smaller than VCLIFF (Extended Data Fig. 5). We note that the linear cliff height\u2013calving relationship with an imposed calving limit (VCLIFF) used here is conservative relative to another proposed calving law20 that assumes a power-law dependence on cliff height and no upper bound on the calving rate. Furthermore, our model numerics preclude regular calving in places undergoing ice-cliff failure, so the computed ice-cliff calving rate can be considered as the sum of all calving processes at thick marine-terminating ice fronts. This allows direct comparison of model calving (Extended Data Fig. 5) with observations. M\u00e9lange can slow calving by providing some back stress at confined calving fronts [62,63], but it has limited effect on the large unconfined widths of Antarctic outlets [64], so it is ignored here.\nEnsemble parameters\uf0c1\nOur primary perturbed physics ensembles use a 14 \u00d7 14 matrix (n = 196) of CREVLIQ and VCLIFF in the hydrofracturing and ice-cliff calving parameterizations described above (Extended Data Table 1). The 14 values of CREVLIQ vary between 0 and 195 m\u22121 yr2 in evenly spaced increments. VCLIFF varies between 0 and 13 km yr\u22121. Previous studies7,8 considered a smaller, arbitrary range of VCLIFF values of up to 5 km yr\u22121; however, observed rates of horizontal ice loss through ice-cliff calving can reach 13 km yr\u22121 at the terminus of Jakobshavn Isbr\u00e6 in West Greenland21, so we limit the top of our parameter range in our main ensembles to this observationally justifiable value. As discussed in the main text, this upper bound might be too small for Antarctic settings with thicker ice margins, taller unconfined ice fronts and higher deviatoric stresses at unbuttressed grounding lines. Select simulations extending the upper bounds of CALVLIQ and VCLIFF above 195 m\u22121 yr2 and 13 km yr\u22121, respectively, are shown in Extended Data Fig. 1. Setting these parameter values to zero (Extended Data Figs. 1, 6) effectively eliminates hydrofracturing and ice-cliff calving, limiting rates of ice loss to processes associated with standard calving, surface mass balance, sub-ice melt and MISI, as in most other continental-scale ice-sheet models.\nEnsemble scoring based on recent observations\uf0c1\nFuture ice-sheet simulations begin in 1950 to allow comparisons with observations over the satellite era. For consistency, initial ice-sheet conditions (ice thickness, bed elevation, velocity, basal sliding coefficients and internal ice and bed temperatures) follow the same procedure as in ref. 8 and are identical in all simulations. Initialization involves a 100,000-kyr spin-up using observed mean annual ocean climatology65 and standard SeaRISE66 atmospheric temperature and precipitation fields [67].", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "a9cea5dae349-6", "text": "Ensemble parameters\uf0c1\nOur primary perturbed physics ensembles use a 14 \u00d7 14 matrix (n = 196) of CREVLIQ and VCLIFF in the hydrofracturing and ice-cliff calving parameterizations described above (Extended Data Table 1). The 14 values of CREVLIQ vary between 0 and 195 m\u22121 yr2 in evenly spaced increments. VCLIFF varies between 0 and 13 km yr\u22121. Previous studies7,8 considered a smaller, arbitrary range of VCLIFF values of up to 5 km yr\u22121; however, observed rates of horizontal ice loss through ice-cliff calving can reach 13 km yr\u22121 at the terminus of Jakobshavn Isbr\u00e6 in West Greenland21, so we limit the top of our parameter range in our main ensembles to this observationally justifiable value. As discussed in the main text, this upper bound might be too small for Antarctic settings with thicker ice margins, taller unconfined ice fronts and higher deviatoric stresses at unbuttressed grounding lines. Select simulations extending the upper bounds of CALVLIQ and VCLIFF above 195 m\u22121 yr2 and 13 km yr\u22121, respectively, are shown in Extended Data Fig. 1. Setting these parameter values to zero (Extended Data Figs. 1, 6) effectively eliminates hydrofracturing and ice-cliff calving, limiting rates of ice loss to processes associated with standard calving, surface mass balance, sub-ice melt and MISI, as in most other continental-scale ice-sheet models.\nEnsemble scoring based on recent observations\uf0c1\nFuture ice-sheet simulations begin in 1950 to allow comparisons with observations over the satellite era. For consistency, initial ice-sheet conditions (ice thickness, bed elevation, velocity, basal sliding coefficients and internal ice and bed temperatures) follow the same procedure as in ref. 8 and are identical in all simulations. Initialization involves a 100,000-kyr spin-up using observed mean annual ocean climatology65 and standard SeaRISE66 atmospheric temperature and precipitation fields [67].\nWe consider three different estimates of recent changes in Antarctic ice mass to test the performance of each ensemble member with a unique combination of model physical parameters (Extended Data Table 1). We use the average annual mass change d\ud835\udc40\u00af/d\ud835\udc61 from 1992\u20132017 (equivalent to a GMSL change of 0.15\u20130.46 mm yr\u22121) provided by the IMBIE assessment4, which is based on a combination of satellite altimetry, gravimetry and surface mass balance estimates. We use the 25-year average to minimize the influence of simulated and observed interannual variability (Extended Data Fig. 1a) on ensemble scoring, although decadal and longer variability68 are not fully captured. Alternative target ranges use mass change calculations based solely on the Gravity Recovery and Climate Experiment (GRACE), following the methodology described in ref. 38 and updated from April 2002 to June 2017. The glacial isostatic adjustment (GIA) component of the GRACE estimates represents the largest source of uncertainty. We use three GIA models69,70,71. For each model we use a range of GIA corrections generated by the authors of69,70,71, assuming a range of viscosities and lithospheric thicknesses69,70,71. The lower bound of our mass change estimates is calculated using the minimum GIA correction from the three models69,70,71 and the upper bound is calculated using the maximum GIA correction. This yields a 2002\u20132017 average estimate of 0.2\u20130.54 mm yr\u22121, close to the central estimate from IMBIE over the same interval. Alternatively, we consider viscosity profiles from each of these studies that have been reported to provide the best fit to observations69,70,71. This substantially narrows and shifts the 2002\u20132017 range towards higher values (0.39 to 0.53 mm yr\u22121), which is impactful on our ensemble scoring and future projections, highlighting the need for more precise modern observations. Although the uncertainty range of estimates based solely on GRACE is smaller, the longer IMBIE record is used as our default training constraint over the modern era.\nLIG ensemble\uf0c1\nLIG simulations use model physics, parameter values and initial conditions identical to those used in our Pliocene and future simulations. The ice-driving atmospheric and oceanic climatology representing conditions between 130 and 125 kyr ago is the same as that used in ref. 8, and is based on a combination of regional atmospheric modelling and proxy-based reconstructions of air and ocean temperatures72. Differences in the timing and magnitude of our modelled Antarctic ice-sheet retreat relative to independent LIG simulations73 reflect the different approaches to LIG climate forcing and structural differences in our ice-sheet models, including the inclusion of hydrofracturing and ice-cliff calving in this study.\nOur ensemble scoring uses a LIG target range of Antarctic ice loss equivalent to 3.1\u20136.1 m, which is assumed to have occurred early in the interglacial between 129 and 128 kyr ago (Extended Data Fig. 1). The range used here is based on a prior estimate of GMSL of 5.9 \u00b1 1.7 m by 128.6 \u00b1 0.8 kyr ago35 (2\u03c3 uncertainty), rounded to the nearest half metre (4.5\u20137.5 m) to reflect the current uncertainty in the magnitude (due to GIA effects and dynamic topography) and timing of LIG sea-level estimates35,74. The Antarctic component is deconvolved from the GMSL value by assuming that Greenland contributed no more than 1 m before 128 kyr ago75,76,77, with an additional 0.4 m contributed by thermosteric effects75. Contributions from mountain glaciers in the early LIG are not known and are not included in our simple accounting. We find that rounding the exact GMSL values from ref. 35 (5.9 \u00b1 1.7 m or 2.8\u20136.2 m after accounting for Greenland and thermosteric components) has no appreciable effect on the outcome of the calibrated ensembles. The target range of 3.1\u20136.1 m used here is lower than the 3.6\u20137.4 m range used in ref. 8, but we emphasize that it is based on a coral record from a single location (Seychelles), and ongoing work may further refine this range. For example, a recent study73 attempting to simultaneously fit relative sea-level data at several locations was able to reproduce early LIG changes observed in the Seychelles without a substantial contribution from Antarctica, but it required a thin lithosphere in the Earth model used to correct for GIA. Conversely, another study78 indicated that a North American ice sheet may have persisted until ~126 kyr ago or later. If true, this would require a substantial Antarctic contribution to GMSL to offset remaining North American ice in the early LIG. These alternative scenarios remain speculative, but they highlight the ongoing uncertainty in the palaeo sea-level records. Our LIG and Pliocene ensemble data (Extended Data Figure 1) are provided as source data to allow others to test the impact of alternative palaeo sea-level interpretations on the future projections.\nPliocene ensemble\uf0c1\nMid-Pliocene simulations also use consistent ice model physics and the same RCM climate forcing described in ref. 8, assuming 400 ppm CO2, an extreme warm austral summer orbit and 2\u2009\u00b0C of ocean warming to represent maximum mid-Pliocene warmth in Antarctica. The ice-sheet simulations are run for 5,000 model years, the approximate duration that the warm orbital parameters are valid (Extended Data Fig. 1). The Pliocene maximum GMSL target range of 11\u201321 m is based on two recent, independent estimates of warm mid-Pliocene (3.26\u20133.03 Myr ago) sea level36,37. In ref. 36, shallow marine sediments are used to estimate the glacial\u2013interglacial range of GMSL variability over this interval. Assuming \u00b15 m of uncertainty in the sea-level reconstructions and up to 5 m of GMSL change contributed by Greenland, at times orbitally out of phase with the timing of Antarctic ice loss36, the central estimate of Antarctica\u2019s contribution to GMSL is 17.8 \u00b1 5 m. This value is adjusted downwards to 16 m, according to an independent estimate derived from Mediterranean cave deposits corrected for geodynamical processes37. Combining the lower central estimate of ref. 37 and the uncertainty range of ref. 36 provides an Antarctic GMSL target range of 11\u201321 m, close to the range of 10\u201320 m used in ref. 8, albeit with considerable uncertainty.\nFuture ensembles\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "a9cea5dae349-7", "text": "Pliocene ensemble\uf0c1\nMid-Pliocene simulations also use consistent ice model physics and the same RCM climate forcing described in ref. 8, assuming 400 ppm CO2, an extreme warm austral summer orbit and 2\u2009\u00b0C of ocean warming to represent maximum mid-Pliocene warmth in Antarctica. The ice-sheet simulations are run for 5,000 model years, the approximate duration that the warm orbital parameters are valid (Extended Data Fig. 1). The Pliocene maximum GMSL target range of 11\u201321 m is based on two recent, independent estimates of warm mid-Pliocene (3.26\u20133.03 Myr ago) sea level36,37. In ref. 36, shallow marine sediments are used to estimate the glacial\u2013interglacial range of GMSL variability over this interval. Assuming \u00b15 m of uncertainty in the sea-level reconstructions and up to 5 m of GMSL change contributed by Greenland, at times orbitally out of phase with the timing of Antarctic ice loss36, the central estimate of Antarctica\u2019s contribution to GMSL is 17.8 \u00b1 5 m. This value is adjusted downwards to 16 m, according to an independent estimate derived from Mediterranean cave deposits corrected for geodynamical processes37. Combining the lower central estimate of ref. 37 and the uncertainty range of ref. 36 provides an Antarctic GMSL target range of 11\u201321 m, close to the range of 10\u201320 m used in ref. 8, albeit with considerable uncertainty.\nFuture ensembles\uf0c1\nWe improve on previous work8 with new atmospheric climatologies used to run future ice-sheet simulations using dynamically downscaled meteorological fields of temperature and precipitation provided by an RCM79 adapted to Antarctica. RCM snapshots are run at 1950 and with increasing levels of effective CO2 (2, 4 and 8 times the preindustrial level) while accounting for topographic changes in the underlying ice sheet as described in ref. 8. The resulting meteorological fields are then time-interpolated and log-weighted to match transient CO2 concentrations following the emissions scenarios simulated here. This technique is computationally efficient and flexible, allowing a number of multi-century emissions scenarios to be explored, including non-standard RCP scenarios (Fig. 1) and those including CDR mitigation (Fig. 3). Unlike in ref. 8, sea surface temperatures and sea ice boundary conditions in the nested RCM come from the same transient NCAR CCSM480 runs that provide the time-evolving sub-surface ocean temperatures used in our sub-ice melt rate calculations. This eliminates the need for an imposed lag between transient greenhouse gas concentrations and equilibrated RCM climates as done previously8. Our revised approach delays the future timing at which surface meltwater begins to appear on ice-shelf surfaces, and the resulting atmospheric temperatures compare favourably with independent CMIP5 and CMIP6 GCMs (Supplementary Figs. 1, 2) and NCAR CESM1.2.2 (Fig. 1h).\nMonthly mean surface air temperatures and precipitation from the RCM are used to calculate the net annual surface mass balance on the ice sheet. These fields are bilinearly interpolated to the relatively fine ice-sheet grid, and temperatures are adjusted for the vertical difference between RCM and ice-sheet elevations using a simple lapse-rate correction. The lapse-rate correction is also applied to precipitation on the basis of a Clausius\u2013Clapeyron-like relation. A two-step zero-dimensional box model using positive-degree days for snow and ice melt captures the basic physical processes of refreezing versus runoff in the snow\u2013firn column8,59. The total surface melt available to influence surface crevassing (Supplementary Fig. 1) is the fraction of meltwater that is not refrozen near the surface, plus any rainwater.\nA spatially dependent bias correction based on reanalysis (Supplementary Fig. 2) could be applied to the RCM forcing, but such corrections are unlikely to remain stationary. Instead, we apply a uniform 2.9\u2009\u00b0C temperature correction, reflecting the austral summer cold bias in the RCM over ice surface elevations lower than 200 m, where surface melt is most likely to begin. The cold bias, caused by an underestimate of net long-wave radiation, is observed in other Antarctic RCMs and GCMs81,82. Correcting for the cold bias and accounting for rainwater increases the total available surface meltwater in our RCP8.5 simulations relative to other studies31 (see Supplementary Information).\nThe +1.5\u2009\u00b0C simulations initially follow a RCP4.5 emission trajectory9, with time-evolving atmospheric fields provided by the RCM and matching sub-surface ocean temperatures from an RCP4.5 CCSM4 simulation80. The ice-driving climatology evolves freely until 2040, when decadal global mean surface air temperatures first reach +1.5\u2009\u00b0C relative to 1850. Once the +1.5\u2009\u00b0C temperature target is reached, the atmosphere and ocean forcings are fixed (maintained) at their 2040 levels for the duration of the simulations. The +2\u2009\u00b0C scenario is also based on RCP4.5, but warming is allowed to evolve until 2060. 21st-century warming does not reach +3\u2009\u00b0C under RCP4.5, so our +3\u2009\u00b0C scenario (roughly representing the NDCs) is based on RCP8.5, with atmospheric and oceanic forcing fixed beyond 2070. Warming trajectories over major Antarctic ice shelves are shown in Supplementary Figs. 1, 2. Ice-sheet ensembles following extended RCP2.6, RCP4.5 and RCP8.5 scenarios9 are shown in Extended Data Fig. 6 for comparison with ref. 8.\nAlternative future ensembles (Extended Data Table 2) truncate the upper bound of the VCLIFF calving parameter from 13 km yr\u22121 (Table 1) to either 11 km yr\u22121 or 8 km yr\u22121, to account for the possibility that 13 km yr\u22121 calving rates observed at Jakobshavn between 2002 and 201521 are not representative of the glacier\u2019s long-term behaviour. This reduces the raw ensembles from n = 196 to n = 168 and n = 126, respectively. An upper bound of 8 km yr\u22121 is difficult to justify because higher values cannot be excluded by the modern, LIG and Pliocene history matching. Furthermore, 8 km yr\u22121 is very close to the validated average value of 7.7 km yr\u22121 in the main ensemble. Using an upper bound of 11 km yr\u22121 instead of 13 km yr\u22121 has only a small effect on future projections (Extended Data Table 2). We consider 13 km yr\u22121 to be a reasonable upper bound for our main ensembles (Fig. 1) because this rate has been observed in nature21 and because ensemble members using this value cannot be excluded on the basis of model performance (Extended Data Fig. 1).\nCoupled ice\u2013Earth\u2013sea level model\uf0c1\nMost simulations use a standard Elastic Lithosphere/Relaxed Asthenosphere (ELRA) representation of vertical bedrock motion [51]. The ELRA model accounts for time-evolving bedrock deformation under changing ice loads, assuming an elastic lithospheric plate above local isostatic relaxation. Alternative simulations (Extended Data Fig. 8) account for full Earth\u2013ice coupling using a viscoelastic (Maxwell) Earth model, combining a radially varying, depth-dependent lithosphere and mantle structure and gravitationally self-consistent sea-level calculations following the methodology described in ref. 12.\nSeismic [83,84] and geodetic [85,86] observations suggest substantial lateral variability in a viscoelastic Earth structure, with lower-than-average viscosities in parts of West Antarctica leading to faster uplift where ice mass is lost at the grounding line. Owing to the current uncertainties in Earth\u2019s viscoelastic properties, we test a broad range of viscosity profiles. These include two end-member profiles described in refs. 12,49; one with a relatively high viscosity profile (HV) consistent with standard, globally tuned profiles; and one with a thinned lithosphere and a low-viscosity zone of 1,019 Pa s in the uppermost upper mantle (LVZ) that is broadly representative of West Antarctica. Here, we test a new profile (BLVZ) similar to LVZ, but assuming a vertical profile with the upper zone one order of magnitude less viscous than in LVZ, as recently proposed for the Amundsen Sea region10. The BLVZ model is consistent with the best-fitting radial Earth model in ref. 10, and uses a lithospheric thickness of 60 km, a shallow upper mantle from 60 km to 200 km depth with a viscosity of 3.98 \u00d7 1018 Pa s, a deep upper mantle from 200 km to 400 km with a viscosity of 1.59 \u00d7 1019 Pa s, a transition zone from 400 km to 670 km depth with a viscosity of 2.51 \u00d7 1019 Pa s, and a lower mantle viscosity of 1 \u00d7 1019 Pa s.", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "a9cea5dae349-8", "text": "Coupled ice\u2013Earth\u2013sea level model\uf0c1\nMost simulations use a standard Elastic Lithosphere/Relaxed Asthenosphere (ELRA) representation of vertical bedrock motion [51]. The ELRA model accounts for time-evolving bedrock deformation under changing ice loads, assuming an elastic lithospheric plate above local isostatic relaxation. Alternative simulations (Extended Data Fig. 8) account for full Earth\u2013ice coupling using a viscoelastic (Maxwell) Earth model, combining a radially varying, depth-dependent lithosphere and mantle structure and gravitationally self-consistent sea-level calculations following the methodology described in ref. 12.\nSeismic [83,84] and geodetic [85,86] observations suggest substantial lateral variability in a viscoelastic Earth structure, with lower-than-average viscosities in parts of West Antarctica leading to faster uplift where ice mass is lost at the grounding line. Owing to the current uncertainties in Earth\u2019s viscoelastic properties, we test a broad range of viscosity profiles. These include two end-member profiles described in refs. 12,49; one with a relatively high viscosity profile (HV) consistent with standard, globally tuned profiles; and one with a thinned lithosphere and a low-viscosity zone of 1,019 Pa s in the uppermost upper mantle (LVZ) that is broadly representative of West Antarctica. Here, we test a new profile (BLVZ) similar to LVZ, but assuming a vertical profile with the upper zone one order of magnitude less viscous than in LVZ, as recently proposed for the Amundsen Sea region10. The BLVZ model is consistent with the best-fitting radial Earth model in ref. 10, and uses a lithospheric thickness of 60 km, a shallow upper mantle from 60 km to 200 km depth with a viscosity of 3.98 \u00d7 1018 Pa s, a deep upper mantle from 200 km to 400 km with a viscosity of 1.59 \u00d7 1019 Pa s, a transition zone from 400 km to 670 km depth with a viscosity of 2.51 \u00d7 1019 Pa s, and a lower mantle viscosity of 1 \u00d7 1019 Pa s.\nTwo sets of coupled ice\u2013Earth\u2013sea level simulations are run for each viscosity profile, with and without hydrofracturing and ice-cliff calving enabled (Extended Data Fig. 8). Simulations with the brittle processes enabled use values of CALVLIQ (105 m\u22121 yr2) and VCLIFF (6 km yr\u22121) close to the ensemble averages. The simulations follow our standard RCP forcing to test the effect of ice\u2013Earth\u2013sea level feedback on future projections. We find that the effects on equivalent sea-level rise are quite small on timescales of a few centuries and similar to those using the ELRA bed model, confirming that the use of the latter in our main ensembles (Fig. 1) is adequate.\nCESM ice-sheet simulations\uf0c1\nTwo additional ice-sheet simulations are run using future atmospheric and oceanic forcing provided by two different RCP8.5 simulations described in ref. 46 and using the NCAR CESM 1.2.2 GCM with CAM5 atmospheric physics87. Ice-sheet model physics and parameter values are identical in both simulations. Hydrofracturing (CALVLIQ) and cliff calving (VCLIFF) parameters use calibrated ensemble averages of 107 m\u22121 yr2 and 7.7 km yr\u22121, consistent with the RCM-driven simulations shown in Figs. 2, 3. The standard RCP8.5 simulation ignores future Antarctic meltwater and dynamic discharge, whereas an alternative simulation accounts for time-evolving and spatially resolved liquid-water and solid-ice inputs around the Antarctic margin (peaking at >2 Sv in the early 22nd century), provided by an offline RCP8.5 ice-sheet simulation including hydrofracturing and ice-cliff calving46. The evolving temperature and precipitation fields from CESM are spatially interpolated and lapse-rate-adjusted to the ice-sheet model grid, using the same surface mass balance scheme used in our main RCM-forced ensembles. Similarly, sub-ice melt rates from CESM are calculated in exactly the same way as those provided by CCSM4 in our main ensembles. Although this discrete two-step coupling between CESM and the ice-sheet model does not account for time-continuous, fully coupled ice\u2013ocean\u2013climate feedback mechanisms, the two simulations (with and without ice-sheet discharge) span the envelope of possible outcomes when two-way meltwater feedback is fully accounted for. The two simulations using CESM with and without meltwater feedback are shown in Fig. 1h for comparison with our main RCM/CCSM4-forced ensembles.\nExtended data figures and tables\uf0c1\nExtended Data Fig. 1 Ensemble observational targets. 196 simulations (grey lines), each using a unique combination of hydrofracturing and ice-cliff calving parameters (Extended Data Table 1) compared with observations (blue dashed boxes). Solid blue lines show simulations without hydrofracturing and ice-cliff calving. Red lines show simulations with maximum parameter values in our main ensemble. Additional simulations (black lines) allow ice-cliff calving rates of up to 26 km yr\u22121, twice the maximum value used in our main ensembles. The vertical heights of the blue boxes represent the likely range of observations. Changes in ice mass above floatation are shown in equivalent GMSL. a, Simulated annual contributions to GMSL in the RCP8.5 ensemble compared with the 1992\u20132017 IMBIE4 observational average (0.15\u20130.46 mm yr\u22121; dashed blue box). b, LIG ensemble simulations from 130 to 125 kyr ago. The height of the dashed blue box shows the LIG target range (3.1\u20136.1 m), the width represents ~1,000-yr age uncertainty34. c, The same LIG simulations as in b, showing the rate of GMSL change contributed by Antarctica, smoothed over a 25-yr window. The peak in the early LIG is mainly caused by marine-based ice loss in West Antarctica. d, The same as b, except for warmer mid-Pliocene conditions. Maximum ice loss is compared with observational estimates of 11\u201321 m (refs. 35,36; blue dashed lines). Note the saturation of the simulated GMSL values near the top of the LIG and Pliocene ensemble range, and the failure of the model to produce realistic LIG or Pliocene sea levels without hydrofracturing and ice-cliff calving enabled (blue lines).\nExtended Data Fig. 2 RCP8.5 ensembles calibrated with alternative GRACE estimates. a, b, The fan charts show the time-evolving uncertainty and range around the median ensemble value (black line) in 10% increments. RCP8.5 ice-sheet model ensembles calibrated with GRACE estimates of annual mass change averaged from 2002\u20132017 using alternative GIA corrections (Methods). Use of GIA corrections produces estimates of mass loss between 2002 and 2017 of 0.2\u20130.54 mm yr\u22121 (a) and 0.39\u20130.53 mm yr\u22121 (b). The more restrictive and higher range of GRACE estimates in b skews the distribution and shifts the ensemble median values of GMSL upwards from 27 cm to 30 cm in 2100 and from 4.44 m to 4.94 m in 2200.\nExtended Data Fig. 3 Last Interglacial and Pliocene ice-sheet simulations. a\u2013e, Ice-sheet simulations with the updated model physics used in our future ensembles and driven with the same LIG and Pliocene climate forcing used in ref. 8. Simulations without hydrofracturing and ice-cliff calving (a, b, d) correspond to blue lines in Extended Data Fig. 1. Simulations using maximum hydrofracturing and ice-cliff calving parameters (c, e) correspond to red lines in Extended Data Fig. 1. a, Modern (1950) ice-sheet simulation. b, c, LIG simulations run from 130 to 125 kyr ago are shown at 125 kyr ago. Values at the top of each panel are the maximum GMSL contribution between 129 and 128 kyr ago. Values in parentheses are the GMSL contribution at 125 kyr ago. d, e, Warm Pliocene simulations. Values shown are the maximum GMSL achieved during the simulations. Smaller values in parentheses show GMSL contributions after 5,000 model years (Extended Data Fig. 2d). Ice mass gain after peak retreat is caused by post-retreat bedrock rebound and enhanced precipitation in the warm Pliocene atmosphere.", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "a9cea5dae349-9", "text": "Extended Data Fig. 2 RCP8.5 ensembles calibrated with alternative GRACE estimates. a, b, The fan charts show the time-evolving uncertainty and range around the median ensemble value (black line) in 10% increments. RCP8.5 ice-sheet model ensembles calibrated with GRACE estimates of annual mass change averaged from 2002\u20132017 using alternative GIA corrections (Methods). Use of GIA corrections produces estimates of mass loss between 2002 and 2017 of 0.2\u20130.54 mm yr\u22121 (a) and 0.39\u20130.53 mm yr\u22121 (b). The more restrictive and higher range of GRACE estimates in b skews the distribution and shifts the ensemble median values of GMSL upwards from 27 cm to 30 cm in 2100 and from 4.44 m to 4.94 m in 2200.\nExtended Data Fig. 3 Last Interglacial and Pliocene ice-sheet simulations. a\u2013e, Ice-sheet simulations with the updated model physics used in our future ensembles and driven with the same LIG and Pliocene climate forcing used in ref. 8. Simulations without hydrofracturing and ice-cliff calving (a, b, d) correspond to blue lines in Extended Data Fig. 1. Simulations using maximum hydrofracturing and ice-cliff calving parameters (c, e) correspond to red lines in Extended Data Fig. 1. a, Modern (1950) ice-sheet simulation. b, c, LIG simulations run from 130 to 125 kyr ago are shown at 125 kyr ago. Values at the top of each panel are the maximum GMSL contribution between 129 and 128 kyr ago. Values in parentheses are the GMSL contribution at 125 kyr ago. d, e, Warm Pliocene simulations. Values shown are the maximum GMSL achieved during the simulations. Smaller values in parentheses show GMSL contributions after 5,000 model years (Extended Data Fig. 2d). Ice mass gain after peak retreat is caused by post-retreat bedrock rebound and enhanced precipitation in the warm Pliocene atmosphere.\nExtended Data Fig. 4 RCP8.5 ensembles calibrated with modern and palaeo observations. The fan charts show the time-evolving uncertainty and range around the median ensemble value (black line) in 10% increments. Mean and median ensemble values are shown at 2100. a, Raw ensemble with a range of plausible model parameters based on glaciological observations (Extended Data Table 1). b, The ensemble trimmed with IMBIE4 (1992\u20132017) estimates of ice mass change. c, The ensemble trimmed with IMBIE rates of ice mass change plus LIG sea-level constraints between 129 and 128 kyr ago34. d, The same as c, except with the addition of maximum mid-Pliocene sea-level constraints35,36 (Extended Data Fig. 1). Future ensembles in the main text (Fig. 1, Table 1) use the combined IMBIE + LIG + Pliocene history matching constraints as shown in d.\nExtended Data Fig. 5 Future retreat of Thwaites Glacier (TG) and Pine Island Glacier (PIG) with +3\u2009\u00b0C global warming. The Amundsen Sea sector of the ice sheet in a nested, high-resolution (1 km) simulation using average calibrated values of hydrofracturing and ice-cliff calving parameters (CALVLIQ = 107 m\u22121 yr2; VCLIF = 7.7 km yr\u22121), consistent with those used in CESM1.2.2-forced simulations (Fig. 1h) and CDR simulations (Fig. 3, Table 1). a\u2013c, The ice sheet in 2050. d\u2013f, The ice sheet in 2100. a, d, Ice-sheet geometry and annually averaged ice-cliff calving rates at thick, weakly buttressed grounding lines. The solid line in all panels is the grounding line and the dashed line is its initial position. Note that simulated ice-cliff calving rates are generally much slower than the maximum allowable value of 7.7 km yr\u22121. Ice shelves downstream of calving ice cliffs are the equivalent of weak m\u00e9lange, incapable of stopping calving64. b, e, Ice surface speed showing streaming and fast flow just upstream of calving ice cliffs where driving stresses are greatest. c, f, Change in ice thickness relative to the initial state. g, GMSL contributions within the nested domain at model spatial resolutions spanning 1\u201310 km.\nExtended Data Fig. 6 Antarctic contribution to sea level under standard RCP forcing. a\u2013c, The fan charts show the time-evolving uncertainty and range around the median ensemble value (thick black line) in 10% increments. The RCP ensembles use the same IMBIE, LIG and Pliocene observational constraints applied to the simulations in Fig. 1. GMSL contributions in simulations without hydrofracturing or ice-cliff calving (excluded from the validated ensembles) are shown for East Antarctica (thin blue line), West Antarctica (thin red line) and the total Antarctic contribution (thin black line). a, RCP2.6; b, RCP4.5; and c, RCP8.5.\nExtended Data Fig. 7 Long-term magnitudes and rates of GMSL rise contributed by Antarctica. a, Ensemble median (50th percentile) projections of GMSL rise contributed by Antarctica with emissions forcing consistent with the +1.5\u2009\u00b0C and +2.0\u2009\u00b0C Paris Agreement ambitions, versus a +3.0\u2009\u00b0C scenario closer to current NDCs. b, Median (50th percentile) rates of GMSL rise in the same emissions scenarios as in a, illustrating a sharp jump in ice loss in the warmer +3.0\u2009\u00b0C scenario after 2060 (also see Fig. 1), and reduced net ice loss before 2060 (black line) caused by increased snowfall. c, Ensemble median (50th percentile) projections of GMSL rise contributed by Antarctica with emissions forcing consistent with standard RCP scenarios, highlighting the potential for extreme GMSL rise under high (RCP8.5) emissions. d, Ensemble median (50th percentile) rates of GMSL rise in the same RCP scenarios as shown in c. Note the much larger vertical-axis scales in c and d relative to a and b.\nExtended Data Fig. 8 Coupled ice\u2013Earth\u2013sea level model simulations. a\u2013c, Simulations without hydrofracturing and ice-cliff calving processes. d\u2013f, Simulations with hydrofracturing and ice-cliff calving enabled (Methods). GMSL contributions are from the WAIS only. Various Earth viscosity profiles (coloured lines) are compared with the ice-sheet model\u2019s standard ELRA formulation (black line). The most extreme viscosity profile (blue line) assumes a thin lithosphere and very weak underlying mantle, like that observed in the Amundsen sea10, but extended continent-wide. a, RCP2.6 without hydrofracturing or ice-cliff calving. b, RCP2.6 with hydrofracturing and ice-cliff calving. c, RCP4.5 without hydrofracturing or ice-cliff calving. d, RCP4.5 with hydrofracturing and ice-cliff calving. e, RCP8.5 without hydrofracturing or ice-cliff calving. f, RCP8.5 with hydrofracturing and ice-cliff calving.\nExtended Data Table 1 Model ensemble parameter values. Parameter values used in unique combinations to generate 196 model ensemble members. Blue and red values correspond to the simulations shown by blue and red lines in Extended Data Fig. 1. Thirteen additional combinations extending CALVLIQ to 390 m\u22121 yr2 and VCLIFF to 26 km yr\u22121 are shown in black in Extended Data Fig. 1. The average calibrated parameter values based on IMBIE, LIG and Pliocene history matching (Extended Data Fig. 1) are CALVLIQ = 107 m\u22121 yr2 and VCLIFF = 7.7 km yr\u22121. The corresponding median values are 105 m\u22121 yr2 and 7 km yr\u22121.", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "a9cea5dae349-10", "text": "Extended Data Fig. 8 Coupled ice\u2013Earth\u2013sea level model simulations. a\u2013c, Simulations without hydrofracturing and ice-cliff calving processes. d\u2013f, Simulations with hydrofracturing and ice-cliff calving enabled (Methods). GMSL contributions are from the WAIS only. Various Earth viscosity profiles (coloured lines) are compared with the ice-sheet model\u2019s standard ELRA formulation (black line). The most extreme viscosity profile (blue line) assumes a thin lithosphere and very weak underlying mantle, like that observed in the Amundsen sea10, but extended continent-wide. a, RCP2.6 without hydrofracturing or ice-cliff calving. b, RCP2.6 with hydrofracturing and ice-cliff calving. c, RCP4.5 without hydrofracturing or ice-cliff calving. d, RCP4.5 with hydrofracturing and ice-cliff calving. e, RCP8.5 without hydrofracturing or ice-cliff calving. f, RCP8.5 with hydrofracturing and ice-cliff calving.\nExtended Data Table 1 Model ensemble parameter values. Parameter values used in unique combinations to generate 196 model ensemble members. Blue and red values correspond to the simulations shown by blue and red lines in Extended Data Fig. 1. Thirteen additional combinations extending CALVLIQ to 390 m\u22121 yr2 and VCLIFF to 26 km yr\u22121 are shown in black in Extended Data Fig. 1. The average calibrated parameter values based on IMBIE, LIG and Pliocene history matching (Extended Data Fig. 1) are CALVLIQ = 107 m\u22121 yr2 and VCLIFF = 7.7 km yr\u22121. The corresponding median values are 105 m\u22121 yr2 and 7 km yr\u22121.\nExtended Data Table 2 Antarctic sea-level contributions with alternative maximum ice-cliff calving rates. Ensemble median GMSL contributions using IMBIE, LIG and Pliocene observational constraints (in metres) relative to 2000. Values in parentheses are the 17th\u201383rd percentiles (likely range). Scenarios refer to the maximum global mean temperature reached relative to pre-industrial (1850) or following extended RCPs, and with the upper bound of the ice-cliff calving parameter (VCLIFF) set at the maximum observed value of 13 km yr\u22121 (n = 196; Table 1), or alternatively at 11 km yr\u22121 (n = 168) or 8 km yr\u22121 (n = 126). Reducing the upper bound of the ice-cliff calving parameter has a relatively small impact on ensemble medians, especially in the near term. The average calibrated value of VCLIFF constrained by observational constraints is 7.7 km yr\u22121, which severely truncates the upper tail of the distributions when using 8 km yr\u22121 as the sampling limit.\nSupplementary Information\uf0c1\nUncertainty in surface melt rates and climate forcing\uf0c1\nAs discussed in the main text and Methods, our ice sheet model accounts for rain and meltwater- induced wet crevassing and hydrofracturing that can trigger the sudden loss of buttressing ice shelves, as mean summer temperatures approach and exceed -1oC. As a result, our future simulations (Fig. 1) are sensitive to the timing when substantial quantities of liquid water appear on vulnerable ice shelf surfaces. In our prior work1, RCP8.5 climate forcing used to run future ice sheet simulations produced substantially more melt than indicated by an independent study2, using different regional and global climate models. Here, we compare the updated climate forcing used in this study with those produced by the CMIP5 GCMs used in ref-2 and 22 state-of-the-art CMIP6 GCMs3.\nSurface melt rates produced by the climate models used in this study (Supplementary Figure 1) are only ~25% as high as those in our previous modeling1, but they remain somewhat higher (especially around the East Antarctic Margin) than those calculated by the empirical temperature- melt relationship used ref.-2. These differences are mainly due to atmospheric temperatures in our model being corrected to account for a cold bias of ~2.9 oC in low elevations over ice surfaces relative to observations4. Similar cold biases of ~2.3 and ~2.4 oC, caused by a deficit of net longwave radiation, are found in the RACMO2 RCM forced by ERA-Interim reanalysis5 and the CESM GCM6. Given the exponential relationship between melt and summer mean (DJF) surface temperature2, our bias-corrected temperatures increase our future melt rates relative to those using uncorrected climate model temperatures, or those using RACMO2 as the bias-correction benchmark2.\nAdditional relatively minor departures from ref-2 are caused by different approaches used to calculate total surface melt from air temperatures. Here, melt rates are calculated by a box model7, using positive degree days for snow and ice melt with standard coefficients8, and accounting for partial refreezing of meltwater1. In our ice sheet model, total surface melt available to influence surface crevassing (Supplementary Figure 1) is the fraction of meltwater not refrozen in the near- surface, plus any rainwater. Under RCP8.5, rainwater in our calculations adds ~10% to total meltwater production in areas of high melt at the end of the 21st century.\nSupplementary Figure 1: Comparison of surface melt and rainwater production rates. Surface water production rates (rain plus meltwater not refrozen in the near surface, m yr-1) in the last decade of the 21st century under RCP8.5 emissions calculated by the surface mass balance scheme in our ice sheet model. a-f, Melt rates from six global climate models (GCMs)9-13 used in a previous assessment2 are compared with the climate models used in this study (g-i). g-i, Surface melt and rainwater rates produced by the regional climate model (RCM) and GCM used in this study. Spatial patterns differ among the climate models. There is more melt water produced on the Ross and Filchner-Ronne ice shelves in the RCM relative to the other models, but the RCM shows less warming over the Amundsen Sea and most of the East Antarctic margin. The two CESM1.2.2 simulations either ignore (h) or include (i) meltwater (freshwater and iceberg discharge) feedbacks between the GCM and ice sheet model (Fig. 1f). As discussed in the main text, the smaller melt rates in i are the result of a strong negative atmospheric warming feedback caused by sea ice expansion when ice sheet discharge is accounted for in the GCM14. The blue to yellow transition in the color bar (750 mm yr-1) is the approximate meltwater production rate preceding the breakup of the Larsen B ice shelf in 20022. Melt and rainwater required to break up thick (>600 m) ice shelves in our hydrofracturing model is closer to 1,400 mm yr-1.\nHere, we compare the timing of future summer warming over four regions of the Antarctic margin (Supplementary Figure 2) simulated by the RCM used to force our main ice sheet model ensembles under RCP8.5 (Fig. 1g,h) relative to ERA5 reanalysis15, five CMIP5 climate models following RCP8.5 used in a previous assessment of future surface melt trajectories2, and 22 CMIP6 GCMs3 following SSP5-8516. The regions include three major buttressing ice shelves (Larsen, Ross, Filcher-Ronne), and the Amundsen Sea, where weakly buttressed outlet glaciers, including Thwaites Glacier, are currently thinning and retreating17. The CMIP6 models sampled here include ACCESS-CM2, ACCESS-ESM1-5, BCC-CSM2-MR, CAMS-CSM1-0, CanESM5, CESM2, CESM2-WACCM, EC-Earth3, EC-Earth3-Veg, FGOALS-f3-L, FIO-ESM-2-0, GFDL-CM4, GFDL-ESM4, INM-CM4-8, INM-CM5-0, IPSL-CM6A-LR, MIROC6, MPI-ESM1-2-HR, MPI- ESM1-2-LR, MRI-ESM2-0, NESM3, NorESM2-LM. This comparison places the climate forcing used in our ice sheet simulations within the context of other state-of-the-art climate models, including a variant of CESM (CESM1.2.2-CAM5) used to test the importance of climate-ice sheet feedbacks in Figure 1h. We focus on the summer melt season, because of its connection to ice- shelf breakup.", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "a9cea5dae349-11", "text": "Here, we compare the timing of future summer warming over four regions of the Antarctic margin (Supplementary Figure 2) simulated by the RCM used to force our main ice sheet model ensembles under RCP8.5 (Fig. 1g,h) relative to ERA5 reanalysis15, five CMIP5 climate models following RCP8.5 used in a previous assessment of future surface melt trajectories2, and 22 CMIP6 GCMs3 following SSP5-8516. The regions include three major buttressing ice shelves (Larsen, Ross, Filcher-Ronne), and the Amundsen Sea, where weakly buttressed outlet glaciers, including Thwaites Glacier, are currently thinning and retreating17. The CMIP6 models sampled here include ACCESS-CM2, ACCESS-ESM1-5, BCC-CSM2-MR, CAMS-CSM1-0, CanESM5, CESM2, CESM2-WACCM, EC-Earth3, EC-Earth3-Veg, FGOALS-f3-L, FIO-ESM-2-0, GFDL-CM4, GFDL-ESM4, INM-CM4-8, INM-CM5-0, IPSL-CM6A-LR, MIROC6, MPI-ESM1-2-HR, MPI- ESM1-2-LR, MRI-ESM2-0, NESM3, NorESM2-LM. This comparison places the climate forcing used in our ice sheet simulations within the context of other state-of-the-art climate models, including a variant of CESM (CESM1.2.2-CAM5) used to test the importance of climate-ice sheet feedbacks in Figure 1h. We focus on the summer melt season, because of its connection to ice- shelf breakup.\nThe evolution of atmospheric warming in the RCM used in our main ensembles (using CCSM4 ocean boundary conditions) is comparable to the subset of CMIP5 GCMs2. When global mean temperatures reach +1.5 oC, +2.0 oC, and +3.0 oC, warming averaged over Antarctica is slightly lagged, reaching +1.48, oC, +1.50 oC, and +1.82 oC, respectively. Both the RCM and CESM1.2.2 used in our study are considerably colder than ERA5 and most CMIP6 GCMs over the main ice shelves. Summer temperatures over the sensitive Larsen and Amundsen Sea regions approach the threshold for producing extensive rain and surface meltwater faster in almost all of the CMIP6 GCMs than either the RCM or CESM1.2.2 (Supplementary Figure 2a-b).\nBias correcting the summer temperatures (TDJF) in the climate models relative to the 40-year average of summer temperatures in ERA5 (\ud835\udc47 (\ud835\udc61) = \ud835\udc47 (\ud835\udc61) \u2212 \ud835\udc47 + \ud835\udc47 ), substantially reduces the range of simulated temperatures among the climate models, especially in the late 20th and early 21st centuries (Supplementary Figure 2e-h). However, we note that the range of bias-corrected temperatures among the models still expands markedly toward the end of the 21st century. Because of the strong cold bias around the periphery of Antarctica in CESM relative to both observations6 and ERA5 (red vs. orange lines in Supplementary Figure 2), corrected temperatures in CESM (Supplementary Figure 2e-h) show more warming in 2100 than the median of the bias-corrected CMIP6 GCMs.\nClearly the wide range of warming rates simulated by these climate models, particularly among CMIP6 GCMs, represents considerable uncertainty in the timing when surface meltwater production and ice shelf loss might begin in the future. The quantified impact of this climatic uncertainty on our ice sheet projections should be explored in future work.\nSupplementary Figure 2: Future atmospheric warming over Antarctic ice shelves. Summer (DJF) surface (2- meter) air temperature (oC) simulated by five CMIP5 and 22 CMIP6 global climate models (GCMs) over the period 1940-2100. CMIP5 models follow RCP8.5 emissions and CMIP6 models follow SSP5-85. GCM temperatures (averaged over 10-year intervals) are compared with ERA5 reanalysis (orange line), the RCM (RCP8.5) used in our main ensembles (blue crosses) and CESM1.2.2 (RCP8.5; red dashed line) used in ice sheet simulations shown in Figure 1h. The inset shows the model domains corresponding to the Larsen, Ross, and Filchner-Ronne ice shelves, and the Amundsen Sea sector of West Antarctica. a-d, Uncorrected, raw model temperatures averaged over the individual model domains. e-h, Bias corrected temperatures using ERA5. Blue crosses show the RCM temperatures at specific times (1950, 2000, and when effective atmospheric CO2 reaches 2 and 4 times preindustrial levels).\nIce shelf hydrofracturing in compressional flow regimes\uf0c1\nIt is conceivable that in regions of compressional ice-shelf flow, liquid water flowing on the surface might tend to reach the margins and run off, instead of penetrating into crevasses and causing hydrofracture. This potential influence of compressional ice flow on hydrofracturing is tested by modifying the model\u2019s wet crevassing (hydrofracturing) scheme (see Methods). In this case, the total meltwater production rate R is reduced by \u00d70.1 as a function of the local ice convergence rate (yr-1) at convergences >0.01, ramping to \u00d71 where convergence is zero.\nWe find that reducing wet crevasse penetration in regions of convergent flow has little influence on our continental-scale results (Supplementary Figure 3). In climate scenarios with minimal surface melt (RCP2.6), Antarctic ice loss is dominated by WAIS retreat in response to ocean- driven thinning of ice shelves and the associated reduction in buttressing. In such instances, the influence of hydrofracturing is minimal and modifications to our wet crevassing scheme are inconsequential. Under more extreme future warming scenarios (RCP8.5), shelf loss is largely driven by massive meltwater production and the sudden onset of widespread meltwater-enhanced calving (hydrofracturing). In the model, this hydrofracturing begins near the calving fronts where the ice is thinnest, convergence and buttressing are minimal18, and air temperatures (melt rates) are highest. Once initiated, meltwater-induced calving reduces convergence and compressional flow in the ice upstream and the meltwater enhanced calving propagates, resulting in the complete loss of major ice shelves, despite the reduction of \ud835\udc514 in convergent flow regimes. Extending these results with a more sophisticated, physically based, time-dependent19 hydrofracturing scheme is the subject of ongoing work. However, these results combined with the relatively high melt rates required to trigger destruction of ice shelves like the Larsen B, add confidence that the model formulation used in our main ensembles is reasonable.\nSupplementary Figure 3: Global mean sea level contributions from Antarctica with a modified hydrofracturing scheme. Simulations follow two future greenhouse gas emissions scenarios, using our nominal model formulation of hydrofracturing used throughout the main text (solid lines), compared with an alternative formulation reducing meltwater influence on crevasse penetration in convergent (compressive) flow regimes (dashed lines).\nReformulation of buttressing at grounding lines\uf0c1\nThe hybrid ice sheet model used here heuristically blends vertically integrated shallow ice/shallow shelf approximations (SIA/SSA)20, with the seaward ice flux at grounding lines imposed as a boundary condition according to an analytical expression relating ice flux to ice thickness21. This expression includes a term \u03b8 representing buttressing by ice shelves, i.e., the amount of back stress caused by pinning points or lateral forces on the ice shelf further downstream. The buttressing factor \u03b8 is defined as the ratio of vertically averaged horizontal deviatoric stress normal to the grounding line, relative to its value if the ice shelf was freely floating with no back stress.\nThe analysis for grounding-line flux and buttressing in ref.6 is limited to one-dimensional flowline geometry. In our standard model20, the expression is applied across individual one-grid-cell-wide segments separating pairs of grounded and floating grid cells, so that the orientation of each single- cell \u201cgrounding-line\u201d segment is parallel to either the x or the y axis. Although this is consistent with the one-dimensional character of the formulation in ref.21, it neglects the actual orientation of the real, slightly wider-scale grounding line, and results in non-isotropic \u03b8 values for u and v staggered-grid velocities.", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "a9cea5dae349-12", "text": "Supplementary Figure 3: Global mean sea level contributions from Antarctica with a modified hydrofracturing scheme. Simulations follow two future greenhouse gas emissions scenarios, using our nominal model formulation of hydrofracturing used throughout the main text (solid lines), compared with an alternative formulation reducing meltwater influence on crevasse penetration in convergent (compressive) flow regimes (dashed lines).\nReformulation of buttressing at grounding lines\uf0c1\nThe hybrid ice sheet model used here heuristically blends vertically integrated shallow ice/shallow shelf approximations (SIA/SSA)20, with the seaward ice flux at grounding lines imposed as a boundary condition according to an analytical expression relating ice flux to ice thickness21. This expression includes a term \u03b8 representing buttressing by ice shelves, i.e., the amount of back stress caused by pinning points or lateral forces on the ice shelf further downstream. The buttressing factor \u03b8 is defined as the ratio of vertically averaged horizontal deviatoric stress normal to the grounding line, relative to its value if the ice shelf was freely floating with no back stress.\nThe analysis for grounding-line flux and buttressing in ref.6 is limited to one-dimensional flowline geometry. In our standard model20, the expression is applied across individual one-grid-cell-wide segments separating pairs of grounded and floating grid cells, so that the orientation of each single- cell \u201cgrounding-line\u201d segment is parallel to either the x or the y axis. Although this is consistent with the one-dimensional character of the formulation in ref.21, it neglects the actual orientation of the real, slightly wider-scale grounding line, and results in non-isotropic \u03b8 values for u and v staggered-grid velocities.\nAlternatively, a more rigorous, isotropic, treatment of \ud835\udf03 can been implemented, by applying the expression in ref.21 to normal flow across a more realistic grounding-line orientation not constrained to one or the other grid axes, following equations 2 and 6 in ref.22 The alternative model treatments of \ud835\udf03 are represented schematically by insets in Supplementary Figure 4a,b. We find that the new treatment of \ud835\udf03 substantially improves the model\u2019s performance23 in the idealized, relatively narrow fjord-like setting of the Marine Ice Sheet Model Intercomparison Project+ (MISMIP+)24, with regards to the transient pace of grounding line retreat and re-advance when compared with models using higher order or full-stokes treatments of englacial stresses. Our new results fall well within the envelope of the multi-model range in the MISMIP+ intercomparison24 (Supplementary Figure 4a,b). In contrast, at the continental scale the new, more rigorous treatment of \ud835\udf03 has a very small effect on the pace of retreat (Supplementary Figure 4c,d), presumably because the dynamics of wide, major Antarctic outlets are adequately represented with the 1-dimensional formulation. The new treatment and further results are described in detail in ref.23.\nSupplementary Figure 4: Effect of reformulated buttressing. a, Time-evolving, mid-channel grounding line position in Experiment Ice1 of the MISMIP+ model intercomparison23, in an idealized, narrow fjord-like setting with reverse-sloped bedrock and channel width of 80 km (modified from Fig. 8b of ref.24). Blue and yellow colors show the response to oceanic basal melt rates applied at time 0, and red colors show the recovery after the basal melt rates are re-zeroed at year 100. Circles and squares show results of our standard model using the old \u03b8 method, with model resolution of 1 km and 10 km respectively. Shaded regions and solid lines show the envelope and mean of multiple other models in the MISMIP+ intercomparison (those using a similar Weertman-type basal sliding scheme). Our standard model retreats faster than other models in the intercomparison. b, Results with our model using the new, more rigorous \u03b8 method described above and 2-km model resolution. This substantially improves model performance relative to the other MISMIP+ models shown in a. Schematic diagrams representing the old versus new \u03b8 methods are shown at the bottom left of a and b, with the model grid represented by the thin black lines, arrows showing ice velocities across the grounding line, and the \u201cactual\u201d grounding line in the new method shown in grey. c and d, Continental-scale Antarctic simulations under RCP8.5 forcing, showing equivalent global mean sea level rise versus time corresponding to net Antarctic ice loss, without ice-cliff calving in c, and with ice-cliff calving in d. Unlike the idealized confined-fjord setting in a and b, these continental-scale Antarctic simulations show only small differences in net ice loss using the old vs. new \u03b8 methods. Without ice-cliff calving in c, the model using the new \u03b8 method (red curve) yields slightly faster ice loss after ~2300, but the differences are small and not important for the purposes of this paper. With ice-cliff calving in d, faster ice loss overwhelms any differences due to the \u03b8 method. The standard \u03b8 method (blue curves) is used in our main ensembles.\nStatistical emulation of model ensembles\uf0c1\nHere, we demonstrate the statistical robustness of the sea level estimates made with the ensembles presented in the main text. While the parameter sampling used in the ensembles is more dense than in our previous work2, many parameter values intermediate to the training set (Table 1) have not been tested, and the sea level projections are not fully probabilistic (i.e. intermediate values are implicitly ascribed zero-probability). To address this, we develop and sample from an Antarctic Ice Sheet model emulator, which is continuous across the prior range of the training data and may be used to generate a much larger ensemble of simulations. We also evaluate the importance of observational (modern and paleo) constraints for limiting emulated probabilistic projections of future sea level rise from Antarctica.\nPhysically based and statistical emulation techniques have been used in several studies of sea level rise and climate change25,26 and specifically to calibrate complex models27,28. Our methodology has similarities to the recent methods of ref.29. We use Gaussian Process (GP) regression30 to construct a statistical emulator designed to mimic the behavior of the numerical ice-sheet model. GP regression is a non-parametric supervised machine learning technique which allows one to map model inputs (e.g., model parameters) to outputs (here, ice volume changes in global-mean sea level equivalent). In contrast to individual deterministic ice-sheet model simulations, GP regression is advantageous because the input parameter space and output prediction space are continuous, with emulation uncertainty inherently estimated for each output. For a set of untested inputs, the corresponding output and its uncertainty can be determined in a fraction of the time it takes to perform a single ice sheet model simulation. A full description and discussion of the emulator and its calibration are provided in a forthcoming manuscript31.\nThe emulator is trained separately on two of the 196-member ensembles described in the main text: the Last Interglacial ensemble and the RCP8.5 scenario. We model the Antarctic ice-sheet contributions to global mean sea level (\ud835\udc53) as the sum of two terms, each with a mean-zero Gaussian process prior:\n\ud835\udc53(\ud835\udf031,\ud835\udf032,\ud835\udc61) = \ud835\udc531(\ud835\udf031,\ud835\udf032) + \ud835\udc532(\ud835\udf031,\ud835\udf032,\ud835\udc61) (S1)\nThe first term represents a parameter-specific intercept, the latter the temporal evolution of the contribution. The priors for each term are specified as:\n\ud835\udc53 (\ud835\udf03 ,\ud835\udf03 )~\ud835\udca2\ud835\udcab(0,\ud835\udefc9\ud835\udc3e (\ud835\udf03 ,\ud835\udf03 ,\ud835\udf03@,\ud835\udf03@ ;l )) (S2)\n\ud835\udc53 (\ud835\udf03 ,\ud835\udf03 ,\ud835\udc61)~\ud835\udca2\ud835\udcab(0,\ud835\udefc9\ud835\udc3e (\ud835\udf03 ,\ud835\udf03 ,\ud835\udf03@,\ud835\udf03@ ;l )\ud835\udc3e (\ud835\udc61,\ud835\udc61@ ;\ud835\udf0f)) (S3)\nand where \ud835\udf037is normalized VMAX, \ud835\udf039 is normalized CREVLIQ, \ud835\udefcE are amplitudes, lE are characteristic length scales in normalized parameter spaces, \u03c4 is the time scale and \ud835\udc3e is a specified correlation function. Because the LIG training data is evaluated at a single time point, there is no temporal term and f2 is excluded in the LIG emulator construction. Each \ud835\udc3eE is defined to be a Mate\u0301rn covariance function with a specified smoothness parameter, \ud835\udefe = 5/2, which governs how responsive the covariance function is to sharp changes in the training data30.\nOptimal hyperparameters (\ud835\udefcE , lE, and \u03c4) of the GP model are found by maximizing the log- likelihood, given the training simulations (Supplementary Table 1). The optimized model can then be conditioned on the training data to predict LIG and RCP8.5 simulation results for parameter values intermediate to those run with the full ice sheet model.", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "a9cea5dae349-13", "text": "\ud835\udc53(\ud835\udf031,\ud835\udf032,\ud835\udc61) = \ud835\udc531(\ud835\udf031,\ud835\udf032) + \ud835\udc532(\ud835\udf031,\ud835\udf032,\ud835\udc61) (S1)\nThe first term represents a parameter-specific intercept, the latter the temporal evolution of the contribution. The priors for each term are specified as:\n\ud835\udc53 (\ud835\udf03 ,\ud835\udf03 )~\ud835\udca2\ud835\udcab(0,\ud835\udefc9\ud835\udc3e (\ud835\udf03 ,\ud835\udf03 ,\ud835\udf03@,\ud835\udf03@ ;l )) (S2)\n\ud835\udc53 (\ud835\udf03 ,\ud835\udf03 ,\ud835\udc61)~\ud835\udca2\ud835\udcab(0,\ud835\udefc9\ud835\udc3e (\ud835\udf03 ,\ud835\udf03 ,\ud835\udf03@,\ud835\udf03@ ;l )\ud835\udc3e (\ud835\udc61,\ud835\udc61@ ;\ud835\udf0f)) (S3)\nand where \ud835\udf037is normalized VMAX, \ud835\udf039 is normalized CREVLIQ, \ud835\udefcE are amplitudes, lE are characteristic length scales in normalized parameter spaces, \u03c4 is the time scale and \ud835\udc3e is a specified correlation function. Because the LIG training data is evaluated at a single time point, there is no temporal term and f2 is excluded in the LIG emulator construction. Each \ud835\udc3eE is defined to be a Mate\u0301rn covariance function with a specified smoothness parameter, \ud835\udefe = 5/2, which governs how responsive the covariance function is to sharp changes in the training data30.\nOptimal hyperparameters (\ud835\udefcE , lE, and \u03c4) of the GP model are found by maximizing the log- likelihood, given the training simulations (Supplementary Table 1). The optimized model can then be conditioned on the training data to predict LIG and RCP8.5 simulation results for parameter values intermediate to those run with the full ice sheet model.\nTaking uniform priors over the input parameters that are consistent with those used by the numerical ice sheet model (i.e., CREVLIQ ~ \ud835\udc48(0,195), VMAX ~ \ud835\udc48(0,13) ) we then apply a Bayesian updating approach to estimate posterior probability distributions for these parameters, conditional upon observational constraints. To do this, we first take 20,000 Latin Hypercube samples from the prior distributions, then weight these based on two different constraints: a uniform LIG distribution, \ud835\udc48(3.1 m, 6.1 m), and a uniform distribution of IMBIE32 trends, \ud835\udc48(0.15 mm yrS7, 0.46 mm yrS7), over 1992-2017. As in the main text, the LIG constraint is based on the maximum Antarctic ice loss between 129 ka and 128 ka, equivalent to the ice loss at 128 ka. The results are posterior probabilities of CREVLIQ/VMAX pairs for each given constraint.\nThese posteriors of CREVLIQ/VMAX are then used to estimate the posterior distributions of AIS sea-level contributions over time. The 5th, 50th, and 95th percentiles of these posterior distributions (in 2100 under RCP8.5) with no constraints, IMBIE constraints only, LIG constraints only, and combined IMBIE and LIG constraints are presented in Supplementary Table 2. The probability distribution over time from 20,000 samples of the combined (IMBIE and LIG) constrained emulator is shown in Supplementary Figure 5b. In Supplementary Figure 6 we show the emulated probability distributions in 2100, subject to each constraint and compared to a histogram of the training set.\nWe note that the emulation results provided here are not directly comparable to the calibrated ensembles in the main text, because those ensembles add a third training constraint based on Pliocene sea level. Rather, these results are intended to complement the main paper by comparing projections that ignore the Pliocene constraints, and to demonstrate that statistically robust GP emulation compares favorably to the binary scoring approach used in Figure 1.\nEmulated distributions closely resemble that of the 196-member training ensemble, with some notable but minor differences that are ascribable to sampling limitations in the original ensemble (e.g., the conditioned training ensemble has 10 simulations at or below its 5th percentile, whereas the constrained ensemble has 1000). As with the training ensemble, the emulated probability distribution without constraints is positively skewed, with a long upper tail that stretches to 63 cm in the 95th percentile by 2100.\nWe find that the prior distribution (Supplementary Figure 6) is qualitatively similar to the IMBIE- constrained distribution, and likewise the LIG-constrained distribution is similar to the IMBIE+LIG-constrained distribution. These results indicate that the IMBIE uniform distribution is not an adequately restrictive constraint on the emulator, although it does slightly reduce the upper bound of projections in 2100 by ~3 cm, shifting the distribution towards lower sea-level contributions. The IMBIE-constrained emulator is consistent with the conclusions of ref.33 that additional information from the satellite record is of limited utility (because simulated ice-mass losses by the end of the 21st century are only weakly correlated with loss trends at the beginning of the 21st century).\nIn contrast, the uniform LIG constraint is more informative for calibrating emulated future projections of Antarctic sea-level contributions. Samples from parameter sets with CREVLIQ<45 and VMAX<4 fall outside the uniform LIG constraint, and the associated likelihoods are near or actually zero (not shown). Conversely, the VMAX/CREVLIQ parameter pairs above these values have greater (non-zero) likelihoods and the associated samples (which typically have higher RCP8.5 emulated sea-level contributions) are accordingly given more weight in the posterior. The resulting posterior distribution shifts towards the high end of the projections, with median projections in 2100 of 34 cm for the LIG-only constraint and 32 cm for the combined constraint distribution. Furthermore, the LIG-constrained distribution posterior has a narrower range than the prior starting in ~2060 and through 2100 (Supplementary Figure 5), demonstrating that future projections are less uncertain when the LIG constraint is applied.\nImportantly, we find the median of GP emulation results is within 1 cm of the projected GMSL contribution in 2100 when compared to the training ensemble (binary scoring) approach used in the main text (Supplementary Table 2, Extended Data Figure 4). The addition of a third training constraint (Pliocene sea level) in the main text slightly increases the central estimate of Antarctica\u2019s GMSL contribution in 2100 from 32 cm (Supplementary Table 2) to 34 cm (Table 1), by further reducing the likelihood of both low and high VMAX/CREVLIQ parameter values.\nSupplementary Table 1: Optimized hyperparameters of the GP emulator found by maximizing the log- likelihoods, given the training ensembles\nSupplementary Table 2: The median and 5th / 95th percentiles of projected Antarctic ice-sheet contributions to GMSL in 2100 (m)\nSupplementary Figure 5: Emulated global mean sea level contributions from Antarctica. Fan charts of the range around the median (black line) in 10% increments from 20,000 RCP8.5 scenario emulator samples, from a the prior and b the posterior calibrated with combined LIG and IMBIE trend constraints using a Bayesian updating approach.\nSupplementary Figure 6: Probabilistic projections of global mean sea level contributions from Antarctica in 2100 under RCP8.5. Projections from 20,000 emulator samples (lines) weighted by different observational constraints. Shown are the prior distribution with no constraints (black), and distributions under the LIG uniform constraint (red), the IMBIE trend uniform constraint (cyan), and the combined LIG and IMBIE trend constraints (blue). Emulated distributions are shown using a kernel density estimation assumes a Silverman bandwidth divided by 2 (to prevent over-smoothing)34. The training ensemble from the main text is shown as a histogram (light blue) scaled for comparison to the emulated distributions.", "source": "https://sealeveldocs.readthedocs.io/en/latest/deconto21.html"}
{"id": "d3958eec8aeb-0", "text": "Li et al. (2023)\uf0c1\nTitle:\nClimate model differences contribute deep uncertainty in future Antarctic ice loss\nCorresponding author:\nDawei Li\nCitation:\nLi, D., DeConto, R. M., & Pollard, D. (2023). Climate model differences contribute deep uncertainty in future Antarctic ice loss. Science Advances, 9(7), eadd7082. doi: 10.1126/sciadv.add7082\nURL:\nhttps://www.science.org/doi/10.1126/sciadv.add7082\nAbstract\uf0c1\nFuture projections of ice sheets in response to different climate scenarios and their associated contributions to sea level changes are subject to deep uncertainty due to ice sheet instability processes, hampering a proper risk assessment of sea level rise and enaction of mitigation/adaptation strategies. For a systematic evaluation of the uncertainty due to climate model fields used as input to the ice sheet models, we drive a three-dimensional model of the Antarctic Ice Sheet (AIS) with the output from 36 climate models to simulate past and future changes in the AIS. Simulations show that a few climate models result in partial collapse of the West AIS under modeled preindustrial climates, and the spread in future changes in the AIS\u2019s volume is comparable to the structural uncertainty originating from differing ice sheet models. These results highlight the need for improved representations of physical processes important for polar climate in climate models.\nIntroduction\uf0c1\nFluctuations of global mean sea level (GMSL) over the past few million years have been dominated by glacial-interglacial cycles. During the Last Glacial Maximum (21 ka ago), formation of the Laurentide Ice Sheet in North America and the Fennoscandian Ice Sheet in Northern Europe and, to a lesser extent, the expansion of Greenland and Antarctic ice sheets contributed to a \u223c120-m drop in GMSL relative to today (1). GMSL during the interglacials was comparable to, although sometimes higher than, the present-day sea level. In contrast, the Last Interglacial (LIG; 129 to 116 ka ago) was not much warmer than preindustrial (\u22120.4\u00b0 to 1.3\u00b0C) (2), but GMSL was 6 to 9 m higher (3, 4), of which \u223c3.1 to 6.1 m may have been contributed by the Antarctic Ice Sheet (AIS) (2, 5). While the LIG is not a precise analog of future sea level, as Earth\u2019s orbital parameters and polar insolation forcing likely played an important role (6), it still hints at a worrisome potential for future sea level rise (SLR) given the \u223c1.2\u00b0C warming that has already occurred.\nAt a rate of 3.58 mm year\u22121 over the period 2006\u20132015, the rise in GMSL is accelerating and is now dominated by melting of land ice, including glaciers and ice sheets (7). Projections of SLR over the 21st century and beyond have been made for various emission scenarios, but they are subject to substantial uncertainty, which becomes greater in scenarios with higher greenhouse gas emissions and hence more warming. Under the assessment by the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC-AR6), following the high greenhouse gas emission scenario of Shared Socioeconomic Pathway 5-8.5 (SSP5-8.5) (8), SLR is likely to reach 0.63 to 1.01 m by 2100, of which 0.03 to 0.34 m is expected to be contributed by the AIS (9). In contrast, another recent statistical analysis of multimodel ice sheet simulations indicates a smaller future contribution from Antarctica (\u22120.01 to 0.1 m likely range) under similar SSP5-8.5 forcing (10), highlighting ongoing uncertainty.\nAs the largest source of uncertainty of SLR beyond 2100, ice loss from the AIS has evaded robust projections. Much of this uncertainty can be attributed to the diversity of numerical ice sheet models (ISMs), which differ not only in spatial resolution, equations of stress balance, numerical schemes, and initialization methods but also in their treatment of key physical processes including grounding line migration, calving, surface mass balance (SMB), and basal processes. The associated uncertainty in the AIS\u2019s response to climate warming has been explored in a number of model intercomparisons, such as the Ice Sheet Model Intercomparison Project (ISMIP; the most recent phase being ISMIP6) (11\u201316). These projects have provided valuable insights by focusing on the difference in ISMs\u2019 response to prescribed changes in climate boundary conditions. For instance, ISM initialization experiments show good agreement in the AIS\u2019s response to changes in SMB, but a much greater spread in the response to ice shelf basal melt (13). Designed to assess how responses differ across the spectrum of ISMs under a nonexhaustive suite of modeled climates, ISMIP6 drove a variety of ISMs with climate fields from a subset of Coupled Model Intercomparison Project Phase 5 (CMIP5) models. As the succeeding generation CMIP6 model output became available to the climate research community, ISM intercomparison projects would benefit from using a more comprehensive set of climate models to take into account a wider and up-to-date range of intermodel uncertainty.\nIt has been recognized that structural differences between climate models can produce divergent quasi-equilibrium states for the AIS in experiments where ISMs are forced by the output of climate models (17); however, there has been no comprehensive assessment of the uncertainty in projected future states of the AIS using the latest generation climate models. In existing ISM intercomparison projects, decentralized model development gives rise to ISMs across a wide spectrum, while often a small subset of available climate models is included to provide climate boundary conditions. Here, we take a complementary approach to evaluate the uncertainty in projected change of the AIS and its contribution to GMSL by driving a single three-dimensional ISM (18) with climate fields from 36 climate models in the CMIP6 archive. The ISM is fine-tuned so that it closely simulates the observed state of the AIS and rates of ice loss under present-day climate conditions (Experiment OBS_INV) (5). Assuming that the ISM is a \u201cperfect\u201d representation of the real AIS, the spread in ISM output reflects the uncertainty associated with past and future climate changes simulated by these CMIP6 models. Such \u201cperfect model\u201d framework has been widely used in climate research to evaluate model predictability, the performance of bias correction and statistical downscaling, etc. (19, 20)\nA series of ISM experiments under this perfect model framework, as documented in Table 1, were carried out to assess the effect of biases in modeled climate on the AIS\u2019s equilibrium state and the uncertainty in past and future trajectories of the AIS due to divergent climate sensitivities displayed by CMIP6 models. We also provide additional ISM experiments to discuss an ice sheet instability mechanism, the effect of observed multidecadal warming of Antarctic subsurface ocean on the AIS, and an alternative modeling strategy with the ISM calibrated per climate model.\nA series of ISM experiments under this perfect model framework, as documented in Table 1, were carried out to assess the effect of biases in modeled climate on the AIS\u2019s equilibrium state and the uncertainty in past and future trajectories of the AIS due to divergent climate sensitivities displayed by CMIP6 models. We also provide additional ISM experiments to discuss an ice sheet instability mechanism, the effect of observed multidecadal warming of Antarctic subsurface ocean on the AIS, and an alternative modeling strategy with the ISM calibrated per climate model.\nTable 1. List of experiments. BSC, basal sliding coefficient; OMF, ocean melt factor; BC, bias-corrected; MICI, marine ice cliff instability.*PD observation: Present-day (PD) climatological mean (averaged over 1981\u20132010), including monthly surface air temperature and precipitation from ERA5 and annual 400-m ocean temperature from World Ocean Atlas 2018 (WOA18).\u2020PD: PD observed state of the AIS specified in Bedmap2.\u2021PI: Preindustrial climate. However, because not all CMIP6 models used in this study have a PI control run, climate fields averaged over the period 1850\u20131869 of historical runs are used here as approximately preindustrial.\u00a71850\u20132100: Historical (1850\u20132014) and SSP5-8.5 (2015\u20132100) scenarios are combined to provide climate forcings for each year over the period 1850\u20132100.\nResults\uf0c1\nNear-equilibrium AIS under raw CMIP6 climates\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/li23sciadv.html"}
{"id": "d3958eec8aeb-1", "text": "A series of ISM experiments under this perfect model framework, as documented in Table 1, were carried out to assess the effect of biases in modeled climate on the AIS\u2019s equilibrium state and the uncertainty in past and future trajectories of the AIS due to divergent climate sensitivities displayed by CMIP6 models. We also provide additional ISM experiments to discuss an ice sheet instability mechanism, the effect of observed multidecadal warming of Antarctic subsurface ocean on the AIS, and an alternative modeling strategy with the ISM calibrated per climate model.\nA series of ISM experiments under this perfect model framework, as documented in Table 1, were carried out to assess the effect of biases in modeled climate on the AIS\u2019s equilibrium state and the uncertainty in past and future trajectories of the AIS due to divergent climate sensitivities displayed by CMIP6 models. We also provide additional ISM experiments to discuss an ice sheet instability mechanism, the effect of observed multidecadal warming of Antarctic subsurface ocean on the AIS, and an alternative modeling strategy with the ISM calibrated per climate model.\nTable 1. List of experiments. BSC, basal sliding coefficient; OMF, ocean melt factor; BC, bias-corrected; MICI, marine ice cliff instability.*PD observation: Present-day (PD) climatological mean (averaged over 1981\u20132010), including monthly surface air temperature and precipitation from ERA5 and annual 400-m ocean temperature from World Ocean Atlas 2018 (WOA18).\u2020PD: PD observed state of the AIS specified in Bedmap2.\u2021PI: Preindustrial climate. However, because not all CMIP6 models used in this study have a PI control run, climate fields averaged over the period 1850\u20131869 of historical runs are used here as approximately preindustrial.\u00a71850\u20132100: Historical (1850\u20132014) and SSP5-8.5 (2015\u20132100) scenarios are combined to provide climate forcings for each year over the period 1850\u20132100.\nResults\uf0c1\nNear-equilibrium AIS under raw CMIP6 climates\uf0c1\nIn the experiment set CMIP6_RAW_PI_CTL (Table 1 and Methods), we investigate the effect of differing modeled preindustrial climates on the equilibrium state of the AIS. The AIS is initialized from the end state of an inverse simulation (21), which infers the characteristics of the AIS bed required to simulate a realistic AIS under the present-day observational climate (Experiment OBS_INV). Here, \u201cpresent day\u201d refers to the 3-year period 1981\u20132010, within the historical period per the CMIP6 protocol (1850\u20132014); \u201cpreindustrial\u201d is defined as the 20-year period 1850\u20131869, under the assumption that, within the first 20 years, anthropogenic forcings had not changed the climate substantially from its pre-1850 state.\nA comparison of simulated present-day summer [December to February (DJF)] near-surface air temperature (T2m) and 400-m annual ocean potential temperature (\u03b8400m) reveals substantial differences between CMIP6 models (Fig. 1). Deviations of modeled temperatures from observation display distinct spatial heterogeneities. For instance, ACCESS-ESM-1-5 has a warm bias in DJF T2m over the ice sheet but a cold bias over the ocean relative to ERA5 (Fig. 1A). Modeled \u03b8400m can be too warm in one ocean sector but too cold in others (Fig. 1B). In addition to subsurface ocean temperatures, air temperature also strongly affects the stability of ice shelves in summer, when most surface melt occurs under the present-day climate. Rheological properties of the glacial ice are, in contrast, affected mainly by annual mean temperature, because seasonal variations in temperature only penetrate \u223c1 m into the ice, a tiny fraction of the typical thickness of the ice sheet or ice shelves. We find substantial intermodel variation in simulated T2m with a warm bias over the ice shelves as much as 8\u00b0C in some models (Fig. 1A).\nFigure 1: Difference between modeled climate fields and observations. (A) Difference in January surface air temperature between 36 CMIP6 climate models and observations (ERA5). (B) Difference in annual mean 400-m ocean temperature between 36 CMIP6 climate models and observations [World Ocean Atlas 2018 (WOA18)]. Climate fields from CMIP6 models and observations are averaged over the period 1981\u20132010.\uf0c1\nThe difference between simulated annual precipitation and that from ERA5 reanalysis dataset (22) generally shows patterns consistent with surface air temperature biases, with warmer models experiencing greater precipitation and vice versa (see the Supplementary Materials). The difference between modeled and observed subsurface ocean temperature at 400 m is less notable, but it is still substantial, as ice shelf basal melt rates are sensitive to ocean temperatures. Under the parameterization scheme used in the ISM, the basal melt rate has a quadratic dependence on \u03b8400m (see Methods) so even modest intermodel differences can substantially change the basal mass balance of ice shelves with important consequences for the buttressed ice upstream.\nA myriad of quasi-equilibrium states of the AIS are reached in 10,000-year runs forced by 36 CMIP6 models\u2019 preindustrial climates (Fig. 2A). In 17 simulations, near-complete collapse of the West AIS (WAIS) contributes >3 m of the GMSL rise (Fig. 3I). In addition, climate forcing from three models with a strong warm bias produces substantial retreat of the East AIS (EAIS), contributing >15 m of the GMSL rise. Climate models with a cold bias in subsurface temperature \u03b8400m, in contrast, generally drive the ISM toward a quasi-equilibrium state with an expanded ice sheet and seaward advance of grounding lines onto continental shelves (Figs. 2A and 3).\nFigure 2: Simulated ice sheets under CMIP6 preindustrial climates. (A) Ice thickness by the end of the control runs forced by raw preindustrial climates from 36 CMIP6 models (Experiment CMIP6_RAW_PI_CTL). (B) Same as (A) but for simulations forced by bias-corrected CMIP6 preindustrial climates (Experiment CMIP6_BC_PI_CTL).\uf0c1\nFigure 3: Intermodel differences in CMIP6 climates and simulated AIS. Scatter plots show intermodel differences in modeled Antarctic climate and resulting states of the AIS forced by 36 CMIP6 climate models, represented by markers of different shapes and colors. (A to D) DJF near-surface (2-m) air temperature (T2m) (\u00b0C, vertical axes) averaged over ice shelves against Antarctic coastal ocean potential temperature at 400-m (\u00b0C, horizontal axes), (E to H) area of floating ice (10 \u00d7 106 km2, vertical axes) against area of grounded ice (106 km2, horizontal axes), and (I to L) contributions to GMSL change from the West AIS (WAIS) (m, vertical axes) against the East AIS (EAIS) (m, horizontal axes). (A) and (B) shows the raw (uncorrected) and bias-corrected preindustrial climates, respectively; (C) and (D) show the changes relative to the 1850\u20131869 period by year 2020 and 2100. Similarly, (E) and (F) and (I) and (J) show ISM results forced by the raw and bias-corrected climates, respectively; (G) and (H) and (K) and (L) show ice sheet changes from the initial preindustrial state at 2020 and 2100, respectively, forced by bias-corrected climates (Experiment CMIP6_BC_1850-2100). Gray squares show 16 to 84 percentile range of intermodel spread.\uf0c1\nThese ISM control experiments highlight the room for improvement in CMIP6 models\u2019 performance in the Antarctic region. The simulations also corroborate the established wisdom that the WAIS is especially sensitive to ocean temperatures: For example, the climate model NESM3 has a mean circum-Antarctic warm bias of 1.5\u00b0C in \u03b8400m (Fig. 3A), but this is sufficient to drive a partial collapse of the WAIS in the ISM on long time scales (Fig. 3I).", "source": "https://sealeveldocs.readthedocs.io/en/latest/li23sciadv.html"}
{"id": "d3958eec8aeb-2", "text": "Figure 3: Intermodel differences in CMIP6 climates and simulated AIS. Scatter plots show intermodel differences in modeled Antarctic climate and resulting states of the AIS forced by 36 CMIP6 climate models, represented by markers of different shapes and colors. (A to D) DJF near-surface (2-m) air temperature (T2m) (\u00b0C, vertical axes) averaged over ice shelves against Antarctic coastal ocean potential temperature at 400-m (\u00b0C, horizontal axes), (E to H) area of floating ice (10 \u00d7 106 km2, vertical axes) against area of grounded ice (106 km2, horizontal axes), and (I to L) contributions to GMSL change from the West AIS (WAIS) (m, vertical axes) against the East AIS (EAIS) (m, horizontal axes). (A) and (B) shows the raw (uncorrected) and bias-corrected preindustrial climates, respectively; (C) and (D) show the changes relative to the 1850\u20131869 period by year 2020 and 2100. Similarly, (E) and (F) and (I) and (J) show ISM results forced by the raw and bias-corrected climates, respectively; (G) and (H) and (K) and (L) show ice sheet changes from the initial preindustrial state at 2020 and 2100, respectively, forced by bias-corrected climates (Experiment CMIP6_BC_1850-2100). Gray squares show 16 to 84 percentile range of intermodel spread.\uf0c1\nThese ISM control experiments highlight the room for improvement in CMIP6 models\u2019 performance in the Antarctic region. The simulations also corroborate the established wisdom that the WAIS is especially sensitive to ocean temperatures: For example, the climate model NESM3 has a mean circum-Antarctic warm bias of 1.5\u00b0C in \u03b8400m (Fig. 3A), but this is sufficient to drive a partial collapse of the WAIS in the ISM on long time scales (Fig. 3I).\nDespite that unrealistic AIS geometries were simulated by under many CMIP6-modeled climates, these experiments are not designed for evaluating CMIP6 climate models\u2019 performance over Antarctica. Here, we have regarded reanalysis datasets as the \u201cobservational truth,\u201d serving as a reference climate for calibrating the ISM model parameters, including the ocean melt rate coefficient and the basal sliding coefficients (BSCs). Because of the scarcity of observations available for Antarctica, reanalysis datasets may have substantial departures from the true climate state in some regions. These control experiments are run for 10,000 years, allowing the AIS to reach a quasi-equilibrium, but it is not clear how close the AIS was to such a state before the dawn of the Industrial Revolution, when anthropogenic climate forcing started to emerge. Furthermore, Earth\u2019s orbital parameters drift substantially over 10,000 years, and the AIS is expected to respond accordingly. The availability of CMIP6 historical simulations, dating back to only 1850, makes the quasi-equilibrium assumption necessary for conducting an intercomparison of the AIS forced by different climate models, but the intrinsic uncertainty in the AIS\u2019s natural variability cautions against judging these climate models based on their respective ISM simulations.\nNear-equilibrium AIS under bias-corrected CMIP6 climates\uf0c1\nThe diverse polar climates simulated by CMIP6 models render the above approach unsuitable for assessing the uncertainty in the AIS\u2019s future trajectory. An alternative strategy is to bias-correct CMIP6 climates against present-day observations. Spatially varying biases in CMIP6 monthly climate fields are calculated and subtracted from the raw model output (Methods). In this approach, we essentially remove CMIP6 models\u2019 biases in present-day climates and focus on their changes from the reference period. However, because of CMIP6 models\u2019 differing sensitivities to anthropogenic forcings, bias-corrected preindustrial climates for Antarctica still display significant intermodel variations, showing a large intermodel spread in preindustrial T2m and \u03b8400m. Mean DJF T2m over ice shelves is up to 4.5 K lower than the present-day reference period. Simulated preindustrial annual mean \u03b8400m averaged along the Antarctic coast is up to 1 K lower than present-day (Fig. 3B). Note that warming proceeds at a faster pace in the atmosphere than the subsurface ocean, underscoring complex processes at play in the Southern Ocean, where vigorous convection and upwelling around Antarctica may suppress the pace of warming (23).\nIn the experiment set CMIP6_BC_PI_CTL, the ISM is initiated from the present-day AIS and runs for 15,000 years until it reaches a quasi-equilibrium but forced with CMIP6 bias-corrected preindustrial climates. Compared with the initial state, the modeled preindustrial AIS in quasi-equilibrium generally shows thinning of the EAIS, consistent with reduced snowfall in a colder preindustrial climate. Under most CMIP6 models, ice shelves around the AIS expand, which is also consistent with lower preindustrial ocean temperatures. Intermodel differences in ice volume of the EAIS and the WAIS are 0.6- and 1.2-m sea level equivalent (SLE), respectively (Fig. 3I).\nProjected changes in Antarctic climate and the AIS\uf0c1\nUnder the SSP5-8.5 scenario, all CMIP6 models included in this study show substantial warming relative to preindustrial in both T2m and \u03b8400m over this century (Figs. 3D and 4). DJF T2m averaged over all Antarctic ice shelf surfaces increases by 0.3 to 2.6 K in 2020 and by 1 to 10 K in 2100; \u03b8400m averaged along the Antarctic coast increases by \u22120.1 to 0.5 K in 2020 and up to 1.6 K in 2100 (Fig. 3, C and D). The amplitude of warming in climate models reveals dependence on the state of simulated reference climate. For instance, CAMS-CSM1-0 and MIROC6 are among the models with the greatest warm bias in T2m (Figs. 1A and 3A), but they also show the least warming (<2 K) by 2100. One of the contributing factors might be that, in preindustrial climates, these models are mostly free of austral summer sea ice, reducing the strength of sea ice-albedo feedback in future warming scenarios.\nFigure 4: Simulated changes in ice thickness since 1850. (A) Changes in ice thickness since 1850 by year 2020 in simulations transiently forced by bias-corrected historical + SSP5-8.5 climates from 36 CMIP6 models (Experiment CMIP6_BC_1850\u20132100). (B) Same as (A) but for year 2100.\uf0c1\nExperiment set CMIP6_BC_1850-2100 are 250-year ISM runs under transient bias-corrected CMIP6 climates in combined historical (1850\u20132014) and SSP5-8.5 (2015\u20132100) scenarios, with the ice sheet initiated from the respective 15,000-year control simulation under the bias-corrected preindustrial climate described previously (Experiment CMIP6_BC_PI_CTL). Climate fields are bias-corrected and drive the ISM year by year, so that an evolution of the AIS is obtained for each CMIP6 model. In this approach, we essentially remove each CMIP6 model\u2019s bias in simulated present-day climate and focus on the course of simulated climate change and associated impact on the AIS, especially on the uncertainty in the AIS\u2019s future projections.\nProjected changes in the Antarctic climate from all CMIP6 models drive a reduction in both AIS volume and the extent of ice shelves (Figs. 3 and 5). The magnitude of ice loss, however, shows a large intermodel spread. CIESM shows the largest warming in atmospheric and oceanic temperatures and drives the most intense Antarctic ice loss. CESM2, CESM2-WACCM, and CNRM-CM6-1 are among the models with the largest warming in T2m by 2100 (Fig. 3C); they also drive some of the largest reductions in ice volume. Counterintuitively, the four variants of EC-Earth3 show greater oceanic warming, but they produce much less 21st century ice loss (Fig. 3, D and H). In the previous three models, ice surface melting and the loss of ice shelves overshadow sub-ice melting due to oceanic warming, which has been the focus of most recent studies on the sensitivity of the AIS, especially its marine-based WAIS portion (24). Climate models with the strongest atmospheric warming also produce the largest WAIS retreat, raising the GMSL by >0.25 m by 2100 (Fig. 3L). A contributing factor for this emerging correlation may be that the ISM used in this study resolves hydrofracturing and ice cliff failure processes, which make the ice shelves prone to collapse triggered by surface melting and thus increase the ISM\u2019s sensitivity to atmospheric warming.", "source": "https://sealeveldocs.readthedocs.io/en/latest/li23sciadv.html"}
{"id": "d3958eec8aeb-3", "text": "Experiment set CMIP6_BC_1850-2100 are 250-year ISM runs under transient bias-corrected CMIP6 climates in combined historical (1850\u20132014) and SSP5-8.5 (2015\u20132100) scenarios, with the ice sheet initiated from the respective 15,000-year control simulation under the bias-corrected preindustrial climate described previously (Experiment CMIP6_BC_PI_CTL). Climate fields are bias-corrected and drive the ISM year by year, so that an evolution of the AIS is obtained for each CMIP6 model. In this approach, we essentially remove each CMIP6 model\u2019s bias in simulated present-day climate and focus on the course of simulated climate change and associated impact on the AIS, especially on the uncertainty in the AIS\u2019s future projections.\nProjected changes in the Antarctic climate from all CMIP6 models drive a reduction in both AIS volume and the extent of ice shelves (Figs. 3 and 5). The magnitude of ice loss, however, shows a large intermodel spread. CIESM shows the largest warming in atmospheric and oceanic temperatures and drives the most intense Antarctic ice loss. CESM2, CESM2-WACCM, and CNRM-CM6-1 are among the models with the largest warming in T2m by 2100 (Fig. 3C); they also drive some of the largest reductions in ice volume. Counterintuitively, the four variants of EC-Earth3 show greater oceanic warming, but they produce much less 21st century ice loss (Fig. 3, D and H). In the previous three models, ice surface melting and the loss of ice shelves overshadow sub-ice melting due to oceanic warming, which has been the focus of most recent studies on the sensitivity of the AIS, especially its marine-based WAIS portion (24). Climate models with the strongest atmospheric warming also produce the largest WAIS retreat, raising the GMSL by >0.25 m by 2100 (Fig. 3L). A contributing factor for this emerging correlation may be that the ISM used in this study resolves hydrofracturing and ice cliff failure processes, which make the ice shelves prone to collapse triggered by surface melting and thus increase the ISM\u2019s sensitivity to atmospheric warming.\nFigure 5: Simulated changes in the AIS\u2019s area and sea level contribution. Top panels show changes in ice area relative to the preindustrial, where black, blue, and red lines represent all, grounded, and floating (shelf) ice, respectively. Bottom panels show changes in the AIS\u2019s contribution to GMSL rise, where black, blue, and red lines are for the whole AIS, the EAIS, and the WAIS, respectively. Results from experiments with marine ice cliff instability (MICI) processes and forced with bias-corrected CMIP6 model climate (Experiment CMIP6_BC_1850-2100) are shown in the left column. Middle column shows results from experiments with MICI processes but forced with raw CMIP6 model climate, while the ISM is tuned separately for each CMIP6 model (Experiment CMIP6_RAW_1850-2100) (see Methods and figs. S13 to S16). Right column is for experiments forced with bias-corrected CMIP6 model climate, while MICI-related processes are turned off (Experiment CMIP6_BC_1850-2100_NO_MICI). In each panel, the full spread (0 to 100th percentile) in 36 simulations is shaded in light gray, and 16th to 84th percentile are in darker gray. The full spread and 16th to 84th percentile of respective variables for grounded ice/EAIS and floating ice/WAIS at 2100 are shown as blue and red boxplots, respectively, to the right of each panel.\uf0c1\nThese 250-year AIS simulations using bias-corrected climates from 36 CMIP6 models reveal both accelerating retreat of the AIS and increasing uncertainty in its future trajectory. Relative to its preindustrial state, the multimodel median rate of ice loss increases by almost an order of magnitude from 2020 to 2100 (Fig. 3, G and H). EAIS and WAIS display contrasting changes over the early stage of warming before 2020: The WAIS loses mass and contributes to a SLR under all CMIP6 models\u2019 bias-corrected climate trajectories, while, under most CMIP6 models (27 of 36), the EAIS gains mass and draws down GMSL (Fig. 3K). Between 1850 and 2020, the EAIS produces a small negative (~\u22120.01 m) multimodel median contribution to GMSL rise, while reduction in the WAIS is more consistent across models. As the 21st century warming proceeds, the EAIS is expected to reverse its trend later and begin to lose mass (Fig. 5C). By 2100, the multimodel median reduction in ice area increases to 6 \u00d7 105 km2, and the multimodel median sea level contribution of the AIS approaches 0.3 m (Fig. 5), with the highest modeled SLR exceeding 1 m. The full range of the AIS\u2019s sea level contribution by 2100 greatly exceeds its multimodel median value as a result of the strong nonlinearity in the ice sheet\u2019s response to temperature change. While the CMIP multimodel mean/median has been shown to produce an accurate representation of modern climate state, and multimodel median sea level projections remain more policy relevant than end-members, we should beware of the existence of low-probability, high-consequence scenarios in future SLR.\nDiscussion\uf0c1\nEffect of MICI on projected ice loss\uf0c1\nThe projected MMM rise in GMSL contributed by the AIS and associated uncertainty in these CMIP6-driven ISM simulations is noticeably greater than those assessed by ISMIP6 (15) and IPCC-AR6 (9). A possible factor might be the \u201cmarine ice cliff instability\u201d (MICI) mechanism, which is accounted for in our ISM but has not been widely implemented in other ISMs. The ISM used in this study includes optional hydrofracturing and ice cliff failure mechanisms (25), which may give rise to MICI (5, 26, 27) under strong future warming scenarios but not in preindustrial and present-day climate conditions. MICI is a newly proposed mechanism, and there have been ongoing discussions concerning its validity. Self-sustaining ice loss triggered by MICI has been proposed to be necessary for explaining the Antarctic contribution to sea level high stands during the LIG and the Pliocene (5, 28) as well as the ice berg keel marks formed in deep water during the last deglaciation in the Amundsen Sea Embayment (29). On the other hand, some suggest that MICI is not well constrained and is not required to explain past sea level high stands (30), it may be mitigated by slow removal of ice shelves (31), and the progress of instability may be slowed by ice-m\u00e9lange buttressing. Recent advances in modeling ice cliff failure reveal that MICI remains a feasible mechanism, but glacier models have shown a higher degree of complexity (32, 33) compared to the parameterization scheme originally implemented in our ISM.\nAlthough key parameters for hydrofracturing and cliff failure have been updated and constrained by sea level proxy data and observational records (5), considering their associated uncertainty, we also carried out alternative experiments without MICI processes (Exp. CMIP6_BC_1850-2100_NO_MICI). Without MICI, the ISM runs show smaller sea level contributions from the AIS by 2100, ranging from \u22120.05 to 0.2 m, with a median of 0.02 m, more in line with the findings of a recent study using statistical emulators of ISMs (10). In the absence of hydrofracturing and ice cliff failure, the warming in near-surface air temperature increases surface melt but does not trigger widespread collapse of ice shelves, and any tall ice cliffs that do emerge where ice shelves are lost remain intact in the model. Ignoring hydrofracturing and ice cliff failure processes puts our model in the lower range among ISMs in terms of its sensitivity to climate warming, so in these simulations without MICI, the resulting uncertainty in future sea level change reflects the combination of widely differing CMIP6 climate fields and a low-sensitivity ISM. However, even without MICI-related processes, the full range of climate-driven sea level uncertainty contributed by the AIS still amounts to 0.25 m by 2100, exceeding uncertainties from other major contributors, including sea water thermal expansion, mountain glaciers, and the Greenland Ice Sheet (7).\nImplications on observed ice sheet changes in recent decades\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/li23sciadv.html"}
{"id": "d3958eec8aeb-4", "text": "Although key parameters for hydrofracturing and cliff failure have been updated and constrained by sea level proxy data and observational records (5), considering their associated uncertainty, we also carried out alternative experiments without MICI processes (Exp. CMIP6_BC_1850-2100_NO_MICI). Without MICI, the ISM runs show smaller sea level contributions from the AIS by 2100, ranging from \u22120.05 to 0.2 m, with a median of 0.02 m, more in line with the findings of a recent study using statistical emulators of ISMs (10). In the absence of hydrofracturing and ice cliff failure, the warming in near-surface air temperature increases surface melt but does not trigger widespread collapse of ice shelves, and any tall ice cliffs that do emerge where ice shelves are lost remain intact in the model. Ignoring hydrofracturing and ice cliff failure processes puts our model in the lower range among ISMs in terms of its sensitivity to climate warming, so in these simulations without MICI, the resulting uncertainty in future sea level change reflects the combination of widely differing CMIP6 climate fields and a low-sensitivity ISM. However, even without MICI-related processes, the full range of climate-driven sea level uncertainty contributed by the AIS still amounts to 0.25 m by 2100, exceeding uncertainties from other major contributors, including sea water thermal expansion, mountain glaciers, and the Greenland Ice Sheet (7).\nImplications on observed ice sheet changes in recent decades\uf0c1\nCentennial and millennial trends in the AIS are dictated by long-term climate change, natural or anthropogenic, but internal variabilities of the climate system may still be important for multidecadal ice sheet changes, e.g., changes in polar ice sheets observed during the satellite era. Few of the ISM simulations driven by bias-corrected CMIP6 climates (Exp. CMIP6_BC_1850-2100) show an Antarctic contribution to GMSL over 1992\u20132017 consistent with that estimated by the Ice Sheet Mass Balance Intercomparison Exercise (IMBIE) team (34, 35). Forced by the multimodel mean outputs from 36 CMIP6 models, net contribution by the AIS during the IMBIE period 1992\u20132017 is minimal (Fig. 6A).\nFigure 6: Simulated rates of GMSL change. (A) Contributions to the mean rate of change in GMSL during the IMBIE period (1992\u20132017) by the AIS in simulations forced by bias-corrected CMIP6 model climates, where the likely ranges estimated by IMBIE are marked by horizontal blue bars. (B) Same as (A) but for the WAIS. (C) Same as (A) but for the EAIS. (D) Same as (A) but for the late-century period 2081\u20132100 under the SSP5-8.5 scenario. Results from each model are shown in gray bars, and the horizontal dashed lines represent the multimodel mean. Gray bars labeled as \u201cCMIP6\u201d represent an ice sheet simulation forced by the multimodel mean climate fields of 36 models, while hollow blue bars are for a similar simulation but with forcings during 1980\u20132019 replaced by observed fields from ERA5 and WOA18.\uf0c1\nIn another simulation with the same climate forcing, but its 1980\u20132019 segment replaced by observational data (Exp. CMIP6_BC_MMM+OBS), Antarctica\u2019s contribution to GMSL rise is more consistent with the IMBIE assessment, as a result of faster retreat of the WAIS and slower growth of the EAIS. A multidecadal warming trend since the 1970s in the circumpolar deep water (CDW) (fig. S12) (36), a relatively warm water mass circulating around Antarctica, may have enhanced basal melting of West Antarctic ice shelves. The ISM presents rates of ice loss comparable to IMBIE estimates when driven by the observed transient climate (fig. S12). Multimodel mean climate fields are essentially devoid of internal climate variabilities\u2014provided that the number of models is large enough\u2014due to cancellation of random phases from models. The observed multidecadal CDW warming trend, which may be partially caused by internal climate variability, cannot\u2014and should not\u2014be expected to be robustly reproduced in CMIP6 historical simulations, and its absence could be a factor for the generally small 1992\u20132017 trends from ISM simulations forced by CMIP6 models.\nISM intercomparison projects\uf0c1\nA number of modeling studies concerning the uncertainty in future SLR contributed by the AIS have been carried out. The ISMIP6-Antarctica project (15) used ISMs from 13 modeling groups and six CMIP5 climate models. A smaller subset of CMIP6 models, all with an equilibrium climate sensitivity (ECS) near the upper end of climate models, has been used in similar ways to assess the future GMSL contributions by ice sheets under different emission scenarios (16). The work presented here complements the scope of existing ISM intercomparison projects. We have included 36 climate models from the CMIP6 ensemble, which encompass a wider range of ECS and more fully represent the contemporary understanding of the climate system and its future changes. CMIP6 models are known to have an overall higher ECS compared with CMIP5 models, primarily as a result of stronger positive cloud feedbacks from refined cloud schemes (37). Although only one ISM is used in this study, we have provided contrasting simulations with and without MICI processes, differing substantially in the sensitivity to atmospheric warming.\nUnder the Representative Concentration Pathway (RCP) 8.5 scenario, a radiative forcing scenario similar to its CMIP6 successor SSP5-8.5, ISMIP6 simulations with 13 different ISMs give an Antarctic contribution to GMSL during the period 2015\u20132100 between \u22127.8 and 30 cm (15). In those simulations, WAIS retreat shows great variance among projections, up to 18-cm SLE, while the EAIS mass change varies between \u22126.1- and 8.3-cm SLE. These ISMIP6 projections present less ice loss and associated uncertainty compared with those in our simulations with the MICI mechanism, which is not considered in ISMIP6. Another contributing factor is the higher ECS of CMIP6 models used here, which generally warm more rapidly under SSP5-8.5 compared with CMIP5 models under RCP8.5.\nEffects of ISM calibration per climate model\uf0c1\nResults discussed so far are all from ISM runs in a \u201csingle-ISM\u201d framework, where the ISM is calibrated on the basis of observational data, with its parameters fixed for all CMIP6 climate models. Nonetheless, calibrating an ISM\u2019s parameters so that, under a prescribed climate, it could simulate that a target ice sheet state is a common practice in the ice sheet modeling community, in which ISM parameters may absorb part of the spread in climate boundary conditions. Ice sheet intercomparison projects, e.g., ISMIP6, were carried out in similar ways, in which ISMs from decentralized development were calibrated separately with their own targets. To assess the effect of ISM tuning on projected Antarctic ice loss, we carried out a series of experiments to tune key ISM parameters for the preindustrial climate simulated by each CMIP6 model (Methods). This essentially results in multiple ISMs, each tailored for the respective CMIP6 model. We then run future projections of the AIS with the raw climate output from CMIP6 models, rather than bias-corrected climate as we did previously.\nWith this \u201cmulti-ISM\u201d approach, the spread in simulated AIS forced by raw CMIP6 1850\u20132100 climate is smaller than that in single-ISM runs (Fig. 5). In comparison with ISMIP6 results, however, the dispersion of simulated Antarctic ice loss by 2100 in multi-ISM runs is still larger than that documented by ISMIP6-Antarctica. This may well be contributed to the more comprehensive set of climate models used in our study and CMIP6 models generally showing a higher climate sensitivity to elevated greenhouse gas levels, despite that the SSP5-8.5 scenario (8) used by CMIP6 models has slightly lower rates of greenhouse gas emissions than RCP8.5\u2014its CMIP5 counterpart used by ISMIP6.", "source": "https://sealeveldocs.readthedocs.io/en/latest/li23sciadv.html"}
{"id": "d3958eec8aeb-5", "text": "Effects of ISM calibration per climate model\uf0c1\nResults discussed so far are all from ISM runs in a \u201csingle-ISM\u201d framework, where the ISM is calibrated on the basis of observational data, with its parameters fixed for all CMIP6 climate models. Nonetheless, calibrating an ISM\u2019s parameters so that, under a prescribed climate, it could simulate that a target ice sheet state is a common practice in the ice sheet modeling community, in which ISM parameters may absorb part of the spread in climate boundary conditions. Ice sheet intercomparison projects, e.g., ISMIP6, were carried out in similar ways, in which ISMs from decentralized development were calibrated separately with their own targets. To assess the effect of ISM tuning on projected Antarctic ice loss, we carried out a series of experiments to tune key ISM parameters for the preindustrial climate simulated by each CMIP6 model (Methods). This essentially results in multiple ISMs, each tailored for the respective CMIP6 model. We then run future projections of the AIS with the raw climate output from CMIP6 models, rather than bias-corrected climate as we did previously.\nWith this \u201cmulti-ISM\u201d approach, the spread in simulated AIS forced by raw CMIP6 1850\u20132100 climate is smaller than that in single-ISM runs (Fig. 5). In comparison with ISMIP6 results, however, the dispersion of simulated Antarctic ice loss by 2100 in multi-ISM runs is still larger than that documented by ISMIP6-Antarctica. This may well be contributed to the more comprehensive set of climate models used in our study and CMIP6 models generally showing a higher climate sensitivity to elevated greenhouse gas levels, despite that the SSP5-8.5 scenario (8) used by CMIP6 models has slightly lower rates of greenhouse gas emissions than RCP8.5\u2014its CMIP5 counterpart used by ISMIP6.\nSome CMIP6 models with a high climate sensitivity happen to display a warm bias in simulated present-day Antarctic climate. For instance, CESM2-WACCM drives one of the largest Antarctic ice loss by 2100 (\u223c1.05 m) in the single-ISM run, but the number reduces to only \u223c0.25-m SLE in the multi-ISM run. Examining the tuned ocean melt factor (OMF) (fig. S13), we can see that, to compensate the warm bias in CESM-WACCM\u2019s 400-m ocean temperature, the OMF has to be reduced to 0.72, much smaller than the OMF (5.0) used in single-ISM runs, which was calibrated on the basis of present-day observations. This, of course, greatly reduces the ISM\u2019s sensitivity to oceanic warming. In the case of MIROC6, which has an exceptionally large warm bias in the surface air temperature, the temperature offset in the ISM\u2019s positive-degree-day scheme (TPD) has to be increased to 4.64 K so that the modeled rate of surface meltwater production is around 100 Gt year\u22121. In other words, for the ISM tuned for MIROC6, ice and snow only melt at temperatures higher than 4.64 K. This is clearly unphysical but not an unexpected outcome of the tuning process. As warm bias in simulated modern polar climate is more prevalent than cold bias among CMIP6 models (Fig. 1A), tuning specifically for each CMIP6 model would generally reduce the ISM\u2019s sensitivity to climatic warming and narrow the spread in projected ice loss.\nThen, we come to the question whether this multi-ISM approach, in comparison with the single-ISM way, is more appropriate in assessing the uncertainty in projected Antarctic ice loss associated with climate models. The multi-ISM way hides climate models\u2019 biases under tailored ISM parameter settings but may resort to parameters that are unphysical or contradicting to observational evidence.\nImplications for Earth system model development\uf0c1\nThe large spread in modeled polar climate in the current generation CMIP6 models would make it highly challenging to conduct intercomparisons of \u201cEarth system models\u201d with embedded, active ice sheets. It is not uncommon for climate models from different modeling centers to share components, and the same ISM or its close variants may be incorporated in several Earth system models. For instance, the Parallel Ice Sheet Model (PISM) is used in NASA GISS and MPI-ESM models, and the Grenoble ice sheet and land ice (GRISLI) model is used in CNRM-CM and IPSL-CM6 (11). Our ISM simulations forced by raw CMIP6 climates have demonstrated that, even with the same ISM, structural differences between atmosphere-ocean models can result in widely varying equilibrium states of the AIS. It has been recognized that simulated paleo\u2013ice sheet volume, such as that during the mid-Pliocene, is highly dependent on climate model\u2013based forcings (17).\nResults from our study highlight that biases in simulated polar climate from state-of-the-art climate models are large enough to drive the AIS to equilibrium states distinctly different from the present day, although the ISM simulates a realistic AIS with observational climate data. This poses a serious challenge to the practice of using paleo sea level to constrain the parameters of ice sheet processes, irrespective of the accuracy of ice volume and sea level reconstructions (38).\nSince the advent of numerical general circulation models in the 1960s, climate models have followed an evolutionary path of increasing complexity with ever more components added for explicit simulation (39). Spanning a hierarchy of models (40), climate modeling has now entered the Earth system model phase, where the most sophisticated models have added biogeochemical cycles and land ice sheets to the atmosphere-land-ocean system. Integrated ice sheet components embedded within Earth system models allow consistent simulations of crucial processes for polar climate change, e.g., the ice-albedo feedback, ice-elevation feedbacks associated with an evolving ice sheet topography, and the climate feedbacks associated with ice sheet meltwater (41\u201343). Results from our study, however, warn of substantial ongoing uncertainty among Earth system models with interactive ice sheets for the evaluation of future SLR. While progress has been made in ice sheet modeling, the uncertainty in future changes of the AIS and associated impacts on GMSL have not been reduced to a level needed for straightforward decision-making, and more work is required. Current greenhouse gas emissions put the climate on track of a >3\u00b0C warming by 2100, and the time window is shrinking for reducing carbon emissions to avoid rapid and unstoppable SLR (5). For more robust sea level projections, improved understanding of processes important for polar climate, including cloud radiative forcing and deep ocean circulations and mixing, is urgently needed.\nMethods\uf0c1\nIce sheet model\uf0c1\nIn this study, we use PSUICE3D (18), a numerical ISM with a hybrid approach to the dynamical equations governing ice sheet and ice shelf flow, which are described by the shallow ice and shallow shelf approximations, respectively, and are combined heuristically by an imposed mass flux condition across the grounding line (44). These hybrid ice dynamics capture the migration of grounding lines and essential mechanisms of ice sheet\u2013ice shelf dynamics, e.g., the marine ice sheet instability (MISI) for an inward-deepening ice sheet bed, while allowing the model to be run on coarse grids (20 km in this study) so that a large ensemble of simulations can be carried out economically on centennial and millennial time scales and on continental spatial scales. Bedrock deformation under the weight of the ice sheet is represented by a local relaxation toward isostatic equilibrium and elastic lithospheric flexure. No explicit basal hydrology is implemented in the model other than allowing basal sliding where the basal temperature reaches the melt point. BSCs of the bed are obtained using an inverse method, in which the model is driven by present-day observational climate and the sliding coefficient at each grid point is tuned iteratively until the local ice thickness equilibrates toward the present-day observed value (21).\nIce sheet SMB is calculated as snowfall minus surface melt, while sublimation at the ice surface is ignored. The fraction of precipitation falling as snow is determined by a parameterized formulation based on the corresponding monthly surface air temperature Ta (45). Ice surface melt is calculated from Ta using a standard positive-degree-day (PDD) scheme with a coefficient of 0.005 m per degree-day, but the temperature baseline for zero melt (parameter TPD) is set at \u22121\u00b0C in single-ISM runs so that, under present-day climate, the total surface melt rate of Antarctic ice shelves is within the observational range (46).\nHeavily parameterized in the current generation ISMs, ocean-induced ice shelf basal melt is recognized as a major source of uncertainty in the AIS\u2019s response to climate change (11, 13, 15). Basal melt of Antarctic ice shelves is strongly influenced by the incursion of warm CDW, which occurs at \u223c10-km spatial scales and daily to subdaily time scales (47) and cannot be faithfully simulated in a coarse resolution (\u223c100-km) ocean model typical of CMIP6 models. Recognizing these limitations, in this study, we use a simple parameterization scheme for basal melt rates, which assumes a quadratic dependence on the 400-m ocean temperature above the pressure melting point of ice (T_o \u2212 T_f)", "source": "https://sealeveldocs.readthedocs.io/en/latest/li23sciadv.html"}
{"id": "e48670af6dee-0", "text": "Little et al. (2019)\uf0c1\nTitle:\nThe Relationship Between U.S. East Coast Sea Level and the Atlantic Meridional Overturning Circulation: A Review\nKey Points:\nThe relationship between the AMOC and coastal sea level is important to flood risk projections and ocean circulation reconstructions\nThe amplitude and pattern of sea level variability associated with AMOC variations is location, forcing, timescale, and model dependent\nFuture research should address the complex spatiotemporal structure of AMOC and the role of near.coast ageostrophic processes\nCorresponding author:\nLittle\nCitation:\nLittle, C. M., Hu, A., Hughes, C. W., McCarthy, G. D., Piecuch, C. G., Ponte, R. M., & Thomas, M. D. (2019). The Relationship between U.S. East Coast sea level and the Atlantic Meridional Overturning Circulation: A review. Journal of Geophysical Research: Oceans, 124, 6435\u00d06458. doi:10.1029/2019JC015152\nURL:\nhttps://agupubs.onlinelibrary.wiley.com/doi/10.1029/2019JC015152\nAbstract\uf0c1\nScientific and societal interest in the relationship between the Atlantic Meridional Overturning Circulation (AMOC) and U.S. East Coast sea level has intensified over the past decade, largely due to (1) projected, and potentially ongoing, enhancement of sea level rise associated with AMOC weakening and (2) the potential for observations of U.S. East Coast sea level to inform reconstructions of North Atlantic circulation and climate. These implications have inspired a wealth of model- and observation-based analyses. Here, we review this research, finding consistent support in numerical models for an antiphase relationship between AMOC strength and dynamic sea level. However, simulations exhibit substantial along-coast and intermodel differences in the amplitude of AMOC-associated dynamic sea level variability. Observational analyses focusing on shorter (generally less than decadal) timescales show robust relationships between some components of the North Atlantic large-scale circulation and coastal sea level variability, but the causal relationships between different observational metrics, AMOC, and sea level are often unclear. We highlight the importance of existing and future research seeking to understand relationships between AMOC and its component currents, the role of ageostrophic processes near the coast, and the interplay of local and remote forcing. Such research will help reconcile the results of different numerical simulations with each other and with observations, inform the physical origins of covariability, and reveal the sensitivity of scaling relationships to forcing, timescale, and model representation. This information will, in turn, provide a more complete characterization of uncertainty in relevant relationships, leading to more robust reconstructions and projections.\nPlain Language Summary\uf0c1\nSea level along the U.S. East Coast is influenced by changes in the density and currents of the North Atlantic Ocean. Indeed, there are simple theoretical considerations that relate indices of basin-scale flow to coastal sea level. Such a relationship could be leveraged to predict future sea level changes and coastal flooding given an expected change in climate and ocean circulation. Alternatively, it could be used to reconstruct ocean circulation from sea level measurements. This paper reviews the nature of this relationship and whether, and when, it is evident in climate models and observations. Although the current generation of large-scale climate and ocean models generally show an antiphase relationship between basin-scale ocean current strength and coastal sea level, the spatial pattern of sea level change differs from theory and between models. Supported by existing and emerging research, the authors hypothesize that these deviations result from important physical processes occurring on the continental shelf and slope, and the complexities of the 3-dimensional ocean circulation. A quantitative assessment of the importance of these processes is critical for understanding past and future climate and sea level changes in this heavily populated and vulnerable region.\nSea Level Variability Along the United States East Coast and Its Societal Importance\uf0c1\nThe densely populated U.S. East Coast is especially vulnerable to the impacts of sea level change, with ~2.4 million people and ~1.4 million housing units between Maine and Florida less than 1 m above local mean high water (Strauss et al., 2012). Here, sea level rise is already having adverse environmental, societal, and economic consequences, including increases in the severity and frequency of coastal flooding (e.g., Ezer & Atkinson, 2014; Moftakhari et al., 2015; Ray & Foster, 2016; Sweet et al., 2018; Wdowinski et al., 2016). Regional rates of sea level rise, and their associated consequences, are projected to increase substantially over the coming century (Figure 1a; Brown et al., 2018; Dahl et al., 2017; Kopp et al., 2014; Little, Horton, Kopp, Oppenheimer, Yip, 2015; Ray & Foster, 2016; Vitousek et al., 2017).\nFigure 1: (a) Monthly mean tide gauge sea level (in millimeters relative to year 2000) at the Battery (New York City; blue line). Projections of relative sea level (RSL) change, relative to year 2000, for RCP 2.6 (blue) and RCP 8.5 emission scenarios (red; Kopp et al., 2014). Shading after the year 2000 indicates 17th to 83rd percentile range of RSL projections. (b) Annual mean RSL (in millimeters, with arbitrary offset) measured at 15 U.S. East Coast tide gauges (Holgate et al., 2013) with long and relatively complete records. (c) Linear trend in RSL along the U.S. East Coast from 1900\u00d02017, in millimeters per year, from a Bayesian reconstruction (panel taken from Piecuch, Huybers, et al., 2018).\uf0c1\nUnderstanding the drivers of future change in relative sea level (RSL, i.e., that observed by tide gauges and relevant to coastal locations; see Gregory et al., 2019), and the ability of numerical models to represent such drivers, is critical. However, this is a complex task, given the many contributing processes that operate over different temporal and spatial scales, including, for example: freshwater input from land and the cryosphere, thermal expansion of sea water, glacial isostatic adjustment, and oceanic mass and volume redistribution (see Kopp et al., 2015; Milne et al., 2009; Stammer et al., 2013, for more thorough reviews of these processes).\nThe relative contributions of these processes to U.S. East Coast RSL vary across space and through time. For example, vertical land motion (due primarily to glacial isostatic adjustment) accounts for the majority of the large-scale spatial variation in recent centennial trends and underlies the high rates of RSL rise in the Mid-Atlantic (Figure 1c; Karegar et al., 2017; Piecuch, Huybers, et al., 2018). However, ongoing climate-related processes - associated with net freshwater input, atmosphere-ocean momentum and buoyancy fluxes, and ocean mass and volume redistribution\u00d1dominate the interannual to multidecadal, spatially variable, U.S. east coast RSL signals during the twentieth century (Figure 1b; Andres et al., 2013; Bingham & Hughes, 2009; Davis & Vinogradova, 2017; Ezer, 2013; Ezer et al., 2013; Frederikse et al., 2017; Goddard et al., 2015; Park & Sweet, 2015; Piecuch et al., 2016; Piecuch, Bittermann, et al., 2018; Piecuch & Ponte, 2015; Thompson & Mitchum, 2014; Woodworth et al., 2014; Yin & Goddard, 2013).", "source": "https://sealeveldocs.readthedocs.io/en/latest/little19.html"}
{"id": "e48670af6dee-1", "text": "Understanding the drivers of future change in relative sea level (RSL, i.e., that observed by tide gauges and relevant to coastal locations; see Gregory et al., 2019), and the ability of numerical models to represent such drivers, is critical. However, this is a complex task, given the many contributing processes that operate over different temporal and spatial scales, including, for example: freshwater input from land and the cryosphere, thermal expansion of sea water, glacial isostatic adjustment, and oceanic mass and volume redistribution (see Kopp et al., 2015; Milne et al., 2009; Stammer et al., 2013, for more thorough reviews of these processes).\nThe relative contributions of these processes to U.S. East Coast RSL vary across space and through time. For example, vertical land motion (due primarily to glacial isostatic adjustment) accounts for the majority of the large-scale spatial variation in recent centennial trends and underlies the high rates of RSL rise in the Mid-Atlantic (Figure 1c; Karegar et al., 2017; Piecuch, Huybers, et al., 2018). However, ongoing climate-related processes - associated with net freshwater input, atmosphere-ocean momentum and buoyancy fluxes, and ocean mass and volume redistribution\u00d1dominate the interannual to multidecadal, spatially variable, U.S. east coast RSL signals during the twentieth century (Figure 1b; Andres et al., 2013; Bingham & Hughes, 2009; Davis & Vinogradova, 2017; Ezer, 2013; Ezer et al., 2013; Frederikse et al., 2017; Goddard et al., 2015; Park & Sweet, 2015; Piecuch et al., 2016; Piecuch, Bittermann, et al., 2018; Piecuch & Ponte, 2015; Thompson & Mitchum, 2014; Woodworth et al., 2014; Yin & Goddard, 2013).\nOf interest in this review paper is RSL variability related to changes in ocean circulation and density that may be causally coupled, or simply correlated, with the Atlantic Meridional Overturning Circulation (AMOC; see section 2). We thus focus on variability in \u201cdynamic sea level\u201d (DSL), that is, the height of the sea surface above the geoid, with the inverse barometer correction applied (Gregory et al., 2019). Secular DSL changes are evident in 21st century climate model simulations and are projected to be a principal driver of acceleration in 21st century sea level and its spatial variation along the east coast (Bilbao et al., 2015; Bouttes et al., 2014; Carson et al., 2016; Chen et al., 2018; Church et al., 2013; Kopp et al., 2014; Little, Horton, Kopp, Oppenheimer, Vecchi, et al., 2015; Little, Horton, Kopp, Oppenheimer, & Yip, 2015; Perrette et al., 2013; Slangen et al., 2014; Yin et al., 2009; Yin, 2012; Yin & Goddard, 2013). Various studies have shown these large-scale regional DSL anomalies to be correlated with a decline in AMOC strength (section 4). However, current-generation climate models also show a wide range in future projections of regional DSL rise. They may also exhibit systematic biases due to poorly resolved processes that influence near-coast DSL (section 6).\nAn improved theoretical and observational basis for AMOC-DSL relationships would enable assessments of the reliability of individual model projections, and climate models more generally, allowing improved estimates of the magnitude, spatial pattern, and time of emergence of expected sea level rise. In addition, a robust \u201csignature\u201d of AMOC (or some other feature of the large-scale circulation) in coastal RSL could be leveraged to infer preinstrumental changes in AMOC and/or climate. Recent improvements to analysis of the tide gauge record, including approaches to cope with data gaps and account for vertical land motion and glacial isostatic adjustment (Kopp, 2013; Piecuch, Huybers, et al., 2017), have intensified the interest in exploiting this relationship to inform reconstructions of ocean variability (e.g., Butler et al., 2015; Kienert & Rahmstorf, 2012; McCarthy et al., 2015). Proxies that predate the tide gauge record offer the opportunity to extend these reconstructions over centennial to millennial timescales (e.g., Kemp et al., 2017, 2018).\nHere, motivated by these considerations, we review evidence for the covariation of AMOC and U.S. East Coast sea level. In section 2, we define AMOC and its relationship to the large-scale circulation of the North Atlantic Ocean. Section 3 presents a simple diagnostic scaling argument between AMOC strength and DSL. Section 4 surveys AMOC-DSL linkages in numerical simulations (where long-period relationships are able to be assessed) and includes a new analysis of the AMOC-DSL scaling coefficient in Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations. Section 5 examines observational linkages between AMOC components and coastal sea level, clarifying the specific components of AMOC (e.g., Gulf Stream) invoked, the regional fingerprint of such linkages, and the timescales over which the relationship has been documented. In section 6, we suggest potential origins of along-coast variations, intersimulation differences in scaling relationships, and discrepancies between models and observations; section 7 highlights new research directions that can help assess these discrepancies more extensively and quantitatively.\nAMOC and the North Atlantic Ocean Circulation\uf0c1\nThe U.S. East Coast borders the western boundary of the North Atlantic Ocean, which is characterized by a spatially and temporally complex system of surface and deep currents (Figure 2).\nFigure 2: Schematic of key AMOC.related components of the North Atlantic Ocean (modfied from Garcia-Ibanez et al., 2018). Abbreviations are as follows: NRG = Northern Recirculation Gyre; LC = Labrador Current; DWBC = Deep Western Boundary Current; IC = Irminger Current; EGIC = East Greenland.Irminger Current. Three source waters for North Atlantic Deep Water are noted: LSW = Labrador Sea Water; ISOW = Iceland-Scotland Overflow Water; DSOW = Denmark Straits Over\u00dfow Water. Box indicates the U.S. East Coast region.\uf0c1\nAt U.S. East Coast latitudes, the large-scale ocean circulation is dominated by two opposing gyres. At subtropical latitudes, southward wind-driven transport in the interior of the gyre is closed by a western boundary current, composed of the Gulf Stream to the north and the Florida and Antilles currents further south. At subpolar latitudes, the North Atlantic Current (NAC) splits into various branches that flow northwards along the eastern side of the subpolar gyre (Rhein et al., 2011). These currents flow cyclonically around the subpolar gyre, contributing to the upper parts of the western boundary currents comprising the East and West Greenland Currents and the Labrador Current. Part of the NAC also flows into the Nordic Seas (e.g., Dickson & Brown, 1994; Sarafanov et al., 2012). Along these high-latitude branches, warm and salty surface waters originating from the tropical and subtropical Atlantic increase in density and transform into North Atlantic Deep Water through a variety of processes, including cooling, mixing, and convection (Marotzke & Scott, 1999; Spall & Pickart, 2001; Thomas et al., 2015).\nIn addition to these large-scale flows, there are important currents along the U.S. East Coast continental shelf, shelf break, and slope: flowing northward over the continental shelf south of Cape Hatteras (the South Atlantic Bight) and southward along the shelf between Cape Hatteras and Nova Scotia (Figure 2). These currents are driven by a combination of local wind and buoyancy forcing as well as interactions with the larger-scale flow field (see section 6). In the South Atlantic Bight, interactions between the shelf current and the Gulf Stream are clearly important, but there is evidence of locally wind driven variability closer to the shore (Lee et al., 1991; Stegmann & Yoder, 1996; Yuan et al., 2017). To the north of Cape Hatteras, the Slope Current has its origins in the Labrador Current and the East Greenland Current (Chapman & Beardsley, 1989; Rossby et al., 2014). Its strength is therefore linked to the AMOC, through the strength of the Labrador Current, as well as through interactions with the Northern Recirculation Gyre (Andres et al., 2013; Zhang, 2008), the Deep Western Boundary Current (e.g. Zhang & Vallis, 2007), and the Gulf Stream (Ezer, 2015).", "source": "https://sealeveldocs.readthedocs.io/en/latest/little19.html"}
{"id": "e48670af6dee-2", "text": "In addition to these large-scale flows, there are important currents along the U.S. East Coast continental shelf, shelf break, and slope: flowing northward over the continental shelf south of Cape Hatteras (the South Atlantic Bight) and southward along the shelf between Cape Hatteras and Nova Scotia (Figure 2). These currents are driven by a combination of local wind and buoyancy forcing as well as interactions with the larger-scale flow field (see section 6). In the South Atlantic Bight, interactions between the shelf current and the Gulf Stream are clearly important, but there is evidence of locally wind driven variability closer to the shore (Lee et al., 1991; Stegmann & Yoder, 1996; Yuan et al., 2017). To the north of Cape Hatteras, the Slope Current has its origins in the Labrador Current and the East Greenland Current (Chapman & Beardsley, 1989; Rossby et al., 2014). Its strength is therefore linked to the AMOC, through the strength of the Labrador Current, as well as through interactions with the Northern Recirculation Gyre (Andres et al., 2013; Zhang, 2008), the Deep Western Boundary Current (e.g. Zhang & Vallis, 2007), and the Gulf Stream (Ezer, 2015).\nIn aggregate, these horizontal and vertical flows result in an \u201coverturning\u201d circulation that transports over 1 PW of heat poleward (Trenberth & Fasullo, 2017). In this paper, this AMOC is defined as the stream function of the zonally and cumulatively vertically integrated meridional velocity of the Atlantic Ocean north of 35\u00b0S (Buckley & Marshall, 2016; Zhang, 2010). In models and observations, the AMOC reveals upper and lower interhemispheric overturning cells of water that are sourced by high-latitude sites of deep water formation in the northern and southern hemispheres respectively (Figure 3).\nFigure 3: The AMOC, averaged over the 1959\u20132012 period, from a 1/12\u00b0 resolution model simulation as described in Hughes et al. (2018). The flow is clockwise around positive values, and the stream function is calculated by integrating the southward velocity both zonally and upwards from the bottom. The black contour is at zero.\uf0c1\nThe upper overturning cell reflects northward transport in the upper ocean currents, including those mentioned earlier in this section, compensated by southward flowing North Atlantic Deep Water at intermediate depths. In models, the maximum of the AMOC stream function is typically located around the latitude of the Gulf Stream separation and at approximately 1,000-m depth. Below this upper cell is a lower cell of Antarctic Bottom Water that originates from sources at high southern latitudes (Buckley & Marshall, 2016; Kuhlbrodt et al., 2007). See Buckley and Marshall (2016) and other reviews in this special issue, particularly Bower et al. (2019), for a more comprehensive description of AMOC structure and variability.\nA Simple Theoretical Basis for AMOC-DSL Covariability\uf0c1\nA diagnostic relationship between the AMOC and DSL can be derived from the zonal momentum equation:\nfrac{rho}{r cos{phi}} frac{D}{Dt} left(u r cos{phi}right) - rho f v + rho f w cot{phi} = -frac{1}{r cos{phi}} frac{partial p}{partial lambda} + F_x, (1)\nwhere r is the Earth\u2019s radius, u is the zonal velocity, v is the meridional velocity, w is the vertical velocity, f is the Coriolis frequency, phi is latitude, lambda is longitude, p is pressure, rho is density, F_x is the eastward viscous force per unit volume, and D/Dt is the material rate of change. For a derivation and discussion of the equations of motion see, for example, Vallis (2006, Chapter 2) and Gill (1982, Chapter 4). If we (1) zonally integrate over the basin and (2) neglect the advection of relative angular momentum (the first term), the term involving w (usually neglected in the Primitive Equations), and the viscous term (assuming we are below the surface Ekman layer, and that any bottom Ekman layer occupies only a small fraction of the zonal integral\u00d1this assumes that we are at depths where it is meaningful to consider the ocean to have sidewalls), this reduces to an integrated geostrophic balance:\nf T = p_E - p_W, (2)\nwhere T is the northward mass transport across the section (the zonal integral of rho v). Equation (2) relates the northward mass transport to the difference between pressure at the eastern end (p_E) and the western end (p_W) of the section. These pressures are bottom pressures, which become equivalent to DSL (with a scaling of approximately 1 cm/mbar of pressure) as the depth tends to zero at the coast.\nThis zonally integrated geostrophic balance can be used to derive a simple scaling between the AMOC and DSL at the western boundary. First, we note that the eastern boundary pressure is very close to being a function of depth alone, independent of latitude, at least below a depth of around 100 m (Hughes et al., 2018; Hughes & de Cuevas, 2001). Subtracting off this reference function of depth in our definition of p (which now should be considered to be a pressure anomaly, referenced to the eastern boundary value), we find that p_E = 0. Then, integrating over depth from the surface (z = 0) to the depth of the maximum in the overturning streamfunction (z = -H), we find that the total northward mass transport above this depth is given by\nQ = int_{-H}^0{T dz} - frac{1}{f} int_{-H}^0{p_W dz} = -frac{H}{f}overline{p_W}, (3)\nwhere overline{p_W} is the western boundary pressure averaged over the depth range above the maximum overturning. The relationship to coastal sea level then follows from the assumption that the depth-averaged pressure in this zone is related to the boundary pressure near the surface, {p_W}_0, which is in turn related to inverse barometer-corrected boundary sea level h_W by rho_0 g h_W = {p_W}_0, where we use a reference density rho_0. Rewriting in terms of this near.surface western boundary pressure anomaly, we find\nQ = -frac{H_e}{f} {p_W}_0 = - frac{H_e}{f} rho_0 g h_W, (4)\nrequiring the definition of an effective layer thickness\nH_e = int_{-H}^0{frac{p_W}{{p_W}_0}dz},  (5)\nwhich may be interpreted as the layer thickness used to multiply the near-surface boundary pressure anomaly (proportional to sea level), in order to get the correct depth-integrated pressure force on the sidewall. If the pressure anomaly (or equivalently the northward transport) is independent of depth above -H, H_e = H. If the zonally integrated flow (or pressure anomaly) is largest at the surface and decreases linearly to zero at the maximum of the overturning, H_e = 0.5 H. Rearranging (5), we find that the coastal sea level signal can be written as\nh_W = -frac{Q}{rho_0}frac{f}{g H_e}, (6)\nin which it is shown how the coastal sea level signal h_W is negatively related to the strength of the overturning Q/rho_0, and the size of the signal is larger if the effective layer thickness H_e is smaller.\nFigure 3 reveals a fairly uniform (or slowly decreasing with increasing depth) northward zonally integrated flow above about 1,000-m depth, balanced by a deeper return flow (with more complicated flows in the top few hundred meters, representing the wind-driven flows superimposed on the large-scale MOC). Assuming f = 10^{-4} s^{-1} (true at a latitude of about 43\u00a1N), equation (6) predicts a sea level change of 1 cm/Sv of meridional transport (less for latitudes closer to the equator, and slightly more for more poleward latitudes). If, rather than constant transport per unit depth above 1,000 m (as in a simple two-layer model), we assume a linear rise from zero at 1,000 m to a maximum at the surface, then pressure at the surface is twice the depth average, leading to a scaling of -2 cm/Sv. Realistic scalings are likely to be between these limits, subject to the assumption of geostrophic balance in equation (2), and the approximation that the vertical profile of the flow remains constant (temporal variations in H_e are proportionally smaller than those in Q). The dependence on f means that this scaling should also lead to smaller sea level signals closer to the equator, again assuming that proportional variations in H_e are smaller than those in f.\nEvidence of an AMOC-DSL Relationship in Numerical Models\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/little19.html"}
{"id": "e48670af6dee-3", "text": "h_W = -frac{Q}{rho_0}frac{f}{g H_e}, (6)\nin which it is shown how the coastal sea level signal h_W is negatively related to the strength of the overturning Q/rho_0, and the size of the signal is larger if the effective layer thickness H_e is smaller.\nFigure 3 reveals a fairly uniform (or slowly decreasing with increasing depth) northward zonally integrated flow above about 1,000-m depth, balanced by a deeper return flow (with more complicated flows in the top few hundred meters, representing the wind-driven flows superimposed on the large-scale MOC). Assuming f = 10^{-4} s^{-1} (true at a latitude of about 43\u00a1N), equation (6) predicts a sea level change of 1 cm/Sv of meridional transport (less for latitudes closer to the equator, and slightly more for more poleward latitudes). If, rather than constant transport per unit depth above 1,000 m (as in a simple two-layer model), we assume a linear rise from zero at 1,000 m to a maximum at the surface, then pressure at the surface is twice the depth average, leading to a scaling of -2 cm/Sv. Realistic scalings are likely to be between these limits, subject to the assumption of geostrophic balance in equation (2), and the approximation that the vertical profile of the flow remains constant (temporal variations in H_e are proportionally smaller than those in Q). The dependence on f means that this scaling should also lead to smaller sea level signals closer to the equator, again assuming that proportional variations in H_e are smaller than those in f.\nEvidence of an AMOC-DSL Relationship in Numerical Models\uf0c1\nNumerical simulations allow analysis of AMOC-DSL relationships that can be compared to the theoretical considerations of the previous section, while incorporating local and large-scale forcing, complex 3-D flows, and ageostrophic processes, to the extent permitted by their resolution. Most analysis of numerical simulations has focused on 21st century, centennial-timescale, AMOC-DSL relationships. In this section, we thus focus on longer timescales, although we contrast these results with selected studies that have examined covariability over shorter timescales, often with a focus on the historical record.\nThe connection between U.S. East Coast sea level rise and the AMOC in coupled climate models was first established by Levermann et al. (2005) through \u201chosing\u201d simulations (in which extreme freshwater forcing is applied to the subpolar North Atlantic). They found that, in a climate model with a relatively coarse (3.75\u00b0 horizontal resolution) ocean, a weakened AMOC is associated with DSL rise in most of the Atlantic basin, with a scaling coefficient of up to \u22125 cm/Sv. Most subsequent numerical simulations that have assessed this relationship show a more complex spatial pattern of DSL change (e.g., Kienert & Rahmstorf, 2012; Landerer et al., 2007; Lorbacher et al., 2010; Yin et al., 2010), and a smaller (less negative) scaling coefficient (e.g., Bingham & Hughes, 2009; Little et al., 2017; Schleussner et al., 2011). However, the correlation between DSL rise over portions of the U.S. East Coast and a decline in AMOC (and, often, a rise in steric height in the western North Atlantic intergyre region) has been repeatedly noted, in simulations forced by future greenhouse gas emission scenarios, freshwater input into the subpolar North Atlantic, or both (e.g., Hu et al., 2009; Hu et al., 2011; Hu & Bates, 2018; Hu & Deser, 2013; Kienert & Rahmstorf, 2012; Krasting et al., 2016; Landerer et al., 2007; Lorbacher et al., 2010; Pardaens et al., 2011; Yin et al., 2010; Yin & Goddard, 2013).\nThe AMOC weakens over the 21st century in most CMIP3 and CMIP5 simulations (Church et al., 2013), with a rate that varies widely across emissions scenarios and models (e.g., Figure 4a; Bakker et al., 2016; Cheng et al., 2013; Heuz\u00e9, 2017; Huber & Zanna, 2017; Schleussner et al., 2011; Weaver et al., 2012).\nFigure 4: (a) Change in maximum AMOC strength for a 28 Coupled Model Intercomparison Project Phase 5 model, RCP4.5-forced, ensemble, from 1976\u20132000 to 2076\u20132100, as calculated by Chen et al. (2018). (b) Ensemble mean dynamic sea level change (m) from 1976\u20132000 to 2076\u20132100.\uf0c1\nThe amplitude and spatial pattern of DSL changes associated with 21st century AMOC weakening has been noted in several studies (Schleussner et al., 2011; Yin et al., 2009). However, such studies have generally considered the ensemble mean DSL change (Figure 4b), or a small subset of available models, and have often focused on the Northeast United States only, limiting analysis of intermodel or regional differences.\nAn assessment of the robustness of the scaling of North Atlantic DSL to AMOC change across climate models is missing in the literature. To fill this gap, we perform a brief analysis using available datasets, including the results of Chen et al. (2018), who investigated the relationship between 21st century changes in DSL and the annual-mean maximum AMOC stream function below 500 m in a large (30-member) CMIP5 ensemble. Models included in this ensemble show an AMOC decline from 1976\u20132000 to 2076\u20132100 ranging from approximately zero to 8 Sv (Figure 4a).\nIn Figure 5, we calculate the AMOC-DSL scaling coefficient for 25 CMIP5 models over this century-long period, at a 1\u00b0 horizontal resolution.\nFigure 5: Map of the ratio of dynamic sea level change to AMOC change (m/Sv; 2076\u20132100 minus 1976\u20132000) for 25 RCP4.5-forced Coupled Model Intercomparison Project Phase 5 models with AMOC weakening larger than 2 Sv.\uf0c1\nThere are broad similarities in the spatial pattern of scaling coefficients and that of the ensemble mean DSL change (Figure 4b), with only a few models showing dramatic differences from the subtropical high/subpolar and coastal low relationship (e.g., MRI-CGCM and FGOALS-g2). However, the amplitude of the scaling coefficient near the U.S. East Coast ranges widely, both north and south of Cape Hatteras, across the ensemble, along with substantial meridional gradients along these coastal regions within individual models.\nThe diversity of model-specific scaling coefficients along the western boundary can also be shown with a regression of DSL change against AMOC change, that is,\n\u2206DSL(x,y,m) = \u03b1(x,y) \u2206AMOC(m) + \u03b5(x,y,m) (7)\nwhere x and y are longitude and latitude, m is the model index, \u03b1 is a local scaling coefficient, and \u03b5 is a residual. (Although the RCP 4.5 scenario is shown, spatial patterns of DSL change, and DSL change associated with AMOC change, do not exhibit strong RCP-dependence; Chen et al., 2018; Little, Horton, Kopp, Oppenheimer, & Yip, 2015; Yin, 2012; Yin et al., 2009).\nLocal regression coefficients, shown in Figure 6b, indicate a meridional tripole in the North Atlantic; models with more AMOC weakening are associated with larger DSL rise in the subtropical gyre and larger DSL fall in most of the subpolar gyre and the tropics. This pattern bears some similarity to the dominant mode of sea surface height variability over the historical record (e.g., Hakkinen & Rhines, 2004; Yin & Goddard, 2013), the multimodel mean 21st century change observed in CMIP simulations (Figure 4b; Little, Horton, Kopp, Oppenheimer, & Yip, 2015; Yin, 2012; Yin et al., 2009, 2010), and a regression of DSL on AMOC strength in a model simulation of the historical period (Figure 6a). Coastal regression coefficients range from approximately \u22121.5 to 0 cm/Sv, with more negative values in U.S. East Coast regions north of Cape Hatteras.", "source": "https://sealeveldocs.readthedocs.io/en/latest/little19.html"}
{"id": "e48670af6dee-4", "text": "There are broad similarities in the spatial pattern of scaling coefficients and that of the ensemble mean DSL change (Figure 4b), with only a few models showing dramatic differences from the subtropical high/subpolar and coastal low relationship (e.g., MRI-CGCM and FGOALS-g2). However, the amplitude of the scaling coefficient near the U.S. East Coast ranges widely, both north and south of Cape Hatteras, across the ensemble, along with substantial meridional gradients along these coastal regions within individual models.\nThe diversity of model-specific scaling coefficients along the western boundary can also be shown with a regression of DSL change against AMOC change, that is,\n\u2206DSL(x,y,m) = \u03b1(x,y) \u2206AMOC(m) + \u03b5(x,y,m) (7)\nwhere x and y are longitude and latitude, m is the model index, \u03b1 is a local scaling coefficient, and \u03b5 is a residual. (Although the RCP 4.5 scenario is shown, spatial patterns of DSL change, and DSL change associated with AMOC change, do not exhibit strong RCP-dependence; Chen et al., 2018; Little, Horton, Kopp, Oppenheimer, & Yip, 2015; Yin, 2012; Yin et al., 2009).\nLocal regression coefficients, shown in Figure 6b, indicate a meridional tripole in the North Atlantic; models with more AMOC weakening are associated with larger DSL rise in the subtropical gyre and larger DSL fall in most of the subpolar gyre and the tropics. This pattern bears some similarity to the dominant mode of sea surface height variability over the historical record (e.g., Hakkinen & Rhines, 2004; Yin & Goddard, 2013), the multimodel mean 21st century change observed in CMIP simulations (Figure 4b; Little, Horton, Kopp, Oppenheimer, & Yip, 2015; Yin, 2012; Yin et al., 2009, 2010), and a regression of DSL on AMOC strength in a model simulation of the historical period (Figure 6a). Coastal regression coefficients range from approximately \u22121.5 to 0 cm/Sv, with more negative values in U.S. East Coast regions north of Cape Hatteras.\nFigure 6: (a) From Woodworth et al. (2014). Regression coefficients of annual mean sea level and overturning transport (at the same latitude) for depths between 100 and 1,300 m using a 1\u00b0 ocean model, for the period 1950\u20132009, without wind forcing. (b) Linear regression coefficient (\u03b1) of DSL change against the change in maximum AMOC strength for the models shown in Figure 5 (m/Sv). (c) Variance in DSL change explained by AMOC change (%). DSL = dynamic sea level; AMOC = Atlantic Meridional Overturning Circulation.\uf0c1\nHowever, regression coefficients in Figure 6b diverge from those obtained through a regression of annual mean DSL on AMOC over the 1950\u20132009 period (Figure 6a) and those predicted by equation 6, particularly along the western boundary, where the CMIP5-derived pattern does not show a universal anticorrelation of sea level and the AMOC. (We note that the single-valued AMOC index used in Figure 6b is different than the meridionally varying index used in Figure 6a. However, we would not expect this to affect the sign of regression coefficients, if AMOC transport changes are meridionally coherent). Perhaps more important than the spatial pattern in Figure 6b is the fact that only a small fraction of intermodel DSL variance is explained by differences in AMOC strength change (Figure 6c). In coastal regions, and in the subpolar gyre, factors unrelated to AMOC strength are principally responsible for the wide spread in 21st century projections of U.S. East Coast DSL rise (Yin et al., 2009, 2010; Kopp et al., 2014; Little, Horton, Kopp, Oppenheimer, & Yip, 2015; Minobe, 2017).\nIt is possible that differences between Figures 6a and 6b originate in a timescale-dependent relationship. This was suggested by Yin and Goddard (2013, their Figure 3) based on (1) similarities between the DSL patterns of observed decadal trends and 21st century model trends; (2) similarities between observed and modeled Empirical Orthogonal Function (EOF) patterns (describing interannual variability); and (3) differences between DSL patterns associated with long-term trends and interannual variability. Similar conclusions were drawn by Lorbacher et al. (2010). Model-derived scaling coefficients for interannual AMOC-DSL relationships north of Cape Hatteras appear to be more consistent than those in Figure 5, and more consistent with the theoretical values in section 2. For example, Bingham and Hughes (2009) find a scaling of -1.7 cm Sv\u22121, Woodworth et al. (2014) find -1.5 cm Sv\u22121, and Little et al. (2017) obtain \u22121.8 cm/Sv. However, the wide spread in scaling coefficients across models under identical forcing (Figure 5) suggests that differences in model representation are critical over longer timescales. Although an analysis of these regional and inter-model differences is beyond the scope of this review, we highlight its importance and discuss possible explanations in sections 6 and 7.\nEvidence of an AMOC-DSL Relationship in Observations\uf0c1\nThe first direct, continuous, basin-wide, observations of the AMOC began in 2004 with the RAPID project (Rapid Climate Change; Cunningham et al., 2007). This record is now complemented by two other basin-wide in situ programs: NOAC at 47\u00b0N (North Atlantic Changes; Mertens et al., 2014) and OSNAP, around 60\u00b0N (Overturning in the Sub-polar North Atlantic; Lozier et al., 2017). Although RAPID observations have revealed a wealth of information, they provide only a 13-year time series at 26\u00b0N at time of writing. This limited record hinders an observation-based assessment of AMOC-DSL relationships, especially over the decadal and longer timescales of primary interest here. Over shorter timescales, Ezer (2015) compared monthly RAPID observations to the Atlantic City-Bermuda tide gauge sea level difference, finding a correlation of 0.27. In the same analysis, Ezer noted substantial differences in correlations, and lag/lead relationships, between the sea level difference and the three individual components of AMOC observed by RAPID (Ekman, Florida Current, and Mid-Ocean transport). Piecuch et al. (2019) also note differing relationships between each of these AMOC components and New England coastal sea level, with only the Ekman component exhibiting strong coherence.\nIn addition to the RAPID record, longer observations of elements of the North Atlantic circulation are available: for example, the Florida Current time series since 1982 (Meinen et al., 2010), the Oleander time series of Gulf Stream transport since 1992 (Rossby et al., 2014), and the position of the Gulf Stream Extension since 1955 (Joyce & Zhang, 2010). Studies based on models (e.g. Saba et al., 2016; Sanchez-Franks & Zhang, 2015) and observations (e.g., Kopp, 2013; McCarthy et al., 2015; Park & Sweet, 2015) have shown strong statistical relationships between US east coast sea level and these metrics at up to multidecadal timescales. We consider evidence in this section for relationships between DSL and these and other elements of the North Atlantic circulation, while emphasizing that changes in the latter do not necessarily imply changes in AMOC, as defined in section 2. We briefly discuss the nature of potential linkages with AMOC in section 6.3.\nLinkages Between DSL and AMOC Components\uf0c1\nThe relationship between coastal DSL and the Gulf Stream has been assessed using theory, observations, and models. Studies have considered the roles of Gulf Stream transport, velocity, and position, both upstream and downstream of the detachment at Cape Hatteras, as well as the strength of the Florida Current.\nEarly studies focused on the relationship between tide gauge observations and the Gulf Stream over seasonal timescales between Florida and Cape Hatteras. Two linkages between ocean circulation and DSL were considered: the cross-stream (shelf) sea level gradient, related to ocean circulation via geostrophy, and the downstream (along-coast) sea level gradient, related via the Bernoulli principle. Montgomery (1941) found little evidence for a relationship of the downstream sea level gradient to velocity (in the Gulf Stream).", "source": "https://sealeveldocs.readthedocs.io/en/latest/little19.html"}
{"id": "e48670af6dee-5", "text": "In addition to the RAPID record, longer observations of elements of the North Atlantic circulation are available: for example, the Florida Current time series since 1982 (Meinen et al., 2010), the Oleander time series of Gulf Stream transport since 1992 (Rossby et al., 2014), and the position of the Gulf Stream Extension since 1955 (Joyce & Zhang, 2010). Studies based on models (e.g. Saba et al., 2016; Sanchez-Franks & Zhang, 2015) and observations (e.g., Kopp, 2013; McCarthy et al., 2015; Park & Sweet, 2015) have shown strong statistical relationships between US east coast sea level and these metrics at up to multidecadal timescales. We consider evidence in this section for relationships between DSL and these and other elements of the North Atlantic circulation, while emphasizing that changes in the latter do not necessarily imply changes in AMOC, as defined in section 2. We briefly discuss the nature of potential linkages with AMOC in section 6.3.\nLinkages Between DSL and AMOC Components\uf0c1\nThe relationship between coastal DSL and the Gulf Stream has been assessed using theory, observations, and models. Studies have considered the roles of Gulf Stream transport, velocity, and position, both upstream and downstream of the detachment at Cape Hatteras, as well as the strength of the Florida Current.\nEarly studies focused on the relationship between tide gauge observations and the Gulf Stream over seasonal timescales between Florida and Cape Hatteras. Two linkages between ocean circulation and DSL were considered: the cross-stream (shelf) sea level gradient, related to ocean circulation via geostrophy, and the downstream (along-coast) sea level gradient, related via the Bernoulli principle. Montgomery (1941) found little evidence for a relationship of the downstream sea level gradient to velocity (in the Gulf Stream).\nAttempts to relate the cross-stream gradient to Gulf Stream fluctuations were more successful. By examining tide gauges along the Florida coastline, and between Charleston and Bermuda, Montgomery (1938) concluded that fluctuations in Gulf Stream strength could be seen in cross-stream sea level measurements. The study of Iselin (1940) supported the utility of tide gauges south of Cape Hatteras (Key West to Charleston) for estimating the Gulf Stream strength. Both studies were based on comparison with shipboard hydrography and related a summer-to-fall increase in sea level to a drop in Gulf Stream transport. Hela (1951) revisited the two earlier studies to relate the annual cycle of sea level difference from Miami to Cat Cay, Bahamas to transport estimates of the Gulf Stream from ship drift (Fuglister, 1948), finding a high correlation (r = 0.95) between the zonal sea level gradient and meridional transport in the Gulf Stream. Blaha (1984) removed local effects of the inverse barometer, seasonal steric effects, river runoff, and local wind stress, to demonstrate that the residual sea level variability had a robust correlation with Gulf Stream transport on seasonal timescales. More recently, Park and Sweet (2015) found an interannual- to decadal-timescale relationship between Florida Current transport and tide gauge observations at three locations in Florida using empirical mode decomposition, with a scaling coefficient determined to be consistent with geostrophic balance.\nSimilar techniques have been used to examine links between Gulf Stream transport variability and sea level in the Mid-Atlantic Bight. Ezer (2013) found a longer-period relationship between Mid-Atlantic Bight DSL and the sea surface gradient across the detached Gulf Stream. The offshore DSL gradient was found to be correlated with sea level at individual tide gauge locations over decadal timescales, as suggested by Yin and Goddard (2013). However, the robustness of these longer period relationships, found using statistical techniques including empirical mode decomposition, has been questioned (Chambers, 2015). Model-based support for observed Florida Current and Gulf Stream correlations is stronger on short timescales: for example, while idealized modeling studies show that an oscillatory transport of Gulf Stream is associated with coherent coastal sea level variations along the southeast U.S. coast (Ezer, 2016), Woodworth et al. (2017) do not see evidence of Florida Current transport variations in annual mean sea level, either averaged south of Cape Hatteras or in the difference of sea level averaged over the coastline north and south of Cape Hatteras.\nCoastal sea level has also been related to the position of the Gulf Stream on leaving the coast at Cape Hatteras, known as the Gulf Stream North Wall (GSNW; Fuglister, 1955). Indices of the GSNW based on sea surface temperature exist since 1966 (Taylor & Stephens, 1980) and based on temperature at 200 m since 1955 (Joyce & Zhang, 2010). The GSNW has been shown to exhibit quasi-decadal fluctuations that are similar to those in sea level data along the U.S. East Coast (McCarthy et al., 2019; Nigam et al., 2018). Kopp (2013) found a significant antiphase relationship between the GSNW index and DSL north of Cape Hatteras and a likely in-phase relationship between GSNW and DSL south of Cape Hatteras. McCarthy et al. (2015) noted the difference of sea level south and north of Cape Hatteras projected onto the surface velocity of the GSNW. Whether these sea level variations reflect AMOC strength changes relies upon an understanding of the interaction of different AMOC components: Early explanations associated an AMOC strengthening with a northward shift in the GSNW (e.g., Eden & Jung, 2001). However, recent literature indicates the inverse; AMOC strengthening drives a southward shift in the GSNW due to coupling between the Gulf Stream, Deep Western Boundary Current, and topography (Joyce & Zhang, 2010; Sanchez-Franks & Zhang, 2015; Yeager, 2015; Zhang & Vallis, 2007).\nAMOC variability may also be related to heat content and density variations in the subtropical and subpolar gyres (Williams et al., 2014). Such changes in gyre properties have been found to be correlated with U.S. East Coast sea level changes (Thompson & Mitchum, 2014). Frederikse et al. (2017) find that, after being adjusted for local atmospheric (wind and pressure) effects and smoothed on decadal timescales, sea level changes from tide gauges north of Cape Hatteras over 1965\u20132014 are correlated with upper-ocean steric height changes in the Labrador Sea and the deep midlatitude North Atlantic intergyre region. This is consistent with the strong relationship between U.S. coastal sea level and Labrador Sea level in the CMIP5 ensemble (Minobe et al., 2017).\nOther studies have considered property differences between gyres, in particular the meridional density gradient, as an indicator of AMOC strength (Butler et al., 2015; De Boer et al., 2010; Kienert & Rahmstorf, 2012; Rahmstorf, 1996; Rahmstorf et al., 2015; Sijp et al., 2012; Thorpe et al., 2001). The meridional density gradient can be related to the gyre-scale sea level gradient, which has been shown to be related to the strength of the AMOC over sufficiently long timescales (multidecadal and longer; Butler et al., 2015). This relationship was investigated by McCarthy et al. (2015), who used differences in DSL north and south of Cape Hatteras as an estimate of the meridional density gradient between the subtropical and subpolar gyres. The meridional gradient projected strongly onto the circulation in the intergyre region and changes in the subpolar heat content on interannual to decadal timescales. Output from a NEMO 0.25\u00b0 simulation related the differences in DSL north and south of the modeled Gulf Stream separation to the meridional heat transport at 40\u00b0N, indicating a relationship to AMOC.\nPossible Sources of Regional, Intermodel, and Model-Observational Discrepancies\uf0c1\nThe diagnostic geostrophic relationship between AMOC transport and U.S. East Coast sea level derived in section 3 implies a scaling coefficient of order \u22121 to \u22122 cm/Sv with little alongshore variation. Although some numerical simulations find coefficients within this range over portions of the U.S. East Coast, a uniform along-coast scaling of AMOC strength and DSL is not evident (section 4). These deviations from theory likely result from neglect of terms in the more complete zonal momentum balance (e.g., friction, nonlinearities, time dependence), or a breakdown in the assumption that U.S. East Coast sea level is related to the depth-averaged boundary pressure via a constant effective layer thickness (He in equation 6). Similarly, intermodel differences under identical forcing must originate in the relative magnitude of neglected dynamical terms, and their treatment in models. Observations of other components of the North Atlantic circulation offer general support for antiphase relationships between large-scale meridional transport and DSL along portions of the U.S. east coast but are constrained by their limited record length and indirect relationship with AMOC (section 5).", "source": "https://sealeveldocs.readthedocs.io/en/latest/little19.html"}
{"id": "e48670af6dee-6", "text": "Possible Sources of Regional, Intermodel, and Model-Observational Discrepancies\uf0c1\nThe diagnostic geostrophic relationship between AMOC transport and U.S. East Coast sea level derived in section 3 implies a scaling coefficient of order \u22121 to \u22122 cm/Sv with little alongshore variation. Although some numerical simulations find coefficients within this range over portions of the U.S. East Coast, a uniform along-coast scaling of AMOC strength and DSL is not evident (section 4). These deviations from theory likely result from neglect of terms in the more complete zonal momentum balance (e.g., friction, nonlinearities, time dependence), or a breakdown in the assumption that U.S. East Coast sea level is related to the depth-averaged boundary pressure via a constant effective layer thickness (He in equation 6). Similarly, intermodel differences under identical forcing must originate in the relative magnitude of neglected dynamical terms, and their treatment in models. Observations of other components of the North Atlantic circulation offer general support for antiphase relationships between large-scale meridional transport and DSL along portions of the U.S. east coast but are constrained by their limited record length and indirect relationship with AMOC (section 5).\nIn this section, we highlight findings from three areas of research that can at least partially account for these regional, intermodel, and model-observational discrepancies via: (1) friction and bathymetry at the coast, (2) local forcing, and (3) temporal and spatial incoherence of AMOC and its components. In section 7, we suggest opportunities to better integrate these findings into the sea level literature.\nFriction and Topographic Influence on Coastal Sea Level\uf0c1\nMost analyses noted in sections 4 and 5 interpret AMOC-DSL relationships based on geostrophy. To understand offshore influences on coastal sea level, however, requires addressing ageostrophic flows and forcing on the slope and shelf, where water column thickness goes to zero and friction is important.\nRecently, Minobe et al. (2017) have addressed coastal DSL onshore of a western boundary current using a reduced gravity, vertical sidewall model. Such a framework bears similarity to that used in other studies of remotely forced coastal sea level variability in western boundary regions (e.g., Hong et al., 2000; Thompson & Mitchum, 2014). In this model, interior DSL gradients are moderated by friction within a coastal boundary layer. Their main result can be written as\nfrac{h_W}{f} = (frac{h_W}{f})_0 + int_y^{y_0} frac{beta h_I}{f^2} dy\u2019\nwhere h_W and h_I are sea level as a function of latitude (y) at the western boundary and in the ocean interior respectively (h_I is taken near the boundary, but to the east of any western boundary current.) The integral is from the y value of interest to a reference point y_0 further north, where frac{h_W}{f} = (frac{h_W}{f})_0. The western boundary sea level is determined from a combination of the interior ocean sea level and the sea level from higher latitudes; coastal sea level anomalies are smaller than those in the interior and shifted toward the equator for reasons which become clearer if the vertical sidewall case is seen as a limiting case of a sloping continental shelf and slope.\nThe southward shift and weakening of the \u201cinterior\u201d sea level signal as it approaches the coast is reminiscent of the linear, barotropic case with a sloping sidewall as explored by Becker and Salmon (1997) following the ideas of Welander (1968). Instead of being controlled by contours of constant f, as in the flat-bottom case, the flow is controlled by contours of constant f/H, where H is the ocean depth. With varying bathymetry, the subpolar gyre intrudes between the coast and the extension of the subtropical gyre, resulting in a reversing pattern of currents along the continental slope, rather than a simple single-signed western boundary current. Similar behavior is found in highly nonlinear and baroclinic cases with a sloping sidewall (e.g., Jackson et al., 2006, their Figure 1). Sea level signals from the interior therefore appear further equatorward at the coast.\nWise et al. (2018) assess the influence of continental shelf bathymetry, using linear dynamics and ocean bottom pressure as the central variable (equivalent to sea level in a single layer case). In this formalism, sea level is \u201cadvected\u201d along contours of gH/f (such contours can be thought of as representing the stream function of a fictitious flow carrying the sea level signal toward the coast at a speed which becomes the long Rossby wave speed over a flat bottom). The \u201cadvection\u201d is toward the west and then toward the equator along the slope, in competition with a \u201cdiffusion\u201d by bottom friction (Figure 7).\nFigure 7: From Wise et al. (2018). Sea level contours (nondimensional; dashed negative) for a given idealized coastal bathymetry along the western boundary of an ocean basin, where x and y are the nondimensional across-shore and alongshore coordinates, respectively. Vertical dotted lines indicate the continental shelf break at x = S and continental slope floor at x = 1. Panels show sea level patterns for different P\u00e9clet numbers: (a) Pa = 0.1, (b) Pa = 0.1, (c) Pa = 10, and (d) Pa = 200. Panels (b)\u2013(d) show only the coastal region.\uf0c1\nAs the coast is approached, the geostrophic shoreward flow becomes balanced by an offshore flow in the bottom Ekman layer, as in Csanady (1978). Friction is required for alongshore sea level gradients to exist without a flow through the coast, as a purely geostrophic balance would imply.\nWhen shelf bathymetry is included, coastal sea level is still determined by the combination of a poleward reference value, and a weighted integral of interior sea level between that poleward latitude and the latitude of interest. However, the coastal sea level anomaly can be smaller than that predicted in the Minobe et al. (2017) configuration: the western pressure signal can all be on the continental slope, with shallower currents causing it to be cancelled out at the coast. Wise et al. (2018) find that coastal DSL depends crucially on the strength of the bottom friction and the shelf bathymetry. The major dependence is on a nondimensional number, the analogue P\u00e9clet number Pa = \u03b2HL/r, where H is the offshore layer thickness, L is the width of the topography, and r is a linear bottom friction coefficient (Figure 7). As friction weakens, the coastal signal shifts further south and becomes weaker compared to the interior sea level.\nEquation 8 is a limiting case for a vertical sidewall, in which the solution becomes independent of the strength or form of the friction. In this linear case, the vertical sidewall limit is found to produce the largest coastal signal, for a given upper layer thickness. The mechanism here can be considered to be a breakdown of the assumption that there exists a meaningful effective layer thickness He. Counterpropagating currents over topography mean the boundary pressure pW can change sign over the upper continental slope, so equation 5 shows that He can become larger than H. Thus, the coastal sea level can be smaller than that implied by the depth-averaged pressure divided by a meaningful effective layer depth. This reduction of the coastal signal can be interpreted as the result of the influence of coastal trapped waves, which carry the interior signal equatorward along the western boundary, as seen for periods of a few days in the model simulations of Ezer (2016). See Hughes et al. (2019) for more detail on the smoothing and \u201cadvective\u201d effect of coastal trapped waves on boundary sea level.\nWe should note, though, that although friction plays a crucial role in communicating sea level changes to the coast, it does so in a manner which does not affect the zonal momentum balance (equation 1), which remains geostrophic.\nLocally (Shelf-) Forced Sea Level Variability\uf0c1\nThe presence of locally forced sea level variability along the shelf may interfere with the simple AMOC-DSL scaling. Similar to section 6.1, ageostrophic dynamics are relevant, although in this case they may also upset the zonal momentum balance.\nLocal meteorological and terrestrial forcing mechanisms, namely, winds, barometric pressure, and river runoff, have long been shown to drive U.S. East Coast sea level variability. Part of this variability can be static in nature, as with the case of inverted barometer effects related to atmospheric pressure, which are found to contribute sizably to variability at many tide gauges (Piecuch & Ponte, 2015; Ponte, 2006). By definition, static signals are not directly related to circulation changes. As such, their separate treatment, and removal if possible, is useful when assessing the relation between tide gauge and AMOC variability.", "source": "https://sealeveldocs.readthedocs.io/en/latest/little19.html"}
{"id": "e48670af6dee-7", "text": "Equation 8 is a limiting case for a vertical sidewall, in which the solution becomes independent of the strength or form of the friction. In this linear case, the vertical sidewall limit is found to produce the largest coastal signal, for a given upper layer thickness. The mechanism here can be considered to be a breakdown of the assumption that there exists a meaningful effective layer thickness He. Counterpropagating currents over topography mean the boundary pressure pW can change sign over the upper continental slope, so equation 5 shows that He can become larger than H. Thus, the coastal sea level can be smaller than that implied by the depth-averaged pressure divided by a meaningful effective layer depth. This reduction of the coastal signal can be interpreted as the result of the influence of coastal trapped waves, which carry the interior signal equatorward along the western boundary, as seen for periods of a few days in the model simulations of Ezer (2016). See Hughes et al. (2019) for more detail on the smoothing and \u201cadvective\u201d effect of coastal trapped waves on boundary sea level.\nWe should note, though, that although friction plays a crucial role in communicating sea level changes to the coast, it does so in a manner which does not affect the zonal momentum balance (equation 1), which remains geostrophic.\nLocally (Shelf-) Forced Sea Level Variability\uf0c1\nThe presence of locally forced sea level variability along the shelf may interfere with the simple AMOC-DSL scaling. Similar to section 6.1, ageostrophic dynamics are relevant, although in this case they may also upset the zonal momentum balance.\nLocal meteorological and terrestrial forcing mechanisms, namely, winds, barometric pressure, and river runoff, have long been shown to drive U.S. East Coast sea level variability. Part of this variability can be static in nature, as with the case of inverted barometer effects related to atmospheric pressure, which are found to contribute sizably to variability at many tide gauges (Piecuch & Ponte, 2015; Ponte, 2006). By definition, static signals are not directly related to circulation changes. As such, their separate treatment, and removal if possible, is useful when assessing the relation between tide gauge and AMOC variability.\nEffects of local winds have been extensively examined in the observational studies of Blaha (1984), Andres et al. (2013), Domingues et al. (2018), and others. Simple regression analyses suggest an important contribution of local winds, particularly the alongshore component, to observed tide gauge variability at interannual to decadal timescales. Setup from onshore winds can also contribute to static variability at the coast (e.g., Thompson, 1986), but separate estimation of these effects has not been examined in detail. Recent studies (Domingues et al., 2018; Li et al., 2014; Little et al., 2017; Piecuch et al., 2016; Woodworth et al., 2014) reinforce the importance of near-coastal winds and barotropic dynamics to explain US east coast tide gauge records over interannual to decadal timescales.\nMuch less studied has been the effect of river runoff. Meade and Emery (1971) found that about 20\u201329% of variations in detrended annual mean sea level in U.S. East Coast tide gauges could be accounted for by changes in riverine input. Their results are consistent with the analysis by Piecuch, Bittermann, et al. (2018), who relate sea level signals to the buoyancy-driven geostrophic coastal currents associated with the runoff. Other studies focusing on different river systems and utilizing different data sets have concluded that riverine input is negligible. For example, Hong et al. (2000) found contributions from runoff to be unimportant relative to winds for tide gauges south of 38\u00b0N (see also Blaha, 1984). Calafat et al. (2018) did not find a relationship between river runoff and decadal modulations in the amplitude of the sea level annual cycle along the South Atlantic Bight. However, beyond the few studies noted here, most US east coast sea level studies have ignored riverine effects.\nRegardless of its origin, the presence of local forcing can lead to large sea level variations that mask the open ocean influence, and thus the emergence of AMOC-associated sea level variability relative to locally forced variability. For example, correlations of DSL and AMOC are weaker in simulations that include wind forcing, particularly close to the coast and along the Northeast U.S. shelf (Figure 8).\nFigure 8: From Woodworth et al. (2014). (a) Correlations of detrended values of annual mean sea level and overturning transport at the same latitude for depths between 100 and 1,300 m using the simulations shown in Figure 6a (without wind forcing). (b) As in Figure 8a, with winds.\uf0c1\nThe fact that atmospheric variability has an almost white spectrum means that locally forced variability will tend to be the dominant influence at higher frequencies, with emergence of the open ocean influence at lower frequencies. Little et al. (2017) conclude, using a climate model ensemble, that coherence with AMOC emerges along the northeast U.S. coast at periods of around 20 years. This conclusion echoes Woodworth et al. (2014), who find that local winds dominate nearshore sea level variability on interannual timescales.\nWe note, however, that local forcing may evolve over longer timescales and may be responsible for some of the model spread seen in Figure 5. For example, Woodworth et al. (2017) suggest that changes in the 20th century wind field may underlie long-period changes in coastal sea level. Furthermore, atmospheric forcing is spatially coherent over very large scales; changes in local forcing may be associated with large-scale patterns of change that also influence AMOC and/or remote regions of the ocean.\nSpatiotemporal Complexity of AMOC, Hydrography, and Current Changes\uf0c1\nThe fact that AMOC is the residual of a spatially and temporally complex system of surface and deep currents (Figure 2; see other reviews in this volume) underscores the relevance of the previous two sections for interpretations of observations: any current used as a proxy for AMOC (e.g., the Florida Current) may be characterized by an ageostrophic momentum balance (e.g., due to inertial terms in western boundary currents, or frictional effects in coastal currents). In fact, it is likely that ageostrophic terms become more important at these smaller scales.\nAn additional important consideration is that currents may be zonally or meridionally compensated, either over shorter timescales, or in the steady state. Observations and modeling studies reveal that changes in AMOC can arise from changes in any of its components, including the interior subtropical gyre (Duchez et al., 2014; Smeed et al., 2018; Zhao & Johns, 2014) and subpolar gyre (Kwon & Frankignoul, 2014; Yeager, 2015), western boundary currents (Beadling et al., 2018; Thomas et al., 2012), and the formation of deep water at high latitude (Medhaug et al., 2011). Additional changes and variability also arise through near-surface Ekman transports (Kanzow et al., 2007), their barotropic compensation (Jayne & Marotzke, 2001), and eddy transports (e.g., Thomas & Zhai, 2013). All of these exhibit varying degrees of zonal and meridional coherence, reflecting a multitude of forcings occurring over different timescales (Wunsch & Heimbach, 2013).\nFor example, the Gulf Stream, by which we refer to the full western boundary current near southern Florida, has two branches: the Florida Current and the Antilles Current, which flows offshore of the Bahama Banks (Figure 2). While the Florida Current carries a larger mean transport (about 32 Sv compared with about 5 Sv in the Antilles Current), both exhibit comparable variability (Lee et al., 1996). Thus, the total western boundary current flow could be constant, but its effect on coastal DSL would vary depending upon the respective contributions of the Florida and Antilles currents. In addition, assessing trends in the volume transport of complex, evolving, western boundary currents is challenging. This difficulty underlies the debate surrounding Ezer et al.\u2019s (2013) conclusion that a Gulf Stream decline was responsible for accelerated sea level rise in the mid-Atlantic Bight (Ezer, 2015; Rossby et al., 2014). The deviation in Gulf Stream transport calculations found across studies is perhaps not surprising, given longitudinally varying changes in the Gulf Stream velocity, width, and position (Dong et al., 2019), and the presence of Gulf Stream meanders, eddies, and recirculation gyres.", "source": "https://sealeveldocs.readthedocs.io/en/latest/little19.html"}
{"id": "e48670af6dee-8", "text": "For example, the Gulf Stream, by which we refer to the full western boundary current near southern Florida, has two branches: the Florida Current and the Antilles Current, which flows offshore of the Bahama Banks (Figure 2). While the Florida Current carries a larger mean transport (about 32 Sv compared with about 5 Sv in the Antilles Current), both exhibit comparable variability (Lee et al., 1996). Thus, the total western boundary current flow could be constant, but its effect on coastal DSL would vary depending upon the respective contributions of the Florida and Antilles currents. In addition, assessing trends in the volume transport of complex, evolving, western boundary currents is challenging. This difficulty underlies the debate surrounding Ezer et al.\u2019s (2013) conclusion that a Gulf Stream decline was responsible for accelerated sea level rise in the mid-Atlantic Bight (Ezer, 2015; Rossby et al., 2014). The deviation in Gulf Stream transport calculations found across studies is perhaps not surprising, given longitudinally varying changes in the Gulf Stream velocity, width, and position (Dong et al., 2019), and the presence of Gulf Stream meanders, eddies, and recirculation gyres.\nUnderstanding the timescales over which the AMOC indicators discussed in section 5 (e.g., the Gulf Stream, and gyre densities) and AMOC strength variations are coherent is critical to their use as proxies of AMOC. There is little evidence for seasonal and interannual variability of the Florida Current or the Gulf Stream (characteristic over the timescales of many studies cited in section 5) to be related to AMOC. Using evidence that Sverdrup balance holds on multiannual to decadal timescales in the interior subtropics (Gray & Riser, 2014; Thomas et al., 2014; Wunsch, 2011), it can be demonstrated that (subtropical) AMOC variability must be mirrored by changes in the western boundary current at these timescales (de Boer & Johnson, 2007; Thomas et al., 2012). The Gulf Stream can therefore be expected to concentrate decadal-period changes in both the wind-driven and the thermohaline circulations, both of which are predicted to weaken in the 21st century (Beadling et al., 2018; Lique & Thomas, 2018; Thomas et al., 2012). However, this finding only applies southward of approximately 35\u00b0N, since the ocean to the north is not in Sverdrup balance (Gray & Riser, 2014; Thomas et al., 2014). Furthermore, there is no satisfactory way of defining the boundary between a western boundary current and the ocean interior when the ocean is dominated by mesoscale eddies (Wunsch, 2008). Models and observations also reveal a strong gyre dependence of AMOC changes, with interannual variability dominating in the subtropical gyre and decadal variability in the subpolar gyre (e.g., Bingham et al., 2007; Wunsch, 2011; Wunsch & Heimbach, 2013; Zhang, 2010). Lozier et al. (2010) used a data-assimilating numerical model to further demonstrate that gyre-dependent AMOC changes might be important on up to multidecadal periods.\nRelatedly, there is evidence that property changes in the subpolar and subtropical gyres may not reflect changes in AMOC over certain timescales. Processes governing ocean density changes in this region on decadal timescales remain unclear (Williams et al., 2015; Buckley & Marshall, 2016; Menary et al., 2015; Piecuch, Ponte, et al., 2017; Robson et al., 2016); remote Rossby wave signals, local atmospheric forcing, changes in deep convection and water mass formation, mean flow advection, and gyre circulation \u201cwobbles\u201d all potentially play a role (Buckley & Marshall, 2016). Although data collected in the subpolar and subtropical gyres suggest southward propagation of deep hydrographic properties on advective (multiannual to decadal) timescales in the Labrador Current and Deep Western Boundary Current of the subtropical gyre (e.g., Molinari et al., 1998; Talley & McCartney, 1982; van Sebille et al., 2011), tracer studies have identified that the majority of water in the Labrador Current does not pass southwards into the subtropical gyre but instead cyclonically recirculates back around within the subpolar gyre (e.g., Bower et al., 2009; Rhein et al., 2002; Zou & Lozier, 2016). Of the deep subpolar water that is advected into the subtropical gyre, the intergyre pathway is not principally via the Deep Western Boundary Current but rather through the interior ocean (Bower et al., 2009; Lozier, 2010; Zhang, 2010), which is compensated by slow upper ocean advective pathways northwards out of the subtropical gyre that reach the greatest transport at depths of approximately 700 m (Burkholder & Lozier, 2011, 2014).\nImplications for Along-Coast Variations and Across-Model Differences\uf0c1\nCollectively, sections 6.1 to 6.3 indicate that U.S. East Coast continental shelf bathymetry, and the evolution of western boundary and coastal currents under local- and large-scale forcing, will influence the local coastal sea level expression associated with a given change in AMOC. The importance of these processes should be expected to vary regionally (e.g., north and south Cape Hatteras, but also within each region); future studies might probe the influence of these smaller scale along-coast variations on local sea level gradients (see section 7).\nFocusing on time-mean sea level on the shelf, Higginson et al. (2015) suggest that coarse resolution models may exhibit errors in the representation of coastal sea level due to inadequate horizontal resolution, the form of the coastal boundary condition, poor representation of processes in shallow water, and/or unresolved continental shelf atmospheric forcing. Sections 6.1 and 6.2 support the importance of the representation of these coastal processes, and imply that differences in the model resolution may underlie some of the spread shown in Figure 5.\nOver the global coastal ocean, Becker et al. (2016) find that climate models have a wide range of success in reproducing the spectral characteristics of observed tide gauge sea level variability. Little et al. (2017) specifically tested the ability of an initial condition ensemble of Community Earth System Model simulations to represent interannual U.S. East Coast DSL variability, finding that Community Earth System Model agrees well with observed tide gauge data along the Northeast U.S. coast, but poorly represents the time-mean and variability of DSL south of Cape Hatteras. The Minobe et al. (2017) framework (section 6.1) also exhibits disagreement with CMIP5 US east coast DSL changes south of ~35\u00b0N (see their Figure 10). This suggests that large-scale models might be particularly limited in the South Atlantic Bight. Here, in addition to complex shelf bathymetry, DSL variability may also be influenced by incoherence between the Gulf Stream and AMOC, the complex vertical and horizontal structure of western boundary currents, the potential effect of rapid western boundary current flow against the prevailing propagation of information in the direction of boundary waves, and the Antilles Current (section 6.3).\nPenduff et al. (2010) find that higher-resolution models (as fine as 0.25\u00b0) show improved representations of variability and time-mean Sea Surface Height (SSH), especially in the eddy rich regions, in comparison to altimetry. Coastal sea level variability also appears improved with finer resolution, and DSL change under strong external forcing appears to be moderated near the coastline in models of higher resolution (Liu et al., 2016). Other high-resolution simulations show substantial modification of the coastal sea level signal (e.g., the two MPI models in Figure 5). Such resolution effects deserve more investigation as simulations become available (see, e.g., Haarsma et al., 2016).\nIn addition to the varied, resolution-dependent, representation of coastal processes and shelf bathymetry in models, which might be expected to disproportionately affect coastal DSL, the spatial variability in the \u201cinterior\u201d DSL change in CMIP5 models implies that more complex changes in the 2-D overturning, or in the 3-D structure of the North Atlantic circulation, are relevant for determining patterns of DSL change. Bouttes et al. (2014) suggest that the underlying driver of differences in large-scale DSL change is related to locations of deep convection. Support for dependence on forcing is also evident in Kienert and Rahmstorf (2012), who find a substantially different DSL response to AMOC changes associated with different forcing (freshwater hosing, CO2 increases, Southern Ocean wind stress changes) within the same climate model.\nPerspective and Future Directions\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/little19.html"}
{"id": "e48670af6dee-9", "text": "Penduff et al. (2010) find that higher-resolution models (as fine as 0.25\u00b0) show improved representations of variability and time-mean Sea Surface Height (SSH), especially in the eddy rich regions, in comparison to altimetry. Coastal sea level variability also appears improved with finer resolution, and DSL change under strong external forcing appears to be moderated near the coastline in models of higher resolution (Liu et al., 2016). Other high-resolution simulations show substantial modification of the coastal sea level signal (e.g., the two MPI models in Figure 5). Such resolution effects deserve more investigation as simulations become available (see, e.g., Haarsma et al., 2016).\nIn addition to the varied, resolution-dependent, representation of coastal processes and shelf bathymetry in models, which might be expected to disproportionately affect coastal DSL, the spatial variability in the \u201cinterior\u201d DSL change in CMIP5 models implies that more complex changes in the 2-D overturning, or in the 3-D structure of the North Atlantic circulation, are relevant for determining patterns of DSL change. Bouttes et al. (2014) suggest that the underlying driver of differences in large-scale DSL change is related to locations of deep convection. Support for dependence on forcing is also evident in Kienert and Rahmstorf (2012), who find a substantially different DSL response to AMOC changes associated with different forcing (freshwater hosing, CO2 increases, Southern Ocean wind stress changes) within the same climate model.\nPerspective and Future Directions\uf0c1\nAn antiphase relationship between large-scale North Atlantic meridional volume transport and U.S. East Coast DSL is broadly evident across a range of numerical simulations and observational analyses. This relationship can be interpreted using the simple geostrophic framework introduced in section 3. However, such a framework is insufficient to explain the widely differing along-coast AMOC-DSL scalings derived in models and observations, or variation across climate models. Furthermore, such an interpretation limits causal attribution: Geostrophy cannot provide information about the forces that drive sea level changes.\nIn this review, we have noted some possible origins for regional, model, timescale, and forcing dependence (section 6). However, we are unable to assess the degree to which each is responsible for variations in local scaling coefficients. Explanations for these deviations are essential to improve confidence in reconstructions of North Atlantic variability derived from tide gauge observations or paleoproxies and projections of coastal sea level change from current-generation climate models.\nWe thus encourage the sea level research community to pursue the following near-term goals: (1) an understanding of the relationship between AMOC and other North Atlantic currents; (2) an understanding of the vertical structure of the AMOC and its variation with respect to local bathymetry; (3) an assessment of the importance of ageostrophic processes to AMOC and related currents; and (4) an effort to connect these research results, including their region (latitude-), model, and timescale dependence, to their origins in heat, momentum, and buoyancy forcing. Such efforts should include new sea level studies, as well as the incorporation of existing and new findings from outside the sea level realm.\nA simple step toward the first and second goals involves broadening the features of the ocean circulation analyzed in models beyond a single AMOC metric (e.g., the basin-wide maximum overturning stream function). Modeled and observed DSL changes have often been compared to AMOC changes at a different latitude, which involves an implicit or explicit assumption that such changes are synchronous and meridionally coherent, which is not supported by the literature cited in section 6.3. Indeed, such a coarse characterization of AMOC may underlie some of the difference in scaling coefficients shown in Figure 5.\nAs noted in section 4, another critical ambiguity of relevance, particularly important to the interpretation of observational analyses, is the coherence of AMOC and western boundary currents. Other important relationships include those between the GSNW and AMOC; Labrador Sea and subpolar gyre steric changes; and subpolar and subtropical gyre steric changes. Higher-resolution simulations can now represent the mean state and variability of coastal currents and indicate that climate-driven changes in these currents may differ from those in the large-scale (e.g., Saba et al., 2016). Although evidence in section 6.3 suggests that many components of AMOC, and subpolar and Nordic Seas buoyancy variability, may be coherent over multidecadal time frames (Pillar et al., 2016), there is evidence that interannual to decadal variability is not, particularly across the intergyre boundary. Modeling studies examining AMOC-DSL relationships can easily include metrics of some of these other AMOC components and indicators (possibly over different timescales), which would improve the scope of their results, and the ability to reconcile with observations.\nThe direct observational record of AMOC variability is limited; in this review, we have focused on the longer observed record of AMOC components. However, the ever extending record of AMOC at 26\u00b0N is now complemented by the OSNAP array, providing some perspective on gyre dependence, the meridional coherence of AMOC, and the relationship with other AMOC components. These AMOC records are complemented by new observational campaigns over the U.S. East coast continental shelf and slope (e.g., Andres et al., 2018, Gawarkiewicz et al., 2018). In addition to these instrumental records, proxy records of both coastal sea level and AMOC are available that are able to resolve decadal-centennial fluctuations (Engelhart & Horton, 2012; Kemp et al., 2017, 2018; Rahmstorf et al., 2015; Thornalley et al., 2018). Complemented by model results, these proxy observations could provide valuable constraints on multidecadal to centennial AMOC-DSL covariability.\nWith respect to the assessment of ageostrophic processes, we note that many modeling centers have begun to provide the output required to compute closed momentum budgets offline (Gregory et al., 2016; Wunsch & Heimbach, 2009; Yeager, 2015). Such budgets, both zonally integrated, and local, would clearly indicate the importance of ageostrophic processes, their time and latitude dependence, and (if possible) differences across a set of models. They could also include the effect of terms, including nonlinearity (Hughes et al., 2019), and, in higher-resolution models, eddy variability (Gr\u00e9gorio et al., 2015; S\u00e9razin et al., 2015), that are not discussed in this review. High-resolution models also offer promise for better resolving the shelf and shelf processes, and they may constitute a means for testing the theories of coastal modulation of interior signals (section 6.1), under a wider range of conditions, forcing, and timescales.\nSuch analyses also move beyond the purely diagnostic, degenerate, statement of force balance supplied by geostrophy, allowing an understanding of the local, regional, basin, and global scale forcing responsible for coastal sea level changes. The incomplete interpretation provided by geostrophy is evident in Goddard et al. (2015), who linked an \u201cextreme\u201d interannual sea level rise event in the northeast US with an abrupt 30% AMOC weakening. However, this event occurred coincident with an anomalously negative North Atlantic Oscillation (NAO) associated with atmospheric pressure and wind anomalies. Piecuch and Ponte (2015) and Piecuch et al. (2016) demonstrated that 50% of this event could be explained by the inverse barometer effect and the remainder could be partly explained by local winds. The 30% drop in the AMOC itself was observed in the Gulf Stream transport (Ezer, 2015) and was explained by wind forcing (Zhao & Johns, 2014). It is thus more appropriate to view the sea level anomaly as driven by all of the forcings (local and remote) associated with the extreme NAO anomaly. Over longer timescales, causality often remains unclear: for example, differences in observed sea level changes along the US east coast have been attributed to changes in Gulf Stream position and strength, AMOC strength, and steric changes. While these changes may be coupled, and serve as indicators of AMOC, they do not identify causal drivers.\nEven if causality can be established under certain forcing and timescales (e.g., interannual, driven by NAO), it does not imply that the same processes and AMOC components (and sea level signatures) are always relevant (e.g., on centennial timescales in the past or future). For example, Kenigson et al. (2018) find that the relationship between DSL and NAO is nonstationary, echoing the results of Andres et al. (2013). Looking farther into the future, 21st century changes in AMOC strength in climate models are principally forced by greenhouse gas-associated heat and buoyancy fluxes in the North Atlantic (Beadling et al., 2018; Bouttes et al., 2014; Slangen et al., 2015), rather than NAO-associated wind stress.", "source": "https://sealeveldocs.readthedocs.io/en/latest/little19.html"}
{"id": "e48670af6dee-10", "text": "Such analyses also move beyond the purely diagnostic, degenerate, statement of force balance supplied by geostrophy, allowing an understanding of the local, regional, basin, and global scale forcing responsible for coastal sea level changes. The incomplete interpretation provided by geostrophy is evident in Goddard et al. (2015), who linked an \u201cextreme\u201d interannual sea level rise event in the northeast US with an abrupt 30% AMOC weakening. However, this event occurred coincident with an anomalously negative North Atlantic Oscillation (NAO) associated with atmospheric pressure and wind anomalies. Piecuch and Ponte (2015) and Piecuch et al. (2016) demonstrated that 50% of this event could be explained by the inverse barometer effect and the remainder could be partly explained by local winds. The 30% drop in the AMOC itself was observed in the Gulf Stream transport (Ezer, 2015) and was explained by wind forcing (Zhao & Johns, 2014). It is thus more appropriate to view the sea level anomaly as driven by all of the forcings (local and remote) associated with the extreme NAO anomaly. Over longer timescales, causality often remains unclear: for example, differences in observed sea level changes along the US east coast have been attributed to changes in Gulf Stream position and strength, AMOC strength, and steric changes. While these changes may be coupled, and serve as indicators of AMOC, they do not identify causal drivers.\nEven if causality can be established under certain forcing and timescales (e.g., interannual, driven by NAO), it does not imply that the same processes and AMOC components (and sea level signatures) are always relevant (e.g., on centennial timescales in the past or future). For example, Kenigson et al. (2018) find that the relationship between DSL and NAO is nonstationary, echoing the results of Andres et al. (2013). Looking farther into the future, 21st century changes in AMOC strength in climate models are principally forced by greenhouse gas-associated heat and buoyancy fluxes in the North Atlantic (Beadling et al., 2018; Bouttes et al., 2014; Slangen et al., 2015), rather than NAO-associated wind stress.\nSeparation of local and remote wind-driven changes in circulation and sea level from remote buoyancy/deep water driven AMOC changes remains a key challenge. Such work will have to illuminate the timescales and climate forcing under which wind and buoyancy forcing are coupled. For example, Woodworth et al. (2014) indicate that wind forcing alone is largely responsible for decadal timescale sea level variability. However, since this study used a standalone ocean model, it is not clear what processes produce low-frequency wind variability. Furthermore, the large spatial scales of atmospheric forcing challenge efforts to isolate the AMOC-forced or remotely forced component of sea level change. Adjoint analyses or perturbation experiments (Heimbach et al., 2011; Pillar et al., 2016; Yeager & Danabasoglu, 2014) may help isolate the roles of wind and buoyancy forcing and elucidate the relevant pathways, state variables, and adjustment processes mediating connections between the open ocean and observed and projected US east coast sea level changes.\nTo conclude, there are many productive areas of research that can help refine our understanding of the relationship between the large-scale climate, AMOC, and coastal sea level. Given their importance to future sea level changes on the U.S. East Coast, and reconstruction of preinstrumental ocean circulation and climate variability, we anticipate the research community will pursue them with vigor.", "source": "https://sealeveldocs.readthedocs.io/en/latest/little19.html"}
{"id": "14d9a88b20c2-0", "text": "Gregory et al. (2019)\uf0c1\nTitle:\nConcepts and Terminology for Sea Level: Mean, Variability and Change, Both Local and Global\nKey Points:\nDescribes concepts and terminology related to sea level, its variability, and changes both locally and globally.\nClarifies language and definitions for better communication in sea-level science\nDiscusses the inconsistencies and ambiguities in sea-level terminology across different disciplines.\nProposes new terminology and recommend replacing certain terms that are unclear or confusing.\nKeywords:\nsea level, concepts, terminology\nCorresponding author:\nJonathan M. Gregory\nCitation:\nGregory, J. M., Griffies, S. M., Hughes, C. W., Lowe, J. A., Church, J. A., Fukimori, I., et al. (2019). Concepts and Terminology for Sea Level: Mean, Variability and Change, Both Local and Global. Surveys in Geophysics, 40(6), 1251\u20131289. doi:10.1007/s10712-019-09525-z\nURL:\nhttps://link.springer.com/article/10.1007/s10712-019-09525-z\nAbstract\uf0c1\nChanges in sea level lead to some of the most severe impacts of anthropogenic climate change. Consequently, they are a subject of great interest in both scientific research and public policy. This paper defines concepts and terminology associated with sea level and sea-level changes in order to facilitate progress in sea-level science, in which communication is sometimes hindered by inconsistent and unclear language. We identify key terms and clarify their physical and mathematical meanings, make links between concepts and across disciplines, draw distinctions where there is ambiguity, and propose new terminology where it is lacking or where existing terminology is confusing. We include formulae and diagrams to support the definitions.\nIntroduction and Motivation\uf0c1\nChanges in sea level lead to some of the most severe impacts of anthropogenic climate change (IPCC 2014). Consequently, they are a subject of great interest in both scientific research and public policy. Since changes in sea level are the result of diverse physical phenomena, there are many authors from a variety of disciplines working on questions of sea-level science. It is not surprising that sea-level terminology is inconsistent across disciplines (for example, \u201cdynamic sea level\u201d has different meanings in oceanography and geodynamics), as well as unclear or ambiguous even within a single discipline. (For instance, \u201ceustatic\u201d is ambiguous in the climate science literature.) We sometimes experience difficulty in finding correct and precise terms to use when writing about sea-level topics, or in understanding what others have written. Such communication problems hinder progress in research and may even confuse discussions about coastal planning and policy.\nThis situation prompted us to revisit the meaning of key sea-level terms, and to recommend definitions along with their rationale. In so doing, we aim to clarify meanings, make links between concepts and across disciplines and draw distinctions where there is ambiguity. We propose new terminology where it is lacking and recommend replacing certain terms that we argue are unclear or confusing. Our goal is to facilitate communication and support progress within the broad realm of sea-level science and related engineering applications.\nIn the next section, we outline the conventions and assumptions we use in our definitions and mathematical derivations. The following three sections (Sects. 3\u20135) contain the definitions, with a subsection for each major term defined, labelled with \u201cN\u201d and numbered consecutively throughout. In Sect. 3 we define five key surfaces: reference ellipsoid, sea surface, mean sea level, sea floor and geoid. We consider the variability and differences in these surfaces in Sect. 4, and quantities describing changes in sea level in Sect. 5. In Sect. 6, we show how relative sea-level change is related to other quantities in various ways. In Sect. 7 we describe how observational data are interpreted using the concepts we have defined. To facilitate sequential reading of this paper, the material of Sects. 3\u20137 is arranged to minimize forward references, though we were unable to avoid all.\nWe give a list of deprecated terms with recommended replacements in Sect. 8, and a list in Sect. 9 of all terms defined, referring to the subsections where they are defined, thus providing an index that also includes our notation. The appendices contain further discussion of some aspects at greater length.\nThe complexity of sea-level science is evident in the detail of the definitions and discussions in this paper. It may therefore be helpful to keep in mind that from the point of view of coastal planning and climate policy there are three quantities of particular interest. Extreme sea level along coasts (i.e., extreme coastal water level) or around offshore marine infrastructure (such as drilling platforms) is of great practical importance because of the enormous damage it can cause to human populations and their built environment and to ecosystems. The expected occurrence of extreme sea level under future climates is therefore relevant to decision-making on a range of time-horizons.\nThe dominant factor in changes of future local extremes is relative sea-level change (RSLC), i.e., the change in sea level with respect to the land (Lowe et al. 2010; Church et al. 2013). Where there is relative sea-level rise, coastal defences have to be raised to afford a constant level of protection against extremes, and low-lying areas are threatened with permanent inundation. Although RSLC depends on many local and regional influences, the majority of coastlines are expected to experience RSLC within a few tens of per cent of global-mean sea-level rise (GMSLR) (Church et al. 2013). Projections of GMSLR are therefore of interest to global climate policy, with both adaptation and mitigation in mind.\nIn general, greater GMSLR is projected for scenarios with higher rates of carbon dioxide emission and on longer timescales. Particular attention is paid, especially by risk-intolerant users, to the probability or possibility of future large changes in sea level (Hinkel et al. 2019). We recommend referring to these as high-end scenarios or projections of RSLC or GMSLR (rather than \u201cextreme\u201d scenarios), to avoid confusion with projections of extreme sea level.\nConventions and Assumptions\uf0c1\nWe here summarize the conventions and assumptions employed in the text and formulae of our definitions.\nFirst Appearance of Terms\uf0c1\nWithin each definition subsection of Sects. 3\u20135, we use bold font for the first appearance of a term whose definition is the subject of another subsection. When we first define a term that does not have its own subsection, it appears with a slanted font. The reader can locate the definitions of terms marked in these ways by looking them up in Sect. 9. In the PDF of this paper, each bold term in Sects. 3\u20138 is a hyperlink to the relevant definition subsection.\nTime-Mean and Changes\uf0c1\nThe sea surface varies on all the timescales of the Earth system, associated with sea-surface waves and tides, meteorological variability (from gustiness of winds to synoptic phenomena such as mid-latitude depressions and tropical cyclones), seasonal, interannual and longer-term internally generated climate variability (e.g., El Ni\u00f1o and the Interdecadal Pacific Oscillation), anthropogenic climate change and naturally forced changes (e.g., by volcanic eruptions, glacial cycles and tectonics). For various purposes of understanding and planning for sea-level variations it is helpful to draw a distinction between a time-mean state and fluctuations within that state. The definition of a \u201cstate\u201d depends on the scientific interest or application. For sea level, the state might be defined by a time-mean long enough to remove tidal influence (about 19 years), or which characterizes a climatological state (conventionally 30 years), but it could be shorter, for example, if interannual variability were regarded as altering the state.\nThus, the time-mean state cannot be absolutely defined, but the concept is necessary. In this paper, mean sea level refers to a time-mean state whose precise definition should be specified when the term is used, and which is understood to be long enough to eliminate the effect of meteorological variations at least. We use symbols with a tilde and time-dependence, e.g., \ud835\udc4b\u0303(\ud835\udc61) for time-varying quantities, and symbols without any distinguishing mark and no time-dependence, e.g., X for time-mean quantities that characterize the state of the system. On longer timescales, the state itself may change, for example, due to anthropogenic influence. We use the symbol \u0394 and the word \u201cchange\u201d to refer to the difference between any two states; thus, \u0394\ud835\udc4b is \u201cchange in X\u201d, e.g., change in relative sea level between the time-mean of 1986\u20132005 and the time-mean of 2081\u20132100. Anthropogenic sea-level change comes mostly through climate change, but there are other influences too, such as impoundment of water on land in reservoirs.\nLocal and Regional\uf0c1\nBy a local quantity, we mean one which is a function of two-dimensional geographical location \ud835\udc2b, specified by latitude and longitude. For some applications, it is important to consider variations of local quantities over distance scales of kilometres or less. Other quantities do not have such pronounced local variation and are typically considered as properties of regions, with distance scales of tens to hundreds of kilometres.\nGlobal Mean Over the Ocean Surface Area\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-1", "text": "Thus, the time-mean state cannot be absolutely defined, but the concept is necessary. In this paper, mean sea level refers to a time-mean state whose precise definition should be specified when the term is used, and which is understood to be long enough to eliminate the effect of meteorological variations at least. We use symbols with a tilde and time-dependence, e.g., \ud835\udc4b\u0303(\ud835\udc61) for time-varying quantities, and symbols without any distinguishing mark and no time-dependence, e.g., X for time-mean quantities that characterize the state of the system. On longer timescales, the state itself may change, for example, due to anthropogenic influence. We use the symbol \u0394 and the word \u201cchange\u201d to refer to the difference between any two states; thus, \u0394\ud835\udc4b is \u201cchange in X\u201d, e.g., change in relative sea level between the time-mean of 1986\u20132005 and the time-mean of 2081\u20132100. Anthropogenic sea-level change comes mostly through climate change, but there are other influences too, such as impoundment of water on land in reservoirs.\nLocal and Regional\uf0c1\nBy a local quantity, we mean one which is a function of two-dimensional geographical location \ud835\udc2b, specified by latitude and longitude. For some applications, it is important to consider variations of local quantities over distance scales of kilometres or less. Other quantities do not have such pronounced local variation and are typically considered as properties of regions, with distance scales of tens to hundreds of kilometres.\nGlobal Mean Over the Ocean Surface Area\uf0c1\nBy global mean, we mean the area-weighted mean over the entire connected surface area of the ocean, i.e., excluding the land. The ocean includes marginal seas connected to the open ocean such as the Mediterranean Sea, Black Sea and Hudson Bay, but excludes inland seas such as the Caspian Sea, the African Great Lakes and the North American Great Lakes. It includes areas covered by sea ice and ice shelves, where special treatment is needed to define the level of the sea surface. We note that observational estimates of the global mean are often made from systems which lack complete coverage.\nFor centennial timescales, we can assume the ocean surface area A is constant, with A = 3.625\u00d710^{14} m^2 (Cogley 2012). It is altered substantially by global-mean sea-level changes of many metres, such as on glacial\u2013interglacial timescales or possibly over future millennia due to ice-sheet changes, and on geological timescales due to plate tectonics. The formulae we give for some quantities describing global-mean changes are not exactly applicable under those circumstances.\nSea-Water Density\uf0c1\nMany of the formulae in this paper involve sea-water density. Although sea-water density is a local quantity, we treat it in many contexts as a globally uniform constant with a representative value \ud835\udf0c\u2217 (e.g., 1028  kg  m \u22123). For the density of freshwater added at the sea surface we use a constant \ud835\udf0cf=1000  kg  m \u22123 for convenience, neglecting the variation of <1% in freshwater density due to temperature.\nVertical Direction and Distance\uf0c1\nBefore considering the vertical location of surfaces, or the local vertical distance between two surfaces, we need to specify the meaning of vertical. Geodesy is concerned with horizontal and vertical distances measured relative to the reference ellipsoid, which is a surface fixed with respect to the solid Earth. Geophysical fluid dynamics, including ocean circulation dynamics, is concerned with horizontal distances on surfaces of constant geopotential, and vertical distances measured perpendicular to such surfaces, especially the geoid. We discuss the two frames of reference (one relative to the reference ellipsoid and the other to the geoid) in the subsections describing those two surfaces. The distinction between the two frames is relevant only to the real world, because numerical ocean circulation models implicitly assume an idealized effective gravity field in which the geoid and the reference ellipsoid are identical (often spherical rather than ellipsoidal). In reality, the geoid has an irregular shape, whose vertical separation from the reference ellipsoid is \u00b1100 m and varies over horizontal length scales of 100s km.\nMost of our formulae involve the local vertical coordinate of surfaces such as \ud835\udc4b(\ud835\udc2b), for which we use the vertical distance above the reference ellipsoid (negative if below). We make this choice in order to give our formulae a well-defined interpretation. The choice of reference frame (with respect either to the reference ellipsoid or to the geoid) does not affect the geophysical definition of a surface, but the numerical value of its vertical coordinate at any given location is not the same in the two frames, because of the substantial difference between their reference surfaces. However, at a given location, there is negligible difference between the two frames regarding the local vertical direction. Hence, we can ignore the difference between the two definitions of \u201cvertical\u201d in evaluating a vertical gradient, the vertical distance \ud835\udc4c(\ud835\udc2b)\u2212\ud835\udc4b(\ud835\udc2b) between two surfaces, or the change in height \u0394\ud835\udc4b(\ud835\udc2b) of a surface.\nSurfaces\uf0c1\nWe here define five key surfaces used in sea-level studies. The reference ellipsoid and the associated terrestrial reference frame (depicted in Fig. 1) are geometrical constructions, chosen by convention. The other four surfaces (compared with the reference ellipsoid in Fig. 2) are geophysically defined and established with some uncertainty from observational data. These and other surfaces, such as datums defined by tides (e.g., mean lower-low water level), are located relative to the reference ellipsoid (Sect. 2.6), by their geodetic height as a function of geodetic location.\nFig. 1: The reference ellipsoid, which is used to locate other surfaces in a terrestrial reference frame, whose origin is the centre of the Earth. The figure shows the construction which defines the geodetic coordinates of an arbitrary point \ud835\udc31 in 3D space. The line between \ud835\udc31 and \ud835\udc2b is normal to the reference ellipsoid, on which \ud835\udc2b lies. The equator is intersected at \ud835\udc29 by the meridian through \ud835\udc2b, and at \ud835\udc290 by the prime meridian, which defines the zero of longitude\nN1 Reference ellipsoid:\nThe surface of an ellipsoidal volume of revolution chosen to approximate the geoid.\nA reference ellipsoid is a conventional geometric construction used to specify locations in a terrestrial reference frame, i.e., relative to the solid Earth. Many reference ellipsoids have been defined by geodesists, and some are intended only for use over limited portions of the globe. A given specification of the reference ellipsoid is time-independent.\nFor purposes relating to global sea level we make the following requirements of the reference ellipsoid.\nIts centre is the time-mean centre of mass of the Earth.\nIts semi-major axis lies in the equatorial plane and its semi-minor axis along the rotation (polar) axis of the Earth.\nIts axis of revolution is the rotation axis.\nIt is fixed with respect to the solid Earth, and it rotates with the Earth.\nThe International Earth Rotation and Reference Systems Service (www.iers.org) defines the International Terrestrial Reference Frame (ITRF). They recommend the GRS80 ellipsoid.\nFor more precise geodetic purposes, the ITRF defines the coordinates and their rates of change of a set of stations on the Earth\u2019s surface. The coordinates are time-dependent because of tectonic motions and true polar wander, i.e., the time-dependence of the Earth\u2019s rotation axis with respect to the solid Earth. The latter phenomenon is neglected in the above specification of the ellipsoid. If the rotation axis is invariant, the last point in our specification above is not necessary because, being a volume of revolution, the reference ellipsoid is symmetrical with respect to rotation about the axis.\nTo locate a point \ud835\udc31 in 3D space in a reference frame based on the reference ellipsoid, we construct a straight line that passes through \ud835\udc31 and is normal to the ellipsoid, which it intersects at \ud835\udc2b. The geodetic height of \ud835\udc31 above the ellipsoid is the distance from \ud835\udc2b to \ud835\udc31 along this line, positive outwards. In our formulae, the vertical coordinate is the geodetic height, which is sometimes called ellipsoidal height. This is not the usual vertical coordinate for models of atmosphere and ocean circulation, which is instead defined relative to the geoid.\nThe geodetic latitude, commonly referred to simply as latitude, is the angle between the equatorial plane and the normal to the ellipsoid. It is different from the geocentric latitude, which is the angle between the equatorial plane and the line from the centre of the Earth to \ud835\udc31. Geodetic and geocentric latitudes are the same for the poles and the equator, but elsewhere geodetic latitude is larger (as can be appreciated from Fig. 1), by up to about 0.2\u02da.", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-2", "text": "For purposes relating to global sea level we make the following requirements of the reference ellipsoid.\nIts centre is the time-mean centre of mass of the Earth.\nIts semi-major axis lies in the equatorial plane and its semi-minor axis along the rotation (polar) axis of the Earth.\nIts axis of revolution is the rotation axis.\nIt is fixed with respect to the solid Earth, and it rotates with the Earth.\nThe International Earth Rotation and Reference Systems Service (www.iers.org) defines the International Terrestrial Reference Frame (ITRF). They recommend the GRS80 ellipsoid.\nFor more precise geodetic purposes, the ITRF defines the coordinates and their rates of change of a set of stations on the Earth\u2019s surface. The coordinates are time-dependent because of tectonic motions and true polar wander, i.e., the time-dependence of the Earth\u2019s rotation axis with respect to the solid Earth. The latter phenomenon is neglected in the above specification of the ellipsoid. If the rotation axis is invariant, the last point in our specification above is not necessary because, being a volume of revolution, the reference ellipsoid is symmetrical with respect to rotation about the axis.\nTo locate a point \ud835\udc31 in 3D space in a reference frame based on the reference ellipsoid, we construct a straight line that passes through \ud835\udc31 and is normal to the ellipsoid, which it intersects at \ud835\udc2b. The geodetic height of \ud835\udc31 above the ellipsoid is the distance from \ud835\udc2b to \ud835\udc31 along this line, positive outwards. In our formulae, the vertical coordinate is the geodetic height, which is sometimes called ellipsoidal height. This is not the usual vertical coordinate for models of atmosphere and ocean circulation, which is instead defined relative to the geoid.\nThe geodetic latitude, commonly referred to simply as latitude, is the angle between the equatorial plane and the normal to the ellipsoid. It is different from the geocentric latitude, which is the angle between the equatorial plane and the line from the centre of the Earth to \ud835\udc31. Geodetic and geocentric latitudes are the same for the poles and the equator, but elsewhere geodetic latitude is larger (as can be appreciated from Fig. 1), by up to about 0.2\u02da.\nTo define the longitude of \ud835\udc31 (\u201cgeodetic\u201d and \u201cgeocentric\u201d are the same for longitude), consider the meridian passing through \ud835\udc2b, which intersects the equator at point \ud835\udc29, and the prime meridian (the Greenwich meridian), which intersects the equator at \ud835\udc290. Viewing the Earth from above, the longitude is the anticlockwise angle between the lines from the centre of the Earth to \ud835\udc290 and to \ud835\udc29.\nFig. 2: Relationship between surfaces relating to sea level. The normal to the reference ellipsoid defines the vertical in the terrestrial reference frame. The normal to the geoid is the vertical coordinate (z) for geophysical fluid dynamics, and anti-parallel to the local effective acceleration g due to gravity. The difference between these two definitions of the vertical direction is greatly exaggerated in this diagram; it is negligible in reality. The local vertical coordinates of mean sea level \ud835\udf02, the geoid G and the sea floor \ud835\udc39 are relative to the reference ellipsoid, while dynamic sea level \ud835\udf01\u0303 is relative to the geoid. The local time-mean thickness of the ocean \ud835\udc3b is the vertical distance between mean sea level and the sea floor. The deviation of atmospheric pressure \ud835\udc5d\u2032\ud835\udc4e from its global mean causes the depression \ud835\udc35 in sea level by the inverse barometer effect\nN2 Sea surface \ud835\udf02\u0303:\nThe time-varying upper boundary of the ocean. The sea-surface height is the geodetic height of the sea surface above the reference ellipsoid (a negative value if below).\nIn ocean areas without floating ice (sea ice, ice shelves or icebergs), the liquid sea surface is the bottom boundary of the atmosphere. In such areas, the existence of a well-defined sea-surface height (SSH)\ud835\udf02\u0303(\ud835\udc2b,\ud835\udc61), that can be represented by a continuous and single-valued mathematical expression, presupposes a space\u2013time averaging, because the instantaneous surface is ill-defined in the presence of some short-timescale phenomena that produce foam and sea spray, such as breaking surface waves and conditions of intense wind. We assume such averaging when speaking about the sea surface.\nIn ocean areas with floating ice, the liquid surface boundary is the bottom of the ice. For those areas, we define the SSH \ud835\udf02\u0303 as the liquid-water equivalent sea surface\ud835\udf02\u0303LWE which the liquid would have if the ice were replaced by an equal mass of sea water of the density \ud835\udf0cs of the surface water in its vicinity. Following Archimedes\u2019 principle,\n\ud835\udf02\u0303LWE = \ud835\udf02\u0303\ud835\udc60 + \ud835\udc64\ud835\udc56\ud835\udc54\ud835\udf0cs, (1)\nwhere \ud835\udf02\u0303\ud835\udc60 is the geodetic height of the liquid sea-water surface (beneath the ice) and \ud835\udc64\ud835\udc56 is the weight per unit area of floating ice. (The depression of \ud835\udf02\u0303\ud835\udc60 relative to \ud835\udf02\u0303 is called the \u201c inverse barometer effect of sea ice\u201d by Griffies and Greatbatch 2012, and \ud835\udf02\u0303LWE is their \u201ceffective sea level\u201d.) Although the liquid-water equivalent sea-surface height is not directly measurable, it is a convenient construct for many practical purposes of sea-level studies, and dynamically justifiable because the hydrostatic pressure and gravity beneath the ice are largely unaffected by the replacement of ice with liquid water.\nThe sea surface varies periodically with various frequencies due to tides . It varies also on all timescales due to sea-surface waves , atmospheric pressure, surface flux exchanges (with the atmosphere), river inflow, variability that is internally generated by ocean dynamics, motion of the sea floor and changes in the mass distribution within the ocean and solid Earth (discussed in many following entries).\nNote that ocean dynamic sea level and ocean dynamic topography are distinct concepts from sea-surface height and from each other.\nN3 Mean sea level (MSL) \ud835\udf02: The time-mean of the  sea surface .\nThe period for the time-mean must be long enough to eliminate the effects of waves and other meteorologically induced fluctuations (as discussed in Sect. 2.2). Predicted tidal variations are subtracted if the period is not long enough to remove time-dependent tides , but permanent tides are included in MSL. For a precise definition of MSL, the period of the time-mean should be specified, and it could be described either with or without dependence on the time of year.\nMSL is located by its geodetic height \ud835\udf02(\ud835\udc2b) above the reference ellipsoid (a negative value if below). In ocean models which regard the geoid and the reference ellipsoid as coincident, \ud835\udf02 is equally the orthometric height of MSL above the geoid. MSL is sometimes called \u201cmean sea surface\u201d. We recommend against using this term, in order to make a clear distinction from \u201csea-surface height\u201d.\nN4 Sea floor \ud835\udc39: The lower boundary of the ocean, its interface with the solid Earth.\nThe sea floor is the part of the surface of the solid Earth (whether bedrock or consolidated sediment, and lying beneath any unconsolidated sediment, e.g., Webb et al. 2013) that is always or sometimes submerged under sea water. The level of the sea floor varies due to solid-Earth tides , accumulation of sediment (with eventual compaction) and vertical land movement on a range of timescales.\nWe specify the instantaneous level of the sea floor by its geodetic height \ud835\udc39\u0303(\ud835\udc2b,\ud835\udc61) (negative over most of the ocean) relative to the reference ellipsoid . The local instantaneous thickness of the ocean (its vertical extent, the depth of the sea floor measured from a ship, a positive quantity sometimes called the depth of the water column) is given by\n\ud835\udc3b\u0303(\ud835\udc2b,\ud835\udc61)=\ud835\udf02\u0303(\ud835\udc2b,\ud835\udc61)\u2212\ud835\udc39\u0303(\ud835\udc2b,\ud835\udc61)\u22650, (2)\ni.e., the vertical distance between the sea surface and the sea floor. The choice of reference surface for vertical coordinates does not affect the value of \ud835\udc3b\u0303, because it is the difference between two vertical coordinates; \ud835\udc3b\u0303 would be the same if SSH and the sea floor were located by heights relative to the geoid rather than the reference ellipsoid. The time-mean thickness of the ocean\ud835\udc3b\n\ud835\udc3b(\ud835\udc2b)=\ud835\udf02(\ud835\udc2b)\u2212\ud835\udc39(\ud835\udc2b)\u22650 (3)\nis likewise related to MSL \ud835\udf02.", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-3", "text": "MSL is located by its geodetic height \ud835\udf02(\ud835\udc2b) above the reference ellipsoid (a negative value if below). In ocean models which regard the geoid and the reference ellipsoid as coincident, \ud835\udf02 is equally the orthometric height of MSL above the geoid. MSL is sometimes called \u201cmean sea surface\u201d. We recommend against using this term, in order to make a clear distinction from \u201csea-surface height\u201d.\nN4 Sea floor \ud835\udc39: The lower boundary of the ocean, its interface with the solid Earth.\nThe sea floor is the part of the surface of the solid Earth (whether bedrock or consolidated sediment, and lying beneath any unconsolidated sediment, e.g., Webb et al. 2013) that is always or sometimes submerged under sea water. The level of the sea floor varies due to solid-Earth tides , accumulation of sediment (with eventual compaction) and vertical land movement on a range of timescales.\nWe specify the instantaneous level of the sea floor by its geodetic height \ud835\udc39\u0303(\ud835\udc2b,\ud835\udc61) (negative over most of the ocean) relative to the reference ellipsoid . The local instantaneous thickness of the ocean (its vertical extent, the depth of the sea floor measured from a ship, a positive quantity sometimes called the depth of the water column) is given by\n\ud835\udc3b\u0303(\ud835\udc2b,\ud835\udc61)=\ud835\udf02\u0303(\ud835\udc2b,\ud835\udc61)\u2212\ud835\udc39\u0303(\ud835\udc2b,\ud835\udc61)\u22650, (2)\ni.e., the vertical distance between the sea surface and the sea floor. The choice of reference surface for vertical coordinates does not affect the value of \ud835\udc3b\u0303, because it is the difference between two vertical coordinates; \ud835\udc3b\u0303 would be the same if SSH and the sea floor were located by heights relative to the geoid rather than the reference ellipsoid. The time-mean thickness of the ocean\ud835\udc3b\n\ud835\udc3b(\ud835\udc2b)=\ud835\udf02(\ud835\udc2b)\u2212\ud835\udc39(\ud835\udc2b)\u22650 (3)\nis likewise related to MSL \ud835\udf02.\nThe shape of the sea floor is sometimes called the bottom topography or the bathymetry, for example in describing it as \u201crough\u201d or \u201csmooth\u201d. These two synonymous terms are also used as names for the quantities \u2212\ud835\udc39, \ud835\udc3a\u2212\ud835\udc39 and \ud835\udf02\u2212\ud835\udc39(=\ud835\udc3b), i.e., the time-mean vertical distance of the sea floor beneath the reference ellipsoid, the geoid or MSL, respectively. In order to be precise, it should be stated which of these alternatives is intended, since G and the reference ellipsoid differ by \u00b1100 m (Sect. 2.6), and G and MSL differ by \u00b11 m, following time-mean ocean dynamic sea level .\nN5 Geoid G: A surface on which the geopotential\u03a6 has a uniform value, chosen so that the volume enclosed between the geoid and the sea floor is equal to the time-mean volume of sea water in the ocean (including the liquid-water equivalent of floating ice).\nThe geopotential is a field of potential energy per unit mass, accounting for the Newtonian gravitational acceleration due to the mass of the Earth plus the centrifugal acceleration arising from the Earth\u2019s rotation. We define the sign of the geopotential such that work is required to move a sea-water parcel from a lower geopotential (deeper in the ocean) to a higher geopotential (shallower in the ocean). Note that this sign convention for the geopotential is opposite to that used in geodesy.\nThe vertical gradient of the geopotential is equal to the local effective gravitational acceleration, g, \ud835\udc54(\ud835\udc2b,\ud835\udc61)=\u2202\u03a6/\u2202\ud835\udc67, usually referred to as \u201cgravitational acceleration\u201d in geophysical fluid dynamics. Hence, the effective gravitational acceleration is normal to the geoid, because the geoid is an equipotential surface, i.e., one on which the geopotential is constant. The Newtonian gravitational acceleration is time-dependent because the distribution of mass in the ocean (liquid and solid), on land (including the land-based cryosphere) and within the solid Earth is generally changing. The centrifugal acceleration is time-dependent because the Earth\u2019s rotation rate and rotation axis are variable.\nFor models of atmosphere and ocean circulation, the vertical unit vector is directed anti-parallel to the effective gravitational acceleration g (or equivalently it is parallel to the local gradient of the geopotential). The height above the geoid of some point \ud835\udc31 is the distance z, measured along the local vertical unit vector, from the geoid to \ud835\udc31. The coordinate z (Fig. 2) is also called the orthometric height of \ud835\udc31. Strictly, the orthometric height is measured along a plumb line, which is always normal to equipotential surfaces, but this distance differs negligibly from that measured along the perpendicular to the reference ellipsoid .\nWe define z such that \ud835\udc67=0 is the geoid, \ud835\udc67>0 is above the geoid, and \ud835\udc67<0 is below. By horizontal we mean aligned with a surface of constant z. This is not strictly an equipotential surface, but the difference is locally negligible. It is, however, very different from a surface of constant geodetic height \ud835\udc67\u2032=\ud835\udc67+\ud835\udc3a, where \ud835\udc3a(\ud835\udc2b) is the geoid height above the reference ellipsoid (\ud835\udc3a<0 where the geoid is below the ellipsoid).\nThe sea surface would coincide with the geoid if the ocean were in a resting steady state in the rotating frame of the earth. Although defining the geoid in this way is conceptually attractive, it is not realistic or practically useful. (See Appendix 1.)\nThe sea surface does not really coincide with the geoid because the ocean is not at rest. (See ocean dynamic sea level .) For example, mean sea level (MSL) north of the Antarctic Circumpolar Current (ACC) is at a higher geopotential than MSL south of the ACC; with respect to the geoid, MSL on the north side is roughly 2 m higher than on the south side.\nReferring to its definition, we choose the geoid as the equipotential surface (out of the infinite set of them) which satisfies\n\u222b(\ud835\udc3a\u2212\ud835\udc39)d\ud835\udc34 = \ud835\udc49 = \u222b\ud835\udc3b d\ud835\udc34 = \u222b(\ud835\udf02\u2212\ud835\udc39) d\ud835\udc34, (4)\nusing Eq. (3) for \ud835\udc3b, and where V is the volume of the global ocean and \ud835\udc34=\u222bd\ud835\udc34 is its surface area. It follows from Eq. (4) that\n\u222b\ud835\udf02 d\ud835\udc34 = \u222b\ud835\udc3a d\ud835\udc34, (5)\ni.e., MSL and geoid height above the reference ellipsoid have equal global means.\nWe define the geoid in terms of MSL \ud835\udf02, rather than the sea-surface height \ud835\udf02\u0303, in order to restrict changes in G and V to those occurring on the timescales of global-mean sea-level rise , rather than on shorter timescales related to meteorological, seasonal and interannual fluctuations. Our definition of the geoid treats it as a geophysical quantity which changes as the Earth system evolves. In some applications, the geoid is defined in a time-independent way as a particular geopotential surface within a particular model of the Earth\u2019s gravity field.\nWe define the geoid to include the permanent ocean tide. With this choice, time-mean ocean dynamic sea level \ud835\udf01 is determined solely by ocean dynamics and density. With the zero-tide convention, which is common in gravity-field models, \ud835\udf01 would include the permanent ocean tide, which is almost +0.1 m at the equator and \u22120.2 m at the poles.\nWe define the geoid as \ud835\udc3a(\ud835\udc2b)=\ud835\udc38(\ud835\udc2b,\u03a6\ud835\udc3a), with a choice of \u03a6\ud835\udc3a such that Eq. (4) is satisfied, where \ud835\udc38(\ud835\udc2b,\u03a6) is the geodetic height of the equipotential surface for geopotential \u03a6. The shapes of the equipotential surfaces, including the geoid, depend on the geographical distribution of mass over the Earth. According to Eq. (4), the global-mean geoid height must change by\n1\ud835\udc34\u222b\u0394\ud835\udc3a d\ud835\udc34 = 1\ud835\udc34\u222b\u0394\ud835\udc39 d\ud835\udc34 + \u0394\ud835\udc49 \ud835\udc34 (6)\nif there is global-mean vertical land movement \u0394\ud835\udc39 affecting the sea floor, or a change \u0394\ud835\udc49 in the volume of the global ocean, whether due to change in density or in mass. Consequently, \u03a6\ud835\udc3a must change such that", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-4", "text": "\u222b\ud835\udf02 d\ud835\udc34 = \u222b\ud835\udc3a d\ud835\udc34, (5)\ni.e., MSL and geoid height above the reference ellipsoid have equal global means.\nWe define the geoid in terms of MSL \ud835\udf02, rather than the sea-surface height \ud835\udf02\u0303, in order to restrict changes in G and V to those occurring on the timescales of global-mean sea-level rise , rather than on shorter timescales related to meteorological, seasonal and interannual fluctuations. Our definition of the geoid treats it as a geophysical quantity which changes as the Earth system evolves. In some applications, the geoid is defined in a time-independent way as a particular geopotential surface within a particular model of the Earth\u2019s gravity field.\nWe define the geoid to include the permanent ocean tide. With this choice, time-mean ocean dynamic sea level \ud835\udf01 is determined solely by ocean dynamics and density. With the zero-tide convention, which is common in gravity-field models, \ud835\udf01 would include the permanent ocean tide, which is almost +0.1 m at the equator and \u22120.2 m at the poles.\nWe define the geoid as \ud835\udc3a(\ud835\udc2b)=\ud835\udc38(\ud835\udc2b,\u03a6\ud835\udc3a), with a choice of \u03a6\ud835\udc3a such that Eq. (4) is satisfied, where \ud835\udc38(\ud835\udc2b,\u03a6) is the geodetic height of the equipotential surface for geopotential \u03a6. The shapes of the equipotential surfaces, including the geoid, depend on the geographical distribution of mass over the Earth. According to Eq. (4), the global-mean geoid height must change by\n1\ud835\udc34\u222b\u0394\ud835\udc3a d\ud835\udc34 = 1\ud835\udc34\u222b\u0394\ud835\udc39 d\ud835\udc34 + \u0394\ud835\udc49 \ud835\udc34 (6)\nif there is global-mean vertical land movement \u0394\ud835\udc39 affecting the sea floor, or a change \u0394\ud835\udc49 in the volume of the global ocean, whether due to change in density or in mass. Consequently, \u03a6\ud835\udc3a must change such that\n1\ud835\udc34\u222b\u0394\ud835\udc3a d\ud835\udc34 = \u0394\u03a6 \ud835\udc3a \ud835\udc34\u222b\u2202\ud835\udc38(\ud835\udc2b,\u03a6) \u2202\u03a6d\ud835\udc34 = \u0394\u03a6 \ud835\udc3a \ud835\udc54, (7)\nif we approximate g as globally uniform.\nVariations and Differences in Surfaces\uf0c1\nIn this section we define terms for time-dependent variations in surfaces (on timescales shorter than those of mean sea-level change) and differences between surfaces.\nN6 Tides: Periodic motions within the ocean, atmosphere and solid Earth due to the rotation of the Earth and its motion relative to the moon and sun. Ocean tides cause the  sea surface to rise and fall.\nThe astronomical tide is the dominant constituent of the ocean tides. It is caused by periodic spatial variations in local gravity. Tidal motion of the land surface and sea floor is due to elastic deformation of the solid Earth by gravitational tidal forces. The diurnal and annual cycles of insolation produce periodic variations in atmospheric pressure and winds (sea breezes), which cause the radiational tide in the atmosphere and ocean (e.g., Williams et al. 2018). The predicted tide is the sum of the astronomical and radiational constituents. Because the ocean and atmosphere are fluids, tidal forces within them cause tidal currents as well as displacements.\nSea-surface height (SSH) can be greatly elevated during a storm by a storm surge , and the consequent extreme sea level is sometimes called a storm tide. The tidal height is the vertical distance of the SSH due to the predicted tide above a local benchmark or a surface which is fixed with respect to the terrestrial reference frame. Often, this surface is a tidal datum, defined by a extremum of the periodic tide, such as mean lower-low water level.\nThe velocity of the ocean tidal currents depends on water depth. Therefore, relative sea-level change (RSLC) affects the tides. In most coastal locations, this interaction alters the tidal variations of the sea surface with respect to mean sea level by less than 10% of the RSLC (Pickering et al. 2017).\nIn most locations, the constituent of the ocean tide with the largest amplitude is the lunar semi-diurnal tide. The orbit of the moon around the Earth modulates the semi-diurnal tide to produce a large amplitude (spring tide) at new and full moon, and a small amplitude (neap tide) at half-moon. There are many smaller periodic constituents associated with the sun and moon. The precession of the plane of the moon\u2019s orbit causes tidal variations with an 18.6-year cycle (the nodal period), affecting extreme sea level on this timescale. There are longer tidal periods.\nThe pole tide is caused by variations of the Earth\u2019s rotation axis relative to the solid Earth, altering the centrifugal acceleration and local gravity. The two largest components of the pole tide have periods of 1 year and about 433 days. The latter is due to the Chandler wobble, which is not strictly periodic and arises from the mechanics of the Earth\u2019s rotation alone (it is a free nutation), rather than being caused by the gravitation of other bodies in the solar system.\nThe time-means of the tidal forces of the moon and sun are nonzero. Hence, in addition to the periodic constituents, the tides have a constant constituent called the permanent tide, which tends to make the Earth and sea surface more oblate. Our definitions of mean sea level and the geoid use the mean-tide convention, including the permanent tide. In gravity models, the zero-tide convention is more usual, in which the permanent ocean tide is subtracted, but the permanent elastic tidal deformation of the solid Earth is retained; an estimate of the latter too is subtracted in the tide-free convention used by GNSS measurements.\nN7 Inverse barometer (IB)\ud835\udc35: The time-dependent hydrostatic depression of the sea surface by atmospheric pressure variations, also called inverted barometer.\nThe ocean is almost incompressible. (A uniform change of 1 hPa over the ocean causes a global-mean sea-level rise of roughly 0.16 mm.) Therefore changes in atmospheric pressure have a negligible effect on the total volume of the ocean. However, they do move sea water around, and the effect on the sea surface depends on the deviation of sea-level pressure \ud835\udc5d\u0303\ud835\udc4e(\ud835\udc2b) from its global (ocean) mean, given by\n\ud835\udc5d\u0303\u2032\ud835\udc4e(\ud835\udc2b,\ud835\udc61) = \ud835\udc5d\u0303\ud835\udc4e(\ud835\udc2b,\ud835\udc61) \u2212 1\ud835\udc34\u222b\ud835\udc5d\u0303\ud835\udc4e(\ud835\udc2b,\ud835\udc61) d\ud835\udc34. (8)\nFor timescales longer than a few days, we can assume the ocean to be in hydrostatic balance. Therefore, the depression of the sea-surface height (SSH) \ud835\udf02\u0303 by IB is \ud835\udc35\u0303=\ud835\udc5d\u0303\u2032\ud835\udc4e/(\ud835\udc54\ud835\udf0cs) where \ud835\udc54(\ud835\udc2b) is the acceleration due to gravity and \ud835\udf0cs(\ud835\udc2b,\ud835\udf02\u0303) the surface sea-water density. That is, when \ud835\udc5d\u0303\u2032\ud835\udc4e>0 then sea level is depressed locally by \ud835\udc35\u0303(\ud835\udc2b), and it is raised when \ud835\udc5d\u0303\u2032\ud835\udc4e<0. The latter effect is an important contribution to storm surge . In a storm or cyclone, \ud835\udc5d\u0303\ud835\udc4e may fall by several 10 hPa, causing SSH to rise by several 100 mm.\nThe global mean of \ud835\udc54\ud835\udf0cs is approximately 9.9\u00d710\u22125 m  Pa \u22121\u22619.9 mm  hPa \u22121, with spatial and temporal variations of about 1% around this value. Hence, for most purposes of sea-level studies we can neglect the spatial variations in g and \ud835\udf0cs, and replace them with constants; thus,\n\ud835\udc35\u0303=\ud835\udc5d\u0303\u2032\ud835\udc4e\ud835\udc54\ud835\udf0c\u2217. (9)\nHence, the global-mean IB correction is zero,\n\u222b\ud835\udc35\u0303(\ud835\udc2b,\ud835\udc61)d\ud835\udc34=0, (10)\nwhich follows by definition of \ud835\udc5d\u0303\u2032\ud835\udc4e.", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-5", "text": "\ud835\udc5d\u0303\u2032\ud835\udc4e(\ud835\udc2b,\ud835\udc61) = \ud835\udc5d\u0303\ud835\udc4e(\ud835\udc2b,\ud835\udc61) \u2212 1\ud835\udc34\u222b\ud835\udc5d\u0303\ud835\udc4e(\ud835\udc2b,\ud835\udc61) d\ud835\udc34. (8)\nFor timescales longer than a few days, we can assume the ocean to be in hydrostatic balance. Therefore, the depression of the sea-surface height (SSH) \ud835\udf02\u0303 by IB is \ud835\udc35\u0303=\ud835\udc5d\u0303\u2032\ud835\udc4e/(\ud835\udc54\ud835\udf0cs) where \ud835\udc54(\ud835\udc2b) is the acceleration due to gravity and \ud835\udf0cs(\ud835\udc2b,\ud835\udf02\u0303) the surface sea-water density. That is, when \ud835\udc5d\u0303\u2032\ud835\udc4e>0 then sea level is depressed locally by \ud835\udc35\u0303(\ud835\udc2b), and it is raised when \ud835\udc5d\u0303\u2032\ud835\udc4e<0. The latter effect is an important contribution to storm surge . In a storm or cyclone, \ud835\udc5d\u0303\ud835\udc4e may fall by several 10 hPa, causing SSH to rise by several 100 mm.\nThe global mean of \ud835\udc54\ud835\udf0cs is approximately 9.9\u00d710\u22125 m  Pa \u22121\u22619.9 mm  hPa \u22121, with spatial and temporal variations of about 1% around this value. Hence, for most purposes of sea-level studies we can neglect the spatial variations in g and \ud835\udf0cs, and replace them with constants; thus,\n\ud835\udc35\u0303=\ud835\udc5d\u0303\u2032\ud835\udc4e\ud835\udc54\ud835\udf0c\u2217. (9)\nHence, the global-mean IB correction is zero,\n\u222b\ud835\udc35\u0303(\ud835\udc2b,\ud835\udc61)d\ud835\udc34=0, (10)\nwhich follows by definition of \ud835\udc5d\u0303\u2032\ud835\udc4e.\nThe inverse-barometer response of the sea surface compensates for the effect of \ud835\udc5d\u0303\u2032\ud835\udc4e on hydrostatic pressure within the ocean, and the subsurface ocean does not feel the fluctuations in atmospheric pressure. Consequently, the ocean behaves dynamically as if the sea-surface height were \ud835\udf02\u0303+\ud835\udc35\u0303, which is called IB-corrected sea-surface height. Its time-mean is \ud835\udf02+\ud835\udc35, the IB-corrected mean sea level. In most climate models, atmospheric pressure variations are not communicated to the ocean. In these models \ud835\udc35\u0303 must be subtracted from the simulated SSH to produce a quantity that varies with \ud835\udc5d\u0303\ud835\udc4e like the observed \ud835\udf02\u0303 does.\nN8 Extreme sea level: The occurrence or the level of an exceptionally high or low local sea-surface height.\nExtremely high sea-surface height (SSH) is caused by meteorological conditions as a storm surge , by sea-surface waves due to various causes and by exceptionally high or low (although predictable) tidal height. When considering coastal impacts, extreme sea level may be called extreme coastal water level. For decadal timescales, the main influence on changes in the frequency distribution of extreme sea level is relative sea-level change (RSLC), whose effect outweighs that of changes in meteorological forcing (Lowe et al. 2010; Church et al. 2013; Vousdoukas et al. 2018). To avoid confusion, we recommend the phrase high-end sea-level change to describe projections of very large RSLC, instead of using the word \u201cextreme\u201d for such projections.\nN9 Storm surge: The elevation or depression of the sea surface with respect to the predicted tide during a storm.\nStorm surges are caused during tropical cyclones and deep mid-latitude depressions by low atmospheric pressure, by strong winds pushing water towards the shore (or away from the shore, causing a negative surge) and by sea-surface waves breaking at the coast. Wave effects are usually excluded or underestimated by tide-gauges. If the actual sea-surface height (SSH) at location \ud835\udc2b and time t due to tide and surge combined (sometimes called the storm tide) is \ud835\udf02\u0303(\ud835\udc2b,\ud835\udc61), and the predicted SSH due to the tide alone is \ud835\udf02\u0303tide(\ud835\udc2b,\ud835\udc61), the storm-surge height\u03c3 is\n\u03c3(\ud835\udc2b,\ud835\udc61)=\ud835\udf02\u0303(\ud835\udc2b,\ud835\udc61)\u2212\ud835\udf02\u0303tide(\ud835\udc2b,\ud835\udc61), (11)\nalso called the surge residual or non-tidal residual.\nThe storm-surge height \u03c3 is the sum of three components: the inverse barometer (IB) effect of low atmospheric pressure, the wind setup caused by the wind-driven current, and the wave setup, which is the elevation of the sea surface due to breaking waves. All three effects are normally present, but intensified by storms. IB and wind setup tend to be more important on wide continental shelves, but wave setup can dominate in some cases (Pedreros et al. 2018), especially in areas of steep sea floor slope.\nThe swash is the uprush and backwash of water over the solid surface (e.g., sand or pebbles) generated by each wave. During the uprush, the swash extends above the wave setup. Its maximum height above the predicted tide, called the wave runup, gives the highest water level of the storm surge.\nParticularly high SSH \ud835\udf02\u0303=\u03c3+\ud835\udf02\u0303tide occurs when the storm surge coincides with high tide. Without the meteorological forcing, storm-surge height \u03c3 would be zero, but since the tide level influences the propagation of the storm-forced signal, \u03c3 and \ud835\udf02\u0303tide are not independent (Horsburgh and Wilson 2007).\nThe skew-surge height is the elevation of the highest sea surface that occurs within a single tidal cycle above the predicted level of the high tide within that cycle. If the actual SSH is \ud835\udf02\u0303(\ud835\udc2b,\ud835\udc61) and the predicted SSH due to the tide alone is \ud835\udf02\u0303tide(\ud835\udc2b,\ud835\udc61), the skew-surge height is\n\u03c3\ud835\udc58(\ud835\udc2b,\ud835\udc61)= max \ud835\udc61(\ud835\udf02\u0303(\ud835\udc2b,\ud835\udc61))\u2212 max \ud835\udc61(\ud835\udf02\u0303tide(\ud835\udc2b,\ud835\udc61)), (12)\nwhere  max \ud835\udc61(\ud835\udc4b(\ud835\udc2b,\ud835\udc61)) means the maximum value of X that occurs at location \ud835\udc2b during the interval of time t from one low tide to the next. For extreme-value analysis, the skew-surge height is preferable to the storm-surge height as a measure of the effect of the meteorological forcing alone in regions where skew-surge height is uncorrelated with tidal height (Williams et al. 2016).\nN10 Sea-surface waves: Waves on the surface of the ocean, usually surface gravity waves caused by winds.\nThe amplitude of a wind wave depends on the strength of the wind, and the time and the distance of open ocean, called the fetch, over which the wind has blown. The sea surface typically exhibits a superposition of many waves of different amplitudes, velocities, frequencies and directions. A swell wave is a wind wave of low frequency which was generated far away.\nA tsunami or seismic sea wave is an extreme sea level event caused by an earthquake, volcano, landslide or other submarine disturbance that suddenly displaces a volume of water. The displacement propagates as a long-wavelength surface gravity wave, but is not a tidal phenomenon, despite it sometimes being called a \u201ctidal wave\u201d.\nThe wave height is the vertical distance from the crest to the trough of a wave, respectively its highest and lowest points. The wave period is the interval of time between the passage of repeated features on the waveform such as crests, troughs or upward crossings of the mean level. The significant wave height is a statistic computed from wave measurements, defined as either the mean of the largest one-third of the wave heights, or four times the standard deviation of wave heights. (These statistics are approximately equal.) The significant wave period is the mean period of the largest one-third of the waves.\nN11 Ocean dynamic sea level \ud835\udf01: The local height of the sea surface above the geoid G, with the inverse barometer correction \ud835\udc35 applied.\nInstantaneous ocean dynamic sea level is defined by\n\ud835\udf01\u0303(\ud835\udc2b,\ud835\udc61)=\ud835\udf02\u0303(\ud835\udc2b,\ud835\udc61)+\ud835\udc35\u0303(\ud835\udc2b,\ud835\udc61)\u2212\ud835\udc3a(\ud835\udc2b). (13)\nIt is determined jointly by ocean density and circulation. The time-mean ocean dynamic sea level is\n\ud835\udf01(\ud835\udc2b)=\ud835\udf02(\ud835\udc2b)+\ud835\udc35(\ud835\udc2b)\u2212\ud835\udc3a(\ud835\udc2b), (14)\nwhose global mean\n1\ud835\udc34\u222b\ud835\udf01(\ud835\udc2b)d\ud835\udc34=0, (15)\nin view of Eqs. (5) and (10).", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-6", "text": "N10 Sea-surface waves: Waves on the surface of the ocean, usually surface gravity waves caused by winds.\nThe amplitude of a wind wave depends on the strength of the wind, and the time and the distance of open ocean, called the fetch, over which the wind has blown. The sea surface typically exhibits a superposition of many waves of different amplitudes, velocities, frequencies and directions. A swell wave is a wind wave of low frequency which was generated far away.\nA tsunami or seismic sea wave is an extreme sea level event caused by an earthquake, volcano, landslide or other submarine disturbance that suddenly displaces a volume of water. The displacement propagates as a long-wavelength surface gravity wave, but is not a tidal phenomenon, despite it sometimes being called a \u201ctidal wave\u201d.\nThe wave height is the vertical distance from the crest to the trough of a wave, respectively its highest and lowest points. The wave period is the interval of time between the passage of repeated features on the waveform such as crests, troughs or upward crossings of the mean level. The significant wave height is a statistic computed from wave measurements, defined as either the mean of the largest one-third of the wave heights, or four times the standard deviation of wave heights. (These statistics are approximately equal.) The significant wave period is the mean period of the largest one-third of the waves.\nN11 Ocean dynamic sea level \ud835\udf01: The local height of the sea surface above the geoid G, with the inverse barometer correction \ud835\udc35 applied.\nInstantaneous ocean dynamic sea level is defined by\n\ud835\udf01\u0303(\ud835\udc2b,\ud835\udc61)=\ud835\udf02\u0303(\ud835\udc2b,\ud835\udc61)+\ud835\udc35\u0303(\ud835\udc2b,\ud835\udc61)\u2212\ud835\udc3a(\ud835\udc2b). (13)\nIt is determined jointly by ocean density and circulation. The time-mean ocean dynamic sea level is\n\ud835\udf01(\ud835\udc2b)=\ud835\udf02(\ud835\udc2b)+\ud835\udc35(\ud835\udc2b)\u2212\ud835\udc3a(\ud835\udc2b), (14)\nwhose global mean\n1\ud835\udc34\u222b\ud835\udf01(\ud835\udc2b)d\ud835\udc34=0, (15)\nin view of Eqs. (5) and (10).\nIn the Coupled Model Intercomparison Project (CMIP), \ud835\udf01\u0303 is stored in the diagnostic named zos, which is defined to have zero mean (Equation H14 of Griffies et al. 2016). However, some models supply it with a nonzero time-dependent mean. If the global mean of the zos diagnostic is found to be nonzero, the global mean should be subtracted uniformly.\nN12 Ocean dynamic topography: An estimate of ocean dynamic sea level computed from the ocean density structure above a reference level where the velocity is either known or assumed to be zero.\nOn any horizontal (see geoid for definition) level z within the ocean, the hydrostatic pressure is given by\n\ud835\udc5d\u0303(\ud835\udc67) = \ud835\udc5d\u0303\ud835\udc4e + \ud835\udc54\u222b\ud835\udf01\u0303\u2212\ud835\udc35\u0303\ud835\udc67\ud835\udf0c\u0303(\ud835\udc67\u2032)d\ud835\udc67\u2032, (16)\nwhich is the sum of the atmospheric pressure \ud835\udc5d\u0303\ud835\udc4e on the sea surface and the weight per unit horizontal area of sea water between z and the sea surface. The coordinate of the sea surface in this case is not \ud835\udf02\u0303 but \ud835\udf02\u0303\u2212\ud835\udc3a=\ud835\udf01\u0303\u2212\ud835\udc35\u0303 by Eq. (13), the height of the sea surface above the geoid, because we are using the orthometric vertical coordinate z, which is the natural choice for ocean dynamics. Equation (9) leads to the horizontal gradient of the atmospheric pressure \u2207\ud835\udc5d\u0303\ud835\udc4e = \u2207\ud835\udc5d\u0303\u2032\ud835\udc4e = \ud835\udc54\ud835\udf0c\u2217\u2207\ud835\udc35\u0303. Consequently, the horizontal gradient of pressure within the ocean is given by\n\u2207\ud835\udc5d\u0303 = \u2207(\ud835\udc5d\u0303\ud835\udc4e + \ud835\udc54\u222b\ud835\udf01\u0303\u2212\ud835\udc35\u0303\ud835\udc67\ud835\udf0c\u0303(\ud835\udc67\u2032)d\ud835\udc67\u2032) (17a)\n= \ud835\udc54\ud835\udf0c\u2217\u2207\u2207\ud835\udc35\u0303+(\ud835\udc54\ud835\udf0c\u2217\u2207\u2207\ud835\udf01\u0303\u2212\ud835\udc54\ud835\udf0c\u2217\u2207\u2207\ud835\udc35\u0303)+\ud835\udc54\u222b\ud835\udf01\u0303\u2212\ud835\udc35\u0303\ud835\udc67\u2207\u2207\ud835\udf0c\u0303(\ud835\udc67\u2032)d\ud835\udc67\u2032 (17b)\n= \ud835\udc54\ud835\udf0c\u2217\u2207\u2207\ud835\udf01\u0303+\ud835\udc54\u222b\ud835\udf01\u0303\u2212\ud835\udc35\u0303\ud835\udc67\u2207\u2207\ud835\udf0c\u0303(\ud835\udc67\u2032)d\ud835\udc67\u2032. (17c)\nIn the first step of this derivation, we used Eq. (9) for the inverse barometer correction \ud835\udc35\u0303, approximated g and sea-surface \ud835\udf0c\u0303=\ud835\udf0c\u2217 as constants, and applied Leibniz\u2019s rule to differentiate the integral, which yields the two terms in parentheses in Eq. (17b), but no term for \ud835\udf0c\u0303 at z because \u2207\u2207\ud835\udc67=0. From Eq. (17c) we obtain\n\u2207\ud835\udf01\u0303(\ud835\udc2b) = 1\ud835\udc54\ud835\udf0c\u2217\u2207\ud835\udc5d\u0303(\ud835\udc2b,\ud835\udc67) \u2212 1\ud835\udf0c\u2217\u222b\ud835\udf01\u0303\u2212\ud835\udc35\u0303\ud835\udc67\u2207\ud835\udf0c\u0303(\ud835\udc2b,\ud835\udc67\u2032)d\ud835\udc67\u2032, (18)\nwhich relates the horizontal gradient of ocean dynamic sea level \ud835\udf01\u0303 to the horizontal hydrostatic pressure gradient at a reference level z and the horizontal density gradient above that level. The second term on the right-hand side is the horizontal gradient of the dynamic heightD\n\ud835\udc37 = \u22121\ud835\udf0c\u2217\u222b\ud835\udf01\u0303\u2212\ud835\udc35\u0303\ud835\udc67\ud835\udf0c\u0303\ud835\udc51\ud835\udc67\u2032 (19)\nof the sea surface relative to z.\nIn much of the ocean interior (below the boundary layer and away from coastal and other strong currents), and taking a time-mean sufficient to eliminate tidal currents, geostrophy is a reasonable approximation, meaning that there is a balance (no net acceleration) between the pressure gradient and Coriolis forces, and all other forces are negligible. Therefore, \ud835\udc2f\u0303\u2243\ud835\udc2f\u0303g, with the geostrophic velocity \ud835\udc2f\u0303g defined by\n\ud835\udc53\ud835\udc24\u00d7\ud835\udf0c\u0303\ud835\udc2f\u0303g=\u2212\u2207\u2207\ud835\udc5d\u0303, (20)\nwhere f is the Coriolis parameter and \ud835\udc24 the vertical unit vector. If we can measure \ud835\udc2f\u0303 at some z and assume it is geostrophic, we arrive at\n\u2207\ud835\udf01\u0303(\ud835\udc2b)=\u2212\ud835\udc53\ud835\udc54\ud835\udf0c\u2217\ud835\udc24\u00d7\ud835\udf0c\u0303\ud835\udc2f\u0303(\ud835\udc2b,\ud835\udc67)\u22121\ud835\udf0c\u2217\u222b\ud835\udf01\u0303\u2212\ud835\udc35\u0303\ud835\udc67\u2207\ud835\udf0c\u0303(\ud835\udc2b,\ud835\udc67\u2032)d\ud835\udc67\u2032, (21)\nfrom Eq. (18).\nAlternatively, if we do not know \ud835\udc2f\u0303 at any z, we assume there exists a level of no motion\ud835\udc67=\u2212\ud835\udc3f, which is a geopotential (horizontal) surface on which \ud835\udc2f\u0303=\ud835\udc2f\u0303g=0, requiring the horizontal hydrostatic pressure gradient to vanish (\u2207\u2207\ud835\udc5d\u0303=0) by Eq. (20). Therefore,\n\u2207\ud835\udf01\u0303(\ud835\udc2b)=\u22121\ud835\udf0c\u2217\u222b\ud835\udf01\u0303 \u2212 \ud835\udc35\u0303 \u2212 \ud835\udc3f\u2207\u2207\ud835\udf0c\u0303(\ud835\udc2b,\ud835\udc67)d\ud835\udc67, (22)", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-7", "text": "\ud835\udc37 = \u22121\ud835\udf0c\u2217\u222b\ud835\udf01\u0303\u2212\ud835\udc35\u0303\ud835\udc67\ud835\udf0c\u0303\ud835\udc51\ud835\udc67\u2032 (19)\nof the sea surface relative to z.\nIn much of the ocean interior (below the boundary layer and away from coastal and other strong currents), and taking a time-mean sufficient to eliminate tidal currents, geostrophy is a reasonable approximation, meaning that there is a balance (no net acceleration) between the pressure gradient and Coriolis forces, and all other forces are negligible. Therefore, \ud835\udc2f\u0303\u2243\ud835\udc2f\u0303g, with the geostrophic velocity \ud835\udc2f\u0303g defined by\n\ud835\udc53\ud835\udc24\u00d7\ud835\udf0c\u0303\ud835\udc2f\u0303g=\u2212\u2207\u2207\ud835\udc5d\u0303, (20)\nwhere f is the Coriolis parameter and \ud835\udc24 the vertical unit vector. If we can measure \ud835\udc2f\u0303 at some z and assume it is geostrophic, we arrive at\n\u2207\ud835\udf01\u0303(\ud835\udc2b)=\u2212\ud835\udc53\ud835\udc54\ud835\udf0c\u2217\ud835\udc24\u00d7\ud835\udf0c\u0303\ud835\udc2f\u0303(\ud835\udc2b,\ud835\udc67)\u22121\ud835\udf0c\u2217\u222b\ud835\udf01\u0303\u2212\ud835\udc35\u0303\ud835\udc67\u2207\ud835\udf0c\u0303(\ud835\udc2b,\ud835\udc67\u2032)d\ud835\udc67\u2032, (21)\nfrom Eq. (18).\nAlternatively, if we do not know \ud835\udc2f\u0303 at any z, we assume there exists a level of no motion\ud835\udc67=\u2212\ud835\udc3f, which is a geopotential (horizontal) surface on which \ud835\udc2f\u0303=\ud835\udc2f\u0303g=0, requiring the horizontal hydrostatic pressure gradient to vanish (\u2207\u2207\ud835\udc5d\u0303=0) by Eq. (20). Therefore,\n\u2207\ud835\udf01\u0303(\ud835\udc2b)=\u22121\ud835\udf0c\u2217\u222b\ud835\udf01\u0303 \u2212 \ud835\udc35\u0303 \u2212 \ud835\udc3f\u2207\u2207\ud835\udf0c\u0303(\ud835\udc2b,\ud835\udc67)d\ud835\udc67, (22)\nusing Eq. (18). There is no motion on \ud835\udc67=\u2212\ud835\udc3f so long as there is a compensation between undulations of dynamic sea level \ud835\udf01\u0303 (on the left-hand side of Eq. 22), and variations of the density structure above \ud835\udc67=\u2212\ud835\udc3f (on the right-hand side). Such exact compensation does not generally occur in the ocean, and the level of no motion does not exist. However, it is a useful approximation in many situations. For example, an anomalous sea-surface high is associated with a depression of the pycnocline in the interior of subtropical gyres (e.g., Figure 3.3 of Tomczak and Godfrey 1994), thus leading to relatively weak flow beneath the pycnocline. In some regions, the approximation is not useful; in particular, sizeable \ud835\udc2f\u0303 occurs at all depths in the Southern Ocean.\nThe ocean dynamic topography is the estimate of ocean dynamic sea level made using Eqs. (21) or (22). Since Eqs. (21) and (22) are unaffected by adding a constant to \ud835\udf01\u0303, the method provides only the difference in \ud835\udf01\u0303 between any two points (i.e., the gradient); it cannot give \ud835\udf01\u0303 for individual points relative to the geoid. Furthermore, it is not applicable in regions where the reference level for motion is below the sea floor , nor for differences between points in basins which are separated by sills that are shallower than the reference level.\nChanges in Sea Level\uf0c1\nThe relationships between quantities determining changes in sea level are summarized in Fig. 3. The phrases \u201csea-level change\u201d (SLC) and \u201csea-level rise\u201d (SLR) are often used in the literature. These make sense when referring to the phenomenon in general, but more specific terms such as relative sea-level change and global-mean sea-level rise should be preferred where relevant.\nFig. 3: Relationships between quantities, defined in Sect. 5, that determine changes in sea level. The lengths of the arrows do not have any significance\u2014they are only illustrative\u2014and the dotted horizontal lines serve only to indicate alignment. All of the quantities are differences between two states, and all except h, \u210e\ud835\udf03 and \u210e\ud835\udc4f are functions of location \ud835\udc2b. Any closed circuit gives an equality, in which a term has a positive sign when traversed in the direction of its arrow, and a negative sign if in the opposite direction to its arrow. For example, \u0394\ud835\udc45\u2212\u0394\ud835\udf02+\u0394\ud835\udc39=0 (Eq. 24) is the circuit marked in red, Eq. (23) in orange, Eq. (38) in blue, and Eq. (54) in green\nN13 Ocean dynamic sea-level change \u0394\ud835\udf01:\nThe change in time-mean ocean dynamic sea level, i.e., the change in IB-corrected mean sea level relative to the geoid.\nFor the difference between two time-mean states of the climate, Eq. (13) gives\n\u0394\ud835\udf01(\ud835\udc2b) = \u0394\ud835\udf02(\ud835\udc2b) + \u0394\ud835\udc35(\ud835\udc2b) \u2212 \u0394\ud835\udc3a(\ud835\udc2b). (23)\nSince the time-mean ocean dynamic sea level \ud835\udf01(\ud835\udc2b) always has a zero global mean by Eq. (15), so does \u0394\ud835\udf01 i.e., global-mean sea-level rise is excluded from ocean dynamic sea-level change. This property depends on Eq. (5) and thus requires a different choice of geopotential to define the geoid in the two states, if there is any change in global-mean sea level.\nN14 Geocentric sea-level change \u0394\ud835\udf02:\nThe change in local mean sea level with respect to the terrestrial reference frame.\nGeocentric sea-level change is the change in the height \ud835\udf02(\ud835\udc2b) of MSL relative to the reference ellipsoid . IB-corrected geocentric sea-level change is \u0394\ud835\udf02 + \u0394\ud835\udc35, i.e., the same with the inverse barometer correction added. Geocentric sea-level change must be distinguished from relative sea-level change .\nN15 Relative sea-level change (RSLC) \u0394\ud835\udc45: The change in local mean sea level relative to the local solid surface, i.e., the  sea floor . Relative sea-level change is also called \u201crelative sea-level rise\u201d (RSLR). (See Sect. 6 for an exposition of the relationship of RSLC to other quantities.)\nBoth the MSL height \ud835\udf02 and the sea floor height \ud835\udc39 may change and thus alter RSL. Hence, RSLC is geodetically expressed as\n\u0394\ud835\udc45(\ud835\udc2b) = \u0394\ud835\udf02(\ud835\udc2b) \u2212 \u0394\ud835\udc39(\ud835\udc2b), (24)\nthe difference between geocentric sea-level change \u0394\ud835\udf02 and vertical land movement \u0394\ud835\udc39 (VLM). IB-corrected relative sea-level change is \u0394\ud835\udc45+\u0394\ud835\udc35, i.e., RSLC with the inverse barometer correction. Relative sea-level change is the quantity registered by a tide-gauge, which measures sea level relative to the solid surface where it is attached.\nSince climate models do not include VLM, they do not distinguish between geocentric and relative sea-level change. In climate models where atmospheric pressure changes \u0394\ud835\udc5d\ud835\udc4e are not applied to the ocean, \u2212\u0394\ud835\udc35 must be added to include the effect of \u0394\ud835\udc5d\ud835\udc4e simulated by the atmosphere model. (Note that this adjustment should not be made to ocean dynamic sea-level change \u0394\ud835\udf01, which by definition is IB-corrected; see Eq. 23.)\nThe term \u201crelative sea level\u201d is not employed in an absolute sense, but only in conjunction with \u201cchange\u201d, because \ud835\udf02\u2212\ud835\udc39 (the analogue of Eq. 24) is simply the depth of the sea floor below MSL, equal to the time-mean thickness of the ocean \ud835\udc3b (Eq. 3).\nIn view of Eq. (3), we may also write RSLC as\n\u0394\ud835\udc45(\ud835\udc2b)=\u0394\ud835\udc3b(\ud835\udc2b), (25)\ni.e., the change in local ocean thickness, making it obvious that RSLC is not meaningful at locations which change from land to sea (transgression) or vice versa (regression), since \ud835\udc3b is undefined on land.", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-8", "text": "Both the MSL height \ud835\udf02 and the sea floor height \ud835\udc39 may change and thus alter RSL. Hence, RSLC is geodetically expressed as\n\u0394\ud835\udc45(\ud835\udc2b) = \u0394\ud835\udf02(\ud835\udc2b) \u2212 \u0394\ud835\udc39(\ud835\udc2b), (24)\nthe difference between geocentric sea-level change \u0394\ud835\udf02 and vertical land movement \u0394\ud835\udc39 (VLM). IB-corrected relative sea-level change is \u0394\ud835\udc45+\u0394\ud835\udc35, i.e., RSLC with the inverse barometer correction. Relative sea-level change is the quantity registered by a tide-gauge, which measures sea level relative to the solid surface where it is attached.\nSince climate models do not include VLM, they do not distinguish between geocentric and relative sea-level change. In climate models where atmospheric pressure changes \u0394\ud835\udc5d\ud835\udc4e are not applied to the ocean, \u2212\u0394\ud835\udc35 must be added to include the effect of \u0394\ud835\udc5d\ud835\udc4e simulated by the atmosphere model. (Note that this adjustment should not be made to ocean dynamic sea-level change \u0394\ud835\udf01, which by definition is IB-corrected; see Eq. 23.)\nThe term \u201crelative sea level\u201d is not employed in an absolute sense, but only in conjunction with \u201cchange\u201d, because \ud835\udf02\u2212\ud835\udc39 (the analogue of Eq. 24) is simply the depth of the sea floor below MSL, equal to the time-mean thickness of the ocean \ud835\udc3b (Eq. 3).\nIn view of Eq. (3), we may also write RSLC as\n\u0394\ud835\udc45(\ud835\udc2b)=\u0394\ud835\udc3b(\ud835\udc2b), (25)\ni.e., the change in local ocean thickness, making it obvious that RSLC is not meaningful at locations which change from land to sea (transgression) or vice versa (regression), since \ud835\udc3b is undefined on land.\nWhen considering sea-level change on geological timescales, in the absence of information about ocean dynamic sea level \ud835\udf01\u0303 or the inverse barometer effect, we might approximate \u0394\ud835\udf01\u0303\u22430 and \u0394\ud835\udc35\u22430, in which case \u0394\ud835\udf02\u2243\u0394\ud835\udc3a from Eq. (23), and \u0394\ud835\udc45\u2243\u0394\ud835\udc3a\u2212\u0394\ud835\udc39 from Eq. (24). This quantity is defined everywhere and thus gives an approximate meaning to RSLC in regions of transgression and regression.\nN16 Steric sea-level change\u0394\ud835\udc45\ud835\udf0c: The part of  relative sea-level change   which is due to the change \u0394\ud835\udf0c in ocean density, assuming the local mass of the ocean per unit area does not change. It is composed of thermosteric sea-level change \u0394\ud835\udc45\ud835\udf03, which is the part due solely to the change \u0394\ud835\udf03 in in-situ temperature, and halosteric sea-level change\u0394\ud835\udc45\ud835\udc46, which is the part due solely to the change \u0394\ud835\udc46 in salinity.\nThe time-mean local mass of the ocean per unit area is\n\ud835\udc5a = \u222b\ud835\udf02\ud835\udc39 \ud835\udf0c d\ud835\udc67 = \ud835\udc3b \u03c1\u0304 with \u03c1\u0304 \u2261 1\ud835\udc3b \u222b\ud835\udf02\ud835\udc39 \ud835\udf0c d\ud835\udc67, (26)\nwhere the first factor \ud835\udc3b = \ud835\udf02 \u2212 \ud835\udc39 is the local time-mean thickness of the ocean (Eq. 3), and the second factor \u03c1\u0304 is the local vertical-mean time-mean density. If we change the density while keeping \ud835\udc5a fixed, the thickness of the ocean changes, because\n0 = \u0394\ud835\udc5a = \u0394\ud835\udc3b|\ud835\udc5a\u03c1\u0304 + H \u0394\u03c1\u0304\u2223\ud835\udc5a (27)\n(by making a linear approximation). Therefore,\n\u0394\ud835\udc3b|\ud835\udc5a =\u2212(\ud835\udc3b/\u03c1\u0304)\u0394\u03c1\u0304 with \u0394\u03c1\u0304 = 1\ud835\udc3b \u222b\ud835\udf02\ud835\udc39\u0394\ud835\udf0cd\ud835\udc67. (28)\nThis would exactly define steric sea-level change in a situation where mass did not move horizontally. But in reality there are horizontal transports, making it impossible to separate density changes due to local changes in properties from those due to the movement of mass. For convenience, we approximate \u03c1\u0304 with the constant \ud835\udf0c\u2217.\nSince the RSLC is given by \u0394\ud835\udc45 = \u0394\ud835\udc3b (without inverse barometer correction, Eq. 25), steric sea-level change is\n\u0394\ud835\udc45\ud835\udf0c = \u22121\ud835\udf0c\u2217\u222b\ud835\udf02\ud835\udc39 \u0394\ud835\udf0cd\ud835\udc67 = \u0394\ud835\udc45\ud835\udf03 + \u0394\ud835\udc45\ud835\udc46 (29)\nwith the density increment decomposed into thermal and haline components (by making a linear approximation)\n\u0394\ud835\udf0c = \u2202\ud835\udf0c\u2202\ud835\udf03\u0394\ud835\udf03 + \u2202\ud835\udf0c\u2202\ud835\udc46\u0394\ud835\udc46, (30)\nand with the corresponding thermosteric and halosteric contributions\n\u0394\ud835\udc45\ud835\udf03 = \u22121\ud835\udf0c\u2217\u222b\ud835\udf02\ud835\udc39\u2202\ud835\udf0c\u2202\ud835\udf03\u0394\ud835\udf03d\ud835\udc67\u0394\ud835\udc45\ud835\udc46 = \u22121\ud835\udf0c\u2217\u222b\ud835\udf02\ud835\udc39\u2202\ud835\udf0c\u2202\ud835\udc46\u0394\ud835\udc46d\ud835\udc67. (31)\nThermosteric sea-level change is often called thermal expansion, because \u2202\ud835\udf0c/\u2202\ud835\udf03<0, so increasing the temperature gives \u0394\ud835\udc45\ud835\udf03>0. (See Appendix 2 regarding the dependence of density on salinity.) Relative sea-level change (without inverse barometer correction) is the sum of steric and manometric sea-level change (Eq. 35).\nN17 Global-mean thermosteric sea-level rise\u210e\ud835\udf03: The part of   global-mean sea-level rise   (GMSLR) which is due to thermal expansion.\nThis quantity is the global mean of local thermosteric sea-level change \u0394\ud835\udc45\ud835\udf03 (due to temperature change, Eq. 31); thus,\n\u210e\ud835\udf03 = 1\ud835\udc34\u222b\u0394\ud835\udc45\ud835\udf03d\ud835\udc34 = \u22121\ud835\udf0c\u2217\ud835\udc34\u222b\u222b\ud835\udf02\ud835\udc39\u2202\ud835\udf0c\u2202\ud835\udf03\u0394\ud835\udf03(\ud835\udc2b,\ud835\udc67)d\ud835\udc67d\ud835\udc34. (32)\nIt is the change in global ocean volume due to change in temperature alone, divided by the ocean surface area. The CMIP variable zostoga is \u210e\ud835\udf03 calculated with respect to a fixed reference state. (Griffies et al. 2016 define the reference to be the initial state of the experiment for CMIP6.) Hence, differences in zostoga between two states give the global-mean thermosteric sea-level rise between those states.\nAlthough halosteric sea-level change \u0394\ud835\udc45\ud835\udc46 (due to salinity change, Eq. 31) can be locally of the same order of magnitude as thermosteric, global-mean halosteric sea-level change is practically zero. In Appendix 2 we detail the physical arguments leading to this conclusion. Salinity change should be excluded when calculating \u210e\ud835\udf03, to avoid including a spurious global-mean halosteric sea-level change. (See Appendix 2 here as well as Appendix H9.5 of Griffies et al. 2016.) However, salinity change must of course be included when calculating \u0394\ud835\udc45\ud835\udc46. It follows that global-mean steric sea-level change, which equals \u210e\ud835\udf03 because global-mean halosteric sea-level change is zero, cannot be calculated as the global mean of local steric sea-level change. This apparent contradiction is due to the inaccuracy of the approximations made following Eq. (28).\nN18 Manometric sea-level change\u0394\ud835\udc45\ud835\udc5a: Definition A: The part of  relative sea-level change  (RSLC) which is not steric, or alternatively Definition B: The part of RSLC which is due to the change \u0394\ud835\udc5a(\ud835\udc2b) in the time-mean local mass of the ocean per unit area, assuming the density does not change. In the following, we show that the two definitions are approximately the same.", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-9", "text": "\u210e\ud835\udf03 = 1\ud835\udc34\u222b\u0394\ud835\udc45\ud835\udf03d\ud835\udc34 = \u22121\ud835\udf0c\u2217\ud835\udc34\u222b\u222b\ud835\udf02\ud835\udc39\u2202\ud835\udf0c\u2202\ud835\udf03\u0394\ud835\udf03(\ud835\udc2b,\ud835\udc67)d\ud835\udc67d\ud835\udc34. (32)\nIt is the change in global ocean volume due to change in temperature alone, divided by the ocean surface area. The CMIP variable zostoga is \u210e\ud835\udf03 calculated with respect to a fixed reference state. (Griffies et al. 2016 define the reference to be the initial state of the experiment for CMIP6.) Hence, differences in zostoga between two states give the global-mean thermosteric sea-level rise between those states.\nAlthough halosteric sea-level change \u0394\ud835\udc45\ud835\udc46 (due to salinity change, Eq. 31) can be locally of the same order of magnitude as thermosteric, global-mean halosteric sea-level change is practically zero. In Appendix 2 we detail the physical arguments leading to this conclusion. Salinity change should be excluded when calculating \u210e\ud835\udf03, to avoid including a spurious global-mean halosteric sea-level change. (See Appendix 2 here as well as Appendix H9.5 of Griffies et al. 2016.) However, salinity change must of course be included when calculating \u0394\ud835\udc45\ud835\udc46. It follows that global-mean steric sea-level change, which equals \u210e\ud835\udf03 because global-mean halosteric sea-level change is zero, cannot be calculated as the global mean of local steric sea-level change. This apparent contradiction is due to the inaccuracy of the approximations made following Eq. (28).\nN18 Manometric sea-level change\u0394\ud835\udc45\ud835\udc5a: Definition A: The part of  relative sea-level change  (RSLC) which is not steric, or alternatively Definition B: The part of RSLC which is due to the change \u0394\ud835\udc5a(\ud835\udc2b) in the time-mean local mass of the ocean per unit area, assuming the density does not change. In the following, we show that the two definitions are approximately the same.\nIf we change the local mass \ud835\udc5a per unit area while keeping density fixed, by Eq. (26) the thickness of the ocean changes by \u0394\ud835\udc3b|\ud835\udf0c=\u0394\ud835\udc5a/\ud835\udf0c\u23af\u23af\u23af, where \ud835\udf0c\u23af\u23af\u23af is the local vertical mean of \ud835\udf0c. (In reality, if the local mass per unit area changes, the density will probably change as well, since mass which is converging horizontally or through the sea surface is unlikely to have \ud835\udf0c=\ud835\udf0c\u23af\u23af\u23af exactly.)\nSince RSLC \u0394\ud835\udc45=\u0394\ud835\udc3b (without inverse barometer correction, Eq. 25), if we approximate \ud835\udf0c\u23af\u23af\u23af with the constant \ud835\udf0c\u2217, we obtain\n\u0394\ud835\udc45\ud835\udc5a \u2243 \u0394\ud835\udc5a\ud835\udf0c\u2217. (33)\nThis is Definition B of \u201cmanometric sea-level change\u201d. The local change in mass \u0394\ud835\udc5a can be estimated from the gravity field, or from the bottom pressure\ud835\udc5d\ud835\udc4f, i.e., the hydrostatic pressure at the sea floor , according to \u0394\ud835\udc5a=(\u0394\ud835\udc5d\ud835\udc4f\u2212\u0394\ud835\udc5d\ud835\udc4e)/\ud835\udc54. (See Appendix 3.) Because of its relationship to \ud835\udc5d\ud835\udc4f, manometric sea-level change is sometimes referred to as the \u201cbottom pressure term\u201d in sea-level change.\nAccording to Definition B, the global mean of \u0394\ud835\udc45\ud835\udc5a vanishes if the mass of the global ocean is constant, since 1/(\ud835\udc34\ud835\udf0c\u2217)\u222b\u0394\ud835\udc5ad\ud835\udc34=0. However, \u0394\ud835\udc45\ud835\udc5a may still be locally nonzero, due to rearrangement of the existing mass of the ocean. If the mass of the global ocean changes, the global mean of \u0394\ud835\udc45\ud835\udc5a is nonzero and equals the barystatic sea-level rise (equality is approximate with Definition B of \u0394\ud835\udc45\ud835\udc5a, exact with Definition A), which is part of global-mean sea-level rise (GMSLR). Despite the correspondence between (local) manometric and (global) barystatic sea-level rise, we argue that these two concepts are sufficiently different to need distinct terms. (See the subsection for barystatic sea-level rise.)\nIf mass and density are both allowed to change, Eq. (26) gives\n\u0394\ud835\udc5a = \u0394\ud835\udc3b \u03c1\u0304 + \ud835\udc3b \u0394\u03c1\u0304 => \u0394\ud835\udc3b = (1/\u03c1\u0304 )(\u0394\ud835\udc5a \u2212 \u222b\ud835\udf02\ud835\udc39\u0394\ud835\udf0cd\ud835\udc67), (34)\nusing the expression for \u0394\u03c1\u0304 from Eq. (28). Again approximating \u03c1\u0304 as \ud835\udf0c\u2217 and substituting from Eqs. (25), (29) and (33), we obtain\n\u0394\ud835\udc45 = \u0394\ud835\udc3b \u2243 \u0394\ud835\udc45\ud835\udf0c + \u0394\ud835\udc45\ud835\udc5a, (35)\ni.e., RSLC (without inverse barometer correction) is the sum of steric sea-level change and manometric sea-level change, which are, respectively, the parts due to change in density and change in mass per unit area. Since \ud835\udc3b is defined only in ocean areas, the formulae are not valid for locations which change from land to sea or vice versa.\nWith \u0394\ud835\udc45\ud835\udc5a defined by Eq. (33), Eq. (35) is only approximate, because of the replacement of \ud835\udf0c\u23af\u23af\u23af with \ud835\udf0c\u2217. We can make Eq. (35) exact if we retain the definition of Eq. (29) for steric sea-level change involving \ud835\udf0c\u2217 and adopt Definition A of \u201cmanometric sea-level change\u201d, as\n\u0394\ud835\udc45\ud835\udc5a \u2261 \u0394\ud835\udc45 \u2212 \u0394\ud835\udc45\ud835\udf0c, (36)\ni.e., \u0394\ud835\udc45\ud835\udc5a is the part of RSLC that is not steric.\nWe propose \u201cmanometric\u201d as a new term because in the existing literature there is no unambiguous and generally used term for \u0394\ud835\udc45\ud835\udc5a. It may be described as the \u201cmass effect on\u201d, \u201cmass contribution to\u201d, \u201cmass component of\u201d or \u201cmass term in\u201d sea level or sea-level change, but these descriptions could equally well refer to GRD -induced sea-level change (the effects of a change in the geographical distribution of mass) or barystatic sea-level rise, so they can be confusing. (\u201cManometric\u201d is an existing word, referring to the measurement of hydrostatic pressure using a column of liquid, a concept that is closely related to bottom pressure.)\nN19 Barystatic sea-level rise\u210e\ud835\udc4f: The part of  global-mean sea-level rise  (GMSLR) which is due to the addition to the ocean of water mass that formerly resided within the land area (as land water storage or land ice) or in the atmosphere (which contains a relatively tiny mass of water), or (if negative) the removal of mass from the ocean to be stored elsewhere. It is also called \u201cbarystatic sea-level change\u201d.\nLand water storage, also called terrestrial water storage, is water on land that is stored as groundwater, soil moisture, water in reservoirs, lakes and rivers, seasonal snow and permafrost. Land ice means ice sheets, glaciers, permanent snow and firn. Barystatic sea-level rise includes contributions from changes in all of these.\nIt does not include changes in the parts of ice shelves and glacier tongues whose weight is supported by the ocean rather than resting on land. (These floating parts constitute the majority of the mass of ice shelves and glacier tongues, but near the grounding line on the seaward side some part of the weight may be supported by the land-based ice.) Where land ice rests on a bed which is below mean sea level, it is already displacing sea water. Therefore, the land ice contribution to barystatic sea-level rise excludes the mass whose liquid-water equivalent volume equals the volume of sea water already displaced. The remainder, which is not currently displacing sea water, is often referred to as the ice mass or volume above flotation in glaciology.\nWe define barystatic sea-level rise as\n\u210e\ud835\udc4f = \u0394\ud835\udc40\ud835\udf0cf\ud835\udc34, (37)", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-10", "text": "We propose \u201cmanometric\u201d as a new term because in the existing literature there is no unambiguous and generally used term for \u0394\ud835\udc45\ud835\udc5a. It may be described as the \u201cmass effect on\u201d, \u201cmass contribution to\u201d, \u201cmass component of\u201d or \u201cmass term in\u201d sea level or sea-level change, but these descriptions could equally well refer to GRD -induced sea-level change (the effects of a change in the geographical distribution of mass) or barystatic sea-level rise, so they can be confusing. (\u201cManometric\u201d is an existing word, referring to the measurement of hydrostatic pressure using a column of liquid, a concept that is closely related to bottom pressure.)\nN19 Barystatic sea-level rise\u210e\ud835\udc4f: The part of  global-mean sea-level rise  (GMSLR) which is due to the addition to the ocean of water mass that formerly resided within the land area (as land water storage or land ice) or in the atmosphere (which contains a relatively tiny mass of water), or (if negative) the removal of mass from the ocean to be stored elsewhere. It is also called \u201cbarystatic sea-level change\u201d.\nLand water storage, also called terrestrial water storage, is water on land that is stored as groundwater, soil moisture, water in reservoirs, lakes and rivers, seasonal snow and permafrost. Land ice means ice sheets, glaciers, permanent snow and firn. Barystatic sea-level rise includes contributions from changes in all of these.\nIt does not include changes in the parts of ice shelves and glacier tongues whose weight is supported by the ocean rather than resting on land. (These floating parts constitute the majority of the mass of ice shelves and glacier tongues, but near the grounding line on the seaward side some part of the weight may be supported by the land-based ice.) Where land ice rests on a bed which is below mean sea level, it is already displacing sea water. Therefore, the land ice contribution to barystatic sea-level rise excludes the mass whose liquid-water equivalent volume equals the volume of sea water already displaced. The remainder, which is not currently displacing sea water, is often referred to as the ice mass or volume above flotation in glaciology.\nWe define barystatic sea-level rise as\n\u210e\ud835\udc4f = \u0394\ud835\udc40\ud835\udf0cf\ud835\udc34, (37)\ni.e., the change in mass \u0394\ud835\udc40 of the global ocean from added freshwater, converted to a change in global ocean volume and divided by the ocean surface area A. Because global-mean halosteric change is negligible, the salinity of the existing sea water does not affect \u210e\ud835\udc4f. Any contribution \ud835\udeff\ud835\udc40 to barystatic sea-level rise can be expressed as its sea-level equivalent (SLE)\ud835\udeff\ud835\udc40/(\ud835\udf0cf\ud835\udc34), using the same formula.\nThe formula provides a convenient method of quantifying the changes in the mass of the ocean if A is constant. However, \u210e\ud835\udc4f and SLE may not accurately indicate the contribution of added mass to global-mean ocean thickness if there is a substantial change to A, as for example in the transition from glacial to interglacial.\nCalculating the global mean of manometric sea-level change \u0394\ud835\udc45\ud835\udc5a from its Definition B (Eq. 33) gives 1/\ud835\udc34\u222b\u0394\ud835\udc45\ud835\udc5ad\ud835\udc34=\u0394\ud835\udc40/(\ud835\udf0c\u2217\ud835\udc34)\u2243\u210e\ud835\udc4f, i.e., approximately equal to the barystatic sea-level change, but not exactly since \ud835\udf0c\u2217\u2260\ud835\udf0cf. With Definition A, the global mean of \u0394\ud835\udc45\ud835\udc5a exactly equals \u210e\ud835\udc4f. (See global-mean sea-level rise .) Despite this relationship between manometric sea-level change and barystatic sea-level rise, we argue that we need distinct terms for them, rather than referring to the latter as the global mean of the former, for two reasons.\nFirst, barystatic sea-level rise is well defined by conservation of water mass on Earth and can be evaluated from the change in mass of other stores of water, e.g., ice sheets and glaciers, without considering the ocean. This has been the usual approach in observational studies of the budget of global-mean sea-level rise, and is the only possibility for diagnosing \u210e\ud835\udc4f from the majority of climate models whose ocean component is Boussinesq or has a linear free surface, and therefore does not conserve water mass. Secondly, the partitioning of RSLC into steric and manometric (Eq. 35) is somewhat arbitrary, because it depends on the choice of \ud835\udf0c\u2217 as a reference density.\nNeither reason for the distinction of \u0394\ud835\udc45\ud835\udc5a and \u210e\ud835\udc4f applies to thermosteric sea-level change; its contribution to global-mean sea-level rise can only be conceived or evaluated as the global mean of the local \u0394\ud835\udc45\ud835\udf03, whose definition by Eq. (31) is well defined.\nIn recent literature, \u201ceustatic\u201d is often used as a synonym for \u201cbarystatic\u201d, whereas in geological literature eustatic sea-level change means either global-mean sea-level rise or global-mean geocentric sea-level rise . Because of this confusion of meaning, we deprecate the term \u201ceustatic\u201d, following the last three assessment reports of the Intergovernmental Panel on Climate Change (Church et al. 2001; Meehl et al. 2007; Church et al. 2013).\nN20 Sterodynamic sea-level change\u0394\ud835\udc4d: Relative sea-level change  due to changes in ocean density and circulation, with  inverse barometer  (IB) correction.\nThis term is the sum of ocean dynamic sea-level change (which includes the IB correction) and global-mean thermosteric sea-level rise ,\n\u0394\ud835\udc4d(\ud835\udc2b)=\u0394\ud835\udf01(\ud835\udc2b)+\u210e\ud835\udf03. (38)\nIt can be diagnosed from ocean models (even those that do not conserve mass as per the commonly used Boussinesq models) as the sum of the changes in zos and zostoga. Sterodynamic sea-level change is the part of relative sea-level change that can be simulated with such models. (As discussed above for ocean dynamic sea-level change \u0394\ud835\udf01, the change in zos calculated from CMIP data should have zero global mean.)\n\u201cSterodynamic\u201d is a term which is newly introduced in this paper. We propose it because in the existing literature there is no clear, simple or generally used term for \u0394\ud835\udc4d. It is a concept that appears in the literature, where it is referred to by various cumbersome phrases, such as \u201cthe oceanographic part of sea-level change\u201d, \u201csteric plus dynamic sea-level change\u201d or \u201csea-level change due to ocean density and circulation change\u201d.\nN21 Vertical land movement (VLM)\u0394\ud835\udc39: The change in the height of the  sea floor  or the land surface.\nVLM has several causes, including isostasy, elastic flexure of the lithosphere, earthquakes and volcanoes (due to tectonics). All of these involve a change in height of the existing solid surface. In contrast, landslides and sedimentation alter the solid surface and its height by transport of materials; some authors count them as VLM. Extraction of groundwater and hydrocarbons may cause subsidence (sinking of the solid surface) by compaction (the reduction in the liquid fraction in the sediment). These anthropogenic effects can be locally large, e.g., in Manila, and can exceed the natural effects by orders of magnitude. Where VLM occurs near the coast, it may cause emergence or submergence of land and thus alter the coastline.\nIsostasy or isostatic adjustment is the process of adjustment of the lithosphere (the crust and the rigid upper part of the mantle) towards a hydrostatic equilibrium in which it is regarded as floating in the asthenosphere (the underlying viscous mantle, which is of higher density than the lithosphere), with an equal pressure everywhere at some notional horizontal level beneath the lithosphere. On geological timescales, isostatic adjustment occurs in response to changes in the mass load of the lithosphere upon the mantle beneath (the asthenosphere and lower mantle), due to erosion, sedimentation or emplacement of igneous rocks.\nOn climate timescales there are large changes in load due to the varying mass of ice on land during glacial\u2013interglacial cycles. (See glacial isostatic adjustment .) Isostatic adjustment occurs over multi-millennial timescales determined by the viscous flow of the mantle beneath the lithosphere. An elastic response of the lithosphere, on annual timescales, occurs in response to changes in load. Although it is small compared with the eventual isostatic response, it is much more rapid, and hence responsible for significant VLM due to contemporary and recent historical changes in land ice, for instance in West Antarctica.\nN22 GRD: Changes in Earth  Gravity, Earth Rotation (and hence centrifugal acceleration) and viscoelastic solid-Earth Deformation.", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-11", "text": "N21 Vertical land movement (VLM)\u0394\ud835\udc39: The change in the height of the  sea floor  or the land surface.\nVLM has several causes, including isostasy, elastic flexure of the lithosphere, earthquakes and volcanoes (due to tectonics). All of these involve a change in height of the existing solid surface. In contrast, landslides and sedimentation alter the solid surface and its height by transport of materials; some authors count them as VLM. Extraction of groundwater and hydrocarbons may cause subsidence (sinking of the solid surface) by compaction (the reduction in the liquid fraction in the sediment). These anthropogenic effects can be locally large, e.g., in Manila, and can exceed the natural effects by orders of magnitude. Where VLM occurs near the coast, it may cause emergence or submergence of land and thus alter the coastline.\nIsostasy or isostatic adjustment is the process of adjustment of the lithosphere (the crust and the rigid upper part of the mantle) towards a hydrostatic equilibrium in which it is regarded as floating in the asthenosphere (the underlying viscous mantle, which is of higher density than the lithosphere), with an equal pressure everywhere at some notional horizontal level beneath the lithosphere. On geological timescales, isostatic adjustment occurs in response to changes in the mass load of the lithosphere upon the mantle beneath (the asthenosphere and lower mantle), due to erosion, sedimentation or emplacement of igneous rocks.\nOn climate timescales there are large changes in load due to the varying mass of ice on land during glacial\u2013interglacial cycles. (See glacial isostatic adjustment .) Isostatic adjustment occurs over multi-millennial timescales determined by the viscous flow of the mantle beneath the lithosphere. An elastic response of the lithosphere, on annual timescales, occurs in response to changes in load. Although it is small compared with the eventual isostatic response, it is much more rapid, and hence responsible for significant VLM due to contemporary and recent historical changes in land ice, for instance in West Antarctica.\nN22 GRD: Changes in Earth  Gravity, Earth Rotation (and hence centrifugal acceleration) and viscoelastic solid-Earth Deformation.\nThese three effects are all caused by changes in the geographical distribution of ocean and solid mass over the Earth. They are often considered together because they occur simultaneously and may interact. Changes in gravitation and rotation alter the geopotential field and hence the geoid \ud835\udc3a(\ud835\udc2b), while deformation of the solid Earth changes the sea floor topography \ud835\udc39(\ud835\udc2b) through vertical land movement . By altering G and \ud835\udc39, GRD induces relative sea-level change (e.g., Tamisiea and Mitrovica 2011; Kopp et al. 2015), which redistributes but does not change the global ocean volume and thus causes no global-mean sea-level rise . GRD-induced relative sea-level change\u0394\ud835\udee4 is defined as\n\u0394\ud835\udee4 = \u0394\ud835\udc3a\u2032 \u2212 \u0394\ud835\udc39\u2032 (39)\n(derived in Sect. 6 as Eq. 51) where \u0394\ud835\udc3a\u2032 and \u0394\ud835\udc39\u2032 are the deviations of the changes in the geoid and in the sea floor from their respective global (ocean) means. By construction, the global (ocean) means of \ud835\udc3a\u2032 and \ud835\udc39\u2032 are each zero; hence, the global (ocean) mean of \u0394\ud835\udee4 is zero.\nWhatever the cause, redistribution of the ocean mass itself has GRD effects, and thereby the ocean affects its own mass distribution and mean sea level (MSL). Thus, MSL, the geoid and the sea floor must all be related in a self-consistent solution, which in the context of glacial isostatic adjustment (GIA) is expressed by the sea-level equation (Farrell and Clark 1976).\nThe ocean GRD effects are called self-attraction and loading (SAL), where \u201cloading\u201d means the weight on the solid Earth. SAL is caused by climatic change in ocean density and circulation (Gregory et al. 2013), which do not involve any change in the mass of the ocean. SAL is also a component of GRD which is caused by changes in land ice and in the solid Earth; thus, SAL contributes to the sea-level effects of GIA, contemporary GRD and mantle dynamic topography as well.\nWe propose the new term \u201cGRD\u201d in the absence of any existing single term to describe this frequently discussed group of effects. GRD-induced relative sea-level change may be described as the \u201cmass effect\u201d, \u201cmass contribution\u201d, \u201cmass component\u201d or \u201cmass term\u201d, but these labels could equally well refer to manometric sea-level change if local, or barystatic sea-level rise if global, so they can be confusing. Moreover, \u201cGRD\u201d is helpful as a label for a concept which unifies SAL, GIA, contemporary GRD and mantle dynamic topography.\nN23 Glacial isostatic adjustment (GIA): GRD  due to ongoing changes in the solid Earth caused by past changes in land ice.\nGIA is caused by the viscous adjustment of the mantle to changes in the load on the lithosphere that occurred when mass was transferred from land ice into the ocean, or the reverse. It is dominated by the ongoing effects of the deglaciation following the Last Glacial Maximum. Due to the reduction in the mass load on land, areas that were beneath former ice sheets are generally rising. This process is sometimes called post-glacial rebound, but that term is unsatisfactory because GIA involves remote vertical land movement as well, both upward and downward. Areas adjacent to the former ice sheets are subsiding as mantle material moves towards the areas of uplift, while land near to the coast is rising and the sea floor is generally subsiding as a result of the increase in the mass of the ocean. The ongoing widespread redistribution of mass also affects the geoid . Together, the changes in geoid and sea floor cause GIA-induced relative sea-level change\u0394\ud835\udee4GIA.\nPrevious changes in land ice during the Holocene contribute to GIA as well, but GIA does not include the contributions from any ongoing change in land ice or ocean mass, whose effects we call contemporary GRD .\nN24 Contemporary GRD: GRD  due to ongoing changes in the mass of water stored on land as ice sheets, glaciers and land water storage.\nSuch transfers of mass cause instantaneous changes in the geoid , and vertical land movement (VLM) on annual timescales due to elastic deformation of the solid Earth, which causes further change to the geoid. Together, these effects produce relative sea-level change (RSLC). There are also slower responses, both VLM and geoid, due to viscous deformation of the asthenosphere. Note that contemporary GRD excludes GIA; the former arises from ongoing change in the mass of water on land, and the latter from past change.\nThe elastic deformation and associated geoid contributions to contemporary GRD-induced relative sea-level change are separately proportional to the mass \u0394\ud835\udc40 which has been added to the ocean. Hence, their sum is\n\u0394\ud835\udee4\ud835\udc5d(\ud835\udc2b)=\u0394\ud835\udc40\ud835\udefe\ud835\udc5d(\ud835\udc2b), (40)\nwhere \ud835\udefe\ud835\udc5d(\ud835\udc2b) is a geographically dependent constant of proportionality, independent of \u0394\ud835\udc40. Since the barystatic sea-level rise is \u0394\ud835\udc40/\ud835\udf0cf\ud835\udc34 (Eq. 37), the RSLC due to the combination of these three effects is\n\u0394\ud835\udc45\ud835\udc5d(\ud835\udc2b) = \u0394\ud835\udc40\ud835\udf19(\ud835\udc2b) where \ud835\udf19(\ud835\udc2b) = \ud835\udefe\ud835\udc5d(\ud835\udc2b) + 1/\ud835\udf0cf\ud835\udc34. (41)\nThe addition of freshwater to the ocean will induce sterodynamic sea-level change as well (e.g., Agarwal et al. 2015).\nThe barystatic\u2013GRD fingerprint \ud835\udf19 is a constant geographical pattern, often called a sea-level fingerprint, or sometimes a static-equilibrium fingerprint to contrast it with the patterns of ocean dynamic sea-level change . \u201cFingerprint\u201d without qualification can be easily confused with climate detection and attribution studies where the same word refers to the patterns caused by particular climate change forcing agents such as greenhouse gases. \u201cStatic-equilibrium\u201d is not informative about the processes concerned. The part of contemporary GRD-induced RSLC due to viscous deformation and associated geoid change cannot be represented by a constant pattern because it depends on convolving the history of mass addition with the time-dependent solid-Earth response.\nN25 Mantle dynamic topography: GRD  due to ongoing changes in the solid Earth caused by mantle convection and plate tectonics.", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-12", "text": "The elastic deformation and associated geoid contributions to contemporary GRD-induced relative sea-level change are separately proportional to the mass \u0394\ud835\udc40 which has been added to the ocean. Hence, their sum is\n\u0394\ud835\udee4\ud835\udc5d(\ud835\udc2b)=\u0394\ud835\udc40\ud835\udefe\ud835\udc5d(\ud835\udc2b), (40)\nwhere \ud835\udefe\ud835\udc5d(\ud835\udc2b) is a geographically dependent constant of proportionality, independent of \u0394\ud835\udc40. Since the barystatic sea-level rise is \u0394\ud835\udc40/\ud835\udf0cf\ud835\udc34 (Eq. 37), the RSLC due to the combination of these three effects is\n\u0394\ud835\udc45\ud835\udc5d(\ud835\udc2b) = \u0394\ud835\udc40\ud835\udf19(\ud835\udc2b) where \ud835\udf19(\ud835\udc2b) = \ud835\udefe\ud835\udc5d(\ud835\udc2b) + 1/\ud835\udf0cf\ud835\udc34. (41)\nThe addition of freshwater to the ocean will induce sterodynamic sea-level change as well (e.g., Agarwal et al. 2015).\nThe barystatic\u2013GRD fingerprint \ud835\udf19 is a constant geographical pattern, often called a sea-level fingerprint, or sometimes a static-equilibrium fingerprint to contrast it with the patterns of ocean dynamic sea-level change . \u201cFingerprint\u201d without qualification can be easily confused with climate detection and attribution studies where the same word refers to the patterns caused by particular climate change forcing agents such as greenhouse gases. \u201cStatic-equilibrium\u201d is not informative about the processes concerned. The part of contemporary GRD-induced RSLC due to viscous deformation and associated geoid change cannot be represented by a constant pattern because it depends on convolving the history of mass addition with the time-dependent solid-Earth response.\nN25 Mantle dynamic topography: GRD  due to ongoing changes in the solid Earth caused by mantle convection and plate tectonics.\nThe dynamics of the interior of the Earth cause vertical land movement , such as the uplift of mid-ocean ridges by upwelling material and the formation of oceanic trenches due to subduction. At the same time, material with different density is redistributed within the Earth, altering the geoid . The consequent GRD-induced relative sea-level change can be very large on geological timescales, amounting to hundreds of metres. Mantle dynamic topography does not include glacial isostatic adjustment (although that is also due to ongoing changes in the solid Earth).\nMantle dynamic topography is often called \u201cdynamic topography\u201d in the solid-Earth literature and also refers to changes in topography on land. We deprecate \u201cdynamic topography\u201d in a sea-level context because it could be confused with ocean dynamic topography .\nN26 Global-mean sea-level rise (GMSLR)h: The increase \u0394\ud835\udc49 in the volume of the ocean divided by the ocean surface area A, also called \u201cglobal-mean sea-level change\u201d (GMSLC). Observational estimation of h is described in Sect. 7.\nBy definition, GMSLR is\n\u210e = \u0394\ud835\udc49/\ud835\udc34 = 1/\ud835\udc34\u0394(\u222b(\ud835\udf02\u2212\ud835\udc39)d\ud835\udc34) = 1/\ud835\udc34\u222b\u0394\ud835\udc45(\ud835\udc2b)d\ud835\udc34 = 1/\ud835\udc34\u222b\u0394\ud835\udc3b(\ud835\udc2b)d\ud835\udc34, (42)\nwhich follows from Eqs. (4), (24) and (25). Hence, GMSLR is the global mean of relative sea-level change \u0394\ud835\udc45 and equals the global mean of the change \u0394\ud835\udc3b in the thickness (or \u201cdepth\u201d) of the ocean. Note that GMSLR differs from global-mean geocentric sea-level rise because GMSLR is unaltered by a global-mean change (1/\ud835\udc34)\u222b\u0394\ud835\udc39d\ud835\udc34 in the level of the sea floor \ud835\udc39, provided the global ocean volume V does not change.\nThe global ocean volume can change due to changes in ocean density or due to changes in ocean mass. Hence, GMSLR is the sum of global-mean thermosteric sea-level rise and barystatic sea-level rise ,\n\u210e=\u210e\ud835\udf03+\u210e\ud835\udc4f. (43)\nA satisfactory explanation of historical observed GMSLR in terms of thermosteric and barystatic contributions has been achieved in recent years thanks to improvements in both observations and models (Church et al. 2011; Gregory et al. 2013; Chambers et al. 2017).\nEquation (43) is implied by the Definition A of manometric sea-level change , as the part of relative sea-level change which is not steric (Eq. 36), whose global mean\n1\ud835\udc34\u222b\u0394\ud835\udc45\ud835\udc5ad\ud835\udc34=1\ud835\udc34\u222b\u0394\ud835\udc45d\ud835\udc34\u22121\ud835\udc34\u222b\u0394\ud835\udc45\ud835\udf0cd\ud835\udc34=\u210e\u2212\u210e\ud835\udf03, (44)\nusing Eq. (42) and recalling that global-mean steric sea-level change is purely thermosteric. By definition, the part of h which is not steric is the part which is due to addition of mass, so it must be the case that\n\u210e\ud835\udc4f=1\ud835\udc34\u222b\u0394\ud835\udc45\ud835\udc5ad\ud835\udc34, (45)\ni.e., barystatic sea-level rise equals the global mean of manometric sea-level change by Definition A.\nThe added mass is unlikely to have exactly the temperature of the existing water to which it is added, implying that changes will probably occur to temperature and hence to density. Because of the nonlinearity of the dependence of \ud835\udf0c on \ud835\udf03, there may be a nonzero contribution to \u210e\ud835\udf03 in consequence. Since this is a steric effect, by definition it is not part of \u210e\ud835\udc4f.\nFrom Definition B (Eq. 33) we obtain an approximate expression for global-mean manometric sea-level change as (1/\ud835\udc34)\u222b\u0394\ud835\udc5a/\ud835\udf0c\u2217d\ud835\udc34=\u0394\ud835\udc40/(\ud835\udf0c\u2217\ud835\udc34), where \u0394\ud835\udc40 is the added mass. This is the same as the expression (Eq. 37) for \u210e\ud835\udc4f except that \ud835\udf0cf is replaced by \ud835\udf0c\u2217. This difference is the result of the approximation in Eq. (33) that \ud835\udf0c\u2217 \u2243 \u03c1\u0304. Physically, it is because manometric sea-level change \u0394\ud835\udc45\ud835\udc5a (a local quantity) is dominated by redistribution of existing sea water, for which \ud835\udf0c\u2217 is a good choice of representative density, whereas barystatic sea-level rise (a global quantity) is due only to addition or subtraction of freshwater of density \ud835\udf0cf, since the redistributive effect is zero in the global mean.\nOn glacial\u2013interglacial and geological timescales, the variation of ocean area cannot be neglected, so GMSLR is ill-defined. However, it is still meaningful to consider global-mean relative sea-level change\u210e\ud835\udc45, which is the change in global-mean ocean thickness\n\u210e\ud835\udc45 = \ud835\udc49+\u0394\ud835\udc49/(\ud835\udc34+\u0394\ud835\udc34) \u2212 \ud835\udc49/\ud835\udc34 = \ud835\udc49/(\ud835\udc34+\u0394\ud835\udc34) (\u0394\ud835\udc49/\ud835\udc49\u2212\u0394\ud835\udc34/\ud835\udc34). (46)\nIf A is constant, \u210e\ud835\udc45 = \u210e. An increase in A (\u0394\ud835\udc34>0) gives a negative contribution to \u210e\ud835\udc45, counteracting the positive contribution from a concomitant increase in V.\nIn geological literature, global-mean sea-level rise is sometimes called \u201ceustatic sea-level change\u201d. Following the last three assessment reports of the Intergovernmental Panel on Climate Change (Church et al. 2001; Meehl et al. 2007; Church et al. 2013), we deprecate \u201ceustatic\u201d because it has become a confusing term, which is also used to mean global-mean geocentric sea-level rise or barystatic sea-level rise .\nN27 Global-mean geocentric sea-level rise\u210e\ud835\udc3a: The global-mean change in  mean sea level  with respect to the terrestrial reference frame.\nThis quantity is the global mean of \u0394\ud835\udf02, the change in MSL relative to the reference ellipsoid . From Eqs. (4) and (5) we have\n\u210e\ud835\udc3a = 1/\ud835\udc34\u222b\u0394\ud835\udf02d\ud835\udc34 = 1/\ud835\udc34\u222b\u0394\ud835\udc3ad\ud835\udc34 = 1/\ud835\udc34(\u0394\ud835\udc49 + \u222b\u0394\ud835\udc39d\ud835\udc34) = \u210e + 1/\ud835\udc34 \u222b\u0394\ud835\udc39 d\ud835\udc34, (47)", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-13", "text": "On glacial\u2013interglacial and geological timescales, the variation of ocean area cannot be neglected, so GMSLR is ill-defined. However, it is still meaningful to consider global-mean relative sea-level change\u210e\ud835\udc45, which is the change in global-mean ocean thickness\n\u210e\ud835\udc45 = \ud835\udc49+\u0394\ud835\udc49/(\ud835\udc34+\u0394\ud835\udc34) \u2212 \ud835\udc49/\ud835\udc34 = \ud835\udc49/(\ud835\udc34+\u0394\ud835\udc34) (\u0394\ud835\udc49/\ud835\udc49\u2212\u0394\ud835\udc34/\ud835\udc34). (46)\nIf A is constant, \u210e\ud835\udc45 = \u210e. An increase in A (\u0394\ud835\udc34>0) gives a negative contribution to \u210e\ud835\udc45, counteracting the positive contribution from a concomitant increase in V.\nIn geological literature, global-mean sea-level rise is sometimes called \u201ceustatic sea-level change\u201d. Following the last three assessment reports of the Intergovernmental Panel on Climate Change (Church et al. 2001; Meehl et al. 2007; Church et al. 2013), we deprecate \u201ceustatic\u201d because it has become a confusing term, which is also used to mean global-mean geocentric sea-level rise or barystatic sea-level rise .\nN27 Global-mean geocentric sea-level rise\u210e\ud835\udc3a: The global-mean change in  mean sea level  with respect to the terrestrial reference frame.\nThis quantity is the global mean of \u0394\ud835\udf02, the change in MSL relative to the reference ellipsoid . From Eqs. (4) and (5) we have\n\u210e\ud835\udc3a = 1/\ud835\udc34\u222b\u0394\ud835\udf02d\ud835\udc34 = 1/\ud835\udc34\u222b\u0394\ud835\udc3ad\ud835\udc34 = 1/\ud835\udc34(\u0394\ud835\udc49 + \u222b\u0394\ud835\udc39d\ud835\udc34) = \u210e + 1/\ud835\udc34 \u222b\u0394\ud835\udc39 d\ud835\udc34, (47)\nwhere h is global-mean sea-level rise (GMSLR) defined by Eq. (42). Thus, global-mean geocentric sea-level rise \u210e\ud835\udc3a differs from GMSLR because the latter is unaltered by a global-mean change (1/\ud835\udc34)\u222b\u0394\ud835\udc39d\ud835\udc34 in the level of the sea floor \ud835\udc39, provided the volume of the ocean does not change. On geological timescales, when the area of the ocean may change, the global-mean change in level of the sea floor is \u0394((1/\ud835\udc34)\u222b\ud835\udc39d\ud835\udc34).\nRelationships Determining Relative Sea-Level Change\uf0c1\nRelative sea-level change (RSLC) is \u0394\ud835\udc45 = \u0394\ud835\udf02 \u2212 \u0394\ud835\udc39 (Eq. 24). By applying the inverse barometer correction, we obtain IB-corrected RSLC\n\u0394\ud835\udc45 + \u0394\ud835\udc35 = \u0394\ud835\udf02 + \u0394\ud835\udc35 \u2212 \u0394\ud835\udc39 (48a)\n= \u0394[\ud835\udf02\u2212\ud835\udc3a+\ud835\udc35] + \u0394[\ud835\udc3a\u2212\ud835\udc39] (48b)\n= \u0394\ud835\udf01 + \u0394[\ud835\udc3a\u2212\ud835\udc39], (48c) where in Eq. (48c) we used the definition of ocean dynamic sea-level change \u0394\ud835\udf01 (Eq. 23) to rewrite the first term. From the definition of the geoid (Eq. 4) we obtain\n1/\ud835\udc34 \u222b \u0394(\ud835\udc3a\u2212\ud835\udc39)d\ud835\udc34 = \u0394\ud835\udc49/\ud835\udc34 = \u210e, (49)\nthe global-mean sea-level rise . Let us write \u0394\ud835\udc3a(\ud835\udc2b)=\u0394\ud835\udc3a\u2032(\ud835\udc2b)+(1/\ud835\udc34)\u222b\u0394\ud835\udc3ad\ud835\udc34 and similarly for \u0394\ud835\udc39, thus defining \u0394\ud835\udc3a\u2032,\u0394\ud835\udc39\u2032 as the local deviations of \u0394\ud835\udc3a,\u0394\ud835\udc39 from their respective global (ocean) means. Therefore,\n\u0394(\ud835\udc3a\u2212\ud835\udc39) = \u0394(\ud835\udc3a\u2032\u2212\ud835\udc39\u2032) + 1/\ud835\udc34 \u222b\u0394(\ud835\udc3a\u2212\ud835\udc39)d\ud835\udc34 = \u0394(\ud835\udc3a\u2032\u2212\ud835\udc39\u2032)+\u210e. (50)\nThis leads to our expression for GRD -induced relative sea-level change (Eq. 39) as\n\u0394\ud835\udee4(\ud835\udc2b)\u2261\u0394[\ud835\udc3a\u2032(\ud835\udc2b)\u2212\ud835\udc39\u2032(\ud835\udc2b)]=\u0394[\ud835\udc3a(\ud835\udc2b)\u2212\ud835\udc39(\ud835\udc2b)]\u2212\u210e. (51)\nSubstituting Eq. (51) in Eq. (48c) gives IB-corrected RSLC as\n\u0394\ud835\udc45(\ud835\udc2b)+\u0394\ud835\udc35(\ud835\udc2b)=\u0394\ud835\udf01(\ud835\udc2b)+\u210e+\u0394\ud835\udee4(\ud835\udc2b), (52)\nthe sum of ocean dynamic sea-level change \u0394\ud835\udf01, global-mean sea-level rise h and GRD-induced RSLC \u0394\ud835\udee4. Using Eqs. (43) and (38) we obtain\n\u0394\ud835\udf01(\ud835\udc2b)+\u210e=\u0394\ud835\udf01(\ud835\udc2b)+\u210e\ud835\udf03+\u210e\ud835\udc4f=\u0394\ud835\udc4d(\ud835\udc2b)+\u210e\ud835\udc4f, (53)\nHence, IB-corrected RSLC is\n\u0394\ud835\udc45(\ud835\udc2b)+\u0394\ud835\udc35(\ud835\udc2b)=\u0394\ud835\udc4d(\ud835\udc2b)+\u210e\ud835\udc4f+\u0394\ud835\udee4(\ud835\udc2b), (54)\nthe sum of sterodynamic sea-level change \u0394\ud835\udc4d(\ud835\udc2b), barystatic sea-level rise \u210e\ud835\udc4f and GRD-induced RSLC. The contemporary GRD -induced RSLC due to a change \ud835\udeff\ud835\udc40\ud835\udc56 in any of the stores of water on land (as land water storage or land ice, e.g., in a lake or an ice sheet) has both a barystatic and a GRD-induced effect on sea level, which are related and may interact (e.g., Gomez et al. 2012). Provided they are both proportional to \ud835\udeff\ud835\udc40\ud835\udc56, we can rewrite Eq. (54) as\n\u0394\ud835\udc45(\ud835\udc2b) + \u0394\ud835\udc35(\ud835\udc2b) = \u0394\ud835\udc4d(\ud835\udc2b) + \u2211\ud835\udc56\ud835\udeff\ud835\udc40\ud835\udc56\ud835\udf19\ud835\udc56 + \u0394\ud835\udee4GIA + \u0394\ud835\udee4\ud835\udc4d, (55)\nwhere \ud835\udf19\ud835\udc56 is the barystatic\u2013GRD fingerprint (Eq. 41) of store i of water, \u0394\ud835\udee4GIA is GIA-induced RSLC, and \u0394\ud835\udee4\ud835\udc4d is the GRD-induced RSLC of ocean mass redistribution (self-attraction and loading) associated with sterodynamic sea-level change. The last term is typically neglected.\nEquation (55) is the means by which MSL projections are derived from coupled atmosphere\u2013ocean general circulation models (AOGCMs). These models do not simulate GRD-induced RSLC (because they have time-independent geoid and sea floor) and are not generally used to compute barystatic sea-level rise (because they do not include adequate representations of land ice or land water storage). RSLR projections are therefore obtained by combining sterodynamic sea-level change simulated by an AOGCM with separately calculated projections of barystatic sea-level rise and GRD-induced RSLC using climate change simulations from the AOGCM applied to models of glaciers, ice sheets and the solid Earth (Church et al. 2013; Kopp et al. 2014; Slangen et al. 2014).", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-14", "text": "the sum of sterodynamic sea-level change \u0394\ud835\udc4d(\ud835\udc2b), barystatic sea-level rise \u210e\ud835\udc4f and GRD-induced RSLC. The contemporary GRD -induced RSLC due to a change \ud835\udeff\ud835\udc40\ud835\udc56 in any of the stores of water on land (as land water storage or land ice, e.g., in a lake or an ice sheet) has both a barystatic and a GRD-induced effect on sea level, which are related and may interact (e.g., Gomez et al. 2012). Provided they are both proportional to \ud835\udeff\ud835\udc40\ud835\udc56, we can rewrite Eq. (54) as\n\u0394\ud835\udc45(\ud835\udc2b) + \u0394\ud835\udc35(\ud835\udc2b) = \u0394\ud835\udc4d(\ud835\udc2b) + \u2211\ud835\udc56\ud835\udeff\ud835\udc40\ud835\udc56\ud835\udf19\ud835\udc56 + \u0394\ud835\udee4GIA + \u0394\ud835\udee4\ud835\udc4d, (55)\nwhere \ud835\udf19\ud835\udc56 is the barystatic\u2013GRD fingerprint (Eq. 41) of store i of water, \u0394\ud835\udee4GIA is GIA-induced RSLC, and \u0394\ud835\udee4\ud835\udc4d is the GRD-induced RSLC of ocean mass redistribution (self-attraction and loading) associated with sterodynamic sea-level change. The last term is typically neglected.\nEquation (55) is the means by which MSL projections are derived from coupled atmosphere\u2013ocean general circulation models (AOGCMs). These models do not simulate GRD-induced RSLC (because they have time-independent geoid and sea floor) and are not generally used to compute barystatic sea-level rise (because they do not include adequate representations of land ice or land water storage). RSLR projections are therefore obtained by combining sterodynamic sea-level change simulated by an AOGCM with separately calculated projections of barystatic sea-level rise and GRD-induced RSLC using climate change simulations from the AOGCM applied to models of glaciers, ice sheets and the solid Earth (Church et al. 2013; Kopp et al. 2014; Slangen et al. 2014).\nAccording to Eqs. (35) or (36), \u0394\ud835\udc45=\u0394\ud835\udc45\ud835\udf0c+\u0394\ud835\udc45\ud835\udc5a, the sum of steric sea-level change \u0394\ud835\udc45\ud835\udf0c and manometric sea-level change \u0394\ud835\udc45\ud835\udc5a, which are the parts due, respectively, to change in density and change in mass per unit area. In general, \u0394\ud835\udc45\ud835\udc5a\u22600 even if \u210e\ud835\udc4f=0, because ocean mass may be redistributed. In particular, because \u0394\ud835\udc45\ud835\udc5a=\u22121/\ud835\udf0cs\u222b\ud835\udf02\ud835\udc39\u0394\ud835\udf0cd\ud835\udc67 is small on the continental shelves (where the ocean is shallow), but ocean dynamics will not permit a strong gradient in \ud835\udf01 to develop across the shelf break, global-mean thermosteric sea-level rise demands a redistribution of ocean mass onto the shelves (Landerer et al. 2007; Yin et al. 2010), with consequent ocean GRD (Gregory et al. 2013).\nObservations of Sea-Level Change\uf0c1\nEstimates of global-mean sea-level rise (GMSLR) for the last century depend mainly on records from tide-gauges. These instruments register coastal relative sea-level change (RSLC) \u0394\ud835\udc45=\u0394\ud835\udf02\u2212\u0394\ud835\udc39 (Eq. 24), which is affected by local vertical land movement (VLM) \u0394\ud835\udc39. VLM is large in some places, with strong geographical gradients.\nGMSLR is calculated as the global mean of RSLC, \u210e=(1/\ud835\udc34)\u222b\u0394\ud835\udc45d\ud835\udc34 (Eq. 42). However, tide-gauges measure \u0394\ud835\udc45 only at points on the coast and thus give a sparse, non-uniform and unrepresentative sampling of the global ocean area. The calculation therefore depends on physically based methods for extrapolation. Considering Eq. (52) in the form\n\u210e = \u0394\ud835\udc45 + \u0394\ud835\udc35 \u2212 \u0394\ud835\udf01 \u2212 \u0394\ud835\udee4 (56)\nwe see that in principle h can be calculated from \u0394\ud835\udc45 from any tide-gauge by applying the inverse barometer (IB) correction \u0394\ud835\udc35, and subtracting local ocean dynamic sea-level change \u0394\ud835\udf01 and local GRD -induced RSLC \u0394\ud835\udee4. The global mean of each of these three adjustments is zero, so Eq. (42) is satisfied. In practice, using historical records, it is necessary to combine many tide-gauges in order to reduce the influence of unforced variability in \ud835\udf01\u0303.\nThe IB adjustment is fairly small and can be made accurately from atmospheric pressure records. Various methods are used to allow for the spatial pattern of \u0394\ud835\udf01, for example by calculating the mean over sets of gauges presumed to be representative of large regions (e.g., Jevrejeva et al. 2008), or by using spatial patterns of \ud835\udf02\u0303 variation observed by satellite altimetry during its shorter period of availability (e.g., Church and White 2011). Because glacial isostatic adjustment (GIA) is the only part of GRD (including VLM) for which a global field is available, most estimates of GMSLR exclude all tide-gauges where GIA is not the only significant contribution to VLM (those affected by earthquakes, anthropogenic subsidence, sediment compactions, etc.). At the tide-gauges which are retained, we adjust for GIA-induced RSLC \u0394\ud835\udee4GIA(\ud835\udc2b) (e.g., Figure 3a of Tamisiea and Mitrovica 2011), estimated by combining solid-Earth models, the sea-level equation and reconstructed histories of deglaciation.\nAlternatively, tide-gauge records may be corrected for VLM using vertical motion calculated from collocated GNSS (e.g., GPS) receivers. Effectively, this transforms RSLC to geocentric sea-level change \u0394\ud835\udf02=\u0394\ud835\udc45+\u0394\ud835\udc39 (Eq. 24). Geoid adjustments must be applied to GNSS-corrected tide-gauge records just as for satellite altimetry, as described in the next paragraph.\nGeocentric sea-level change \u0394\ud835\udf02(=\u0394\ud835\udf01\u2212\u0394\ud835\udc35+\u0394\ud835\udc3a, Eq. 23) has been measured over most of the global ocean since the early 1990s by satellite radar altimetry, using instruments which are located in a terrestrial reference frame (equivalent to the reference ellipsoid), and measure their vertical distance from the sea surface. To study the contemporary causes of observed geocentric sea-level change we must subtract \u0394\ud835\udc3aGIA(\ud835\udc2b), the effect of GIA on the geoid (e.g., Figure 3b of Tamisiea and Mitrovica 2011), from IB-corrected geocentric sea-level change, thus:\n\u0394\ud835\udf02 + \u0394\ud835\udc35 \u2212 \u0394\ud835\udc3a GIA = \u0394\ud835\udf01 + \u0394\ud835\udc3aNGIA, (57)\nwhere \u0394\ud835\udc3aNGIA = \u0394\ud835\udc3a \u2212 \u0394\ud835\udc3aGIA is due to ongoing redistribution of water mass on the Earth\u2019s surface.\nTo convert global-mean geocentric sea-level rise \u210e\ud835\udc3a=(1/\ud835\udc34)\u222b\u0394\ud835\udf02d\ud835\udc34 to GMSLR h requires an adjustment for the global mean of \u0394\ud835\udc39, according to Eq. (47). Although several processes can produce large local VLM, the only large global-mean effect is GIA. There is no contemporary GMSLR associated with GIA, so Eq. (49) gives (1/\ud835\udc34)\u222b\u0394\ud835\udc39GIAd\ud835\udc34=(1/\ud835\udc34)\u222b\u0394\ud835\udc3aGIAd\ud835\udc34\u21d2(1/\ud835\udc34)\u222b\u0394\ud835\udc3aNGIAd\ud835\udc34=\u210e+(1/\ud835\udc34)\u222b\u0394\ud835\udc39NGIAd\ud835\udc34. Hence, the global mean of Eq. (57) becomes\n\u210e\ud835\udc3a = \u210e + 1/\ud835\udc34\u222b\u0394\ud835\udc39GIA d\ud835\udc34 + 1/\ud835\udc34\u222b\u0394\ud835\udc39NGIA d\ud835\udc34, (58)", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-15", "text": "Geocentric sea-level change \u0394\ud835\udf02(=\u0394\ud835\udf01\u2212\u0394\ud835\udc35+\u0394\ud835\udc3a, Eq. 23) has been measured over most of the global ocean since the early 1990s by satellite radar altimetry, using instruments which are located in a terrestrial reference frame (equivalent to the reference ellipsoid), and measure their vertical distance from the sea surface. To study the contemporary causes of observed geocentric sea-level change we must subtract \u0394\ud835\udc3aGIA(\ud835\udc2b), the effect of GIA on the geoid (e.g., Figure 3b of Tamisiea and Mitrovica 2011), from IB-corrected geocentric sea-level change, thus:\n\u0394\ud835\udf02 + \u0394\ud835\udc35 \u2212 \u0394\ud835\udc3a GIA = \u0394\ud835\udf01 + \u0394\ud835\udc3aNGIA, (57)\nwhere \u0394\ud835\udc3aNGIA = \u0394\ud835\udc3a \u2212 \u0394\ud835\udc3aGIA is due to ongoing redistribution of water mass on the Earth\u2019s surface.\nTo convert global-mean geocentric sea-level rise \u210e\ud835\udc3a=(1/\ud835\udc34)\u222b\u0394\ud835\udf02d\ud835\udc34 to GMSLR h requires an adjustment for the global mean of \u0394\ud835\udc39, according to Eq. (47). Although several processes can produce large local VLM, the only large global-mean effect is GIA. There is no contemporary GMSLR associated with GIA, so Eq. (49) gives (1/\ud835\udc34)\u222b\u0394\ud835\udc39GIAd\ud835\udc34=(1/\ud835\udc34)\u222b\u0394\ud835\udc3aGIAd\ud835\udc34\u21d2(1/\ud835\udc34)\u222b\u0394\ud835\udc3aNGIAd\ud835\udc34=\u210e+(1/\ud835\udc34)\u222b\u0394\ud835\udc39NGIAd\ud835\udc34. Hence, the global mean of Eq. (57) becomes\n\u210e\ud835\udc3a = \u210e + 1/\ud835\udc34\u222b\u0394\ud835\udc39GIA d\ud835\udc34 + 1/\ud835\udc34\u222b\u0394\ud835\udc39NGIA d\ud835\udc34, (58)\nrecalling that the global means of \u0394\ud835\udc35 and \u0394\ud835\udf01 are zero. In response to the shift of mass from the land (as ice) into the ocean since the Last Glacial Maximum, and the consequent mantle adjustment, the sea floor is subsiding on average, giving a trend in (1/\ud835\udc34)\u222b\u0394\ud835\udc39GIAd\ud835\udc34 of about \u22120.3  mm  year \u22121 (Tamisiea and Mitrovica 2011). Thus, \u210e\ud835\udc3a<\u210e due to GIA. Contemporary changes in land ice cause elastic deformation of the sea floor. This gives a negative (1/\ud835\udc34)\u222b\u0394\ud835\udc39NGIAd\ud835\udc34 which reduces \u210e\ud835\udc3a by about 8% of the barystatic sea-level rise (Frederikse et al. 2017).\nDeprecated Terms and Recommended Replacements\uf0c1\nDeprecated term\nRecommended replacement\nEustatic sea-level change\nBarystatic sea-level rise or barystatic sea-level change\nfor global-mean sea-level rise due to change in the mass of\nthe ocean, but not its density\nGlobal-mean sea-level rise for the global mean of\nrelative sea-level change, due to the change in the volume\nof the ocean\nGlobal-mean geocentric sea-level rise for the global\nmean of change in mean sea level relative to the terrestrial\nreference frame, due to the combined effects of change in\nthe volume of the ocean and change in the level of the sea\nfloor\nDynamic topography\nOcean dynamic sea level for mean sea level above the\ngeoid due to ocean dynamics\nOcean dynamic topography for ocean dynamic sea level\nestimated from ocean density\nSea-level change due to mantle dynamic topography for\nGRD-induced relative sea-level change due to solid-Earth\ndynamics\nMean sea surface\nMean sea level (MSL)\nMean sea-level change\nor local sea-level change\nRelative sea-level change (RSLC) or relative sea-level\nrise (RSLR) for the change in mean sea level relative to the\nland\nGeocentric sea-level change for the change in mean sea\nlevel relative to the terrestrial reference frame\nGlobal sea-level change\n(GSLC)\nGobal-mean sea-level rise (GMSLR) or global-mean sea-\nlevel change (GMSLC) for the global mean of relative sea-\nlevel change, due to the change in the volume of the ocean\nGlobal-mean geocentric sea-level rise for the global-mean\nchange in mean sea level relative to the terrestrial\nreference frame\nExtreme sea level\nExtreme sea level for the occurrence of exceptionally\nhigh local sea surface due to short-term phenomena, or\nextreme coastal water level when considering coastal impacts.\nHigh-end sea-level change for projections or scenarios\nof very large RSLR or GMSLR\nSea-level change due to\nthermal expansion\nThermosteric sea-level change for contribution to\nrelative sea-level change\nGlobal-mean thermosteric sea-level rise for contribution\nto global-mean sea-level change\nSea-level change due to\noceanographic processes or\nsteric plus dynamic sea-\nlevel change\nSterodynamic sea-level change for the change in relative\nsea-level due to change in ocean density and circulation\nSea-level fingerprint or\nstatic-equilibrium\nfingerprint\nBarystatic\u2013GRD fingerprint for the sum of the RSLC from\nGRD (elastic and geoid) and the barystatic sea-level rise due\nto the addition of a unit mass of water to the global ocean\nPost-glacial rebound (PGR)\nGlacial isostatic adjustment (GIA)\nMass effect on, mass term\nin, mass component of, or\nmass contribution to sea\nlevel or to sea-level\nchange\nBarystatic sea-level rise for the contribution to global-\nmean sea-level rise from the change of mass of the global\nocean (associated with changes in mass of water and ice on\nland), as opposed to global-mean thermosteric sea-level rise\nManometric sea-level change for the contribution to\nrelative sea-level change due to change in the local mass of\nthe ocean per unit area, as opposed to steric sea-level\nchange\nGRD-induced relative sea-level change for the effects on\nrelative sea level from geoid change and vertical land\nmovement, as opposed to steric, ocean dynamic and barystatic\nsea-level change\nBottom pressure term in\nsea-level change\nManometric sea-level change\nList of Defined Terms and Notations\uf0c1\nThis table gives the entry number or section (not the page number) in which each term is defined. In the PDF, each term is a hyperlink to the relevant text. The rows for which there is no entry number are included only to define notation.\nAbove flotation\nN19\nAltimetry\nSection 7\nA\nArea of the global ocean\nAsthenosphere\nN21\nAstronomical tide\nN6\n\ud835\udc5d\ud835\udc4e\nAtmospheric pressure at the\nsea surface\n\u210e\ud835\udc4f\nBarystatic sea-level rise\nN19\n\ud835\udf19\nBarystatic\u2013GRD fingerprint\nN24\nBathymetry\nN4\nBottom pressure\nN18\nBottom topography\nN4\nChandler wobble\nN6\nCompaction\nN21\nContemporary GRD\nN24\n\ud835\udf0c\nDensity of water\nDepth of the water column\nN4\nD\nDynamic height\nN12\ng\nEffective gravitational acceleration\nN5\nEllipsoidal height\nN1\nEquipotential surface\nN5\nEustatic sea-level change\nN19\nExtreme coastal water level\nN8\nExtreme sea level\nN8\nFetch\nN10\nFree nutation\nN6\nGeocentric latitude\nN1\n\u0394\ud835\udf02\nGeocentric sea-level change\nN14\nGeodetic height\nN1\nGeodetic latitude\nN1\nG\nGeoid\nN5\nGeoid height\nN5\n\u03a6\nGeopotential\nN5\nGeostrophy\nN12\nvg\nGeostrophic velocity\nN12\n\u0394\ud835\udee4GIA\nGIA-induced relative sea-level change\nN23\nGlacial isostatic  adjustment (GIA)\nN23\nGlobal mean\nSection 2.4\n\u210e\ud835\udc3a\nGlobal-mean geocentric sea-level rise\nN27\n\u210e\ud835\udc45\nGlobal-mean relative sea-level change\nN26\nh\nGlobal-mean sea-level rise (GMSLR)\nN26\n\u210e\ud835\udf03\nGlobal-mean thermosteric sea-level rise\nN17\nGravitational acceleration\nN5\nGRD\nN22\n\u0394\ud835\udee4\nGRD-induced relative sea-level change\nN22\nGreenwich meridian\nN1\nHalosteric sea-level change \u0394\ud835\udc45\ud835\udc46\nN16\nHigh-end\nN8\nHorizontal\nN5\nIB-corrected geocentric  sea-level change\nN14\nIB-corrected mean sea level\nN7", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-16", "text": "N19\nAltimetry\nSection 7\nA\nArea of the global ocean\nAsthenosphere\nN21\nAstronomical tide\nN6\n\ud835\udc5d\ud835\udc4e\nAtmospheric pressure at the\nsea surface\n\u210e\ud835\udc4f\nBarystatic sea-level rise\nN19\n\ud835\udf19\nBarystatic\u2013GRD fingerprint\nN24\nBathymetry\nN4\nBottom pressure\nN18\nBottom topography\nN4\nChandler wobble\nN6\nCompaction\nN21\nContemporary GRD\nN24\n\ud835\udf0c\nDensity of water\nDepth of the water column\nN4\nD\nDynamic height\nN12\ng\nEffective gravitational acceleration\nN5\nEllipsoidal height\nN1\nEquipotential surface\nN5\nEustatic sea-level change\nN19\nExtreme coastal water level\nN8\nExtreme sea level\nN8\nFetch\nN10\nFree nutation\nN6\nGeocentric latitude\nN1\n\u0394\ud835\udf02\nGeocentric sea-level change\nN14\nGeodetic height\nN1\nGeodetic latitude\nN1\nG\nGeoid\nN5\nGeoid height\nN5\n\u03a6\nGeopotential\nN5\nGeostrophy\nN12\nvg\nGeostrophic velocity\nN12\n\u0394\ud835\udee4GIA\nGIA-induced relative sea-level change\nN23\nGlacial isostatic  adjustment (GIA)\nN23\nGlobal mean\nSection 2.4\n\u210e\ud835\udc3a\nGlobal-mean geocentric sea-level rise\nN27\n\u210e\ud835\udc45\nGlobal-mean relative sea-level change\nN26\nh\nGlobal-mean sea-level rise (GMSLR)\nN26\n\u210e\ud835\udf03\nGlobal-mean thermosteric sea-level rise\nN17\nGravitational acceleration\nN5\nGRD\nN22\n\u0394\ud835\udee4\nGRD-induced relative sea-level change\nN22\nGreenwich meridian\nN1\nHalosteric sea-level change \u0394\ud835\udc45\ud835\udc46\nN16\nHigh-end\nN8\nHorizontal\nN5\nIB-corrected geocentric  sea-level change\nN14\nIB-corrected mean sea level\nN7\nIB-corrected relative sea-level change\nN15\nIB-corrected sea-surface height\nN7\n\ud835\udf03\nIn-situ temperature of ocean water\nB\nInverse barometer (IB)\nN7\nInverted barometer\nN7\nIsostasy\nN21\nIsostatic adjustment\nN21\nLand ice\nN19\nLand water storage\nN19\nLatitude\nN1\nLevel of no motion\nN12\nLiquid-water equivalent sea\nsurface\nN2\nLithosphere\nN21\nLocal\nSection 2.3\nLongitude\nN1\n\u0394\ud835\udc45\ud835\udc5a\nManometric sea-level change\nN18\nMantle dynamic topography\nN25\nM\nMass of the global ocean\n\ud835\udf02\nMean sea level (MSL)\nN3\nMean-tide\nN6\nNeap tide\nN6\nNodal period\nN6\nOcean\nSection 2.4\n\ud835\udf01\nOcean dynamic sea level\nN11\n\u0394\ud835\udf01\nOcean dynamic sea-level\nchange\nN13\nOcean dynamic topography\nN12\nOcean GRD\nN22\nm\nOcean mass per unit area\nOrthometric height\nN5\nPermanent tide\nN6\nPole tide\nN6\nPost-glacial rebound\nN23\nPredicted tide\nN6\nPrime meridian\nN1\nRadiational tide\nN6\nReference ellipsoid\nN1\nRegression\nN15\n\u0394\ud835\udc45\nRelative sea-level change\n(RSLC)\nN15\n\ud835\udf0c\u2217\nRepresentative density of\nocean water\nS\nSalinity of ocean water\nF\nSea floor\nN4\nSea surface\nN2\nSea-level equation\nN22\nSea-level equivalent (SLE)\nN19\nSea-level fingerprint\nN24\nSea-surface height (SSH)\nN2\nSea-surface waves\nN10\nSeismic sea wave\nN10\nSelf-attraction and loading\n(SAL)\nN22\nSignificant wave height\nN10\nSignificant wave period\nN10\nSkew-surge height\nN9\nSpring tide\nN6\nState\nSection 2.2\nStatic-equilibrium\nfingerprint\nN24\n\u0394\ud835\udc45\ud835\udf0c\nSteric sea-level change\nN16\n\u0394\ud835\udc4d\nSterodynamic sea-level\nchange\nN20\nStorm surge\nN9\nStorm tide\nN6\n\u03c3\nStorm-surge height\nN9\nSubsidence\nN21\nSurge residual\nN9\nSwash\nN9\nSwell wave\nN10\nTerrestrial reference frame\nN1\nTerrestrial water storage\nN19\nThermal expansion\nN16\nThermosteric sea-level\nchange \u0394\ud835\udc45\ud835\udf03\nN16\nH\nThickness of the ocean\nN4\nTidal currents\nN6\nTidal datum\nN6\nTidal height\nN6\nTide-free\nN6\nTide-gauge\nN15\nTides\nN6\nTransgression\nN15\nTrue polar wander\nN1\nTsunami\nN10\nVertical\nN1\n\u0394\ud835\udc39\nVertical land movement\n(VLM)\nN21\nV\nVolume of the global ocean\nWave height\nN10\nWave period\nN10\nWave runup\nN9\nWave setup\nN9\nWind setup\nN9\nWind wave\nN10\nZero-tide\nN6\nAppendix 1: No Resting Steady State Exists for a Realistic Ocean\uf0c1\nA state of rest requires zero acceleration parallel to the surface, which must therefore be an equipotential. This condition is satisfied by the geoid because it is an equipotential surface by definition. However, zero acceleration at the surface is not a sufficient condition for the ocean to remain at rest. If there are any horizontal density gradients within the ocean, there will be pressure gradients beneath the horizontal surface, producing forces that will set the ocean into motion. So another necessary condition for zero ocean circulation is the absence of density gradients along horizontal surfaces, i.e., density is a function of depth only. This configuration is quite unlike the real state of the ocean.\nAppendix 2: Why We Can Ignore Global Halosteric Sea-Level Change\uf0c1\nWhen freshwater enters the ocean, such as from melting continental ice sheets, it adds to the ocean mass and in turn increases global-mean sea level (barystatic sea-level rise). Ocean salinity also changes due to the dilution of sea water, thus suggesting a role for a global halosteric sea-level change (Munk 2003; Levitus et al. 2005). However, the net effect on global-mean sea level is almost entirely barystatic since the global halosteric effect is negligible (Lowe and Gregory 2006). We can understand why this is so by recognizing that freshwater entering the ocean sees its salinity increase while the ambient sea water is itself freshened. These compensating salinity changes (which are often ignored, as by Munk 2003 and Levitus et al. 2005) have corresponding compensating sea-level changes, thus bringing the global halosteric effect to near zero. We demonstrate this effect in the following subsections, by considering a two-bucket thought experiment where one bucket holds freshwater (bucket-1) and the other holds sea water (bucket-2). We ask how the total water volume changes upon homogenizing the water in the two buckets, while conserving the masses of freshwater and salt. As we will see, the total volume of homogenized water is very nearly equal to the sum of the volume initially in the two separate buckets (to within 0.1%).\nConservation of Mass for Freshwater and Salt\uf0c1\nLet the two buckets contain water of mass \ud835\udc40\ud835\udc5b, volume \ud835\udc49\ud835\udc5b, salinity \ud835\udc46\ud835\udc5b, and density \ud835\udf0c\ud835\udc5b, \ud835\udc5b=1,2, and assume they have equal Conservative Temperature and equal pressure. Now homogenize the water from the two buckets into a single larger bucket, and assume no change in pressure nor any heat of mixing so that Conservative Temperature also remains unchanged. The total mass of freshwater and salt is unchanged upon homogenizing, so that\n\ud835\udc40 = \ud835\udc401 + \ud835\udc402; \ud835\udc40\ud835\udc46 = \ud835\udc401\ud835\udc461 + \ud835\udc402\ud835\udc462, (59)\nwhere M is the total mass and S is the salinity of the homogenized water. Return the homogenized water to the original buckets, placing the same mass \ud835\udc401 back into the first bucket and mass \ud835\udc402 into the second bucket.\nDependence of Density on Salinity\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-17", "text": "Conservation of Mass for Freshwater and Salt\uf0c1\nLet the two buckets contain water of mass \ud835\udc40\ud835\udc5b, volume \ud835\udc49\ud835\udc5b, salinity \ud835\udc46\ud835\udc5b, and density \ud835\udf0c\ud835\udc5b, \ud835\udc5b=1,2, and assume they have equal Conservative Temperature and equal pressure. Now homogenize the water from the two buckets into a single larger bucket, and assume no change in pressure nor any heat of mixing so that Conservative Temperature also remains unchanged. The total mass of freshwater and salt is unchanged upon homogenizing, so that\n\ud835\udc40 = \ud835\udc401 + \ud835\udc402; \ud835\udc40\ud835\udc46 = \ud835\udc401\ud835\udc461 + \ud835\udc402\ud835\udc462, (59)\nwhere M is the total mass and S is the salinity of the homogenized water. Return the homogenized water to the original buckets, placing the same mass \ud835\udc401 back into the first bucket and mass \ud835\udc402 into the second bucket.\nDependence of Density on Salinity\uf0c1\nThe dimensionless coefficients \ud835\udefc\u2261\ud835\udf0c\u22121\u2202\ud835\udf0c/\u2202\ud835\udf03 and \ud835\udefd\u2261\ud835\udf0c\u22121\u2202\ud835\udf0c/\u2202\ud835\udc46, which are used to compute steric sea-level change (Eq. 31), measure the relative change in the in-situ density as a function of temperature and salinity. Because \u2202\ud835\udf0c/\u2202\ud835\udf03 is generally negative, the volume of a given parcel of sea water increases as its temperature rises; this phenomenon is called thermal expansion. By analogy, since \u2202\ud835\udf0c/\u2202\ud835\udc46>0, the corresponding effect for salinity is sometimes called \u201chaline contraction\u201d. This is a misleading analogy, because if the salinity has increased but the mass has not changed, some freshwater must have been replaced by salt, so the parcel is materially altered, unlike in the case of adding heat. If salt is added to the parcel but no mass is removed, the salinity, mass and volume of the parcel will all increase. The notion of \u201chaline contraction\u201d has led some previous authors to draw incorrect conclusions about the effect on sea level from adding freshwater to the ocean. We here aim to clarify this situation.\nThe change in the volume of water due to homogenization depends on the value of \ud835\udefd. For the surface ocean, representative values are \ud835\udf0c=1028  kg  m \u22123 and \ud835\udc46=0.035, while for freshwater \ud835\udf0c=\ud835\udf0cf=1000  kg  m \u22123 and \ud835\udc46=0. Hence, a representative \ud835\udefd\u2248(1/1000)(1028\u22121000)/(0.035\u22120)=28/35=0.8. This coefficient has a roughly 5% relative variation across the ocean, with most of that variation determined by temperature rather than salinity. (See Roquet et al. 2015, as well as Figure 1 in Griffies et al. 2014.) Since our concern is with salinity changes, we take \ud835\udefd to be constant in the following.\nComputing the Change in Total Volume\uf0c1\nThe change in total volume upon homogenization is the sum of the changes in the two buckets,\n\ud835\udeff\ud835\udc49=\ud835\udeff\ud835\udc491+\ud835\udeff\ud835\udc492. (60)\nSince the mass of water in the two buckets remains the same before and after homogenization, the volume in the two buckets is altered only due to changes in their respective densities\n\ud835\udeff\ud835\udf0c\ud835\udc5b=\ud835\udeff(\ud835\udc40\ud835\udc5b/\ud835\udc49\ud835\udc5b)=\u2212(\ud835\udf0c\ud835\udc5b/\ud835\udc49\ud835\udc5b)\ud835\udeff\ud835\udc49\ud835\udc5b\u21d2\ud835\udeff\ud835\udf0c\ud835\udc5b/\ud835\udf0c\ud835\udc5b=\u2212\ud835\udeff\ud835\udc49\ud835\udc5b/\ud835\udc49\ud835\udc5b, (61)\ni.e., the relative density increases as the relative volume decreases. Because the buckets have the same temperature in our experiment, relative density changes occur only through salinity changes, according to\n\ud835\udeff\ud835\udf0c\ud835\udc5b/\ud835\udf0c\ud835\udc5b=\ud835\udefd\ud835\udeff\ud835\udc46\ud835\udc5b=\u2212\ud835\udeff\ud835\udc49\ud835\udc5b/\ud835\udc49\ud835\udc5b, (62)\nin which case the change in total volume is\n\ud835\udeff\ud835\udc49=\ud835\udeff\ud835\udc491+\ud835\udeff\ud835\udc492=\u2212(\ud835\udc491\ud835\udefd\ud835\udeff\ud835\udc461+\ud835\udc492\ud835\udefd\ud835\udeff\ud835\udc462). (63)\nMass conservation for salt means that\n\ud835\udeff(\ud835\udc40\ud835\udc46)=\ud835\udeff(\ud835\udc401\ud835\udc461)+\ud835\udeff(\ud835\udc402\ud835\udc462)=0. (64)\nFurthermore, since mass in the two buckets is unchanged, salt conservation leads to\n\ud835\udc401\ud835\udeff\ud835\udc461+\ud835\udc402\ud835\udeff\ud835\udc462=0, (65)\nso that salinity in one bucket rises while that in the other falls. Making use of this result in Eq. (63) leads to our desired expression for total volume change\n\ud835\udeff\ud835\udc49=\u2212\ud835\udefd\ud835\udeff\ud835\udc461(\ud835\udc491\u2212\ud835\udc492\ud835\udc401/\ud835\udc402)=\u2212\ud835\udefd\ud835\udc491\ud835\udeff\ud835\udc461(1\u2212\ud835\udf0c1/\ud835\udf0c2). (66)\nConnecting to Thickness Changes\uf0c1\nEquation (66) provides an expression for the change in total volume upon homogenizing two buckets of water with equal Conservative Temperatures, equal pressures, but with differing salinities. To connect to sea level, assume an equal cross-sectional area, A, for the buckets, so that the volume of water is given by \ud835\udc49\ud835\udc5b=\ud835\udc34\u210e\ud835\udc5b, where \u210e\ud835\udc5b is the thickness of the water in the bucket. Equation (66) then says that upon homogenization, the thickness of water changes by\n\ud835\udeff\u210e=\u2212\ud835\udefd\u210e1\ud835\udeff\ud835\udc461(1\u2212\ud835\udf0c1/\ud835\udf0c2),(67)\nand that the total thickness of the homogenized water is given by\n\u210enew=\u210e1+\u210e2+\ud835\udeff\u210e=\u210e2+\u210e1[1\u2212\ud835\udefd\ud835\udeff\ud835\udc461(1\u2212\ud835\udf0c1/\ud835\udf0c2)]. (68)\nAs expected, we see that \ud835\udeff\u210e=0 only when \ud835\udefd=0 or \ud835\udf0c1=\ud835\udf0c2. The first is never true, and the second is not true in the general case of differing temperatures (in which case there are thermosteric changes ignored in our discussion).\nAn Ocean Example\uf0c1\nTo explore the oceanic implications of Eq. (68), assume bucket-1 initially has freshwater with density \ud835\udf0c1=\ud835\udf0cf, whereas bucket-2 initially has sea water with density \ud835\udf0c2=\ud835\udf0cs=\ud835\udf0cf+\ud835\udf0c\u2032. The salinity change for bucket-1 is \ud835\udeff\ud835\udc461=\ud835\udc46, since this bucket went from its original freshwater concentration to the homogenized sea water with salinity S. The halosteric-induced thickness change (Eq. 67) is thus given by\n\ud835\udeff\u210e=\u2212\u210e1\ud835\udefd\ud835\udc46(\ud835\udf0c\u2032/\ud835\udf0cs)<0. (69)\nHow large is this effect? For the case of an upper ocean with salt concentration \ud835\udc46=0.035, sea-water density \ud835\udf0cs=1028 kg  m \u22123\u21d2\ud835\udf0c\u2032=28 kg  m \u22123 and \ud835\udefd=0.8, we have\n\ud835\udeff\u210e=\u2212\u210e1\u00d70.8\u00d70.035\u00d7(28/1028)\u2248\u2212\u210e1\u00d77.6\u00d710\u22124. (70)\nTo within roughly 8 parts in 104, the change in thickness of the ocean column is nearly identical to the thickness of freshwater added to the ocean. For example, if we add one metre of freshwater into the upper ocean (\u210e1=1 m ), then the change in sea level is equal to one metre minus the tiny amount 0.76 mm . Hence, as emphasized by Lowe and Gregory (2006), we can generally ignore the contribution to global-mean sea level from global halosteric effects.\nAppendix 3: Bottom Pressure\uf0c1\nThe hydrostatic pressure at the ocean sea floor is commonly referred to as the ocean bottom pressure \ud835\udc5d\u0303\ud835\udc4f, usually calculated as\n\ud835\udc5d\u0303\ud835\udc4f=\ud835\udc5d\u0303\ud835\udc4e+\ud835\udc54\ud835\udc5a\u0303, (71)", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "14d9a88b20c2-18", "text": "An Ocean Example\uf0c1\nTo explore the oceanic implications of Eq. (68), assume bucket-1 initially has freshwater with density \ud835\udf0c1=\ud835\udf0cf, whereas bucket-2 initially has sea water with density \ud835\udf0c2=\ud835\udf0cs=\ud835\udf0cf+\ud835\udf0c\u2032. The salinity change for bucket-1 is \ud835\udeff\ud835\udc461=\ud835\udc46, since this bucket went from its original freshwater concentration to the homogenized sea water with salinity S. The halosteric-induced thickness change (Eq. 67) is thus given by\n\ud835\udeff\u210e=\u2212\u210e1\ud835\udefd\ud835\udc46(\ud835\udf0c\u2032/\ud835\udf0cs)<0. (69)\nHow large is this effect? For the case of an upper ocean with salt concentration \ud835\udc46=0.035, sea-water density \ud835\udf0cs=1028 kg  m \u22123\u21d2\ud835\udf0c\u2032=28 kg  m \u22123 and \ud835\udefd=0.8, we have\n\ud835\udeff\u210e=\u2212\u210e1\u00d70.8\u00d70.035\u00d7(28/1028)\u2248\u2212\u210e1\u00d77.6\u00d710\u22124. (70)\nTo within roughly 8 parts in 104, the change in thickness of the ocean column is nearly identical to the thickness of freshwater added to the ocean. For example, if we add one metre of freshwater into the upper ocean (\u210e1=1 m ), then the change in sea level is equal to one metre minus the tiny amount 0.76 mm . Hence, as emphasized by Lowe and Gregory (2006), we can generally ignore the contribution to global-mean sea level from global halosteric effects.\nAppendix 3: Bottom Pressure\uf0c1\nThe hydrostatic pressure at the ocean sea floor is commonly referred to as the ocean bottom pressure \ud835\udc5d\u0303\ud835\udc4f, usually calculated as\n\ud835\udc5d\u0303\ud835\udc4f=\ud835\udc5d\u0303\ud835\udc4e+\ud835\udc54\ud835\udc5a\u0303, (71)\nwhere the first term is the atmospheric pressure at the liquid-water equivalent sea surface and the second term is the weight of the mass per unit area \ud835\udc5a\u0303(\ud835\udc2b) of sea water, given by Eq. (26). This formula makes two approximations. First, hydrostatic pressure does not exactly equal the weight per unit area of the fluid above it because of the curvature of the Earth (Ambaum 2008). Second, g should appear within the vertical integral of density to obtain m (Eq. 26), because g depends on z. However, these approximations are entirely adequate for sea-level studies.\nThe difference in bottom pressure between two states\n\u0394\ud835\udc5d\ud835\udc4f=\u0394\ud835\udc5d\ud835\udc4e+\ud835\udc54\u0394\ud835\udc5a, (72)\nthat is, the sum of the change in local atmospheric pressure and the change in the weight of the local ocean. Using Eqs. (26) and (25) to replace \u0394\ud835\udc5a,\n\u0394\ud835\udc5d\ud835\udc4f=\u0394\ud835\udc5d\ud835\udc4e+\ud835\udc54\ud835\udf0c\u2217\u0394\ud835\udc3b+\ud835\udc54\u222b\ud835\udf02\ud835\udc39\u0394\ud835\udf0c(\ud835\udc67)d\ud835\udc67, (73)\nwhere \ud835\udc3b=\ud835\udf02\u2212\ud835\udc39 is the time-mean thickness of the ocean (Eq. 3). This form separates the change in pressure due to sea water into one term (the second) due to the change in the local thickness of the ocean, and another (the third) which is proportional to the local vertical-mean change in sea-water density.", "source": "https://sealeveldocs.readthedocs.io/en/latest/gregory19.html"}
{"id": "1a5e23fee427-0", "text": "Horton et al. (2018)\uf0c1\nTitle:\nMapping Sea-Level Change in Time, Space, and Probability\nKeywords:\nsea level, climate change, Holocene, Last Interglacial, Mid-Pliocene Warm Period, sea-level rise projections\nCorresponding author:\nHorton\nCitation:\nHorton, B. P., Kopp, R. E., Garner, A. J., Hay, C. C., Khan, N. S., Roy, K., & Shaw, T. A. (2018). Mapping Sea-Level Change in Time, Space, and Probability. Annual Review of Environment and Resources, 43(1), 481\u2013521. doi:10.1146/annurev-environ-102017-025826\nURL:\nhttps://www.annualreviews.org/doi/10.1146/annurev-environ-102017-025826\nAbstract\uf0c1\nFuture sea-level rise generates hazards for coastal populations, economies, infrastructure, and ecosystems around the world. The projection of future sea-level rise relies on an accurate understanding of the mechanisms driving its complex spatio-temporal evolution, which must be founded on an understanding of its history. We review the current methodologies and data sources used to reconstruct the history of sea-level change over geological (Pliocene, Last Interglacial, and Holocene) and instrumental (tide-gauge and satellite altimetry) eras, and the tools used to project the future spatial and temporal evolution of sea level. We summarize the understanding of the future evolution of sea level over the near (through 2050), medium (2100), and long (post-2100) terms. Using case studies from Singapore and New Jersey, we illustrate the ways in which current methodologies and data sources can constrain future projections, and how accurate projections can motivate the development of new sea-level research questions across relevant timescales.\nIntroduction\uf0c1\nAs recorded instrumentally and reconstructed from geological proxies, sea levels have risen and fallen throughout Earth\u2019s history, on timescales ranging from minutes to millions of years. Sea-level projections depend on establishing a robust relationship between sea level and climate forcing, but the vast majority of instrumental records contain less than 60 years of data, which are from the late twentieth and early twenty-first centuries (1-3). This brief instrumental period captures only a single climate mode of rising temperatures and sea level within a baseline state that is climatically mild by geological standards. Complementing the instrumental records, geological proxies provide valuable archives of the sea-level response to past climate variability, including periods of more extreme global mean surface temperature (e.g., 4-7). Ultimately, information from the geological record can help assess the relationship between sea level and climate change, providing a firmer basis for projecting the future (8), but current ties between past changes and future projections are often vague and heuristic. Greater interconnections between the two sub-disciplines are key to major progress.\nThe linked problems of characterizing past sea-level changes and projecting future sea-level rise face two fundamental challenges. First, regional and local sea-level changes vary substantially from the global mean (9). Understanding regional variability is critical to both interpreting records of past changes and generating local projections for effective coastal risk management (e.g., 9, 10). Second, uncertainty is pervasive in both records of past changes and in the physical and statistical modeling approaches used to project future changes (e.g., 11), and it requires careful quantification and statistical analysis (12). Quantification of uncertainty becomes particularly important for decision analysis related to future projections (e.g., 13).\nHere, we review the mechanisms that drive spatial variability, as well as their contributions to the uncertainty in mapping sea level on different timescales. We describe methodologies and data sources for piecing together lines of evidence related to past and future sea level to map changes in space, time, and probability. We review the sources and statistical methods applied to proxy [Pliocene, Last Interglacial (LIG) and Holocene] and instrumental (tide gauges and satellites) data, and the statistical and physical modeling approaches used to project future sea-level changes. Finally, we highlight two case study regions - Singapore and New Jersey - to illustrate the way in which proxy and instrumental data can improve future projections, and conversely how future projections can guide the development of new sea-level research questions to further constrain projections.\nMechanisms for global, regional, and local relative sea-level changes\uf0c1\nRelative sea level (RSL) is defined as the difference in elevation between the sea surface and the land. Global mean sea level (GMSL) is defined as the areal mean of either RSL or sea-surface height over the global ocean. It is often approximated by taking various forms of weighted means of individual RSL records, sometimes with corrections for specific local processes. Over the twentieth century, GMSL trends (14) were dominated by increases in ocean mass due to melting of land-based glaciers (e.g., 15) and ice sheets (e.g., 16), and by thermal expansion of warming ocean water. Changes in land water storage due to dam construction and groundwater withdrawal also made a small contribution (e.g., 17). Over a variety of timescales, RSL differs from GMSL, because of key driving processes such as atmosphere/ocean dynamics, the static-equilibrium effects of ocean/cryosphere/hydrosphere mass redistribution on the height of the geoid and the Earth\u00d5s surface, glacio-isostatic adjustment (GIA), sediment compaction, tectonics, and mantle dynamic topography (MDT). The driving processes are spatially variable and cause RSL change to vary in rate and magnitude among regions (Figure 1).\nFigure 1: Mapping uncertainty of sea-level drivers on different timescales based on available estimates. The length of colored bars along the x-axis represents the characteristic timescale over which a process may occur, rather than the total time duration over which the process has been active. The color scale represents the range in magnitude of relative sea-level change driven by a process over an event or observed/predicted timescale. It does not imply a specific relationship of the change in amplitude with timescale, given the nonlinear nature of many of these processes. The color scheme for glacial eustasy is also scaled to encompass predicted changes in global mean sea level of decimeters in the next several decades to meters over the next several centuries. (b) The uncertainty of instrumental and proxy recorders of sea level. The x (age) axis represents the time span over which the proxy may be used (given the temporal range of the dating method used to determine its age), rather than the proxy\u2019s temporal uncertainty. To estimate the contribution of a given process, the vertical and temporal resolution of a chosen instrument or proxy cannot exceed the magnitude and rate of sea-level change driven by that process.\uf0c1\nAtmosphere/ocean dynamics are the dominant driver of spatial heterogeneity in RSL on annual and multidecadal timescales (18-21), as well as a significant driver on longer timescales during periods with limited land-ice changes, such as the Common Era (22-25). The highest rates of RSL rise over the past two decades (greater than 15 mm/year) have occurred in the western tropical Paci\u00dec (18, 26), although the pattern appears to have reversed since 2011 (27). Observations and numerical model simulations (18, 28) con\u00derm that the intensification of trade winds, which occurs when the Paci\u00dec Decadal Oscillation (PDO) exhibits a negative trend, accounts for the amplitude and spatial pattern of RSL rise in the western tropical Paci\u00dec. In the western North Atlantic Ocean, changes in the strength and/or position of the Gulf Stream impact RSL trends differently north and south of North Carolina, where the Gulf Stream separates from the US Atlantic coast and turns toward northern Europe (19, 22, 23, 29). In fact, there is a .30-cm difference in sea-surface height between New Jersey and North Carolina (29). Climate models project that by the late twenty-\u00derst century, associated with a decline in the Atlantic Meridional Overturning Circulation (AMOC), ocean dynamic sea-level rise of up to 0.2 to 0.3 m could occur along the western boundary of the North Atlantic (30). However, coastal ocean dynamic variability in the western North Atlantic has been largely driven over the past few decades by local winds, with limited evidence for coupling to AMOC strength (21, 31).", "source": "https://sealeveldocs.readthedocs.io/en/latest/horton18.html"}
{"id": "1a5e23fee427-1", "text": "Atmosphere/ocean dynamics are the dominant driver of spatial heterogeneity in RSL on annual and multidecadal timescales (18-21), as well as a significant driver on longer timescales during periods with limited land-ice changes, such as the Common Era (22-25). The highest rates of RSL rise over the past two decades (greater than 15 mm/year) have occurred in the western tropical Paci\u00dec (18, 26), although the pattern appears to have reversed since 2011 (27). Observations and numerical model simulations (18, 28) con\u00derm that the intensification of trade winds, which occurs when the Paci\u00dec Decadal Oscillation (PDO) exhibits a negative trend, accounts for the amplitude and spatial pattern of RSL rise in the western tropical Paci\u00dec. In the western North Atlantic Ocean, changes in the strength and/or position of the Gulf Stream impact RSL trends differently north and south of North Carolina, where the Gulf Stream separates from the US Atlantic coast and turns toward northern Europe (19, 22, 23, 29). In fact, there is a .30-cm difference in sea-surface height between New Jersey and North Carolina (29). Climate models project that by the late twenty-\u00derst century, associated with a decline in the Atlantic Meridional Overturning Circulation (AMOC), ocean dynamic sea-level rise of up to 0.2 to 0.3 m could occur along the western boundary of the North Atlantic (30). However, coastal ocean dynamic variability in the western North Atlantic has been largely driven over the past few decades by local winds, with limited evidence for coupling to AMOC strength (21, 31).\nGravitational, rotational, and elastic deformational effects - also called static-equilibrium effects - reshape sea level nearly instantaneously in response to the redistribution of mass be.tween the cryosphere, the ocean, and the terrestrial hydrosphere (32-35). These effects are linked to the change in self-gravitation of the ice sheets and liquid water, the response of the Earth\u2019s rotational vector to the redistribution of mass at the Earth\u2019s surface, and the elastic response of the solid Earth surface to changing surface loads (Figure 2b,c). Unique RSL change geometries, sometimes called \u201cfingerprints,\u201d can be associated with the melting of different ice sheets and glaciers, and this response scales linearly with the magnitude of a marginal ice-mass change (32, 34). The dominant self-gravitation signal will result in a RSL fall near a shrinking land ice mass, which will be compensated by a RSL rise in the far \u00deeld that will be greater than the GMSL signal expected from the water mass in\u00dfux. The exact spatial pattern of RSL change depends on the geometry of the melting undergone by the ice reservoir. Recent studies (36, 37) have examined how mass loss centered in different portions of an ice sheet or glacial region will affect RSL differently. For example, New Jersey experiences a RSL fall in response to mass loss in southern.most Greenland, even though it experiences a modest (approximately 50% of the global mean) RSL rise in response to uniform melting across Greenland (Figure 2b).\nFigure 2: (a) Dynamic sea-level contribution to sea surface height (millimeter/year) from 2006-2100 under the RCP8.5 experiment of the Community Earth System Model, as archived by Coupled Model Intercomparison Project Phase 5 (30). Elastic fingerprints of projections of (b) Greenland ice-sheet mass loss and (c) West Antarctic ice-sheet mass loss, presented as ratios of RSL change to GMSL change (140). (d) Contribution of glacio-isostatic adjustment (GIA) to present-day relative sea level (RSL) change (millimeter/year), calculated using the ICE-5G ice loading history (52), combined with a maximum-likelihood solid-Earth model identified through a Kalman smoother tide-gauge analysis (119). Modi\u00deed from Kopp et al. (24).\uf0c1\nPliocene:\nepoch in the geologic timescale that extends from 5.3 million to 1.8 million years ago, during which the Earth experienced a transition from relatively warm climates to the prevailing cooler climates of the Pleistocene; includes the Mid-Pliocene Warm Period (.3.2 to 3.0 million years ago), which is the most recent period in geologic time with temperatures comparable to those projected for the twenty-first century.\nLast Interglacial:\nthe interglacial stage prior to the current Holocene interglacial (an interglacial is a geological interval of warmer global average temperature, characterized by the absence of large ice sheets in North America and Europe); the Last Interglacial extends from approximately 129,000 to 116,000 years ago, corresponds to Marine Isotope Stage5e and is also known as the Eemian.\nHolocene:\ncurrent geological epoch, beginning approximately 11,650 years ago, after the last glacial period; the start of the Holocene is formally defined by chemical (delta^{18}O) shifts in an ice core from northern Greenland that reflect climate warming.\nRelative sea level (RSL):\nheight of the sea surface at a specific location, measured with respect to the height of the surface of the solid Earth.\nDynamic sea level:\nsea-surface height variations produced by oceanic and atmospheric circulation and by temperature and salinity distributions.\nGlobal mean sea level (GMSL):\nareal average height of relative sea level (or, in some uses, sea-surface height) over the Earth\u2019s oceans combined; influenced primarily by the volume of seawater and the size and shape of the ocean basins; in the geological literature, GMSL is classically referred to as \u201ceustatic sea level\u201d.\nStatic-equilibrium effects:\ngravitational, elastic, and rotational effects of mass redistribution at the Earth surface, which lead to changes in both sea-surface height and the height of the solid Earth; these combined effects give rise to what are known as \u201csea-level fingerprints,\u201d or the geographic pattern of sea-level change following the rapid melting of ice sheets and glaciers.\nOver longer timescales, GIA arises as the viscoelastic mantle responds to the transfer of mass between land-based ice sheets and the global ocean during a glacial cycle. GIA induces deformation of the solid Earth, as well as changes in the Earth\u00d5s gravitational \u00deeld and its rotational state (38-43). After a change in surface load, the elastic component of the deformation is recovered nearly instantaneously, but the viscoelastic properties of the underlying mantle determine the characteristics of the recovery over longer timescales. In general, this recovery takes place over thousands of years, although in localized regions underlain by low-viscosity mantle, it can take place over decades to centuries (e.g., 44). On a global scale, at least in the Quaternary period, the system does not reach isostatic equilibrium, because it is interrupted by the initiation of another glacial cycle. The deformation that is observed today is the overprint of a series of glacial cycles that extend from the Pliocene through the Pleistocene glacial cycles and into the Holocene (7, 45, 46).\nGIA models simulate the evolution of the solid Earth as a function of the rheological structure and ice-sheet history (42, 47, 48). During the glacial phase of a glaciation-deglaciation cycle, the depression of land beneath ice sheets causes a migration of mantle material away from ice-load centers. This migration results in the formation of a forebulge in regions adjacent to ice sheets (e.g., the mid-Atlantic coast of the United States). Following the ice-sheet retreat, mantle material flows toward the former load centers. These centers experience postglacial rebound, while the forebulge retreats and collapses. In regions located beneath the centers of Last Glacial Maximum ice sheets (e.g., Northern Canada and Fennoscandia), postglacial uplift has resulted in RSL records characterized by a continuous fall; rates of present-day uplift greater than 10 mm/year occur in these near-\u00deeld locations (42). In the former forebulges, land is subsiding at a rate that varies with distance from the former ice centers. Along the US Atlantic coast, rates of present-day subsidence reach a maximum amplitude of close to 2 mm/year (49). In regions distal from the former ice sheet, the GIA signal is much smaller (50). These regions are characterized by present-day GIA-induced rates of RSL change that are near constant or show a slight fall (<0.3 mm/year), due to hydro-isostatic loading (continental levering) and to a global fall in the ocean surface linked to the hydro-and glacio-isostatic loading of the bottom of the Earth\u2019s ocean basins (equatorial ocean syphoning) (Figure 2d, 51).", "source": "https://sealeveldocs.readthedocs.io/en/latest/horton18.html"}
{"id": "1a5e23fee427-2", "text": "GIA models simulate the evolution of the solid Earth as a function of the rheological structure and ice-sheet history (42, 47, 48). During the glacial phase of a glaciation-deglaciation cycle, the depression of land beneath ice sheets causes a migration of mantle material away from ice-load centers. This migration results in the formation of a forebulge in regions adjacent to ice sheets (e.g., the mid-Atlantic coast of the United States). Following the ice-sheet retreat, mantle material flows toward the former load centers. These centers experience postglacial rebound, while the forebulge retreats and collapses. In regions located beneath the centers of Last Glacial Maximum ice sheets (e.g., Northern Canada and Fennoscandia), postglacial uplift has resulted in RSL records characterized by a continuous fall; rates of present-day uplift greater than 10 mm/year occur in these near-\u00deeld locations (42). In the former forebulges, land is subsiding at a rate that varies with distance from the former ice centers. Along the US Atlantic coast, rates of present-day subsidence reach a maximum amplitude of close to 2 mm/year (49). In regions distal from the former ice sheet, the GIA signal is much smaller (50). These regions are characterized by present-day GIA-induced rates of RSL change that are near constant or show a slight fall (<0.3 mm/year), due to hydro-isostatic loading (continental levering) and to a global fall in the ocean surface linked to the hydro-and glacio-isostatic loading of the bottom of the Earth\u2019s ocean basins (equatorial ocean syphoning) (Figure 2d, 51).\nGlobal models of the GIA process have contributed to our knowledge of solid Earth geodynamics through the constraints they provide on the effective viscosity of the mantle. They also provide a means to constrain the evolution of land-based ice sheets and ocean bathymetry over a glacial cycle (e.g., 42, 52), which can in turn be used to provide boundary conditions for tests of global climate models under paleoclimate conditions (e.g., 53). Global GIA models have traditionally relied on a simple Maxwell representation of the Earth\u00d5s rheology and on spherically symmetric models of the Earth\u00d5s mantle viscosity. Research is currently underway to include complex rheologies and lateral heterogeneity in mantle viscosity in GIA models, features that may be of substantial importance in regions with a complex geological structure, such as West Antarctica (e.g., 44).\nLocally, RSL can also change in response to sediment compaction driven by natural processes and by anthropogenic groundwater and hydrocarbon withdrawal (e.g., 54, 55). Many coastlines are located on plains composed of unconsolidated or loosely consolidated sediments, which com.pact under their own weight as the pressure of overlying sediments leads to a reduction in pore space (54, 56). Sediment compaction can occur over a range of depths and timescales. In the Mississippi Delta, Late Holocene subsidence due to shallow compaction has been estimated to be as high as 5 mm/year (57). Anthropogenic groundwater or hydrocarbon withdrawal can accelerate sediment compaction. For example, from 1958-2006 CE, subsidence in the Mississippi Delta was 7.6 \u00b1 0.2 mm/year, with a peak rate of 9.8 \u00b1 0.3 mm/year prior to 1991 that corresponded to the period of maximum oil extraction (58). Many other deltaic regions, including the Ganges, Chao Phraya, and Pasig Deltas, experience high rates of subsidence, linked to a combination of natural and anthropogenic sediment compaction, and they exhibit some of the highest rates of present-day RSL rise (59). Deeper, often poorly understood, processes also contribute to coastal subsidence, including thermal subsidence and fault motion (60).\nOn some coastlines, deformation caused by tectonics can be an important driver of RSL change. Indeed, reconstructions of RSL can be used to estimate the presence and rate of vertical land motion caused by coastal tectonics at regional spatial scales (e.g., 61). Coastlines may have near-instantaneous or gradual rates of uplift or subsidence due to coseismic movement associated with earthquakes or longer-term post-or interseismic deformation. Geodetic measurements of the 2011 Tohoku-oki and the 2004 Indian Ocean megathrust earthquakes revealed several meters of near-instantaneous coseismic vertical land motion (e.g., 62), which were followed by postseismic recovery that quickly exceeded the amount of coseismic change (63, 64). Based on a collection of bedrock thermochronometry measurements (65), gradual rates of vertical land motion from tectonics vary from <0.01 mm/year to 10 mm/year. Stable, cratonic regions (e.g., central and western Australia, central North America, and eastern Scandinavia) exhibit negligible vertical land motion rates of <0.01 mm/year. Rates are higher (0.01-0.1 mm/year) along passive margins (e.g., southeastern Australia, Brazil, and the US Atlantic coast) and the highest vertical land motion rates (1- 10 mm/year) are found in several tectonically active mountainous areas (e.g., the Coastal Mountains of British Columbia, Papua New Guinea, and the Himalayas). Most of these rate estimates are integrated over several millions to tens of millions of years [and may include influence from other low-frequency signals such as MDT or karstification (66)], and therefore have insufficient resolution to reveal temporal variations on shorter timescales (65).\nA common approach to calculate long-term tectonic vertical land motion uses LIG shore.lines, often inappropriately assuming that, once tectonically corrected, the elevation of GMSL at the LIG was .5 m above present. However, when calculating long-term tectonics from LIG shorelines, uncertainty in LIG GMSL and departures from GMSL due to GIA in response to glacial-interglacial cycles and excess polar ice-sheet melt relative to present-day values must be considered (67, 68). Instrumental observations (e.g., global positioning system, interferometric synthetic-aperture radar) of vertical land motion can provide the resolution to decipher temporal variations in rates, although the observation period is too short to capture the full period over which these processes operate.\nMDT refers to the surface undulations induced by mantle \u00dfow (69, 70). One of the most important consequences of MDT studies is their influence on estimates of long-term GMSL and RSL change (69). Several geophysical approaches have been developed to model global and regional MDT. Husson & Conrad (71) proposed that the dynamic effect of longer-term (~10^8 years) change in tectonic velocities on GMSL could be up to ~80 m from a model based on boundary layer theory. Conrad & Husson (72) used a forward model of mantle flow based on the present-day mantle structure and plate motions to estimate that the current rate of GMSL rise induced by MDT is <1 m/million years. An increasing body of evidence suggests that MDT can contribute to regional RSL change at rates of >1 m/100 kyr (e.g., 73, 74). The uncertainties due to MDT in RSL reconstructions become increasingly large further back in time (73, 75). Observationally, MDT is essentially indistinguishable from long-term tectonic change.\nGlacial isostatic adjustment (GIA):\nresponse of the solid Earth to mass redistribution during a glacial cycle; isostasy refers to a concept whereby deformation takes place in an attempt to return the Earth to a state of equilibrium; GIA refers to isostatic deformation related to ice and water loading during a glacial cycle\nSediment compaction:\nreduction in the volume of sediments caused by a decrease in pore space, which has the effect of lowering the height of the solid Earth surface; can occur naturally or due to the anthropogenic extraction of fluids (such as water and fossil fuels) from the pore space.\nMantle dynamic topography (MDT):\ndifferences in the height of the surface of the solid Earth caused by density-driven flow within the Earth\u2019s mantle.\nPast and current observations of sea-level change\uf0c1\nReconstructions of Relative Sea Levels from Proxy Data\uf0c1\nGeological reconstructions of RSL are derived from sea-level proxies, the formation of which was controlled by the past position of sea level (76). Sea-level proxies, which have a systematic and qunatifiable relationship with contemporary tides (77), include sedimentary, geomorphic, archeological, and fixed biological indicators, as well as coral reefs, coral microatolls, salt-marsh flora, and salt-marsh fauna (Figure 1b). The relationship of a proxy to sea level is de\u00dened by its \u201cindicative meaning,\u201d which describes the central tendency (reference water level) and vertical range (indicative range) of its relationship with tidal level(s).", "source": "https://sealeveldocs.readthedocs.io/en/latest/horton18.html"}
{"id": "1a5e23fee427-3", "text": "Glacial isostatic adjustment (GIA):\nresponse of the solid Earth to mass redistribution during a glacial cycle; isostasy refers to a concept whereby deformation takes place in an attempt to return the Earth to a state of equilibrium; GIA refers to isostatic deformation related to ice and water loading during a glacial cycle\nSediment compaction:\nreduction in the volume of sediments caused by a decrease in pore space, which has the effect of lowering the height of the solid Earth surface; can occur naturally or due to the anthropogenic extraction of fluids (such as water and fossil fuels) from the pore space.\nMantle dynamic topography (MDT):\ndifferences in the height of the surface of the solid Earth caused by density-driven flow within the Earth\u2019s mantle.\nPast and current observations of sea-level change\uf0c1\nReconstructions of Relative Sea Levels from Proxy Data\uf0c1\nGeological reconstructions of RSL are derived from sea-level proxies, the formation of which was controlled by the past position of sea level (76). Sea-level proxies, which have a systematic and qunatifiable relationship with contemporary tides (77), include sedimentary, geomorphic, archeological, and fixed biological indicators, as well as coral reefs, coral microatolls, salt-marsh flora, and salt-marsh fauna (Figure 1b). The relationship of a proxy to sea level is de\u00dened by its \u201cindicative meaning,\u201d which describes the central tendency (reference water level) and vertical range (indicative range) of its relationship with tidal level(s).\nUnder the uniformitarian assumption that the indicative meaning is constant in time, the indicative meaning can be determined empirically by direct measurement of modern analogs. The reconstruction begins with \u00deeld measurement of the elevation of a paleo sea-level proxy with respect to a common datum (e.g., mean tide level). The vertical uncertainty of a RSL reconstruction is primarily related to the indicative range of the sea-level proxy (Figure 1b). For proxies that form in intertidal settings, including most sedimentary, fixed biological, and geomorphic indicators, vertical uncertainties are proportional to the magnitude of local tidal range. In contrast, the vertical distribution of corals varies among species and is driven by light attenuation, along with a host of other factors (78). Although vertical RSL uncertainties are not systematically larger for older reconstructions, paleo-tidal range change (see, e.g., 79) or variations in the relationship of a proxy to sea level over time may introduce unquantifiable uncertainties.\nPaleo sea-level proxies are dated to provide a chronology for past RSL changes. The method used to date a proxy dictates the age range over which it may be used (Figure 1b). Sea-level proxies can be dated directly using radiometric methods. Radiocarbon dating is used to obtain chronologies over decades to the last .50,000 years, whereas methods such as U-series or luminescence dating can be used over hundreds of thousands of years (80). Sea-level proxies may also be dated by correlation with marine oxygen isotope stages, magnetic reversals, or other chronologies using bio-or chemostratigraphy. The age uncertainties of RSL reconstructions increase over time (e.g., 8, 68).\nThree geological intervals have been the particular focus of attention for sea-level reconstructions, because they provide analogues for future predicted changes: the Mid-Pliocene Warm Period (MPWP), the LIG stage, and the Holocene.\nSea-level proxy:\nany physical, biological, or chemical feature with a systematic and quantifiable relationship to sea level at its time of formation.\nMid-Pliocene Warm Period (~3.2 to 3.0 million years ago)\uf0c1\nThe MPWP is the most recent period in geologic time with temperatures comparable to those projected for the twenty-first century (e.g., 81). The period is characterized by a series of 41-kyr, orbitally paced climate cycles marked by three abrupt shifts in the stacked oxygen isotope record (82, 83). During this time, atmospheric CO2 ranged between approximately 350 and 450 ppm, and the configuration of oceans and continents was similar to today\u00d5s, which permits feasible comparison of oceanic and atmospheric conditions in models of Pliocene and modern climate (84, 85). Global climate model simulations estimate peak global mean surface temperatures between 1.9-3.6 C above preindustrial (86).\nBoth modeling and field evidence suggest that polar ice sheets were smaller during the MPWP, but constraints on the magnitude of GMSL maxima are highly uncertain. Early reconstructions of Pliocene sea levels have been derived from estimates of global ice volume from the temperature-corrected oxygen isotope composition of foraminifera and ostracods (e.g., 87), although the analytical uncertainties (~\u00b110 m) and the uncertainties associated with separating the ice volume, temperature, and diagenetic signals may be greater than the estimated magnitude of GMSL change from the present (8). Therefore, attention has focused on geomorphic proxy reconstructions from paleoshoreline deposits (e.g., 88, 89) or erosional features caused by sea-level fluctuations such as disconformities on atolls (e.g., 90). Estimating GMSL during the Pliocene is complicated by the amount of time elapsed since the formation of sea-level proxies, which allows processes operating over long timescales, such as tectonic uplift or MDT, to create differences between RSL and GMSL of up to tens of meters (e.g., 74). The uncertain contribution of RSL change from MDT makes reconstructions from this period highly challenging, although increasing the number and spatial distribution of RSL reconstructions from the Pliocene may help to derive a GMSL estimate consistent with model predictions of GIA and MDT that use a unique and internally consistent set of physical conditions (7).\nLast Interglacial (~129,000-116,000 years ago)\uf0c1\nDuring the LIG, global mean surface temperature was comparable to or slightly warmer than present, although the peak LIG CO2 concentration of .285 ppm (e.g., 91) was considerably less than that of the present (.400 ppm). Global mean sea-surface temperature was .0.5 \u00b1 0.3.C above its late nineteenth-century level (92). Model simulations indicate little global mean surface temperature change during the Last Inter.glacial stage, whereas combined land and ocean proxy data imply .1.C of warming, but with possible spatio-temporal sampling biases (93). Due to higher orbital eccentricity during the LIG, polar warming was more extreme (94). Greenland surface temperatures peaked .5-8.C above preindustrial levels (95), and Antarctic temperatures were .3-5.C warmer (96), both comparable to late twenty-first-century projections under Representative Concentration Pathway (RCP) 8.5 (97).\nLIG RSL reconstructions are much more abundant than those for the MPWP (e.g., 4, 6, 68, 78, 98; see also Figure 3c). Geomorphic (marine terraces, shore platforms, beachrock, beach deposits and ridges, abrasion and tidal notches, and cheniers), sedimentary (lagoonal deposits), coral reef, and geochemical sea-level proxies are used to reconstruct RSL changes during this period (e.g., 68). Compilations of RSL data combined with spatio-temporal statistical and GIA modeling indicate that peak GMSL was extremely likely >6 m but unlikely >9 m above present (6, 99). These estimates are in agreement with site-speci\u00dec, GIA-corrected coastal records in the Seychelles at 7.6 \u00b1 1.7 m (4) and in Western Australia at 9 m (100) above present (Figure 3c).\nGMSL during the LIG may have experienced multiple peaks, possibly associated with orbitally driven, asynchronous land-ice minima at the two poles (e.g., 8, 99). A significant fraction of the Greenland ice sheet remained intact throughout the LIG period, with recent alternative reconstructions limiting the peak Greenland GMSL contribution to .2 m (95) or 4-6 m (101) of the ice sheet\u00d5s total 7-m sea-level equivalent mass. Thermal expansion and the melting of mountain glaciers together likely contributed .1 m (102, 103). This implies a significant contribution to LIG GMSL from Antarctic ice melt. However, there is little direct observational evidence of mass loss from the Antarctic region. Additional constraints from RSL reconstructions in mid-to high-latitude regions may help to partition contributions from Greenland and Antarctica (104).\nEstimates of LIG GMSL have not yet incorporated the effects of MDT, which may contribute as much as 4 \u00b1 7m(1.) to RSL change in some regions (e.g., Southwestern Australia) (73). In contrast to MPWP, the magnitudes of RSL change due to GIA and MDT are roughly the same order, although the spatial pattern associated with the two processes should be distinct (e.g., 4, 73). Whether a formal accounting for MDT would significantly alter the estimated height of the LIG highstand is unknown.\nRepresentative Concentration Pathway (RCP):", "source": "https://sealeveldocs.readthedocs.io/en/latest/horton18.html"}
{"id": "1a5e23fee427-4", "text": "GMSL during the LIG may have experienced multiple peaks, possibly associated with orbitally driven, asynchronous land-ice minima at the two poles (e.g., 8, 99). A significant fraction of the Greenland ice sheet remained intact throughout the LIG period, with recent alternative reconstructions limiting the peak Greenland GMSL contribution to .2 m (95) or 4-6 m (101) of the ice sheet\u00d5s total 7-m sea-level equivalent mass. Thermal expansion and the melting of mountain glaciers together likely contributed .1 m (102, 103). This implies a significant contribution to LIG GMSL from Antarctic ice melt. However, there is little direct observational evidence of mass loss from the Antarctic region. Additional constraints from RSL reconstructions in mid-to high-latitude regions may help to partition contributions from Greenland and Antarctica (104).\nEstimates of LIG GMSL have not yet incorporated the effects of MDT, which may contribute as much as 4 \u00b1 7m(1.) to RSL change in some regions (e.g., Southwestern Australia) (73). In contrast to MPWP, the magnitudes of RSL change due to GIA and MDT are roughly the same order, although the spatial pattern associated with the two processes should be distinct (e.g., 4, 73). Whether a formal accounting for MDT would significantly alter the estimated height of the LIG highstand is unknown.\nRepresentative Concentration Pathway (RCP):\none of a set of four standardized pathways, developed by the global climate modeling and integrated assessment modeling communities, describing possible future pathways of climate forcing over the twenty-first century; Extended Concentration Pathways extended the RCPs to the end of the twenty-third century\nFigure 3: Reconstructions of global mean sea level (GMSL) and relative sea level (RSL) (6, 25, 119) from (a) the instrumental period, (b)the Holocene, and (c) the Last Interglacial. (a) GMSL estimates during the Instrumental Period from Dangendorf et al. (2017) (118) (green), Hay et al. (2015; Gaussian process regression (GPR)) (119) (dark blue), Hay et al. (2015; Kalman smoothing (KS)) (119) (light blue), Jevrejeva et al. (2014) (117) (orange), and Church & White (2011) (116) (purple), as well as individual RSL records from tide gauges obtained from the Permanent Service for Mean Sea Level (PSMSL). (b) GMSL (and sea-level equivalent signal) derived from far-field data (purple: Lambeck et al. (2014) (46), with 2-sigma uncertainty range) and from GIA models [ICE-5G (Peltier 2004) (52) (red); ICE-6G (Peltier et al. 2015) (42) (blue); Bradley et al. 2016 (111) (black)]. RSL data from Southern Disko Bugt (175, 176); Arisaig, Scotland (177); West Guangdong, southern China (178); Northeastern Brazil (179); South Shetland Island, Antarctica (180); and Langebaan Lagoon, South Africa (181). (c) GMSL estimate from Kopp et al. (6) and RSL reconstructions from Barbados (182-192) interpreted using coral depth distributions presented in Hibbert et al. (78), the Netherlands (193) as interpreted by Kopp et al. (6), the Red Sea continuous delta-18O record (green crosses) with probabilistic model and 95% confidence interval shown (green shading) (194), the Seychelles (195), and Western Australia (100, 196-206) where coral data are interpreted as a lower limit on RSL. Unless otherwise indicated, model uncertainties are 1-sigma, whereas data uncertainties are 2-sigma. Error bars cross at the median of the vertical probability distribution and midpoint of the age distribution of each data point. U-series data are screened following guidelines presented in Hibbert et al. (2016) (78) or Dutton et al. (2015) (195). With the exception of the Red Sea dataset, RSL reconstructions have not been corrected for tectonic motion. To demonstrate the potential in\u00dfuence of tectonics on RSL reconstructions, we plot data from Barbados (C1) using uncorrected elevations (solid lines) and elevations corrected for tectonic uplift (dashed lines).\uf0c1\nThe Holocene (11,700 years ago to present)\uf0c1\nA global temperature reconstruction for the early to middle Holocene (from ~9.5-5.5 ka), derived from both marine and terrestrial proxies, suggests a global mean surface temperature ~0.8C higher than preindustrial temperatures (105). This estimate, however, conflicts with climate models that simulate a warming trend through the Holocene. The discrepancy may be due to uncertainties in both the seasonality of proxy reconstructions and the sensitivity of climate models to orbital forcing (106). Recent evidence suggests that estimates of global temperatures may be biased by sub-seasonal sensitivity of marine and coastal temperature estimates from the North Atlantic, with pollen records from North America and Europe instead suggesting a later period of peak warmth from .5.5-3.5 ka and temperatures .0.6.C warmer than the late nineteenth century (107).\nThe Holocene has more abundant and highly resolved RSL reconstructions than previous interglacial periods (Figure 3b, 45). These reconstructions are sourced from sedimentary (wet.land, deltaic, estuarine, lagoonal facies), geomorphic (beachrock, tidal and abrasional notches), archaeological, coral reef, coral microatoll, and other biological sea-level proxies. The abundance of RSL data from this period, combined with the preservation of near-\u00deeld glacial deposits, has contributed to the development of a relatively well-constrained history of ice-sheet retreat, particularly in the Northern Hemisphere (108). However, questions remain about Antarctic and Greenland contributions to GMSL (e.g., 109, 110), the timing of when (prior to the twentieth century rise) land-ice contributions to GMSL ceased (e.g., 46, 111, 112), and the magnitude and timescale of internal variability in glaciers, ice sheets, and the ocean.\nGiven the resolution of Holocene data, detailed sea-level reconstructions from this period are important for constraining local to regional processes and providing estimates of rates of change. GIA is the dominant process driving spatial variability during the Holocene (45). Records from locations formerly covered by ice sheets (near-field regions such as Antarctica, Greenland, Canada, Sweden, and Scotland) reveal a complex pattern of RSL fall from a maximum marine limit due to the net effect of inputs from melting of land-based ice sheets and glacio-isostatic uplift. Rates of RSL fall in near-field regions during the early Holocene were up to -69 \u00b1 9 m/ka (45). Regions near the periphery of ice sheets (intermediate-field locations such as the mid-Atlantic and Pacific coasts of the United States, and northwestern Europe and the Caribbean) display fast rates of RSL rise (up to 10 \u00b1 1 m/ka) in the early Holocene in regions near the center of forebulge collapse. Regions far from ice sheets exhibit a mid-Holocene highstand, the timing (between 8 and 4 ka) and magnitude (between <1 and 6 m) of which vary among South American, African, Asian, and Oceania regions. With diminishing contributions from GIA and melting of land-based ice sheets during the past several millennia, lower amplitude local-to regional-scale processes, such as steric effects or ocean dynamics, are manifested in RSL records (22).\nAlthough the past two millennia (the Common Era) may not be a direct analog for future changes, semi-empirical relationships between high-resolution RSL reconstruction can be paired with temperature reconstructions (e.g., 113) that show periods of both warming (e.g., Medieval Climate Anomaly) and cooling (e.g., Little Ice Age) to show climate forcing on timescales (multi.decadal to multicentennial) and magnitudes relevant to future climate and sea-level scenarios (e.g., 25). The more complete geologic record in the Common Era permits the reconstruction of continuous time series of decimeter-scale RSL change over this period using salt-marsh sequences and coral microatolls (5). The resolution of reconstructions is comparable to future sea-level changes over the next decades to centuries, which enables an examination of regional dynamic variability in sea level that is not possible for earlier periods (24). In addition, the GIA signal is approximately linear over the Common Era and, therefore, it is easier to quantify its contribution to RSL.\nTide gauge:\ndevice for measuring the height of the sea surface with respect to a reference height fixed to the solid Earth.\nReconstructions of Relative Sea Level from Instrumental Data\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/horton18.html"}
{"id": "1a5e23fee427-5", "text": "Although the past two millennia (the Common Era) may not be a direct analog for future changes, semi-empirical relationships between high-resolution RSL reconstruction can be paired with temperature reconstructions (e.g., 113) that show periods of both warming (e.g., Medieval Climate Anomaly) and cooling (e.g., Little Ice Age) to show climate forcing on timescales (multi.decadal to multicentennial) and magnitudes relevant to future climate and sea-level scenarios (e.g., 25). The more complete geologic record in the Common Era permits the reconstruction of continuous time series of decimeter-scale RSL change over this period using salt-marsh sequences and coral microatolls (5). The resolution of reconstructions is comparable to future sea-level changes over the next decades to centuries, which enables an examination of regional dynamic variability in sea level that is not possible for earlier periods (24). In addition, the GIA signal is approximately linear over the Common Era and, therefore, it is easier to quantify its contribution to RSL.\nTide gauge:\ndevice for measuring the height of the sea surface with respect to a reference height fixed to the solid Earth.\nReconstructions of Relative Sea Level from Instrumental Data\uf0c1\nTide-gauge measurements of RSL date back to at least the eighteenth century, with archived records available for Amsterdam beginning in 1700, Liverpool beginning in 1768, and Stockholm beginning in 1774 (114). Originally put in place to monitor tides for shipping purposes, most of the earliest records are located in northern Europe and along the coasts of North America, and many contain persistent data gaps through time. It was not until the mid-twentieth century that most of the current tide-gauge network, which includes tide gauges in the Southern Hemisphere and the Arctic Ocean, became operational (115). Contained in each tide-gauge record is the combined effect of local, regional, and global sea-level processes that take place over timescales ranging from minutes to centuries. The Permanent Service for Mean Sea Level compiles the world\u00d5s tide-gauge records into two databases: raw unprocessed time series are contained in the metric database; and the revised local reference database contains the time series referenced to a common datum (1).\nToday, sea levels are on a long-term rising trend along a large majority of coastlines (Figure 3a; see also 26, 115, 116). Rates of RSL change derived from tide-gauge data varied both spatially and temporally during the twentieth century, and decadal rates of GMSL rise show large variations throughout this period (116). Dense tide-gauge records along the US Atlantic coast have resulted in numerous studies that show rates of RSL rise exceeding GMSL rise. This sea-level rise has been attributed to the combination of GIA, ocean dynamics, and land-based ice melt (20, 49). Tide-gauge records from Alaska, northern Canada, and Fennoscandia illustrate the impact of GIA on local and regional sea level (Figure 3b). These regions, which were covered by ice during the Last Glacial Maximum, are experiencing RSL changes that are dominated by ongoing postglacial rebound of the solid Earth. As the land uplifts at rates >10 mm/year, the result is a RSL fall (48).\nGiven the regional variability in sea level, and the spatio-temporal sparsity of the tide-gauge network, inferring GMSL over the nineteenth and twentieth centuries is a difficult task. The first attempts to compute GMSL involved regional averaging of small subsets of tide gauges (2). The tide gauges included in these subsets had to satisfy multiple criteria, including being located far from regions experiencing significant sea-level changes due to GIA and having at least 60 years of observations with minimal data gaps. Resulting subsets ranged from 9 to 22 sites and estimates of GMSL fall in the range of 1.7-1.8 mm/year. Extending the simple regional averaging technique, Jevrejeva et al. (115, 117) used a \u201cvirtual station\u201d approach that sequentially averages pairs of tide gauges to produce a single virtual tide gauge in each region. This approach, with a GMSL estimate over the twentieth century of 1.9 \u00b1 0.3 mm/year and 3.1 \u00b1 0.6 mm/year over 1993-2009 (Figure 4), produces a more robust estimate of the uncertainty than the simple averaging technique by better addressing the spatial sparsity in the tide-gauge network. More recently, Dangendorf et al. (118) extended the virtual station approach. They simulated local geoid changes and observations of vertical land motion to correct the tide gauges for local sea level effects, resulting in a 1901-1990 GMSL estimate of 1.1 \u00b1 0.3 mm/year and a 1993-2012 estimate of 3.1 \u00b1 1.4 mm/year.\nFigure 4: Rates of sea-level rise, and the 1-sigma uncertainty range, over the twentieth century (green dots) and over the satellite altimetry era (blue dots) derived from tide-gauge and satellite altimetry observations. The time windows for reach reconstruction are as follows: (a) 1993-2014 (VM2; 127); (b) 1993-2014 (VM1; 127);(c) 1993-2010 (125); (d) 1993-2009 (117); (e) 1901-1990, 1993-2012 (118); ( f ) 1901-1990 (GPR; 119); (g) 1901-1990, 1993-2010 (KS; 119); (h) 1900-1999, 1993-2009 (117); (i) 1900-2009 (121); ( j) 1901-1990, 1993-2009 (116); (k) 1992-2010 (120); (l) 1993-2010 (26); (m) 1904-2003 (3); (n) 1880-1990 (207).\uf0c1\nTackling the problem of spatio-temporal sparsity differently, Hay et al. (119) combined the tide-gauge records with process-based models of the underlying physics driving global and regional sea-level change using two techniques: a multi-model Kalman smoother and Gaussian process regression. These two methodologies estimate GMSL by first estimating, from the tide-gauge record, the magnitudes of the individual processes contributing to local and global sea level, then summing the individual contributors to produce GMSL estimates. During 1901-1990, the Kalman smoother and Gaussian process regression techniques produced GMSL rise estimates of 1.2 \u00b1 0.2 mm/year and 1.1 \u00b1 0.4 mm/year, respectively. During the altimetry era, from 1993-2010, the Kalman smoother technique estimates that GMSL rose at 3.0 \u00b1 0.7 mm/year (Figure 4).\nSatellite altimetry:\nmeasurement of the height of the sea surface through satellite-based techniques such as radar altimetry.\nSince 1993, the long but incomplete tide-gauge record has been supplemented with near-global satellite altimetry observations. Satellite altimeter missions have provided maps of absolute sea level every 10 days within approximately \u00b1 66o, permitting changes in the sea surface to be determined for the majority of the world ocean (120). Unlike tide gauges, which are inherently only located along the world\u00d5s coastlines, satellite altimetry observations have provided new insight into previously unobserved ocean basins. The combination of tide gauge and altimetry observations has the potential to shed new insights on both GMSL and RSL; however, combining these two data sources is also not a simple task. For example, coastal processes and vertical land motion, which are not observed by satellite altimeters, can be the dominant processes captured in tide-gauge records.\nAccurately characterizing and separating sea-level noise from sea-level signal is an ongoing challenge (116, 121). In empirical orthogonal function approaches, satellite altimetry observations are used to determine the dominant global patterns of sea surface height change over the past .25 years. The magnitudes of these patterns are then constrained over the twentieth century with the tide-gauge observations. GMSL estimates using this technique for 1901-1990 are approximately 1.5 \u00b1 0.2 mm/year (116), whereas over the longer time period of 1900-2009, GMSL estimates increase to 1.7 \u00b1 0.2 mm/year (Figure 4, 116, 121). It is a matter for debate as to whether the observed dominant short-term patterns of variability over the satellite era are the most appropriate ones to characterize patterns of long-term variability over the tide-gauge era (122).", "source": "https://sealeveldocs.readthedocs.io/en/latest/horton18.html"}
{"id": "1a5e23fee427-6", "text": "Satellite altimetry:\nmeasurement of the height of the sea surface through satellite-based techniques such as radar altimetry.\nSince 1993, the long but incomplete tide-gauge record has been supplemented with near-global satellite altimetry observations. Satellite altimeter missions have provided maps of absolute sea level every 10 days within approximately \u00b1 66o, permitting changes in the sea surface to be determined for the majority of the world ocean (120). Unlike tide gauges, which are inherently only located along the world\u00d5s coastlines, satellite altimetry observations have provided new insight into previously unobserved ocean basins. The combination of tide gauge and altimetry observations has the potential to shed new insights on both GMSL and RSL; however, combining these two data sources is also not a simple task. For example, coastal processes and vertical land motion, which are not observed by satellite altimeters, can be the dominant processes captured in tide-gauge records.\nAccurately characterizing and separating sea-level noise from sea-level signal is an ongoing challenge (116, 121). In empirical orthogonal function approaches, satellite altimetry observations are used to determine the dominant global patterns of sea surface height change over the past .25 years. The magnitudes of these patterns are then constrained over the twentieth century with the tide-gauge observations. GMSL estimates using this technique for 1901-1990 are approximately 1.5 \u00b1 0.2 mm/year (116), whereas over the longer time period of 1900-2009, GMSL estimates increase to 1.7 \u00b1 0.2 mm/year (Figure 4, 116, 121). It is a matter for debate as to whether the observed dominant short-term patterns of variability over the satellite era are the most appropriate ones to characterize patterns of long-term variability over the tide-gauge era (122).\nAs the satellite altimetry record length grows, so does the satellite-derived time series of (near) global mean sea surface height (123, 124). These estimates of 2.6-3.2 mm/year (125-127) are obtained by computing area weighted averages of the near global sea surface height fields. It is now possible to use the 25-year altimetry record to estimate the acceleration in GMSL since 1993. This acceleration of 0.084 \u00b1 0.025 mm/year^2 (128) represents a starting point for putting recent GMSL estimates into historical context. Developing new statistically robust methodologies to combine the satellite altimetry data with the tide gauge observations is an important and daunting task, and it is necessary in order to quantify local and regional accelerations over the twentieth century.\nAttribution of Twentieth-Century Global Mean Sea-Level Change\uf0c1\nAttribution studies focus on the extent to which twentieth (and early twenty-first) century GMSL can be affirmatively tied to the effects of human-caused warming (129). These studies\u00d1relying on a variety of both physical modeling and statistical techniques\u00d1generally agree that a large portion of the twentieth-century rise, including most GMSL rise over the past quarter of the twentieth century, is tied to anthropogenic warming (25, 130-132).\nFor example, Slangen et al. (132) used a suite of physical models of global climate and land-ice surface mass balance, together with correction terms for omitted factors, to compare GMSL with and without natural forcing. They found that natural forcing could account for approximately 50% of the modeled historical GMSL change from 1900-2005, and only approximately 10% of modeled historical GMSL change from 1970-2005. Kopp et al. (25) calibrated a statistical model to the relationship between temperature and rate of sea-level change over the past two millennia, and found that\u00d1had the twentieth-century global mean surface temperature been the same as the average over 500-1800 CE\u00d1twentieth-century GMSL rise would have been approximately 35% (90% probable range: .13 to +59%) of its instrumental value.\nProjections of future sea-level rise\uf0c1\nOur knowledge of past and present changes in sea level can help us understand and predict its future evolution. Methods used to project sea-level changes in the future can be categorized along two basic axes: (1) the degree to which they disaggregate the different drivers of sea-level change, and (2) the extent to which they attempt to characterize probabilities of future outcomes (Figure 5). The former axis separates projections that tabulate individual processes - including projections focused on central ranges, scenarios attempting to assess upper bounds of plausible sea-level rise, and probabilistic bottom-up projections - from semi-empirical approaches based on global climate and sea-level statistics, as well as some expert judgement-based approaches. The latter axis separates approaches focused on assessing either central or extreme outcomes from fully probabilistic approaches.\nFigure 5: Taxonomy of sea-level rise projections methods. The horizontal axis separates methods based on the degree to which they disaggregate the different drivers of sea-level change. The vertical axis separates methods based on the extent to which they attempt to characterize probabilities of future outcomes.\uf0c1\nSea-level rise projections published in the past several years have largely been conditional on different RCPs (133). The RCPs represent a range of possible future climate forcing path.ways, including a high-emission pathway with continued growth of CO2 emissions (RCP8.5), a moderate-emission pathway with stabilized emissions (RCP4.5), and a low-emission pathway consistent with the Paris Agreement\u00d5s goal (134) of net-zero CO2 emissions in the second half of this century (RCP2.6). The use of the RCPs enables comparisons among projections from different studies and different methods (135-142).\nBottom-Up Approaches\uf0c1\nMost projections are based on a bottom-up accounting of contributions from different driving factors of global and regional sea-level change. Estimates of different contributing factors may be based on a quantitative or semi-quantitative literature meta-analysis. For example, climate models such as those included in the Coupled Model Intercomparison Projection Phase 5 are often used to inform projections of thermal expansion and dynamic sea-level change as well as to drive models of glacier surface mass balance. Alternatively, estimates of factors that contribute to sea-level rise may also be based on the output of a single model study of complex processes such as marine-ice sheet dynamics [e.g., the use of DeConto & Pollard (143) in Kopp et al. (144)] or on simpli\u00deed models that capture the core dynamics of a process such as ocean heat uptake in response to climate forcing (135, 142). Estimates of sea-level contributions may also be based on heuristic judgements, for example, of the plausible acceleration of ice \u00dfow through outlet glaciers (145).\nCentral-range estimates\uf0c1\nIn the literature, many bottom-up estimates focus on characterizing central ranges for key contributing factors, de\u00dened by a median, a single low quantile, and a single high quantile (e.g., 146, 147), typically the 17th and 83rd or 5th and 95th percentile values.\nHigh-end estimates\uf0c1\nHigh-end (sometimes referred to as \u201cworst-case\u201d) bottom-up estimates complement central-range estimates. Pfeffer et al. (145) constructed a high-end (2.0 m GMSL rise by 2100) sea-level rise scenario based on plausible accelerations of Greenland ice discharge, determined partially by the fastest local, annual rates of ice-sheet discharge currently observed. This estimate has subsequently been debated, and additional contributions from thermal expansion [based on an Earth system model (148)], groundwater discharge, and Antarctica (e.g., 55) have been suggested, raising the high-end projection to .2.6 m. Furthermore, the highest among DeConto & Pollard\u00d5s (143) ensemble of Antarctic simulations exceeded 1.7 m of sea-level rise from Antarctica alone in 2100 under RCP8.5, suggesting that high-end outcomes well in excess of 3 m of GMSL rise by 2100 cannot be excluded under RCP8.5.\nProbabilistic approaches\uf0c1\nProbabilistic approaches build on both the central range and high-end approaches, aiming to estimate a single, comprehensive probability distribution of sea-level rise from a bottom-up accounting of different components. The relationship between central range projections and probabilistic projections can be relatively straightforward. The central range projections are often presented with 1 or 2. putative standard errors (e.g., 147), which have a natural probabilistic interpretation if a particular distributional form is assumed. The relationship between high-end estimates and probabilistic projections is interpreted in a broader variety of ways. For example, Kopp et al. (140) highlighted the agreement between the 99.9th percentile of their RCP8.5 GMSL projection (2.5 m) and other high-end estimates, whereas Jevrejeva et al. (126) used the 95th percentile of an RCP8.5 projection (1.8 m) as an upper limit.", "source": "https://sealeveldocs.readthedocs.io/en/latest/horton18.html"}
{"id": "1a5e23fee427-7", "text": "Central-range estimates\uf0c1\nIn the literature, many bottom-up estimates focus on characterizing central ranges for key contributing factors, de\u00dened by a median, a single low quantile, and a single high quantile (e.g., 146, 147), typically the 17th and 83rd or 5th and 95th percentile values.\nHigh-end estimates\uf0c1\nHigh-end (sometimes referred to as \u201cworst-case\u201d) bottom-up estimates complement central-range estimates. Pfeffer et al. (145) constructed a high-end (2.0 m GMSL rise by 2100) sea-level rise scenario based on plausible accelerations of Greenland ice discharge, determined partially by the fastest local, annual rates of ice-sheet discharge currently observed. This estimate has subsequently been debated, and additional contributions from thermal expansion [based on an Earth system model (148)], groundwater discharge, and Antarctica (e.g., 55) have been suggested, raising the high-end projection to .2.6 m. Furthermore, the highest among DeConto & Pollard\u00d5s (143) ensemble of Antarctic simulations exceeded 1.7 m of sea-level rise from Antarctica alone in 2100 under RCP8.5, suggesting that high-end outcomes well in excess of 3 m of GMSL rise by 2100 cannot be excluded under RCP8.5.\nProbabilistic approaches\uf0c1\nProbabilistic approaches build on both the central range and high-end approaches, aiming to estimate a single, comprehensive probability distribution of sea-level rise from a bottom-up accounting of different components. The relationship between central range projections and probabilistic projections can be relatively straightforward. The central range projections are often presented with 1 or 2. putative standard errors (e.g., 147), which have a natural probabilistic interpretation if a particular distributional form is assumed. The relationship between high-end estimates and probabilistic projections is interpreted in a broader variety of ways. For example, Kopp et al. (140) highlighted the agreement between the 99.9th percentile of their RCP8.5 GMSL projection (2.5 m) and other high-end estimates, whereas Jevrejeva et al. (126) used the 95th percentile of an RCP8.5 projection (1.8 m) as an upper limit.\nThe first published probabilistic GMSL projections were developed by Titus & Narayanan (149) for the US Environmental Protection Agency, based on a suite of coupled simple physical models with parameters informed by structured expert elicitation. Probabilistic approaches experienced a resurgence in the past half-decade, in part because of concerns regarding the adequacy of communication about high-end uncertainty in IPCC AR5 sea-level projections (126, 137, 138, 140). Probabilistic studies have been largely constrained to use the climate scenarios run by large model intercomparison projects. However, some more recent probabilistic studies rely on simple coupled models of different components, allowing for more flexible simulations (135, 136, 141, 142, 150).\nTop-Down Approaches\uf0c1\nTop-down approaches for estimating GMSL focus on comprehensive metrics of change, rather than a bottom-up accounting of individual driving factors. Most top-down studies are semi-empirical in nature.\nSemi-empirical approaches\uf0c1\nSemi-empirical approaches rely on historical statistical relationships between GMSL change and driving factors such as temperature. One of the earliest GMSL projections (151) used such a relationship, fitting approximated GMSL as a lagged linear function of global mean surface temperature; their relationship (roughly 16 cm/\u00fbC) would yield a likely twenty-first century GMSL rise of approximately 0.2-0.3 m under RCP2.6, and 0.4-0.8 m under RCP8.5. They noted, however, the potential for rapid loss of marine-based ice in Antarctica to raise their projections significantly. This particular study did not formally account for uncertainty in the relationship between temperature and sea level, and thus would fall at the lower end of our probabilistic axis. However, uncertainty analysis is straightforward with simple parametric approaches, and subsequent semi-empirical studies have generally been highly probabilistic.\nThe current generation of semi-empirical approaches began with Rahmstorf (152), who fitted the historical rate of GMSL change as a function of temperature disequilibrium. Combining a semi-empirical approach that includes uncertainty estimates on key parameters with probabilistic projections of the global mean surface temperature response to different forcing scenarios can yield formally complete probability distributions of future GMSL rise. Such projections are, however, sensitive to the choice of calibration data set\u00d1an additional level of uncertainty not typically formally quantified within a single study\u00d1preventing a formal probabilistic evaluation. These choices can have a significant impact. For example, Kopp et al. (144), using a calibration based on reconstructions of temperature and GMSL over the past two millennia, project a rise of 0.3-0.9 m (at the 90% confidence level) over the twenty-first century under RCP4.5, whereas Schaeffer et al. (153), using a calibration based on a single geological reconstruction from North Carolina (5), project 0.6-1.2 m.\nExpert judgement\uf0c1\nIn the course of scientific practice, experts integrate many streams of information to revise their assessments of the world and the way it behaves; Bayes\u2019 theorem, as used in formal statistical analyses, is a formalization of this process. On some level, all projections of future change are based on expert judgement, frequently expressed within the deliberative context of a scientific publication or assessment panel.\nA variety of approaches - some relatively informal, others based on more rigorous social scientific practices - use this integration process executed by individuals as an object of study in its own right, and extract from it estimates of the likelihood of different future outcomes. In the sea-level realm, structured expert elicitation\u00d1a formal method in which experts are guided in the interpretation of probabilities in a workshop setting before having their responses weighted based on their performance on calibration questions\u00d1has been used to assess the probability distribution of future ice-sheet changes (154). Less structured, more informal expert surveys have also been used to assess the response of GMSL as a whole to different forcing scenarios (155).\nMethods of Using Sea-Level Rise Projections\uf0c1\nThe approaches described above are \u201cscience-first\u201d approaches \u00d1 focused on integrating a variety of lines of information to produce a scientific judgement about future global and/or regional sea-level changes. These approaches are not generally designed to produce projections that can be directly used in a decision process. Yet, in the absence of ongoing dialogue between scientists and decision makers, this distinction can give rise to confusion. For example, approaches focused exclusively on central ranges omit information about high-end outcomes that can be crucial for risk management, whereas approaches focused exclusively on high-end estimates could lead to excessively costly and overly cautious decisions. Bottom-up probabilistic approaches and semi-empirical approaches can provide self-consistent information about both central tendencies and high-end outcomes, but relying on results from a single estimated probability distribution can mask ambiguity and potentially provide a false sense of security about the (un)likelihood of extreme outcomes (156). Caveats expressed in primary scientific literature are frequently lost in the translation to assessment reports.\nScenario approaches\uf0c1\nOne approach to dealing with these challenges is to use the underlying scientific literature - drawing on multiple methodologies - to develop scenarios against which decisions can be tested. For example, the National Research Council defined a range of heuristically motivated \u201cplausible variations in GMSL rise,\u201d spanning 50-150 cm between the 1980s and 2100, which they recommended be used for engineering sensitivity analyses (157). In some contexts, such scenario-based projections are categorized together with scientific projections. We argue that this is a categorization error: Discrete scenarios for decision analysis can be scientifically justified only when based on projections developed using the suite of scientific approaches discussed above.\nProbabilistic approaches and deep uncertainty\uf0c1\nOne motivation for developing complete probability distributions for future sea-level rise is their direct utility in specific decision frameworks. For example, bene\u00det-cost analyses employ probability distributions of future change as an input; probabilistic projections are thus crucial for assessing metrics such as the social cost of greenhouse gas emissions (e.g., 158). Similarly, probability distributions of future sea-level rise can be combined with probability distributions of future storm tides to estimate future flood prob.abilities (e.g., 159, 160). However, some decision makers have expressed confusion regarding the distinction between Bayesian probabilities of future changes and historical, frequentist probability distributions for variables such as storm tides in a stationary climate. Although the reality of climate change means that no probability distribution can be truly based on the assumption of stationarity, the familiarity of such assumptions can mask deep uncertainty and lead to overconfidence (156).", "source": "https://sealeveldocs.readthedocs.io/en/latest/horton18.html"}
{"id": "1a5e23fee427-8", "text": "Scenario approaches\uf0c1\nOne approach to dealing with these challenges is to use the underlying scientific literature - drawing on multiple methodologies - to develop scenarios against which decisions can be tested. For example, the National Research Council defined a range of heuristically motivated \u201cplausible variations in GMSL rise,\u201d spanning 50-150 cm between the 1980s and 2100, which they recommended be used for engineering sensitivity analyses (157). In some contexts, such scenario-based projections are categorized together with scientific projections. We argue that this is a categorization error: Discrete scenarios for decision analysis can be scientifically justified only when based on projections developed using the suite of scientific approaches discussed above.\nProbabilistic approaches and deep uncertainty\uf0c1\nOne motivation for developing complete probability distributions for future sea-level rise is their direct utility in specific decision frameworks. For example, bene\u00det-cost analyses employ probability distributions of future change as an input; probabilistic projections are thus crucial for assessing metrics such as the social cost of greenhouse gas emissions (e.g., 158). Similarly, probability distributions of future sea-level rise can be combined with probability distributions of future storm tides to estimate future flood prob.abilities (e.g., 159, 160). However, some decision makers have expressed confusion regarding the distinction between Bayesian probabilities of future changes and historical, frequentist probability distributions for variables such as storm tides in a stationary climate. Although the reality of climate change means that no probability distribution can be truly based on the assumption of stationarity, the familiarity of such assumptions can mask deep uncertainty and lead to overconfidence (156).\nSea-level rise projections, particularly for the second half of this century and beyond, exhibit ambiguity. Projections have no uniquely specifiable probability distribution, and different approaches yield distributions that differ considerably. The \u00deeld of decision making under un.certainty has developed several approaches to cope with ambiguity (e.g., 161). Some approaches rely on employing multiple probability distributions, which can reveal the robustness (or lack thereof ) of a probability-based judgement to the underlying uncertainty in scientific knowledge that may not be captured within a single probability distribution. Possibility theory (162) provides one approach for combining multiple lines of evidence to produce a \u201cprobability box\u201d that bounds the upper and lower limits of different quantiles of a probability distribution, revealing areas of relatively low and relatively high ambiguity. We apply a simpler but related approach below, summarizing literature projections for different scenarios in \u201cvery likely\u201d ranges that are constructed from the minima of 5th-percentile projections and maxima of 95th-percentile projections.\nDeep uncertainty:\nalso known as ambiguity or Knightian uncertainty; describes uncertainties for which it is not possible to develop a single, well-characterized probability distribution\nSea-Level Rise Projections\uf0c1\nWe summarize recent literature projections of GMSL rise for 2050, 2100, 2150, and 2300, as well as recent studies on multi-millennial sea-level rise commitments (Table 1, Figure 6a). Most of these studies are based on the RCPs, which allow the quantile projections produced by different studies to be directly compared to one another.\nSea-level rise projections conditional on different RCPs do not, however, align with the differ.ent temperature targets laid out in the 2015 Paris Agreement, which aims to hold \u201cthe increase in the global average temperature to well below 2 C above pre-industrial levels and [pursue] efforts to limit the temperature increase to 1.5.C above pre-industrial levels\u201d (134, paragraph 2-1a). Among the RCPs, both the 2.0C and 1.5C Paris Agreement temperature targets are most consistent with RCP2.6, although some RCP4.5 projections are consistent with 2.0.C. Thus, there has also been a recent set of studies focused on different scenarios consistent with these goals, providing another point for cross-study comparison (163-166).\nIn order to compare values across different studies that use different temporal baselines, we have normalized sea-level projections:\nSLR_{Adj} = SLR left(frac{t}{(Y-Y_0)} right), (1)\nwhere SLR_{Adj} is the normalized sea-level rise projection, SLR is the sea-level rise reported in the study, t is the time range in years (e.g., in the case of 2050 projections, t = 50), Y is the study end year, and Y_0 is the study baseline year. In cases where a range of years is used for either the study endpoint, or for the study baseline, we use the central year from the range for Equation 1 above.\nTable 1: Global mean sea-level rise projections (median, 17th to 83rd percentile range, and 5th to 95th percentile range). Studies have been categorized as probabilistic (projections that sample uncertainty for different driving factors and present multiple quantiles in the original study), semi-empirical (projections made with a model that uses a statistical relationship between global mean temperature and GMSL, without computing individual factors), or central range (projections that are either not semi-empirical and also do not sample uncertainty for different driving factors, or that focus the original study exclusively on a central, low, and high quantile). Probabilistic models include Kopp14 (140), Grinsted15 (137), Jackson16 (138), Kopp17 (144), Nauels17a (142), Jackson18 (164), and Rasmussen18 (165). Semi-empirical models include Jevrejeva12 (139), Schaeffer12 (153), Kopp16 (25), Bittermann17 (163), and Jackson18 (164). Central range models include Perrette13 (208), Slangen14 (147), Mengel16 (141), Schleussner16 (166), Bakker17 (135), Goodwin17 (136), Nauels17b (209), and Wong17 (150).\nYear\nPercentile range projections\n50 (median)\n17-83\n5-95\nProbabilistic projections\nKopp14\nRCP8.5\n2050\n0.29\n0.24-0.34\n0.21-0.38\n2100\n0.79\n0.62-1.00\n0.52-1.21\n2150\n1.30\n1.00-1.80\n0.80-2.30\n2300\n3.18\n1.75-5.16\n0.98-7.37\nRCP4.5\n2050\n0.26\n0.21-0.31\n0.18-0.35\n2100\n0.59\n0.45-0.77\n0.36-0.93\n2150\n0.90\n0.60-1.30\n0.40-1.70\n2300\n1.92\n0.70-3.49\n0.00-5.31\nRCP2.6\n2050\n0.25\n0.21-0.29\n0.18-0.33\n2100\n0.50\n0.37-0.65\n0.29-0.82\n2150\n0.70\n0.50-1.10\n0.30-1.50\n2300\n1.42\n0.32-2.88\n0.22-4.70\nGrinsted15 - RCP8.5\n2100\n0.80\n0.58-1.20\n0.45-1.83\nJackson16 - RCP8.5 High-end\n2050\n0.27\n0.20-0.34\n0.17-0.44\n2100\n0.80\n0.60-1.16\n0.49-1.60\nJackson16 - RCP8.5\n2100\n0.72\n0.52-0.94\n0.35-1.13\nJackson16 - RCP4.5\n2100\n0.52\n0.34-0.69\n0.21-0.81\nKopp17 - RCP8.5\n2050\n0.31\n0.22-0.40\n0.17-0.48\n2100\n1.46\n1.09-2.09\n0.83-2.43\n2150\n4.09\n3.17-5.47\n2.92-5.98\n2300\n11.69\n9.80-14.09\n9.13-15.52\nKopp17 - RCP4.5\n2050\n0.26\n0.18-0.36\n0.14-0.43\n2100\n0.91\n0.66-1.25\n0.50-1.58\n2150\n1.72\n1.21-2.72\n0.90-3.22\n2300\n4.21\n2.75-5.95\n2.11-6.96", "source": "https://sealeveldocs.readthedocs.io/en/latest/horton18.html"}
{"id": "1a5e23fee427-9", "text": "0.90\n0.60-1.30\n0.40-1.70\n2300\n1.92\n0.70-3.49\n0.00-5.31\nRCP2.6\n2050\n0.25\n0.21-0.29\n0.18-0.33\n2100\n0.50\n0.37-0.65\n0.29-0.82\n2150\n0.70\n0.50-1.10\n0.30-1.50\n2300\n1.42\n0.32-2.88\n0.22-4.70\nGrinsted15 - RCP8.5\n2100\n0.80\n0.58-1.20\n0.45-1.83\nJackson16 - RCP8.5 High-end\n2050\n0.27\n0.20-0.34\n0.17-0.44\n2100\n0.80\n0.60-1.16\n0.49-1.60\nJackson16 - RCP8.5\n2100\n0.72\n0.52-0.94\n0.35-1.13\nJackson16 - RCP4.5\n2100\n0.52\n0.34-0.69\n0.21-0.81\nKopp17 - RCP8.5\n2050\n0.31\n0.22-0.40\n0.17-0.48\n2100\n1.46\n1.09-2.09\n0.83-2.43\n2150\n4.09\n3.17-5.47\n2.92-5.98\n2300\n11.69\n9.80-14.09\n9.13-15.52\nKopp17 - RCP4.5\n2050\n0.26\n0.18-0.36\n0.14-0.43\n2100\n0.91\n0.66-1.25\n0.50-1.58\n2150\n1.72\n1.21-2.72\n0.90-3.22\n2300\n4.21\n2.75-5.95\n2.11-6.96\nFigure 6: (a) Near-term (2050; left), mid-term (2100; center), and long-term (2300; right) sea-level rise projections for RCP2.6, RCP4.5, and RCP8.5 scenarios, respectively, as well as for scenarios stabilizing global mean temperature at 1.5 C (Stab1.5) and 2.0.C (Stab2.0) above preindustrial levels. Shown are the 5th-95th percentile ranges (thin bars), 17th-83rd percentile ranges (thick bars), and median (circles) global mean sea-level (GMSL) rise projections (in meters). The AR5 \u201clikely\u201d ranges of 2050 and 2100 sea-level rise for each RCP scenario are shown by colored shading on the left and center panels, respectively. Gray shading on the right-most panel represents the range of IPCC AR5 2300 sea-level rise projections. (b) Decomposition of uncertainty in GMSL projections, following the DP16 projections of Kopp et al. (144). Red represents within-scenario variance due to the Antarctic ice sheet (AIS), cyan the variance due to the Greenland ice sheet (GIS), blue the variance due to glaciers and ice caps (GIC), green the variance due to thermal expansion (TE), and purple the variance due to land-water storage (LWS). The yellow line represents the total variance, pooling across RCP2.6, RCP4.5, and RCP8.5 (Scen). Until the 2040s, cross-scenario variance is negligible, leading to a total variance across RCPs that is slightly smaller than the variance within RCP4.5 (represented by the sum of all other contributions). In the second half of the twenty-first century, across-scenario variance grows to dominate uncertainty.\uf0c1\nProjections for 2050\uf0c1\nNear-term projections (through 2050) exhibit minimal sensitivity to emission pathways and a relatively small spread among studies (135, 138-141, 144, 150, 163). Across various RCPs and temperature scenarios, median GMSL projections in these studies range from 0.2-0.3 m. A conservative interpretation of these different studies would place the very likely GMSL rise between 2000 and 2050, across possible forcing pathways, at 0.1-0.5 m, with the bene\u00det of transitioning from rapid emission growth to rapid emission decline being <0.1 m (Table 1, Figure 6a).\nProjections for 2100\uf0c1\nIn the second half of the century and beyond, the spread in projections grows substantially due to both alternative methods and emissions uncertainty. Within a single forcing pathway, uncertainty in the response of the polar ice sheets to climate changes becomes increasingly dominant (Figure 6b), but uncertainty across scenarios becomes at least as large and often larger. Across RCPs and studies, median projections for total twenty-first-century GMSL rise range from as low as 0.4 m under RCP2.6 (25, 141) to as high as 1.5 m under RCP8.5 in simulations allowing for an aggressively unstable Antarctic ice sheet (150). Scenario choice exerts a great deal of influence, with median projections ranging from 0.4 to 0.8 m under RCP2.6, 0.5 to 0.9 m under RCP4.5, and 0.7 to 1.5 m under RCP8.5 (25, 135-142, 144, 147, 150). Assessing across studies yields a very likely GMSL rise of 0.2-1.0 m under RCP2.6, 0.2-1.6 m under RCP4.5, and 0.4-2.4 m under RCP8.5 (Table 1, Figure 6a).\nStudies attempting to assess the difference in GMSL rise between 1.5C and 2.0C warmer worlds that are consistent with goals of the Paris Agreement largely occupy the space of RCP2.6 and the cooler fraction of RCP4.5 projections. Excluding one older semi-empirical study (153), normalized projections of median 2100 sea-level rise range from 0.4-0.6 m under a scenario in which global average temperatures stabilize at 1.5.C (163) and from 0.5-0.7 m under a scenario in which global average temperatures stabilize at 2.0.C (164). Across studies, very likely ranges are 0.2-1.0 m under 1.5.C stabilization and 0.2-1.1 m under 2.0.C stabilization (163-166).\nProjections for 2150\uf0c1\nAcross the past three and a half decades, the end of the twenty-first-century has remained the endpoint of most GMSL projections, even as that endpoint has crept closer. With the twenty-second century now within the lifetime of some infrastructure investments, a small number of studies have looked beyond (140, 142, 144). Across three studies, median estimates of GMSL rise between 2000 and 2150 range from 0.6-0.9 m under RCP2.6, 0.9-1.7 m under RCP4.5, and 1.3-4.1 m under RCP8.5. Across studies, very likely ranges are 0.3-1.5 m under RCP2.6, 0.4-3.2 m under RCP4.5, and 0.8-6.0 m under RCP8.5.\nAmong studies focused on the difference between 1.5C and 2.0C of warming, two (163, 165) have projected 2150 sea-level rise. Median projections extend from 0.5 m to 0.7 m for 1.5C of warming and from 0.7 m to 0.9 m for 2.0C of warming. Very likely ranges are 0.3-1.5 m for 1.5.C and 0.4-1.8 m for 2.0C.\nProjections for 2300\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/horton18.html"}
{"id": "1a5e23fee427-10", "text": "Projections for 2150\uf0c1\nAcross the past three and a half decades, the end of the twenty-first-century has remained the endpoint of most GMSL projections, even as that endpoint has crept closer. With the twenty-second century now within the lifetime of some infrastructure investments, a small number of studies have looked beyond (140, 142, 144). Across three studies, median estimates of GMSL rise between 2000 and 2150 range from 0.6-0.9 m under RCP2.6, 0.9-1.7 m under RCP4.5, and 1.3-4.1 m under RCP8.5. Across studies, very likely ranges are 0.3-1.5 m under RCP2.6, 0.4-3.2 m under RCP4.5, and 0.8-6.0 m under RCP8.5.\nAmong studies focused on the difference between 1.5C and 2.0C of warming, two (163, 165) have projected 2150 sea-level rise. Median projections extend from 0.5 m to 0.7 m for 1.5C of warming and from 0.7 m to 0.9 m for 2.0C of warming. Very likely ranges are 0.3-1.5 m for 1.5.C and 0.4-1.8 m for 2.0C.\nProjections for 2300\uf0c1\nThe same three studies providing 2150 RCP projections (140, 142, 144) also provide projections through 2300, the temporal endpoint of the extensions of the RCPs. [Kopp et al.\u2019s (140) projections are extended to 2300 in Kopp et al. (144).]. One semi-empirical study (167) also provides projections on this timescale. Unsurprisingly, the difference among scenarios is extremely large by 2300 \u00d1 by which time, the extension of RCP2.6 is characterized by an atmospheric CO2 concentration lower than today, whereas the extension of RCP8.5 is characterized by a CO2 concentration of nearly 2,000 ppm. Median estimates of GMSL rise between 2000 and 2300 range from 1.0-2.0 m under RCP2.6, 1.7-4.2 m under RCP4.5, and 3.2-11.7 m under RCP8.5. Across studies, very likely ranges are .0.2 to 4.7 m under RCP2.6, 0.0 to 7.0 m under RCP4.5, and 1.0 to 15.5 m under RCP8.5 (Figure 6a).\nKopp et al. (144) provide two sets of projections, one (labeled K14), based on an extension of Kopp et al. (140) that, for ice sheets, is largely consistent with the IPCC AR5, and one (labeled DP16) incorporating results from the Antarctic ice-sheet model of DeConto & Pollard (143). The difference between these two projections highlights the importance of Antarctic ice-sheet behavior on this timescale. In K14, the 90% credible projections are -0.2 to 4.7 m under RCP2.6, 0.0 to 5.3 m under RCP4.5, and 1.0 to 7.4 m under RCP8.5. In DP16, the corresponding projections are 0.5-3.0 m under RCP2.6, 2.1-7.0 m under RCP4.5, and 9.1-15.6 m under RCP8.5. The incorporation of the results of a mechanistic model for the Antarctic ice sheet narrows the projection range under low emissions but shifts and fattens it under high emissions.\nMulti-millennial projections\uf0c1\nThe effects of climate change on sea level are not felt instantaneously; rather, due to the slow response time of deep ocean heat uptake and the sluggish response of ice sheets, they play out over millennia. The long-term sea-level response to a given emission future is sometimes called a \u201csea-level commitment\u201d (168). Levermann et al. (168) use a combination of physical models for ocean warming, glaciers, ice caps, and ice-sheet contributions to assess the sea-level change arising from two millennia of exposure to a constant temperature. Over 2,000 years, they find a sea-level commitment of approximately 2.3 m/C of warming. They note, however, that over longer time periods Greenland exhibits an abrupt threshold of ice loss between 0.8 and 2.2.C that ultimately adds approximately 6 m to GMSL. Incorporating this abrupt threshold yields a relationship, they conclude, that is consistent with paleo-sea-level constraints from the LIG, the MPWP, and Marine Isotope Stage 11 (approximately 411-401 thousand years ago). Over two millennia, they project a commitment of 1.4-5.2 m from 1.C of warming, 3.0- 7.7 m from 2.C of warming, and 6.0-12.1 m from 4.C of warming. Over ten millennia, these numbers increase to 1.5-10.9 m, 3.5-13.5 m, and 12.0-16.0 m. Clark et al. (169) use physical models to consider not only the translation between temperature and long-term sea-level change, but also the translation between emissions and temperature. For a scenario in which 1,280 Gt C are emitted after the year 2000 - roughly comparable to RCP4.5, and leading to a peak warming of approximately 2.5.C above preindustrial levels - they find a 10,000-year sea-level commitment in excess of 20 m. They estimate that historical CO2 emissions have already locked in 1.2-2.2 m of sea-level rise, and phasing emissions down to zero over the course of the next .90 years will lock in another ~9m.\nA few additional studies have focused on individual drivers of sea-level rise and the possible long-term contributions to sea level from specific mechanisms. Numerous studies have used Earth system models of intermediate complexity to assess the long-term thermal expansion contribution to GMSL rise, which amounts to approximately 0.2-0.6 m/.C (11). Zickfeld et al. (170) found that the slow response time of the oceans is important even for their response to short-lived climate forcers. For example, if CH4 emissions cease, 75% of the CH4-induced thermal expansion persists for 100 years, and approximately 40% persists for 500 years.\nIn addition, other studies have used coupled ice-sheet/ice-shelf models to examine the long.term response of the Antarctic ice sheet to RCP forcings. Golledge et al. (171) found that RCP2.6 would lead to 0.1-0.2 m of GMSL rise from Antarctica by 2300 and 0.4-0.6 m by 5000 CE, whereas RCP4.5 would lead to 0.6-1.0 m by 2300 and 2.8-4.3 m by 5000 CE, and RCP8.5 would lead to 1.6-3.0 m by 2300 and 5.2-9.3 m by 5000 CE. DeConto & Pollard (143), using an ice-sheet model that accounts for marine ice-sheet instability, ice-shelf hydrofracturing, and ice-cliff collapse, found that RCP2.6 would lead to approximately .0.5 to +2.4 m of GMSL rise from Antarctica by 2500 CE, whereas RCP4.5 would lead to 2.0-7.1 m and RCP8.5 to 9.7-17.6 m.\nMarine Isotope Stages:\nwarm and cool periods in Earth paleoclimate inferred from oxygen isotope data from deep sea core samples; timescale was developed by Cesare Emiliani in the 1950s as a standard to correlate Quaternary climate records.\nSynthesis\uf0c1\nBayesian and related probabilistic approaches are becoming increasingly widespread in reconstructing the spatio-temporal history of GMSL and RSL (e.g., 12, 25, 119). Bayesian reasoning represents a formal, probabilistic extension of the method of multiple working hypotheses, involving the identification of either a discrete or continuous set of alternative hypotheses or an assessment of the strength of prior evidence for each hypothesis. To date, however, probabilistic analyses of past and future changes have largely transpired in different domains. One of the ad.vantages of the rigor provided by formal approaches is that this need not be the case. Uncertainty quantification in future projections can guide the identification of useful research questions for paleo-sea level science, and the resulting improvements in understanding the past can lead to re\u00dened future projections.", "source": "https://sealeveldocs.readthedocs.io/en/latest/horton18.html"}
{"id": "1a5e23fee427-11", "text": "In addition, other studies have used coupled ice-sheet/ice-shelf models to examine the long.term response of the Antarctic ice sheet to RCP forcings. Golledge et al. (171) found that RCP2.6 would lead to 0.1-0.2 m of GMSL rise from Antarctica by 2300 and 0.4-0.6 m by 5000 CE, whereas RCP4.5 would lead to 0.6-1.0 m by 2300 and 2.8-4.3 m by 5000 CE, and RCP8.5 would lead to 1.6-3.0 m by 2300 and 5.2-9.3 m by 5000 CE. DeConto & Pollard (143), using an ice-sheet model that accounts for marine ice-sheet instability, ice-shelf hydrofracturing, and ice-cliff collapse, found that RCP2.6 would lead to approximately .0.5 to +2.4 m of GMSL rise from Antarctica by 2500 CE, whereas RCP4.5 would lead to 2.0-7.1 m and RCP8.5 to 9.7-17.6 m.\nMarine Isotope Stages:\nwarm and cool periods in Earth paleoclimate inferred from oxygen isotope data from deep sea core samples; timescale was developed by Cesare Emiliani in the 1950s as a standard to correlate Quaternary climate records.\nSynthesis\uf0c1\nBayesian and related probabilistic approaches are becoming increasingly widespread in reconstructing the spatio-temporal history of GMSL and RSL (e.g., 12, 25, 119). Bayesian reasoning represents a formal, probabilistic extension of the method of multiple working hypotheses, involving the identification of either a discrete or continuous set of alternative hypotheses or an assessment of the strength of prior evidence for each hypothesis. To date, however, probabilistic analyses of past and future changes have largely transpired in different domains. One of the ad.vantages of the rigor provided by formal approaches is that this need not be the case. Uncertainty quantification in future projections can guide the identification of useful research questions for paleo-sea level science, and the resulting improvements in understanding the past can lead to re\u00dened future projections.\nProbabilistic projections allow the identification of the major drivers of variance and, thus, the areas where investigation has the potential to yield the greatest reduction in that variance. For example, the DP16 of Kopp et al. (144), RSL projections in New Jersey (Figure 7) and Singapore (Figure 8) both are highly sensitive to the fate of the Antarctic ice sheet. Physical uncertainty in the Antarctic response (distinct from scenario uncertainty) accounts for at least ~25% of projection variance at both sites throughout the twenty-first century. In Singapore, the second largest contributor to projection variance for much of the century is the geological background (e.g., land subsidence), and the third largest contributor is atmosphere/ocean dynamics. By contrast, in New Jersey, atmosphere/ocean dynamics are the dominant contributor to variance through most of the century, whereas uncertainty in the geological background is negligible. This analysis would, thus, guide research to improve RSL projections in both localities toward the Antarctic, but it also highlights the importance of the geological background in Singapore and of a better characterization of North Atlantic atmosphere/ocean dynamics (Figures 7 and 8).\nFigure 7: (a) Geological reconstruction of past relative sea level (RSL) in Atlantic City, New Jersey. Red boxes indicate sea-level index points. The yellow-orange curve indicates annual tide-gauge data. The gray curve is a prediction of past RSL at Atlantic City from a spatio-temporal empirical hierarchical model (25) \u00det to a database of western North Atlantic sea-level proxies and tide-gauge data. (b) Projections of RSL change in Atlantic City, New Jersey, under the RCP2.6 (green), RCP4.5 (orange), and RCP8.5 (purple) emission scenarios, from the DP16 projections of Kopp et al. (144). Lines indicate median projections; boxes indicate 5th-95th percentile projections for 2100, relative to 2000 CE. (c) Drivers of the uncertainty in the RSL projections of b. Wedges indicate the fractional contributions of different processes to the total variance, pooled across the three RCPs and using RCP4.5 as a baseline [(red) AIS, Antarctic ice sheet; (cyan) GIS, Greenland ice sheet; (blue) GIC, glaciers and ice caps; (green) TE, global mean thermal expansion; (magenta) LWS, global mean land-water storage; (yellow) DSL, dynamic sea level; (grey) Geo, nonclimatic, geological background processes]. The Scen (yellow-orange) line represents the total variance pooled across all emission scenarios.\uf0c1\nFigure 8: (a) Geological reconstruction of past relative sea level (RSL) in Singapore. Red boxes indicate sea-level index points. The orange curve indicates annual tide-gauge data at Raffles Light House, and the gray curve is a prediction of past RSL from an empirical hierarchical model (25) \u00det to the proxy and tide-gauge data. (b) Projections of future RSL change at Raf\u00dfes Light House, Singapore, under the RCP2.6 (green), RCP4.5 (orange), and RCP8.5 (purple) emission scenarios, from the DP16 projections of Kopp et al. (144). Lines indicate median projections; boxes indicate 5th-95th percentile projections for 2100, relative to 2000 CE. (c) Drivers of uncertainty in the RSL projections in panel b. Wedges indicate the fractional contribution of different processes to the total variance, pooled across the three RCPs and using RCP4.5 as a baseline [(red) AIS, Antarctic ice sheet; (cyan) GIS, Greenland ice sheet; (blue) GIC, glaciers and ice caps; (green) TE, global mean thermal expansion; (magenta) LWS, global mean land-water storage; (yellow) DSL, dynamic sea level; (grey) Geo, nonclimatic, geological background processes]. The Scen (yellow-orange) line represents the total variance pooled across all emission scenarios.\uf0c1\nThe deep uncertainty regarding the behavior of marine-based parts of the Antarctic ice sheet has been noted since the earliest days of modern GMSL rise projections (e.g., 151), based on geological considerations. The Antarctic response during past warm periods serves as an important diagnostic of the performance of models used to project ice-sheet behavior in future warm cli.mates. For example, DeConto & Pollard\u00d5s (143) estimates of the Antarctic contribution to GMSL during the LIG (3.6-7.4 m) and MPWP (5-15 m) serve as a filter on ensemble members viewed as having reasonable physical parameterizations. Under both high-and low-emissions scenarios, LIG behavior correlates with sea-level contributions in 2100 (r = 0.52 for RCP2.6 and r = 0.35 for RCP8.5), whereas Pliocene behavior correlates strongly (r = 0.67) with behavior under RCP8.5. The Pliocene correlation is even stronger (r = 0.83) for RCP8.5 in 2500, as is the LIG correlation for RCP2.6 (r = 0.61). These modeling results support the heuristic idea that the LIG provides information relevant to the long-term future in a low-emission world and that the Pliocene and other warmer past periods provide information relevant to a higher-emission world. Unfortunately, whereas significant progress may be possible over the next decade in understanding the LIG, knowledge about sea level during earlier periods may be problematic in light of the potentially major contributions from MDT (73).\nThe variance analysis also indicates the need to improve geological rate estimates in Singapore (Figure 8c). Under RCP4.5, the central 90% RSL projection for 2050 is 4-47 cm (144). The geological contribution to RSL in 2050 is estimated at -5 \u00b1 8 cm. If the geological contribution were known precisely to be equal to its median estimate of .1.0 mm/year, the range shrinks to 7-44 cm (a 14% reduction in range width). A less literal interpretation of the particular values used in this projection would view the signi\u00decant variance contribution as a flag for further investigation. The spread of geological background rates around the Singapore coast ranges from .2.4 \u00b1 1.5 mm/year to 0.0 \u00b1 2.0 mm/year, suggesting up to .6 mm/year of spread that could be reduced by using records longer than the tide-gauge era (140).", "source": "https://sealeveldocs.readthedocs.io/en/latest/horton18.html"}
{"id": "1a5e23fee427-12", "text": "The variance analysis also indicates the need to improve geological rate estimates in Singapore (Figure 8c). Under RCP4.5, the central 90% RSL projection for 2050 is 4-47 cm (144). The geological contribution to RSL in 2050 is estimated at -5 \u00b1 8 cm. If the geological contribution were known precisely to be equal to its median estimate of .1.0 mm/year, the range shrinks to 7-44 cm (a 14% reduction in range width). A less literal interpretation of the particular values used in this projection would view the signi\u00decant variance contribution as a flag for further investigation. The spread of geological background rates around the Singapore coast ranges from .2.4 \u00b1 1.5 mm/year to 0.0 \u00b1 2.0 mm/year, suggesting up to .6 mm/year of spread that could be reduced by using records longer than the tide-gauge era (140).\nAnother regionally important factor indicated by the variance decomposition is atmosphere/ ocean dynamics, estimated to contribute 1 \u00b1 5 cm to RSL change between 2000 and 2050 for Singapore. As with the geological component, the precise quantitative value should be viewed with caution. The global climate models used to estimate RSL do not resolve the details of atmospheric and ocean circulation in the Java Sea and through the Singapore Strait. The potential importance of this contribution should motivate studies with regional ocean models. Indeed, geological reconstructions also suggest the potential significance of this term. Meltzner et al. (172) found coral microatoll evidence at Belitung, in the Java Sea, for mid-Holocene \u00b160-cm swings in RSL, with peak rates of change reaching 13 \u00b1 4 mm/year for roughly half a century. Were such a swing to happen over the next half century, it would dwarf other drivers of RSL change. This finding emphasizes the value of understanding the relevant physical processes and ensuring the models used to project future RSL changes can reasonably reproduce them.\nA similar example arises in New Jersey. In 2050 under RCP4.5, the central 90% projection for total RSL is 19-65 cm, to which atmosphere/ocean dynamics contribute -7 to 18 cm (Figure 7c). Eliminating atmosphere/ocean dynamics uncertainty would reduce the range to 26-60 cm (a 26% reduction in width). This broad range is driven primarily by the uncertain response of the Gulf Stream, the North Atlantic Oscillation, the AMOC, and possibly El Nino-Southern Oscillation to warming. On shorter timescales, dynamics involving these systems are likely responsible for the migrating \u201chot spots\u201d of sea-level change observed along the US Atlantic Coast (e.g., 31). The uncertain atmosphere/ocean dynamics contribution motivates paleo-sea level studies focused on understanding multidecadal-scale and centennial-scale variability along the Atlantic coast of North America. Studies of RSL change over the past millennium suggest variability of more than a decimeter (173). The spatial pattern of this past variability along the coast suggests the same atmosphere/ocean dynamics factors that are involved in future projections (rather than, for example, land-ice changes) are the most likely drivers (22, 24). This variability thus provides a historical test case for the coupled climate models used to project future atmosphere/ocean dynamic RSL change.\nConclusion\uf0c1\nWith 11% of the world population living in coastal areas less than 10 m above sea level (174), rising seas represent one of the main sources of future economic and ecological risk. Although records from the instrumental era provide useful information in constraining the future evolution of sea level, the geological record presents us with a history of climatic changes under a wide range of different boundary conditions (e.g., paleogeographic configurations) and climatic forcings (e.g., atmospheric CO2 levels and orbital regimes). To better constrain the response of the climate system to current and future anthropogenic greenhouse forcing, it is necessary to study these geological periods. Given the serious risks associated with sea-level rise, reconstructions of RSL are particularly important. However, claims of ties between past changes and future projections are not always formally established. It is only if both geological reconstructions and projections are made cognizant of uncertainty and spatial variability that a range of specific connections between past and future changes can be made and turned into useful information for planners and decision makers. Although projections of future sea level will always remain uncertain, greater interconnections between the two sub-disciplines could lead to significant progress in constraining their characteristics.\nSummary Points\uf0c1\nRelative sea level (RSL) differs from global mean sea level (GMSL), because driving processes\u00d1such as atmosphere/ocean dynamics, the static-equilibrium effects of ocean/cryosphere/hydrosphere mass redistribution on the height of the geoid and the Earth\u00d5s surface, glacio-isostatic adjustment (GIA), sediment compaction, tectonics, and mantle dynamic topography (MDT)\u00d1are spatially variable and cause RSL change to vary in rate and magnitude among regions.\nGeological reconstructions of RSL are derived from sea-level proxies, the formation of which were controlled by the past position of sea level. We summarize the response of sea level to past climatic changes during three geological intervals that provide analogues for future predicted changes: the Mid-Pliocene Warm Period, the Last Interglacial, and the Holocene.\nEstimates of GMSL rise over the twentieth century (1.1-1.9 mm/year) are derived from the temporally and spatially sparse tide gauge network, whereas more recent estimates (2.6-3.2 mm/year) are also obtained using satellite altimetry observations of sea surface height.\nA large portion of the twentieth-century rise, including most GMSL rise over the past quarter of the twentieth century, is tied to anthropogenic warming.\nMethods used to project sea-level changes in the future vary both in the degree to which they disaggregate the different drivers of sea-level change and the extent to which they attempt to characterize probabilities of future outcomes.\nA review of recent GMSL rise projections shows that, across methodologies and emission scenarios, median values of future sea-level range from 0.2-0.3 m (2050), 0.4-1.5 m (2100), 0.6-4.1 m (2150), and 1.0-11.69 m (2300), with 95th percentile projections for RCP8.5 (a high-emission scenario) reaching as high as 2.4 m in 2100, and 15.5 m in 2300.\nFuture Issues\uf0c1\nIncreasing the spatial and temporal distribution, improving the resolution, and incorporating geological sea-level reconstructions into uni\u00deed, freely accessible databases may improve insights into the relative contribution of climatic and geophysical processes into present and future sea-level change.\nRecognition of the sizable contributions of MDT to RSL change over millions of years has complicated reconstruction of sea level during the Pliocene, the last time global mean temperatures were as high as projected for this century. Reducing uncertainty of MDT may allow more useful constraints on future sea level.\nCharacterize the impact of more complex mantle rheologies on models of the GIA process and incorporate this knowledge in regional and local reconstructions of past sea-level change.\nMore rigorous uncertainty quantification in geological sea-level reconstructions will facilitate more accurate use of geological sea level to constrain future sea-level projections; conversely, analyzing uncertainty in sea-level rise projections can help identify research priorities for both paleo sea-level reconstruction and process studies.\nIn order to obtain estimates of local sea-level accelerations over the last century, it will be necessary to combine the tide gauge and satellite altimetry observations in a statistically robust framework.\nSustained dialogue between scientists and decision-makers, not just \u201cscience-first\u201d assessment, is necessary to ensure that scientific sea-level rise projections are used in a way that respects both scientific knowledge and its uncertainties.\nReferences\uf0c1\nHolgate SJ, Matthews A, Woodworth PL, Rickards LJ, Tamisiea ME, et al. 2013. New data systems and products at the permanent service for mean sea level. J. Coast. Res. 29:493-504\nDouglas BC. 1991. Global sea level rise. J. Geophys. Res. Oceans 96(C4):6981-92\nHolgate SJ. 2007. On the decadal rates of sea level change during the twentieth century. Geophys. Res. Lett. 34(1):L01602\nDutton A, Webster JM, Zwartz D, Lambeck K, Wohlfarth B. 2015. Tropical tales of polar ice: evidence of Last Interglacial polar ice sheet retreat recorded by fossil reefs of the granitic Seychelles islands. Quat. Sci. Rev. 107:182-96\nKemp AC, Horton BP, Donnelly JP, Mann ME, Vermeer M, Rahmstorf S. 2011. Climate related sea-level variations over the past two millennia. PNAS 108(27):11017-22\nKopp RE, Simons FJ, Mitrovica JX, Maloof AC, Oppenheimer M. 2009. Probabilistic assessment of sea level during the Last Interglacial Stage. Nature 462(7275):863-67", "source": "https://sealeveldocs.readthedocs.io/en/latest/horton18.html"}
{"id": "1a5e23fee427-13", "text": "Characterize the impact of more complex mantle rheologies on models of the GIA process and incorporate this knowledge in regional and local reconstructions of past sea-level change.\nMore rigorous uncertainty quantification in geological sea-level reconstructions will facilitate more accurate use of geological sea level to constrain future sea-level projections; conversely, analyzing uncertainty in sea-level rise projections can help identify research priorities for both paleo sea-level reconstruction and process studies.\nIn order to obtain estimates of local sea-level accelerations over the last century, it will be necessary to combine the tide gauge and satellite altimetry observations in a statistically robust framework.\nSustained dialogue between scientists and decision-makers, not just \u201cscience-first\u201d assessment, is necessary to ensure that scientific sea-level rise projections are used in a way that respects both scientific knowledge and its uncertainties.\nReferences\uf0c1\nHolgate SJ, Matthews A, Woodworth PL, Rickards LJ, Tamisiea ME, et al. 2013. 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Gulf Stream\u00d5s induced sea level rise and variability along the U.S. mid-Atlantic coast. J. Geophys. Res. Oceans 118(2):685-97\nKopp RE. 2013. Does the mid-Atlantic United States sea level acceleration hot spot re\u00dfect ocean dynamic variability? Geophys. Res. Lett. 40(15):3981-85\nLittle CM, Piecuch CG, Ponte RM. 2017. On the relationship between the meridional overturning circulation, alongshore wind stress, and United States East Coast sea level in the Community Earth System Model Large Ensemble. J. Geophys. Res. Oceans 122(6):4554-68\nKemp AC, Bernhardt CE, Horton BP, Kopp RE, Vane CH. 2014. Late Holocene sea-and land-level change on the U.S. southeastern Atlantic coast. Mar Geol. 357:90-100\nKemp AC, Hawkes AD, Donnelly JP, Vane CH, Horton BP. 2015. Relative sea-level change in Con.necticut (USA) during the last 2200 yrs. Earth Planet. Sci. Lett. 428:217-229\nKopp RE, Hay CC, Little CM, Mitrovica JX. 2015. Geographic variability of sea-level change. Curr. Clim. Change Rep. 1(3):192-204\nKopp RE, Kemp AC, Bittermann K, Horton BP, Donnelly JP. 2016. Temperature-driven global sea-level variability in the Common Era. PNAS 113(11):1434-41\nNerem RS, Chambers DP, Choe C, Mitchum GT. 2010. Estimating mean sea level change from the TOPEX and Jason Altimeter missions. Mar. Geod. 33(sup1):435-46\nHamlington BD, Cheon SH, Thompson PR, Merri\u00deeld MA, Nerem RS, et al. 2016. An ongoing shift in Paci\u00dec Ocean sea level. J. Geophys. Res. Oceans 121(7):5084-97\nMcGregor S, Gupta AS, England MH. 2012. Constraining wind stress products with sea surface height observations and implications for Paci\u00dec Ocean sea level trend attribution. J. Clim. 25(23):8164-76\nYin J, Goddard PB. 2013. Oceanic control of sea level rise patterns along the East Coast of the United States. Geophys. Res. Lett. 40(20):5514-20\nTaylor KE, Stouffer RJ, Meehl GA. 2012. An overview of CMIP5 and the experiment design. Bull. Am. Meteorol. 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{"id": "1a5e23fee427-14", "text": "Nerem RS, Chambers DP, Choe C, Mitchum GT. 2010. Estimating mean sea level change from the TOPEX and Jason Altimeter missions. Mar. Geod. 33(sup1):435-46\nHamlington BD, Cheon SH, Thompson PR, Merri\u00deeld MA, Nerem RS, et al. 2016. An ongoing shift in Paci\u00dec Ocean sea level. J. Geophys. Res. Oceans 121(7):5084-97\nMcGregor S, Gupta AS, England MH. 2012. Constraining wind stress products with sea surface height observations and implications for Paci\u00dec Ocean sea level trend attribution. J. Clim. 25(23):8164-76\nYin J, Goddard PB. 2013. Oceanic control of sea level rise patterns along the East Coast of the United States. Geophys. Res. Lett. 40(20):5514-20\nTaylor KE, Stouffer RJ, Meehl GA. 2012. An overview of CMIP5 and the experiment design. Bull. Am. Meteorol. Soc. 93(4):485-98\nValle-Levinson A, Dutton A, Martin JB. 2017. Spatial and temporal variability of sea level rise hot spots over the eastern United States. Geophys. Res. 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{"id": "bccc98a2faca-0", "text": "Hallberg et al. (2013)\uf0c1\nTitle:\nSensitivity of Twenty-First-Century Global-Mean Steric Sea Level Rise to Ocean Model Formulation\nCorresponding author:\nRobert Hallberg\nKeywords:\nSea level, Climate change, Ocean models\nCitation:\nHallberg, R., Adcroft, A., Dunne, J. P., Krasting, J. P., & Stouffer, R. J. (2013). Sensitivity of Twenty-First-Century Global-Mean Steric Sea Level Rise to Ocean Model Formulation. Journal of Climate, 26(9), 2947\u00d02956. doi: 10.1175/jcli-d-12-00506.1\nURL:\nhttps://journals.ametsoc.org/view/journals/clim/26/9/jcli-d-12-00506.1.xml\nAbstract\uf0c1\nTwo comprehensive Earth system models (ESMs), identical apart from their oceanic components, are used to estimate the uncertainty in projections of twenty-first-century sea level rise due to representational choices in ocean physical formulation. Most prominent among the formulation differences is that one (ESM2M) uses a traditional z-coordinate ocean model, while the other (ESM2G) uses an isopycnal-coordinate ocean. As evidence of model fidelity, differences in twentieth-century global-mean steric sea level rise are not statistically significant between either model and observed trends. However, differences between the two models\u2019 twenty-first-century projections are systematic and both statistically and climatically significant. By 2100, ESM2M exhibits 18% higher global steric sea level rise than ESM2G for all four radiative forcing scenarios (28-49 mm higher), despite having similar changes between the models in the near-surface ocean for several scenarios. These differences arise primarily from the vertical extent over which heat is taken up and the total heat uptake by the models (9% more in ESM2M than ESM2G). The fact that the spun-up control state of ESM2M is warmer than ESM2G also contributes by giving thermal expansion coefficient that are about 7% larger in ESM2M than ESM2G. The differences between these models provide a direct estimate of the sensitivity of twenty-first-century sea level rise to ocean model formulation, and, given the span of these models across the observed volume of the ventilated thermocline, may also approximate the sensitivities expected from uncertainties in the characterization of interior ocean physical processes.\nIntroduction\uf0c1\nGlobal-mean sea level has been rising throughout the twentieth century, with increased rates in recent decades (Church et al. 2011). The leading contributors have been documented as the melting of land ice (snow, mountain glaciers, and ice sheets) and the steric rise in sea level due to a warming and expanding ocean (Church et al. 2011), with smaller contributions from climatic and anthropogenic changes in land-water storage (Milly et al. 2003). Projecting twenty-first-century sea level rise (SLR) is of great societal importance but is subject to uncertainties in our understanding of the underlying physical processes. The dynamic response of marine-terminated ice sheets to warming oceans is poorly understood and has the potential to contribute to SLR at rates with a plausible order of magnitude of 10 mm yr^{-1} (Holland et al. 2008; Pfeffer et al. 2008). Because the response of clouds under changing climate is a leading order uncertainty in the earth\u2019s changing radiative budget, and because of the close connection between this budget, ocean heat uptake, and SLR, the cloud response is another substantial cause of uncertainty in SLR. Similarly, uncertainties in the radiative forcing due to aerosols and the overall sensitivity of the feedbacks in the coupled system generally can also contribute to un.certainty in projections of SLR.\nThe ocean contribution to SLR is closely related to its net uptake of heat, although the properties of the water taking up that heat are of leading order importance to SLR. Additionally, interior ocean mixing of heat and salinity generally cause seawater to contract because of nonlinearities of the equation of state, even though they do not alter the net heat content of the ocean (Griffies and Greatbatch 2012). Changes in ocean circulation play a leading order role in determining where the temperature will increase because of the ocean circulation response to climate change, and hence in detecting steric sea level rise (e.g., Gnanadesikan et al. 2007a; Winton et al. 2013). Interior ocean diapycnal mixing and ocean mixed layer processes play a major role in regulating the ocean\u2019s long-term uptake of heat (e.g., Dalan et al. 2005), but the explicit specification of diapycnal mixing in climate models remains largely empirical. Ocean models can also exhibit numerical artifacts, such as spurious diapycnal mixing (Griffies et al. 2000) or excessive entrainment in overflows (Legg et al. 2006), that can complicate their ability to project SLR for the real world. There is also evidence that representation of the rectified effects of ocean mesoscale eddies are an important source of uncertainty in the ocean circulation response to climate change (Hallberg and Gnanadesikan 2006; Farneti et al. 2010), and hence potentially for heat uptake and SLR. With such a broad range of processes contributing, it is worthwhile to estimate the overall magnitude of the contributions of oceanic uncertainties to uncertainties in projections of steric sea level rise.\nThis study examines global-mean steric sea level rise (GSSLR) from four climate change scenarios from two Earth system models (ESMs) that are identical apart from their ocean components. We utilize this framework to identify and quantify the uncertainties in GSSLR attributable to limitations in our understanding of the physics of the ocean and the numerical portrayal of the ocean\u2019s dynamics. This approach is thus different than the typical ensemble survey of coupled model inter-comparison for uncertainty estimation, as it allows us to roughly distinguish ocean-derived GSSLR differences from atmospherically forced GSSLR differences, be.cause it avoids convolving issues relating to drift in sea level and overweighting z-coordinate ocean models (with very similar lineages and algorithmic choices) in the ensemble. This study finds systematic 18% differences in GSSLR between the two models. While these differences are large enough to warrant a more thorough study, they do not fundamentally alter previous estimates of sea level rise that can be expected to occur in the twenty-fist century.\nThe earth system models\uf0c1\nThis study uses two comprehensive earth system models with identical atmospheric, land surface, sea ice, and ocean ecosystem components, differing only in their physical ocean components (Dunne et al. 2012). The ESM2M uses a 50-level z*-coordinate ocean model, built with the Modular Ocean Model, version 4.1 (MOM4p1) code (Griffies 2009). The ESM2G uses a 63-layer isopycnal-coordinate version of the Generalized Ocean Layer Dynamics (GOLD) ocean model (Hallberg and Adcroft 2009). Both use nominal horizontal resolutions of 1\u02da with a tripolar fold over the Arctic. Both have comprehensive sets of physical parameterizations representative of the state-of-the-art z-coordinate and isopycnal-coordinate ocean climate models, as described in Dunne et al. (2012). Both ocean models conserve heat, salt, and mass to numerical round off, and both use proper freshwater mass flux surface boundary conditions, instead of artificially converting them into virtual salt fluxes. Neither model\u2019s atmosphere was changed or retuned from the Geophysical Fluid Dynamics Laboratory (GFDL) Climate Model, version 2.1 (CM2.1) (Anderson et al. 2004). The runs presented here use the temporally evolving concentrations of well-mixed radiatively active gases and aerosols (Lamarque et al. 2010) prescribed by phase 5 of the Coupled Model Intercomparison Project (CMIP5) for the historical period up to 2005, and the four standardized Representative Concentration Pathways (RCPs) (Moss et al. 2010; Taylor et al. 2012). The RCP scenarios are labeled with the approximate global-mean radiative forcing anomalies due to well-mixed gases at the end of the twenty-first century (e.g., RCP8.5 has about an 8.5 W m 22 radiative heating anomaly relative to the preindustrial control in 1850). The various RCP scenarios are based on plausible choices for anthropogenic emissions. The atmospheric concentrations of CO2 differ, particularly in the latter half of the twenty-first century. While the radiative forcing for RCP8.5 increases strongly throughout the twenty-first century, the radiative forcing in RCP2.6 peaks in midcentury before declining. RCP4.5 and RCP6.0 have radiative forcing in the twenty-first century between RCP8.5 and RCP2.6.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hallberg13.html"}
{"id": "bccc98a2faca-1", "text": "Both models have been spun up with 1860 radiative forcing for over 1000 years (2560 years for ESM2M and 1160 years for ESM2G), until their global-mean heat budgets were well balanced before starting their respective control runs. The ESM2M control runs exhibit a slight warming averaged over the volume of the ocean (dT/dt = -0.038\u02daC century^{-1} averaged over a 500-yr-long control run), while ESM2G has an even smaller cooling (dT/dt = -0.010\u02daC century^{-1}). The ocean heat (and steric sea level) budgets for the control runs of these models are thus much closer to balance than in most coupled climate models of this resolution (Sen Gupta et al. 2012). The 500-yr-long 1860 control run of ESM2G has an average steric sea level drop of 0.023 mm yr^{-1}, while ESM2M\u2019s has an average steric sea level rise of 0.074 mm yr^{-1}. In these runs, the standard deviation of the detrended annual-mean global-mean steric sea level anomaly is 2.3 mm for ESM2G and 1.8 mm for ESM2M, and they are used as uncertainty estimates in the figures presented later.\nThere are some pertinent differences in the spun-up ocean control states of the two models, both in the ocean interior and at the surface. As shown in Figure 1, the main thermocline extends too deeply in ESM2M and is too shallow in ESM2G relative to observations (see also Dunne et al. 2012). While the models use explicit diapycnal diffusivities of similar magnitudes in the main thermocline, ESM2M includes both parameterizations that indirectly enhance diapycnal mixing (e.g., Gnanadesikan et al. 2007b) and numerically induced diapycnal mixing (Ilicak et al. 2012; Griffies et al. 2000). The overly sharp thermocline in ESM2G may indicate that it is underrepresenting mixing processes in the thermocline. Below the thermocline, ESM2G uses an enhanced diapycnal diffusivity relative to ESM2M, following the prescription of Gargett (1984), while both models use similar abyssal tidal mixing parameterizations following Simmons et al. (2004). Under historical climate forcing, ESM2M is an average of 1\u02daC warmer relative to the observed climatology for 1980-2000, while ESM2G is 0.25\u02daC cooler than the climatology (Figure 1, middle). The root-mean-square (RMS) temperature errors relative to climatology for ESM2G are substantially smaller than for ESM2M below 500 m, while ESM2M has smaller RMS errors above 500 m, converging to similar RMS errors at the surface (Figure 1, right). Differences in the parameterizations of other processes, such as eddy mixing, could also contribute substantially to differences in both the oceans\u2019 mean states and to GSSLR. The annual-mean near-surface temperatures in 1980-2000 of the historical simulations average 0.4\u02daC colder in ESM2G than ESM2M, with smaller differences in midlatitudes and zonal-mean differences exceeding 1.5\u02daC between 50\u02da and 75\u02daN. The northern sea ice is more extensive than observed, especially in ESM2G, and the southern sea ice is less extensive than observed, especially in ESM2M (Dunne et al. 2012). These differences between the spun-up mean states of the two models figure prominently in their differing projections of GSSLR.\nFigure 1: (left) Horizontal-mean potential temperatures from ESM2M (red) and ESM2G (blue) averaged over years 1981-2000 of the historical runs, along with the observed horizontal-mean temperature from the World Ocean Atlas, 2001 (WOA2001) (dashed) (Conkright et al. 2002). (middle) As in (left), but for horizontal-mean temperature bias from ESM2M and ESM2G relative to observed. (right) As in (left), but for horizontal RMS temperature errors for ESM2M and ESM2G. The WOA2001 dataset was chosen as a reference because most of the observations are from the 1980s and 1990s, giving a consistent comparison with this time average from the models.\uf0c1\nProjected global steric sea level rise\uf0c1\nThe GSSLR for the historical and twenty-first-century projections under the four RCP scenarios are shown in Figure 2. This figure includes both thermosteric and halosteric contributions, although the focus here is on exploring the thermosteric differences, since the global-mean differences in the halosteric sea level rise are relatively small. The two models are statistically similar through.out the twentieth century, including responses of similar magnitudes to major volcanic eruptions such as Krakatoa (1883), Agung (1963), and Pinatubo (1991). The mean rate of GSSLR in the latter twentieth century in both models (1.16 mm yr^{-1} for ESM2M and 1.10 mm yr^{-1} for ESM2G) is slightly higher than observational estimates of sea level rise from thermal expansion of 0.8 \u00b1 0.15 mm yr^{-1} for 1972\u00d02008 (Church et al. 2011), while observed global-mean halosteric sea level rise is much smaller, just 0.04 \u00b1 0.02 mm yr^{-1} averaged from 1955 to 2003 (Ishii et al. 2006), and not as well constrained observationally.\nFigure 2: Global-mean steric sea level from concentration-forced simulations with ESM2M (red) and ESM2G (blue), relative to the mean for 1861-1900, for ensembles of historical runs with four members for ESM2M and seven members for ESM2G (up to 2005) and for the four CMIP5 standardized RCPs (starting in 2005). The marks to the right of the plot are projected to 2100 from linear fits over the last 40 years, with errors estimated from the variance during that same period. Long-term mean steric sea level drifts from the control runs of +0.076 mm y^{-1} and -0.025 mm yr^{-1} have been subtracted from ESM2M and ESM2G, respectively. The three black lines show the observationally based estimate of thermosteric SLR from 1972 to 2008 of 0.80 \u00b1 0.15 mm yr^{-1} Church et al. (2011); the vertical offset for these black lines is arbitrary.\uf0c1\nIn the twenty-first-century scenarios, there are systematic and statistically significant differences between the two models. By the middle of the twenty-first century, ESM2M exhibits a significantly larger GSSLR than ESM2G, and by the end of the twenty-first century (2081-2100), the 20-yr-averaged GSSLR relative to 1881-1900 is about 18% higher in ESM2M than in ESM2G for each of the four RCP scenarios (Fig. 2). Put differently, the values of GSSLR attained by ESM2G by the end of the twenty-first century are reached 28, 21, 16, and 11 years earlier by ESM2M for scenarios RCP2.6, RCP4.5, RCP6.0, and RCP8.5, respectively. Figure 2 also shows that the ocean formulation is responsible, both directly and indirectly via differences in the spun-up mean ocean state, for an uncertainty in projections of GSSLR that is of comparable magnitude to the differences between successive RCP forcing scenarios.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hallberg13.html"}
{"id": "bccc98a2faca-2", "text": "Figure 2: Global-mean steric sea level from concentration-forced simulations with ESM2M (red) and ESM2G (blue), relative to the mean for 1861-1900, for ensembles of historical runs with four members for ESM2M and seven members for ESM2G (up to 2005) and for the four CMIP5 standardized RCPs (starting in 2005). The marks to the right of the plot are projected to 2100 from linear fits over the last 40 years, with errors estimated from the variance during that same period. Long-term mean steric sea level drifts from the control runs of +0.076 mm y^{-1} and -0.025 mm yr^{-1} have been subtracted from ESM2M and ESM2G, respectively. The three black lines show the observationally based estimate of thermosteric SLR from 1972 to 2008 of 0.80 \u00b1 0.15 mm yr^{-1} Church et al. (2011); the vertical offset for these black lines is arbitrary.\uf0c1\nIn the twenty-first-century scenarios, there are systematic and statistically significant differences between the two models. By the middle of the twenty-first century, ESM2M exhibits a significantly larger GSSLR than ESM2G, and by the end of the twenty-first century (2081-2100), the 20-yr-averaged GSSLR relative to 1881-1900 is about 18% higher in ESM2M than in ESM2G for each of the four RCP scenarios (Fig. 2). Put differently, the values of GSSLR attained by ESM2G by the end of the twenty-first century are reached 28, 21, 16, and 11 years earlier by ESM2M for scenarios RCP2.6, RCP4.5, RCP6.0, and RCP8.5, respectively. Figure 2 also shows that the ocean formulation is responsible, both directly and indirectly via differences in the spun-up mean ocean state, for an uncertainty in projections of GSSLR that is of comparable magnitude to the differences between successive RCP forcing scenarios.\nThe first reason for the higher GSSLR in ESM2M than in ESM2G is simply because it takes up more heat. This is readily evident in Fig. 3 (bottom), where ESM2M warms substantially more than comparable ESM2G simulations, with volume-mean temperature increasing about 9% more in ESM2M than in ESM2G. These differences in heat uptake are primarily found over the broad depth range from 200 to 2000 m (Fig. 4, left). The warming itself is much more strongly surface intensified in both models than are the differences between the models, and it is quite similar at the surface (apart from RCP2.6, where near-surface temperatures start diverging around 2050, as seen in Fig. 3); this point is discussed further below. To leading order, the heat is being taken up primarily in the thermocline of both models, but the main thermocline is deeper in ESM2M than in ESM2G, giving a greater volume of water to warm. As shown in Fig. 4 (middle left), the density changes contributing to the differences in GSSLR between the models are broadly distributed over the top 2500 m of the models, with roughly equal contributions coming from the depth ranges of 0\u2013600 m, 600\u20131200 m, and 1200\u20132500 m. By contrast, well over half the total GSSLR comes from the topmost 600 m in all the cases. Differences in salinity changes compensate or augment the GSSLR differences because of differences in thermal changes at varying depths (Fig. 4, right), but when vertically integrated, the differences in salinity changes between the models contribute less than 0.2 mm to the difference in GSSLR. The larger heat uptake in ESM2M than ESM2G accounts for about half the difference in GSSLR between the models.\nFigure 3: (top) Time series of global-mean SST, relative to the mean for 1880\u20131920, from ESM2M (red) and ESM2G (blue) for ensembles of historical runs and the four CMIP5 radiative scenarios. The values on the right are projections to 2100 from linear fits over the last 40 years, with error bars indicating the variance from these trends over the same 40-yr period. (bottom) Time series of globally integrated heat content anomalies, expressed as volume-mean ocean temperature anomalies in degrees Celsius.\uf0c1\nFigure 4: (left) Vertical profiles of the horizontal-mean temperature change for ESM2M (red) and ESM2G (blue) averaged over a 40-yr period relative to 1861\u20131900. The historical intervals are a century apart (1961\u20132000), while for RCP2.6 and RCP8.5, the intervals are two centuries apart (2061\u20132100). (middle left) Vertical profiles of the horizontal-mean contributions to GSSLR (spatially integrated density anomalies divided by the ocean\u2019s surface area and a mean density) from the same runs. (middle right) Profiles of the difference in contribution to GSSLR, ESM2M minus ESM2G. (right) Vertical profiles of the dominant terms in the differences between ESM2M and ESM2G in GSSLR contributions for RCP8.5. The average of the models\u2019 temperature changes acting on the difference between the models\u2019 thermal expansion coefficient differences (blue) and the differences in water-mass property changes acting on the mean thermal expansion and haline contraction coefficients of the two models (solid black) explain almost the entire signal shown in the third panel. The dashed and dotted lines show the separate profiles of GSSLR contributions from the temperature and salinity change differences, respectively, acting on the mean of the models\u2019 thermal expansion and haline contraction coefficients.\uf0c1\nA second factor in the differing GSSLR between these two models is the difference in the thermal expansion coefficients where the heating occurs; the thermal expansion coefficient is a strongly increasing function of temperature and pressure, so the two models could be taking up similar amounts of heat, but in different locations, leading to differing amounts of GSSLR (see, e.g., Griffies and Greatbatch 2012). This effect is evident in Fig. 4 (left and middle-left panels), where the contributions to GSSLR are relatively concentrated in the warmer near-surface waters compared with the heat uptake, and it is explicitly diagnosed for RCP8.5 in Fig. 4 (right). ESM2G has a sharper thermocline than ESM2M, and is, on average, about 1.25\u00b0C colder than ESM2M at the same depths below the topmost few hundred meters (Fig. 1, middle), with differences in thermal expansion coefficients based on the horizontal-mean temperatures peaking at about 750-m depth, where it is 14% larger in the ESM2M historical run than in ESM2G (and 8% larger than for observed temperatures; in ESM2G it is 6% smaller than observed). The thermal expansion coefficients have smaller relative differences above 750 m because the water is warmer, on average, and they have smaller relative differences below 1000 m because of the effects of pressure. Averaged over the whole volume of the ocean, the simulated thermal expansion coefficient averaged from 1981 to 2000 is 1.1% smaller than observed in ESM2G and 6.6% larger than observed in ESM2M. For RCP8.5, between 1870 and 2090 the volume-mean thermal expansion coefficient increases by about 2.8% in both cases. When weighted by the models\u2019 temperature changes, the mean thermal expansion coefficients are 4% smaller than observed for ESM2G and 3.1% larger than observed for ESM2M for 1981\u20132000 and increase in the simulations by 10.4% and 11.0% between 1870 and 2090 for RCP8.5. The fact that the warming of the top 2000 m occurs, on average, some 40 m deeper in ESM2M than ESM2G (Fig. 4) also tends to give larger GSSLR in ESM2M than ESM2G, but only by about 0.5%, and it is a minor contributor to the GSSLR differences between the models. The simple fact that the thermal expansion coefficient is a strong function of temperature, and that the control state of ESM2M is warmer than ESM2G, accounts for a roughly 7% larger GSSLR in ESM2M than ESM2G.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hallberg13.html"}
{"id": "bccc98a2faca-3", "text": "Nonoceanic factors that might affect GSSLR, such as atmospheric feedbacks and differences in sea ice that have confounded previous attribution efforts (see Bindoff et al. 2007), do not contribute directly in this study, since those components are identical. However, surface differences in the spun-up mean state of the coupled models can lead to different responses in the atmosphere or sea ice. For instance, the global-mean SSTs in the ESM2G RCP2.6 simulation cool substantially in the latter half of the twenty-first century (Fig. 3, top), tracking the decline in the radiative forcing of RCP2.6, as high-latitude haloclines form in both the Northern and Southern Hemispheres and the sea ice expands. These ice-covered haloclines locally limit the otherwise large ocean heat loss, and the ocean\u2019s warming (Fig. 3, bottom) is not greatly slowed by this global-mean near-surface cooling, even as the lower-latitude surface cooling slows the uptake of heat by warmer waters and sea level rise slows (Fig. 2). Other scenarios exhibit somewhat similar behavior, although they figure less prominently in the differences between the two models\u2019 projections of GSSLR than in RCP2.6.\nThe RCP8.5 simulations are particularly intriguing, in that the sea surface temperature anomalies exhibit strikingly similar histories throughout the twenty-first century (Fig. 3, top), and by the end of the twenty-first century, summertime sea ice is too limited to do much in either model, but there are still 9% differences in integrated heat uptake (Fig. 3) and 18% differences in GSSLR (Fig. 2). In the near-surface waters (an average from 0 to 400 m is shown in Figs. 5a,b), which dominate the GSSLR signals, both models exhibit temperature changes that are remarkably similar both in magnitude (ESM2M warms just 4% more than ESM2G) and in their spatial patterns. These near-surface temperature changes include both contributions that are directly forced by the uptake of heat from the atmosphere and internal redistributions of heat tied to circulation changes, such as the spinup of the Antarctic Circumpolar Current and the weakening of the Gulf Stream. Some of the heating differences between the models may reflect a deeper rapidly ventilated thermocline in ESM2M than in ESM2G. The volume of water between 50\u00b0N and 50\u00b0S that is ventilated within 50 years (as measured by a passive \u201cideal age\u201d tracer) is roughly 20% larger in ESM2M than ESM2G (172-m versus 141-m average thicknesses in 1981\u20132000). If the surface warming signal is partly acting as a Dirichlet boundary condition for the ocean\u2019s interior temperature, this greater volume of rapidly ventilated water would lead to a larger heat uptake and GSSLR. These relative differences in the volumes of ventilated water are similar to the differences in the volumes of water warmer that some temperatures appropriate to the thermocline (e.g., 12\u00b0C). Whether the differences in ventilation drive the differences in near-surface stratification (see Fig. 1) or whether it is the reverse is beyond the scope of this paper; certainly, there is a connection between them and with the amount of heat that the upper ocean can take up on time scales of decades. However, these near-surface heating differences are not the dominant driver of GSSLR differences in the RCP8.5 simulations.\nFigure 5: Temperature change for RCP8.5 averaged over the years 2081\u20132100, relative to 1861\u20131900 and corrected for long-term mean drifts, for (left) ESM2G and (right) ESM2M and averaged over the depth ranges of (a),(b) 0\u2013400 m and (c),(d) 800\u20131200 m. The horizontal-mean temperature changes are 1.59\u00b0, 1.66\u00b0, 0.56\u00b0, and 0.73\u00b0C in (a)\u2013(d), respectively. Between 0 and 400 m, the average warming is 4% larger in ESM2M than ESM2G, but between 800 and 1200 m, the average warming is 29% larger in ESM2M than ESM2G.\uf0c1\nAt a depth of 800\u20131200 m in the RCP8.5 scenario (Figs. 5c,d), the heat uptake is of profoundly different magnitude between the models (the temperature increase is 29% larger in ESM2M than ESM2G), but still with very similar patterns. This depth is chosen for greater scrutiny because there is a peak in the difference in SLR contributions from water-mass changes between the models at about 1000 m (Fig. 4, right). Both exhibit warming (and an increase in salinity) in the western Atlantic because of a slowdown of the Atlantic meridional overturning circulation with a somewhat stronger warming signal in ESM2M than ESM2G. The Pacific is comparable to the Atlantic in the integrated heat change difference between the models in the 800\u20131200-m depth range and actually dominates the horizontally averaged steric sea level rise difference because there is no compensating salinity signal. The North Pacific signal is too deep for any of the water involved to have been directly influenced by the surface heat flux anomalies; instead, it is due to circulation changes. The broad warming of the eastern Pacific in both models is consistent with a broad downward displacement of the isopycnals of approximately 100 m in both models. The cooling signals on the western side of the Pacific basin are consistent with a vertical contraction of the subtropical gyres as the overlying waters become more strongly stratified. The temperature signal at about 1000 m in the Pacific is much larger in ESM2M than ESM2G, primarily because the vertical temperature gradients at this depth are much larger in ESM2M than ESM2G (Fig. 1). These deep temperature signals, which make up a large portion of the overall GSSLR difference, illustrate the importance of the ocean\u2019s initial state in determining the details of its forced GSSLR signal.\nDiscussion and summary\uf0c1\nThis study examines the differences between the GSSLR projected by two earth system models, which differ only in their ocean components, in order to estimate the uncertainties in twenty-first-century GSSLR projections arising solely from uncertainties in the numerical representation of ocean dynamics and parameterizations of physical processes in the ocean. The interior ocean\u2013mean states of these two models have water-mass biases that broadly straddle the observed properties of the ocean, and their ocean components might be considered cutting-edge geopotential- and isopycnal-coordinate ocean climate models. ESM2G exhibits twenty-first-century GSSLR that is consistently 18% smaller than in ESM2M for all four radiative forcing scenarios. Differences in the amount of heat taken up by the two models would account for a 9% difference in GSSLR, while differences in the thermal expansion coefficient due to different control states would account for a 7% difference. While these differences are highly statistically significant, they are also small enough to suggest that uncertainties in the ocean do not qualitatively alter the expected magnitude of twenty-first-century GSSLR.\nThere are two significant caveats to the findings reported here. The first is that since neither of these models explicitly resolves ocean eddies, the role of ocean eddies in rectifying distributions of ocean heat uptake (e.g., B\u00f6ning et al. 2008), and thus modulating GSSLR, is a source of uncertainty that cannot be addressed here. The second caveat is that these results only apply to the time scales out to 2100. For longer-term projections, the abyssal and deep-ocean responses are much more important. Given the very large differences in the abyssal circulation between the models, which can be detected in the models\u2019 very different ideal age distributions (see Fig. 13 of Dunne et al. 2012) and lead to the models\u2019 dramatically different abyssal temperatures (Fig. 1, left), the two models studied here can be expected to have quite different magnitudes of GSSLR for time scales of multiple centuries to millennia. For instance, the differences in the spun-up temperature profiles between the models (Fig. 1), which accumulated over the course of spin-up runs of over a thousand years, would cause steric sea level differences between the models of approximately 0.6 m, relative to the models\u2019 identical pre-spin-up initial conditions.\nThe regions where the GSSLR differences appear are also regions where models have profoundly different interior ocean biases. This observation suggests that accurately capturing the ocean\u2019s mean state, especially the stratification (which regulates how circulation changes translate into density changes), the thermocline depth (which appears to partially control the volume of water over which heat is taken up in the twenty-first century), and the mean temperatures (which substantially impact the thermal expansion coefficient) are useful steps toward reducing uncertainties in projections of twenty-first-century sea level rise. To the extent that the uncertainties in projected rise and biases in the spun-up state of the ocean have striking similarities and may have similar causes, or that the biases in the spun-up state directly affect projections of GSSLR, the utility of coupled climate models to accurately predict GSSLR might be appraised by evaluating simulated interior ocean temperature and stratification biases.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hallberg13.html"}
{"id": "bccc98a2faca-4", "text": "There are two significant caveats to the findings reported here. The first is that since neither of these models explicitly resolves ocean eddies, the role of ocean eddies in rectifying distributions of ocean heat uptake (e.g., B\u00f6ning et al. 2008), and thus modulating GSSLR, is a source of uncertainty that cannot be addressed here. The second caveat is that these results only apply to the time scales out to 2100. For longer-term projections, the abyssal and deep-ocean responses are much more important. Given the very large differences in the abyssal circulation between the models, which can be detected in the models\u2019 very different ideal age distributions (see Fig. 13 of Dunne et al. 2012) and lead to the models\u2019 dramatically different abyssal temperatures (Fig. 1, left), the two models studied here can be expected to have quite different magnitudes of GSSLR for time scales of multiple centuries to millennia. For instance, the differences in the spun-up temperature profiles between the models (Fig. 1), which accumulated over the course of spin-up runs of over a thousand years, would cause steric sea level differences between the models of approximately 0.6 m, relative to the models\u2019 identical pre-spin-up initial conditions.\nThe regions where the GSSLR differences appear are also regions where models have profoundly different interior ocean biases. This observation suggests that accurately capturing the ocean\u2019s mean state, especially the stratification (which regulates how circulation changes translate into density changes), the thermocline depth (which appears to partially control the volume of water over which heat is taken up in the twenty-first century), and the mean temperatures (which substantially impact the thermal expansion coefficient) are useful steps toward reducing uncertainties in projections of twenty-first-century sea level rise. To the extent that the uncertainties in projected rise and biases in the spun-up state of the ocean have striking similarities and may have similar causes, or that the biases in the spun-up state directly affect projections of GSSLR, the utility of coupled climate models to accurately predict GSSLR might be appraised by evaluating simulated interior ocean temperature and stratification biases.\nThe fact that it is the lower thermocline that dominates the GSSLR differences between the models, and not the upper main thermocline that dominates GSSLR itself, suggests that differences in the processes that set and alter the interior ocean water-mass properties in these density ranges may largely explain the differences between these two models. Formation of mode waters and intermediate waters are problematic for many of the coupled models that are included in CMIP5 (e.g., Downes et al. 2011) and are a focus of ongoing development. The two models also represent very differently the overflows (e.g., Legg et al. 2006) that are an integral part of the ocean\u2019s overturning circulation and the formation of water masses that are found at this depth. Increasing diapycnal diffusion is well known to broaden the lower thermocline. Ilicak et al. (2012) diagnose that ESM2M has spurious (numerically induced) diapycnal mixing that is about a third of the size of the explicitly parameterized intended mixing, while that in ESM2G is only about an eighth as large. While this global diagnostic cannot say where this spurious mixing is occurring, it could help explain both the greater breadth of the main thermocline and the deeper penetration of heat in ESM2M compared to ESM2G. Greater scrutiny of the models\u2019 representation of the processes that control the water-mass structure and location of the lower main thermocline might be of particular value for further reducing the oceanic uncertainty in projections of GSSLR.\nThe biggest uncertainties in projecting twenty-first-century sea level rise are in how much mass the Antarctic and Greenland ice sheets will lose dynamically. Twenty-first-century SLR due to ice sheet dynamics is unknown to within about 1 m of sea level rise (e.g., Pfeffer et al. 2008); while recent rates of observed ice sheet mass loss would only contribute approximately 130 \u00b1 40 mm in the twenty-first century, this increases to between 450 and 700 mm if observed accelerations in ice sheet mass loss continue (Rignot et al. 2011). A second major source of uncertainty is what radiative forcing scenario humans will collectively choose for our planet, here differing between the highest and lowest CMIP5 scenarios by about 125 mm of GSSLR by 2100. Uncetainties in the representation of the dynamics of the ocean and atmosphere and of key physical processes, such as clouds or small-scale ocean mixing, also map significantly onto uncertainties in projected GSSLR. The various coupled climate models used in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report give 5% and 95% estimates of twenty-first-century GSSLR that differ by \u00b142% from the mean for a given forcing scenario (Meehl et al. 2007), or a range of about 190 mm. Since these IPCC models are largely independent, this value is likely to be dominated by atmospheric differences, especially in changing cloud distributions, although ocean differences will also contribute. The comparison presented here suggests that the uncertainty in twenty-first-century steric sea level rise due only to the ocean model formulation and physical processes in the ocean is approximately 28\u201349 mm (depending on the forcing scenario).\nTo put these results into the long-term perspective, it is important to recognize that the uncertainties in twenty-first-century GSSLR arising from the ocean (of order 0.05 m) are small compared with the potential sea level rise stemming from interactions between the oceans and ice sheets (of order 1 m). While additional work to improve our ability to capture the physics and dynamics of the ocean in numerical models will be useful, and the role of ocean eddies in modulating GSSLR is largely unexplored, by far the most prominent open questions regarding the ocean\u2019s role in sea level rise center on the interactions between the oceans and ice sheets and how they will evolve in coming centuries.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hallberg13.html"}
{"id": "8e1a60b11d1e-0", "text": "Dangendorf et al. (2021)\uf0c1\nTitle:\nData-driven reconstruction reveals large-scale ocean circulation control on coastal sea level\nKey Points:\nRegional coastal sea levels are largely dominated by sterodynamic sea-level variations\nSteric sea level signals originate from open ocean regions often thousands of kilometers away\nBetter understanding of sterodynamic sea-level variations is key for robust near-term coastal sea-level estimates\nKeywords:\nsteric dynamic sea level, coastal sea level, tide gauge, Empirical Orthogonal Functions\nCorresponding author:\nDangendorf\nCitation:\nDangendorf, S., Frederikse, T., Chafik, L., Klinck, J. M., Ezer, T., & Hamlington, B. D. (2021). Data-driven reconstruction reveals large-scale ocean circulation control on coastal sea level. Nature Climate Change, 11(6), 514\u2013520. doi:10.1038/s41558-021-01046-1\nURL:\nhttps://www.nature.com/articles/s41558-021-01046-1\nAbstract\uf0c1\nUnderstanding historical and projected coastal sea-level change is limited because the impact of large-scale ocean dynamics is not well constrained. Here, we use a global set of tide-gauge records over nine regions to analyse the relationship between coastal sea-level variability and open-ocean steric height, related to density fluctuations. Interannual-to-decadal sea-level variability follows open-ocean steric height variations along many coastlines. We extract their common modes of variability and reconstruct coastal sterodynamic sea level, which is due to ocean density and circulation changes, based on steric height observations. Our reconstruction, tested in Earth system models, explains up to 91% of coastal sea-level variability. Combined with barystatic components related to ocean mass change and vertical land motion, the reconstruction also permits closure of the coastal sea-level budget since 1960. We find ocean circulation has dominated coastal sea-level budgets over the past six decades, reinforcing its importance in near-term predictions and coastal planning.\nIntroduction\uf0c1\nThe ability to predict and estimate future coastal sea-level changes depends on a thorough understanding of the observational record. Recent studies provide evidence that the global sea-level budget \u2014 the comparison of observed sea-level rise with the sum of individual contributions \u2014 can be reasonably closed with independent observations from remote sensing techniques and Argo floats since 2005 (refs. 1,2,3) but also with a combination of observations and reanalysis estimates since 1900 (ref. 4). This points to notable progress since the 2013 fifth assessment report of the Intergovernmental Panel on Climate Change [5]. The budget has also been closed regionally for larger areas off the coast since 2005 (refs. 6,7) and at basin scales since the 1950s [4,8]. However, at the coast, where information is most needed, budget assessments have higher uncertainty due to the number of additional processes that cancel out in the global mean. These include: changes in the sterodynamic component [9], due to ocean circulation change and steric (density-driven) expansion; gravitational, rotational and deformational effects accompanying global barystatic (ocean mass-driven) sea-level changes; and vertical land motion induced by glacial isostatic adjustment, tectonics or local subsidence.\nFor barystatic sea level and vertical land motion, a number of observations and model estimates now provide constraints at decadal [10] to century scales11. Specifically, the barystatic estimates due to ice-mass loss, terrestrial water storage and glacier melting and their representation at individual locations have considerably improved [4,8].\nHowever, the role of steric sea-level changes and their signature along shallow coastlines is still poorly understood [12,13]. The steric component, defined as the depth integral of density changes in the ocean, is the dominant driver of sea-level variability in the (deep) open ocean (Fig. 1a) with mostly minor contributions coming from ocean-bottom pressure14 (Fig. 1b). In contrast, at the coast where the ocean\u2019s depth decreases to zero, the resulting steric contribution vanishes as well (Fig. 1a). Thus, changes in ocean density will necessarily lead to larger expansion and contraction of the water column in the deep ocean than at the shallow coast15, driving a sea-surface height gradient between the two. This gradient needs to be balanced and hence forces changes in ocean-bottom pressure, with the latter becoming the dominant contributor to sea-level variability at the coast (Fig. 1b). However, due to a wide variety of ocean dynamic processes, coastal sea-level variability cannot be directly derived from steric sea-level changes in the nearby open ocean12,16,17 (Fig. 1c). Due to the lack of this direct relation between the open-ocean steric effects and coastal sea level, both the geographical origin and the underlying processes of the resulting coastal sterodynamic sea-level variations (hereafter SDSL) are poorly understood, inhibiting their proper quantification6,18. Particularly challenging in many coastal regions is the presence of strong boundary currents and coastally trapped waves that mediate open-ocean steric effects to the coast and introduce, due to their coast-parallel flow and propagation, substantial alongshore coherence in sea level often extending over thousands of kilometres17. Indeed, sea-level signals at the continental coasts often originate from perturbations at remote locations13,16, hindering the simple across-shelf integration of steric height from the nearby deep ocean as previously described by ref. 12. While global ocean reanalyses should provide a physically consistent solution for simulating coastal SDSL, they currently face challenges such as drifts and biases due to air\u2013sea fluxes and ocean mixing errors, coarse model resolution or the assimilation of observations that become sparse back in time19. As a consequence, they poorly reproduce observations at the coast20,21 (particularly spatial trends; Extended Data Fig. 1). These knowledge and modelling gaps about past SDSL changes are critical to resolve given that sea-level information is most needed at the coast. Together with the improved information about non-steric processes, these factors call for an alternative, and ideally data-driven, approach for estimating SDSL in the coastal zone.\nFig. 1: Relative roles of ocean-bottom pressure and steric components for coastal SDSL. a,b, Shown is the explained SDSL variance through steric height (a) and ocean-bottom pressure (b) in a historical ocean simulation with the CNRM-CM6-1-HR ESM. c, Schematic of the relationship between deep-ocean steric expansion and ocean-bottom pressure changes on the shallow shelf. The exchange is largely controlled by boundary currents and coastally trapped waves.\nHere, we reassess coastal sea-level changes in light of increasing data and knowledge of the non-steric contributions and by introducing a two-step statistical framework for estimating coastal SDSL changes. In the first step, we investigate the statistical link between coastal SDSL variability and open-ocean steric height to identify the source regions that communicate with the coast and discuss our current understanding of the physical processes that are involved. In a second step, we use this statistical link to reconstruct coastal SDSL solely on the basis of open-ocean steric height by applying a regression approach based on empirical orthogonal functions (EOFs). Finally, we use the reconstructed SDSL estimates to analyse the coastal sea-level budget for nine selected regions.\nIdentification of regions of common variability\uf0c1\nWe start by identifying the geographic source regions of coastal SDSL variability. We select 89 tide-gauge records spanning the period from 1960 to 2012 (the chosen period is constrained by the availability the different datasets; Methods), grouped into nine regions of coherent variability (North Sea, Northwest Atlantic north/south of Cape Hatteras, Northeast Pacific, Hawaii, Japan Sea, West Australia, New Zealand and Western Pacific) and shown in Fig. 2a and Extended Data Fig. 2. These records are first corrected for vertical land motion and barystatic sea-level components to isolate density-related SDSL signals (Methods). Then we follow the principal idea presented in refs. 22,23 for the North Sea and the Northwest Atlantic north of Cape Hatteras and correlate the tide-gauge residuals (hereafter SDSLTG) with steric height time series from improved (via mapping methods and correction schemes for instrumental biases) gridded temperature and salinity fields over the upper 2,000\u2009m (ref. 24) in the adjacent open ocean. A comparison with other steric products can be found in Methods. As source regions, we define all locations showing a significant correlation (P\u2009\u2264\u20090.05) with the corresponding regional mean of SDSLTG.", "source": "https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html"}
{"id": "8e1a60b11d1e-1", "text": "Here, we reassess coastal sea-level changes in light of increasing data and knowledge of the non-steric contributions and by introducing a two-step statistical framework for estimating coastal SDSL changes. In the first step, we investigate the statistical link between coastal SDSL variability and open-ocean steric height to identify the source regions that communicate with the coast and discuss our current understanding of the physical processes that are involved. In a second step, we use this statistical link to reconstruct coastal SDSL solely on the basis of open-ocean steric height by applying a regression approach based on empirical orthogonal functions (EOFs). Finally, we use the reconstructed SDSL estimates to analyse the coastal sea-level budget for nine selected regions.\nIdentification of regions of common variability\uf0c1\nWe start by identifying the geographic source regions of coastal SDSL variability. We select 89 tide-gauge records spanning the period from 1960 to 2012 (the chosen period is constrained by the availability the different datasets; Methods), grouped into nine regions of coherent variability (North Sea, Northwest Atlantic north/south of Cape Hatteras, Northeast Pacific, Hawaii, Japan Sea, West Australia, New Zealand and Western Pacific) and shown in Fig. 2a and Extended Data Fig. 2. These records are first corrected for vertical land motion and barystatic sea-level components to isolate density-related SDSL signals (Methods). Then we follow the principal idea presented in refs. 22,23 for the North Sea and the Northwest Atlantic north of Cape Hatteras and correlate the tide-gauge residuals (hereafter SDSLTG) with steric height time series from improved (via mapping methods and correction schemes for instrumental biases) gridded temperature and salinity fields over the upper 2,000\u2009m (ref. 24) in the adjacent open ocean. A comparison with other steric products can be found in Methods. As source regions, we define all locations showing a significant correlation (P\u2009\u2264\u20090.05) with the corresponding regional mean of SDSLTG.\nFig. 2: Origin and reconstruction of coastal SDSL changes. a, Spatial correlation patterns between the detrended SDSL residuals at tide gauges (SDSLTG, grey dots) and detrended steric height from the open ocean for nine coastal regions. Only significant correlations (P\u2009\u2264\u20090.05) are shown. Note that in some regions, correlation patterns of different regions may overlap. b, Illustration of the reconstruction of SDSLEOF in observations (top) and in validation experiments with ESMs (here illustrated by the CNRM-CM6-1-HR ESM, bottom) for the Northwest Atlantic south of Cape Hatteras. Shadings represent the 95% confidence intervals (CI) from all Monte-Carlo samples. c, Correlation and trend differences between reconstructed SDSLEOF and the a priori known SDSLTG in the validation experiments with 12 ESMs. Also shown is the correlation between SDSLEOF and SDSLTG in actual observations (orange dots). TG, tide gauge; NW, northwest; NE, northeast; NCH, north of Cape Hatteras; SCH, south of Cape Hatteras.\nFor all regions, significant correlations are widely spread over the oceans and often extend thousands of kilometres away from the tide-gauge sites (Fig. 2a globally and Extended Data Fig. 3 for expanded views into each region). Along eastern boundaries the correlation patterns range from the (sub)tropics to high latitudes with narrowing bands of high correlations along the continental slope moving poleward. In the Atlantic (Extended Data Fig. 3a), steric sea-level variations near the Strait of Gibraltar have recently been linked to both local wind forcing and Atlantic Meridional Overturning Circulation changes16,25, while further north along the Portuguese coastline, sea-level variability is tightly connected to longshore wind forcing13,26,27,28. The along-shelf coherence (Extended Data Fig. 3a) is consistent with the hypothesis that coastally trapped waves communicate SDSL variations from the eastern boundary into the North Sea16,17,28. A similar, but much more pronounced, correlation pattern can be found in the Northeast Pacific, where the largest correlations, r\u2009>\u20090.9, occur around the Equator and off the California coast (Extended Data Fig. 3d). This is consistent with ref. 29, who demonstrated that coastal sea levels along the Californian coastline vary in concert with fluctuations in equatorial trade winds and longshore winds generated around the Aleutian Low. Westerlies in the western and central Pacific generate equatorial Kelvin waves, which first propagate eastward along the Equator and then, after being reflected at the eastern boundary, travel northward as coastal Kelvin waves16,30.\nFor the western regions in the Atlantic and Pacific, correlations indicate a dynamic connection to the western boundary currents (Kuroshio and Gulf Stream), although with an interesting distinction in the Atlantic north and south of Cape Hatteras31 (Extended Data Fig. 3b,c). North of Cape Hatteras the correlation pattern follows the continental slope into the Labrador Sea and the Subpolar Gyre. This agrees with ref. 23, who provided evidence that Labrador Sea density anomalies (driven by both atmospheric processes in the upper layers and variations in the Deep Western Boundary Current at intermediate and deeper levels) propagate southward as coastally trapped waves32. South of Cape Hatteras, however, highest correlations are directly centred on the Gulf Stream pathway. This is consistent with the suggestion that coastal sea-level variability in this region is linked to a fast barotropic response of the coastal ocean to (overturning-related) large-scale heat divergence in the open ocean33,34 and/or subtle variations in the strength and position of the Gulf Stream35.\nIn the Indo-Pacific regions (West Australia and Western Pacific), coastal SDSL variations are highly coherent even between widely separated regions leading to overlapping correlation patterns extending from the Bay of Bengal into the Central Pacific (Extended Data Fig. 3g,i). These signals are linked to the El Ni\u00f1o/Southern Oscillation and primarily driven by equatorial trade winds36. These trade winds induce westward propagating equatorial Rossby waves, which first cross the Indonesian throughflow region and then travel poleward as coastally trapped waves along the west coast of Australia37,38. The coasts of New Zealand show coherence with the larger South Pacific Gyre region as well as the warm subtropical currents in the Tasman Sea extending onto the southwestern Australian continental shelves. Sasaki39 used an eddy-resolving ocean general circulation model to show that long baroclinic Rossby waves, forced by wind stress curl over the subtropical gyre, are an important driver of New Zealand\u2019s decadal sea-level variability. For gauges at Hawaii, a typical example of an open-ocean site surrounded by steeply sloping topography, highest correlations are pronounced locally northeast of the islands, indicating a more local control of coastal sea-level variations.\nIn summary, for all nine regions the identified correlation patterns are consistent with known processes induced by ocean dynamics (like wave guides and propagation characteristics) that have also been identified in basic ocean simulation experiments16. This underpins the physical nature of the statistical relationship and suggests that coastal SDSL changes are primarily remotely forced by perturbations in the open ocean and transferred to the coast (Fig. 1c) through the action of (coastally trapped) Kelvin and Rossby waves.\nReconstruction of SDSL at the coast\uf0c1\nThe large-scale coherence between coastal and open-ocean steric sea level indicates that a purely data-driven reconstruction of SDSL signals along the coast might be possible. Here, we apply an EOF regression approach40 to compute the covariance relationship between coastal SDSLTG and steric height from each source region over 1960 to 2012. This relationship is then used to analyse SDSLTG solely on the basis of steric height in the open ocean (hereafter, SDSLEOF; Methods). The EOF effectively filters the common signal and removes noise from both datasets. The regression character further allows for a scaling of the steric height, which becomes necessary if signals are either amplified (for example, due to resonance processes generated by winds) or damped (for example, due to bottom friction) when travelling towards the coast. We note, however, that the EOF does not consider any time lags, which might play a role if baroclinic Rossby waves with long travel times are involved in the transfer.", "source": "https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html"}
{"id": "8e1a60b11d1e-2", "text": "In summary, for all nine regions the identified correlation patterns are consistent with known processes induced by ocean dynamics (like wave guides and propagation characteristics) that have also been identified in basic ocean simulation experiments16. This underpins the physical nature of the statistical relationship and suggests that coastal SDSL changes are primarily remotely forced by perturbations in the open ocean and transferred to the coast (Fig. 1c) through the action of (coastally trapped) Kelvin and Rossby waves.\nReconstruction of SDSL at the coast\uf0c1\nThe large-scale coherence between coastal and open-ocean steric sea level indicates that a purely data-driven reconstruction of SDSL signals along the coast might be possible. Here, we apply an EOF regression approach40 to compute the covariance relationship between coastal SDSLTG and steric height from each source region over 1960 to 2012. This relationship is then used to analyse SDSLTG solely on the basis of steric height in the open ocean (hereafter, SDSLEOF; Methods). The EOF effectively filters the common signal and removes noise from both datasets. The regression character further allows for a scaling of the steric height, which becomes necessary if signals are either amplified (for example, due to resonance processes generated by winds) or damped (for example, due to bottom friction) when travelling towards the coast. We note, however, that the EOF does not consider any time lags, which might play a role if baroclinic Rossby waves with long travel times are involved in the transfer.\nTo test the robustness of the reconstruction against overfitting and to assess uncertainties, we use ocean simulations from 12 Earth system models (ESM) over the period 1850\u20132012 with historical forcing (Supplementary Table 2). In the ESMs coastal SDSL, open-ocean steric height and ocean-bottom pressure variations are a priori known and therefore form an ideal testbed for the EOF approach (using source regions similarly determined in each ESM as for the observational record; Methods). We extract in total 12,000 realizations of 53-yr periods to calibrate the reconstruction (with randomly varied model parameters; Methods) and use an independent, random 53-yr period (from the remaining model years) for validation. The resulting time series are displayed, as an example, for the Northwest Atlantic south of Cape Hatteras in Fig. 2b and for all regions in Extended Data Fig. 4. In all model runs, the EOF reconstruction mimics coastal SDSL variations reasonably well, which is reflected in significant correlation coefficients over all models and subsamples providing only subtle differences between calibration and validation periods (Fig. 2c). EOF reconstructions in tropical and subtropical coastal regions with known links to the El Ni\u00f1o/Southern Oscillation show slightly larger correlations (median r\u2009\u2265\u20090.86, P\u2009\u2264\u20090.05) than those at higher latitudes (for example, the Northwest Atlantic north of Cape Hatteras) or in large continental shelf seas (for example, the North Sea) (median r\u2009=\u20090.64\u20130.77, P\u2009\u2264\u20090.05). This is probably related to increased and atmospherically forced barotropic variability in these records, which might mask the remotely forced and density induced SDSL variations28,41,42. Similarly well reconstructed are linear trends in the ESMs (Fig. 2d). These usually agree with the model internal true coastal SDSL signal within a range \u00b10.7\u2009mm\u2009yr\u20131 in all subsamples and regions and show little evidence for systematic trend biases (median trend differences are of the order of \u00b10.06\u2009mm\u2009yr\u20131 over both calibration and validation periods) (Fig. 2d). Overall, this demonstrates the skill of the EOF approach in reconstructing coastal SDSL from open-ocean steric height and motivates its application to observations.\nThe SDSLEOF reconstructions based on open-ocean steric height observations from the source regions are again displayed, as an example, for the Northwest Atlantic south of Cape Hatteras in Fig. 2b and for all regions in Extended Data Fig. 4. We generated an ensemble of 5,000 SDSLEOF reconstructions at each site, which is based on varying barystatic sea-level corrections at tide-gauge records (Methods) and randomly varied parameter choices in the EOF approach (Methods). In agreement with the ESM experiments, the ensemble SDSLEOF reconstructions show significant median correlations to SDSLTG that range from r\u2009=\u20090.62 (P\u2009\u2264\u20090.05) in the Northwest Atlantic south of Cape Hatteras to r\u2009=\u20090.95 (P\u2009\u2264\u20090.05) in the Western Pacific (Fig. 2c). In the three regions that are directly influenced by western boundary currents (Northwest Atlantic south of Cape Hatteras, Japan Sea and New Zealand), SDSLEOF displays slightly lower (but still good) agreement with coastal residual sea level than in the other regions. This is probably related to the more complex dynamics involving mesoscale eddy activity and slowly propagating Rossby waves39,43,44 that are hard to capture in the EOF approach without any consideration of time lags. Such time lags seem to play a minor role in regions dominated by coastally trapped waves, which typically have travel times below a month from the source regions to the coasts26,30. Overall, the EOF reconstructions display an encouraging performance in transferring open-ocean steric height signals toward the coast that exceeds those from standard reanalysis products (Extended Data Fig. 1) and even holds for longer timescales as further discussed in the budget assessment below.\nImplications for the coastal sea-level budget\uf0c1\nTaking advantage of the improved representation of SDSL variability at the coast, we finally reassess the total coastal sea-level budget for each region by adding the barystatic component back to the reconstructed SDSL component and comparing it to the vertical land motion corrected coastal sea level in each region. This budget is displayed in Fig. 3 for linear (Fig. 3a,b and Table 1) and nonlinear trends (Fig. 3c) during 1960 to 2012. In all regions the trend budget can be closed within the respective uncertainties (Fig. 3b and Table 1) that are, particularly in Northern Europe and North America, dominated by vertical land motion (Fig. 3b). Median differences to observations are everywhere within a range \u00b10.2\u2009mm\u2009yr\u20131. The only exception is Hawaii, where the median trend is overestimated by 0.4\u2009mm\u2009yr\u20131. We note, however, that there are also substantial uncertainties in the underlying steric products (Extended Data Fig. 5 and Methods) that may account for these differences. At all locations, except Hawaii and the Japan Sea, SDSL components explain the major fraction of the total trend budget (Fig. 3a).\nFig. 3: Coastal sea-level budget over 1950 to 2012. a, Shown are (as pie diagrams for each region) the fractions of the coastal trend budget that are explained by SDSLEOF and barystatic components. b, The linear trend budget of coastal sea level for nine regions after correcting each tide gauge for glacial isostatic adjustment and residual vertical land motion. Blue bars represent regional averages, while the stacked blue/orange bars represent the budget estimated with SDSLEOF and barystatic sea level. c, The rates derived from a nonlinear trend for each component and region. All shadings and error bars represent 95% CI derived from the 5,000-member ensemble.\nTable 1 Linear trend budget. Linear trends for coastal sea level (corrected for vertical land motion), the total budget and each contributor over the period 1960 to 2012. All trends are given as a median of the 5,000-member ensemble with the 95% CIs provided in brackets. GRD, gravity, rotation and deformation. NW Atlantic NCH/SCH, Northwest Atlantic north/south of Cape Hatteras; NE Pacific, Northeast Pacific.\nRegion\nObservations\n(mm\u2009yr\u20131)\nBudget\n(mm\u2009yr\u20131)\nSDSLMEFOF\n(mm\u2009yr\u20131)\nBarystatic GRD\n(mm\u2009yr\u20131)\nNorth Sea\n2.01 (1.30;2.76)\n2.09 (1.58;2.52)\n1.73 (1.28;2.09)\n0.36 (0.17;0.56)\nNW Atlantic\nNCH\n1.43 (0.78;2.40)\n1.42 (1.02;1.87)\n0.76 (0.50;1.14)\n0.65 (0.39;0.87)\nNW Atlantic\nSCH\n1.40 (0.52;2.32)\n1.48 (1.12;1.80)\n0.76 (0.56;0.98)\n0.72 (0.42;0.97)\nNE Pacific\n1.23 (0.20;2.26)\n1.40 (0.97;1.80)\n1.02 (0.89;1.20)", "source": "https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html"}
{"id": "8e1a60b11d1e-3", "text": "Table 1 Linear trend budget. Linear trends for coastal sea level (corrected for vertical land motion), the total budget and each contributor over the period 1960 to 2012. All trends are given as a median of the 5,000-member ensemble with the 95% CIs provided in brackets. GRD, gravity, rotation and deformation. NW Atlantic NCH/SCH, Northwest Atlantic north/south of Cape Hatteras; NE Pacific, Northeast Pacific.\nRegion\nObservations\n(mm\u2009yr\u20131)\nBudget\n(mm\u2009yr\u20131)\nSDSLMEFOF\n(mm\u2009yr\u20131)\nBarystatic GRD\n(mm\u2009yr\u20131)\nNorth Sea\n2.01 (1.30;2.76)\n2.09 (1.58;2.52)\n1.73 (1.28;2.09)\n0.36 (0.17;0.56)\nNW Atlantic\nNCH\n1.43 (0.78;2.40)\n1.42 (1.02;1.87)\n0.76 (0.50;1.14)\n0.65 (0.39;0.87)\nNW Atlantic\nSCH\n1.40 (0.52;2.32)\n1.48 (1.12;1.80)\n0.76 (0.56;0.98)\n0.72 (0.42;0.97)\nNE Pacific\n1.23 (0.20;2.26)\n1.40 (0.97;1.80)\n1.02 (0.89;1.20)\n0.38 (\u20130.02;0.71)\nHawaii\n1.55 (1.24;1.89)\n1.18 (0.71;1.58)\n0.47 (0.27;0.67)\n0.71 (0.31;1.05)\nJapan Sea\n1.29 (0.89;1.75)\n1.13 (0.64;1.60)\n0.48 (0.12;0.81)\n0.65 (0.35;0.96)\nWest Australia\n1.48 (1.11;1.85)\n1.60 (1.10;2.04)\n0.89 (0.61;1.19)\n0.71 (0.34;1.03)\nNew Zealand\n1.74 (1.16;2.35)\n1.66 (1.12;2.11)\n0.99 (0.64;1.25)\n0.66 (0.32;0.99)\nThe budget terms also explain the observed interannual variability, which is expressed by an explained variance ranging from 38% at sites in the Northwest Atlantic south of Cape Hatteras to 91% along the Californian coast in the Northeast Pacific (Fig. 2c and Extended Data Fig. 4). The temporal variability is largely dominated by the SDSL component at all sites (Fig. 3c), although barystatic sea level through ice-mass loss and natural and anthropogenic terrestrial water storage variations (Methods) adds an accelerating signal to the rates. Largest accelerations in barystatic sea level are found around the Hawaiian Islands, where rates have been increasing from close to 0 to >2\u2009mm\u2009yr\u20131 since the late 1990s. However, in the total budget, this acceleration has been reversed by strong negative anomalies in the SDSL components since the early 2000s (Fig. 3c). In contrast, Northern European coastlines only exhibit a small barystatic sea-level signal with an average rate of 0.4 (0.2; 0.6)\u2009mm\u2009yr\u20131 over 1960 to 2012 but this is (despite the large uncertainties in different steric products) counterbalanced by the largest average SDSL rates of all sites (Fig. 3b). In the Northeast Pacific, SDSL shows the well-known sea-level suppression since the 1970s45, while at gauges in the Western Pacific and West Australia, SDSL is characterized by a sustained acceleration from close-to-zero rates before the 1980s to >14\u2009mm\u2009yr\u20131 in the 2010s (in an opposite direction to the negative SDSL rates at Hawaii); a value that is six times larger than the simultaneous barystatic sea-level rise. This acceleration has previously been attributed to anthropogenic forcing46 and represents the most pronounced SDSL sea-level change signal of all sites. Further accelerations in the SDSL terms can be seen in the Japan Sea and New Zealand since the early 1980s and along the coasts of Northeast America north of Cape Hatteras since the 1990s but their magnitudes are far smaller than those seen in the tropical Indo-Pacific regions and an attribution to natural and anthropogenic forcing has not yet been achieved.\nThe large site-specific rates also suggest substantial regional SDSL deviations from the simultaneous global mean (Fig. 4b) that are considerably larger than the spatial variations that have been contributed by barystatic sea level. Such deviations are important for coastal planning purposes, particularly at engineering-relevant timescales of a few decades. To generalize the potential of coastal SDSL variations to deviate from the global mean at varying timescales, we calculate moving trends for window sizes between 10 and 53\u2009yr for both coastal SDSL and global mean steric sea level and assess their respective ratio (Fig. 4). At decadal timescales (~10\u2009yr), local variations can be several hundred times larger or smaller than the global mean in any region considered here. This number decreases with increasing timescale but regional deviations can still be as large as ten, six and three times the simultaneous global mean for periods of 20, 30 and 50\u2009yr, respectively. Given the dominance of SDSL variations at these timescales (Fig. 3c), this indicates that the key to more robust near-term coastal sea-level estimates for the coming decades clearly lies in a better understanding of SDSL variations and their geographical origin.\nFig. 4: Scaling of local and global SDSL. a, The maximum ratio between coastal SDSLEOF and global mean steric sea level observed for different periods and each of the nine regions between 1960 and 2012. The ratios have been derived from moving trends calculated for window sizes ranging from 10 to 53\u2009yr. Three periods at 20, 30 and 50\u2009yr have been highlighted, demonstrating that SDSL can differ by up to ten, six and three times from the global mean. The tick black line highlights the factor 1 indicating variations of magnitude equal to the global mean. The corresponding SDSL time series, smoothed with a singular spectrum analysis using an embedding dimension of 10\u2009yr, are shown in b.\nOur results represent a notable advance in estimating drivers of regional coastal sea level over the past 53\u2009yr. Regardless of the accelerating barystatic sea-level terms around the globe, coastal sea-level variations are still largely dominated by the SDSL terms. This highlights the urgent need for a better understanding of the underlying physics to provide robust, near-term sea-level predictions. Our analysis represents a step in this direction as it demonstrates that for all analysed regions, coastal SDSL signals originate from the open ocean that are often thousands of kilometres away from individual sites. This reinforces the key role of large-scale ocean circulation in transferring the steric signal to the coast. The transfer can accurately be approximated using the EOF technique introduced here and allows for, together with the other components, improved closure of the coastal sea-level budget. Further modelling studies, such as those recently undertaken for the Northern European Shelf28,47, are required to clarify the involved oceanographic processes and to develop dynamical downscaling procedures that allow for more robust projections along the coast48.\nMethods\uf0c1\nTide-gauge data and corrections\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html"}
{"id": "8e1a60b11d1e-4", "text": "Fig. 4: Scaling of local and global SDSL. a, The maximum ratio between coastal SDSLEOF and global mean steric sea level observed for different periods and each of the nine regions between 1960 and 2012. The ratios have been derived from moving trends calculated for window sizes ranging from 10 to 53\u2009yr. Three periods at 20, 30 and 50\u2009yr have been highlighted, demonstrating that SDSL can differ by up to ten, six and three times from the global mean. The tick black line highlights the factor 1 indicating variations of magnitude equal to the global mean. The corresponding SDSL time series, smoothed with a singular spectrum analysis using an embedding dimension of 10\u2009yr, are shown in b.\nOur results represent a notable advance in estimating drivers of regional coastal sea level over the past 53\u2009yr. Regardless of the accelerating barystatic sea-level terms around the globe, coastal sea-level variations are still largely dominated by the SDSL terms. This highlights the urgent need for a better understanding of the underlying physics to provide robust, near-term sea-level predictions. Our analysis represents a step in this direction as it demonstrates that for all analysed regions, coastal SDSL signals originate from the open ocean that are often thousands of kilometres away from individual sites. This reinforces the key role of large-scale ocean circulation in transferring the steric signal to the coast. The transfer can accurately be approximated using the EOF technique introduced here and allows for, together with the other components, improved closure of the coastal sea-level budget. Further modelling studies, such as those recently undertaken for the Northern European Shelf28,47, are required to clarify the involved oceanographic processes and to develop dynamical downscaling procedures that allow for more robust projections along the coast48.\nMethods\uf0c1\nTide-gauge data and corrections\uf0c1\nWe make use of a set of 89 annual tide-gauge records from nine coastal regions taken from the online portal of the Permanent Service for Mean Sea Level in Liverpool49 and listed in Supplementary Table 1. The nine coastal regions have been selected on the basis of previous studies demonstrating that their tide-gauge records show similar dynamic sea-level variability4,21,25,29,36,39,43. In each region, individual records have been chosen on the basis of criteria such as data availability (>75%, except of a few exceptions primarily in the Indo-Pacific) and homogeneity (visual inspections and data flags). The individual records, together with their corresponding virtual stations and a cross-correlation matrix, are shown in Extended Data Fig. 2. Nine clusters of pronounced positive correlations appear, thus underpinning the coherence within each region. Existing data gaps have been filled with the local realizations from the hybrid sea-level reconstruction from ref. 50. The local realizations from the hybrid reconstruction include a local residual process from the Kalman Smoother that accounts for local effects such as vertical land motion (but does not contribute to the sea-level fields in the ocean and the corresponding global mean sea level) and therefore almost perfectly mimics their long-term trends50,51. They are also highly correlated with the real tide gauges (Supplementary Table 1). The gap-filling is a requirement for the EOF approach outlined below and avoids issues with benchmark differences when being merged to regional means52. We note, however, that the median percentage of data gaps is only 6% over all sites (Supplementary Table 1) and thus has a negligible influence on our results. Our major aim here is to investigate the SDSL variability in each of these regions. A challenge in this regard stems from the fact that tide-gauge records are affected by numerous different additional processes (vertical land motion and barystatic sea level) that may mask the actual SDSL signals. To isolate the SDSL variability at each site, we therefore initially remove vertical land motion and barystatic components. Each of these corrections comes with notable uncertainties. These uncertainties are considered here and build the basis for a probabilistic ensemble assessment with 5,000 members.\nThe first correction corresponds to vertical land motion, which primarily affects coastal sea level at lowest frequencies and induces spatially varying trends between individual locations. To correct for vertical land motion, we fit a linear trend to the differences between each tide-gauge record (before the gap-filling) and the nearest-neighbour time series from the hybrid reconstruction (that does not include the residual component and is corrected for its median glacial isostatic adjustment field) from ref. 50, which combines a process-based Kalman Smoother51 with ordinary EOF reconstructions53. As the Kalman Smoother aligns a series of predescribed processes (barystatic fingerprints, dynamic sea-level changes from climate models and 161 glacial isostatic adjustment models but excluding non-climatic local vertical land motion; ref. 51) to a global set of tide gauges, the difference between the hybrid reconstruction and tide gauges should, next to model errors, predominantly be driven by local vertical land motion51. The basic idea is similar to the Gaussian process approach used in ref. 54 for future projections and estimates based on the difference between tide-gauge records and satellite altimetry10 but it has the advantage of providing much longer residual series covering the entire length of tide-gauge records back to 1900 (that is, the period over which the hybrid reconstruction is available). As a preliminary cross-validation, we compare our estimates to the vertical land motion dataset from ref. 4. Their dataset is based on Global Navigation Satellite System observations and differences between tide gauges and nearby satellite altimetry but corrected for the nonlinear crustal components of present-day barystatic sea-level change and, therefore, is directly comparable to ours. The corrections are only available at 65 out of our 89 tide-gauge sites. Both datasets are significantly correlated (r\u2009=\u20090.78, P\u2009\u2264\u20090.05) with a root mean square difference of 0.8\u2009mm\u2009yr\u20131 (which is substantially smaller than that from satellite altimetry minus tide gauge (1.22\u2009mm\u2009yr\u20131); ref. 55) but vertical land motion estimates from the hybrid reconstruction show a higher correlation to linear trends from tide-gauge observations (r\u2009=\u20090.91, P\u2009\u2264\u20090.05) than those from ref. 4 (r\u2009=\u20090.67, P\u2009\u2264\u20090.05) (Extended Data Fig. 6). For this reason, as well as the fact that the hybrid reconstruction provides vertical land motion estimates at more stations than the ref. 4 dataset, we proceed with the hybrid reconstruction-based vertical land motion estimates. The largest uncertainty in the hybrid reconstruction-based vertical land motion estimates stems from the 161 glacial isostatic adjustment models used in the Kalman Smoother from ref. 53 that consider different solid-Earth parameters (lithosphere thickness and mantle viscosity) and varying global deglaciation histories over the past 20,000\u2009yr. The second uncertainty in the vertical land motion estimates is related to fitting of the linear trend to noisy data. This uncertainty has been modelled considering that the residuals are normally distributed but temporally correlated. To consider both uncertainties in the budget assessment, we perturb the vertical land motion estimates with random noise from the fitting uncertainty as well as the uncertainty from the 161 glacial isostatic adjustment models (considering their spatial correlation). This results in a 5,000-member ensemble of plausible vertical land motion corrections at each site.\nThe next components that we remove from the tide-gauge records are the barystatic terms due to contemporary mass redistribution. Here, we make use of a 5,000-member ensemble by ref. 4 that combines sea-level contributions from ice-sheet56,57,58,59,60, glacier11,61 and terrestrial water storage62,63,64,65 observations and reanalysis estimates and accounts for observational and model uncertainties. The barystatic effects have little effect on interannual variability of sea level but they are highly nonlinear and produce large spatial variability between individual locations (Fig. 3b). Removing the two 5,000-member ensembles of vertical land motion and barystatic sea level results in an ensemble of SDSLTG residuals including the uncertainties resulting from the initial corrections.", "source": "https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html"}
{"id": "8e1a60b11d1e-5", "text": "The next components that we remove from the tide-gauge records are the barystatic terms due to contemporary mass redistribution. Here, we make use of a 5,000-member ensemble by ref. 4 that combines sea-level contributions from ice-sheet56,57,58,59,60, glacier11,61 and terrestrial water storage62,63,64,65 observations and reanalysis estimates and accounts for observational and model uncertainties. The barystatic effects have little effect on interannual variability of sea level but they are highly nonlinear and produce large spatial variability between individual locations (Fig. 3b). Removing the two 5,000-member ensembles of vertical land motion and barystatic sea level results in an ensemble of SDSLTG residuals including the uncertainties resulting from the initial corrections.\nIn addition to vertical land motion and barystatic effects, tide-gauge records are also affected by the barotropic response of the ocean to atmospheric forcing. This consists of barotropic wind forcing and the inverted barometer response to sea-level pressure fluctuations over the oceans and represents a dominant fraction of the sea-level spectrum from intra-annual to decadal scales42. While the barotropic wind forcing term is usually considered as an inherent process of SDSL, it may introduce large variability of opposite sign at different locations27,28 and mask the actual SDSL variability seen by a tide gauge41. The latter may particularly be the case, when SDSL signals have, for instance, been initiated by wind forcing in remote regions affected by different atmospheric circulation systems than those responsible for the local barotropic signals. For this reason, we initially remove these wind and pressure effects from each tide-gauge record for the correlation and EOF analyses. Note, however, that we later add this component back to SDSL for the overall validation and the budget assessment. Thus, the SDSLEOF components shown in Figs. 1\u20133 in fact represent SDSL plus atmospheric pressure effects. As an estimate of these effects, we use the outputs from barotropic simulations with the MIT global circulation model forced with atmospheric reanalysis winds and sea-level pressure from the twentieth century reanalysis66 over the period 1871\u20132012. Further details on the model configuration and detailed validations can be found in refs. 21,42. The wind and pressure components are most important at higher latitudes, where stratification is weak, and they introduce both spatially varying temporal trends as well as pronounced intra-annual to decadal variability [42].\nSteric height data\uf0c1\nWe estimate steric changes from a gridded temperature24 and salinity reconstruction67 on the basis of hydrographic profiles covering the upper 2,000\u2009m of the ocean over the 1960 to 2012 period using the TEOS-10 GSW software for MATLAB68. This temperature and salinity reconstruction is based on an optimal interpolation approach, which uses the CMIP5 multimodel ensemble to derive correlation scales and to set the initial field. We note that there are many other gridded temperature and salinity datasets available that use different mapping methods than ref. 24. Three of these datasets have additionally been analysed here: ref. 69 and EN4 (EN4.2.1.)70 with two different mechanical bathythermograph (MBT) and expendable bathythermograph (XBT) bias corrections schemes following refs. 71,72. There are notable differences in linear trends calculated from each of the steric height datasets over 1960 to 2012 (Extended Data Fig. 5a\u2013d) that are particularly pronounced in areas of major ocean circulation systems (>2\u2009mm\u2009yr\u20131)73. These large differences between individual products may be partly related to the distinct mesoscale eddy activity that is not resolved by hydrographic observations as well as the different mapping approaches in each reconstruction24. They also feed in the SDSLEOF reconstruction (that essentially covers information from these circulation systems) when applied to each dataset individually (Extended Data Fig. 5e,f). However, the SDSLEOF reconstruction based on the ref. 24 dataset has the smallest trend differences to the SDSLTG in most regions (Extended Data Fig. 5) and also provides the best representation of variability (Extended Data Fig. 5f). It is interesting to note that regions with the largest interproduct trend spread also show the largest spread in correlations to SDSLTG with ref. 24 data providing far better agreement than all other products. For this reason, and since the dataset from ref. 24 has been shown to represent a methodological improvement over former reconstructions, we limit our analysis in the main paper to this particular dataset.\nEOF reconstruction\uf0c1\nThe EOF approach assumes that two or more sets of variables share a certain degree of similar variability, which can be expressed by distinct spatial patterns (EOF modes) for each individual variable (here, steric height from the open ocean and SDSLTG at the coast) and a common principal component (PC) corresponding to each spatial pattern. In the literature, similar approaches (but using canonical correlation analysis74 or cyclostationary EOFs40) have been used to reconstruct sparse/short climatic data (for example, precipitation) on the basis of covariates covering much longer periods than the variable of interest (for example, sea-level pressure or sea-surface temperature). Here, we use this approach to transfer steric height estimates from the source regions (identified with the correlation patterns in Fig. 2a) to the coast represented by the tide-gauge residuals after removing vertical land motion, barystatic sea level and (barotropic) wind and pressure effects (SDSLTG). This is done in three steps:\nWe calculate EOFs over the 1960\u20132012 period between detrended and smoothed (using a randomly chosen smoothing window between 3 and 5\u2009yr) steric height and SDSLTG. This produces several different modes with variable-specific spatial patterns and common PCs. In our reconstruction, we only use a subsample of these modes that share a certain degree of variance in each region. We randomly varied the corresponding threshold, such that only those modes are considered that cumulatively explain between 92 and 98% of the variance of the entire coupled field. On average, this resulted in the consideration of five (West Pacific) to nine (North Sea) modes in the different regions.\nThe spatial pattern of the steric height from the EOF analysis is then projected back onto the entire (1960\u20132012) non-detrended and non-smoothed steric height fields from the source region to produce a series of each PC.\nFinally, the PCs from step 2, now solely based on steric height from the open ocean, are projected onto the spatial patterns from tide-gauge residuals (SDSLTG), which produces an EOF-based SDSL reconstruction (SDSLEOF) over the entire 1960\u20132012 period at each site.\nThe SDSLEOF reconstructions are then evaluated as spatial averages over all sites in each region. By using varying barystatic corrections and by considering randomly varied parameter choices, we produce 5,000 ensemble members that are used to assess uncertainties of the EOF reconstruction. The EOF approach has two major advantages compared to simple field averages over the source region as formerly used in refs. 22,23 While a simple area average assumes that the steric signal from the open ocean is one on one transferred toward the coast, there are factors at play that may dampen or amplify the signal while propagating from the open ocean toward the coast. The regression character of the EOF approach explicitly takes this into account and scales the signal to match the variability seen at tide gauges. Furthermore, EOF analysis decomposes a field into common modes. As typical for many other atmospheric or oceanographic time series, most of the variance of the entire field is contained in the first few modes, while local effects move as noise into lower EOFs. Thus, the EOF approach is robust against local outliers. To test the stability of the EOF reconstruction against increasing data uncertainties in the steric products before the 1980s, we also calculated a second 5,000-member ensemble on the basis of PCs calculated since solely 1980 (Extended Data Fig. 7). We do not find any significant differences in the reconstructions based on PCs calculated over the entire period or only since 1980. Correlations are, in all cases, >0.98 with the only exception being the three western boundary currents where the correlation coefficients are between 0.92 and 0.94. The trends are also not significantly different between the two ensembles (Extended Data Fig. 7b).\nEarth system models\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html"}
{"id": "8e1a60b11d1e-6", "text": "The spatial pattern of the steric height from the EOF analysis is then projected back onto the entire (1960\u20132012) non-detrended and non-smoothed steric height fields from the source region to produce a series of each PC.\nFinally, the PCs from step 2, now solely based on steric height from the open ocean, are projected onto the spatial patterns from tide-gauge residuals (SDSLTG), which produces an EOF-based SDSL reconstruction (SDSLEOF) over the entire 1960\u20132012 period at each site.\nThe SDSLEOF reconstructions are then evaluated as spatial averages over all sites in each region. By using varying barystatic corrections and by considering randomly varied parameter choices, we produce 5,000 ensemble members that are used to assess uncertainties of the EOF reconstruction. The EOF approach has two major advantages compared to simple field averages over the source region as formerly used in refs. 22,23 While a simple area average assumes that the steric signal from the open ocean is one on one transferred toward the coast, there are factors at play that may dampen or amplify the signal while propagating from the open ocean toward the coast. The regression character of the EOF approach explicitly takes this into account and scales the signal to match the variability seen at tide gauges. Furthermore, EOF analysis decomposes a field into common modes. As typical for many other atmospheric or oceanographic time series, most of the variance of the entire field is contained in the first few modes, while local effects move as noise into lower EOFs. Thus, the EOF approach is robust against local outliers. To test the stability of the EOF reconstruction against increasing data uncertainties in the steric products before the 1980s, we also calculated a second 5,000-member ensemble on the basis of PCs calculated since solely 1980 (Extended Data Fig. 7). We do not find any significant differences in the reconstructions based on PCs calculated over the entire period or only since 1980. Correlations are, in all cases, >0.98 with the only exception being the three western boundary currents where the correlation coefficients are between 0.92 and 0.94. The trends are also not significantly different between the two ensembles (Extended Data Fig. 7b).\nEarth system models\uf0c1\nTo test the performance of the EOF technique, we apply it to the historical runs of 11 ESMs from the Coupled Model Intercomparison Project Phase 5 (CMIP5) [75], which are all listed in Supplementary Table 2. As CMIP5 models usually have a horizontal resolution that barely exceeds one degree, we additionally included one eddy-permitting model (CNRM-CM6-1-HR; ref. 76) from the HighResMIP initiative. CNRM-CM6-1-HR has a resolution of 25\u2009km, providing a more realistic representation of the coastal zone than its CMIP5 counterparts and many ocean reanalyses19. We decided to use ESMs rather than ocean reanalyses because the latter suffer from (regionally varying) drifts due to sparse data assimilation, uncertainties in air\u2013sea fluxes and mixing errors19, while ESMs are entirely consistent without data assimilation. All simulations have been linearly de-drifted using the pre-industrial control run (PiControl). ESMs have the advantage of providing predescribed components of the sea-surface height (\u2018zos\u2019), ocean-bottom pressure (\u2018pbl\u2019) and global mean thermosteric sea-level changes (\u2018zostoga\u2019). As the ESMs are volume- rather than mass-conserving, we sum zos and zostoga and subsequently subtract pbl to derive steric height from each model (one might also estimate steric height from temperature and salinity profiles in each model, which is, however, more time consuming). We sample coastal sea-level (zos\u2009+\u2009zostoga) at the grid points closest to the tide-gauge locations and perform a similar correlation analysis with steric height to identify the source regions. Then the EOF technique is applied in a similar fashion (with 1,000 randomly varied smoothing factors and mode-selection thresholds) as for observations. We compare the reconstruction to both the available 53-yr calibration periods as well as a randomly selected and independent validation period of 53 consecutive years that have not been used for calibration. There are three factors to keep in mind when using ESMs as a testbed for the EOF approach. First, the resolution of ESMs is, even in CNRM-CM6-1-HR, still too coarse to fully resolve coastal processes. Second, the model provides \u2018perfect observations\u2019 at each location without gaps and measurement errors. Third, we do not have corrections for barotropic wind forcing available for the ESMs as we apply for real observations. While the first two factors spatially smooth the observations and therefore tend to increase the covariance compared to real observations, the missing barotropic correction may lead to a slightly degraded performance in high latitude regions compared to reality.\nStatistics\uf0c1\nAll correlations and regressions were performed after removing linear trends. Statistical significance and error estimates for the correlation analyses are computed using Fisher\u2019s z-transform77. While the test does not account for temporal correlations in the data, it is much more time-efficient and leads to barely different source regions than with repeated simulations using autoregressive processes. Uncertainties of linear trends are calculated assuming that the residuals are temporally correlated following an autoregressive process of the order one. Nonlinear trends in the different budget components have been calculated by a singular spectrum analysis with an embedding dimension of ten using the MATLAB package from ref. 78.\nExtended data\uf0c1\nExtended Data Fig. 1: Performance of ocean reanalysis in simulating SDSL variability and trends. Shown are linear trends of SDSL as simulated by the a SODAsi.378, b SODA 2.2.480, c ORA S481, d ORA20C82,83, and e GECCO214 reanalysis over the common period from 1960 to 2012. For all reanalysis systems, the model internal global average has been replaced by ref. 24. In b and d, data is only available until 2008 and 2009, respectively. Grey dots show the 89 tide-gauge locations used in this study. f Linear trends in SDSLTG from the virtual stations of the nine coastal regions (grey bars) are compared to trends calculated from SDSL as simulated by the five ocean reanalysis systems (nearest-neighbour series). d, Correlations between detrended SDSLTG and SDSL from the five ocean reanalysis systems. The grey shadings separate the different regions from each other.\nExtended Data Fig. 2: Tide-gauge coherence and virtual stations for each region. a, Cross-Correlation matrix for the 89 tide-gauge records ordered by region. Black boxes mark the locations of the selected tide-gauge records for each region. b, The observed tide-gauge records (corrected for vertical land motion; coloured lines) together with the virtual station for each region (thick black line) that has been built based on gap-filled records (see Methods). The percentage of total data availability in each region is given in brackets.\nExtended Data Fig. 3: Origin of coastal SDSL changes. Spatial correlation patterns between the SDSL residuals at tide gauges (SDSLTG, grey dots) and steric height24 from the open ocean used to assemble Fig. 1a but for each of the nine coastal regions separately. Only significant correlations (P \u2264 0.05) are shown. a, North Sea, b NW Atlantic north of Cape Hatteras, c NW Atlantic south of Cape Hatteras, d NE Pacific, e Hawaii, f Japan Sea, g West Australia, h New Zealand, and i West Pacific.\nExtended Data Fig. 4: Reconstruction of coastal SDSL changes. Extension of Fig. 2b illustrating the reconstruction of SDSLEOF in observations (top) and in validation experiments with ESMs (here illustrated by the CNRM-CM6-1-HR, bottom) for each of the nine coastal regions. a, North Sea, b Northwest Atlantic north of Cape Hatteras, c Northwest Atlantic south of Cape Hatteras, d Northeast Pacific, e Hawaii, f Japan Sea, g West Australia, h New Zealand, and i West Pacific.\nExtended Data Fig. 5: Linear trends in steric height and comparison of different observational products. Shown are the linear trends in steric height calculated over the upper 2000m for different gridded observational products. a, ref. 24 and 67, b ref. 68, c EN469 with ref. 70 corrections, and d EN4 with ref. 71 corrections. The grey dots mark the locations of tide-gauge records used in this study. e, Linear trends for the SDSLEOF reconstructions in each region using the four different data products (grey bars = ref. 24 and67; blue = ref. 68; turquoise = EN469 with ref. 70 corrections; yellow = EN469 with ref. 71 corrections. f, Same as e but showing the correlation between SDSLEOF based on the different products and SDSLTG.", "source": "https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html"}
{"id": "8e1a60b11d1e-7", "text": "Extended Data Fig. 3: Origin of coastal SDSL changes. Spatial correlation patterns between the SDSL residuals at tide gauges (SDSLTG, grey dots) and steric height24 from the open ocean used to assemble Fig. 1a but for each of the nine coastal regions separately. Only significant correlations (P \u2264 0.05) are shown. a, North Sea, b NW Atlantic north of Cape Hatteras, c NW Atlantic south of Cape Hatteras, d NE Pacific, e Hawaii, f Japan Sea, g West Australia, h New Zealand, and i West Pacific.\nExtended Data Fig. 4: Reconstruction of coastal SDSL changes. Extension of Fig. 2b illustrating the reconstruction of SDSLEOF in observations (top) and in validation experiments with ESMs (here illustrated by the CNRM-CM6-1-HR, bottom) for each of the nine coastal regions. a, North Sea, b Northwest Atlantic north of Cape Hatteras, c Northwest Atlantic south of Cape Hatteras, d Northeast Pacific, e Hawaii, f Japan Sea, g West Australia, h New Zealand, and i West Pacific.\nExtended Data Fig. 5: Linear trends in steric height and comparison of different observational products. Shown are the linear trends in steric height calculated over the upper 2000m for different gridded observational products. a, ref. 24 and 67, b ref. 68, c EN469 with ref. 70 corrections, and d EN4 with ref. 71 corrections. The grey dots mark the locations of tide-gauge records used in this study. e, Linear trends for the SDSLEOF reconstructions in each region using the four different data products (grey bars = ref. 24 and67; blue = ref. 68; turquoise = EN469 with ref. 70 corrections; yellow = EN469 with ref. 71 corrections. f, Same as e but showing the correlation between SDSLEOF based on the different products and SDSLTG.\nExtended Data Fig. 6: Validation of the vertical land motion (VLM) correction. Comparison between observed trends (after the removal of barystatic gravitation, rotation and deformation terms) and residual VLM plus Glacial Isostatic Adjustment from the difference between tide gauges and the hybrid reconstruction from ref. 50 as well as the observed trends and residual VLM from Global Navigation Satellite System plus Glacial Isostatic Adjustment and the difference between tide-gauge and satellite altimetry as calculated by ref. 4 (Fred).\nExtended Data Fig. 7: Validation of the EOF approach. a, Shown are the time series of SDSLEOF based on reconstructions using principal components that have been calculated and regressed on the steric height from the open-ocean over the entire 1960 to 2012 period (and as used in the main paper) as well as those based on principal components that have been calculated (and regressed on the steric height from the open-ocean) over the period from 1980\u20132012. The grey shading marks the corresponding validation period from 1960\u20131979. b, The corresponding linear trends of SDSLEOF over the common period from 1960\u20132012. Shadings and error bars represent the 95% confidence intervals.", "source": "https://sealeveldocs.readthedocs.io/en/latest/dangendorf21.html"}
{"id": "9435f63cacce-0", "text": "Chen and Tung (2018)\uf0c1\nTitle:\nGlobal surface warming enhanced by weak Atlantic overturning circulation\nKey Points:\nThe role of AMOC has shifted its primary role from transporting surface heat northwards to storing heat in the deeper Atlantic, thereby buffering global surface warming.\nDuring an accelerating phase from the mid-1990s to the early 2000s, the AMOC stored about half of the global excess heat, contributing to a slowdown in global warming.\nChanges in the AMOC since the 1940s are best explained by multidecadal variability, rather than a trend forced by human activities.\nRecently, the AMOC and oceanic heat uptake have weakened, suggesting a period of rapid global surface warming.\nKeywords:\nAtlantic meridional overturning circulation, Global surface warming, Ocean heat storage, Multidecadal variability, Climate change, Oceanic heat uptake\nCorresponding author:\nKa-Kit Tung\nCitation:\nChen, X., & Tung, K.-K. (2018). Global surface warming enhanced by weak Atlantic overturning circulation. Nature, 559(7714), 1\u201314. doi:10.1038/s41586-018-0320-y\nURL:\nhttps://www.nature.com/articles/s41586-018-0320-y\nAbstract\uf0c1\nEvidence from palaeoclimatology suggests that abrupt Northern Hemisphere cold events are linked to weakening of the Atlantic Meridional Overturning Circulation (AMOC) [1], potentially by excess inputs of fresh water [2]. But these insights \u2014 often derived from model runs under preindustrial conditions \u2014 may not apply to the modern era with our rapid emissions of greenhouse gases. If they do, then a weakened AMOC, as in 1975\u20131998, should have led to Northern Hemisphere cooling. Here we show that, instead, the AMOC minimum was a period of rapid surface warming. More generally, in the presence of greenhouse-gas heating, the AMOC\u2019s dominant role changed from transporting surface heat northwards, warming Europe and North America, to storing heat in the deeper Atlantic, buffering surface warming for the planet as a whole. During an accelerating phase from the mid-1990s to the early 2000s, the AMOC stored about half of excess heat globally, contributing to the global-warming slowdown. By contrast, since mooring observations began [3,4,5] in 2004, the AMOC and oceanic heat uptake have weakened. Our results, based on several independent indices, show that AMOC changes since the 1940s are best explained by multidecadal variability [6], rather than an anthropogenically forced trend. Leading indicators in the subpolar North Atlantic today suggest that the current AMOC decline is ending. We expect a prolonged AMOC minimum, probably lasting about two decades. If prior patterns hold, the resulting low levels of oceanic heat uptake will manifest as a period of rapid global surface warming.\nMain\uf0c1\nAs an analogy of the flow of energy in our climate system, consider the filling of a bucket of water from a tap at the top. The feed rate of the tap is an analogue of the top-of-atmosphere radiative imbalance\u2014the net heating\u2014of our planet, with the water level in the bucket analogous to surface warming. The sink at the bucket bottom drains into a larger bucket below (the deeper oceans). If the drain rate is the same as the feed rate from the tap at the top, the water level in the bucket does not rise (hiatus of surface warming). If the drain is plugged, the water level will rise rapidly in the bucket (rapid surface warming). AMOC controls about half of the variation of this \u2018drain rate\u2019.\nFigure 1 quantifies the energy budget of our climate system, using the subsurface ocean heat content (OHC) measured mostly by a system of autonomous profiling Argo floats, during a period, 2000\u20132014, when the \u2018drain rate\u2019 was large. The total OHC, as approximated by that in the upper 1,500 m of the oceans, is increasing at a rate of about 0.42 \u00b1 0.02 W m\u22122, consistent with radiative imbalance7. The upper 200 m roughly corresponds to the mixed layer globally. Through wind and turbulent mixing, variations of sea surface temperature (SST) and mixed-layer OHC are highly statistically correlated (r\u2009=\u20090.82 in 13-month running mean). Figure 1 shows that both were in a warming slowdown for this period. Why the upper 200 m OHC was in a warming slowdown is clear: the increase in heat storage below 200 m, about 89 zettajoules (1 ZJ\u2009=\u20091021 J). This amount of heat is equivalent to 180 years of the world\u2019s energy consumption at the current rate, and any future variation even within this observed range will have important consequences for the surface temperature.\nFigure 1: Quantifying the global heat budget and the partition among ocean basins in the two periods 2000\u20132004 and 2005\u20132014. The SST from ERSST.v4 is shown as a black curve and the 0\u2212200-m OHC from the ISHII and Scripps datasets (see Methods) is shown as an orange curve, showing that they co-vary and that both are in a warming slowdown, while the total OHC, as approximated by the 0\u22121,500-m OHC (red curve), is increasing at the regressed linear rate of 0.42 W m\u22122 (red dashed straight line). This excess heat from forcing is sequestered below 200 m. The orange-shaded region represents the additional amount of heat stored in the 200\u22121,500 m layer since 2000, about 89 ZJ. One zettajoule is equivalent to twice the world\u2019s annual energy consumption. If this additional storage were absent, the upper 200 m would have increased at the rapid rate of the red curve. We adjusted the data for the Southern Ocean to remove a possible artefact due to the rapid transition from no-Argo to the Argo observing platform around 2002\u2212200328. The inset shows the division of the 89 ZJ of global ocean increase in heat storage in the 200\u22121,500 m layer into the four ocean basins and two periods. 35\u00b0 S marks the northern boundary of the Southern Ocean and the southern boundary of the Atlantic, Pacific and Indian oceans. The error bars are one-standard-deviation errors of the linear regression.\nIf the radiative imbalance and the heat storage below 200 m were to remain the same, the 0\u20131,500 m OHC would still increase at the same rate as the radiative imbalance, but the 0\u2013200 m OHC curve would lie on the 0\u20131,500 m curve, increasing at the same rate, or about 0.23 \u00b0C per decade. Our best estimate for the next two decades, allowing for some increase in ocean storage, is 70% of that rate, at 0.16 \u00b0C per decade (see Methods), close to the 25-year trend of 0.177 \u00b0C per decade of the last rapid warming period in the twentieth century [8].\nThe inset of Figure 1 shows how the global increase in OHC storage between 200 m and 1,500 m are partitioned among the various oceans. The Pacific and the Indian oceans dominate the horizontal exchanges of heat in the upper 300 m [9,10], and the Atlantic and the Southern oceans dominate the vertical redistribution11. They accounted for about 70% of the global heat storage increase in the 200\u20131,500 m layer during 2000\u20132014, divided between the North Atlantic, which is dominant before 2005, and the Southern Ocean after 2005. The subsurface warming in the Southern Ocean started in 1993 according to the data available (see below), and was attributed to the southward displacement and intensification of the circumpolar jet [8], caused in large part by the Antarctic ozone hole [12]. The North Atlantic\u2019s role appears to be cyclic on decadal timescales, with AMOC in an accelerating phase before 2005.\nAMOC transports warm saline surface water found in the subtropical Atlantic to the subpolar Atlantic, where heat loss to the cold atmosphere increases its density. Aided by its high salinity it sinks and returns southward at depth. When AMOC is stronger (weaker), more (less) of the warm and saline water is found in the subpolar Atlantic, and subsequent sinking subducts more (less) heat there, as demonstrated in Figure 2. The contrast is dramatic between periods when AMOC is increasing and when it is decreasing. Why AMOC sometimes accelerates or declines is more complicated. It could be responding to external forcing, for example, such as the freshening of the subpolar waters from melting ice at the end of the Little Ice Age [13]. Or, AMOC could be part of a natural, multidecadal variability involving feedbacks between the density effect of salinity on deep convection in Labrador and the Nordic Seas, and the subsequent induced northward transport of surface salinity reinforcing the deep convection [14].", "source": "https://sealeveldocs.readthedocs.io/en/latest/chentung18.html"}
{"id": "9435f63cacce-1", "text": "The inset of Figure 1 shows how the global increase in OHC storage between 200 m and 1,500 m are partitioned among the various oceans. The Pacific and the Indian oceans dominate the horizontal exchanges of heat in the upper 300 m [9,10], and the Atlantic and the Southern oceans dominate the vertical redistribution11. They accounted for about 70% of the global heat storage increase in the 200\u20131,500 m layer during 2000\u20132014, divided between the North Atlantic, which is dominant before 2005, and the Southern Ocean after 2005. The subsurface warming in the Southern Ocean started in 1993 according to the data available (see below), and was attributed to the southward displacement and intensification of the circumpolar jet [8], caused in large part by the Antarctic ozone hole [12]. The North Atlantic\u2019s role appears to be cyclic on decadal timescales, with AMOC in an accelerating phase before 2005.\nAMOC transports warm saline surface water found in the subtropical Atlantic to the subpolar Atlantic, where heat loss to the cold atmosphere increases its density. Aided by its high salinity it sinks and returns southward at depth. When AMOC is stronger (weaker), more (less) of the warm and saline water is found in the subpolar Atlantic, and subsequent sinking subducts more (less) heat there, as demonstrated in Figure 2. The contrast is dramatic between periods when AMOC is increasing and when it is decreasing. Why AMOC sometimes accelerates or declines is more complicated. It could be responding to external forcing, for example, such as the freshening of the subpolar waters from melting ice at the end of the Little Ice Age [13]. Or, AMOC could be part of a natural, multidecadal variability involving feedbacks between the density effect of salinity on deep convection in Labrador and the Nordic Seas, and the subsequent induced northward transport of surface salinity reinforcing the deep convection [14].\nFig. 2: The OHC linear trend in the Atlantic basin. The trend is zonally averaged over two periods, when AMOC is increasing (a) and decreasing (b). The two periods are chosen according to the observed AMOC trends in Fig. 3a. ISHII data are used in the first period and Scripps data are used in the second period. Stippling indicates areas of statistical significance at the 95% confidence level. The linear trend is unreliable in the Southern Ocean prior to 2005, and so that region is masked.\nAMOC is commonly believed to be slowing on centennial timescales owing to global warming. The RAPID/MOCHA mooring array, deployed in 20043 off the coast of Florida to monitor AMOC, soon afterwards recorded its weakening4. The decadal decline, however, is ten times larger than the predicted forced response5, causing concerns about its long-term trend and possible deficiencies of the models used. Figure 3a, constructed from various independent proxies from 1945 to the present (see Extended Data Fig. 1 for unfiltered time series and Extended Data Fig. 2 for error bars), shows that it is dominated instead by reversing phases. The weakening AMOC, by 3.7 Sverdrups (Sv) since 2005 measured by the RAPID/MOCHA array, was actually preceded by an acceleration15,16. Altimetry data of sea-surface heights (SSH) available since 199317 were used to deduce18 via geostrophic balance that at 41\u00b0 N AMOC sped up by 4 Sv from the early 1990s to 2005, consistent with Zhang\u2019s subsurface fingerprint proxy6. We use multiple independent proxies to infer subpolar AMOC strength back in time to 1945. Many of the proxies used here have been validated by models: Zhang\u2019s subsurface temperature fingerprint was highly coherent with AMOC strength6,19,20 at low frequencies in the model (GFDL CM2.1) at mid-latitudes. The subpolar gyre SST proxy21, and the upper ocean subpolar salinity proxy20 were also model-validated. Along with the long record of tide gauges along the east coast of the USA22, these proxies consistently indicate a period of low AMOC from the mid-1970s to the 1990s. The shading in Fig. 3 shows that this period coincided with a period of rapid surface warming. See also Extended Data Fig. 3 for the coincidence of Atlantic OHC change and global surface warming. See Methods for model\u2013observation reconciliation.\nFigure 3: AMOC and GSTA variations. a, Mid and subpolar latitude AMOC strength, as calculated at 41\u00b0 N using altimetry measurements, from ref. 18 (red, two-year running mean, Sverdrup scale shown on the right); inferred from integrated subpolar salinity in 0\u20131,500 m and 45\u201365\u00b0 N in the Atlantic as a proxy, using the ISHII (dark blue) and Scripps (purple) datasets, with a two-year running mean. The green curve is the subpolar salinity, similarly calculated but using EN4. The AMOC fingerprint6 (dark blue) and the accumulated sea-level index (turquoise) calculated from historical tide gauge measurements22 were smoothed with 10-year and 7-year low-pass filters, respectively, from their sources. The subpolar gyre SST index21 in orange is also a two-year running mean. See Methods for details. The inset shows RAPID-measured AMOC at 26\u00b0 N. b, Shown are GSTA from HadCRUT4.6 (black), the nonlinear secular trend (close to the 100-year linear trend) (brown) and variation about the trend for timescales longer than decadal (multidecadal variability (MDV), red). The inset shows the SST spatial pattern associated with MDV obtained by regressing SST onto its time series. The blue curve is the smoothed version of GSTA obtained as the sum of the secular trend and MDV. The faint lines around the solid lines are from 100 ensemble members of the HadCRUT4.6, which assess the range of uncertainty of the data used in the solid lines.\nWe call AMOC+ (AMOC\u2013) the phase when the AMOC strength is above (below) climatology (based on the subpolar salinity, which has a long record with no trend). The high (+) phase consists of two rapid subphases. The increasing subphase (AMOCup) started in 1993, from the low point in AMOC\u2013, first slowly and then rapidly, peaking in 2005. It is then followed by a rapid decreasing subphase (AMOCdown) (2005 to the present) (Fig. 3a). At low values of overturning (AMOC\u2013) the strength is relatively level even though there are short-term fluctuations, because a slower poleward transport of saline water from the tropical Atlantic makes it difficult to speed up the sinking in the subpolar North Atlantic except through slower processes: The surface water could slowly become more saline through the reduction of fresh water outflow from land glaciers and from the Arctic Ocean23. The northward transport of warm and saline water increased more rapidly since 1999, and started a negative feedback as the warm surface water increased glacier melt and freshwater outflow. The previous AMOCdown subphase of 1965\u20131974 started with the gradual freshening of the north Atlantic waters, as can be inferred from the decreasing salinity in the subpolar region, braking the AMOC. Incidentally, both SSH at 41\u00b0 N and RAPID at 26\u00b0 N showed a simultaneous, short-lived 30% drop in AMOC strength in 2009\u201320105, partially caused by an extreme negative episode of atmospheric North Atlantic Oscillation that affected the wind field5 over both areas.\nWater masses in the subpolar and subtropical gyres are different and transports across gyre boundaries need not be continuous14. For vertical heat subduction, it is mainly the subpolar AMOC that is our focus in Fig. 3a. Signals from salinity proxies at the subpolar Atlantic have almost reached the previous low. The subpolar gyre SST has started to warm. The deep Labrador Sea density, which is known to lead by 7\u201310 years changes in wider basin AMOC15,16, has stopped declining since 2014 (Extended Data Fig. 4). The subtropical region is more prone to higher-frequency perturbations14, and the RAPID time series is experiencing its short-term oscillations (two so far) after the recovery from the large dip in 2010 so the decadal trend may be difficult to see. Nevertheless, it appears to have stabilized at that latitude. Previously, when AMOC reached its lowest AMOC\u2013 value after 1975, that level phase lasted two and a half decades. Although we have data only for one cycle, its observed non-sinusoidal pattern characterized by a prolonged flat minimum separated by steep peaks is as expected from the physical arguments presented above.", "source": "https://sealeveldocs.readthedocs.io/en/latest/chentung18.html"}
{"id": "9435f63cacce-2", "text": "Water masses in the subpolar and subtropical gyres are different and transports across gyre boundaries need not be continuous14. For vertical heat subduction, it is mainly the subpolar AMOC that is our focus in Fig. 3a. Signals from salinity proxies at the subpolar Atlantic have almost reached the previous low. The subpolar gyre SST has started to warm. The deep Labrador Sea density, which is known to lead by 7\u201310 years changes in wider basin AMOC15,16, has stopped declining since 2014 (Extended Data Fig. 4). The subtropical region is more prone to higher-frequency perturbations14, and the RAPID time series is experiencing its short-term oscillations (two so far) after the recovery from the large dip in 2010 so the decadal trend may be difficult to see. Nevertheless, it appears to have stabilized at that latitude. Previously, when AMOC reached its lowest AMOC\u2013 value after 1975, that level phase lasted two and a half decades. Although we have data only for one cycle, its observed non-sinusoidal pattern characterized by a prolonged flat minimum separated by steep peaks is as expected from the physical arguments presented above.\nThe longer Global-mean Surface Temperature Anomaly (GSTA) record shown in Fig. 3b, together with its low-frequency variation24,25, consists of a secular trend and a multidecadal variability (MDV), defined to be on timescales that are decadal or longer. The spatial pattern associated with MDV (inset to Fig. 3b) has the pattern of an interhemispheric seesaw in the Atlantic, with the North Atlantic being the centre of action, consistent with model results26. When the MDV is increasing it doubles the GSTA warming rate over the 100-year trend of 0.08 K per decade, and is associated with a period of rapid warming in the late and also the early twentieth century. That secular trend of 0.08 K per decade, statistically significant at over 95% confidence level against a second-order autoregressive (AR(2)) red noise, has been attributed to the underlying anthropogenic global warming trend27. The regressed spatial pattern associated with the secular trend resembles the model-predicted response from greenhouse warming24,25. The MDV in the GSTA is related to the Atlantic Multidecadal Oscillation (AMO) (see Methods), the latter having a record extending back several hundred years.\nThe previous period of low overturning in the AMOC\u2212 phase, from 1975 to the 1990s, coincided with a period of rapid global warming at the surface. This is more than a coincidence because the energy budget involved can be quantified. We do not have reliable subsurface data for the period when the surface warming was rapid. However, the change from that period can be quantified so that an estimate can be made for what would happen if that change were absent. During 2000\u20132005, in the AMOCup subphase, 52% of the global increase between 200 m and 1,500 m is sequestered in the Atlantic. Together with the heat sequestrated in the Southern Ocean, it contributed to a period of global warming slowdown. When this additional heat storage is absent, a period of rapid surface warming is expected to reoccur.\nAlthough the Argo programme was launched around 2000, its coverage in the Southern Ocean did not become adequate until 2005. To validate the data on OHC we compare satellite SSH* (the asterisk indicates the deviation of SSH from its global mean) available since 1993 (Fig. 4a and b) to the thermosteric sea level rise (due to thermal expansion of the water column) (Fig. 4c and d) calculated using OHC above 1,500 m. The comparison is surprisingly good north of 35\u00b0 S. Notable exceptions are as expected; they include areas with no Argo measurements: shallow maritime areas west of the Caribbean islands, and the deep mid-Atlantic Ocean below 1,500 m, which was not included in our OHC. South of 35\u00b0 S the linear trend in the Argo data is not reliable across 2003 during the transition from no-Argo to Argo measurements28. The two datasets consistently show that in the subpolar Atlantic there is increasing (decreasing) heat storage when AMOC is increasing (decreasing). The southward (northward) displacement of the Gulf Stream at mid-latitudes created some compensating cooling (warming)21. In the AMOC\u2019s rapidly decreasing subphase, some heat is entrained in the subtropical gyre. The Southern Hemisphere north of 35\u00b0 S is mostly featureless. South of 35\u00b0 S, mesoscale patterns of warming can be seen in SSH*, which is also reflected in the OHC after 2004, but not before, owing to data quality. These mesoscale eddies in the linear trend occurring south of the Antarctic Circumpolar Current may be due to its recent strengthening, and its increased baroclinic instability [29].\nFigure 4: Contrasting thermosteric SSH* patterns for increasing and decreasing AMOC. a, c, Linear SSH* trend when AMOC is increasing; b, d, Linear SSH* trend when AMOC is decreasing. a and b show SSH* from remote sensing, compared with the steric sea level calculated using OHC in c and d. SSH* is SSH with its global mean subtracted, reflecting mostly the thermosteric part of SSH (see Methods).\nThe increased sea level (Fig. 4b) and warmer SST (Extended Data Fig. 5d) in the western subtropical Atlantic may have led to strong hurricanes and their destructive power, and the surprising string of category-5 hurricanes making landfall towards the end of the decreasing phase of the AMOC, instead of at the peak of the AMOC, when the mean SST of the entire North Atlantic is the warmest and the basin-wide hurricane number is the highest30.\nClimate-model runs under preindustrial conditions demonstrated the existence of multidecadal variation in AMOC, and its associated Atlantic SST variation: the AMOC+ (AMOC\u2212) phase corresponds to warm (cold) SST and Northern Hemisphere mean surface temperature6,19. This prevailing paradigm has permeated popular perceptions about the future climate consequence of an AMOC weakened by global warming, similar to the abrupt switch back into icy conditions of the Younger Dryas during the last deglaciation2. Over the past few decades, however, there is a positive trend of warmer subsurface water in the subpolar Atlantic (Extended Data Fig. 6), rendering the mean state lighter (see the temperature\u2013salinity diagram in Extended Data Fig. 7). Deep convections can now carry more heat downward. In the presence of greenhouse heating from above and warmer SSTs, AMOC\u2019s role in sequestering heat becomes important in the current global surface energy budget (Fig. 1). When AMOC is more constant, as in the AMOC\u2212 phase, little additional heat is sequestered in the Atlantic, contributing to a more rapid surface warming as more heat from radiative imbalance remains on the surface and the upper 200 m of the global oceans. We note, however, that we have discussed here only one component of a complex system: global heat balance is maintained by the combined ocean and atmosphere systems and a change in the transport of one regional component may affect the partitioning of change between other parts of the ocean or of the atmosphere, depending on the timescales involved.\nMethods\uf0c1\nUpdated AMOC indices\uf0c1\nWe reproduced the unfiltered monthly AMOC indices (Extended Data Fig. 1). Their correlation coefficient with Zhang\u2019s unfiltered AMOC fingerprint is listed on the right. All correlations are statistically significant at over 95% confidence level.\nAMOC indices in Fig.3a\uf0c1\nExtended Data Fig. 1 shows that all unfiltered AMOC proxies used in Fig. 3a are correlated with Zhang\u2019s fingerprint AMOC proxy at over 95% confidence level. Zhang showed20 that in the Geophysical Fluid Dynamics Laboratory model the fingerprint proxy is highly coherent with the model AMOC Index, defined as the zonal integrated maximum Atlantic overturning at 40\u00b0 N, at decadal and multidecadal scales. This is the reason that the fingerprint is shown smoothed with a 10-year low-pass filter. This fingerprint is calculated using the detrended 400-m subsurface temperature. (It was updated to 2017 by the author with permission to use.)\nOur subpolar upper ocean salinity index is defined as the average over 45\u00b0\u201365\u00b0 N in the Atlantic basin and integrated over 0\u20131,500 m. The two undetrended salinity indices shown in Fig. 3 and Extended Data Fig. 1 are from three data sources. The first index is based on ISHII and Scripps. ISHII data have not been updated since 2012 and Scripps data are only available since 2004; they are connected at 2012 when calculating the correlation coefficient with Zhang\u2019s fingerprint AMOC proxy. The data source for the second salinity index is from EN4 (version 4.2.1).", "source": "https://sealeveldocs.readthedocs.io/en/latest/chentung18.html"}
{"id": "9435f63cacce-3", "text": "Methods\uf0c1\nUpdated AMOC indices\uf0c1\nWe reproduced the unfiltered monthly AMOC indices (Extended Data Fig. 1). Their correlation coefficient with Zhang\u2019s unfiltered AMOC fingerprint is listed on the right. All correlations are statistically significant at over 95% confidence level.\nAMOC indices in Fig.3a\uf0c1\nExtended Data Fig. 1 shows that all unfiltered AMOC proxies used in Fig. 3a are correlated with Zhang\u2019s fingerprint AMOC proxy at over 95% confidence level. Zhang showed20 that in the Geophysical Fluid Dynamics Laboratory model the fingerprint proxy is highly coherent with the model AMOC Index, defined as the zonal integrated maximum Atlantic overturning at 40\u00b0 N, at decadal and multidecadal scales. This is the reason that the fingerprint is shown smoothed with a 10-year low-pass filter. This fingerprint is calculated using the detrended 400-m subsurface temperature. (It was updated to 2017 by the author with permission to use.)\nOur subpolar upper ocean salinity index is defined as the average over 45\u00b0\u201365\u00b0 N in the Atlantic basin and integrated over 0\u20131,500 m. The two undetrended salinity indices shown in Fig. 3 and Extended Data Fig. 1 are from three data sources. The first index is based on ISHII and Scripps. ISHII data have not been updated since 2012 and Scripps data are only available since 2004; they are connected at 2012 when calculating the correlation coefficient with Zhang\u2019s fingerprint AMOC proxy. The data source for the second salinity index is from EN4 (version 4.2.1).\nThe sea-level index was obtained as in ref. 22 by calculating the sea-level difference between the average of a group of linearly detrended, deseasonalized tide-gauge measurements south of 35\u00b0 N and that to the north. It is accumulated in time, shifted to the right by 4.8 years and smoothed with a 7-year lowpass filter.\nThe subpolar gyre SST index was obtained by \u2018detrending\u2019 the subpolar gyre SST by the subtraction of the global mean SST. It is averaged over the subpolar gyre region, defined by ref. 21.\nWillis\u2019 AMOC strength at 41\u00b0 N was calculated [18] using altimetry SSH measurements and geostrophic approximation for the zonal-mean northward velocity vertically integrated above 1,130 m. It is not detrended or accumulated.\nError bars for data used in Fig. 3\uf0c1\nThe error bars for the salinity time series used in Fig. 3a are plotted in Extended Data Fig. 2. The uncertainty at each gridpoint is provided by each data source: ISHII, Scripps and EN4. The error bar of the salinity time series at each time is computed as the combination of the gridpoint uncertainty and one standard deviation due to the averaging in space. The uncertainty of the SSH-deduced AMOC strength was given by ref. 18. The measurement and sampling errors at each time gridpoint were \u00b112%. The uncertainty of tide-gauge data was discussed by ref. 22, and that of Zhang\u2019s fingerprint proxy by ref. 30. The uncertainty of the global surface temperature data from HadCRUT4.6 was assessed by the data source using 100 ensemble members that span the uncertainty range of the data.\nCalculation of warming scenarios\uf0c1\nWe emphasize that this is not a prediction, but a scenario calculation. In our current climate system, the OHC in the upper 1,500 m of the global oceans increases at the rate of 0.42 W m\u22122, which is approximately the top-of-atmosphere radiative imbalance. Apart from short-term variations of radiative imbalance such as those due to volcanic eruptions, it is reasonable to assume that for the next two decades there will not be an appreciable change in radiative imbalance, barring an unexpected development of carbon sequestration technology.\nScenario 1\uf0c1\nIf the OHC storage below 200 m remains the same (no increases), then the radiative imbalance of the 0.42 W m\u22122 heats only the top 200 m of the global oceans. That is, the increase of OHC in the top 200 m of the oceans is responsible for the increase in the entire 1,500 m of the column. The top 200 m of the global ocean then warms at the rate calculated as: 0.42 W m\u22122 divided by the heat capacity of 200 m of the ocean\u2009=\u20090.23 \u00b0C per decade. This is equivalent to that obtained for a \u2018slab\u2019 ocean of 200 m thick.\nScenario 2\uf0c1\nAs for Scenario 1 except that only the Atlantic and the Southern oceans\u2019 heat content below 200 m remain the same for the next two decades. The Pacific and the Indian oceans continue to increase their OHC at the current rate. The warming rate is 70% of that for Scenario 1 because at present the Atlantic and the Southern oceans together are responsible for 70% of the OHC increase in the upper 1,500 m of the oceans. This is probably the more likely scenario because we have argued in the main text that AMOC is likely to remain relatively constant during the next two decades. The subsurface Southern Ocean has been warming since at least 1993, caused by the southward displacement and intensification of the westerly jet, which cannot continue much longer, first because the proposed cause (the ozone hole) has diminished in importance as the ozone hole heals, and second because there is not much more room for the jet\u2019s southward displacement. So the increase in warming will probably stop.\nModel AMOC and reconciliation with recent observations\uf0c1\nObservational results in Fig. 3a show that there was a positive trend from 1993 to 1999, with a small peak in 1996. The rapid rising trend from 1999 to 2005 is statistically significant at the over 95% confidence level. This is seen in all proxies, most clearly in the less smoothed data (SSH and subpolar salinity). This claim is supported by observation of SSH-deduced AMOC strength, tide-gauges, the subpolar salinity proxy, and also the Zhang fingerprint proxy. (The last proxy, because of 10-year smoothing, does not show the smaller peak in the mid-1990s). A model reanalysis also showed an acceleration prior to 2005 followed by a decline at 26\u00b0 N, and a peak in the mid-1990s as well as one in 2005 at 45\u00b0 N16. AMOC in models is sensitive to resolution and subgrid parameterization31, resulting in little consensus among reanalysis (and hindcast) products. With one exception16 these products do not agree with the RAPID observation at 26\u00b0 N. The exception is the GloSea5 model, which has a higher, eddy-permitting resolution than previous reanalyses. Supplementary figure 1 of ref. 16 shows two peaks, one at 1995 and one at 2005. The 1995 peak is slightly higher than the 2005 peak, and is referred to thus in the main text of ref. 16: \u201cThe AMOC at 45\u00b0 N is representative of the changes in the subpolar gyre, with the AMOC decreasing from a maximum in the mid-1990s, followed by a slight increase (Fig. 1d)\u201d. The peak in 2005 was not mentioned. However, the result on the 1995 peak should be treated with care, as the authors themselves stated in the supplementary information of ref. 16: \u201cIt is likely that there will be a period of spinup, where the deep ocean (where there are few observational constraints) adjusts, which may explain the divergence in trend. Hence we disregard the first few years of each experiment. There is also a shock in 1992 when the altimeter data is introduced, which may contribute to the increase in AMOC strength between 1989 and 1995. Hence we choose the period to analyse starting from January 1995, and join the two analyses in January 2002.\u201d The relative magnitude of the 1995 peak and the 2005 peak may be unreliable as it was obtained by joining two reanalyses, one starting from 1989 and one from 1995 with \u201cdivergence in trend\u201d16.\nThe observed SSH data since 1992 can be used to deduce AMOC strength using geostrophic approximation, bypassing the problems of shock and subsequent adjustment when the same SSH data were introduced in model assimilation.\nSST changes during different phases of AMOC\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/chentung18.html"}
{"id": "9435f63cacce-4", "text": "The observed SSH data since 1992 can be used to deduce AMOC strength using geostrophic approximation, bypassing the problems of shock and subsequent adjustment when the same SSH data were introduced in model assimilation.\nSST changes during different phases of AMOC\uf0c1\nThe upper branch of the climatological AMOC brings warm and saline surface water from the subtropical North Atlantic to its subpolar latitudes. When the overturning is stronger, more of this warm water is found in the subpolar northern latitudes. In the Southern Hemisphere, more of the cold water from the region of the Antarctic Circumpolar Current is brought northward into the Southern subtropics. Consequently a characteristic signature in the Atlantic SST is an opposite-signed multidecadal anomaly, with warming to the north and smaller cooling to the south when the overturning is stronger (AMOC+), and the reverse pattern when it is weaker (AMOC\u2013) (Extended Data Fig. 5a, b). This ocean-induced SST variability is centered in the subpolar North Atlantic20. The observed tendency during the last two subphases of the AMOC is as expected (Extended Data Fig. 5c, d): As AMOC slows after 2005, the SST tends towards a cooler North Atlantic and warmer subtropics. Accompanying the strong cooling in the subpolar gyre is an interesting intense warming after 2005 in the northwest Atlantic, centered in the Gulf of Main, which was recently simulated in a high-resolution climate model32 as due to the northward displacement of the Gulf Stream when AMOC slows. The inverse relationship between Gulf Stream\u2019s northward displacement and AMOC strength was found6 to be caused by the Labrador Current retreat and the bottom vortex stretching33.\nAMO\uf0c1\nIn long coupled atmosphere\u2013ocean model runs under preindustrial conditions (without increasing greenhouse gases) the AMO is the SST manifestation of AMOC variations, and the two time series are approximately in phase19. The definition of AMO in ref. 19 is the mean of Atlantic SST north of 45\u00b0 N, which may lead the subtropical SST anomaly by two years. A more traditional definition of AMO is the mean Atlantic SST north of the Equator34, with an approximately one-year phase difference. It has been shown24, using the space-time perspective of rotated empirical orthogonal function analysis, that the AMO is mainly responsible for the observed global mean surface temperature variation on multidecadal timescales. The two are in phase during the industrial era. Since the AMOC and the global mean surface temperature variation are not in phase (as shown in Fig. 3), it follows that during the industrial era, AMOC and AMO are off phase, possibly by a quarter cycle, although AMOC\u2019s time series is too short for an accurate determination of the phase information.\nDuring the positive phase of AMO, SST is warm in the North Atlantic and surrounding continents. Therefore, Northern Hemisphere mean surface temperature is warm during the positive phase and cool during the negative phase of the AMO. Using multiproxy data in the Northern Hemisphere the AMO time series can be extended back several hundred years35. The longest instrumental temperature record exists in central England, and it was used27 to reconstruct the AMO timeseries back to the Little Ice Ages. An even longer record of ice cores in Greenland, in the northern Atlantic, exists, and a statistically significant at the over 95% confidence level AMO signal can be found36 extending back to 800 AD that is coherent with the instrumental record of central England27 during their overlapping period. It appears that AMO is a recurrent phenomenon of period around 65\u201370 years and that it is robust in the preindustrial era, with the Atlantic and the surrounding areas warm during the positive phase and cold during the negative phase. From climate model preindustrial control runs, it seems that AMO is a surface manifestation of AMOC variation. Furthermore, based on palaeoclimate evidence of cold events when AMOC slows down abruptly, a common perception is that a slowdown in AMOC would lead to a cold Northern Hemisphere. The mechanism relies on the dominant role of AMOC (and its Gulf Stream) in horizontally transporting surface heat from the tropics to the mid- and high-latitude Atlantic, where it releases some heat to the cold atmosphere before sinking in the subpolar Atlantic. The heat released to the atmosphere makes Europe warmer (when wind blows in that direction) than it should be for its latitude.\nCalculating SSH* from altimetry data\uf0c1\nSSH* is SSH with its global mean subtracted. SSH contains both the thermosteric part (due to thermal expansion of the entire water column) and the ocean water mass addition that is due to melting land ice. It is known that the ocean will adjust to any change in ocean mass rapidly through the propagation of gravity waves, and will reach a new equilibrium globally within a couple of months37. Therefore, the subtraction of the global mean largely removes the mass contribution from SSH.\nExtended data figures and tables\uf0c1\nExtended Data Fig. 1: Unfiltered AMOC proxy time series in monthly resolution. The thick solid lines are 13-month running means. The numbers to the right of each time series show the correlation coefficient with the unfiltered AMOC subsurface temperature fingerprint of Zhang. Data are taken from refs 20,21,22. All of the correlation coefficients are above 95% confidence level. The accumulated sea-level index is shifted to the right by 4.8 years in this figure. Without the time shift, its correlation with the AMOC proxy is practically zero (r\u2009=\u20090.06).\nExtended Data Fig. 2: Error bars for the three salinity time series shown in Fig. 1. The colour lines are monthly values of uncertainty, superimposed on the 13-month means of the time series. psu, practical salinity units.\nExtended Data Fig. 3: Coincidence of the three AMOC phases with global warming slowdown and acceleration. a, Global mean surface temperature. b, OHC north of 45\u00b0 N in the Atlantic. c, Salinity north of 45\u00b0 N in the Atlantic.\nExtended Data Fig. 4: Deep Labrador Sea density. Average density in the 1,000\u20131,500 m layer of the Labrador Sea, regionally averaged over the ocean area shown in the inset, from the three data sources given. A leading signal for stronger AMOC is the increased deep Labrador Sea salinity (and hence density). The signal propagates southward along the western boundary at depth, changing the cross-basin zonal gradient, and hence the geostrophic southward velocity13. The return flow then strengthens the upper branch of AMOC with a lag of 7\u201310 years15,16.\nExtended Data Fig. 5: SST patterns during different AMOC phases. a, When AMOC is below climatology. b, When AMOC is above climatology, SST detrended. c, SST linear trend when AMOC is increasing. d, When AMOC is decreasing.\nExtended Data Fig. 6: Linear trends, from 1950 to 2017, of temperature, salinity and density. a\u2013c, Trends in temperature (a), salinity (b) and density (c) as a function of depth. Solid curves indicate where the trend is statistically significant at 95% confidence level.\nExtended Data Fig. 7: Temperature\u2013salinity diagram. The subpolar Atlantic Ocean (45\u00b0\u201365\u00b0 N) for each depth between 300 m and 1,500 m for the two periods, with the mean of 2000\u20132016 in red and the mean of 1920\u20131940 in blue. The dots shown are the five winter month values (NDJFM). At these depths the seasonal cycle is very small [38].", "source": "https://sealeveldocs.readthedocs.io/en/latest/chentung18.html"}
{"id": "e85a386fd775-0", "text": "Zika et al. (2021)\uf0c1\nTitle:\nRecent Water Mass Changes Reveal Mechanisms of Ocean Warming\nCorresponding author:\nZika\nCitation:\nZika, J. D., Gregory, J. M., McDonagh, E. L., Marzocchi, A., & Clement, L. (2021). Recent Water Mass Changes Reveal Mechanisms of Ocean Warming. Journal of Climate, 34(9), 3461-3479. doi: 10.1175/jcli-d-20-0355.1\nKeywords:\nOcean, Water masses/storage, Climate change, Heat budgets/fluxes, Climate variability, Trends\nAbstract\uf0c1\nOver 90% of the buildup of additional heat in the Earth system over recent decades is contained in the ocean. Since 2006, new observational programs have revealed heterogeneous patterns of ocean heat content change. It is unclear how much of this heterogeneity is due to heat being added to and mixed within the ocean leading to material changes in water mass properties or is due to changes in circulation that redistribute existing water masses. Here we present a novel diagnosis of the \u201cmaterial\u201d and \u201credistributed\u201d contributions to regional heat content change between 2006 and 2017 that is based on a new \u201cminimum transformation method\u201d informed by both water mass transformation and optimal transportation theory. We show that material warming has large spatial coherence. The material change tends to be smaller than the redistributed change at any geographical location; however, it sums globally to the net warming of the ocean, whereas the redistributed component sums, by design, to zero. Material warming is robust over the time period of this analysis, whereas the redistributed signal only emerges from the variability in a few regions. In the North Atlantic Ocean, water mass changes indicate substantial material warming while redistribution cools the subpolar region as a result of a slowdown in the meridional overturning circulation. Warming in the Southern Ocean is explained by material warming and by anomalous southward heat transport of 118 \u00b1 50 TW through redistribution. Our results suggest that near-term projections of ocean heat content change and therefore sea level change will hinge on understanding and predicting changes in ocean redistribution.\nIntroduction\uf0c1\nOver the past 50 years, as atmospheric greenhouse gas concentrations have increased, the ocean has absorbed more than 10 times as much heat as all other components of the climate system combined (Rhein et al. 2013). This warming showed substantial spatial variability between 1993 and 2005, being up to 10 times as much in some regions as the global average (Zhang and Church 2012). It is unclear whether this variability is due to geographical variation in the interior propagation of surface warming versus redistribution of existing heat within the ocean.\nOcean warming is an important issue because ocean thermal expansion is the largest projected contribution to global mean sea level rise in the twenty-first century (Church et al. 2013). Numerical climate models disagree on the pattern and amplitude of ocean heat content (OHC) change and hence on sea level rise under anthropogenic greenhouse warming (Gregory et al. 2016). Understanding how heat has been taken up and redistributed by the ocean is essential for predicting future changes in sea level.\nNumerical ocean models forced with historical atmospheric conditions have proved to be useful tools in quantifying how variability in atmospheric forcing can set variability in OHC (Drijfhout et al. 2014) and sea level (Penduff et al. 2011) at interannual to decadal time scales. However, such models can be unrealistic for simulating multidecadal climate change because of model drift and inaccuracies in long-term changes in atmospheric forcing, particularly global mean heat fluxes (Grif\u00dees et al. 2009). On the other hand, coupled ocean atmosphere climate models are routinely used to capture the effect of long-term climate forcing. But such models only accurately simulate past unforced variability in regional OHC when, by chance, their internal variability is in phase with the observed system.\nAn advance in terms of numerical ocean climate modeling has come from the separation of OHC change into an \u201cadded\u201d and a \u201credistributed\u201d component in climate model simulations, where the former is due to change in the surface heat flux, and the latter due to rearrangement of existing OHC because of altered ocean heat transports (Banks and Gregory 2006). This decomposition is analogous to the \u201canthropogenic\u201d and \u201cnatural\u201d decomposition that has revolutionized our under standing of oceanic carbon records (Khatiwala et al. 2013). Here we will present a novel method to diagnose the \u201cmaterial\u201d component of OHC change, which we will show is closely related to the \u201cadded\u201d component introduced by Banks and Gregory (2006).\nRecent work has aimed to reconstruct the drivers of OHC change based on observationally derived air\u00d0sea boundary conditions. Zanna et al. (2019) for example used surface temperature anomalies combined with a tracer-based approach to reconstruct the role of anomalous surface heat fluxes in centennial heat content change. Roberts et al. (2017) estimated the contribution of air\u00d0sea heat flux changes in setting mixed layer and full-depth-integrated OHC budgets over recent decades and inferred the role of ocean circulation as a residual. Here we aim to circumvent reliance on such boundary conditions and infer the mechanisms of ocean heat content change directly based on water mass changes.\nWater mass-based methods have been used to decompose local temperature and salinity changes into a dynamic \u201cheave\u201d component and an apparently material component at constant density based on a one-dimensional view of the water column (Bindoff and McDougall 1994). However, their analysis did not distinguish between material processes and horizontal advection, insofar as they affect the water mass properties of an individual water column.\nHere we introduce a new method based on water mass theory, called the minimum transformation method, which we use to estimate recent drivers of three-dimensional OHC change. In section 2 we will review water mass theory and establish the relationship between changes in water masses as de\u00dened by their temperature and salinity and material changes in seawater temperature. We will describe in section 3 how this theory is translated into a practical method to estimate material changes in water masses and map these into geographical space. We present an application of this minimum transformation method to recent data over the Argo period in section 4 and give results in section 5. We discuss the results and compare them with existing work in section 6, and we give conclusions in section 7.\nWater mass theory\uf0c1\nWater mass analysis has long been used in physical oceanography to trace the origin of waters (Montgomery 1958). In the latter half of the twentieth century a quantitative framework emerged to describe the relationship between water masses, air\u00d0sea fluxes, and mixing [Walin 1982; see the review by Groeskamp et al. (2019)]. Recent work has seen this framework advanced in two ways specifically relevant to our work here: to multiple tracer dimensions to understand the thermodynamics of ocean circulation (Nycander et al. 2007; Zika et al. 2012; Doos et al. 2012; Groeskamp et al. 2014; Hieronymus et al. 2014) and to unsteady problems to understand the ocean\u00d5s role in transient climate change (Palmer and Haines 2009; Evans et al. 2014; Zika et al. 2015a,b; Evans et al. 2017, 2018).\nAn example of the utility of the water mass transformation framework in understanding transient change is provided by Zika et al. (2015a). They demonstrate that the distribution of water in salinity coordinates is influenced by the water cycle and turbulent mixing, the latter only being able to collapse the range of salinities the ocean covers. This means that changes in the width of the salinity distribution indicate an enhancement of the water cycle and/or a reduction in that rate at which salt is mixed. In this project we extend this concept to consider how changes in the temperature-salinity distribution relate to material changes in water masses.\nMaterial changes in Conservative Temperature Theta (hereinafter simply \u201ctemperature\u201d or T) following the motion of an incompressible fluid are related to Eulerian changes and advection by\nfrac{DT}{Dt} = frac{partial T}{partial t} + bf{u} cdot nabla{T}, (1)\nwhere bf{u} is the 3D velocity vector and frac{DT}{Dt} is the material derivative, which is related to sources and sinks of heat and irreversible mixing. Conservative Temperature is used here since it is a more accurate \u201cheat\u201d variable than potential temperature (McDougall 2003), although the later is still routinely used in ocean models, including the one analyzed in section a of appendix A.\nEven if a perfect record of frac{partial T}{partial t} were available at a fixed location, we would not know the relative roles of advection (bf{u} cdot nabla{T}) and material processes (frac{DT}{Dt}). To separate them, we consider the water mass perspective as an alternative to the Eulerian perspective. The following theory draws directly from Hieronymus et al. (2014).", "source": "https://sealeveldocs.readthedocs.io/en/latest/zika21.html"}
{"id": "e85a386fd775-1", "text": "An example of the utility of the water mass transformation framework in understanding transient change is provided by Zika et al. (2015a). They demonstrate that the distribution of water in salinity coordinates is influenced by the water cycle and turbulent mixing, the latter only being able to collapse the range of salinities the ocean covers. This means that changes in the width of the salinity distribution indicate an enhancement of the water cycle and/or a reduction in that rate at which salt is mixed. In this project we extend this concept to consider how changes in the temperature-salinity distribution relate to material changes in water masses.\nMaterial changes in Conservative Temperature Theta (hereinafter simply \u201ctemperature\u201d or T) following the motion of an incompressible fluid are related to Eulerian changes and advection by\nfrac{DT}{Dt} = frac{partial T}{partial t} + bf{u} cdot nabla{T}, (1)\nwhere bf{u} is the 3D velocity vector and frac{DT}{Dt} is the material derivative, which is related to sources and sinks of heat and irreversible mixing. Conservative Temperature is used here since it is a more accurate \u201cheat\u201d variable than potential temperature (McDougall 2003), although the later is still routinely used in ocean models, including the one analyzed in section a of appendix A.\nEven if a perfect record of frac{partial T}{partial t} were available at a fixed location, we would not know the relative roles of advection (bf{u} cdot nabla{T}) and material processes (frac{DT}{Dt}). To separate them, we consider the water mass perspective as an alternative to the Eulerian perspective. The following theory draws directly from Hieronymus et al. (2014).\nWe characterize water masses by their T and Absolute Salinity S_A (IOC/SCOR/IAPSO 2010; hereinafter simply \u201csalinity\u201d or S). The volume v of water per unit temperature and salinity and at temperature T^* and salinity S^* is\nv(T^*, S^*) = frac{partial^2}{partial T partial S} int_{T<T^*, S<S^*}dV, (2)\nwhere the integral is over elements dV of ocean volume that are cooler than T^* and fresher than S^*. An estimate of v that is based on recent observational analysis is given in Fig. 1a. (These data are described in detail in section 4.)\nFigure 1: Portrait of changing ocean water masses: (a) inventory of ocean volume in Conservative Temperature vs Absolute Salinity coordinates (mean of 2006-17 inclusive) and (b) change in water mass volume between the early half and late half of the period divided by the six years (Sv). According to water mass theory, changes in air-sea heat and freshwater fluxes and/or changes in rates of diffusion are required for these changes to occur.\uf0c1\nConsidering all of the water in the ocean and retaining the incompressibility assumption, the only way v can change is via transformation - that is, by making water parcels warmer, colder, saltier, or fresher as described by the following continuity equation [derived formally in Hieronymus et al. (2014)]:\nfrac{partial v}{partial t} + frac{partial}{partial T} (v dot{T}) + frac{partial}{partial S} (v dot{S}) = 0, (3)\nwhere dot{T} is the average material derivative of T within a water mass. That is,\ndot{T}(T^*, S^*) = frac{1}{v} frac{partial^2}{partial T partial S}  int_{T<T^*, S<S^*}frac{DT}{Dt} dV, (4)\nand likewise dot{S} is the average material derivative of S. An estimate of recent changes in v is given in Figure 1b.\nIn Eq. (3) the terms vdot{T} and vdot{S} are the transformation rates in the temperature direction (Sv g^{-1} kg^{-1}; 1 Sv = 10^6 m^3 s^{-1}) and salinity direction (Sv C\u02da^{-1}) respectively. Equation (3) states that the amount of water between two closely spaced isotherms (T and T + partial T) and isohalines (S and S + partial S) will go up if more water is made warmer at T than at T + partial T and/or more water is made saltier at S than at S + partial S.\nWhen the system is in a statistically steady state the water mass distribution v remains constant such that\nfrac{partial}{partial T} overline{v dot{T}} + frac{partial}{partial S} overline{v dot{S}} = 0, (5)\nwhere the overbar represents a sufficiently long time average. In this steady case, the vector field described by overline{v dot{T}} and overline{v dot{S}} can be characterized by a thermohaline streamfunction (Zika et al. 2012; Groeskamp et al. 2014).\nHere, we will not attempt to estimate this steady-state component of water mass transformation [e.g., as Groeskamp et al. (2017) have done]. Rather we will attempt to quantify only the component required to explain changes in v. That is, we aim to quantify the anomaly in the transformation rate (v dot{T})\u2019 such that v dot{T} = overline{v dot{T}} + (v dot{T})\u2019, and likewise for (v dot{S})\u2019, with\nfrac{partial v}{partial t} + frac{partial}{partial T} (v dot{T})\u2019 + frac{partial}{partial S} (v dot{S})\u2019 = 0, (6)\nNote that a steady-state component like Eq. (5) can always be added to (v dot{T})\u2019  and (v dot{S})\u2019 such that Eq. (6) is still satisfied. Hwever, we seek only the net change in water mass transformation required to explain changes in v and therefore seek the smallest (in a root-mean-square sense) values of dot{T}\u2019 and dot{S}\u2019 that satisfy Eq. (6). That is, we seek the smallest change in air-sea heat and freshwater fluxes and mixing - in a net sense - that can explain changes in water masses. We call this the minimum transformation.\nHere we will use changes in v to infer the minimum transformation and therefore estimate v dot{T}\u2019. This will allow us to estimate the material processes influencing ocean temperature change.\nThe minimum transformation method\uf0c1\nWe now apply water mass theory to understand changes in a discrete set of water masses describing the ocean over two time periods. We will then describe the application of a minimum transformation method that exploits an \u201cearth mover\u00d5s distance\u201d (EMD) algorithm to estimate the amount of material warming required to affect changes in those water masses.\nDiscrete water masses\uf0c1\nConsider the set of N discrete water masses with the ith water mass defined by the limits [T_i^{min}, S_i^{min}, mathbf{x}_i^{min}] and [T_i^{max}, S_i^{max}, mathbf{x}_i^{max}]. Essentially, our water masses are hypercubes in T\u00d0S\u00d0x\u00d0y\u00d0z space (more arbitrary space-and tim-dependent regions can be defined without affecting the method described below). To indicate whether water is within the ith water mass we define a boxcar function Pi_i such that\nbegin{equation}\nPi_i(mathbf{x}, t) = begin{cases}1, & T_i^{min} leq T(mathbf{x}, t) < T_i^{max}, S_i^{min} leq S(mathbf{x}, t) < S_i^{max} text{and} mathbf{x}_i^{min} leq mathbf{x} < mathbf{x}_i^{max}\\\n0, & text{otherwise}.  end{cases}\nend{equation}\nThe volume of water in the ith water mass at time t is then iiint{Pi_i(mathbf{x}, t) dV}.\nWe consider two time periods: an early period (t_0 - Delta t leq t < t_0) and a late period (t_0 leq t < t_0 + Delta t). The average volume of the ith water mass over the early period is V1_i and the average volume of the jth water mass over the late period is V2_j such that\nV1_i = frac{1}{Delta t} int_{t_0 - Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) dV dt\nand\nV2_j = frac{1}{Delta t} int_{t_0}^{t_0 + Delta t} iiint Pi_i(mathbf{x}, t) dV dt, (8)\nand the average temperature and salinity of water within V1_i is\nT1_i = frac{1}{Delta t V1_i} int_{t_0 - Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) T(mathbf{x}, t) dV dt\nand", "source": "https://sealeveldocs.readthedocs.io/en/latest/zika21.html"}
{"id": "e85a386fd775-2", "text": "Discrete water masses\uf0c1\nConsider the set of N discrete water masses with the ith water mass defined by the limits [T_i^{min}, S_i^{min}, mathbf{x}_i^{min}] and [T_i^{max}, S_i^{max}, mathbf{x}_i^{max}]. Essentially, our water masses are hypercubes in T\u00d0S\u00d0x\u00d0y\u00d0z space (more arbitrary space-and tim-dependent regions can be defined without affecting the method described below). To indicate whether water is within the ith water mass we define a boxcar function Pi_i such that\nbegin{equation}\nPi_i(mathbf{x}, t) = begin{cases}1, & T_i^{min} leq T(mathbf{x}, t) < T_i^{max}, S_i^{min} leq S(mathbf{x}, t) < S_i^{max} text{and} mathbf{x}_i^{min} leq mathbf{x} < mathbf{x}_i^{max}\\\n0, & text{otherwise}.  end{cases}\nend{equation}\nThe volume of water in the ith water mass at time t is then iiint{Pi_i(mathbf{x}, t) dV}.\nWe consider two time periods: an early period (t_0 - Delta t leq t < t_0) and a late period (t_0 leq t < t_0 + Delta t). The average volume of the ith water mass over the early period is V1_i and the average volume of the jth water mass over the late period is V2_j such that\nV1_i = frac{1}{Delta t} int_{t_0 - Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) dV dt\nand\nV2_j = frac{1}{Delta t} int_{t_0}^{t_0 + Delta t} iiint Pi_i(mathbf{x}, t) dV dt, (8)\nand the average temperature and salinity of water within V1_i is\nT1_i = frac{1}{Delta t V1_i} int_{t_0 - Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) T(mathbf{x}, t) dV dt\nand\nS1_i = frac{1}{Delta t V1_i} int_{t_0 - Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) S(mathbf{x}, t) dV dt, (9)\nrespectively; likewise for V2_j we have\nT2_j = frac{1}{Delta t V2_j} int_{t_0}^{t_0 + Delta t} iiint Pi_j(mathbf{x}, t) T(mathbf{x}, t) dV dt\nand\nS2_j = frac{1}{Delta t V2_j} int_{t_0}^{t_0 + Delta t} iiint Pi_j(mathbf{x}, t) S(mathbf{x}, t) dV dt. (10)\nTo change the set of volumes V1_i into the set of volumes V2_j requires a transformation of water in T-S space. When water transforms, it changes its T and S and can also move geographically.\nTo understand how water is transformed from the physical location and physical properties of one water mass to another we use the shorthand tilde{x}(t+Delta t | mathbf{x}, t) for the position of a water parcel at time t + Delta t conditional on it previously being at position mathbf{x} at time t. That is,\ntilde{x}(t+Delta t | mathbf{x}, t) = mathbf{x} + int_t^{t+Delta t} mathbf{u}[tilde{x}(t^* | mathbf{x}, t), t^*] dt^*, (11)\nwhere, as previously, mathbf{u} is the 3D velocity vector. We describe the transformation rate between the early and late water masses with the matrix mathbf{g}. The ith column and jth row of this matrix g_{ij} correspond to the average rate of transformation of water from early water mass i to late water mass j such that\ng_{ij} = frac{1}{Delta t^2} int_{t_0 - Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) Pi_j[tilde{x}(t + Delta t | mathbf{x}, t),t]dV dt. (12)\nIn Eq. (12) the term Pi_i(mathbf{x}, t) Pi_j[tilde{x}(t + Delta t | mathbf{x}, t),t] isolates water that was in the ith water mass at time t and was subsequently in the jth water mass at some time Delta t later. The quantity g_{ij} is therefore the average rate (m^3 s^{-1}) at which water in the ith early water mass is transformed into the jth late water mass.\nSince the total volume of water is conserved between the early and late periods all the water from the early water masses (V1_i) must be transformed into late water masses. Likewise, all water masses from the late period (V2_j) are made from water masses of the early period. That is,\nV1_i = Delta t sum_{j=1}^N g_{ij}\nand\nV2_j = Delta t sum_{i=1}^N g_{ij}. (13)\nThe average temperature change of water that transforms from V1_i to V2_j is then\nDelta T_{ij} = frac{1}{Delta t^2 g_{ij}} int_{t_0-Delta t}^{t_0} iiint Pi_i(mathbf{x}, t) Pi_j[tilde{x}(t + Delta t | mathbf{x}, t),t]{T[tilde{x}(t + Delta t | mathbf{x}, t),t]-T(mathbf{x}, t)} dV dt, (14)\nwhere the temperature change of individual parcel is related to the Lagrangian derivative by\nT[tilde{x}(t + Delta t | mathbf{x}, t),t] - T(mathbf{x}, t) = int_t^{t + Delta t} frac{DT}{Dt}[tilde{x}(t^*|mathbf{x},t),t^*]dt^*. (15)\nWe can write Eq. (14) as\nDelta T_{ij} = mathcal{T}2_{ji} - mathcal{T}1_{ij}, (16)\nwhere mathcal{T}2_{ji} is the volume-weighted average temperature of the water in the jth late water mass that was previously in the ith early water mass and mathcal{T}1_{ij} is the volume-weighted average temperature of the water in the ith early water mass that is later in the jth late water mass.\nThe transformation g_{ij} involves a range of water parcels with a range of temperatures T(mathbf{x}, t), whose mean is mathcal{T}1_{ij},in the early period moving to a range of temperatures T[tilde{x}(t + Delta t | mathbf{x}, t),t], whose mean is mathcal{T}2_{ji}, in the late period. To simplify this problem, we assume that in both periods the water masses are well mixed. This means that we expect that the mean temperature of any sample of water parcels from water mass i in the early period will equal the mean temperature of the water mass as a whole, and in particular this is true for the sample of parcels that ends up in water mass j in the late period. Thus mathcal{T}1_{ij} = T1_i with this assumption. By a similar argument, mathcal{T}2_{ji} = T2_j, and hence the average T and S change of water transforming from the ith early to the jth late water mass as the difference of the average T and S of the two water masses. That is, Delta T_{ij} = T2_j - T1_j and Delta S_{ij} = S2_j - S1_j.\nThis above approximation preserves the following equality relating the change in global volume-weighted temperature to the transformation matrix:\nsum_{j=1}^N V2_j T2_j - sum_{i=1}^N V1_i T1_i = Delta t sum_{i=1}^Nsum_{j=1}^N g_{ij} (T2_j - T1_i), (17)\nand likewise for the volume-weighted salinity.\nWe have effectively discretized the continuum of trajectories from early to late water masses into a finite set of discrete trajectories. This discretization clearly leads to some information loss; however, such losses are unavoidable in any computationally feasible inverse method.", "source": "https://sealeveldocs.readthedocs.io/en/latest/zika21.html"}
{"id": "e85a386fd775-3", "text": "where mathcal{T}2_{ji} is the volume-weighted average temperature of the water in the jth late water mass that was previously in the ith early water mass and mathcal{T}1_{ij} is the volume-weighted average temperature of the water in the ith early water mass that is later in the jth late water mass.\nThe transformation g_{ij} involves a range of water parcels with a range of temperatures T(mathbf{x}, t), whose mean is mathcal{T}1_{ij},in the early period moving to a range of temperatures T[tilde{x}(t + Delta t | mathbf{x}, t),t], whose mean is mathcal{T}2_{ji}, in the late period. To simplify this problem, we assume that in both periods the water masses are well mixed. This means that we expect that the mean temperature of any sample of water parcels from water mass i in the early period will equal the mean temperature of the water mass as a whole, and in particular this is true for the sample of parcels that ends up in water mass j in the late period. Thus mathcal{T}1_{ij} = T1_i with this assumption. By a similar argument, mathcal{T}2_{ji} = T2_j, and hence the average T and S change of water transforming from the ith early to the jth late water mass as the difference of the average T and S of the two water masses. That is, Delta T_{ij} = T2_j - T1_j and Delta S_{ij} = S2_j - S1_j.\nThis above approximation preserves the following equality relating the change in global volume-weighted temperature to the transformation matrix:\nsum_{j=1}^N V2_j T2_j - sum_{i=1}^N V1_i T1_i = Delta t sum_{i=1}^Nsum_{j=1}^N g_{ij} (T2_j - T1_i), (17)\nand likewise for the volume-weighted salinity.\nWe have effectively discretized the continuum of trajectories from early to late water masses into a finite set of discrete trajectories. This discretization clearly leads to some information loss; however, such losses are unavoidable in any computationally feasible inverse method.\nNote that, even if the ith water mass for the early period has the same temperature and salinity bounds as the ith water mass of the late period, the distribution of properties within the water mass can change. That is, in general T1_j \u2260 T2_i and S1_j \u2260 S2_i, so g_{ij} is always a transformation, even with i = j. For example, assume the ith water mass has temperature bounds 1\u02da and 2\u02daC and that the water between those bounds is on average at 1.9\u02daC in the early period and 1.1\u02daC in the late period. Groeskamp et al. (2014) called this a \u201clocal effect\u201d and included it as a separate term in their formulation. Here, we find it convenient to consider the transformation from the ith early water mass at 1.9\u02daC to the ith late water mass at 1.1\u02daC to be yet another transformation - no different than between any other pair of water masses.\nWe relate the transformation rate to the average material temperature tendency required to warm the ith early water mass to form the range of destination water masses it arrives at in the late period. That is,\ndot{T}_i = frac{1}{V1_i} sum_{j=1}^N (T2_j - T1_i) g_{ij}. (18)\nWe use dot{T} to define a 3D material temperature change field Delta T_{material} such that\nDelta T_{material}(mathbf{x}) = int_{t_0-Delta t}^{t_0} sum_{i=1}^N Pi_i(mathbf{x}, t) dot{T}_i dt\napprox frac{1}{Delta t} int_{t_0-Delta t}^{t_0} left{int_t^{t + Delta t}frac{DT\u2019}{Dt}[tilde{x}(t^*|mathbf{x},t),t^*]dt^*right} dt. (19)\nNote here that we are relating dot{T}_i only to the anomaly of the Lagrangian tendency (i.e., frac{DT\u2019}{Dt} rather than frac{DT}{Dt}) as it appears in Eq. (19). This is because our dot{T}_i describes only the changes in the transformation rate required to explain changes in the water mass distribution [as in Eq. (6)]. There can be (and indeed is) an additional \u201cmean\u201d transformation rate that leads to cycles of water in T-S space but does not lead to any changes in water mass inventories with time (Groeskamp et al. 2014). Implicit in Eq. (19) is the assumption that the anomalous warming of a particular water mass occurred evenly (in a volume-and time-weighted sense) over the regions and times during which that water mass existed in the early period.\nWe will contrast the inferred material warming at one location mathbf{x} against the total warming\nDelta T(mathbf{x}) = int_{t_0 - Delta t}^{t_0} T(mathbf{x}, t + Delta t) - T(mathbf{x}, t) dt/Delta t,\nwith the residual of the two being a redistribution component such that\nDelta T_{material} = Delta T - Delta T_{redistribution}.\nBy construction, Delta T_{redistribution} accounts for the advective redistribution of temperature (mathbf{u} cdot nabla{T}), which does not affect the underlying water masses and therefore is not accounted for in Delta T_{material}.\nFinding the minimum transformation using an EMD algorithm\uf0c1\nOur goal now is to estimate the transformation matrix mathbf{g}. Out of the in\u00denite number of choices that could satisfy Eq. (13),we will look for the smallest (in a least squares sense) possible transformation required to change the distribution. We call this the minimum transformation.\nPrevious studies have diagnosed transformation rates from time-dependent changes in water mass distributions by searching for a minimum least squares solution on a regular T-S (Evans et al. 2014) or density-spiciness grid (Portela et al. 2020). Because of the dramatic variations in volume per unit temperature and salinity of the World Ocean (Fig. 1b) we choose to describe the distribution in an unstructured way. Furthermore, we exploit recent advances in the area of \u201coptimal transportation theory\u201d - in particular, the EMD algorithm that is mentioned at the beginning of section 3 (Pele and Werman 2008, 2009).\nThe EMD solves the hypothetical problem of moving earth from a set of mounds, each with varying amounts of earth, into a set of holes with varying amounts of empty space to be filled, where the total volume of the mounds is equal to that of the holes. In our case the \u201cmounds\u201d are the early water masses and the \u201choles\u201d are the late water masses. The optimization problem is to find the set of transfers (from a mound to a hole, or the early to late water masses) that gives the smallest possible total of mass-weighted distance (the product of the mass and the distance of a transfer) that needs to be traveled in order to empty the mounds and fill the holes. For the EMD algorithm, we require a distance metric mathbf{d} ,which is a matrix whose ith column and jth row d_{ij} is the cost of moving water from the ith early water mass to the jth late water mass. The EMD algorithm then estimates mathbf{g} such that Eq. (13) is satis\u00deed and the following total mass-weighted \u201cdistance\u201d is minimized:\nsum_{j=1}^Nsum_{i=1}^N g_{ij} d_{ij}. (21)\nWe use the following distance metric:\nd_{ij} = (T1_i - T2_j)^2 + [a(S1_i - S2_j)]^2 + delta_{ij}, (22)\nwhere temperature and salinity differences are squared so that the distance is positive definite and long trajectories in T\u00d0S space are penalized more than short ones and a is a constant that scales the salinity change relative to the temperature change and whose choice is described in the next section. The intent of delta_{ij} is to permit movement between water masses that are adjacent geographically without additional penalty but at the same time to stop direct exchange between geographically disconnected water masses, for example between water masses in the Southern Ocean and the Arctic. To achieve this we set delta_{ij} = 0 where the ith and jth water masses are in the same or adjacent geographical regions and delta_{ij} >> max{(T1_i - T2_j)^2 + [a(S1_i - S2_j)]^2} otherwise (in practice we use delta_{ij} = 10^6 in the latter case). Regions that share a meridional or zonal boundary are considered to be adjacent. The Arctic and North Paci\u00dec Oceans are not considered to be adjacent, whereas the Indian Ocean and equatorial Paci\u00dec regions are considered to be adjacent.", "source": "https://sealeveldocs.readthedocs.io/en/latest/zika21.html"}
{"id": "e85a386fd775-4", "text": "sum_{j=1}^Nsum_{i=1}^N g_{ij} d_{ij}. (21)\nWe use the following distance metric:\nd_{ij} = (T1_i - T2_j)^2 + [a(S1_i - S2_j)]^2 + delta_{ij}, (22)\nwhere temperature and salinity differences are squared so that the distance is positive definite and long trajectories in T\u00d0S space are penalized more than short ones and a is a constant that scales the salinity change relative to the temperature change and whose choice is described in the next section. The intent of delta_{ij} is to permit movement between water masses that are adjacent geographically without additional penalty but at the same time to stop direct exchange between geographically disconnected water masses, for example between water masses in the Southern Ocean and the Arctic. To achieve this we set delta_{ij} = 0 where the ith and jth water masses are in the same or adjacent geographical regions and delta_{ij} >> max{(T1_i - T2_j)^2 + [a(S1_i - S2_j)]^2} otherwise (in practice we use delta_{ij} = 10^6 in the latter case). Regions that share a meridional or zonal boundary are considered to be adjacent. The Arctic and North Paci\u00dec Oceans are not considered to be adjacent, whereas the Indian Ocean and equatorial Paci\u00dec regions are considered to be adjacent.\nOur motivation for using EMD is simply to find the smallest amount of transformation (in a least squares sense) required to explain observed water mass change. If T-S changes in the ocean could be explained purely by adiabatic redistribution of existing water masses, then our method would prioritize this solution. Our initial guess is therefore this adiabatic solution (i.e., where g_{ij} = 0 for all i and j). The EMD algorithm finds the smallest deviation possible from this adiabatic case. We cannot rule out larger compensating transformations having taken place. In principle, solutions given different initial guesses (e.g., an initial guess for mathbf{g} that is based on a numerical simulation) could be explored. We leave this to future work.\nFigure 2 summarizes the minimum transformation method schematically. In the schematic just four early and four late water masses are de\u00dened with two in one geographical area and two in another. The minimum transformation moves water from the ith early to the ith late water masses in all four cases (i.e., g_{ii} \u2260 0 for all i). In addition, a substantial amount of water is moved from the second early water mass to the first late water mass (g_{21}) and from the third early water mass to the fourth late water mass (g_{34}). The observed change in temperature is therefore explained by a material warming of 2\u02da and 1\u02daC of the two warmer shallower water masses and of 0.5\u02daC for the cooler deeper water masses. The remainder of the Eulerian pattern of temperature change is explained by redistribution. This schematic representation is vastly simplified as compared to our actual implementation of the minimum transformation method, which is described in the next section.\nFigure 2: Schematic describing a simplified hypothetical implementation of the minimum transformation method. (left) Between a late and an early period, surface waters warm, especially to the south, where the ocean is fresher and the upper ocean layer becomes thicker. (center) The ocean is split into a southern region containing water masses 1 and 3 and a northern region containing water masses 2 and 4. Between the early and late periods, water masses 1 and 4 increase in volume and 2 and 3 reduce in volume. Taking into account the changing temperatures, salinities, and volumes of the early and late water masses, the \u201cminimum transformations\u201d g_{ij} are found using the EMD algorithm. These suggest modest warming of each water mass with some of early water mass 2 transforming to become late water mass 1 (g_{21}) and some of early water mass 3 transforming to become late water mass 4 (g_{34}). (right) The total temperature change is heterogeneous. A warming of 2\u02daC explains changes in water mass 1, a warming of 1\u02daC explains changes in water mass 2, and a warming of 0.5\u02daC explains changes in water masses 3 and 4. This warming is projected onto the location of those water masses in the early period to show the \u201cmaterial change.\u201d The residual of the total and material changes is then explained by a \u201credistribution\u201d that involves intense subsurface warming in the southern region and intense subsurface cooling in the northern region.\uf0c1\nData and application of the minimum transformation method\uf0c1\nObservational estimates of T and S come from the objective analysis provided by the Enact Ensemble (V4.0, hereinafter EN4; Good et al. 2013). EN4 has a 1\u02da-by-1\u02da horizontal resolution with 42 vertical levels. We analyze each month between 2006 and 2017 inclusive. We split these data into two time periods: an early period between 2006 and 2011 inclusive and a late period between 2012 and 2017 inclusive (i.e., t_0 = 0000 1 January 2007 and Delta t = 6 years).\nWe then define a discrete set of water masses for each time period by splitting the ocean into nine geographical regions and within each region by splitting up the ocean according to T-S bins. Our nine geographical regions are the Southern Ocean south of 35\u02daS, the subtropical Pacific and Atlantic Oceans between 35\u02da and 10\u02daS, the Indian Ocean north of 35\u02daS, the tropical Pacific and Atlantic Oceans between 10\u02daS and 10\u02daN, the North Pacific north of 10\u02daN, the Atlantic Ocean between 10\u02da and 40\u02daN, and the Atlantic and Arctic Ocean north of 40\u02daN. To avoid discontinuities in our resulting analysis we transition linearly from one region to another over a 10\u02da band (Figure 5).\nWe define T and S bin boundaries ([T_{min}, T_{max}] and [S_{min}, S_{max}] respectively) using a quadtree. The quadtree starts with a single (obviously oversized) bin with T boundaries [-6.4\u02da,96\u02daC] and S boundaries [-5.2, 46 g kg^{-1}] in which the entirety of the ocean\u2019s seawater resides. The single bin is then split into four equally sized bins with the same aspect ratio as the original bin. The same process of splitting into four is repeated for any bin whose volume change is greater than a threshold of 62 times 10^{12} m^3 (equivalent to the volume of a 5\u02da longitude by 5\u02da latitude region at the equator with a depth of 200 m) or until the bin size is 0.4\u02daC by 0.2 g kg^{-1}. Average volumes for each water mass are shown in Figure 3. In the supplementary text we show that changing the size of these bins by a factor of 2 does not substantially change our results. The quadtree is applied within each region and for the change between the late and early periods. This results in bin edges defining N = 1447 water masses. These bins are then used to dedine both the early water masses and the late water masses.\nFigure 3: Gray lines show Conservative Temperature T and Absolute Salinity S bounds of each water mass (or \u201cbin\u201d) generated using a quadtree for each geographical region. The average T and S of the water found within each bin are shown by the location of each marker, and the volume is represented by the color scale (log10m3). Inventories and mean T and S values represent the entire period (2006-17 inclusive). Inset panels show masks associated with each geographical region.\uf0c1\nWe choose the constant a to be the ratio of a typical haline contraction coefficient to a typical thermal expansion coefficient (a = beta_0/alpha_0 = 4.28). This does not mean that transformations along density surfaces are necessarily preferred; rather, the squares in Eq. (22) mean that density-compensated changes in T and S are penalized as much as changes of the same magnitude where one of the signs is reversed. The inferred Delta T_{material} for each water mass is shown in Figure 4. We have tested the sensitivity of our method to varying a by a factor of 2 and found only negligible changes in inferred warming (see section b of appendix A).\nFigure 4: Each symbol shows Delta T_{material}, the average warming required for each early water mass in order to transform them into the set of late water masses.\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/zika21.html"}
{"id": "e85a386fd775-5", "text": "Figure 3: Gray lines show Conservative Temperature T and Absolute Salinity S bounds of each water mass (or \u201cbin\u201d) generated using a quadtree for each geographical region. The average T and S of the water found within each bin are shown by the location of each marker, and the volume is represented by the color scale (log10m3). Inventories and mean T and S values represent the entire period (2006-17 inclusive). Inset panels show masks associated with each geographical region.\uf0c1\nWe choose the constant a to be the ratio of a typical haline contraction coefficient to a typical thermal expansion coefficient (a = beta_0/alpha_0 = 4.28). This does not mean that transformations along density surfaces are necessarily preferred; rather, the squares in Eq. (22) mean that density-compensated changes in T and S are penalized as much as changes of the same magnitude where one of the signs is reversed. The inferred Delta T_{material} for each water mass is shown in Figure 4. We have tested the sensitivity of our method to varying a by a factor of 2 and found only negligible changes in inferred warming (see section b of appendix A).\nFigure 4: Each symbol shows Delta T_{material}, the average warming required for each early water mass in order to transform them into the set of late water masses.\uf0c1\nIn section a of appendix A, we compare the results of our method applied to synthetic data from a climate model simulation with an added-heat variable explicitly simulated by the model. We find good agreement between added heat and our inferred Delta T_{material} and between simulated redistributed heat and our inferred Delta T_{redistributed} when ocean temperature and salinity are fed in as \u201cdata\u201d to the method. Section b of appendix A also explores sensitivity of our results to parameter choices. The uncertainties we place on OHC change are \u00b12 standard deviations of a bootstrap ensemble, also described in section c of appendix A.\nTo produce maps of the total, material and redistributed contributions to the heat content we multiply the density and heat capacity of seawater by the respective temperature change and vertically integrate these through the entire water column. Our method also produces a material salinity change. We leave discussion of those data to future work.\nResults\uf0c1\nPatterns of total OHC change between early and late periods are heterogeneous (Figure 5a). There are basin-scale patches of decreasing heat content in the western equatorial and tropical Pacific, in the Pacific sector of the Southern Ocean, in the subtropical south Indian Ocean, and in the subpolar North Atlantic. Warming is seen most strongly in the tropical eastern Pacific, South Atlantic Ocean, and subtropical North Atlantic. These changes are highly sensitive to the specific observation years chosen and the length of the epochs reflecting the regional time scale of variability associated with the redistributed component. Uncertainty is far larger than the signal in the majority of regions (stippling in Figure 5a) and coincident with previously identified regions of large sea level anomaly variability (Penduff et al. 2011).\nFigure 5: Heterogeneous pattern of total and redistributed heat content change contrast against robust material heat content change: (a) change in depth-integrated ocean heat content between 2006-11 and 2012-17 inclusive, (b) inferred redistributed heat, and (c) inferred material heat content change based on changing water masses for the same period. Regions where the magnitude of the signal is less significant (less than 2 standard deviations of a bootstrap ensemble) are stippled.\uf0c1\nHowever, there are a few regions (e.g., patches of the Southern Ocean and North Atlantic) where the regional redistributed signal is robust and emerges from the uncertainty (Figure 5b). The patterns of redistributed heat observed in the Pacific are consistent with interdecadal Pacific oscillation (IPO)-driven thermosteric sea level variability (Lyu et al. 2017). The IPO was typically positive in the late period and negative in the early period (see https://psl.noaa.gov/gcos_wgsp/Timeseries/ for these data).\nMaterial heat content change shows a smaller amplitude but more coherent signal than redistributed heat (Figures 5b,c). Material warming is seen across almost the entirety of the globe, with maxima in the Southern Hemisphere and Atlantic subtropical convergence zones (Maximenko et al. 2009), consistent with model simulations of passive ocean heat uptake due to anthropogenic greenhouse warming (Gregory et al. 2016). In such model simulations, anomalous heat fluxes into the ocean predominate at mid-to high latitudes and this heat is distributed throughout the ocean largely passively via subduction (downwelling) in the North Atlantic and the Southern Ocean (Marshall et al. 2015).\nStrikingly, the uncertainty in material heat content change is far smaller than that of total OHC change (stippling in Figure 5c). This suggests that heat was added to and distributed within the ocean persistently over the Argo period and that this warming is not an artifact of a particularly warm year or years.\nZonally integrating the net OHC change reveals a signal of roughly the same magnitude as its uncertainty at all latitudes (Figure 6a). Zonally integrated redistributed heat likewise has a small signal to uncertainty ratio except in the Southern Ocean (Figure 6a). Accumulating the redistributed heat contribution from north to south gives the meridional heat transport due to redistribution. Broadly, heat is redistributed from north to south with a southward cross-equatorial transport of 73 \u00b1 60 TW between the two epochs (Figure 6c).\nFigure 6: Material heat content change is accumulating in the tropics and subtropics, whereas existing heat is being redistributed southward. (a) Total heat content change (gray), redistribution contribution (blue), and material contribution (red). (b) Contributions to material heat content change from the Indian (green), Pacific (orange), and Atlantic (yellow) Oceans. (c) Meridional heat transport due to redistribution in the Southern Ocean (blue), Atlantic (cyan), and Indian plus Pacific Oceans (magenta). Shaded areas represent \u00b12 standard deviations of a bootstrap ensemble.\uf0c1\nMaterial heat content change (Figure 6a) is larger than its uncertainty at most latitudes and shows a peak at 35\u02daS and at 15\u02da and 35\u02daN. The material heat content change peaks at 35\u02daS and 35\u02daN are collocated with climatological wind stress curl minima, where material warming due to anomalous surface heat fluxes may be accumulating due to convergence of surface Ekman transport.\nTable 1 shows material, redistributed, and total heat content changes by ocean basin. Material heat content change is distributed among the Indian, South Paci\ufb01c, and South Atlantic basins approximately according to their area. However, the tropical and subtropical North Atlantic stores close to 20% of the global ocean\u2019s material heat content change despite representing less than 10% of its area (Table 1). An outsized role for the North Atlantic in storing material heat content change in the climate system has also been foreseen in numerical modeling studies (Lee et al. 2011).\nTable 1: Material, redistribution, and total contributions to heat content change by ocean basin in terawatts and area as fraction of global ocean area. Heat content change estimates are based on differences between the periods 2006\u201311 and 2012\u201317 inclusive. Uncertainties are \u00b12 standard deviations. The Southern Ocean is de\ufb01ned as the entire ocean south of 32\u02daS. The South Paci\ufb01c, South Atlantic, and Indian Ocean estimates exclude the ocean south of 32S. The North Atlantic is split into a region south of and a region north of 44\u02daN. The latter includes the Arctic Ocean.\nMaterial\nRedistributed\nTotal\nArea fraction\nSouthern Ocean\n90 \u00b1 18\n118 \u00b1 50\n208 \u00b1 63\n0.27\nSouth Pacific\n53 \u00b1 16\n226 \u00b1 22\n28 \u00b1 22\n0.15\nNorth Pacific\n82 \u00b1 25\n261 \u00b1 55\n21 \u00b1 54\n0.23\nIndian Ocean\n45 \u00b1 10\n213 \u00b1 25\n32 \u00b1 30\n0.12\nSouth Atlantic\n34 \u00b1 11\n6 \u00b1 7\n40 \u00b1 7\n0.06\nNorth Atlantic (<44\u02daN)\n75 \u00b1 33\n20 \u00b1 17\n95 \u00b1 46\n0.10\nNorth Atlantic (>44\u02daN)\n19 \u00b1 6\n240 \u00b1 13\n220 \u00b1 16\n0.08\nGlobal Ocean\n398 \u00b1 81\n0\n398 \u00b1 81\n1.00\nWe identify robust redistributed warming signals in the subtropical North Atlantic and Southern Ocean. Warming in the subtropical North Atlantic is compensated by cooling in the subpolar North Atlantic consistent with a 40 \u00b1 13 TW southward transport of heat across 44\u02daN (Figure 6c). Southward heat redistribution across 32S brings 118 \u00b1 50 TW into the Southern Ocean.\nDiscussion\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/zika21.html"}
{"id": "e85a386fd775-6", "text": "Table 1: Material, redistribution, and total contributions to heat content change by ocean basin in terawatts and area as fraction of global ocean area. Heat content change estimates are based on differences between the periods 2006\u201311 and 2012\u201317 inclusive. Uncertainties are \u00b12 standard deviations. The Southern Ocean is de\ufb01ned as the entire ocean south of 32\u02daS. The South Paci\ufb01c, South Atlantic, and Indian Ocean estimates exclude the ocean south of 32S. The North Atlantic is split into a region south of and a region north of 44\u02daN. The latter includes the Arctic Ocean.\nMaterial\nRedistributed\nTotal\nArea fraction\nSouthern Ocean\n90 \u00b1 18\n118 \u00b1 50\n208 \u00b1 63\n0.27\nSouth Pacific\n53 \u00b1 16\n226 \u00b1 22\n28 \u00b1 22\n0.15\nNorth Pacific\n82 \u00b1 25\n261 \u00b1 55\n21 \u00b1 54\n0.23\nIndian Ocean\n45 \u00b1 10\n213 \u00b1 25\n32 \u00b1 30\n0.12\nSouth Atlantic\n34 \u00b1 11\n6 \u00b1 7\n40 \u00b1 7\n0.06\nNorth Atlantic (<44\u02daN)\n75 \u00b1 33\n20 \u00b1 17\n95 \u00b1 46\n0.10\nNorth Atlantic (>44\u02daN)\n19 \u00b1 6\n240 \u00b1 13\n220 \u00b1 16\n0.08\nGlobal Ocean\n398 \u00b1 81\n0\n398 \u00b1 81\n1.00\nWe identify robust redistributed warming signals in the subtropical North Atlantic and Southern Ocean. Warming in the subtropical North Atlantic is compensated by cooling in the subpolar North Atlantic consistent with a 40 \u00b1 13 TW southward transport of heat across 44\u02daN (Figure 6c). Southward heat redistribution across 32S brings 118 \u00b1 50 TW into the Southern Ocean.\nDiscussion\uf0c1\nRecent anomalous southward heat transport in the North Atlantic has been well documented and has been attributed to a downturn in the Atlantic meridional overturning circulation (Smeed et al. 2014; Bryden et al. 2020). Observed heat transport anomalies equate to a downturn in meridional heat transport equivalent to -23 \u00b1 60 TW for the period 2006-11 versus 2012\u201317 at 26\u02daN in the Atlantic [see appendix B for details of this calculation, which is based on data from Bryden et al. (2020)], which is consistent with our estimate of the change in redistribution heat transport of -23 \u00b1 19 TW (Figure 6; uncertainties are \u00b12 standard deviations).\nThe large apparent meridional heat transport we have identified in the Southern Ocean was previously identified by Roberts et al. (2017) based on the residual of observed OHC change and estimates of air-sea heat fluxes. Their approach captures additional heat in the system where it is fluxed into the ocean while our approach estimates how that heat is distributed. Nonetheless, the correspondence between our results and theirs is reassuring and perhaps not surprising if the redistribution signal is large as both approaches indicate.\nThe approach of Zanna et al. (2019) is more directly comparable to ours. They reconstruct the passive contribution to ocean warming since 1850 by propagating SST anomalies into the ocean interior using Green\u2019s functions. They report changes for a much longer time frame (1955-2017 as opposed to our 2006-17), and therefore magnitudes of warming estimates are not comparable, but a comparison of patterns of change is relevant. In terms of our zonally averaged material warming and their \u201cpassive warming\u201d the two datasets share peaks at approximately 35\u02daS and 35\u02daN potentially attributable to surface Ekman convergence (see their Fig. 3).\nZanna et al. (2019) report relatively small amounts of passive warming at low-latitude regions while we report a peak in material warming there. This may suggest that the material warming we estimate at low latitudes is in fact related to interannual to decadal variability. An explanation of this may be that the lower low-latitude SST corresponds to a predominance of a negative IPO (Lyu et al. 2017), leading to anomalous ocean heat uptake over our study period. This is a commonly cited explanation for the so-called global warming hiatus discussed in the 2010s (Whitmarsh et al. 2015).\nZanna et al. (2019) compare their inferred passive warming between 1955 and 2017 to the warming observed in situ. Based on this they find evidence of a southward redistribution of heat in the Northern Hemisphere but no substantial southward redistribution in the Southern Hemisphere. This suggests that the southward redistribution of heat inferred by both Roberts et al. (2017) and this study in the Southern Hemisphere may be a more recent occurrence. Indeed, two recent studies have shown that the Southern Hemisphere dominance of ocean heat content change during the twenty-first century is not consistently represented in historical climate simulations and is likely linked to internal variability (Bronselaer and Zanna 2020; Rathore et al. 2020).\nHere we have exclusively analyzed the Hadley Centre\u2019s EN4 dataset. Sensitivity to observational coverage is mitigated in part by our consideration of data during the Argo observing period (2006-17). We consider uncertainties to have been reasonably estimated based on our bootstrapping approach, which subsamples those years (see section c of appendix A). Because of EN4\u2019s mapping approach, however, regions where minimal observations were made (e.g., the marginal ice zones in the Southern Hemisphere and below 2000 m) will likely have muted trend estimates. This issue will require special attention when our method is applied to the pre-Argo period and in particular with regard to salinity observations, which are less numerous than temperature observations (Clement et al. 2020).\nConclusions\uf0c1\nIn summary we have shown the following:\nWater mass changes between 2006-11 and 2012-17 can be interpreted in terms of material warming across the globe and with the highest concentrations in the tropical and subtropical North Atlantic Ocean, consistent with simulations of the addition of heat into the ocean due to greenhouse forcing.\nThe majority of the variance in ocean heat content change at scales of 1\u02da-by-1\u02da over that period can be explained by a redistribution of existing water masses within the ocean.\nThe inferred redistribution indicates a downturn in northward meridional heat transport into the subpolar North Atlantic of 40 \u00b1 13 TW and an anomalous southward heat transport into the Southern Ocean of 118 \u00b1 50 TW.\nThe material warming signal that we have inferred is generally weaker than redistribution, but the signal is far less sensitive to changes in the years over which the analysis was carried out. This suggests that material warming may be giving a robust indication of slow thermodynamic changes in the ocean. This could be a result of anthropogenic forcing, although that would be remarkable since the midpoints of the early and late periods are only 6 years apart.\nWe expect the strength of the material warming signal to increase into the future as the ocean warms. However, since the redistribution signal is so large, circulation changes and variability must be understood if near-term ocean temperature variability and regional sea level change are to be projected accurately.", "source": "https://sealeveldocs.readthedocs.io/en/latest/zika21.html"}
{"id": "a4e559be412f-0", "text": "Hughes et al. (2010)\uf0c1\nTitle:\nIdenti\ufb01cation of jets and mixing barriers from sea level and vorticity measurements using simple statistics\nKey Points:\nSkewness and kurtosis in sea level data can be used to identify oceanic fronts and mixing barriers.\nRegions indicative of strong jets are associated with zero skewness and low kurtosis.\nGeostrophic relative vorticity was the preferred variable to represent local dynamics.\nKeywords:\nskewness, kurtosis, sea level, vorticity, jet, meander, mixing, AVISO, altimetry\nCorresponding author:\nChris W. Hughes\nCitation:\nHughes, C. W., Thompson, A. F., & Wilson, C. (2010). Identification of jets and mixing barriers from sea level and vorticity measurements using simple statistics. Ocean Modelling, 32(1\u20132), 44\u201357. doi:10.1016/j.ocemod.2009.10.004\nURL:\nhttps://doi.org/10.1016/j.ocemod.2009.10.004\nAbstract\uf0c1\nThe probability density functions (PDFs) of sea level and geostrophic relative vorticity are examined using satellite altimeter data. It is shown that departures from a Gaussian distribution can generally be repre.sented by two functions, and that the spatial distribution of these two functions is closely linked to the skewness and kurtosis of the PDF. The patterns indicate that strong jets tend to be identi\ufb01ed by a zero contour in skewness coinciding with a low value of kurtosis. A simple model of the statistics of a mean.dering frontal region is presented which reproduces these features. Comparisons with mean currents and sea surface temperature gradients con\ufb01rm the identi\ufb01cation of these features as jets, and con\ufb01rm the existence of several Southern Ocean jets unresolved by drifter data. Diagnostics from a range of idealized eddying model simulations show that there is a strong, simple relationship between kurtosis of potential vorticity and effective diffusivity. This suggests that kurtosis may provide a simple method of mapping mixing barriers in the ocean.\nIntroduction\uf0c1\nMore than a decade of precise satellite altimeter measurements has produced long time series of sea level h, over most of the global ocean. As a way of representing the different variations seen in different regions, it is common to plot the root-mean-square devi.ation of sea level from its mean, r.h., or the geostrophic eddy kinetic energy (EKE), large values of which tend to be associated with strong, eddying currents. More recently, Thompson and Demirov (2006) noted that there is further interesting information in the skewness $S(h)$ of the sea level distribution, which tends to be positive on the poleward side of strong eastward currents, and negative on the equatorward side. They interpreted this as indica.tive of the intermittent passage of warm core eddies or warm meanders across points poleward of a jet, and of cold core eddies or meanders on the equatorward side.\nThis prompts the question of whether higher moments of variability contain further information, and how those moments might be interpreted. More generally, what is the spatial variation in the PDF of sea level, and what causes that variation? In considering this question, we found that sea level, being a non-local variable from a dynamical point of view, is sometimes more dif\ufb01cult to interpret than the more localized relative vorticity, so in much of the work presented here we focus on the PDF of relative vorticity $zeta$.\nWe show below that, in fact, maps of skewness $S$ and kurtosis $K$ contain most of the information which can be reliably extracted from PDFs at each position. These are de\ufb01ned as\n$$ S(chi) = frac{frac{1}{n}sum_nchi^3}{(frac{1}{n}sum_nchi^2)^{frac{3}{2}}} $$, (1)\n$$ K(chi) = frac{frac{1}{n}sum_nchi^4}{(frac{1}{n}sum_nchi^2)^2} $$, (2)\nP3=2 ;\n1 x2\nn Pn\nwhere $chi$ is the deviation of some quantity from its mean value. Skewness is a measure of asymmetry of the PDF. Where rare, large events predominantly have one sign, this is the sign of the skewness; a Gaussian distribution is symmetric and therefore has a skewness of zero. Kurtosis is traditionally described as a measure of \u2018\u2018peakiness\u201d of the PDF. High kurtosis means that rare, large amplitude events occur more frequently than would be expected for a Gaussian distribution, producing a more sharply peaked PDF with broader tails than a Gaussian. Low kurtosis means that events much larger than typical are rarer than would be expected from a Gaussian distribution, and the associated PDF tends to be \ufb02at near its peak, or even bimodal, and drops to small values faster than a Gaussian. The smallest possible kurtosis is 1, and this results from a variable taking only two possible values, with equal probability. A Gaussian distribution leads to a kurtosis of 3. For this reason, the quantity $K - 3$ is often used, sometimes termed excess \u2018\u2018kurtosis\u201d and sometimes simply \u2018\u2018kurtosis\u201d . We will use the definition given above and, when 3 is subtracted, this will be stated explicitly.\nOur dataset consists of the AVISO gridded sea level anomaly (corrected for tides and inverse barometer effect) supplied weekly on a 1/3 degree Mercator grid. While the grid is 1/3 degree, the spacing between altimeter tracks is 0.72 degrees of longitude for ERS/Envisat, and 2.78 degrees for Topex or Jason, so we should not expect to resolve all features less than about 100 km across. We use the \u2018\u2018reference\u201d version of the data in which sampling is always from two altimeters (Topex/Poseidon or Jason 1 and ERS or Envisat) in the same two orbits, and consider 690 weeks spanning the period 5th April 1995\u201311th June 2008 which follows the period when ERS-1 was not in the standard 35-day repeat orbit. Geostrophic relative vorticity anomalies are calculated by \ufb01rst-order centered differencing of the sea level to give geostrophic velocity, and the same form of differencing to then give vorticity at the same grid points as the sea level data. These are divided by the local Coriolis parameter $f$ so that positive values represent cyclonic, and negative values anti-cyclonic, relative vorticity.\nAs we are interested in the shape of the PDFs rather than their widths, we consider only time series which have had their means removed and have been divided by their standard deviations. In fact, we also subtract an annual and semiannual cycle and a linear trend, simultaneously \u00det to each time series. It is also worth noting a limitation of the geostrophic relative vorticity calculation. The effect of nonlinear terms in the momentum equation is such that the geostrophic velocity (and hence vorticity) is an underestimate in cyclonic vortices, and an overestimate in anticyclonic vortices. This potential bias should be kept in mind, although it is not particularly important for the main issue we consider here, which focuses on the step-like structure in jets.\nBinning the resulting normalized PDFs from each grid point into bins 0.01 standard deviations wide, and averaging over the globe (excluding the band within 5 degrees of the equator in the case of vorticity, to avoid the equatorial singularity), produces the average PDFs shown on both logarithmic and linear scales in Fig. 1. The dashed lines show the corresponding Gaussian PDF for reference. We see that the average shape of the PDF for both sea level and relative vorticity is fairly close to Gaussian, but significantly above Gaussian in the wings and centre of the distribution (and below Gaussian in between). Gille and Sura (submitted for publication) look at the overall global relationship between skewness and kurtosis seen from such PDFs, and similar characterization of the velocity PDFs from altimetry has been investigated by Schorghofer and Gille (2002) and Gille and Llewellyn-Smith (2000). This average shape, however, conceals a large geographic variation. Characterization of this spatial variability is the subject of the next section.\nFig. 1: Global average, normalized PDF of (left) sea level, and (right) geostrophic relative vorticity $zeta/f$f from gridded altimetry. The same data are shown on (top) logarithmic and (bottom) linear scales. In each panel, the dotted line is the corresponding Gaussian PDF.\nSpatial variations of the PDFs\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/hughes10.html"}
{"id": "a4e559be412f-1", "text": "As we are interested in the shape of the PDFs rather than their widths, we consider only time series which have had their means removed and have been divided by their standard deviations. In fact, we also subtract an annual and semiannual cycle and a linear trend, simultaneously \u00det to each time series. It is also worth noting a limitation of the geostrophic relative vorticity calculation. The effect of nonlinear terms in the momentum equation is such that the geostrophic velocity (and hence vorticity) is an underestimate in cyclonic vortices, and an overestimate in anticyclonic vortices. This potential bias should be kept in mind, although it is not particularly important for the main issue we consider here, which focuses on the step-like structure in jets.\nBinning the resulting normalized PDFs from each grid point into bins 0.01 standard deviations wide, and averaging over the globe (excluding the band within 5 degrees of the equator in the case of vorticity, to avoid the equatorial singularity), produces the average PDFs shown on both logarithmic and linear scales in Fig. 1. The dashed lines show the corresponding Gaussian PDF for reference. We see that the average shape of the PDF for both sea level and relative vorticity is fairly close to Gaussian, but significantly above Gaussian in the wings and centre of the distribution (and below Gaussian in between). Gille and Sura (submitted for publication) look at the overall global relationship between skewness and kurtosis seen from such PDFs, and similar characterization of the velocity PDFs from altimetry has been investigated by Schorghofer and Gille (2002) and Gille and Llewellyn-Smith (2000). This average shape, however, conceals a large geographic variation. Characterization of this spatial variability is the subject of the next section.\nFig. 1: Global average, normalized PDF of (left) sea level, and (right) geostrophic relative vorticity $zeta/f$f from gridded altimetry. The same data are shown on (top) logarithmic and (bottom) linear scales. In each panel, the dotted line is the corresponding Gaussian PDF.\nSpatial variations of the PDFs\uf0c1\nSkewness and kurtosis are the first two in an infinite series of moments which characterize the shape of the PDF, following the mean and standard deviation which characterize its position and width. However, it is not immediately clear that these are the parameters best suited to describing the spatial variations in shape. Furthermore, as kurtosis is particularly sensitive to rogue large values in a dataset (it is sometimes used as an indicator of bad data), it is quite possible for much of the shape of the PDF to be invisible to the kurtosis in cases where one particularly large value occurs. For this reason, we seek to characterize the typical variations in shape of the PDF, ignoring the very extreme wings of the distribution.\nTo do this, we use empirical orthogonal function (EOF) analysis. This is often used to calculate spatial patterns associated with the principal modes of variability of time series given at each grid point. Here, instead of time, we are using the x-axis of the normalized PDF graph at each grid point. Rather than calculate EOFs of the complete PDF, we choose fist to subtract the Gaussian PDF so that we will clearly be mapping departures from Gaussian behavior. We obtain a set of orthonormal eigenvectors, the first of which explains the largest possible amount of spatial variability in the PDF, the second of which describes as much as possible of the remaining variability after removing the effect of the first mode, and so on. The associated eigenvalues give the amount of variance explained by each mode.\nThere are not enough points in a time series at one point to produce a PDF with such high resolution as in Fig. 1, so here we increase the bin size to 0.1 standard deviations, and consider only the 80 points between -4 and +4 standard deviations (this avoids the inclusion of any very extreme values). The analysis was also repeated with a bin size of 0.4 standard deviations, and only 20 points per PDF, with very similar results to those presented here.\nThe first 15 eigenvalues of the resulting EOFs are plotted in Fig. 2, as percentages of the total variance (diamonds for the sea level EOFs and crosses for relative vorticity). In both cases, the first two eigenvalues stand clearly above the background continuum, together explaining 28.8% of the sea level variance and 22.7% of relative vorticity variance. In the case of sea level, the second two EOFs may also plausibly be said to stand above the background. Inspection of the associated eigenvectors clearly shows the remaining EOFs to be associated with statistical noise, representing simply the exchange of probability between neighbouring bins (using coarser bins reduces the amplitude of this noise, leaving the first two EOFs to account for 61.7% of variance for sea level and 60.6% for relative vorticity, but does not lead to identification of any more significant modes).\nFig. 2: Eigenvalues of the first 15 EOFs of the PDFs for (diamonds) sea level and (crosses) relative vorticity. Eigenvalues are normalized so that they sum to 100, and each represents the percentage of variance explained by the corresponding eigenvector.\nSince we are interested in relating the variations in PDFs to skewness and kurtosis, it would be nice if the EOFs fell naturally into symmetric and antisymmetric categories. They do not, but the importance of symmetry is clear from the fact that very nearly symmetric and antisymmetric functions can be formed from the obvious pairs of EOFs. If we take the first two EOFs of sea level, we can construct from these by a rotation, two different orthonormal vectors $mathbf{C}$ and $mathbf{D}$ chosen to minimize the quantity $(mathbf{C} +mathbf{C}^r)^2 + (mathbf{D} -mathbf{D}^r)^2$, where the superscript $r$ represents the reverse of the vector (i.e. the components listed in reverse order). This minimizes the sum of the squares of the symmetrical component of $mathbf{C}$ and the antisymmetric component of $mathbf{D}$. In other words, $mathbf{C}$ represents a linear combination of the first two EOFs which is close to antisymmetric, and $mathbf{D}$ an orthogonal linear combination which is close to symmetric. The results of such a minimization applied to the pairs of EOFs identified from Fig. 2 are shown in Fig. 3. The solid lines are constructed from pairs of EOFs of the sea level PDFs, and dashed lines from relative vorticity. To show how closely these approximate the ideal symmetry, crosses represent the exactly antisymmetric or exactly symmetric components of the corresponding sea level EOF curves. Success in this minimization is not inevitable. For example, no combination of the first and third EOFs can produce anything like a symmetric and antisymmetric pair of functions. This success suggests that it is meaningful to combine the EOFs in this way.\nFig. 3: Rotated eigenvectors of the first 4 EOFs (solid) of the PDFs for sea level and the first 2 EOFs (dashed) for relative vorticity. Crosses are half of the corresponding sea level vector plus or minus its reverse, illustrating the corresponding perfectly symmetrical or antisymmetric curves.\nThe projection of the PDFs onto these rotated EOFs is shown in Figs. 4 and 5. The pattern of the first rotated EOF for sea level is clearly very similar to the skewness map presented by Thompson and Demirov (2006). Major eastward currents are delineated by the boundary between large positive and large negative values, and preferred paths of eddies, such as in the Alaskan Stream along the Aleutian island chain at the northern boundary of the Paci\u00dec (Ueno et al., 2009), and southwest of Australia (Morrow et al., 2004) also stand out. The tropical Paci\u00dec is also prominent. As Thompson and Demirov (2006) point out, this is the result of the dominance of the large 1997\u00d01998 El Nino event in the region. This highlights a disadvantage of considering sea level: large scale sea level signals can dominate the time series at a given point, but there may be little or no associated current or other dynamical change at that point. Dynamically, sea level is a non-local variable on time scales of several days or longer. For this reason, the localization of physical processes is better determined using vorticity or potential vorticity. This is illustrated for relative vorticity in Fig. 5. The spatial pattern for the first rotated EOF is clearly related to that for sea level (with a sign change since a positive localized sea level anomaly represents an anticyclonic circulation), but the relative vorticity map shows finer scales and more localized structures (particularly in the Southern Ocean) than the corresponding map based on sea level. Using relative vorticity also avoids a dominant influence of the El Nino event, making it possible to pick out clear structures to the west of Hawaii and Central America.\nFig. 4: Projection of the sea level PDFs onto the first and second rotated eigenvectors from Fig. 3.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hughes10.html"}
{"id": "a4e559be412f-2", "text": "Fig. 3: Rotated eigenvectors of the first 4 EOFs (solid) of the PDFs for sea level and the first 2 EOFs (dashed) for relative vorticity. Crosses are half of the corresponding sea level vector plus or minus its reverse, illustrating the corresponding perfectly symmetrical or antisymmetric curves.\nThe projection of the PDFs onto these rotated EOFs is shown in Figs. 4 and 5. The pattern of the first rotated EOF for sea level is clearly very similar to the skewness map presented by Thompson and Demirov (2006). Major eastward currents are delineated by the boundary between large positive and large negative values, and preferred paths of eddies, such as in the Alaskan Stream along the Aleutian island chain at the northern boundary of the Paci\u00dec (Ueno et al., 2009), and southwest of Australia (Morrow et al., 2004) also stand out. The tropical Paci\u00dec is also prominent. As Thompson and Demirov (2006) point out, this is the result of the dominance of the large 1997\u00d01998 El Nino event in the region. This highlights a disadvantage of considering sea level: large scale sea level signals can dominate the time series at a given point, but there may be little or no associated current or other dynamical change at that point. Dynamically, sea level is a non-local variable on time scales of several days or longer. For this reason, the localization of physical processes is better determined using vorticity or potential vorticity. This is illustrated for relative vorticity in Fig. 5. The spatial pattern for the first rotated EOF is clearly related to that for sea level (with a sign change since a positive localized sea level anomaly represents an anticyclonic circulation), but the relative vorticity map shows finer scales and more localized structures (particularly in the Southern Ocean) than the corresponding map based on sea level. Using relative vorticity also avoids a dominant influence of the El Nino event, making it possible to pick out clear structures to the west of Hawaii and Central America.\nFig. 4: Projection of the sea level PDFs onto the first and second rotated eigenvectors from Fig. 3.\nFig. 5: Projection of the relative vorticity PDFs onto the first and second rotated eigenvectors from Fig. 3.\nThe projections of sea level and relative vorticity PDFs onto the second rotated EOFs bear a similar relationship to each other (without the sign change, since the second rotated EOF is close to symmetrical). Strong currents now stand out as low values of the projection, and these features are more clearly de\u00dened in the relative vorticity plot.\nFrom the forms of the EOFs, we expect the projections to be closely related to skewness and kurtosis respectively, and Fig. 6 shows that this is the case for relative vorticity (the equivalent maps for sea level skewness and kurtosis are not shown, but bear a similar relation to the sea level EOF projections). The EOF projections can be described as slightly \u201ccleaner\u201d: definition of some features is better, such as the Loop Current in the Gulf of Mexico, and features along the Falklands shelf. There are also some isolated spots of large skewness and kurtosis which are not visible in the EOF maps, which suggests that they may be due to rogue data points (a few time series which have been checked are consistent with this, consisting of a rather \u00dfat curve with one sudden spike). A problem with the gridding in the region north of Iceland and Norway also shows up much more clearly in skewness and kurtosis than in the EOF maps. However, it can generally be said that maps of skewness and kurtosis are capturing the same spatial variability as the two EOF maps and, since only two EOFs are above the background noise for relative vorticity, that means that skewness and kurtosis capture all that can currently be captured about spatial variations in the PDF of relative vorticity. In the case of sea level, the spatial patterns associated with the third and fourth rotated EOFs (not shown) appear very noisy except in the vicinity of the very strongest currents, suggesting that they do contain physically meaningful information, but only in these select regions.\nFig. 6: Skewness and kurtosis of relative vorticity time series.\nIt is difficult to assess the statistical noise levels on these estimates, as the weekly sea level maps are not independent. A standard result estimates the standard error on skewness as $sqrt{6/n}$, and that on kurtosis as $sqrt{24/n}$, where $n$ is the number of independent samples, although kurtosis has a strongly asymmetric distribution, having a minimum value of 1, Gaussian value of 3 and in\u00denite maximum possible value for a continuous PDF. As a guide, the 5 and 95 percentiles for skewness and kurtosis generated from a Gaussian distribution sampled at a \u00denite number $n$ of independent times have been calculated by Monte Carlo simulation (using 100,000 random input time series) for $n = 690$ (the number of points in the time series), $n = 300$, and $n = 100$. The results are shown in Table 1. The strongest justification for the significance of these results, however, is the spatial coherence and physical plausibility of the resulting patterns.\nTable 1: Values of skewness ($S$), kurtosis minus 3 $(K - 3)$ and projections of rotated EOF1 and rotated EOF2 generated by chance from \u00denite samples of length $n$ taken from Gaussian distributions. The 5th and 95th percentiles are given.\n$n$\n%\n$S$\n$K - 3$\nEOF1\nEOF2\n690\n5\n-0.14\n-0.36\n-0.10\n-0.11\n95\n0.14\n0.16\n0.10\n0.07\n300\n5\n-0.21\n-0.48\n-0.15\n-0.16\n95\n0.21\n0.29\n0.15\n0.12\n100\n5\n-0.36\n-0.73\n-0.26\n-0.27\n95\n0.36\n0.51\n0.26\n0.23\nInterpretation of low kurtosis regions\uf0c1\nAs stated in the introduction, the lowest possible kurtosis is 1, and occurs when the variable ($zeta/f$ or $h$) is always at one of two values, and occupies those two values with equal probability. Consider a sharp jet, which may be approximated as a step in sea level. If that jet meanders, then sea level within the region over which it meanders will always be at one of two values (either to the left, or to the right of the jet). Along some line, the jet will spend equal amounts of time to the left and to the right of that line. On that line, the kurtosis of sea level would be 1.\nOff the line, the fraction of time spent in each state varies, becoming more asymmetrical with distance from the centre line until beyond the limit of meanders where sea level becomes constant. If the fractions of time spent at each value are $A$ at the lower value, and $B = 1 - A$ at the higher value, then it is simple to calculate that $K = -3 + 1/P$, $S = (A -B)/sqrt{P}$, $S^2 = -4 + 1/P$, where $P = AB$ has a maximum possible value of 1/4. It will be noticed that this rather extreme situation gives the relationship $K = S^2 + 1$. This in fact represents the minimum possible $K$ for a given $S$ (Pearson, 1916). Idealized though this model is, it does capture the main features surrounding jets in Fig. 6: low kurtosis and zero skewness at the centre (mean position) of the jet, with kurtosis growing to large positive values on either side, as skewness grows to large positive values on one side and large negative values on the other side of the jet.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hughes10.html"}
{"id": "a4e559be412f-3", "text": "0.10\n0.07\n300\n5\n-0.21\n-0.48\n-0.15\n-0.16\n95\n0.21\n0.29\n0.15\n0.12\n100\n5\n-0.36\n-0.73\n-0.26\n-0.27\n95\n0.36\n0.51\n0.26\n0.23\nInterpretation of low kurtosis regions\uf0c1\nAs stated in the introduction, the lowest possible kurtosis is 1, and occurs when the variable ($zeta/f$ or $h$) is always at one of two values, and occupies those two values with equal probability. Consider a sharp jet, which may be approximated as a step in sea level. If that jet meanders, then sea level within the region over which it meanders will always be at one of two values (either to the left, or to the right of the jet). Along some line, the jet will spend equal amounts of time to the left and to the right of that line. On that line, the kurtosis of sea level would be 1.\nOff the line, the fraction of time spent in each state varies, becoming more asymmetrical with distance from the centre line until beyond the limit of meanders where sea level becomes constant. If the fractions of time spent at each value are $A$ at the lower value, and $B = 1 - A$ at the higher value, then it is simple to calculate that $K = -3 + 1/P$, $S = (A -B)/sqrt{P}$, $S^2 = -4 + 1/P$, where $P = AB$ has a maximum possible value of 1/4. It will be noticed that this rather extreme situation gives the relationship $K = S^2 + 1$. This in fact represents the minimum possible $K$ for a given $S$ (Pearson, 1916). Idealized though this model is, it does capture the main features surrounding jets in Fig. 6: low kurtosis and zero skewness at the centre (mean position) of the jet, with kurtosis growing to large positive values on either side, as skewness grows to large positive values on one side and large negative values on the other side of the jet.\nThe observed values of $K$ are, inevitably, never as low as this extreme model would predict. This prompts a slightly more sophisticated model: instead of constant sea level to either side of the jet, add Gaussian noise to the sea level on either side. Thus, we consider the situation in which there is a sharp step in sea level across the jet, which meanders, but there is also random sea level variability producing a Gaussian PDF either side of the step (for simplicity, we choose the standard deviations of the Gaussians to be the same on each side of the step). The time series at any point is then a random variation about a certain mean at times when the point is to the north of the jet, and a random variation about a different mean at times when the point is to the south of the jet. The resulting PDF consists of the sum of two Gaussian PDFs, with centres separated by a distance $d$ (the size of the step). We measure $d$ in units of the Gaussian standard deviation, so that $d$ represents the ratio of step size to the size of the Gaussian noise. We now define $A$ as the integral of the Gaussian centered at the lower value (i.e. the probability of being on the low side of the step), and $B = 1 - A$ is the integral of the second Gaussian. Again, we will have $A = B = 0.5$ at the mean central position of the jet, with $A$ decreasing and $B$ increasing to one side of that point, and the converse on the other side.\nAt the jet centre, the sum of two Gaussians with small separation would produce a PDF with a flatter centre region than a single Gaussian alone (and hence kurtosis less than 3). For larger separation ($d > 2$) the PDF becomes bimodal, and kurtosis becomes even smaller, dropping towards 1 as the separation of the Gaussians becomes larger (when the noise to either side of the jet becomes a small fraction of the size of the step).\nFig. 7: Time series of relative vorticity (plotted as $zeta/f$) from two points with particularly low kurtosis, from (top) the Gulf Stream extension and (bottom) the Agulhas Return Current. Panels to the right show the corresponding PDF, calculated by kernel density estimation using a Gaussian kernel of standard deviation 0.2.\nFig. 7  shows the time series, and associated normalized PDF, for $zeta/f$ at two points of particularly low kurtosis in the Gulf Stream extension and the Agulhas Return Current. In both cases the vorticity clearly spends about half its time in the vicinity of one value, and half its time close to another value, with clusters about those two values overlapping to a degree, but clearly separate. This is reflected in the bimodal PDFs.\nThe model remains simplified, but this has the advantage that it can be solved analytically for skewness and kurtosis as a function of $A$ and $d$. The resulting relationships (derived in Appendix A) are\n$$ K - 3 = frac{d^4P(1-6P)}{(1 + d^2P)^2} $$, (3)\n$$ S = frac{d^3P(A-B)}{(1+d^2P)^{3/2}} $$, (4)\n$$ S^2 = frac{d^6P^2(1-4P)}{(1+d^2P)^3} $$, (5)\nremembering that $B = 1 - A$ and $P = AB$. At the mean position of the jet, $A = B = 1/2$ giving a skewness of zero, and reducing (3) to $K = 3 - 2/(1 + 4/d^2)^2$. A series of curves, each corresponding to changing $A$ at constant $d$ (i.e. representing how skewness and kurtosis would vary across a jet for a particular ratio of noise to step size) is shown as the thin black curves in Fig. 8. The different curves represent integer values of $d$ from 1 to 6 (inner\u00d0outer), showing how the distance from the Gaussian values $S = 0$, $K = 3$ increases as the step size $d$ increases in comparison to the noise. To understand this plot, consider a jet with negative skewness to the south (for relative vorticity, an eastward jet in the southern hemisphere would show this pattern, for sea level it would be a northern hemisphere jet). As we move from south to north, we follow one of the curves in an anticlockwise direction. Far to the south, the noise dominates over the influence of the jet and the PDF is a single Gaussian ($P = 0$), producing $S = 0$, $K = 3$. As the influence of sea level from the other side of the jet becomes stronger ($P$ increases), skewness decreases and kurtosis increases, reaching a maximum at $P = 1/(d^2+12)$. Kurtosis then starts to decrease while skewness continues to decrease until it reaches a minimum at $P = 2/(d^2+12)$, where $K = 3 + 3S^2/2$. Kurtosis drops below 3 at $P = 1/6$, decreasing to its minimum at the centre of the jet where $P = 1/4$, $S = 0$. Then kurtosis starts to rise and the curve follows the positive skewness branch to the right and up, returning finally to $S = 0$, $K = 3$ far to the north.\nFig. 8: The relationship between skewness and kurtosis in the vicinity of a front. Thin curves represent the relationship resulting from the simple model described in the text. Each curve corresponds to a particular ratio d of step size to noise (values d .1\u00d06 are plotted), with curves becoming larger as d increases (noise decreases). For relative vorticity, the curve is followed anticlockwise when passing from poleward to equatorward of an eastward jet. Crosses are values at points in the vicinity of the Agulhas Return Current. The thick line with diamonds is the trajectory described by statistics averaged at constant meridional distance from the centre of the current.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hughes10.html"}
{"id": "a4e559be412f-4", "text": "Fig. 8: The relationship between skewness and kurtosis in the vicinity of a front. Thin curves represent the relationship resulting from the simple model described in the text. Each curve corresponds to a particular ratio d of step size to noise (values d .1\u00d06 are plotted), with curves becoming larger as d increases (noise decreases). For relative vorticity, the curve is followed anticlockwise when passing from poleward to equatorward of an eastward jet. Crosses are values at points in the vicinity of the Agulhas Return Current. The thick line with diamonds is the trajectory described by statistics averaged at constant meridional distance from the centre of the current.\nFor small $d$ (small step size compared to noise), the trajectories remain close to $S = 0$, $K = 3$, extending further from this point as $d$ increases. In fact, allowing all values of $d$ produces a family of curves which \u00dell the entire allowed space $K geq S^2 + 1$. Only for $d > 2$ does the PDF become bimodal at the jet centre, at which point we would then have $K < 2.5$, although for more general distributions, the PDF can only be guaranteed to be bimodal if $K < S^2 + 1.512$ (Klaassen et al., 2000).\nThere are many ways in which this model is oversimplified. Noise is the same (and Gaussian) on either side of the jet, and the jet is still modelled as a step function. A slightly more realistic model has also been investigated numerically, modelling the jet as $a(t)tanh{(chi - chi_0(t))} + b(t)$, with Gaussian random time series for $a$, $b$, and $chi_0$. Results from this are not shown as the curves produced are very similar (though not identical) to those given by the simpler model, and do not seem to provide much greater insight. Two main criteria determine whether the trajectory forms a wide loop about the point $S = 0$, $K = 3$: the jet must meander by more than its width, and the sea level noise either side of the jet must be smaller than the sea level step across the jet.\nWe have illustrated the actual skewness-kurtosis relationship for the Agulhas return current in Fig. 8. The centre of the jet at each longitude between 23.3\u02daE and 50\u02daE was defined as the point of minimum kurtosis in a narrow latitude range south of Africa. Kurtosis and skewness were then regridded, shifting each longitude to the north or south so that it was centered on the jet centre. Skewness and kurtosis at all points from 10 grid points south to 10 grid points north of the centre (a total range of about 4.8 degrees) are plotted in the figure as grey crosses. Then skewness and kurtosis were averaged at constant northward distance from the jet centre, and the resulting trajectory plotted as the thick line in Fig. 8.\nAlthough the relationship does not lie along a particular constant $d$ curve, it is clear that the trajectory forms a fairly broad loop around $S = 0$, $K = 3$, often outside the $d = 2$ contour, and with minimum $K$ below 2.5 consistent with the observed bimodal distribution, and with the interpretation as a meandering jet. The asymmetry is interesting, suggesting that noise is more significant in the Antarctic Circumpolar Current (ACC) to the south of the jet, and that the meanders are the more dominant signal on the northern side, in the Indian Ocean. Thus, although kurtosis falls below 3 only in a small region around the mean jet position, the statistics remain consistent with interpretation as the effect of a meandering jet to a distance of several degrees either side of the jet.\nIt will not have escaped the reader\u00d5s attention that the discussion has been in terms of sea level, whereas most of the illustrations are of relative vorticity. While it is clear that a jet must be associated with a drop in sea level, the associated vorticity pattern is not so clear, except to note that, as velocity is a maximum at the jet centre (assuming an eastward jet), relative vorticity must be cyclonic on the poleward side and anticyclonic on the equatorward side of the jet, and small far from the jet. It is not inevitable that the strongest gradient in relative vorticity lies at the jet centre.\nIn one sense, it does not matter. The arguments above apply if there is a sharp, meandering front in any quantity, and the low kurtosis region can then be taken to represent the mean position of that front. However, there is a more concrete model which is rather appealing, which is clearest if we consider things in terms of potential vorticity (PV). One model of a jet, recently reviewed by Dritschel and McIntyre (2008, D&M hereafter, see also references therein), is as the result of a step in PV. In this paradigm, jets represent a barrier to the mixing of PV, so PV tends to become mixed to two different, constant values either side of a jet, with a sharp gradient across the jet. In turn, inverting the PV distribution shows that such a PV staircase actually implies the existence of a jet at the position of the PV step, so a positive feedback exists tending to maintain this configuration. As PV is materially conserved, time series of PV in the vicinity of the jet will be close to the ideal of switching between two constant values which produces the lowest possible kurtosis values for a given skewness.\nOur time series is, of necessity, relative vorticity rather than PV. However, if we assume we are in a dynamical regime in which variations of PV are dominated by vorticity rather than thickness variations (or if we assume a constant relationship between thickness and relative vorticity changes), then the time series of relative vorticity at a fixed point (so that $f$ is constant) will be equivalent to time series of PV. In this case, we can see that the low kurtosis regions are consistent with the existence of a PV step at the jet centre. This prompts the question of whether kurtosis bears a relationship to the presence of mixing barriers, which will be considered in the next section.\nFirst, though, we turn our attention to the many sharply-de\u00dened low kurtosis features which are clear in Figs. 5 and 6. The Gulf Stream, Kuroshio, and Agulhas Return Current are clear, but there are many other features, particularly in the Southern Ocean, which could also plausibly represent jets or frontal features. From our model, the centres of jets which meander strongly should be characterized by regions where the zero contour of skewness coincides with a value of kurtosis less than 3. In Fig. 9 we plot these contours in black, using $zeta/f$ skewness and kurtosis, and insisting on a degree of spatial continuity by using a 5 by 5 grid point smoothed version of the fields. The contours are superimposed on a map (top) of mean surface geostrophic \u00dfow speed based on the Rio05 mean dynamic topography (Rio and Hernandez, 2004). It is immediately clear that the technique correctly identifies not only the major eastward-\u00dfowing jets, but a number of weaker, mid-ocean jets in all ocean basins. There are, however, significant disagreements with the Rio05 data, most notably in the Southern Ocean. Here, agreement is generally good in the northern parts of the ACC, but is less good further south, especially in the eastern Paci\u00dec sector where a number of apparent jets are identified which are absent from Rio05.\nHowever, small-scale features in the Rio05 data rely for their detection primarily on the surface drifter data, and these southern regions of the ACC are precisely where the density of drifter data drops off. It may be that there are really jets in these regions, but they are not resolved by the measurements available to produce the Rio05 map. In order to test this possibility, we have turned to sea surface temperature (SST) gradients. These are not always indicative of surface currents, but the fact that the ACC is to first-order an equivalent barotropic \u00dfow (Killworth, 1992; Killworth and Hughes, 2002) means that temperature at any depth does tend to be a good proxy for the dynamic topography in this region (Sun and Watts, 2001). In order to calculate a mean SST gradient, we have used merged infrared and microwave satellite data from the Mersea Odyssea project, downloaded from ftp://ftp.ifremer.fr/ ifremer/medspiration/data/l4hrsstfnd/eurdac/glob/odyssea. The data are provided as daily fields at 0.1 degree resolution. Over the period 1st October 2007 to 12th May 2009, 451 fields were available. These were differentiated to produce temperature gradients and each field inspected by eye to check for obvious artifacts. On this basis, 30 daily fields were eliminated. The remaining 421 fields of SST gradient were averaged, and regridded onto the AVISO altimetry grid.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hughes10.html"}
{"id": "a4e559be412f-5", "text": "However, small-scale features in the Rio05 data rely for their detection primarily on the surface drifter data, and these southern regions of the ACC are precisely where the density of drifter data drops off. It may be that there are really jets in these regions, but they are not resolved by the measurements available to produce the Rio05 map. In order to test this possibility, we have turned to sea surface temperature (SST) gradients. These are not always indicative of surface currents, but the fact that the ACC is to first-order an equivalent barotropic \u00dfow (Killworth, 1992; Killworth and Hughes, 2002) means that temperature at any depth does tend to be a good proxy for the dynamic topography in this region (Sun and Watts, 2001). In order to calculate a mean SST gradient, we have used merged infrared and microwave satellite data from the Mersea Odyssea project, downloaded from ftp://ftp.ifremer.fr/ ifremer/medspiration/data/l4hrsstfnd/eurdac/glob/odyssea. The data are provided as daily fields at 0.1 degree resolution. Over the period 1st October 2007 to 12th May 2009, 451 fields were available. These were differentiated to produce temperature gradients and each field inspected by eye to check for obvious artifacts. On this basis, 30 daily fields were eliminated. The remaining 421 fields of SST gradient were averaged, and regridded onto the AVISO altimetry grid.\nThe resulting SST gradient plot is shown in the lower panel of Fig. 9, with our putative jet contours superimposed. It is clear that the Southern Ocean contours do indeed correspond with frontal features which were unresolved in the Rio05 data. In order to test how robust these comparisons are, we have repeated them with the Maximenko and Niiler (2005) dynamic topography, and with 7.25 years of SST data from the coarser-resolution AMSR-E microwave temperature measurements (Wentz and Meissner, 2004). The resulting pictures (not shown) are very similar, with a little smoothing of the SST gradient, and a little less smoothing of the geostrophic \u00dfow speed (at the expense of more small-scale noise).\nFig. 9: Magnitude of the mean current (top) and mean sea surface temperature gradient (bottom), with black contours superimposed where the skewness/kurtosis relationship implies the mean centre of a jet or front to lie.\nOne final feature worth noting is that the identified path of the Kuroshio seems to be on the northern flank of the jet itself. The same is also true if sea level is used to identify this jet (not shown). This may be a result of the different averaging periods used for the mean current and the skewness and kurtosis; preliminary calculations using different subsets of the altimeter data produce more variation in results around the Kuroshio than elsewhere. Close inspection of the Gulf Stream also reveals some fine scale structure in the vorticity diagnostics which are not present in the sea level equivalents. It may be that, by combining the two analyses, more detailed information about the lateral structure of the jets can be extracted.\nIn summary, the pattern of a low kurtosis zone at the centre of a change in sign of skewness seems to be a reliable method of identifying meandering jets or frontal zones. When applied to time series of relative vorticity, this has allowed us to identify several jets previously unresolved by drifter data. In the next section, we will consider whether these low kurtosis zones also represent mixing barriers.\nDoes low kurtosis imply a mixing barrier?\uf0c1\nAs discussed above, the PV staircase model reviewed by D&M implies that jets occur at steps in PV, and that they act as mixing barriers. In fact D&M make the argument that mixing across a jet requires the presence of vortices with PV anomalies larger than the PV step which is associated with the jet. This sounds very similar to the criterion necessary for the formation of a low kurtosis region. If vortices are considered to be the \u00d4\u00d4noise\u00d3 on either side of the jet, then low kurtosis at the jet centre only occurs when the noise is smaller than the step, suggesting that low kurtosis should qualitatively be an indicator of a mixing barrier.\nIn order to test this suggestion, we turn to a set of idealized model experiments, initially run in order to investigate the effect of topography on jets and mixing in a zonal channel (Thompson, 2009). These are two-layer, quasigeostrophic simulations in a doubly-periodic channel, forced by an implicit zonal momentum flux which maintains a constant difference between the total zonal transports in the upper and lower layers. These model runs are not chosen because they are supposed to model particular parts of the real ocean, but because they explore a wide range of jet types and behaviors, including intermittent jets, meridionally-drifting jets, and topographically-steered jets, as well as steady, zonal jets. Another reason for the model choice is that the mixing diagnostics have already been performed, making it simple to compare mixing with kurtosis.\nFour model experiments are considered. Experiment 1 is a \u00dfat-bottomed channel, and produces four, steady, eastward jets, with weaker westward flow in-between. Experiment 32 has sinusoidal topography as a function of latitude only, and produces a sequence of jets which form in regions of strong background PV gradient, but drift north or south to regions of weak PV gradient, where they decay. Experiment 84 has topography which is sinusoidal in both latitude and longitude, producing a series of three strongly-steered eastward jets, with weaker westward \u00dfow in between. Experiment 87 has similar topography, but only one strong eastward jet, which is more weakly steered and which intermittently breaks up in a bout of strong mixing. More details of these model runs are given in Thompson (2009). Mean and eddy kinetic energies vary by a factor of more than 40 between experiments, which clearly represent a wide range of conditions and kinds of jet.\nFlow fields and PV kurtosis maps for the top layer are shown in Fig. 10 (in the case of experiment 32, this is a plot of zonally-aver aged \u00dfow and kurtosis as a function of time and latitude, with kurtosis calculated using a moving window). It is clear that kurtosis is robustly low at the centre of the jets. For these experiments, the effective diffusivity $K_{eff}$ of upper layer PV was calculated as a function of time and equivalent latitude using the methodology of Shuckburgh and Haynes (2003). In order to compare across the range of experiments, it was found most effective to normalize the diffusivity by the square root of the domain-averaged EKE. The resulting normalized diffusivities would have dimensions of length, but the experiments were all non-dimensionalized using the Rossby radius $R_0$ as the length scale, and $R_0/U$ for time, where $U$ is the average imposed velocity difference between layer 1 and layer 2, so the normalized diffusivity should be multiplied by $R_0$ to give a dimensional value.\nFig. 10. Kurtosis of upper layer PV (shaded) and upper layer streamfunction (contours) for the four model experiments considered here. Plots are time averages, except for experiment 32, which is a zonal average as a function of time, the kurtosis being a running average over 20 time units.\nThe time-averaged values of $K_{eff}$, normalized by $sqrt{EKE}$, were compared with zonally-averaged values of PV kurtosis (in the case of experiments 84 and 87 the average was not zonal but along mean streamlines, because the mean flow is strongly-steered by topography). The resulting relationship between kurtosis and $K_{eff}/sqrt{EKE}$ is plotted for all experiments in Fig. 11. There is not just a qualitative relationship between the two, at low values of diffusivity there appears to be a strong, universal, linear relationship. As a guide (not any kind of formal \u00det), the straight line $K_{eff}/sqrt{EKE} = (K - 1.3)/30$ has been drawn, which appears to fit the distribution fairly well.\nFig. 11: Scatter plot of surface layer normalized effective diffusivity against zonally-averaged kurtosis of PV (along stream-averaged for experiments 84 and 87) for the four numerical experiments. The solid line represents a suggested suitable linear relationship, but it is not a formal \u00det. Values of the normalizing constant, non-dimensional domain-averaged $sqrt{EKE}$, are listed for each experiment.", "source": "https://sealeveldocs.readthedocs.io/en/latest/hughes10.html"}
{"id": "a4e559be412f-6", "text": "Fig. 10. Kurtosis of upper layer PV (shaded) and upper layer streamfunction (contours) for the four model experiments considered here. Plots are time averages, except for experiment 32, which is a zonal average as a function of time, the kurtosis being a running average over 20 time units.\nThe time-averaged values of $K_{eff}$, normalized by $sqrt{EKE}$, were compared with zonally-averaged values of PV kurtosis (in the case of experiments 84 and 87 the average was not zonal but along mean streamlines, because the mean flow is strongly-steered by topography). The resulting relationship between kurtosis and $K_{eff}/sqrt{EKE}$ is plotted for all experiments in Fig. 11. There is not just a qualitative relationship between the two, at low values of diffusivity there appears to be a strong, universal, linear relationship. As a guide (not any kind of formal \u00det), the straight line $K_{eff}/sqrt{EKE} = (K - 1.3)/30$ has been drawn, which appears to fit the distribution fairly well.\nFig. 11: Scatter plot of surface layer normalized effective diffusivity against zonally-averaged kurtosis of PV (along stream-averaged for experiments 84 and 87) for the four numerical experiments. The solid line represents a suggested suitable linear relationship, but it is not a formal \u00det. Values of the normalizing constant, non-dimensional domain-averaged $sqrt{EKE}$, are listed for each experiment.\nFor kurtosis values significantly higher than 3, the relationship becomes looser. There is no reason to expect a relationship at these high $K$ values, so this is unsurprising. The relationship is also significantly worse for experiment 32, which again is not surprising as the value at each latitude is an average over times when there is low mixing and times when there is high mixing at that latitude. The surprise is that it works as well as it does, and falls on roughly the same range of values as the other experiments. Fig. 12: The same values of normalized effective diffusivity from Fig. 11, plotted as a function of effective latitudinal coordinate measured in Rossby radii. The dashed line is the value which would be predicted from kurtosis of PV, using the linear relationship suggested in Fig. 11.\nFig. 12 uses the linear scaling proposed in Fig. 11 to plot normalized $K_{eff}$ as a function of latitude for each experiment, together with the value which would be predicted from the kurtosis (dashed lines). This shows how well kurtosis captures the structure as well as values at the minima of diffusivity. There is a tendency to underestimate diffusivity where jets are drifting (experiment 32) or intermittent (experiment 87), in which case our simple model is no longer adequate, but even here there is a reasonable correspondence. Much better fits can be found for individual experiments by adding quadratic terms, but that is at the expense of universality, since the quadratic terms differ strongly between experiments.\nFig. 12: The same values of normalized effective diffusivity from Fig. 11, plotted as a function of effective latitudinal coordinate measured in Rossby radii. The dashed line is the value which would be predicted from kurtosis of PV, using the linear relationship suggested in Fig. 11.\nConclusions and discussion\uf0c1\nMeandering jets in the ocean are associated with a characteristic pattern of skewness and kurtosis of sea level and, more clearly, relative vorticity. The mean position of the jet or front lies along the zero contour of skewness, which is also a region of low (less than 3) kurtosis. This can be explained using a model in which the jet or front represents a sharp step in sea level or relative vorticity, and meanders over a distance wider than the width of the step. We find little evidence that more useful data can be extracted from the spatial variation of PDFs beyond what is apparent from skewness and kurtosis. Using this relationship we have identified several Southern Ocean jets which were previously unresolved by drifter-based climatologies.\nThe fact that these features are seen more clearly in relative vorticity than in sea level suggests the use of a model of a jet as a step in PV, between two regions of well-mixed PV, as discussed recently by D&M. In this model, when the jump in PV across the step is larger than the eddy variations to either side, the step acts as a mixing barrier. These are precisely the conditions in which time series of PV would exhibit low kurtosis at the mean position of the jet centre. That led us to ask whether low kurtosis regions were indicative of the presence of a mixing barrier.\nAcross a wide variety of idealized model experiments, we find a strong, universal, linear relationship between PV kurtosis and effective diffusivity normalized by the square root of domain-averaged EKE. The relationship is particularly strong at low values of kurtosis, which represent the strongest mixing barriers. This suggests that the regions of low kurtosis from the relative vorticity time series may indeed represent mixing barriers in the ocean.\nThere are a couple of difficulties with linking the model experiments and our interpretation to the data. The data only tell us about relative vorticity, not PV. Variations in $f$ are not a problem, as the time series are at constant latitude, but if thickness variations are not either small or simply related to relative vorticity variations, then the time series we have may not be representative of PV variations. The second problem is that the relationship we find is between PV kurtosis and a diffusivity normalized by the square root of domain-averaged EKE. In the real ocean, what would be the appropriate region over which to average? Using local EKE in the model diagnostics results in significantly more scatter in the relationship, so some degree of spatial averaging is clearly needed, perhaps over an eddy Rhines scale? These difficulties mean that it would be premature to produce quantitative estimates of real ocean diffusivities using this method: a study is needed using more realistic ocean model geometry to determine how best to apply the relationship we find.\nKurtosis does, however, have two advantages over effective diffusivity: it is very simple to calculate, and it is a local quantity, meaning that maps are easily produced, unlike effective diffusivity which only varies in one spatial dimension (although it is less obvious how to produce time series of kurtosis than of diffusivity). This means that it may be useful for quick identifications of mixing barriers in a number of contexts. For example, it would be simple to extend the present analysis to subsurface regions in an ocean model, permitting the investigation of the three-dimensional geometry of mixing barriers. Similarly, the ideas should apply equally well to atmospheric data. As White (1980) showed, a similar pattern (a zero skewness contour between two regions of significant skewness of opposite signs, coinciding with a region of low kurtosis) occurs in maps derived from 500 mbar geopotential height, though not at 1000 mbar. As with sea level, it may be that this picture would be sharpened by considering relative vorticity or PV.\nThere is a good case to make skewness and kurtosis (whether it is of sea level, relative vorticity, or PV) standard diagnostics to be used to assess the realism of eddying ocean models, as well as to understand the dynamics of jets and mixing.\nAppendix A. Derivation of statistics for a PDF which is the sum of two Gaussians\uf0c1\nIf we write the Gaussian distribution with standard deviation $sigma$ as\n$$ G(chi, sigma) = frac{1}{sigmasqrt{2pi}}expleft({-chi^2/2sigma^2}right) $$, (6)\nwhich has been normalized so that its integral is 1, then integration by parts shows that\n$$ int_{-infty}^{infty}{chi^2 , G(chi, sigma) dchi} = sigma^2 $$, (7)\n$$ int_{-infty}^{infty}{chi^4 , G(chi, sigma) dchi} = 3sigma^4 $$, (8)\nand odd moments of $G$ are zero by symmetry.\nThe PDF which consists of two Gaussians separated by $d$ standard deviations is\n$$ p = A G(chi + Bsigma d, sigma) + B G(chi - A sigma d, sigma) $$, (9)\nwhere $B = 1 - A$, and the origin has been chosen so that the mean value of the PDF is zero (to construct this, note that the distances of the Gaussian centres from the origin must be inversely proportional to their integrals $A$ and $B$, and that the distance between the Gaussians is de\u00dened to be $sigma d$). The second moment of this distribution, which we will set to 1, is then given by", "source": "https://sealeveldocs.readthedocs.io/en/latest/hughes10.html"}
{"id": "a4e559be412f-7", "text": "There is a good case to make skewness and kurtosis (whether it is of sea level, relative vorticity, or PV) standard diagnostics to be used to assess the realism of eddying ocean models, as well as to understand the dynamics of jets and mixing.\nAppendix A. Derivation of statistics for a PDF which is the sum of two Gaussians\uf0c1\nIf we write the Gaussian distribution with standard deviation $sigma$ as\n$$ G(chi, sigma) = frac{1}{sigmasqrt{2pi}}expleft({-chi^2/2sigma^2}right) $$, (6)\nwhich has been normalized so that its integral is 1, then integration by parts shows that\n$$ int_{-infty}^{infty}{chi^2 , G(chi, sigma) dchi} = sigma^2 $$, (7)\n$$ int_{-infty}^{infty}{chi^4 , G(chi, sigma) dchi} = 3sigma^4 $$, (8)\nand odd moments of $G$ are zero by symmetry.\nThe PDF which consists of two Gaussians separated by $d$ standard deviations is\n$$ p = A G(chi + Bsigma d, sigma) + B G(chi - A sigma d, sigma) $$, (9)\nwhere $B = 1 - A$, and the origin has been chosen so that the mean value of the PDF is zero (to construct this, note that the distances of the Gaussian centres from the origin must be inversely proportional to their integrals $A$ and $B$, and that the distance between the Gaussians is de\u00dened to be $sigma d$). The second moment of this distribution, which we will set to 1, is then given by\n$$ int_{-infty}^{infty}{chi^2 , p dchi} = A int_{-infty}^{infty}{(chi - B sigma d)^2 G(chi, sigma)} dchi + B int_{-infty}^{infty}{(chi + A sigma d)^2 G(chi, sigma)} dchi $$. (10)\nExpanding the squared terms, odd terms in $chi$ integrate to zero, and even terms were evaluated above, so this gives, after some gathering of terms,\n$$ 1 = sigma^2(1 + d^2P) $$, (11)\nwhere $P = AB$, or\n$sigma = (1 + d^2P)^{-1/2}$. (12)\nThe same procedure can be applied to the third and fourth moments, leading to\n$$ S = sigma^3 d^3 P(A - B) $$, (13)\nand\n$$ K = 3sigma^4 + d^2 sigma^4 P[6 + d^2(1 - 3P)] $$. (14)\nSubstituting for $sigma$ and simplifying then leads to (3) and (4).", "source": "https://sealeveldocs.readthedocs.io/en/latest/hughes10.html"}
{"id": "1ea2eff08fb1-0", "text": "DeConto and Pollard (2016)\uf0c1\nTitle:\nContribution of Antarctica to past and future sea-level rise\nKey Points:\nAntarctic ice sheet (AIS) mass loss contributed significantly to past sea-level rise during warmer periods.\nModel predicts over 1 m sea-level rise by 2100, 15 m by 2500 if emissions continue unabated.\nAtmospheric warming might become the dominant driver of AIS while ocean warming will delay recovery of the AIS\nKeywords:\nAntarctic ice sheet, sea-level rise, climate change, greenhouse gas emissions, ice sheet modelling\nCorresponding author:\nRobert M. DeConto\nCitation:\nDeConto, R. M., & Pollard, D. (2016). Contribution of Antarctica to past and future sea-level rise. Nature, 531(7596), 591\u2013597. doi:10.1038/nature17145\nURL:\nhttps://www.nature.com/articles/nature17145\nAbstract\uf0c1\nPolar temperatures over the last several million years have, at times, been slightly warmer than today, yet global mean sea level has been 6\u20139\u2009metres higher as recently as the Last Interglacial (130,000 to 115,000 years ago) and possibly higher during the Pliocene epoch (about three million years ago). In both cases the Antarctic ice sheet has been implicated as the primary contributor, hinting at its future vulnerability. Here we use a model coupling ice sheet and climate dynamics\u2014including previously underappreciated processes linking atmospheric warming with hydrofracturing of buttressing ice shelves and structural collapse of marine-terminating ice cliffs\u2014that is calibrated against Pliocene and Last Interglacial sea-level estimates and applied to future greenhouse gas emission scenarios. Antarctica has the potential to contribute more than a metre of sea-level rise by 2100 and more than 15\u2009metres by 2500, if emissions continue unabated. In this case atmospheric warming will soon become the dominant driver of ice loss, but prolonged ocean warming will delay its recovery for thousands of years.\nEditorial Summary: A 500-year model of Antarctica\u2019s contribution to future sea-level rise\uf0c1\nRobert DeConto and David Pollard use a newly improved numerical ice-sheet model calibrated to Pliocene and Last Interglacial sea-level estimates to develop projections of Antarctica\u2019s evolution over the next five centuries, driven by a range of greenhouse gas scenarios. The modelling shows that the Antarctic ice sheet has the potential to contribute between almost nothing, to contributing more than a metre of sea-level rise by 2100 and more than 15 metres by 2500. The startling high-end estimate arises from unabated emissions and previously underappreciated mechanisms: ice-fracturing by surface meltwater and collapse of large ice cliffs. The low end shows that a scenario of strong climate mitigation can radically reduce societal exposure to higher sea levels.\nIntroduction\uf0c1\nReconstructions of the global mean sea level (GMSL) during past warm climate intervals including the Pliocene (about three million years ago)1 and late Pleistocene interglacials2,3,4,5 imply that the Antarctic ice sheet has considerable sensitivity. Pliocene atmospheric CO2 concentrations were comparable to today\u2019s (~400 parts per million by volume, p.p.m.v.)6, but some sea-level reconstructions are 10\u201330\u2009m higher1,7. In addition to the loss of the Greenland Ice Sheet and the West Antarctic Ice Sheet (WAIS)2, these high sea levels require the partial retreat of the East Antarctic Ice Sheet (EAIS), which is further supported by sedimentary evidence from the Antarctic margin8. During the more recent Last Interglacial (LIG, 130,000 to 115,000 years ago), GMSL was 6\u20139.3\u2009m higher than it is today2,3,4, at a time when atmospheric CO2 concentrations were below 280\u2009p.p.m.v. (ref. 9) and global mean temperatures were only about 0\u20132\u2009\u00b0C warmer10. This requires a substantial sea-level contribution from Antarctica of 3.6\u20137.4\u2009m in addition to an estimated 1.5\u20132\u2009m from Greenland11,12 and around 0.4\u2009m from ocean steric effects10. For both the Pliocene and the LIG, it is difficult to obtain the inferred sea-level values from ice-sheet models used in future projections.\nMarine ice sheet and ice cliff instabilities\uf0c1\nMuch of the WAIS sits on bedrock hundreds to thousands of metres below sea level (Fig. 1a)13. Today, extensive floating ice shelves in the Ross and Weddell Seas, and smaller ice shelves and ice tongues in the Amundsen and Bellingshausen seas (Fig. 1b) provide buttressing that impedes the seaward flow of ice and stabilizes marine grounding zones (Fig. 2a). Despite their thickness (typically about 1\u2009km near the grounding line to a few hundred metres at the calving front), a warming ocean has the potential to quickly erode ice shelves from below, at rates exceeding 10\u2009m\u2009yr\u22121\u2009\u00b0C\u22121 (ref. 14). Ice-shelf thinning and reduced backstress enhance seaward ice flow, grounding-zone thinning, and retreat (Fig. 2b). Because the flux of ice across the grounding line increases strongly as a function of its thickness15, initial retreat onto a reverse-sloping bed (where the bed deepens and the ice thickens upstream) can trigger a runaway Marine Ice Sheet Instability (MISI; Fig. 2c)15,16,17. Many WAIS grounding zones sit precariously on the edge of such reverse-sloped beds, but the EAIS also contains deep subglacial basins with reverse-sloping, marine-terminating outlet troughs up to 1,500\u2009m deep (Fig. 1). The ice above floatation in these East Antarctic basins is much thicker than in West Antarctica, with the potential to raise GMSL by around 20\u2009m if the ice in those basins is lost13. Importantly, previous ice-sheet simulations accounting for migrating grounding lines and MISI dynamics have shown the potential for repeated WAIS retreats and readvances over the past few million years18, but could only account for GMSL rises of about 1\u2009m during the LIG and 7\u2009m in the warm Pliocene, which are substantially smaller than geological estimates.\nFigure 1: Antarctic sub-glacial topography and ice sheet features. a, Bedrock elevations13 interpolated onto the 10-km polar stereographic ice-sheet model grid and used in Pliocene, LIG, and future ice-sheet simulations. b, Model surface ice speeds and grounding lines (black lines) show the location of major ice streams, outlet glaciers, and buttressing ice shelves (seaward of grounding lines) relative to the underlying topography in a. Features and place names mentioned in the text are also shown. AS, Amundsen Sea; BS, Bellingshausen Sea; WDIC, WAIS Divide Ice Core. The locations of the Pine Island, Thwaites, Ninnis, Mertz, Totten, and Recovery glaciers are shown. Model ice speeds (b) are shown after equilibration with a modern atmospheric and ocean climatology (see Methods).\nFigure 2: Schematic representation of MISI and MICI and processes included in the ice model. Top-to-bottom sequences (a\u2013c and d\u2013f) show progressive ice retreat into a subglacial basin, triggered by oceanic and atmospheric warming. The pink arrow represents the advection of warm circumpolar deep water (CDW) into the shelf cavity. a, Stable, marine-terminating ice-sheet margin, with a buttressing ice shelf. Seaward ice flux is strongly dependent on grounding-line thickness h. Sub-ice melt rates increase with open-ocean warming and warm-water incursions into the ice-shelf cavity. b, Thinning shelves and reduced buttressing increase seaward ice flux, backing the grounding line onto reverse-sloping bedrock. c, Increasing h with landward grounding-line retreat leads to an ongoing increase in ice flow across the grounding line in a positive runaway feedback until the bed slope changes. d, In addition to MISI (a\u2013c), the model physics used here account for surface-meltwater-enhanced calving via hydrofracturing of floating ice (e), providing an additional mechanism for ice-shelf loss and initial grounding-line retreat into deep basins. f, Where oceanic melt and enhanced calving eliminate shelves completely, subaerial cliff faces at the ice margin become structurally unstable where h exceeds 800\u2009m, triggering rapid, unabated MICI retreat into deep basins.", "source": "https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html"}
{"id": "1ea2eff08fb1-1", "text": "Figure 1: Antarctic sub-glacial topography and ice sheet features. a, Bedrock elevations13 interpolated onto the 10-km polar stereographic ice-sheet model grid and used in Pliocene, LIG, and future ice-sheet simulations. b, Model surface ice speeds and grounding lines (black lines) show the location of major ice streams, outlet glaciers, and buttressing ice shelves (seaward of grounding lines) relative to the underlying topography in a. Features and place names mentioned in the text are also shown. AS, Amundsen Sea; BS, Bellingshausen Sea; WDIC, WAIS Divide Ice Core. The locations of the Pine Island, Thwaites, Ninnis, Mertz, Totten, and Recovery glaciers are shown. Model ice speeds (b) are shown after equilibration with a modern atmospheric and ocean climatology (see Methods).\nFigure 2: Schematic representation of MISI and MICI and processes included in the ice model. Top-to-bottom sequences (a\u2013c and d\u2013f) show progressive ice retreat into a subglacial basin, triggered by oceanic and atmospheric warming. The pink arrow represents the advection of warm circumpolar deep water (CDW) into the shelf cavity. a, Stable, marine-terminating ice-sheet margin, with a buttressing ice shelf. Seaward ice flux is strongly dependent on grounding-line thickness h. Sub-ice melt rates increase with open-ocean warming and warm-water incursions into the ice-shelf cavity. b, Thinning shelves and reduced buttressing increase seaward ice flux, backing the grounding line onto reverse-sloping bedrock. c, Increasing h with landward grounding-line retreat leads to an ongoing increase in ice flow across the grounding line in a positive runaway feedback until the bed slope changes. d, In addition to MISI (a\u2013c), the model physics used here account for surface-meltwater-enhanced calving via hydrofracturing of floating ice (e), providing an additional mechanism for ice-shelf loss and initial grounding-line retreat into deep basins. f, Where oceanic melt and enhanced calving eliminate shelves completely, subaerial cliff faces at the ice margin become structurally unstable where h exceeds 800\u2009m, triggering rapid, unabated MICI retreat into deep basins.\nSo far, the potential for MISI to cause ice-sheet retreat has focused on the role of ocean-driven melting of buttressing ice shelves from below16,18,19,20. However, it is often overlooked that the major ice shelves in the Ross and Weddell seas and the many smaller shelves and ice tongues buttressing outlet glaciers are also vulnerable to atmospheric warming. Today, summer temperatures approach or just exceed 0\u2009\u00b0C on many shelves21, and their flat surfaces near sea level mean that little atmospheric warming would be needed to dramatically increase the areal extent of surface melting and summer rainfall.\nMeltwater on ice-shelf surfaces causes thinning if it percolates through the shelf to the ocean. If refreezing occurs, the ice is warmed, reducing its viscosity and speeding its flow22. The presence of rain and meltwater can also influence crevassing and calving rates23 (hydrofracturing) as witnessed on the Antarctic Peninsula\u2019s Larson B ice shelf during its sudden break-up in 200224. Similar dynamics could have affected the ice sheet during ancient warm intervals25, and given enough future warming, could eventually affect many ice shelves and ice tongues, including the major buttressing shelves in the Ross and Weddell seas.\nAnother physical mechanism previously underappreciated at the ice-sheet scale involves the mechanical collapse of ice cliffs in places where marine-terminating ice margins approach 1\u2009km in thickness, with >90\u2009m of vertical exposure above sea level26. Today, most Antarctic outlet glaciers with deep beds approaching a water depth of 1\u2009km are protected by buttressing ice shelves, with gently sloping surfaces at the grounding line (Fig. 2d). However, given enough atmospheric warming above or ocean warming below (Fig. 2e), ice-shelf retreat can outpace its dynamically accelerated seaward flow as buttressing is lost and retreating grounding lines thicken15. In places where marine-terminating grounding lines are thicker than 800\u2009m or so, this would produce >90\u2009m subaerial cliff faces that would collapse (Fig. 2f) simply because longitudinal stresses at the cliff face would exceed the yield strength (about 1\u2009MPa) of the ice26.\nMore heavily crevassed and damaged ice would reduce the maximum supported cliff heights. If a thick, marine-terminating grounding line began to undergo such mechanical failure, its retreat would continue unabated until temperatures cooled enough to reform a buttressing ice shelf, or the ice margin retreated onto bed elevations too shallow to support the tall, unstable cliffs25. If protective ice shelves were suddenly lost in the vast areas around the Antarctic margin where reverse-sloping bedrock is more than 1,000\u2009m deep (Fig. 1a), exposed grounding-line ice cliffs would quickly succumb to structural failure, as is happening in the few places where such conditions exist today (the Helheim and Jakobsavn glaciers on Greenland and the Crane Glacier on the Antarctic Peninsula), hinting that a Marine Ice Cliff Instability (MICI) in addition to MISI could be an important contributor to past and future ice-sheet retreat.\nOur three-dimensional ice sheet\u2013ice shelf model25,27 (Methods) predicts the evolution of continental ice thickness and temperature as a function of ice flow (deformation and sliding) and changes in mass balance via precipitation, runoff, basal melt, oceanic melt under ice shelves and on vertical ice faces, calving, and tidewater ice-cliff failure. The model captures MISI (Fig. 2a\u2013c) by accounting for migrating grounding lines and the buttressing effects of ice shelves with pinning points and side-shear. To capture the dynamics of MICI (Fig. 2d\u2013f), new physical treatments of surface-melt and rainwater-enhanced calving (hydrofracturing) and grounding-line ice-cliff dynamics have been added25. Including these processes was found to increase the model\u2019s contribution to Pliocene GMSL from +7\u2009m (ref. 18) to +17\u2009m (ref. 25). The model formulation used here is similar to that described in ref. 25, but with improvements in the treatment of calving, thermodynamics, and climate\u2013ice\u2013ocean coupling (Methods).\nThe Antarctic Ice Sheet in the Pliocene\uf0c1\nThe warm mid-Pliocene and LIG provide complementary targets for model performance, via the ability to produce ~5\u201320\u2009m and ~3.5\u20137.5\u2009m GMSL from Antarctica, respectively. These two time periods highlight model sensitivities to different processes, because Pliocene summer air temperatures were capable of producing substantial surface meltwater, especially during warm austral summer orbits28. Conversely, LIG temperatures were cooler29, with limited potential for surface meltwater production. Instead, ocean temperatures30 could have been the determining factor in LIG ice retreat31.\nTo simulate Pliocene and LIG ice sheets, we couple the ice model to a high-resolution, atmospheric regional climate model (RCM) adapted to Antarctica and nested within a global climate model (GCM; see Methods). The RCM captures the orographic details of ice shelves and adjacent ice-sheet margins, which is critical here because the new calving and grounding line processes are mechanistically linked to the atmosphere.\nHigh-resolution ocean modelling beneath time-evolving ice shelves on palaeoclimate timescales exceeds existing capabilities. Instead, we use a modern ocean climatology32 interpolated to our ice-sheet grid, with uniformly imposed sub-surface ocean warming providing melt rates on sub-ice-shelf and calving-front surfaces exposed to sea water. The RCM climatologies and imposed ocean warming are applied to quasi-equilibrated initial ice-sheet states, with atmospheric temperatures and the precipitation lapse-rate corrected as the ice sheet evolves.\nAs in ref. 25, the Pliocene simulation uses a RCM climatology with 400\u2009p.p.m.v. CO2, a warm austral summer orbit28, and 2\u2009\u00b0C imposed ocean warming to represent maximum mid-Pliocene warmth (Extended Data Fig. 1). The model produces an 11.3-m contribution to GMSL rise, reflecting a reduction in its sensitivity of about 6\u2009m relative to the formulation in ref. 25, but within the range of plausible sea-level estimates1,7. Pliocene retreat is triggered by meltwater-induced hydrofracturing of ice shelves, which relieves backstress and initiates both MISI and MICI retreat into the deepest sectors of WAIS and EAIS marine basins.\nThe Antarctic Ice Sheet during the LIG\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html"}
{"id": "1ea2eff08fb1-2", "text": "The Antarctic Ice Sheet in the Pliocene\uf0c1\nThe warm mid-Pliocene and LIG provide complementary targets for model performance, via the ability to produce ~5\u201320\u2009m and ~3.5\u20137.5\u2009m GMSL from Antarctica, respectively. These two time periods highlight model sensitivities to different processes, because Pliocene summer air temperatures were capable of producing substantial surface meltwater, especially during warm austral summer orbits28. Conversely, LIG temperatures were cooler29, with limited potential for surface meltwater production. Instead, ocean temperatures30 could have been the determining factor in LIG ice retreat31.\nTo simulate Pliocene and LIG ice sheets, we couple the ice model to a high-resolution, atmospheric regional climate model (RCM) adapted to Antarctica and nested within a global climate model (GCM; see Methods). The RCM captures the orographic details of ice shelves and adjacent ice-sheet margins, which is critical here because the new calving and grounding line processes are mechanistically linked to the atmosphere.\nHigh-resolution ocean modelling beneath time-evolving ice shelves on palaeoclimate timescales exceeds existing capabilities. Instead, we use a modern ocean climatology32 interpolated to our ice-sheet grid, with uniformly imposed sub-surface ocean warming providing melt rates on sub-ice-shelf and calving-front surfaces exposed to sea water. The RCM climatologies and imposed ocean warming are applied to quasi-equilibrated initial ice-sheet states, with atmospheric temperatures and the precipitation lapse-rate corrected as the ice sheet evolves.\nAs in ref. 25, the Pliocene simulation uses a RCM climatology with 400\u2009p.p.m.v. CO2, a warm austral summer orbit28, and 2\u2009\u00b0C imposed ocean warming to represent maximum mid-Pliocene warmth (Extended Data Fig. 1). The model produces an 11.3-m contribution to GMSL rise, reflecting a reduction in its sensitivity of about 6\u2009m relative to the formulation in ref. 25, but within the range of plausible sea-level estimates1,7. Pliocene retreat is triggered by meltwater-induced hydrofracturing of ice shelves, which relieves backstress and initiates both MISI and MICI retreat into the deepest sectors of WAIS and EAIS marine basins.\nThe Antarctic Ice Sheet during the LIG\uf0c1\nSummer air temperatures in the RCM are slightly warmer at 116\u2009kyr ago than 128\u2009kyr ago, but remain below freezing in both cases, with little to no surface melt (Extended Data Fig. 2). As a result, substantial oceanic warming >4\u2009\u00b0C is required to initiate WAIS retreat at 128\u2009kyr ago, which occurs once an ocean-melt threshold is reached in the stability of the Thwaites grounding line (Extended Data Fig. 3a and d). Allowing two-way coupling between the RCM and the ice-sheet model (Methods) captures dynamical atmospheric feedbacks as the ice margin retreats. This enhances retreat (Extended Data Fig. 3b, e), but still requires >4\u2009\u00b0C of ocean warming to produce a >3.5\u2009m increase in GMSL. We find that by accounting for the additional influence of circum-Antarctic ocean warming on the RCM atmosphere (Methods), the GMSL contribution increases to >6.5\u2009m with just 3\u2009\u00b0C sub-surface ocean warming (Extended Data Fig. 3c and f), despite the cooler orbit of the Earth 128\u2009kyr ago. The ocean-driven continental warming at 128\u2009kyr ago agrees with ice core records29 and supports a Southern Ocean control on the timing of ice-sheet retreat30,31, possibly through Northern Hemisphere influences on the ocean meridional overturning circulation33.\nAlternative simulations (Fig. 3) use time-evolving atmospheric and oceanic climatologies (Methods) based on marine and ice-core proxy reconstructions29. These time-continuous simulations produce GMSL contributions of 6\u20137.5\u2009m early in the interglacial, followed by a prolonged plateau and rapid recovery of the ice sheet beginning around 115\u2009kyr ago. This result matches the magnitude, temporal pattern, and rate of LIG sea-level change in ref. 3. (Fig. 3a), and the simulated recovery of the WAIS satisfies the presence of ice >70\u2009kyr ago at the bottom of the WAIS Divide Ice Core34.\nFigure 3: Ice-sheet simulations and Antarctic contributions to GMSL through the LIG driven by a time-evolving, proxy-based atmosphere\u2013ocean climatology. a, Change in GMSL in LIG simulations starting at 130\u2009kyr ago and initialized with a modern ice sheet (blue) or a bigger LGM ice sheet representing glacial conditions at the onset of the LIG (red). A probabilistic reconstruction of Antarctica\u2019s contribution to GMSL is shown in black3 with uncertainties (16th and 84th percentiles) as dashed lines. b, c, Ice-sheet thickness at the time of maximum retreat using modern initial conditions (b) and using glacial initial conditions (c). Ice-free land surfaces are brown. The bigger sea-level response when initialized with the \u2018glacial\u2019 ice sheet is caused by deeper bed elevations and the ~3,000-yr lagged bedrock response to ice retreat50, which enhances bathymetrically sensitive MISI dynamics. d, The same simulation as b without the new model physics accounting for meltwater-enhanced calving or ice-cliff failure27. GMSL contributions are shown at top left.\nCombined with estimates of Greenland ice loss11,12,35 and ocean thermal effects10, the simulated, Antarctic contributions to Pliocene and LIG sea level are in much better agreement with geological estimates2,3,4 than previous versions of our model18,27, which lacked these new treatments of meltwater-enhanced calving and ice-margin dynamics, suggesting that the new model is better suited to simulations of future ice response.\nFuture simulations\uf0c1\nUsing the same model physics and parameter values as used in the Pliocene and LIG simulations, we apply the ice-sheet model to long-term future simulations (Methods). Here, atmospheric forcing is provided by high-resolution RCM simulations (Extended Data Fig. 4) following three extended Representative Carbon Pathway (RCP) scenarios (RCP2.6, RCP4.5 and RCP8.5)36. Future circum-Antarctic ocean temperatures used in our time-evolving sub-ice melt-rate calculations come from matching, high-resolution (1\u00b0) National Center for Atmospheric Research (NCAR) CCSM4 simulations (ref. 37, Extended Data Fig. 5). The simulations begin in 1950 to provide some hindcast spinup, and are run for 550 years to 2500.\nThe RCP scenarios (Fig. 4) produce a wide range of future Antarctic contributions to sea level, with RCP2.6 producing almost no net change by 2100, and only 20\u2009cm by 2500. Conversely, RCP4.5 causes almost complete WAIS collapse within the next five hundred years, primarily owing to the retreat of Thwaites Glacier into the deep WAIS interior. The Siple Coast grounding zone remains stable until late in the simulation, thanks to the persistence of the buttressing Ross Ice Shelf (see Supplementary Video 2). In RCP4.5, GMSL rise is 32\u2009cm by 2100, but subsequent retreat of the WAIS interior, followed by the fringes of the Wilkes Basin and the Totten Glacier/Law Dome sector of the Aurora Basin produces 5\u2009m of GMSL rise by 2500.\nFigure 4: Future ice-sheet simulations and Antarctic contributions to GMSL from 1950 to 2500 driven by a high-resolution atmospheric model and 1\u00b0 NCAR CCSM4 ocean temperatures. a, Equivalent CO2 forcing applied to the simulations, following the RCP emission scenarios in ref. 36, except limited to 8\u2009\u00d7\u2009PAL (preindustrial atmospheric level, where 1 PAL\u2009=\u2009280\u2009p.p.m.v.). b, Antarctic contribution to GMSL. c, Rate of sea-level rise and approximate timing of major retreat and thinning in the Antarctic Peninsula (AP), Amundsen Sea Embayment (ASE) outlet glaciers, AS\u2013BS, Amundsen Sea\u2013Bellingshausen Sea; the Totten (T), Siple Coast (SC) and Weddell Sea (WS) grounding zones, the deep Thwaites Glacier basin (TG), interior WAIS, the Recovery Glacier, and the deep EAIS basins (Wilkes and Aurora). d, Antarctic contribution to GMSL over the next 100 years for RCP8.5 with and without a +3\u2009\u00b0C adjustment in ocean model temperatures in the Amundsen and Bellingshausen seas as shown in Extended Data Fig. 5d. e\u2013g, Ice-sheet snapshots at 2500 in the RCP2.6 (e), RCP4.5 (f) and RCP8.5 (g) scenarios. Ice-free land surfaces are shown in brown. h, Close-ups of the Amundsen Sea sector of WAIS in RCP8.5 with bias-corrected ocean model temperatures.", "source": "https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html"}
{"id": "1ea2eff08fb1-3", "text": "Figure 4: Future ice-sheet simulations and Antarctic contributions to GMSL from 1950 to 2500 driven by a high-resolution atmospheric model and 1\u00b0 NCAR CCSM4 ocean temperatures. a, Equivalent CO2 forcing applied to the simulations, following the RCP emission scenarios in ref. 36, except limited to 8\u2009\u00d7\u2009PAL (preindustrial atmospheric level, where 1 PAL\u2009=\u2009280\u2009p.p.m.v.). b, Antarctic contribution to GMSL. c, Rate of sea-level rise and approximate timing of major retreat and thinning in the Antarctic Peninsula (AP), Amundsen Sea Embayment (ASE) outlet glaciers, AS\u2013BS, Amundsen Sea\u2013Bellingshausen Sea; the Totten (T), Siple Coast (SC) and Weddell Sea (WS) grounding zones, the deep Thwaites Glacier basin (TG), interior WAIS, the Recovery Glacier, and the deep EAIS basins (Wilkes and Aurora). d, Antarctic contribution to GMSL over the next 100 years for RCP8.5 with and without a +3\u2009\u00b0C adjustment in ocean model temperatures in the Amundsen and Bellingshausen seas as shown in Extended Data Fig. 5d. e\u2013g, Ice-sheet snapshots at 2500 in the RCP2.6 (e), RCP4.5 (f) and RCP8.5 (g) scenarios. Ice-free land surfaces are shown in brown. h, Close-ups of the Amundsen Sea sector of WAIS in RCP8.5 with bias-corrected ocean model temperatures.\nIn RCP8.5, increased precipitation causes an initial, minor gain in total ice mass (Fig. 4d), but rapidly warming summer air temperatures trigger extensive surface meltwater production38 and hydrofracturing of ice shelves by the middle of this century (Extended Data Fig. 4). The Larsen C is one of the first shelves to be lost, about 2055. Around the same time, major thinning and retreat of outlet glaciers commences in the Amundsen Sea Embayment, beginning with Pine Island Glacier (Fig. 4h), and along the Bellingshausen margin. Massive meltwater production on shelf surfaces, and eventually on the flanks of the ice sheet, would quickly overcome the buffering capacity of firn39. In the model, the meltwater accelerates WAIS retreat via its thermomechanical influence on ice rheology (Methods) and the influence of hydrofacturing on crevassing and structural failure of the retreating margin. Antarctica contributes 77\u2009cm of GMSL rise by 2100, and continued loss of the Ross and Weddell Sea ice shelves drives WAIS retreat from three sides simultaneously (the Amundsen, Ross, and Weddell seas), all with reverse-sloping beds into the deep ice-sheet interior. As a result, WAIS collapses within 250 years. At the same time, steady retreat into the Wilkes and Aurora basins, where the ice above floatation is >2,000\u2009m thick, adds substantially to the rate of sea-level rise, exceeding 4\u2009cm\u2009yr\u22121 (Fig. 4c) in the next century, which is comparable to maximum rates of sea-level rise during the last deglaciation40. At 2500, GMSL rise for the RCP8.5 scenario is 12.3\u2009m. As in our LIG simulations, atmosphere\u2013ice sheet coupling accounting for the warming feedback associated with the retreating ice sheet adds an additional 1.3\u2009m of GMSL to the RCP8.5 scenario (Fig. 4b).\nThe CCSM4 simulations providing the model\u2019s sub-ice-shelf melt rates (Extended Data Fig. 5) underestimate the penetration of warm Circum-Antarctic Deep Water into the Amundsen and Bellingshausen seas observed in recent decades41. As a result, the model fails to capture recent, 21st-century thinning and grounding-line retreat along the southern Antarctic Peninsula42 and the Amundsen Sea Embayment43. Correcting for the ocean-model cool bias along this sector of coastline improves the position of Pine Island and Thwaites grounding lines relative to observations42,43 (Fig. 4h) and increases GMSL rise by 9\u2009cm at 2100 (mainly due to the accelerated retreat of Pine Island Glacier), but the correction has little effect on longer timescales (Extended Data Table 1). Ocean warming is important to the behaviour of individual outlet glaciers early in the simulations, but we find that most of the long-term sea-level rise in RCP4.5 and RCP8.5 scenarios is caused by atmospheric warming and the onset of extensive surface meltwater production, rather than ocean warming as implied by other recent studies44,45,46. Without atmospheric warming, the magnitude of RCP8.5 ocean warming in CCSM4 is insufficient to cause the major retreat of the WAIS or East Antarctic basins; and even with >3\u2009\u00b0C additional warming in the Amundsen and Bellingshausen seas it takes several thousand years for WAIS to retreat via ocean-driven MISI dynamics alone (Extended Data Fig. 6). We note that despite the 10-km grid resolution, the model simulates major ice streams well (Fig. 1), including their internal variability18. However, during drastic subglacial-basin retreat the internal variability is quickly overtaken as grounding lines recede into deep interior catchments (see Supplementary Video 10).\nLarge Ensemble analysis\uf0c1\nTo better utilize Pliocene and LIG geological constraints on model performance, we perform a Large Ensemble analysis (Methods) to explore the uncertainty associated with the primary parameter values controlling (1) relationships between ocean temperature and sub-ice-shelf melt rates, (2) hydrofracturing (crevasse penetration in relation to surface liquid water supply), and (3) maximum rates of marine-terminating ice-cliff failure. The combination of Pliocene and LIG sea level targets is ideal, because Pliocene retreat is dominated by processes associated with (2) and (3), while the LIG is dominated by process (1).\nBoth Pliocene and LIG ensembles are run with combinations of widely ranging parameter values associated with the three processes, and the combinations are scored by their ability to simulate target ranges of Pliocene and LIG Antarctic sea-level contributions (Methods). The filtered subsets of parameter values capable of reproducing both targets are then used in ensembles of future RCP scenarios (Extended Data Table 2), providing both an envelope of possible outcomes and an estimate of the model\u2019s parametric uncertainty (Fig. 5). Importantly, the ensemble analysis supports our choice of \u2018default\u2019 model parameters used in the nominal Pliocene, LIG, and future simulations (Fig. 4, Extended Data Table 2). The lack of substantial ice-sheet retreat in the optimistic RCP2.6 scenario remains unchanged, but the Large Ensemble analysis substantially increases our RCP4.5 and RCP8.5 2100 sea-level projections to 49\u2009\u00b1\u200920\u2009cm and 105\u2009\u00b1\u200930\u2009cm, if higher (>10\u2009m instead of >5\u2009m) Pliocene sea-level targets are used. Adding the ocean temperature correction in the Amundsen and Bellingshausen seas (Fig. 4d and h) further increases the 2100 projections in RCP2.6, RCP4.5 and RCP8.5 to 16\u2009\u00b1\u200916\u2009cm, 58\u2009\u00b1\u200928\u2009cm and 114\u2009\u00b1\u200936\u2009cm, respectively (see Methods and Extended Data Tables 1 and 2).\nFigure 5: Large Ensemble model analyses of future Antarctic contributions to GMSL. a, RCP ensembles to 2500. b, RCP ensembles to 2100. Changes in GMSL are shown relative to 2000, although the simulations begin in 1950. Ensemble members use combinations of model parameters (Methods) filtered according to their ability to satisfy two geologic criteria: a Pliocene target of 10\u201320\u2009m GMSL and a LIG target of 3.6\u20137.4\u2009m. c and d are the same as a and b, but use a lower Pliocene GMSL target of 5\u201315\u2009m. Solid lines are ensemble means, and the shaded areas show the standard deviation (1\u03c3) of the ensemble members. The 1\u03c3 ranges represent the model\u2019s parametric uncertainty, while the alternate Pliocene targets (a and b versus c and d) illustrate the uncertainty related to poorly constrained Pliocene sea-level targets. Mean values and 1\u03c3 uncertainties at 2500 and 2100 are shown.\nLong-term commitment to elevated sea level\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html"}
{"id": "1ea2eff08fb1-4", "text": "Figure 5: Large Ensemble model analyses of future Antarctic contributions to GMSL. a, RCP ensembles to 2500. b, RCP ensembles to 2100. Changes in GMSL are shown relative to 2000, although the simulations begin in 1950. Ensemble members use combinations of model parameters (Methods) filtered according to their ability to satisfy two geologic criteria: a Pliocene target of 10\u201320\u2009m GMSL and a LIG target of 3.6\u20137.4\u2009m. c and d are the same as a and b, but use a lower Pliocene GMSL target of 5\u201315\u2009m. Solid lines are ensemble means, and the shaded areas show the standard deviation (1\u03c3) of the ensemble members. The 1\u03c3 ranges represent the model\u2019s parametric uncertainty, while the alternate Pliocene targets (a and b versus c and d) illustrate the uncertainty related to poorly constrained Pliocene sea-level targets. Mean values and 1\u03c3 uncertainties at 2500 and 2100 are shown.\nLong-term commitment to elevated sea level\uf0c1\nOcean warming alone may be limited in its potential to trigger massive, widespread ice loss, but the multi-millennial thermal response time of the ocean47 will have a profound influence on the ice sheet\u2019s recovery. In simulations run 5,000 years into the future, we conservatively assume no ocean warming beyond 2300 and simply maintain those ocean temperatures while the atmosphere cools assuming different scenarios of CO2 drawdown beginning in 2500 (Methods). For RCP8.5 and natural CO2 drawdown, GMSL continues to rise until 3500 with a peak of about 20\u2009m, after which the warm ocean inhibits the re-advance of grounding lines into deep marine basins for thousands of years (Extended Data Fig. 7). Even in the moderate RCP4.5 scenario with rapidly declining CO2 after 2500, WAIS is unable to recover until the global ocean cools, implying a multi-millennial commitment to several metres of sea-level rise despite human-engineered CO2 drawdown.\nGiven uncertainties in model initial conditions, simplified hybrid ice dynamics, parameterized sub-ice melt, calving, structural ice-margin failure, and the ancient sea-level estimates used in our Large Ensemble analysis, the rates of ice loss simulated here should not be viewed as actual predictions, but rather as possible envelopes of behaviour (Fig. 5) that include processes not previously considered at the continental scale. These are among the first continental-scale simulations with model physics constrained by ancient sea-level estimates, simultaneously accounting for high-resolution atmosphere\u2013ice sheet coupling and ocean model temperatures.\nHowever, several important processes are lacking and should be included in future work. In particular, the model lacks two-way coupling between the ice sheet and the ocean. This is especially relevant for RCP8.5, in which >1 Sv of freshwater and icebergs would be supplied to the Southern Ocean during peak retreat (Extended Data Fig. 8). Rapid calving and ice-margin collapse also implies ice m\u00e9lange in restricted embayments that could provide buttressing and a negative feedback on retreat. The loss of ice mass would also have a strong effect on relative sea level at the margin owing to gravitational and solid-earth deformation effects48, which could affect MISI and MICI dynamics because of their strong dependency on bathymetry. Future simulations should include coupling with Earth models that account for these processes. Improved ancient sea-level estimates are also needed to further constrain model physics and to reduce uncertainties in future RCP scenarios (Fig. 5).\nDespite these limitations, our new model physics are shown to be capable of simulating two very different ancient sea-level events: the LIG, driven primarily by ocean warming and MISI dynamics, and the warmer Pliocene, in which surface meltwater and MICI dynamics are also important. When applied to future scenarios with high greenhouse gas emissions, our palaeo-filtered model ensembles show the potential for Antarctica to contribute >1\u2009m of GMSL rise by the end of this century, and >15\u2009m metres of GMSL rise in the next 500 years. In RCP8.5, the projected onset of major ice-sheet retreat occurs sooner (about 2050), and is substantially faster (>4\u2009cm\u2009yr\u22121 after 2100) and higher (Figs 4 and 5) than implied by other recent studies44,45,49. These differences are mainly due to our addition of model physics linking surface meltwater and ice dynamics via hydrofracturing of buttressing ice shelves and structural failure of marine-terminating ice cliffs. In addition, we use (1) freely evolving grounding-line dynamics that preclude the need for empirically calibrated retreat rates49, (2) highly resolved atmosphere and ocean model components rather than intermediate-complexity climate models45 or simplified climate forcing44, and (3) calibration based on major retreat during warm palaeoclimates rather than recent minor retreat driven by localized ocean forcing.\nAs in these prior studies, we also find that ocean-driven melt is an important driver of grounding-line retreat where warm water is in contact with ice shelves, but in scenarios with high greenhouse gas emissions we find that atmospheric warming soon overtakes the ocean as the dominant driver of Antarctic ice loss. Surface meltwater may lead to the ultimate demise of the major buttressing ice shelves (Supplementary Videos 8 and 9) and extensive grounding-line retreat, but it is the long thermal memory of the ocean that will inhibit the recovery of marine-based ice for thousands of years after greenhouse gas emissions are curtailed.\nMethods\uf0c1\nIce sheet\u2013ice shelf model\uf0c1\nWe use an established ice-sheet model, with hybrid ice dynamics following the formulation described in ref. 27, and an internal condition on ice velocity at the grounding line15 that captures MISI (Fig. 2a\u2013c) by accounting for migrating grounding lines and the buttressing effects of ice shelves with pinning points and side shear. Bedrock deformation under changing ice loads is modelled as an elastic lithospheric plate above local isostatic relaxation. A grid resolution of 10\u2009km is used for all simulations, the finest resolution computationally feasible for long-term continental simulations. The model includes newly added treatments of hydrofracturing and ice cliff failure (Fig. 2d\u2013f) described in ref. 25 and extended here. Basal sliding coefficients are determined by an inverse method51, iteratively matching ice-surface elevations to observations until a quasi-equilibrium is reached. In this case, inverted sliding coefficients are derived from a modern (preindustrial) surface climatology, using the same RCM used in our Pliocene, LIG, and future simulations.\nIn addition to the Pliocene and LIG targets highlighted here, the ice sheet\u2013ice shelf model has been shown capable of simulating: (1) the modern ice sheet, including grounding-line positions, ice thicknesses, velocities, ice streams, and ice shelves (Fig. 1b), (2) the Last Glacial Maximum (LGM) extent27, (3) the timing of post-LGM retreat18, and (4) the ability of the ice sheet to regrow to its modern extent following retreat25.\nCalving and hydrofracturing\uf0c1\nCalving depends on the combined penetration depths of surface and basal crevasses, relative to total ice thickness23,26,52,53. Crevasse depths are parameterized according to the divergence of the ice velocity field52, with an additional contribution depending on the logarithm of ice speed that crudely represents the accumulated strain history (ice damage) along a flow path25. Rapid calving is imposed as ice thickness falls below 200\u2009m for unconfined embayments. The 200-m criterion is decreased in confined embayments according to 200\u2009\u00d7\u2009max[0, min[1, (\u03b1\u2009\u2212\u200940)/20]], where \u03b1 is the \u2018arc to open ocean\u2019 (in degrees), crudely representing the effects of ice m\u00e9lange in narrow seaways. The unconfined onset thickness of 200\u2009m was increased from its value of 150\u2009m in ref. 25 in order to improve modern Ross and Weddell Sea calving-front locations. A similar dependence on \u03b1 is imposed for oceanic sub-ice-shelf melt rates, as described below.\nSurface crevasses are additionally deepened (hydrofractured) as they fill with liquid water, which is assumed to depend on the grid-scale runoff of surface melt and rainfall available after refreezing23,53. The crevasse-depth dependence on surface runoff plus rainfall rate R (in metres per year) has been modified slightly for low R values. The R used in equation (B.6) of ref. 25 is changed to:\n0 for R < 1.5 m yr^{-1}\n4*1.5*(R-1.5) for 1.5 m yr^{-1} < R < 3 m yr^{-1}\nR^2 for R > 3 m yr^{-1} (as before)", "source": "https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html"}
{"id": "1ea2eff08fb1-5", "text": "Calving and hydrofracturing\uf0c1\nCalving depends on the combined penetration depths of surface and basal crevasses, relative to total ice thickness23,26,52,53. Crevasse depths are parameterized according to the divergence of the ice velocity field52, with an additional contribution depending on the logarithm of ice speed that crudely represents the accumulated strain history (ice damage) along a flow path25. Rapid calving is imposed as ice thickness falls below 200\u2009m for unconfined embayments. The 200-m criterion is decreased in confined embayments according to 200\u2009\u00d7\u2009max[0, min[1, (\u03b1\u2009\u2212\u200940)/20]], where \u03b1 is the \u2018arc to open ocean\u2019 (in degrees), crudely representing the effects of ice m\u00e9lange in narrow seaways. The unconfined onset thickness of 200\u2009m was increased from its value of 150\u2009m in ref. 25 in order to improve modern Ross and Weddell Sea calving-front locations. A similar dependence on \u03b1 is imposed for oceanic sub-ice-shelf melt rates, as described below.\nSurface crevasses are additionally deepened (hydrofractured) as they fill with liquid water, which is assumed to depend on the grid-scale runoff of surface melt and rainfall available after refreezing23,53. The crevasse-depth dependence on surface runoff plus rainfall rate R (in metres per year) has been modified slightly for low R values. The R used in equation (B.6) of ref. 25 is changed to:\n0 for R < 1.5 m yr^{-1}\n4*1.5*(R-1.5) for 1.5 m yr^{-1} < R < 3 m yr^{-1}\nR^2 for R > 3 m yr^{-1} (as before)\nThis supposes that minimal hydrofracturing occurs for relatively small R values. The linear segment between 1.5\u2009m\u2009yr\u22121and 3\u2009m\u2009yr\u22121 intersects the R2 parabola as a tangent at R\u2009=\u20093. This modification prevents small amounts of recession in some East Antarctic basins for modern conditions, where small amounts of summer melt and rainfall occur.\nStructural failure of ice cliffs\uf0c1\nTo account for structural ice-cliff failure26,54 (MICI in Fig. 2), a wastage rate of ice W is applied locally to the grid cell adjacent to tidewater grounding lines with no floating ice, if the required stresses at the exposed cliff face exceed the yield strength of ice. This condition depends on the subaerial cliff height at the interpolated grounding line relative to the maximum ice thickness that can be supported, modified locally to account for any meltwater-enhanced crevasse penetration (hydrofracturing), and any reductions in crevassing caused by backstress. For dry crevassing at an ice margin with no hydrofracturing and no buttressing (backstress), the maximum exposed cliff height is 100\u2009m, assuming an ice yield strength of 1\u2009MPa25,26. The formulation of W results in a steep ramp in wastage rates of 0\u20133\u2009km\u2009yr\u22121, where exposed ice cliffs ramp from 80\u2009m to 100\u2009m. The maximum wastage rate of 3\u2009km\u2009yr\u22121 used as our default is conservatively chosen, based on recent observations of the Jakobshavn Isbrae Glacier (up to ~12\u2009km\u2009yr\u22121) and the Crane Glacier (~5\u2009km\u2009yr\u22121) following the loss of their ice-buttressing shelves55,56,57.\nOther modifications to ice-sheet model physics\uf0c1\nThe model is modified from ref. 25 to include a more physically based parameterization of the vertical flow of surface mobile liquid water (runoff and rainfall) through moulins and other fracture systems towards the base22,58, which affects the vertical temperature profiles within the ice sheet. Vertical sub-grid-scale columns of liquid water are assumed to exist, through which the water freely drains while exchanging heat by conduction with the surrounding ambient ice that cools and can freeze some or all of the liquid water within the ice interior.\nWe use uniform parameter values everywhere: we set the fractional area of sub-grid columns to overall area to be 0.1, and the horizontal scale of drainage elements to be 10\u2009m (R in ref. 22, used in the calculations of conductive heat exchange with ambient ice). The fractional area includes both large moulins and any downward movement of liquid water in crevasses or cracks of all scales, which would be prevalent in the future melting scenarios investigated here. Offline sensitivity tests show low sensitivity of our model behaviour to these values, but further investigation is warranted.\nFor reasonable numerical behaviour, the horizontal heat exchange needs to be part of the time-implicit vertical diffusive heat solution for ambient ice temperature in the main model. To avoid an iterative procedure in cases where all liquid water is frozen before reaching the bed, a time-explicit calculation of the water penetration is made first, and one of the following measures is applied in the time-implicit ice-temperature step: (1) the conductive heat exchange coefficient at all levels is reduced by a constant factor for the column, so that the liquid penetrates to the lowest layer but no further; and (2) the conductive coefficient is set to zero below the depth of furthest penetration. Both methods give very similar results in idealized single-column tests; method (1) was used for all runs here. In cases with greater surface liquid flux, there is no reduction of coefficients and some water reaches the base.\nA minor bug fix is corrected in the calculation of vertical velocities within the ice (w\u2032 in ref. 27), which previously did not account for the removal of ice at the base due to oceanic melting. This only affects advection of temperature in ice shelves, and has negligible effects on results.\nIce-sheet initial conditions\uf0c1\nIce-sheet initial conditions and basal sliding coefficients are provided by a 100-kyr inverse simulation following the methodology in ref. 51, using mass-balance forcing provided by a bias-corrected RCM climatology and modern observed ocean temperatures (described below). In the inverse procedure, basal sliding coefficients under modern grounded ice are adjusted iteratively to reduce the misfit with observed ice thickness, with grounding-line positions fixed to observed locations. The LIG simulation using \u2018glacial\u2019 initial conditions (Fig. 3) uses the same basal sliding coefficients (along with a relatively slippery value for modern ocean beds), but initialized from a previous simulation of the LGM with a prescribed, cold glacial climate representing conditions at ~20\u2009kyr ago. The total ice volume in the modern and glacial ice sheets is 26.55\u2009\u00d7\u2009106\u2009km3 and 32.30\u2009\u00d7\u2009106\u2009km3, respectively, equivalent to bedrock-compensated GMSL values of 56.80\u2009m and 62.28\u2009m.\nAtmospheric coupling\uf0c1\nAtmospheric climatologies providing surface mass-balance inputs to the ice model are provided by decadal averages of meteorological fields from the RegCM3 RCM59, adapted to Antarctica with a polar stereographic grid and small modifications of model physics for polar regions. The RCM uses a 40-km grid, over a generous domain spanning Antarctica and surrounding oceans, nested within the GENESIS v3 Global Climate Model60,61. The GCM and RCM share the same radiation code62 and orbitally dependent calculations of shortwave insolation, important for the Pliocene and LIG palaeoclimate simulations.\nAnomaly methods are used to correct a small <2\u2009\u00b0C Antarctic cold bias in the RCM:\nT = T_{exp} + T_{obs} - T_{ctl}\nP = P_{exp} * P_{obs} / P_{ctl}\nwhere T is monthly surface air temperature and P is monthly precipitation. Subscripts \u2018exp\u2019, \u2018obs\u2019 and \u2018ctl\u2019 refer to model experiment, observed modern climatology, and model modern control, respectively. A modern (1950) RCM simulation is used for the model modern control, and the ALBMAP data set [63] is used for observed modern climatology.\nIn the climatic correction for the difference between the ice-model surface elevation and the interpolated elevation in the climate model or observational data set27, precipitation is now corrected as well as temperature. As before, air temperature T (in degrees Celsius) is shifted by \u0394T\u2009=\u2009\u03b3\u0394z, where \u03b3\u2009=\u2009\u22120.008\u2009\u00b0C\u2009m\u22121 is the lapse rate (that is, the decrease in atmospheric temperature with respect to altitude) and \u0394z is the elevation difference. Now, precipitation P is multiplied by a Clausius\u2013Clapeyron-like factor:\nP * 2^{\u2206T/10}", "source": "https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html"}
{"id": "1ea2eff08fb1-6", "text": "Atmospheric coupling\uf0c1\nAtmospheric climatologies providing surface mass-balance inputs to the ice model are provided by decadal averages of meteorological fields from the RegCM3 RCM59, adapted to Antarctica with a polar stereographic grid and small modifications of model physics for polar regions. The RCM uses a 40-km grid, over a generous domain spanning Antarctica and surrounding oceans, nested within the GENESIS v3 Global Climate Model60,61. The GCM and RCM share the same radiation code62 and orbitally dependent calculations of shortwave insolation, important for the Pliocene and LIG palaeoclimate simulations.\nAnomaly methods are used to correct a small <2\u2009\u00b0C Antarctic cold bias in the RCM:\nT = T_{exp} + T_{obs} - T_{ctl}\nP = P_{exp} * P_{obs} / P_{ctl}\nwhere T is monthly surface air temperature and P is monthly precipitation. Subscripts \u2018exp\u2019, \u2018obs\u2019 and \u2018ctl\u2019 refer to model experiment, observed modern climatology, and model modern control, respectively. A modern (1950) RCM simulation is used for the model modern control, and the ALBMAP data set [63] is used for observed modern climatology.\nIn the climatic correction for the difference between the ice-model surface elevation and the interpolated elevation in the climate model or observational data set27, precipitation is now corrected as well as temperature. As before, air temperature T (in degrees Celsius) is shifted by \u0394T\u2009=\u2009\u03b3\u0394z, where \u03b3\u2009=\u2009\u22120.008\u2009\u00b0C\u2009m\u22121 is the lapse rate (that is, the decrease in atmospheric temperature with respect to altitude) and \u0394z is the elevation difference. Now, precipitation P is multiplied by a Clausius\u2013Clapeyron-like factor:\nP * 2^{\u2206T/10}\nRates of surface snowfall and rainfall are now consistently multiplied by a factor \u03c1w/\u03c1i\u2009\u2248\u20091.1, where \u03c1w and \u03c1i are the densities of liquid water and of ice respectively. This consistently converts between the units of most climate models and climatological databases (metres of liquid water equivalent per year) and the ice-model surface budget terms (metres of ice equivalent per year).\nOceanic sub-ice shelf and calving-face melt rates\uf0c1\nDirect coupling of high-resolution ocean models and ice sheets remains challenging. For present-day simulations we use a parameterization of sub-ice shelf melt rates, similar to that used by other model groups64. The parameterization27 links oceanic melt rates to the nearest observed (or modelled) ocean temperatures:\nOM = (KT\u03c1wCw/\u03c1iLf) abs(To - Tf) (To - Tf)\nwhere To is ocean temperature interpolated from the nearest point in an observational (or ocean model) gridded data set, Tf is the local freezing-point temperature at the depth of the ice base, and Cw is the specific heat of ocean water. The transfer factor KT\u2009=\u200915.77\u2009m\u2009yr\u22121\u2009\u00b0C\u22121 results in a combined coefficient (KT\u03c1wCw/\u03c1iLf) of 0.224\u2009m\u2009yr\u22121\u2009\u00b0C\u22122. The depth dependence on Tf produces higher melt rates at the grounding line, as observed, and the dependence on T0\u2009\u2212\u2009Tf is quadratic65. Although spatially coarse observational data sets and standard GCM ocean models fail to capture detailed ocean current systems below ice-shelf cavities, this approach (Extended Data Fig. 6e and f) is preferable to the ad hoc prescription of single temperatures and transfer coefficients along individual sectors of the Antarctic margin as in ref. 27.\nThe effects of confined geography on ocean currents are represented by reducing basal melting depending on the total arc to open ocean \u03b1, representing the concavity of the coastline25. The melt rate computed from ocean temperatures as above is multiplied by the factor: max[0, min[1, alpha - 20) / 20]]\nThis effect, combined with the reduction of thin-ice calving with a similar dependence on \u03b1 described above, allows ice to expand into interior basins during cool-climate recovery after major retreats of marine-based ice, as presumably occurred many times in West Antarctica over the last several million years66.\nMelting of vertical ice surfaces in direct contact with ocean water is derived from the oceanic melt rate (OM) of surrounding grid cells, but is increased by a scaling factor of 10, producing more realistic calving front positions and in better agreement with hydrographic melt rate observations and detailed modelling67. Present-day sub-ice shelf and calving-face melt rates described here use the 1\u00b0 resolution World Ocean Atlas32,68 temperatures at 400-m depth, interpolated to the time-evolving ice model grid and propagated under ice-shelf surfaces using contiguous neighbour iteration to provide To. The depth of 400\u2009m represents typical observed levels of Circum-Antarctic Deep Water, a main source of warm-water incursions into the Amundsen Sea Embayment today69.\nPliocene simulation\uf0c1\nOur default Pliocene simulation uses the same nested GCM\u2013RCM climatology used in a prior study25, with 400\u2009p.p.m.v. CO2 and a generic warm austral summer orbit28 (Extended Data Fig. 1). Ocean temperatures are increased uniformly by 2\u2009\u00b0C everywhere in the Southern Ocean. The resulting Antarctic contribution of 11.3\u2009m GMSL implies >15\u2009m GMSL rise if an additional ~5\u2009m contribution from Greenland70 and the steric effects of a warm Pliocene ocean are also considered. This result is ~6\u2009m less than in ref. 25, reflecting a reduction in the sensitivity of the model with the changes described above.\nLIG simulations\uf0c1\nThe LIG spans a ~20-kyr interval with greenhouse-gas atmospheric mixing ratios comparable to the pre-industrial Holocene9. Opportunities for Antarctic ice-sheet retreat within this interval include a peak in the duration of Antarctic summers coeval with a boreal summer insolation maximum at 128\u2009kyr ago, and an Antarctic summer insolation maxima one half-precession cycle later at 116\u2009kyr ago (Extended Data Fig. 2). We target these two orbital time slices because they contrast radiatively long and weak (128\u2009kyr ago) versus short and intense Antarctic summers (116\u2009kyr ago), both of which have been postulated to be important drivers of ice volume on glacial\u2013interglacial timescales71.\nLIG simulations that include climate\u2013ice sheet feedback asynchronously couple the GCM\u2013RCM and the ice-sheet model. In this case, the nested RCM land (ice) surface boundary conditions are updated at the end of the initial retreat at ice model-year 5000 and the ice-sheet model is rerun using the updated climatology. This improves the representation of ice-climate feedbacks via albedo, ocean surface conditions (sea surface temperatures and sea ice), and dynamical effects of the changing topography on the atmosphere. We find that explicitly including climate\u2013ice feedbacks improves model performance, relative to simple lapse-rate adjustments.\nLIG simulations (Extended Data Table 1; Extended Data Fig. 3d, e) apply anomaly-corrected RCM mass-balance forcing at each LIG time slice, using the appropriate greenhouse gas9,72 and orbital values73 in the nested GCM\u2013RCM. Ocean temperatures are provided by the World Ocean Atlas data set32, with incremental warming of 1\u20135\u2009\u00b0C applied uniformly over the Southern Ocean grid domain.\nTo allow the RCM atmosphere to respond to a warmer Southern Ocean in addition to applying elevated ocean temperatures to the ice model, we increase the southward ocean-heat convergence in the nested GCM\u2013RCM using the methodology described in ref. 28, effectively warming the Southern Ocean sea surface temperatures by ~2\u2009\u00b0C and reducing sea-ice extent. Accounting for the effect of a warmer Southern Ocean on the overlying atmosphere produces more LIG ice-sheet retreat for a given ocean warming, improving our model\u2013data fit. With this technique, only 3\u2009\u00b0C of assumed sub-surface ocean warming is required to produce >6\u2009m GMSL rise from Antarctica at either LIG orbital time slice, reinforcing the notion of a dominant oceanic control on LIG ice-sheet retreat.", "source": "https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html"}
{"id": "1ea2eff08fb1-7", "text": "LIG simulations that include climate\u2013ice sheet feedback asynchronously couple the GCM\u2013RCM and the ice-sheet model. In this case, the nested RCM land (ice) surface boundary conditions are updated at the end of the initial retreat at ice model-year 5000 and the ice-sheet model is rerun using the updated climatology. This improves the representation of ice-climate feedbacks via albedo, ocean surface conditions (sea surface temperatures and sea ice), and dynamical effects of the changing topography on the atmosphere. We find that explicitly including climate\u2013ice feedbacks improves model performance, relative to simple lapse-rate adjustments.\nLIG simulations (Extended Data Table 1; Extended Data Fig. 3d, e) apply anomaly-corrected RCM mass-balance forcing at each LIG time slice, using the appropriate greenhouse gas9,72 and orbital values73 in the nested GCM\u2013RCM. Ocean temperatures are provided by the World Ocean Atlas data set32, with incremental warming of 1\u20135\u2009\u00b0C applied uniformly over the Southern Ocean grid domain.\nTo allow the RCM atmosphere to respond to a warmer Southern Ocean in addition to applying elevated ocean temperatures to the ice model, we increase the southward ocean-heat convergence in the nested GCM\u2013RCM using the methodology described in ref. 28, effectively warming the Southern Ocean sea surface temperatures by ~2\u2009\u00b0C and reducing sea-ice extent. Accounting for the effect of a warmer Southern Ocean on the overlying atmosphere produces more LIG ice-sheet retreat for a given ocean warming, improving our model\u2013data fit. With this technique, only 3\u2009\u00b0C of assumed sub-surface ocean warming is required to produce >6\u2009m GMSL rise from Antarctica at either LIG orbital time slice, reinforcing the notion of a dominant oceanic control on LIG ice-sheet retreat.\nThe two time-continuous LIG simulations using prescribed climatologies (Fig. 3) use bias-corrected, present-day RCM climatologies with a uniform, time-evolving perturbation derived from the average of Antarctic ice-core climatologies compiled in ref. 29. Southern Ocean temperatures are treated similarly, with World Ocean Atlas temperatures32 increased according to the average of circum-Antarctic LIG anomalies29. Only records from marine drill-cores poleward of 45\u00b0\u2009S are used in the averages, but we note that there is considerable uncertainty in the proxy sea surface temperature estimates (>2\u2009\u00b0C)29. This approach also assumes that the proxy sea surface temperatures reflect changes at sub-surface depths (~400\u2009m), which is uncertain. The resulting anomalies are applied to the ice sheet model at 130\u2009kyr ago, 125\u2009kyr ago, 120\u2009kyr ago, and 115\u2009kyr ago and the ice-sheet model is run continuously from 130\u2009kyr ago to 115\u2009kyr ago. The pairs of air and ocean temperature perturbations applied at each 5-kyr LIG timestep are 1.97\u00b0 and 1.70\u00b0, 1.41\u00b0 and 1.51\u00b0, 0.83\u00b0 and 1.09\u00b0, \u22121.57\u00b0 and 0.31\u00b0, respectively.\nThe time-continuous LIG simulations are initialized from either a present-day initial ice state (Fig. 1b), or from a prior Last Glacial Maximum simulation with 5.76\u2009\u00d7\u2009106\u2009km3 more ice than today. The latter initial condition may better represent the ice sheet at the onset of the LIG and leads to a greater potential sea-level rise owing to the deeper bed conditions early in the deglaciation, which enhances the bathymetrically sensitive MISI dynamics.\nThe proxy-forced LIG simulation clearly supports a maximum Antarctic contribution to GMSL early in the interglacial period (Fig. 3). However, we note that owing to the demonstrated influence of Southern Ocean temperature on the timing of retreat and the uncertain magnitude and chronology of our imposed forcing29, these results cannot definitively rule out maximum Antarctic retreat at the end of the LIG, as has also been proposed4,74\nFuture simulations\uf0c1\nBecause of the new ice-model physics that directly involve the atmosphere via meltwater enhancement of crevassing and calving, highly resolved atmospheric climatologies are needed at spatial resolutions beyond those of most GCMs. However, multi-century RCM simulations are computationally infeasible. To accommodate the need for long but high-resolution climatologies, the nested GCM\u2013RCM is run to equilibrium with 1\u2009\u00d7\u2009PAL, 2\u2009\u00d7\u2009PAL, 4\u2009\u00d7\u2009PAL and 8\u2009\u00d7\u2009PAL CO2. In the ice-sheet simulations, CO2 follows the extended RCP greenhouse gas emissions36 to the year 2500, and the climate at any time is the average of the two appropriate surrounding RCM solutions, weighted according to the logarithm of the concentration of CO2. The RCM climatologies follow total equivalent CO2, which accounts for all radiatively active trace gases in the RCP timeseries. In RCP8.5, equivalent CO2 forcing exceeds 8\u2009\u00d7\u2009PAL after 2175, but it is conservatively limited here to a maximum of 8\u2009\u00d7\u2009PAL (Fig. 4a). A 10-yr lag is imposed in the RCM climatologies to reflect the average offset between sea surface temperatures and surface air temperatures in the equilibrated RCM (with equilibrated sea surface temperatures from the parent GCM) and the transient response of the real ocean\u2019s mixed layer.\nOcean temperatures in the RCP scenarios are provided by high-resolution (0.5\u00b0 atmosphere and 1\u00b0 ocean) NCAR CCSM437 ocean model output, following the RCP2.6, RCP4.5, and RCP8.5 greenhouse gas emissions scenarios run to 2300. Ocean temperatures beyond the limit of the CCSM4 simulations at 2300 are conservatively maintained at their 2300 values. As with the World Ocean Atlas, water temperatures at 400-m depth (between ocean model z-levels 30 and 31) are used in the parameterization of oceanic sub-ice melt (oceanic melt rate) described above. The CCSM4 underestimates the wind-driven warming of Antarctic Shelf Bottom Water41 in the Amundsen and Bellingshausen seas associated with recent increases in melt rates and grounding-line retreats20,42,43. To account for this, additional warming is added to the Amundsen and Bellingshausen sectors of the continental margin. We find the addition of 3\u2009\u00b0C to the CCSM4 ocean temperatures increases melt rates to 25\u201330\u2009m\u2009yr\u22121 (Extended Data Fig. 5f). While still less than observed, this substantially improves grounding-line positions in the Amundsen Sea (Pine Island Glacier in particular) from 1950 to 2015. When applied to RCP4.5 and RCP8.5, the ocean-bias correction accelerates twenty-first-century WAIS retreat (Fig. 4d, g, h) but is found to have little effect beyond 2100 (Extended Data Table 1).\nExtended RCP greenhouse gas scenarios36 are available up to 2500, beyond which we assume two different scenarios: (1) natural decay of CO275,76 and no further anthropogenic emissions, or (2) engineered, fast drawdown towards pre-industrial levels with an e-folding time of 100 years. These choices are not intended to be definitive, but serve to illustrate the ice-sheet response to a wide range of possible long-term future forcings.", "source": "https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html"}
{"id": "1ea2eff08fb1-8", "text": "Ocean temperatures in the RCP scenarios are provided by high-resolution (0.5\u00b0 atmosphere and 1\u00b0 ocean) NCAR CCSM437 ocean model output, following the RCP2.6, RCP4.5, and RCP8.5 greenhouse gas emissions scenarios run to 2300. Ocean temperatures beyond the limit of the CCSM4 simulations at 2300 are conservatively maintained at their 2300 values. As with the World Ocean Atlas, water temperatures at 400-m depth (between ocean model z-levels 30 and 31) are used in the parameterization of oceanic sub-ice melt (oceanic melt rate) described above. The CCSM4 underestimates the wind-driven warming of Antarctic Shelf Bottom Water41 in the Amundsen and Bellingshausen seas associated with recent increases in melt rates and grounding-line retreats20,42,43. To account for this, additional warming is added to the Amundsen and Bellingshausen sectors of the continental margin. We find the addition of 3\u2009\u00b0C to the CCSM4 ocean temperatures increases melt rates to 25\u201330\u2009m\u2009yr\u22121 (Extended Data Fig. 5f). While still less than observed, this substantially improves grounding-line positions in the Amundsen Sea (Pine Island Glacier in particular) from 1950 to 2015. When applied to RCP4.5 and RCP8.5, the ocean-bias correction accelerates twenty-first-century WAIS retreat (Fig. 4d, g, h) but is found to have little effect beyond 2100 (Extended Data Table 1).\nExtended RCP greenhouse gas scenarios36 are available up to 2500, beyond which we assume two different scenarios: (1) natural decay of CO275,76 and no further anthropogenic emissions, or (2) engineered, fast drawdown towards pre-industrial levels with an e-folding time of 100 years. These choices are not intended to be definitive, but serve to illustrate the ice-sheet response to a wide range of possible long-term future forcings.\nFuture high-resolution ocean-model output is not available on multi-millennial timescales. In our long (5,000-year) future simulations (Extended Data Fig. 7), CCSM4 ocean temperatures at 400\u2009m depth are assumed to remain at their 2300 values for thousands of years beyond 2300 (until 7000). This assumption is based on the thermal inertia of the deep ocean (thousands of years)47, its longwave radiative feedback on atmospheric temperatures77, and its relative isolation from surface variations. The response of the intermediate and deep ocean to atmospheric and surface-ocean warming before 2300 is heavily lagged in time, and consequently deep-ocean temperatures would continue to rise long after CO2 levels and surface temperatures began to decline after 250077. However, at some point several thousand years later, intermediate- and deep-ocean waters would start to cool if CO2 levels decay as in Extended Data Fig. 7. The trajectory of these temperatures would vary spatially and depend on details of the ocean circulation. To our knowledge, the state of the ocean as it recovers from a greenhouse gas perturbation over these timescales is largely unknown, as relevant coupled atmosphere\u2013ocean global climate model simulations at the resolution and duration appropriate to our ice model have not been run. Consequently, our assumption of constant 400-m ocean temperatures after 2300, although likely to be conservative beyond 2500, may be questionable for the latter parts of the simulations assuming fast, engineered CO2 drawdown. However, assuming the slow, natural pace of CO2 recovery76, atmospheric concentrations would remain above twice the current level of carbon dioxide (2\u2009\u00d7\u2009CO2) for thousands of years in the RCP8.5 scenario (Extended Data Fig. 7). Assuming a global temperature sensitivity of ~3\u2009\u00b0C per doubling of CO2, our ocean temperatures applied to the long RCP8.5 scenario are probably conservative over the duration of the simulation.\nGeologically constrained Large Ensemble analysis of future ice-sheet retreat\uf0c1\nTo quantify model uncertainty due to poorly known parameter values, ensembles of future RCP scenarios are performed with varying model parameters affecting sub-ice oceanic melt rates, meltwater-enhanced calving (hydrofracturing) and marine-terminating ice cliff failure. Ensemble members use the high-resolution atmospheric and ocean forcing described in the main text and above. Alternative ensembles are run both with and without the bias correction of CCSM4 ocean temperatures in the Amundsen and Bellingshausen Seas. The three parameters and four values used for each are as follows.\nOCFAC is the coefficient in the parameterization of sub-ice-shelf oceanic melt, which is proportional to the square of the difference between nearby ocean water temperature at 400-m depth, and the pressure-melting point of ice. It corresponds to K in equation (17) of ref. 27. The relationship between proximal ocean conditions and melting at the base of floating ice shelves remains a challenging topic of ongoing research78, and a simple parameterization64 is used here. Ensemble values of OCFAC are 0.1, 1, 3 and 10 times the default value of 0.224\u2009m\u2009yr\u22122\u2009\u00b0C\u22122.\nCREVLIQ is the coefficient in the parameterization of hydrofracturing due to surface liquid. It replaces the constant 100 in equation (B.6) of ref. 25, and is the additional crevasse depth due to surface melt plus rainfall rate, with a quadratic dependence. This crudely represents the complex relationship between surface water and crevasse propagation, and basic model sensitivity is shown in supplementary figure 7b of ref. 25. Values of CREVLIQ are 0\u2009m, 50\u2009m, 100\u2009m and 150\u2009m per (m yr\u22121)\u22122.\nVCLIF is the maximum rate of horizontal wastage due to ice-cliff structural failure. It replaces the default value of 3,000 (3\u2009km\u2009yr\u22121) in equation (A.4) of ref. 25. Its magnitude is based on observed retreat rates of modern large ice cliffs, and basic model sensitivity is shown in supplementary figure 7a of ref. 25. Values of VCLIF are 0\u2009km\u2009yr\u22121, 1\u2009km\u2009yr\u22121, 3\u2009km\u2009yr\u22121 and 5\u2009km\u2009yr\u22121.\nMedium-range, default values of OCFAC, CREVLIQ, and VCLIF used in our nominal Pliocene (Extended Data Fig. 1), LIG (Fig. 3), and Future (Fig. 4) simulations are OCFAC\u2009=\u20091 (corresponding to 0.224\u2009m\u2009yr\u22122\u2009\u00b0C\u22122), CREVLIQ\u2009=\u2009100\u2009m per (m yr\u22121)\u22122, and VCLIF\u2009=\u20093\u2009km\u2009yr\u22121, respectively.\nSimulations for the Pliocene and LIG scenarios are run with all possible combinations of these parameter values, that is, 64 (=43) runs (Extended Data Table 2). Each run is subject to a pass/fail test that its equivalent GMSL rise falls within the observed ranges for the LIG (3.6\u20137.4\u2009m) and the Pliocene (10\u201320\u2009m). The filtered subset of parameter combinations that pass (15 out of 64) are then used in an ensemble of future RCP scenarios. An additional ensemble calculation is performed using the same LIG criteria, but a lower accepted range for Pliocene sea-level rise (5\u201315\u2009m), to reflect the large uncertainty in Pliocene sea-level reconstructions1 (29 out of 64 passed this test). The mean and 1\u03c3 range of each ensemble are shown for the three RCP scenarios in Fig. 5, providing both an envelope of possible outcomes and an estimate of the model\u2019s parametric uncertainty. Two alternative sets of future RCP ensembles are run with the ocean-temperature bias correction in the Amundsen and Bellingshausen seas shown in Extended Data Fig. 5. This increases Antarctica\u2019s GMSL contribution by ~9\u2009cm over the next century in both RCP8.5 and RCP8.5, but has almost no effect on longer timescales (Extended Data Tables 1, 2). In the RCP2.6 ensemble calibrated against the higher >10\u2009m Pliocene sea-level targets, the ocean-bias correction increases both the ensemble-mean and 1\u03c3 standard deviation to 16\u2009\u00b1\u200916\u2009cm in 2100 and 62\u2009\u00b1\u200976\u2009cm in 2500 (Extended Data Table 1). The increased variance is caused by three simulations in the RCP2.6 ensemble set, in which the stability of the Thwaites Glacier grounding line is exceeded and the WAIS retreats into the deep interior. Although the ensemble members with bias-corrected ocean temperatures are generally more consistent with observations of recent retreat in the Amundsen\u2013Bellingshausen sector, the validity of the bias correction in the long-term future is unknown.", "source": "https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html"}
{"id": "1ea2eff08fb1-9", "text": "Simulations for the Pliocene and LIG scenarios are run with all possible combinations of these parameter values, that is, 64 (=43) runs (Extended Data Table 2). Each run is subject to a pass/fail test that its equivalent GMSL rise falls within the observed ranges for the LIG (3.6\u20137.4\u2009m) and the Pliocene (10\u201320\u2009m). The filtered subset of parameter combinations that pass (15 out of 64) are then used in an ensemble of future RCP scenarios. An additional ensemble calculation is performed using the same LIG criteria, but a lower accepted range for Pliocene sea-level rise (5\u201315\u2009m), to reflect the large uncertainty in Pliocene sea-level reconstructions1 (29 out of 64 passed this test). The mean and 1\u03c3 range of each ensemble are shown for the three RCP scenarios in Fig. 5, providing both an envelope of possible outcomes and an estimate of the model\u2019s parametric uncertainty. Two alternative sets of future RCP ensembles are run with the ocean-temperature bias correction in the Amundsen and Bellingshausen seas shown in Extended Data Fig. 5. This increases Antarctica\u2019s GMSL contribution by ~9\u2009cm over the next century in both RCP8.5 and RCP8.5, but has almost no effect on longer timescales (Extended Data Tables 1, 2). In the RCP2.6 ensemble calibrated against the higher >10\u2009m Pliocene sea-level targets, the ocean-bias correction increases both the ensemble-mean and 1\u03c3 standard deviation to 16\u2009\u00b1\u200916\u2009cm in 2100 and 62\u2009\u00b1\u200976\u2009cm in 2500 (Extended Data Table 1). The increased variance is caused by three simulations in the RCP2.6 ensemble set, in which the stability of the Thwaites Glacier grounding line is exceeded and the WAIS retreats into the deep interior. Although the ensemble members with bias-corrected ocean temperatures are generally more consistent with observations of recent retreat in the Amundsen\u2013Bellingshausen sector, the validity of the bias correction in the long-term future is unknown.\nExtended data figures and tables\uf0c1\nExtended Data Figure 1: Warm mid-Pliocene climate and ice-sheet simulation. a, January (warmest monthly mean) difference in 2-m (surface) air temperature simulated by the RCM relative to a preindustrial control simulation with 280\u2009p.p.m.v. CO2 and present-day orbit. The temperature difference is lapse-rate-corrected to account for the change in ice-sheet geometry and surface elevations. The Pliocene simulation uses 400\u2009p.p.m.v. CO2, a warm austral summer orbit, and assumes a retreated WAIS to represent maximum Pliocene warm conditions. b, The Pliocene ice-sheet is shown after 5,000 model years, driven by the RCM climate in a, and assuming 2\u2009\u00b0C ocean warming relative to a modern ocean climatology32. In the model formulation used here, maximum Pliocene ice-sheet retreat with default model parameters is equivalent to 11.26\u2009m GMSL, about 6\u2009m less than in ref. 25.\nExtended Data Figure 2: LIG greenhouse gases, orbital parameters, and RCM climates. a, Greenhouse gas concentrations9,72 converted to radiative forcing shows the LIG interval (light red bar) and the best opportunity for ice-sheet retreat. b, Summer insulation at 70\u00b0 latitude in both hemispheres73 (red, south; blue, north) and summer duration at 70\u00b0\u2009S (black)79 shown over the last 150\u2009kyr, and the two orbital time slices (vertical dashed black lines at 128\u2009kyr ago and 116\u2009kyr ago). c, Table showing the greenhouse gas atmospheric mixing ratios (CO2 in parts per million by volume; CH4 and N2O in parts per billion by volume) and orbital parameters (eccentricity, obliquity, precession) used in the GCM\u2013RCM at the LIG time slices (dashed lines 1 and 2 in a and b), respectively. d\u2013f, January (warmest monthly mean) differences in 2-m surface air temperature relative to a preindustrial control simulation at 128\u2009kyr ago (d), 116\u2009kyr ago (e), and the present-day (2015) (f). Simulated austral summer temperatures at 116\u2009kyr ago (e) with relatively high-intensity summer insolation is warmer than the long-duration summer orbit at 128\u2009kyr ago (d), but unlike the Pliocene (Extended Data Fig. 1a), neither LIG climatology is as warm as the present day, producing little to no rain or surface melt on ice-shelf surfaces.\nExtended Data Figure 3: Effect of Southern Ocean warming on Antarctic surface air temperatures and the ice sheet at 128\u2009kyr ago. a\u2013c, January (warmest monthly mean) differences in 2-m surface air temperature at 128\u2009kyr ago, relative to a preindustrial control simulation (top row). GHG, greenhouse gas; SST, sea surface temperature. d, e, Ice-sheet thickness (m) after 5,000 model years, driven by the corresponding climate in a\u2013c. a and d, Without climate\u2013ice sheet coupling (present-day ice extent and surface ocean temperatures in the RCM), and prescribed 5\u2009\u00b0C sub-surface ocean warming felt only by the ice sheet. b and e, With asynchronous coupling between the RCM atmosphere and ice sheet, and prescribed 5\u2009\u00b0C sub-surface ocean warming felt only by the ice sheet. c and f, With asynchronous coupling between the RCM atmosphere and ice sheet, prescribed 3\u2009\u00b0C sub-surface ocean warming felt by the ice sheet, and ~2\u2009\u00b0C surface ocean warming felt by the RCM atmosphere. c shows the locations of East Antarctic ice cores (EDC, EPICA Dome C; V, Vostock; DF, Dome F; EDML, EPICA Dronning Maud Land) indicating warming early in the interglacial29 and previously attributed to WAIS retreat80; this warming is similar to that simulated in c from a combination of ice-sheet retreat and warmer Southern Ocean temperatures, supporting the notion that the timing of LIG retreat was largely driven by far-field ocean influences, rather than local astronomical forcing.\nExtended Data Figure 4: RCM climates used in future, time-continuous RCP scenarios and evolving ice-surface melt rates linked to hydrofracturing model physics. a\u2013d, January surface (2-m) air temperatures simulated by the RCM at the present-day (2015) (a), twice the present level of carbon dioxide, 2\u2009\u00d7\u2009CO2 (b), 4\u2009\u00d7\u2009CO2 (c), and 8\u2009\u00d7\u2009CO2 (d) with the retreating ice sheet. The colour scale is the same in all panels. Yellow to red colours indicate temperatures above freezing with the potential for summer rain, and surface meltwater production. e\u2013h, Evolving ice-surface meltwater production (in metres per year) in the time-evolving RCP8.5 ice-sheet simulations, driven by a time-continuous RCM climatology (Methods) following the RCP8.5 greenhouse gas time series (Fig. 4a). Black lines show the positions of grounding lines and ice-shelf calving fronts at discrete time intervals\u2014e, 2050; f, 2100; g, 2150; and h, 2500\u2014with superposed meltwater production rates.\nExtended Data Figure 5: NCAR CCSM4 ocean temperatures and oceanic sub-ice-shelf melt rates. a, RCP2.6 ocean warming at 400-m depth, shown as the difference of decadal averages from 1950\u20131960 to 2290\u20132300. b, Same as a but for RCP4.5. c, Same as a but for RCP8.5. d, CCSM4 RCP8.5 ocean warming from 1950\u20131960 to 2010\u20132020 showing little to no warming in the Amundsen and Bellingshausen seas. The red line shows the area of imposed, additional ocean warming. e, f, Oceanic melt rates at 2015 calculated by the ice-sheet model from interpolated CCSM4 temperatures (e), and with +3\u2009\u00b0C adjustment in the Amundsen and Bellingshausen seas (f), corresponding to the area within the red line in d.", "source": "https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html"}
{"id": "1ea2eff08fb1-10", "text": "Extended Data Figure 4: RCM climates used in future, time-continuous RCP scenarios and evolving ice-surface melt rates linked to hydrofracturing model physics. a\u2013d, January surface (2-m) air temperatures simulated by the RCM at the present-day (2015) (a), twice the present level of carbon dioxide, 2\u2009\u00d7\u2009CO2 (b), 4\u2009\u00d7\u2009CO2 (c), and 8\u2009\u00d7\u2009CO2 (d) with the retreating ice sheet. The colour scale is the same in all panels. Yellow to red colours indicate temperatures above freezing with the potential for summer rain, and surface meltwater production. e\u2013h, Evolving ice-surface meltwater production (in metres per year) in the time-evolving RCP8.5 ice-sheet simulations, driven by a time-continuous RCM climatology (Methods) following the RCP8.5 greenhouse gas time series (Fig. 4a). Black lines show the positions of grounding lines and ice-shelf calving fronts at discrete time intervals\u2014e, 2050; f, 2100; g, 2150; and h, 2500\u2014with superposed meltwater production rates.\nExtended Data Figure 5: NCAR CCSM4 ocean temperatures and oceanic sub-ice-shelf melt rates. a, RCP2.6 ocean warming at 400-m depth, shown as the difference of decadal averages from 1950\u20131960 to 2290\u20132300. b, Same as a but for RCP4.5. c, Same as a but for RCP8.5. d, CCSM4 RCP8.5 ocean warming from 1950\u20131960 to 2010\u20132020 showing little to no warming in the Amundsen and Bellingshausen seas. The red line shows the area of imposed, additional ocean warming. e, f, Oceanic melt rates at 2015 calculated by the ice-sheet model from interpolated CCSM4 temperatures (e), and with +3\u2009\u00b0C adjustment in the Amundsen and Bellingshausen seas (f), corresponding to the area within the red line in d.\nExtended Data Figure 6: Effect of future ocean warming only. a, Antarctic contribution to future GMSL rise in long, 5,000-yr ice-sheet simulations driven by sub-surface ocean warming simulated by CCSM4, following RCP8.5 (black line), with a +3\u2009\u00b0C adjustment in the Amundsen and Bellingshausen seas (blue line; see Extended Data Fig. 5) and a warmer +5\u2009\u00b0C adjustment (red line). Atmospheric temperatures and precipitation are maintained at their present values. b\u2013d, Ice-sheet thickness at model-year 5,000, driven by sub-surface ocean forcing from CCSM4 (b) and from CCSM4 with a +3\u2009\u00b0C (c) or +5\u2009\u00b0C (d) adjustment in the Amundsen and Bellingshausen seas. Note the near-complete loss of ice shelves, but modest grounding-line retreat in b, the retreat of Pine Island Glacier in c, and the near-complete collapse of WAIS once a stability threshold in the Thwaites Glacier grounding line is reached in d.\nExtended Data Figure 7: The long-term future of the ice sheet and GMSL over the next 5,000 years following RCP8.5 and RCP4.5. a, Equivalent CO2 forcing following RCP8.5 until the year 2500, and then assuming zero emissions after 2500 and allowing a natural relaxation of greenhouse gas levels (red) or assuming a fast, engineered drawdown (blue) with an e-folding timescale of 100 years. b. Antarctic contribution to GMSL over the next 5,000 years, following the greenhouse gas scenarios in a. c, The same as a, except showing long-term RCP4.5 greenhouse gas forcing. d, The same as b, except following the RCP4.5 scenarios in c. The insets in b and d show the ice sheet (and remaining sea-level rise) after 5,000 model years in RCP8.5 and RCP4.5, respectively, assuming fast CO2 drawdown (blue lines), highlighting the multi-millennial commitment to a loss of marine-based Antarctic ice, even in the moderate RCP4.5 scenario. Note the different y-axes in RCP8.5 versus RCP4.5.\nExtended Data Figure 8: Freshwater input to the Southern Ocean. Total freshwater and iceberg flux from 1950 to 2500, following the future RCP scenarios shown in Fig. 4b. Freshwater input calculations include contributions from ice loss above and below sea level and exceed 1\u2009Sv in RCP8.5.\nExtended Data Table 1: Summary of Antarctic contributions to GMSL during the Pliocene, LIG, future centuries, and future millennia. Antarctic contributions to GMSL for the Pliocene and LIG simulations (rows 1\u20139) with +2\u2009\u00b0C ocean warming in the Pliocene and incrementally imposed ocean warming in the LIG simulations. Values shown represent ice retreat at the end of quasi-equilibrated 5000-yr simulations. Time-continuous LIG simulations forced by proxy-based atmosphere and ocean climatologies (rows 10\u201312) list maximum GMSL contributions occurring early in the LIG (Fig. 3a). The remaining rows list Antarctic contributions to GMSL at specific times (years as shown) in time-dependent future simulations. Ensemble means and standard deviations (1\u03c3) of the RCP ensemble members listed in Extended Data Table 2 are also shown. Future GMSL contributions are shown relative to 2000.\nExtended Data Table 2: Ensemble simulations of Pliocene, LIG, and future Antarctic contributions to GMSL. Varying combinations of three model parameters (first column) correspond to OCFAC, CREVLIQ and VCLIF, respectively (see Methods). The resulting GMSL contributions of each ensemble member driven by Pliocene and LIG climatologies are shown in the second and third columns. Combinations of model parameters satisfying Pliocene and LIG sea-level targets are assigned a Large Ensemble number (LE#) in the fourth column. Default model parameter values (LE# 12) and resulting Pliocene and LIG GMSL rise are in bold type. Four future ensembles using alternative sets of the palaeo-filtered Large Ensemble members and following RCP2.5, RCP4.5 and RCP8.5 emissions scenarios are shown at right. The top two ensembles use 29 combinations of parameter values that satisfy LIG sea-level targets and a range of Pliocene sea-level targets between 5\u2009m and 15\u2009m. The bottom two ensembles use a more restricted set of 15 parameter combinations that satisfy a higher Pliocene target range >10\u2009m. Future RCP ensembles at left correspond to the GMSL time series in Fig. 5. The two ensemble sets at far right include the ocean-temperature bias correction described in the text, Fig. 4 and Extended Data Fig. 5. Antarctic GMSL contributions for each ensemble member are shown at 2100 and 2500. Ensemble means and 1\u03c3 standard deviations are also shown. GMSL contributions in future ensembles are relative to 2000.\nSupplementary information\uf0c1\nRCP2.6 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 470 kb)\nRCP4.5 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 522 kb)", "source": "https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html"}
{"id": "1ea2eff08fb1-11", "text": "Supplementary information\uf0c1\nRCP2.6 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 470 kb)\nRCP4.5 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 522 kb)\nRCP8.5 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 584 kb)\nRCP2.6 oceanic melt rates (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 593 kb)\nRCP4.5 oceanic melt rates (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 691 kb)\nRCP8.5 oceanic melt rates (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 808 kb)\nRCP2.6 surface melt-water production (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 477 kb)\nRCP4.5 surface melt-water production (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 594 kb)\nRCP8.5 surface melt-water production (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 778 kb)\nRCP8.5 ice-surface speeds (norm of ice-surface velocities (m a-1)) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 918 kb)\nNature Podcast Discussion\uf0c1\nAdam Levy: Prediction is very difficult, especially about the future. This saying, attributed to physicist Niels Bohr, is often used to refer to quantum mechanics. But climate scientists know it applies to their research too.\nAfter all, how do you work out what the future holds for the climate when you\u2019ve only got one planet? You\u2019re still learning how it works, and you can\u2019t carry out carefully controlled studies. Well, the typical approach is to build computer models that simulate the relevant laws of physics and can be checked against the real world.\nBut what if you only have limited data from the real world, and how do you cope with processes that haven\u2019t even happened yet, but might come into play in the future? These are questions that scientists looking at the Antarctic are grappling with. We only have satellite data of Antarctica from the last few decades, so scientists have to work hard to make the most of the information we have.", "source": "https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html"}
{"id": "1ea2eff08fb1-12", "text": "RCP8.5 ice-surface speeds (norm of ice-surface velocities (m a-1)) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 918 kb)\nNature Podcast Discussion\uf0c1\nAdam Levy: Prediction is very difficult, especially about the future. This saying, attributed to physicist Niels Bohr, is often used to refer to quantum mechanics. But climate scientists know it applies to their research too.\nAfter all, how do you work out what the future holds for the climate when you\u2019ve only got one planet? You\u2019re still learning how it works, and you can\u2019t carry out carefully controlled studies. Well, the typical approach is to build computer models that simulate the relevant laws of physics and can be checked against the real world.\nBut what if you only have limited data from the real world, and how do you cope with processes that haven\u2019t even happened yet, but might come into play in the future? These are questions that scientists looking at the Antarctic are grappling with. We only have satellite data of Antarctica from the last few decades, so scientists have to work hard to make the most of the information we have.\nBut understanding what\u2019s going to happen to Antarctica\u2019s ice is vital to understanding how global warming will impact the world.\nRobert DeConto: There\u2019s just so much potential sea level rise locked up in Antarctica there. There\u2019s such a vast amount of ice.\nAdam Levy: This is Rob DeConto from the University of Massachusetts who reporters in this week\u2019s nature.\nHe\u2019s been trying to peer into the future by modeling how Antarctica contributes to sea level rise.\nRobert DeConto: So even a small fraction of Antarctica being mobilized and going into the ocean is going to have a global impact.\nAdam Levy: Because it could have such a big influence. Lots of different groups have tried simulating Antarctica\u2019s future and have come up with a broad range of results.\nHere\u2019s Tamsin Edwards of the Open University who published a study a few months ago on future ice loss in the Antarctic.\nTamsin Edwards: I would say it\u2019s the the biggest unknown in future sea level rise.\nAdam Levy: But why? What makes it so hard to pin down?\nTamsin Edwards: Pretty much everything about it. All of these different ways in which ice can flow, can crack, can be lost and gained, it makes quite a complicated picture.\nAdam Levy: Both Tamsin Edwards and Rob DeConto have used models to try to get to grips with this problem, but they\u2019re somewhat divided about what their models should be based on. Here\u2019s Tamsin again.\nTamsin Edwards: So we kind of assumed that if the model is good at simulating the recent past, it\u2019s more likely to be good at predicting the future.\nAdam Levy: But Rob thinks there\u2019s only so much that the last few decades can teach us.\nRobert DeConto: In the very recent past, the climate and the oceans have been certainly not as warm as they\u2019re predicted to become in the next century. So we compare the results that we get with geologic records.\nAdam Levy: Geologic records that just means records of the climate from the distant past, deduced from things like the erosion of now inland cliffs.\nRob favors using data like these because there\u2019ve been times in the Earth\u2019s past where the climate has looked pretty similar to today\u2019s situation.\nRobert DeConto: 125,000 years ago, the world looks a lot like it does today. Similar climate, and yet sea level was between six and nine meters higher.\nAdam Levy: So where Tamsin\u2019s model uses direct observations of Antarctica from the last few decades, Rob\u2019s uses our understanding of sea levels from thousands of years ago.\nBut whatever you are checking your model against, you can never be sure it\u2019ll apply to the future. Says Tamsin\nTamsin Edwards: If you\u2019re calibrating with past data, and that includes paleo climate data as well, because you never find a perfect analog of the future in paleo climate. There are always different things going on, so you have to bear that in mind when you\u2019re thinking about your predictions and be a bit cautious.\nAdam Levy: And the same goes for models based on today\u2019s climate. It\u2019s not a done deal that tomorrow will behave like today. And what if Antarctica loses ice in different ways tomorrow than it does today? Rob\u2019s model includes certain processes that we haven\u2019t observed in Antarctica. For example, the possibility that melt water on top of ice could make ice cliffs unstable.\nThis could cause ice to collapse into the sea much faster than we\u2019re seeing today. Rob says his model is only accurate if he includes these kind of dramatic processes. But it\u2019s not easy to build these processes into a model.\nRobert DeConto: I would say that these are just really the first baby steps to try to incorporate processes like these in the models.\nAdam Levy: But Tamsin is not convinced that including processes like this, that we\u2019ve not really seen taking place yet, is the best bet.\nTamsin Edwards: We haven\u2019t seen direct evidence of this. I would say that really says we have to put it in the models. Basically at the moment. It\u2019s an exciting time. The jury\u2019s out.\nAdam Levy: So whereas Tamsin\u2019s model is limited to the behavior we know to have happened in Antarctica, Rob\u2019s includes processes that may or may not arise in the future.\nThey\u2019re both trying to make the best use of limited information. And so to the results: According to these different models, how much is the Antarctic going to contribute to sea level rise by 2100? We\u2019ll get to what these numbers mean in a minute, but first his Tamsin\u2019s estimate.\nTamsin Edwards: We came up with the most likely of about 10 centimeters, quite low, and we came up with a prediction that there was only a 1-in-20 chance it would be more than 30 centimeters by the end of the century.\nAdam Levy: How about Rob\u2019s model?\nRobert DeConto: We\u2019re getting something between 64 centimeters and a little over a meter.\nAdam Levy: It\u2019s a huge difference. Yes, the two models used slightly different scenarios of greenhouse gas emissions, and yes, there are plenty of other uncertainties, but the difference is still striking. And Rob\u2019s results could mean, for example, that low lying island nations could have to evacuate sooner than was previously anticipated.\nRobert DeConto: You know, I hope we\u2019re wrong.\nAdam Levy: Understandable, when Rob\u2019s model also predicts over 10 meters of sea level rise 500 years from now. And remember, Antarctica is just one piece of the sea level rise puzzle added to other sources of sea level rise, like the Greenland ice sheet. Even Tamsin\u2019s estimate could lead to sea level rises of about a meter by the end of the century. A huge challenge for coastal cities around the world.\nBut such big uncertainties mean that it\u2019s hard for the world to know what to prepare itself for. Rob is hopeful that techniques like his and Tamsin\u2019s could be combined in the future to take advantage of both recent observations and geological records.\nTamsin, on the other hand, thinks that for the time being, it\u2019s good that we have a range of models tackling the problem in different ways.\nTamsin Edwards: We may come up with some super ice sheet model that captures everything perfectly, but it\u2019s a good idea to have different models with different approaches and that they\u2019d be independent and you can compare their results.\nAdam Levy: After all, if you can\u2019t compare lots of different Earths, at least you can compare lots of different models.\nPodcaster: The details of both those model studies are available at nature.com/nature. You heard from Tamsin Edwards, whose paper came out in Nature in December, and Rob DeConto, whose paper is out this week.", "source": "https://sealeveldocs.readthedocs.io/en/latest/decontopollard16.html"}
{"id": "ad4932bbfb3a-0", "text": "Index", "source": "https://sealeveldocs.readthedocs.io/en/latest/genindex.html"}
{"id": "3ca884893a78-0", "text": "Kuhlbrodt and Gregory (2012)\uf0c1\nTitle:\nOcean heat uptake and its consequences for the magnitude of sea level rise and climate change\nKey Points:\nThe spread of the OHU efficiency explains half of the spread in total OHU\nMost models are biased towards a too weak stratification and a too strong OHU\nThe Southern Ocean and its stratification dominate global OHU in the models\nCorresponding author:\nKuhlbrodt\nKeywords:\nCMIP5 models, climate change, ocean heat uptake, sea level rise\nCitation:\nKuhlbrodt, T., and J. M. Gregory (2012), Ocean heat uptake and its consequences for the magnitude of sea level rise and climate change, Geophys. Res. Lett., 39, L18608, doi:10.1029/2012GL052952\nURL:\nhttps://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2012GL052952\nAbstract\uf0c1\nUnder increasing greenhouse gas concentrations, ocean heat uptake moderates the rate of climate change, and thermal expansion makes a substantial contribution to sea level rise. In this paper we quantify the differences in projections among atmosphere-ocean general circulation models of the Coupled Model Intercomparison Project in terms of transient climate response, ocean heat uptake efficiency and expansion efficiency of heat. The CMIP3 and CMIP5 ensembles have statistically indistinguishable distributions in these parameters. The ocean heat uptake efficiency varies by a factor of two across the models, explaining about 50% of the spread in ocean heat uptake in CMIP5 models with CO2 increasing at 1%/year. It correlates with the ocean global-mean vertical profiles both of temperature and of temperature change, and comparison with observations suggests the models may overestimate ocean heat uptake and underestimate surface warming, because their stratification is too weak. The models agree on the location of maxima of shallow ocean heat uptake (above 700 m) in the Southern Ocean and the North Atlantic, and on deep ocean heat uptake (below 2000 m) in areas of the Southern Ocean, in some places amounting to 40% of the top-to-bottom integral in the CMIP3 SRES A1B scenario. The Southern Ocean dominates global ocean heat uptake; consequently the eddy-induced thickness diffusivity parameter, which is particularly influential in the Southern Ocean, correlates with the ocean heat uptake efficiency. The thermal expansion produced by ocean heat uptake is 0.12 m YJ^{-1}, with an uncertainty of about 10% (1 YJ = 10^{24} J).\nIntroduction\uf0c1\nOcean heat uptake moderates the rate of time-dependent climate change. Thermal expansion of sea-water is a consequence of ocean heat uptake and one of the major contributors to global-mean sea level rise [Church et al., 2011]. Our general aim in this paper is to quantify the differences in predictions of the magnitude and distribution of ocean heat uptake, and its consequences for global-mean surface air temperature change and thermal expansion, among atmosphere\u00d0ocean general circulation models (which we henceforth refer to simply as \u201cmodels\u201d, for convenience) used for projections of anthropogenic climate change.\nWe analyse results from 22 models that participated in the Coupled Model Intercomparison Project Phase 3 (CMIP3), and from the 20 models in the CMIP5 project whose data were available at the time of writing this paper (Spring 2012). See Figure 1 and Table 1 in Text S1 in the auxiliary material, for a list.1 We mainly use the control experiments and experiments with atmospheric CO_2 concentration increasing at 1%/year (details in the auxiliary material).\nOcean Heat Uptake Efficiency and Transient Climate Response\uf0c1\nGregory and Forster [2008] showed that there is an approximately linear relationship between the global mean surface air temperature change \u0394Ta and the radiative forcing F (due to greenhouse gases etc.): \u0394Ta = F/\u03c1, with the climate resistance \u03c1 in W m\u22122 K\u22121. This relationship holds well for observations and model simulations of recent decades, and for projections of climate change under a continuously increasing forcing, which is a characteristic of most scenarios considered for the 21st century. The basis of this relationship is that the difference between the radiative forcing and the radiative feedback yields the net heat flux N into the climate system: N = F \u2212 \u0394Ta, and N can be approximated by N \u2243 \u03ba\u0394Ta. The climate resistance \u03c1 is thus the sum of \u03b1, the climate feedback parameter, and \u03ba, which is identified as the ocean heat uptake efficiency because nearly all the added heat is stored in the ocean [e.g., Church et al., 2011].\nFollowing Gregory and Forster [2008], the ocean heat uptake efficiency \u03ba, the climate feedback parameter \u03b1 and the climate resistance \u03c1were calculated for CMIP5 by ordinary least squares regression (OLS) of decadal-meanN, F-N and F respectively against \u0394Ta under the standard idealized scenario of CO2 increasing at 1% per year, giving a forcing F(t) = F2\u00d7t/70 which is linear with time t in years, where F2\u00d7 is obtained from experiments in which CO2 is instantaneously increased and then held constant [Andrews et al., 2012] (Table 1 in Text S1). The transient climate response (TCR) was calculated, following its definition, as \u0394Tafor the time-mean of years 61\u201380 in this scenario (Figure 1 and Table 1 in Text S1). The coefficient of variation (ratio of ensemble standard deviation to ensemble mean) of TCR is about 20% in CMIP5.\nFigure 1: The ocean heat uptake efficiency \u03ba (blue bars), the climate feedback parameter \u03b1 (red bars), the transient climate response (crosses) and the expansion efficiency of heat \u03f5 (circles) for the CMIP3 (numbers) and the CMIP5 (letters) models. The total bar length is the climate resistance \u03c1 = \u03b1 + \u03ba. The models are arranged in order of \u03ba. See Table 1 in Text S1 in the auxiliary material for an alphabetical list of the models. It can be seen from this diagram that TCR and \u03ba are anticorrelated (the crosses are further left towards the bottom), but there is no relationship between \u03ba and \u03b1 or \u03f5 (the red bars and the circles do not show any tendency from top to bottom). For several technical reasons, not all parameters could be calculated for every model.\uf0c1\nWe see that \u03b1 obtained by this method agrees closely with \u03b1 obtained from the CO2step-increase experiments [Andrews et al., 2012]. F2\u00d7 is not correlated with \u03b1 or \u03ba. Whereas Gregory and Forster [2008] found \u03b1 and \u03bato be independent in CMIP3, they have a correlation of 0.56 in CMIP5, significant at the 5% level (one-tailed). This is due principally to the models GFDL-ESM2G and GFDL-ESM2M, which have\u03b1 and \u03ba that are both larger than in any other model (except for alpha of MIROC5). Without these models, the correlation is insignificant (0.32). Further investigation of these models is needed to establish whether there is a link between their large \u03b1 and large \u03ba.\nThe definition of \u03c1 implies that TCR = F2\u00d7/\u03c1 = F2\u00d7/(\u03b1 + \u03ba). Thus, a larger \u03ba gives a smaller TCR (correlation of \u03baand TCR is \u22120.76). Excluding GFDL-ESM2G and GFDL-ESM2M, so that\u03ba is uncorrelated with \u03b1, we can compute the fraction of the across-model variance of TCR explained by\u03ba by comparing var(F2\u00d7/(\u03b1 + \u03ba)) with var(\u3008F2\u00d7\u3009/(\u3008\u03b1\u3009 + \u03ba)), where the angle brackets denote the model mean (see the auxiliary material for further comment on the method). The fraction explained is about 10%.\nBo\u00e9 et al. [2009, 2010] present evidence from CMIP3 suggesting that ocean heat uptake has a much stronger influence than this on surface warming. Their strong relationship, however, depends particularly on a cluster of five models [Bo\u00e9 et al., 2009, Figure 3b]. In the high-latitude Southern Ocean region which was analysed for that figure, three of these models (csiro_mk3_0, giss_e_h and giss_e_r) have an extremely weak ocean temperature stratification. Another model (ncar_pcm1) has the lowest climate sensitivity of any CMIP3 model. We therefore suspect that the correlation could be strong by chance rather than from a common physical behaviour exhibited by these models.", "source": "https://sealeveldocs.readthedocs.io/en/latest/kuhlbrodtgregory12.html"}
{"id": "3ca884893a78-1", "text": "We see that \u03b1 obtained by this method agrees closely with \u03b1 obtained from the CO2step-increase experiments [Andrews et al., 2012]. F2\u00d7 is not correlated with \u03b1 or \u03ba. Whereas Gregory and Forster [2008] found \u03b1 and \u03bato be independent in CMIP3, they have a correlation of 0.56 in CMIP5, significant at the 5% level (one-tailed). This is due principally to the models GFDL-ESM2G and GFDL-ESM2M, which have\u03b1 and \u03ba that are both larger than in any other model (except for alpha of MIROC5). Without these models, the correlation is insignificant (0.32). Further investigation of these models is needed to establish whether there is a link between their large \u03b1 and large \u03ba.\nThe definition of \u03c1 implies that TCR = F2\u00d7/\u03c1 = F2\u00d7/(\u03b1 + \u03ba). Thus, a larger \u03ba gives a smaller TCR (correlation of \u03baand TCR is \u22120.76). Excluding GFDL-ESM2G and GFDL-ESM2M, so that\u03ba is uncorrelated with \u03b1, we can compute the fraction of the across-model variance of TCR explained by\u03ba by comparing var(F2\u00d7/(\u03b1 + \u03ba)) with var(\u3008F2\u00d7\u3009/(\u3008\u03b1\u3009 + \u03ba)), where the angle brackets denote the model mean (see the auxiliary material for further comment on the method). The fraction explained is about 10%.\nBo\u00e9 et al. [2009, 2010] present evidence from CMIP3 suggesting that ocean heat uptake has a much stronger influence than this on surface warming. Their strong relationship, however, depends particularly on a cluster of five models [Bo\u00e9 et al., 2009, Figure 3b]. In the high-latitude Southern Ocean region which was analysed for that figure, three of these models (csiro_mk3_0, giss_e_h and giss_e_r) have an extremely weak ocean temperature stratification. Another model (ncar_pcm1) has the lowest climate sensitivity of any CMIP3 model. We therefore suspect that the correlation could be strong by chance rather than from a common physical behaviour exhibited by these models.\nThe time-integrated heat uptake in the 1%/year CO2 scenario up to year 70 is H2\u00d7 = \u222b070N(t) dt \u2243 35F2\u00d7\u03ba/(\u03ba + \u03b1) (in W year m\u22122). Across the CMIP5 1%/year CO2 scenarios, it has a coefficient of variation of about 10%. Using the same CMIP5 models and method as for TCR (see also the auxiliary material), we find that H2\u00d7 has a correlation of 0.92 with F2\u00d7\u03ba/(\u03ba + \u03b1), and the fraction of variance of H2\u00d7 explained by \u03ba is \u223c50%. Thus \u03ba influences heat uptake more than it influences surface warming because of its appearance in the numerator of H2\u00d7. (In the auxiliary material, we derive a formula for var(H2\u00d7) in terms of var(\u03ba) and var(TCR).)\nThe distributions of \u03ba, \u03b1, \u03c1 and TCR are not significantly different for the CMIP3 and CMIP5 ensembles according to Kolmogorov\u2013Smirnov tests. In both ensembles, \u03ba varies by about a factor of 2. Investigating the reasons for this substantial spread motivates the next section.\nVertical Distribution of Temperature and Temperature Change\uf0c1\nOcean heat uptake efficiency depends on how fast the heat can be transported downwards. We put forward the hypothesis that a model with a weak vertical temperature gradient in the control state has a larger capacity for downward heat transport (e.g. because a large diapycnal mixing coefficient erodes the stratification) and therefore should have a larger \u03ba.The hypothesis applies to net global-mean vertical heat transport, comprising diapycnal mixing and other processes.\nFigure 2a shows the global-mean vertical temperature profile from the control runs of the CMIP3 and CMIP5 models (the average over the first 20 years that are parallel to the 1%/year CO2 runs) and from observations (WOA05 [Locarnini et al., 2006]), each profile being expressed as a difference from its surface temperature. This confirms that in the top 2000 m most models are less stratified than the real ocean. To elucidate the relationship between \u03ba and the global temperature profiles, we use a simple measure of the vertical temperature gradient, namely the vertical temperature difference Tz between two layers, 0\u2013100 m and 1500\u20132000 m (similar to Bo\u00e9 et al. [2009]). The relationship of \u03ba to Tz is shown in Figure 3a and is negative, as expected (r = \u22120.35 with p= 0.07 [one-sided]). HadGEM2-ES (model J) has a very small\u03ba and is strongly stratified in the uppermost layers, being closer to the observed profile than most other models, particularly in the top 500 m. The \u03ba-Tz relationship therefore suggests that \u03ba tends to be too large in AOGCMs.\nFigure 2: (a) Globally averaged temperature profiles for the control runs of the CMIP3 and CMIP5 models shown as difference from surface temperature, with observations for comparison (dash-dotted; WOA05 [Locarnini et al., 2006]). NorESM1-M is an outlier in that it is unusually weakly stratified in the top 200 m, giving a large\u03ba, but very strongly stratified in the 500 m or so below, giving a large Tz. Another outlier is giss_e_r with an extremely weak stratification. (b) Change of the temperature profiles in the 1%/year CO2 runs, divided by the vertical integral between 0 m and 2000 m. Units are dimensionless (\u201cDL\u201d). (c) Change of the temperature profiles in the CMIP3 models during the observational record [Levitus et al., 2012] (\u201cLev12\u201d), scaled as in Figure 2b. Shown is the difference of a 20-year average (2000 to 2019) from the SRES A1B runs minus a 20-year average from 20C3M (1945\u20131964). Two models (red, orange) overestimate surface warming because of their too small total heat uptake. To some extent, a few models capture the surface intensification (\u201cSFI\u201d [light green]: bccr_bcm2_0, gfdl_cm2_0, gfdl_cm2_1, miub_echo_g, mri_cgcm2_3_2a) seen in the observations (dash-dotted). Also note the shallow subsurface maximum warming in observations, but not in models, for which we have no explanation.\nFigure 3: The ocean heat uptake efficiency \u03ba [W m\u22122 K\u22121] against (a) the globally averaged vertical temperature difference Tz in the control runs, (b) its change \u0394Tz in the 1%/year CO2runs, scaled with the total warming, and (c) the quasi-Stokes diffusivity parameter\u03baGM for those CMIP3 models where it is a constant. The black lines are regression lines. The CMIP3 models have red numbers while the CMIP5 models have black letters (see Table 1 in Text S1 for key). Blue crosses on the horizontal axis denote the values of Tz from WOA05 and of \u0394Tz from Levitus et al. [2012].\nThe change of the global vertical temperature profile averaged over the years 61\u201380 of the 1%/year CO2 runs is shown in Figure 2b. The profiles were scaled with (i.e., divided by) their vertical integral between 0 m and 2000 m in order to compare their shapes rather than the total warming. The amount of warming in the top 100 m, as compared to the deeper layers, varies considerably across the models. As Figure 3b shows, the variation of \u03ba across models is strongly related to \u0394Tz, defined as the change of (the scaled) Tz in the 1%/year CO2 runs. The correlation (r = \u22120.66) is significant at the 99% level (p < 0.01). If \u0394Tz is large, then the temperature increase at the surface is larger than at depth, indicating that most heat has been taken up at the surface. This goes along with a small \u03ba. Conversely, models that distribute the additional heat further down have a smaller \u0394Tz and a larger \u03ba.\nThe \u03ba-Tz relationship suggests most models will probably transport heat too deeply. Consistent with this, Figure 2c shows that the observed warming over recent decades [Levitus et al., 2012] is more strongly surface-intensified than in the CMIP3 simulations of the same period.\nGeographical Distribution of Ocean Heat Uptake\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/kuhlbrodtgregory12.html"}
{"id": "3ca884893a78-2", "text": "Figure 3: The ocean heat uptake efficiency \u03ba [W m\u22122 K\u22121] against (a) the globally averaged vertical temperature difference Tz in the control runs, (b) its change \u0394Tz in the 1%/year CO2runs, scaled with the total warming, and (c) the quasi-Stokes diffusivity parameter\u03baGM for those CMIP3 models where it is a constant. The black lines are regression lines. The CMIP3 models have red numbers while the CMIP5 models have black letters (see Table 1 in Text S1 for key). Blue crosses on the horizontal axis denote the values of Tz from WOA05 and of \u0394Tz from Levitus et al. [2012].\nThe change of the global vertical temperature profile averaged over the years 61\u201380 of the 1%/year CO2 runs is shown in Figure 2b. The profiles were scaled with (i.e., divided by) their vertical integral between 0 m and 2000 m in order to compare their shapes rather than the total warming. The amount of warming in the top 100 m, as compared to the deeper layers, varies considerably across the models. As Figure 3b shows, the variation of \u03ba across models is strongly related to \u0394Tz, defined as the change of (the scaled) Tz in the 1%/year CO2 runs. The correlation (r = \u22120.66) is significant at the 99% level (p < 0.01). If \u0394Tz is large, then the temperature increase at the surface is larger than at depth, indicating that most heat has been taken up at the surface. This goes along with a small \u03ba. Conversely, models that distribute the additional heat further down have a smaller \u0394Tz and a larger \u03ba.\nThe \u03ba-Tz relationship suggests most models will probably transport heat too deeply. Consistent with this, Figure 2c shows that the observed warming over recent decades [Levitus et al., 2012] is more strongly surface-intensified than in the CMIP3 simulations of the same period.\nGeographical Distribution of Ocean Heat Uptake\uf0c1\nThe projected ocean heat uptake (OHU, i.e., the increase in ocean heat content) in model simulations with an increasing CO2 content has a distinct regional structure. We analyse this for the CMIP3 SRES A1B scenario, for which we have the largest number of models available. For comparison, the same analysis for the 1% CO2 runs of CMIP3 and CMIP5 can be found in the auxiliary material. They show generally less heat uptake because \u222bF dt is smaller, but the geographical features are similar.\nThe ensemble-mean top-to-bottom integrated OHU is shown inFigure 4a. It was calculated as the difference between the 20-year averages 2080\u20132099 and 1980\u20131999. It is largest in the Southern Ocean, in a band around 40\u00b0S, with maxima in the Argentine Basin and south of Africa. This leads to a clear signal in steric sea level rise [cf.Pardaens et al., 2011, Figure 2], which is predominantly thermosteric in the Southern Ocean. The models agree on these features (R > 1, thin black contours), and they are also visible in the top 700 m alone (Figure 4b), which accounts for up to 50% of the heat uptake in the full depth.\nFigure 4: Vertically integrated ocean heat uptake (colour shading; in GJ m\u22122) in the ensemble average of the SRES A1B scenario of 17 CMIP3 models for (a) the total water column, (b) the upper 700 m and (c) below 2000 m. Thick black line: zonal total in 1015 J m\u22121 (scale in the upper left corner), with \u00b11 standard deviation (dotted). Note the different scales in Figure 4c. Black contours show the ratio R of ensemble mean and ensemble standard deviation (solid: R > 1, thick solid: R = 1, dashed: R < 1). For Figures 4a and 4b, R> 1 in most areas indicating agreement across models. An exception are the deep-water formation regions in the Southern Ocean and the North Atlantic. In Figure 4c the models mainly show OHU in the Southern Ocean.\nOHU below 2000 m is substantial in several large areas of the Southern Ocean (Figure 4c), including the Argentine basin and the area west of the Drake Passage, where there are maxima of top-to-bottom OHU. The pattern bears resemblance to observations [Purkey and Johnson, 2010]. In these areas, the deep OHU can amount to up to 40% of the total. In the deep-water formation areas in the Southern Ocean and in the North Atlantic the ensemble mean OHU displays minima above 700 m. The models show a large spread in these areas (R < 1).\nThe zonal total heat uptake (thick black line in the left hand side of the panel, dotted: one standard deviation) confirms that the global maximum of OHU per degree latitude is in the mid-latitude Southern Ocean [Stouffer et al., 2006]. Therefore, the stratification in that region could have a particularly large influence on \u03ba.In the large majority of the models, the Southern Ocean stratification is strongly influenced by the parameterization of the eddy-induced tracer transports. Consistent with this, we find that the quasi-Stokes diffusivity parameter\u03baGM(often called the eddy-induced thickness diffusivity) has a significant influence on\u03ba (Figure 3c). When \u03baGM is small, the isopycnal layers are steep, leading to a strong horizontal density gradient [Kuhlbrodt et al., 2012, Figure 1c] but a weak stratification and thus a large \u03ba.\nExpansion Efficiency of Heat\uf0c1\nThe expansion efficiency of heat [Russell et al., 2000], as a property of a model in m YJ^{\u22121} (1 YJ \u2261 1024 J), is defined as \u03f5 = hx/H, where hx is the global mean sea level rise due to thermal expansion and Hthe global-integral OHU. We calculate\u03f5 by OLS regression of hx against H, using results from 1%/year CO2 and all available 21st-century scenarios.\nIn all models, there is an excellent scenario-independent linear relationship, but\u03f5 varies across models (Figure 1 and Table 1 in Text S1) because the thermal expansivity of sea water (1/\u03c1) \u2202\u03c1/\u2202T increases with pressure and temperature. Therefore, the magnitude of thermal expansion depends on the latitudes and depths at which the heat is actually stored; this pattern depends on the model, but not on the scenario for a given model.\nThe ranges of \u03f5 in the CMIP3 and CMIP5 ensembles are similar: 0.12 \u00b1 0.01 m YJ\u22121 in CMIP3 and 0.11 \u00b1 0.01 m YJ\u22121 in CMIP5. This is consistent with the observational estimates for 0 m to 2000 m, 1955\u20132010 [Levitus et al., 2012], from which we infer \u03f5 = 0.12 \u00b1 0.01 m YJ\u22121. The observational estimates by Church et al. [2011] for 1972\u20132008 for the full ocean depth indicate \u03f5 = 0.15 \u00b1 0.03 m YJ\u22121, which is slightly higher but not significantly different. We did not find any correlation of \u03f5 with \u03ba, Tz or \u0394Tz, although such relationships would be plausible. It might well be that the stratification in the individual regions which are particularly important to OHU (section 4) influences \u03f5more than global-mean properties do.\nConcluding Remarks\uf0c1\nOur analysis of CMIP3 and CMIP5 model results indicates that model spread in ocean vertical heat transport processes is responsible for a substantial part of the spread in predictions of global-mean ocean heat uptake (about 50% in the CMIP5 1%CO2/year experiments), and for some of the spread in predictions of surface warming. Since most AOGCMs have weaker global-mean stratification than observed, it is possible that they generally overestimate ocean heat uptake and underestimate surface warming [Forest et al., 2008]. The ocean heat uptake in CMIP5 1%CO2/year experiments has a spread of about 10%, and there is also a spread of about 10% in the expansion efficiency of heat \u03f5, due to the different spatial distribution of the warming in the models. These factors contribute roughly equally to the spread of thermal expansion projection in response to CO2. Comparison, analysis and evaluation of model processes of ocean interior heat transport is essential to make progress in reducing uncertainties in projections of the magnitude and distribution of ocean heat uptake and the consequent sea-level rise.", "source": "https://sealeveldocs.readthedocs.io/en/latest/kuhlbrodtgregory12.html"}
{"id": "d4e5a3445e08-0", "text": "Chen et al. (2017)\uf0c1\nTitle:\nThe increasing rate of global mean sea-level rise during 1993\u20132014\nKey Points:\nThe global mean sea level (GMSL) rose from 2.2 \u00b1 0.3\u2009mm\u2009yr\u22121 in 1993 to 3.3 \u00b1 0.3\u2009mm\u2009yr\u22121 in 2014, indicating an acceleration in sea-level rise during this period.\nThe mass loss from the Greenland Ice Sheet significantly increased during this period, accounting for less than 5% of the GMSL rate in 1993 but more than 25% in 201\nThe mass contributions to GMSL, which include glacier mass loss, Greenland and Antarctic ice sheets, and anthropogenic terrestrial water storage, increased from about 50% in 1993 to 70% in 2014, indicating their growing role in sea-level rise.\nKeywords:\nGlobal mean sea-level rise, acceleration, Greenland Ice Sheet, Mass contributions, Satellite altimetry\nCorresponding author:\nXianyao Chen\nCitation:\nChen, X., Zhang, X., Church, J. A., Watson, C. S., King, M. A., Monselesan, D., et al. (2017). The increasing rate of global mean sea-level rise during 1993\u20132014. Nature Climate Change, 7(7), 492\u2013495. doi:10.1038/nclimate3325\nURL:\nhttps://www.nature.com/articles/nclimate3325\nAbstract\uf0c1\nGlobal mean sea level (GMSL) has been rising at a faster rate during the satellite altimetry period (1993\u20132014) than previous decades, and is expected to accelerate further over the coming century1. However, the accelerations observed over century and longer periods2 have not been clearly detected in altimeter data spanning the past two decades3,4,5. Here we show that the rise, from the sum of all observed contributions to GMSL, increases from 2.2 \u00b1 0.3\u2009mm\u2009yr\u22121 in 1993 to 3.3 \u00b1 0.3\u2009mm\u2009yr\u22121 in 2014. This is in approximate agreement with observed increase in GMSL rise, 2.4 \u00b1 0.2\u2009mm\u2009yr\u22121 (1993) to 2.9 \u00b1 0.3\u2009mm\u2009yr\u22121 (2014), from satellite observations that have been adjusted for small systematic drift, particularly affecting the first decade of satellite observations6. The mass contributions to GMSL increase from about 50% in 1993 to 70% in 2014 with the largest, and statistically significant, increase coming from the contribution from the Greenland ice sheet, which is less than 5% of the GMSL rate during 1993 but more than 25% during 2014. The suggested acceleration and improved closure of the sea-level budget highlights the importance and urgency of mitigating climate change and formulating coastal adaption plans to mitigate the impacts of ongoing sea-level rise.\nMain\uf0c1\nProjections of future sea levels must be based on a sound understanding of historical changes in GMSL and its underlying processes, as well as recent changes in the rate of rise1. In a previous study, the apparent decrease in the rate of GMSL rise from 3.2\u2009mm\u2009yr\u22121 in the first decade of satellite altimetry to 2.8\u2009mm\u2009yr\u22121 in the second was suggested to be primarily a result of natural interannual variability, related to water exchange between ocean and land during El Ni\u00f1o/Southern Oscillation (ENSO) cycles3. After removing this variability, the underlying rate of GMSL rise was 3.3 \u00b1 0.4\u2009mm\u2009yr\u22121 for both decades, with neither deceleration nor acceleration of GMSL inferred over 1993 to 2014. This lack of observed acceleration of GMSL contrasts with a simultaneously increased contribution from the Greenland ice sheet (GIS) and a less certain increase from the Antarctica ice sheet (AIS) overall7, and is inconsistent with the positive acceleration presented in century-long tide gauge data8 and global mean sea-level reconstructions2.\nBy comparing tide gauge and satellite altimeter sea-level observations, a recent study6 identified a possible systematic drift within the altimeter record, particularly affecting the first six years (1993\u20131999). This systematic error erroneously elevates the GMSL trend during 1993\u20131998 by between 0.9 \u00b1 0.5 and 1.5 \u00b1 0.5\u2009mm\u2009yr\u22121, depending on whether a glacial isostatic adjustment (GIA) or Global Positioning System (GPS) data set was used to correct for the effects of land motion at tide gauges used in the bias estimation process. After removing these biases, the estimated rate of GMSL rise from 1993 to mid-2014 was between 2.6 \u00b1 0.4 and 2.9 \u00b1 0.4\u2009mm\u2009yr\u22121, with a positive but not statistically significant acceleration of 0.041 \u00b1 0.058\u2009mm\u2009yr\u22122, compared with a not statistically significant deceleration of \u22120.057 \u00b1 0.058\u2009mm\u2009yr\u22122 for unadjusted data.\nGMSL rise results from the ocean thermal expansion, loss of mass from glaciers9, the GIS and the AIS7, and changes in land water storage from climate variability and anthropogenic effects10,11. To study how the rate of the GMSL rise varies during the satellite period, we investigate the time-varying intrinsic trend in GMSL and these contributing components by separating them from their interannual variability using an adaptive data analysis approach.\nAn intrinsic trend is defined as \u2018an intrinsically fitted monotonic function or a function in which there can be at most one extremum within a given data span\u201912. Unlike the commonly used linear polynomial trend that requires a priori assumptions regarding stationarity and linearity of time series, the intrinsic trend is not defined by a predetermined functional form of the trend and, hence, is more adaptive to the underlying physical properties of observations. The method we apply to derive the intrinsic trend in GMSL and its components is ensemble empirical mode decomposition (EEMD)13, which is based on the empirical mode decomposition (EMD) method designed for adaptive analysis of nonlinear and non-stationary time series14 (see Methods and Supplementary Information) and has only recently been applied to sea-level trend estimation8. The main benefit of using EMD is that it can separate non-stationary oscillations (such as natural variations on different timescales) from the long-term trend, and the trend is found empirically without any assumptions about its shape.\nFigure 1a presents the unadjusted GMSL from four different processing groups, and the adjusted CSIRO GMSL derived using vertical land motion (VLM) estimates at tide gauges based on GIA and GPS6. We note there is not yet a homogeneously reprocessed altimeter data set that addresses the likely systematic bias estimated by ref. 6. In the absence of such a data set, an assessment of all available records (including the adjusted record from ref. 6) is entirely appropriate. The intrinsic trend and interannual variability of each time series are shown in Fig. 1a, b, respectively. The significance of the intrinsic trend is tested against a null hypothesis of red background noise with the same lag-1 autocorrelation as the raw time series (Supplementary Fig. 1), and it is shown that the increase in the intrinsic trend of the GPS-based adjusted GMSL record is statistically significant during the recent decade (Supplementary Fig. 2).\nFigure 1: Global mean sea level (GMSL). Curves show the GPS-based and GIA-based adjusted GMSL, and unadjusted GMSL from four different groups. a, GMSL and the time-varying secular trend from EEMD analysis. b, The interannual variability of GMSL. c, The instantaneous rate of GMSL rise. The uncertainties of the derived interannual variability, intrinsic secular trend, and its instantaneous rate are shown in coloured shades.", "source": "https://sealeveldocs.readthedocs.io/en/latest/chen17.html"}
{"id": "d4e5a3445e08-1", "text": "Figure 1a presents the unadjusted GMSL from four different processing groups, and the adjusted CSIRO GMSL derived using vertical land motion (VLM) estimates at tide gauges based on GIA and GPS6. We note there is not yet a homogeneously reprocessed altimeter data set that addresses the likely systematic bias estimated by ref. 6. In the absence of such a data set, an assessment of all available records (including the adjusted record from ref. 6) is entirely appropriate. The intrinsic trend and interannual variability of each time series are shown in Fig. 1a, b, respectively. The significance of the intrinsic trend is tested against a null hypothesis of red background noise with the same lag-1 autocorrelation as the raw time series (Supplementary Fig. 1), and it is shown that the increase in the intrinsic trend of the GPS-based adjusted GMSL record is statistically significant during the recent decade (Supplementary Fig. 2).\nFigure 1: Global mean sea level (GMSL). Curves show the GPS-based and GIA-based adjusted GMSL, and unadjusted GMSL from four different groups. a, GMSL and the time-varying secular trend from EEMD analysis. b, The interannual variability of GMSL. c, The instantaneous rate of GMSL rise. The uncertainties of the derived interannual variability, intrinsic secular trend, and its instantaneous rate are shown in coloured shades.\nWe derive the rate of the time-varying intrinsic trend by calculating its first-order temporal derivative (Fig. 1c). Consistent with previous studies3, the unadjusted GMSL exhibits a slightly decreasing rate of rise from about 3.5\u2009mm\u2009yr\u22121 during the first decade to 3.0\u20133.3\u2009mm\u2009yr\u22121 during the second. In contrast, the rate of the GPS-based adjusted GMSL rise increases by 0.5\u2009mm\u2009yr\u22121 from about 2.4 \u00b1 0.2 (1\u03c3) mm\u2009yr\u22121 in 1993 to around 2.9 \u00b1 0.3\u2009mm\u2009yr\u22121 in 2014 (2.8 \u00b1 0.2 to 3.2 \u00b1 0.3\u2009mm\u2009yr\u22121 for the GIA-based adjusted GMSL). That is, the time-varying trend of the adjusted altimeter data suggests an acceleration in GMSL in agreement with ref. 6, with the dominant increase in the rate of rise occurring in the recent decade.\nFigure 1b shows the interannual variability of all GMSL records derived by EEMD. It includes a significant drop of water level related to the transfer of water from the ocean to the land during the strong La Ni\u00f1a event in 2011 and the subsequent rapid recovery in the following two years15. This interannual variability agrees well with the interannual variability of the land water storage based on the global hydrological model16 and the interannual variability of the thermosteric sea level17, and is significantly correlated (0.42 for the unadjusted CSIRO-based time series, and up to 0.56 for the others) with the ENSO index18. By definition of the EMD method, this interannual variability does not contribute to the intrinsic trend over the whole period.\nWe determined global mean steric sea-level (GMSSL) anomalies using a range of subsurface measurements of temperature and salinity data sets19. The GMSSLs from these data sets exhibit wide discrepancies owing to the inhomogeneous observations in the ocean, different data quality control procedures, XBT (expendable bathythermograph) bias corrections, mapping methods and model structures20. These discrepancies are especially pronounced until 2005 when sufficient spatial data coverage was obtained from Argo floats. We select ocean temperature\u2013salinity data sets that do not have obvious discontinuities in the GMSSL time series and whose linear trend of GMSSL during the Argo period (2005\u20132014) remains within the 2\u03c3 range of that derived from three Argo gridded data sets (Supplementary Table 1). Figure 2 shows monthly GMSSL anomalies, interannual variability and the intrinsic trends from seven data sets based on the above selection criteria.\nFigure 2: Global mean steric sea level (GMSSL). Coloured curves show the global mean steric sea level from seven data sets. a, The GMSSL and its time-varying secular trend. b, The interannual variability of GMSSL. c, The instantaneous rate of GMSSL rise. The uncertainties of the derived interannual variability, intrinsic secular trend, and its instantaneous rate are shown in coloured shades. In c, the dots denote the median of all GMSSL records at each year, with the uncertainty estimated using the median statistical method. Note that the different length of the GMSSL time series affects the median rates over the last few years, and consequently affects the budget over the last few years as shown in Fig. 4.\nEven with these relatively strict criteria, the GMSSLs of the selected ocean temperature\u2013salinity data sets still exhibit remarkable differences over the whole period. The instantaneous rate of the GMSSL of some models indicates acceleration, whereas others not. To reduce the impact of the skewness, we estimate the instantaneous rate of GMSSL rise as the median of that derived from seven data sets at each year. The derived mean thermal expansion contribution is about 0.94 \u00b1 0.16\u2009mm\u2009yr\u22121 during 1993\u20132014, which is equivalent to about 0.48 \u00b1 0.08\u2009W\u2009m\u22122 net surface heat flux into the ocean, and consistent with the observed top-of-atmosphere heat imbalance21. The ensemble estimate of the GMSSL rise suggests little acceleration during the satellite altimetry period.\nThe main contributions to the global ocean mass changes are from the GIS, the AIS and glaciers. The GIS and AIS mass changes are investigated using the estimates based on altimetry, gravimetry and mass flux data for 1993\u201320127, and the GRACE observations during 2003\u20132014 by adjusting its trend to match the published data over 2003\u2013200922 (Supplementary Fig. 5). The glacier data are estimated from a glacier mass balance model driven by gridded climate observations9.\nFigure 3 shows that all three sources of mass loss exhibit an increasing contribution to GMSL. The rate of glacier mass loss increased over 1993 to 2005, from 0.60 \u00b1 0.15 to 0.87 \u00b1 0.21\u2009mm\u2009yr\u22121 GMSL equivalent, but is then nearly unchanged up to 2013 (Fig. 3c). The GIS mass loss increased from around 0.11 \u00b1 0.03\u2009mm\u2009yr\u22121 in 1993 to around 0.85 \u00b1 0.03\u2009mm\u2009yr\u22121 in 2014, approaching an average acceleration of 0.03\u2009mm\u2009yr\u22122. The rate of the AIS mass loss is around 0.22 \u00b1 0.02\u2009mm\u2009yr\u22121 in 1993, and only slightly increases to 0.31 \u00b1 0.02\u2009mm\u2009yr\u22121 in 2014. These trends agree quantitatively with previous linear estimates7,9 over the whole satellite period, and contribute to the acceleration of GMSL.\nFigure 3: Global mean ocean mass change. Curves show the land-glacier, AIS and GIS and anthropogenic TWS contributions to GMSL. a\u2013c, Each mass component and its secular trend (a), the interannual variability (b), and the instantaneous rate (c) of the ocean mass change. In c, the black dots and their error bars show the rate of thermal expansion, GMSSL, from Fig. 2 for comparison with the mass change rate. The uncertainties of the derived interannual variability, intrinsic secular trend, and their instantaneous rates are shown in coloured shades.\nAnother contribution to changes in the global ocean mass is from terrestrial water storage (TWS), including that associated with anthropogenic activities (groundwater extraction, irrigation, impoundment in reservoirs, wetland drainage, and deforestation) and natural climate variability. Here, the anthropogenic TWS changes are based on the estimates of ref. 11, with their groundwater depletion being replaced with the estimates of ref. 10, which are 20% smaller. This smaller estimate is consistent with 80% of the extracted ground water making its way to the ocean23. The intrinsic trend and its instantaneous rate of the anthropogenic TWS show a slightly increased contribution to GMSL from around 0.11 \u00b1 0.04\u2009mm\u2009yr\u22121 during the first decade to about 0.24 \u00b1 0.06\u2009mm\u2009yr\u22121 during the second (Fig. 3c).", "source": "https://sealeveldocs.readthedocs.io/en/latest/chen17.html"}
{"id": "d4e5a3445e08-2", "text": "Figure 3: Global mean ocean mass change. Curves show the land-glacier, AIS and GIS and anthropogenic TWS contributions to GMSL. a\u2013c, Each mass component and its secular trend (a), the interannual variability (b), and the instantaneous rate (c) of the ocean mass change. In c, the black dots and their error bars show the rate of thermal expansion, GMSSL, from Fig. 2 for comparison with the mass change rate. The uncertainties of the derived interannual variability, intrinsic secular trend, and their instantaneous rates are shown in coloured shades.\nAnother contribution to changes in the global ocean mass is from terrestrial water storage (TWS), including that associated with anthropogenic activities (groundwater extraction, irrigation, impoundment in reservoirs, wetland drainage, and deforestation) and natural climate variability. Here, the anthropogenic TWS changes are based on the estimates of ref. 11, with their groundwater depletion being replaced with the estimates of ref. 10, which are 20% smaller. This smaller estimate is consistent with 80% of the extracted ground water making its way to the ocean23. The intrinsic trend and its instantaneous rate of the anthropogenic TWS show a slightly increased contribution to GMSL from around 0.11 \u00b1 0.04\u2009mm\u2009yr\u22121 during the first decade to about 0.24 \u00b1 0.06\u2009mm\u2009yr\u22121 during the second (Fig. 3c).\nRegarding the natural variability of TWS, global values are not reliable before the GRACE mission in 2002. Interannual fluctuations of TWS based on the continental water balance model are estimated as about 0.25\u2009mm\u2009yr\u22121 (GMSL equivalent) during 1993\u2013199824, whereas the GRACE observations during 2002\u20132012 suggested a natural TWS contribution to GMSL of around \u22120.71 \u00b1 0.20\u2009mm\u2009yr\u22121 (ref. 25). This rate is approximately consistent with the 5.5\u2009mm fall in GMSL over 2002\u20132012 in the interannual variability (Fig. 1b), which is highly correlated with the La Ni\u00f1a-like variability in the Pacific15, when precipitation decreases over the ocean and increases over the land. Because of the strong ENSO-related interannual variability, there can be significant trends in TWS over periods of a decade or shorter. Therefore, short-period linear trend estimates do not adequately represent the time series over the whole satellite altimeter period, and it is likely that the total trend is small (but poorly quantified).\nUsing time series of GMSL, GMSSL and all components of global ocean mass change, Fig. 4 shows the instantaneous budget of GMSL over the satellite period. The thermal expansion component is about 50% of the total contributions in 1993. Although the rate of this contribution did not change much throughout the record, by the end of the record it is reduced to about 30% of the sum of the contributions because of the acceleration in the global ocean mass component, consistent with a previous estimate of the changing relative roles of ocean thermal expansion and ocean mass26. The ocean mass change is initially dominated by the contribution of glacier mass loss, with smaller contributions from the GIS and AIS mass loss and anthropogenic TWS changes. But in the recent decade, the acceleration of the mass loss from the GIS was the largest, and its contribution to the GMSL became almost equal to that from thermal expansion and glaciers by 2014. The year-by-year contribution from the AIS mass loss is nearly constant while the glacier contribution increases slowly.\nFigure 4: Instantaneous closure of the global mean sea-level budget. Yearly instantaneous rate of change of the GPS-based adjusted (black dots) and mean unadjusted GMSL (grey stars) and that of the GMSSL, and ocean mass contributions from the GIS, the AIS, the anthropogenic TWS and glaciers, and ocean thermal expansion (each shown in coloured shades, ordered from top to bottom). The blue dots denote the sum of the instantaneous rates of change of each component with its uncertainty estimated as the square root of the sum of the squares of the uncertainty in each instantaneous rate, as shown in previous figures. The time series of the loss of mass from the glaciers and the anthropogenic TWS stops in 2012, and 2009, respectively. Their rates in the years up to 2014 are assumed unchanged and shown in a lighter colour.\nIn all future projection scenarios of the Fifth Assessment Report of the Intergovernmental Panel on Climate Change27, the largest contribution to changes in GMSL is the ocean thermal expansion, accounting for 30\u201355% of the projection, whereas the glaciers are the second largest, accounting for 15\u201335%. Our analysis of recent observations shows that the acceleration of ocean thermal expansion during 1993\u20132014 is not significant. Climate model simulations indicate the fall in ocean heat content following the 1991 volcanic eruption of Mount Pinatubo and the subsequent recovery has probably resulted in a rate of thermal expansion about 0.5\u2009mm\u2009yr\u22121 higher than would be expected from greenhouse gas forcing alone28. The recovery in ocean thermal expansion following major volcanic eruption takes more than 15 years28,29. Thus, the underlying acceleration of thermal expansion in response to the anthropogenic forcing may emerge over the next decade or so, resulting in a further acceleration in the rate from that reported here and recent estimates30. In contrast to the lack of observed acceleration in the ocean thermal expansion, there has been a significant acceleration in the mass contributions, dominated by the increased GIS mass loss. This results in an approximate closure of the sea level budget throughout the study period from 1993 to 2014 and, importantly, both the sum of contributions and the GPS (and GIA)-based adjusted altimeter rates indicate an acceleration in sea level over the satellite altimeter period.\nThis approximate but improved closure of the sea-level budget throughout 1993\u20132014 is progress with respect to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, and increases confidence in our observations and understanding of recent changes in sea level. The study period is still short and ongoing observations are required to understand the longer-term significance of this finding, and to identify the contributions of decadal and multi-decadal variations that are unresolved in the 20-year-long records. The estimated increase in the rate of rise has important implications for projections of sea-level rise and for society.\nMethods\uf0c1\nData\uf0c1\nSatellite altimetry\uf0c1\nWe use six different altimetry-based monthly sea-level data from four processing groups: Archiving Validation and Interpretation Satellite Oceanographic Center (AVISO; https://podaac.jpl.nasa.gov/dataset/MERGED_TP_J1_OSTM_OST_GMSL_ASCII_V4); Colorado University (CU, Release 4; http://sealevel.colorado.edu/files/2015_rel4/sl_ns_global.txt); Goddard Space Flight Center (GSFC; https://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level.html); Commonwealth Scientific and Industrial Research Organization (CSIRO) and University of Tasmania (ftp://ftp.marine.csiro.au/pub/legresy/gmsl_files/CSIRO_Alt_refined.csv); adjusted CSIRO data set using a model of glacial isostatic adjustment to estimate vertical land motion at tide gauges; and adjusted CSIRO data set using GPS data to estimate vertical land motion at tide gauges. All six data sets are based on TOPEX, Jason-1 and OSTM/Jason-2 data. The global average is computed over 66\u00b0\u2009S\u201366\u00b0\u2009N for AVISO, CU and GSFC, but over 65\u00b0\u2009S\u201365\u00b0\u2009N for CSIRO. Detailed descriptions of each data set are available in the corresponding websites.\nSteric sea-level data sets\uf0c1\nWe use seven products describing the global ocean monthly temperature\u2013salinity to compute the global mean steric sea level. Two of these are objective analyses based on optimal interpolation without constraints from ocean model dynamics, and five are reanalyses based on data assimilation with models. From 20 global ocean temperature\u2013salinity data sets [19], we select a subset of seven ocean temperature\u2013salinity data sets that do not have obvious discontinuities in the GMSSL time series and whose linear trends of GMSSL during the Argo period (2005\u20132014) remain within the 2\u03c3 range of that derived from three Argo gridded data sets. Supplementary Table 1 provides the basic information of these data sets.\nLand glaciers\uf0c1\nThe global yearly glacier mass data set used in this paper is produced with a glacier model driven by gridded climate observations [9].\nGreenland and Antarctic ice sheets\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/chen17.html"}
{"id": "d4e5a3445e08-3", "text": "Data\uf0c1\nSatellite altimetry\uf0c1\nWe use six different altimetry-based monthly sea-level data from four processing groups: Archiving Validation and Interpretation Satellite Oceanographic Center (AVISO; https://podaac.jpl.nasa.gov/dataset/MERGED_TP_J1_OSTM_OST_GMSL_ASCII_V4); Colorado University (CU, Release 4; http://sealevel.colorado.edu/files/2015_rel4/sl_ns_global.txt); Goddard Space Flight Center (GSFC; https://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level.html); Commonwealth Scientific and Industrial Research Organization (CSIRO) and University of Tasmania (ftp://ftp.marine.csiro.au/pub/legresy/gmsl_files/CSIRO_Alt_refined.csv); adjusted CSIRO data set using a model of glacial isostatic adjustment to estimate vertical land motion at tide gauges; and adjusted CSIRO data set using GPS data to estimate vertical land motion at tide gauges. All six data sets are based on TOPEX, Jason-1 and OSTM/Jason-2 data. The global average is computed over 66\u00b0\u2009S\u201366\u00b0\u2009N for AVISO, CU and GSFC, but over 65\u00b0\u2009S\u201365\u00b0\u2009N for CSIRO. Detailed descriptions of each data set are available in the corresponding websites.\nSteric sea-level data sets\uf0c1\nWe use seven products describing the global ocean monthly temperature\u2013salinity to compute the global mean steric sea level. Two of these are objective analyses based on optimal interpolation without constraints from ocean model dynamics, and five are reanalyses based on data assimilation with models. From 20 global ocean temperature\u2013salinity data sets [19], we select a subset of seven ocean temperature\u2013salinity data sets that do not have obvious discontinuities in the GMSSL time series and whose linear trends of GMSSL during the Argo period (2005\u20132014) remain within the 2\u03c3 range of that derived from three Argo gridded data sets. Supplementary Table 1 provides the basic information of these data sets.\nLand glaciers\uf0c1\nThe global yearly glacier mass data set used in this paper is produced with a glacier model driven by gridded climate observations [9].\nGreenland and Antarctic ice sheets\uf0c1\nGreenland and Antarctic ice sheet records during 1993\u20132012 available at http://imbie.org/data-downloads [7] are used in this study. To extend the records to the end of 2014, observations based on the GRACE satellite are used. Noting the potential GIA error in GRACE, especially for Antarctica31, we adjusted the trend of the GRACE records so that they agreed with the published trends over 2003\u20132009. Then two records are connected in 2003. After 2003, the GRACE record is used. The derived monthly time series are shown in Supplementary Fig. 5.\nAnthropogenic terrestrial water storage\uf0c1\nThe yearly data of anthropogenic terrestrial water storage are extracted from the century-long time series [11], after their groundwater depletion is replaced with the most recent estimates [10].\nEnsemble empirical mode decomposition method\uf0c1\nThe main method used in this study is ensemble empirical mode decomposition (EEMD) [13], which was developed on the basis of the empirical mode decomposition (EMD)14 method. The EMD and EEMD methods have been applied to oceanic and climatic time series analysis32, and are also used to study regional [8,33,34] and global sea-level variability35. Here we briefly introduce the general decomposition procedure and mainly introduce the tests used to assess statistical significance and the estimation of the uncertainty of the intrinsic secular trend derived by the EMD/EEMD method.\nDecomposition and intrinsic secular trend\uf0c1\nIn EMD, a time series x(t) is decomposed into a set of amplitude\u2013frequency-modulated oscillatory functions (so-called intrinsic mode functions, IMFs) Cj(t), j = 1,2, \u2026 n and a residual R(t): x(t) = \u2211 j=1nCj(t) + R(t) through a sifting process. The following is undertaken: (1) locate all maxima and minima and connect all maxima (minima) with a cubic spline as an upper (lower) envelope of the time series; (2) compute the difference between the time series and the mean of the upper and lower envelopes to yield a new time series h(t); (3) for the time series h(t), repeat steps 1 and 2 until upper and lower envelopes are symmetric with respect to zero mean under the stopping criteria13,14, then an IMF, Cj(t), is derived as the time series h(t); and (4) subtract Cj(t) from original time series to yield a residual R(t) and treat R(t) as the original time series and repeat steps 1\u20133 until the residual R(t) becomes a monotonic function or a function with only one extremum; then, the whole sifting process is completed and all IMFs and the residual function, namely, the intrinsic trend of x(t), are obtained.\nThe EEMD approach is based on EMD13. In EEMD, multiple noise realizations are added to the time series x(t), from which an ensemble average of the corresponding IMFs is extracted to yield scale-consistent signals. The main steps in the EEMD are as follows: (1) add a white noise series to the targeted data; (2) decompose the data with the added white noise into IMFs; (3) repeat step 1 and 2 again and again, but with different white noise series each time; and (4) obtain (ensemble) means of the respective IMFs of the decompositions as the final result. The advantage of the EEMD is that by using an ensemble mean, non-physical oscillations due to random data errors are reduced and thus low-frequency modes are more accurate.\nIt is proved that the added white noise with the variance \u03c3 will have at most  impact on the resulting IMFs13, where N is the number of ensemble members. When N increases, this impact is negligibly small. In this paper, we always use the white noise with variance \u03c3 = 0.2 relative to the variance of the original time series, and N = 1,000 ensemble members.\nAs demonstrated in previous applications of the EEMD method involving trend analysis of global mean surface temperature36, global land surface air temperature37, and the sea-level observations along the eastern US coast8,33, the residual function R(t) is derived by removing any, but not a predetermined, variability on shorter timescales than the length of time series, as represented by the IMFs Cj(t). Consequently, R(t) can take any unspecified shape and will preserve the potential variability on longer timescales than the length of time series. For the observations used here (22 year duration for the altimetry), the relatively high-frequency variability on the interannual timescales will be shown by summing all of the IMFs, that is, \u2211 j=1nCj(t) and the residual R(t) will be regarded as the intrinsic trend.\nIt should be noted that the intrinsic trend R(t) is in the same unit as the raw time series (in this case for the global mean sea level used here, the unit is millimetres). Taking the first-order time derivative of the time-varying intrinsic trend yields the instantaneous rate of the trend, in units of millimetres per year for global mean sea-level rise, which provides more time-varying information on how the intrinsic trend has evolved within the given time region, compared with a typical fitted polynomial and the time-varying estimations based on the sliding window approach38,39.\nThe validity of the intrinsic trend is strongly based on the specified data duration. The properties of the trend beyond the data length require further investigation with more observations. In this study, the potential decadal variability of GMSL on the timescale longer than the length of satellite altimetry cannot be separated from the secular trend, which implies that the accelerated GMSL may partially reflect the internal decadal variability, as well as the effects of the anthropogenic forcing.\nSignificant test of the intrinsic secular trend\uf0c1\nTo test the statistical significance of the intrinsic secular trend, one needs to reject a null hypothesis that it arises by chance for stochastic processes with zero means at given confidence levels. In climate sciences, two widely used null hypotheses are that the underlying processes are noise characterized as white (that is, no temporal correlation) or red (with lag temporal correlation). There are many methods to test the statistical significance of a linear, curve-fitted, or time-varying trend against a white or red noise null hypothesis33,40,41,42. Here we applied one approach developed for testing the time-varying trend derived by the EMD/EEMD method37. Although the detail of the statistical significance test is given in their Supplementary Section 2, the general procedures of this approach are introduced as follows, in order for the integrity of this work.", "source": "https://sealeveldocs.readthedocs.io/en/latest/chen17.html"}
{"id": "d4e5a3445e08-4", "text": "It should be noted that the intrinsic trend R(t) is in the same unit as the raw time series (in this case for the global mean sea level used here, the unit is millimetres). Taking the first-order time derivative of the time-varying intrinsic trend yields the instantaneous rate of the trend, in units of millimetres per year for global mean sea-level rise, which provides more time-varying information on how the intrinsic trend has evolved within the given time region, compared with a typical fitted polynomial and the time-varying estimations based on the sliding window approach38,39.\nThe validity of the intrinsic trend is strongly based on the specified data duration. The properties of the trend beyond the data length require further investigation with more observations. In this study, the potential decadal variability of GMSL on the timescale longer than the length of satellite altimetry cannot be separated from the secular trend, which implies that the accelerated GMSL may partially reflect the internal decadal variability, as well as the effects of the anthropogenic forcing.\nSignificant test of the intrinsic secular trend\uf0c1\nTo test the statistical significance of the intrinsic secular trend, one needs to reject a null hypothesis that it arises by chance for stochastic processes with zero means at given confidence levels. In climate sciences, two widely used null hypotheses are that the underlying processes are noise characterized as white (that is, no temporal correlation) or red (with lag temporal correlation). There are many methods to test the statistical significance of a linear, curve-fitted, or time-varying trend against a white or red noise null hypothesis33,40,41,42. Here we applied one approach developed for testing the time-varying trend derived by the EMD/EEMD method37. Although the detail of the statistical significance test is given in their Supplementary Section 2, the general procedures of this approach are introduced as follows, in order for the integrity of this work.\nFor any time series x(t) with time-varying secular trend R(t) derived by the EEMD method, the statistical significance test includes: (1) computing the lag-1 autocorrelation \u03b1 of the time series x(t). If \u03b1 = 0 then the null hypothesis that the white background noise is applied; if \u03b1 > 0, then the null hypothesis that the red background noise is applied; (2) generating 5,000 samples of red noise time series with the same temporal data length of x(t) and the lag-1 autocorrelation \u03b1; (3) deriving the intrinsic trend of each generated red noise time series by using the EEMD method. This yields an empirical probability density function of the intrinsic trends, which is approximately normally distributed, at any temporal locations; (4) comparing the intrinsic trend of the studied time series with the two-standard-deviation spread value of the trends of the red noise time series (around 95% of confidence) at any temporal locations. If the former is larger, the intrinsic trend of the studied time series is considered statistically significant and the null hypothesis that the intrinsic trend of the time series is from noise could be rejected; (5) taking the first-order time derivative of the intrinsic trend yields its instantaneous rate. If the intrinsic trend is statistically significant, we will consider its instantaneous rate is significant.\nIn this approach, the noise time series are generated on the basis of the AR(1) process x(t) = \u03b1x(t \u2212 \u0394t) + w(t), where the coefficient \u03b1 is the autoregressive parameter (that is, lag-1 correlation coefficient), \u0394t is the sampling rate and w(t) is the white noise with the unit standard deviation. A more general case is to generate the red noise on the basis of the ARMA(p, q) process43,44. Empirically, the selection of the red noise model may change the probability density function shape of the EEMD trends of each red noise time series, but it will not change the general patterns of the statistical significance test if we go through all possibilities of the lag-1 autocorrelation from 0 to 0.99. In this study, we adopt the AR(1) model.\nTaking the GPS-based adjusted GMSL time series as an example, Supplementary Figs 2\u20134 present the analysis of its intrinsic trend, and the test of its statistical significance. Supplementary Fig. 2 shows that the lag-1 autocorrelation coefficient of the GPS-based adjusted GMSL is \u03b1 = 0.84. With this lag-1 autocorrelation coefficient, 5,000 AR(1) time series are generated and then decomposed by the EEMD method to derive their intrinsic trend (Supplementary Fig. 2a). Both thick black lines in Supplementary Fig. 2a are two-standard-deviation spread lines of the trend of AR(1) time series. Note that these intrinsic trends of the background noise are dimensionless. To test the statistical significance of the intrinsic trend of GPS-based adjusted GMSL time series, which is in the same unit of millimetres, we divide it by the standard deviation of the linearly detrended GMSL time series (red line in Supplementary Fig. 2a) and compare it with two standard deviations of the intrinsic trend of the red background noise at each temporal location. If the former is larger, the trend of GMSL is considered statistically significant. Supplementary Fig. 2b, c presents the comparison at two randomly selected years 1999 and 2009, respectively, in which the trend of GMSL time series is not statistically different from the trend of AR(1) red noise with 0.84 lag-1 autocorrelation in 1999, but significantly different in 2009. In Supplementary Fig. 2a, comparing the temporal variability of the intrinsic secular trend of the GPS-based adjusted GMSL time series with the two-standard-deviation line (around 95% confidence) of the intrinsic trend of the 5,000 AR(1) processes with 0.84 lag-1 autocorrelation shows that the intrinsic trend of GPS-based adjusted GMSL becomes statistically significant since 2005.\nAs for the definition of the intrinsic trend12, this statistical significance test is also valid only during the studied period, because the properties of the intrinsic trend beyond the data length may change a lot, and so their statistical significance.\nTo test the time series with different lag-1 autocorrelation, Supplementary Fig. 3 shows the two-standard-deviation line (around 95% confidence) of the intrinsic secular trend of the 5,000 AR(1) processes with the lag-1 autocorrelation ranging from 0 to 0.99. The trend spread depends on the value of lag-1 autocorrelation. When the noise is getting redder (larger lag-1 autocorrelation), the corresponding spreads become wider37.\nBased on the 95% confidence levels of different AR(1) time series with lag-1 autocorrelation ranging from 0 to 0.99, the statistical significance of the intrinsic secular trend of the GMSL, the GMSSL, and the global ocean mass change can be tested, as shown in Supplementary Fig. 4a\u2013c, respectively.\nEstimation of the uncertainty of the intrinsic trend\uf0c1\nTo estimate the uncertainties in the intrinsic trend, the down sampling approach36 is applied. This method is also used to study the increasing flooding hazard in Miami Beach, Florida [34].\nFor the monthly time series of global mean sea level, global mean steric sea level, or the Greenland and Antarctic ice sheet mass loss, we randomly pick a value of the time series for each calendar year to represent the entire annual average. This step can theoretically yield 12 (ref. 22) different time series for 22 years of monthly data. We randomly choose 1,000 series and re-compute their intrinsic secular trend, and then obtain the mean of the trend, and the spread of the trends provides the confidence interval. For the yearly time series of glacier and anthropogenic terrestrial water storage time series, we randomly pick up a value of the time series within two standard deviations of the time series to represent the spread of the time series, and choose 1,000 different series and re-compute their intrinsic secular trend. The rate of the intrinsic trend is obtained by computing the mean of the time derivative of each intrinsic trend and its uncertainty. This approach can also be applied to estimate the uncertainty of the other IMFs of the time series if the timescale of the function is longer than a month.\nSince the higher-frequency variability of the time series is gradually separated using EEMD, the uncertainty of the intrinsic trend is generally less than the uncertainty estimation of the linear trend of original whole time series. The uncertainty of the intrinsic trend at the start and end of the data range is relatively large given the edge effects. This is unavoidable for any temporally local analysis method, such as the Gibbs effect of the Fourier transform and the \u2018cone of influence\u2019 of wavelet analysis45. Compared with these methods, the temporal locality of EEMD is smaller, and so are the uncertainties at the two ends, as discussed in the study of uncertainty of the global sea surface temperature [36].", "source": "https://sealeveldocs.readthedocs.io/en/latest/chen17.html"}
{"id": "d4e5a3445e08-5", "text": "Based on the 95% confidence levels of different AR(1) time series with lag-1 autocorrelation ranging from 0 to 0.99, the statistical significance of the intrinsic secular trend of the GMSL, the GMSSL, and the global ocean mass change can be tested, as shown in Supplementary Fig. 4a\u2013c, respectively.\nEstimation of the uncertainty of the intrinsic trend\uf0c1\nTo estimate the uncertainties in the intrinsic trend, the down sampling approach36 is applied. This method is also used to study the increasing flooding hazard in Miami Beach, Florida [34].\nFor the monthly time series of global mean sea level, global mean steric sea level, or the Greenland and Antarctic ice sheet mass loss, we randomly pick a value of the time series for each calendar year to represent the entire annual average. This step can theoretically yield 12 (ref. 22) different time series for 22 years of monthly data. We randomly choose 1,000 series and re-compute their intrinsic secular trend, and then obtain the mean of the trend, and the spread of the trends provides the confidence interval. For the yearly time series of glacier and anthropogenic terrestrial water storage time series, we randomly pick up a value of the time series within two standard deviations of the time series to represent the spread of the time series, and choose 1,000 different series and re-compute their intrinsic secular trend. The rate of the intrinsic trend is obtained by computing the mean of the time derivative of each intrinsic trend and its uncertainty. This approach can also be applied to estimate the uncertainty of the other IMFs of the time series if the timescale of the function is longer than a month.\nSince the higher-frequency variability of the time series is gradually separated using EEMD, the uncertainty of the intrinsic trend is generally less than the uncertainty estimation of the linear trend of original whole time series. The uncertainty of the intrinsic trend at the start and end of the data range is relatively large given the edge effects. This is unavoidable for any temporally local analysis method, such as the Gibbs effect of the Fourier transform and the \u2018cone of influence\u2019 of wavelet analysis45. Compared with these methods, the temporal locality of EEMD is smaller, and so are the uncertainties at the two ends, as discussed in the study of uncertainty of the global sea surface temperature [36].\nThe above uncertainty estimation of the intrinsic trend does not take into account systematic (non-averaging) error terms present in the time series. For the case of the adjusted GMSL time series, uncertainty associated with the bias drift estimation for each mission needs to be considered. The above uncertainty estimation method can be applied to each realization of the time series, with each realization generated sampling the bias drifts and intra/inter-mission bias and associated uncertainties. Applying the EEMD analysis to each time series and estimating the uncertainty of the derived intrinsic trend gives a joint uncertainty estimation of the instantaneous rate of the GPS-based adjusted GMSL rise (not shown). The slightly higher uncertainty of the instantaneous rate of the GMSL change (from \u00b10.6\u2009mm\u2009yr\u22121 during 1993 to \u00b10.4\u2009mm\u2009yr\u22121 during 2014) reflects the different mission lengths and the split between TOPEX side A and side B in the early part of the record.", "source": "https://sealeveldocs.readthedocs.io/en/latest/chen17.html"}
{"id": "bdedab7bad2b-0", "text": "Sadai et al. (2020)\uf0c1\nTitle:\nFuture climate response to Antarctic Ice Sheet melt caused by anthropogenic warming\nCorresponding author:\nShaina Sadai\nCitation:\nSadai, S., Condron, A., DeConto, R., & Pollard, D. (2020). Future climate response to Antarctic Ice Sheet melt caused by anthropogenic warming. Science Advances, 6(39), eaaz1169. doi:10.1126/sciadv.aaz1169\nURL:\nhttps://www.science.org/doi/10.1126/sciadv.aaz1169\nAbstract\uf0c1\nMeltwater and ice discharge from a retreating Antarctic Ice Sheet could have important impacts on future global climate. Here, we report on multi-century (present-2250) climate simulations performed using a coupled numerical model integrated under future greenhouse-gas emission scenarios IPCC RCP4.5 and RCP8.5, with meltwater and ice discharge provided by a dynamic-thermodynamic ice sheet model. Accounting for Antarctic discharge raises subsurface ocean temperatures by >1\u02daC at the ice margin relative to simulations ignoring discharge. In contrast, expanded sea ice and 2\u02daC to 10\u02daC cooler surface air and surface ocean temperatures in the Southern Ocean delay the increase of projected global mean anthropogenic warming through 2250. In addition, the projected loss of Arctic winter sea ice and weakening of the Atlantic Meridional Overturning Circulation are delayed by several decades. Our results demonstrate a need to accurately account for meltwater input from ice sheets in order to make confident climate predictions.\nIntroduction\uf0c1\nObservational evidence indicates that the West Antarctic Ice Sheet (WAIS) is losing mass at an accelerating rate (1, 2). Recent advances in ice sheet modeling have improved our understanding of Antarctic Ice Sheet (AIS) evolution in response to anthropogenic greenhouse gas forcing and show that the AIS could contribute substantially to sea level rise by the end of this century (3-6). A more accurate understanding of the impacts that this evolution might have on atmospheric and oceanic dynamics is needed to constrain possible future changes in the climate system. However, ice sheet physics are not adequately represented in the current generation of global climate models (GCM) used in future projections (7, 8). The AIS is considered a tipping element within the climate system (9) with the potential to contribute several tens of centimeters of global mean sea level rise in the next two centuries, but the climate system response to such large-scale ice loss is not well constrained, especially beyond 2100.\nToday, freshwater input to the ocean is increasing in response to climatic warming, largely from a combination of net precipitation and increasing riverine input resulting from an invigorated hydrologic cycle, and the loss of sea and land ice (10). Previous modeling work investigating the relative impacts of freshwater forcing in the North Atlantic versus the Southern Ocean (11, 12) has demonstrated that the location and magnitude of the additional freshwater are central to the modeled climate response. Methodology for modeling the climatic impact of freshwater perturbations has also varied widely in terms of strength, duration, and location of meltwater input: Historically, so-called \u201chosing\u201d approaches added water uniformly within given latitude bands (11-14), while more recent work has applied freshwater forcing at specific locations around global coastlines or spread according to iceberg movements (6, 15-19). Despite differences in model resolution and representation of Earth system processes, several elements of the climate response to freshwater perturbations in the Southern Ocean have been broadly consistent, such as a decrease in surface air temperatures (SATs) over the Southern Ocean, a decrease in the strength of the Atlantic Meridional Overturning Circulation (AMOC), and the expansion of Southern Ocean sea ice.\nHere, we present results from a series of climate model simulations performed using a high-resolution, fully coupled, ocean-atmosphere-cryosphere-land model, Community Earth System Model (CESM) 1.2.2 with Community Atmospheric Model 5 (CAM5) atmospheric physics (20), under Representative Concentration Pathway (RCP) 4.5 and RCP8.5 (10) spanning 2005-2250 (see Materials and Methods). In our freshwater forcing simulations, referred to throughout the paper as RCP4.5FW and RCP8.5FW, time-evolving freshwater (liquid melt-water and solid ice) input from Antarctica is provided from a continental ice sheet/ice shelf model (3) responding to the same atmospheric forcing scenarios. The control runs (RCP4.5CTRL and RCP8.5CTRL) have no additional freshwater forcing beyond what is already simulated by the CESM model. To account for spatial and temporal variations in runoff and to improve on classic hosing experiments, we released time-variant AIS meltwater and ice discharge into the ocean at the nearest surface-level coastal grid cell to where ice calving and/or ocean melt is occurring in the ice sheet model (Fig. 1A; see Materials and Methods) such that considerable volumes of meltwater and ice enter the ocean from the Amundsen Coast of West Antarctica, including Pine Island and Thwaites glaciers. In our experiments, liquid melt-water and solid ice discharge from the AIS are input separately to account for the latent heat of melting the solid component. In both RCP scenarios, the solid ice component dominates the discharge, with 62 to 87% of the total discharge being ice in RCP8.5FW and 71 to 86% in RCP4.5 (fig. S1). This is due to ice model advances that include hydrofracturing and ice-cliff calving. Here, we use the term \u201cAIS discharge\u201d to refer to the total freshwater forcing from the ice sheet model from both the solid ice and liquid meltwater components.\nIn RCP4.5FW, total discharge increases throughout the 21st century and remains between 0.4 and 0.8 sverdrup (sverdrup = 10^6 m^3/s) from 2050 to 2250; in contrast, the meltwater input in RCP4.5CTRL never exceeds 0.1 sverdrup (Fig. 1D). In RCP8.5FW, AIS discharge is dominated by the retreat of the WAIS in the ice sheet model during the 21st century, peaking at >2 sverdrup around ~2125 when the Ross Ice Shelf has collapsed and the inland ice behind it drains into the Ross Sea. Discharge then remains above 1 sverdrup through 2200 due to increasing contributions from the East Antarctic Ice Sheet (EAIS). This is in sharp contrast to RCP8.5CTRL in which discharge increases steadily throughout the run but never exceeds 0.2 sverdrup (Fig. 1D). As such, our methodology allows a direct comparison of the climate response to changing atmospheric greenhouse gas concentrations with and without a major Antarctic meltwater contribution that accounts for both the liquid meltwater and solid ice components of AIS discharge (see Materials and Methods). While projected changes in meltwater and ice discharge from Greenland are not included in our simulations, their potential impacts on climate are discussed in Materials and Methods.\nFigure 1: Freshwater forcing quantities and salinity response. (A) Spatially distributed, time-varying freshwater forcing from AIS discharge, which includes both the liquid meltwater and solid ice components, was input at the surface level around the continental margin. Forcing in September 2121 CE is shown here. (B) Combined liquid and solid forcing components are shown in relation to the global mean surface temperature in RCP8.5. Solid components are the dominant portion of the forcing, as seen in fig. S1. (C) Decadal (2121-2130) sea surface salinity anomaly based on the difference between RCP8.5FW and RCP8.5CTRL, reflecting the freshwater input during peak ice sheet retreat. (D) Same as in (B) except for RCP4.5.\uf0c1\nResults\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/sadai20.html"}
{"id": "bdedab7bad2b-1", "text": "In RCP4.5FW, total discharge increases throughout the 21st century and remains between 0.4 and 0.8 sverdrup (sverdrup = 10^6 m^3/s) from 2050 to 2250; in contrast, the meltwater input in RCP4.5CTRL never exceeds 0.1 sverdrup (Fig. 1D). In RCP8.5FW, AIS discharge is dominated by the retreat of the WAIS in the ice sheet model during the 21st century, peaking at >2 sverdrup around ~2125 when the Ross Ice Shelf has collapsed and the inland ice behind it drains into the Ross Sea. Discharge then remains above 1 sverdrup through 2200 due to increasing contributions from the East Antarctic Ice Sheet (EAIS). This is in sharp contrast to RCP8.5CTRL in which discharge increases steadily throughout the run but never exceeds 0.2 sverdrup (Fig. 1D). As such, our methodology allows a direct comparison of the climate response to changing atmospheric greenhouse gas concentrations with and without a major Antarctic meltwater contribution that accounts for both the liquid meltwater and solid ice components of AIS discharge (see Materials and Methods). While projected changes in meltwater and ice discharge from Greenland are not included in our simulations, their potential impacts on climate are discussed in Materials and Methods.\nFigure 1: Freshwater forcing quantities and salinity response. (A) Spatially distributed, time-varying freshwater forcing from AIS discharge, which includes both the liquid meltwater and solid ice components, was input at the surface level around the continental margin. Forcing in September 2121 CE is shown here. (B) Combined liquid and solid forcing components are shown in relation to the global mean surface temperature in RCP8.5. Solid components are the dominant portion of the forcing, as seen in fig. S1. (C) Decadal (2121-2130) sea surface salinity anomaly based on the difference between RCP8.5FW and RCP8.5CTRL, reflecting the freshwater input during peak ice sheet retreat. (D) Same as in (B) except for RCP4.5.\uf0c1\nResults\uf0c1\nThe impact of applying spatially varying freshwater forcing is immediately apparent in the salinity field (Fig. 1 and fig. S2). By the end of the 21st century, the sea surface salinity (SSS) in the RCP8.5FW experiment is reduced by up to \u22125 practical salinity unit (psu) (compared to RCP8.5CTRL) over most of the Southern Ocean and begins spreading northward (Fig. 1 and fig. S2). By the time of peak WAIS retreat, around year 2120, the negative SSS anomaly exceeds \u221215 psu around the Antarctic margin, especially in the Amundsen and Bellingshausen seas and portions of the Ross and Weddell seas (Fig. 1C). By the middle of the 22nd century, the anomaly has spread pervasively throughout all the ocean basins, to depths of ~4000 m (fig. S2). In RCP4.5FW, the ice sheet collapse does not peak and decline in the same way as RCP8.5FW but rather is maintained throughout most of the run, resulting in a persistent and steady freshwater forcing (Fig. 1, B and D). The associated salinity anomaly patterns are spatially similar to the RCP8.5FW simulation but lower in magnitude (\u22121 to \u22122 psu) and remain confined to the Southern Ocean (fig. S2).\nPrescribing AIS discharge from the ice sheet model has a profound impact on sea ice. Accurately capturing this response is important because seasonal freeze and melt cycles in the Southern Ocean act as a deepwater pump (21); thus, changes in sea ice are linked to changes in Southern Ocean overturning. The balance between brine rejection from sea ice formation, freshwater forcing, and associated changes in ocean convection also lead to alterations in air-sea heat exchange that can trap warm waters at depths and increase melt rates under neighboring ice shelves (22). Substantial changes in sea ice extent affect the radiative balance through sea ice albedo feedbacks and can markedly affect ecosystems. For example, shifts in sea ice formation have already begun to affect penguin colonies (23) and will likely have wide-reaching effects on microfauna communities, krill abundance, and larger ocean predators (24).\nIn our simulations, sea ice expands in both RCP4.5FW and RCP8.5FW, despite the strongly elevated radiative forcing (Fig. 2). The large AIS discharge in both simulations reduces salinity, raises the freezing temperature, and stratifies the water column around the coast. This, in turn, reduces convection, suppresses Southern Ocean overturning, and leads to a substantial buildup in perennial sea ice extent and thickness. Spatially, the greatest sea ice growth in the perturbation experiments is within the South Pacific sector, where the freshwater input is largest. Sea ice accumulates within the first few decades in both the RCP4.5 and RCP8.5 AIS discharge experiments, compared to the control simulations. In RCP8.5FW, Southern Ocean sea ice extent reaches a maximum in the 2120\u2019s during peak AIS discharge, with sea ice thickness exceeding 10 m in the Amundsen, Bellingshausen, and Ross seas and parts of the EAIS margin (Fig. 2). As the freshwater forcing from AIS discharge declines following WAIS collapse, sea ice extent and thickness also begin to decline, although >10-m-thick sea ice still persists in several regions in year 2200 (fig. S3, A and C). After peak AIS discharge has occurred in RCP8.5FW in the 2120\u2019s, sea ice extent and thickness markedly decline in this scenario. This is in contrast to RCP4.5FW, where >5-m-thick perennial sea ice persists into the 22nd century, despite the substantial anthropogenic greenhouse gas forcing (fig. S3, B and D). In contrast to the large quantities of sea ice produced in the perturbation experiments, sea ice never expands in RCP4.5CTRL and RCP8.5CTRL and declines over the course of those runs, with minimal sea ice in the Southern Ocean by 2100, and no austral winter sea ice by 2200 (Fig. 2A and fig. S3).\nFigure 2: Sea ice response to freshwater forcing. (A) Time series of Southern Ocean sea ice area in February showing the extent of perennial sea ice in austral summer. Lower anthropogenic radiative forcing allows for a much greater sea ice area in the 22nd century in RCP4.5FW, despite a similar magnitude of freshwater forcing to that of RCP8.5FW. (B to E) February sea ice thickness decadally averaged for 2121\u20132130 for (B) RCP8.5FW, (C) RCP4.5FW, (D) RCP8.5CTRL, and (E) RCP4.5CTRL. Note the difference in scale for (D) and (E).\nProjected changes in sea ice resulting from accelerated AIS discharge produces a strong albedo feedback that delays atmospheric warming in both perturbation experiments (Fig. 1, B and D). Spatially, the cooler temperatures relative to the control simulations are maximized directly over the Antarctic continental margin where the AIS discharge perturbation is applied (Fig. 3, A and B). The effect of the freshwater forcing from AIS discharge on global mean surface temperature (GMST) reaches a maximum at the time of peak ice sheet retreat in RCP8.5FW, with GMST values 2.5\u00b0C lower than the control run (Fig. 1B and fig. S4). This finding demonstrates that AIS mass loss could provide a negative feedback on anthropogenic warming, despite catastrophic impacts to the climate system as a whole, and substantial contributions to sea level rise. It is important to note, although, that while the rate of anthropogenic warming is mitigated somewhat until Antarctica is largely exhausted of ice, global temperatures still rise substantially above present-day values in both RCP4.5FW and RCP8.5FW (Fig. 1, B and D, and table S1).", "source": "https://sealeveldocs.readthedocs.io/en/latest/sadai20.html"}
{"id": "bdedab7bad2b-2", "text": "Figure 2: Sea ice response to freshwater forcing. (A) Time series of Southern Ocean sea ice area in February showing the extent of perennial sea ice in austral summer. Lower anthropogenic radiative forcing allows for a much greater sea ice area in the 22nd century in RCP4.5FW, despite a similar magnitude of freshwater forcing to that of RCP8.5FW. (B to E) February sea ice thickness decadally averaged for 2121\u20132130 for (B) RCP8.5FW, (C) RCP4.5FW, (D) RCP8.5CTRL, and (E) RCP4.5CTRL. Note the difference in scale for (D) and (E).\nProjected changes in sea ice resulting from accelerated AIS discharge produces a strong albedo feedback that delays atmospheric warming in both perturbation experiments (Fig. 1, B and D). Spatially, the cooler temperatures relative to the control simulations are maximized directly over the Antarctic continental margin where the AIS discharge perturbation is applied (Fig. 3, A and B). The effect of the freshwater forcing from AIS discharge on global mean surface temperature (GMST) reaches a maximum at the time of peak ice sheet retreat in RCP8.5FW, with GMST values 2.5\u00b0C lower than the control run (Fig. 1B and fig. S4). This finding demonstrates that AIS mass loss could provide a negative feedback on anthropogenic warming, despite catastrophic impacts to the climate system as a whole, and substantial contributions to sea level rise. It is important to note, although, that while the rate of anthropogenic warming is mitigated somewhat until Antarctica is largely exhausted of ice, global temperatures still rise substantially above present-day values in both RCP4.5FW and RCP8.5FW (Fig. 1, B and D, and table S1).\nFigure 3: Air and ocean temperatures. (A) SAT difference (RCP8.5FW minus RCP8.5CTRL), decadally averaged for 2121\u20132130, shows strong cooling throughout the Southern Ocean. (B) Same as in (A), but for RCP4.5FW minus RCP4.5CTRL. Note that the cooling is limited to the Southern Hemisphere. (C) Decadally averaged sea surface temperature (SST) difference (RCP8.5FW minus RCP8.5CTRL) for 2121\u20132130 showing Southern Ocean cooling spreading to the equator and parts of the Northern Hemisphere. (D) Same as in (C), except for RCP4.5FW minus RCP4.5CTRL. (E) Subsurface ocean temperature difference (RCP8.5FW minus RCP8.5CTRL) at 400-m water depth, representative of continental shelf depths at the mouth of ice shelf cavities. Warming is concentrated in the Ross Sea. (F) Same as in (E), but for RCP4.5FW minus RCP4.5CTRL, showing warming concentrated in the Weddell Sea.\nFreshwater forcing from AIS discharge strongly modifies the trajectory of polar climate in both hemispheres. During peak WAIS collapse, when the SAT in the Arctic (north of 60\u00b0N) is up to 2.5\u00b0C cooler in RCP8.5FW compared to RCP85CTRL, the decline in Arctic winter sea ice is slowed such that complete loss of Arctic sea ice is delayed by ~30 years (fig. S5). In the Southern Ocean, expanded sea ice growth suppresses surface warming, particularly in the Amundsen Sea region of Antarctica where sea ice formation is maximized. The resultant sea ice cooling feedback is so strong that SATs in portions of the Southern Ocean are colder after 2100 than at the beginning of the simulation in the early 21st century (fig. S6). This effect is seen in both RCP4.5FW and RCP8.5FW. The cooling effect persists until the end of the run under RCP4.5FW, as steady ice loss continues throughout the simulation. In contrast, the cooling effect disappears in RCP8.5FW after the peak in AIS discharge\u2014when the West and East Antarctic basins become exhausted of ice and temperatures over the Southern Ocean begin to rise rapidly, ending >10\u00b0C warmer than the start of the run (fig. S6).\nGlobal sea surface temperatures (SSTs) increase because of anthropogenic emissions in all simulations. Under RCP8.5FW, the Southern Ocean is an exception as SSTs cool by as much as 2\u00b0C during the 21st century and through the period of peak AIS discharge, as compared to the start of the run (fig. S7). Compared to RCP8.5CTRL, we find that SSTs in RCP8.5FW are significantly lower, with a 2\u00b0 to 10\u00b0C cooling in the Southern Hemisphere at the time of peak AIS discharge during the 2120s, while a slight warming of ~2\u00b0C is observed in the North Atlantic and subtropical Pacific (Fig. 3C). The spatial patterns of temperature anomalies in RCP4.5FW are similar to those in RCP8.5FW, but of smaller magnitude. For example, SSTs in the Southern Hemisphere are 1\u00b0 to 3\u00b0C cooler, while in the North Atlantic and subtropical Pacific, the warming is, at most, ~0.5\u00b0 to 1\u00b0C (Fig. 3D).\nThe cooling response of Southern Ocean surface waters contrasts with subsurface warming at depths (~400 m) broadly representative of sills at the entrances of ice shelf cavities around the ice sheet margin. This juxtaposition is caused by the expanded sea ice cover, increased surface stratification in the upper water column, and reduced vertical mixing as seen in other studies (18). The subsurface warming in RCP8.5FW is more intense in our simulation relative to other recent studies (6, 18), because our integrations are run forward long enough to capture peak in AIS discharge associated with maximum WAIS retreat in the early 22nd century. The strongest subsurface ocean warming in RCP8.5FW is in the Ross Sea, where temperatures at 400-m water depth are ~2\u00b0 to 4\u00b0C warmer than in RCP8.5CTRL in the 2120s (Fig. 3E). The strongest warming in RCP4.5FW is observed in the Weddell Sea at this time (Fig. 3F), although as noted previously, the WAIS does not undergo the same rapid collapse in this scenario. By 2250, temperatures are up to 3\u00b0C warmer in RCP4.5FW and up to 6\u00b0C warmer in RCP8.5FW, as compared to the start of run averages (fig. S8). The subsurface warming effect remains confined to the Southern Ocean, south of the Antarctic Circumpolar Current, as large parts of the deep ocean display the same cooling anomaly seen in the SSTs (fig. S9).\nThe contrasting surface cooling and subsurface warming have clear implications for the future stability of the AIS. A previous ice sheet modeling study (6) using an intermediate-complexity climate model to capture ice-climate feedbacks found that the subsurface ocean warming feedback dominates over changes in SATs, but the ice sheet model did not account for processes like ice shelf hydrofracturing (3), which is sensitive to SATs and surface melt, so the relative importance of these competing feedbacks (subsurface ocean warming versus atmospheric cooling) has yet to be fully tested. Here, we find rapid increases in subsurface temperatures in the Ross and Weddell seas during the 21st century in RCP8.5FW (fig. S8). The warming subsequently slows into the start of the 22nd century as the temperatures over the Southern Ocean briefly decrease because of sea ice growth. In the later part of the 22nd century through the end of the simulations, atmospheric warming increases much more rapidly than ocean temperatures, which may point to SAT becoming the dominant control on ice loss. Determining the relative impacts of these two competing feedbacks will require dynamic coupling of ice sheet/ice shelf models with global climate models.\nPast changes in the AMOC strength are associated with rapid shifts in past climate (25). In addition, observational records show that the AMOC has slowed since the 1950s (26). In previous Southern Ocean freshwater forcing experiments (11, 14), a low-salinity anomaly was found to spread northward into the North Atlantic, suppressing deepwater formation. However, those experiments applied the freshwater forcing uniformly over a large region of the Southern Ocean rather than at the location of ice and meltwater discharge at the ocean surface around the Antarctic margin. In our experiments, the low-salinity anomaly spreads throughout the Southern Ocean, but it does not reach the North Atlantic at sufficient strength to inhibit overturning. This difference could be a result of the salinity perturbation in these earlier studies being applied across the Southern Ocean, rather than specific locations adjacent to the ice sheet as in this study (27).", "source": "https://sealeveldocs.readthedocs.io/en/latest/sadai20.html"}
{"id": "bdedab7bad2b-3", "text": "The contrasting surface cooling and subsurface warming have clear implications for the future stability of the AIS. A previous ice sheet modeling study (6) using an intermediate-complexity climate model to capture ice-climate feedbacks found that the subsurface ocean warming feedback dominates over changes in SATs, but the ice sheet model did not account for processes like ice shelf hydrofracturing (3), which is sensitive to SATs and surface melt, so the relative importance of these competing feedbacks (subsurface ocean warming versus atmospheric cooling) has yet to be fully tested. Here, we find rapid increases in subsurface temperatures in the Ross and Weddell seas during the 21st century in RCP8.5FW (fig. S8). The warming subsequently slows into the start of the 22nd century as the temperatures over the Southern Ocean briefly decrease because of sea ice growth. In the later part of the 22nd century through the end of the simulations, atmospheric warming increases much more rapidly than ocean temperatures, which may point to SAT becoming the dominant control on ice loss. Determining the relative impacts of these two competing feedbacks will require dynamic coupling of ice sheet/ice shelf models with global climate models.\nPast changes in the AMOC strength are associated with rapid shifts in past climate (25). In addition, observational records show that the AMOC has slowed since the 1950s (26). In previous Southern Ocean freshwater forcing experiments (11, 14), a low-salinity anomaly was found to spread northward into the North Atlantic, suppressing deepwater formation. However, those experiments applied the freshwater forcing uniformly over a large region of the Southern Ocean rather than at the location of ice and meltwater discharge at the ocean surface around the Antarctic margin. In our experiments, the low-salinity anomaly spreads throughout the Southern Ocean, but it does not reach the North Atlantic at sufficient strength to inhibit overturning. This difference could be a result of the salinity perturbation in these earlier studies being applied across the Southern Ocean, rather than specific locations adjacent to the ice sheet as in this study (27).\nTo assess the impact of Antarctic discharge on future AMOC strength, we calculated the maximum overturning values throughout the full depth range of the water column in the Atlantic Ocean from 20\u00b0 to 50\u00b0N. In both RCP8.5 simulations, an almost complete collapse of the overturning circulation is seen, with the strength of the AMOC decreasing from 24 sverdrup in 2005 to 8 sverdrup by 2250 (Fig. 4A). In RCP8.5FW, the collapse of the overturning circulation (based on the timing when overturning strength drops below 10 sverdrup for 5 consecutive years) is delayed by 35 years, relative to RCP8.5CTRL (Fig. 4A). The largest difference in AMOC in these simulations corresponds to the timing of peak discharge around 2120. The stronger AMOC in RCP8.5FW may be a contributing factor to the higher SST and SAT temperatures in the North Atlantic at this time as compared to RCP8.5CTRL. In RCP4.5FW, the strength of the overturning declines in the beginning of the run and settles into a lower equilibrium of 19 sverdrup, but it does not fully collapse. After 2200, AMOC begins to recover in RCP4.5CTRL but remains suppressed in RCP4.5FW (Fig. 4A).\nFigure 4: North Atlantic Ocean heat transport, AMOC, and global precipitation. (A) Time series of the AMOC strength in sverdrup (Sv). (B) Decadally averaged precipitation difference for 2121\u20132130 (RCP8.5FW minus RCP8.5CTRL). (C) Northward heat transport difference for 2121\u20132130 (RCP8.5FW minus RCP8.5CTRL). (D) Same as in (B), except for RCP4.5FW minus RCP4.5CTRL.\nIn our model simulations, the AIS discharge\u2013forced changes in the AMOC act to increase northward heat transport in the Atlantic Ocean (Fig. 4C). In our RCP8.5FW experiment, we find that during the period of maximum AIS discharge, the largest change in northward heat transport (compared to RCP8.5CTRL) is between 20\u00b0 and 40\u00b0N, with an increase of ~0.16 PW (1 PW = 1015 W). A similar pattern emerges in the RCP4.5 simulations, but to a lesser extent. Last, the delayed warming in the Southern Hemisphere and enhanced warming in the North Hemisphere associated with a stronger AMOC in our perturbation simulations result in a northward shift in the intertropical convergence zone under both RCP4.5FW and RCP8.5FW scenarios. The patterns of precipitation change in the RCP8.5FW and RCP4.5FW simulations relative to the control simulations are broadly similar in both experiments, although the magnitude of the changes is smaller in the RCP4.5FW scenario (Fig. 4, B and D).\nDiscussion\uf0c1\nIn summary, our climate model simulations show that future changes in meltwater and ice discharge from the AIS will have major implications for both regional and global climates. The multi-century simulations shown here (i) span the interval of peak AIS discharge in the 22nd century (under RCP8.5), (ii) account for spatially distributed (surface) and temporally varying freshwater forcing, and (iii) partition the fresh water into liquid meltwater and solid ice discharge simulated by an ice sheet model (3). The simulations highlight the potential importance of AIS discharge on the trajectory of future global climate. Our results point to a more complicated picture of WAIS stability based on standalone ice-sheet simulations that do not account for ice-ocean-atmosphere interactions. By including the freshwater forcing from AIS discharge in future greenhouse gas forcing scenarios, we find that the increased stratification of the Southern Ocean and the large-scale expansion of sea ice cause subsurface warming that could accelerate sub-ice melt rates and ice shelf thinning. At the same time, sea ice\u2013driven surface cooling provides a strong negative feedback that could mitigate surface melt and hydrofracturing of ice shelves. Last, we find a delay in the future decline in AMOC strength that enhances northward heat transport. The results shown here clearly demonstrate the need for interactive, or fully synchronous, simulations of ice sheets with fully coupled global climate models to more accurately assess the future stability of the AIS and the broader global climate impacts of substantial ice loss from Antarctica (6).\nMaterial and Methods\uf0c1\nModel configuration\uf0c1\nThree model simulations were conducted using CESM 1.2.2 with CAM5 physics (20). Model integrations were conducted using a 1\u00b0 grid resolution for the ocean and sea ice components, with a displaced pole over Greenland, and a finite-volume 0.9\u00b0 \u00d7 1.25\u00b0 grid for the atmosphere and land components. The ocean model contains 60 vertical layers, and there are 30 vertical layers representing the atmosphere. Integrations were initialized from 20th century restart files and run under IPCC RCP4.5 and RCP8.5 greenhouse gas forcing scenarios from 2005 to 2250.\nAIS discharge forcing\uf0c1\nFor the RCP4.5 and RCP8.5 perturbation simulations (RCP4.5FW and RCP8.5FW), the AIS discharge data were obtained from previous offline ice sheet model simulations, driven by the same RCP4.5 and RCP8.5 emission scenarios (3). In our CESM simulations, discharge from the AIS is spatially and temporally distributed and differentiates between liquid and solid components (fig. S1). Partitioning of liquid and solid components within CESM has the advantage of taking into account the latent heat of melting for the solid component. Accounting for latent heat has been found to be an important component in ocean response (19). Liquid components from the ice sheet model include sub-ice ocean melt, cliff face melt, and parameterized vertical flow, while solid components represent ice calving and basal refreezing (3). Using the ice sheet model component quantities allows for a larger magnitude of input as opposed to using ice sheet volume change as done in previous studies (18). The freshwater flux from the polar stereographic ice sheet model grid is spatially interpolated and applied as a perturbation at the nearest surface level coastal grid cells following each longitude band in the CESM gx1v6 grid. This provides input at 320 grid cell locations around the continental margin. For the RCP8.5 control run (RCP8.5CTRL), freshwater runoff is calculated by the standard CESM with no additional forcing from the ice sheet model. Because of computational limitations, no control run was done for RCP4.5, and instead, the data from the CCSM4 b.e11.BRCP45C5CN.f09_g16.001 run were obtained from Earth System Grid and used as a control (referred to as RCP4.5CTRL).", "source": "https://sealeveldocs.readthedocs.io/en/latest/sadai20.html"}
{"id": "bdedab7bad2b-4", "text": "AIS discharge forcing\uf0c1\nFor the RCP4.5 and RCP8.5 perturbation simulations (RCP4.5FW and RCP8.5FW), the AIS discharge data were obtained from previous offline ice sheet model simulations, driven by the same RCP4.5 and RCP8.5 emission scenarios (3). In our CESM simulations, discharge from the AIS is spatially and temporally distributed and differentiates between liquid and solid components (fig. S1). Partitioning of liquid and solid components within CESM has the advantage of taking into account the latent heat of melting for the solid component. Accounting for latent heat has been found to be an important component in ocean response (19). Liquid components from the ice sheet model include sub-ice ocean melt, cliff face melt, and parameterized vertical flow, while solid components represent ice calving and basal refreezing (3). Using the ice sheet model component quantities allows for a larger magnitude of input as opposed to using ice sheet volume change as done in previous studies (18). The freshwater flux from the polar stereographic ice sheet model grid is spatially interpolated and applied as a perturbation at the nearest surface level coastal grid cells following each longitude band in the CESM gx1v6 grid. This provides input at 320 grid cell locations around the continental margin. For the RCP8.5 control run (RCP8.5CTRL), freshwater runoff is calculated by the standard CESM with no additional forcing from the ice sheet model. Because of computational limitations, no control run was done for RCP4.5, and instead, the data from the CCSM4 b.e11.BRCP45C5CN.f09_g16.001 run were obtained from Earth System Grid and used as a control (referred to as RCP4.5CTRL).\nRecent observations show a northward expansion of sea ice in some sectors of the Southern Ocean and a cooling of the ocean surface (28). However, models from phase 5 of the Coupled Model Intercomparison Project (CMIP5) predict a sea ice decline over the modern period continuing into the future (8). Since freshwater forcing from the ice sheets is lacking in the current suite of climate models, inaccurate freshwater runoff has been suggested as the cause of discrepancies between models and observations (8). Previous climate simulations using CESM1 (CAM5) for 1980\u20132013 (17) found that after an initial adjustment period, sea ice area showed no increase in response to freshwater forcing, suggesting that other methods could be at play in driving recently observed sea ice trends. Modeling studies of future climate response to freshwater forcing in the Southern Ocean show expansion of sea ice extent in response to freshwater perturbations (18, 29). There may be a threshold beyond which AIS discharge becomes a dominant control on sea ice formation. The forcing applied in (17) was much less than applied in our long-term future simulations. That study (17) found that sea ice response was insensitive to the perturbation depth where the fresh water was added to the ocean. Our study uses a forcing scheme similar to that recently used in (18), with fresh water applied at the surface only. Other groups have shown distinct regional differences in sea ice sensitivity, suggesting that regional differences in freshwater perturbations will be important for assessing future ice response (22).\nFuture changes in Greenland Ice Sheet discharge\uf0c1\nIn all our experiments, freshwater input from the Greenland Ice Sheet uses the default CESM freshwater forcing scheme. While a consideration of Greenland Ice Sheet freshwater forcing is outside of the scope of this paper, inclusion of both ice sheets via dynamic coupling with global climate models will be an important step for future research and for accurately projecting future climate states. In particular, increased meltwater discharge from Greenland has been shown to slow the AMOC (6), which could offset (to some degree) the stronger overturning circulation projected in our simulations as a response to increased AIS discharge. We hypothesize that a weakened AMOC might reduce the increased northward transport of heat simulated by our model simulations and cool the North Atlantic sector.", "source": "https://sealeveldocs.readthedocs.io/en/latest/sadai20.html"}
{"id": "494096f52fd1-0", "text": "Please activate JavaScript to enable the search functionality.", "source": "https://sealeveldocs.readthedocs.io/en/latest/search.html"}
{"id": "f4751a4b49b7-0", "text": "Yin et al. (2020)\uf0c1\nTitle:\nResponse of Storm-Related Extreme Sea Level along the U.S. Atlantic Coast to Combined Weather and Climate Forcing\nKeywords:\nMeridional overturning circulation, Extreme events, Sea level, Storm surges, Climate change, Climate models\nCorresponding author:\nJianjun Yin\nCitation:\nYin, J., Griffies, S. M., Winton, M., Zhao, M., & Zanna, L. (2020). Response of Storm-Related Extreme Sea Level along the U.S. Atlantic Coast to Combined Weather and Climate Forcing. Journal of Climate, 33(9), 3745\u20133769. doi: 10.1175/jcli-d-19-0551.1\nURL:\nhttps://journals.ametsoc.org/view/journals/clim/33/9/jcli-d-19-0551.1.xml\nAbstract\uf0c1\nStorm surge and coastal flooding caused by tropical cyclones (hurricanes) and extratropical cyclones (nor\u2019easters) pose a threat to communities along the Atlantic coast of the United States. Climate change and sea level rise are altering the statistics of these extreme events in a rather complex fashion. Here we use a fully coupled global weather/climate modeling system (GFDL CM4) to study characteristics of extreme daily sea level (ESL) along the U.S. Atlantic coast and their response to global warming. We find that under natural weather processes, the Gulf of Mexico coast is most vulnerable to storm surge and related ESL. New Orleans is a striking hotspot with the highest surge efficiency in response to storm winds. Under a 1% per year atmospheric CO2 increase on centennial time scales, the anthropogenic signal in ESL is robust along the U.S. East Coast. It can emerge from the background variability as soon as in 20 years, or even before global sea level rise is taken into account. The regional dynamic sea level rise induced by the weakening of the Atlantic meridional overturning circulation facilitates this early emergence, especially during wintertime coastal flooding associated with nor\u2019easters. Along the Gulf Coast, ESL is sensitive to the modification of hurricane characteristics under the CO2 forcing.\nIntroduction\uf0c1\nThe U.S. Atlantic coast (including both the East Coast and the Gulf of Mexico coast) is an active region for tropical and extratropical storms. Geographically, this densely populated coastal region is surrounded by a broad (100\u2013300 km) and shallow (<100 m) continental shelf (Fig. 1a), making it particularly vulnerable to severe storm surge and associated socioeconomic damages and life loss. Notable examples include Hurricane Katrina in 2005 (Fritz et al. 2007) and Superstorm Sandy in 2012 (Sobel 2014), as well as more recent wintertime coastal flooding caused by \u201cbombogenesis\u201d (Buell 2018).\nFigure 1: Geometry and bathymetry along the U.S. Atlantic coast. (a) The U.S. Atlantic coastline in nature is highlighted by the red color. Large coastal cities are marked from north to south and west: Halifax, Boston, New York, Baltimore, Charleston, Miami, Tampa, New Orleans, and Houston/Galveston. (b) Representation of coastal geometry and bathymetry (km) in CM4. Coastal ocean grid boxes in red, green, and purple indicate the NE (north of Cape Hatteras), SE (Cape Hatteras to the south tip of Florida), and GOM regions. The color scale uses 100-m intervals for 0\u2013500-m depth and 500-m intervals below 500 m.\nThe twenty-first-century outlook of storm surge often invokes the \u201cnoise + trend\u201d model, namely, global sea level rise (SLR) will lead to elevated storm surge (USGCRP 2017). However, the real world situation is more complex. Storm surge critically depends on such storm characteristics as intensity, frequency, size, path, translational speed, and landfall angle (Simpson 1974; Weisberg and Zheng 2006; Irish et al. 2008; Rego and Li 2009; Hall and Sobel 2013). In addition to chaotic/stochastic \u201cnoise\u201d processes, the generation, development, and propagation of tropical cyclones (TCs) and extratropical cyclones (ECs) over the North Atlantic and North America are influenced by El Ni\u00f1o\u2013Southern Oscillation (ENSO) (Hirsch et al. 2001; Donnelly and Woodruff 2007), the North Atlantic Oscillation (Elsner et al. 2000; Ezer and Atkinson 2014), the Atlantic multidecadal variability (Zhang and Delworth 2006), anthropogenic greenhouse gas and aerosol forcing (Mann and Emanuel 2006; Lin et al. 2012; Little et al. 2015; Garner et al. 2017; Rahmstorf 2017; Marsooli et al. 2019), and other factors. These factors mutually interact and modify sea surface temperature (SST), ocean heat distribution, vertical wind shear, meridional temperature gradient, large-scale oceanic and atmospheric circulation, and regional and global sea level. Given their distinct spatiotemporal scales and possible opposing effects on storms and storm surge, it remains scientifically challenging to study sea level extremes and their impact along the U.S. Atlantic coast in the face of natural and anthropogenic climate variability and change.\nHere we address this challenge using a fully coupled global climate model (CM4) recently developed at the Geophysical Fluid Dynamics Laboratory (GFDL) of NOAA. Under the protocol of phase 6 of the Coupled Model Intercomparison Project (CMIP6) (Eyring et al. 2016), a series of climate change experiments have been performed with CM4. With these simulations, we focus on weather\u2013climate interactions and their combined effect on storm-related extreme daily sea level (ESL) along the U.S. Atlantic coast. The paper is organized as follows. Section 2 describes the model and daily sea level analysis methods. Section 3 evaluates the model performance in sea level simulations. Section 4 presents characteristics and statistics of ESL under natural weather processes. Their response to CO2 forcing is described in section 5, followed by the conclusions and discussion of model limitations toward the end.\nModel, data, and methods\uf0c1\nThe GFDL CM4 climate model\uf0c1\nCM4 is the latest generation of the climate models developed and used at GFDL (Held et al. 2019). The atmospheric model (AM4.0) (Zhao et al. 2018a,b) adopts finite-volume cubed-sphere dynamical core with 96 (~1.0\u00b0 grid spacing) or 192 (~0.5\u00b0 grid spacing) grid boxes per cube face. It has 33 vertical levels and the model top is located at 1 hPa. The model incorporates updated physics such as a double-plume scheme for shallow and deep convection and single-moment cloud microphysics. Due to improvements in model resolution, physics, and dynamics, CM4 can better simulate strong TCs and ECs over the North Atlantic and North America with hurricane-force winds, reasonable storm tracks, seasonal cycle, and interannual variability (Zhao et al. 2018a), although the strongest (e.g., category 4 and 5) hurricanes are not simulated (Fig. 2).\nFigure 2: Simulations of TC and EC in the long-term piControl of CM4. (a) Global map of TC tracks. (b) TCs over the North Atlantic. Black contours (hPa) indicate the mean subtropical high during June\u2013October. (c) Global map of EC tracks. (d) ECs over the North Atlantic and North America. Black contours (\u00b0C) indicate the near-surface temperature and its gradient during December\u2013February. The color scale denotes daily winds (m s\u22121) associated with storms.\nWe use a Lagrangian approach and the 6-h data for detecting and tracking TCs and ECs in the CM4 simulations (Fig. 2) (Zhao et al. 2009). Among multiple criteria, TCs should have a maximum surface wind speed of at least 14 m s\u22121 and their trajectories must last at least 3 days. In addition, TCs should have a warm core of at least 1\u00b0C above the surrounding temperatures between 300 and 500 hPa, thus allowing TCs to be distinguished from ECs and other storms. The relative vorticity at 850 hPa in TCs should be greater than 1.6 \u00d7 10^{\u22124} s^{\u22121}. We use the sea level pressure field to identify ECs that should have a maximum wind speed of 25 m s\u22121 and last for at least 3 days. Detailed algorithms and codes for detecting and tracking storms can be found at https://www.gfdl.noaa.gov/tstorms/.", "source": "https://sealeveldocs.readthedocs.io/en/latest/yin2020.html"}
{"id": "f4751a4b49b7-1", "text": "Figure 2: Simulations of TC and EC in the long-term piControl of CM4. (a) Global map of TC tracks. (b) TCs over the North Atlantic. Black contours (hPa) indicate the mean subtropical high during June\u2013October. (c) Global map of EC tracks. (d) ECs over the North Atlantic and North America. Black contours (\u00b0C) indicate the near-surface temperature and its gradient during December\u2013February. The color scale denotes daily winds (m s\u22121) associated with storms.\nWe use a Lagrangian approach and the 6-h data for detecting and tracking TCs and ECs in the CM4 simulations (Fig. 2) (Zhao et al. 2009). Among multiple criteria, TCs should have a maximum surface wind speed of at least 14 m s\u22121 and their trajectories must last at least 3 days. In addition, TCs should have a warm core of at least 1\u00b0C above the surrounding temperatures between 300 and 500 hPa, thus allowing TCs to be distinguished from ECs and other storms. The relative vorticity at 850 hPa in TCs should be greater than 1.6 \u00d7 10^{\u22124} s^{\u22121}. We use the sea level pressure field to identify ECs that should have a maximum wind speed of 25 m s\u22121 and last for at least 3 days. Detailed algorithms and codes for detecting and tracking storms can be found at https://www.gfdl.noaa.gov/tstorms/.\nThe oceanic model of CM4 is based on the Modular Ocean Model version 6 (MOM6). It uses the arbitrary Lagrangian\u2013Eulerian algorithm in the vertical to allow for the combination of different vertical coordinates including geopotential, isopycnal, and terrain following. The model adopts the C-grid stencil in the horizontal and is configured on a tripolar grid. It has a 0.25\u00b0 eddy-permitting horizontal grid spacing (~20 km at midlatitudes) and 75 hybrid vertical layers down to the 6500-m maximum bottom depth. On the shelf, the vertical grid spacing can be as fine as 2 m. The ocean model configuration used here as part of CM4 is documented by Adcroft et al. (2019).\nMOM6 roughly resolves important bays and estuaries embedded along the U.S. Atlantic coastline and their connections to the open ocean, such as Massachusetts Bay, Long Island Sound, Delaware Bay, and Chesapeake Bay (Fig. 1b). However, the model resolution is not fine enough to resolve smaller bays and harbors such as Tampa Bay, Galveston Bay, and New York Harbor, as well as the chains of barrier islands east of North Carolina and south of Florida to Texas. MOM6 realistically represents the broad and gently sloping continental shelf and the sharp ocean deepening across the shelf break. Previous research showed that accurate representation of coastal geometry and bathymetry is important in capturing the fine structures of storm surge (Resio and Westerink 2008; Rego and Li 2010; Mori et al. 2014).\nIn terms of SLR and storm surge, CM4 simulates ocean steric and dynamic effects. Like many other CMIP6 models, CM4 does not incorporate an ice sheet component, and therefore cannot simulate land ice melt and its increasing contribution to global SLR in a warming climate (Chen et al. 2017). In addition, CM4 does not simulate tides which can interact with storm surge constructively and nonlinearly and lead to the so-called tide surge (Rego and Li 2010; Muis et al. 2019). Incorporating these processes would further heighten ESL during severe storms. Other model limitations will be discussed in the discussion and conclusions section (section 6).\nCMIP6 experiments with CM4 and CM4HR\uf0c1\nAs summarized in Table 1, the standard version of CM4 (1.0\u00b0 atmosphere and 0.25\u00b0 ocean) has been used to carry out the CMIP6 experiments including the Diagnostic, Evaluation and Characterization of Klima (DECK) and the Scenario Model Intercomparison Project (ScenarioMIP) (Eyring et al. 2016; O\u2019Neill et al. 2016). A 250-yr model spinup was carried out prior to the DECK runs. Meanwhile, a higher-resolution version of CM4 (CM4HR) has also been configured (0.5\u00b0 atmosphere and 0.25\u00b0 ocean). CM4HR has been used for the High Resolution Model Intercomparison Project (HighResMIP) of CMIP6 (Haarsma et al. 2016). Daily and even hourly data critical for conducting storm and storm surge analysis have been saved. In this study, we focus on the simulations with the standard CM4 and present available results from CM4HR, thus showing the impact of atmospheric model resolution.\nTable 1: CMIP6 Experiments with GFDL CM4 and CM4HR used in this study.\nDaily sea level analysis\uf0c1\nIn the preindustrial control simulation (piControl) of CM4, we calculate daily mean sea level anomalies (SLA; \u0394hc) for a particular day and location according to\n\u0394hc = \u0394\u03b7c + \u0394bc,  (1)\nwhere \u0394bc = \u2212\u0394pc/\u03c10g,  (2)\n\u0394\u03b7c(x,y,t)=\u03b7c(x,y,t)\u2212\u02dc\u03b7c(x,y,t1), and (3)\n\u0394pc(x,y,t)=pc(x,y,t)\u2212\u02dcpc(x,y,t1),t1=1,2,\u2026,365. (4)\nThe subscript c denotes piControl. The terms \u03b7c, \u02dc\u03b7c, and \u0394\u03b7c are daily dynamic sea level (relative to a time invariant geoid), its climatology and anomaly, respectively. By definition, all of these terms have a zero global mean. Along the coast, daily fluctuations of \u03b7c mainly reflect ocean rise and fall associated with transient weather processes and corresponding coastal waves. On interannual and longer time scales, \u03b7c is also influenced by large-scale ocean circulation, climate modes, and external forcing. CM4 incorporates the effects on \u03b7c of ocean temperature, salinity, and mass redistribution, as well as rainfall, evaporation, and river runoff (Griffies et al. 2014).\nBecause CM4 does not explicitly simulate the inverse barometer effect on sea level, we diagnose its contribution (\u0394bc) using sea level pressure anomalies and an equilibrium relationship [Eqs. (2) and (4)] (Ponte 2006). The terms pc,\u02dcpc, and \u0394pc are daily sea level pressure and its climatology and anomaly, respectively. In this study, \u02dc\u03b7c and \u02dcbc are removed when calculating SLA values [Eqs. (1), (3), and (4)]. But it should be noted that the absolute surge is generally higher during warm seasons than cold seasons due to the seasonal cycles (see below).\nUnder anthropogenic CO2 forcing, the ocean absorbs most of the excess heat due to radiative imbalance at the top of the atmosphere, and thus causing global mean thermosteric SLR (\u0394Ge). The term \u0394Ge in CM4 can be diagnosed as \u0394Ge(t)=\u22121/A\u222b_A \u222b_{-H}^{\u03b7e} 1/\u03c10 \u0394\u03c1 dz dA, (5)\nwhere \u0394\u03c1 is the anomaly of in situ density of seawater, \u03c10 is the reference seawater density, A is the global ocean surface area, H is the ocean depth, and \u03b7e is the dynamic sea level in the CO2 experiments. The subscript e denotes CO2 experiments. In these experiments, SLA (\u0394he) without global thermosteric SLR is calculated as \u0394he = \u0394\u03b7e + \u0394be,  (6)\nwhere \u0394\u03b7e and \u0394be are computed relative to \u02dc\u03b7c and \u02dcbc in piControl:\n\u0394\u03b7e(x,y,t) = \u03b7e(x,y,t)\u2212\u02dc\u03b7c(x,y,t1),  (7)\n\u0394pe(x,y,t) = pe(x,y,t)\u2212\u02dcpc(x,y,t1) + \u03f5, t1 = 1,2,\u2026,365. (8)\nIn addition to daily weather processes, regional trends of \u03b7e and pe and the change of their seasonal cycles under the CO2 forcing also contribute to \u0394\u03b7e and \u0394be. Note that \u03b5 is a small correction term due to the redistribution of air mass loading between the land and ocean in the CO2 experiments. SLA with global thermosteric SLR is calculated as \u0394he(x, y, t) + \u0394Ge(t).", "source": "https://sealeveldocs.readthedocs.io/en/latest/yin2020.html"}
{"id": "f4751a4b49b7-2", "text": "Under anthropogenic CO2 forcing, the ocean absorbs most of the excess heat due to radiative imbalance at the top of the atmosphere, and thus causing global mean thermosteric SLR (\u0394Ge). The term \u0394Ge in CM4 can be diagnosed as \u0394Ge(t)=\u22121/A\u222b_A \u222b_{-H}^{\u03b7e} 1/\u03c10 \u0394\u03c1 dz dA, (5)\nwhere \u0394\u03c1 is the anomaly of in situ density of seawater, \u03c10 is the reference seawater density, A is the global ocean surface area, H is the ocean depth, and \u03b7e is the dynamic sea level in the CO2 experiments. The subscript e denotes CO2 experiments. In these experiments, SLA (\u0394he) without global thermosteric SLR is calculated as \u0394he = \u0394\u03b7e + \u0394be,  (6)\nwhere \u0394\u03b7e and \u0394be are computed relative to \u02dc\u03b7c and \u02dcbc in piControl:\n\u0394\u03b7e(x,y,t) = \u03b7e(x,y,t)\u2212\u02dc\u03b7c(x,y,t1),  (7)\n\u0394pe(x,y,t) = pe(x,y,t)\u2212\u02dcpc(x,y,t1) + \u03f5, t1 = 1,2,\u2026,365. (8)\nIn addition to daily weather processes, regional trends of \u03b7e and pe and the change of their seasonal cycles under the CO2 forcing also contribute to \u0394\u03b7e and \u0394be. Note that \u03b5 is a small correction term due to the redistribution of air mass loading between the land and ocean in the CO2 experiments. SLA with global thermosteric SLR is calculated as \u0394he(x, y, t) + \u0394Ge(t).\nIn summary of the analysis methods, we distinguish SLA in piControl (\u0394hc) and CO2 experiments (\u0394he + \u0394Ge) to emphasize that the latter also includes global thermosteric SLR and regional dynamic SLR in addition to storm surge and other factors. Storm surge refers to the change in sea surface height relative to the predicted tide during a storm (Gregory et al. 2019). Strictly, it should not include any factors that would affect sea level in the absence of a storm. Thus, we choose to use the term \u201cESL\u201d in the following to discuss high-end (extreme) daily sea levels, which incorporate all the above effects represented in CM4.\nObservational and reanalysis data\uf0c1\nIn terms of data\u2013model comparison for evaluation purposes, we use the daily tide gauge data provided by the University of Hawaii Sea Level Center (Caldwell et al. 2015) (https://uhslc.soest.hawaii.edu/). We choose long-term high-quality stations mostly along the U.S. Atlantic coast (Table 2). The data are detrended and deseasonalized. It should be noted that this comparison is not ideal since tide gauges, often located inside bays or harbors, are point measurements, while the model results represent averaged values over the coastal ocean grid cells. For the altimetry data of dynamic sea level, we use the multisatellite merged gridded dataset from the Copernicus Marine Environment Service (http://marine.copernicus.eu/). The daily anomaly data with a 0.25\u00b0 spatial resolution span 1993\u20132017 (Pujol et al. 2016). The long-term mean dynamic sea level is based on the period of 1993\u20132012. For sea level pressure, we use the NCEP/NCAR reanalysis for the 1948\u20132018 period (Kalnay et al. 1996). The daily data have a 2.5\u00b0 spatial resolution (https://www.esrl.noaa.gov).\nTable 2: Daily tide gauge data used in the present study. (Note that the linear trends are not directly comparable due to different data length at different stations.)\nEvaluating sea level simulations in piControl of CM4\uf0c1\nCM4 captures the pronounced features of the long-term mean dynamic sea level observed by satellites (Figs. 3a,b). These features include the peak-to-peak range, the asymmetry associated with the gyre circulation, the sharp gradients across the Gulf Stream, Kuroshio, and the Antarctic Circumpolar Current, and the contrast between subpolar and subtropical regions and between the Pacific and Atlantic basins.\nFigure 3: Dynamic sea level \u03b7 in the altimetry data and piControl simulations of CM4. (a),(b) Long-term mean (m). (c),(d) Seasonal cycle as quantified by the difference between September and March (m). (e),(f) Daily variability as quantified by the standard deviation of the detrended and deseasonalized daily dynamic sea level (m). (left) Altimetry data and (right) CM4 simulations.\nCM4 simulates a seasonal cycle of the dynamic sea level \u02dc\u03b7c similar to the observations (Figs. 3c,d). In the Northern Hemisphere, the dynamic sea level is higher by up to 0.2 m during early autumn than during early spring, especially along the Gulf Stream and Kuroshio and nearby regions. This is mainly due to seasonal heating and cooling of the ocean, as well as seasonal changes of prevailing winds and ocean circulation. In CM4, \u02dc\u03b7c along the U.S. Atlantic coast resembles that in the ocean interior, and shows increasing amplitudes from the north toward the south (Fig. 4a). In nature, annual and semiannual long tides also contribute to higher coastal sea levels during late summer and early autumn (Sweet et al. 2018). In the tropical Pacific, the belt-like feature reflects the north\u2013south shift of the ITCZ and associated trade winds. Compared with ocean interior, \u02dc\u03b7c reduces in some shelf regions such as in the Okhotsk Sea, South of Alaska, along the west coast, and on the northeast shelf of North America. The shallow ocean column on shelf limits the magnitude of seasonal thermal expansion and contraction.\nFigure 4: Daily climatology and seasonal cycle of dynamic sea level \u02dc\u03b7 and the inverse barometer effect \u02dcb at large coastal cities in the 150-yr piControl of CM4. (a) Dynamic sea level climatology. (b) Inverse barometer effect climatology. The long-term mean at each city is removed for better comparison. Notice the different y-axis scales in (a) and (b).\nThe jet-like Gulf Stream and deep western boundary current are better simulated in CM4 compared with previous model generations (Adcroft et al. 2019; Held et al. 2019). CM4 somewhat underestimates mesoscale eddy activities along the Gulf Stream, Loop Current, and Kuroshio, as well as the associated daily variability of dynamic sea level (Figs. 3e,f). This is partly due to the eddy-permitting (rather than eddy \u201cresolving\u201d) resolution of the ocean model. While most of the mesoscale eddies do not directly impact coastal sea levels, the warm-core rings could cause sudden TC intensification due to their anomalously high heat content (Goni et al. 2009). A notable example is Hurricane Katrina, which rapidly intensified to a category 5 hurricane after passing over a warm-core ring prior to its landfall near New Orleans (Jaimes and Shay 2009). Recent studies also suggest that in addition to direct impacts through winds and pressure, coastal storms could disrupt the Gulf Stream flow, thereby indirectly influencing sea level along the U.S. East Coast (Ezer et al. 2017; Ezer 2018, 2019).\nAs for surface meteorological factors, CM4 reproduces the deepening of the Icelandic low during winter and the enhanced variability of sea level pressure and surface winds along the U.S. East Coast (Figs. 5a,b). During summer, the strength and position of the North Atlantic subtropical high are realistic in the CM4 simulations (Figs. 5c,d). At higher latitudes, the summertime weather variability reduces compared with wintertime. The seasonal cycle of the inverse barometer effect (i.e., the amplitude of \u02dcbc) is less than 0.1 m along the U.S. Atlantic coast and its seasonal variation differs at different locations (Fig. 4b).\nFigure 5: Sea level pressure (hPa) and its variability in the NCEP\u2013NCAR reanalysis and piControl simulations of CM4. (a),(b) Mean sea level pressure (contours) and its daily variability (shading) as quantified by the standard deviation during winter (November\u2013March). (c),(d) Mean sea level pressure and its daily variability during summer (June\u2013October). (left) NCEP\u2013NCAR reanalysis and (right) CM4 simulations.\nCharacterizing storm-related ESL in piControl\uf0c1\nStatistics of SLA along the U.S. Atlantic coast\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/yin2020.html"}
{"id": "f4751a4b49b7-3", "text": "As for surface meteorological factors, CM4 reproduces the deepening of the Icelandic low during winter and the enhanced variability of sea level pressure and surface winds along the U.S. East Coast (Figs. 5a,b). During summer, the strength and position of the North Atlantic subtropical high are realistic in the CM4 simulations (Figs. 5c,d). At higher latitudes, the summertime weather variability reduces compared with wintertime. The seasonal cycle of the inverse barometer effect (i.e., the amplitude of \u02dcbc) is less than 0.1 m along the U.S. Atlantic coast and its seasonal variation differs at different locations (Fig. 4b).\nFigure 5: Sea level pressure (hPa) and its variability in the NCEP\u2013NCAR reanalysis and piControl simulations of CM4. (a),(b) Mean sea level pressure (contours) and its daily variability (shading) as quantified by the standard deviation during winter (November\u2013March). (c),(d) Mean sea level pressure and its daily variability during summer (June\u2013October). (left) NCEP\u2013NCAR reanalysis and (right) CM4 simulations.\nCharacterizing storm-related ESL in piControl\uf0c1\nStatistics of SLA along the U.S. Atlantic coast\uf0c1\nAccording to the correlation of SLA \u0394hc, we divide the U.S. Atlantic coast into three regions: northeast (NE), southeast (SE), and the Gulf of Mexico (GOM) (Fig. 1b). In piControl of CM4, the standard deviation \u03c3 of SLA shows a clear separation of coastal and interior ocean dynamics, roughly along the 100-m isobaths with lower \u03c3 values (Fig. 6a). Vigorous mesoscale eddies dominate in ocean interior, while wind surge and coastal waves dominate variability near the coast (Hughes et al. 2019). The bowl-shaped coastline can enhance coastal SLA variability, such as from Cape Cod to Cape Hatteras, east of Georgia, along the Florida Panhandle, and south of Louisiana and Texas. The coastal SLA variability in CM4 is consistent with the estimate from the tide gauge data, with slightly underestimated magnitudes at some sites (Fig. 6a).\nFigure 6: Characteristics and statistics of SLA (\u0394hc) variability along the U.S. Atlantic coast in the 150-yr piControl of CM4. (a) The standard deviation (m), (b) skewness, and (c) kurtosis. Colored circles indicate the tide gauge observations (Table 2). The black line shows the 100-m isobath.\nSkewness and kurtosis describe the shape of the probability distribution of SLA at different locations (see appendix A). Figure 6b shows a positive skewness of SLA along the U.S. Atlantic coast. A positive skewness indicates a longer tail at the positive end than the negative end, which occurs when ocean surge dominates in magnitude over ocean fall due to the passing of storms. TCs and ECs tend to propagate northeastward just offshore of the NE and SE coast (Fig. 2). This preferred storm track is related to the dynamics of the subtropical (Bermuda\u2013Azores) high during summer (Elsner et al. 2000) and the midlatitude baroclinicity during winter (Lunkeit et al. 1998; Brayshaw et al. 2011). The northeasterly wind on the west and northwest side of these cyclones can cause large positive SLA values through shoreward Ekman transport. For the GOM, the northward movement (i.e., translational speed) of landfalling TCs perpendicular to the coastline causes stronger landward winds and ocean surge on the east side than the seaward winds and ocean fall on the west side. Land friction also slows down seaward winds and therefore reduces the magnitude of negative storm surge.\nKurtosis measures the \u201ctailedness\u201d of the SLA distribution and is a useful indicator of large storm surge and coastal vulnerability to ESL. Its value is sensitive to rare and extreme events that can lead to catastrophe. In piControl of CM4, the geographical map of kurtosis shows a striking hotspot around New Orleans with values greater than 10 (Fig. 6c). Enhanced values are also found along the west coast of Florida and the south coast of Texas. The kurtosis pattern along the coast is consistent with extreme surge height.\nIn addition to the moments of SLA, we also evaluate return levels of ESL by fitting the generalized Pareto distribution to the ESL values with the peak-over-threshold method (Coles et al. 2001; Arns et al. 2013) (see appendix B for details). Along the NE coast, the 1-, 10- and 100-yr return levels are generally underestimated in CM4 compared with the tide gauge data, particularly at New York (Fig. 7). The tide gauge at the Battery is inside of New York Harbor. Local large storm surge at lower Manhattan is influenced and amplified by the dynamics of the harbor and Hudson River, which are not resolved in CM4 (Blumberg et al. 2015). The ESL return levels along the SE and GOM coast are better simulated in CM4, despite the lack of the most catastrophic event like the >2-m daily surge at Galveston induced by Hurricane Carla in September 1961 (Fig. 7).\nFigure 7: Comparison of SLA variability and ESL events between (left) the tide gauge data and the control simulations of (middle) CM4 and (right) CM4HR. The daily data have been detrended and deseasonalized. Six cities in the NE, SE, and GOM regions with high-quality tide gauge data are chosen: Halifax, Boston, New York (at the Battery), Charleston, Miami (at Virginia Key), and Galveston. The gray dashed lines upward show the 1-, 10- and 100-yr return levels, respectively. The shape k, scale \u03c3, and location \u03b8 parameters (with the standard error) of the GPD fit are shown at the upper-right corner; see appendix B for details. The ESLs induced by Hurricanes Sandy and Carla are marked at New York and Galveston, respectively. Notice that the tide gauge data are point measurements at coast, while the model data are the area averaged values over the coastal ocean grid cells.\nAlong the GOM coast, large spikes in the simulated SLA time series are caused by landfalling TCs/hurricanes during summer and early autumn with August as the peak month (Fig. 8a), also evidenced by the long positive tail of the SLA histogram. The GOM coast is relatively quiet during winter and spring. On the NE coast, the SLA time series show a periodic wave-packet-like pattern: its variability is largely suppressed in summer but amplified in winter (Fig. 8c). Thus, most ESL events in this region occur during cold seasons associated with ECs/nor\u2019easters (Colle et al. 2010, 2015). Nonetheless, some of the North Atlantic TCs/hurricanes can occasionally strike this northerly region during late summer and early autumn. In fact, the record high daily surge of 1.2 m at New York in the tide gauge data was induced by Sandy in October 2012 (Fig. 7), which was a large tropical\u2013extratropical system at landfall with an unusual path perpendicular to the New Jersey shoreline (Hall and Sobel 2013). It exceeds the simulated extreme surge height at New York by CM4 and contributes to the higher 100-yr return level of ESL in the tide gauge data (Fig. 7).\nFigure 8: Time series of SLA (\u0394hc) at New Orleans and New York in piControl of CM4. (a) SLA time series of a representative 1-yr period at New Orleans. (b) Contributions of wind surge \u0394\u03b7c and pressure surge \u0394bc to large positive surge events (\u0394hc > 0.2 m) at New Orleans. (c),(d) As in (a) and (b), but for New York. Note that (b) and (d) use the 150-yr piControl with seasonal cycles removed. Notice the different y-axis scales between different panels.\nWind\u2013surge relationship\uf0c1\nThe piling up of seawater against the coast by winds is the dominant factor in storm surge. Generally, the wind effect accounts for roughly 80%\u201390% of the total surge height (Figs. 8b,d and 9a,b). The remainder is mainly due to the inverse barometer effect induced by the low central pressure of storms. In the following discussion, we focus on the wind surge part of the SLA.", "source": "https://sealeveldocs.readthedocs.io/en/latest/yin2020.html"}
{"id": "f4751a4b49b7-4", "text": "Figure 8: Time series of SLA (\u0394hc) at New Orleans and New York in piControl of CM4. (a) SLA time series of a representative 1-yr period at New Orleans. (b) Contributions of wind surge \u0394\u03b7c and pressure surge \u0394bc to large positive surge events (\u0394hc > 0.2 m) at New Orleans. (c),(d) As in (a) and (b), but for New York. Note that (b) and (d) use the 150-yr piControl with seasonal cycles removed. Notice the different y-axis scales between different panels.\nWind\u2013surge relationship\uf0c1\nThe piling up of seawater against the coast by winds is the dominant factor in storm surge. Generally, the wind effect accounts for roughly 80%\u201390% of the total surge height (Figs. 8b,d and 9a,b). The remainder is mainly due to the inverse barometer effect induced by the low central pressure of storms. In the following discussion, we focus on the wind surge part of the SLA.\nFigure 9: Large daily surge event induced by a strong and large TC in piControl of CM4. During this event, a surge of up to 1.8 m (\u0394hc) occurs along the GOM coast on 24 Aug, year 138. (a) Daily dynamic sea level anomalies \u0394\u03b7c (m) associated with this event. (b) SLA due to the inverse barometer effect \u0394bc (m). (c) Daily surface wind vector and speed (m s\u22121). (d) Daily precipitation (cm day\u22121). (e) Surface current vector and speed (m s\u22121). (f) SST anomalies (\u00b0C) associated with the cool wake. Contours in (a), (b), (d), and (f) are daily sea level pressure anomalies (hPa) associated with the TC. The green line shows the storm track except in (c), where the line colors indicate the storm maximum daily winds (m s\u22121) during its propagation.\nWind stress at the ocean surface can be calculated based on the following empirical bulk aerodynamic formula:\n\u03c4 = Cd \u03c1air U10 U10, (9)\nwhere \u03c4 is the wind stress vector, Cd a drag coefficient, \u03c1air surface air density, and U10 and U10 the wind speed and vector at 10 m above the sea, respectively, computed relative to the ocean surface currents. According to Eq. (9), the wind stress magnitude is a quadratic function of 10-m wind speed. The value of Cd can increase with the increase of wind speed (Large and Pond 1981; Weisberg and Zheng 2008). At the high end of the wind spectrum associated with hurricanes and strong ECs, however, Cd reduces with the increase of wind speed (Powell et al. 2003; Oey et al. 2007).\nAt the coast, storm surge creates a sea surface slope and an adverse pressure gradient in the offshore (x) direction. This pressure gradient tends to balance wind stress at the ocean surface:\n\u2202\u03b7/\u2202x \u2248 \u03c4/(\u03c10 g H). (10)\nHere \u03b7 is dynamic sea level, \u03c10 the reference seawater density, g the gravitational acceleration, and H the ocean depth. At the coastal regions where H reduces, the sea surface slope becomes steeper and storm surge becomes higher (Pugh 1987).\nThe warm, semi-enclosed, and oval-shaped GOM has a basin size, geometry, and bathymetry favorable for wind setup from rotating synoptic systems (Fig. 1). When a counterclockwise rotating hurricane enters the gulf from the Caribbean Sea, water piles up at the coast due to the longshore winds and resultant shoreward Ekman transport (Hope et al. 2013). At landfall, the strongest wind is typically at its eastern and northeastern sector (Fig. 10a). So a storm track slightly west of New Orleans could realize the worst-case scenario of storm surge for the city. The intense southeasterly storm wind blows almost perpendicular into the funneling land geometry east of the Mississippi river delta, and is therefore highly efficient at raising coastal water levels (As-Salek 1998). In piControl of CM4, the wind surge height at New Orleans scales up well (r = 0.75) with the local/nearby wind speed following a quadratic relationship (Figs. 10c,d). This wind\u2013surge relationship, as classified by the Saffir\u2013Simpson scale (Simpson 1974; Needham and Keim 2014), highlights the nonlinear increase in coastal vulnerability as a storm intensifies.\nFigure 10: Simulated wind\u2013surge relationship in piControl of CM4. (a) Typical wind pattern for large surges at New Orleans. (b) Typical wind pattern for large surges at New York. Shading shows the correlation of large daily surge at New Orleans and New York with daily wind speed. Contours and vectors are linear regressions of sea level pressure (hPa m\u22121) and u\u03c5 winds (m s\u22121 m\u22121) on the large surge values. (c) Scatterplot of large daily wind surge at New Orleans and New York as a function of local wind speed. The nonlinear fit is based on a quadratic wind\u2013surge relationship. (d) The quadratic wind\u2013surge relationship at nine cities along the Atlantic coast. Values in the legend indicate the fit correlation.\nDuring the landfall of a GOM hurricane, the maximum sustained wind, intense storm precipitation, and coastal surge center almost coincide (Figs. 9a,c,d). The downpour, while capable of causing inland flooding, can further increase the coastal surge height by dumping a large amount of water at the ocean surface in a short time (Wong and Toumi 2016). Over the shallow continental shelf waters, it can take a few days for the water bulge to spread and disperse through surface gravity and coastal waves. This enhancement of surge height by heavy rainfall does not work as efficiently along the NE and SE coast in part due to the narrower continental shelf. CM4 simulates the TC intensification in the GOM after passing over warm core rings north of the Loop Current (Figs. 9c,e). Due to the storm-induced ocean vertical mixing and divergent Ekman transport away from the TC center, a cool wake is evident behind the TC propagation in the CM4 simulations (Fig. 9f).\nFor New York, a large wind surge typically occurs when the low pressure system is located to the south and the alongshore winds induce shoreward Ekman transport (Figs. 10b,c,d). The surge at Baltimore and Miami shows weak or even no correlation with local/nearby winds. Baltimore is located in the Chesapeake Bay, where the surge is limited by the bay geometry. In nature, large storm surges in the Chesapeake Bay do exist provided that coastal storms push large amounts of waters into the bay (Ezer 2018, 2019). The narrow passage connecting the bay and open ocean is represented by one grid cell in CM4 (Fig. 1b), which may not be sufficient for simulating large inflow events. Although Miami is next to the open ocean and at the forefront of hurricane paths, the continental shelf offshore is exceptionally narrow (Fig. 1). In addition, Miami is at the southern tip of the Florida peninsula with a convex-shaped coastline. These features make storm surge less efficient at concentrating its energy. The observed tide gauge data confirm that the daily surge around Miami has not exceeded 0.4 m since the 1990s (Fig. 7). Strong winds, heavy rainfall, and big ocean waves during hurricanes are of more serious concern at Miami.\nCharacterizing response of ESL to CO2 forcing\uf0c1\nOur assessment above suggests that CM4 offers a previously unavailable modeling framework to study weather\u2013climate interactions and their combined effect on storm surge and related ESL. Next we consider a series of climate change experiments with CM4 under the CMIP6 protocol (Table 1) (Eyring et al. 2016). Among these simulations, we focus on the 1% per year increase in atmospheric CO2 concentration experiment (1pctCO2), supplemented with the companion experiments including the historical simulations, the twenty-first-century projections under two Shared Socioeconomic Pathways (SSP2\u20134.5 and SSP5\u20138.5) scenarios (O\u2019Neill et al. 2016), and the idealized instantaneous CO2 quadrupling (abrupt 4xCO2) run. The responses of the weather\u2013climate system and storm-related ESL are qualitatively similar between these experiments and increase in magnitude with the increase in external forcing. The results from these different experiments allow us to quantify the range of the ESL response.\nSimulated changes in weather, climate, and sea level in 1pctCO2\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/yin2020.html"}
{"id": "f4751a4b49b7-5", "text": "Characterizing response of ESL to CO2 forcing\uf0c1\nOur assessment above suggests that CM4 offers a previously unavailable modeling framework to study weather\u2013climate interactions and their combined effect on storm surge and related ESL. Next we consider a series of climate change experiments with CM4 under the CMIP6 protocol (Table 1) (Eyring et al. 2016). Among these simulations, we focus on the 1% per year increase in atmospheric CO2 concentration experiment (1pctCO2), supplemented with the companion experiments including the historical simulations, the twenty-first-century projections under two Shared Socioeconomic Pathways (SSP2\u20134.5 and SSP5\u20138.5) scenarios (O\u2019Neill et al. 2016), and the idealized instantaneous CO2 quadrupling (abrupt 4xCO2) run. The responses of the weather\u2013climate system and storm-related ESL are qualitatively similar between these experiments and increase in magnitude with the increase in external forcing. The results from these different experiments allow us to quantify the range of the ESL response.\nSimulated changes in weather, climate, and sea level in 1pctCO2\uf0c1\nIn 1pctCO2 of CM4, both global mean surface temperature and global thermosteric SLR display upward trends during the 150-yr model simulation (Fig. 11a). Global thermosteric SLR (\u0394Ge) initially lags the surface temperature response, due to the gradual downward heat penetration and enormous thermal inertia of the ocean, and shows a faster acceleration after year 50. Note that \u0394Ge is 0.09 m at year 70 (time of CO2 doubling) and 0.34 m at year 140 (time of CO2 quadrupling); \u0394Ge in 1pctCO2 is corrected by removing a slow drift of the deep ocean in piControl. As a consequence of excess heat uptake mainly by the upper layers, the ocean becomes more stratified in 1pctCO2.\nFigure 11: Simulated climate change and SLR in 1pctCO2 of CM4. (a) Time series of global mean surface air temperature anomalies, SST anomalies, and global thermosteric SLR. (b) Time series of dynamic SLR at large cities along the East and Gulf Coast.\nIn the North Atlantic and along the U.S. East Coast, ocean dynamics plays an important role in regionally modifying SLR (Levermann et al. 2005; Yin et al. 2009; Ezer 2015). In response to 1pctCO2, the Atlantic meridional overturning circulation (AMOC) weakens, which results in a 0.1-m dynamic SLR along NE at year 70 and 0.2-m dynamic SLR at year 140 in 1pctCO2 (Figs. 11b and 12a). CM4 simulates a vigorous AMOC in piControl with interannual to multidecadal variability (Figs. 13a,b). The regional enhancement of SLR along NE (on the top of global mean SLR) due to AMOC weakening is a robust feature in the previous CMIP3 (Yin et al. 2009) and CMIP5 (Yin 2012) simulations and projections, although the exact magnitude can vary across models. Compared with the previous results (Yin et al. 2009; Yin 2012; Yin and Goddard 2013), the dynamic SLR signal in CM4 extends farther southward to north of Miami (Fig. 12a). This extension may in part be due to the refined oceanic model resolution and associated representation of the continental shelf geometry and western boundary current in CM4 compared with previous model generations. Detailed mechanisms are worthy of further investigation in the future. The reduced current shear, cross-current dynamic sea level gradient, and baroclinicity tend to reduce the ocean mesoscale eddy activities (Fig. 12b).\nFigure 12: Simulated ocean changes during years 131\u2013150 in 1pctCO2 of CM4 relative to piControl. (a) Dynamic sea level anomalies (m) with a zero global mean. Contours are the long-term mean dynamic sea level (m) in piControl. (b) Response of the ocean mesoscale eddies. Shading shows the anomalies of the standard deviation of daily dynamic sea level (m). Contours are the standard deviation in piControl. To calculate the eddy-related changes in dynamic sea level, the background and large-scale SLR in 1pctCO2 is removed. (c) Pattern of SST anomalies (\u00b0C) with the global mean value removed. The green box indicates the main development region of TCs. (d) Pattern of ocean heat content anomalies (109 J m\u22122) with the global mean value removed.\nFigure 13: Upper bound of AMOC-induced dynamic SLR under CO2 forcing. (a) Atlantic meridional overturning streamfunction (Sv) as a function of latitude and depth (m) in the long-term piControl. (b) Time series of the AMOC index defined as the maximum Atlantic overturning streamfunction values north of 30\u00b0N in piControl and the CO2 experiments. (c) Global map of dynamic sea level changes (m) during years 131\u2013150 of abrupt 4xCO2 relative to piControl. (d) Time series of dynamic SLR in abrupt 4xCO2 at large coastal cities. The smooth curves are the exponential fit to the dynamic SLR at New York (NE), Charleston (SE), and New Orleans (GOM).\nGiven the importance of this dynamic SLR, it is of interest to quantify its upper bound in the stronger abrupt 4xCO2 experiment. In response to the instantaneous CO2 quadrupling, the AMOC quickly spins down and the dynamic SLR equilibrates at about 0.40 m along NE after 80 years, 0.27 m along SE, and 0.10 m along GOM (Figs. 13c,d). The e-folding time of the response is 27, 11, and 8 years, respectively. The longer response time scale at NE is likely due to the slower baroclinic processes in the higher latitudes associated with the modification of ocean density properties under CO2 forcing.\nAs for weather processes in a warming climate, CM4 simulates an increase in the strength (i.e., based on the maximum sustained wind and central pressure) of strong TCs/hurricanes over the North Atlantic, and a decrease in the annual count of all TCs after 100 years in 1pctCO2 (Figs. 14a,c) (Knutson et al. 2013, 2019). Despite warmer SSTs in the TC main development region (10\u00b0\u201325\u00b0N, 80\u00b0\u201320\u00b0W) (Fig. 12c), a greater warming in the tropical upper troposphere leads to a decrease in the lapse rate and an increase in static stability, which tend to inhibit atmospheric convection and TC formation in 1pctCO2 (Vecchi and Soden 2007; Knutson et al. 2008; Sobel et al. 2016). Previous studies show that the hurricane intensity may have increased during the past decades (Emanuel 2005), with stronger intensity for longer period of time (Ezer 2018). The track density map reveals that the reduction in TC frequency in CM4 mainly occurs east of the Caribbean Sea so that the number of landfalling TCs/hurricanes along the U.S. Atlantic coast remains almost unchanged (Fig. 14a). Meanwhile, extreme storm precipitation increases along the U.S. Atlantic coast in the CO2 experiments (Fig. 15), although the annual precipitation does not.\nFigure 14: Response of TC and EC in 1pctCO2 of CM4. (a),(b) Changes in TC and EC track density (number per decade) during the 150-yr simulations of 1pctCO2. Shading shows the anomalies and contours show the mean in piControl. The track density is evaluated over 2\u00b0 \u00d7 2\u00b0 boxes. (c),(d) TC and EC count (number per year) over the North Atlantic and North America as a function of time. Notice the different scales between (a) and (b), and between (c) and (d).\nFigure 15: Responses of daily (left) winds, (center) precipitation, and (right) sea level pressure anomaly along the (top) NE, (middle) SE, and (bottom) GOM coast in 1pctCO2 of CM4. The histograms use 150-yr simulations. The y axis indicates the total number of days summed over all coastal ocean grid points in the NE, SE, and GOM regions. A logarithm scale is used to better show the tail.", "source": "https://sealeveldocs.readthedocs.io/en/latest/yin2020.html"}
{"id": "f4751a4b49b7-6", "text": "Figure 14: Response of TC and EC in 1pctCO2 of CM4. (a),(b) Changes in TC and EC track density (number per decade) during the 150-yr simulations of 1pctCO2. Shading shows the anomalies and contours show the mean in piControl. The track density is evaluated over 2\u00b0 \u00d7 2\u00b0 boxes. (c),(d) TC and EC count (number per year) over the North Atlantic and North America as a function of time. Notice the different scales between (a) and (b), and between (c) and (d).\nFigure 15: Responses of daily (left) winds, (center) precipitation, and (right) sea level pressure anomaly along the (top) NE, (middle) SE, and (bottom) GOM coast in 1pctCO2 of CM4. The histograms use 150-yr simulations. The y axis indicates the total number of days summed over all coastal ocean grid points in the NE, SE, and GOM regions. A logarithm scale is used to better show the tail.\nThe total number of ECs/nor\u2019easters offshore of the U.S. East Coast shows a more significant reduction after 100 years in 1pctCO2 of CM4 (Fig. 14b). On global scales, polar amplification of global warming can lead to a reduced meridional temperature gradient near the surface at midlatitudes, especially during wintertime (Holland and Bitz 2003; Colle et al. 2015; Shaw et al. 2016). Regionally, SST anomalies in 1pctCO2 show a \u201cwarm\u2013cool\u2013warm\u201d tripolar pattern (relative to the global mean) among the regions north of the Gulf Stream, east of the subpolar gyre, and in the Nordic seas (Fig. 12c) (Rahmstorf et al. 2015). In particular, the larger ocean warming on the northeast U.S. continental shelf extends from the surface to the bottom of the shelf ocean, and is mainly caused by the weakening of the AMOC (Saba et al. 2015; Caesar et al. 2018). Recently, this region has been identified as one of the hotspots for marine heat waves (Fr\u00f6licher et al. 2018; IPCC 2019) that could impact marine ecosystems (Pershing et al. 2015). This faster ocean warming, along with the faster land surface warming, reduces the temperature contrast across the Gulf Stream as well as across the land\u2013sea boundary, thereby weakening the near-surface baroclinicity and storm track intensity of ECs/nor\u2019easters during winter.\nCompared with the SST anomalies, the maximum increase in heat content of the entire ocean column occurs at the offshore side of the shelf break (Fig. 12d). The dynamic SLR along the U.S. East Coast, the tripolar SST anomaly pattern, and the faster ocean heat accumulation along the shelf break are consistent manifestations and consequences of the AMOC weakening in CM4.\nResponse of ESL to CO2 forcing\uf0c1\nFigure 16 compares the SLA distribution in the historical, SSP projection, 1pctCO2, and abrupt 4xCO2 runs with (\u0394he + \u0394Ge) and without (\u0394he) global thermosteric SLR. It is evident that the increase in CO2 forcing progressively shifts the probability density function (PDF) curve to the right and toward higher values. In the historical run, the shift is relatively small due to the anthropogenic aerosol forcing largely counteracting greenhouse gas forcing until about 1990, which leaves insufficient time for sea level response (Held et al. 2019). The shift is more significant in the historical run without anthropogenic aerosol and land use forcing, in the SSP projections, and in 1pctCO2, and is strongest in the abrupt 4xCO2 run.\nFigure 16: Progressive responses of ESL to different strength of external forcing. The histograms indicate the distributions of SLA values in piControl, 1pctCO2, abrupt 4xCO2, the historical runs (with and without anthropogenic aerosol and land use forcing), and SSP projection runs of CM4. (a) SLA in piControl (\u0394hc) and climate change experiments without global thermosteric SLR (\u0394he). (b) SLA with global thermosteric SLR (\u0394he + \u0394Ge). The y axis indicates the total number of surge days summed over all coastal ocean grid points in the NE, SE, and GOM regions. All values have been normalized to a 150-yr period for comparison. (left) The piControl with idealized 1pctCO2 and abrupt 4xCO2 simulations and (right) piControl with the historical and SSP projection runs, for (top) NE, (middle) SE, and (bottom) GOM.\nWithout global thermosteric SLR, the nearly uniform shift of the PDF curve in 1pctCO2 and the elevated daily surge height along the NE and SE coast is mainly attributable to the AMOC-induced dynamic SLR (Fig. 16a). The Kolmogorov\u2013Smirnov statistical test indicates that the shift of the PDF curve is statistically significant. Along the GOM coast, the overall shift of the PDF curve to the right is relatively small, except having a disproportionately longer tail (Fig. 16a). This heightening of ESL is consistent with the increase in TC intensity under the CO2 forcing (Fig. 15). Adding global thermosteric SLR substantially widens the SLA distribution, and reduces its skewness and kurtosis (Fig. 16b).\nIn piControl of CM4, the return levels for 1-, 10- and 100-yr ESL events differ dramatically among three major coastal cities (Fig. 17) (see appendix B). The tightly packed return levels at Miami are lowest, in sharp contrast with the highest and widely separated return levels at New Orleans, especially for the 1-in-100-year events (0.26 m at Miami vs 1.83 m at New Orleans) (Tebaldi et al. 2012). SLA at Miami shows small variability and a lack of tail at both ends of its histogram (Fig. 17b). The opposite occurs at New Orleans with large surge spikes and a long histogram tail (Fig. 17c), while the surge at New York is in the middle (Fig. 17a).\nFigure 17: Time of emergence of the anthropogenic signal in ESL in 1pctCO2 of CM4, for (a) New York, (b) Miami, and (c) New Orleans. Blue and red colors denote SLA in piControl (\u0394hc) and 1pctCO2 (\u0394he + \u0394Ge), respectively. Horizontal dashed lines denote the 1-, 10-, and 100-yr return levels of daily sea level in the 150-yr piControl based on the GPD method. Triangles and diamonds indicate TOE in ESL height and frequency, respectively. Rectangles denote permanent exceedance by the rising mean sea level. Shown are the (left) time series and (right) histogram of SLA.\nIn climate change studies, the time of emergence (TOE) of the anthropogenic signal is an important quantity for detection and attribution purposes (Diffenbaugh and Scherer 2011; Hawkins and Sutton 2012). Under CO2 forcing, the anthropogenic signal can emerge in terms of ESL height or frequency or both. With 1pctCO2 of CM4, we quantify and compare TOE in terms of ESL height and frequency with and without global thermosteric SLR (see appendix C for the TOE calculation method). With global thermosteric SLR (\u0394he + \u0394Ge), TOE in ESL height of the 1-yr events occurs at year 23, 22, and 70 for New York, Miami, and New Orleans, respectively (Fig. 17). It is longer and later for the 10-yr events, and occurs at year 69 and 50 for New York and Miami, respectively. At New Orleans, the 10-yr signal emerges in ESL frequency (at year 86) rather than in ESL height. For the more extreme 100-yr event, TOE in ESL frequency can be identified at year 64 and 55 for New York and Miami, respectively. However, the 100-yr signal cannot be detected at New Orleans. This is mainly due to the large natural variability and a slower SLR at New Orleans due to ocean steric and dynamic effects in CM4.", "source": "https://sealeveldocs.readthedocs.io/en/latest/yin2020.html"}
{"id": "f4751a4b49b7-7", "text": "Figure 17: Time of emergence of the anthropogenic signal in ESL in 1pctCO2 of CM4, for (a) New York, (b) Miami, and (c) New Orleans. Blue and red colors denote SLA in piControl (\u0394hc) and 1pctCO2 (\u0394he + \u0394Ge), respectively. Horizontal dashed lines denote the 1-, 10-, and 100-yr return levels of daily sea level in the 150-yr piControl based on the GPD method. Triangles and diamonds indicate TOE in ESL height and frequency, respectively. Rectangles denote permanent exceedance by the rising mean sea level. Shown are the (left) time series and (right) histogram of SLA.\nIn climate change studies, the time of emergence (TOE) of the anthropogenic signal is an important quantity for detection and attribution purposes (Diffenbaugh and Scherer 2011; Hawkins and Sutton 2012). Under CO2 forcing, the anthropogenic signal can emerge in terms of ESL height or frequency or both. With 1pctCO2 of CM4, we quantify and compare TOE in terms of ESL height and frequency with and without global thermosteric SLR (see appendix C for the TOE calculation method). With global thermosteric SLR (\u0394he + \u0394Ge), TOE in ESL height of the 1-yr events occurs at year 23, 22, and 70 for New York, Miami, and New Orleans, respectively (Fig. 17). It is longer and later for the 10-yr events, and occurs at year 69 and 50 for New York and Miami, respectively. At New Orleans, the 10-yr signal emerges in ESL frequency (at year 86) rather than in ESL height. For the more extreme 100-yr event, TOE in ESL frequency can be identified at year 64 and 55 for New York and Miami, respectively. However, the 100-yr signal cannot be detected at New Orleans. This is mainly due to the large natural variability and a slower SLR at New Orleans due to ocean steric and dynamic effects in CM4.\nThe early TOE in ESL at New York is facilitated by the AMOC-induced dynamic SLR in this region (Figs. 11b and 12a). The anthropogenic signal first shows up in wintertime ESL events and coastal flooding associated with nor\u2019easters. The early TOE at Miami is primarily due to the weak background SLA variability especially the low surge height in piControl. More significantly in 1pctCO2, the 1-, 10- and 100-yr return levels of ESL are permanently exceeded at Miami by the rising mean sea level at year 71, 92, and 102, respectively (Fig. 17b). By contrast, New Orleans shows no permanent exceedance. We find that along the U.S. East Coast, the anthropogenic emergence occurs even before global thermosteric SLR is taken into account.\nImpact of the atmospheric model resolution\uf0c1\nThe refined atmospheric model resolution (0.5\u00b0) in CM4HR leads to more intense TCs/hurricanes with stronger winds and smaller size in the control simulation (Fig. 18). These magnify SLA extremes at both ends, but with a greater influence on the positive side along the SE and GOM coast (Fig. 19). For example, the highest daily surge at the GOM coast increases from 1.8 m in CM4 to 2.3 m in CM4HR. The simulations of ECs in CM4 and CM4HR are similar due to their large size relative to TCs. Compared with CM4, the return levels of the 1-, 10- and 100-yr ESL are higher in CM4HR, closer to those for the tide gauge data (Fig. 7). We find that in abrupt 4xCO2, the responses of storm-related ESL and the impact factors are qualitatively similar between CM4 and CM4HR, including storm characteristics, surge statistics, and oceanic and atmospheric circulation, as well as global and regional sea level (Fig. 19).\nFigure 18: Large daily surge event induced by a strong TC in the control run of CM4HR. During this event, a surge of up to 2.3 m (\u0394hc) occurs along the GOM coast on 1 Sep, year 80. (a) Daily dynamic sea level anomalies \u03b7c (m) associated with this event. (b) SLA due to the inverse barometer effect \u0394bc (m). (c) Daily surface wind vector and speed (m s\u22121). (d) Daily precipitation (cm day\u22121). (e) Surface current vector and speed (m s\u22121). (f) SST anomalies (\u00b0C) associated with the cool wake. Contours in (a), (b), (d), and (f) are daily sea level pressure anomalies (hPa) associated with the TC. The green line shows the storm track except in (c), where the line colors indicate the storm maximum daily winds (m s\u22121) during its propagation. Note that Fig. 9 shows similar plots but for CM4.\nFigure 19: Histograms of SLA in the 150-yr control and abrupt 4xCO2 runs of CM4 and CM4HR. (left) SLA in the control run (\u0394hc) and in the CO2 run without global thermosteric SLR (\u0394he) and (right) SLA in the control run (\u0394hc) and in the CO2 run with global thermosteric SLR (\u0394he + \u0394Ge), for (top) NE, (middle) SE, and (bottom) GOM.\nConclusions and model limitations\uf0c1\nIn the present study, we use a seamless and self-consistent global modeling framework (GFDL CM4) to study weather\u2013climate interactions and their combined effect on extreme sea level along the U.S. Atlantic coast. Thanks to recent progress in model development and improvement, some outstanding questions of significant societal concerns can be answered now for the first time. We compare the characteristics of storm-related ESL among the NE, SE, and GOM regions and their responses to CO2 forcing. We find that under internal weather processes, the low-lying Gulf Coast is most vulnerable to hurricanes and related storm surge. New Orleans is a striking hotspot with the highest surge efficiency in response to storm winds. In response to a 1% per year atmospheric CO2 increase, the elevated surge height along the U.S. East Coast is mainly caused by the background SLR, while that along the Gulf Coast is sensitive to the modification of hurricane characteristics by the external forcing.\nOur results confirm previous findings (e.g., Yin et al. 2009) that among the densely populated coastal regions worldwide, the U.S. East Coast is special and more vulnerable in terms of dynamic SLR (Fig. 13c). The AMOC-induced regional SLR facilitates the early emergence of the anthropogenic signal in daily surge, especially during wintertime flooding associated with nor\u2019easters. The weakening of AMOC in the CO2 experiments is mainly caused by thermohaline processes (Gregory et al. 2005; Stouffer et al. 2006; Hu et al. 2009; IPCC 2019). On shorter time scales, recent research showed that it is the atmospheric wind and pressure that influenced annual mean sea level along the U.S. northeast coast (Piecuch et al. 2019). While different possible factors need to be explored, our results here from the new CMIP6 simulations stress that the active and important role of AMOC in weather, climate, regional dynamic SLR, and storm-related ESL should not be underestimated, particularly for the twenty-first century.\nNonetheless, given the complexity of SLR and storm surge along the U.S. Atlantic coast, there are important caveats about model limitations. In nature, the highest water level typically occurs during tide surge. In addition to tidal ranges, the surge\u2013tide nonlinear interactions depend on multiple factors such as the timing of landfall, the distance to the storm, and the slope of the continental shelf (Rego and Li 2010). CM4 does not simulate tides as well as wave setup or run-up, therefore underestimating the highest water level during storm surge. CM4 does not implement a wetting and drying scheme to represent the intrusion of seawaters and coastal inundation during storm surge (Hubbert and McInnes 1999). The ESL analysis based on the daily mean data can underestimate the peak hourly surge. Uncertainties also come from the lack of the strongest (e.g., category 4 and 5) hurricanes in CM4 and CM4HR, as well as the underestimated return levels of ESL (Fig. 7). An increase in the return level in piControl could delay TOE in 1pctCO2.", "source": "https://sealeveldocs.readthedocs.io/en/latest/yin2020.html"}
{"id": "f4751a4b49b7-8", "text": "Our results confirm previous findings (e.g., Yin et al. 2009) that among the densely populated coastal regions worldwide, the U.S. East Coast is special and more vulnerable in terms of dynamic SLR (Fig. 13c). The AMOC-induced regional SLR facilitates the early emergence of the anthropogenic signal in daily surge, especially during wintertime flooding associated with nor\u2019easters. The weakening of AMOC in the CO2 experiments is mainly caused by thermohaline processes (Gregory et al. 2005; Stouffer et al. 2006; Hu et al. 2009; IPCC 2019). On shorter time scales, recent research showed that it is the atmospheric wind and pressure that influenced annual mean sea level along the U.S. northeast coast (Piecuch et al. 2019). While different possible factors need to be explored, our results here from the new CMIP6 simulations stress that the active and important role of AMOC in weather, climate, regional dynamic SLR, and storm-related ESL should not be underestimated, particularly for the twenty-first century.\nNonetheless, given the complexity of SLR and storm surge along the U.S. Atlantic coast, there are important caveats about model limitations. In nature, the highest water level typically occurs during tide surge. In addition to tidal ranges, the surge\u2013tide nonlinear interactions depend on multiple factors such as the timing of landfall, the distance to the storm, and the slope of the continental shelf (Rego and Li 2010). CM4 does not simulate tides as well as wave setup or run-up, therefore underestimating the highest water level during storm surge. CM4 does not implement a wetting and drying scheme to represent the intrusion of seawaters and coastal inundation during storm surge (Hubbert and McInnes 1999). The ESL analysis based on the daily mean data can underestimate the peak hourly surge. Uncertainties also come from the lack of the strongest (e.g., category 4 and 5) hurricanes in CM4 and CM4HR, as well as the underestimated return levels of ESL (Fig. 7). An increase in the return level in piControl could delay TOE in 1pctCO2.\nWithout an ice sheet model, CM4 cannot simulate the impacts of Greenland melt on sea level, AMOC and geoid changes along the U.S. East Coast (Kopp et al. 2010; Bakker et al. 2016). Finally, CM4 does not simulate climate-unrelated factors. Most of the U.S. Atlantic coast is influenced by land subsidence, particularly at New Orleans and along the Texas coast (Nienhuis et al. 2017), which can increase relative SLR and exacerbate the impact of storm surge and coastal flooding (Table 2). By contrast, land uplift in some of the New England coastal regions can offset and mitigate the dynamic SLR (Karegar et al. 2016).\nIdeally, projections of SLR and storm-related ESL along the U.S. Atlantic coast should take all these factors into account. We trust that future model development will continue to address these and other limitations and further improve the model\u2019s ability and capacity, thereby providing more accurate information for effective planning and preparedness along the U.S. Atlantic coast.\nAppendix\uf0c1\nAppendix A: Calculation of Skewness and Kurtosis of SLA\uf0c1\nSkewness and kurtosis describe the shape of the probability distribution of SLA (Hughes et al. 2010). In piControl, the skewness of SLA values is the third standardized moment\nskew = E [ ( \u0394hc \u2212 \u03bc / \u03c3 )^3 ], (A1)\nwith \u03bc and \u03c3 being the long-term mean and standard deviation of \u0394hc, and E the expectation operator. The kurtosis is the fourth standardized moment and is computed by\nkurt = E [ ( \u0394hc \u2212 \u03bc / \u03c3)^4 ]. (A2)\nThe kurtosis of a normal (Gaussian) distribution is 3. Sometimes it is useful to compare the kurtosis of a distribution to this value (the so-called excess kurtosis). In this study, we use the original calculation of kurtosis based on Eq. (A2). Large kurtosis values indicate more extreme outliners in the distribution.\nAppendix B: Return Level and Period of ESL in piControl\uf0c1\nWe use the peak-over-threshold method (Coles et al. 2001; Arns et al. 2013) to calculate return levels of storm-related ESL corresponding to particular return periods in the 150-yr piControl. We set the 99th percentile of SLA (\u0394hc) as the threshold to extract the subset of extreme values. We fit the empirical distribution of the subset with the generalized Pareto distribution (GPD).\ny = p(x|k,\u03c3,\u03b8)= (1/\u03c3) (1 + k (x \u2212 \u03b8)/ \u03c3)^{\u22121\u22121/k} , k \u2260 0\n= (1/\u03c3) e^{\u2212(x\u2212\u03b8)/\u03c3}, k = 0,   (B1)\nfor x \u2265 \u03b8 when k > 0, and \u03b8 \u2264 x \u2264 \u03b8 \u2212 \u03c3/k when k < 0. Here y is the PDF of GPD; k, \u03c3, and \u03b8 are the shape, scale, and location parameters, respectively. For k = 0, GPD becomes the exponential distribution. Given a particular return period T (1, 10, or 100 years) of ESL events, the corresponding return level zT is\nzT  = \u03b8 + \u03c3/k { [ (1 \u2212 F(\u03b8)) / p ]^k \u2212 1 }, k \u2260 0= \u03b8 + \u03c3log [ (1 \u2212 F(\u03b8)) / p ], k = 0   (B2)\nwhere p and F(\u03b8) are the probability of the event and cumulative density function, respectively.\nAppendix C: Time of Emergence of ESL in 1pctCO2\uf0c1\nFor the 1-in-1-year ESL events, we use a 20-yr moving window and the 99.73 percentile of SLA (empirical 1-yr event return level) as the threshold to extract the event samples (Si, i = year 20, 21, \u2026, 150). For example, S20 and S21 denote the subset exceeding the 99.73 percentile of SLA during years 1\u201320 and 2\u201321, respectively. We then identify the median value of Si in piControl (m^i_c) and 1pctCO2 (m^i_e). The subscripts c and e denote piControl and CO2 experiments, respectively. The mean Mc and standard deviation \u03c3c of m^i_c are\nMc = 1/131 \u2211^150_{i=20} m^i_c,\n\u03c3c = [\u2211^150_{i=20} (m^i_c - Mc)^2 / 131 ]^{1/2}.\n(C1)\nIn 1pctCO2, TOE in ESL height of the 1-yr events is defined as the year i beyond which m^i_e permanently exceeds (Mc + 2\u03c3c). If the anthropogenic signal emerges within the first 20 years, TOE is marked as year 20. For the 10-yr events, we follow the same detection procedure except using a 50-yr moving window instead to increase the sample size and the 99.97 percentile as the threshold. We do not evaluate TOE in ESL height for the 100-yr event due to its extreme rareness in the 150-yr simulations of CM4.\nTo quantify TOE in ESL frequency, we count the occurrence time above the 1- and 10-yr return level in piControl using a 20- and 50-yr moving window, respectively. TOE in ESL frequency is defined as the year beyond which the occurrence time in 1pctCO2 permanently exceeds the mean plus two standard deviation of the occurrence time in piControl (similar to the method above for ESL height). For the 100-yr event, TOE is the year beyond which its occurrence time in 1pctCO2 within a 50-yr moving window permanently exceeds 1 (i.e., \u22652).", "source": "https://sealeveldocs.readthedocs.io/en/latest/yin2020.html"}
{"id": "0bbafafddd15-0", "text": "Bamber et al. (2022)\uf0c1\nTitle:\nIce Sheet and Climate Processes Driving the Uncertainty in Projections of Future Sea Level Rise: Findings From a Structured Expert Judgement Approach\nKey Points:\nGreenland surface melt is a dominant uncertainty in 21st century contributions from the ice sheets\nIce shelf buttressing is the dominant uncertainty in Antarctic ice dynamics in the 21st century\nEast Antarctic ice dynamics only play a significant role in the 22nd century for a high temperature scenario\nKeywords:\nice sheets, sea level rise, expert judgement, uncertainty\nCorresponding author:\nBamber\nCitation:\nBamber, J. L., Oppenheimer, M., Kopp, R. E., Aspinall, W. P., & Cooke, R. M. (2022). Ice Sheet and Climate Processes Driving the Uncertainty in Projections of Future Sea Level Rise: Findings From a Structured Expert Judgement Approach. Earth\u2019s Future, 10(10). https://doi.org/10.1029/2022ef002772\nURL:\nhttps://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022EF002772\nAbstract\uf0c1\nThe ice sheets covering Antarctica and Greenland present the greatest uncertainty in, and largest potential contribution to, future sea level rise. The uncertainty arises from a paucity of suitable observations covering the full range of ice sheet behaviors, incomplete understanding of the influences of diverse processes, and limitations in defining key boundary conditions for the numerical models. To investigate the impact of these uncertainties on ice sheet projections we undertook a structured expert judgement study. Here, we interrogate the findings of that study to identify the dominant drivers of uncertainty in projections and their relative importance as a function of ice sheet and time. We find that for the 21st century, Greenland surface melting, in particular the role of surface albedo effects, and West Antarctic ice dynamics, specifically the role of ice shelf buttressing, dominate the uncertainty. The importance of these effects holds under both a high-end 5\u00b0C global warming scenario and another that limits global warming to 2\u00b0C. During the 22nd century the dominant drivers of uncertainty shift. Under the 5\u00b0C scenario, East Antarctic ice dynamics dominate the uncertainty in projections, driven by the possible role of ice flow instabilities. These dynamic effects only become dominant, however, for a temperature scenario above the Paris Agreement 2\u00b0C target and beyond 2100. Our findings identify key processes and factors that need to be addressed in future modeling and observational studies in order to reduce uncertainties in ice sheet projections.\nPlain Language Summary\uf0c1\nThe ice sheets covering Antarctica and Greenland are the largest source of future sea level rise but projections of their behavior are extremely uncertain. This is partly because of processes that are poorly understood in terms of their importance and potential contribution in the future. To investigate these issues and the relative importance of different processes in driving uncertainties in projections we solicited expert judgements from a group of scientists actively working on the topic. This exercise revealed that the dominant factors controlling the uncertainties depends on how far into the future one looks and the warming scenario assumed. For the 21st century, surface melting on the Greenland ice sheet is a dominant source of uncertainty alongside possible ice flow instabilities in West Antarctica. The East Antarctic Ice Sheet, the largest ice mass by an order of magnitude, does not play a significant role until the 22nd century and only for relatively high levels of future warming, based on the expert judgements. These findings quantify the relative role of different processes in driving uncertainty and indicate key areas for future focus to improve ice sheet projections and reduce the uncertainty in future sea level rise estimates.\nIntroduction\uf0c1\nSubstantial sea level rise (SLR) is considered to be one of the most serious consequences of climate warming (Bamber et al., 2019). The largest contributors and uncertainty in projecting future SLR are the ice sheets that cover Antarctica and Greenland (Bamber et al., 2019; Fox-Kemper et al., 2021). These ice sheets respond over timescales ranging from diurnal, for example, tides (Gudmundsson, 2006) to multi-millennial, for example, changes in climate at the end of the last glacial, 12,000 years BP (Huybrechts, 2002).\nObservations of the ice sheets at high temporal resolution, however, are limited to just the last few decades and may not be adequate to assess or constrain projections of deterministic numerical models (Fox-Kemper et al., 2021). Conditions at the base of an ice sheet are important for determining its sensitivity to external forcing (Ritz et al., 2015) but are unlikely ever to be definitively observable, due to inaccessibility. During the 1990s, satellite observations indicated relatively rapid and large amplitude changes in ice dynamics in the Amundsen Sea Embayment of West Antarctica and in Greenland that were not reproduced by the numerical models available at that time (Vaughan & Arthern, 2007). This required a re-evaluation of the sensitivity of the numerical models to external forcing. More recently, a process called the Marine Ice Cliff Instability (MICI) has been hypothesized to have contributed to SLR high-stands in the last interglacial and further back in time (DeConto & Pollard, 2016). Including MICI in numerical models can result in a dramatic increase in ice sheet sensitivity to external forcing (DeConto & Pollard, 2016; DeConto et al., 2021) but its importance to past ice sheet behavior and its relevance to the contemporary Antarctic Ice Sheet is unclear, and disputed (Bassis et al., 2021; Edwards et al., 2019).\nThese two examples of our limited understanding of ice sheet processes illustrate the problem of determining epistemic uncertainties associated with major natural systems that are under-sampled or sparsely observed (Attenberg et al., 2015). Other factors, such as poorly constrained model input data and boundary conditions, present significant challenges for deterministic modeling approaches. The limitations of ice sheet model projections are highlighted in a recent study comparing contemporary observations with an ensemble of state-of-the-art models and the spread in their hindcasts and projections (Aschwanden et al., 2021). Few models are able to reproduce the observations, and for the AIS, estimates are uncertain even on the sign of the contribution both in the recent past and near future.\nAdditionally, all three present-day ice sheets possess hypothesized instabilities (including the MICI), the details of which are outlined in Note S1 in Supporting Information S1. Note that we partition the Antarctic Ice Sheet into the West (WAIS) and East (EAIS) Antarctic Ice Sheets due to the different factors that influence their behavior (see Note S1 in Supporting Information S1 and other studies, e.g., Seroussi et al., 2020). Paleo-proxy records suggest that instabilities drove abrupt ice loss in the past (Liu et al., 2016; Wise et al., 2017). In all three cases, however, the instability thresholds are likely to be state- and rate-dependent and difficult, therefore, to constrain reliably. These factors create a further profound challenge for future SLR projections based on deterministic numerical modeling.\nNonetheless, projections and their uncertainties are required for quantifying SLR estimates for decision support (as are so-called \u201cworst-case\u201d and high-end scenarios (R. E. Kopp et al., 2019; Stammer et al., 2019)). Several approaches have been employed to tackle the gap between policy needs and limitations in deterministic model projections. These include, for example, a plausibility experiment addressing the question \u201cwhat is the most extreme physically-plausible dynamic response of the ice sheets\u201d (Pfeffer et al., 2008). That study concluded that a SLR in excess of 2 m by 2100CE was \u201cimplausible\u201d but without assigning a probability to their upper limit or any other estimates. Interestingly, their estimate for the upper bound for the SLR contribution from the AIS, 62 cm, is roughly half that of 105 cm from the first numerical model simulation that included the MICI process (DeConto & Pollard, 2016). This latter value has, however, been revised in the most recent simulations down to 60 cm for the 95th percentile (DeConto et al., 2021), which is similar to the plausibility limit estimated by Pfeffer et al. (2008) for the AIS. This suggests that the plausibility value in Pfeffer et al., 2008 may be an underestimate for a low probability (>99th percentile) response. Probabilistic approaches, conditioned on expert community assessment, expert judgement and process modeling have also been developed (Robert E. Kopp et al., 2014).", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber22.html"}
{"id": "0bbafafddd15-1", "text": "Nonetheless, projections and their uncertainties are required for quantifying SLR estimates for decision support (as are so-called \u201cworst-case\u201d and high-end scenarios (R. E. Kopp et al., 2019; Stammer et al., 2019)). Several approaches have been employed to tackle the gap between policy needs and limitations in deterministic model projections. These include, for example, a plausibility experiment addressing the question \u201cwhat is the most extreme physically-plausible dynamic response of the ice sheets\u201d (Pfeffer et al., 2008). That study concluded that a SLR in excess of 2 m by 2100CE was \u201cimplausible\u201d but without assigning a probability to their upper limit or any other estimates. Interestingly, their estimate for the upper bound for the SLR contribution from the AIS, 62 cm, is roughly half that of 105 cm from the first numerical model simulation that included the MICI process (DeConto & Pollard, 2016). This latter value has, however, been revised in the most recent simulations down to 60 cm for the 95th percentile (DeConto et al., 2021), which is similar to the plausibility limit estimated by Pfeffer et al. (2008) for the AIS. This suggests that the plausibility value in Pfeffer et al., 2008 may be an underestimate for a low probability (>99th percentile) response. Probabilistic approaches, conditioned on expert community assessment, expert judgement and process modeling have also been developed (Robert E. Kopp et al., 2014).\nStructured expert judgement (SEJ) using calibrated expert responses provides a formal, rigorous, reproducible and well-established framework for tackling this type of problem (Aspinall, 2010; Bamber & Aspinall, 2013; Oppenheimer et al., 2016). SEJ can capture epistemic uncertainties that are challenging for deterministic modeling approaches to identify (Attenberg et al., 2015). There is, for example, evidence available to the expert about past ice sheet behavior that is difficult to incorporate into a deterministic numerical model. An example of this is paleo sea level records that indicate a rapid SLR of 2\u20134 cm/yr for multiple centuries at around 14.6\u201314.3 Kyr BP, known as Meltwater Pulse 1A (Liu et al., 2016). This entailed an 8\u201315 m SLR which must have been associated with one or more ice sheet instabilities, but the precise source, dynamics and forcing mechanism(s) are unclear (Liu et al., 2016). The longer-term sea level record, covering glacial-interglacial cycles clearly shows a pattern of slow ice sheet growth and rapid decay, providing further evidence of instabilities in ice sheet behavior during or entering a warming inter-glacial period, such as the one we are in today. Further evidence from the paleo-sea level record comes from the last interglacial period when the sea level high stand was about 5\u201310 m above present-day (Gulev et al., 2021) and when global mean temperatures peaked at about 0.9\u00b0C and averaged 0.2\u00b0C above the pre-industrial value for global sea surface temperatures (Turney et al., 2020). These data provide the expert with evidence that ice sheets can generate high rates of SLR (circa 4 m/century) over centennial timescales and that they can be sensitive to relatively small temperature perturbations.\nPreviously, we reported the key findings from an SEJ elicitation undertaken in 2018 via two workshops, one held in the USA and the other in the UK, involving 22 experts in total (hereafter B19) (Bamber et al., 2019). The primary findings presented in B19 were the respective contributions to SLR from each ice sheet, for each time period and temperature change scenario considered. For the high temperature scenario (5\u00b0C by 2100; roughly equivalent to the high end emissions scenario RCP8.5), the 95th percentile ice sheet contribution to SLR was 178 cm at 2100CE. When combined with the contribution from glaciers and thermal expansion of the oceans this implied about a 10% chance of exceeding a SLR of 2 m by 2100CE (Bamber et al., 2019) (Figure 1), comparable with the plausibility experiment discussed earlier (Pfeffer et al., 2008) and the high-end scenario for SLR in the Sixth Assessment Report of the IPCC (Fox-Kemper et al., 2021). We present, in Figure 1, these findings expressed in terms of SLR as a function of time for different probabilities from 5 to 95%. This is useful for practitioners who will have different level of risk tolerance depending on the asset and hazard or who may be concerned about the probability of exceeding a specific value of SLR by a certain date (M. Oppenheimer et al., 2019). For example, the blue dashed lines indicate the probability of exceeding 1 m of SLR by 2100 (50%) or 2150 (\u223c90%) for the high temperature scenario. For 2 m of SLR it is 10% and 30%, respectively. The full table of values for 1%\u201399.9% are given in the Table S1 in Supporting Information S1.\nFigure 1: Projected substantial sea level rise (SLR) as a function of time for different probabilities between the 5th and 95th percentile for the High temperature scenario (5\u00b0C by 2100). The dashed blue lines indicate the probability of equaling or exceeding a given SLR at a specific date in the future: in this case 1 m by 2100 and 2150 (green) or 2 m (red) by those dates.\nWhat was not considered in B19 was which ice sheet processes are responsible for the projected upper SLR values, and which of these processes dominate the uncertainty in future projections as a function of temperature scenario and ice sheet. This requires further and deeper interrogation of the expert judgements at the process level. This is what is presented here. To our knowledge, this is the first quantitative analysis of the relative importance of the processes that influence the uncertainty in ice sheet projections using SEJ as opposed to deterministic modeling, which has various limitations as mentioned above.\nMaterials and Methods\uf0c1\nThe overall approach and methodology used in the SEJ was presented in detail in B19 and we, therefore, summarize only the salient points here. To determine the integrated SLR contribution for each ice-sheet the participating experts quantified their uncertainties for three key physical processes relevant to ice-sheet mass balance: accumulation (A), surface runoff (R) and discharge (D). They did this for each of the Greenland, West Antarctic, and East Antarctic ice sheets (GrIS, WAIS, and EAIS, respectively) and for two schematic temperature change scenarios. The first temperature trajectory (denoted L for low) stabilizes in 2100CE at +2\u00b0C above pre-industrial global mean surface air temperature (defined as the average for 1850\u20131900), and the second (denoted H for High) stabilizes in 2100 at +5\u00b0C (Figure S1 in Supporting Information S1). Projections of contributions to SLR from the three ice sheets were elicited for four dates: 2050, 2100, 2200, and 2300 CE.\nThe experts were weighted according to an impartial and rigorous approach that assesses each expert\u2019s informativeness and statistical accuracy via a set of seed or calibration questions from their field based on a well established methodology (Bamber et al., 2019; Cooke, 1991). The calibration questions were used to provide an impartial, repeatable measure of how well an expert is able to characterize their (un)certainty in the system under study (Cooke, 1991). The approach is similar to, for example, weighting a multi-member numerical model ensemble based on the ability to reproduce a desired property of the system being modeled. For each process, temperature and epoch, the experts provided a 5th, 50th, and 95th percentile sea level equivalent anomaly with respect to the 2000\u20132010 mean (i.e., a change from the historical value). Using the expert weights and Monte Carlo sampling, probability distributions were obtained for each process and ice sheet (Bamber et al., 2019). How these were then combined to produce a total SLR contribution is discussed in Note S2 in Supporting Information S1 but is not important here as we focus, in this paper, on the individual process probability distributions and, in particular, how their relative importance changes with time and temperature scenario.", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber22.html"}
{"id": "0bbafafddd15-2", "text": "Materials and Methods\uf0c1\nThe overall approach and methodology used in the SEJ was presented in detail in B19 and we, therefore, summarize only the salient points here. To determine the integrated SLR contribution for each ice-sheet the participating experts quantified their uncertainties for three key physical processes relevant to ice-sheet mass balance: accumulation (A), surface runoff (R) and discharge (D). They did this for each of the Greenland, West Antarctic, and East Antarctic ice sheets (GrIS, WAIS, and EAIS, respectively) and for two schematic temperature change scenarios. The first temperature trajectory (denoted L for low) stabilizes in 2100CE at +2\u00b0C above pre-industrial global mean surface air temperature (defined as the average for 1850\u20131900), and the second (denoted H for High) stabilizes in 2100 at +5\u00b0C (Figure S1 in Supporting Information S1). Projections of contributions to SLR from the three ice sheets were elicited for four dates: 2050, 2100, 2200, and 2300 CE.\nThe experts were weighted according to an impartial and rigorous approach that assesses each expert\u2019s informativeness and statistical accuracy via a set of seed or calibration questions from their field based on a well established methodology (Bamber et al., 2019; Cooke, 1991). The calibration questions were used to provide an impartial, repeatable measure of how well an expert is able to characterize their (un)certainty in the system under study (Cooke, 1991). The approach is similar to, for example, weighting a multi-member numerical model ensemble based on the ability to reproduce a desired property of the system being modeled. For each process, temperature and epoch, the experts provided a 5th, 50th, and 95th percentile sea level equivalent anomaly with respect to the 2000\u20132010 mean (i.e., a change from the historical value). Using the expert weights and Monte Carlo sampling, probability distributions were obtained for each process and ice sheet (Bamber et al., 2019). How these were then combined to produce a total SLR contribution is discussed in Note S2 in Supporting Information S1 but is not important here as we focus, in this paper, on the individual process probability distributions and, in particular, how their relative importance changes with time and temperature scenario.\nIn addition, we also investigate the role of various drivers of changes in D, A and R. To achieve this, we draw on additional qualitative information acquired during the 2018 SEJ (Note S3 in Supporting Information S1) supported, where available, with relevant literature related to developments in ice sheet process understanding and observations of past and recent ice sheet behavior. Specifically, we examine probability distributions for the SLR contributions of each ice sheet individually, considering the physical mechanisms that drive the response of those ice sheets via atmospheric, oceanic, or internal and surface forcings. In so doing, we quantify the rank-order of factors or processes that are influencing projection uncertainties in relation to each ice sheet independently, and where future research effort could reap the greatest benefits by addressing those sources of uncertainty. Some of the processes display non-Gaussian distributions with long upper tails, which can only be explored and characterized using a probabilistic approach (e.g., Figure 2).\nFigure 2: Indicative probability distribution plots for substantial sea level rise (SLR) contributions by 2100CE from the three ice sheets and for three physical processes, identified on the x-axis (runoff from East Antarctic Ice Sheet (EAIS) is omitted as this is presumed zero under either temperature rise scenario). Results are derived from expert elicitation for the 2100L (low +2\u00b0C) global temperature trajectory (left hand curves) and for the 2100H (high +5\u00b0C) global temperature trajectory (right hand curves); probability density curves are approximate and extend from values corresponding to a 99% chance of SLR being exceeded to a 1% chance of SLR being exceeded. The 5th, 95th and 50th percentile values of the distributions are shown by red and black rectangles, respectively.\nIce-Sheet Processes and Drivers\uf0c1\nAccumulation, A, and surface runoff, R, relate to what is termed the surface mass balance (SMB) of the ice sheet and are modulated, primarily, by atmospheric processes such as moisture content (affecting snowfall), air mass circulation, cloud cover, surface albedo, air temperature and wind speed (Paterson, 1994). Discharge, D, relates to the speed of the ice at the point that it reaches the ocean, known as the grounding line, where the ice first comes into contact with the ocean (Van der Veen, 1999). It is influenced by forces acting on the ice column including the buttressing effect of floating ice downstream of the grounding line (Van der Veen, 1999). Variations in ocean heat content, due to either changes in water temperature or circulation, can affect the strength of the buttressing force. Thus, discharge is primarily forced by the physical state of the ocean and SMB primarily by atmospheric conditions. In general, changes in discharge are related to ice dynamics, which have a longer time-constant compared to SMB and tend to vary smoothly in time. Surface melting can, however, affect calving rates and ice shelf collapse by hydrofracture and sub-shelf melting so that each process is not necessarily entirely independent (Lai et al., 2020). These correlations may be important when assessing the integrated response of the ice sheet to external forcing (Bamber et al., 2019) but here we consider each process independently as a function of the forcing.\nSome processes that affect A, R, and D are comparatively well understood, such as the relationship between ice thickness and strain rate in the ice, while others are either poorly understood or poorly constrained. In particular, all three ice sheets may possess thresholds in their behavior beyond which an irreversible response in part of the ice sheet is initiated. However, the precise location of the threshold in parameter space is highly uncertain (Bassis et al., 2021; DeConto & Pollard, 2016; Edwards et al., 2019; Gregory et al., 2004, 2020; Joughin et al., 2014; Seroussi et al., 2020). The relative importance of various factors influencing A, R, and D were elicited as part of the SEJ workshops (Note S3 in Supporting Information S1 and (Bamber et al., 2019)).\nResults and Discussion\uf0c1\nIn the following discussion we consider the 5th, 50th, and 95th percentile SLR contribution values for different processes and the numbers are presented in that order in centimeters. Figures 2 and 3 are distribution plots that approximate the probability density functions, plotted along the y axis for 2100 and 2200, respectively. Similar plots for 2050 and 2300, alongside the tabulated percentile values are provided in Figures S2 and S3 in Supporting Information S1.\nFigure 3: As for Figure 2 but for 2200.\nFor 2100L, the dominant processes in terms of SLR contribution and uncertainty are GrIS runoff, [0.06, 4.4, 36] cm and WAIS dynamics, [0, 4.8, 42] cm, respectively, although EAIS dynamics becomes a significant factor at the 95th percentile (Table 1). The total SLR from the ice sheets for 2100L is [\u22125, 18, 73] cm. Thus, GrIS runoff and WAIS dynamics account for approximately half of the median total contribution from the ice sheets. The large 5th\u201395th percentile credible range for GrIS runoff is surprising given that SMB is considered to be a relatively well understood and reliably modeled component of ice sheet mass balance (Hofer et al., 2019). It is noteworthy, however, that both the modeled runoff magnitude and trend from a recent SMB intercomparison exercise varied by a factor 3 between models despite using identical climate forcing fields for 1980\u20132012 (Hofer et al., 2019). Thus, while the process may be well understood, there remain tuneable parameters in the models, such as albedo, that have a controlling influence on the sensitivity of runoff to changes in the climate forcing (Hofer et al., 2019). In addition, the record mass loss in 2019 over the GrIS, more than double the mean for 2003\u20132018, was driven primarily by exceptionally high runoff rather than any other process (Sasgen et al., 2020). As a consequence, we examine in further detail the potential factors that might be causing the large uncertainty in runoff for the GrIS.", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber22.html"}
{"id": "0bbafafddd15-3", "text": "Results and Discussion\uf0c1\nIn the following discussion we consider the 5th, 50th, and 95th percentile SLR contribution values for different processes and the numbers are presented in that order in centimeters. Figures 2 and 3 are distribution plots that approximate the probability density functions, plotted along the y axis for 2100 and 2200, respectively. Similar plots for 2050 and 2300, alongside the tabulated percentile values are provided in Figures S2 and S3 in Supporting Information S1.\nFigure 3: As for Figure 2 but for 2200.\nFor 2100L, the dominant processes in terms of SLR contribution and uncertainty are GrIS runoff, [0.06, 4.4, 36] cm and WAIS dynamics, [0, 4.8, 42] cm, respectively, although EAIS dynamics becomes a significant factor at the 95th percentile (Table 1). The total SLR from the ice sheets for 2100L is [\u22125, 18, 73] cm. Thus, GrIS runoff and WAIS dynamics account for approximately half of the median total contribution from the ice sheets. The large 5th\u201395th percentile credible range for GrIS runoff is surprising given that SMB is considered to be a relatively well understood and reliably modeled component of ice sheet mass balance (Hofer et al., 2019). It is noteworthy, however, that both the modeled runoff magnitude and trend from a recent SMB intercomparison exercise varied by a factor 3 between models despite using identical climate forcing fields for 1980\u20132012 (Hofer et al., 2019). Thus, while the process may be well understood, there remain tuneable parameters in the models, such as albedo, that have a controlling influence on the sensitivity of runoff to changes in the climate forcing (Hofer et al., 2019). In addition, the record mass loss in 2019 over the GrIS, more than double the mean for 2003\u20132018, was driven primarily by exceptionally high runoff rather than any other process (Sasgen et al., 2020). As a consequence, we examine in further detail the potential factors that might be causing the large uncertainty in runoff for the GrIS.\nTable 1: 5th, 50th, and 95th Percentile Elicited Estimates for SLR Contributions by Each Ice Sheet and Each Process (G Denotes GrIS, W WAIS, E EAIS; A Denotes Accumulation, R Runoff, D Discharge). Note: GrIS, Greenland ice sheet; EAIS, East Antarctic Ice Sheet; SLR, sea level rise; WAIS, West Antarctic Ice Sheet. The orange shaded cells denote values that are greater than 25% of the total combined SLR contribution from the ice sheets in the final column. The totals are not the sum of the components because of dependencies between processes and ice sheets (see Note S3 in Supporting Information S1). NB all numbers in the table exclude the 2000\u20132010 baseline of 0.7 mm/yr because this was added post-hoc to the values elicited from the experts (Bamber et al., 2019).\nFor each of the three primary processes elicited (D, A, R), there are several potential atmospheric, oceanic or ice-sheet variables that could act as drivers of change. To identify which factors were considered important, during the SEJ workshops we asked the experts to rank climate drivers in relation to the primary ice sheet processes. Here, qualitative information about the rank order of the drivers was obtained rather than the quantiles elicited for the three processes: D, A, and R (see Note S3 and Figures S4\u2013S6 in Supporting Information S1). Not all experts answered all sections of the rationale questionnaire and our findings are based, therefore, on the qualitative responses that were obtained. As such, these should be regarded as indicative of the relative importance of different drivers.\nAs part of the elicitation, factors influencing A and R were grouped into SMB processes that could be modified by changes in atmospheric moisture or circulation, albedo changes and changes in summer sea ice extent; the influences of these factors were elicited separately for floating and for grounded ice (Figure 4 and Figure S4 in Supporting Information S1).\nFigure 4: Expert judgements on the relative role to the overall uncertainty for six drivers of changes in ice dynamics: buttressing by ice shelves, basal traction, transverse stresses, hydrofracturing, ice cliff instability, and dissipation after iceberg formation at exit gates; and two drivers for changes in surface mass balance (SMB): atmospheric moisture and circulation, and albedo. Note that buttressing is directly related to the initiation and evolution of MISI and also hydrofracture and ice cliff instability. Descriptive definitions for these factors are provided in the Note S3 in Supporting Information S1. SMB processes were considered separately for grounded and floating ice and shown here are the results for the former only. This figure is for the three ice sheets at 2100, 2200, and 2300 for the High temperature scenario only. SMB and D are scaled according to their relative contribution to the integrated ice sheet substantial sea level rise. The equivalent plot for the Low temperature scenario including floating ice is shown in Figure S4 in Supporting Information S1 and for the High scenario including ice shelves in Figure S5 in Supporting Information S1.\nFrom these expert judgements, changes in albedo are determined to be the dominant control on the SMB response of the GrIS (Figure 4). This is not surprising as surface albedo is the single most important variable in modulating the surface energy balance of the GrIS and, as a consequence, melt rates (Fitzgerald et al., 2012). Nonetheless, that GrIS runoff has a comparable uncertainty range to WAIS discharge for both temperature scenarios for 2100 was an unexpected result and we examine, therefore, both the modeling and observational evidence that supports this finding.\nAlbedo is sensitive to several variables that are poorly constrained in climate models, including changes in cloud cover characteristics and extent (Hofer et al., 2019), impurity and algal content of the surface (Tedstone et al., 2020), and the seasonality of changes in precipitation and air temperature. For example, most General Circulation Models (GCMs) project the largest temperature increase in the Arctic to occur in winter (Koenigk et al., 2013) as reflected by the observational record (Hanna et al., 2021), resulting in increased winter precipitation. This can act to reduce runoff by depositing a high-albedo insulating snow layer in winter (Day et al., 2013). Conversely, increased summertime precipitation can have the opposite effect as it results in greater rainfall, which acts to accelerate melting and reduce the surface albedo (Fausto et al., 2016). Indeed, non-radiative energy fluxes such as rain are generally poorly captured in GCMs, and hence also regional climate models, but will become increasingly important as temperatures rise above the freezing point of water (Fausto et al., 2016). Hence, seasonal atmospheric changes play a critical role in modulating R, but are, in general, not well constrained by GCMs.\nChanges in future cloud cover are inconsistent between climate models and these discrepancies can have a greater impact on R than the difference in radiative forcing between RCP2.6 and RCP8.5, for example, (Hofer et al., 2019). Since 1985, despite a step-change increase in D in about 2005, SMB has dominated the mass loss trends on the GrIS (King et al., 2020), and the ice sheet currently dominates the land ice contribution to SLR (Sasgen et al., 2020). These trends are generally not well captured by ice sheet models forced by GCM output (Goelzer et al., 2020). For example, the ensemble mean SLR for the GrIS under RCP8.5 from the latest ice sheet model intercomparison exercise (ISMIP6) is 9.0 cm with a 5th\u201395th range of \u00b15.0 cm by 2100 (Goelzer et al., 2020). RCP8.5 results in a warming over Greenland by 2100 of about 9\u201310\u00b0C above pre-industrial, yet the mean present-day rate of mass loss from the ice sheet for 2010\u20132019 is already equivalent to 8 cm/century (Sasgen et al., 2020), suggesting that the models used have a weak sensitivity to climate forcing relative to recent observations. Further, a recent study using a glacier-resolving ice sheet model combined with a comprehensive uncertainty analysis obtained a 16th\u201384th (equivalent to one sigma) percentile range of 14\u201333 cm for RCP8.5 by 2100 for the GrIS (Aschwanden et al., 2019). The authors of that study concluded that the uncertainty was driven by the climate forcing and surface processes, in agreement with our interpretation of the expert judgements presented here (c.f. Figures 2 and 4). We conclude that these are the primary factors responsible for the elicited uncertainties in GrIS runoff, which are comparable with WAIS discharge for both 2100L and 2100H scenarios.", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber22.html"}
{"id": "0bbafafddd15-4", "text": "Changes in future cloud cover are inconsistent between climate models and these discrepancies can have a greater impact on R than the difference in radiative forcing between RCP2.6 and RCP8.5, for example, (Hofer et al., 2019). Since 1985, despite a step-change increase in D in about 2005, SMB has dominated the mass loss trends on the GrIS (King et al., 2020), and the ice sheet currently dominates the land ice contribution to SLR (Sasgen et al., 2020). These trends are generally not well captured by ice sheet models forced by GCM output (Goelzer et al., 2020). For example, the ensemble mean SLR for the GrIS under RCP8.5 from the latest ice sheet model intercomparison exercise (ISMIP6) is 9.0 cm with a 5th\u201395th range of \u00b15.0 cm by 2100 (Goelzer et al., 2020). RCP8.5 results in a warming over Greenland by 2100 of about 9\u201310\u00b0C above pre-industrial, yet the mean present-day rate of mass loss from the ice sheet for 2010\u20132019 is already equivalent to 8 cm/century (Sasgen et al., 2020), suggesting that the models used have a weak sensitivity to climate forcing relative to recent observations. Further, a recent study using a glacier-resolving ice sheet model combined with a comprehensive uncertainty analysis obtained a 16th\u201384th (equivalent to one sigma) percentile range of 14\u201333 cm for RCP8.5 by 2100 for the GrIS (Aschwanden et al., 2019). The authors of that study concluded that the uncertainty was driven by the climate forcing and surface processes, in agreement with our interpretation of the expert judgements presented here (c.f. Figures 2 and 4). We conclude that these are the primary factors responsible for the elicited uncertainties in GrIS runoff, which are comparable with WAIS discharge for both 2100L and 2100H scenarios.\nIn Table 1, the dominant processes driving the median and 95th percentile SLR are highlighted in orange. For both temperature scenarios and all epochs GrIS runoff and WAIS dynamics are the two processes dominating the uncertainty. EAIS dynamics becomes important mainly for the High temperature scenario except for 2300L where the 95th percentile value is about 26% of the total SLR. This suggests that improvements in modeling these two processes would reduce SLR projection uncertainty. This is, however, not limited to improvements in ice sheet modeling but also in reducing uncertainties in the driving climate forcing that influences GrIS runoff on the one hand and WAIS dynamics on the other. The former relates to atmospheric processes while the latter is primarily oceanic.\nSome drivers shown in Figure 4 are not independent of others (see also Note S3 in Supporting Information S1). Ice shelf buttressing, for example, will be affected by hydrofracture, ice cliff instability and dissipation of icebergs, which are also the three processes that control the MICI. The results are shown for each ice sheet and for three time periods, 2100, 2200, and 2300. For the GrIS, basal traction is considered the dominant process in influencing discharge for all time periods. This is not unexpected, as floating tongues and ice shelves are limited in extent in Greenland. The second most important process is buttressing but this decreases with time as the ice sheet shrinks in size, its marine margins recede and floating tongues disappear. For 2100L and H, GrIS dynamics provides the third largest uncertainty, after GrIS runoff and WAIS discharge (Figure 2). By 2200, however, it has been overtaken by WAIS accumulation (2200L and 2200H) and EAIS dynamics for 2200H (Figure 4), most likely because of a retreating marine margin over time.\nFor 2100H, WAIS discharge [0.1, 15, 91] cm and GrIS runoff [0.2, 11, 74] cm again account for close to half the median total ice sheet contribution of 51 cm [\u22121, 43, 170] and dominate the uncertainty with 5th\u201395th percentile credible ranges of 91 and 74 cm, respectively. However, for this high-end warming scenario, which after accounting for polar amplification, implies a temperature increase over the Antarctic Ice Sheet of about +7\u00b0C to +10\u00b0C, EAIS dynamics is responsible for the third largest uncertainty with a 5th\u201395th percentile range of 54 cm (Table 1). For 2100H relative to 2100L, the 5th\u201395th percentile credible range has roughly doubled for WAIS discharge and GrIS runoff, but approximately trebled for EAIS dynamics. This indicates that the experts consider that instabilities in the latter could be triggered by 2100 under +5\u00b0C warming, while for both temperature scenarios the experts infer it is plausible that the marine ice sheet instability (MISI) would be invoked for the WAIS with the amplitude of the response sensitive to temperature. This is in contrast with the latest ice sheet model intercomparison project for Antarctica, where the sign and sensitivity of the WAIS response to warming scenario, for example, varies between models (Seroussi et al., 2020).\nFor the WAIS, buttressing is the dominant ice sheet process for all the time periods considered (Figure 4), reflecting the view that this is the primary control on the MISI and grounding line migration rates (Schoof, 2007). However, its relative importance declines from 2100 to 2300, with ice cliff instability increasing in significance, presumably as ice shelves recede or collapse, leaving exposed ice cliffs\u2014close to the grounding line\u2014that may be susceptible to ice cliff failure (Seroussi et al., 2020). The MISI is driven by changes in the amount of buttressing afforded by floating ice shelves that \u201cprotect\u201d the inland, grounded ice. This, in turn, is sensitive to sub-shelf melting which is affected by changes in ocean temperature and/or circulation. The experts considered two drivers for changes in ocean circulation in the elicitation process. These were alterations to: (a) circumpolar deep water intrusion onto the continental shelf (CDW) and (b) the meridional overturning circulation (AMOC). Of these, experts considered the first to be by far the most important for influencing Antarctic sub-shelf melt rates over all the time periods and both temperature scenarios. For the GrIS, changes in the AMOC were considered most important as the former two are primarily related to Southern Ocean circulation (Figure S6 in Supporting Information S1).\nGravitational, rotational and solid Earth deformation (collectively GRD) effects have been hypothesized to influence the stability of grounding lines on retrograde slopes (Whitehouse et al., 2019) and were considered as part of the rationale analysis but have been demonstrated to be of second order importance (Larour et al., 2019) (Note S4 and Figure S7 in Supporting Information S1). Over millennial timescales they may, however, be of first-order significance (Pan et al., 2021).\nFor the EAIS, the experts concluded that buttressing is the dominant and primary factor for all time periods (Figure 4). It is interesting to note that for 2200H the 95th percentile estimate for EAIS discharge is larger than any other ice sheet process and hydro-fracture is considered to be increasingly important (Table S2 in Supporting Information S1) and also, but to a lesser extent, for 2100H (Figure 4). This is consistent with recent evidence that suggests that as much as 60% of Antarctic ice shelf area is vulnerable to hydrofracture from surface meltwater, including almost all of the Filchner Ronne, Ross and Amery ice shelves that buttress large drainage basins in East Antarctica (Lai et al., 2020).\nConversely, because runoff is limited over both the WAIS and EAIS at present, it is considered to play a limited role in direct mass loss (as opposed to an indirect role in accelerating ice shelf collapse) under the high temperature scenario up to 2100 (Figure 2 and Table 1) and even up to 2200 (Figure 2, Table 1). Hence, albedo changes are considered to be of limited importance over grounded ice for both Antarctic ice sheets. In this case, it is changes in moisture content and circulation that are identified as the dominant control on SMB. Thus, for example, increased accumulation of the WAIS has a 5% probability of mitigating the ice sheet contribution to SLR by at least 65 cm for 2200H. This is also reflected in ice sheet model simulations using climate model output, particularly for the EAIS (Seroussi et al., 2020). The experts conclude that changes in summer sea ice extent will have some impact on ice shelf SMB for all three ice sheets up to 2200 (Figures S4 and S5 in Supporting Information S1), with the largest contribution over the GrIS.", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber22.html"}
{"id": "0bbafafddd15-5", "text": "For the EAIS, the experts concluded that buttressing is the dominant and primary factor for all time periods (Figure 4). It is interesting to note that for 2200H the 95th percentile estimate for EAIS discharge is larger than any other ice sheet process and hydro-fracture is considered to be increasingly important (Table S2 in Supporting Information S1) and also, but to a lesser extent, for 2100H (Figure 4). This is consistent with recent evidence that suggests that as much as 60% of Antarctic ice shelf area is vulnerable to hydrofracture from surface meltwater, including almost all of the Filchner Ronne, Ross and Amery ice shelves that buttress large drainage basins in East Antarctica (Lai et al., 2020).\nConversely, because runoff is limited over both the WAIS and EAIS at present, it is considered to play a limited role in direct mass loss (as opposed to an indirect role in accelerating ice shelf collapse) under the high temperature scenario up to 2100 (Figure 2 and Table 1) and even up to 2200 (Figure 2, Table 1). Hence, albedo changes are considered to be of limited importance over grounded ice for both Antarctic ice sheets. In this case, it is changes in moisture content and circulation that are identified as the dominant control on SMB. Thus, for example, increased accumulation of the WAIS has a 5% probability of mitigating the ice sheet contribution to SLR by at least 65 cm for 2200H. This is also reflected in ice sheet model simulations using climate model output, particularly for the EAIS (Seroussi et al., 2020). The experts conclude that changes in summer sea ice extent will have some impact on ice shelf SMB for all three ice sheets up to 2200 (Figures S4 and S5 in Supporting Information S1), with the largest contribution over the GrIS.\nFinally, we asked the experts whether they considered the recent (decadal) trends in mass balance for the GrIS and WAIS, as observed from satellite data, were due predominantly to internal variability (IV) or external forcing (EF) (Figure 5). This is an important question for four reasons. First, these same observations are used to initialize numerical ice sheet models (DeConto et al., 2021; Seroussi et al., 2020). To do this, it is necessary to assign the recent trends to either IV or to EF, or some combination of the two. That is because, as for GCMs, ice sheet models are not aimed at reproducing the conditions of one particular day, a season or a year, but to model climatically forced trends. Second, this is a central question for process understanding and also for probabilistic approaches that are conditioned on the observations, as are semi empirical models (Little et al., 2013). Third, recent observations have been used to calibrate tuneable parameters in an ice sheet model (DeConto et al., 2021). This requires assigning the trend in the observations to IV or EF. Note that model calibration and initialization are not, in general, the same process. Fourth, observations are an important tool for verifying the performance of a numerical model but only if the signal(s) in the observations can be assigned to some combination of IV and EF (Randall et al., 2007). The experts concluded that the trends in Greenland are predominantly driven by EF, whereas for the WAIS there was no consensus and no certainty (Figure 5) as was also the case in a previous SEJ exercise (Bamber & Aspinall, 2013).\nFigure 5: Expert judgements for whether internal variability (IV) or external forcing (EF) is the dominant driver of recent (last two decade) observational trends in mass balance for the Greenland Antarctic ice sheets (GrIS) and West Antarctic Ice Sheet (WAIS).\nConclusions\uf0c1\nThe findings just described, which are drawn from the SEJ exercise presented in B19, are generally consonant with recently reported observational evidence but are in sharp contrast to the latest ice sheet model intercomparison analyses in terms of both the dominant drivers of uncertainty and their magnitudes (Goelzer et al., 2020; Seroussi et al., 2020). An important contribution we have been able to provide through our analysis is to express these influences\u2014on sea level projections and associated uncertainties\u2014in probabilistic terms. We can, thus, quantify the relative role of different processes not just for their median response but also for the tails of the distributions, which are lower probability but higher impact. Where the distributions display high kurtosis (e.g., WAIS dynamics and GrIS runoff) the median and standard deviation do not capture the full uncertainty and risk associated with that process. In IPCC assessment reports prior to the AR6 (Fox-Kemper et al., 2021) this has been a major limitation in their sea level rise projections, which were limited to the likely range, equivalent to \u00b1 one standard deviation (Bamber et al., 2019).\nWe found that for all time periods out to 2300 CE, quantified uncertainties are dominated by WAIS dynamics and GrIS runoff. The former is influenced by the marine ice sheet instability, MISI, which in turn, is influenced by changes in ocean circulation and heat content in ways that are not well understood or, as yet, adequately modeled (Seroussi et al., 2020). Subglacial topography has an important controlling influence on the initiation of the MISI and how rapidly it evolves but is imperfectly known for many key sectors of the WAIS (Cornford et al., 2020; Rosier et al., 2021). GrIS runoff is relatively well understood as a process, but is sensitive to climate drivers that are poorly captured in GCMs and, therefore, imperfectly represented in future projections. For example, changes in cloud properties, such as optical depth, altitude and seasonality, can have a dramatic impact on melt rates but are inconsistent between GCMs and are known to be poorly modeled in general (Hofer et al., 2019). Runoff is also sensitive to albedo. Relatively small concentrations of both inorganic and organic material on the ice sheet surface can have a significant impact on albedo and, therefore, melting, but this is a factor that is yet to be included in ice sheet models (Williamson et al., 2020). The seasonality of both temperature and precipitation changes over Greenland has a strong influence on SMB trends but is also not consistently projected by GCMs. Reducing future uncertainties in ice sheet projections will require, therefore, improvements in ice sheet process understanding and modeling of those processes as well as more robust projections of the climate forcing for a given greenhouse gas emissions pathway.\nAn important challenge, building on this analysis, is to extend and refine our expert judgement elicitation so that we can better quantify critical parameters, variables and processes related to model projections of ice sheet contributions to sea level rise. For instance, while the uncertainties in our experts\u2019 assessments likely include some elements that relate to processes that are not formally identified in the present exercise, an elicitation could be designed that would enable us to disaggregate these complexities, and their associated uncertainties, in more detail. This would allow us to quantify the role of additional factors in limiting process certainty. As is usual with structured elicitations of this type, such additional findings\u2014based on informed expert judgements\u2014will almost certainly highlight specific topics meriting further research and analysis. As discussed above, this is not limited to ice sheet processes but also to the climate projections used to force them.\nSupporting Information\uf0c1\nIce Sheet Instabilities\uf0c1\nFor the Greenland Ice Sheet (GrIS), a potential key threshold relates to a concept termed the \u2018small ice cap instability\u2019 (Maqueda et al., 1998). This instability originates from a positive feedback between changes in surface elevation and increased runoff, i.e. it is linked to surface mass balance (SMB). As the ice sheet loses mass, the surface elevation lowers, resulting in warmer surface temperature and increased melting. When the amount of surface melting exceeds the total accumulation, via snowfall, the ice sheet is no longer sustainable in the long-term. The increase in global temperature required to pass this threshold has been estimated to lie between +0.8 to +3.2 \u030aC above pre-industrial with a best estimate of +1.6 \u030aC (Robinson et al., 2012). Recent evidence from satellite observations suggests that the GrIS had reached a state of persistent ice loss by about 2005 (King et al., 2020) and that it experienced its largest recorded mass loss, equivalent to 1.5 mm sea level equivalent, in 2018. About 60% of the mass loss over the last three decades is attributable to SMB and the rest to discharge (King et al., 2020; Sasgen et al., 2020). Whether the GrIS would completely disintegrate or reach a new, smaller metastable state is a topic of current debate (Gregory et al., 2020; Robinson et al., 2012).", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber22.html"}
{"id": "0bbafafddd15-6", "text": "An important challenge, building on this analysis, is to extend and refine our expert judgement elicitation so that we can better quantify critical parameters, variables and processes related to model projections of ice sheet contributions to sea level rise. For instance, while the uncertainties in our experts\u2019 assessments likely include some elements that relate to processes that are not formally identified in the present exercise, an elicitation could be designed that would enable us to disaggregate these complexities, and their associated uncertainties, in more detail. This would allow us to quantify the role of additional factors in limiting process certainty. As is usual with structured elicitations of this type, such additional findings\u2014based on informed expert judgements\u2014will almost certainly highlight specific topics meriting further research and analysis. As discussed above, this is not limited to ice sheet processes but also to the climate projections used to force them.\nSupporting Information\uf0c1\nIce Sheet Instabilities\uf0c1\nFor the Greenland Ice Sheet (GrIS), a potential key threshold relates to a concept termed the \u2018small ice cap instability\u2019 (Maqueda et al., 1998). This instability originates from a positive feedback between changes in surface elevation and increased runoff, i.e. it is linked to surface mass balance (SMB). As the ice sheet loses mass, the surface elevation lowers, resulting in warmer surface temperature and increased melting. When the amount of surface melting exceeds the total accumulation, via snowfall, the ice sheet is no longer sustainable in the long-term. The increase in global temperature required to pass this threshold has been estimated to lie between +0.8 to +3.2 \u030aC above pre-industrial with a best estimate of +1.6 \u030aC (Robinson et al., 2012). Recent evidence from satellite observations suggests that the GrIS had reached a state of persistent ice loss by about 2005 (King et al., 2020) and that it experienced its largest recorded mass loss, equivalent to 1.5 mm sea level equivalent, in 2018. About 60% of the mass loss over the last three decades is attributable to SMB and the rest to discharge (King et al., 2020; Sasgen et al., 2020). Whether the GrIS would completely disintegrate or reach a new, smaller metastable state is a topic of current debate (Gregory et al., 2020; Robinson et al., 2012).\nThe West Antarctic Ice Sheet (WAIS) is termed a marine ice sheet because most of the bedrock it rests on lies below sea level, in some places by as much as 2,500 m (Bamber et al., 2009). In addition, the ice sheet also rests, predominantly, on a retrograde bed slope: one that deepens inland. These two conditions are hypothesised to be necessary (but not sufficient) to invoke the Marine Ice Sheet Instability (MISI) whereby the grounding line is inherently unstable and can rapidly migrate inland (Schoof, 2007; Seroussi et al., 2020). Recent evidence indicates that part of the WAIS may already be experiencing irreversible grounding line retreat as a result of MISI (Joughin et al., 2014). Unlike the GrIS instability mechanism, the WAIS MISI is a dynamic response driven predominantly by ocean forcing.\nThe East Antarctic Ice Sheet (EAIS) has several marine basins, which could be vulnerable to oceanic erosion but are currently protected by regions of ice grounded above sea level or on prograde bed slopes (Bamber et al., 2009). For the two major marine basins, Aurora and Wilkes, this \u201csafety band\u201d is just tens of kilometers wide (Fig S1 and S2 of (Bamber et al., 2009). In addition, the two largest ice shelves in Antarctica, the Filchner Ronne and Ross, buttress large catchments in both the WAIS and EAIS. Inclusion of enhanced calving via hydrofracture and ice cliff failure (both components that contribute to marine ice cliff instability, MICI) in numerical models can lead to a significant loss of ice from the EAIS by 2100CE under RCP8.5 conditions (DeConto and Pollard, 2016). More recently, the rate of mass loss has been revised downward using updated climate forcing and calibration data (DeConto et al., 2021). Nonetheless, significant mass loss was predicted from the EAIS over the present century for RCP8.5 and a recent study suggests that as many as 60% of Antarctic ice shelves - which buttress inland ice - are vulnerable to hydrofracture if inundated by meltwater (Lai et al., 2020).\nExplaining variation between ice sheets\uf0c1\nIn a given year, under a given temperature scenario, sea level rise (SLR) from the ice sheets is simply the sum of contributions from EAIS, WAIS and GrIS:\nSLR(ice sheets) = EAIS + WAIS + GrIS\nA natural question is how much the uncertainty of each ice sheet contribution influences the uncertainty in enumerating SLR(ice sheets). Suppose we could observe EAIS=x. Given this information our expectation for SLR is represented as E(SLR | EAIS = x). As we let x vary over its range, E(SLR | EAIS = x) will also vary. The question is, by how much? If EAIS had no effect on SLR, then the expected SLR value would not depend on x at all and would always be equal to the unconditional expectation E(SLR). On the other hand, if E(SLR | EAIS = x) varied substantially, that would mean that the value of EAIS has a big role in determining the value of SLR. We can capture that effect by comparing the variance of E(SLR | EAIS = x) as x varies, to the unconditional variance of SLR. This ratio is called (inappropriately) the \u2018correlation ratio\u2019 (CR), though is better thought of as the fraction of variance of SLR explained by variations in EAIS:\nCR (SLR, EAIS) = Var(E(SLR | EAIS = x)) / Var(SLR).\nWhen the variation of EAIS explains all the variation in SLR, then the above ratio is one.\nFor contributions from the three ice sheets, EAIS, WAIS and GrIS, if their variations are independent then:\nVar(SLR) = Var(EAIS) + Var(WAIS) + Var(GrIS)\nand the correlation ratios sum to one.\nHowever, if the variations in individual ice sheet contributions are positively correlated then the sum of the correlation ratios is greater than one. In this case knowing, say, that EAIS = 2m tells us something about contributions from WAIS and GrIS. The following table gives the correlation ratios calculated from the expert judgements for High and Low temperature stabilization scenarios (H, L), for 2300CE and 2100CE.\nFraction of variance of SLR explained by each ice sheet\n2300H\n2300L\n2100H\n2100L\nEAIS\n0.75\n0.41\n0.49\n0.30\nGrIS\n0.19\n0.32\n0.34\n0.39\nWAIS\n0.61\n0.63\n0.67\n0.57\nsum\n1.55\n1.36\n1.49\n1.26\nWe observe that in all cases the correlation ratios sum to more than one, and that exceedances are greater for High temperature stabilization scenarios. This suggests the experts jointly consider ice sheet responses could be more strongly correlated under higher temperature trajectories, and possibly become even more so further ahead into the future. For instance, there is the implication that, under the High temperature scenario, variations in EAIS contributions could be the major influence on total SLR uncertainty by 2300CE (CR 0.49 \u2192 0.75), while the related effect of GrIS variations will be much reduced (CR 0.34 \u2192 0.19)\nWe do not extend this type of analysis down to the physical ice mass processes operating at the individual ice sheets: those processes are inter-dependent, sometimes with tail correlations, and each expert assessed such dependences for themself when making judgements on ice sheet contributions. While it might be possible to decompose, expert by expert, the variance of SLR into components \u2013 expressing numerically the way these processes appear to act at each individual ice sheet \u2013 more insight is gained by examining their joint appraisal of importance rankings for these drivers (Bamber et al, 2019).\nDefinitions of driving processes included in the rationale questionnaire\uf0c1\nSix ice dynamic drivers and three SMB drivers were included in the expert rationale questionnaire, designed to provide an indication of the rationales for the uncertainties for each of the three ice sheet process elicited: accumulation, A, and runoff, R, (contributing to SMB) and discharge, D, across the grounding line. In the case of the rationale questionnaire, quantile values were not elicited but instead the relative rank order of each factor in driving the change in A, R or D (Bamber et al, 2019). Here, we provide brief descriptors for these drivers\nButtressing, B:", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber22.html"}
{"id": "0bbafafddd15-7", "text": "Fraction of variance of SLR explained by each ice sheet\n2300H\n2300L\n2100H\n2100L\nEAIS\n0.75\n0.41\n0.49\n0.30\nGrIS\n0.19\n0.32\n0.34\n0.39\nWAIS\n0.61\n0.63\n0.67\n0.57\nsum\n1.55\n1.36\n1.49\n1.26\nWe observe that in all cases the correlation ratios sum to more than one, and that exceedances are greater for High temperature stabilization scenarios. This suggests the experts jointly consider ice sheet responses could be more strongly correlated under higher temperature trajectories, and possibly become even more so further ahead into the future. For instance, there is the implication that, under the High temperature scenario, variations in EAIS contributions could be the major influence on total SLR uncertainty by 2300CE (CR 0.49 \u2192 0.75), while the related effect of GrIS variations will be much reduced (CR 0.34 \u2192 0.19)\nWe do not extend this type of analysis down to the physical ice mass processes operating at the individual ice sheets: those processes are inter-dependent, sometimes with tail correlations, and each expert assessed such dependences for themself when making judgements on ice sheet contributions. While it might be possible to decompose, expert by expert, the variance of SLR into components \u2013 expressing numerically the way these processes appear to act at each individual ice sheet \u2013 more insight is gained by examining their joint appraisal of importance rankings for these drivers (Bamber et al, 2019).\nDefinitions of driving processes included in the rationale questionnaire\uf0c1\nSix ice dynamic drivers and three SMB drivers were included in the expert rationale questionnaire, designed to provide an indication of the rationales for the uncertainties for each of the three ice sheet process elicited: accumulation, A, and runoff, R, (contributing to SMB) and discharge, D, across the grounding line. In the case of the rationale questionnaire, quantile values were not elicited but instead the relative rank order of each factor in driving the change in A, R or D (Bamber et al, 2019). Here, we provide brief descriptors for these drivers\nButtressing, B:\nThis is the influence of back stresses on the grounded ice from floating ice shelves. Discharge is determined by the force balance acting at the grounding line. This force balance is comprised of several terms. On one side is the gravitational driving stress that results in ice flow. Opposing this are transverse stresses (TS) such as at the margins of the glacier or ice stream, basal traction (BT) and the backstress at the grounding line due to the buttressing effect of floating ice.\nBasal traction, BT:\nSee Buttressing. BT is the resistive force between the glacier bed and the ice in contact with it. For a frozen bed, this term is not relevant but fast-moving ice at the margins of the ice sheets the bed is not frozen, water is present, and basal sliding occurs. For ice streams, as much as 90% of the ice motion can be due to basal sliding, which is controlled by BT.\nTransverse stresses, TS:\nSee Buttressing. TS are largely determined by the large difference in ice speed between the slow-flow margins of a glacier and the fast-moving central trunk. TS act as a resistive force to ice motion and are influenced by damage characteristics of the ice, which in turn is a function of strain history and ice rheology.\nHydrofracture, HF:\nHF is a process that enhances crevasse propagation on both ice shelves and grounded ice. It weakens the ice by accelerating crevasse growth via water filled crevasses. HF is a key process in the MICI as it leads to rapid ice shelf collapse, with sufficient surface melting.\nIce cliff instability, IC:\nIC is linked to HF and MICI. After rapid ice shelf collapse, an ice cliff forms at the grounding line (ice above sea level). Above a critical height, this ice cliff is unstable, resulting in brittle failure (the shear stress exceeds the yield stress of ice).\nDissipation of icebergs, DI:\nThis is related to IC and MICI. During IC, icebergs are formed, which, depending on the geometry of the ice shelf and bathymetry beneath can accumulate in an embayment or become rafter on a sill or alternatively can be advected away from the ice edge by ocean currents.\nAtmospheric moisture and circulation, AM:\nIn a changing climate, the predominant patterns of atmospheric circulation and strength of multi-annual oscillations such as the Pacific Decadal Oscillation or Arctic Oscillation may change affecting both the source and magnitude of precipitation regionally. Circulation changes can also influence surface ocean heat transport, which in turn can affect buttressing but here we were only concerned with its influence on SMB.\nAlbedo, AL:\nChanges in surface AL have a large impact on the radiative energy balance of the snow or ice surface, which affects melt rates. Several factors that are currently not included in SMB models are known to influence albedo such as organic and inorganic impurities deposited or growing on the surface.\nSea ice, SI:\nSI acts as a barrier to moisture and heat exchange between the atmosphere and ocean and changes in sea ice extent or concentration can, therefore, influence both of these factors locally, affecting rates of precipitation and air temperatures.\nImportance of gravitational, rotational and deformation effects\uf0c1\nRecent observations and developments in numerical modeling have suggested that gravitational, rotational and solid Earth deformation (GRD) effects on regional sea level and isostatic bedrock elevation caused by changes in ice mass loading could have a stabilising effect on, in particular, grounding line migration associated with MISI. Fig S7 shows the results of the experts\u2019 judgement on the importance of GRD for the stability of the three ice sheets where D implies decreasing stability, I is increasing stability and N is no impact. The GrIS has limited sectors that satisfy the MISI criteria: a retrograde bed slope that is below sea level close to, or at, the present- day grounding line. Consequently, GRD effects are considered of negligible significance here. The WAIS is the ice sheet that is most susceptible to the MISI and is thus the ice sheet where GRD may act as a negative, stabilising feedback. However, only 50% of the experts consider this to be the case and recent modeling suggest the effect is, however, small (Larour et al., 2019). For the EAIS, about a third of the experts consider GRD to be of relevance and, as for the WAIS, any reduction in grounding line migration due to GRD effects is likely to be small (Larour et al., 2019). Consequently, we do not discuss GRD effects further and consider them to be of second- order importance.\nSupporting Figures\uf0c1\nFigure S1: The two temperature scenarios prescribed: L (+2\u00b0 C) and H (+5\u00b0 C)\nFigure S2: Indicative probability distribution plots for SLR contributions by 2050CE from the three ice sheets and for three physical processes, identified on the x-axis (runoff from EAIS is omitted as this is presumed zero under either temperature rise scenario). Results are derived from expert elicitation for the 2050L (low +2\u00b0C) global temperature trajectory (left hand curves) and for the 2050H (high +5\u00b0C) global temperature trajectory (right hand curves); probability density curves are approximate and extend from values corresponding to a 99% chance of SLR being exceeded to a 1% chance of SLR being exceeded. Median values are shown by the black rectangle and the total SLR contribution from the ice sheets is shown in orange.\nFigure S3: As for figure S2 but for 2300.\nFigure S4: Expert judgements on the relative role of the three drivers for changes in SMB: atmospheric moisture and circulation (AM), albedo (AL) and sea ice extent (SI) for both grounded and floating ice for the Low temperature scenario.\nFigure S5: Expert judgements on the relative role of the three drivers for changes in SMB: atmospheric moisture and circulation (AM), albedo (AL) and sea ice extent (SI) for both grounded and floating ice for the Low temperature scenario.\nFigure S6: Expert judgements on the relative role of the two ocean processes: circumpolar deep water (CDW) and the Atlantic Meridional Overturning Circulation (AMOC) for the High temperature scenario.\nFigure S7: Relative importance of GRD effects for decreasing ice stability (D), increasing it (I) or having no effect (N).\nSupporting Tables\uf0c1\nTable S1: SLR for different probabilities from 1-99.9% and at ten year increments from 2010- 2300. All values are relative to the year 2000 baseline for the High temperature scenario. Values are in cms.\nTable S2: Change in process significance between Low and High temperature scenarios for ice dynamic processes.\nTable S3: As for Table S1 but for SMB processes.", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber22.html"}
{"id": "9597ccc3a71c-0", "text": "van de Wal et al. (2022)\uf0c1\nTitle:\nA High-End Estimate of Sea Level Rise for Practitioners\nKey Points:\nA high-end estimate of sea level rise in 2100 and 2300\nDecisionmaker/practitioner perspective on high-end\nTiming of collapse of ice shelves critical\nCorresponding author:\nRoderik S. W. van de Wal\nCitation:\nvan de Wal, R. S. W., Nicholls, R. J., Behar, D., McInnes, K., Stammer, D., Lowe, J. A., et al. (2022). A High\u2010End Estimate of Sea Level Rise for Practitioners. Earth\u2019s Future, 10(11), e2022EF002751. doi:10.1029/2022ef002751\nURL:\nhttps://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022EF002751\nAbstract\uf0c1\nSea level rise (SLR) is a long-lasting consequence of climate change because global anthropogenic warming takes centuries to millennia to equilibrate for the deep ocean and ice sheets. SLR projections based on climate models support policy analysis, risk assessment and adaptation planning today, despite their large uncertainties. The central range of the SLR distribution is estimated by process-based models. However, risk-averse practitioners often require information about plausible future conditions that lie in the tails of the SLR distribution, which are poorly defined by existing models. Here, a community effort combining scientists and practitioners builds on a framework of discussing physical evidence to quantify high-end global SLR for practitioners. The approach is complementary to the IPCC AR6 report and provides further physically plausible high-end scenarios. High-end estimates for the different SLR components are developed for two climate scenarios at two timescales. For global warming of +2\u00b0C in 2100 (RCP2.6/SSP1-2.6) relative to pre-industrial values our high-end global SLR estimates are up to 0.9 m in 2100 and 2.5 m in 2300. Similarly, for a (RCP8.5/SSP5-8.5), we estimate up to 1.6 m in 2100 and up to 10.4 m in 2300. The large and growing differences between the scenarios beyond 2100 emphasize the long-term benefits of mitigation. However, even a modest 2\u00b0C warming may cause multi-meter SLR on centennial time scales with profound consequences for coastal areas. Earlier high-end assessments focused on instability mechanisms in Antarctica, while here we emphasize the importance of the timing of ice shelf collapse around Antarctica. This is highly uncertain due to low understanding of the driving processes. Hence both process understanding and emission scenario control high-end SLR.\nPlain Language Summary\uf0c1\nTaking a co-production approach between scientists and practioners, we provide high-end sea level rise (SLR) estimates for practitioner application based on an expert evaluation of physical evidence and approaches currently used in policy environments to understand high end risk. We do this for two global warming scenarios, a modest and a strong one, for two time slices 2100 and 2300. The large and growing differences between the scenarios beyond 2100 emphasize the long-term benefits of mitigation. However, even a modest warming may cause multi-meter SLR on centennial time scales with profound consequences for coastal areas. Earlier high-end assessments focused on instability mechanisms in Antarctica, while here we emphasize the importance of the timing of ice shelf collapse around Antarctica as well as how practitioners use high end projections to frame risk. We stress that both emission scenario and limited physical understanding control the outcome.\nIntroduction\uf0c1\nSea level rise (SLR) is a key aspect of climate change, with important consequences for coastal societies and low-lying areas, especially small islands, deltas, and coastal cities (Oppenheimer et al., 2019). Human interference in the climate system leads to a continuing gradual warming and expansion of ocean water (i.e., the steric effect), mass loss from glaciers and polar ice sheets. Most of these effects continue long after emissions have slowed or stopped. Climate models simulating physical processes are used to reconstruct historical sea level change (excluding the ice sheet contribution), and consequently provide a method to project SLR given specific future anthropogenic CO2 emissions and associated warming of the Earth system. Such a process-based approach provides robust estimates of changes in the central part of the SLR distribution for projections and published studies using this method are in general agreement. However, estimating the tails of the distribution, which includes the ice sheet contribution remains contentious as not all the relevant processes are sufficiently understood or represented in the models, leading to variations between projections and multiple views of how the upper tail of the SLR distribution will evolve in future.\nHigh-end SLR projections provide information about the upper tail of the probability distribution of SLR, and are especially important for decisionmakers and practitioners (collectively referred to as practitioners) assessing long-term risks and adaptation responses. High-end projections, though by definition unlikely to occur, can provide information for adaptation planning, that is, defining a plausible \u201cworst case\u201d SLR to consider in an adaptation plan (Hinkel et al., 2015; Nicholls, Hanson, et al., 2021; Vogel et al., 2016). In addition, high-end estimates provide insight on potential adaptation limits, tipping points and thresholds, and the level of climate mitigation required to keep SLR adaptation manageable in the future. In this context, it is also important to consider the long-term commitment of SLR, requiring high-end projections for time horizons well beyond 2100.\nWe emphasize that high-end SLR information does not replace the quantification of the more likely central parts of the SLR distribution, but rather supplements these estimates. For example, a default adaptation plan may follow the median projection, with high-end estimates used to inform the development of contingency options that can be applied in the case that high-end SLR manifests. Such a planning approach is known as \u201cadaptive planning\u201d or \u201cdynamic adaptive planning\u201d in the literature (Haasnoot et al., 2013; Ranger et al., 2013). This is particularly the case when there are long lead times for action (i.e., the time to plan, design, finance, obtain support and implement the work) and long operational lives, such as for storm surge barriers or nuclear power stations, or where there is significant path-dependency for decisions (e.g., when decisions have a long legacy that may preclude future options such as choosing between protection and retreat). Therefore, a \u201clikely\u201d range as used by Oppenheimer et al. (2019) as the central 66% of the probability distribution is not always sufficient (Hinkel et al., 2015).\nObtaining estimates of high-end SLR can be approached in a statistical sense with probabilistic projections, as provided by Kopp et al. (2017, 2019) and Le Bars et al. (2017), but this approach may not capture possible contributions from processes not yet understood or included in climate models. To overcome this some studies define every percentile of conditional probability distributions based on an underlying assumption, such as including the Antarctic contribution from a single study (e.g., Goodwin et al., 2017). This suggests a higher confidence in the outcomes than is warranted by current physical understanding and is potentially misleading to practitioners since it does not reflect or communicate limits in our physical understanding of these processes. An alternative approach that provides estimates to address these difficulties are structured expert elicitation studies which have also been applied to provide estimates of high-end SLR (Bamber et al., 2019). They attempt to capture the uncertainty due to the lack of knowledge (Lempert et al., 2003; Oppenheimer et al., 2019) that exists in model projections without relying on models, and which is impossible to constrain using a deterministic modeling approach. This approach combines the ad hoc judgment of a group of experts. However, the considerations regarding which processes are included, and which are not, is not made explicit and the interpretation of these estimates by experts is not necessarily the same as those of uninformed practitioners because they do not know the considerations of the experts. For this reason, in this paper, we prefer to use expert judgment based on physical reasoning to arrive at estimates which cannot be constrained by deterministic modeling. This is outlined in the Greenland and Antarctic sections and provides a transparent attribution of cause and effect.", "source": "https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html"}
{"id": "9597ccc3a71c-1", "text": "Obtaining estimates of high-end SLR can be approached in a statistical sense with probabilistic projections, as provided by Kopp et al. (2017, 2019) and Le Bars et al. (2017), but this approach may not capture possible contributions from processes not yet understood or included in climate models. To overcome this some studies define every percentile of conditional probability distributions based on an underlying assumption, such as including the Antarctic contribution from a single study (e.g., Goodwin et al., 2017). This suggests a higher confidence in the outcomes than is warranted by current physical understanding and is potentially misleading to practitioners since it does not reflect or communicate limits in our physical understanding of these processes. An alternative approach that provides estimates to address these difficulties are structured expert elicitation studies which have also been applied to provide estimates of high-end SLR (Bamber et al., 2019). They attempt to capture the uncertainty due to the lack of knowledge (Lempert et al., 2003; Oppenheimer et al., 2019) that exists in model projections without relying on models, and which is impossible to constrain using a deterministic modeling approach. This approach combines the ad hoc judgment of a group of experts. However, the considerations regarding which processes are included, and which are not, is not made explicit and the interpretation of these estimates by experts is not necessarily the same as those of uninformed practitioners because they do not know the considerations of the experts. For this reason, in this paper, we prefer to use expert judgment based on physical reasoning to arrive at estimates which cannot be constrained by deterministic modeling. This is outlined in the Greenland and Antarctic sections and provides a transparent attribution of cause and effect.\nThe approach builds on Stammer et al. (2019), where they quantify high-end SLR by synthesizing all the available physical evidence across observations, model sensitivity studies and modeled SLR scenario studies, and then assess and synthesize this information. Importantly, this approach aims to meet practitioner needs, which depend less on precise estimates of likelihood and more on evidence that is sufficiently credible, salient, and legitimate to support adaptation planning, including financing (Cash et al., 2003, 2002). \u201cSalient\u201d is used here in the context of relevance to practical needs. Within this framework, projections supported by multiple lines of evidence and eliciting broader confidence from the scientific community are of greater value as compared to projections further along the tail that feature fewer lines of evidence, and hence have lower confidence. This is an expansion of the approach based on building blocks (Stammer et al., 2019), in which the building blocks represent the amount of SLR beyond the likely range that practitioners will consider according to their risk-averseness, emission scenarios, and how these evolve over time. It is key that the main processes are considered explicitly. The work is based on a WCRP grand challenge workshop on this topic where a wide variety of people were invited (\u223c25 scientists and \u223c10 practitioners) including experts on all relevant sea level components and experts on the application of SLR information. The estimates for the specific components are made by a subset of authors as outlined in the acknowledgment statement.\nBecause the level of understanding of each sea level component differs, we employ different methods to assess each of them separately. For example, the understanding of the thermal expansion of the ocean and the glacier-melt component is sufficient to use distributions derived from climate models directly. For those components, we assume that all necessary knowledge of the high-end is captured in the distribution. However, for the Greenland and Antarctic ice sheet components the uncertainty is much larger, as understanding of physical processes is more limited, and hence a robust and reliable probability density function does not exist. We, therefore, choose to apply a process-based expert judgment to the available lines of evidence to estimate a high-end ice sheet contribution. By following this approach we deviate from (Fox-Kemper et al., 2021), which provides a high-end scenario with and without a specific Antarctic instability mechanism and includes structured expert elicitation. Hence, we take a complementary approach where we explicitly and transparently assess the physical processes leading to a high-end estimate for Greenland and Antarctica.\nThe aim of this paper is to develop high-end projections that are most strongly supported by physical evidence and yet are also salient for the decision and practitioner environment. We derive new high-end estimates based on present physical understanding and demonstrate a methodological approach that may be regularly updated as the science evolves and improves, especially knowledge on ice sheets. Table S1 lists the author\u2019s contribution by section. Throughout this paper, we follow the definition of technical terms as defined in the glossary of the IPCC AR6 report (Matthews et al., 2021).\nPractitioner Perspectives on High-End Sea Level Projections\uf0c1\nThis paper explicitly considers practitioner perspectives in addition to SLR science to promote developing salient projections (e.g., Hinkel et al., 2019). Risk-averse practitioners need to consider low likelihood, high consequence SLR futures that poses challenges to adaptation, in addition to median outcomes (Fox-Kemper et al., 2021; Garner et al., 2018; Haasnoot et al., 2020; Hall et al., 2019; Hinkel et al., 2015; Nicholls, Hanson, et al., 2021). While median SLR projections have been relatively stable over time, several high-end projections have emerged, especially in recent years (e.g., DeConto & Pollard, 2016). However, these high-end projections have not been reviewed systematically from a user perspective, and most adaptation practitioners find them challenging to use, if they use them at all. Those practitioners that have applied them have had to develop their own understanding and guidance, including expertise on sea level science. This constitutes a high overhead to application when adaptation is often poorly funded.\nAn influential approach linking scientific exploration and decision requirements advises that scientific influence on decisions depends on the \u201csalience, credibility, and legitimacy\u201d of the information presented from the decision perspective (Cash et al., 2003, 2002). Of particular importance for high-end SLR projections is salience, defined as \u201cthe relevance of information for an actor\u2019s decision choices, or for the choices that affect a given stakeholder.\u201d In our view, salience for high-end SLR projections derives from two factors.\nFirst, scientific information used for decision-making must consider all the major uncertainties and ambiguities across experts and models (Gold, 1993; Jones et al., 2014; Simpson et al., 2016). This requirement may be at odds with the physics-based design of SLR projections. For example, the SLR scenarios provided by IPCC AR4 did not assign values outside the central likely range as information was absent (Meehl et al., 2007). In AR5, the possibility of several tenths of a meter above the likely range was considered as a high-end possibility, reflecting rapid melting of the Antarctica and Greenland ice sheets: these processes, however were poorly understood and not captured directly in the physics-based design (Church et al., 2013). While this exclusion is explicitly stated and makes sense from a physical science perspective, practitioners may misuse the results, as they will expect/assume that IPCC SLR scenarios cover all major uncertainties. AR6 moved to an emulator approach and covered a wider range of probabilities than earlier assessments reflecting the increased understanding of key physical processes that was unavailable for earlier assessments: the central range of estimates to 2100 is similar to earlier estimates, but also addresses high-impact/low-probability outcomes (Section 5), and provides a range of values from the literature. This evolution of the IPCC reports reflect increased understanding and provides improved treatment of the risk management context for adaptation planning, but alternative interpretations as presented here are possible, thereby increasing the understanding of high-end estimates.\nSecond, salience requires a differentiation between scientific endeavors in general and what is sometimes called \u201cactionable science,\u201d which in the climate field is intended to support risk assessment and adaptation planning/investment (Bamzai et al., 2021; Beier et al., 2017; Moss et al., 2013; Vogel et al., 2016). New studies that challenge prior lines of evidence should be carefully reviewed, assessed, and debated before any application or incorporation into guidance (Nicholls, Hanson, et al., 2021). This avoids the \u201cwhiplash effect\u201d wherein planners and all their efforts are undermined each time a new study questions their adopted projections. In this respect, we advocate this work to be used alongside (Fox-Kemper et al., 2021) rather than replacing it.", "source": "https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html"}
{"id": "9597ccc3a71c-2", "text": "First, scientific information used for decision-making must consider all the major uncertainties and ambiguities across experts and models (Gold, 1993; Jones et al., 2014; Simpson et al., 2016). This requirement may be at odds with the physics-based design of SLR projections. For example, the SLR scenarios provided by IPCC AR4 did not assign values outside the central likely range as information was absent (Meehl et al., 2007). In AR5, the possibility of several tenths of a meter above the likely range was considered as a high-end possibility, reflecting rapid melting of the Antarctica and Greenland ice sheets: these processes, however were poorly understood and not captured directly in the physics-based design (Church et al., 2013). While this exclusion is explicitly stated and makes sense from a physical science perspective, practitioners may misuse the results, as they will expect/assume that IPCC SLR scenarios cover all major uncertainties. AR6 moved to an emulator approach and covered a wider range of probabilities than earlier assessments reflecting the increased understanding of key physical processes that was unavailable for earlier assessments: the central range of estimates to 2100 is similar to earlier estimates, but also addresses high-impact/low-probability outcomes (Section 5), and provides a range of values from the literature. This evolution of the IPCC reports reflect increased understanding and provides improved treatment of the risk management context for adaptation planning, but alternative interpretations as presented here are possible, thereby increasing the understanding of high-end estimates.\nSecond, salience requires a differentiation between scientific endeavors in general and what is sometimes called \u201cactionable science,\u201d which in the climate field is intended to support risk assessment and adaptation planning/investment (Bamzai et al., 2021; Beier et al., 2017; Moss et al., 2013; Vogel et al., 2016). New studies that challenge prior lines of evidence should be carefully reviewed, assessed, and debated before any application or incorporation into guidance (Nicholls, Hanson, et al., 2021). This avoids the \u201cwhiplash effect\u201d wherein planners and all their efforts are undermined each time a new study questions their adopted projections. In this respect, we advocate this work to be used alongside (Fox-Kemper et al., 2021) rather than replacing it.\nRelevant examples of high-end scenarios in planning exist in other fields. These support sound risk management, while adhering to a reasonable standard of practice to ensure appropriate resource allocation to the level of risk aversion. Accordingly, planners have found it advisable to frame high-end risk with a standard that balances risk management objectives with finite resources, avoiding large opportunity costs where possible. For example, the UK National Risk Register defines a \u201creasonable worst-case scenario\u201d (RWCS) for use in planning. This is defined as \u201cthe worst plausible manifestation of that particular risk (once highly unlikely variations have been discounted) to enable relevant bodies to undertake proportionate planning\u201d (HM Government, 2020). The RWCS \u201cis designed to exclude theoretically possible scenarios which have so little probability of occurring that planning for them would be likely to lead to disproportionate use of resources\u201d (Memorandum Submitted by the Government Office for Science and the Cabinet Office, 2011). The US Army Corps of Engineers selected a \u201cmaximum probable flood\u201d for design purposes after the Great Mississippi River Flood of 1927. This is the \u201cgreatest flood having a reasonable probability of occurrence\u201d and was preferred over a larger \u201cmaximum possible flood\u201d, reflecting a meteorological sequence that, though reflective of historic events, was deemed highly implausible (Jadwin, 1928). This reasonableness standard has stood the test of time, including periodic review, and may be modified in the future to reflect changes to climate, land use, or other factors as appropriate.\nFor SLR, an example of a salient approach is The Thames Estuary Plan (TE2100), which addresses management of future coastal flood risk for London, UK. It was one of the first long-term adaptation plans to address deep uncertainty (sometimes popularized as the unknown unknowns) with consideration of both more likely and high-end SLR (Ranger et al., 2013). The term \u201cH++\u201d was created by TE2100 to describe a highly unlikely but possible high-end range of SLR. While most attention is focused on the definite upper bound, the high-end represents a range of values. H++ was designed to support a \u201cdynamic robustness\u201d planning approach that allows for consideration of a wide range of adaptation options as SLR observations and science develop over time (Ranger et al., 2013). This approach examines which extreme adaptation options should be kept open, whilst actively planning for smaller more likely SLR estimates and regularly reviewing the observed rates of SLR and the robustness of SLR projections. In TE2100, an upper-end SLR exceeding 4.2 m in 2100 was initially adopted for planning. This includes a strom surge component which is not expected to change greatly in future. In 2009, after consideration of emerging science and observations, especially Greenland and West Antarctica, the 2100 upper-end SLR projection was revised downwards to 2.7 m, of which 2 m is the time-mean SLR (Lowe et al., 2009). This revised value is still used in practice today (Environmental Agency Guidance, 2021; Palmer et al., 2018). Hence, TE2100 demonstrates an adaptive process of science evaluation and revision of a salient high-end scenario for adaptation planning. This inspires the estimates in this paper.\nHow We Develop a High-End Estimate\uf0c1\nTo avoid overreliance on single studies, for example, as illustrated in the (Griggs, 2017) approach, we consider SLR-related processes that are ideally supported by multiple lines of independent evidence. Our approach to construct high-end SLR estimates uses information on SLR components that meet the following three requirements: (a) there is sufficient physical understanding of the relevant processes involved; (b) this understanding can be linked to a quantitative estimate of the associated SLR; (c) there is evidence to explain why the estimates we produce are expected to be in the upper tail of the range of responses. For SLR components where robust distributions are available, two times the standard deviation is warranted in view of the need to sample in the tail. For some components there is sufficient quantitative understanding to use the tail of a probability density function derived from physical models, but not for all components. In particular, the mean and variance of the ice sheet components are poorly constrained, and they cannot be derived directly from climate models. This continues to complicate development of a high-end estimate.\nAdditionally, the covariance between sea level components is largely unknown because only the ocean component of SLR is directly derived from a large ensemble of climate models in which the relevant processes are coupled. The other sea level components are calculated off-line from climate and land-ice models, and hence require ad-hoc assumptions about the co-variance between components (Lambert et al., 2021), similar to what has been done in Fox-Kemper et al. (2021) or via a covariance controlled by temperature changes (Palmer et al., 2020). To address this problem, we provide a range of high-end values based on the assumption that the different components (glaciers, Greenland, Antarctica, steric expansion, land water storage change [LWSC]) are fully dependent (covariances all equal to 1, maximizing the uncertainty, and hence the upper end of the range) or fully independent (covariance all equal to 0, minimizing the uncertainty, providing a lower end of the range). At present, this is the only fully transparent way to consider the co-variance between for instance the Greenland and Antarctic component. Additionally, it spans the full range of possible outcomes. However, it is unlikely that the complexity of processes involved, and the climate change patterns themselves are fully correlated or fully independent. To illustrate this one can think of the importance of atmospheric circulation changes and basal melt to high end. The first process is important in Greenland and the second in Antarctica. To what end both will change in a similar way is not known, hence full dependency is unlikely. At the same time global warming plays a role in both processes, hence fully independency is also unlikely.\nFor this reason, practitioners can decide whether to treat the uncertainties as fully independent, fully dependent, or in between depending on their level of risk-averseness. For the independent case (all co-variances zero), we take the median values of AR6 for the different components and define the high-end to be characterized by two standard deviations above the median value. For the dependent case we can simply add the estimates of the different components.\nThe problem of estimating high-end values for SLR is therefore not only about constraining the uncertainty in the component with the largest uncertainty, but also about understanding how the uncertainty in the SLR components are correlated with each other. The first problem is due to insufficient process understanding of the dynamics of the Antarctic ice sheet. The second problem is due to the surface mass balance (SMB) of the Greenland ice sheet, which requires Earth system models with fully coupled interactive ice sheets models to solve.", "source": "https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html"}
{"id": "9597ccc3a71c-3", "text": "For this reason, practitioners can decide whether to treat the uncertainties as fully independent, fully dependent, or in between depending on their level of risk-averseness. For the independent case (all co-variances zero), we take the median values of AR6 for the different components and define the high-end to be characterized by two standard deviations above the median value. For the dependent case we can simply add the estimates of the different components.\nThe problem of estimating high-end values for SLR is therefore not only about constraining the uncertainty in the component with the largest uncertainty, but also about understanding how the uncertainty in the SLR components are correlated with each other. The first problem is due to insufficient process understanding of the dynamics of the Antarctic ice sheet. The second problem is due to the surface mass balance (SMB) of the Greenland ice sheet, which requires Earth system models with fully coupled interactive ice sheets models to solve.\nHere, we restrict ourselves to two time slices (2100 and 2300) and two climate scenarios (RCP2.6/SSP1-2.6 and RCP8.5/SSP5-8.5) which we call for simplicity the low and high scenario. The detailed physical reasoning behind the estimates of the individual cryospheric components is discussed in detail in Section 4 (Glaciers), Section 5 (Greenland), and Section 6 (Antarctica). Section 7 combines the storylines for the different SLR components in an estimate of the high-end global mean SLR for the four scenarios being 2100 and 2300 low and high-temperature change. We focus on the year 2100 because there is significantly more information available for this time horizon than for any other date in time. Moreover, the physical understanding decreases significantly after this time horizon. We focus on 2300 to highlight the long time-scales involved for SLR, the necessity for adaptation and the benefits of mitigation. The scenarios rely strongly on the well-known representative concentration pathways of RCP2.6/SSP1-2.6, which has a median response at 2100 of just under 2\u00b0C, and RCP8.5/SSP5-8.5 which has a median around 5\u00b0C in 2100 and 8\u00b0C\u201310\u00b0C in 2300. These correspond loosely to the core goal of the Paris Agreement and unmitigated emissions, respectively, and provide a significant range in future conditions. We limit our analyses to these scenarios because current understanding of the Antarctic response is not precise enough to distinguish intermediate scenarios between RCP2.6/SSP1-2.6 and RCP8.5/SSP5-8.5, as discussed in Section 7 in more detail. For each of the four scenarios, we provide a range in the high-end estimate of SLR constraint by the dependent or independent addition of the different components.\nThe method provides estimates of the high-end of projected global sea level change, and does not include the wide range of processes that contribute to regional sea level variations, nor does it consider regional and local vertical land motion, needed to determine the relative sea level changes at a particular coastal location, and that lead to changes in the frequency and magnitude of extreme sea level events at all time scales. Additionally, practitioners need to consider for example, bathymetric effects, possible changes in tides or surges and other near coastal processes. All these local effects and the possible changes therein need to be assessed separately, in particular human-induced subsidence (Nicholls, Lincke, et al., 2021). We in effect assume that the global terms contribute significantly to the uncertainty in local SLR at most locations, but the local terms in the uncertainty budget vary in importance with location. Hence we focus on what is common to all locations. A simple additional step that practitioners could take is to realize that a large Antarctic contribution will influence regional sea level with higher values far from Antarctica due to gravitational effects. Operational tools to include this effect and all the other local to regional processes already exist and are applicable to any global scenario.\nGlaciers\uf0c1\nIn this section, we detail the physical reasoning behind the estimates of the individual cryospheric components starting with glaciers (Section 4, Greenland Section 5 and Antarctica Section 6), as they do not immediately follow from the IPCC model ensemble results. Sections 4\u20136, 4\u20136, 4\u20136 have a similar structure starting with the processes which are relevant and ending with an evaluation of the high-end contribution of the specific component. They each have a figure illustrating how the relevant processes contribute to high-end SLR. The critical processes are eventually per cryospheric component summarized in Table 1 for each scenario.\nTable 1: Overview of Ciritical Processes for High-End Estimate of the Cryospheric Components of Sea Level Rise Per Time Scale and Scenario\n2100-low\n2100-high\n2300-low\n2300-high\nGlaciers\nTemperature increase\nTemperature increase\nTemperature increase, glacier\nmass equilibrium\nTemperature increase, amount of glacier ice\nGreenland\nTemperature increase,\noutlet glacier\nacceleration\nTemperature increase,\nalbedo feedbacks,\natmospheric\ncirculation changes\nTemperature increase\nTemperature increase, albedo feedbacks,\natmospheric circulation changes, tipping points\nAntarctica\nSMB, BMB, switch in\nflow below shelves\nSMB, shelf collapse,\nBMB, calving,\nhydrofracturing\nSMB, shelf collapse, BMB,\ncalving, hydrofracturing\nMISI, MICI, basal sliding\nThe Glacier Model Intercomparison Project Phase 2 (GlacierMIP2; Marzeion et al., 2020), is a community effort based on CMIP5 model runs estimating the mass loss of global glaciers. It includes 11 different glacier models, of which seven include all the glaciers outside of Greenland and Antarctica, and four are regional. The glacier models are forced by up to 10 General Circulation Models (GCMs) per RCP scenario, such that a total of 288 ensemble members form the basis of this most recent estimate of glacier mass change projections for the 21st century. Compared to this, projections that include the 23rd century are sparse and based on individual models (e.g., Goelzer et al., 2012; Marzeion et al., 2012). Some information about long-term glacier mass change can be obtained from equilibrium experiments (e.g., Levermann et al., 2013; Marzeion et al., 2018).\nProcesses for Glaciers Relevant for High-End SLR Scenarios\uf0c1\nTemperature changes are critical to calculate glacier volume changes. Through the spatial distribution of glaciers on the land surface and a strong bias to Arctic latitudes, glaciers experience roughly twice the temperature anomalies of the global mean (Marzeion et al., 2020). Biases of projected spatial patterns of temperature increase, particularly concerning Arctic Amplification (stronger temperature change at high latitude), thus have the potential to impact projected glacier mass loss. However, we assume that the GCM ensemble size of GlacierMIP2 is large enough to adequately represent this uncertainty.\nOther processes which may play a role are related to debris cover and ice-ocean interaction. Only one of the glacier models taking part in GlacierMIP2 includes a parameterization of frontal ablation/calving (Huss & Hock, 2015), such that there is potential for underestimation of mass loss in the GlacierMIP2 ensemble as important ice-ocean interaction processes are not represented. However, frontal ablation and calving will most strongly affect mass loss of ice currently below mean sea level (Farinotti et al., 2019), and hence they will contribute relatively little to SLR since that constitutes only 15% of the total glacier mass. Additionally, the mass loss projected in GlacierMIP2 for 2100 under RCP2.6/SSP1-2.6 indicates that the number of tidewater glaciers will be greatly reduced even under low emissions and will retreat from contact with the ocean. Thus, ice-ocean interaction may have strong effects on the timing of mass loss within the 21st century, but this is unlikely to play a large role at the end of the 21st century or later, and for greater temperature increases.\nNone of the global models and only one of the regional models in GlacierMIP2 (Kraaijenbrink et al., 2017) includes effects of debris cover on glacier mass balance. Strong surface mass loss has the potential to cause the surface accumulation of debris layers (e.g., Kirkbride & Deline, 2013) thick enough to insulate the ice below it, thus reducing melt rates (e.g., Nicholson & Benn, 2006). At the same time, a thin debris cover layer could enhance melt rates. The lack of representation of debris cover in GlacierMIP2 is estimated to be unlikely to have a significant impact on the considered high-end range of projections.\nEvaluation of the High-End Contribution for Glaciers\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html"}
{"id": "9597ccc3a71c-4", "text": "Other processes which may play a role are related to debris cover and ice-ocean interaction. Only one of the glacier models taking part in GlacierMIP2 includes a parameterization of frontal ablation/calving (Huss & Hock, 2015), such that there is potential for underestimation of mass loss in the GlacierMIP2 ensemble as important ice-ocean interaction processes are not represented. However, frontal ablation and calving will most strongly affect mass loss of ice currently below mean sea level (Farinotti et al., 2019), and hence they will contribute relatively little to SLR since that constitutes only 15% of the total glacier mass. Additionally, the mass loss projected in GlacierMIP2 for 2100 under RCP2.6/SSP1-2.6 indicates that the number of tidewater glaciers will be greatly reduced even under low emissions and will retreat from contact with the ocean. Thus, ice-ocean interaction may have strong effects on the timing of mass loss within the 21st century, but this is unlikely to play a large role at the end of the 21st century or later, and for greater temperature increases.\nNone of the global models and only one of the regional models in GlacierMIP2 (Kraaijenbrink et al., 2017) includes effects of debris cover on glacier mass balance. Strong surface mass loss has the potential to cause the surface accumulation of debris layers (e.g., Kirkbride & Deline, 2013) thick enough to insulate the ice below it, thus reducing melt rates (e.g., Nicholson & Benn, 2006). At the same time, a thin debris cover layer could enhance melt rates. The lack of representation of debris cover in GlacierMIP2 is estimated to be unlikely to have a significant impact on the considered high-end range of projections.\nEvaluation of the High-End Contribution for Glaciers\uf0c1\nGlaciers store less than 1% of the global ice mass (Farinotti et al., 2019), and contributed 0.7 mm/yr over the period 2010\u20132018 (Hugonnet et al., 2021). Their potential to contribute to SLR is thus limited by their total mass, and which is estimated to be 0.32 \u00b1 0.08 m SLE (Farinotti et al., 2019). However, this limit does not affect their contribution within the 21st century: even under RCP8.5/SSP5-8.5, GlacierMIP2 projects that 64% \u00b1 20% of the glacier mass will remain by 2100. At the same time, the GlacierMIP2 projections show that the glacier contribution strongly depends on the temperature increase itself and less on precipitation changes, both affecting the SMB (Figure 1). This temperature increase is reasonably constrained by the large set of CMIP model ensemble and shows a Gaussian distribution.\nFigure 1: Causal relation between processes leading to a high-end contribution of Glaciers to sea level rise (SLR). Climate forcing leads to patterns of temperature (\u0394T) and precipitation (\u0394P) change over the globe (colored stripes global mean change). These local climate variables control the surface mass balance (SMB) and thereby the volume change of glaciers which determines the SLR by the glacier component. Ice dynamics are usually highly simplified in glacier models and therefore omitted here.\nHence, both climate and appropriate physical processes are captured in the GlacierMIP2 projections and therefore a high-end estimate for glaciers is based on the mean and twice the standard deviation of the GlacierMIP2 experiment as outlined in our definition of a high-end estimate in Section 3. Table 1 and Figure 1 illustrate the critical processes required for a high-end estimate of the glacier contribution. Similar tables and figures are presented in the later ice Sections to demonstrate and contrast the different processes for the different cryospheric components. Table 3 provides the references to the papers from which we derived the actual values to estimate the high-end range. Our final high-end values for the glaciers are based on the GlacierMIP2 result: 0.079 \u00b1 0.056 m of ice volume change under RCP2.6/SSP1-2.6 and 0.159 \u00b1 0.086 m under RCP8.5/SSP5-8.5 in 2100. We convert these to sea level equivalents by correcting for the fact that approximately 15% of the glacier volume is below sea level and arrive at a high-end estimate of 0.15 m sea level equivalents under RCP2.6/SSP1-2.6 and 0.27 m under RCP8.5/SSP5-8.5 (being the mean plus twice the standard deviation). By 2300, glaciers might approach stabilization under RCP2.6/SSP1-2.6 after having contributed 0.28 m to SLR (Cazenave et al., 2018). Their contribution would be limited by their current ice mass above flotation of 0.32 \u00b1 0.08 m (Farinotti et al., 2019), for higher emission scenarios, which is then by definition the highest contribution possible.\nTable 3: summarizes all the references used for the different high-end estimates of all the components and provides a comparison to the results of Fox-Kemper et al. (2021).\nGreenland\uf0c1\nCurrently, substantial ice mass loss is observed in Greenland (Bamber et al., 2018; Cazenave et al., 2018; A. Shepherd et al., 2020) with a rate over the period 2010\u20132019 equivalent to 0.7 mm/yr Global Mean Sea Level Rise (GMSLR; Fox-Kemper et al., 2021). This is to a large extent driven by a change in the SMB, but also by increased dynamic loss of ice via marine-terminating outlet glaciers (Csatho et al., 2014; Enderlin et al., 2014; King et al., 2020; Van Den Broeke, 2016).\nProcesses\uf0c1\nFor the 21st century outlet glaciers remain important (Choi et al., 2021; Wood et al., 2021), but for longer time scales changes in SMB are expected to dominate mass loss from the Greenland ice sheet, in particular for high-emission forcing, as some marine-terminating outlet glaciers begin to retreat onto land (e.g., F\u00fcrst et al., 2015). Since the IPCC AR5 report, several new studies with projections for Greenland up to 2100 have been published that were broadly consistent with the AR5 (e.g., Calov et al., 2018; F\u00fcrst et al., 2015; Golledge et al., 2019; Vizcaino et al., 2015). More recent studies, as also reported by Fox-Kemper et al. (2021), however, have obtained significantly larger mass loss rates with values of up to 33 cm by 2100 (Aschwanden et al., 2019; Hofer et al., 2020; Payne et al., 2021). This can be explained by a larger sensitivity used for converting air temperature to melt, and averaging of the forcing over a large domain and applying a spatially constant scalar anomaly, an approach that has been disputed (F\u00fcrst et al., 2015; Gregory & Huybrechts, 2006; Van De Wal, 2001).\nThe Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6) ensemble mean results indicated a contribution of 0.096 \u00b1 0.052 m for RCP8.5/SSP5-8.5 in 2100 for a representative range of CMIP5 GCMs (Goelzer et al., 2020), where an unaccounted contribution for committed sea level of 6 \u00b1 2 mm is additionally added (Goelzer et al., 2020; Price et al., 2011). However, recent results with CMIP6 forcing show a larger range with one model suggesting a contribution of 256 mm (Hofer et al., 2020; Payne et al., 2021). These results were obtained with a limited number of CMIP6 models, some of which are known to exhibit a large climate sensitivity and therefore may be biased high. The ISMIP6 results based on CMIP5 therefore provide a reasonable estimate of the uncertainty caused by GCMs, but they do not include an estimate of the uncertainty due to the more detailed and accurate Regional Climate Models (RCMs), which are forced by GCMs to arrive at detailed mass balance changes. ISMIP6 results are based on only one RCM used for downscaling the GCM results to SMB changes.", "source": "https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html"}
{"id": "9597ccc3a71c-5", "text": "The Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6) ensemble mean results indicated a contribution of 0.096 \u00b1 0.052 m for RCP8.5/SSP5-8.5 in 2100 for a representative range of CMIP5 GCMs (Goelzer et al., 2020), where an unaccounted contribution for committed sea level of 6 \u00b1 2 mm is additionally added (Goelzer et al., 2020; Price et al., 2011). However, recent results with CMIP6 forcing show a larger range with one model suggesting a contribution of 256 mm (Hofer et al., 2020; Payne et al., 2021). These results were obtained with a limited number of CMIP6 models, some of which are known to exhibit a large climate sensitivity and therefore may be biased high. The ISMIP6 results based on CMIP5 therefore provide a reasonable estimate of the uncertainty caused by GCMs, but they do not include an estimate of the uncertainty due to the more detailed and accurate Regional Climate Models (RCMs), which are forced by GCMs to arrive at detailed mass balance changes. ISMIP6 results are based on only one RCM used for downscaling the GCM results to SMB changes.\nUncertainties in modeling SMB have been further addressed using a common historical forcing (1980\u20132012) and comparing the output of 13 different SMB models for the Greenland ice sheet (Fettweis et al., 2020). They found that the ensemble mean produced the best estimate of SMB compared to observations, but the difference in surface melting between models was as much as a factor 3 (from 134 to 508 Gt/yr) and the trend in runoff also differed by a similar amount (from 4.0 to 13.4 Gt/yr/yr) for the common period 1980\u20132012. Combining the uncertainties in modeling SMB with those for the projected climate forcing indicates that the SMB component is poorly constrained and has large uncertainties, despite having dominated recent mass loss trends in Greenland (Van Den Broeke, 2016).\nFurther uncertainties in projections for the Greenland ice sheet related to specific processes include: (a) the importance of firn saturation which buffers meltwater prior to run off, (b) albedo lowering by darkening of the surface caused by dust or algal growth, (c) the strength of melt-albedo and height-SMB feedback mechanisms, both leading to additional mass loss, and (d) calving, all being processes that are poorly constrained and often not included in SMB models. Considering these processes has the potential to increase the contribution of Greenland and widen the uncertainty distribution. Furthermore, it is known that the current generation of GCMs do not capture recently observed atmospheric circulation changes (Delhasse et al., 2018, 2020; Fettweis et al., 2017; Hanna et al., 2018), and it is not yet clear whether these changes are forced by climate change or natural variability. Delhasse et al. (2018) estimated that Greenland atmospheric blocking, leading to persistence of enhanced warm air advection from the South and changes in cloudiness (Hofer et al., 2019), may lead to a doubling of mass loss due to SMB changes over the 21st century. This is an estimate for 2040\u20132050 which does not capture the positive albedo feedback arising from an expanding ablation zone, so we consider the doubling of the mass loss due to SMB changed caused on circulation changes as a lower bound of this effect. In all these studies, projections are made based by stand-alone climate models, lacking many of the feedbacks discussed above (Fyke et al., 2018).\nIn contrast to the Antarctic ice sheet (discussed in the next Section), only a limited contribution of the dynamics of the outlet glaciers is to be expected (F\u00fcrst et al., 2015; Goelzer et al., 2020; Nick et al., 2013), This is because they occupy only a small fraction of the ice sheet perimeter, whereas in Antarctica the majority of the perimeter is in direct contact with the ocean.\nPaleo-simulations may be important for constraining near-future mass loss from the Antarctic ice sheet, but provide few constraints for the Greenland ice sheet for the future transient nature of high-end ice mass loss estimates on century time scales. They merely offer insight about sea level high stands during characteristic warm periods in the past.\nEvaluation of the High-End Contribution for Greenland\uf0c1\nCritically important for generating a high-end estimate for the Greenland ice sheet is the SMB as expressed in Figure 2. SMB and ocean changes are the driver for changes in outlet glaciers and ice sheet dynamics. While SMB and outlet glacier changes have contributed to observed SLR changes, SMB changes are expected to become more important on longer time scales and with stronger forcing. Changes in ice sheet dynamics are expected to be limited. For a high-end estimate of the Greenland ice sheet there is most likely a strong divergence between the low warming and the high warming scenario, particularly beyond 2100. A recent study (No\u00ebl et al., 2021), based on a regional climate model forced with a GCM, indicates that the SMB over the ice sheet is negative for a global warming above 2.7 K for a constant topography, ignoring elevation-change-related feedbacks. If so, no processes adding mass to the ice sheet will exist and this has been argued to be a \u201ctipping-point\u201d for the ice sheet. On the other hand, this is challenged by studies including dynamical changes of the topography (Gregory et al., 2020; Le clec\u2019h et al., 2019) because the ice sheet may evolve to a smaller equilibrium state. The importance of the existence of a tipping-point is merely on the millennial time scales, but a negative SMB at least suggests a strong nonlinear response to a large climate forcing. Table 1 illustrates the critical processes to consider when estimating a high-end contribution for the Greenland ice sheet. For the 21st century, we estimate the high-end estimate for the +5\u00b0C scenario to be around 0.30 m, being twice the ISMIP6 results (Goelzer et al., 2020) where the factor two arises from the possible atmospheric circulation changes (Church et al., 2013; Delhasse et al., 2018, 2020) that are not captured in the models. This factor of two should be interpreted as the deep uncertainty around the SMB changes in a changing climate caused by a poor understanding of modeling circulation changes and surface processes affecting the albedo. At this point, our approach deviates from Fox-Kemper et al. (2021) who use expert judgment as part of their lines of evidence.\nFigure 2: Causal relation between processes leading to a high-end contribution of Greenland to sea level rise (SLR). Critical processes are albedo, ocean forcing and atmospheric circulation changes. These three processes impact the surface mass balance (SMB). Outlet glaciers change by changes in SMB and ocean forcing and SMB also influences the dynamics of the main ice sheet, where the ocean affects the outlet glaciers, together controlling the SLR.\nFor a +2\u00b0C scenario there seem to be few processes that can be large, hence we use the upper end of the very likely range assessed by AR6 being 0.10 m as the high-end estimate (Fox-Kemper et al., 2021). The omission of feedbacks and circulation changes are judged to only be important for large perturbations, justifying excluding them for a high-end estimate. Consequently, high-end projections in 2300 for a +2\u00b0C scenario are still constrained and estimated to be 0.3 m, as the SMB is the main driving process. The few studies, based on intermediate complexity climate models (Table 13.8, Church et al., 2013) suggest a high-end contribution of 1.2 m in 2300 from the Greenland ice sheet under a high scenario. A more recent but similar result is obtained using an intermediate complexity model coupled to an ice sheet model (Van Breedam et al., 2020). Here, we suggest, following the projections in 2100, to include a factor 2 based on the possible atmospheric circulation changes above, as the deep uncertainty in the SMB, thereby arriving at a high-end estimate of 2.5 m for Greenland under a +8\u00b0C\u201310\u00b0C scenario in 2300. This is close to the structured expert judgment by Bamber et al. (2019), but higher than the experiment by Aschwanden where the degree-day factors are constrained by the observational period 2000\u20132015 (Fox-Kemper et al., 2021).\nAntarctica\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html"}
{"id": "9597ccc3a71c-6", "text": "Figure 2: Causal relation between processes leading to a high-end contribution of Greenland to sea level rise (SLR). Critical processes are albedo, ocean forcing and atmospheric circulation changes. These three processes impact the surface mass balance (SMB). Outlet glaciers change by changes in SMB and ocean forcing and SMB also influences the dynamics of the main ice sheet, where the ocean affects the outlet glaciers, together controlling the SLR.\nFor a +2\u00b0C scenario there seem to be few processes that can be large, hence we use the upper end of the very likely range assessed by AR6 being 0.10 m as the high-end estimate (Fox-Kemper et al., 2021). The omission of feedbacks and circulation changes are judged to only be important for large perturbations, justifying excluding them for a high-end estimate. Consequently, high-end projections in 2300 for a +2\u00b0C scenario are still constrained and estimated to be 0.3 m, as the SMB is the main driving process. The few studies, based on intermediate complexity climate models (Table 13.8, Church et al., 2013) suggest a high-end contribution of 1.2 m in 2300 from the Greenland ice sheet under a high scenario. A more recent but similar result is obtained using an intermediate complexity model coupled to an ice sheet model (Van Breedam et al., 2020). Here, we suggest, following the projections in 2100, to include a factor 2 based on the possible atmospheric circulation changes above, as the deep uncertainty in the SMB, thereby arriving at a high-end estimate of 2.5 m for Greenland under a +8\u00b0C\u201310\u00b0C scenario in 2300. This is close to the structured expert judgment by Bamber et al. (2019), but higher than the experiment by Aschwanden where the degree-day factors are constrained by the observational period 2000\u20132015 (Fox-Kemper et al., 2021).\nAntarctica\uf0c1\nCurrently significant ice mass loss is observed in West-Antarctica (Bamber et al., 2018; Cazenave et al., 2018; Rignot et al., 2019; A. Shepherd et al., 2018): over the period 2010\u20132019 Antarctica contributed 0.4 mm/yr to GMSL rise (Fox-Kemper et al., 2021). Most studies indicate that ice loss in West Antarctica follows from increased rates of sub-ice shelf melting caused by ocean circulation changes, in particular in the Amundsen Sea sector (Adusumilli et al., 2018; Paolo et al., 2015), but it is questioned whether this is the result of anthropogenic climate change or natural variability in the ocean as suggested by Jenkins et al. (2018) or by a combination of both processes (Holland et al., 2019). Against this background, it is important to consider which processes may lead to substantial continued or accelerated mass loss from Antarctica, and therefore its contribution to high-end sea level scenarios. In addition, it needs to be considered whether there are instabilities in the system which influence high-end estimates. We explore this in more detail than for the previous two components because of the large uncertainty and the large potential contribution to SLR from Antarctica.\nProcesses in Antarctica Relevant for High-End Sea Level Scenarios\uf0c1\nA major uncertainty in future Antarctic mass losses resulting in high-end SLR is connected to the possibility of rapid and/or irreversible ice losses through instabilities in marine-based parts of the ice sheet, as hypothesized for the Marine Ice Sheet Instability (MISI) and the Marine Ice Cliff Instability (MICI), see Pattyn et al. (2018) for further explanation. MISI is a self-reinforcing mechanism within marine ice sheets that lie on a bed that slopes down towards the interior of the ice sheet. If these instabilities are activated it might be that they overshadow climate forcing scenarios. At present, floating ice shelves exert back stress on the inland ice, limiting the flow of ice off the continent and resulting in a stable ice sheet configuration. In the absence of ice-shelf buttressing caused by loss of the shelf or substantial thinning, ice sheets on a bed sloping towards the interior are, under certain circumstances, inherently unstable (Schoof, 2007; Sergienko & Wingham, 2019, 2021), and stable grounding line positions can only be reached when the bed slopes in the opposite direction (sloping bed upwards to the interior; Pattyn et al., 2012). If ice shelf buttressing remains, however, stable grounding line positions can also be reached on downward sloping beds for specific geometric configurations (Cornford et al., 2020; Gudmundsson et al., 2012; Haseloff & Sergienko, 2018; Sergienko & Wingham, 2019). Weak buttressing may not prevent grounding-line retreat, but may slow it.\nAntarctic ice shelves modulate the grounded ice flow, and their thinning and weakening is crucial in the timing and magnitude of major ice mass loss or the onset of MISI. This onset of rapid MISI is controlled by the timing of ice shelf breakup or collapse, and the resulting loss of buttressing that otherwise would prevent MISI from occurring. Ice sheet models demonstrate that the permanent removal of all Antarctic ice shelves leads to MISI, West Antarctic ice sheet collapse, and 2\u20135 m SLR over several centuries (Sun et al., 2020).\nThe MICI hypothesis of rapid, unmitigated calving of thick ice margins triggered by ice shelf collapse has been included in an ice sheet model by DeConto and Pollard (2016); DeConto et al. (2021) and Pollard et al. (2015). Including the MICI processes was partly motivated by inconsistencies with reconstructed paleo sea level proxies (Bertram et al., 2018; DeConto & Pollard, 2016), but also has a sound physical process based support (Bassis et al., 2021; Crawford et al., 2021). Like MISI, the onset of MICI is triggered by the loss of buttressing ice shelves facilitating the creation of ice cliffs which subsequently destabilize. Its onset also depends on the magnitude of ocean and atmospheric warming. A major difference is the more rapid calving of the ice cliffs at the front of the ice sheet inducing a faster retreat.\nImportantly, without the disintegration of buttressing ice shelves, neither MISI nor MICI can operate and the dynamic mass loss contribution from Antarctica to SLR is limited. The current atmospheric state is too cold for a large contribution from surface melt. Further, a few degrees of Antarctic warming leads to more snow accumulation, partly offsetting the increases in oceanic melt and the resulting loss of ice by changes in the ice flow (Seroussi et al., 2020). However, the possibility of larger changes induced by ocean processes cannot be excluded. It has been argued that, in particular, the waters below the Filchner-Ronne ice-shelf could warm by more than 2\u00b0C as a result of changes in ocean circulation (Hellmer et al., 2012). Both observations (Darelius et al., 2016; Ryan et al., 2020) and models (Hazel & Stewart, 2020; Naughten et al., 2017) support this as a possibility, although a recent study (Naughten et al., 2021) suggests that such a change in circulation may be unlikely under the climate scenarios considered here for the 21st century. The LARMIP experiments (Levermann et al., 2020) provide an indication that the impact of such a change could be on the order of 0.2 m global mean SLR by 2100.\nObservations of basal melt are hampered by the inaccessibility of the sub-ice-shelf cavities, and modeling of basal melt is challenging both because of the lack of observational validation and the limited resolution of the cavities that is possible in models covering continental scales. To date, most ocean model components within coupled climate models do not include the regions beneath the ice shelves. Simplified parameterizations of sub-shelf cavity circulation have been developed, such as the PICO-model (Reese et al., 2018), or the cross-sectional plume model (Lazeroms et al., 2018, 2019; Pelle et al., 2019). Alternatively (Jourdain et al., 2020), propose a parameterization of sub-shelf melt based on the use of low-resolution CMIP5 ocean models, calibrated to observed melt rates (see also Favier et al., 2019). Rather than attempting to explicitly resolve the sub-shelf circulation (Levermann et al., 2020), estimated the Antarctic contribution based on low-resolution ocean temperature change with a linear response function capturing all the uncertainties. This approach ignores dampening or self-amplifying processes and concentrates on the forced response but includes a dynamical response of the ice sheet itself.", "source": "https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html"}
{"id": "9597ccc3a71c-7", "text": "Observations of basal melt are hampered by the inaccessibility of the sub-ice-shelf cavities, and modeling of basal melt is challenging both because of the lack of observational validation and the limited resolution of the cavities that is possible in models covering continental scales. To date, most ocean model components within coupled climate models do not include the regions beneath the ice shelves. Simplified parameterizations of sub-shelf cavity circulation have been developed, such as the PICO-model (Reese et al., 2018), or the cross-sectional plume model (Lazeroms et al., 2018, 2019; Pelle et al., 2019). Alternatively (Jourdain et al., 2020), propose a parameterization of sub-shelf melt based on the use of low-resolution CMIP5 ocean models, calibrated to observed melt rates (see also Favier et al., 2019). Rather than attempting to explicitly resolve the sub-shelf circulation (Levermann et al., 2020), estimated the Antarctic contribution based on low-resolution ocean temperature change with a linear response function capturing all the uncertainties. This approach ignores dampening or self-amplifying processes and concentrates on the forced response but includes a dynamical response of the ice sheet itself.\nIdeally, sub-shelf circulation and ocean melt should be represented in three dimensions, at the high spatial resolution, and interactively coupled with the ice sheet and the ocean models (Comeau et al., 2022; Smith et al., 2021). This represents a significant ongoing modeling challenge (e.g., Van Westen & Dijkstra, 2021), together with uncertainties in the bathymetry, limiting confidence in future projections of ice shelf loss.\nIt is also critical to consider other processes than basal melt or circulation changes that can lead to disintegration of the major ice shelves. In particular, one needs to consider calving and surface melt that can enhance ice shelf surface crevassing and hydrofracturing. While hydrofracturing is an important process to reduce or eliminate buttressing and facilitate ice sheet instability, fracturing without surface melt also weakens the ice shelves, particularly along their margins. This is observed in the Amundsen Sea region (Lhermitte et al., 2020), but is not yet fully implemented and validated in large-scale ice sheet models, hindering an estimate of the timing of ice shelf collapse.\nAs the pace of future atmospheric warming and the capacity of firn to absorb melt water remain uncertain, predictions of ice shelf surface melting by 2100 and subsequent ice shelf disintegration under RCP8.5/SSP5-8.5 vary widely. Based on a regional climate model (Trusel et al., 2015), compiled melt rates under warming scenarios. Under RCP8.5/SSP5-8.5, several small ice shelves will be exposed by 2100 to melt rates exceeding the values observed at the time that the Larsen-B ice-shelf broke up in 2002. However, the major ice shelves (e.g., Filchner-Ronne, Ross Amery) remain stable over this century, but likely not over longer time scales. These melt rates contrast with the results of independent simulations using simpler climate models and a different scheme to calculate surface melt (DeConto & Pollard, 2016) that suggest a much faster disintegration of the ice shelves. An updated assessment (DeConto et al., 2021) confirms the ice shelf stability for this century, but also shows a rapid disintegration soon after under RCP8.5/SSP5-8.5. An intercomparison study showed that the increased melt is partly compensated by increased accumulation (Seroussi et al., 2020), regardless of the emissions scenario followed. It shows disintegration of some small ice shelves, but not the big shelves which constrain high-end contributions to 2100. Soon after 2100, this is likely not the case any longer under RCP8.5/SSP5-8.5. So this facilitates the construction of high-end estimates for 2100 and 2300. For 2100, we can assume that the consequence in terms of SLR is not yet visible, but for 2300 we can be sure that the ice sheet has had sufficient time to start reacting to the break-up of ice shelves under strong forcing scenarios.\nWhat If the Major Ice Shelves Break Up?\uf0c1\nBoth MISI and MICI might be important for SLR if and when ice shelves collapse. Ice-shelf collapse, therefore, can be considered the key prerequisite for these instabilities to commence. By \u201cinstability\u201d we imply that, once initiated, the process of retreat continues irrespective of the applied climate forcing. MISI is a dynamic response of the ice sheet to a change in the buttressing conditions, whereas MICI might lead to direct mass loss via tall collapsing cliffs, which also may be a self-sustaining process. Research on MICI has focused on the critical height at which vertical ice cliffs become unstable (Bassis & Walker, 2012; Clerc et al., 2019; Parizek et al., 2019) and plausible rates of calving and retreat (Schlemm & Levermann, 2019). Estimates of ice-cliff calving have also used observations of calving ice-fronts in Greenland as a constraint (e.g., DeConto & Pollard, 2016), although Greenland glaciers might not be representative of the behavior of wider and thicker outlet glaciers in Antarctica that have lost their ice shelves. The importance of the ice cliff calving mechanism, while likely relevant to high-end sea level scenarios if ice shelves are lost, is currently disputed in the literature (Fox-Kemper et al., 2021).\nA second major uncertainty in the response of ice margins once shelves are lost is the uncertainty about the physics of the basal friction conditions near the grounding line, which could further enhance seaward ice flow (Pattyn et al., 2018; Tsai et al., 2015). As a result, the few existing ice model projections for 2300 vary considerably (Bulthuis et al., 2019; Golledge et al., 2015; Levermann et al., 2020), but should all be considered physically plausible and thereby provide independent lines of evidence for a high-end SLR (see, Table 3 for values).\nThe Antarctic Buttressing Model Intercomparison project (ABUMIP; Sun et al., 2020) shows that instantaneous and sustained loss of all Antarctic ice shelves leads to multi-meter SLR over several centuries (1\u201312 m in 500 yr from present). The participating models did not include MICI, and the variation in magnitude of ice loss was found to be related to subglacial processes, where plastic friction laws generally lead to enhanced ice loss. This experiment should be considered as an upper bound as artificially regrowth of ice shelves was prevented, and other dampening effects were ignored.\nPaleo evidence of past ice loss might provide some constraints on the uncertainty in ice sheet models, but available data are mostly restricted to total ice loss and remain limited in their ability to constrain rates of ice loss (Dutton et al., 2015).\nRegardless of the processes driving ice loss on the ice shelves, the retreat of ice also leads to an instantaneous and time-delayed response of the underlying bedrock and an immediate reduction in gravitational attraction between the ice sheet and the nearby ocean. The resulting reduction of relative sea level at the grounding line may stabilize its retreat, providing a negative feedback (Barletta et al., 2018; DeConto et al., 2021; Gomez et al., 2010, 2015; Larour et al., 2019; Pollard et al., 2017) showed that these effects do little to slow the pace of retreat until after the mid-twenty-third century in the Amundsen Sea region. Coulon et al. (2021) also find that the West-Antarctic ice sheet destabilizes for high-forcing regardless of the mantle viscosity. At the same time, Kachuck et al. (2020) and Pan et al. (2022) indicate that the weak viscosity in West-Antarctica might significantly reduce the West-Antarctic contribution over the next 150 yr, because the rapid bedrock uplift compensates the grounding line retreat. Altogether, this suggests that for the shorter time scales over the next centuries, it cannot be excluded that this negative feedback plays a role, but improved 3D viscosity models are needed to quantify this effect.\nEvaluation of the High-End Contribution for Antarctica\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html"}
{"id": "9597ccc3a71c-8", "text": "The Antarctic Buttressing Model Intercomparison project (ABUMIP; Sun et al., 2020) shows that instantaneous and sustained loss of all Antarctic ice shelves leads to multi-meter SLR over several centuries (1\u201312 m in 500 yr from present). The participating models did not include MICI, and the variation in magnitude of ice loss was found to be related to subglacial processes, where plastic friction laws generally lead to enhanced ice loss. This experiment should be considered as an upper bound as artificially regrowth of ice shelves was prevented, and other dampening effects were ignored.\nPaleo evidence of past ice loss might provide some constraints on the uncertainty in ice sheet models, but available data are mostly restricted to total ice loss and remain limited in their ability to constrain rates of ice loss (Dutton et al., 2015).\nRegardless of the processes driving ice loss on the ice shelves, the retreat of ice also leads to an instantaneous and time-delayed response of the underlying bedrock and an immediate reduction in gravitational attraction between the ice sheet and the nearby ocean. The resulting reduction of relative sea level at the grounding line may stabilize its retreat, providing a negative feedback (Barletta et al., 2018; DeConto et al., 2021; Gomez et al., 2010, 2015; Larour et al., 2019; Pollard et al., 2017) showed that these effects do little to slow the pace of retreat until after the mid-twenty-third century in the Amundsen Sea region. Coulon et al. (2021) also find that the West-Antarctic ice sheet destabilizes for high-forcing regardless of the mantle viscosity. At the same time, Kachuck et al. (2020) and Pan et al. (2022) indicate that the weak viscosity in West-Antarctica might significantly reduce the West-Antarctic contribution over the next 150 yr, because the rapid bedrock uplift compensates the grounding line retreat. Altogether, this suggests that for the shorter time scales over the next centuries, it cannot be excluded that this negative feedback plays a role, but improved 3D viscosity models are needed to quantify this effect.\nEvaluation of the High-End Contribution for Antarctica\uf0c1\nA chain of processes illustrated in Figure 3 control the contribution from Antarctica to SLR. The stability of the ice shelves is central, and this is controlled by surface melt, bottom melt, calving and hydrofracturing. The relative importance of these factors changes because of regional climate change as estimated by global climate models. The uncertainty in the regional climate in the southern hemisphere is generally larger than in the northern hemisphere, increasing uncertainties in the Antarctic component (Heuz\u00e9 et al., 2013; Russell et al., 2018). Once the ice shelves are broken up, the dynamics of the ice sheet, including the MISI and MICI mechanisms, control how much ice is lost. All studies for a 5\u00b0C warming at the end of the century indicate a multi-meter contribution to GMSL from Antarctica on longer than a century time scale. Major ice shelves will disintegrate eventually under that magnitude of warming. The timing of the disintegration is uncertain, but unlikely to have a large effect on high-end SLR already during the 21st century. For this reason, we consider the upper range of Bulthuis et al. (2019), Golledge et al. (2019, 2015), and Levermann et al. (2020), to estimate the high-end contribution of the Antarctic Ice Sheet in 2100 to be 0.39 m for a +2\u00b0C scenario (Levermann et al., 2020) and 0.59 m for a +5\u00b0C scenario, which is close to the results by Edwards et al. (2021). We do this as no formal probability distributions are available for the likelihood of ice shelf collapse and cliff instability. The study by DeConto and Pollard (2016) is not included for our estimates for 2100, because of a potential overestimation of surface melt rates which initiates shelf disintegration too early. For 2300, only a limited number of ice dynamical studies exist, but they all agree that several meters of SLR from Antarctica is possible because of ice shelf collapse, and limited constraints on instability mechanisms and ice dynamics. Based on Bulthuis et al. (2019), DeConto et al. (2021), and Golledge et al. (2015), we estimate a high-end contribution to be 1.35 m for a +2\u00b0C scenario and 6 m for a +8\u00b0C\u201310\u00b0C scenario in 2300. A more recent study by DeConto et al. (2021) including improved estimates for surface melt rates is included for the 2300 estimates. So, despite the different physics of all those studies, we believe that we can combine those studies for a high-end estimate because they agree on the onset of shelf disintegration around 2100 and far ahead of 2300. For the +8\u00b0C\u201310\u00b0C scenario, we take the average of the three dynamical studies, while realizing that constraints on the rates of mass loss are highly uncertain and vary strongly among the models.\nFigure 3: Causal relation between processes leading to a high-end contribution of Antarctica to sea level rise (SLR). The Antarctic climate response affects Surface Melt and Bottom Melt, which together with Calving and Hydrofracturing determine the stability of the ice shelves. If the ice shelves break up, the dynamics encompassing instability mechanisms like Marine Ice Sheet Instability (MISI) and Marine Ice Cliff Instability (MICI) and basal sliding control the final contribution of the Antarctic ice sheet to high-end SLR.\nTable 1 illustrates the critical processes for a high-end estimate for the Antarctic contribution.\nIn summary, it is not only the poor understanding of the dynamics of ice flow, but also the limited understanding of the processes controlling the break-up of the major ice shelves that determines the uncertainty in the timing and magnitude of the Antarctic contribution to sea level. When combined, this leads to the Antarctic component having the largest uncertainties in the sea level projections.\nLines of Evidence for High-End Scenarios\uf0c1\nIn Sections 4\u20136, 4\u20136, 4\u20136, we discussed the contribution of cryospheric components to SLR, which largely follow from CMIP climate model outputs applied as offline-forcing for ice sheet model simulations. The critical processes for the different components are summarized in Table 1.\nIn this section, we integrate these components into a total high-end SLR estimate focusing on the time slices 2100 and 2300 and the two temperature scenarios because there is a reasonable sample of studies available. The multiple lines of evidence enable us to go beyond single studies or even single multimodel experiments and provide a more complete synthesis of the plausible physical response, thereby creating estimates that are more salient to practitioners. Such an approach has been used for other seemingly intractable problems such as narrowing the range of Equilibrium Climate Sensitivity (Sherwood et al., 2020) as used in AR6.\nFor Greenland and Antarctica, the lines of evidence include an assessment of the physical processes. While we cannot define a precise percentile for the total high-end SLR, our interpretation of the multiple lines of evidence as outlined in the Greenland and Antarctic Sections above, is that it lies in the tail and comprises an unlikely outcome. Circulation changes may be important for high-end estimates but only under high forcing for Greenland, instability mechanisms and basal processes and uncertainty in timing of ice shelf collapse result in the high-estimate for Antarctica under a high forcing. For low forcing the SMB changes control the high-estimate for Greenland and the basal melt rate changes control the high-estimate for Antarctica.\nSince for longer time scales and higher temperature scenarios, the Antarctic ice sheet contribution dominates the uncertainty in SLR, we can essentially obtain an estimate of high-end SLR by combining the cryospheric components and adding known contributions from thermal expansion and land water changes. Here, the thermal expansion component of SLR and its contribution to the high-end follows directly from the thermal expansion of sea water assessed by Fox-Kemper et al. (2021) as the resulting mean plus twice the standard deviation. The LWSC results mainly from groundwater changes and is partly induced by socio-economic changes and partly due to climate change. In a review by Bierkens and Wada (2019), the upper end of the socio-economic contribution is estimated to be 0.9 mm/yr, and the climate driven component is estimated to be 40 mm in 2100, independent of the scenario (Karabil et al., 2021). This is partly offset by the projections for more dams being built in the early 22nd century (Hawley et al., 2020; Zarfl et al., 2015). Recent papers argue for possible changes in precipitation (Wada et al., 2012), endorheic basin storage changes (Reager et al., 2016; Wang et al., 2018) and increased droughts (Pokhrel et al., 2021), all affecting SLR in a positive or a negative sense. As the LWSC components remains small in all cases and it is not critical for a high-end estimate, here we simply follow (Fox-Kemper et al., 2021).", "source": "https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html"}
{"id": "9597ccc3a71c-9", "text": "For Greenland and Antarctica, the lines of evidence include an assessment of the physical processes. While we cannot define a precise percentile for the total high-end SLR, our interpretation of the multiple lines of evidence as outlined in the Greenland and Antarctic Sections above, is that it lies in the tail and comprises an unlikely outcome. Circulation changes may be important for high-end estimates but only under high forcing for Greenland, instability mechanisms and basal processes and uncertainty in timing of ice shelf collapse result in the high-estimate for Antarctica under a high forcing. For low forcing the SMB changes control the high-estimate for Greenland and the basal melt rate changes control the high-estimate for Antarctica.\nSince for longer time scales and higher temperature scenarios, the Antarctic ice sheet contribution dominates the uncertainty in SLR, we can essentially obtain an estimate of high-end SLR by combining the cryospheric components and adding known contributions from thermal expansion and land water changes. Here, the thermal expansion component of SLR and its contribution to the high-end follows directly from the thermal expansion of sea water assessed by Fox-Kemper et al. (2021) as the resulting mean plus twice the standard deviation. The LWSC results mainly from groundwater changes and is partly induced by socio-economic changes and partly due to climate change. In a review by Bierkens and Wada (2019), the upper end of the socio-economic contribution is estimated to be 0.9 mm/yr, and the climate driven component is estimated to be 40 mm in 2100, independent of the scenario (Karabil et al., 2021). This is partly offset by the projections for more dams being built in the early 22nd century (Hawley et al., 2020; Zarfl et al., 2015). Recent papers argue for possible changes in precipitation (Wada et al., 2012), endorheic basin storage changes (Reager et al., 2016; Wang et al., 2018) and increased droughts (Pokhrel et al., 2021), all affecting SLR in a positive or a negative sense. As the LWSC components remains small in all cases and it is not critical for a high-end estimate, here we simply follow (Fox-Kemper et al., 2021).\nA summary overview of the different components to SLR is shown in Table 2. Assuming perfect correlation between all contributions, the total global high-end SLR estimate in 2100 amounts to 0.86 and 1.55 m for +2\u00b0C and +5\u00b0C, respectively. Focusing on 2300, these numbers increase considerably to 2.5 and 10.4 m, for +2\u00b0C and +8\u00b0C\u201310\u00b0C, respectively. Alternatively, assuming total independence of contributions, the high-end rise is 0.72 and 1.27 m for 2100 and 2.2 and 8.6 m in 2300, for +2\u00b0C and +8\u00b0C\u201310\u00b0C, respectively. Hence, the assumption of independence significantly lowers the estimates; for a high scenario, the difference is around 0.3 m in 2100 and nearly 2 m in 2300.\nTable 2: The High-End Estimates for the Different Sea Level Components, and Their Sum\n2100    2100    2300    2300\n+2\u00b0C    +5\u00b0C    +2\u00b0C    +8\u00b0C\u201310\u00b0C\nGlaciers        0.15a   0.27    0.28    0.32\nGreenland       0.10    0.29    0.39    2.5\nAntarctica      0.39    0.59    1.35    6\nThermal expansion       0.18    0.36    0.35    1.51\nLWSC    0.04    0.04    0.10    0.10\nTotal high-end estimateb        Upper end of the range  0.9     1.6     2.5     10\nLower end of the range  0.7     1.3     2.2     9\n^a Values are presented relative to 1995\u20132014 in meters. To compare to a baseline of 1986\u20132005 as used in AR5 and SROCC add 0.03 m for total sea level and 0.01 m for individual components.\n^b The high-end of the range follows from the assumption of perfect correlation (all covariances between the components equal to one), the low-end of the range follows from the assumption of fully uncorrelated (all covariances between the components equal to zero).\nSimply summing all high-end components implies a perfect dependency between all the components which is unlikely, as explained above. It would for instance imply that enhanced basal melting in Antarctica is perfectly correlated to specific atmospheric conditions surrounding the Greenland ice sheet. Alternatively, less risk-averse users could assume that all components are independent of each other, which is also not very likely. The high-end estimates should be considered in the context of the mean and likely ranges reported by the IPCC assessments. This also implies that users who are less risk-averse, or have the ability, to iteratively build resilience, can decide to consider the mean values for all components from an IPCC assessment and add the high-end contribution from Antarctica and Greenland to develop a tailored, but still transparent high-end estimate. In this way, the high-end components and how best to sum them encourage discussion between sea level scientists and practitioners and co-production of the most appropriate SLR scenarios for the respective needs, including the development of storylines (T. G. Shepherd & Lloyd, 2021). For a more easily accessible approach, and because both perfect correlation and full independence of all components seem unlikely based on today\u2019s understanding, practitioners might simply average the high end estimate projections in this paper between the two to derive a single, high end projection for use in planning, if that is more useful than a range.\nTable 2 also indicates that the high-end estimate for GMSL in 2100 for a significant warming of +5\u00b0C does differ from the conclusions drawn by Fox-Kemper et al. (2021) and Oppenheimer et al. (2019), who argue that a GMSL of 2 m cannot be excluded, as supported by results from an expert elicitation process (Bamber et al., 2019). Table 3 shows the detailed differences between this study and (Fox-Kemper et al., 2021) for Greenland and Antarctica showing lower values in this study for Greenland in 2100 for both scenarios and for Greenland and Antarctic for the 2\u00b0C scenario in 2300. A reason might be that the expert elicitation used by Fox-Kemper et al. (2021) was influenced by DeConto and Pollard (2016) which is not used here. However, the closed nature of the expert elicitation method does not allow a firm conclusion.\nTable 3: A Comparison Between This Paper and the IPCC AR6 Values\nReferences^a    Approach/processes      This paper      AR6 (Table 9.8 and Table 9.11)  Remarks\n2100 +2\u00b0C\nThermal expansion       Fox-Kemper et al. (2021)        AR6 assessment  0.18b   0.18\nGlaciers        Marzeion et al. (2020)  Temperature change, ensemble 10 climate models, 10 glacier models       0.15    0.11\nGreenland       Fox-Kemper et al. (2021)        AR6 assessment, medium confidence       0.10    0.30    <<cAR6\nAntarctica      Levermann et al. (2020) Basal melt for 16 ice sheet models      0.39    0.25    >>AR6\nLand water storage change       Fox-Kemper et al. (2021)        AR6 assessment  0.04    0.04\nTotal           Range depending on correlation (Section 3)      0.72\u20130.86       0.79\n2100 +5\u00b0C\nThermal expansion       Fox-Kemper et al. (2021)        AR6 assessment  0.36    0.36\nGlaciers        Marzeion et al. (2020)  Temperature change, ensemble 10 climate models, 10 glacier models       0.27    0.20\nGreenland       Delhasse et al. (2018, 2020) and Goelzer et al. (2020)  ISMIP6 assessment including circulation changes and missing feedbacks leading to deep uncertainty       0.29    0.59    <<AR6\nAntarctica      Bulthuis et al. (2019), DeConto et al. (2021), and Golledge et al. (2015)       Mixture basal melt and ice dynamical studies    0.59    0.56\nLand water storage change       Fox-Kemper et al. (2021)        AR6 assessment  0.04    0.04\nTotal           Range depending on correlation (Section 3)      1.27\u20131.55       1.60\n2300 +2\u00b0C", "source": "https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html"}
{"id": "9597ccc3a71c-10", "text": "References^a    Approach/processes      This paper      AR6 (Table 9.8 and Table 9.11)  Remarks\n2100 +2\u00b0C\nThermal expansion       Fox-Kemper et al. (2021)        AR6 assessment  0.18b   0.18\nGlaciers        Marzeion et al. (2020)  Temperature change, ensemble 10 climate models, 10 glacier models       0.15    0.11\nGreenland       Fox-Kemper et al. (2021)        AR6 assessment, medium confidence       0.10    0.30    <<cAR6\nAntarctica      Levermann et al. (2020) Basal melt for 16 ice sheet models      0.39    0.25    >>AR6\nLand water storage change       Fox-Kemper et al. (2021)        AR6 assessment  0.04    0.04\nTotal           Range depending on correlation (Section 3)      0.72\u20130.86       0.79\n2100 +5\u00b0C\nThermal expansion       Fox-Kemper et al. (2021)        AR6 assessment  0.36    0.36\nGlaciers        Marzeion et al. (2020)  Temperature change, ensemble 10 climate models, 10 glacier models       0.27    0.20\nGreenland       Delhasse et al. (2018, 2020) and Goelzer et al. (2020)  ISMIP6 assessment including circulation changes and missing feedbacks leading to deep uncertainty       0.29    0.59    <<AR6\nAntarctica      Bulthuis et al. (2019), DeConto et al. (2021), and Golledge et al. (2015)       Mixture basal melt and ice dynamical studies    0.59    0.56\nLand water storage change       Fox-Kemper et al. (2021)        AR6 assessment  0.04    0.04\nTotal           Range depending on correlation (Section 3)      1.27\u20131.55       1.60\n2300 +2\u00b0C\nThermal expansion       Fox-Kemper et al. (2021)        AR6 assessment  0.35    0.35\nGlaciers        Goelzer et al. (2012) and Marzeion et al. (2012)        Temperature change, single parameterized glacier models 0.28    0.29\nGreenland       Fox-Kemper et al. (2021)        AR6 assessment  0.39    1.28    <<AR6\nAntarctica      Bulthuis et al. (2019), DeConto et al. (2021), and Golledge et al. (2015)       Four ice dynamical studies with a range of physical processes simulated 1.35    1.56\nLand water storage change       Fox-Kemper et al. (2021)        AR6 assessment  0.1     0.1\nTotal           Range depending on correlation (Section 3)      2.19\u20132.47       3.1\n2300 +8\u00b0C\u201310\u00b0C\nThermal expansion       Fox-Kemper et al. (2021)        AR6 assessment  1.51    1.51\nGlaciers        Farinotti et al. (2019) Temperature change, all glaciers melted 0.32    0.32\nGreenland       Church et al. (2013), Delhasse et al. (2018, 2020)      SMB changes including deep uncertainty  2.5     2.23\nAntarctica      Bulthuis et al. (2019), DeConto et al. (2021), and Golledge et al. (2015)       Four ice dynamical studies with a range of physical processes simulated 6       13.54   <<AR6\nLand water storage change       Fox-Kemper et al. (2021)        AR6 assessment  0.10    0.10\nTotal           Range depending on correlation (Section 3)      8.59\u201310.43      16.2\n^a Reference used to compile the values in this study.\n^b Values are in meters relative to a baseline period of 1995\u20132014.\n^c >>/<< indicates more than 20% difference between this study and AR6. We used from AR6 the highest 83rd percentile projections across all probability distributions considered, including low confidence processes.\nIn 2300, the contribution of the Antarctic ice sheet is poorly constrained, so the high-end estimate is considerably higher than most previous estimates (Church et al., 2013; Oppenheimer et al., 2019), but not as high as (Fox-Kemper et al., 2021). This points to the large uncertainties in projecting sea levels over multiple centuries which arises from: (a) the poorly constrained timing of the collapse of major ice shelves around Antarctica, and (b) the limited understanding of ice-dynamical and subglacial processes. For 2100, the difference for Greenland seems to arise from the difference in structured expert judgment and our physical assessment of the literature.\nAll the high-end scenarios imply a major adaptation challenge due to SLR, especially beyond 2100 (Haasnoot et al., 2020). What we present builds on a combination of model results and an assessment of different studies leading to lines of evidence per component, thereby providing practical and flexible guidance to practitioners. Further discussions between sea level scientists and practitioners facilitate the application of this knowledge most effectively. We recommend that these storylines should be updated at regular intervals (consistent to the IPCC process), reflecting the evolution of the body of knowledge. This provides a more robust update process than a whiplash response due to single new papers, which may contain high-profile results but lack community consensus or understanding.\nTable 2 indicates that the projected temperature has a large effect on the projected high-end SLR during the 21st century and beyond. It also shows that the long timescales associated with slow processes in the ocean and ice sheets provide a strong incentive for mitigation. An SLR of 10 m by 2300 would be extremely challenging and costly, suggesting the need for a near-universal retreat from the present coastline including the most developed and valuable areas, or alternatively, protection/advance on a scale that is hard to envisage, even where artificial protection is the norm today. For a 2\u00b0C temperature rise, a high-end 2.5 m rise by 2300 would still present significant challenges, but with rates of SLR that are much slower, offering a wider range of adaptation options and choices. Current experience of rapidly subsiding cities (Nicholls & Tol, 2006) demonstrates that protection for such a magnitude of SLR is feasible if desired and it can be financed. Hence, both from an adaptation and mitigation perspective, smaller temperature increases are preferred.\nConsidering 2050, there is little difference between low and high-temperature scenarios, as the tails of the distribution are more constrained on decadal time scales. This reflects that the major source of uncertainty\u2014the break-up of major ice shelves in Antarctica\u2014is not foreseen over these time scales.\nAddressing 2150 as a time horizon is desirable as many decisions extend over a century (i.e., beyond 2100), but difficult scientifically because of the uncertainty in the timing of a possible break-up of the major Antarctica ice shelves. A first attempt is offered by Fox-Kemper et al. (2021). We argue that there is no evidence for an early break-up of major ice shelves combined with a major loss of grounded Antarctic ice mass influencing the high-end estimate during the 21st century. At the same time, DeConto et al. (2021) indicate a break up of major ice shelves around 2100 or soon after for the high-forcing scenario. The rate of mass loss which might then occur either by enhanced basal sliding or marine ice cliff and shelf instability is poorly constrained, making it extremely difficult to provide a high-end SLR for 2150. It illustrates the high uncertainty in the acceleration of Antarctic ice mass loss. This uncertainty affects the high-end estimate for 2300 much less than for 2150 under the high forcing scenario, as by then the major ice shelves are assumed to have broken up, and sufficient time has passed to allow for accelerated Antarctic ice mass loss. Hence, the precise timing is for this reason less critical at this time scale. For low +2\u00b0C forcing scenarios, the prevailing view (DeConto et al., 2021) is that ice shelf break up will occur in fewer regions and therefore the high-end contribution of Antarctica will be considerably lower irrespective of the time scale.", "source": "https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html"}
{"id": "9597ccc3a71c-11", "text": "Considering 2050, there is little difference between low and high-temperature scenarios, as the tails of the distribution are more constrained on decadal time scales. This reflects that the major source of uncertainty\u2014the break-up of major ice shelves in Antarctica\u2014is not foreseen over these time scales.\nAddressing 2150 as a time horizon is desirable as many decisions extend over a century (i.e., beyond 2100), but difficult scientifically because of the uncertainty in the timing of a possible break-up of the major Antarctica ice shelves. A first attempt is offered by Fox-Kemper et al. (2021). We argue that there is no evidence for an early break-up of major ice shelves combined with a major loss of grounded Antarctic ice mass influencing the high-end estimate during the 21st century. At the same time, DeConto et al. (2021) indicate a break up of major ice shelves around 2100 or soon after for the high-forcing scenario. The rate of mass loss which might then occur either by enhanced basal sliding or marine ice cliff and shelf instability is poorly constrained, making it extremely difficult to provide a high-end SLR for 2150. It illustrates the high uncertainty in the acceleration of Antarctic ice mass loss. This uncertainty affects the high-end estimate for 2300 much less than for 2150 under the high forcing scenario, as by then the major ice shelves are assumed to have broken up, and sufficient time has passed to allow for accelerated Antarctic ice mass loss. Hence, the precise timing is for this reason less critical at this time scale. For low +2\u00b0C forcing scenarios, the prevailing view (DeConto et al., 2021) is that ice shelf break up will occur in fewer regions and therefore the high-end contribution of Antarctica will be considerably lower irrespective of the time scale.\nThese new high-end estimates provide practitioners with a range of plausible, transparent, and salient high-end sea level estimates that reflect our current physical understanding and reflect the author\u2019s views that it is not possible with the current level of understanding to match these to precise likelihoods. Further, it encourages practitioners to consider their vulnerability and adaptation options without misleading them about the level of understanding. In this way sea level scientists and practitioners can learn together about the application and co-develop appropriate bespoke solutions. How practioners decide to use these numbers, including the low/high ranges should in our view depend on their risk-averseness, among other factors, which they have to evaluate themselves.\nWe also purposely choose to define high-end estimates for low/+2\u00b0C and high/+5\u00b0C in 2100 and +8\u00b0C\u201310\u00b0C in 2300 temperature increase, with respect to the pre-industrial levels. We cannot provide a likelihood for either of these emissions-driven warming scenarios, and moreover it is also not possible at present to define a high-end for an intermediate emissions or temperature rise scenario (e.g., RCP4.5). While it is obvious that this will be intermediate to the values in Table 2, more detailed specification is not possible due to limited understanding of the time scales and strengths of the feedbacks of the ice components for an intermediate scenario. Essentially, we are convinced that the ice shelves will break-up under high scenarios, but whether they will largely remain intact under lower scenarios is highly uncertain thereby making a distinction between RCP4.5 and RCP2.6/SSP1-2.6 impossible with present levels of knowledge. In addition, there are fewer studies available for a robust high-end estimate for RCP4.5. Irrespective of the scenario (Fox-Kemper et al., 2021) estimate the sea level commitment associated with historical estimates to be 0.7\u20131.1 m up to 2300, which could probably be considered as the lower end of SLR to consider for practitioners.\nDiscussion\uf0c1\nIn this paper, we have attempted to provide physically based high-end estimates of global SLR to 2100 and 2300 by providing specific high-end numbers for SLR under the assumption of a +2\u00b0C and +5\u00b0C global mean temperature increase (in 2100). In particular, we aimed to provide practitioners with salient well-supported information on low likelihood, high-consequence cases that complement those provided by Fox-Kemper et al. (2021). These high-end estimates can be debated and tailored to individual risk-averse decisions in adaptation planning and implementation, supporting more sound risk management, while adhering to a reasonable standard of practice to ensure appropriate resource allocation. In this way, planners have information available allowing them to frame high-end risk using a standard that balances risk management objectives with finite resources, while avoiding large opportunity costs where possible.\nThis approach is different than that taken by Fox-Kemper et al. (2021), in particular for projected sea level contributions from Greenland and Antarctica, and we highlight that our approach does not replace that of Fox-Kemper et al. (2021), but instead complements it. Details of the difference are given in Table 3.\nWe present a range for the high-end estimates, which is defined by the assumptions of how the different components are correlated. The choice of where in this range a user chooses to focus will depend on aspects such as their level of risk aversion and ideally will arise for any particular application through a detailed dialogue between the practitioners and sea level experts.\nHence, as an expert sea level community group we have attempted to quantify the processes controlling the sea level contribution from the different components based largely on the same evidence as used by Fox-Kemper et al. (2021). The independent assessment of the literature presented here results in a different outcome. A key difference in the methods is that here we emphasize that the Antarctic contribution is likely to be controlled by the timing of the loss of major ice shelves around Antarctica. We attempted to follow lines of physical evidence which represent a snapshot of the current knowledge, and this will evolve as knowledge improves. As new physical insights emerge, so individual components of the analysis could be repeated by sub-groups of experts (e.g., for Antarctica), resulting in an update of Table 3. In this way, the approach is modular and comparatively easy to update.\nIn this respect, the improved use of climate models including a dynamical ice sheet component will fill knowledge gaps with respect to the quantification of feedbacks which are not yet included in the modeling frameworks, and an improved understanding of correlations between different components of the climate system that contribute to global SLR. In addition, growing observational time series will also constrain the physics of the slow processes controlling ice shelf and ice sheet evolution. A strong focus on the timing of thinning and breakup of the Antarctic ice shelves is a critical aspect. At the same time, we also acknowledge that most studies fail to convincingly address the paleo sea level record and this requires further investigation, which may affect future high-end sea level estimates.\nThis work was originally inspired by questions focusing on \u201cwhat is a credible high-end SLR for different timeframes?\u201d, to aid climate risk assessment and adaptation planning. In addition, it demonstrates the large benefits of greenhouse gas mitigation for SLR over many centuries, which have only been explored in DeConto et al. (2021). Practitioners can use the high-end estimates to \u201cstress-test\u201d decisions for high-end SLR and develop robust adaptive plans that acknowledge uncertainties about SLR and identify short-term actions and long-term options to adapt as necessary. While our results suggest a plausible high-end, there are still aspects of sea level that are not well understood or which we cannot yet quantify and which might impact a future estimate of high-end SLR, especially on timescales beyond 2100. These include processes associated with the Antarctic ice sheet that are not well understood but which have the potential to cause rapid SLR: better understanding might impact future estimates of the high-end. Qualitatively this is consistent with the rapid expansion of high-end SLR uncertainty identified by Fox-Kemper et al. (2021) from 2100 to 2150, which is over a timescale of high interest to risk-adverse practitioners. Future research on high-end estimates in 2150 would be especially valuable, including under intermediate forcing scenarios (e.g., SSP3).\nFirst, among these uncertainties is the rate of ice loss caused by MICI in Antarctica. The only continental-scale model attempting to quantify the contribution of MICI to future SLR, uses constraints based on observations of calving at the termini of large marine-terminating glaciers in Greenland. However, the geometry of some Antarctic outlet glaciers is very different to the relatively narrow, m\u00e9lange-filled fjordal settings in Greenland. For example, Thwaites Glacier in West Antarctica is about 10 times wider than Jakobshavn and drains a deep basin in the heart of West Antarctica >2 km deep in places. While MICI has not commenced at Thwaites, the ongoing loss of shelf ice and the retreat of the grounding line onto deeper bedrock could eventually produce a much taller and wider calving front than anything observed on Earth today. Hence models that include MICI in Antarctica, but limit calving rates to those observed on Greenland could be too conservative (e.g., DeConto et al., 2021) and should not be considered an upper bound on the possible SLR contribution from Antarctica. Similar uncertainties also exist for basal processes controlling the rate of mass loss once buttressing ice shelves are lost, with a large simulated range in SLR from Antarctica in response to strong imposed forcing (Sun et al., 2020).", "source": "https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html"}
{"id": "9597ccc3a71c-12", "text": "First, among these uncertainties is the rate of ice loss caused by MICI in Antarctica. The only continental-scale model attempting to quantify the contribution of MICI to future SLR, uses constraints based on observations of calving at the termini of large marine-terminating glaciers in Greenland. However, the geometry of some Antarctic outlet glaciers is very different to the relatively narrow, m\u00e9lange-filled fjordal settings in Greenland. For example, Thwaites Glacier in West Antarctica is about 10 times wider than Jakobshavn and drains a deep basin in the heart of West Antarctica >2 km deep in places. While MICI has not commenced at Thwaites, the ongoing loss of shelf ice and the retreat of the grounding line onto deeper bedrock could eventually produce a much taller and wider calving front than anything observed on Earth today. Hence models that include MICI in Antarctica, but limit calving rates to those observed on Greenland could be too conservative (e.g., DeConto et al., 2021) and should not be considered an upper bound on the possible SLR contribution from Antarctica. Similar uncertainties also exist for basal processes controlling the rate of mass loss once buttressing ice shelves are lost, with a large simulated range in SLR from Antarctica in response to strong imposed forcing (Sun et al., 2020).\nSecond, the timing when Antarctic ice shelves might be lost remains a key unknown. Shelf collapse may be caused by hydrofracturing, but this process is poorly understood. Some models assume hydrofracturing occurs if surface melt exceeds a threshold, but due to limited observations, the threshold is poorly constrained, as is the role of interannual variability in the melt, accumulation, and the detailed physics of the firn layer. For the break-up of the Larsen B Ice Shelf in 2002, this variability was probably important, but there is insufficient data for a robust calibration. In addition, break-up of ice shelves has been observed in response to processes triggered by ocean warming, processes which are not yet well quantified and that are omitted from all major existing models.\nThird, most models are unable to capture the magnitude of SLR in previous warm periods in Earth history, suggesting that there are either processes missing or that the importance of the processes that are included are underestimated. Antarctica lost ice during these warm periods, but we do not know understand why, even not, if we use the lower estimates of Last Interglacial highstands as recently published (Dyer et al., 2021).\nBecause of these \u201cUnknown Unknowns\u201d, a flexible approach to risk and adaptation assessment is advisable recognizing the uncertainties of future SLR and realizing that major mitigation will prevent locking in a catastrophic commitment to SLR over multiple centuries. The fact that multiple lines of evidence are needed to build a salient and credible high-end estimate also implies that the publication of a single new study should not change the approach\u2014overreaction and a whiplash approach needs to be prevented. However, it also implies that the evidence leading to the high-end values need to be periodically revisited at regular timescales to IPCC assessments.", "source": "https://sealeveldocs.readthedocs.io/en/latest/vandewal22.html"}
{"id": "d99c4c73a912-0", "text": "Slangen et al. (2022)\uf0c1\nTitle:\nThe evolution of 21st century sea-level projections from IPCC AR5 to AR6 and beyond\nKeywords:\nSea-level changes, Numerical modelling, Climate change, Coastal change\nCorresponding author:\nAim\u00e9e B.A. Slangen\nCitation:\nSlangen, A. B. A., Palmer, M. D., Camargo, C. M. L., Church, J. A., Edwards, T. L., Hermans, T. H. J., et al. (2022). The evolution of 21st century sea-level projections from IPCC AR5 to AR6 and beyond. Cambridge Prisms: Coastal Futures, 1. https://doi.org/10.1017/cft.2022.8\nURL:\nhttps://www.cambridge.org/core/journals/cambridge-prisms-coastal-futures/article/evolution-of-21st-century-sealevel-projections-from-ipcc-ar5-to-ar6-and-beyond/BECA28410452901A67B01B68F9B358E0\nAbstract\uf0c1\nSea-level science has seen many recent developments in observations and modelling of the different contributions and the total mean sea-level change. In this overview, we discuss (1) the evolution of the Intergovernmental Panel on Climate Change (IPCC) projections, (2) how the projections compare to observations and (3) the outlook for further improving projections. We start by discussing how the model projections of 21st century sea-level change have changed from the IPCC AR5 report (2013) to SROCC (2019) and AR6 (2021), highlighting similarities and differences in the methodologies and comparing the global mean and regional projections. This shows that there is good agreement in the median values, but also highlights some differences. In addition, we discuss how the different reports included high-end projections. We then show how the AR5 projections (from 2007 onwards) compare against the observations and find that they are highly consistent with each other. Finally, we discuss how to further improve sea-level projections using high-resolution ocean modelling and recent vertical land motion estimates.\nImpact statement\uf0c1\nSea-level rise is an important aspect of climate change, with potentially large consequences for coastal communities around the world. Sea-level change is therefore an active area of research that has seen many developments in the past decades. Based on the available research, the Intergovernmental Panel on Climate Change (IPCC) provides regular updates on sea-level projections which are used by policymakers and for adaptation planning. In this review, we compare the sea-level projections from different IPCC reports in the past 10 years and explain what has changed in the methods used and in the numbers presented. We also compare observed changes from the 2021 IPCC report to projected changes from the 2013 IPCC report, for the overlapping period 2007\u20132018, and find that they are highly consistent. Finally, we share some potential future research directions on improving sea-level projections.\nIntroduction\uf0c1\nPresent-day sea-level change (SLC) is primarily a consequence of human-induced climate change, which will impact people and communities all over the world. From a decision-making perspective, knowing how much the sea level will rise, and when, can help to decide which protective measures need to be taken at which point in time. Therefore, sea-level projections are among the most anticipated outcomes of the Intergovernmental Panel on Climate Change (IPCC) assessment reports (ARs). While sea-level extremes are also an important consideration for future coastal hazards, in this review we focus our attention on projections of mean sea level.", "source": "https://sealeveldocs.readthedocs.io/en/latest/slangen22.html"}
{"id": "d99c4c73a912-1", "text": "Impact statement\uf0c1\nSea-level rise is an important aspect of climate change, with potentially large consequences for coastal communities around the world. Sea-level change is therefore an active area of research that has seen many developments in the past decades. Based on the available research, the Intergovernmental Panel on Climate Change (IPCC) provides regular updates on sea-level projections which are used by policymakers and for adaptation planning. In this review, we compare the sea-level projections from different IPCC reports in the past 10 years and explain what has changed in the methods used and in the numbers presented. We also compare observed changes from the 2021 IPCC report to projected changes from the 2013 IPCC report, for the overlapping period 2007\u20132018, and find that they are highly consistent. Finally, we share some potential future research directions on improving sea-level projections.\nIntroduction\uf0c1\nPresent-day sea-level change (SLC) is primarily a consequence of human-induced climate change, which will impact people and communities all over the world. From a decision-making perspective, knowing how much the sea level will rise, and when, can help to decide which protective measures need to be taken at which point in time. Therefore, sea-level projections are among the most anticipated outcomes of the Intergovernmental Panel on Climate Change (IPCC) assessment reports (ARs). While sea-level extremes are also an important consideration for future coastal hazards, in this review we focus our attention on projections of mean sea level.\nIn the past 15 years, process-based sea-level projections (i.e., projections which use models to simulate the physical processes and interactions contributing to sea-level change) in the IPCC reports have developed from global-mean only (AR4, Meehl et al., Reference Meehl, Stocker, Collins and Zhao2007) to regional projections (AR5, Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a). More recent reports focused on the Antarctic contribution (Special Report on Oceans and Cryosphere in a Changing Climate SROCC, Oppenheimer et al., Reference Oppenheimer, Glavovic, Hinkel, van de Wal, Magnan, Abd-Elgawad, Cai, Cifuentes-Jara, DeConto, Ghosh, Hay, Isla, Marzeion, Meyssignac and Sebesvari2019), and provided projections consistent with the assessed Equilibrium Climate Sensitivity (ECS) (AR6, Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a). The research community has dedicated significant research effort and published many papers on improving the understanding and modelling of the different contributions to SLC, such as ice sheets, glaciers and sterodynamic changes (e.g., Gregory et al., Reference Gregory, Bouttes, Griffies, Haak, Hurlin, Jungclaus, Kelley, Lee, Marshall, Romanou, Saenko, Stammer and Winton2016; Nowicki et al., Reference Nowicki, Payne, Larour, Seroussi, Goelzer, Lipscomb, Gregory, Abe-Ouchi and Shepherd2016; The IMBIE Team, 2018, 2019; Hock et al., Reference Hock, Bliss, Marzeion, Giesen, Hirabayashi, Huss, Radic and Slangen2019). Since AR5, new global mean and regional projections have been published, using various methods: for instance based on fully coupled climate models (Slangen et al., Reference Slangen, Katsman, van de Wal, Vermeersen and Riva2012; Kopp et al., Reference Kopp, Horton, Little, Mitrovica, Oppenheimer, Rasmussen, Strauss and Tebaldi2014; Slangen et al., Reference Slangen, Carson, Katsman, van de Wal, K\u00f6hl, Vermeersen and Stammer2014a; Carson et al., Reference Carson, K\u00f6hl, Stammer, Slangen, Katsman, van de Wal, Church and White2015; Jackson and Jevrejeva, Reference Jackson and Jevrejeva2016; Buchanan et al., Reference Buchanan, Oppenheimer and Kopp2017; Palmer et al., Reference Palmer, Gregory, Bagge, Calvert, Hagedoorn, Howard, Klemann, Lowe, Roberts, Slangen and Spada2020), reduced-complexity models (Perrette et al., Reference Perrette, Landerer, Riva, Frieler and Meinshausen2013; Schleussner et al., Reference Schleussner, Lissner, Fischer, Wohland, Perrette, Golly, Rogelj, Childers, Schewe, Frieler, Mengel, Hare and Schaeffer2016; Nauels et al., Reference Nauels, Meinshausen, Mengel, Lorbacher and Wigley2017), semi-empirical models (Kopp et al., Reference Kopp, Kemp, Bittermann, Horton, Donnelly, Gehrels, Hay, Mitrovica, Morrow and Rahmstorf2016; Mengel et al., Reference Mengel, Levermann, Frieler, Robinson, Marzeion and Winkelmann2016; Bakker et al., Reference Bakker, Wong, Ruckert and Keller2017; Bittermann et al., Reference Bittermann, Rahmstorf, Kopp and Kemp2017; Goodwin et al., Reference Goodwin, Haigh, Rohling and Slangen2017; Wong et al., Reference Wong, Bakker, Ruckert, Applegate, Slangen and Keller2017; Jackson et al., Reference Jackson, Grinsted and Jevrejeva2018; Jevrejeva et al., Reference Jevrejeva, Jackson, Grinsted, Lincke and Marzeion2018), structured expert judgement (SEJ) (Bamber et al., Reference Bamber, Oppenheimer, Kopp, Aspinall and Cooke2019), or a mixture of methods (Grinsted et al., Reference Grinsted, Jevrejeva, Riva and Dahl-Jensen2015; Kopp et al., Reference Kopp, DeConto, Bader, Hay, Horton, Kulp, Oppenheimer, Pollard and Strauss2017; Le Bars et al., Reference Le Bars, Drijfhout and De Vries2017; Le Cozannet et al., Reference Le Cozannet, Manceau and Rohmer2017a). There have also been a number of reviews, including a database of sea-level projections (Garner et al., Reference Garner, Weiss, Parris, Kopp RE, Horton RM, Overpeck and Arbor2018), reviews on developments following AR5 (Clark et al., Reference Clark, Church, Gregory and Payne2015; Slangen et al., Reference Slangen, Adloff, Jevrejeva, Leclercq, Marzeion, Wada and Winkelmann2017a), overviews of processes and timescales (Horton et al., Reference Horton, Kopp, Garner, Hay, Khan, Roy and Shaw2018a; Hamlington et al., Reference Hamlington, Gardner, Ivins, Lenaerts, Reager, Trossman, Zaron, Adhikari, Arendt, Aschwanden, Beckley, Bekaert, Blewitt, Caron, Chambers, Chandanpurkar, Christianson, Csatho, Cullather, DeConto, Fasullo, Frederikse, Freymueller, Gilford, Girotto, Hammond, Hock, Holschuh, Kopp, Landerer, Larour, Menemenlis, Merrifield, Mitrovica, Nerem, Nias, Nieves, Nowicki, Pangaluru, Piecuch, Ray, Rounce, Schlegel, Seroussi, Shirzaei, Sweet, Velicogna, Vinogradova, Wahl, Wiese and Willis2020), reviews on coastal sea-level change (e.g., Van de Wal et al., Reference Van de Wal, Zhang, Minobe, Jevrejeva, Riva, Little, Richter and Palmer2019) and reviews integrating risk and adaptation assessments (e.g., Nicholls et al., Reference Nicholls, Hanson, Lowe, Slangen, Wahl, Hinkel and Long2021).", "source": "https://sealeveldocs.readthedocs.io/en/latest/slangen22.html"}
{"id": "d99c4c73a912-2", "text": "One thing that all sea-level projections have in common, despite the different approaches and methodologies, is an uncertainty that grows substantially through time. The uncertainties in regional sea-level projections over the coming years to decades result primarily from internal climate variability (see e.g., Palmer et al., Reference Palmer, Gregory, Bagge, Calvert, Hagedoorn, Howard, Klemann, Lowe, Roberts, Slangen and Spada2020, their Figure 11). On decadal to centennial timescales, uncertainties depend on the future forcings (such as greenhouse gas emissions) and the response of the climate system; and on the modelling uncertainty associated with simulating the different contributions to SLC. The forcing uncertainty can be assessed using different emissions or radiative forcing scenarios, varying from scenarios with net-zero CO2 emissions by 2050 to scenarios with a tripling of the present-day CO2 emissions by 2100. The modelling uncertainty can be relatively well quantified for some contributions, such as global mean thermal expansion. For other contributions, such as (multi)-century timescale ice mass loss of the Antarctic Ice Sheet, the uncertainty is characterised as \u2018deep uncertainty\u2019, which means that experts do not know or cannot agree on appropriate conceptual models or the probability distributions used (Lempert et al., Reference Lempert, Popper and Bankes2003; Kopp et al., Reference Kopp, Oppenheimer, O\u2019Reilly, Drijfhout, Edwards, Fox-Kemper, Garner, Golledge, Hermans, Hewitt, Horton, Krinner, Notz, Nowicki, Palmer, Slangen and Xiao2022). These contributions are therefore a topic of much research and debate (e.g., Oppenheimer et al., Reference Oppenheimer, Glavovic, Hinkel, van de Wal, Magnan, Abd-Elgawad, Cai, Cifuentes-Jara, DeConto, Ghosh, Hay, Isla, Marzeion, Meyssignac and Sebesvari2019).\nIn addition to studies on future sea-level projections, much research has been focused on understanding past observations. A lot of progress has been made in the closing of the sea-level budget for the 20th century, which compares the sum of the observed contributions to the total observed changes, on global (e.g., Gregory et al., Reference Gregory, White, Church, Bierkens, Box, Van Den Broeke, Cogley JG. Fettweis, Hanna, Huybrechts, Konikow, Leclercq, Marzeion, Oerlemans, Tamisiea, Wada, Wake and Van De Wal2013; Chambers et al., Reference Chambers, Cazenave, Champollion, Dieng, Llovel, Forsberg, von Schuckmann and Wada2016; Cazenave et al., Reference Cazenave2018; Frederikse et al., Reference Frederikse, Landerer, Caron, Adhikari, Parkes, Humphrey, Dangendorf, Hogarth, Zanna, Cheng and Wu2020) and basin scales (e.g., Slangen et al., Reference Slangen, Van De Wal, Wada and Vermeersen2014b; Frederikse et al., Reference Frederikse, Riva, Kleinherenbrink, Wada, van den Broeke and Marzeion2016; Rietbroek et al., Reference Rietbroek, Brunnabend, Kusche, Schr\u00f6ter and Dahle2016; Frederikse et al., Reference Frederikse, Jevrejeva, Riva and Dangendorf2018; Wang et al., Reference Wang, Church, Zhang, Gregory, Zanna and Chen2021b). These budget studies have led to important advances in the understanding of sea-level change and its contributing processes on global and regional scales. In addition, the observations can be compared with model simulations (Church et al., Reference Church, Monselesan, Gregory and Marzeion2013c; Meyssignac et al., Reference Meyssignac, Slangen, Melet, Church, Fettweis, Marzeion, Agosta, Ligtenberg, Spada, Richter, Palmer, Roberts and Champollion2017; Slangen et al., Reference Slangen, Meyssignac, Agosta, Champollion, Church, Fettweis, Ligtenberg, Marzeion, Melet, Palmer, Richter, Roberts and Spada2017b; Oppenheimer et al., Reference Oppenheimer, Glavovic, Hinkel, van de Wal, Magnan, Abd-Elgawad, Cai, Cifuentes-Jara, DeConto, Ghosh, Hay, Isla, Marzeion, Meyssignac and Sebesvari2019) to test, understand and improve the model representation of the different processes. This has turned out to be challenging, especially for the earlier part of the 20th century: SROCC stated that only 51% of the 1901\u20131990 observed global mean sea-level (GMSL) change could be explained by models, due to \u2018the inability of climate models to reproduce some observed regional changes\u2019, in particular before 1970. The agreement between models and observations increased to 91% for 1971\u20132015 and 99% for 2006\u20132015 (Oppenheimer et al., Reference Oppenheimer, Glavovic, Hinkel, van de Wal, Magnan, Abd-Elgawad, Cai, Cifuentes-Jara, DeConto, Ghosh, Hay, Isla, Marzeion, Meyssignac and Sebesvari2019).\nIt is also possible to evaluate past projections against observations that have been made since. For instance, for total SLC, Wang et al. (Reference Wang, Church, Zhang and Chen2021a) found an almost identical GMSL trend in the observations and AR5 projections for the period 2007\u20132018. Lyu et al. (Reference Lyu, Zhang and Church2021) compared observations and climate model output of ocean warming for the purpose of constraining projections. They found a high correlation for the Argo period (2005\u20132019) and concluded that the observational record over this period is currently the most useful constraint for projections of ocean warming. Such evaluations against the already realised SLC are important to provide further insights and build confidence in sea-level projections.\nHere, we will first discuss \u2018how we got here\u2019: recent methodological developments in process-based sea-level projections for the 21st century, with a brief recap of the IPCC sea-level projection methods up to IPCC AR5, followed by a discussion of the key differences between AR5, SROCC and AR6 projections (section \u2018Key advances in sea-level projections up to IPCC AR6\u2019). Next, we discuss \u2018where we are\u2019, by evaluating AR5 projections of SLC (which start from 2007 onwards) against observational time series (up to 2018), both for total GMSL and for individual contributions (section \u2018Comparison of the AR5 model simulations with observations\u2019). Finally, we discuss \u2018where we\u2019re going\u2019: how can sea-level projections be better tailored for coastal information (section \u2018Moving towards local information\u2019). Throughout this review, we adopt the sea-level terminology defined by Gregory et al. (Reference Gregory, Griffies, Hughes, Lowe, Church, Fukimori, Gomez, Kopp, Landerer, Le Cozannet, Ponte, Stammer, Tamisiea and van de Wal2019) and we refer to Box 9.1 of IPCC AR6 (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a) for a summary of the key drivers of SLC.\nKey advances in sea-level projections up to IPCC AR6\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/slangen22.html"}
{"id": "d99c4c73a912-3", "text": "Here, we will first discuss \u2018how we got here\u2019: recent methodological developments in process-based sea-level projections for the 21st century, with a brief recap of the IPCC sea-level projection methods up to IPCC AR5, followed by a discussion of the key differences between AR5, SROCC and AR6 projections (section \u2018Key advances in sea-level projections up to IPCC AR6\u2019). Next, we discuss \u2018where we are\u2019, by evaluating AR5 projections of SLC (which start from 2007 onwards) against observational time series (up to 2018), both for total GMSL and for individual contributions (section \u2018Comparison of the AR5 model simulations with observations\u2019). Finally, we discuss \u2018where we\u2019re going\u2019: how can sea-level projections be better tailored for coastal information (section \u2018Moving towards local information\u2019). Throughout this review, we adopt the sea-level terminology defined by Gregory et al. (Reference Gregory, Griffies, Hughes, Lowe, Church, Fukimori, Gomez, Kopp, Landerer, Le Cozannet, Ponte, Stammer, Tamisiea and van de Wal2019) and we refer to Box 9.1 of IPCC AR6 (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a) for a summary of the key drivers of SLC.\nKey advances in sea-level projections up to IPCC AR6\uf0c1\nThere have been substantial methodological and scientific advances in sea-level projections since the publication of the IPCC First Assessment Report in 1990 (Warrick and Oerlemans, Reference Warrick and Oerlemans1990). The use of global climate models (GCMs) in IPCC sea-level projections dates back to the IPCC Third Assessment Report (Church et al., Reference Church, Gregory, Huybrechts, Kuhn, Lambeck, Nhuan, Qin and Woodworth2001). In IPCC AR4, climate models from the third phase of the Climate Model Intercomparison Project (CMIP3) were used as the \u2018backbone\u2019 of the process-based GMSL projections (Meehl et al., Reference Meehl, Stocker, Collins and Zhao2007), with a similar approach adopted for AR5 using the CMIP5 generation of climate models (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a). A major change for the AR5 was the inclusion of regional projections (following Slangen et al., Reference Slangen, Katsman, van de Wal, Vermeersen and Riva2012). The IPCC Special Report on Global Warming of 1.5\u00b0 for the first time assessed GMSL based on warming levels (Hoegh-Guldberg et al., Reference Hoegh-Guldberg, Jacob, Taylor, Bindi, Brown, Camilloni, Diedhiou, Djalante, Ebi, Engelbrecht, Guiot, Hijioka, Mehrotra, Payne, Seneviratne, Thomas, Warren, Zhou, Masson-Delmotte, Zhai, P\u00f6rtner and Waterfield2018). The SROCC added new information on the dynamical ice sheet contribution to the AR5 projections (Oppenheimer et al., Reference Oppenheimer, Glavovic, Hinkel, van de Wal, Magnan, Abd-Elgawad, Cai, Cifuentes-Jara, DeConto, Ghosh, Hay, Isla, Marzeion, Meyssignac and Sebesvari2019). The main advance in AR6 was the use of physics-based emulators to ensure consistency of the sea-level projections with the AR6-assessed ECS and global surface air temperature (GSAT).\nWe will now discuss some of the key differences of the global mean and regional sea-level projections in IPCC AR6 relative to AR5 and SROCC, by explaining what has been done differently, why these changes were made, and what the effects are on the projections. We do not include the SR1.5 projections in this discussion (Hoegh-Guldberg et al., Reference Hoegh-Guldberg, Jacob, Taylor, Bindi, Brown, Camilloni, Diedhiou, Djalante, Ebi, Engelbrecht, Guiot, Hijioka, Mehrotra, Payne, Seneviratne, Thomas, Warren, Zhou, Masson-Delmotte, Zhai, P\u00f6rtner and Waterfield2018), as the SR1.5 report made a literature-based assessment of GMSL changes for 1.5\u00b0 and 2\u00b0, but did not produce new projections.\nBefore we discuss the projections, we note that the interpretation and communication of the uncertainties in sea-level projections has varied across the different IPCC assessment reports (Kopp et al., Reference Kopp, Oppenheimer, O\u2019Reilly, Drijfhout, Edwards, Fox-Kemper, Garner, Golledge, Hermans, Hewitt, Horton, Krinner, Notz, Nowicki, Palmer, Slangen and Xiao2022). IPCC reports use calibrated uncertainty language, in which the confidence level is a qualitative reflection of the evidence and agreement, whereas the likelihood metric is a quantitative measure of uncertainty, expressed probabilistically (Box 1.1, Chen et al., Reference Chen, Rojas, Samset, Cobb, Diongue Niang, Edwards, mori, Faria, Hawkins, Hope, Huybrechts, Meinshausen, Mustafa, Plattner, Tr\u00e9guier, Masson-Delmotte, Zhai, Pirani and Zhou2021). For the medium confidence projections in AR5, the 5\u201395th percentile range of the model ensemble was interpreted as the likely range (the central range with about two-thirds probability, 17\u201383%), with the uncertainty range of all contributions inflated relative to the model spread to account for structural uncertainties arising from the CMIP5 model ensemble. For the sea-level projections in AR6 (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a, Section 9.6), the likely range was redefined as the central range with at least two-thirds probability, encompassing the outer 17th to 83rd percentiles of the probability distributions considered in a p-box (e.g., Le Cozannet et al., Reference Le Cozannet, Manceau and Rohmer2017a). That is, the definition of likely range in AR5, SROCC and AR6 is comparable but not exactly the same, and the way of determining the range from the available information is different. The AR6 medium confidence projections include estimated distributions for each emissions scenario with two different methodological choices for the Antarctic ice sheet (see Table 1). AR6 also presented a set of lowconfidence projections, which include additional contributions from ice sheet processes and estimates for which there is less agreement and/or less evidence (see Table 1).\nTable 1: High-level summary of the methods used in the AR5, SROCC and AR6 reports to project global mean and regional SLC (1\u00b0 \u00d7 1\u00b0 resolution) to 2100. Note: This is an adapted version of Table 9.7 in Fox-Kemper et al. (Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a).", "source": "https://sealeveldocs.readthedocs.io/en/latest/slangen22.html"}
{"id": "d99c4c73a912-4", "text": "Table 1: High-level summary of the methods used in the AR5, SROCC and AR6 reports to project global mean and regional SLC (1\u00b0 \u00d7 1\u00b0 resolution) to 2100. Note: This is an adapted version of Table 9.7 in Fox-Kemper et al. (Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a).\nThe methodologies of the projections in AR5, SROCC and AR6 are briefly summarised in Table 1; for more details, we refer to Chapter 13 of AR5 (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a), Chapter 4 of SROCC (Oppenheimer et al., Reference Oppenheimer, Glavovic, Hinkel, van de Wal, Magnan, Abd-Elgawad, Cai, Cifuentes-Jara, DeConto, Ghosh, Hay, Isla, Marzeion, Meyssignac and Sebesvari2019) and Chapter 9 of AR6 (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a). We focus on three major elements of the projections that have changed: (1) the use of CMIP5 versus CMIP6 model output and consistency with the assessed ECS (section \u2018Updated climate model information and the use of emulators\u2019); (2) differences in the approaches to project the contributions to SLC (section \u2018Differences in the projected contributions to SLC\u2019); (3) the way the reports addressed potential outcomes outside the likely range (section \u2018Sea-level projections outside the likely range\u2019).\nUpdated climate model information and the use of emulators\uf0c1\nThe majority of the sea-level projections for the 21st century since AR5 have been based on CMIP5 climate model output (Taylor et al., Reference Taylor, Stouffer and Meehl2012), forced by Representative Concentration Pathways (RCP, Meinshausen et al., Reference Meinshausen, Smith, Calvin, Daniel, Kainuma, Lamarque, Matsumoto, Montzka, Raper, Riahi, Thomson, Velders and DPP2011), which are scenarios of future greenhouse gas concentrations and aerosol emissions. The projections in AR6 used information from CMIP6 climate models (Eyring et al., Reference Eyring, Bony, Meehl, Senior, Stevens, Stouffer and Taylor2016), which were forced by Shared Socioeconomic Pathways (SSP, O\u2019Neill et al., Reference O\u2019Neill, Kriegler, Riahi, Ebi, Hallegatte, Carter, Mathur and van Vuuren2014): scenarios of socio-economic development (including for instance population change, urbanisation and technological development) in combination with radiative forcing changes (GHG emissions and concentrations). These scenarios are noted as SSPx \u2212 y, where x denotes the SSP pathway (SSP1 sustainability, SSP2 middle-of-the-road, SSP3 regional rivalry, SSP4 inequality, SSP5 fossil fuel-intensive) and y the radiative concentration level in 2100 in W/m2. AR6 used five illustrative SSP scenarios: SSP1\u20131.9 (very low emissions), SSP1\u20132.6 (low emissions), SSP2\u20134.5 (intermediate emissions), SSP3\u20137.0 (high emissions) and SSP5\u20138.5 (very high emissions).\nThe ECS from the CMIP6 model ensemble has a higher average and a wider range compared to the CMIP5 model ensemble and compared to the AR6 assessment of ECS (Forster et al., Reference Forster, Storelvmo, Armour, Collins, Dufresne, Frame, Lunt, Mauritsen, Palmer, Watanabe, Wild, Zhang, Masson-Delmotte, Zhai, Pirani and Zhou2021). The consequences of this change in ECS distribution for projections of GMSL change were investigated by Hermans et al. (Reference Hermans, Gregory, Palmer, Ringer, Katsman and Slangen2021), who used CMIP6 data in combination with the AR5 methodology. They found that, while the projected change in GSAT median and range increased substantially from CMIP5 to CMIP6 (from 1.9 (1.1\u20132.6) K to 2.5 (1.6\u20133.5) K under SSP2-RCP4.5, see their Table S2 for additional scenarios), the upper end of the GMSL likely range projections at 2100 increased by only 3\u20137 cm across all scenarios (see their Figures 1 and 3), due to the delayed response of SLC to temperature changes. However, they also found an increase in the end-of-century GMSL rates of up to ~20%, suggesting that differences between CMIP5 and CMIP6-based GMSL projections could become substantially larger on longer time scales.\nFigure 1: Comparison of 21st century projections of global mean SLC in AR5, SROCC and AR6. Total GMSL and individual contributions, between 1995 and 2014 and 2100 (m), median values and likely ranges of medium confidence projections, for (a) RCP2.6/SSP1\u20132.6 and (b) RCP8.5/SSP5\u20138.5. See also Table 9.8 in Fox-Kemper et al. (Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a) for comparative numbers of GMSL projections. AR6 low confidence projections for SSP1\u20132.6 and SSP5\u20138.5 in grey for Greenland, Antarctica and GMSL. Corrections for the differences in baseline period between AR5 (1986\u20132005) and AR6 (1995\u20132014) were done following IPCC AR6, Table 9.8.\nFigure 2: Comparison of regional relative sea-level change w.r.t. the global mean sea-level change in AR5 and AR6 (2020\u20132100) (%), based on median values, for (a) IPCC AR5 RCP4.5, global mean of 0.46 m and (b) IPCC AR6 SSP2\u20134.5, global mean of 0.51 m.", "source": "https://sealeveldocs.readthedocs.io/en/latest/slangen22.html"}
{"id": "d99c4c73a912-5", "text": "Figure 1: Comparison of 21st century projections of global mean SLC in AR5, SROCC and AR6. Total GMSL and individual contributions, between 1995 and 2014 and 2100 (m), median values and likely ranges of medium confidence projections, for (a) RCP2.6/SSP1\u20132.6 and (b) RCP8.5/SSP5\u20138.5. See also Table 9.8 in Fox-Kemper et al. (Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a) for comparative numbers of GMSL projections. AR6 low confidence projections for SSP1\u20132.6 and SSP5\u20138.5 in grey for Greenland, Antarctica and GMSL. Corrections for the differences in baseline period between AR5 (1986\u20132005) and AR6 (1995\u20132014) were done following IPCC AR6, Table 9.8.\nFigure 2: Comparison of regional relative sea-level change w.r.t. the global mean sea-level change in AR5 and AR6 (2020\u20132100) (%), based on median values, for (a) IPCC AR5 RCP4.5, global mean of 0.46 m and (b) IPCC AR6 SSP2\u20134.5, global mean of 0.51 m.\nFigure 3: Comparison of observations (IPCC AR6, available up to 2018) and projections (IPCC AR5, available from 2007) of GMSL change. (a) Total GMSL and (b-f) individual contributions in (m) with respect to the period 1986\u20132005; all uncertainties recomputed to represent the likely range. Text in panels compares rates (mm/yr) of observations for 2006\u20132018 (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a, Table 9.5) to rates of projections for 2007\u20132018 (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a); rates rounded to nearest 0.1 mm/yr; time periods used for rates differ by 1 year, allowing for traceability to the IPCC reports. Note that AR5 included the Greenland peripheral glaciers in the glacier contribution, whereas AR6 included it in the Greenland contribution; we have therefore subtracted a Greenland peripheral glacier estimate of 0.1 mm/yr from the AR6 Greenland observations in (c) and added it to the AR6 glacier observations in (d), both for the time series and the rates (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a, Table 13.1; Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021b, Table 9.SM.2). The AR5 observed glacier change is added to (d) for reference (using the 1993\u20132010 linear rate from Table 13.1 of Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a).\nOne of the novel aspects of AR6 was the use of a physically-based emulator, which allowed for projections of 21st century GSAT and SLC that were consistent with the AR6 assessment of ECS (Forster et al., Reference Forster, Storelvmo, Armour, Collins, Dufresne, Frame, Lunt, Mauritsen, Palmer, Watanabe, Wild, Zhang, Masson-Delmotte, Zhai, Pirani and Zhou2021). The AR6 used a simple two-layer energy balance model (e.g., Geoffroy et al., Reference Geoffroy, Saint-Martin, Bellon, Voldoire, Olivi\u00e9 and Tyt\u00e9ca2013). Previous studies have used this two-layer model to successfully emulate CMIP5 model projections of GSAT and global mean thermosteric SLC to 2300 (Palmer et al., Reference Palmer, Harris and Gregory2018; Yuan and Kopp, Reference Yuan and Kopp2021). The AR6 emulator ensemble was constrained using four observational targets, including historical GSAT change and ocean heat uptake (Smith et al., Reference Smith, Nicholls, Armour, Collins, Forster, Meinshausen, Palmer, Watanabe, Masson-Delmotte, Zhai, Pirani and Zhou2021). The projected ocean heat uptake was translated to global mean thermosteric SLC using CMIP6-based estimates of expansion efficiency (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021b). The GSAT changes were also used as input for the land-ice contributions to GMSL rise, which were generated with additional emulators applied to suites of coordinated community efforts for the ice sheet (LARMIP-2, Levermann et al., Reference Levermann, Winkelmann, Albrecht, Goelzer, Golledge, Greve, Huybrechts, Jordan, Leguy, Martin, Morlighem, Pattyn, Pollard, Quiquet, Rodehacke, Seroussi, Sutter, Zhang, Van Breedam, Calov, Deconto, Dumas, Garbe, Gudmundsson, Hoffman, Humbert, Kleiner, Lipscomb, Meinshausen, Ng, Nowicki, Perego, Price, Saito, Schlegel, Sun and Van De Wal2020; ISMIP6, Nowicki et al., Reference Nowicki, Payne, Larour, Seroussi, Goelzer, Lipscomb, Gregory, Abe-Ouchi and Shepherd2016) and glacier model (GlacierMIP2, Marzeion et al., Reference Marzeion, Hock, Anderson, Bliss, Champollion, Fujita, Huss, Immerzeel, Kraaijenbrink, Malles, Maussion, Radi\u0107, Rounce, Sakai, Shannon, van de Wal and Zekollari2020) simulations carried out for AR6.\nDifferences in the projected contributions to SLC\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/slangen22.html"}
{"id": "d99c4c73a912-6", "text": "Differences in the projected contributions to SLC\uf0c1\nIn AR5, the assessments of glacier and ice sheet contributions were based on a range of individual models and publications. The only difference in the SROCC projections with respect to AR5 was the reassessment of the Antarctic dynamics contribution, by replacing the AR5 Antarctic scenario-independent ice dynamic projections with scenario-dependent process-based model estimates (Levermann et al., Reference Levermann, Winkelmann, Nowicki, Fastook, Frieler, Greve, Hellmer, Martin, Meinshausen, Mengel, Payne, Pollard, Sato, Timmermann, Wang and Bindschadler2014; Golledge et al., Reference Golledge, Kowalewski, Naish, Levy, Fogwill and Gasson2015; Ritz et al., Reference Ritz, Edwards, Durand, Payne, Peyaud and Hindmarsh2015; Bulthuis et al., Reference Bulthuis, Arnst, Sun and Pattyn2019; Golledge et al., Reference Golledge, Keller, Gomez, Naughten, Bernales, Trusel and Edwards2019). This led to a decrease in 21st century GMSL change compared with AR5 for the RCP2.6 scenario, and an increase for the RCP8.5 scenario (medians and likely ranges; Figure 1a,b). However, the scenario-dependence in SROCC may have been amplified because two model estimates did not include accumulation changes (Levermann et al., Reference Levermann, Winkelmann, Nowicki, Fastook, Frieler, Greve, Hellmer, Martin, Meinshausen, Mengel, Payne, Pollard, Sato, Timmermann, Wang and Bindschadler2014; Ritz et al., Reference Ritz, Edwards, Durand, Payne, Peyaud and Hindmarsh2015), which are projected to increase with warming and partially counteract dynamic losses (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a).\nFor the AR6 projections, statistical emulators were applied to the ISMIP6 and GlacierMIP2 outputs, using the Gaussian process model described in Edwards et al. (Reference Edwards, Nowicki, Marzeion, Hock, Goelzer, Seroussi, Jourdain, Slater, Turner, Smith, McKenna, Simon, Abe-Ouchi, Gregory, Larour, Lipscomb, Payne, Shepherd, Agosta, Alexander, Albrecht, Anderson, Asay-Davis, Aschwanden, Barthel, Bliss, Calov, Chambers, Champollion, Choi, Cullather, Cuzzone, Dumas, Felikson, Fettweis, Fujita, Galton-Fenzi, Gladstone, Golledge, Greve, Hattermann, Hoffman, Humbert, Huss, Huybrechts, Immerzeel, Kleiner, Kraaijenbrink, Le clec\u2019h, Lee, Leguy, Little, Lowry, Malles, Martin, Maussion, Morlighem, O\u2019Neill, Nias, Pattyn, Pelle, Price, Quiquet, Radi\u0107, Reese, Rounce, R\u00fcckamp, Sakai, Shafer, Schlegel, Shannon, Smith, Straneo, Sun, Tarasov, Trusel, Van Breedam, van de Wal, van den Broeke, Winkelmann, Zekollari, Zhao, Zhang and Zwinger2021). For LARMIP-2, results for Antarctic ice sheet dynamics were emulated using an impulse-response function model following (Levermann et al., Reference Levermann, Winkelmann, Albrecht, Goelzer, Golledge, Greve, Huybrechts, Jordan, Leguy, Martin, Morlighem, Pattyn, Pollard, Quiquet, Rodehacke, Seroussi, Sutter, Zhang, Van Breedam, Calov, Deconto, Dumas, Garbe, Gudmundsson, Hoffman, Humbert, Kleiner, Lipscomb, Meinshausen, Ng, Nowicki, Perego, Price, Saito, Schlegel, Sun and Van De Wal2020), augmented by a parametric surface-mass balance model following AR5. There were several motivations for using these emulators: (1) to constrain the projections to the assessed ECS range, an approach that represents a marked change from previous IPCC reports; (2) to be able to make projections across all five illustrative SSP scenarios of AR6, as the ice sheet and glacier contributions were mostly based on CMIP5 RCP scenarios; and (3) to sample modelling uncertainties more thoroughly, estimating probability distributions for the contributions. The use of simple climate models and emulators is a trade-off between a more complete exploration of the uncertainties which can be done due to the computational speed of the emulators (compared to the full ice sheet and glacier models, which are limited by constraints of computing and person time), and the potential biases introduced by the necessary assumptions of a simpler model (Edwards et al., Reference Edwards, Nowicki, Marzeion, Hock, Goelzer, Seroussi, Jourdain, Slater, Turner, Smith, McKenna, Simon, Abe-Ouchi, Gregory, Larour, Lipscomb, Payne, Shepherd, Agosta, Alexander, Albrecht, Anderson, Asay-Davis, Aschwanden, Barthel, Bliss, Calov, Chambers, Champollion, Choi, Cullather, Cuzzone, Dumas, Felikson, Fettweis, Fujita, Galton-Fenzi, Gladstone, Golledge, Greve, Hattermann, Hoffman, Humbert, Huss, Huybrechts, Immerzeel, Kleiner, Kraaijenbrink, Le clec\u2019h, Lee, Leguy, Little, Lowry, Malles, Martin, Maussion, Morlighem, O\u2019Neill, Nias, Pattyn, Pelle, Price, Quiquet, Radi\u0107, Reese, Rounce, R\u00fcckamp, Sakai, Shafer, Schlegel, Shannon, Smith, Straneo, Sun, Tarasov, Trusel, Van Breedam, van de Wal, van den Broeke, Winkelmann, Zekollari, Zhao, Zhang and Zwinger2021). The Gaussian process emulator performed well for the cumulative change in time, but did not account for temporal correlation, so the rates could not be estimated from the emulator. As a consequence, in contexts where rates were needed, AR6 used simpler parametric emulators, based on approaches used in AR5.", "source": "https://sealeveldocs.readthedocs.io/en/latest/slangen22.html"}
{"id": "d99c4c73a912-7", "text": "A comparison of the GMSL projections to 2100 in the different reports reveals a number of differences (Figure 1a,b). In the land ice contributions, we see a narrowing of the likely ranges for glaciers (under both scenarios) and the Greenland ice sheet (under SSP5\u20138.5), and a widening of the Antarctic ice sheet likely range. The latter is wider as it is based on a p-box bounding distribution functions from the ISMIP6 emulator and LARMIP-2 (Table 1), where the presented likely range spans from the lowest 17th to the highest 83rd percentile of the considered methods. The ECS-constrained temperature projections in AR6 (section \u2018Updated climate model information and the use of emulators\u2019) used as input to the land ice emulators show a marked reduction in the width of the likely range at 2100 (~0.7 K for SSP1\u20132.6; ~1.9 K for SSP5\u20138.5) compared with the 21 CMIP5 models used as the basis of the AR5 sea-level projections (~1.6 K for RCP2.6; ~2.8 K for RCP8.5), which could also be one of the reasons for the reduced width of the glacier and Greenland likely ranges. The glacier range may also be slightly underestimated because each region is emulated independently, which means the projections do not account for covariances in the regional uncertainties apart from those associates with a common dependence on temperature (Marzeion et al., Reference Marzeion, Hock, Anderson, Bliss, Champollion, Fujita, Huss, Immerzeel, Kraaijenbrink, Malles, Maussion, Radi\u0107, Rounce, Sakai, Shannon, van de Wal and Zekollari2020; Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a, Section 9.5). However, the AR5 glacier and Greenland uncertainties were open-ended (\u2265 66% ranges) and essentially estimated with expert judgement, at a time of far less information from \u2013 and confidence in \u2013 these process-based models, so the narrowing range is also consistent with an improving evidence base. The land-water storage contribution is reduced in AR6 compared with AR5 due to the use of a different methodology which now links land-water storage changes to global population under SSP scenarios (Kopp et al., Reference Kopp, Horton, Little, Mitrovica, Oppenheimer, Rasmussen, Strauss and Tebaldi2014), in combination with a larger negative reservoir impoundment contribution from Hawley et al. (Reference Hawley, Hay, Mitrovica and Kopp2020).\nAR5 used different methodologies for estimating the uncertainties in GMSL (Figure 1a,b) and regional SLC (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013b). In contrast, the AR6 GMSL (Figure 1a,b) and regional projected uncertainties are combined in the same way, with the different contributions all treated as conditionally independent given GSAT, which is an input for the emulator (Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021b). The total projected GMSL for SSP1\u20132.6 has increased in AR6 compared with RCP2.6 projections in AR5 and SROCC, with a similar likely range (Figure 1a), but with different relative contributions of each component. For SSP5\u20138.5, the AR6 GMSL projections are 4 cm lower than RCP8.5 in SROCC but 6 cm higher than RCP8.5 in AR5 (Figure 1b), due to differences in the model estimates included (from AR5 to SROCC) and in both models used and the methods used to combine the models (from SROCC to AR6) of the projected Antarctic contribution.\nThe regional projections (Figure 2) show that SLC is spatially highly variable, due to a combination of ocean dynamic changes, gravitational, rotational and deformation (GRD) effects in response to present-day mass changes, and long-term Glacial Isostatic Adjustment (GIA). There is an overall agreement in the patterns between AR5 and AR6. Some differences arise from the vertical land motion (VLM) contribution, which included only GIA in AR5 and also other VLM contributions, such as tectonics, compaction or anthropogenic subsidence, in AR6: compare for instance the larger ratios along the US East Coast ( Figure 2b) to the VLM contribution in Figure 9.26 from Fox-Kemper et al. (Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a). The increased contribution from Antarctica compared to AR5, in combination with the ocean dynamics contribution, leads to a more widespread below-average SLC in the Antarctic Circumpolar Current region.\nSea-level projections outside the likely range\uf0c1\nOne of the key uncertainties in sea-level projections is the dynamic contribution of the ice sheets (i.e., processes related to the flow of the ice). AR5 assessed the likely dynamical contribution of the Antarctic Ice Sheet by 2100 at \u22122 to 18.5 cm, but also noted that \u2018Based on current understanding, only the collapse of marine-based sectors of the Antarctic ice sheet, if initiated, could cause global mean sea level to rise substantially above the likely range during the 21st century. There is medium confidence that this additional contribution would not exceed several tenths of a metre of sea level rise during the 21st century\u2019. An ice sheet estimate based on SEJ was available at the time of AR5 but this could not be supported by other lines of evidence (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a). Including the SEJ estimates would have led to an assessment that could not be transparently linked to physical evidence, as the reasoning of the experts involved in the SEJ exercise is undocumented, and it was decided not to use it for the AR5 assessment.", "source": "https://sealeveldocs.readthedocs.io/en/latest/slangen22.html"}
{"id": "d99c4c73a912-8", "text": "Sea-level projections outside the likely range\uf0c1\nOne of the key uncertainties in sea-level projections is the dynamic contribution of the ice sheets (i.e., processes related to the flow of the ice). AR5 assessed the likely dynamical contribution of the Antarctic Ice Sheet by 2100 at \u22122 to 18.5 cm, but also noted that \u2018Based on current understanding, only the collapse of marine-based sectors of the Antarctic ice sheet, if initiated, could cause global mean sea level to rise substantially above the likely range during the 21st century. There is medium confidence that this additional contribution would not exceed several tenths of a metre of sea level rise during the 21st century\u2019. An ice sheet estimate based on SEJ was available at the time of AR5 but this could not be supported by other lines of evidence (Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a). Including the SEJ estimates would have led to an assessment that could not be transparently linked to physical evidence, as the reasoning of the experts involved in the SEJ exercise is undocumented, and it was decided not to use it for the AR5 assessment.\nAfter AR5, following for instance Sutton (Reference Sutton2019), low probability estimates were increasingly used in the context of risk assessment and to discuss less likely outcomes for risk-averse users (e.g., Le Cozannet et al., Reference Le Cozannet, Nicholls, Hinkel, Sweet, McInnes, Van de Wal, Slangen, Lowe and White2017b; Hinkel et al., Reference Hinkel, Church, Gregory, Gregory, Lambert, McInnes, Nicholls, Church, van der Pol and van de Wal2019; Nicholls et al., Reference Nicholls, Hanson, Lowe, Slangen, Wahl, Hinkel and Long2021). SROCC argued that stakeholders with a low risk tolerance might use the SEJ numbers (e.g., their Figure 4.2). Model results including marine ice cliff instability (MICI, Deconto and Pollard, Reference Deconto and Pollard2016) were not used in the main projections of SROCC because the too high surface melt rates led to an uncertain timing and magnitude in the simulated ice loss. In AR6, a set of low confidence projections was presented (shown in grey in Figure 1a,b) which build on the medium confidence projections. These projections include additional contributions for the ice sheets, estimated using a p-box approach (e.g., Le Cozannet et al., Reference Le Cozannet, Manceau and Rohmer2017a), considering SEJ (Bamber et al., Reference Bamber, Oppenheimer, Kopp, Aspinall and Cooke2019) together with an improved model-based estimate for Antarctica which included MICI (DeConto et al., Reference DeConto, Pollard, Alley, Velicogna, Gasson, Gomez, Sadai, Condron, Gilford, Ashe, Kopp, Li and Dutton2021). It is important to note that the low confidence ranges represent the breadth of literature estimates available at the time, but that they are not incorporated in the assessed likely ranges.\nThe AR6 low confidence projections suggest that by 2100, under SSP1\u20132.6 ( Figure 1a), there is a potential Greenland contribution outside the likely range, based on SEJ. For Antarctica, the medium confidence SSP1\u20132.6 projections already include a wide range of values, so the impact of SEJ and MICI estimates in the lowconfidence projections is less distinct. Under SSP5\u20138.5 (Figure 1b), the upper values of the AR6 low confidence projections for both ice sheets are considerably larger than the corresponding medium confidence estimates. This reflects the deep uncertainty in the literature on the Antarctic contribution (see also Box 9.4 in Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a). What is needed to reduce this deep uncertainty is primarily a better understanding of the physical processes. This will lead to more physically-based model projections with larger ensembles, which will allow for a better exploration of the uncertainties.\nComparison of the AR5 model simulations with observations\uf0c1\nIn the previous section, we discussed \u2018how we got here\u2019: the developments that led to the most recent IPCC projections. However, it is also relevant to see \u2018where we are\u2019, by comparing the observed sea-level change against sea-level projections for their overlapping period. We evaluate the assessed likely ranges of the AR5 projections (from 2007 onwards, Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a) against the assessed observational time series from AR6 (up to 2018, Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a, Table 9.5), both for the total GMSL and the individual contributions (Figure 3).\nFor GMSL, Antarctica, Greenland and thermal expansion, the observational timeseries are close to the centre of the projections and the estimated rates of change are highly consistent (Figure 3a,b,c,e). The observed glacier timeseries in AR6 is at the lower end of the projections, even though the observed rates entirely fall within the likely range of the projected rates (Figure 3d). It is worth noting that the AR5 included glaciers peripheral to the Greenland Ice Sheet in the glacier projections (their Table 13.5), which according to the observations in their Table 13.1 adds a contribution in the order of 0.1 mm/yr. In AR6, this was included in the Greenland contribution. To facilitate the comparison, we have included the observed Greenland peripheral glacier estimate in Figure 3d (Glaciers) and subtracted it from the observations in Figure 3c (Greenland), based on linear rates presented in Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a and Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a. In addition, the glacier contributions since AR5 suggest a smaller glacier contribution, both in observations and projections (for the observations: grey dashed line in Figure 3d based on Church et al., Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer, Unnikrishnan, Stocker, Qin, Plattner and Midgley2013a, Table 13.1 shows a higher rate than AR6, for the projections: Marzeion et al., Reference Marzeion, Leclercq, Cogley and Jarosch2015). The observed rate of land-water change is larger than the projected central value, but the observed time series, despite its interannual variability, mostly falls within the projected likely range. The observed rate of change is at the upper bound of the likely range projections (Figure 3f).\nWang et al. (Reference Wang, Church, Zhang and Chen2021a) also evaluated GMSL and regional projections from AR5 and SROCC against different tide gauge and altimetry time series for the period 2007\u20132018. They found that the GMSL trends for 2007\u20132018 from AR5 projections are almost identical to observed trends and well within the 90% confidence interval. They also showed significant local differences between observations and models, which could be improved with better VLM estimates and minimisation of the internal variability.", "source": "https://sealeveldocs.readthedocs.io/en/latest/slangen22.html"}
{"id": "d99c4c73a912-9", "text": "Wang et al. (Reference Wang, Church, Zhang and Chen2021a) also evaluated GMSL and regional projections from AR5 and SROCC against different tide gauge and altimetry time series for the period 2007\u20132018. They found that the GMSL trends for 2007\u20132018 from AR5 projections are almost identical to observed trends and well within the 90% confidence interval. They also showed significant local differences between observations and models, which could be improved with better VLM estimates and minimisation of the internal variability.\nA study by Lyu et al. (Reference Lyu, Zhang and Church2021) focused on ocean warming, with the purpose of constraining projections. They compared the observations of ocean temperature by the Argo array (2005\u20132019) with model simulations from the CMIP5 and CMIP6 databases. They found that (1) the range of CMIP6 has shifted upwards compared with CMIP5; (2) there is a high correlation between observations and models over the Argo period; (3) the emergent constraint indicates that the larger trend of thermosteric SLC in the CMIP6 archive needs to be taken with caution. This supports the AR6 approach, where an emulator was used to constrain the thermosteric SLC of CMIP6 models with the assessed ECS range (section \u2018Updated climate model information and the use of emulators\u2019), leading to thermosteric SLC projections similar to AR5 and the constrained Lyu et al. (Reference Lyu, Zhang and Church2021) projections.\nMoving towards local information\uf0c1\nAR5 was the first IPCC assessment report to show regional sea-level projections in addition to GMSL projections, by including the effects of changes in ocean density and circulation, GIA and GRD effects (Table 1). SROCC built on AR5 but explored regional changes in sea-level extremes in more depth. In AR6 as a whole, even stronger emphasis was put on regional climate changes and on using regional information for impacts and risk assessment, in particular in Chapter 10 (Doblas-Reyes et al., Reference Doblas-Reyes, S\u00f6rensson, Almazroui, Dosio, Gutowski, Haarsma, Hamdi, Hewitson, Kwon, Lamptey, Maraun, Stephenson, Takayabu, Terray, Turner, Zuo, Masson-Delmotte, Zhai, Pirani and Zhou2021), Chapter 12 (Ranasinghe et al., Reference Ranasinghe, Ruane, Vautard, Arnell, Coppola, Cruz, Dessai, Islam, Rahimi, Ruiz, Sillmann, Sylla, Tebaldi, Wang, Zaaboul, Masson-Delmotte, Zhai, Pirani and Zhou2021) and the Interactive Atlas (Guti\u00e9rrez et al., Reference Guti\u00e9rrez, Jones, Narisma, Alves, Amjad, Gorodetskaya, Grose, Klutse, Krakovska, Li, Mart\u00ednez-Castro, Mearns, Mernild, Ngo-Duc, van den Hurk, Yoon, Masson-Delmotte, Zhai, Pirani and Zhou2021). The IPCC authors and the IPCC Technical Support Unit also collaborated with NASA to develop the NASA/IPCC Sea Level Projection Tool (https://sealevel.nasa.gov/ipcc-ar6-sea-level-projection-tool) to provide easy access to global and regional projections. As the need for more detailed sea-level information is becoming increasingly evident (e.g., Le Cozannet et al., Reference Le Cozannet, Nicholls, Hinkel, Sweet, McInnes, Van de Wal, Slangen, Lowe and White2017b; Hinkel et al., Reference Hinkel, Church, Gregory, Gregory, Lambert, McInnes, Nicholls, Church, van der Pol and van de Wal2019; Nicholls et al., Reference Nicholls, Hanson, Lowe, Slangen, Wahl, Hinkel and Long2021; Durand et al., Reference Durand, van den Broeke, Le Cozannet, Edwards, Holland, Jourdain, Marzeion, Mottram, Nicholls, Pattyn, Paul, Slangen, Winkelmann, Burgard, van Calcar, Barr\u00e9, Bataille and Chapuis2022), we discuss a couple of potential future research avenues which may help to further improve sea-level projections on a regional to local scale.\nHigh-resolution ocean modelling\uf0c1\nOcean dynamic SLC is a major driver of spatial sea-level variability, which is typically derived from CMIP5 and CMIP6 GCM simulations. However, the extent to which GCMs can provide local information is limited because of their relatively low atmosphere and ocean grid resolutions, which are constrained by computational costs. The typical ocean grid resolution of CMIP5 models is approximately 1\u00b0 by 1\u00b0 (~100 km). Although the ocean components of some CMIP6 models operate at a 0.25\u00b0 resolution, the resolution of most CMIP6 models has not increased much relative to CMIP5, and the CMIP5 and CMIP6 simulations of ocean dynamic SLC show similar features (Lyu et al., Reference Lyu, Zhang and Church2020). These relatively coarse resolutions may lead to misrepresentations of ocean dynamic SLC, particularly in coastal regions in which small-scale and tidal processes and bathymetric features are important. Increasing the resolution of the GCMs requires significant additional computational resources as well as more explicit modelling of high-resolution processes that are currently parameterized.\nAs an alternative, GCMs can be dynamically downscaled using high-resolution atmosphere or ocean models. Emerging research demonstrates the value of dynamical downscaling for SLC simulations in coastal regions such as the Northwestern European Shelf (Figure 4; Hermans et al., Reference Hermans, Tinker, Palmer, Katsman, Vermeersen and Slangen2020; Chaigneau et al., Reference Chaigneau, Reffray, Voldoire and Melet2022; Hermans et al., Reference Hermans, Katsman, Camargo, Garner, Kopp and Slangen2022), the Southern Ocean (Zhang et al., Reference Zhang, Church, Monselesan and McInnes2017), the Mediterranean Sea (Sannino et al., Reference Sannino, Carillo, Iacono, Napolitano, Palma, Pisacane and Struglia2022), the marginal seas in the Northwest Pacific Ocean (Liu et al., Reference Liu, Minobe, Sasaki and Terada2016; Kim et al., Reference Kim, Kim, Jeong, Lee, Byun and Cho2021), the marginal seas near China (Jin et al., Reference Jin, Zhang, Church and Bao2021) and the Brazilian continental shelf (Toste et al., Reference Toste, Assad and Landau2018), on both annual and sub-annual timescales. Additionally, dynamical downscaling can offer a framework in which local changes in tides, surges and waves can be resolved in conjunction with time-mean SLC and incorporated into sea-level projections (Kim et al., Reference Kim, Kim, Jeong, Lee, Byun and Cho2021; Chaigneau et al., Reference Chaigneau, Reffray, Voldoire and Melet2022), as it allows for modelling changes at higher temporal frequencies. Dynamical downscaling requires GCM output as boundary conditions, which means that the regional solutions due to the explicit modelling of higher resolution processes should always be considered in the context of the GCM model that is driving the regional model. For instance, for the South China Sea, Jin et al. (Reference Jin, Zhang, Church and Bao2021) found that \u2018the downscaled results driven by ensemble mean forcings are almost identical to the ensemble average results from individually downscaled cases\u2019. However, more extensive analysis of the uncertainties associated with dynamical downscaling remains to be done. As a result, the dynamical downscaling of ocean simulations has not yet been systematically applied in the context of regional and local sea-level projections.\nFigure 4: Ocean dynamic SLC northwest of Europe, as simulated by (a) the CMIP5 GCM HadGEM2-ES and (b) dynamically downscaled using regional ocean model NEMO-AMM7, and by (c) the CMIP5 GCM MPI-ESM-LR and (d) dynamically downscaled, for the scenario RCP8.5 (2074\u20132099 minus 1980\u20132005). Figure adapted from Hermans et al. (Reference Hermans, Tinker, Palmer, Katsman, Vermeersen and Slangen2020).\nVertical land motion\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/slangen22.html"}
{"id": "d99c4c73a912-10", "text": "Figure 4: Ocean dynamic SLC northwest of Europe, as simulated by (a) the CMIP5 GCM HadGEM2-ES and (b) dynamically downscaled using regional ocean model NEMO-AMM7, and by (c) the CMIP5 GCM MPI-ESM-LR and (d) dynamically downscaled, for the scenario RCP8.5 (2074\u20132099 minus 1980\u20132005). Figure adapted from Hermans et al. (Reference Hermans, Tinker, Palmer, Katsman, Vermeersen and Slangen2020).\nVertical land motion\uf0c1\nIn addition to the ocean and ice contributions, relative SLC is affected by VLM (Table 1), which may amplify or even dominate the SLC experienced at coastal locations. AR5 and SROCC used GIA models to estimate the VLM contribution to SLC, whereas AR6 based its VLM estimate on the geological background rate at tide gauge stations, derived using the Gaussian Process Model from (Kopp et al., Reference Kopp, Horton, Little, Mitrovica, Oppenheimer, Rasmussen, Strauss and Tebaldi2014; Table 1). Neither method provides a satisfactory answer, given that the former excludes non-GIA VLM contributions, and the latter requires assumptions regarding the spatio-temporal extrapolation of the tide-gauge derived background rates to areas without tide gauge information by using a GIA model as a prior. AR6, therefore, stated that \u2018there is low to medium confidence in the GIA and VLM projections employed in this Report. In many regions, higher-fidelity projections would require more detailed regional analysis\u2019.\nWork published after the IPCC AR6 literature deadline has provided new observation-based estimates of VLM for 99 coastal cities based on InSAR observations (Wu et al., Reference Wu, Wei and D\u2019Hondt2022) and along the world\u2019s coastlines using GNSS data (Oelsmann et al., Reference Oelsmann, Passaro, Dettmering, Schwatke, S\u00e1nchez and Seitz2021). However, even with better observational estimates, significant assumptions are required when extrapolating these into the future. Both AR5 and AR6 assume VLM rates remain constant over time, an assumption that is wrong in regions that are tectonically active (where VLM will be nonlinear and stochastic) or where VLM occurs in response to groundwater and gas extractions (which is strongly dependent on societal choices). A potential solution is to use expanded geological reconstructions of paleo sea level on millennial time scales to constrain long-term average trends (Horton et al., Reference Horton, Shennan, Bradley, Cahill, Kirwan, Kopp and Shaw2018b).\nConclusions and future perspectives\uf0c1\nIn this overview, we have discussed several aspects of sea-level projections: recent developments in the projections, how they compare against observations, and potential future research directions: \u2018how we got here\u2019 (section \u2018Key advances in sea-level projections up to IPCC AR6\u2019), \u2018where we are\u2019 (section \u2018Comparison of the AR5 model simulations with observations\u2019) and \u2018where we\u2019re going\u2019 (section \u2018Moving towards local information\u2019).\nKey differences between AR5, SROCC and AR6 include the use of new climate model information (CMIP6) and the use of emulators to constrain the projections to the AR6 assessment of Equilibrium Climate Sensitivity (section \u2018Updated climate model information and the use of emulators\u2019), new information for the different projected contributions to sea-level change (section \u2018Differences in the projected contributions to SLC\u2019), and the treatment of projections outside the likely range (section \u2018Sea-level projections outside the likely range\u2019).\nThe likely range projections of GMSL and regional SLC at 2100 show relatively modest changes from AR5 to SROCC and AR6, given approximately equivalent climate change scenarios (sections \u2018Updated climate model information and the use of emulators\u2019 and \u2018Differences in the projected contributions to SLC\u2019): under RCP2.6/SSP1\u20132.6 from 0.25\u20130.58 m (AR5) to 0.33\u20130.62 m (AR6); under RCP8.5/SSP5\u20138.5 from 0.49\u20130.95 m (AR5) to 0.63\u20131.01 m (AR6). Substantial reductions in the uncertainty of the Greenland and glacier contributions to GMSL at 2100 under SSP5\u20138.5 for AR6 are counterbalanced by an increase in the Antarctic uncertainty, which leads to relatively small changes in overall uncertainty at 2100 between AR5 and AR6.\nIn AR6, the explicit inclusion of low confidence projections highlighted the deep uncertainty associated with the dynamical ice sheet contribution (section \u2018Sea-level projections outside the likely range\u2019), which was communicated through the use of \u2018low-likelihood high-impact\u2019 storylines (IPCC, Reference Masson-Delmotte, Zhai, Pirani, Connors, P\u00e9an, Berger, Caud, Chen, Goldfarb, Gomis, Huang, Leitzell, Lonnoy, JBR, Maycock, Waterfield, Yelek\u00e7i, Yu and Zhou2021; Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, A\u00f0algeirsd\u00f3ttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sall\u00e9e, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a). Regional SLC projections based on the low confidence projections were also provided by AR6, but we highlight that more work is needed on understanding and physical modelling of the ice sheet contributions, and on the potential for different regional estimates associated with the partitioning of Greenland and Antarctic ice mass loss.\nOur comparison of AR5 projections with observations for the period 2007\u20132018 shows that the rates of change agree within uncertainties for GMSL and for individual contributions (section \u2018Comparison of the AR5 model simulations with observations\u2019), which is in line with previous studies focusing on total sea-level change (Wang et al., Reference Wang, Church, Zhang and Chen2021a) and the ocean heat uptake contribution (Lyu et al., Reference Lyu, Zhang and Church2021). Monitoring the projections against observed changes is important as it can help to constrain future projections.\nIn terms of future developments of sea-level projections (section \u2018Moving towards local information\u2019), we highlight the need for dynamical ocean downscaling to represent processes missing in GCMs, such as tidal effects and local currents in shelf sea regions, to better estimate future ocean dynamic SLC. This would also improve simulations of key small-scale processes at the ocean-ice interface that affect the climatic drivers of ice sheets and therefore projections of their future evolution. It would also lead to a better quantification of the effects on mean SLC on, for example, tidal characteristics and wave propagations to understand the potential compounding effects on future coastal flood hazards. A second aspect that is relevant to relative sea-level projections, in particular in low-lying delta regions, is the need for improved VLM observational estimates and projections. This will particularly impact coastal SLC projections, as flood risks depend on (and in some parts of the world are dominated by) the movement of the land in addition to the changes in water level.\nIn this paper, we have focused on sea-level projections up to 2100. However, it is important to note that sea-level change does not stop in 2100. Currently, projections beyond 2100 are typically based on different methods compared with the projections up to 2100, due to a lack of model simulations and literature. For instance, in AR6 the time series were extended to 2150 assuming constant ice sheet rates post 2100 and the Gaussian process emulators were substituted with parametric fits. Unfortunately, the use of different methods tends to lead to discontinuities in the time series. To fill this gap, we need better understanding and process modelling of the different components, such that consistent methods can be used to generate long-term projections for the next IPCC assessment report and beyond. This will allow investigations of for instance the sea-level response to surface warming overshoot scenarios, or the inclusion of tipping points in sea-level projections (e.g., Lenton et al., Reference Lenton, Rockstr\u00f6m, Gaffney, Rahmstorf, Richardson, Steffen and Schellnhuber2019). These are only some of the many potential research avenues associated with long-term sea-level projections, all of which are important to investigate given the long-lasting commitment and widespread consequences of future sea-level rise.", "source": "https://sealeveldocs.readthedocs.io/en/latest/slangen22.html"}
{"id": "c18462502844-0", "text": "Li et al. (2022)\uf0c1\nTitle:\nThe Impact of Horizontal Resolution on Projected Sea-Level Rise Along US East Continental Shelf With the Community Earth System Model\nKey Points:\nThe high resolution (HR) Community Earth System Model reduces biases in dynamic sea level (DSL) and circulation on US east continental shelf\nCompared to the low resolution model, the HR projects enhanced (reduced) trends of DSL rise along the US south (north) east continental shelf\nDifferent DSL rise patterns are related to different Gulf Stream reductions under a weakening Atlantic Meridional Overturning Circulation\nCorresponding author:\nDapeng Li\nCitation:\nLi, D., Chang, P., Yeager, S. G., Danabasoglu, G., Castruccio, F. S., Small, J., et al. (2022). The Impact of Horizontal Resolution on Projected Sea\u2010Level Rise Along US East Continental Shelf With the Community Earth System Model. Journal of Advances in Modeling Earth Systems, 14(5), e2021MS002868. doi:10.1029/2021ms002868\nURL:\nhttps://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021MS002868\nAbstract\uf0c1\nThe Intergovernmental Panel on Climate Change Fifth Assessment Report lists sea-level rise as one of the major future climate challenges. Based on pre-industrial and historical-and-future climate simulations with the Community Earth System Model, we analyze the projected sea-level rise in the Northwest Atlantic Ocean with two sets of simulations at different horizontal resolutions. Compared with observations, the low resolution (LR) model simulated Gulf Stream does not separate from the shore but flows northward along the entire coast, causing large biases in regional dynamic sea level (DSL). The high resolution (HR) model improves the Gulf Stream representation and reduces biases in regional DSL. Under the RCP8.5 future climate scenario, LR projects a DSL trend of 1.5\u20132 mm/yr along the northeast continental shelf (north of 40\u00b0 N), which is 2\u20133 times the trend projected by HR. Along the southeast shelf (south of 35\u00b0 N), HR projects a DSL trend of 0.5\u20131 mm/yr while the DSL trend in LR is statistically insignificant. The different spatial patterns of DSL changes are attributable to the different Gulf Stream reductions in response to a weakening Atlantic Meridional Overturning Circulation. Due to its poor representation of the Gulf Stream, LR projects larger (smaller) current decreases along the north (south) east continental slope compared to HR. This leads to larger (smaller) trends of DSL rise along the north (south) east shelf in LR than in HR. The results of this study suggest that the better resolved ocean circulations in HR can have significant impacts on regional DSL simulations and projections.\nPlain Language Summary\uf0c1\nProjecting future sea-level rise has great socioeconomic value. Based on long-term global high-resolution Community Earth System Model simulations, we analyze future sea-level rise in the Northwest Atlantic Ocean. Two identical sets of simulations were conducted with different horizontal resolutions. Comparisons between the two sets of simulations show different sea-level rise projections along the US east continental shelf between the low-resolution (LR) and high-resolution (HR) models. At the northeast shelf, HR projects a sea-level rise of 0.8 mm/yr, less than half of the trend (1.7 mm/yr) projected by LR. At the southeast shelf, HR projects a sea-level rise of 0.6 mm/yr, while the trend in LR is statistically insignificant at only 0.15 mm/yr. We attribute the different sea-level rise projections to the different ocean circulations simulated in LR and HR. Under global warming, LR projects a decrease in Gulf Stream flow along the entire east continental slope, while the decrease in Gulf Stream strength is confined to the southeast continental slope in HR. This study provides an explanation for the discrepancy in regional sea-level rise projections between low- and high-resolution climate models and thus improves our understanding of projected future sea-level rise.\nIntroduction\uf0c1\nSea-level rise has been listed as one of the major impacts of global warming by the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (Collins et al., 2013). Based on an analysis of an urban protection data set, Hallegatte et al. (2013) predicted an increase in the cost of global flooding from \u223c$6 billion/year in 2005 to $60\u201363 billion/year in 2050 due to future sea-level rise and land subsidence. With \u223c41% of global population residing in coastal areas (Mart\u00ednez et al., 2007), understanding future coastal sea-level rise is of great socioeconomic importance.\nThe US east coast has been recognized as one of the hot spots for future sea-level rise (Little et al., 2019; Yin et al., 2009). Based on Geophysical Fluid Dynamics Laboratory (GFDL) Climate Model (CM) global simulations at 1\u02da horizontal resolution, Yin et al. (2009) reported \u223c20 cm future dynamical sea level (DSL) rise off the US northeast coast. By decomposing the DSL rise into local steric height and mass transport components, they found: (a) negative and positive (referenced to global mean) local steric height increases in coastal and open ocean regions; (b) a large cancellation between the negative local steric height and the positive mass transport in coastal regions. Studies also indicate that DSL along the US east coast is related to the Atlantic Meridional Overturning Circulation (AMOC). Based on \u201chosing\u201d experiments (in which freshwater forcing is artificially applied at the subpolar North Atlantic Ocean), Levermann et al. (2005) first showed DSL rises near the North America coasts under a weakening AMOC. They attribute the changes in DSL to changes in geostrophic circulation (Levermann et al., 2005). Near the US northeast coasts, the same DSL and AMOC relation has been repeatedly documented in subsequent climate simulations forced by future global warming scenarios (Landerer et al., 2007; Little et al., 2017; Yin et al., 2009). By comparing 25 different models (at \u223c1\u02da horizontal resolution) participating in the Coupled Model Intercomparison Project Phase 5 (CMIP5), Little et al. (2019) showed that most models exhibit DSL rises near the US northeast coast with decreasing AMOC. However, large uncertainty exists in projected future DSL rises given the spread across different models (Little et al., 2019).\nMost climate simulations submitted for CMIPs are based on standard resolution (a nominal horizontal resolution of 1\u02da) climate models (e.g., Flato et al., 2013). Recent advancements of computing power and storage capacity have enabled high resolution (HR) climate simulations. Based on comparisons of a pair of century long CESM simulations at the standard resolution (1\u02da) and high-resolution (0.1\u02da ocean and sea ice; and 0.25\u02da atmosphere and land), Small et al. (2014) showed that the HR CESM produces more realistic regional simulations than the standard resolution model. Using a longer and much more comprehensive set of CESM simulations than in Small et al. (2014), Chang et al. (2020) found that HR CESM significantly improves climate simulations in many aspects at both basin and regional scales. Chang et al. (2020) further showed that increasing model horizontal resolution can affect future climate projections, in line with previous studies (Roberts et al., 2020; van Westen et al., 2020). By analyzing GFDL CM simulations with different horizontal resolutions, Saba et al. (2016) showed that the warming rate projected by HR is almost double the rate projected by LR in the North Atlantic continental shelf. They suggested that the enhanced warming in HR was associated with improved ocean circulation.", "source": "https://sealeveldocs.readthedocs.io/en/latest/li22james.html"}
{"id": "c18462502844-1", "text": "Most climate simulations submitted for CMIPs are based on standard resolution (a nominal horizontal resolution of 1\u02da) climate models (e.g., Flato et al., 2013). Recent advancements of computing power and storage capacity have enabled high resolution (HR) climate simulations. Based on comparisons of a pair of century long CESM simulations at the standard resolution (1\u02da) and high-resolution (0.1\u02da ocean and sea ice; and 0.25\u02da atmosphere and land), Small et al. (2014) showed that the HR CESM produces more realistic regional simulations than the standard resolution model. Using a longer and much more comprehensive set of CESM simulations than in Small et al. (2014), Chang et al. (2020) found that HR CESM significantly improves climate simulations in many aspects at both basin and regional scales. Chang et al. (2020) further showed that increasing model horizontal resolution can affect future climate projections, in line with previous studies (Roberts et al., 2020; van Westen et al., 2020). By analyzing GFDL CM simulations with different horizontal resolutions, Saba et al. (2016) showed that the warming rate projected by HR is almost double the rate projected by LR in the North Atlantic continental shelf. They suggested that the enhanced warming in HR was associated with improved ocean circulation.\nThe refinement in model horizontal resolution improves sea level simulations. Higginson et al. (2015) suggested that models with coarse resolution may produce erroneous coastal sea level due to inadequate model resolution. By comparing global ocean sea-ice simulations at four different horizontal resolutions (2\u02da, 1\u02da, 0.5\u02da, and 0.25\u02da), Penduff et al. (2010) showed that the 0.25\u02da resolution model can capture sea-level variability more realistically than the others in ocean eddy active regions. Thus, the impacts of model horizontal resolution on future sea-level change deserve focused exploration (Little et al., 2019). In this study, we examine the benefits of HR climate simulations by analyzing the projected sea level change in the Northwest Atlantic Ocean. The novelty of this work lies in the fact that the pair of HR and LR CESM simulations analyzed in this work are much longer than those analyzed in previous studies. They consist of a 500-year preindustrial control (CTRL) simulation and a 250-year (1850\u20132100) historic and future transient (TNST) climate simulation branched from CTRL (Chang et al., 2020). These multi-century simulations completed by the International Laboratory for High-Resolution Earth System Prediction (iHESP) are much longer than the simulation period (1950\u20132050, 100 years) specified in the High Resolution Model Intercomparison Project (HighResMIP, Haarsma et al., 2016). The long integration time reduces model drift and thus potentially improves the fidelity of simulation results. The objectives of this work are to (a) compare LR and HR CESM with observations to validate model results, (b) estimate the long-term sea-level trends along the US east continental shelf in HR and LR, (c) explore how refinement in model resolution impacts ocean circulation and sea-level projections. The reason we focus on ocean circulation is because previous studies have shown DSL rises near the US east coast are associated with a weakening AMOC (Levermann et al., 2005; Little et al., 2017; Yin et al., 2009). However, previous sea-level projections near the US east coasts are all based on LR models. Here we revisit this issue and compare HR and LR projected sea-level rise. Although the resolution of HR is much higher than that of LR (see Table 1 for details), HR is still too coarse to fully resolve small scale dynamical processes near the coasts. Regional downscaling with higher resolution is needed to simulate the full range of coastal dynamics relevant to sea-level rise. The manuscript is structured in five sections. Sections 2 and 3 describe data and methods, respectively. Section 4 presents results and discussion, followed by a summary in Section 5.\nTable 1: Four 250-Year CESM Simulations Analyzed in This Study\nResolution   |  TNST/CTRL   |   Nominal horizontal resolution for ocean and sea-ice (atmosphere and land)   |   Vertical layers for ocean (atmosphere)     |    Climate forcing\nLR      TNST    1 (1)   60 (30) 1850\u20132005: Historic forcing, 2006\u20132100: RCP 8.5\nLR      CTRL    1 (1)   60 (30) 251-500 model year: Climate forcing of 1850\nHR      TNST    0.1 (0.25)      62 (30) 1850\u20132005: Historic forcing, 2006\u20132100: RCP 8.5\nHR      CTRL    0.1 (0.25)      62 (30) 251-500 model year: Climate forcing of 1850\nNote. LR and HR stand for low and high resolution, respectively. TNST and CTRL stand for historic/future-transient and pre-industrial control simulations, respectively. TNST simulations were branched from respective CTRL simulations at year 250.\nData\uf0c1\nCESM CTRL and TNST Climate Simulations\uf0c1\nA comprehensive overview of the CESM CTRL and TNST climate simulations completed as a part of the iHESP partnership is presented in Chang et al. (2020). Here, we present a brief summary of the CESM simulations (Table 1). The CESM CTRL and TNST simulations are designed following the CMIP5 protocol (Taylor et al., 2012). The CTRL experiment is a 500-year simulation forced with perpetual climate forcing for year 1850. The TNST simulation is branched from the CTRL simulation at year 250 and forced with historic climate forcing from 1850 to 2005 and RCP 8.5 emission scenario climate forcing from 2,006 to 2,100. The model code base is CESM1.3 and the component models include the Parallel Ocean Program version 2 (POP2; Danabasoglu et al., 2012; Smith et al., 2010) for the ocean, the spectral element dynamical core (SE-dycore) Community Atmosphere Model version 5 (CAM5; Neale et al., 2012) for the atmosphere, the Community Land Model version 4 (Lawrence et al., 2011) for the land, and the Community Ice Code version 4 (Hunke & Lipscomb, 2008) for the sea ice. For HR CESM, the nominal horizontal resolutions are 0.1\u02da for the ocean and sea ice and 0.25\u02da for the atmosphere and land, with 62 vertical levels for the ocean and 30 hybrid sigma vertical levels for the atmosphere. For LR CESM, the nominal horizontal resolution is 1\u00b0 for all the component models with 60 vertical levels for the ocean and 30 hybrid sigma vertical levels for the atmosphere. Both POP2 and CAM5 utilize stretched vertical grids.\nFor global simulations, the deep ocean typically takes thousands of years to reach an equilibrium (Danabasoglu, 2004; Griffies et al., 2014). Due to the relatively short spin-up time (250 years), model drift exists in the CESM simulations (see Chang et al., 2020). The impacts of such drift, however, can be minimized by referencing TNST to CTRL simulations (Griffies et al., 2014; van Westen et al., 2020). In this work, we compute the projected change in field \u201cx\u201d as: \u2206 x = (x(TNST)2 \u2013 x(TNST)1) \u2013 (x(CTRL)2 \u2013 x(CTRL)1), where x(TNST) and x(CTRL) stand for a variable x from TNST and CTRL simulations, respectively, and the subscripts 1 and 2 denote two different time windows. The CESM outputs monthly averaged fields. All the displayed results in Section 4 are yearly averages determined from monthly model outputs.\nObservational Datasets\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/li22james.html"}
{"id": "c18462502844-2", "text": "For global simulations, the deep ocean typically takes thousands of years to reach an equilibrium (Danabasoglu, 2004; Griffies et al., 2014). Due to the relatively short spin-up time (250 years), model drift exists in the CESM simulations (see Chang et al., 2020). The impacts of such drift, however, can be minimized by referencing TNST to CTRL simulations (Griffies et al., 2014; van Westen et al., 2020). In this work, we compute the projected change in field \u201cx\u201d as: \u2206 x = (x(TNST)2 \u2013 x(TNST)1) \u2013 (x(CTRL)2 \u2013 x(CTRL)1), where x(TNST) and x(CTRL) stand for a variable x from TNST and CTRL simulations, respectively, and the subscripts 1 and 2 denote two different time windows. The CESM outputs monthly averaged fields. All the displayed results in Section 4 are yearly averages determined from monthly model outputs.\nObservational Datasets\uf0c1\nFive observational datasets are used to evaluate model results. The first is the sea surface height (SSH) above geoid obtained from satellite altimeters between 1993 and 2019 (Taburet et al., 2019). It includes data observed from all altimeter missions, and the temporal and spatial resolutions are daily and 0.25\u02da, respectively. The second is the climatological mean near-surface velocity from drifters (Laurindo et al., 2017). The time period for the climatological mean is 1979\u20132020 and the spatial resolution is 0.25\u02da. The third data set is the World Ocean Atlas (WOA) climatological mean temperature and salinity (Locarnini et al., 2018; Zweng et al., 2019). The time period for climatological mean is 2005\u20132017 and the spatial resolution is 0.25. The fourth data set is the ETOPO5 bathymetry with a spatial resolution of 5 min (NGDC, 1993). The four observational data sets above may not be fully representative at the coasts due to their resolutions and/or lack of measurements. Therefore, they can only be used to compare LR and HR simulation in the open ocean off the coast. The last data set is AMOC measured by the RAPID-MOC array at 26.5\u00b0 N (McCarthy et al., 2015). The measurements started from April 2004 and are still in progress. All CESM simulations and observational data sets are publicly available and the access to the datasets is provided in the acknowledgment section.\nMethods\uf0c1\nSSH Decomposition\uf0c1\nThe methods to decompose SSH (\u03b7) are discussed in detail in Griffies et al. (2014) and Griffies and Greatbatch (2012). Here, we summarize the key equations in this section. More detailed information of the relevant equations and derivations is presented in the Supporting Information.\nFor a hydrostatic fluid, \u03b7 tendency can be decomposed as:\nurn:x-wiley:19422466:media:jame21583:jame21583-math-0024 (1)\nwhere urn:x-wiley:19422466:media:jame21583:jame21583-math-0025 is the gravitational acceleration, urn:x-wiley:19422466:media:jame21583:jame21583-math-0026 is the surface density, urn:x-wiley:19422466:media:jame21583:jame21583-math-0027 and urn:x-wiley:19422466:media:jame21583:jame21583-math-0028 are the pressure at the surface and the bottom, urn:x-wiley:19422466:media:jame21583:jame21583-math-0029 is the water depth, urn:x-wiley:19422466:media:jame21583:jame21583-math-0030 is the in-situ density, urn:x-wiley:19422466:media:jame21583:jame21583-math-0031 and urn:x-wiley:19422466:media:jame21583:jame21583-math-0032 are the vertical and time coordinates, respectively (Equation (13) in Griffies et al., 2014). The first term on the right-hand side of Eq (1) measures sea-level change associated with mass change and it\u2019s related to barotropic mass transport and surface mass flux (see Equations (47\u201349) in Griffies et al. (2014) and the Supporting Information for details). The second term on the right-hand side of Equation (1) measures sea-level change associated with local density change. This decomposition was first used by Gill and Niller (1973) to analyze sea-level fluctuation. Landerer et al. (2007) and Yin et al. (2009) later used this decomposition to interpret climate models simulated sea-level patterns under global warming.\nFor the POP2 model, which uses the Boussinesq approximation and zero surface water flux, SSH explicitly computed by the model is the DSL (Griffies et al., 2014). DSL (urn:x-wiley:19422466:media:jame21583:jame21583-math-0033) is defined as the anomaly from the global mean sea level: urn:x-wiley:19422466:media:jame21583:jame21583-math-0034, where urn:x-wiley:19422466:media:jame21583:jame21583-math-0035 is the globally averaged sea level (Griffies et al., 2014), and urn:x-wiley:19422466:media:jame21583:jame21583-math-0036 is zero at every time step in POP2. Thus, all terms in Equation (1) should be interpreted as anomalies from the global mean when decomposing the POP2 SSH field. Since the bottom pressure is not available from POP2 output, we estimate the mass transport term as the residual between SSH and local steric height.\nBoussinesq Approximation and Sterodynamic Sea-Level\uf0c1\nMany ocean models including POP2 employ the Boussinesq approximation which conserves the volume rather than the mass of a fluid parcel. Greatbatch (1994) showed that Boussinesq models do not account for sea-level changes associated with the net expansion (or contraction) of the global ocean. Further comparison between Boussinesq and non-Boussinesq models shows: (a) very similar large-scale sea level patterns (see Figure 3 in Griffies & Greatbatch, 2012); (b) corrections are needed in Boussinesq models to study the impact on earth rotation and geoid associated with water mass redistribution (Bryan, 1997; Kopp et al., 2010). For assessing future sea-level change with a Boussinesq model, the only correction required is to add a globally uniform, time-varying factor known as the global mean steric sea-level (Greatbatch, 1994; Griffies et al., 2014). Since this correction is globally uniform, it has no dynamical effects (Greatbatch, 1994).\nThe global mean steric sea level (urn:x-wiley:19422466:media:jame21583:jame21583-math-0037) is computed as the global average of local steric sea level (urn:x-wiley:19422466:media:jame21583:jame21583-math-0038):\nurn:x-wiley:19422466:media:jame21583:jame21583-math-0039\n(2)\nurn:x-wiley:19422466:media:jame21583:jame21583-math-0040\n(3)\nwhere urn:x-wiley:19422466:media:jame21583:jame21583-math-0041 indicates a global average, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0042 kg/m3 is the reference density (van Westen & Dijkstra, 2021). Since density changes can result from temperature and salinity changes, local steric height (urn:x-wiley:19422466:media:jame21583:jame21583-math-0043) can be decomposed into thermosteric and halosteric components. Although local thermosteric and halosteric heights can be of the same order of magnitude, the global mean halosteric height is zero (Gregory et al., 2019). Thus, urn:x-wiley:19422466:media:jame21583:jame21583-math-0044 is essentially due to thermosteric component and is referred to as global mean thermosteric sea-level (Gregory et al., 2019). The sum of DSL and global mean thermosteric sea-level (correcting for the Boussinesq approximation) is referred to as the sterodynamic sea-level (Gregory et al., 2019).", "source": "https://sealeveldocs.readthedocs.io/en/latest/li22james.html"}
{"id": "c18462502844-3", "text": "The global mean steric sea level (urn:x-wiley:19422466:media:jame21583:jame21583-math-0037) is computed as the global average of local steric sea level (urn:x-wiley:19422466:media:jame21583:jame21583-math-0038):\nurn:x-wiley:19422466:media:jame21583:jame21583-math-0039\n(2)\nurn:x-wiley:19422466:media:jame21583:jame21583-math-0040\n(3)\nwhere urn:x-wiley:19422466:media:jame21583:jame21583-math-0041 indicates a global average, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0042 kg/m3 is the reference density (van Westen & Dijkstra, 2021). Since density changes can result from temperature and salinity changes, local steric height (urn:x-wiley:19422466:media:jame21583:jame21583-math-0043) can be decomposed into thermosteric and halosteric components. Although local thermosteric and halosteric heights can be of the same order of magnitude, the global mean halosteric height is zero (Gregory et al., 2019). Thus, urn:x-wiley:19422466:media:jame21583:jame21583-math-0044 is essentially due to thermosteric component and is referred to as global mean thermosteric sea-level (Gregory et al., 2019). The sum of DSL and global mean thermosteric sea-level (correcting for the Boussinesq approximation) is referred to as the sterodynamic sea-level (Gregory et al., 2019).\nThe sterodynamic sea-level changes only account for changes in sea-level associated with ocean circulation and density changes (Gregory et al., 2019), while the actual sea-level can be influenced by other processes such as glacial melting, changes in land-water storage, and vertical land motion. The current version of CESM does not include these processes. Thus, sea-level changes associated with these processes are not considered in this study.\nExternally Forced Sea-Level Changes\uf0c1\nIn this study, we are interested in the externally forced sea-level changes. By referencing TNST to CTRL simulations, sea-level changes in response to anthropogenic climate forcing can be extracted (a schematic is presented in Figure S1 in the Supporting Information S1). While internal variability can give rise to large decadal fluctuations in sea-level in the North Atlantic Ocean (Chafik et al., 2019; Griffies & Bryan, 1997; Yeager, 2020), externally forced sea-level changes are expected to manifest as robust long-term trends. Hence we use linear trend analysis with significance tests to identify externally forced sea-level changes. Given that externally forced sea-level changes may not necessarily be linear with time, we also examine sea-level differences between present and future time periods. The two analysis methods give very similar spatial patterns of sea-level response to the RCP8.5 CO2 emission scenario.\nResults and Discussion\uf0c1\nEvaluation of Model Simulations Against Observations\uf0c1\nWe first compare the model results with the existing observations before discussing future sea-level projections. Figure 1 shows DSL mean and variance from the satellite observations, HR, and LR simulations. For the mean DSL, HR shows two major improvements over LR: (a) HR reduces mean DSL bias along the entire US east continental shelf; and (b) HR produces more realistic mean DSL patterns along the Gulf Stream extension than LR (Figures 1a\u20131c). Along the northeast continental shelf (north of Cape Hatteras, marked as the blue star in Figures 1a\u20131c), HR reduces the negative DSL bias of \u223c40 cm in LR. Along the southeast shelf (south of Cape Hatteras), HR reduces the positive DSL bias of \u223c20 cm in LR (Figures 1a\u20131c). In addition, HR improves the Gulf Stream separation point over LR, although the overshooting issue still exists. The Gulf Stream separation point was determined from visual inspection. A non-biased method is to select a (fixed) DSL/SSH isoline and quantify the separation latitude, for example, as was done for the East Australian Current (Cetina-Heredia et al., 2014). Observations show that the Gulf Stream leaves the US east coast near Cape Hatteras at 35\u00b0 N (Figure 1a). HR simulated Gulf Stream meanders past 35\u00b0 N and separates from the coast close to 40\u00b0 N, while LR simulated Gulf Stream does not show a clear separation from the coasts (Figures 1b-1c). The attachment of the Gulf Stream to the coast is a common issue in coarse resolution ocean model simulations (Chassignet & Marshall, 2008; Dengg et al., 1996; Saba et al., 2016; Schoonover et al., 2017). A realistic Gulf Stream separation has been found when model horizontal resolution increases up to 1/50urn:x-wiley:19422466:media:jame21583:jame21583-math-0048 (equivalent to 1.5 km in mid latitudes), and the effects of submesocale processes are explicitly represented (Chassignet & Xu, 2017). Despite this shortcoming, the simulated mean DSL along the Gulf Stream extension is much closer to observations in HR than in LR. For DSL variance, HR and the observations show similar spatial patterns along the continental shelf with large variance in the south and small variance in the north, even though the magnitudes in HR are larger than observations (Figures 1d-1e). In contrast, LR produces opposite spatial patterns with small (large) variance along the south (north) east shelf (Figure 1f). In the Gulf Stream extension region, the variance in HR is closer to observations than LR (Figures 1d\u20131f). This improvement is likely attributed to the better representation of oceanic mesoscale eddies in HR, which has been listed as one of the existing problems for coarse resolution climate model projections of future sea-level change (Fasullo & Nerem, 2018).\nFigure 1: Left column: mean dynamic sea level (DSL) from Altimeter observation (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: Variance of daily DSL from Altimeter observation (d), HR (e) and LR (f). For the variance of observed sea level, we first compute anomalies from the global mean and then compute variance. For (e)\u2013(f), we directly compute variance of model sea surface height output. The time period for climatological mean and variance is 1993\u20132019. The blue star in (a)\u2013(c) denotes Cape Hatteras.\nDSL and surface currents are related through the geostrophic relationship for large-scale ocean circulations such as the Gulf Stream. Thus, the reduced DSL bias in HR is associated with improved Gulf Stream circulation. Compared with drifter observations, LR simulates a too weak Gulf Stream current both along the US southeast continental slope (south of Cape Hatteras) and in the extension region (Figures 2a\u20132c). Specifically, along the southeast continental slope, the near surface current speed in LR is only 40\u201360 cm/s, less than half of the observed values of 120\u2013140 cm/s. In contrast, HR simulated current speed is \u223c120 cm/s or greater (Figure 2b), much closer to the observations. At \u223c40\u00b0 N, HR and observations show southwestward shelf currents, which are absent in LR (Figures 2d\u20132f). The improved ocean circulations due to refined model resolution has also been reported in other models (Chassignet et al., 2020; Saba et al., 2016). In the Gulf Stream extension region, the current speed in LR is 10\u201320 cm/s, much less than the current speed of \u223c50 cm/s in both HR and observations. However, the aforementioned overshooting problem is evident in both LR and HR (Figures 2b-2c). Although HR clearly shows an improved representation of the Gulf Stream and its extension compared to those of LR, it does not completely eliminate all the biases, particularly the overshooting bias.", "source": "https://sealeveldocs.readthedocs.io/en/latest/li22james.html"}
{"id": "c18462502844-4", "text": "Figure 1: Left column: mean dynamic sea level (DSL) from Altimeter observation (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: Variance of daily DSL from Altimeter observation (d), HR (e) and LR (f). For the variance of observed sea level, we first compute anomalies from the global mean and then compute variance. For (e)\u2013(f), we directly compute variance of model sea surface height output. The time period for climatological mean and variance is 1993\u20132019. The blue star in (a)\u2013(c) denotes Cape Hatteras.\nDSL and surface currents are related through the geostrophic relationship for large-scale ocean circulations such as the Gulf Stream. Thus, the reduced DSL bias in HR is associated with improved Gulf Stream circulation. Compared with drifter observations, LR simulates a too weak Gulf Stream current both along the US southeast continental slope (south of Cape Hatteras) and in the extension region (Figures 2a\u20132c). Specifically, along the southeast continental slope, the near surface current speed in LR is only 40\u201360 cm/s, less than half of the observed values of 120\u2013140 cm/s. In contrast, HR simulated current speed is \u223c120 cm/s or greater (Figure 2b), much closer to the observations. At \u223c40\u00b0 N, HR and observations show southwestward shelf currents, which are absent in LR (Figures 2d\u20132f). The improved ocean circulations due to refined model resolution has also been reported in other models (Chassignet et al., 2020; Saba et al., 2016). In the Gulf Stream extension region, the current speed in LR is 10\u201320 cm/s, much less than the current speed of \u223c50 cm/s in both HR and observations. However, the aforementioned overshooting problem is evident in both LR and HR (Figures 2b-2c). Although HR clearly shows an improved representation of the Gulf Stream and its extension compared to those of LR, it does not completely eliminate all the biases, particularly the overshooting bias.\nFigure 2: Left column: mean near surface velocity from drifter observations (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: mean near surface velocity from drifter observations (d), HR (e) and LR (f) zoomed into the US northeast continental shelf and slope. The velocity is sampled at 15-m depth. The time period for the climatological mean is 1979\u20132020. Red star in (d) indicates Boston, Massachusetts. For clarity, vectors are plotted at every four grid points in (a), every 10 grid points in (b), and every grid point in (c) to approximate a spatial resolution of 1urn:x-wiley:19422466:media:jame21583:jame21583-math-0050 (the resolutions of drifter, HR and LR are 0.25urn:x-wiley:19422466:media:jame21583:jame21583-math-0051, 0.1urn:x-wiley:19422466:media:jame21583:jame21583-math-0052 and 1urn:x-wiley:19422466:media:jame21583:jame21583-math-0053, respectively). To highlight small-scale circulations, vectors are plotted on every 2 grid points in (d), every 5 grid points in (e), and every grid point in (f). This yields an approximate spatial resolution of 0.5urn:x-wiley:19422466:media:jame21583:jame21583-math-0054 for both observations (d) and HR (e), and 1urn:x-wiley:19422466:media:jame21583:jame21583-math-0055 for LR (f).\nIn addition to improved DSL and ocean circulations, HR reduces biases in near surface temperature and salinity along the northeast continental shelf (Figure 3). Compared to the WOA climatology, HR reduces the warm temperature and high salinity biases of LR in the Gulf of Maine (Figure 3). These bias reductions may be attributed to the improved ocean circulation in HR (Figures 2d\u20132f). In LR, the overshooting Gulf Stream brings warm and saline water to the Gulf of Maine, causing \u223c4\u00b0 C bias in near surface temperature and \u223c3 g/kg bias in near surface salinity (Figure 3). In HR, the southwestward shelf current transports cold and fresh water from the Gulf of St. Lawrence and the Labrador Sea to the Gulf of Maine, reducing the temperature and salinity biases (Figure 3). Although HR improves surface salinity in the Gulf of Maine, it shows a negative salinity bias (\u223c\u22121 g/kg) in the Gulf of St. Lawrence (Figures 3d\u20133f). The low salinity water there may explain the negative salinity bias in the Gulf of Maine as southwestward shelf currents move from the Gulf of St. Lawrence to the Gulf of Maine.\nFigure 3: Left column: mean temperature at 15-m depth from World Ocean Atlas (WOA), (a), high resolution (HR) (b), and low resolution (LR) (c). Right column: mean salinity at 15-m depth from WOA (d), HR (e) and LR (f). Arrows are the mean velocities at 15-m depth from drifter observations (a), (d), HR (b), (e), and LR (c), (f). The averaging time period for temperature and salinity is 2005\u20132017. Red star indicates Boston, Massachusetts. Vectors are plotted on every two grid points in (a), (d), every 5 grid points in (b), (e), and every grid point in (c), (f). This yields an approximate spatial resolution of 0.5urn:x-wiley:19422466:media:jame21583:jame21583-math-0057 for both drifter (a), (d) and HR (b), (e), and 1urn:x-wiley:19422466:media:jame21583:jame21583-math-0058 for LR (c), (f).\nProjected Future Sea-Level Rise\uf0c1\nUnder the future RCP 8.5 emission scenario, both LR and HR project increasing DSL trends along the US east continental shelf but with different amplitudes (Figures 4a and 4d). Along the northeast shelf (north of 40\u00b0 N), LR projects a DSL trend of 1.5\u20132 mm/yr, more than double the DSL trend of 0.5\u20131 mm/yr projected by HR. Along the southeast shelf (south of 35\u00b0 N), HR shows a DSL trend of 0.5\u20131 mm/yr, while LR shows a statistically insignificant trend of less than 0.5 mm/yr. Although LR and HR project different DSL trends along the US east shelf, the global mean thermosteric sea-level rise is in close agreement between the two models (Figure 5). This is consistent with the finding by Van Westen et al. (2020) and may be attributed to the fact that the global mean thermosteric sea-level rise is related to ocean heat uptake, which is largely determined by the RCP8.5 emission scenario specified in LR and HR. Between 2,001 and 2,100, LR and HR project a similar average trend of \u223c3 mm/yr for global mean thermosteric sea-level rise (Figure 5).\nFigure 4: Trends of dynamic sea level (DSL) (a), (d), local steric height component (b), (e), and mass transport component (c), (f) from the low resolution (LR) (left column) and high resolution (HR) (right column). Trends are computed from the TNST simulations from 2,001 to 2,100 and corrected by the CTRL simulations to account for potential model drift (see Section 2.1). Black dots indicate the regions where trends are statistically insignificant (p > 0.1). Global mean thermosteric sea-level rise is removed in (b), (e). Red, blue, and black stars mark Boston, Cape Hatteras, and Jacksonville, respectively. The difference of DSL, local steric height, and mass transport components between two time periods shows similar spatial patterns as Figure 4. We present that plot in Figure S2 in the Supporting Information S1.\nFigure 5: Global mean thermosteric sea-level relative to 1,850. Shaded areas are from 2,001 to 2,100, when global mean thermosteric sea-level starts to increase due to global warming.", "source": "https://sealeveldocs.readthedocs.io/en/latest/li22james.html"}
{"id": "c18462502844-5", "text": "Figure 4: Trends of dynamic sea level (DSL) (a), (d), local steric height component (b), (e), and mass transport component (c), (f) from the low resolution (LR) (left column) and high resolution (HR) (right column). Trends are computed from the TNST simulations from 2,001 to 2,100 and corrected by the CTRL simulations to account for potential model drift (see Section 2.1). Black dots indicate the regions where trends are statistically insignificant (p > 0.1). Global mean thermosteric sea-level rise is removed in (b), (e). Red, blue, and black stars mark Boston, Cape Hatteras, and Jacksonville, respectively. The difference of DSL, local steric height, and mass transport components between two time periods shows similar spatial patterns as Figure 4. We present that plot in Figure S2 in the Supporting Information S1.\nFigure 5: Global mean thermosteric sea-level relative to 1,850. Shaded areas are from 2,001 to 2,100, when global mean thermosteric sea-level starts to increase due to global warming.\nFigures 4b\u20134e, 4f show the trends of local steric height and mass transport components (both are relative to global mean, see Section 3) in the Northwest Atlantic Ocean. For both LR and HR, negative and positive local steric height trends mostly occur in continental shelf and open ocean regions, respectively. This indicates that the local steric height increase is lower than the global mean in continental shelf and greater than the global mean in the open ocean. This is because the local steric height is a depth integral (Equation (3)), so that the steric response increases with water depth. The negative local steric height trends in continental shelf are compensated by positive mass transport trends (Figures 4c and 4f). These are consistent with the model simulation results reported by Yin et al. (2009). Different contributions of local steric height and mass transport to DSL are noted between LR and HR (Figure 4). Here we choose two regions (marked as the 3\u00b0 \u00d7 3\u00b0 black boxes in Figures 4a and 4d) to analyze the difference between LR and HR. At the northeast shelf near Boston, Massachusetts (highlighted as the red star in Figure 4), the larger increases in mass transport and the smaller decreases in local steric height lead to larger increases in DSL in LR (Figure 4, Table 2). We further quantify the relative contributions of mass transport and local steric height to the difference in DSL trends between LR and HR. At the northeast shelf box region, LR and HR project DSL rises of 1.66 and 0.8 mm/yr, respectively (Table 2, Figure 6a). The difference in projected DSL rise (0.86 mm/yr) results from the difference in local steric height and mass transport (Figures 6b and 6c). Between LR and HR, the difference in local steric height is 0.55 mm/yr (see the fourth row in Table 2), accounting for 64% of the DSL difference (0.86 mm/yr). The difference in mass transport accounts for the remaining 36% of the DSL difference. The same analysis performed for the southeast shelf box region reveals the difference in mass transport (0.32 mm/yr) accounts for 65% of the DSL trend difference (0.49 mm/yr), and the difference in local steric height accounts for the remaining (Table 2, Figures 6d\u20136f). Because the mass transport is estimated as the residual between DSL and local steric height (see Section 3), we next focus on comparing the differences in local steric height between LR and HR.\nTable 2: Contributions of Local Steric Height and Mass Transport to Dynamic Sea Level (DSL) Trends on the Northeast Shelf Near Boston, Massachusetts and on the Southeast Shelf Near Jacksonville, Florida\nBoston, Massachusetts   DSL     Local steric height     Mass transport\nLR      1.66 urn:x-wiley:19422466:media:jame21583:jame21583-math-0064 0.19      \u22122.55 urn:x-wiley:19422466:media:jame21583:jame21583-math-0065 0.11     4.22 urn:x-wiley:19422466:media:jame21583:jame21583-math-0066 0.20\nHR      0.80 urn:x-wiley:19422466:media:jame21583:jame21583-math-0067 0.26      \u22123.10 urn:x-wiley:19422466:media:jame21583:jame21583-math-0068 0.23     3.91 urn:x-wiley:19422466:media:jame21583:jame21583-math-0069 0.16\nLR\u2013HR   0.86    0.55    0.31\nJacksonville, Florida   DSL     Local steric height     Mass transport\nLR      0.15 urn:x-wiley:19422466:media:jame21583:jame21583-math-0070 0.20      \u22122.74 urn:x-wiley:19422466:media:jame21583:jame21583-math-0071 0.14     2.89 urn:x-wiley:19422466:media:jame21583:jame21583-math-0072 0.14\nHR      0.64 urn:x-wiley:19422466:media:jame21583:jame21583-math-0073 0.29      \u22122.57 urn:x-wiley:19422466:media:jame21583:jame21583-math-0074 0.14     3.21 urn:x-wiley:19422466:media:jame21583:jame21583-math-0075 0.21\nHR\u2013LR   0.49    0.17    0.32\nNote. The trends and 95% confidence intervals are computed with the time series in Figure 6 from 2,001 to 2,100. The unit is mm/yr.\nFigure 6: Time series of dynamic sea level, local steric height and mass transports on the northeast shelf near Boston, Massachusetts (a\u2013c) and on the southeast shelf near Jacksonville, Florida (d\u2013f). The values are spatially averaged within the boxes highlighted in Figures 4a and 4d. Thin and thick lines are yearly mean and 10-year running mean, respectively. Shaded areas in (a\u2013f) are from 2,001 to 2,100, when Atlantic Meridional Overturning Circulation strength starts to decrease (see Figure 9d).\nTwo factors contribute to the local steric height differences between LR and HR: bathymetry and in-situ density. Along the US southeast continental shelf, bathymetry in LR is deeper than that in HR and ETOPO5 (Figures 7a\u20137c). In addition, the land-sea mask in LR does not accurately represent the coastline due to the coarse horizontal resolution (Figures 7c and 7f). In the Gulf of Maine, HR resolves small scale bathymetry features such as the Northeast channel, Jordan Basin, Wilkinson Basin, and Georges Basin (Figure 7d). These features are completely missing in LR. Given that the local steric height is a depth integral, the misrepresented bathymetry in LR causes biases in local steric height. Within the Gulf of Maine (highlighted as the black box in Figure 7d), the maximum depth in HR is 330 m, 50% deeper than the maximum depth of 220 m in LR (Figures 7e-7f, Figure 8). In addition to bathymetry difference, LR and HR project different density changes in the future (Figure 8a). Since both density and bathymetry affect local steric height, we next explore the impacts of the two factors on local steric height in the Gulf of Maine box region.\nFigure 7: Left column: bathymetry contours along the US east continental shelf from ETOPO5 (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: bathymetry in the Gulf of Maine from ETOPO5 (d), HR (e) and LR (f). In (d), JB, WB, GB, and NC stand for the Jordan basin, Wilkinson basin, Georges basin, and Northeast channel, respectively. The black box in (d) indicates the region for spatially averaged profiles shown in Figure 8.\nFigure 8: Depth profiles of in-situ density change (a), temperature change (b), and salinity change (c) averaged in the Gulf of Maine. The region for spatial averaging is highlighted in Figure 7 (d). The change is calculated as the difference of the mean values between 2,081-2,100 and 2,001\u20132,020 in the TNST simulations and corrected with the CTRL simulations to account for potential model drift.", "source": "https://sealeveldocs.readthedocs.io/en/latest/li22james.html"}
{"id": "c18462502844-6", "text": "Two factors contribute to the local steric height differences between LR and HR: bathymetry and in-situ density. Along the US southeast continental shelf, bathymetry in LR is deeper than that in HR and ETOPO5 (Figures 7a\u20137c). In addition, the land-sea mask in LR does not accurately represent the coastline due to the coarse horizontal resolution (Figures 7c and 7f). In the Gulf of Maine, HR resolves small scale bathymetry features such as the Northeast channel, Jordan Basin, Wilkinson Basin, and Georges Basin (Figure 7d). These features are completely missing in LR. Given that the local steric height is a depth integral, the misrepresented bathymetry in LR causes biases in local steric height. Within the Gulf of Maine (highlighted as the black box in Figure 7d), the maximum depth in HR is 330 m, 50% deeper than the maximum depth of 220 m in LR (Figures 7e-7f, Figure 8). In addition to bathymetry difference, LR and HR project different density changes in the future (Figure 8a). Since both density and bathymetry affect local steric height, we next explore the impacts of the two factors on local steric height in the Gulf of Maine box region.\nFigure 7: Left column: bathymetry contours along the US east continental shelf from ETOPO5 (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: bathymetry in the Gulf of Maine from ETOPO5 (d), HR (e) and LR (f). In (d), JB, WB, GB, and NC stand for the Jordan basin, Wilkinson basin, Georges basin, and Northeast channel, respectively. The black box in (d) indicates the region for spatially averaged profiles shown in Figure 8.\nFigure 8: Depth profiles of in-situ density change (a), temperature change (b), and salinity change (c) averaged in the Gulf of Maine. The region for spatial averaging is highlighted in Figure 7 (d). The change is calculated as the difference of the mean values between 2,081-2,100 and 2,001\u20132,020 in the TNST simulations and corrected with the CTRL simulations to account for potential model drift.\nTo study the impact of bathymetry on local steric height, we integrate HR projected density changes (urn:x-wiley:19422466:media:jame21583:jame21583-math-0076) from the surface to the depths used in LR (urn:x-wiley:19422466:media:jame21583:jame21583-math-0077) and HR (urn:x-wiley:19422466:media:jame21583:jame21583-math-0078), respectively (so the only difference is bathymetry between LR and HR. The reason why we do not use urn:x-wiley:19422466:media:jame21583:jame21583-math-0079 is because urn:x-wiley:19422466:media:jame21583:jame21583-math-0080 has a shallow bias and urn:x-wiley:19422466:media:jame21583:jame21583-math-0081 has no values between urn:x-wiley:19422466:media:jame21583:jame21583-math-0082 and urn:x-wiley:19422466:media:jame21583:jame21583-math-0083 (see Figure 8a). The two calculations yield urn:x-wiley:19422466:media:jame21583:jame21583-math-0084 = 4.2 cm, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0085 = 8.4 cm. Thus, if LR projects same density change as HR and the only difference is bathymetry, then the bias in LR bathymetry can lead up to 50% difference in local steric height changes in that region. To study the impact of density on local steric height, we integrate the projected density changes of LR (urn:x-wiley:19422466:media:jame21583:jame21583-math-0086) and HR (urn:x-wiley:19422466:media:jame21583:jame21583-math-0087) from the surface to urn:x-wiley:19422466:media:jame21583:jame21583-math-0088 (so the only difference is density between LR and HR. The reason why we do not use urn:x-wiley:19422466:media:jame21583:jame21583-math-0089 is because urn:x-wiley:19422466:media:jame21583:jame21583-math-0090 has no values between urn:x-wiley:19422466:media:jame21583:jame21583-math-0091 and urn:x-wiley:19422466:media:jame21583:jame21583-math-0092 (see Figure 8a). The two calculations yield urn:x-wiley:19422466:media:jame21583:jame21583-math-0093 = 4.2 cm, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0094 = 8.3 cm. Thus, if HR uses the same bathymetry as LR and the only difference is density changes, then the difference in density projections can cause \u223c50% difference in local steric height changes in that region.\nBoth temperature and salinity changes contribute to density changes. In the Gulf of Maine box region, HR projects a 5\u00b0 C increase in surface temperature from 2001 to 2100, \u223c40% larger than the temperature increase (3.6\u00b0 C) projected by LR (Figure 8b). The enhanced warming projected by HR is consistent with Saba et al. (2016), who showed larger warming rates along the Northwest Atlantic shelf in climate models with higher horizontal resolutions. In addition to enhanced warming, HR also projects larger salinity increases in the entire water column than LR (Figure 8c). The large salinity increases partially compensate the density decreases due to high temperature, leading to reduced density decreases (even density increases at 70 m depth) in HR than that in LR (Figure 8). Note that the density increases near 70 m in HR (Figure 8a) contribute negatively to the local steric height changes.\nAssociations With AMOC\uf0c1\nPrevious studies have related DSL changes in the North Atlantic Ocean to AMOC (Chafik et al., 2019; Little et al., 2017; Yin et al., 2009). We start by comparing AMOC overturning streamfunctions between LR and HR. For the mean states (the mean states were computed as the averages over the last 100 years (400\u2013500) of the control simulations, Figures 9a and 9b), differences are noted (a) below 3,000-m depth in the Atlantic basin, and (b) in mid latitudes (\u223c40\u00b0N) between 800 and 1,400 m depth. The former difference may be related to the Nordic Seas overflow parameterization (Danabasoglu et al., 2010), which is used in LR and disabled in HR. At \u223c40\u00b0N and between 800 and 1,400 m depth, the mean AMOC transport in LR (20\u201322 Sv, 1 Sv = 106 m3/s) is stronger than that (mostly 16\u201320 Sv) in HR. One factor that may explain such difference is the mixed layer depth (MLD) bias in the north Atlantic deep water formation regions. By comparing LR, HR and observed MLD, Chang et al. (2020) showed LR contains large positive bias in the north Atlantic deep water formation regions such as Labrador Sea (see their Figure 15). MLD bias there may affect deep water formation and AMOC variability (Yeager et al., 2021). Exploring the impacts of MLD and deep water formation on AMOC is beyond the scope of this work. A study assessing the contributions of the Labrador Sea water formation to AMOC can be found in Yeager et al. (2021).\nFigure 9: Atlantic Meridional Overturning Circulation (AMOC) overturning streamfunction climatological mean for low resolution (LR) (a) and high resolution (HR) (b). AMOC overturning streamfunctions are averaged during the last 100 years (year 401\u2013500) of the CTRL simulations to minimize model drift. (c) Comparison of AMOC overturning streamfunctions from LR, HR and RAPID observations at 26.5\u00b0N. The observed AMOC overturning streamfunction is averaged from April 2004 to March 2020. LR and HR AMOC overturning streamfunctions are averaged from 1986 to 2005. This time period is chosen to avoid the impact of the RCP8.5 CO2 forcing (starts from 2006) on AMOC simulations. (d) AMOC strength from the TNST simulations and corrected by the CTRL simulations. AMOC strength is calculated as the AMOC overturning streamfunction at 26.5\u00b0N and 1000-m depth.", "source": "https://sealeveldocs.readthedocs.io/en/latest/li22james.html"}
{"id": "c18462502844-7", "text": "Figure 9: Atlantic Meridional Overturning Circulation (AMOC) overturning streamfunction climatological mean for low resolution (LR) (a) and high resolution (HR) (b). AMOC overturning streamfunctions are averaged during the last 100 years (year 401\u2013500) of the CTRL simulations to minimize model drift. (c) Comparison of AMOC overturning streamfunctions from LR, HR and RAPID observations at 26.5\u00b0N. The observed AMOC overturning streamfunction is averaged from April 2004 to March 2020. LR and HR AMOC overturning streamfunctions are averaged from 1986 to 2005. This time period is chosen to avoid the impact of the RCP8.5 CO2 forcing (starts from 2006) on AMOC simulations. (d) AMOC strength from the TNST simulations and corrected by the CTRL simulations. AMOC strength is calculated as the AMOC overturning streamfunction at 26.5\u00b0N and 1000-m depth.\nFigure 9c presents the climatological mean (1986\u20132005) AMOC overturning streamfunctions at 26.5\u00b0N. Compared to the RAPID observations (Smeed et al., 2014, 2018), LR and HR show realistic vertical structures in the upper 2,000 m, with the maximum values at 1,000-m depth. Below 3,000-m depth, model biases are evident and LR is in closer agreement with observations than HR. The large differences between HR and observations maybe related to the aforementioned overflow parameterization (Chang et al., 2020; Danabasoglu et al., 2010). By comparing AMOC simulations from multiple global models, Danabasoglu et al. (2014) showed that large biases between models and RAPID observations at depth are common if the overflows are not parameterized. Under the RCP8.5 emission scenario, LR and HR project similar reductions of AMOC strength (\u223c8 Sv) from 2,001 to 2,100 (Figure 9d, AMOC strength is defined as the AMOC overturning streamfunction at 26.5\u00b0N and 1,000-m depth).\nAs the AMOC strength decreases, LR and HR project weakened Gulf Stream currents but with different amplitudes (Figure 10). LR projects a decrease in near surface current speed along the entire US east continental slope with the largest decrease occurring at 40\u00b0 N. For HR, the current speed decreases are mainly confined along the southeast continental slope. The spatial patterns of current speed trends are related to the mean ocean circulation (Figure 2). LR simulated Gulf Stream does not have a clear separation point from the shore, and it moves northward along the entire continental slope (Figures 2c and 2f). As a result, the weakening Gulf Stream currents affect the entire east continental slope. HR simulated Gulf Stream leaves US east continental slope at \u223c40\u00b0 N (Figure 2b), so the effects of weakening Gulf Stream are mainly confined along the southeast slope. For 1 Sv of AMOC reduction, HR projects a larger decrease in Gulf Stream currents at the southeast continental slope compared to LR (Figure 10, Figures 11a, 11b). In addition to the large Gulf Stream reductions, HR shows narrow bands of enhanced current speed on the landside of the Gulf Stream. The increases in current speed are associated with the shift of Gulf Stream path. At 31.5\u00b0 N, the mean Gulf Stream currents (indicated by the 80 and 120 cm/s velocity contours in Figure 11d) slightly shift toward the continental slope as the Gulf Stream weakens. LR also shows enhanced current speed on the landside of Gulf Stream but the enhancements are only noticed in a few grid points. At 31.5\u00b0 N, the continental slope and shift in Gulf Stream path are completely absent in LR (Figure 11c).\nFigure 10: Regressions of velocity speed at 15-m depth on Atlantic Meridional Overturning Circulation strength from low resolution (a) and high resolution (b). Regressions are computed from the TNST simulations from 2,001 to 2,100 and corrected by the CTRL simulations to account for potential model drift (see Section 2.1). Black dots indicate the regions where regressions are statistically insignificant (p > 0.1). Green lines in (a) denote the cross sections for Figure 11.\nFigure 11: Top panel: Regressions of velocity speed on Atlantic Meridional Overturning Circulation strength across 31.5\u00b0 N from low resolution (LR) (a) and high resolution (HR) (b). Bottom panel: velocity speed averaged during historical time (2,001\u20132,020, solid contours) and future time (2,081\u20132,100, dashed contours) across 31.5\u00b0 N from LR (c) and HR (d). The cross-section is highlighted as the green line in Figure 10a. In (a)\u2013(b), regressions are computed from the TNST simulations from 2,001 to 2,100 and corrected by the CTRL simulations to account for potential model drift (see Section 2.1). Black dots indicate the regions where regressions are statistically insignificant (p > 0.1). In (c)\u2013(d), contours with same color have the same velocity speed and the unit of contour labels is cm/s.\nBased on geostrophic balance (e.g., urn:x-wiley:19422466:media:jame21583:jame21583-math-0103, where urn:x-wiley:19422466:media:jame21583:jame21583-math-0104 is the meridional geostrophic velocity, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0105 is the Coriolis parameter), large DSL gradient exists across the Gulf Stream. As the AMOC strength decreases, the weakened Gulf Stream currents reduce the DSL gradient across the Gulf Stream. This can lead to DSL rises on the landside of the Gulf Stream and DSL decreases in the open ocean. Compared to HR, LR projects larger current speed decreases along the northeast continental slope, and smaller current speed decreases along the southeast continental slope (Figure 10). This will lead to larger DSL rises along the northeast shelf and smaller DSL rises along the southeast shelf, in line with the projected DSL trends shown in Figures 4a and 4d. In addition to the different Gulf Stream reductions between LR and HR, the landward shift in the Gulf Stream path projected by HR can also affect regional DSL patterns in the future. These suggest that the better resolved Gulf Stream in HR can have significant impacts on regional DSL projections.\nHere we examine the difference in DSL patterns between LR and HR with geostrophic balance. The geostrophic balance is typically valid in the open ocean and the mid shelf (Fewings & Lentz, 2010). At the inner shelf and coastal zone, geostrophic balance does not hold because of the significance of friction, wave and wind stress (Fewings & Lentz, 2010; Little et al., 2019; Thorpe, 2007). Although HR shows significant improvement on ocean circulation compared to LR, HR is still too coarse to fully resolve coastal dynamics. A regional downscaling with higher resolution is needed to further explore how coastal sea-level responds to a weakening Gulf Stream and AMOC.\nSummary and Conclusions\uf0c1\nIn this study, we analyze DSL rise along the US east continental shelf in a pair of HR and LR CESM simulations. This study is motivated by Little et al. (2019), who pointed out the need for exploring sea-level rise near the US east coast when HR climate simulations are available. Three major findings from the analysis are listed below.\nHR reduces biases in DSL and ocean circulation along the US east continental shelf and the Gulf Stream extension region\nBoth LR and HR models project DSL rise along the US east shelf under the RCP8.5 emission scenario, consistent with previous projections based on LR climate models (Landerer et al., 2007; Little et al., 2017; Yin et al., 2009)\nCompared to LR, HR projects smaller trends of DSL rise along the northeast shelf (north of 40\u00b0 N), and larger trends of DSL rise along the southeast shelf (south of 35\u00b0 N). The different DSL patterns are attributable to the difference in Gulf Stream changes in response to a weakening AMOC", "source": "https://sealeveldocs.readthedocs.io/en/latest/li22james.html"}
{"id": "c18462502844-8", "text": "Here we examine the difference in DSL patterns between LR and HR with geostrophic balance. The geostrophic balance is typically valid in the open ocean and the mid shelf (Fewings & Lentz, 2010). At the inner shelf and coastal zone, geostrophic balance does not hold because of the significance of friction, wave and wind stress (Fewings & Lentz, 2010; Little et al., 2019; Thorpe, 2007). Although HR shows significant improvement on ocean circulation compared to LR, HR is still too coarse to fully resolve coastal dynamics. A regional downscaling with higher resolution is needed to further explore how coastal sea-level responds to a weakening Gulf Stream and AMOC.\nSummary and Conclusions\uf0c1\nIn this study, we analyze DSL rise along the US east continental shelf in a pair of HR and LR CESM simulations. This study is motivated by Little et al. (2019), who pointed out the need for exploring sea-level rise near the US east coast when HR climate simulations are available. Three major findings from the analysis are listed below.\nHR reduces biases in DSL and ocean circulation along the US east continental shelf and the Gulf Stream extension region\nBoth LR and HR models project DSL rise along the US east shelf under the RCP8.5 emission scenario, consistent with previous projections based on LR climate models (Landerer et al., 2007; Little et al., 2017; Yin et al., 2009)\nCompared to LR, HR projects smaller trends of DSL rise along the northeast shelf (north of 40\u00b0 N), and larger trends of DSL rise along the southeast shelf (south of 35\u00b0 N). The different DSL patterns are attributable to the difference in Gulf Stream changes in response to a weakening AMOC\nThe improved ocean circulation associated with refined horizontal resolution has been reported in numerous studies (Chassignet et al., 2020; Saba et al., 2016; van Westen et al., 2020). Here we show that the HR CESM simulates realistic Gulf Stream currents along the southeast continental slope and southwestward shelf currents along the northeast shelf. The southwestward shelf currents carry cold and fresh water from the Labrador Sea to Gulf of Maine, reducing warm temperature and high salinity bias. These results are consistent with Saba et al. (2016), who showed improved regional circulations and reduced temperature and salinity bias in the HR GFDL CM simulations. In addition to reduced biases in ocean circulation, HR better resolves small scale features of bathymetry and coastline. These make HR more suitable for regional sea-level study than LR. Jean-Michel et al. (2021) reported a global reanalysis product with a horizontal resolution of 1/12urn:x-wiley:19422466:media:jame21583:jame21583-math-0108 called GLORYS12. Such HR data products provide valuable information for regional studies.\nIn response to a weakening AMOC under global warming, both LR and HR models project decreasing Gulf Stream currents but at different spatial locations. The weakening Gulf Stream currents occur along the entire east continental slope in LR, while they are confined along the southeast continental slope in HR. The difference in Gulf Stream changes is related to the mean ocean circulation patterns. Compared with observations, LR simulated Gulf Stream does not show a clear separation from the shore. Thus, the weakening Gulf Stream currents affect the entire east continental slope. In contrast, HR simulated Gulf Stream leaves the shore at \u223c40\u00b0 N (HR still contains bias given the observed separation point at \u223c35\u00b0 N), so the effects of weakening Gulf Stream are confined along the southeast continental slope. The decreasing Gulf Stream currents can lead to DSL rise on the landside of the Gulf Stream through geostrophic balance. In this study, we focus on the contribution of ocean circulation to DSL. In addition to ocean circulation, sea-level can be influenced by many other processes such as coastal trapped waves (Hughes et al., 2019) and atmospheric forcing (Chafik et al., 2019; Llovel et al., 2018). Based on observational and reanalysis data, Chafik et al. (2019) demonstrated a high correlation between along-shelf winds and sea level along the European coast. Yin et al. (2020) analyzed GFDL simulations and showed the Gulf of Mexico coasts, particularly New Orleans, are most vulnerable to storm related extreme sea-level under global warming. Here we do not consider atmospheric forcing because the role of atmospheric variability on low frequency sea-level changes is still in debate. Woodworth et al. (2014) argued winds can generate low frequency sea-level changes near the coasts, while Little et al. (2019) suggested atmospheric forcing dominates high frequency sea-level variability. The low frequency sea-level variability is mainly associated with AMOC reductions (Little et al., 2017; Yin et al., 2009). Future work is encouraged to explore how atmospheric variability impacts future sea-level changes. Due to the volume conservation constraint in the ocean model used here, the simulated DSL changes do not account for global mean sea-level changes due to volume expansion or contraction. The global mean sea-level change can be estimated with the globally averaged steric height (Greatbatch, 1994; Yin et al., 2010). Under the future RCP 8.5 emission scenario, LR and HR models project similar global mean thermosteric sea-level rise of \u223c3 mm/yr from 2,001 to 2,100. Including the global mean thermosteric sea-level rise, HR projects a sterodynamic sea-level rise of 3.5\u20134 mm/yr along the east shelf. In contrast, LR projects a smaller trend (3\u20133.5 mm/yr) along the southeast shelf, and a larger trend (4.5\u20135 mm/yr) along the northeast shelf. These trends do not account for sea-level rise due to glacial melting. Thus, future work may focus on exploring the contributions of glacial melting to sea-level rise. Recent studies have consistently shown that HR climate models produce overall more realistic simulations than LR models (Chang et al., 2020; Griffies et al., 2015; Saba et al., 2016; Small et al., 2014; van Westen et al., 2020). Higher horizontal resolutions enable to resolve more baroclinic modes. These baroclinic modes contains vertical structures and therefore high vertical resolutions become important. Stewart et al. (2017) showed increasing vertical resolutions can lead to \u223c 30% increases in SSH variance south of 40\u00b0 S. The benefits of HR models can not only be used to learn physical mechanisms but also to diagnose parametrization schemes (Bachman et al., 2020). However, due to high computing costs, HR model ensembles and future projections are still scarce. As of now, only 7 models have completed and published their HR simulation results following CMIP6 HighResMIP protocol (Haarsma et al., 2016). We encourage future efforts to focus on creating more ensembles and simulating different future climate scenarios to improve the robustness of future projections. Another option to reach this goal would be to reduce LR models biases with accurate subgrid parameterizations. Recent advancement of machine learning may help solve this problem (Guillaumin & Zanna, 2021).", "source": "https://sealeveldocs.readthedocs.io/en/latest/li22james.html"}
{"id": "e1b1028b405a-0", "text": "Bamber et al. (2019)\uf0c1\nTitle:\nIce sheet contributions to future sea-level rise from structured expert judgment\nKey Points:\nPotential contributions of ice sheets to future sea-level rise (SLR) remain the largest source of uncertainty in SLR projections\nFor a +2 \u00b0C temperature scenario, consistent with the Paris Agreement, the study estimates a median SLR contribution of 26 cm by 2100, with a 95th percentile value of 81 cm. For a +5 \u00b0C temperature scenario, more consistent with unchecked emissions growth, the corresponding values are 51 cm and 178 cm, respectively.\nBeyond 2100, uncertainty and projected SLR increase rapidly. For the +5 \u00b0C scenario, the 95th percentile ice sheet contribution by 2200 is 7.5 m due to instabilities in both West and East Antarctica.\nScenarios of 21st century global total SLR exceeding 2 m should be used for planning purposes.\nKeywords:\nsea-level rise, climate predictions, ice sheets, Greenland, Antarctica\nCorresponding author:\nJonathan L. Bamber\nCitation:\nBamber, J. L., Oppenheimer, M., Kopp, R. E., Aspinall, W. P., & Cooke, R. M. (2019). Ice sheet contributions to future sea-level rise from structured expert judgment. Proceedings of the National Academy of Sciences, 116(23), 11195\u201311200. doi:10.1073/pnas.1817205116\nURL:\nhttps://www.pnas.org/doi/full/10.1073/pnas.1817205116\nSignificance\uf0c1\nFuture sea level rise (SLR) poses serious threats to the viability of coastal communities, but continues to be challenging to project using deterministic modeling approaches. Nonetheless, adaptation strategies urgently require quantification of future SLR uncertainties, particularly upper-end estimates. Structured expert judgement (SEJ) has proved a valuable approach for similar problems. Our findings, using SEJ, produce probability distributions with long upper tails that are influenced by interdependencies between processes and ice sheets. We find that a global total SLR exceeding 2 m by 2100 lies within the 90% uncertainty bounds for a high emission scenario. This is more than twice the upper value put forward by the Intergovernmental Panel on Climate Change in the Fifth Assessment Report.\nAbstract\uf0c1\nDespite considerable advances in process understanding, numerical modeling, and the observational record of ice sheet contributions to global mean sea-level rise (SLR) since the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change, severe limitations remain in the predictive capability of ice sheet models. As a consequence, the potential contributions of ice sheets remain the largest source of uncertainty in projecting future SLR. Here, we report the findings of a structured expert judgement study, using unique techniques for modeling correlations between inter- and intra-ice sheet processes and their tail dependences. We find that since the AR5, expert uncertainty has grown, in particular because of uncertain ice dynamic effects. For a +2 \u00b0C temperature scenario consistent with the Paris Agreement, we obtain a median estimate of a 26 cm SLR contribution by 2100, with a 95th percentile value of 81 cm. For a +5 \u00b0C temperature scenario more consistent with unchecked emissions growth, the corresponding values are 51 and 178 cm, respectively. Inclusion of thermal expansion and glacier contributions results in a global total SLR estimate that exceeds 2 m at the 95th percentile. Our findings support the use of scenarios of 21st century global total SLR exceeding 2 m for planning purposes. Beyond 2100, uncertainty and projected SLR increase rapidly. The 95th percentile ice sheet contribution by 2200, for the +5 \u00b0C scenario, is 7.5 m as a result of instabilities coming into play in both West and East Antarctica. Introducing process correlations and tail dependences increases estimates by roughly 15%.\nIntroduction\uf0c1\nGlobal mean sea-level rise (SLR), which during the last quarter century has occurred at an accelerating rate (1), averaging about +3 mm\u22c5y\u22121, threatens coastal communities and ecosystems worldwide. Adaptation measures accounting for the changing hazard, including building or raising permanent or movable structures such as surge barriers and sea walls, enhancing nature-based defenses such as wetlands, and selective retreat of populations and facilities from areas threatened by episodic flooding or permanent inundation, are being planned or implemented in several countries. Risk assessment for such adaptation efforts requires projections of future SLR, including careful characterization and evaluation of uncertainties (2) and regional projections that account for ocean dynamics, gravitational and rotational effects, and vertical land motion (3). During the nearly 40 y since the first modern, scientific assessments of SLR, understanding of the various causes of this rise has advanced substantially. Improvements during the past decade include closing the historic sea-level budget, attributing global mean SLR to human activities, confirming acceleration of SLR since the nineteenth century and during the satellite altimetry era, and developing analytical frameworks for estimating regional and local mean sea level and extreme water level changes. Nonetheless, long-term SLR projections remain acutely uncertain, in large part because of inadequate understanding of the potential future behaviors of the Greenland and Antarctic ice sheets and their responses to future global climate change. This limitation is especially troubling, given that the ice sheet influence on SLR has been increasing since the 1990s (4) and has overtaken mountain glaciers to become the largest barystatic (mass) contribution to SLR (5). In addition, for any given future climate scenario, the ice sheets constitute the component with the largest uncertainties by a substantial margin, especially beyond 2050 (6).\nAdvances since the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (7) include improved process understanding and representation in deterministic ice sheet models (8, 9), probabilistic projections calibrated against these models and the observational record (10), and new semiempirical models, based on the historical relationship between temperature and sea-level changes. Each of these approaches has limitations that stem from factors including poorly understood processes, poorly constrained boundary conditions, and a short (\u223c25 y) satellite observation record of ice sheets that does not capture the time scales of internal variability in the ice sheet climate system. As a consequence, it is unclear to what extent recent observed ice sheet changes (11) are a result of internal variability (ice sheet weather) or external forcing (ice sheet climate).\nWhere other methods are intractable for scientific or practical reasons, structured expert judgement (SEJ), using calibrated expert responses, provides a formal approach for estimating uncertain quantities according to current scientific understanding. It has been used in a wide range of applications, including natural and anthropogenic hazards such as earthquakes, volcanic eruptions, vector-borne disease spread, and nuclear waste security (12). That said, it should not be regarded as a substitute for fundamental research into driving processes, but instead as a source of complementary insights into the current state of knowledge and, in particular, the extent of the uncertainties (12). An SEJ study conducted in advance of the AR5 (13) (hereafter BA13) provided valuable insights into the uncertainties around ice sheet projections, as assessed at that time.\nSince then, regional- and continental-scale, process-based modeling of ice sheets has advanced substantially (8, 9, 14\u201316), with the inclusion of new positive feedbacks that could potentially accelerate mass loss, and negative feedbacks that could potentially slow it. These include solid Earth and gravitational processes (17, 18), Antarctic marine ice cliff instability (19), and the influences of organic and inorganic impurities on the albedo of the Greenland Ice Sheet (20). The importance of these feedbacks is an area of continuing research. Therefore, alternative approaches must be exploited to assess future SLR and, critically, its associated uncertainties (21), to serve the more immediate needs of the science and policy communities.\nHere, we report the findings of an SEJ exercise undertaken in 2018 via separate, 2-d workshops held in the United States and United Kingdom, involving 22 experts (hereafter SEJ2018). Details of how experts were selected are provided in SI Appendix, Note 1. The questions and format of the workshops were identical, so that the findings could be combined using an impartial weighting approach (Methods). SEJ (as opposed to other types of expert elicitation) weights each expert using objective estimates of their statistical accuracy and informativeness (22), determined using experts\u2019 uncertainty evaluations over a set of seed questions from their field with ascertainable values (Methods). The approach is analogous to weighting climate models based on their skill in capturing a relevant property, such as the regional 20th century surface air temperature record (23). In SEJ, the synthetic expert (i.e., the performance weighted [PW] combination of all of the experts\u2019 judgments) in general outperforms an equal weights (EW) combination in terms of statistical accuracy and informativeness, as illustrated in SI Appendix, Fig. S3. The approach is particularly effective at identifying those experts who are able to quantify their uncertainties with high statistical accuracy for specified problems rather than, for example, experts with restricted domains of knowledge or even high scientific reputation (12).", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber19.html"}
{"id": "e1b1028b405a-1", "text": "Since then, regional- and continental-scale, process-based modeling of ice sheets has advanced substantially (8, 9, 14\u201316), with the inclusion of new positive feedbacks that could potentially accelerate mass loss, and negative feedbacks that could potentially slow it. These include solid Earth and gravitational processes (17, 18), Antarctic marine ice cliff instability (19), and the influences of organic and inorganic impurities on the albedo of the Greenland Ice Sheet (20). The importance of these feedbacks is an area of continuing research. Therefore, alternative approaches must be exploited to assess future SLR and, critically, its associated uncertainties (21), to serve the more immediate needs of the science and policy communities.\nHere, we report the findings of an SEJ exercise undertaken in 2018 via separate, 2-d workshops held in the United States and United Kingdom, involving 22 experts (hereafter SEJ2018). Details of how experts were selected are provided in SI Appendix, Note 1. The questions and format of the workshops were identical, so that the findings could be combined using an impartial weighting approach (Methods). SEJ (as opposed to other types of expert elicitation) weights each expert using objective estimates of their statistical accuracy and informativeness (22), determined using experts\u2019 uncertainty evaluations over a set of seed questions from their field with ascertainable values (Methods). The approach is analogous to weighting climate models based on their skill in capturing a relevant property, such as the regional 20th century surface air temperature record (23). In SEJ, the synthetic expert (i.e., the performance weighted [PW] combination of all of the experts\u2019 judgments) in general outperforms an equal weights (EW) combination in terms of statistical accuracy and informativeness, as illustrated in SI Appendix, Fig. S3. The approach is particularly effective at identifying those experts who are able to quantify their uncertainties with high statistical accuracy for specified problems rather than, for example, experts with restricted domains of knowledge or even high scientific reputation (12).\nThe participating experts quantified their uncertainties for three physical processes relevant to ice sheet mass balance: accumulation, discharge, and surface runoff. They did this for each of the Greenland, West Antarctic, and East Antarctic ice sheets (GrIS, WAIS, and EAIS, respectively), and for two schematic temperature change scenarios. The first temperature trajectory (denoted L) stabilized in 2100 at +2 \u00b0C above preindustrial global mean surface air temperature (defined as the average for 1850\u20131900), and the second (denoted H) stabilized at +5 \u00b0C (SI Appendix, Fig. S1). The experts generated values for four dates: 2050, 2100, 2200, and 2300. Experts also quantified the dependence between accumulation, runoff, and discharge within each of the three ice sheets, and between each ice sheet for discharge only, for the H scenario in 2100. We used temperature trajectories rather than emissions scenarios to isolate the experts\u2019 judgements about the relationship between global mean surface air temperature change and ice sheet changes from judgements about climate sensitivity.\nAn important and unique element of SEJ2018 was the elicitation of intra- and inter-ice sheet dependencies (SI Appendix, Note 1.5). Two features of dependence were elicited: a central dependence and an upper tail dependence. The former captures the probability that one variable exceeds its median given that the other variable exceeds its median, whereas the latter captures the probability that one variable exceeds its 95th percentile given that the other exceeds its 95th percentile. It is well known that these two types of dependence are, in general, markedly different, a property that is not captured by the usual Gaussian dependence model. The latter always imposes tail independence, regardless of the degree of central dependence, and can produce large errors when applied inappropriately (24). For example, if GrIS discharge exceeds its 95th percentile, what is the probability that runoff will also exceed its 95th percentile? This probability may be substantially higher than the independent probability of 5%, and ignoring tail dependence may lead to underestimating the probability of high SLR contributions. On the basis of each expert\u2019s responses, a joint distribution was constructed to capture the dependencies among runoff, accumulation, and discharge for GrIS, WAIS, and EAIS, with dependence structures chosen, per expert, to capture central and tail dependences (Methods and SI Appendix, Note 1.5). In BA13, heuristic dependency values were applied on the basis of simple assumptions about the response of processes to a common forcing.\nTo help interpret the findings, experts were also asked to provide qualitative and rank-order information on what they regard to be the leading processes that could influence ice dynamics and surface mass balance (snowfall minus ablation); henceforth, this is termed the descriptive rationale. Further details can be found in the SI Appendix. The combined sea-level contribution from all processes and ice sheets was determined assuming either independence or dependence. Here, we focus on the findings with dependence; we examine the effect of the elicited dependencies and the approach taken in SI Appendix, Note 1.5.\nThe ice sheet contributions were expressed as anomalies from the 2000\u20132010 mean states, which were predefined (SI Appendix, Table S7). The baseline sea-level contribution for this period was prescribed as 0.76 mm\u22c5y\u22121 (0.56, 0.20, and 0.00 mm\u22c5y\u22121 for GrIS, WAIS, and EAIS, respectively) and has been added to the elicited values discussed here. This is close to an observationally derived value of 0.79 mm\u22c5y\u22121 for the same period, which was published subsequently to the SEJ workshops (4).\nResults and Discussion\uf0c1\nFig. 1 shows the probability density functions (PDFs) for both temperature trajectory scenarios for the combined ice sheet contributions, assuming some dependencies exist between ice sheet processes, as elicited from the expert group (SI Appendix, Note 1.5). The associated numerical values are detailed in Table 1, and plots for all four epochs are provided in SI Appendix, Fig. S2. They display similar characteristics to Fig. 1. The PDFs were generated using Monte Carlo sampling from the intrinsic range obtained from the expert responses (22). All PDFs are non-Gaussian and exhibit an extended upper tail, especially for the H temperature scenario. We believe this reflects the experts\u2019 joint view that large amplitude, nonlinear instabilities could be triggered at this higher temperature, even by 2050. For example, for 2050, the median [and likely range, defined as the 17\u201383% probability range, as in the AR5 (25)] of the ice sheet contributions are 10 cm (5\u201318 cm) for the L scenario and 12 cm (6\u201324 cm) for the H scenario. The tail behavior is discussed further in SI Appendix, Note 1.1. By 2100, the differences between the scenarios grow larger, with projected contributions of 26 cm (12\u201353 cm) and 51 cm (22\u2013113 cm; Fig. 2 and Table 1).\nFig. 1: PDFs for the L (blue) and H (red) temperature scenarios for the combined ice sheet SLR contributions at (A) 2100 and (B) 2300. All four time intervals are shown in SI Appendix, Fig. S2. The horizontal bars show the fifth, 17th, 50th (median), 83rd, and 95th percentile values. The baseline rate of 0.76 mm\u22c5a\u22121 is included. Note that there is more than a factor five change in the x axis scales.\nTable 1: Projected sea-level rise contributions from each ice sheet and combined. Individual ice sheet and total sea-level contributions for both temperature scenarios and for the four periods considered: 2050, 2100, 2200, and 2300. All values assume the dependencies elicited for the 2100 H case. Because the PDFs are not Gaussian, the mean and median values differ; the latter is a better measure of central tendency. All values are cumulative from 2000 and include the baseline imbalance for 2000\u20132010 of 0.76 mm y\u22121. The AR5-defined likely range (17\u201383%) is provided alongside the 90% credible interval. PW01 denotes the performance weighted combination of experts based on their calibration score.\nYear and ice sheet      Low     High\nMean \u00b1 SD       50%     5\u201395%   17\u201383%  Mean \u00b1 SD       50%     5\u201395%   17\u201383%\n2050\n\u2003PW01 SLR       11 \u00b1 8  10      1\u201327    5\u201318    15 \u00b1 12 12      1\u201338    6\u201324\n\u2003GrIS   7 \u00b1 5   5       2\u201318    3\u201311    9 \u00b1 7   6       2\u201327    4\u201314\n\u2003WAIS   7 \u00b1 8   5       0\u201323    1\u20137     5 \u00b1 6   4       0\u201318    1\u201310", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber19.html"}
{"id": "e1b1028b405a-2", "text": "Fig. 1: PDFs for the L (blue) and H (red) temperature scenarios for the combined ice sheet SLR contributions at (A) 2100 and (B) 2300. All four time intervals are shown in SI Appendix, Fig. S2. The horizontal bars show the fifth, 17th, 50th (median), 83rd, and 95th percentile values. The baseline rate of 0.76 mm\u22c5a\u22121 is included. Note that there is more than a factor five change in the x axis scales.\nTable 1: Projected sea-level rise contributions from each ice sheet and combined. Individual ice sheet and total sea-level contributions for both temperature scenarios and for the four periods considered: 2050, 2100, 2200, and 2300. All values assume the dependencies elicited for the 2100 H case. Because the PDFs are not Gaussian, the mean and median values differ; the latter is a better measure of central tendency. All values are cumulative from 2000 and include the baseline imbalance for 2000\u20132010 of 0.76 mm y\u22121. The AR5-defined likely range (17\u201383%) is provided alongside the 90% credible interval. PW01 denotes the performance weighted combination of experts based on their calibration score.\nYear and ice sheet      Low     High\nMean \u00b1 SD       50%     5\u201395%   17\u201383%  Mean \u00b1 SD       50%     5\u201395%   17\u201383%\n2050\n\u2003PW01 SLR       11 \u00b1 8  10      1\u201327    5\u201318    15 \u00b1 12 12      1\u201338    6\u201324\n\u2003GrIS   7 \u00b1 5   5       2\u201318    3\u201311    9 \u00b1 7   6       2\u201327    4\u201314\n\u2003WAIS   7 \u00b1 8   5       0\u201323    1\u20137     5 \u00b1 6   4       0\u201318    1\u201310\n\u2003EAIS   0 \u00b1 2   0       \u22124\u20134    \u22122\u20131    0 \u00b1 4   0       \u22126\u20137    \u22123\u20132\n2100\n\u2003PW01 SLR       32 \u00b1 25 26      3\u201381    12\u201353   67 \u00b1 56 51      7\u2013178   22\u2013112\n\u2003GrIS   19 \u00b1 16 13      2\u201357    7\u201331    33 \u00b1 30 23      2\u201399    10\u201360\n\u2003WAIS   13 \u00b1 16 8       \u22123\u201344   2\u201323    27 \u00b1 33 18      \u22125\u201393   3\u201346\n\u2003EAIS   3 \u00b1 6   0       \u22128\u201312   \u22123\u20134    6 \u00b1 17  2       \u221211\u201346  \u22124\u201311\n2200\n\u2003PW01 SLR       89 \u00b1 72 72      5\u2013231   30\u2013149  204 \u00b1 260       130     5\u2013750   40\u2013251\n\u2003GrIS   49 \u00b1 47 34      5\u2013149   19\u201379   77 \u00b1 69 55      3\u2013216   23\u2013122\n\u2003WAIS   37 \u00b1 45 26      \u221224\u2013128 1\u201376    80 \u00b1 113        51      \u221225\u2013324 \u22123\u2013138\n\u2003EAIS   4 \u00b1 15  2       \u221215\u201334  \u22126\u201310   48 \u00b1 158        6       \u221229\u2013398 \u221210\u201319\n2300\n\u2003PW01 SLR       155 \u00b1 137       120     0\u2013426   47\u2013259  310 \u00b1 322       225     14\u2013988  87\u2013466\n\u2003GrIS   78 \u00b1 75 55      7\u2013237   30\u2013145  130 \u00b1 117       98      7\u2013349   39\u2013225\n\u2003WAIS   67 \u00b1 88 44      \u221247\u2013248 6\u2013131   117 \u00b1 136       83      \u221236\u2013384 7\u2013228\n\u2003EAIS   10 \u00b1 41 3       \u221229\u201396  \u22128\u201324   63 \u00b1 195        10      \u221253\u2013498 \u221214\u201351\nFig. 2: Median and likely range (17th\u201383rd percentile as used in the AR5) estimates of the ice sheet SLR contributions for different temperature scenarios and different studies. AR5 RCP ice sheet contributions are shown for RCP 2.6 and RCP 8.5 by combining contributions from the different sources (gray bars). BA13 is shown for the elicited temperature increase of 3.5 \u00b0C by 2100 (orange bar). This study (SEJ2018, in blue) is shown for the L and H temperature scenarios using solid lines. Dashed lines are interpolated from the L and H findings, using stochastic resampling of the distributions assuming a linear relationship between pairs of L and H samples.\nThe relative contribution of each ice sheet to total SLR (used here to refer to the sum of the three ice sheet contributions) depends on the temperature scenario. To demonstrate this, we compare the mean projections for the three ice sheets for the overall 2100 H distribution, for the same distribution conditional on the total contribution being above the median total projection (>51 cm), and the same distribution conditional on the total being above the 90th percentile (>141 cm). In the unconditional distribution, GrIS dominates the mean projection, contributing 33 cm (49%) of the 67-cm total, compared with 27 cm for WAIS and 6 cm for EAIS: proportions that approximately mirror the present-day contributions (4). The GrIS share declines for larger total contributions. For the mean of the upper half of total SLR projections, GrIS contributes 49 cm (46%) of 106 cm total compared with 44 cm for WAIS and 13 cm for EAIS; for the mean of the top decile, GrIS contributes 60 cm (30%) of the 194-cm total compared with 95 cm for WAIS and 39 cm for EAIS.\nStatistically, the declining GrIS share and declining GrIS/AIS ratio reflect a higher mean estimate but slightly less skewed distribution for GrIS than for WAIS, and a long tail for EAIS (Fig. 3), as well as the assessed dependence structure between different terms. Physically, this is likely a result of the role of highly nonlinear dynamic processes coming into play for marine sectors of the AIS that are needed to achieve the higher values of total SLR, whereas at lower total SLR values, more linear processes dominate. It is also noteworthy that the fifth percentiles for both temperature scenarios and for all epochs are less than their current values, suggesting a scenario in which increased snowfall, primarily over the AIS (Table 1), plausibly compensates for any changes in ice dynamics and enhanced melting over the GrIS.\nFig. 3: Individual ice sheet contributions to SLR for 2100 L (A) and H (B) temperature scenarios, assuming dependences between the ice sheets in terms of the processes of accumulation, runoff, and discharge. PDFs were generated from 50,000 realizations of the relevant SEJ distributions. Horizontal bars indicate the fifth, 50th, and 95th percentile values (i.e., the 90% credible range). Also shown are the likely range (17th\u201383rd percentile) as defined in the AR5 and the total AIS contribution (WAIS plus EAIS assuming the inter ice sheet dependencies elicited). Note that this is not simply the sum of WAIS and EAIS contributions because of inter-ice sheet dependencies. The AIS values are compared with a recent emulator approach (30) in SI Appendix, Fig. S11.", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber19.html"}
{"id": "e1b1028b405a-3", "text": "Statistically, the declining GrIS share and declining GrIS/AIS ratio reflect a higher mean estimate but slightly less skewed distribution for GrIS than for WAIS, and a long tail for EAIS (Fig. 3), as well as the assessed dependence structure between different terms. Physically, this is likely a result of the role of highly nonlinear dynamic processes coming into play for marine sectors of the AIS that are needed to achieve the higher values of total SLR, whereas at lower total SLR values, more linear processes dominate. It is also noteworthy that the fifth percentiles for both temperature scenarios and for all epochs are less than their current values, suggesting a scenario in which increased snowfall, primarily over the AIS (Table 1), plausibly compensates for any changes in ice dynamics and enhanced melting over the GrIS.\nFig. 3: Individual ice sheet contributions to SLR for 2100 L (A) and H (B) temperature scenarios, assuming dependences between the ice sheets in terms of the processes of accumulation, runoff, and discharge. PDFs were generated from 50,000 realizations of the relevant SEJ distributions. Horizontal bars indicate the fifth, 50th, and 95th percentile values (i.e., the 90% credible range). Also shown are the likely range (17th\u201383rd percentile) as defined in the AR5 and the total AIS contribution (WAIS plus EAIS assuming the inter ice sheet dependencies elicited). Note that this is not simply the sum of WAIS and EAIS contributions because of inter-ice sheet dependencies. The AIS values are compared with a recent emulator approach (30) in SI Appendix, Fig. S11.\nDirect comparison with the AR5 is complicated by the use of different external forcings. Our L scenario is slightly warmer than the median projection for Representative Concentration Pathway (RCP) 2.6, and cooler than the median projection for RCP 4.5 at 2100 (2081\u20132100 global mean warming of +1.9 \u00b0C compared with medians of +1.6 \u00b0C and +2.4 \u00b0C, for RCP 2.6 and RCP 4.5, respectively), whereas our H scenario is roughly comparable to the median projection for RCP8.5 (2081\u20132100 global mean warming of +4.5 \u00b0C compared with a median of +4.3 \u00b0C for RCP 8.5), although with different trajectories (SI Appendix, Fig. S1). Our two temperature scenarios were chosen to assess the potential consequences, in terms of SLR, of the goal of the COP21 Paris agreement to keep global temperatures below +2 \u00b0C above preindustrial and of a scenario closer to business as usual, as opposed to matching a specific RCP. For comparison, the AR5 likely range ice sheet SLR contribution for RCP8.5 at 2100 is 6\u201335 cm, with a median of 19 cm (7) (Fig. 2). As mentioned, comparing our findings with those from the AR5 requires transforming temperatures and percentiles to match those used in the AR5. Nonetheless, given these caveats, it is clear the SEJ median and upper value of the likely range (83rd percentile) are statistically significantly larger than the corresponding AR5 values (Fig. 2). Our likely range upper bound is almost three times the AR5 value for RCP 8.5 (94 vs. 35 cm, estimated by summing the individual components considered in the AR5 and, hence, assuming perfect dependence). This is driven, primarily, by larger uncertainty ranges for the WAIS and GrIS contributions (Fig. 3), possibly resulting from experts\u2019 consideration of the aforementioned nonlinear processes. We note also that the uncertainties have grown substantially in comparison with BA13, where the elicited temperature increase above preindustrial was +3.5 \u00b0C (indicated by the orange line in Fig. 2). In comparison, our current findings result in a larger uncertainty range at a lower temperature increase (Fig. 2). There has been recent consideration of the benefits of limiting warming to +1.5 \u00b0C (26) and what difference this would make compared with the Paris Agreement +2 \u00b0C. The reduction in the sea-level contribution from the ice sheets at this lower temperature for our study is broadly in line with the findings of the Intergovernmental Panel on Climate Change Special Report on 1.5 \u00b0C, which obtained a value of 10 cm reduction in global mean sea level from all sources (26).\nAnother important point is the positive skews of the distributions, which result in long upper tails that are less apparent in the AR5 values (limited to the likely range). For example, the median values obtained here and in the AR5 for RCP2.6 differ by 8 cm (Fig. 2), but the 83rd percentile from the SEJ is about 100% larger (51 vs. 25 cm). This becomes even more important if considering probabilities beyond the likely range defined in the AR5, such as the very likely range (the 90th percentile confidence interval). This is apparent from the values in Table 1. Kurtosis provides a quantitative measure of tail behavior and is discussed in SI Appendix, Note 1.1.\nFig. 3 illustrates the PDFs for 2100 L and H temperature trajectories for each ice sheet. The 90% credible intervals for the GrIS and WAIS (approximately equivalent to the very likely range in Intergovernmental Panel on Climate Change terminology) are broadly similar to one another in both scenarios (c.f. the 90% credible interval bars in Fig. 3 A and B). For the 2100 L and H scenarios, the EAIS uncertainty ranges are about a factor of three and two smaller, respectively. Median values for the GrIS and WAIS are broadly comparable (13/8 cm for L and 23/18 cm for H), whereas the EAIS median values are 0 and 2 cm for L and H, respectively. Both the WAIS and GrIS show a strong skew with a long positive tail, which is absent for the EAIS for 2100 L but begins to emerge for 2100 H. There is, consequently, a substantial difference between the high-end, 95th percentile values considered here versus the 83rd percentile value presented in the AR5, which is far more pronounced than differences between the fifth and 17th percentiles (Fig. 3). For WAIS under 2100 H, the difference between the 83rd and 95th percentile is a factor two (Fig. 3 and Table 1), and a factor four for the EAIS. This is also seen when considering the total SLR from the ice sheets. For 2200 H, the 83rd and 95th percentiles are 251 and 750 cm, respectively (Table 1). By limiting consideration only to the likely range, the AR5 results miss this tail behavior, which is a critical component of risk management.\nThe present SEJ demonstrates a shift in expert opinion since BA13 (i.e., in 2012), when it was found that the GrIS had the narrowest 90% credible range but the largest median SLR rate (13). Here, the GrIS still has the largest median value (for both L and H), but the upper tail of the distribution is now comparable to that of the WAIS (Fig. 3A). It is difficult to determine the basis for this, but we note that the experts overwhelmingly believe that the recent (last 2 decades) acceleration in mass loss from the GrIS is predominantly a result of external forcing, rather than internal variability. Of the 22 experts, 18 judge the acceleration is largely or entirely a result of external forcing (SI Appendix, Fig. S9A and Table S6). This is an important and statistically significant shift from the findings in BA13. In contrast, for the WAIS, opinion remains divided, with seven experts indicating their view that it is largely a result of internal variability, seven placing more weight on external forcing, and eight giving equal weights to each. This reflects the earlier conclusions of BA13.\nThe findings of SEJ2018 cannot be directly compared with BA13 because the target questions differ, as do the temperature scenarios. The closest comparison that can be made between SEJ2018 and BA13 is for the latter\u2019s cumulative 5/50/95% SLR values of 10/29/84 cm for 2010\u20132100, which comprised two-thirds from GrIS, one-third from WAIS, and a negligible amount from EAIS, for a temperature increase based on experts\u2019 judgement of +3.5 \u00b0C (13). For SEJ2018, we obtain \u22125/18/73 cm for +2 \u00b0C rise and \u22121/43/170 cm for +5 \u00b0C rise (integrated over 2000\u20132100). Fig. 2 compares the likely range in BA13 and the various temperature markers used here and in the AR5. It is evident that opinion has shifted toward a stronger ice sheet response and a larger credible range, for a given temperature change, than was considered plausible by the experts 6 y ago.", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber19.html"}
{"id": "e1b1028b405a-4", "text": "The present SEJ demonstrates a shift in expert opinion since BA13 (i.e., in 2012), when it was found that the GrIS had the narrowest 90% credible range but the largest median SLR rate (13). Here, the GrIS still has the largest median value (for both L and H), but the upper tail of the distribution is now comparable to that of the WAIS (Fig. 3A). It is difficult to determine the basis for this, but we note that the experts overwhelmingly believe that the recent (last 2 decades) acceleration in mass loss from the GrIS is predominantly a result of external forcing, rather than internal variability. Of the 22 experts, 18 judge the acceleration is largely or entirely a result of external forcing (SI Appendix, Fig. S9A and Table S6). This is an important and statistically significant shift from the findings in BA13. In contrast, for the WAIS, opinion remains divided, with seven experts indicating their view that it is largely a result of internal variability, seven placing more weight on external forcing, and eight giving equal weights to each. This reflects the earlier conclusions of BA13.\nThe findings of SEJ2018 cannot be directly compared with BA13 because the target questions differ, as do the temperature scenarios. The closest comparison that can be made between SEJ2018 and BA13 is for the latter\u2019s cumulative 5/50/95% SLR values of 10/29/84 cm for 2010\u20132100, which comprised two-thirds from GrIS, one-third from WAIS, and a negligible amount from EAIS, for a temperature increase based on experts\u2019 judgement of +3.5 \u00b0C (13). For SEJ2018, we obtain \u22125/18/73 cm for +2 \u00b0C rise and \u22121/43/170 cm for +5 \u00b0C rise (integrated over 2000\u20132100). Fig. 2 compares the likely range in BA13 and the various temperature markers used here and in the AR5. It is evident that opinion has shifted toward a stronger ice sheet response and a larger credible range, for a given temperature change, than was considered plausible by the experts 6 y ago.\nThe rather high median and 95% values for 2100 SLR (Fig. 2 and Table 1), found here, likely reflect recent studies that have explored, in particular, AIS sensitivity to CO2 forcing during previous warm periods (27, 28) and new positive feedback processes such as the Marine Ice Cliff Instability (19), alongside the increasing evidence for a secular trend in Arctic climate (29) and subsequent increasing GrIS mass loss (4). A recent study (30) has used an emulator approach to reexamine the potential role of the Marine Ice Cliff Instability in explaining past sea level and how this affects projections, and we can compare our AIS results with the projections reported in ref. 30. Our results lie between the emulation with Marine Ice Cliff Instability and without, lying closer to the latter for the median values (SI Appendix, Fig. S11). Uncertainties for the H temperature scenario grow rapidly beyond 2100, with 90th percentile credible ranges of \u221210 to 740 cm and \u22129 to 970 cm for 2200 and 2300, respectively. Limiting projections to the likely range largely obscures the real, and potentially critical, extent of the deep uncertainties evident in this study.\nGlobal Total SLR Projections\uf0c1\nTo place these results in the context of total SLR projections, including contributions from ocean thermal expansion, glaciers, and land-water storage, we use a probabilistic SLR projection framework (3). Specifically, we substitute Monte Carlo samples from the PW01 joint probability distribution in SEJ2018 for the ice sheet values used in Kopp et al. (3), while keeping the remaining projections for other components of SLR. For thermal expansion and glaciers, these projections are driven by CMIP5 model projections, using an approach similar to that of AR5. For land-water storage, the projections are based on semiempirical relationships among population, dam construction, and groundwater withdrawal (3). We combine the L scenario ice sheet projections with the other components from the +2.0 \u00b0C scenario developed by Rasmussen et al. (31), and for the H scenario with those for RCP 8.5 from Kopp et al. (3).\nCompared with other SLR projections for 2050 developed over the last 6 y (32), the 2050 L projections are broadly comparable (very likely range of 16\u201349 cm), whereas the 2050 H projections are somewhat fatter tailed, with the very likely range extending up to 61 cm (Table 2). This compares with the 20 studies compiled by Horton et al. (32), which spanned from 12 cm at the low end of fifth percentile projections to 48 cm at the high end of 95th percentile projections. There are relatively few +2 \u00b0C studies to compare with our 2100 L projections, but those that are compiled in Horton et al. (32) range from 0.2 m at the low end of fifth percentile projections to 1.1 m at the high end of the 95th percentile projections. The SEJ2018 distributions fall on the high side of this range, with a median projection of 0.7 m and a 90th percentile range of 0.4\u20131.3 m.\nTable 2: Total global-mean sea-level rise projections. Produced by combining PW01 ice sheet projections with thermal expansion, glacier, and land water storage distributions from Kopp et al (3).\nCentimeters above 2000 CE       50%     17\u201383%  5\u201395%   1\u201399%\n2050 L  30      22\u201340   16\u201349   10\u201361\n2050 H  34      26\u201347   21\u201361   16\u201377\n2100 L  69      49\u201398   36\u2013126  21\u2013163\n2100 H  111     79\u2013174  62\u2013238  43\u2013329\nThe 2100 H projections fall within the existing range of RCP 8.5 projections, which have extended upward in recent years, substantially beyond the AR5 range. The 2100 H median projection of 1.1 m falls midway between the AR5 projection of 0.7 m and the 1.5 m that Kopp et al. (6) projected using the Antarctic ice sheet projections of DeConto and Pollard (19), which provided an initial attempt at explicit, continental-scale physical modeling of ice shelf hydrofracturing and marine ice cliff instability. The very likely range of 0.6\u20132.4 m falls within the 0.4\u20132.4-m low-fifth percentile to high-95th percentile range in the compilation of Horton et al. (32). This comparison emphasizes the skewness of the expert distribution: although the median projection falls in the middle of recently published projections, the 95th percentile tracks the high end of published projections. Although none of these studies is entirely independent of the others, taken together, they provide strong support for recent coastal planning scenarios that anticipate SLR well above the AR5 range (33\u201335).\nConclusions\uf0c1\nThis study suggests that experts\u2019 judgments of uncertainties in projections of the ice sheet contribution to SLR have grown during the last 6 y and since publication of the AR5. This is likely a consequence of a focused effort by the glaciological community to refine process understanding and improve process representation in numerical ice sheet models. It may also be related to the observational record, which indicates continued increase in mass loss from both the AIS and GrIS during this time. This negative learning (36, 37) may appear a counter intuitive conclusion, but is not an uncommon outcome: as understanding of the complexity of a problem improves, so can uncertainty bounds grow. We note that for risk management applications, consideration of the upper tail behavior of our SLR estimates is crucial for robust decision making. Limiting attention to the likely range, as was the case in the Intergovernmental Panel on Climate Change AR5, may be misleading and will likely lead to a poor evaluation of the true risks. We find it plausible that SLR could exceed 2 m by 2100 for our high-temperature scenario, roughly equivalent to business as usual. This could result in land loss of 1.79 M km2, including critical regions of food production, and displacement of up to 187 million people (38). A SLR of this magnitude would clearly have profound consequences for humanity.\nMaterials and Methods\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber19.html"}
{"id": "e1b1028b405a-5", "text": "Conclusions\uf0c1\nThis study suggests that experts\u2019 judgments of uncertainties in projections of the ice sheet contribution to SLR have grown during the last 6 y and since publication of the AR5. This is likely a consequence of a focused effort by the glaciological community to refine process understanding and improve process representation in numerical ice sheet models. It may also be related to the observational record, which indicates continued increase in mass loss from both the AIS and GrIS during this time. This negative learning (36, 37) may appear a counter intuitive conclusion, but is not an uncommon outcome: as understanding of the complexity of a problem improves, so can uncertainty bounds grow. We note that for risk management applications, consideration of the upper tail behavior of our SLR estimates is crucial for robust decision making. Limiting attention to the likely range, as was the case in the Intergovernmental Panel on Climate Change AR5, may be misleading and will likely lead to a poor evaluation of the true risks. We find it plausible that SLR could exceed 2 m by 2100 for our high-temperature scenario, roughly equivalent to business as usual. This could result in land loss of 1.79 M km2, including critical regions of food production, and displacement of up to 187 million people (38). A SLR of this magnitude would clearly have profound consequences for humanity.\nMaterials and Methods\uf0c1\nExperts were convened in two separate 2-d workshops, one in Washington, DC, drawing on experts working in North America, followed by one near London, drawing on European experts. The experts were notified in advance of the objectives of the exercise and received examples of questions to be asked, along with a description of the method to be applied for analyzing their responses (SI Appendix, Note 4). To minimize misunderstandings and ambiguities and to clarify issues and aspects of the problem, group discussion of the target questions was allowed before experts individually (and privately) completed each of the three categories of questions. These comprised seed questions used for calibration of the experts, target questions for eliciting judgments on topics for which our goal was to quantify uncertainties, and a set of descriptive rationale questions, through which experts could articulate or summarize their reasoning about the target items (SI Appendix, Note 3). The period for answering questions was unlimited, but in practice was about 6\u20138 h overall. At the conclusion of the first day, responses were collated and preliminary probability distributions were developed from EW and from performance weights combination solutions, using the Classical Model Decision Maker approach (22). These preliminary outcomes were presented to the experts on the second day, and they were given an opportunity to discuss and, if they wished, to revise their initial judgments. Although a broad discussion revealed what motivated many of the responses and provided a basis for our interpretation here of the key contributory factors, few experts changed any of their responses after this provisional presentation.\nAfter the elicitation, the target item uncertainty distributions were recalculated with the Classical Model to conform to the goal of achieving optimal statistical accuracy with minimal credible bounds (e.g., high informativeness). This is accomplished by forming a weighted combination of those experts for which the hypothesis that their probabilistic assessments were statistically accurate would be not rejected at the 0.01 level (denoted PW01). The threshold 0.01 was chosen to achieve robust representation of experts from both workshops while enforcing standard scientific constraints on statistical hypotheses. On this basis, the judgments of six US and two European experts were preferred, and the outcomes of pooling their judgments are shown in SI Appendix, Table S1, for each of the temperature scenarios. Instead of choosing a statistical rejection threshold based on standard hypothesis testing, the Classical Model also allows choosing an optimal threshold that maximizes the statistical accuracy and informativeness of the resulting combination. The effect of this optimization is a moderate reduction in the 90th percentile credible range relative to the PW01 combination.\nThe Classical Model Decision Maker combined score is an asymptotic strictly proper scoring rule if experts get zero weight when their P value drops below some threshold (22). This means that, with such a cutoff, an expert receives their maximal expected weight in the long run by, and only by, stating percentiles that reflect their true beliefs. The weight of an expert is determined by his/her statistical accuracy and informativeness. For comparison, an equally weighted combination of the eight preferred experts (denoted EW01) is formed. EW01\u2019s credible intervals are wider than those of PW01 (SI Appendix, Note 1.1). We use PW01 here to provide robust representation from both panels, as explained here. All combinations concern the experts\u2019 joint distributions, based on the elicited dependence information. Expert scoring is shown in SI Appendix, Table S3, where further details can be found. Rutgers, Princeton University, and Resources for the Future (RFF) considered this study to be exempt from requiring informed consent.\nSupplementary Information\uf0c1\nDetermining expert quantiles\uf0c1\nThirteen experts participated in the expert elicitation on contribution to sea level rise from ice sheets, held at RFF, Washington DC, USA on Jan 25-26. Nine experts participated in a similar elicitation held near London, UK on Feb 20-21, 2018. The two elicitations used the same elicitation protocol. The assessments concerned Accumulation, Runoff and Discharge for GrIS, WAIS and EAIS for the time \uf0b4 temperature scenarios shown in Figure S1. Experts were chosen based on whether they were research active in the topic, assessed on their publications over the last ~5 years and involvement in related initiatives such as NASA SeaRise, Delta Commission (Netherlands Govt), EU Ice2Sea project, Ice Sheet MIPS etc. A working minimum group size, from previous experience, is about six experts and more than 20 provides diminishing returns in terms of the performance of the synthetic pooled expert. We also wished to obtain a balance in age, gender and specialism within the broad field of ice sheets and SLR and to avoid accessing multiple experts from the same group. In addition to the 22 that participated, nine experts were invited who could not attend (4) or did not wish to (5).\nThe participating experts are listed below\nUS elicitation: Robert Bindschadler, Rob DeConto, Natalya Gomez, Ian Howat, Ian Joughin, Shawn Marshall, Sophie Nowicki, Stephen Price, Eric Rignot, Ted Scambos, Christian Schoof, Helene Seroussi, Ryan Walker\nEU elicitation: Ga\u00ebl Durand, Johannes Fuerst, Hilmar Gudmundsson, Anders Levermann, Frank Pattyn, Catherine Ritz, Ingo Sasgen, Aimee Slangen, Bert Wouters\nThe assessments were combined using equal weighting and performance-based weighting. In the EU expert panel, one expert provided judgments based on a conceptual interpretation of the three processes, Accumulation, Runoff and Discharge, that differed significantly from the definitional framework outlined in the questionnaire; the expert acknowledged this to be the case upon enquiry, and their judgments were not included in subsequent processing. In the US panel one expert misinterpreted the baseline values, as a result, their uncertainty judgments contained systematic discrepancies in relation to others in the panel. Unfortunately, there was not an opportunity to re-visit and correct this expert\u2019s evaluations in a timely manner, and so the relevant inputs were removed from the analysis reported here.\nThe combined assessments were convolved to obtain the overall ice sheet contribution to global sea level rise using dependence information provided by the experts\nOverall Results\uf0c1\nIn this exercise experts quantified their 5th, 50th and 95th percentiles for accumulation, for discharge and for runoff for each of GrIS, WAIS and EAIS as anomalies from the 2000-2010 baseline trend (see Supplementary note 5).\nThey also quantified their dependence between these quantities at 2100 with 5\u02da C warming with respect to pre-industrial. This same dependence structure was applied for all other scenarios. As an extension, more articulated dependence structures could be elicited for the different scenarios and applied to the present assessments. In the terminology of SEJ, a Decision Maker (DM) is a \u201csynthetic pooled expert\u201d that is some weighted combination of experts. Equal Weights (EW) is sometime referred to as \u201cone person one vote\u201d. Performance Weighting (PW) is where experts are weighted based on measures of their informative and accuracy quantified using a set of calibration questions or items (described in greater detail in SI Note 1.2).\nThe results with Performance Weighting (PW) are shown in Table S1 in yellow. For the final results, it was decided to use the performance weighted combination of all experts whose statistical accuracy (P- value) was greater than 0.01 (PW01). EW denotes Equal Weighted combinations.", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber19.html"}
{"id": "e1b1028b405a-6", "text": "EU elicitation: Ga\u00ebl Durand, Johannes Fuerst, Hilmar Gudmundsson, Anders Levermann, Frank Pattyn, Catherine Ritz, Ingo Sasgen, Aimee Slangen, Bert Wouters\nThe assessments were combined using equal weighting and performance-based weighting. In the EU expert panel, one expert provided judgments based on a conceptual interpretation of the three processes, Accumulation, Runoff and Discharge, that differed significantly from the definitional framework outlined in the questionnaire; the expert acknowledged this to be the case upon enquiry, and their judgments were not included in subsequent processing. In the US panel one expert misinterpreted the baseline values, as a result, their uncertainty judgments contained systematic discrepancies in relation to others in the panel. Unfortunately, there was not an opportunity to re-visit and correct this expert\u2019s evaluations in a timely manner, and so the relevant inputs were removed from the analysis reported here.\nThe combined assessments were convolved to obtain the overall ice sheet contribution to global sea level rise using dependence information provided by the experts\nOverall Results\uf0c1\nIn this exercise experts quantified their 5th, 50th and 95th percentiles for accumulation, for discharge and for runoff for each of GrIS, WAIS and EAIS as anomalies from the 2000-2010 baseline trend (see Supplementary note 5).\nThey also quantified their dependence between these quantities at 2100 with 5\u02da C warming with respect to pre-industrial. This same dependence structure was applied for all other scenarios. As an extension, more articulated dependence structures could be elicited for the different scenarios and applied to the present assessments. In the terminology of SEJ, a Decision Maker (DM) is a \u201csynthetic pooled expert\u201d that is some weighted combination of experts. Equal Weights (EW) is sometime referred to as \u201cone person one vote\u201d. Performance Weighting (PW) is where experts are weighted based on measures of their informative and accuracy quantified using a set of calibration questions or items (described in greater detail in SI Note 1.2).\nThe results with Performance Weighting (PW) are shown in Table S1 in yellow. For the final results, it was decided to use the performance weighted combination of all experts whose statistical accuracy (P- value) was greater than 0.01 (PW01). EW denotes Equal Weighted combinations.\nTotal ice-sheet SLR is the sum of SLR from all three ice sheets: however, this is a sum of stochastic variables. For 2300H the total mean of 287 cm is the sum of 63 cm, 113 cm and 111 cm, but the quantiles do not sum in this way. For 2300H, the total 95th percentile, 966cm, is smaller than 498 cm + 332 cm + 378 cm = 1208 cm. Adding stochastic variables requires knowledge of their joint distribution. The quantiles will add only if the variables are completely rank dependent (sometimes called co- monotonic). In this case one variable is at or above its 95th percentile if and only if the others are as well. The chance of that happening is then 5%, which means that the sum of the 95th percentiles is exceeded with probability 5%. If the variables are independent, then the chance that all three are at or above their respective 95th percentiles is 0.053 = 0.000125. In this case the 95th percentile will be much lower than the sum of the separate 95th percentiles. In fact, if the three ice sheets are independent the 95th percentile of PW01 (Figure S9b) is 823 cm. The difference 966 cm \u2212 823 cm reflects the effect of the dependence.\nThe choice of a cutoff for statistical accuracy (P-value) beneath which experts are unweighted is imposed by the theory of strictly proper scoring rules (see Supplementary Information section 1.2). The scoring rule theory does not say what this cutoff should be, only that there should be some positive lower bound to the admissible statistical accuracy scores. Optimal performance weighting (PWOpt) chooses a cutoff which optimizes the scores of the resulting combination. PW01 reflects the choice to include all those experts who have acceptable statistical accuracy so as to ensure wider representation. The distributions of PW01 are somewhat wider than those of PWOpt. With the optimal cutoff of 0.399, only experts 3 and 14 are weighted. Cutoff = 0.01 forms a weighted combination of eight experts whose statistical accuracy is above 0.01; these are experts 3,6,8,9,12,14,24 and 27. EW01 forms an equal weighted combination of these same eight experts. All combinations concern the experts\u2019 joint distributions based on the elicited dependence information.\nExpert Scoring\uf0c1\nThe expert judgment methodology applied here is termed the \u201cClassical Model\u201d because of its analogy to classical hypothesis testing (1). The key idea is that experts are treated as statistical hypotheses. Experts were given a PowerPoint presentation to explain the basic features of the method (see SI Section 8), on which this section is based. Expert scoring is shown in Table S2. For detailed explanations please refer to (2), especially the online supplementary material (Appendix A).\nAn expert\u2019s statistical accuracy is the P-value (column 2 in Table S2) at which we would falsely reject the hypothesis that an expert\u2019s probability assessments are statistically accurate. Roughly, an expert is statistically accurate if, in a statistical sense, 5% of the realizations fall beneath his/her 5th percentile, 45% of the realizations fall between the 5th and 50th percentile, etc. High values (near 1) are good, low values (near 0) reflect low statistical accuracy. An expert\u2019s informativeness is measured as the Shannon relative information in the expert\u2019s distribution relative to a uniform background measure over an interval containing all experts\u2019 percentile assessments and the realizations, variable-wise. Columns 3 and 4 give the average information scores for each expert for all variables (column 3) and all calibration variables (column 4). The number of calibration variables is shown in column 5 for each expert (in this case all experts assessed all 16 calibration variables). The product of columns 2 and 4 is the combined score for each expert. Note that statistical accuracy scores vary over seven orders of magnitude whereas information scores vary within a factor three. Therefore, by design, the ratios of the products of combined scores are dominated by the statistical accuracy. If an expert\u2019s P-value is above a cut-off value (in this case P=0.01) then the expert is weighted with weight proportional to the combined score. Normalized weights for weighted experts are shown in column 6.\nA combination of the experts\u2019 distributions is termed a \u201cdecision maker\u201d (DM). Column 7 gives each expert\u2019s Shannon relative information with respect to the equal weight (EW) DM (1). These dimensionless numbers indicate the divergence among the experts themselves and are compared with perturbations caused by dropping a single expert or a single calibration variable (Supplementary Tables 3 and 4). Note that the scores in column 7 are somewhat smaller than the scores in column 3. This suggests that EW is somewhat more informative than the background measure, relative to which the experts\u2019 informativeness is measured in column 3.\nOther DMs in Table 2, besides EW, are PW01, the performance weighted combination of the eight weighted experts, and PWOpt, the performance weighted combination with the cutoff chosen to optimize the combined score of the DM. Indeed, the combined score of PWOpt (0.4914) is (only) slightly greater than that of PW01 (0.4795). As is typical in such studies, the information of EW is about half that of PWOpt. Very roughly, this translates to EW\u2019s average 90% confidence bands being twice as large as those of PWOpt. Similarly, EW\u2019s statistical accuracy (P-value) is inferior to that of PWOpt. This is an \u201cin-sample\u201d comparison since DM\u2019s are compared on the same set over which PWOpt is optimized. For \u201cout-of-sample\u201d comparisons see below.\nSix of the 13 US experts had a statistical accuracy score above 0.01. This is a high number for SEJ studies, especially considering the fact that 16 calibration variables were used, constituting a more powerful statistical test than the traditional number of ten calibration items. Two of the eight EU experts had a statistical accuracy score above 0.01, which is in line with most SEJ studies. There is very little difference between the scores of PWOpt and PW01, though there are modest differences in SLR predictions (see Table S1). A scoring system is asymptotically strictly proper if and only if an expert obtains his/her highest expected score in the long run by, and only by, stating percentiles corresponding to his/her true beliefs. The combined score is an asymptotic strictly proper scoring rule if experts get zero weight when their P-value drops below some threshold (1). If (s)he tries to game the system to maximize his/her expected weight, (s)he will eventually figure out that (s)he must say exactly what (s)he thinks. Honesty is the only optimal strategy. The theory does not say what the cut-off value should be, so that is often chosen by optimization.", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber19.html"}
{"id": "e1b1028b405a-7", "text": "Other DMs in Table 2, besides EW, are PW01, the performance weighted combination of the eight weighted experts, and PWOpt, the performance weighted combination with the cutoff chosen to optimize the combined score of the DM. Indeed, the combined score of PWOpt (0.4914) is (only) slightly greater than that of PW01 (0.4795). As is typical in such studies, the information of EW is about half that of PWOpt. Very roughly, this translates to EW\u2019s average 90% confidence bands being twice as large as those of PWOpt. Similarly, EW\u2019s statistical accuracy (P-value) is inferior to that of PWOpt. This is an \u201cin-sample\u201d comparison since DM\u2019s are compared on the same set over which PWOpt is optimized. For \u201cout-of-sample\u201d comparisons see below.\nSix of the 13 US experts had a statistical accuracy score above 0.01. This is a high number for SEJ studies, especially considering the fact that 16 calibration variables were used, constituting a more powerful statistical test than the traditional number of ten calibration items. Two of the eight EU experts had a statistical accuracy score above 0.01, which is in line with most SEJ studies. There is very little difference between the scores of PWOpt and PW01, though there are modest differences in SLR predictions (see Table S1). A scoring system is asymptotically strictly proper if and only if an expert obtains his/her highest expected score in the long run by, and only by, stating percentiles corresponding to his/her true beliefs. The combined score is an asymptotic strictly proper scoring rule if experts get zero weight when their P-value drops below some threshold (1). If (s)he tries to game the system to maximize his/her expected weight, (s)he will eventually figure out that (s)he must say exactly what (s)he thinks. Honesty is the only optimal strategy. The theory does not say what the cut-off value should be, so that is often chosen by optimization.\nIn the Classical Model, the optimization works as follows: starting with a cutoff beneath the lowest P- value includes all experts with weight proportional to their combined scores. The combined score of the resulting DM is stored. Taking the expert with the lowest P-value, we next exclude that expert, normalize the remaining combined scores, compute the resulting DM, apply this DM to the calibration variables and store the resulting DM\u2019s combined score. Then we remove the next lowest P-value expert and repeat. With N expert P-values this results in N-1 different DM\u2019s. We choose the DM whose combined score is the highest. In this case, setting the cut-off at 0.399 and retaining experts 3 and 14 produced the highest scoring DM. With this scoring system it is impossible that a weighted expert has a lower P-value than an unweighted expert, even though doing so might produce a higher DM score. This system can thus be regarded as optimal weighting under a strictly proper scoring rule constraint. The theory was developed in the 1980s and is detailed in (1) and (2).\nThe Classical Model has been applied in hundreds of expert panels and has been validated both in- and out-of-sample (2-5). In the absence of observations of the variables of interest, out-of-sample validation comes down to cross-validation whereby the calibration variables are repeatedly separated into subsets of training- and test variables. The PW model is initialized on the training variables and scored on the test variables. The superiority of PW over EW in terms of statistical accuracy and informativeness has been demonstrated using this approach.\nRobustness on Experts\uf0c1\nRobustness on experts examines the effect on the PW01 \u201cdecision maker\u201d (i.e. the synthetic pooled expert) of losing individual experts. Experts are removed one at a time and PW01 is recomputed. Table S3 shows the resulting information and P-values of the \u201cperturbed\u201d PW01. The rightmost column of Table S4 shows the divergence among the experts themselves. Comparison with the rightmost column of table S3 shows that the scoring results are very robust against loss of a single expert.\nA more complete sense of robustness would examine the effect of the method of recruitment of experts and of the elicitation team. Before the Classical Model was adopted for the European uncertainty analysis of accident consequence codes for nuclear power plants (6), the authorities in Brussels required that parallel elicitations be carried out using the same elicitation protocol, but with different elicitation teams independently recruiting different experts. The findings in this case indicate a strong convergence of elicitation results from the two groups (6). Such an approach is generally far beyond the budgets of most applications. However, the results here (Table S1) show good general agreement on SLR between the US and European panels who were elicited separately. A different type of robustness is gleaned from the 14 year running expert judgment assessments of risks from the Montserrat volcano (7). Those assessments concerned a consistent elicitation method, applied to the same variables under changing conditions, with some exchanging of participating experts over elicitations. The approach showed good consistency of performance for volcanic hazard assessment purposes, over more than seventy repeat elicitations.\nRobustness on Items\uf0c1\nSeed variables are removed one at a time and PW01 is recomputed. These scores are extremely robust against loss of a seed variable. Comparing the rightmost columns of Supplementary Tables 3 and 5 shows that the perturbation caused by loss of a single calibration variable is very small relative to the divergence among the experts themselves.\nDependence Elicitation\uf0c1\nDependence and especially tail dependence are unfamiliar concepts for many scientists. A PowerPoint presentation was given to the experts, before the elicitation, to introduce these notions, where the reader can find precise definitions (see Supplementary Section 8 for links). Figure S6 from the presentation shows how aggregation affects uncertainty. 3 sigma or one in 1000 upper tail events are depicted for the sum of 10 zero mean normal variables. If the variables have a pairwise correlation of 0.5, the distribution dilates such that the 3 sigma event coincides with the sigma event of the sum of independent Normals. If this pairwise correlation is realized with an upper tail dependent copula, the 3 sigma event coincides with the 7 sigma event for independent Normals. Thus an event whose probability is 1/1000 (3 sigma will appear to be an event with probability 1.28*10^{-12} (7 sigma)) when tail dependence is present but ignored.\nThe dependence elicitation for pairs of variables was accomplished by eliciting conditional exceedance probabilities: for central correlation, experts answered: \u201cwhat is the probability that variable X exceeds its median given that variable Y has exceeded its median?\u201d. Numerical and verbal answers were accepted (Table S8). For upper tail dependence, \u201cmedian\u201d was replaced by \u201c95th percentile\u201d in the above question and verbal responses were elicited as indicated in Table S8.\nThree random variables (Runoff, Discharge and Accumulation) for each of the three ice sheets yield 36 pairs of variables. Potential dependences between ice sheets were also identified. Based on judgments of size and relevance, the analysis team pared this down to 10 pairs corresponding to the colored nodes in Figure S8, in addition to 3 inter-ice sheet relations. This structure is a \u201cdependence vine\u201d for determining a high dimensional joint distribution based on bivariate and conditional bivariate distributions. Unspecified (conditional) bivariate distributions are conditionally independent, making it easy to extend a partially specified structure to the minimally informative realization of the specified structure.\nThe basic \u201cdependence vine\u201d for expert 14, as an example, is shown in Figure S8. The ellipses represent the variables (GA = Greenland Accumulation; WD = West Antarctica Discharge; etc). The dependences, represented by arcs, are quantified by assessing exceedance probabilities. The colored nodes are those between which dependence is assessed. Conditional independence is assumed elsewhere. Calculations and sampling were performed with the freeware UNINET. This exposition of vine theory is necessarily incomplete; a Wiki page provides more background and references. A full exposition is in (8, 9).\nFor each of the eight experts with P-value > 0.01, a comparable regular vine was constructed using the dependence information elicited from each individual expert. These eight joint distributions were combined with the various weighting schemes shown in Table S2.\nFrom expert quantiles to SLR\uf0c1\nThe procedure of going from expert quantiles to distributions for SLR is as follows (for detailed information see (2), especially the online supplementary material Appendix A):\nFor each variable we determine an \u201cintrinsic range\u201d (IR), the smallest interval that contains all expert assessments plus the realization (in case of seed variables) + a 10% overshoot below and above (10% is a parameter that can be adjusted in the code)\nWe put a background measure on each IR. In the code the user can choose between the uniform and log-uniform background measure. Log-uniform is indicated when experts reason in orders of magnitude. In this case all background measures are uniform. Other choices could be made but would require re-coding.", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber19.html"}
{"id": "e1b1028b405a-8", "text": "Three random variables (Runoff, Discharge and Accumulation) for each of the three ice sheets yield 36 pairs of variables. Potential dependences between ice sheets were also identified. Based on judgments of size and relevance, the analysis team pared this down to 10 pairs corresponding to the colored nodes in Figure S8, in addition to 3 inter-ice sheet relations. This structure is a \u201cdependence vine\u201d for determining a high dimensional joint distribution based on bivariate and conditional bivariate distributions. Unspecified (conditional) bivariate distributions are conditionally independent, making it easy to extend a partially specified structure to the minimally informative realization of the specified structure.\nThe basic \u201cdependence vine\u201d for expert 14, as an example, is shown in Figure S8. The ellipses represent the variables (GA = Greenland Accumulation; WD = West Antarctica Discharge; etc). The dependences, represented by arcs, are quantified by assessing exceedance probabilities. The colored nodes are those between which dependence is assessed. Conditional independence is assumed elsewhere. Calculations and sampling were performed with the freeware UNINET. This exposition of vine theory is necessarily incomplete; a Wiki page provides more background and references. A full exposition is in (8, 9).\nFor each of the eight experts with P-value > 0.01, a comparable regular vine was constructed using the dependence information elicited from each individual expert. These eight joint distributions were combined with the various weighting schemes shown in Table S2.\nFrom expert quantiles to SLR\uf0c1\nThe procedure of going from expert quantiles to distributions for SLR is as follows (for detailed information see (2), especially the online supplementary material Appendix A):\nFor each variable we determine an \u201cintrinsic range\u201d (IR), the smallest interval that contains all expert assessments plus the realization (in case of seed variables) + a 10% overshoot below and above (10% is a parameter that can be adjusted in the code)\nWe put a background measure on each IR. In the code the user can choose between the uniform and log-uniform background measure. Log-uniform is indicated when experts reason in orders of magnitude. In this case all background measures are uniform. Other choices could be made but would require re-coding.\nFor each expert and each variable, we fit a density that is minimally informative with respect to the background measure and complies with the expert\u2019s quantile assessments. For the uniform background, this is a piecewise uniform density. This density \u201cadds as little as possible\u201d to the expert\u2019s assessment. Note that fitting a two-parameter family such as the Gaussian distribution will often be unable to match 3 quantiles.\n4) ASSUMING INDEPENDENCE\na. With N experts we form the EW combination by simple averaging of the experts\u2019 densities. DO NOT average the quantiles; that can give a very overconfident result.\nb. With PW, we take a weighted average of densities.\nc. Simple Monte Carlo sampling is used to build a distribution for SLR. For each ice sheet we sample D, R and A and store D+R-A.\nd. Monte Carlo sampling is used to build a distribution of total SLR as SLRGr + SLREAIS + SLRWAIS. Again, do not sum the quantiles.\nWITH DEPENDENCE, we build a joint density for each expert based on the elicited exceedance probabilities. This cannot be done with generic software. XL add-ons like @Risk and Crystal Ball impose the assumption of the Gaussian copula. Based on a pilot elicitation with the 2012 experts, we anticipated that tail dependence could be significant, rendering the Gaussian copula inappropriate. For each expert we obtain a distribution for total SLR, and we take a weighted average of these densities to find the combined distribution for SLR. Each expert\u2019s total SLR distributions incorporates his/her dependence.\nSteps (1) \u2013 (3) can be done with freeware EXCALIBUR (EXpert CALIBRation). Step (4) can be done with Freeware UNICORN (UNCertainty analysis wIth CORelatioNs)\u2013 which has limited dependence modeling capability). Step (5) uses freeware UNINET which is much more powerful. All these programs can be downloaded from http://www.lighttwist.net/wp/.\nExperts\u2019 rationales\uf0c1\nThis section summarizes and collates the expert responses to the rationale questionnaire that is reproduced in supplementary  note 6. For description of the process considered see note 6.\nIt is apparent that SEJ2018 value spreads for Antarctic Ice Sheet contribution to sea level rise in 2100CE lie above Edwards et al (2019)(10) no-MICI but are substantially lower than the 50th and 95th percentile MICI values obtained using the emulator in (10).\nBriefing note sent to experts prior to elicitation\uf0c1\nThe following briefing note was sent to all experts prior to the elicitation:\nEliciting Ice Sheets\u2019 Contribution to Sea Level Rise\nSept 28, 2017\nIntroduction: Probabilistic prediction for Ice Sheet contributions to Sea Level Rise\uf0c1\nWith global warming, ice sheets in Greenland and Antarctica are likely to become the primary agents of Sea Level Rise (SLR) in the coming decades and centuries. In their normally slow, march to the sea, glaciers draining the ice sheets exhibit dynamics which are highly variable from place to place, with neighboring glaciers or ice streams responding in markedly different ways to the same external forcing. Dynamic models must account for things like bedrock properties (including slipperiness and topography), ice shelf buttressing, precipitation, melt water effects on ice stiffness, grounding line migration, ocean currents, and ice cliff instability. Some of these features are directly observable, many are not.\nGlaciologists focusing on individual glaciers must contend with many uncertainties when predicting future ice mechanics and dynamics out to, say 2100CE, or even 2300CE. Point predictions, whatever their pedigree, are of limited value when the uncertainties are very large. Scientists must therefore make probabilistic predictions; they must say, in effect \u201cMy best estimate is a +0.2mm contribution to SLR by 2100CE from this particular glacier, and I am 90% confident the contribution will be between - 3mm and +6mm\u201d. A narrative might explain, say, \u201cthe contribution could actually be negative (the ice sheet would actually grow) if warming and changing atmospheric and ocean circulation increased winter precipitation inland while leaving the buttressing ice shelves largely intact; a very high contribution might result if increased storminess and shifting ocean currents break up ice shelves or summer coastal precipitation causes increased calving and instability\u201d. Capturing the narrative behind the uncertainty assessments is essential for understanding and communicating our current state of knowledge.\nThat is the easy part. Judging the cumulative future effects of the main ice sheets on sea level rise raises a host of new questions and methodological challenges, lying further outside most physical scientists\u2019 comfort zone. What might be the joint impacts of ice sheet responses on SLR if extreme conditions were encountered under global climate change?\nA proof of concept\uf0c1\nWe describe a proof-of-concept demonstration for using expert judgments to constrain quantitative estimates of dependences in potentially correlated processes that affect the ice sheet (2), and indicate some preliminary trial results. We also explore the influence on these results of different ways of combining expert judgments (3).\nA talk on this subject was given at the Banff research center in 2013 by Roger Cooke and can be streamed from http://www.birs.ca/events/2013/5-day-workshops/13w5146/videos/watch/201305221037-Cooke.html\nA talk on performance weighting was given at the Centers for Disease Control and Prevention in Atlanta GA on May 23, 2017 by Willy Aspinall, and may be streamed at https://www.youtube.com/watch?v=FPC-h-br8i8&feature=youtu.be\nA recent study extending (Bamber and Aspinall, 2013, henceforth B&A) made a first pass at assessing dependences between macro process variables relating to the Greenland, West Antarctica and East Antarctica ice sheets. Estimates of contributions to SLR were based on the B&A protocol. A typical question was\nIn the case of Greenland, for a global mean annual Surface Average Temperature rise of 3\u00b0C by 2100 with respect to pre-industrial, what will be the integrated contribution, in mm to SLR relative to 2000- 2010 of the following:\ni) accumulation\n5% value: ___________ 95% value: ___________ 50%value: ____________\nii) runoff\n5% value: ___________ 95% value: ___________ 50%value: ____________\niii) discharge\n5% value: ___________ 95% value: ___________ 50%value:: ____________\nSimilar questions were directed to West and East Antarctica, and to different temperatures, out to 2200.\nThe dependence elicitation was based on exceedance probabilities, as pioneered in the 1990\u2019s by uncertainty analyses for nuclear power plants in the US and in Europe. Whereas the earlier nuclear work used only the 50% exceedance probabilities, our ice sheet follow-on study asked also for 95% exceedance probabilities.\nWithin ice sheet process dependencies to 2100CE\uf0c1\nGreenland Ice Sheet, 2100 3\u00b0C warming\nGiven discharge >= your 50% value, what is probability that runoff also >= your 50% =____", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber19.html"}
{"id": "e1b1028b405a-9", "text": "A talk on this subject was given at the Banff research center in 2013 by Roger Cooke and can be streamed from http://www.birs.ca/events/2013/5-day-workshops/13w5146/videos/watch/201305221037-Cooke.html\nA talk on performance weighting was given at the Centers for Disease Control and Prevention in Atlanta GA on May 23, 2017 by Willy Aspinall, and may be streamed at https://www.youtube.com/watch?v=FPC-h-br8i8&feature=youtu.be\nA recent study extending (Bamber and Aspinall, 2013, henceforth B&A) made a first pass at assessing dependences between macro process variables relating to the Greenland, West Antarctica and East Antarctica ice sheets. Estimates of contributions to SLR were based on the B&A protocol. A typical question was\nIn the case of Greenland, for a global mean annual Surface Average Temperature rise of 3\u00b0C by 2100 with respect to pre-industrial, what will be the integrated contribution, in mm to SLR relative to 2000- 2010 of the following:\ni) accumulation\n5% value: ___________ 95% value: ___________ 50%value: ____________\nii) runoff\n5% value: ___________ 95% value: ___________ 50%value: ____________\niii) discharge\n5% value: ___________ 95% value: ___________ 50%value:: ____________\nSimilar questions were directed to West and East Antarctica, and to different temperatures, out to 2200.\nThe dependence elicitation was based on exceedance probabilities, as pioneered in the 1990\u2019s by uncertainty analyses for nuclear power plants in the US and in Europe. Whereas the earlier nuclear work used only the 50% exceedance probabilities, our ice sheet follow-on study asked also for 95% exceedance probabilities.\nWithin ice sheet process dependencies to 2100CE\uf0c1\nGreenland Ice Sheet, 2100 3\u00b0C warming\nGiven discharge >= your 50% value, what is probability that runoff also >= your 50% =____\nGiven discharge >= your 95% value, what is probability that runoff also >= your 95% =____\nGiven accumulation >= your 50% value, what is probability that discharge also >= your 50% =____\nGiven accumulation >= your 50% value, what is probability that runoff also >= your 50% =____\nIn answering questions concerning the 95% exceedances, the experts had to consider whether factors likely to produce extreme values in one variable would also produce extreme values in the other.\nAn extensive procedures guide for structured expert judgment emerging from these nuclear studies has informed many subsequent applications, including B&A. Following the Classical Model for structured expert judgment (Cooke 1991; Cooke and Goossens 2008), calibration variables from the experts\u2019 field were used by B&A to score the experts\u2019 statistical accuracy and informativeness. True values of calibration variables are known post hoc, they preferably concern near term future measurements, but can also involve unfamiliar intersections of past data or literature. An illustrative calibration variable from B&A was\nThere are nine main glacier/ice caps on Iceland. What was their 2009/2010 average climatic balance Bclim, in Kg/m2? (please indicate gain by +value, loss by -value)\n5% value: ___________ 95% value: ___________ 50%value: ____________\nBased on extensive experience with the Classical Model, an equally weighted combination of experts tends to give statistically accurate assessments exhibiting wide confidence bounds (low information). The goal of the Classical Model is to demonstrate high statistical accuracy with narrow confidence bounds. This is accomplished by differentially weighting the experts so as to favor those with high statistical accuracy and high information. Recent background on the Classical Model for climate uncertainty quantification may be found here. Other recent applications are summarized here, a Wikipedia page gives some background, and an extensive study of out-of-sample validation with complete mathematical exposition in supplementary material is here.\nDependence and aggregation\uf0c1\nThe SLR contribution of, say, the Jakobshaven glacier in western Greenland up to 2100CE is a random variable; it can be described mathematically by giving a range of possible values and a probability that each value would be realized. Quantifying the uncertainty in the contribution to SLR from the Greenland and Antarctic ice sheets involves adding together hundreds of random variables. Adding random variables is not like adding ordinary numbers. In adding two random variables, say the Jakobshaven and the Petermann glaciers\u2019 contributions to SLR by 2100CE, we must consider all possible combinations of values for Jakobshaven and for Petermann, and consider the probability that these values arise together. Suppose the contribution from Jakobshaven were very large. According to the above narrative, that suggests certain influencing factors are in play; how would these influences affect the Petermann glacier, 1274 km to the north? If they would also tend to induce high contribution values for the Petermann, then this could indicate a positive dependence between the SLR contributions of the two glaciers. If, on the contrary, the drivers of elevated ice mass loss in the west of Greenland were conducive to more stable conditions in the north, then the interglacier dependence might be negative.\nThe more random variables we aggregate, the more important the effects of long range, global correlations can become, a feature which our intuitions easily under-appreciate. A neglected weak global correlation of \uf072 = 0.2 when summing 500 normal variables underestimates the confidence interval of the sum by an order of magnitude. Global correlations also amplify the correlation of aggregations. In the above example, the correlation between the sum of the first 250 variables and the sum of the second 250 variables is 0.992. In contemplating the uncertainty in the effects of hundreds of glaciers, we must consider the overall effects of these dependencies.\nTail Dependence\uf0c1\nThe correlation coefficient represents a sort of average association between two random variables. This often yields an adequate measure of their association, but not always. The linkage between two variables may be primarily due to factors driving the extreme values, not the more mundane, central values.\nFor example, under normal conditions it may be that the mass loss at Jakobshaven and at Petermann vary according to local weather conditions, which are largely uncorrelated. However, very large mass loss at Jakobshaven would implicate large scale warming factors, which in turn could imply large mass loss at Petermann as well. In such cases one speaks of positive tail dependence between the two variables, here glacier processes. Tail dependence can be positive or negative, can affect the upper or lower tails of distributions, or both, and bears no direct relation to the ordinary correlation. Thus, two Gaussian variables are always tail independent. Given that one of them exceeds its rth percentile, the probability that the second also exceeds its own rth percentile tends toward the independent value of (100-r)% as r tends to 100% regardless of the correlation, provided it is strictly between 1 and \u22121.\nIn other words, a very high value of one variable tends not to entrain a high value of the other with two Gaussian variables, but this will not be true for variables characterized by other distributions.\nResults\uf0c1\nThe calculations were performed by Aspinall and Cooke defining a regular vine, using the experts\u2019 responses. Regular vines capture dependence in terms of nested bivariate and conditional bivariate distributions on the ranks of random variables, called copulae. The copulae are chosen to mimic the elicited exceedance probabilities. Our highest weighted experts evinced tail dependence between Greenland Discharge and Greenland Runoff, between West Antarctica Discharge and West Antarctica Runoff, and between West Antarctica Discharge and East Antarctica Discharge. Although the actual values of tail dependence varied between experts, they were comparable in magnitude. Other variables exhibited median dependence without tail dependence.\nTable 1 presents the overall results for the case of +3\u02daC global warming by 2100CE, and enables us to gauge the effects of dependence and of performance weighting. \u201cEW\u201d denotes the combination based on equal weighting of all nine experts, \u201cPW\u201d denotes the optimal performance weighting in which two experts were weighted, based on statistical accuracy and informativeness4. \u201cIndep\u201d signifies that experts\u2019 dependence information was not used. The contribution to SLR was computed, per ice sheet, as Runoff + Discharge \u2212 Accumulation as if these were independent random variables. \u201ctail indep\u201d signifies that tail dependence was ignored and dependence was based only on the 50% exceedance probabilities. \u201ctail dep\u201d includes the information on tail dependence.\nTable 1: \u201cEW\u201d denotes the combination based on equal weighting of all experts, \u201cPW\u201d denotes the optimal performance weighting in which the experts were weighted. \u201cIndep\u201d signifies that no dependence information was used. \u201ctail indep\u201d signifies that dependence was based only on the 50% exceedance probabilities. \u201ctail dep\u201d includes the information on tail dependence.", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber19.html"}
{"id": "e1b1028b405a-10", "text": "In other words, a very high value of one variable tends not to entrain a high value of the other with two Gaussian variables, but this will not be true for variables characterized by other distributions.\nResults\uf0c1\nThe calculations were performed by Aspinall and Cooke defining a regular vine, using the experts\u2019 responses. Regular vines capture dependence in terms of nested bivariate and conditional bivariate distributions on the ranks of random variables, called copulae. The copulae are chosen to mimic the elicited exceedance probabilities. Our highest weighted experts evinced tail dependence between Greenland Discharge and Greenland Runoff, between West Antarctica Discharge and West Antarctica Runoff, and between West Antarctica Discharge and East Antarctica Discharge. Although the actual values of tail dependence varied between experts, they were comparable in magnitude. Other variables exhibited median dependence without tail dependence.\nTable 1 presents the overall results for the case of +3\u02daC global warming by 2100CE, and enables us to gauge the effects of dependence and of performance weighting. \u201cEW\u201d denotes the combination based on equal weighting of all nine experts, \u201cPW\u201d denotes the optimal performance weighting in which two experts were weighted, based on statistical accuracy and informativeness4. \u201cIndep\u201d signifies that experts\u2019 dependence information was not used. The contribution to SLR was computed, per ice sheet, as Runoff + Discharge \u2212 Accumulation as if these were independent random variables. \u201ctail indep\u201d signifies that tail dependence was ignored and dependence was based only on the 50% exceedance probabilities. \u201ctail dep\u201d includes the information on tail dependence.\nTable 1: \u201cEW\u201d denotes the combination based on equal weighting of all experts, \u201cPW\u201d denotes the optimal performance weighting in which the experts were weighted. \u201cIndep\u201d signifies that no dependence information was used. \u201ctail indep\u201d signifies that dependence was based only on the 50% exceedance probabilities. \u201ctail dep\u201d includes the information on tail dependence.\nIce sheet contribution to SLR by 2100CE with +3\u02daC warming [mm] mean stdev 5% 50% 95% Expert combination method EW indep 615 270 238 581 1120 PW Indep 335 200 71 307 719 PW tail indep 337 216 64 305 749 PW tail dep 338 229 71 292 785 The largest effect is wrought by using performance-based weighting instead of expert equal weighting. The mean SLR of \u201cEW indep\u201d is nearly twice that of the PW combinations, and the 5- 50- and95- percentiles are substantially shifted upwards, relative to any of the alternative combinations. Focusing on the PW combinations, the effect of including dependence information is most visible in the 95th percentiles; the corresponding means are notably consistent. Including ice sheet inter-dependence, without tail dependence, raises the 95th percentile by +37 mm relative to the independent case; including tail dependence raises this percentile by +66mm relative to the independent case.\nThese are \u201clinear pooling methods\u201d; other methods have also been proposed for ice sheet uncertainty quantification, for a discussion see Bamber et al (2016).\nConclusions\uf0c1\nPredicting the cumulative effect of ice sheets on Sea Level Rise by 2100CE involves large uncertainties. Developing science-based quantifications of these uncertainties obliges scientists to venture outside their comfort zone of deterministic model-based predictions and deal with expert subjective uncertainty assessments. Adding information on dependence and tail dependence increased the values of the upper tail 95th percentiles of the performance weight combination. However, that increase effect was dominated by the reduction in SLR predictions produced by restricting the elicitation solution to our statistically accurate experts.\nReference values for ice-sheet processes\uf0c1\nIn the elicitation workshops, there was extensive discussion of how to define ice sheet contributions to sea level over future periods of time in relation to the temperature rise trajectories shown in Fig. S1. It was agreed that the ice sheet contributions would be expressed as anomalies from the 2000-2010 mean mass change states, as pre-defined in Table S7. On this basis, the net baseline sea-level contributions for this period were prescribed as 0.76 mm yr-1 for overall SLR, and 0.56, 0.20, and 0.00 mm yr-1 for GrIS, WAIS, and EAIS, respectively. (The resulting joint contribution of the three ice sheets is close to an observationally-derived value of 0.79 mm yr-1 for the same period, which was published subsequently to the SEJ workshops (4)).\nFor the SLR results presented in the main text, baseline contributions \u2013 integrated over the relevant time periods (i.e. from 2000CE to 2050CE; 2100CE; 2200CE and 2300CE) \u2013 have been added to the elicited SLR values reported in Supplementary note 1.\nTable S8: Reference probabilities assumed for estimating central and tail dependencies.\nPrompts for discussion of rationales\uf0c1\nSome of the questions below give you options for answering that are not independent (e.g., on the second question, buttressing is not independent of hydrofracturing). In such cases, indicate the option that best captures your overall judgment. In cases where you feel more than one answer is absolutely necessary to best characterize your judgment, feel free to fit in more than one response. Where changes are referred to and a future period is specified, these are for the difference between the future period and the base period, 2000-2010.\nMass change observations and assumptions\uf0c1\nAre the recent ~decadal trends in mass balance largely due to internal variability of the atmosphere/ice/ocean/climate system or anthropogenic forcing, for each ice sheet overall?\nSheet: GrIS WAIS EAIS\nIV EF IV EF (no trend) (no trend)\nDynamical processes\uf0c1\nHow will changes in near-field gravitational and vertical land motion due to past and future ice sheet unloading affect marine ice sheet instability: Decrease instability (D), Increase instability (I), or No significant change (N)?\nSheet GrIS WAIS EAIS\nD I N\nAmong buttressing by ice shelves (B), basal traction (BT), transverse stresses (TS), hydrofracturing (HF), ice cliff instability (IC), and dissipation after iceberg formation at exit gates (DI), which one will be the most important for controlling the overall 21st, 22nd, and 23rd century discharge rate and grounding line migration for key ice streams and outlet glaciers (recognizing time variations in the role of each)? Key ice streams are those that you expect to control overall discharge for that ice sheet.\n2\u00b0C scenario: Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd B BT TS HF IC DI\n5\u00b0C scenario: Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd B BT TS HF IC DI\nSurface mass balance\uf0c1\nBetween atmospheric circulation/moisture transport changes (AM) and albedo changes (AC), which do you consider more important for determining surface mass balance of grounded ice during the 21st, 22nd, and 23rd century.\n2\u00b0C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd AM AC\n5\u00b0C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd AM AC\nAmong changes in summer sea ice extent (SI), atmospheric circulation/moisture transport changes (AM), and albedo changes (AC), which do you consider most important for determining surface mass balance and rate of thinning of ice shelves in 21st, 22nd, and 23rd century?\n2\u00b0C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd SI AM AC\n5\u00b0C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd SI AM AC\nOcean processes\uf0c1\nAmong Antarctic circumpolar current changes (ACC), changes in intrusion of circumpolar deep water onto continental shelf (CDW), and changes in AMOC (MOC), which do you consider will have the largest effect on sub-shelf basal melt rates during the 21st, 22nd, and 23rd century?\n2\u00b0C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd ACC CDW MOC\n5\u00b0C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd ACC CDW MOC\nPolar Amplification\uf0c1\nPlease provide the polar amplification factor (e.g., 1.5x, 2x) or range of factors that you used in your estimates.", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber19.html"}
{"id": "e1b1028b405a-11", "text": "Surface mass balance\uf0c1\nBetween atmospheric circulation/moisture transport changes (AM) and albedo changes (AC), which do you consider more important for determining surface mass balance of grounded ice during the 21st, 22nd, and 23rd century.\n2\u00b0C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd AM AC\n5\u00b0C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd AM AC\nAmong changes in summer sea ice extent (SI), atmospheric circulation/moisture transport changes (AM), and albedo changes (AC), which do you consider most important for determining surface mass balance and rate of thinning of ice shelves in 21st, 22nd, and 23rd century?\n2\u00b0C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd SI AM AC\n5\u00b0C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd SI AM AC\nOcean processes\uf0c1\nAmong Antarctic circumpolar current changes (ACC), changes in intrusion of circumpolar deep water onto continental shelf (CDW), and changes in AMOC (MOC), which do you consider will have the largest effect on sub-shelf basal melt rates during the 21st, 22nd, and 23rd century?\n2\u00b0C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd ACC CDW MOC\n5\u00b0C scenario Sheet GrIS WAIS EAIS 21st 22nd 23rd 21st 22nd 23rd 21st 22nd 23rd ACC CDW MOC\nPolar Amplification\uf0c1\nPlease provide the polar amplification factor (e.g., 1.5x, 2x) or range of factors that you used in your estimates.\n2050 2100 2200 2300 1.5\u00b0C 2.0\u00b0C 2\u00b0C 5\u00b0C 2\u00b0C 5\u00b0C 2\u00b0C 5\u00b0C North South\nLow-probability, high-consequence scenarios\uf0c1\nAre there high-outcome scenarios above the 95% values you provided that deserve attention? If so, what are they?\nAmbiguity relating to discharge versus sea level contribution\uf0c1\nThe questionnaire provided to experts asked for their estimate of changes in discharge (defined as the ice flux across the grounding line) that would contribute to SLR. For ice grounded below sea level, such as in large sectors of the WAIS and parts of the EAIS, the change in volume of discharge and the sea level contribution are not the same quantity. This is because it is only the volume above flotation (VAF) that contributes to SLR, while the change in discharge includes ice below flotation that will be displaced by sea water.\nThis issue was identified during the second SEJ workshop held in Europe and to address it we asked all experts what value they were using for discharge: total discharge or VAF (the same as sea level equivalent). Of the 22 experts, four stated they had calculated total discharge and the rest VAF. Of these four, one had a high calibration score and a strong weighting in the PW01 solutions and a correction to these discharge values for the WAIS and EAIS were considered necessary. To do this, we utilized the output of a thermomechanical ice sheet model coupled to a solid earth deformation model in a climate forced deglaciation experiment (11, 12) and calculated the ratio of total discharge to VAF. This is shown in Figure S12 alongside the gradients for the ratio for the WAIS, EAIS and AIS. For the WAIS, the ratio changes after a volume loss of about 1 m sea level equivalent (SLE), while for the EAIS it is relatively constant. For the EAIS discharge we used a constant ratio, while for the WAIS it varied as a function of the discharge anomaly. The change in gradient is only significant for the 2300 L and H and 2200 H scenarios, where WAIS discharge anomaly exceeds 1 m for this expert.\nFigure S12: The ratio of volume above flotation to total ice discharge for a present-day deglaciation experiment for the Antarctic ice sheet. Fig a) AIS, b) WAIS, c) EAIS. Blue dots represent the first 400 years, red dots are for the remaining 20 Kyr.\nElicitation questions\uf0c1\nThe Elicitation questions are available as a pdf and Excel file at https://doi.org/10.5523/bris.23k1jbtan6sjv2huakf63cqgav", "source": "https://sealeveldocs.readthedocs.io/en/latest/bamber19.html"}
{"id": "294d6099ce82-0", "text": "Yuan and Kopp (2021)\uf0c1\nTitle:\nEmulating Ocean Dynamic Sea Level by Two-Layer Pattern Scaling\nKey Points:\nAn emulator for DSL changes is developed based on a two-layer energy balance model and a two-layer pattern scaling technique\nThe two-layer emulator can better capture the evolution of DSL in corresponding coupled GCMs than scaling of global mean surface temperature\nThe two-layer emulator allows estimation of the probability of future DSL changes in various emission scenarios over multiple centuries\nCorresponding author:\nYuan\nCitation:\nYuan, J., & Kopp, R. E. (2021). Emulating ocean dynamic sea level by two-layer pattern scaling. Journal of Advances in Modeling Earth Systems, 13, e2020MS002323, https://doi.org/10.1029/2020MS002323\nURL:\nhttps://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020MS002323\nAbstract\uf0c1\nOcean dynamic sea level (DSL) change is a key driver of relative sea level (RSL) change. Projections of DSL change are generally obtained from simulations using atmosphere-ocean general circulation models (GCMs). Here, we develop a two-layer climate emulator to interpolate between emission scenarios simulated with GCMs and extend projections beyond the time horizon of available simulations. This emulator captures the evolution of DSL changes in corresponding GCMs, especially over middle and low latitudes. Compared with an emulator using univariate pattern scaling, the two-layer emulator more accurately reflects GCM behavior and captures non-linearities and non-stationarity in the relationship between DSL and global-mean warming, with a reduction in global-averaged error during 2271-2290 of 36%, 24%, and 34% in RCP2.6, RCP4.5, and RCP8.5, respectively. Using the emulator, we develop a probabilistic ensemble of DSL projections through 2300 for four scenarios: Representative Concentration Pathway (RCP) 2.6, RCP 4.5, RCP 8.5, and Shared Socioeconomic Pathway (SSP) 3-7.0. The magnitude and uncertainty of projected DSL changes decrease from the high-to the low-emission scenarios, indicating a reduced DSL rise hazard in low- and moderate-emission scenarios (RCP2.6 and RCP4.5) compared to the high-emission scenarios (SSP3-7.0 and RCP8.5).\nPlain Language Summary\uf0c1\nAs climate warms, sea-level rise poses a major threat to coastal communities and ecosystems. A key driver of local sea level change is ocean dynamic sea level change, which is associated with changes in ocean density and circulation. The primary tools used to project changes in dynamic sea level are atmosphere-ocean general circulation models, which are computationally expensive. Here we develop an emulator for dynamic sea level changes that is, built upon a two-layer energy balance model. Considering both the rapid response of well-mixed surface layer and the delayed response of the deep ocean to forcing, the emulator facilitates the estimation of probability distributions of future dynamic sea level change under different emission scenarios and the extension of projections beyond the time horizon of available simulations from some atmosphere-ocean general circulation models. This emulator captures the evolution of dynamic sea level changes in the atmosphere-ocean general circulation models to which it is tuned, including the non-linear and non-stationary relationship between the dynamic sea level and global warming. The emulator thus facilitates the estimation of future local sea-level changes.\nIntroduction\uf0c1\nSea-level rise impacts coastal communities and ecosystems through permanent inundation, increasingly common tidal flooding, and increasingly frequent and severe storm-driven flooding. Global-mean sea level (GMSL) is rising at an accelerating rate, and under most scenarios is projected to continue accelerating over the 21st century (Oppenheimer et al., 2019). Regional relative sea level (RSL) change differs from global-mean sea-level change due to a variety of processes operating on diverse timescales, including the gravitational, rotational, and deformational effects associated with mass redistribution and ocean dynamic effects associated with changes in surface winds, ocean currents, and heat and freshwater fluxes (Gregory et al., 2016, 2019; Kopp et al., 2015; Perrette et al., 2013; Stammer et al., 2013).\nAtmosphere-ocean general circulation models (GCMs) are the primary tool used to project ocean dynamic sea level (DSL) change, but the computational demands of these models limit the utility of GCM ensembles for estimating the likelihood of different levels of future sea-level change. Ensembles such as the Coupled Model Intercomparison Project Phase 5 (CMIP5, Landerer et al., 2014; Taylor et al., 2012) are composed of models contributed based on voluntary effort, not the product of systematic experimental design; as such, they are an \u201censemble of opportunity\u201d rather than a probabilistic ensemble (Tebaldi & Knutti, 2007). The CMIP future projection experiments are driven by a small number of forcing scenarios - Representative Concentration Pathways (RCPs) in the case of CMIP5 - and model simulations are of different lengths; some simulations run the RCPs to the year 2100, while others extend these to 2300.\nThe computationally intensive nature of GCMs makes it challenging to produce large perturbed-physics ensembles that represent uncertainties in key feedback parameters, as well as to simulate forcing conditions intermediate between the RCPs. Simple climate models (SCMs) provide an alternative tool for estimating the uncertainties of future projections at the global scale, as they can capture the overall physics of climate evolution and can be run very fast even on a personal computer (Held et al., 2010; Meinshausen et al., 2011; Millar et al., 2017; Perrette et al., 2013). However, SCMs represent the climate at a highly aggregated (e.g., global or hemispheric) scale, and thus cannot produce spatial patterns of climate change at each time step.\nPattern scaling approaches are often used to translate the global mean surface air temperature (GSAT) change into regional-scale changes for impact analysis (Mitchell, 2003; Rasmussen et\u00a0al., 2016; Santer, 1990; Tebaldi & Arblaster,\u00a02014; Tebaldi et al.,2011). Generally speaking, pattern scaling uses a simple statistical model (often, linear regression) to relate local climatic changes to a variable such as GSAT change, assum.ing the patterns of local response to external forcing remain constant under increased forcing (Tebaldi & Arblaster, 2014).\nSome previous studies use the pattern scaling approach to estimate the uncertainty in DSL projections (Bilbao et\u00a0al.,\u00a02015; M. D. Palmer et\u00a0al.,\u00a02020; Perrette et\u00a0al.,\u00a02013). For example, Perrette et\u00a0al. (2013) regressed DSL change on GSAT. At New York City, they found that r2 values across models vary between 0.02 and 0.85, and also that the linear relationship between DSL and GSAT becomes weaker after the 21st century. Bilbao et\u00a0al.\u00a0(2015) examined the relationship between DSL and several variables, including GSAT, global-mean sea-surface temperature, ocean volume mean temperature, and global-mean thermosteric sea-level rise (GMTSLR). They found that GSAT performed best in predicting 21st-century DSL change in a high emissions scenario (RCP 8.5), while ocean-volume mean temperature and GMTSLR performed better in lower emissions scenarios (RCP 2.6 and 4.5). They speculated that this difference reflects a more important role for surface warming relative to deep warming in a more strongly forced scenario. They found that, across models and scenarios, area-weighted average root mean square error in pattern-scaled 2081\u20132100 DSL change ranged from ~1 to 3\u00a0cm.\nBuilding upon Bilbao et al. (2015)\u2019s speculation about the relative importance of shallow and deep warming under different scenarios, we developed a bivariate pattern scaling, which uses a multiple linear regression with two predictors: GSAT and global-mean deep ocean temperature change. The two temperature changes can be generated by a two-layer energy-balance model (2LM) (Held et al., 2010; Winton et al., 2010), which has proved to be a useful tool for understanding the responses of climate system to climate forcing (Geoffroy et al, 2013a, 2013b). Shallow and deep temperatures from a 2LM have previously been employed in an emulator to extend 21st century CMIP5 projections of GMTSLR to 2300 (M. D. Palmer et al., 2018), and M. D. Palmer et al. (2020) used GSAT from the two-layer model and univariate pattern scaling (based on GSAT) to emulate CMIP5 projections of DSL change.", "source": "https://sealeveldocs.readthedocs.io/en/latest/yuankopp21.html"}
{"id": "294d6099ce82-1", "text": "Building upon Bilbao et al. (2015)\u2019s speculation about the relative importance of shallow and deep warming under different scenarios, we developed a bivariate pattern scaling, which uses a multiple linear regression with two predictors: GSAT and global-mean deep ocean temperature change. The two temperature changes can be generated by a two-layer energy-balance model (2LM) (Held et al., 2010; Winton et al., 2010), which has proved to be a useful tool for understanding the responses of climate system to climate forcing (Geoffroy et al, 2013a, 2013b). Shallow and deep temperatures from a 2LM have previously been employed in an emulator to extend 21st century CMIP5 projections of GMTSLR to 2300 (M. D. Palmer et al., 2018), and M. D. Palmer et al. (2020) used GSAT from the two-layer model and univariate pattern scaling (based on GSAT) to emulate CMIP5 projections of DSL change.\nIn this study, we develop an emulator for DSL changes using both GSAT and deep-ocean temperature change projected by a 2LM. Here we drive the 2LM with radiative forcings from the Finite Amplitude Impulse Response model (FaIR), a SCM which includes a reduced-complexity carbon cycle and calculates atmospheric CO2 concentrations, radiative forcing and temperature changes based on emissions (Millar et al., 2017; Smith et al., 2017, 2018). FaIR was designed to more accurately reflect the temporal evolution of GSAT in response to a pulse emission, and it has been used in previous studies to produce observation-constrained future projections (Millar et al., 2017; Smith et al., 2017, 2018). In this study, we develop an emulator for GMTSLR and DSL change using surface and deep-ocean temperature changes generated by the FaIR-2LM (Section 2.2). As the univariate pattern scaling fails to capture the delayed response of the deep ocean to warming, we employ FaIR-2LM and two-layer pattern scaling to project future DSL changes, taking into account uncertainty in climate sensitivity, and demonstrate their ability to interpolate between climate scenarios run by GCMs. Compared to M. D. Palmer et al. (2018, 2020), which also use a 2LM to emulate GMTSLR or DSL projections, our approach differs in: (1) employing radiative forcings calculated based on emissions; (2) applying a format of 2LM considering efficacy factor of deep ocean heat uptake; (3) using both surface and deep-ocean temperature for pattern scaling (more details are described in supporting information).\nSection 2 describes data and methodology, including the details of FaIR-2LM, the calibration of the FaIR.2LM based on selected CMIP5 GCMs, the two-layer pattern scaling methodology, and the application of this system to emulate DSL projections. Section 3 evaluates the performance of the two-layer pattern scaling. Section 4 shows the resulting ensemble of DSL projections. Finally, Section 5 discusses and summarizes the results.\nData and Methods\uf0c1\nData\uf0c1\nWe use the zos variable from five CMIP5 general circulation models (GCMs) in RCP 2.6, 4.5, and 8.5 sce.narios: MPI-ESM-LR, bcc-csm1-1, HadGEM2-ES, GISS-E2-R, IPSL-CM5A-LR. These five GCMs are used because they were used to calibrate the parameters of the 2LM by Geoffroy et al. (2013) and provide multi-century data (to 2300) for zos in all three scenarios. DSL is taken as zos with its global mean removed, consistent with the definition of Gregory et al. (2019). The drift is removed from DSL by subtracting a linear function of time fitted to the pre-industrial control simulation from each scenario experiments, at each grid point. In addition, we remove the climatology in a baseline period (1986-2005) from DSL. The global mean surface air temperature (GSAT) and GMTSLR from the five models in the three scenarios are also used to evaluate the performance of FaIR-2LM.\nFaIR-Two Layer Model (FaIR-2LM) and Calibration\uf0c1\nThis study develops a hybrid SCM model by replacing the temperature module in FaIR 1.3 (Smith et al., 2018) with a 2LM. In FaIR 1.3, GSAT changes are the sum of two components, representing fast and slow responses to effective radiative forcing (ERF) (Equation 22 in Smith et al., 2018). The fast and slow components of temperature changes in FaIR 1.3 mathematically depend on multiple coefficients (e.g., thermal response timescales) that are obtained from the ensemble mean of multiple CMIP5 models (Geoffroy, et al., 2013b). Since these components do not have an unambiguous physical meaning, it is challenging to link them to sea-level change. Therefore, we replace the temperature module in FaIR 1.3 by the 2LM to construct FaIR.2LM. In each step of FaIR-2LM, the 2LM is driven by radiative forcing from FaIR 1.3, and produces the GSAT anomaly, which feeds back to the FaIR carbon cycle (Figure S1).\nFigure S1: Schematic diagram of the FaIR-2LM (modified from Figure 1 of Smith et al. 2018).\uf0c1\nWe employ a 2LM that includes an efficacy term for deep ocean heat uptake (Geoffroy, et al., 2013a; Held et al., 2010; Winton et al., 2010):\nC frac{dT}{dt} = mathcal{F} - lambda T - epsilon gamma (T - T_0)  (1)\nC_0 frac{dT_0}{dt} = gamma (T - T_0) (2)\nwhere mathcal{F} denotes the adjusted radiative forcing, C and C_0 are the heat capacity of the well-mixed upper layer and the deep ocean layer, respectively, and T and T_0 represent the global mean temperature anomalies of the upper and lower layer, respectively. Following Equation 22 in Geoffroy, et al. (2013b) and using C = 8.2 W yr m^{-2} K^{-1} and C_0 = 109 W yr m^{-2} K^{-1} based on an average across multiple CMIP5 GCMs (Geoffroy, et al., 2013a), we estimate the average depths of the upper layer and lower layer are 86 m and 1141 m, respectively. T is equivalent to GSAT perturbation (Held et al., 2010). lambda is the parameter for climate feedback, gamme is the coefficient of deep ocean heat uptake, and epsilon is the efficacy factor of deep ocean heat uptake, which represents the uneven spatial distribution of heat exchanges between the two layers.\nTo calibrate FaIR-2LM, we adjust parameter settings (listed in Table 1) based on previous studies (Forster et al., 2013; Geoffroy, Saint-Martin, et al., 2013a; Zelinka et al., 2014). The radiative forcing in FaIR-2LM is driven by the default emission trajectory for each scenario in FaIR 1.3, but scaled by two parameters determined for each GCM: (1) the radiative forcing of CO_2 doubling (F_{2 times CO_2}) reported by Forster et al. (2013), and (2) the present-day aerosol forcing (a*f_{pd}) estimated in previous studies (Forster et al., 2013; Zelinka et al., 2014), or -0.9 W m^{-2} - the median of range estimated by the Fifth Assessment Report of Intergovernmental Panel on Climate Change (IPCC AR5) (Stocker et al., 2013) - for models not reported in previous studies. The five parameters in Equations 1 and 2 (i.e., lambda, gamma, epsilon, C, C_0) are the same as those in Geoffroy et al. (2013) for the corresponding GCMs.\nTable 1: FaIR-2LM Parameters adjusted to match the GSAT in CMIP5 GCMs. \\(\\lambda\\) (W m-2 K-1), \\(\\gamma\\) (W m-2 K-1), \\(\\epsilon\\), C (W yr m-2 K-1), and \\(C_0\\) (W yr m-2 K-1) are reported by Geoffroy et al. (2013). The units for \\(F_{2 \\times CO_2}\\) and \\(af_{pd}\\) are W m-2.\nCMIP5 GCMs\n\\(\\lambda\\)\n\\(\\gamma\\)\n\\(\\epsilon\\)\nC\n\\(C_0\\)\n\\(F_{2 \\times CO_2}\\)\n\\(af_{pd}\\)\nbcc-csm1-1\n1.28\n0.59\n1.27\n8.4\n56", "source": "https://sealeveldocs.readthedocs.io/en/latest/yuankopp21.html"}
{"id": "294d6099ce82-2", "text": "To calibrate FaIR-2LM, we adjust parameter settings (listed in Table 1) based on previous studies (Forster et al., 2013; Geoffroy, Saint-Martin, et al., 2013a; Zelinka et al., 2014). The radiative forcing in FaIR-2LM is driven by the default emission trajectory for each scenario in FaIR 1.3, but scaled by two parameters determined for each GCM: (1) the radiative forcing of CO_2 doubling (F_{2 times CO_2}) reported by Forster et al. (2013), and (2) the present-day aerosol forcing (a*f_{pd}) estimated in previous studies (Forster et al., 2013; Zelinka et al., 2014), or -0.9 W m^{-2} - the median of range estimated by the Fifth Assessment Report of Intergovernmental Panel on Climate Change (IPCC AR5) (Stocker et al., 2013) - for models not reported in previous studies. The five parameters in Equations 1 and 2 (i.e., lambda, gamma, epsilon, C, C_0) are the same as those in Geoffroy et al. (2013) for the corresponding GCMs.\nTable 1: FaIR-2LM Parameters adjusted to match the GSAT in CMIP5 GCMs. \\(\\lambda\\) (W m-2 K-1), \\(\\gamma\\) (W m-2 K-1), \\(\\epsilon\\), C (W yr m-2 K-1), and \\(C_0\\) (W yr m-2 K-1) are reported by Geoffroy et al. (2013). The units for \\(F_{2 \\times CO_2}\\) and \\(af_{pd}\\) are W m-2.\nCMIP5 GCMs\n\\(\\lambda\\)\n\\(\\gamma\\)\n\\(\\epsilon\\)\nC\n\\(C_0\\)\n\\(F_{2 \\times CO_2}\\)\n\\(af_{pd}\\)\nbcc-csm1-1\n1.28\n0.59\n1.27\n8.4\n56\n3.23\n-0.9\nGISS-E2-R\n2.03\n1.06\n1.44\n6.1\n134\n3.78\n-0.9\nHadGEM2-ES\n0.61\n0.49\n1.54\n7.5\n98\n2.93\n-1.23\nIPSL-CM5A-LR\n0.79\n0.57\n1.14\n8.1\n100\n3.1\n-0.68\nMPI-ESM-LR\n1.21\n0.62\n1.42\n8.5\n78\n4.09\n-0.9\nGSAT produced by the calibrated FaIR-2LM is compared with that from the corresponding GCMs in the three scenarios (Fig. S2). For the five GCMs, the GSAT simulated by FaIR-2LM is close to the GSAT from the corresponding GCM, with the root mean square error (RMSE) determined over the entire simulation period in a range of 0.15-0.23 K for RCP2.6, 0.14-0.32 K for RCP4.5, and 0.20-0.43 K for RCP8.5.\nGMTSLR is driven by the thermal expansion of sea water volume due to the increase in ocean heat uptake. To calibrate GMTSLR in FaIR-2LM to match a specific GCM, we first correct the drift in the GCM\u2019s GMTSLR field by removing the linear trend in the pre-industrial control simulation, assuming the drift is not sensitive to the external forcing (Hobbs et al., 2016).\nThen, we emulate GMTSLR based on the T and T_0 from FaIR-2LM following the approach described in Kuhlbrodt and Gregory (2012):\n{GMTSLR} = sigma times (C Delta T + C_0 Delta T_0)  (3)\nwhere sigma is the expansion efficiency of heat in units of 10^{-24} m J^{-1}. The sigma value is calibrated by optimizing GMTSLR emulated from FaIR-2LM to match the GMTSLR simulated from the corresponding GCM.\nTwo-Layer Pattern Scaling\uf0c1\nUnivariate pattern scaling is based on a linear relation between regional changes in a climate variable (DSL for this study) and global mean responses of climate change, such as GSAT (T):\nDSL(t,x,y) = alpha(x,y) T(t) + b(x,y) + epsilon(t,x,y)  (4)\nwhere x and y denote longitudes and latitudes, t represents the time, b is an intercept term, and epsilon is the residual term. Here, alpha captures the scaling relationship between DSL and GSAT (Figure 1). The five GCMs agree that the linear response of DSL to surface warming is positive over the Arctic and sub-polar Atlantic, and negative over the southeastern Pacific and the southern areas of Southern Ocean.\nFigure 1: Changes in DSL in response to changes in deep ocean temperature (first column) and global-mean surface air temperature (second column) in bivariate pattern scaling. The third column is the response of DSL changes to global-mean surface air temperature in univariate pattern scaling. The first five rows display the maps of slopes obtained from a GCM over the period of 1981-2300. The sixth row shows the multi-model mean of slopes. The areas where the slopes from the five models agree in sign are hatched. White areas are lands. Units are m K^{-1}.\uf0c1\nIn the bivariate pattern scaling approach, we regress the DSL anomaly on both T (GSAT anomaly) and T_0 (deep-ocean temperature anomaly) from FaIR-2LM:\nDSL(t_i,x,y) = alpha(x,y) T(t_i) + beta(x,y) T_0(t_i) + b(x,y) + epsilon(t,x,y)  (5)\nwhere t_i denotes years in three scenarios, i = 1, 2, 3. For each GCM, we estimate the fields of alpha, beta, b, and epsilon by regressing projections from all three emissions scenarios (RCPs 2.6, 4.5, and 8.5) on T and T_0 on a grid cell-by-grid cell basis. alpha represents changes in zos in response to changes in surface temperature in the period 1981\u20132300, while beta represents the response of changes in zos to changes in deep-ocean temperature at the same period (Figure 1). Consistent with the univariate scaling pattern, the five GCMs agree that the upper-layer response, represented by alpha, is positively correlated with warming over the most areas of Arctic and northern edge of the Southern Ocean, and negatively correlated with warming over the southeastern Pacific and the southern areas of Southern Ocean. The deep-layer response represented by beta is positively correlated with warming over the Indian and tropical and southern Pacific Oceans, and negatively correlated with warming over most areas of the Southern Ocean and Arctic. These reflect opposite behaviors between rapid and sustained changes in DSL over the Arctic, the Indian and tropical and southern Pacific Oceans, and a consistent DSL fall in both rapid and sustained changes over the Southern Ocean.\nThere is little agreement on either surface- or deep-layer slopes across the five GCMs over most parts of the Atlantic basin (Figure 1). This may reflect limited skill in simulating strong western boundary currents (e.g., the Atlantic Meridional Overturning Circulation (AMOC)) in the GCMs, which have a relatively coarse (~1\u02da) spatial resolution in ocean component (Small et al., 2014) and so poorly capture non-linear mesoscale processes in the ocean current (Hallberg, 2013). Near the eastern coast of North America, DSL is closely related to AMOC (Goddard et al., 2015), which is expected to weaken in a warming climate (Caesar et al., 2018). Low skill in capturing AMOC behavior can affect the DSL projections in the Atlantic basin as well as its coasts (van Westen et al., 2020). As the coefficients of pattern scaling depend on the simulations by the GCMs, they also do not explicitly resolve the non-linear mesoscale process of the ocean current. Therefore, we should interpret the DSL changes predicted by the two-layer emulator with cautions over the regions where non-linear mesoscale effects of ocean current are strong.\nProjecting DSL Using FaIR-2LM and Patterns\uf0c1\nWe use two steps to generate a probabilistic ensemble of DSL projections. First, we generate an ensemble of surface and deep-ocean temperature pairs using FaIR-2LM. The planetary energy balance at the top of the atmosphere (Zelinka et al., 2020) is:\n\\[N = \\mathcal{F} + \\lambda T   (6)\\]", "source": "https://sealeveldocs.readthedocs.io/en/latest/yuankopp21.html"}
{"id": "294d6099ce82-3", "text": "There is little agreement on either surface- or deep-layer slopes across the five GCMs over most parts of the Atlantic basin (Figure 1). This may reflect limited skill in simulating strong western boundary currents (e.g., the Atlantic Meridional Overturning Circulation (AMOC)) in the GCMs, which have a relatively coarse (~1\u02da) spatial resolution in ocean component (Small et al., 2014) and so poorly capture non-linear mesoscale processes in the ocean current (Hallberg, 2013). Near the eastern coast of North America, DSL is closely related to AMOC (Goddard et al., 2015), which is expected to weaken in a warming climate (Caesar et al., 2018). Low skill in capturing AMOC behavior can affect the DSL projections in the Atlantic basin as well as its coasts (van Westen et al., 2020). As the coefficients of pattern scaling depend on the simulations by the GCMs, they also do not explicitly resolve the non-linear mesoscale process of the ocean current. Therefore, we should interpret the DSL changes predicted by the two-layer emulator with cautions over the regions where non-linear mesoscale effects of ocean current are strong.\nProjecting DSL Using FaIR-2LM and Patterns\uf0c1\nWe use two steps to generate a probabilistic ensemble of DSL projections. First, we generate an ensemble of surface and deep-ocean temperature pairs using FaIR-2LM. The planetary energy balance at the top of the atmosphere (Zelinka et al., 2020) is:\n\\[N = \\mathcal{F} + \\lambda T   (6)\\]\nwhere N is the radiative imbalance at the top of the atmosphere. The equilibrium climate sensitivity (ECS) is given by T when N = 0, and mathcal{F} = F_{2 times CO_2}. Therefore, lambda is related to F_{2 times CO_2} and ECS by\nlambda = - F_{2 times CO_2} / ECS  (7)\nThe uncertainty of F_{2 times CO_2} is small relative to the spread of lambda, while ECS largely determine the uncertainty of lambda. Therefore, we adopt the best estimation in the Intergovernmental Panel on Climate Change Fifth Assessment Report (AR5) for F_{2 times CO_2} = 3.71 W m^{-2} (Collins et al., 2013). We produce initial distributions of ECS, gamma, and gamma_{epsilon} based on the literature constraints (Figure S4) outlined below:\nECS: Based on multiple lines of evidence, the uncertainties of ECS estimated by AR5 are likely in the range 1.5\u02daC-4.5\u02daC with high confidence, extremely unlikely less than 1\u02daC and very unlikely greater than 6\u02daC (Collins et al., 2013). In the AR5 terminology, likely denotes a probability of at least 66%, very unlikely a probability of less than 10%, and extremely unlikely a probability of less than 5% (Mastrandrea et al., 2010). Therefore, we construct a log-normal distribution for ECS with parameters optimized to match a 5th percentile of 1\u02daC, a 17th percentile of 1.5\u02daC, an 83rd percentile of 4.5\u02daC, and a 90th percentile of 6\u02daC.\ngamma: We treat gamma as normally distribution, with mean 0.67 W m^{-2} K^{-1} and standard deviation 0.15 W m^{-2} K^{-1} derived from the 16 GCMs in the CMIP5 archive (Geoffroy et al., 2013).\ngamma_{epsilon}: As the efficacy factor of heat uptake is related to deep-ocean heat uptake (Held et al., 2010), we use gamma_{epsilon} instead of epsilon to maintain the covariance between gamma and epsilon. We calculate the mean of 0.86 W m^{-2} K^{-1} and standard deviation 0.29 W m^{-2} K^{-1} of gamma_{epsilon} based on the products of gamma and epsilon from 16 GCMs in CMIP5 archive (Geoffroy, et al., 2013a). The distribution of gamma_{epsilon} is constructed as a normal distribution with the multi-model mean and the multi-model standard deviation.\nTCR: Under a zero-layer approximation which considers the 1%/yr increase in CO_2 until doubling scenario occurring on a timescale long enough that the upper ocean is in approximate equilibrium and short enough that the deep-ocean temperature has not yet responded substantially, Transient Climate Response (TCR) can be obtained by (Jimenez-de-la-Cuesta & Mauritsen, 2019):\n{TCR} = - frac{F_{2 times CO_2}}{lambda - gamma_{epsilon}}  (8)\nUncertainty in the TCR can be constrained adequately by varying only lambda and gamma_{epsilon} under the zero-layer approximation. Therefore, although there are significant uncertainties of C and C_0 among GCMs, we use fixed values because the uncertainties of these parameters are not necessary to represent uncertainty in the TCR. In this study, we set C = 8.2 W m^{-2} K^{-1} and C_0 = 109 W m^{-2} K^{-1} based on the multi-model mean of GCMs from Coupled Model Intercomparison Project Phase 5 (CMIP5) archive (Geoffroy, et al., 2013a).\nWe then generate a 100,000-member ensemble of ECS, gamma and gamma_{epsilon} based on these distributions via Monte Carlo sampling. As gamma_{epsilon}} should be larger than 0, we discard parameter sets in which gamma_{epsilon}} < 0 or gamma_{epsilon}} > 2 times 0.86 to keep the mean of gamma_{epsilon}} in parameter sets to be 0.86 W m^{-2} K^{-1}. Therefore, 99734 parameter sets are kept. An ensemble of lambda is then computed by the best estimation of F_{2 times CO_2} and the ensemble of ECS based on Equation 6 (Figure S4). The median (central 66% range) of lambda is \u22121.39 (\u22122.4 to \u22120.8) W m^{-2} K^{-1}. As the likely range of ECS estimated by AR5 is equivalent to the central 90% range of ECS estimated by CMIP5 GCMs, the uncertainty range of lambda estimated by FaIR-2LM is larger than that estimated by ensemble of GCMs (Geoffroy et al., 2013). The spread of TCR is estimated as a diagnostic by substituting the ensemble of lambda, gamma_{epsilon}, and best estimation of F_{2 times CO_2} into Equation 8. The uncertainty of TCR is in a central 66% range of 1.1\u20132.3\u02daC, with a 95th percentile of 2.9\u02daC. This is consistent with but slightly narrower than the TCR estimated by AR5, which is likely between 1\u02daC and 2.5\u02daC, and is extremely unlikely greater than 3\u02daC.\nWe apply Latin hypercube sampling (LHS, Stein, 1987) to the parameter sets of lambda, gamma, gamma_{epsilon} by sampling 1,000 sets from the 99,734 parameter sets. For each parameter, LHS divides the probability density function of the 99,734 samples into 1,000 portions that have equal area. A sample is taken from each portion randomly so that the 1,000 sample sets cover the multidimensional distribution of the three parameters. Finally, we applied 1,000 parameter sets together with the fixed parameters (F_{2 times CO_2}, C, C0) to the FAIR-2LM and generate a 1,000-member probabilistic ensemble of temperature pair time-series.\nWe compare the spread in GSAT projected by FaIR-2LM with the likely ranges estimated by AR5 for four different periods (Collins et al., 2013) (Table 3 and Figure S5). The mean of the probabilistic ensemble is slightly lower than the mean estimate of GSAT from AR5 in all four periods of RCP2.6 and RCP4.5, and in the 21st century for RCP8.5. Compared with AR5 likely ranges, the central 66% probability range of GSAT from FaIR-2LM is generally consistent: narrower in all four periods of RCP2.6, narrower in the first two periods but wider in the last two periods in RCP4.5, and wider in the first two periods but narrower in the last two periods in RCP8.5.\nWe project GMTSLR based on Equation 3 using the probabilistic ensemble of surface and deep-ocean temperature projections from FaIR-2LM. The C, C_0 and expansion efficiency of heat sigma (0.113 times 10^{-24 m}) used here are adopted from the multi-model ensemble mean of CMIP5 archive (Geoffroy, et al., 2013a; Kuhlbrodt & Gregory, 2012).", "source": "https://sealeveldocs.readthedocs.io/en/latest/yuankopp21.html"}
{"id": "294d6099ce82-4", "text": "We apply Latin hypercube sampling (LHS, Stein, 1987) to the parameter sets of lambda, gamma, gamma_{epsilon} by sampling 1,000 sets from the 99,734 parameter sets. For each parameter, LHS divides the probability density function of the 99,734 samples into 1,000 portions that have equal area. A sample is taken from each portion randomly so that the 1,000 sample sets cover the multidimensional distribution of the three parameters. Finally, we applied 1,000 parameter sets together with the fixed parameters (F_{2 times CO_2}, C, C0) to the FAIR-2LM and generate a 1,000-member probabilistic ensemble of temperature pair time-series.\nWe compare the spread in GSAT projected by FaIR-2LM with the likely ranges estimated by AR5 for four different periods (Collins et al., 2013) (Table 3 and Figure S5). The mean of the probabilistic ensemble is slightly lower than the mean estimate of GSAT from AR5 in all four periods of RCP2.6 and RCP4.5, and in the 21st century for RCP8.5. Compared with AR5 likely ranges, the central 66% probability range of GSAT from FaIR-2LM is generally consistent: narrower in all four periods of RCP2.6, narrower in the first two periods but wider in the last two periods in RCP4.5, and wider in the first two periods but narrower in the last two periods in RCP8.5.\nWe project GMTSLR based on Equation 3 using the probabilistic ensemble of surface and deep-ocean temperature projections from FaIR-2LM. The C, C_0 and expansion efficiency of heat sigma (0.113 times 10^{-24 m}) used here are adopted from the multi-model ensemble mean of CMIP5 archive (Geoffroy, et al., 2013a; Kuhlbrodt & Gregory, 2012).\nA projection of DSL is constructed as follows: 1) a pair of alpha and beta is randomly picked with replacement from the pool of two-layer patterns produced in Section 2.3; 2) a temperature pair from the 1000 members is combined with the pair of alpha and beta in an equation:\n{DSL}(t, x, y) = alpha(x, y) T(t) + beta(x, y) T_0(t) + b(x, y)  (9)\nEvaluation of Two-Layer Pattern Scaling\uf0c1\nTo evaluate the prediction skill of the two-layer pattern scaling, we compare the DSL changes simulated from a GCM with the DSL changes emulated by the two-layer pattern scaling (widehat{{DSL}}) based on FAIR-2LM using the key parameters (i.e. parameters in Table 1) in the same GCM. Two metrics are used: (1) absolute values of the residual differences between widehat{{DSL}} changes and DSL changes during a period at each grid point, and (2) global average of the absolute values obtained from the metric 1 (Table S1). These two metrics are applied to both bivariate pattern scaling and univariate pattern scaling, to examine the improvement of bivariate approach comparing with the univariate approach.\nIn 2271-2290, for instance, the global-averaged climatology of | DSL - widehat{{DSL}} | (score obtained by the second metric) from the two-layer pattern scaling is less than that from the univariate pattern scaling (bottom row Figure 2), with a reduction of 36%, 24%, and 34% in RCP2.6, RCP4.5, and RCP8.5, respectively. The spatial pattern of R = DSL - widehat{{DSL}} is derived from both approaches are various across GCMs (Figures S6-S10). The 5-model ensemble averaged climatology of | R | in both approaches is higher over high latitudes (e.g., Arctic, subpolar Northern Atlantic, Southern Ocean) than over middle to low latitudes, but is generally lower in two-layer pattern scaling than in univariate pattern scaling (first two rows Figure 2). As the pattern-scaling method cannot resolve DSL change due to unforced variability, the relatively large | R | over the high latitudes may be due to the relatively high unforced variability over these regions (Bilbao et al., 2015).\nWe further compare the time evolution of widehat{{DSL}} predicted by the two-layer pattern scaling approaches with the evolution of DSL in corresponding GCMs through the period 1981-2290. As case studies, we pick two grid cells: one in the western Pacific near the Philippines (14.5\u02daN, 127\u02daE), and the other over the North Atlantic near the coast of New York City [NYC] (40\u02daN, 73\u02daW) (solid black dots in Figure 2). The grid point near the Philippines is selected because it is in the tropical Pacific, where DSL rise associated with the deep ocean temperature rise is strongest, while the grid point near the NYC is selected represent a coastal area that some projections find experiences significant DSL changes in response to changes in AMOC.\nFigure 2: Differences between DSL simulated by GCMs (zos) and DSL (widehat{{zos}}) predicted by univariate pattern scaling (univariate, first row) and two-layer pattern scaling (two-layer, second row) over the period 2271-2290 for the ensemble mean of 5 GCMs in three scenarios: RCP2.6, RCP4.5, RCP8.5 (Units: m). The third row shows the global mean of the | {zos} - (widehat{{zos}} | in 1TS and 2TS, respectively. Black dots on maps denote the two grid cells used for the plot in Figure 3.\uf0c1\nAt the western Pacific grid cell, in RCP 2.6, the relationship between DSL and GSAT anomaly displays a hook-like shape, indicating continued rise in DSL as GSAT stabilizes and declines in response to negative emissions (Figure 3a). The delayed adjustment of DSL may be due to the continuous warming of deep layer (T_0) when GSAT is stabilized, because the ocean is not yet equilibrated with the elevated forcing. In response to changes in T_0, the deep ocean density is still changing even without changing circulation in the deep ocean (England, 1995), so DSL continues to change. This hook-like shape is captured by the two-layer pattern scaling approach but not by the univariate pattern scaling. Compare to the DSL simulated by a GCM, the RMSE of the predicted DSL is smaller if using the two-layer pattern scaling approach than using the univariate pattern scaling approach. The average RMSE across the five GCMs is reduced 26% if we use the approach from the two-layer pattern scaling instead of the univariate pattern scaling (Table 3). Across the five GCMs, although the relationship between DSL and GSAT is diverse in RCP4.5 and RCP8.5, DSL projected by the two-layer technique is consistently closer than that predicted by the univariate technique to the DSL simulated by the GCMs. The sole exception is for bcc-csm1-1 in RCP8.5, for which the simulated DSL projection is quite linearly associated with GSAT. The average of RMSEs across the 5 GCMs decrease from the univariate pattern scaling approach to the two-layer pattern scaling approach by 35% in RCP4.5 and by 33% in RCP8.5 (Table 3).\nFigure 3: widehat{{zos}} predicted by univariate pattern scaling and two-layer pattern scaling at the grid cell (a) over Western Pacific (14.5\u02daN, 127\u02daE) and (b) over the North Atlantic (40\u02daN, 73\u02daW) for the five models in the three scenarios. The zos simulated by corresponding GCMs is shown by scatters in which colors indicate years. Root mean square errors between the widehat{{zos}} and zos determined over the entire simulating period for each GCM are shown in parentheses of legend (units: m).\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/yuankopp21.html"}
{"id": "294d6099ce82-5", "text": "Figure 3: widehat{{zos}} predicted by univariate pattern scaling and two-layer pattern scaling at the grid cell (a) over Western Pacific (14.5\u02daN, 127\u02daE) and (b) over the North Atlantic (40\u02daN, 73\u02daW) for the five models in the three scenarios. The zos simulated by corresponding GCMs is shown by scatters in which colors indicate years. Root mean square errors between the widehat{{zos}} and zos determined over the entire simulating period for each GCM are shown in parentheses of legend (units: m).\uf0c1\nAt the North Atlantic grid cell, the relationship between DSL and GSAT also displays non-linear features for all the five models, especially in low- and moderate-emission scenarios (Figure 3b). These non-linear features, which may arise from the delayed response of deep branch of AMOC, cannot be captured by univariate pattern scaling but are captured to a large extent by the two-layer pattern scaling (lines in Figure 3). The value of the two-layer approach is highlighted by the clear non-linearity of the DSL response when viewed as a function of GSAT anomaly. Compare to the univariate approach, the RMSE between the DSL simulated by GCMs and the DSL predicted by the two-layer pattern scaling is smaller, with a reduction of 19%, 16%, and 13% for RCP2.6, RCP4.5, and RCP8.5, respectively. The method of two-layer pattern scaling generally has a better performance in emulating the DSL from the corresponding GCM than the univariate pattern scaling, as the two-layer pattern scaling includes one more predictor than univariate pattern scaling, allowing it to capture the delayed adjustment of DSL. The delayed adjustment of DSL due to the deep-ocean warming is important for the DSL projections, as different areas present different features that may reveal the regional variation in deep-ocean circulation (Held et al., 2010).\nProjections of DSL\uf0c1\nThe procedure described in Section 2.4 allows us to produce a 1000-member probabilistic ensemble of DSL projections not only for the three CMIP5 scenarios: RCP2.6, RCP4.5, and RCP8.5, but also for any other scenarios with an emission pathway between these three scenarios. We demonstrate this capability using SSP3-7.0, a CMIP6 scenario that has forcing intermediate between RCP4.5 and RCP8.5 (O\u2019Neill et al., 2016) and is closer than either to no-policy reference scenarios from most integrated assessment models (Riahi et al., 2017). The emission pathway of SSP3-7.0 used to drive the FaIR-2LM is taken from the Reduced Complexity Model Intercomparison Project (Nicholls et al., 2020).\nThe five projections using parameters calibrated to the five GCMs respectively are within the 66% range of the 1000-member ensemble for both surface and deep-ocean temperature in the three RCPs (Figure 4). By 2300, the median estimates (66% range) of the surface temperature relative the period of 1986-2005 are 0.5\u02daC (0.2-1.0\u02daC) for RCP2.6, 2.2\u02daC (1.2-3.6\u02daC) for RCP4.5, 7.4\u02daC (4.5-11.7\u02daC for RCP8.5, and 5.3\u02daC (3.2-8.6\u02daC) for SSP3-7.0.\nBased on the projections of temperature pairs, we also produced projections of GMTSLR for the four scenarios (Figure 4). The spread of GMTSLR ensemble encapsulates the GMTSLR time series from the 5 GCMs (Figure 4). During the period of 2081-2100, the median estimates (66% range) of the GMTSLR relative the period of 1986-2005 are 0.12 (0.07-0.18) m for RCP2.6, 0.16 (0.10-0.24) m for RCP4.5, 0.19 (0.12-0.27) m for SSP3-7.0, and 0.24 (0.15-0.34) m for RCP8.5. This compares to Oppenheimer et al. (2019)\u2019s projected median estimates (66% ranges) of 0.14 (0.10-0.18) m for RCP2.6, 0.19 (0.14-0.23) m for RCP4.5, and 0.27 (0.21-0.33) m for RCP8.5. By 2300, the median estimates (66% range) of GMTSLR relative to the period of 1986-2005 are 0.20 (0.12-0.33) m for RCP2.6, 0.43 (0.25-0.68) m for RCP4.5, 0.85 (0.50-1.33) m for SSP3-7.0, and 1.15 (0.69-1.76) m for RCP8.5. As climate warms, the projections of DSL changes increase along with the increase in GMTSLR. In the five GCMs, although the contributions of DSL changes to the local sterodynamic sea level (DSL+GMTSLR; Gregory et al., 2019) changes are small at some locations (i.e., regions marked by the light and dark gray shadings in Figure S11), in others the ratio of DSL change with respect to the GMTSLR changes are fairly significant. For instance, DSL changes at some regions (e.g., Arctic, North Atlantic, and Southern Ocean) are greater than 50% of the GMTSLR during the period of 2271-2290 (identified by yellow contours in Figure S11).\nFigure 4: Ensemble projections of CO_2 concentrations (first row), GSAT (second row), deep-ocean temperature (third row), and GMTSLR (fourth row) changes relative to the baseline period 1986-2005 under the four scenarios. Shadings represents the 66% range, dark blue lines the median of probabilistic ensemble projections. The projection calibrated to the five GCMs in the three RCP scenarios are shown on top of the shadings (orange lines).\uf0c1\nCompared with the GSAT and GMTSLR spread in 2300 estimated by M. D. Palmer et al. (2018), the FaIR.2LM projections have a slightly lower median for all the three RCPs. The 66% range of both surface temperature and GMTSLR estimated by FaIR-2LM is comparable to the 90% range of that estimated by M. D. Palmer et al. (2018) because we adopt a distribution of lambda based on the AR5 assessment of equilibrium climate sensitivity (Collins et al., 2012), which is broader than the 90% range estimated by the CMIP5 multi-model ensemble emulated by M. D. Palmer et al. (2018).\nComparing the DSL projections between the period of 2081-2100 and the period of 2271-2290 (Figure 5), the median estimate is lower and the 66% range of uncertainty is narrower at the end of 21st century than that at the end of 23rd century in moderate-to high-emission scenarios (RCP4.5, SSP3-7.0 and RCP8.5). But in RCP2.6, the median estimate and 66% uncertainty range are comparable in magnitude between these two periods. In both periods, the median DSL anomaly projections across the four scenarios share many similar features (Figure 5). Over the Arctic region, a weak increase in DSL is observed over the Chukchi Sea and the Beaufort Sea in RCP2.6. In the higher emission scenarios, the increase in DSL extends to the whole Arctic basin with intensified amplitudes. The changes in DSL over the North Atlantic are dominated by a negative anomaly under RCP2.6, and display positive anomalies over much of the North Atlantic under RCP8.5 and SSP3-7.0. The ensemble spread of the 5th-95th range of DSL projections are relatively large over the Southern Ocean, Arctic and Subpolar Atlantic than other areas. The large uncertainties over these areas, consistent with previous literatures (M. D. Palmer et al., 2020; Perrette et al., 2013; Yin, 2012), may be interpreted by the diverse characteristics simulated by GCMs that do not explicitly resolve non-linear mesoscale processes of the ocean current over these areas (van Westen et al., 2020).", "source": "https://sealeveldocs.readthedocs.io/en/latest/yuankopp21.html"}
{"id": "294d6099ce82-6", "text": "Comparing the DSL projections between the period of 2081-2100 and the period of 2271-2290 (Figure 5), the median estimate is lower and the 66% range of uncertainty is narrower at the end of 21st century than that at the end of 23rd century in moderate-to high-emission scenarios (RCP4.5, SSP3-7.0 and RCP8.5). But in RCP2.6, the median estimate and 66% uncertainty range are comparable in magnitude between these two periods. In both periods, the median DSL anomaly projections across the four scenarios share many similar features (Figure 5). Over the Arctic region, a weak increase in DSL is observed over the Chukchi Sea and the Beaufort Sea in RCP2.6. In the higher emission scenarios, the increase in DSL extends to the whole Arctic basin with intensified amplitudes. The changes in DSL over the North Atlantic are dominated by a negative anomaly under RCP2.6, and display positive anomalies over much of the North Atlantic under RCP8.5 and SSP3-7.0. The ensemble spread of the 5th-95th range of DSL projections are relatively large over the Southern Ocean, Arctic and Subpolar Atlantic than other areas. The large uncertainties over these areas, consistent with previous literatures (M. D. Palmer et al., 2020; Perrette et al., 2013; Yin, 2012), may be interpreted by the diverse characteristics simulated by GCMs that do not explicitly resolve non-linear mesoscale processes of the ocean current over these areas (van Westen et al., 2020).\nFigure 5: Projection of DSL changes at median estimation (first column) and range of 17th-83rd percentile averaged over the period of 2081-2100 in four scenarios (a) relative to the baseline period 1986-2005. (b) is the same with (a) except for the period of 2271-2290. Units are m.\uf0c1\nAt the illustrative grid point near Philippines over western Pacific (Figure 6a), the 66% range of the probabilistic ensemble encapsulates DSL projections from 2 of the 5 GCMs in the three RCPs, while the 90% range of the probabilistic ensemble contains DSL projections from all the 5 GCMs in the three RCPs, except for HadGEM2-ES in RCP2.6. At the grid point near NYC, the projected DSL changes estimated by the probabilistic ensemble exhibits a fat tail, with a median projection in RCP 8.5 of 0.13 m and a 95th percentile projection of 0.8 m by the end of 23rd century. By contrast, RCP 2.6 exhibits a much narrower range, with a median of 0 m and a 95th percentile of 0.08 m. The 66% range of the projected DSL uncertainties encapsulates 2 of 5 GCM projections. The 90% range of the probabilistic ensemble only encapsulates the DSL projections from three over five GCMs in RCP2.6 and RCP4.5, but encapsulates the DSL projections from all five GCMs in RCP8.5. The emulator fails to capture multidecadal variability in DSL, a limitation which would be expected because the emulator is constructed based on the pattern scaling approach.\nFigure 6: Ensemble projections of DSL changes relative to the baseline period 1986-2005 at the grid cells near Philippines over the western Pacific (upper panel) and near NYC over the North Atlantic (lower panel) for the four scenarios: RCP2.6, RCP4.5, SSP3-7.0, and RCP8.5. Shadings represent the projections produced by the two-layer emulator, with light and dark shadings indicating the 90% and 66% range, respectively, and dark blue lines the median of probabilistic ensemble projections. The black lines represent the projections produced by the univariate emulator, with the dashed and solid lines indicating the 90% and 66% range, respectively. The projection of DSL changes smoothed by 20-years running average in the five GCMs are shown on top of the shadings (colored lines). Units: m.\uf0c1\nTo compare with the DSL projections derived from two-layer pattern scaling, we also produced the DSL projections based on univariate pattern scaling following the same procedure (Figures S12 and S14). The median and 17th-83rd range of DSL projections derived from univariate pattern scaling are similar in patterns (Figure S12). However, differences of both median and spreads of the DSL projections between univariate and two-layer pattern scaling vary across regions, especially over high latitudes in high-emission scenarios (Figure S13). Specifically, compared to the univariate emulator, the median of DSL projected by the two-layer emulator is lower over the Pacific and Indian Ocean, and higher over Arctic, Atlantic and Southern Ocean in the period of 2081-2100, but the opposite in the period of 2271-2290. In addition, the 17th-83rd range of the DSL projected by the two-layer emulator is wider than that by the univariate emulator over the Arctic. The area-weighted increases in DSL spread over the Arctic are 0.02 m in RCP2.6, 0.03 m in RCP4.5, and 0.04 m in RCP8.5 during 2081-2100, and are 0.006 m in RCP2.6, 0.008 m in RCP4.5, 0.009 m in RCP8.5 during 2271-2290. For the grid cell near Philippines, despite the shift in median, the distributions of DSL projections derived from univariate pattern scaling exhibit a different shape from that derived from two-layer pattern scaling (Figure 6). In 2290, the 90% range of DSL projection from the univariate emulator is close to that from the two-layer emulator, slightly narrower by 0.03 m for RCP2.6, 0.02 m for RCP4.5, and 0.01 m for SSP3-7.0 and RCP8.5. The two-layer pattern scaling leads to not only a shift of the distribution but also a different shape of the distribution of the DSL projections, compared to that derived from univariate pattern scaling. There are more DSL projections simulated by GCMs encapsulated within the 90% range of the probabilistic ensemble of DSL projections derived from two-layer pattern scaling than that by the univariate pattern scaling (Figure 6). For the grid cell near the NYC, the shape of DSL distributions derived from univariate pattern scaling is similar to that derived from two-layer pattern scaling, except the spread of the DSL projections derived from univariate pattern scaling is slightly narrower than that derived from the two-layer pattern scaling, with the 90% range of DSL projection in 2290 narrower by 0.03 m for RCP2.6, 0.01 m for RCP4.5, and 0.03 m for SSP3-7.0 and RCP8.5 (Figure 6). The greatest difference is in RCP 2.6, where the difference in the 90% range is by far the largest compared to the overall range.\nTable 2: The Averaged RMSE Between the DSL Simulated by GCMs and the DSL Predicted by Univariate/Two-Layer Pattern Scaling Across Five Models. Note: The averaged RMSEs and the reduction of RMSE from univariate pattern scaling approach to two-layer pattern scaling are calculated for the three RCP scenarios, respectively.\nDiscussion and Conclusions\uf0c1\nWe have developed a probabilistic ensemble of DSL projections through 2300 using a novel two-layer emulator. Replacing the climate module in the FaIR simple climate model with a two-layer energy-balance model, we developed FaIR-2LM, which produces projections of global average temperature in the well-mixed upper layer (T) for rapid responses to radiative forcing, and in the deep ocean layer (T_0) for delayed responses. Calibrated by the parameters for each GCMs, the GSAT (Figure S2) and GMTSLR (Figure S3) emulated by FaIR-2LM generally follow that from the corresponding GCM, with RMSE <0.43 K for GSAT and <0.05 m for GMTSLR. A two-layer pattern scaling based on surface and deep-ocean temperature is used to project DSL. During the period 2271-2290, for instance, the DSL predicted by the two-layer pattern scaling are closer to the DSL simulated by the corresponding GCM than that predicted by the univariate pattern scaling (Figure 2). At two selected grid cells (near the coast of Philippines and NYC), the time evolution of DSL projections predicted by the two-layer emulator more accurately reflects GCM behavior and captures non-linearities and non-stationarity in the relationship between DSL and global-mean warming, comparing with that predicted by the univariate technique (Figure 3).", "source": "https://sealeveldocs.readthedocs.io/en/latest/yuankopp21.html"}
{"id": "294d6099ce82-7", "text": "Table 2: The Averaged RMSE Between the DSL Simulated by GCMs and the DSL Predicted by Univariate/Two-Layer Pattern Scaling Across Five Models. Note: The averaged RMSEs and the reduction of RMSE from univariate pattern scaling approach to two-layer pattern scaling are calculated for the three RCP scenarios, respectively.\nDiscussion and Conclusions\uf0c1\nWe have developed a probabilistic ensemble of DSL projections through 2300 using a novel two-layer emulator. Replacing the climate module in the FaIR simple climate model with a two-layer energy-balance model, we developed FaIR-2LM, which produces projections of global average temperature in the well-mixed upper layer (T) for rapid responses to radiative forcing, and in the deep ocean layer (T_0) for delayed responses. Calibrated by the parameters for each GCMs, the GSAT (Figure S2) and GMTSLR (Figure S3) emulated by FaIR-2LM generally follow that from the corresponding GCM, with RMSE <0.43 K for GSAT and <0.05 m for GMTSLR. A two-layer pattern scaling based on surface and deep-ocean temperature is used to project DSL. During the period 2271-2290, for instance, the DSL predicted by the two-layer pattern scaling are closer to the DSL simulated by the corresponding GCM than that predicted by the univariate pattern scaling (Figure 2). At two selected grid cells (near the coast of Philippines and NYC), the time evolution of DSL projections predicted by the two-layer emulator more accurately reflects GCM behavior and captures non-linearities and non-stationarity in the relationship between DSL and global-mean warming, comparing with that predicted by the univariate technique (Figure 3).\nTable 3: Comparison of the Distributions of GSAT Anomaly (Relative to 1986-2005) Projected by FaIR-2LM With the Distributions of Global-Mean Surface Temperature Assessed by AR5 (Collins et al., 2013) in RCP 2.6, RCP4.5, SSP3-7.0 and RCP 8.5 (the 2nd and 3rd Columns, units: \u02daC). Note: Means are given without parentheses; likely range (for AR5) and 17th-83rd percentile range (for FaIR-2LM) are given in parentheses. The fourth column is similar with previous columns except for the GMTSLR projected by FAIR-2LM (Units: m).\nBy perturbating the key parameters, FaIR-2LM allows emulation of projected global-mean surface and deep-ocean temperature pairs and GMTSLR for emissions scenarios (e.g., SSP3-7.0; Figures 4 and 5) beyond those run by the GCMs to which it is calibrated. Compared with the likely ranges assessed by AR5 in the RCP 2.6, 4.5 and 8.5, the FaIR-2LM performs well in emulating the GSAT spread (Table 2 and Figure S5). By 2300, the ensembles of GSAT and GMTSLR estimated by FaIR-2LM have a slightly lower median and a slightly wider 90% range than the estimations by M. D. Palmer et al. (2018), likely because we use the uncertainty of ECS from AR5, which has a larger range than that estimated by CMIP5 multi-model ensemble.\nWe produce probabilistic ensembles of DSL projections for four different emissions scenarios. Characteristics of median DSL projections during 2271-2290 include increases in DSL along most of the coast around the Pacific and Indian Oceans and a decrease in DSL over the Southern Ocean in all four scenarios, as well as increased DSL over the Arctic and along the North Atlantic Current in moderate to high emissions scenarios (Figure 5). The 66% range (17th-83rd percentile) of uncertainties are small over the middle and low latitudes, and are relatively large over the Southern Ocean, Arctic and North Atlantic, where the simulations of GCMs are diverse due to the challenges of capturing the complex physical processes, such as deep water formation in the subpolar Atlantic, the Antarctic circumpolar current, and ice-albedo feedback in polar regions (Flato et al., 2013; Landerer et al., 2014; Wang et al., 2014). The ensemble of DSL projections also allows us to examine the trajectories of the DSL projections and their uncertainties at specific locations (Figure 6). At selected locations in the North Atlantic and Western Pacific, the 90% range of DSL spread generally encapsulates the time series of DSL changes relative to the baseline period from the 5 GCMs.\nThe two-layer emulator provides a useful tool to explore the uncertainty of DSL projections over multiple centuries with computational resources that are much less than a GCM requires. It can be calibrated to match assessments of key values like the equilibrium climate sensitivity, and allows the flexibility of simulating forcing conditions intermediate between the RCPs as the patterns are common for different scenarios. However, we should note that the errors between the DSL predicted by two-layer emulator and DSL simulated by the corresponding GCMs are small in middle and low latitudes but relatively large in high latitudes (e.g., the Southern Ocean, Arctic, and subpolar Atlantic). In addition, the two-layer emulator cannot explicitly resolve the non-linear mesoscale effects of the ocean current due to the coarse resolutions of the CMIP5 GCMs that the two-layer pattern scaling relies on. Comparing with the predicted DSL derived from univariate approach, the improvement of using the two-layer approach on predicting DSL has a similar magnitude with the uncertainty of DSL projections over the middle and low latitudes in RCP2.6 and RCP4.5 scenarios during the period of 2271-2290. But the improvement is limited comparing to the uncertainty of DSL projections in RCP8.5. As the non-linear responses of DSL are more obvious in the RCP2.6 and RCP4.5 than in RCP8.5, the notable improvement of using the two-layer approach over the middle- and low-latitudes in the RCP2.6 and RCP4.5 highlight the advantage on improving the DSL projections in these two scenarios.\nLoss of land ice (e.g., Greenland Ice Sheet and Antarctic Ice Sheet) is an important contributor not only to GMSL but also to RSL. Glacio-isostatic adjustment (GIA) caused by changes in ice sheet mass loading induces local vertical land motion and associated changes in local sea level. Mass loss of an ice sheet also reduces the gravitational attraction that pulls sea water toward it, causing water to migrate away with a distinct spatial pattern, or \u201cfingerprint\u201d, of sea level change to the global ocean (Mitrovica et al., 2009). Freshwater flux from a melting ice sheet may drastically alter the salinity profile of the near-by ocean, bringing about complex feedbacks involving near-surface ocean stratification, sea ice formation, and corresponding changes in surface temperature, winds, and ocean currents (Bronselaer et al., 2018; Sadai et al., 2020) - each process could have its impact in RSL. Among these factors, only freshwater flux from the ice sheet can significantly affect both global climate and DSL (e.g., Golledge et al., 2019). Despite the importance of polar ice sheets, their contributions to DSL are not included in the current generation coupled climate models. Our study, relying on outputs from climate models participating the CMIP5 project, thus cannot take into account the effects of evolving ice sheets on DSL. In more comprehensive analyses, the effect of land-ice loss should be considered.\nReferences\uf0c1\nBilbao, R. A. F., Gregory, J. M., & Bouttes, N. (2015). 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{"id": "294d6099ce82-10", "text": "Stein, M. (1987). Large sample properties of simulations using latin hypercube sampling. Technometrics, 29, 143\u2013151. https://doi.org/10.1080/00401706.1987.10488205\nStocker, T. F., Qin, D., Plattner, G.-K., Tignor, M. M. B., Allen, S. K., Boschung, J., et al. (2013). Climate change 2013: The physical science basis. Contribution of working group I to the Fifth assessment Report of the intergovernmental panel on climate change. (1\u20131535). Cambridge, United Kingdom and New York, NY: Cambridge University Press.\nTaylor, K. E., Stouffer, R. J., & Meehl, G. A. (2012). An overview of CMIP5 and the experiment design. Bulletin of the American Meteorological Society, 93, 485\u2013498. https://doi.org/10.1175/BAMS-D-11-00094.1\nTebaldi, C., & Arblaster, J. M. (2014). Pattern scaling: Its strengths and limitations, and an update on the latest model simulations. Climatic Change, 122, 459\u2013471. https://doi.org/10.1007/s10584-013-1032-9\nTebaldi, C., Arblaster, J. M., & Knutti, R. (2011). Mapping model agreement on future climate projections. Geophysical Research Letters, 38, L23701. https://doi.org/10.1029/2011GL049863\nTebaldi, C., & Knutti, R. (2007). The use of the multi-model ensemble in probabilistic climate projections. Philosophical Transactions of The Royal Society Mathematical, Physical and Engineering Sciences, 365, 2053\u20132075. https://doi.org/10.1098/rsta.2007.2076\nvan Westen, R. M., Dijkstra, H. A., van der Boog, C. G., Katsman, C. A., James, R. K., Bouma, T. J., et al. (2020). Ocean model resolution dependence of Caribbean sea-level projections. Scientific Reports, 10, 14599. https://doi.org/10.1038/s41598-020-71563-0\nWang, C., Zhang, L., Lee, S.-K., Wu, L., & Mechoso, C. R. (2014). A global perspective on CMIP5 climate model biases. Nature Climate Change, 4, 201\u2013205. https://doi.org/10.1038/nclimate2118\nWinton, M., Takahashi, K., & Held, I. M. (2010). Importance of ocean heat uptake efficacy to transient climate change. Journal of Climate, 23, 2333\u20132344. https://doi.org/10.1175/2009JCLI3139.1\nYin, J. (2012). Century to multi-century sea level rise projections from CMIP5 models. Geophysical Research Letters, 39. https://doi.org/10.1029/2012GL052947\nZelinka, M. D., Andrews, T., Forster, P. M., & Taylor, K. E. (2014). Quantifying components of aerosol-cloud-radiation interactions in cli.mate models. Journal of Geophysical Research: Atmospheres, 119, 7599\u20137615. https://doi.org/10.1002/2014JD021710\nZelinka, M. D., Myers, T. A., McCoy, D. T., Po-Chedley, S., Caldwell, P. M., Ceppi, P., et al. (2020). Causes of Higher Climate Sensitivity in CMIP6 Models. Geophysical Research Letters, 47, e2019GL085782. https://doi.org/10.1029/2019GL085782", "source": "https://sealeveldocs.readthedocs.io/en/latest/yuankopp21.html"}
{"id": "0b3d18ead65a-0", "text": "Church et al. (2013)\uf0c1\nTitle:\nEvaluating the ability of process based models to project sea-level change\nKey Points:\nEvaluation of CMIP5 and other process-based models using observations\nProcess-based models, when properly calibrated, can reproduce a significant portion of the observed sea-level rise.\nOcean thermal expansion and glacier melting are the two dominant contributors to sea-level rise\nThe models\u2019 ability to reproduce observed sea-level rise has improved significantly, increasing confidence in their projections for the 21st century.\nKeywords:\nsea level, climate change, projections\nCorresponding author:\nJohn A. Church\nCitation:\nChurch, J. A., Monselesan, D., Gregory, J. M., & Marzeion, B. (2013). Evaluating the ability of process based models to project sea-level change. Environmental Research Letters, 8(1), 014051. doi:10.1088/1748-9326/8/1/014051\nURL:\nhttps://iopscience.iop.org/article/10.1088/1748-9326/8/1/014051\nAbstract\uf0c1\nWe evaluate the ability of process based models to reproduce observed global mean sea-level change. When the models are forced by changes in natural and anthropogenic radiative forcing of the climate system and anthropogenic changes in land-water storage, the average of the modelled sea-level change for the periods 1900\u20132010, 1961\u20132010 and 1990\u20132010 is about 80%, 85% and 90% of the observed rise. The modelled rate of rise is over 1 mm yr\u22121 prior to 1950, decreases to less than 0.5 mm yr\u22121 in the 1960s, and increases to 3 mm yr\u22121 by 2000. When observed regional climate changes are used to drive a glacier model and an allowance is included for an ongoing adjustment of the ice sheets, the modelled sea-level rise is about 2 mm yr\u22121 prior to 1950, similar to the observations. The model results encompass the observed rise and the model average is within 20% of the observations, about 10% when the observed ice sheet contributions since 1993 are added, increasing confidence in future projections for the 21st century. The increased rate of rise since 1990 is not part of a natural cycle but a direct response to increased radiative forcing (both anthropogenic and natural), which will continue to grow with ongoing greenhouse gas emissions.\nIntroduction\uf0c1\nA complete understanding of 20th century sea-level rise has been lacking, with the observed rise over recent decades being larger than projections in the Intergovernmental Panel on Climate Change (IPCC) Third (TAR, Church et al 2001) and Fourth Assessment Reports (AR4, Hegerl et al 2007). As a result, sea-level projections for the 21st century and beyond have been controversial. The omission of \u2018rapid\u2019 dynamic ice sheet contributions from the AR4 projections, because of the lack of a published basis for estimating them, compounded this problem. Rahmstorf et al (2007) argued that the observed sea-level rise since 1990 was at or above the upper limit of the TAR projections, and Rahmstorf et al (2012a) argued that both the TAR and AR4 projections were biased low. However, using an improved understanding of the impact of volcanic eruptions on sea level, Church et al (2011a) described the comparison slightly differently, finding that while the observed rise was in the upper quartile of the AR4 projections there was no inconsistency between observations and projections from 1990. Semi-empirical models (SEMs; Rahmstorf 2007, Horton et al 2008, Vermeer and Rahmstorf 2009, Grinsted et al 2010, Jevrejeva et al 2010, 2011, Rahmstorf et al 2012b) have been proposed as an alternative way to estimate future sea-level rise.\nUsing observations of 20th century temperatures, Bittermann et al (2013) [B13] compared SEM forecasts of 20th century sea-level rise to the observations. They concluded that, when both tide-gauge reconstructions of global mean sea-level and paleo sea-level data were used to estimate the parameters of their SEMs, their forecasts for 1900\u20132000 (range of 13\u201330 cm) were in agreement with the observations (14\u201326 cm). For the period 1961\u20132003, they also found that when the SEM was trained using the Church and White (2011) [CW11] estimates of GMSL and paleo data up to 1960, the predicted rate of 2.0 mm yr\u22121 (range of 1.9\u20132.3 mm yr\u22121) agreed with the observations within the uncertainties. However, using the Jevrejeva et al (2008) estimate of GMSL, with or without the paleo data, resulted in sea-level projections that were biased high by up to 70%. B13 challenged the sea-level process model community to test their projections for the same period.\nHere we evaluate the ability of process based models (the basis of 21st century projections) to simulate 20th century global averaged sea-level rise. These process based models are dependent on our physical understanding of the climate system built up over many years. Modelling sea level requires simulations of oceanic and atmospheric global and regional temperatures. In contrast to the SEMs, the process based models are forced by greenhouse gas concentrations and simulate temperature changes, rather than using observed temperature or radiative forcing changes as input, and they are not trained with observed sea levels and are therefore not sensitive to uncertainties in them. This study builds upon recent progress in understanding the 20th century sea-level budget (Church et al 2011b, Moore et al 2011, Gregory et al 2013a) but focuses clearly on model results and their ability to project sea-level change. We compare individual contributions to sea level calculated with the World Climate Research Programme Coupled Model Intercomparison Project Phase 5 (CMIP5) model results with observations (section 2) and compare the sum of these terms to the observed sea-level rise since 1900, 1961 and 1990, as in B13. We discuss the possibility that some fraction of 20th century sea-level change is possibly due to internally generated variability that is unlikely to be simulated in phase and amplitude by the models (section 3). We also discuss the implications of the results for the observed increase in the rate of rise and for future projection of 21st century sea-level rise (section 4).\nSea-level response to historical radiative forcing and anthropogenic intervention in the water cycle\uf0c1\nOcean thermal expansion\uf0c1\nOcean thermal expansion (figure 1(a)) is available for 25 atmosphere\u2013ocean general circulation models (AOGCMs) participating in the CMIP5 experiment. The simulations used here have been forced with the best estimates of historical radiative forcings up to 2005 and then radiative forcing from the RCP4.5 scenario (Moss et al 2010, Taylor et al 2012) until 2010. However, the preindustrial spin-up and the control simulation for these models assumed zero volcanic forcing and thus the sudden imposition of the negative volcanic forcing in the historical simulations from 1850 results in a negative bias in the estimated ocean thermal expansion (Gregory 2010). To overcome this bias, we have added 0.1 mm yr\u22121 (\u00b10.05 mm yr\u22121) ocean thermal expansion to the model results (Gregory 2010, Gregory et al 2013b). We compare the model results to the observational estimates based on the analysis of Domingues et al (2008), updated to 2012 for the upper 700 m, the Levitus et al (2012) analysis from 700 to 2000 m, and a linear trend from 1992 to 2011 for the ocean below 2000 m (Purkey and Johnson 2010). From 1970, when the amount of observational data increases significantly, the models and the observations are not significantly different and the observations are near the centre of the model simulated range.\nFigure 1: Comparisons of modelled and observed (a) ocean thermal expansion (observations in blue), (b) glacier contributions, (c) changes in terrestrial storage (the sum of aquifer depletion and reservoir storage) and (d) and the rate of change (10 year centred average) for the terms in (a) to (c). Individual model simulations are shown by grey lines with the model average shown in black (thermal expansion) and purple (glaciers). The estimated glacier contributions estimated by Cogley (2009, green), Leclercq et al (2011, red) and using the model of Marzeion et al (2012, dark blue) forced by observed climate are also shown in (b). All curves in (a) and (b) are normalized over the period 1980\u20131999 and the colours in (d) are matched to earlier panels.", "source": "https://sealeveldocs.readthedocs.io/en/latest/church13.html"}
{"id": "0b3d18ead65a-1", "text": "Figure 1: Comparisons of modelled and observed (a) ocean thermal expansion (observations in blue), (b) glacier contributions, (c) changes in terrestrial storage (the sum of aquifer depletion and reservoir storage) and (d) and the rate of change (10 year centred average) for the terms in (a) to (c). Individual model simulations are shown by grey lines with the model average shown in black (thermal expansion) and purple (glaciers). The estimated glacier contributions estimated by Cogley (2009, green), Leclercq et al (2011, red) and using the model of Marzeion et al (2012, dark blue) forced by observed climate are also shown in (b). All curves in (a) and (b) are normalized over the period 1980\u20131999 and the colours in (d) are matched to earlier panels.\nModelled thermal expansion (figures 1(a), (d)) falls slightly following the volcanic eruption of Santa Maria in 1902. The rate of expansion is then relatively constant up until the eruption of Mt Agung in 1963 when there is a significant fall in sea level. There are similar falls in sea level following the eruptions of El Chichon in 1982 and Mt Pinatubo in 1991. The increase in sulfur dioxide emissions by more than a factor of two from 1950 to 1975 (Smith et al 2011) results in an increasingly negative aerosol forcing that partially offsets the increasing greenhouse gas concentrations leading to a slower rate of warming (and thermal expansion) after 1960 (Church et al 2011b). Over the 20th century, there is a clear increase in the rate of rise with the fastest rate occurring from 1993. This latter increase is a result of increasing greenhouse gas concentrations, recovery from impacts of the Mt Pinatubo eruption (Gregory et al 2006, Gleckler et al 2006, Church et al 2005, Domingues et al 2008, Gregory et al 2013a) and falling sulfur dioxide emissions from 1975 to 2000 (Smith et al 2011).\nGlacier contributions\uf0c1\nMarzeion et al (2012) use an (offline) glacier model forced by regional surface temperatures and precipitation from AOGCM CMIP5 climate simulations to estimate glacier contributions for the 20th century (figures 1(b), (d), grey and purple lines). Their model is calibrated using individual glacier mass balance observations also used by Cogley (2009), such that the Marzeion et al (2012) results are neither strictly independent from the Cogley (2009) results, nor from observations. However, the dependency is very weak, since only about 0.1% of all the world\u2019s glaciers are included in these observations (substantially less in terms of surface area and ice volume, and with a mean time series length of only 15 years). Two different validation methods in Marzeion et al (2012) show that the model is able to reconstruct observed glacier changes independent of the observations, such that the combined contribution of all the glaciers to sea level is in fact only weakly dependent on the observations of individual glacier contributions. From 1950, the model results (15 available models) used by Marzeion et al are not significantly different from the observed estimated changes in glacier mass of Cogley (2009) and the estimates based on glacier length from Leclercq et al (2011). The Marzeion et al modelled rate of rise is almost constant during the first half of the century up until 1960 but larger than the Leclercq et al estimate (that also relies on Cogley), then smaller until the 1990s (figure 1(d)), after which it increases. Loss of glacier area at low altitudes combined with the stabilization of temperatures for the 1950\u20131975 period could have contributed to this slowing of the rate of glacier contribution.\nGreenland and Antarctic contributions\uf0c1\nThe contributions of the Greenland and Antarctic Ice Sheets for the 20th century are poorly determined. Observational estimates for 1993\u20132011 (Shepherd et al 2012) indicate a net contribution of about 11 mm, about two thirds of this from Greenland. Models of surface mass balance (using AOGCM results) for Greenland agree with the increased surface mass loss over the last two decades but indicate little impact on sea level over previous decades, and with divergent results for the first half of the 20th century. (See Gregory et al (2013a) for a full discussion.) Recent model results for four major Greenland outlet glaciers (Helheim, Jakobshavn, Petermann and Kangerdlugssuaq) forced by changes in ocean temperatures (Nick et al 2009, and personal communication) indicate a contribution of order 0.6 mm yr\u22121 for 2000\u201310, consistent with the observational estimates. However, we are unaware of any completed model simulations of the Greenland Ice Sheet contribution for the 20th century using the new generation of ice sheet models.\nFor Antarctica, Levermann et al (2012) have recently completed an ice sheet model simulation for the 20th century using ocean temperatures on the shelf near Antarctica and atmosphere\u2013ice exchange from the CMIP5 AOGCMs, with an allowance for a delay of the warming to penetrate underneath the ice shelves. The 20th century contribution is only 4 mm, mostly since 1990, similar to recent observational estimates (Shepherd et al 2012).\nThese results indicate significant progress in modelling ice sheet response to climate and ocean forcing. However, as they are as yet incomplete, we have not included these new model results here. Instead, we include estimates of these terms in section 3 and discuss the implications in section 4.\nLand-water storage\uf0c1\nInternally generated climate variability influences the amount of water stored as soil moisture and in lakes, rivers and reservoirs. On short timescales, the rate of change in the storage can be several millimetres leading to rapid rates of sea-level change (Boening et al 2012). However, over decadal timescales the net contribution is small (Ngo-Duc et al 2005) and hence for the comparison we ignore this contribution.\nThere are also direct human related interventions in the hydrological cycle that impact the amount of water stored on land. This occurs principally through the building of reservoirs (Chao et al 2008, Lettenmaier and Milly 2009) and the depletion of groundwater (Konikow 2011, Wada et al 2012). For reservoir storage, we use the estimates of Chao et al with no allowance for seepage (as in Gregory et al 2013a). We assume that the reservoirs are on average 85% full (with a range of 70\u2013100%). For groundwater depletion, we average the observational estimates of Konikow (2011) and model results of Wada et al (2012). Over the first half of the 20th century, both of these terms are small (figure 1(c)). After 1950, the significant increase in the rate of dam building leads to negative contribution to sea-level change. From the 1980s, a slowing in the rate of dam building and an increase in the rate of groundwater depletion leads to a small positive contribution to sea-level rise (figures 1(c) and (d)).\nObserved and modelled sea-level change 1900\u20132012\uf0c1\nWe compare the sum of the ocean thermal expansion, glacier and estimated land-water contributions (available for 13 models) with observational estimates of global mean sea level of CW11 and Ray and Douglas (2011) [RD]; figure 2. Both estimates are similar over the 20th century (RD has a slightly larger trend), with a broad maximum in the rate of rise from 1930 to 1950, a minimum about 1960 and then a rising trend to the end of the records. Both series have a minimum in the rate of rise in the 1920s and a maximum in the 1970s, but it is unclear if these two features are robust or an indication of the inadequacy of the available sea-level data.", "source": "https://sealeveldocs.readthedocs.io/en/latest/church13.html"}
{"id": "0b3d18ead65a-2", "text": "There are also direct human related interventions in the hydrological cycle that impact the amount of water stored on land. This occurs principally through the building of reservoirs (Chao et al 2008, Lettenmaier and Milly 2009) and the depletion of groundwater (Konikow 2011, Wada et al 2012). For reservoir storage, we use the estimates of Chao et al with no allowance for seepage (as in Gregory et al 2013a). We assume that the reservoirs are on average 85% full (with a range of 70\u2013100%). For groundwater depletion, we average the observational estimates of Konikow (2011) and model results of Wada et al (2012). Over the first half of the 20th century, both of these terms are small (figure 1(c)). After 1950, the significant increase in the rate of dam building leads to negative contribution to sea-level change. From the 1980s, a slowing in the rate of dam building and an increase in the rate of groundwater depletion leads to a small positive contribution to sea-level rise (figures 1(c) and (d)).\nObserved and modelled sea-level change 1900\u20132012\uf0c1\nWe compare the sum of the ocean thermal expansion, glacier and estimated land-water contributions (available for 13 models) with observational estimates of global mean sea level of CW11 and Ray and Douglas (2011) [RD]; figure 2. Both estimates are similar over the 20th century (RD has a slightly larger trend), with a broad maximum in the rate of rise from 1930 to 1950, a minimum about 1960 and then a rising trend to the end of the records. Both series have a minimum in the rate of rise in the 1920s and a maximum in the 1970s, but it is unclear if these two features are robust or an indication of the inadequacy of the available sea-level data.\nThe sum of the modelled ocean thermal expansion, glacier, and terrestrial storage contributions from 1900 to 2010 (figure 2(a)) ranges from 110 mm to almost 200 mm with a model average of 153 mm. The spread of models encompasses the GMSL estimate of CW11 but is slightly less than RD. The average of the model results explains about 80% of the observed rise. The average modelled rate of sea-level rise (figure 2(b)) is more than 1 mm yr\u22121 prior to 1950, as a result of early 20th century warming and thermal expansion and increased glacier melting, but is somewhat less than the observed rate over 1930\u201350. The average modelled rate of rise decreases to less than 0.5 mm yr\u22121 in the 1960s before increasing again to reach a maximum of 3 mm yr\u22121 in 2000, about double the 20th century average and substantially greater than the modelled rate of rise in the first half of the 20th century. The slower rate of rise from 1950 to 1980 is likely a result of the impact of volcanic eruptions, the increase in tropospheric aerosol loading (emissions peak in the 1970s) on the modelled ocean thermal expansion and glacier melting contributions, a loss of glacier area following early 20th century melting and an increase in the rate of reservoir storage.\nFigure 2: The sum of the modelled contributions from ocean thermal expansion, increased glacier melting and changes in land-water storage. The light grey lines are individual models with the black line the model mean. The 20th estimates of global mean sea level are indicated by the blue (CW11) and green (RD) lines with the shading indicating the uncertainty estimates (two standard deviations). The satellite altimeter data since 1993 is shown in red. The adjusted model mean (dashed black line) is the model mean after an allowance for the impact of natural variability on glacier contributions and a potential long-term ice sheet contribution are included. The results are given (a) for the period 1900\u20132010, (b) the rates of sea-level change for the same period, (c) for 1961\u20132010, and (d) for 1990\u20132010. The dotted black line is after inclusion of the Shepherd et al (2012) ice sheet observational estimates but excluding the peripheral glacier contribution (to avoid double counting). The red dot is the average rate from the altimeter record.\nFor the period since 1961 (figure 2(c)), the modelled rise ranges from about 50 to 110 mm and encompasses the observed rise of close to 90 mm, with the model average rise of 75 mm explaining about 85% of the observed rise. Since 1990 (the start of the projections for the TAR and the AR4; figure 2(d)), the modelled sea-level rise ranges from 30 to 65 mm and encompasses the observed rise of about 55 mm, with the average model rise of 51 mm explaining over 90% of the observed rise. The model average rate over 1993\u20132010 of 3 mm yr\u22121 is almost equal to the rate of 3.2 \u00b1 0.4 mm yr\u22121 observed with satellite altimeters (with both rates being very linear). The increased rate of the modelled rise from 1980 to 2000, and particularly after 1993, is a result of continued increases in greenhouse gas concentrations, the recovery of the climate system from the series of volcanic eruptions (particularly Mt Pinatubo in 1993), decreasing sulfur dioxide emissions from 1975 to 2000 and increasing land-water contributions.\nOther effects on sea-level change\uf0c1\nThere are at least two potential additional contributions to 20th century sea-level change. Firstly, the ice sheets are often assumed to have been in a state of approximate mass balance, hence making zero net contribution to sea level before the major increase in greenhouse gas emissions of the 20th century. However, the long response time of the Antarctic and (to a lesser extent) Greenland ice sheets means that there may be a small ongoing contribution to sea-level change due to climate change in previous centuries or millennia (Huybrechts et al 2011). An ongoing contribution of 0.0\u20130.2 mm yr\u22121 was considered in the sea-level budget studies of Gregory et al (2013a) and Church et al (2011b). Here we have added a 0.1 mm yr\u22121 contribution to the above modelled estimates (10 mm over the 20th century).\nSecondly, there may be contributions related to internally generated variability on decadal timescales (Delworth and Knutson 2000). Marzeion et al (2012) have also computed glacier mass changes using observed rather than simulated temperature change (figure 1(b), blue line). An additional contribution of about 20 mm is estimated to occur between 1920 and 1960, with the largest additional contribution in the 1930s (the difference between the blue and purple lines in figure 1(b)). While the Leclercq et al (2011) estimates from measurements of glacier length indicate a smaller overall contribution during the 20th century, they also give a greater rate of mass contribution from 1920 to 1940 than for earlier and later periods. These additional early 20th century contributions are a result of a regional warming over Greenland during this period (Chylek et al 2004).\nWhen these two terms are added to the AOGCM results, the sea-level rise over the 20th century (figure 2(a), dashed line) is 176 mm, which is over 90% of the observed GMSL estimate, and both observed time series lie within the model spread (the individual model results have not been replotted after the addition of these terms). The modelled rate of rise in the first half of the 20th century is now closer to the observed rate and the observed rate lies within the spread of the model rates through nearly all of the century, although the timing of the faster rate of rise occurs slightly earlier in the model results than in the observations. There is little change to the simulations from the additional terms for the periods since 1961 and 1990 and the average model results for these periods remain within 20% of the observed rise (figures 2(c), (d)). The observational estimates (Shepherd et al 2012) indicate a small 20th century ice sheet contribution that would further close the gap between the observed and modelled sea-level rise to about 10% or better, as depicted by the dotted lines in figure 2.\nDiscussion\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/church13.html"}
{"id": "0b3d18ead65a-3", "text": "Secondly, there may be contributions related to internally generated variability on decadal timescales (Delworth and Knutson 2000). Marzeion et al (2012) have also computed glacier mass changes using observed rather than simulated temperature change (figure 1(b), blue line). An additional contribution of about 20 mm is estimated to occur between 1920 and 1960, with the largest additional contribution in the 1930s (the difference between the blue and purple lines in figure 1(b)). While the Leclercq et al (2011) estimates from measurements of glacier length indicate a smaller overall contribution during the 20th century, they also give a greater rate of mass contribution from 1920 to 1940 than for earlier and later periods. These additional early 20th century contributions are a result of a regional warming over Greenland during this period (Chylek et al 2004).\nWhen these two terms are added to the AOGCM results, the sea-level rise over the 20th century (figure 2(a), dashed line) is 176 mm, which is over 90% of the observed GMSL estimate, and both observed time series lie within the model spread (the individual model results have not been replotted after the addition of these terms). The modelled rate of rise in the first half of the 20th century is now closer to the observed rate and the observed rate lies within the spread of the model rates through nearly all of the century, although the timing of the faster rate of rise occurs slightly earlier in the model results than in the observations. There is little change to the simulations from the additional terms for the periods since 1961 and 1990 and the average model results for these periods remain within 20% of the observed rise (figures 2(c), (d)). The observational estimates (Shepherd et al 2012) indicate a small 20th century ice sheet contribution that would further close the gap between the observed and modelled sea-level rise to about 10% or better, as depicted by the dotted lines in figure 2.\nDiscussion\uf0c1\nOcean thermal expansion and the increased melting of glaciers are the two dominant contributions to 20th century sea-level rise in the simulations, with a smaller contribution from changes in land-water storage. Each of these components has its own unique temporal dependence. The model results indicate that most of the variation in the thermal expansion and glacier contributions to global mean sea level is a response to radiative forcing of the climate system from changes in concentrations of greenhouse gases, stratospheric volcanic aerosol and tropospheric anthropogenic aerosol. Observations in the latter half of the 20th century provide strong support for and confidence in the model simulations of these components. However, since parameters in the glacier model are estimated from observations in the latter half of the 20th century, the evaluation of the glacier models is not a fully independent test of their skill.\nNot all 20th century sea-level rise is necessarily externally forced. There is evidence for an enhanced glacier contribution in the first half of the 20th century (Marzeion et al 2012, Leclercq et al 2011). Since climate models can simulate early 20th century global averaged temperature well (Stott et al 2000), the difference between the two glacier estimates may be partly related to regional climate changes (rather than global averaged temperatures), although natural variability impacts both regional and global averaged temperatures (Delworth and Knutson 2000). The extent to which internally generated climate variability can lead to enhanced sea-level rise deserves further investigation. If the apparent impact during the first half of the 20th century was repeated in the future, it would increase projections for the 21st century by the order of 20 mm. However this additional sea-level rise will enter the calibrations of SEMs that use global averaged temperatures (or radiative forcing) and thus will impact the SEM projections.\nThe range of the model simulations over the three periods, and particularly since 1961 and 1990, encompasses the observed sea-level rise with the model mean within 20% (about 10% since 1990) of the observed rise. Experience with multi-model ensembles is that they generally outperform individual models (Weigel et al 2008, 2010), but specific results are not available for sea level. The agreement of observations with the model mean represents a significant improvement since the IPCC TAR (Church et al 2001) and AR4 (Hegerl et al 2007) and is a reason for increased confidence in the next generation of global mean sea-level projections. This agreement also means that it should now be possible to attribute 20th century sea-level rise to the various climate forcings. Reasons for the improvement include allowance for the omission of volcanic forcing in the spin-up of the AOGCMs, more complete representation of the radiative forcing driving the AOGCMs, a larger initial glacier mass (Arendt et al 2012) and more complete observations of glacier mass loss (Cogley 2009). Also, the Marzeion et al glacier model is able to reconstruct observed glacier changes independent of the observations and is an important part of the improved representation of 20th century sea-level rise.\nSignificant challenges remain. It is likely that the model spread does not cover the full range of possibilities because of systematic uncertainties that are common to many models. Hence, the model spread found here (about 40% of the observed rise for the 20th century and more than 50% since 1961) may underestimate the full uncertainty, particularly as it was not possible to include models of the ice sheet components. The observational estimates of ice sheet contributions since 1993 further close the gap between the observed and modelled sea-level rise to 10% or better. This evaluation is also incomplete as the ice sheet contributions to date are only a small fraction for the potential longer-term contributions. Careful comparison of the new generation of ice sheet simulations with observations is required to critically evaluate them.\nChambers et al (2012) argue there is an apparent 60 year cycle in the observed sea-level record. Similar variability is present in the forced simulations of the first half of the 20th century but is enhanced when the additional glacier contributions are included in the sum of terms. For the latter half of the 20th century, the observed minimum in the rate of sea-level rise in the 1960s (a deceleration from 1940 to 1970) and the subsequent increase in rate to about twice the 20th century average at the end of the record is present in the forced sea-level estimates. This increase is principally in response to increasing greenhouse gas concentrations and a combination of changing volcanic forcing and tropospheric aerosol loading, leading to a larger ocean thermal expansion and increased glacier melting. There is an additional contribution of less than 20% from anthropogenic interference in the hydrological cycle (figures 1(c) and (d)). Thus, the observed increased rate of rise since 1990 is not part of a natural cycle but a direct response to increased radiative forcing (both anthropogenic and natural) of the climate system. This radiative forcing will continue to increase with ongoing greenhouse gas emissions. The simulation of the observed 20th century sea-level rise and its variability within the uncertainties is a reason for increased confidence in projections of 21st century sea-level rise in future projections.", "source": "https://sealeveldocs.readthedocs.io/en/latest/church13.html"}
{"id": "5078fc646d68-0", "text": "Church and White (2011)\uf0c1\nTitle:\nSea-Level Rise from the Late 19th to the Early 21st Century\nKeywords:\nSea level, Climate change, Satellite altimeter, Tide gauge\nCorresponding author:\nChurch\nCitation:\nChurch, J. A. & White, N. J. (2011). Sea-Level Rise from the Late 19th to the Early 21st Century. Surveys in Geophysics, 32, 585\u2013602.\nURL:\nhttps://link.springer.com/article/10.1007/s10712-011-9119-1\nAbstract\uf0c1\nWe estimate the rise in global average sea level from satellite altimeter data for 1993\u00d02009 and from coastal and island sea-level measurements from 1880 to 2009. For 1993-2009 and after correcting for glacial isostatic adjustment, the estimated rate of rise is 3.2 \u00b1 0.4 mm year$^{-1}$ from the satellite data and 2.8 \u00b1 0.8 mm year$^{-1}$ from the in situ data. The global average sea-level rise from 1880 to 2009 is about 210 mm. The linear trend from 1900 to 2009 is 1.7 \u00b1 0.2 mm year$^{-1}$ and since 1961 is 1.9 \u00b1 0.4 mm year$^{-1}$. There is considerable variability in the rate of rise during the twentieth century but there has been a statistically significant acceleration since 1880 and 1900 of 0.009 \u00b1 0.003 mm year$^{-2}$ and 0.009 \u00b1 0.004 mm year$^{-2}$, respectively. Since the start of the altimeter record in 1993, global average sea level rose at a rate near the upper end of the sea level projections of the Intergovernmental Panel on Climate Change\u00d5s Third and Fourth Assessment Reports. However, the reconstruction indicates there was little net change in sea level from 1990 to 1993, most likely as a result of the volcanic eruption of Mount Pinatubo in 1991.\nIntroduction\uf0c1\nRising sea levels have important direct impacts on coastal and island regions where a substantial percentage of the world\u2019s population lives (Anthoff et al. 2006). Sea levels are rising now and are expected to continue rising for centuries, even if greenhouse gas emissions are curbed and their atmospheric concentrations stabilized. Rising ocean heat content (and hence ocean thermal expansion) is an important element of climate change and sea-level rise. The remaining contributions to sea-level rise come principally from the melting of land ice: glaciers and ice caps (which include the small glaciers and ice caps fringing the major ice sheets) and the major ice sheets of Antarctica and Greenland, with additional contributions from changes in the storage of water on (or in) land. (See Church et al. 2010 for a summary of issues). Correctly estimating historical sea-level rise and representing global ocean heat uptake in climate models are both critical to projecting future climate change and its consequences. The largest uncertainty in projections of sea-level rise up to 2100 is the uncertainty in global mean sea level (GMSL) and thus improving estimates of GMSL rise (as well as regional variations in sea level) remains a high priority.\nSince late 1992, high quality satellite altimeters (TOPEX/Poseidon, Jason-1, and OSTM/Jason-2) have provided near global measurements of sea level from which sea-level rise can be estimated. However, this altimeter record is still short (less than 20 years) and there is a need to know how sea level has varied over multi-decadal and longer time scales. Quantifying changes in the rate of sea-level rise and knowing the reasons for such changes are critical to improving our understanding of twentieth century sea-level rise and improving our projections of sea-level change for the twenty first century and beyond.\nFor the period prior to the altimeter record, estimates of sea-level change are dependent on a sparsely distributed network of coastal and island tide-gauge measurements (Wood.worth and Player 2003). Even today, there are many gaps in the global network of coastal and island sea-level measurements and the network was sparser early in the twentieth century and in the nineteenth century. Many previous studies have used the individual sea-level records (corrected for vertical land motion) to estimate the local rate of sea-level rise (as a linear trend; e.g. Douglas 1991) and some studies attempted to detect an acceleration in the local rate of sea-level rise (Woodworth 1990; Woodworth et al. 2009; Douglas 1992). However, these individual records have considerable interannual and decadal var.iability and thus long records are required to get accurate estimates of the local trends in sea level (Douglas 2001). These authors assumed that these long-term trends are either representative of the global averaged rise or a number of records have been averaged, in some cases regionally and then globally, to estimate the global average rate of rise. However, the modern satellite record has made it clear that sea level is a dynamic quantity and it does not rise uniformly around the globe.\nSea level at any location contains the in\u00dfuences of local and regional meteorological effects (including storm surges), modes of climate variability (for example the El Nino-Southern Oscillation) and long-term trends (from both the ocean surface and land move.ments), including the impact of anthropogenic climate change. As the altimeter record has clearly demonstrated, GMSL has much less short term variability (more than an order of magnitude) than sea level at individual locations because while the volume of the oceans is nearly constant the distribution changes with time. While the variability at individual locations can be minimised by low pass filtering, there remains significant energy at yearly to decadal periods that may be either positively or negatively correlated between stations, thus confounding estimates of GMSL rise when few records are available.\nTo date, there have been two approaches to determining time series of GMSL from coastal and island tide gauges. The first and most straight forward approach averages the sea-level records (corrected for land motion) from individual locations. When there are only a small number of locations with continuous records, this approach is relatively straight forward, although care must be taken to remove data inhomogeneities. When more gauges are used, the records usually have different lengths and starting times. It is then necessary to average the rates of rise over some time step and integrate the results to get the sea-level change. Holgate and Woodworth (2004) used this approach and Jevrejeva et al. (2006) used a virtual station method of averaging neighbouring station sea-level changes in several regions and then averaging to get the global mean sea-level change. No attempt was made to interpolate between the locations of observations and thus to estimate deep ocean sea level. Thus these are essentially estimates of coastal sea-level change. However, note that White et al. (2005) argued that over longer periods the rates of coastal and global rise are similar.\nThe second approach uses spatial functions which represent the large-scale patterns of variability to interpolate between the widely distributed coastal and island sea-level observations and thus to estimate global sea level (as distinct from coastal sea level). This technique was first developed by Chambers et al. (2002) for interannual sea-level variability and extended by Church et al. (2004) to examine sea-level trends. The Church et al. approach uses the Reduced Space Optimal Interpolation technique (Kaplan et al. 2000) developed for estimating changes in sea-surface temperature and atmospheric pressure. The spatial functions used are the empirical orthogonal functions (EOFs) of sea-level variability estimated from the satellite altimeter data set from TOPEX/Poseidon, Jason-1 and OSTM/Jason-2 satellite data, which now cover the period from January 1993 into 2011. We use data from January 1993 through December 2009 in this paper.\nHere, we update previous estimates of GMSL rise for the period of the instrumental record using a longer (17 years) altimeter data set and an expanded in situ sea-level observational data set extending back to 1860. We use the Reduced Space Optimal Interpolation technique to quantify the rate of sea-level rise and the changes in the rate since 1880.\nMethods and Data\uf0c1\nIn Situ Sea-Level Data\uf0c1\nWe use monthly sea-level data downloaded from the Permanent Service for Mean Sea Level (PSMSL; Woodworth and Player 2003) web site (http://www.psmsl.org) in August 2010. Careful selection and editing criteria, as given by Church et al. (2004) were used. The list of stations used in the reconstruction is available on our web site at http://www.cmar.csiro.au/sealevel/sl_data_cmar.html. Tide gauge records are assigned to the nearest locations (with good satellite altimeter data) on the 1\u02da-by-1\u02da grid of the satellite altimeter based EOFs. Where more than one record is assigned to a single grid point they are averaged. Changes in height from 1 month to the next are stored for use in the reconstruction.", "source": "https://sealeveldocs.readthedocs.io/en/latest/churchwhite11.html"}
{"id": "5078fc646d68-1", "text": "The second approach uses spatial functions which represent the large-scale patterns of variability to interpolate between the widely distributed coastal and island sea-level observations and thus to estimate global sea level (as distinct from coastal sea level). This technique was first developed by Chambers et al. (2002) for interannual sea-level variability and extended by Church et al. (2004) to examine sea-level trends. The Church et al. approach uses the Reduced Space Optimal Interpolation technique (Kaplan et al. 2000) developed for estimating changes in sea-surface temperature and atmospheric pressure. The spatial functions used are the empirical orthogonal functions (EOFs) of sea-level variability estimated from the satellite altimeter data set from TOPEX/Poseidon, Jason-1 and OSTM/Jason-2 satellite data, which now cover the period from January 1993 into 2011. We use data from January 1993 through December 2009 in this paper.\nHere, we update previous estimates of GMSL rise for the period of the instrumental record using a longer (17 years) altimeter data set and an expanded in situ sea-level observational data set extending back to 1860. We use the Reduced Space Optimal Interpolation technique to quantify the rate of sea-level rise and the changes in the rate since 1880.\nMethods and Data\uf0c1\nIn Situ Sea-Level Data\uf0c1\nWe use monthly sea-level data downloaded from the Permanent Service for Mean Sea Level (PSMSL; Woodworth and Player 2003) web site (http://www.psmsl.org) in August 2010. Careful selection and editing criteria, as given by Church et al. (2004) were used. The list of stations used in the reconstruction is available on our web site at http://www.cmar.csiro.au/sealevel/sl_data_cmar.html. Tide gauge records are assigned to the nearest locations (with good satellite altimeter data) on the 1\u02da-by-1\u02da grid of the satellite altimeter based EOFs. Where more than one record is assigned to a single grid point they are averaged. Changes in height from 1 month to the next are stored for use in the reconstruction.\nThe number of locations with sea-level data available for the reconstruction is larger than in our earlier 2004 (Church et al. 2004) and 2006 (Church and White 2006) studies, particularly prior to 1900 (Figure 1). In the 1860s there are only 7-14 locations available, all north of 30\u02daN. In the 1870s, there is one record available South of 30\u02daN but still none in the southern hemisphere and it is only in the second half of the 1880s (Fort Denison, Sydney, Australia starts in January 1886) that the first southern hemisphere record becomes available. While we attempted the reconstruction back to 1860, the results showed greater sensitivity to details of the method prior to the 1880s when the first southern hemisphere record is available (see below for further discussion). As a result, while we show the reconstruction back to 1860, we restricted the subsequent analysis (computation of trends, etc.) to after 1880. The number of locations with data available increases to 38 in 1900 (from 71 individual gauges), including several in the southern hemisphere, to about 85 locations in 1940 (from 130 individual gauges but with still less than 10 in the southern hemisphere), and to about 190 in 1960 (from about 305 individual gauges with about 50 locations in the southern hemisphere). The number of locations peaks in May 1985 at 235 (from 399 individual gauges, with slightly less than one-third in the ocean-dominated southern hemisphere; Figure 1). The largest gaps are in the Southern Ocean, the South Atlantic Ocean and around Africa (Figure 1f). Through the 1990s there are at least 200 locations available from between 370 and 400 gauges. For the last few years there are fewer records available because of the unavoidable delay in the transmission by national authorities of monthly and annual mean information to the PSMSL. In December 2009, there are 135 locations available from 250 gauges.\nFigure 1: The number and distribution of sea-level records available for the reconstruction. (a) The number of locations for the globe and the northern and southern hemispheres. (b-f) indicate the distribution of gauges in the 1880s, 1910s, 1930s, 1960s and 1990s. The locations indicated have at least 60 months of data in the decade and the number of records are indicated in brackets.\uf0c1\nSea-level measurements are affected by vertical land motion. Corrections for local land motion can come from long-term geological observations of the rate of relative local sea-level change (assuming the relative sea-level change on these longer times scales is from land motions rather than changing ocean volume), or from models of glacial isostatic adjustment, or more recently from direct measurements of land motion with respect to the centre of the Earth using Global Positioning System (GPS) observations. Here, the ongoing response of the Earth to changes in surface loading following the last glacial maximum were removed from the tide-gauge records using the same estimate of glacial isostatic adjustment (GIA; Davis and Mitrovica 1996; Milne et al. 2001) as in our earlier study (Church et al. 2004).\nWe completed the analysis with and without correction of the sea-level records for atmospheric pressure variations (the \u201cinverse barometer\u201d effect). The HadSLP2 global reconstructed atmospheric pressure data set (Allan and Ansell 2006) was used for this correction.\nWe tested the impact of correcting the tide-gauge measurements for terrestrial loading and gravitational changes resulting from dam storage (Fiedler and Conrad 2010). For the large number of tide gauges used in the period of major dam building after 1950 (mostly over 200), the impact on global mean sea level is only about 0.05 mm year^{-1} (smaller than the 0.2 mm year^{-1} quoted by Fiedler and Conrad, which is for a different less globally-distributed set of gauges). Tests of similar corrections for changes in the mass stored in glaciers and ice caps, and the Greenland and Antarctic Ice Sheets show that these effects have an even smaller impact on GMSL.\nSatellite Altimeter Data Processing Techniques\uf0c1\nThe TOPEX/Poseidon, Jason-1 and OSTM/Jason-2 satellite altimeter missions measure sea surface height (SSH) relative to the centre of mass of the Earth along the satellite ground track. A number of instrumental and geophysical corrections must be applied. Every 10 days (one cycle) virtually global coverage of the world\u00d5s ocean, between 66\u02daN and S, is achieved. Our gridded data set as used here goes to 65\u02daN and S.\nOur satellite altimeter data processing mostly follows the procedures, and uses the edits and tests, recommended by the providers of the satellite altimeter data sets, and are similar to those described in Leuliette et al. (2004). The documents for the three missions used are Benada (1997) for TOPEX/Poseidon, Aviso (2003) for Jason-1 and CNES (2009) for OSTM/Jason-2.\nOrbits from the most recent versions of the Geophysical Data Records (GDR \u00deles; MGDR-B for TOPEX/Poseidon, GDR-C for Jason-1 and GDR-T for OSTM/Jason-2) are used. GDR corrections from the same \u00deles for tides, wet troposphere, dry troposphere, ionosphere, sea-state bias (SSB), inverse barometer correction (when required) and the mean sea surface are applied in accordance with these manuals, except for some TOPEX/ Poseidon corrections: firstly, the TOPEX/Poseidon wet troposphere correction has been corrected for drift in one of the brightness temperature channels (Ruf 2002) and offsets related to the yaw state of the satellite (Brown et al. 2002). Secondly, the inverse barometer correction (when used) has been recalculated using time-variable global-mean over-ocean atmospheric pressure, an improvement on the GDR-supplied correction which assumes a constant global-mean over-ocean atmospheric pressure. This approach makes the correction used for TOPEX/Poseidon consistent with the Jason-1 and OSTM/Jason-2 processing.", "source": "https://sealeveldocs.readthedocs.io/en/latest/churchwhite11.html"}
{"id": "5078fc646d68-2", "text": "Satellite Altimeter Data Processing Techniques\uf0c1\nThe TOPEX/Poseidon, Jason-1 and OSTM/Jason-2 satellite altimeter missions measure sea surface height (SSH) relative to the centre of mass of the Earth along the satellite ground track. A number of instrumental and geophysical corrections must be applied. Every 10 days (one cycle) virtually global coverage of the world\u00d5s ocean, between 66\u02daN and S, is achieved. Our gridded data set as used here goes to 65\u02daN and S.\nOur satellite altimeter data processing mostly follows the procedures, and uses the edits and tests, recommended by the providers of the satellite altimeter data sets, and are similar to those described in Leuliette et al. (2004). The documents for the three missions used are Benada (1997) for TOPEX/Poseidon, Aviso (2003) for Jason-1 and CNES (2009) for OSTM/Jason-2.\nOrbits from the most recent versions of the Geophysical Data Records (GDR \u00deles; MGDR-B for TOPEX/Poseidon, GDR-C for Jason-1 and GDR-T for OSTM/Jason-2) are used. GDR corrections from the same \u00deles for tides, wet troposphere, dry troposphere, ionosphere, sea-state bias (SSB), inverse barometer correction (when required) and the mean sea surface are applied in accordance with these manuals, except for some TOPEX/ Poseidon corrections: firstly, the TOPEX/Poseidon wet troposphere correction has been corrected for drift in one of the brightness temperature channels (Ruf 2002) and offsets related to the yaw state of the satellite (Brown et al. 2002). Secondly, the inverse barometer correction (when used) has been recalculated using time-variable global-mean over-ocean atmospheric pressure, an improvement on the GDR-supplied correction which assumes a constant global-mean over-ocean atmospheric pressure. This approach makes the correction used for TOPEX/Poseidon consistent with the Jason-1 and OSTM/Jason-2 processing.\nCalibrations of the TOPEX/Poseidon data against tide gauges have been performed by Gary Mitchum and colleagues (see, e.g., Nerem and Mitchum 2001). Here and in earlier publications, we have used the calibrations up to the end of 2001 (close to the end of the TOPEX/Poseidon mission). One of the problems these calibrations address is the changeover to the redundant \u201cside B\u201d altimeter electronics in February 1999 (at the end of cycle 235) due to degradation of the \u00d4\u00d4side A\u00d5\u00d5 altimeter electronics which had been in use since the start of the mission. An alternative processing approach to address the side A to side B discontinuity is to use the separate Chambers et al. (2003) SSB models for TOPEX sides A and B without any use of the Poseidon data, as this correction does not address the substantial drift in the Poseidon SSH measurements, especially later in the mission. No tide-gauge calibrations are applied to Jason-1 or OSTM/Jason-2 data. The altimeter data sets as used here are available on our web site at http://www.cmar.csiro.au/sealevel/sl_data_cmar.html.\nThe Analysis Approach\uf0c1\nThe full details of our approach to estimating historical sea level were reported in Church et al. (2004). Briefly, the reconstructed sea level H^r(x, y, t) is represented as\nH^r(x, y, t) = U^r(x, y) alpha(t) + epsilon\nwhere U^r(x, y) is a matrix of the leading empirical orthogonal functions (EOFs) calculated from monthly satellite altimeter data mapped (using a Gaussian filter with a length scale of 300 km applied over a square with sides of 800 km) to a one degree by one degree grid for the ice free oceans between 65\u00fbS and 65\u00fbN, epsilon is the uncertainty, x and y are latitude and longitude and t is time. This matrix is augmented by an additional \u201cmode\u201d that is constant in space and used to represent any global average sea-level rise. In the reduced space optimal interpolation, the amplitude of the constant mode and these EOFs are calculated by minimising the cost function\nS(alpha) = (K U^r alpha - H^0)^T M^{-1} (K U^r alpha - H^0) + alpha^T Lambda alpha\nThis cost function minimises the difference between the reconstructed sea levels and the observed coastal and island sea levels H^0, allowing for a weighting related to the observational uncertainties, omitted EOFs and also down-weights higher order EOFs. K is a sampling operator equal to 1 when there is observed sea-level data available and 0 otherwise, Lambda is the diagonal matrix of the eigenvalues of the covariance matrix of the altimeter data and M is the error covariance matrix given by\nM = R + KU\u2019 Lambda\u2019 U\u2019^{T}K^T\nwhere R is the matrix of the covariance of the instrumental errors (assumed diagonal here) and the primes indicate the higher order EOFs not included in the reconstruction.\nThe EOFs are constructed from the covariances of the altimeter sea-level data after removal of the mean. Any overall increase in sea level as a result of ocean thermal expansion or the addition of mass to the ocean is difficult to represent by a finite number of EOFs. We therefore include an additional \u201cmode\u201d which is constant in space to represent this change in GMSL.\nBecause the sea-level measurements are not related to a common datum, we actually work with the change in sea level between time steps and then integrate over time to get the solution. The least squares solution provides an estimate of the amplitude of the leading EOFs, global average sea-level and error estimates.\nChristiansen et al. (2010) tested the robustness of various reconstruction techniques, including an approach similar to that developed by Church et al. (2004) using thermosteric sea level calculated from climate model results. They used an ensemble of model results (derived by randomising the phase of the principal components of the model sea level, see Christiansen et al. (2010) for details). For a method similar to that used here (including the additional \u201cconstant\u201d mode and for a 20 year period for determining the EOFs), the trend in the ensemble mean reconstruction was within a few percent of the true value when 200 gauges were available (with about a 10% variation for the inter.quartile range of individual estimates, decreasing to about 5% when a 50 year period for determining the EOFs was available). When only 40 gauges were used, the ensemble mean trend was biased low by a little under 10% (with an interquartile range of about 15%). They further showed that the reconstructions tend to overestimate the interannual variability and that a longer period for determining the EOFs is important in increasing the correlation between the reconstructed and model year to year variability. Reconstructions that do not use the constant mode perform poorly compared to those that do. These results are similar to our own tests with climate model simulations, with the reconstruction tending to have a slightly smaller trend. Christiansen et al. also found a simple mean of the tide gauges reproduces the trend with little bias in the ensemble mean and about a 10% variation in the interquartile range. However, the simple mean has larger interannual variations and correlates less well with the model interannual variability.\nThe GMSL estimates are not sensitive to the number of EOFs (over the range 4\u00d020 plus the constant mode) used in the reconstruction, although the average correlation between the observed and reconstructed signal increases and the residual variance decreases when a larger number of EOFs is used. For the long periods considered here and with only a small number of records available at the start of the reconstruction period, we used only four EOFs which explain 45% of the variance, after removal of the trend.\nComputation of EOFs\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/churchwhite11.html"}
{"id": "5078fc646d68-3", "text": "Christiansen et al. (2010) tested the robustness of various reconstruction techniques, including an approach similar to that developed by Church et al. (2004) using thermosteric sea level calculated from climate model results. They used an ensemble of model results (derived by randomising the phase of the principal components of the model sea level, see Christiansen et al. (2010) for details). For a method similar to that used here (including the additional \u201cconstant\u201d mode and for a 20 year period for determining the EOFs), the trend in the ensemble mean reconstruction was within a few percent of the true value when 200 gauges were available (with about a 10% variation for the inter.quartile range of individual estimates, decreasing to about 5% when a 50 year period for determining the EOFs was available). When only 40 gauges were used, the ensemble mean trend was biased low by a little under 10% (with an interquartile range of about 15%). They further showed that the reconstructions tend to overestimate the interannual variability and that a longer period for determining the EOFs is important in increasing the correlation between the reconstructed and model year to year variability. Reconstructions that do not use the constant mode perform poorly compared to those that do. These results are similar to our own tests with climate model simulations, with the reconstruction tending to have a slightly smaller trend. Christiansen et al. also found a simple mean of the tide gauges reproduces the trend with little bias in the ensemble mean and about a 10% variation in the interquartile range. However, the simple mean has larger interannual variations and correlates less well with the model interannual variability.\nThe GMSL estimates are not sensitive to the number of EOFs (over the range 4\u00d020 plus the constant mode) used in the reconstruction, although the average correlation between the observed and reconstructed signal increases and the residual variance decreases when a larger number of EOFs is used. For the long periods considered here and with only a small number of records available at the start of the reconstruction period, we used only four EOFs which explain 45% of the variance, after removal of the trend.\nComputation of EOFs\uf0c1\nFor each altimeter mission the along-track data described above are smoothed onto a 1\u02da-by-1\u02da-by-1 month grid for the permanently ice-free ocean from 65\u02daS to 65\u02daN. The smoothing uses an e-folding length of 300 km and covers 90% of the global oceans. The three data sets are combined by matching means at each grid point (rather than just the global average) over the common periods between TOPEX/Poseidon and Jason-1 and between Jason-1 and OSTM/Jason-2. This is an attempt to overcome the problem of different geographically correlated errors in the missions, for example due to different sea-state bias corrections. The overlap between TOPEX/Poseidon and Jason-1 was from 15-January-2002 to 21-August-2002 (T/P cycles 344-365, J-1 cycles 1-22) or, effectively, February to July 2002 in our monthly data sets. The overlap between Jason-1 and OSTM/ Jason-2 was from 12-July-2008 to 26-January-2009 (J-1 cycles 240-259 and J-2 cycles 1-20) or, effectively, August to December 2008 in our monthly data sets.\nSeparate versions of the altimeter data sets with and without the inverse barometer correction and with and without the seasonal signal are produced, as follows:\nOnly whole years (in this case 17 years) are used.\nGrid points with gaps in the time series (e.g. due to seasonal sea ice) are ignored.\nThe data are area (cos(latitude)) weighted.\nThe global-mean trend is removed.\nThe GIA correction appropriate for this data is applied (Mark Tamisiea, NOC Liverpool, private communication).\nIn the original (Church et al. 2004; Church and White 2006) reconstructions, the EOFs were defined with the 9 and 12 years (respectively) of TOPEX/Poseidon and Jason-1 satellite altimeter data available at those times. There are now 17 years of monthly satellite altimeter data available, almost twice as long as the original series. This longer time series should be able to better represent the variability and result in an improved reconstruction of global average sea level, as found by Christiansen et al. (2010). After removing the global average trend and the seasonal (annual plus semi-annual) signal, the first four EOFs account for 29, 8, 5 and 4% of the variance (Figure 2). If the seasonal signal is not removed, the first four EOFs account for 24, 18, 14 and 4% of the variance. These EOFs characterise the large-scale interannual variability, particularly that associated with the El Nino-Southern Oscillation phenomenon, and for the case where the seasonal signal has not been removed, also include the seasonal north/south oscillation of sea level.\nFigure 2: The EOFs used in the sea-level construction. The four EOFs on the left include the seasonal signal and represent a combination of the seasonal signal and interannual variability. The corresponding four EOFs on the right are after the seasonal signal has been removed from the altimeter data. The EOFs are dimensionless and of unit length.\uf0c1\nSensitivity of the Results\uf0c1\nTo complete the reconstruction, we need to specify two parameters: the instrumental error covariance matrix R and the relative weighting of the \u201cconstant\u201d mode to the EOFs. Church and White (2006) used the first differences between sets of nearby sea-level records to compute an average error estimate of the first differences of 50 mm and assumed errors were independent of and between locations (i.e. the error covariance matrix was diagonal). When the seasonal signal was removed, tests indicated the residual variance increased when a smaller error estimate was used but was not sensitive to the selection of larger values. Similarly, the residual variance increased when the weighting of the \u00d4\u00d4constant\u00d5\u00d5 mode was less than 1.5 times the first EOF but was not sensitive to larger values. The computed trends for the 1880\u00d02009 increased slightly (0.06 mm year -1 or about 4%) when the relative weighting was increased by 33% from 1.5 to 2.0 or the error estimate was decreased by 40% to 30 mm. Prior to 1880 when there were less than 15 locations available and none in the southern hemisphere, there was considerably greater sensitivity to the parameter choice than for the rest of the record and hence we focus on results after 1880. When the seasonal signal was retained in the solution, a larger error estimate of 70 mm was appropriate. This solution also had a larger residual variance and a slightly greater sensitivity in the trend to the parameter choice and hence we focus on the solution with the seasonal signal removed, as in our earlier studies.\nAs a further test of the effectiveness of the EOFs to represent the interannual variability in GMSL, we computed EOFs using shorter periods of 9 and 12 years, similar to our earlier analyses (Church et al. 2004; Church and White 2006). The resulting estimates are well within the uncertainties.\nThe atmospheric pressure correction makes essentially no difference to the GMSL time series for the computations with the seasonal signal removed and no difference to the computations including the seasonal signal after about 1940. However, prior to 1940, the correction does make a significant difference to the GMSL calculated with the seasonal signal included. These results suggests some problem with the atmospheric correction prior to 1940 and as a result we decided not to include this correction in the results. This issue seems to be related to the HadSLP2 data set not resolving the annual cycle and, possibly, the spatial patterns well for the Southern Hemisphere south of 30 S for the 1920s and 1930s, presumably because of sparse and changing patterns of input data at this time and in this region. This is being investigated further.\nResults\uf0c1\nWe present results for two periods: from 1880 to 2009 and the satellite altimeter period from January 1993 to December 2009. The latter is only a partial test of the reconstruction technique because the EOFs used were actually determined for this period.", "source": "https://sealeveldocs.readthedocs.io/en/latest/churchwhite11.html"}
{"id": "5078fc646d68-4", "text": "As a further test of the effectiveness of the EOFs to represent the interannual variability in GMSL, we computed EOFs using shorter periods of 9 and 12 years, similar to our earlier analyses (Church et al. 2004; Church and White 2006). The resulting estimates are well within the uncertainties.\nThe atmospheric pressure correction makes essentially no difference to the GMSL time series for the computations with the seasonal signal removed and no difference to the computations including the seasonal signal after about 1940. However, prior to 1940, the correction does make a significant difference to the GMSL calculated with the seasonal signal included. These results suggests some problem with the atmospheric correction prior to 1940 and as a result we decided not to include this correction in the results. This issue seems to be related to the HadSLP2 data set not resolving the annual cycle and, possibly, the spatial patterns well for the Southern Hemisphere south of 30 S for the 1920s and 1930s, presumably because of sparse and changing patterns of input data at this time and in this region. This is being investigated further.\nResults\uf0c1\nWe present results for two periods: from 1880 to 2009 and the satellite altimeter period from January 1993 to December 2009. The latter is only a partial test of the reconstruction technique because the EOFs used were actually determined for this period.\nThe reconstructed and satellite estimates of GMSL have somewhat different error sources. The two largest uncertainties for the reconstructed sea level are the incomplete global coverage of sea-level measurements (particularly in the southern hemisphere), and uncertainties in land motions used to correct the sea-level records. The former contributes directly to the formal uncertainty estimates that are calculated on the basis that the sea-level records are independent. In estimating uncertainties on linear trends and accelerations, we recognise the series are autocorrelated and the number of effective degrees of freedom is only a quarter of the number of years of data. Previous tests using various GIA models suggest an additional uncertainty in trends of about \u00b10.1 mm year^{-1} (Church et al. 2004) that should be added in quadrature to the uncertainty in the trend estimate from the time series (but not for estimates of the acceleration in the rate of rise). The annual time series of GMSL and the estimated uncertainty estimates are available at http://www.cmar.csiro.au/sealevel/sl_data_cmar.html.\n1993-2009\uf0c1\nThe global mean sea level can be computed cycle-by-cycle (every 10 days) directly from the along track satellite data or from the mapped (monthly) satellite data. After averaging the cycle-by-cycle data set over 3 cycles these two estimates for the Jason-1 mission (February 2002 to January 2009; Figure 3) are very similar; the differences have a standard deviation of 1.0 mm. The trends are different by only 0.2 mm year^{-1}, with the trend from the gridded data set being higher numerically, but not statistically different from the trend from the along-track data set.\nFigure 3: Comparison of the satellite-altimeter estimates of GMSL from the along-track data (including all ocean areas where valid data are available) and the mapped data (for a fixed grid) for the duration of the Jason-1 altimeter mission.\uf0c1\nThe reconstructed and altimeter GMSL both increase from 1993 to the end of the record (Figure 4). The larger year-to-year variability of the reconstructed signal (compared with the altimeter record) of ~4-5 mm is less than the one standard deviation uncertainty estimates of about \u00b17 mm. For almost all of the record, the reconstruction is within the one standard deviation uncertainty estimate of the altimeter record. The uncertainty of the reconstruction increases slightly in the last couple of years because of the smaller number of tide gauge records available through the PSMSL.\nFigure 4: Global average sea level from 1990 to 2009 as estimated from the coastal and island sea-level data (blue with one standard deviation uncertainty estimates) and as estimated from the satellite altimeter data from 1993 (red). The satellite and the in situ yearly averaged estimates have the same value in 1993 and the in situ data are zeroed in 1990. The dashed vertical lines indicate the transition from TOPEX Side A to TOPEX Side B, and the commencement of the Jason-1 and OSTM/Jason-2 records.\uf0c1\nAfter correcting for the GIA, the linear trend from the altimeter data from January 1993 to December 2009 is 3.2 \u00b1 0.4 mm year^{-1} (note the GIA values appropriate for correcting the altimeter data are different to that necessary for the in situ data). The uncertainty range (1 standard deviation) comes from fitting a linear trend to the data using uncertainties on the annual averages of 5 mm and is consistent with an updated error budget of altimeter sea-level trend uncertainties (Ablain et al. 2009). They estimate the largest uncertainties are related to the wet tropospheric (atmospheric water vapour) correction, the bias uncertainty of successive missions, orbit uncertainty and the sea-state bias correction. These total to about 0.4 mm year -1, similar to our uncertainty estimate. The reconstructed global average sea-level change over the same period is almost the same as for the altimeter data. However, as a result of different interannual variability, the trend of 2.8 \u00b1 0.8 mm year^{-1} is smaller but not significantly different to the altimeter estimate after correction for glacial isostatic adjustment.\n1880-2009\uf0c1\nThe GMSL time series (Figure 5) are not significantly different from our earlier 2006 result (Church and White 2006). The total GMSL rise (Figure 5) from January 1880 to December 2009 is about 210 mm over the 130 years. The trend over this period, not weighted by the uncertainty estimates, is 1.5 mm year^{-1} (1.6 mm year^{-1} when weighted by the uncertainty estimates). Although the period starts 10 years later in 1880 (rather than 1870), the total rise (Figure 5) is larger than our 2006 estimate of 195 mm mostly because the series extends 8 years longer to 2009 (compared with 2001).\nFigure 5: Global average sea level from 1860 to 2009 as estimated from the coastal and island sea-level data (blue). The one standard deviation uncertainty estimates plotted about the low passed sea level are indicated by the shading. The Church and White (2006) estimates for 1870-2001 are shown by the red solid line and dashed magenta lines for the 1 standard deviation errors. The series are set to have the same average value over 1960-1990 and the new reconstruction is set to zero in 1990. The satellite altimeter data since 1993 is also shown in black.\uf0c1\nThe interannual variability is mostly less than the one standard deviation uncertainty estimates, which range from ~25 mm in 1880 to a minimum of ~6 mm in 1988 (as shown in Figure 5, where the yearly GMSL time series is plotted over the envelope of smoothed (\u00b13 year boxcar) 1 standard deviation limits). However, there are a number of features which are comparable to/larger than the uncertainty estimates. Firstly, there is a clear increase in the trend from the first to the second half of the record; the linear trend from 1880 to 1935 is 1.1 \u00b1 0.7 mm year^{-1} and from 1936 to the end of the record the trend is 1.8 \u00b1 0.3 mm year^{-1}. The period of relatively rapid sea-level rise commencing in the 1930s ceases abruptly in about 1962 after which there is a fall in sea level of over 10 mm over 5 years. Starting in the late 1960s, sea level rises at a rate of almost 2.4 mm year^{-1} for 15 years from 1967 and at a rate of 2.8 \u00b1 0.8 mm year^{-1} from 1993 to the end of the record. There are brief interruptions in the rise in the mid 1980s and the early 1990s.", "source": "https://sealeveldocs.readthedocs.io/en/latest/churchwhite11.html"}
{"id": "5078fc646d68-5", "text": "Figure 5: Global average sea level from 1860 to 2009 as estimated from the coastal and island sea-level data (blue). The one standard deviation uncertainty estimates plotted about the low passed sea level are indicated by the shading. The Church and White (2006) estimates for 1870-2001 are shown by the red solid line and dashed magenta lines for the 1 standard deviation errors. The series are set to have the same average value over 1960-1990 and the new reconstruction is set to zero in 1990. The satellite altimeter data since 1993 is also shown in black.\uf0c1\nThe interannual variability is mostly less than the one standard deviation uncertainty estimates, which range from ~25 mm in 1880 to a minimum of ~6 mm in 1988 (as shown in Figure 5, where the yearly GMSL time series is plotted over the envelope of smoothed (\u00b13 year boxcar) 1 standard deviation limits). However, there are a number of features which are comparable to/larger than the uncertainty estimates. Firstly, there is a clear increase in the trend from the first to the second half of the record; the linear trend from 1880 to 1935 is 1.1 \u00b1 0.7 mm year^{-1} and from 1936 to the end of the record the trend is 1.8 \u00b1 0.3 mm year^{-1}. The period of relatively rapid sea-level rise commencing in the 1930s ceases abruptly in about 1962 after which there is a fall in sea level of over 10 mm over 5 years. Starting in the late 1960s, sea level rises at a rate of almost 2.4 mm year^{-1} for 15 years from 1967 and at a rate of 2.8 \u00b1 0.8 mm year^{-1} from 1993 to the end of the record. There are brief interruptions in the rise in the mid 1980s and the early 1990s.\nThe linear trend from 1900 to 2009 is 1.7 \u00b1 0.2 mm year^{-1} and from 1961 to 2009 is 1.9 \u00b1 0.4 mm year^{-1}. However, there are significant departures from a linear trend. We estimate an acceleration in GMSL by fitting a quadratic to the time series, taking account of the time variable uncertainty estimates. From 1880 to 2009, the acceleration (twice the quadratic coefficient) is 0.009 \u00b1 0.003 mm year^{-2} (one standard deviation). This estimate is slightly less than but not significantly different from the (one standard deviation) estimate of Church and White (2006) of 0.013 \u00b1 0.003 mm year^{-2}, but still significantly different from zero at the 95% level. From 1900 to 2009, the acceleration is also 0.009 \u00b1 0.004 mm year^{-2}. If the variable uncertainty estimates are ignored the equivalent accelerations are 0.010 and 0.012 mm year^{-2}.\nDiscussion\uf0c1\nThere are other recent estimates of changes in GMSL for this period widely available (Jevrejeva et al. 2006; Holgate and Woodworth, 2004; Fig. 6). They all agree approximately with our updated GMSL time series and the longer of these estimates (Jevrejeva et al. 2006) also has an acceleration in the 1930s and a pause in the rise commencing in the 1960s. These changes are also present in a number of individual sea-level records (Woodworth et al. 2009). However, note that the interannual variability in the Jevrejeva et al. series is unrealistically large in the early part of the record and larger than their uncertainty estimates. The Jevrejeva et al. estimate of sea level prior to 1850 (Jevrejeva et al. 2008) indicates an acceleration in the rate of rise commencing at the end of the eighteenth century. Note that their pre-1850 estimate uses only three-sea level records. We do not attempt to extend our construction back prior to 1860. If instead of the recon.struction technique, we employed a straight average of tide gauges, the overall trend back to 1910 is very similar but there is larger interannual variability (Figure 6). Prior to 1910, the variability is even larger (consistent with the results of Christiansen et al. (2010), with unrealistic decadal trends of \u00b110 mm year^{-1}.\nOne source of error is the poor corrections for land motion. Bouin and Wooppelmann (2010) used GPS time series for correcting tide-gauge records for land motion from all sources and estimated a global average sea-level rise of 1.8 mm year^{-1} for the twentieth century, consistent with the present results and early studies (e.g. Douglas 1991). These GPS series are just now beginning to be long enough to provide useful constraints on land motion from all sources (not just GIA).\nA significant non-climatic influence on sea level is the storage of water in dams and the depletion of ground water from aquifers, some of which makes it into the ocean. Chao et al. (2008) estimated that about 30 mm of sea-level equivalent is now stored in man-made dams and the surrounding soils; most of this storage occurred since the 1950s. Globally, the rate of dam entrapment has slowed significantly in the last decade or two. The depletion of ground water (Konikow et al. personal communication; Church et al. in preparation) offsets perhaps a third of this terrestrial storage over the last two decades and the rate of depletion has accelerated over the last two decades.\nFigure 6: Global average sea level from 1860 to 2009 as estimated from the coastal and island sea-level data (blue) compared with estimates of Jevrejeva et al. (2006, brown), Holgate and Woodworth (2004, red) and from a simple average of the gauges (yellow). All series are set to have the same average value over 1960-1990 and the reconstructions are set to zero in 1990. The satellite altimeter data since 1993 is also shown in black.\uf0c1\nWe remove this direct (non-climate) anthropogenic change in terrestrial water storage (both dam storage and aquifer depletion) from our observations to focus on the sea-level change related to climatic influences. The resulting time series (Figure 7) shows a slightly faster rate of sea-level rise since about 1960 and a slightly larger acceleration for the periods since 1880 and 1900. Terrestrial storage contributed to the sea level fall in the 1960s but does not fully explain it. The volcanic eruptions of Mt Agung in 1963, El Chichon in 1982 and Mt Pinatubo in 1991 probably contribute to the small sea level falls in the few years following these eruptions (Church et al. 2005; Gregory et al. 2006; Domingues et al. 2008) but it has not yet been possible to quantitatively explain the mid 1960s fall in sea level (Church et al. in preparation).\nFigure 7: Global average sea level from 1860 to 2009 as estimated from the coastal and island sea-level data (grey) and after correcting for the changes in terrestrial storage associated with the building of dams and the deletion of aquifers (blue). Note these series are virtually identical before 1950.\uf0c1\nThe acceleration in the rate of sea-level rise since 1880 is in qualitative agreement with the few available long (mostly northern hemisphere) sea-level records and longer term estimates of sea level from geological (e.g. salt-marsh) data (for example Donnelly et al. 2004; Gehrels et al. 2006). These data mostly indicate an acceleration at the end of the nineteenth or start of the twentieth century (see Woodworth et al. 2011, this volume, for a summary and references).", "source": "https://sealeveldocs.readthedocs.io/en/latest/churchwhite11.html"}
{"id": "5078fc646d68-6", "text": "Figure 6: Global average sea level from 1860 to 2009 as estimated from the coastal and island sea-level data (blue) compared with estimates of Jevrejeva et al. (2006, brown), Holgate and Woodworth (2004, red) and from a simple average of the gauges (yellow). All series are set to have the same average value over 1960-1990 and the reconstructions are set to zero in 1990. The satellite altimeter data since 1993 is also shown in black.\uf0c1\nWe remove this direct (non-climate) anthropogenic change in terrestrial water storage (both dam storage and aquifer depletion) from our observations to focus on the sea-level change related to climatic influences. The resulting time series (Figure 7) shows a slightly faster rate of sea-level rise since about 1960 and a slightly larger acceleration for the periods since 1880 and 1900. Terrestrial storage contributed to the sea level fall in the 1960s but does not fully explain it. The volcanic eruptions of Mt Agung in 1963, El Chichon in 1982 and Mt Pinatubo in 1991 probably contribute to the small sea level falls in the few years following these eruptions (Church et al. 2005; Gregory et al. 2006; Domingues et al. 2008) but it has not yet been possible to quantitatively explain the mid 1960s fall in sea level (Church et al. in preparation).\nFigure 7: Global average sea level from 1860 to 2009 as estimated from the coastal and island sea-level data (grey) and after correcting for the changes in terrestrial storage associated with the building of dams and the deletion of aquifers (blue). Note these series are virtually identical before 1950.\uf0c1\nThe acceleration in the rate of sea-level rise since 1880 is in qualitative agreement with the few available long (mostly northern hemisphere) sea-level records and longer term estimates of sea level from geological (e.g. salt-marsh) data (for example Donnelly et al. 2004; Gehrels et al. 2006). These data mostly indicate an acceleration at the end of the nineteenth or start of the twentieth century (see Woodworth et al. 2011, this volume, for a summary and references).\nIn addition to the overall increase in the rate of sea-level rise, there is also considerable variability in the rate. Using the yearly average data, we computed trends for successive 16 year periods (close to the length of the altimeter data set) from 1880 to the present (Figure 8). We find maxima in the rates of sea-level rise of over 2 mm year^{-1} in the 1940s and 1970s and nearly 3 mm year^{-1} in the 1990s (Figure 8). As in earlier studies (using 10 and 20 year windows; Church and White 2006; Church et al. 2008), the most recent rate of rise over these short 16 year windows is at the upper end of a histogram of trends but is not statistically higher than the peaks during the 1940s and 1970s. Consistent with the findings of Christiansen et al. (2010), our computed variability in the rates of rise are almost a factor of two less than those where an average of tide gauges (Holgate and Woodworth 2004; Holgate 2007) is used to estimate GMSL. The rate of sea-level rise since 1970 has now been quantitatively explained (Church et al. in preparation) by a gradual increase in ocean thermal expansion, with fluctuations at least partly related to volcanic eruptions, and an increasing cryospheric contribution. The contribution from glaciers and ice caps (Cogley 2009), and the Greenland Ice Sheet (Rignot et al. 2008, 2011) both increased in the 1990s. There are also recent indications of an increasing contribution from the West Antarctic Ice Sheet (Rignot et al. 2011). The larger rate of rise in the 1940s may be related to larger glacier and ice-cap contributions (Oerlemanns et al. 2007) and higher temperatures over Greenland resulting in larger sea-level contributions at that time.\nFigure 8: Linear trends in sea level over successive 16 year periods for the yearly averaged reconstructed sea-level data. The trend from the satellite altimeter data are shown at the end of the time series.\uf0c1\nThe rate of sea-level rise as measured both by the satellite altimeter record and the in situ reconstruction of about 3 mm year^{-1} since 1993 is near the upper end of the sea-level projections for both the Intergovernmental Panel on Climate Change\u2019s Third (Church et al. 2001) and Fourth (Meehl et al. 2007 - see also Hunter 2010) Assessment Reports. However, note that the in situ data also indicates that there was little net change in GMSL from 1990 to 1993, most likely as a result of the volcanic eruption of Mount Pinatubo in 1991 (Domingues et al. 2008; Church et al. in preparation).\nSignificant progress has been made during the last decade in estimating and understanding historical sea-level rise. However, much remains to be done. Of particular importance is the maintenance and continuation of the observing network and associated infrastructure such as the PSMSL archive. The in situ sea-level data set continues to provide a very valuable contribution to our understanding of late nineteenth, twentieth and early twenty first century sea-level rise. Data archaeology and paleo observations to extend the spatial and temporal coverage of in situ sea-level observations need to be vigorously pursued. Modern GPS measurements at tide-gauge locations, which are now beginning to provide valuable information on vertical land motion (e.g., Bouin and Woppelmann 2010) should be continued and expanded. This applies in particular to the use of in situ data to monitor the accuracy of satellite altimeter measurement systems. Increasing the number and geographical distribution of these GPS observations is a priority. Of course a major priority is maintaining a continuous record of high-quality satellite-altimeter observations of the oceans and continuing to improve the International Terrestrial Reference Frame and maintaining and expanding the associated geodetic networks. These improved observations need to be combined with more elegant analysis of the observations, including, for example, considering changes in the gravitational field associated with evolving mass distributions on the Earth and using observations of sea-level rise, ocean thermal expansion and changes in the cryosphere in combined solutions.\nAcknowledgments:\nThis paper is a contribution to the Commonwealth Scientific Industrial Research Organization (CSIRO) Climate Change Research Program. J. A. C. and N. J. W. were partly funded by the Australian Climate Change Science Program. NASA & CNES provided the satellite altimeter data, PSMSL the tide-gauge data.\nReferences\uf0c1\nAblain MA, Cazenave A, Valladeau G, Guinehut S (2009) A new assessment of the error budget of global mean sea level rate estimated by satellite altimetry over 1993-2008. Ocean Sci 5:193-2001\nAllan R, Ansell T (2006) A new globally complete monthly historical gridded mean sea level pressure dataset (HadSLP2): 1850-2004. J Clim 19:5816-5842\nAnthoff D, Nicholls RJ, Tol RSJ, Vafeidis AT (2006) Global and regional exposure to large rises in sea-level: a sensitivity analysis. Tyndall Centre for climate change Research Working paper 96\nAviso (2003) AVISO and PODAAC user handbook - IGDR and GDR jason products. Edition 2.0. SMM.MU-M5-OP-13184-CN\nBenada JR (1997) PO.DAAC Merged GDR (TOPEX/POSEIDON) Generation B user\u2019s handbook, version 2.0, JPL D-11007\nBouin MN, Woppelmann G (2010) Land motion estimates from GPS at tide gauges: a geophysical evaluation. Geophys J Int 180:193-209. doi:10.1111/j.1365-246X.2009.04411.x\nBrown S, Ruf CS, Keihm SJ (2002) Brightness temperature and path delay correction for TOPEX micro.wave radiometer yaw state bias. Technical report to the TOPEX/Poseidon Science Working Team, 8 August 2002, University of Michigan\nChambers DP, Melhaff CA, Urban TJ, Fuji D, Nerem RS (2002) Low-frequency variations in global mean sea level: 1950\u00d02000. J Geophys Res 107:3026. doi:10.129/2001JC001089\nChambers DP, Hayes SA, Reis JC, Urban TJ (2003) New TOPEX sea state bias models and their effect on global mean sea level. J Geophys Res 108:3305. doi:10.1029/2003JC001839", "source": "https://sealeveldocs.readthedocs.io/en/latest/churchwhite11.html"}
{"id": "5078fc646d68-7", "text": "References\uf0c1\nAblain MA, Cazenave A, Valladeau G, Guinehut S (2009) A new assessment of the error budget of global mean sea level rate estimated by satellite altimetry over 1993-2008. Ocean Sci 5:193-2001\nAllan R, Ansell T (2006) A new globally complete monthly historical gridded mean sea level pressure dataset (HadSLP2): 1850-2004. J Clim 19:5816-5842\nAnthoff D, Nicholls RJ, Tol RSJ, Vafeidis AT (2006) Global and regional exposure to large rises in sea-level: a sensitivity analysis. Tyndall Centre for climate change Research Working paper 96\nAviso (2003) AVISO and PODAAC user handbook - IGDR and GDR jason products. Edition 2.0. SMM.MU-M5-OP-13184-CN\nBenada JR (1997) PO.DAAC Merged GDR (TOPEX/POSEIDON) Generation B user\u2019s handbook, version 2.0, JPL D-11007\nBouin MN, Woppelmann G (2010) Land motion estimates from GPS at tide gauges: a geophysical evaluation. Geophys J Int 180:193-209. doi:10.1111/j.1365-246X.2009.04411.x\nBrown S, Ruf CS, Keihm SJ (2002) Brightness temperature and path delay correction for TOPEX micro.wave radiometer yaw state bias. Technical report to the TOPEX/Poseidon Science Working Team, 8 August 2002, University of Michigan\nChambers DP, Melhaff CA, Urban TJ, Fuji D, Nerem RS (2002) Low-frequency variations in global mean sea level: 1950\u00d02000. J Geophys Res 107:3026. doi:10.129/2001JC001089\nChambers DP, Hayes SA, Reis JC, Urban TJ (2003) New TOPEX sea state bias models and their effect on global mean sea level. J Geophys Res 108:3305. doi:10.1029/2003JC001839\nChao BF, Wu YH, Li YS (2008) Impact of artificial reservoir water impoundment on global sea level. Science 320:212\u00d0214. doi:10.1126/science.1154580\nChristiansen B, Schmith T, Thejll P (2010) A surrogate ensemble study of sea level reconstructions. J Clim 23:4306\u00d04326. doi:10.1175/2010JCLI3014.1\nChurch JA, White NJ (2006) A 20th century acceleration in global sea-level rise. Geophys Res Lett 33:L10602. doi:10.1029/2005GL024826\nChurch JA, Gregory JM, Huybrechts P, Kuhn M, Lambeck K, Nhuan MT, Qin D, Woodworth PL (2001) Changes in Sea Level. In: Houghton JT, Ding Y, Griggs DJ, Noguer M, van der Linden P, Dai X, Maskell K, Johnson CI (eds) Climate change 2001: the scientific basis. Contribution of working group 1 to the third assessment report of the intergovernmental panel on climate change. Cambridge University Press, Cambridge\nChurch JA, White NJ, Coleman R, Lambeck K, Mitrovica JX (2004) Estimates of the regional distribution of sea-level rise over the 1950 to 2000 period. J Clim 17:2609\u00d02625\nChurch JA, White NJ, Arblaster J (2005) Signi\u00decant decadal-scale impact of volcanic eruptions on sea level and ocean heat content. Nature 438:74\u00d077. doi:10.1038/nature04237\nChurch J, White N, Aarup T, Wilson SW, Woodworth P, Domingues C, Hunter J, Lambeck K (2008) Understanding global sea levels: past, present and future. Sustain Sci 3:9\u00d022. doi:10.1007/ s11625-008-0042-4\nChurch JA, Woodworth PL, Aarup T, Wilson SW (eds) (2010) Understanding sea-level rise and variability. Wiley-Blackwell Publishing, Chichester\nCNES (2009) OSTM/Jason-2 Products Handbook. SALP-MU-M-OP-15815-CN\nCogley JG (2009) Geodetic and direct mass-balance measurements: comparison and joint analysis. Ann Glaciol 50:96-100\nDavis JL, Mitrovica JX (1996) Glacial isostatic adjustment and the anomalous tide gauge record of eastern North America. Nature 379:331\u00d0333\nDomingues CM, Church JA, White NJ, Gleckler PJ, Wijffels SE, Barker PM, Dunn JR (2008) Improved estimates of upper-ocean warming and multi-decadal sea-level rise. Nature 453:1090\u00d01093. doi: 10.1038/nature07080\nDonnelly JP, Cleary P, Newby P, Ettinger R (2004) Coupling instrumental and geological records of sea level change: evidence from southern New England of an increase in the rate of sea level rise in the late 19th century. Geophys Res Lett 31:L05203. doi:10.1029/2003GL018933\nDouglas BC (1991) Global sea level rise. J Geophys Res 96:6981\u00d06992\nDouglas BC (1992) Global sea level acceleration. J Geophys Res 97:12,699-12,706\nDouglas BC (2001) Sea level change in the era of the recording tide gauge. In: Douglas BC, Michael S, Kearney MS, Leatherman SP (eds) Sea level rise. International Geophysical Series, vol 75, Academic Press, San Diego\nFiedler JW, Conrad CP (2010) Spatial variability of sea level rise due to water impoundment behind dams. Geophys Res Lett 37:L12603. doi:10.1029/2010GL043462\nGehrels WR, Marshall WA, Gehrels MJ, Larsen G, Kirby JR, Eirksson J, Heinemeier J, Shimmield T (2006) Rapid sea-level rise in the North Atlantic Ocean since the \u00derst half of the nineteenth century. The Holocene 16:949\u00d0965. doi:10.1177/0959683606hl986rp\nGregory JM, Lowe JA, Tett SFB (2006) Simulated global-mean sea-level changes over the last half.millenium. J Clim 19:4576\u00d04591\nHolgate SJ (2007) On the decadal rates of sea level change during the twentieth century. Geophys Res Lett 34:L01602. doi:10.1029/2006GL028492\nHolgate SJ, Woodworth PL (2004) Evidence for enhanced coastal sea level rise during the 1990s. Geophys Res Lett 31:L07305. doi:10.1029/2004GL019626\nHunter J (2010) Estimating sea-level extremes under conditions of uncertain sea-level rise. Clim Chang 99:331\u00d0350. doi:10.1007/s10584-009-9671-6\nJevrejeva S, Grinsted A, Moore JC, Holgate S (2006) Nonlinear trends and multi-year cycles in sea level records. J Geophys Res 111:C09012. doi:10.1029/2005JC003229\nJevrejeva S, Moore JC, Grinsted A, Woodworth PL (2008) Recent global sea level acceleration started over 200 years ago. Geophys Res Lett 35:L08715. doi:08710.01029/02008GL033611\nKaplan A, Kushnir Y, Cane MA (2000) Reduced space optimal interpolation of historical marine sea level pressure. J Clim 13:2987\u00d03002\nLeuliette EW, Nerem RS, Mitchum GT (2004) Calibration of TOPEX/Poseidon and Jason Altimeter Data to construct a continuous record of mean sea level change. Mar Geodesy 27:79\u00d094. doi:10.1080/ 01490410490465193\nMeehl GA, Stocker TF, Collins WD, Friedlingstein P, Gaye AT, Gregory JM, Kitoh A, Knutti R, Murphy JM, Noda A, Raper SCB, Watterson IG, Weaver AJ, Zhao Z-C (2007) Global climate projections. In: Qin D, Solomon S, Manning M,\nMarquis M, Averyt K, Tignor MMB, Miller HL Jr, Chen Z (eds) Climate change 2007: the physical science basis. Contribution of working group 1 to the fourth assessment report of the intergovernmental panel on climate change. Cambridge University Press, Cambridge", "source": "https://sealeveldocs.readthedocs.io/en/latest/churchwhite11.html"}
{"id": "5078fc646d68-8", "text": "Holgate SJ (2007) On the decadal rates of sea level change during the twentieth century. Geophys Res Lett 34:L01602. doi:10.1029/2006GL028492\nHolgate SJ, Woodworth PL (2004) Evidence for enhanced coastal sea level rise during the 1990s. Geophys Res Lett 31:L07305. doi:10.1029/2004GL019626\nHunter J (2010) Estimating sea-level extremes under conditions of uncertain sea-level rise. Clim Chang 99:331\u00d0350. doi:10.1007/s10584-009-9671-6\nJevrejeva S, Grinsted A, Moore JC, Holgate S (2006) Nonlinear trends and multi-year cycles in sea level records. J Geophys Res 111:C09012. doi:10.1029/2005JC003229\nJevrejeva S, Moore JC, Grinsted A, Woodworth PL (2008) Recent global sea level acceleration started over 200 years ago. Geophys Res Lett 35:L08715. doi:08710.01029/02008GL033611\nKaplan A, Kushnir Y, Cane MA (2000) Reduced space optimal interpolation of historical marine sea level pressure. J Clim 13:2987\u00d03002\nLeuliette EW, Nerem RS, Mitchum GT (2004) Calibration of TOPEX/Poseidon and Jason Altimeter Data to construct a continuous record of mean sea level change. Mar Geodesy 27:79\u00d094. doi:10.1080/ 01490410490465193\nMeehl GA, Stocker TF, Collins WD, Friedlingstein P, Gaye AT, Gregory JM, Kitoh A, Knutti R, Murphy JM, Noda A, Raper SCB, Watterson IG, Weaver AJ, Zhao Z-C (2007) Global climate projections. In: Qin D, Solomon S, Manning M,\nMarquis M, Averyt K, Tignor MMB, Miller HL Jr, Chen Z (eds) Climate change 2007: the physical science basis. Contribution of working group 1 to the fourth assessment report of the intergovernmental panel on climate change. Cambridge University Press, Cambridge\nMilne GA, Davis JL, Mitrovica JX, Scherneck H-G, Johansson JM, Vermeer M, Koivula H (2001) Space-geodetic constraints on glacial isostatic adjustment in Fennoscandia. Science 291:2381\u00d02385\nNerem RS, Mitchum GT (2001) Chapter 6 of Sea level rise\u00d1history and consequences. In: Douglas BC, Kearney MS, Leatherman SP (eds) Academic Press, London\nOerlemanns J, Dyurgerov M, van de Wal RSW (2007) Reconstructing the glacier contribution to sea-level rise back to 1850. The Cryosphere 1:59-65\nRignot E, Box JE, Burgess E, Hanna E (2008) Mass balance of the Greenland Ice Sheet from 1958 to 2007. Geophys Res Lett 35:L20502. doi:10.1029/2008GL035417\nRignot E, Velicogna I, van den Broeke MR, Monaghan A, Lenaerts J (2011) Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise. Geophys Res Lett 38:L05503. doi: 10.1029/2011GL046583\nRuf CS (2002) TMR drift correction to 18 GHz brightness temperatures, Revisited. Report to TOPEX Project, 3 June, 2002\nWhite NJ, Church JA, Gregory JM (2005) Coastal and global averaged sea-level rise for 1950 to 2000. Geophys Res Lett 32:L01601. doi:10.1029/2004GL021391\nWoodworth PL (1990) A search for accelerations in records of European mean sea level. Int J Climatol 10:129\u00d0143\nWoodworth PL, Player R (2003) The permanent service for mean sea level: an update to the 21st century. J Coastal Res 19:287\u00d0295\nWoodworth PL, White NJ, Jevrejeva S, Holgate SJ, Church JA, Gehrels WR (2009) Evidence for the accelerations of sea level on multi-decade and century timescales. Int J Climatol 29:777\u00d0789. doi: 10.1002/joc.1771\nWoodworth PL, Menendez M, Gehrels WR (2011) Evidence for Century-time scale Acceleration in mean sea levels and for recent changes in extreme sea levels. Surveys in Geophysics, This Volume", "source": "https://sealeveldocs.readthedocs.io/en/latest/churchwhite11.html"}
{"id": "63dd50a3dfc4-0", "text": "Couldrey et al. (2021)\uf0c1\nTitle:\nWhat causes the spread of model projections of ocean dynamic sea-level change in response to greenhouse gas forcing?\nKey Points:\nOcean model diversity in AOGCMs is a key source of uncertainty in sea-level projections under greenhouse gas forcing.\nIncreased air-sea heat flux sets the broad pattern of dynamic sea-level change; wind stress and freshwater flux have localized effects.\nNonlinear dynamic sea-level responses occur with simultaneous flux perturbations, especially in the Arctic and North Atlantic\nKeywords:\nsea-level rise, ocean heat uptake, climate change, climate modeling, ocean model diversity, air-sea flux perturbations, FAFMIP\nCorresponding author:\nMatthew P. Couldrey\nCitation:\nCouldrey, M. P., Gregory, J. M., Dias, F. B., Dobrohotoff, P., Domingues, C. M., Garuba, O., et al. (2021). What causes the spread of model projections of ocean dynamic sea-level change in response to greenhouse gas forcing? Climate Dynamics, 56(1\u20132), 155\u2013187. doi:10.1007/s00382-020-05471-4\nURL:\nhttps://link.springer.com/article/10.1007/s00382-020-05471-4\nAbstract\uf0c1\nSea levels of different atmosphere\u2013ocean general circulation models (AOGCMs) respond to climate change forcing in different ways, representing a crucial uncertainty in climate change research. We isolate the role of the ocean dynamics in setting the spatial pattern of dynamic sea-level (\u03b6) change by forcing several AOGCMs with prescribed identical heat, momentum (wind) and freshwater flux perturbations. This method produces a \u03b6 projection spread comparable in magnitude to the spread that results from greenhouse gas forcing, indicating that the differences in ocean model formulation are the cause, rather than diversity in surface flux change. The heat flux change drives most of the global pattern of \u03b6 change, while the momentum and water flux changes cause locally confined features. North Atlantic heat uptake causes large temperature and salinity driven density changes, altering local ocean transport and \u03b6. The spread between AOGCMs here is caused largely by differences in their regional transport adjustment, which redistributes heat that was already in the ocean prior to perturbation. The geographic details of the \u03b6 change in the North Atlantic are diverse across models, but the underlying dynamic change is similar. In contrast, the heat absorbed by the Southern Ocean does not strongly alter the vertically coherent circulation. The Arctic \u03b6 change is dissimilar across models, owing to differences in passive heat uptake and circulation change. Only the Arctic is strongly affected by nonlinear interactions between the three air-sea flux changes, and these are model specific.\nIntroduction\uf0c1\nSea-level rise presently is and will continue to be an important consequence of anthropogenically forced climate change. Global mean thermosteric sea-level rise, due to thermal expansion of a warming ocean, accounts for 30\u201355% of the global mean sea-level rise (GMSLR) projected for the years 2081\u20132100 (Church et al. 2013). The remainder results mostly from ocean mass gain due to melting land ice (glaciers and ice sheets). Regional sea-level changes are much more complicated, involving ocean and climate dynamics as well as solid-Earth processes, typically not included in coupled climate models. The latter can make up 50% or more of regional sea-level change pattern by the end of the 21st Century (Slangen et al. 2012; Stammer et al. 2013).\nAs part of the Coupled Model Intercomparison Project (CMIP), atmosphere\u2013ocean general circulation models (AOGCMs) simulate anthropogenic sea-level change related to changes in climate dynamics by starting from a near-equilibrium (i.e. well spun-up) preindustrial control state (piControl) and running forward with time-varying forcing agents (greenhouse gases, anthropogenic aerosol, etc.). In these models, ocean dynamic sea level, \u03b6, is defined at each location and time as\n\u03b6 = \u03b7 \u2212 \u03b7\u0305 (1)\nwhere \u03b7 is the local sea-surface height relative to a surface on which the geopotential has a uniform constant value, and \u03b7\u0305 is its global mean over the ocean area. \u03b7 is termed \u2018sterodynamic sea level\u2019 according to recent terminology conventions (Gregory et al. 2019). By definition, the global mean of \u03b6 is zero, but locally it is not zero due to ocean circulation and horizontal density gradients. Using CMIP terminology, \u03b6 is the variable \u2018zos\u2019 (Griffies et al. 2016). The sterodynamic sea-level change (\u0394\u03b7) that an individual location experiences may differ substantially from the global mean thermosteric sea-level rise (GMSLR, \u0394\ud835\udf02\u2212), because of changes in ocean circulation and density. This present work focuses on the spatial pattern in ocean dynamic sea-level change\n\u2206\u03b6(x,y,t) = \u0394\ud835\udf02(\ud835\udc65,\ud835\udc66,\ud835\udc61) \u2212 \u2206\u03b7\u0305(\ud835\udc61),(2)\nprojected to occur over the coming century due to anthropogenic greenhouse gas forced climate change. Accordingly, \u0394\u03b6 is calculated from CMIP output as the difference between the \u2018zos\u2019 fields in a forcing experiment relative to a control state (see Sects. 2.2 and 2.3 for details). In results from AOGCMs from CMIP\u2019s fifth phase (CMIP5), the spatial standard deviation of the multi-model mean \u0394\u03b6 projected under scenario RCP4.5 by 2081\u20132100 is 0.06 m, which is 30% of the multi-model mean GMSLR due to thermal expansion (Gregory et al. 2016). Thus, in some locations, \u0394\u03b7 is more than twice its global mean, because of ocean dynamic sea-level change. Moreover, different AOGCMs predict diverse spatial patterns and magnitudes of sea-level change (Slangen et al. 2014). The global mean of the inter-model standard deviation of \u0394\u03b6 in the same projections is also about 0.06 m; in other words, the systematic uncertainty in predicting the pattern of dynamic sea-level change is of first order, being about the same magnitude as the pattern itself (see also Fig. 3). It is this spread among AOGCMs that we seek to investigate: one of the largest uncertainties affecting regional impacts of anthropogenic sea-level and climate change this century and beyond.\nPart of the spread among AOGCMs comes from their different representations of forcing agents, especially anthropogenic aerosol (Melet and Meyssignac 2015). The idealized scenario of increasing the concentration of CO2 by 1% per year, called \u20181pctCO2\u2019 is simpler to interpret than more complex experiments with differing time profiles of numerous types of climate forcing (Eyring et al. 2016). After seven decades, 1pctCO2 reaches a similar magnitude of radiative forcing to RCP 4.5 by the end of the twenty-first century.\nDeveloping a more complete understanding of the climate response to idealized 1pctCO2 forcing provides insight into how we expect the climate to respond to moderate greenhouse gas and aerosol emissions by the end of this century. However, even when AOGCMs are forced with this simple, idealized setup, they produce a range of climate response, primarily because of their differing climate sensitivities (i.e. the degree of surface warming that results per radioactive forcing). Differences in the representation of cloud feedback mechanisms in atmosphere models accounts for the greatest uncertainty in climate sensitivity (Ceppi et al. 2017). The control climate, which is different for each model, also contributes to the spread (Bouttes and Gregory 2014), e.g. via the strength of the ice coverage and water vapour feedbacks (Hu et al. 2017), and sea-surface temperature (SST) biases (He and Soden 2016). These and other factors affect the spatial patterns and magnitudes of the air-sea fluxes of heat, freshwater, and momentum, which are the drivers of \u0394\u03b6. Unpacking the influence of oceanic processes from atmospheric processes is therefore difficult in experiments like 1pctCO2.\nPrevious work has investigated how the diversity in the changes of air-sea fluxes of heat, freshwater and momentum contribute to the spread in projections of sea-level change. A typical approach is to force a single model with ensembles of boundary conditions like SST (Huber and Zanna 2017) or air-sea flux change (Bouttes and Gregory 2014) to mimic the spread of fully coupled simulations. These studies find that forcing individual models with a variety of boundary conditions produces a large spread of ocean responses, in terms of sea-level change (Bouttes and Gregory 2014), ocean heat uptake (OHU) and circulation change (Huber and Zanna 2017). While these studies demonstrate that models are sensitive to surface fluxes, the uncertainty that results from the diversity of ocean model structure in coupled models has not yet been assessed.", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-1", "text": "Developing a more complete understanding of the climate response to idealized 1pctCO2 forcing provides insight into how we expect the climate to respond to moderate greenhouse gas and aerosol emissions by the end of this century. However, even when AOGCMs are forced with this simple, idealized setup, they produce a range of climate response, primarily because of their differing climate sensitivities (i.e. the degree of surface warming that results per radioactive forcing). Differences in the representation of cloud feedback mechanisms in atmosphere models accounts for the greatest uncertainty in climate sensitivity (Ceppi et al. 2017). The control climate, which is different for each model, also contributes to the spread (Bouttes and Gregory 2014), e.g. via the strength of the ice coverage and water vapour feedbacks (Hu et al. 2017), and sea-surface temperature (SST) biases (He and Soden 2016). These and other factors affect the spatial patterns and magnitudes of the air-sea fluxes of heat, freshwater, and momentum, which are the drivers of \u0394\u03b6. Unpacking the influence of oceanic processes from atmospheric processes is therefore difficult in experiments like 1pctCO2.\nPrevious work has investigated how the diversity in the changes of air-sea fluxes of heat, freshwater and momentum contribute to the spread in projections of sea-level change. A typical approach is to force a single model with ensembles of boundary conditions like SST (Huber and Zanna 2017) or air-sea flux change (Bouttes and Gregory 2014) to mimic the spread of fully coupled simulations. These studies find that forcing individual models with a variety of boundary conditions produces a large spread of ocean responses, in terms of sea-level change (Bouttes and Gregory 2014), ocean heat uptake (OHU) and circulation change (Huber and Zanna 2017). While these studies demonstrate that models are sensitive to surface fluxes, the uncertainty that results from the diversity of ocean model structure in coupled models has not yet been assessed.\nThe change of the Atlantic Meridional Overturning Circulation (AMOC) strength in response to climate change is model specific, and is believed to be a key factor setting the pattern of North Atlantic sea-level change (Yin et al. 2009; Hawkes 2013; Bouttes et al. 2014). Globally, ocean heat uptake has been related to the degree of AMOC weakening (Xie and Vallis 2012; Rugenstein et al. 2013; Kostov et al. 2014). However, more recently, the correlation between OHU and AMOC strength was shown to arise because both are affected by mesoscale eddy transfer (Saenko et al. 2018), where OHU is more intense and deep reaching with decreasing mesoscale eddy transfer. The ocean components of most CMIP5 and CMIP6 models are not able to resolve mesoscale eddies, so their effects are parameterized in different ways across models. It is therefore plausible that the differing representations of mesoscale and other unresolved phenomena are likely to contribute to the spread of sea-level projections among AOGCMs, through their influence on seawater properties (e.g. temperature, salinity and density) and ocean transports of heat and salt.\nThe Flux-Anomaly-Forced Model Intercomparison Project (FAFMIP) outlines a protocol for forcing different AOGCMs with perturbations to their air-sea fluxes\u2014heat, freshwater, and momentum\u2014to systematically explore the oceanic response to CO2-forced climate change (Gregory et al. 2016). The key goal of FAFMIP is to replicate the oceanic response to 1pctCO2 forcing, while excluding the model spread due to changes in air-sea fluxes. Initial FAFMIP results have highlighted the importance of the heat flux perturbation in setting much of the global pattern of \u0394\u03b6, and that both the wind stress and heat flux perturbations set the Southern Ocean dipole (Gregory et al. 2016).\nBuilding on previous findings, we present in this study: (1) new sea-level results based on AOGCM simulations forced with simultaneous rather than separate flux perturbations, (2) an intercomparison of the roles of temperature and salinity-driven density changes, and (3) further examination of the decomposition of ocean heat content (OHC) changes due to changes in temperature and transport. Our study also includes new CMIP6 simulations and paves the way for possible forthcoming FAFMIP analyses.\nThis paper is structured as follows: an explanation of the configuration of model experiments and analysis methods is given in Sect. 2. In Sect. 3.1, the sea-level responses to FAFMIP and 1pctCO2 forcing are compared, followed by a comparison of the 1pctCO2 sea-level response from CMIP5 and CMIP6 in Sect. 3.2. The response of AOGCMs to individually applied surface flux perturbations (heat, freshwater and momentum) is assessed in Sect. 3.3, while nonlinear interactions between these flux perturbations are described in Sect. 3.4. A decomposition of ocean heat uptake based on a subset of the AOGCMs is presented in Sect. 3.5. Results are discussed in Sect. 4 and the conclusions are laid out in Sect. 5. An appendix with further notes on the decomposition of ocean heat uptake is included in \u201cAppendix\u201d.\nMethods\uf0c1\nPerturbation of air-sea fluxes\uf0c1\nThe FAFMIP protocol presents a method that mimics the effect of 1pctCO2 forcing on the ocean but applies identical perturbations to each model (Gregory et al. 2016). The perturbations are the multi model mean changes in the air-sea fluxes of heat, freshwater, and momentum from 1pctCO2 simulations averaged over the 61st-80th years of forcing relative to the piControl state. This period covers the time where CO2 concentration reaches double its preindustrial values (at year 70). The suite of CMIP5 AOGCMs available at the time to derive the required surface flux perturbations for the FAFMIP protocol comprises 13 members; CNRM-CM5, CSIRO-Mk3-6-0, CanESM2, GFDL-ESM2G, HadGEM2-ES, MIROC-ESM, MIROC5, MPI-ESM-LR, MPI-ESM-MR, MPI-ESM-P, MRI-CGCM3, NorESM1-ME, and NorESM1-M. It was decided that all perturbations should be derived from a common set of models to allow for consistent comparison of model-mean sea-level change and the associated spread (Gregory et al. 2016). Further details about FAFMIP and the protocol, including the perturbation files can be found at https://www.fafmip.org.\nTime-dependent CO2 and other forcing causes a varying magnitude of sea-level change, while the spatial pattern is relatively time-invariant (Hawkes 2013; Perrette et al. 2013; Slangen et al. 2014; Bilbao et al. 2015). This phenomenon of \u2018pattern scaling\u2019 means that time-dependent forcing is not necessary for our investigation of the spatial structure. Therefore, in the interest of simplicity the FAFMIP flux perturbations are applied as a constant forcing for the full 70 years of each experiment, with no time-variation except for the annual cycle.\nExperiments\uf0c1\nFAFMIP perturbations to the fluxes of heat, water and momentum (Fig. 1) were applied in five different experiments, as listed below. All perturbations were applied at the air-sea interface in direct contact with seawater surface, such that sea ice is not directly affected. However, there will be indirect effects on sea ice due to the redistribution of heat and freshwater in response to all the perturbations. The heat and freshwater fluxes are defined positive downward into the ocean, and the momentum flux perturbations are positive eastward and northward. FAFMIP experiments were run by nine modelling groups using 13 AOGCMs (Table 1).\nFig. 1: Annual means of downward flux perturbations applied in FAFMIP experiments at the ocean surface for heat, water, eastward momentum, and northward momentum, a\u2013d respectively. Perturbations are the multi model mean surface flux anomalies from simulations forced with 1% per year rising CO2 concentrations averaged over years 61\u201380\nTable 1 Key features of the main AOGCMs studied, where dashes in Ocean horizontal resolution indicate a spatially varying resolution", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-2", "text": "Time-dependent CO2 and other forcing causes a varying magnitude of sea-level change, while the spatial pattern is relatively time-invariant (Hawkes 2013; Perrette et al. 2013; Slangen et al. 2014; Bilbao et al. 2015). This phenomenon of \u2018pattern scaling\u2019 means that time-dependent forcing is not necessary for our investigation of the spatial structure. Therefore, in the interest of simplicity the FAFMIP flux perturbations are applied as a constant forcing for the full 70 years of each experiment, with no time-variation except for the annual cycle.\nExperiments\uf0c1\nFAFMIP perturbations to the fluxes of heat, water and momentum (Fig. 1) were applied in five different experiments, as listed below. All perturbations were applied at the air-sea interface in direct contact with seawater surface, such that sea ice is not directly affected. However, there will be indirect effects on sea ice due to the redistribution of heat and freshwater in response to all the perturbations. The heat and freshwater fluxes are defined positive downward into the ocean, and the momentum flux perturbations are positive eastward and northward. FAFMIP experiments were run by nine modelling groups using 13 AOGCMs (Table 1).\nFig. 1: Annual means of downward flux perturbations applied in FAFMIP experiments at the ocean surface for heat, water, eastward momentum, and northward momentum, a\u2013d respectively. Perturbations are the multi model mean surface flux anomalies from simulations forced with 1% per year rising CO2 concentrations averaged over years 61\u201380\nTable 1 Key features of the main AOGCMs studied, where dashes in Ocean horizontal resolution indicate a spatially varying resolution\nExperiment 1 In FAF-passiveheat, the heat flux perturbation (Fig. 1a) is applied to a \u2018passive added temperature\u2019 tracer, Ta. FAF-passiveheat is a control (similar to piControl), since its climate is not perturbed and experiences only internal variability while the extra tracer allows for the passive uptake of the heat perturbation to be quantified. Ta is initially set to 0 everywhere and the forcing, F, is applied at the surface like a heat flux (none of it penetrates below the surface, like shortwave radiation does). It is transported within the ocean via the same schemes that each model uses to advect and diffuse temperature, T, without affecting the evolution of the ocean state at all because it is passive. Since the perturbation has positive and negative values locally, Ta can be positive and negative. While the input of the passive added heat tracer via the prescribed surface heat flux is identical across models, the geographic patterns of its distribution in the ocean will differ across models, depending on each model\u2019s preindustrial circulation and parameterized tracer transports. The FAF-passiveheat experiment makes it possible to consistently compare the unperturbed tracer uptake across models, which is necessary for a decomposition of the heat uptake in each model when forced with transient climate change (Sect. 2.4).\nExperiment 2 In FAF-heat, the heat flux perturbation F is applied as a forcing to ocean temperature, T. (Note that we call it a \u201cforcing\u201d because it is an external perturbation to the climate system, but it is not a radiative forcing, such as is given by CO2 increase.) The perturbation is strongly positive in the North Atlantic and in the Southern Ocean (Fig. 1a). Relative to annual mean climatological heat fluxes, the perturbation reduces the North Atlantic (north of the equator) basin-mean upward heat flux by about 50% (the precise amount varies between models). In the Southern Ocean south of 45\u00b0 S, the perturbation is roughly 160% of the climatological flux and of opposite sign, switching the basin into a region of net ocean heat uptake. To avoid the atmosphere\u2019s tendency to eliminate the SST anomaly through an opposing air-sea flux, a further passive tracer is used, called the redistributed temperature tracer, Tr which is initialized to equal T at the start and is transported within the ocean in the just the same ways as T but is not forced by the surface heat flux perturbation. The atmosphere is decoupled from the SST of T, and instead sees the surface field of Tr (Fig. 2). The result is that the perturbation gets added to the ocean, where it accumulates and modifies seawater density, and changes ocean transport, but the atmosphere does not absorb any of the added heat and is only modified by changes to surface Tr that arise indirectly through the changing ocean circulation. In FAF-heat, fields of Tr and T quickly diverge from each other by a value approximately equal to Ta. Sub-grid scale schemes (e.g. boundary layer schemes; neutral diffusion; parameterized eddy advection) have nonlinear effects on the transport of temperature that we ignore, meaning that T is assumed equal to Tr\u2009+\u2009Ta (Gregory et al. 2016). In FAF-passiveheat, Tr (if introduced and treated in the same way) would be identical to T, because no forcing is applied to T. By comparing the distribution of Ta in FAF-heat (whose circulation changes) against FAF-passiveheat (whose circulation follows the steady state) it is possible to identify regions where the changing circulation stores added heat \u2018actively\u2019 (i.e. unlike a passive tracer).\nFig. 2: Treatment of surface heat flux perturbation in FAF-heat and FAF-all, redrawn from (Gregory et al. 2016). Q is the net surface heat from the atmosphere and sea ice into the ocean and F is the flux perturbation. The SST used to calculate the surface heat flux to atmosphere and sea ice is coupled to a redistributed temperature tracer Tr, which does not feel F\nExperiment 3 The water flux perturbation is derived from the CMIP5 \u2018wfo\u2019 diagnostic, which is the sum of precipitation, evaporation, river inflow and water fluxes between floating ice and seawater. There is no perturbation applied over land. The freshwater flux perturbation applied in FAF-water has a very small global annual average, and mainly redistributes freshwater (Fig. 1b). The perturbation is broadly consistent with the \u201cwet gets wetter, dry gets drier\u201d pattern (Held and Soden 2006), reinforcing evaporation in the mid latitudes (by about 10%), and adding freshwater elsewhere (also about 10% reinforcement): namely the equatorial Pacific, the Southern Ocean, the Arctic Ocean, and the high latitude North Pacific and North Atlantic.\nExperiment 4 The surface momentum perturbation applied in FAF-stress is mainly characterized by a reinforcement and southward shift of the Southern Ocean westerlies (Fig. 1c). Between 45\u00b0 and 65\u00b0 S, the perturbation strengthens the westerlies by about 10%. The perturbation has smaller effects on the zonal and meridional downward momentum fluxes in the mid latitudes (Fig. 1c, d). The perturbation is added to the momentum balance of the ocean surface, such that it does not directly affect sub-grid scale parameterization schemes (e.g. planetary boundary closures) that depend on wind stress or ice stress.\nExperiment 5 All three perturbations are applied together in the FAF-all experiment. This experiment serves two purposes: to assess how well the perturbations mimic the effect of CO2 forcing as in 1pctCO2, and to determine the extent to which the perturbations counteract or amplify each other\u2019s effects on sea level when applied simultaneously. If the flux perturbations interact with each other when applied together in FAF-all, then the FAF-all sea-level response will not equal the sum of the sea-level responses to the individual perturbations. This aspect of the FAFMIP design was not tested by Gregory et al. (2016), since no results for FAF-all were available at the time from the five pre-CMIP6 models analysed.\nCalculation of change due to perturbations\uf0c1\n\u2206\u03b6 can be derived from CMIP output as the difference in the \u2018zos\u2019 field from a forced experiment relative to the \u2018zos\u2019 field in an unforced control state. Although \u2018zos\u2019 is usually defined to have a zero global area mean (Griffies et al. 2016), for some models it was necessary to subtract the nonzero area mean. This study is focused on the regional sea-level changes expected by the end of the twenty-first century. Because exponentially increasing CO2 concentration, such as in 1pctCO2, gives a radiative forcing which increases linearly in time, and the FAFMIP perturbations correspond to 1pctCO2 forcing at year 70, 70 years of time invariant FAFMIP forcing integrates to approximately the same as a 100-year time integral of 1pctCO2 forcing. \u2206\u03b6 is therefore calculated from the final decade (years 61\u201370) of the perturbation experiments (FAF-stress, -water etc.), and from years 91\u2013100 of 1pctCO2 experiments for comparison. This approach means the amplitudes of \u2206\u03b6 will be approximately similar, but in any case, the spatial pattern of \u2206\u03b6 is the object of interest in this study.", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-3", "text": "Experiment 5 All three perturbations are applied together in the FAF-all experiment. This experiment serves two purposes: to assess how well the perturbations mimic the effect of CO2 forcing as in 1pctCO2, and to determine the extent to which the perturbations counteract or amplify each other\u2019s effects on sea level when applied simultaneously. If the flux perturbations interact with each other when applied together in FAF-all, then the FAF-all sea-level response will not equal the sum of the sea-level responses to the individual perturbations. This aspect of the FAFMIP design was not tested by Gregory et al. (2016), since no results for FAF-all were available at the time from the five pre-CMIP6 models analysed.\nCalculation of change due to perturbations\uf0c1\n\u2206\u03b6 can be derived from CMIP output as the difference in the \u2018zos\u2019 field from a forced experiment relative to the \u2018zos\u2019 field in an unforced control state. Although \u2018zos\u2019 is usually defined to have a zero global area mean (Griffies et al. 2016), for some models it was necessary to subtract the nonzero area mean. This study is focused on the regional sea-level changes expected by the end of the twenty-first century. Because exponentially increasing CO2 concentration, such as in 1pctCO2, gives a radiative forcing which increases linearly in time, and the FAFMIP perturbations correspond to 1pctCO2 forcing at year 70, 70 years of time invariant FAFMIP forcing integrates to approximately the same as a 100-year time integral of 1pctCO2 forcing. \u2206\u03b6 is therefore calculated from the final decade (years 61\u201370) of the perturbation experiments (FAF-stress, -water etc.), and from years 91\u2013100 of 1pctCO2 experiments for comparison. This approach means the amplitudes of \u2206\u03b6 will be approximately similar, but in any case, the spatial pattern of \u2206\u03b6 is the object of interest in this study.\nDecadal fields of \u03b6 are calculated to reduce (but cannot not totally eliminate) the effect of unforced interannual variability, reflecting our interest in understanding the climate response to forcing by the end of this century. A change (i.e. \u2206\u03b6) is deemed significant for our purposes if its magnitude is more than twice the decadal standard deviation (a 95% interval for a normal distribution) of variability determined at that location in the relevant control simulation (i.e. piControl for 1pctCO2 and FAF-passiveheat for all other experiments). Decadal mean fields of \u03b6 are calculated for each decade of control simulation, and the threshold for significance is taken to be double the standard deviation across the decadal averages. Insignificant \u2206\u03b6 features (within\u2009\u00b1\u20092 standard deviations) are set to 0 for plotting purposes.\nThe steric sea-level responses to each perturbation can be decomposed into the thermosteric (\u2206\u03b6T) and halosteric (\u2206\u03b6S) components:\n\u0394\ud835\udf01\ud835\udc47=\u222b\ud835\udf02\ud835\udc3b(\ud835\udefc\u0394\ud835\udc47\u0394\ud835\udc67)\u2212\ud835\udc59\ud835\udf03, (3)\n\u0394\ud835\udf01\ud835\udc46=\u2212\u222b\ud835\udf02\ud835\udc3b\ud835\udefd\u0394\ud835\udc46\u0394\ud835\udc67. (4)\nThe thermosteric sea-level change (resulting from temperature change), \u2206\u03b6T (3), is the depth integral (from the surface, \u03b7, to the full ocean depth, H, with a layer thickness \u0394z) of the change in temperature (\u2206T, \u00b0C) multiplied by the seawater thermal expansion coefficient (\u03b1, \u00b0C\u22121) with the global mean thermosteric sea-level change, \ud835\udc59\ud835\udf03, removed. We focus on the thermosteric component with its global mean removed to because the spatial pattern of change is the quantity of interest for this study, not the global mean change. The temperature change is the difference in potential temperature from the forced experiment relative to the control (FAF-passiveheat) averaged over the final decade. A similar Eq. (4) can be constructed for the halosteric component of sea-level change, using the change in salinity (S) and the haline contraction coefficient of seawater (\u03b2, dimensionless). Since saline water of a given mass has a smaller volume than the same mass of freshwater, a minus sign converts contraction to expansion, which is more readily comparable with \u2206\u03b6 and \u2206\u03b6T. The halosteric change typically has a near-zero global mean because total ocean salinity changes are small, making only a very small or negligible contribution to the global mean sea-level change (Gregory et al. 2019). \u03b1 and \u03b2 were calculated using the mean temperature, salinity and pressure fields of the final decade of the control simulation using standard nonlinear equations of state (McDougall and Barker 2011).\nA sensitivity test (not shown) found that the calculation of \u2206\u03b6T and \u2206\u03b6S is not strongly affected by the choice of decade used to derive \u03b1 and \u03b2; the effect of the temperature and salinity changes on \u03b1 and \u03b2 are small and it is the spatial patterns of \u0394\ud835\udc47 and \u0394\ud835\udc46 that set \u2206\u03b6T and \u2206\u03b6S. Note that the dynamic sea-level change will differ from the steric change (the sum of \u2206\u03b6T and \u2206\u03b6S) in locations where there is a large barotropic redistribution of density such as the subpolar North Atlantic and the Arctic (Lowe and Gregory 2006; Yin et al. 2010). The dynamic and steric sea-level changes will also differ in locations such as shelf seas, where the change in mass loading of the full water column (a non-steric effect) can be large (Landerer et al. 2007; Yin et al. 2010).\nWe quantify the part of dynamic sea-level change that is non-steric, \u0394\ud835\udf01\ud835\udc41, as\n\u0394\ud835\udf01\ud835\udc41=\u0394\ud835\udf01\u2212\u0394\ud835\udf01\ud835\udc47\u2212\u0394\ud835\udf01\ud835\udc46.(5)\nIn plots of \u0394\ud835\udf01\ud835\udc41, we subtract the area mean to reveal the spatial pattern of non-steric sea-level change, since spatial anomalies are the quantity of interest for this work. According to recent terminology conventions (Gregory et al. 2019), \u0394\ud835\udf01 is related to other components of sea-level change through\n\u0394\ud835\udf01=\u0394\ud835\udc35+\u0394\ud835\udc45\ud835\udc5a+\u0394\ud835\udf01\ud835\udc47+\u0394\ud835\udf01\ud835\udc46\u2212\u0394\u0393\u2212\ud835\udc59\ud835\udc4f,(6)\nwhere \u0394\ud835\udc35 is the change due to the inverse barometer effect, \u0394\ud835\udc45\ud835\udc5a is the manometric sea-level change (due to change in ocean mass per unit area), \u0394\u0393 is the change due gravitational, rotational and deformational (GRD) effects from the redistribution of mass over the surface of the planet, \ud835\udc59\ud835\udc4f is the barystatic change (due to addition of water to the ocean, mostly from land ice). The difference between the dynamic sea-level change and the steric change in the real world is\n\u0394\ud835\udf01\u2212\u0394\ud835\udf01\ud835\udc47\u2212\u0394\ud835\udf01\ud835\udc46=\u0394\ud835\udf01\ud835\udc41=\u0394\ud835\udc35+\u0394\ud835\udc45\ud835\udc5a\u2212\u0394\u0393\u2212\ud835\udc59\ud835\udc4f.(7)\nHowever, in the AOGCMs considered in this study (Table 1) \u0394\u0393 and \ud835\udc59\ud835\udc4f are zero because these processes are not represented. \u0394\ud835\udc35 is not readily quantifiable from these models, but is assumed to be small and average to near zero over long time periods since it is of most relevance on meteorological rather than climate timescales (Ponte 2006; Gregory et al. 2019). Therefore, maps of \u0394\ud835\udf01\ud835\udc41 relative to its global area mean in these models reveals the spatial pattern of \u0394\ud835\udc45\ud835\udc5a, the manometric sea-level change. This sea-level component is broadly analogous to the \u2018barotropic component\u2019 of sea-level change discussed in previous literature, although they are calculated differently (e.g. see Lowe and Gregory 2006).\nDecomposition of ocean heat content change\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-4", "text": "In plots of \u0394\ud835\udf01\ud835\udc41, we subtract the area mean to reveal the spatial pattern of non-steric sea-level change, since spatial anomalies are the quantity of interest for this work. According to recent terminology conventions (Gregory et al. 2019), \u0394\ud835\udf01 is related to other components of sea-level change through\n\u0394\ud835\udf01=\u0394\ud835\udc35+\u0394\ud835\udc45\ud835\udc5a+\u0394\ud835\udf01\ud835\udc47+\u0394\ud835\udf01\ud835\udc46\u2212\u0394\u0393\u2212\ud835\udc59\ud835\udc4f,(6)\nwhere \u0394\ud835\udc35 is the change due to the inverse barometer effect, \u0394\ud835\udc45\ud835\udc5a is the manometric sea-level change (due to change in ocean mass per unit area), \u0394\u0393 is the change due gravitational, rotational and deformational (GRD) effects from the redistribution of mass over the surface of the planet, \ud835\udc59\ud835\udc4f is the barystatic change (due to addition of water to the ocean, mostly from land ice). The difference between the dynamic sea-level change and the steric change in the real world is\n\u0394\ud835\udf01\u2212\u0394\ud835\udf01\ud835\udc47\u2212\u0394\ud835\udf01\ud835\udc46=\u0394\ud835\udf01\ud835\udc41=\u0394\ud835\udc35+\u0394\ud835\udc45\ud835\udc5a\u2212\u0394\u0393\u2212\ud835\udc59\ud835\udc4f.(7)\nHowever, in the AOGCMs considered in this study (Table 1) \u0394\u0393 and \ud835\udc59\ud835\udc4f are zero because these processes are not represented. \u0394\ud835\udc35 is not readily quantifiable from these models, but is assumed to be small and average to near zero over long time periods since it is of most relevance on meteorological rather than climate timescales (Ponte 2006; Gregory et al. 2019). Therefore, maps of \u0394\ud835\udf01\ud835\udc41 relative to its global area mean in these models reveals the spatial pattern of \u0394\ud835\udc45\ud835\udc5a, the manometric sea-level change. This sea-level component is broadly analogous to the \u2018barotropic component\u2019 of sea-level change discussed in previous literature, although they are calculated differently (e.g. see Lowe and Gregory 2006).\nDecomposition of ocean heat content change\uf0c1\nWe can decompose OHC change into components due to changes in ocean temperature and in transport. Following Gregory et al. (2016), we let \u03a6 represent the transport operator that encompasses all processes that affect heat transport, including resolved and parameterized advection, diffusion, and convection. That is, \u03a6(\ud835\udc47)=\u2212\u2207\u2219(\ud835\udc62\ud835\udc62\ud835\udc47+\ud835\udc43\ud835\udc43), the convergence of temperature due to the three dimensional resolved velocity field \ud835\udc62\ud835\udc62 and parameterized subgrid-scale tracer transport processes \ud835\udc43\ud835\udc43. In \u03a6(\ud835\udc47) parentheses around \ud835\udc47 indicates the action of ocean tracer transport on the temperature within the parentheses. At steady state, the ocean has an unperturbed temperature, \ud835\udc47\u2212, and an unperturbed three-dimensional transport, \u03a6\u2212, where overlines indicate a long time average over the control run. The convergence of unperturbed temperature transport, \u03a6\u2212(\ud835\udc47\u2212), is zero in the steady state, except at the surface where it balances the surface heat flux.\nForced climate change modifies the surface fluxes. It alters the ocean temperature by an amount T\u2032, relative to the unperturbed state by the addition of heat, and the transport by \u03a6\u2032 through changing both the wind driven and density driven transports. As a result, the convergence \u03a6(\ud835\udc47) of heat is modified as well and is no longer zero. Hence, interior temperature changes according to\n\u2202\ud835\udc47\u2032\u2202\ud835\udc61=[\u03a6\u2212 + \u03a6\u2032](T\u2212 + \ud835\udc47\u2032) = \u03a6\u2212(\ud835\udc47\u2032)+\u03a6\u2032(T\u2212) + \u03a6\u2032(\ud835\udc47\u2032), (8)\nwhere [\u03a6\u2212+\u03a6\u2032](\ud835\udc47\u2212+\ud835\udc47\u2032) is symbolically the action of both the unperturbed and perturbed transport acting on the unperturbed and perturbed temperature. Note also that \u03a6\u2212(\ud835\udc47\u2212)=0.\nThus we distinguish three different causes of temperature change that arise from the convergence of: \u03a6\u2212(\ud835\udc47\u2032), transport of the added heat by the unperturbed transport processes; \u03a6\u2032(\ud835\udc47\u2212), changes in the ocean transport redistributing unperturbed heat; and \u03a6\u2032(\ud835\udc47\u2032), perturbation in the transport that redistributes the added heat (8).\nIf the oceans absorbed the added heat from anthropogenic climate change like a passive tracer that does not affect ocean circulation or other transport processes, then OHU would be driven entirely by the first term, \u03a6\u2212(\ud835\udc47\u2032). This term is therefore the \u201cpassive uptake of added heat\u201d. In reality, the ocean circulation and subgrid scale processes are affected by temperature change and other surface flux changes, so the other terms play a part. The second term is a pure redistribution, whose global volume integral is small (but not precisely zero because \ud835\udc47\u2212 can be fluxed to the atmosphere). The final term is of second order in perturbation quantities, but it is not always negligible.\nConsider the following illustrative situation in a convective zone of the Labrador Sea, where climate change causes increased heat flux into the ocean, and the ocean temperature gets warmer at around 250 m depth. Positive \u03a6\u2212(\ud835\udc47\u2032) describes the change in temperature that results from the unperturbed circulation and subgrid processes that passively transport the additional heat downwards. However, these transport processes are weakened by the input of \ud835\udc47\u2032 because the air-sea heat input strengthens stratification and weakens downward heat transport by convection. The weakened downward transport carries less additional heat than in the passive case; and \u03a6\u2032(\ud835\udc47\u2032) is weakly negative because \u03a6\u2032 is negative. Finally, weakened downward transport means that less heat from lower latitudes gets brought northward and downward, causing strongly negative \u03a6\u2032(\ud835\udc47\u2212).\nFAFMIP experiments and diagnostics allow for the three contributions to the change in the convergence of heat to be distinguished. We can express the change in ocean heat content (\u2206h, Jm\u22122) due to each contribution by converting the appropriate temperature (T) field using a reference heat capacity for seawater (cp0\u2009=\u20094000 J kg\u22121 K\u22121), a reference density (\u03c10 = 1026 kg m\u22123) and the ocean grid cell vertical thickness (\u0394z, m). Differencing particular experiments and temperature fields (T, Ta, or Tr) yields different components of OHC change. Further notes on the time evolution of Tr, Ta and T, describing how different temperature change terms are grouped in the decomposition are included in the \u201cAppendix\u201d.\nThe OHC change due all three convergences of temperature in (8), \u0394h, is\n\u0394\u210e=\u0394\ud835\udc47\ud835\udc50\ud835\udc5d0\ud835\udf0c0\u0394\ud835\udc67, (9)\nwhere \u2206T, is the difference of the model\u2019s temperature field (T) between the final decades of FAF-heat and FAF-passiveheat (9). In FAF-heat, the heat flux changes the transport processes (\u03a6\u2032 \u2260 0) and the temperature (\ud835\udc47\u2032 \u2260 0) and, thus there is a change in heat content due to all three types of temperature convergence.\nThe OHC change due to passive uptake of additional heat, \u0394\u210e[\u03a6\u23af\u23af\u23af\u23af\u23af(\ud835\udc47\u2032)] is\n\u0394\u210e[\u03a6\u23af\u23af\u23af\u23af\u23af(\ud835\udc47\u2032)]=\ud835\udc47\u23af\u23af\u23af\u23af\ud835\udc4e\ud835\udc50\ud835\udc5d0\ud835\udf0c0\u0394\ud835\udc67, (10)\nwhere the notation \u0394\u210e[\u2026] symbolically represents the change in OHC due to the convergence of temperature enclosed by the square brackets. Since passive temperature is initially 0, its decadal mean change by the end of simulation is simply \ud835\udc47\u2212\ud835\udc4e, the time mean Ta from FAF-passiveheat for the years 61\u201370.\nThe OHC change due to the redistribution of unperturbed temperature, \u0394\u210e[\u03a6\u2032(\ud835\udc47\u23af\u23af\u23af\u23af)] is\n\u0394\u210e[\u03a6\u2032(\ud835\udc47\u23af\u23af\u23af\u23af)]=\u0394\ud835\udc47\ud835\udc5f\ud835\udc50\ud835\udc5d0\ud835\udf0c0\u0394\ud835\udc67, (11)\nwhere \u2206Tr is the difference between FAF-heat redistributed temperature, Tr, and FAF-passiveheat T, averaged over the final decade.\nThe OHC change due to the perturbation in the transport redistributing the added heat, \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2032)] is", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-5", "text": "The OHC change due all three convergences of temperature in (8), \u0394h, is\n\u0394\u210e=\u0394\ud835\udc47\ud835\udc50\ud835\udc5d0\ud835\udf0c0\u0394\ud835\udc67, (9)\nwhere \u2206T, is the difference of the model\u2019s temperature field (T) between the final decades of FAF-heat and FAF-passiveheat (9). In FAF-heat, the heat flux changes the transport processes (\u03a6\u2032 \u2260 0) and the temperature (\ud835\udc47\u2032 \u2260 0) and, thus there is a change in heat content due to all three types of temperature convergence.\nThe OHC change due to passive uptake of additional heat, \u0394\u210e[\u03a6\u23af\u23af\u23af\u23af\u23af(\ud835\udc47\u2032)] is\n\u0394\u210e[\u03a6\u23af\u23af\u23af\u23af\u23af(\ud835\udc47\u2032)]=\ud835\udc47\u23af\u23af\u23af\u23af\ud835\udc4e\ud835\udc50\ud835\udc5d0\ud835\udf0c0\u0394\ud835\udc67, (10)\nwhere the notation \u0394\u210e[\u2026] symbolically represents the change in OHC due to the convergence of temperature enclosed by the square brackets. Since passive temperature is initially 0, its decadal mean change by the end of simulation is simply \ud835\udc47\u2212\ud835\udc4e, the time mean Ta from FAF-passiveheat for the years 61\u201370.\nThe OHC change due to the redistribution of unperturbed temperature, \u0394\u210e[\u03a6\u2032(\ud835\udc47\u23af\u23af\u23af\u23af)] is\n\u0394\u210e[\u03a6\u2032(\ud835\udc47\u23af\u23af\u23af\u23af)]=\u0394\ud835\udc47\ud835\udc5f\ud835\udc50\ud835\udc5d0\ud835\udf0c0\u0394\ud835\udc67, (11)\nwhere \u2206Tr is the difference between FAF-heat redistributed temperature, Tr, and FAF-passiveheat T, averaged over the final decade.\nThe OHC change due to the perturbation in the transport redistributing the added heat, \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2032)] is\n\u0394\u210e[\u03a6\u2032(\ud835\udc47\u2032)]=\u0394\ud835\udc47\ud835\udc4e\ud835\udc50\ud835\udc5d0\ud835\udf0c0\u0394\ud835\udc67, (12)\nwhere \u0394\ud835\udc47\ud835\udc4e is the difference of Ta between FAF-heat and FAF-passiveheat (12).\nModels analysed\uf0c1\nDifferent suites of models are analysed in different parts of this work, subject to the availability of output fields. The first analysis required sea-surface height above geoid, \u03b6, ocean temperature, and seawater salinity, available from 13 FAFMIP AOGCMs (Table 1), although less than the full set of output for all experiments was available for CESM2, GISS-E2-R-CC and MIROC6. The ocean heat budget decomposition in Sect. 3.5 required 3-D fields of redistributed and added temperature, available for ten FAFMIP models (the exceptions being CESM2, GISS-E2-R-CC and MIROC6). A comparison of the sea-level response to 1pctCO2 forcing was also performed for a suite of 19 CMIP5 models and 16 CMIP6 models listed in Table 2. The \u2018zos\u2019 fields of MIROC5, CAMS-CSM1-0 and GISS-E2-1-G required correction for the inverse barometer effect due to sea ice loading, following (Griffies et al. 2016).\nTable 2: List of models from CMIP5 and CMIP6 that appear in Fig. 4\nFrom the 13 models that have performed FAFMIP experiments, five are from the CMIP5 era, seven from CMIP6, and one (HadCM3) is pre-CMIP5. All ocean model components of models feature similar horizontal resolution (roughly 1-by-1 degree of latitude), and so unresolved features such as mesoscale eddies are parameterized. Even the finest of these ocean grids (MPI-ESM1-2-HR, about 0.4-by-0.4 degrees of latitude) is \u2018eddy-permitting\u2019 and not \u2018eddy-resolving\u2019, as it can resolve some large ocean eddies, but it still employs an eddy flux parameterization to represent unresolved mesoscale and sub-mesoscale processes. While horizontal resolution is broadly similar across models, details such as the vertical grids or refined resolution near the equator are model-specific.\nResults\uf0c1\nFAF-all versus 1pctCO2\uf0c1\nThis section explores the diversity in \u0394\u03b6 in FAF-all versus 1pctCO2, to demonstrate the extent to which patterns of \u0394\u03b6 are generated by ocean processes rather than by the patterns and magnitude of all fluxes.\nThe spatial pattern of the sea-level response to all flux perturbations applied simultaneously (FAF-all, Fig. 3a) is similar to the pattern that results from 1pctCO2 forcing (Fig. 3c). The agreement between responses to 1pctCO2 and FAF-all forcing is an intended feature of the experimental design and shows that the mean pattern of CO2-forced sea-level change can be reproduced when the models are forced instead with perturbations to their surface fluxes. The spatial standard deviation of \u2206\u03b6 is a useful scalar that summarizes the magnitude (or heterogeneity) of the spatial pattern of dynamic sea-level change. The spatial standard deviation of \u2206\u03b6 is 0.082 m for FAF-all; larger than 0.059 m for 1pctCO2, indicating a stronger spatial pattern in FAF-all.\nFig. 3: Ocean dynamic sea-level response \u0394\u03b6 to greenhouse gas forcing in 1pctCO2 runs (above) and FAF-all runs (below) for 11 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0. Mean across models (above) and standard deviation across models (below)\nThe three prominent features of regional sea-level change identified in previous work (Church et al. 2013; Slangen et al. 2014; Gregory et al. 2016) are apparent here: (1) the Southern Ocean meridional gradient with positive \u0394\u03b6 north of 55\u00b0 S and negative \u0394\u03b6 at higher latitudes, (2) the meridional dipole of positive \u0394\u03b6 in the northern North Atlantic against weakly negative \u0394\u03b6 in the southern North Atlantic, and (3) positive \u0394\u03b6 in the Arctic.\nThe large positive \u0394\u03b6 in the North Atlantic is greater in magnitude in FAF-all than 1pctCO2. This is due to the \u201cNorth Atlantic redistribution feedback\u201d, wherein the heat flux perturbation (which is strongly positive in the North Atlantic) causes the AMOC to decline (Winton et al. 2013; Gregory et al. 2016). The weakening of the AMOC reduces the northward heat transport, thus redistributing the OHC, leading to cooler SST at high latitudes, and reinforcing ocean heat uptake there (by reducing the heat loss from the ocean to the atmosphere). This occurs because the atmosphere is coupled to the redistributed temperature, Tr, and therefore \u201csees\u201d a cooling in the North Atlantic due to redistribution, but does not respond to the added heat, which it cannot see. Because of this feedback, the heat input into the North Atlantic is about double what it would be in a 1pctCO2 simulation. By comparing FAF-heat experiments with two corresponding pairs of an AOGCM and an OGCM, Todd et al. (2020) find, however, that the AMOC weakening is greater by only about 10% in the AOGCM case due to the feedback. Their finding is consistent with our results, where the total OHC change in FAF-heat is about 10% greater (due to the redistribution feedback) than the time- and area-integral of the imposed perturbation. The feedback is a complicating feature of the simulation design, but does not diminish the utility of the experiments, because the imposed heat flux perturbation is the same for all models. The degree of AMOC weakening (and ocean heat transport change) shown by each model reflects the sensitivity of each model to common forcing, regardless of whether it resulted directly from the forcing or through the redistribution feedback.", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-6", "text": "The three prominent features of regional sea-level change identified in previous work (Church et al. 2013; Slangen et al. 2014; Gregory et al. 2016) are apparent here: (1) the Southern Ocean meridional gradient with positive \u0394\u03b6 north of 55\u00b0 S and negative \u0394\u03b6 at higher latitudes, (2) the meridional dipole of positive \u0394\u03b6 in the northern North Atlantic against weakly negative \u0394\u03b6 in the southern North Atlantic, and (3) positive \u0394\u03b6 in the Arctic.\nThe large positive \u0394\u03b6 in the North Atlantic is greater in magnitude in FAF-all than 1pctCO2. This is due to the \u201cNorth Atlantic redistribution feedback\u201d, wherein the heat flux perturbation (which is strongly positive in the North Atlantic) causes the AMOC to decline (Winton et al. 2013; Gregory et al. 2016). The weakening of the AMOC reduces the northward heat transport, thus redistributing the OHC, leading to cooler SST at high latitudes, and reinforcing ocean heat uptake there (by reducing the heat loss from the ocean to the atmosphere). This occurs because the atmosphere is coupled to the redistributed temperature, Tr, and therefore \u201csees\u201d a cooling in the North Atlantic due to redistribution, but does not respond to the added heat, which it cannot see. Because of this feedback, the heat input into the North Atlantic is about double what it would be in a 1pctCO2 simulation. By comparing FAF-heat experiments with two corresponding pairs of an AOGCM and an OGCM, Todd et al. (2020) find, however, that the AMOC weakening is greater by only about 10% in the AOGCM case due to the feedback. Their finding is consistent with our results, where the total OHC change in FAF-heat is about 10% greater (due to the redistribution feedback) than the time- and area-integral of the imposed perturbation. The feedback is a complicating feature of the simulation design, but does not diminish the utility of the experiments, because the imposed heat flux perturbation is the same for all models. The degree of AMOC weakening (and ocean heat transport change) shown by each model reflects the sensitivity of each model to common forcing, regardless of whether it resulted directly from the forcing or through the redistribution feedback.\nWhen the different AOGCMs are forced with identical surface flux perturbations in FAF-all, the spread in sea-level response (Fig. 3d) is similar to the spread that results from 1pctCO2 forcing (Fig. 3b). The largest spread of sea-level change among the 11 models (measured as the standard deviation across models) is focused on the same three regions in FAF-all as in 1pctCO2\u2014the Arctic, the Southern Ocean, and the North Atlantic\u2014and is of similar magnitude. The area mean of inter-model standard deviation is 0.045 m in 1pctCO2, and 0.046 m in FAF-all. This evidence indicates that much of the spread in projections of the dynamic sea-level response to climate forcing arises due to differences in ocean model formulation, rather than in the surface flux forcing from the diverse atmosphere models. This conclusion is different from that of Huber and Zanna (2017), who found that the parametric uncertainty of a given model is too small to explain the spread of ocean responses to climate change. The dynamic sea-level responses of the individual AOGCMs to FAF-all forcing are included in the \u201cAppendix\u201d (Fig. 13 in \u201cAppendix\u201d).\nSea-level response to 1% per year CO2 forcing in CMIP5 and CMIP6\uf0c1\nThere is strong similarity between the sea-level responses to 1pctCO2 forcing from the much larger CMIP5/6 ensembles (Fig. 4a, c) and the sea-level responses to our smaller suite of FAFMIP models (Fig. 3), especially in the North Atlantic, Arctic, and Southern oceans. This similarity indicates that the FAFMIP-participant models form a representative subset of the wider CMIP5 and CMIP6 ensembles. It also suggests that the findings of FAFMIP are likely to be applicable to a wider range of models than the 13 FAFMIP models analysed here.\nFig. 4: Multi model mean projections of \u2206\u03b6 (left) from 1pctCO2 forcing experiments averaged over years 91\u2013100 for 19 CMIP5 models (a), 16 CMIP6 models (c). Standard deviation of the model spread (right). Models used are described in Table 2\nThe 1pctCO2 response in the two different CMIP eras is similar (Fig. 4a, c), in agreement with recent findings (Lyu et al. 2020). The similarity of responses of models from the different eras indicates that models from across the eras may be analysed together as one ensemble, rather than separately. The current generation of AOGCMs show diverse sea-level responses in the Arctic, Southern Ocean, North Atlantic and North Pacific (Fig. 4d), much like the previous generation (Fig. 4b), indicating a continuing need to focus on these regions.\nThe CMIP5 ensemble uses ten different ocean components (ignoring version differences) among its 19 members (Table 2). In the 16 different CMIP6 AOGCMs shown, there are eight different ocean model components. In the CMIP6 ensemble, six models use a version of NEMO (Nucleus for European Modelling of the Ocean), three use POP (Parallel Ocean Program), two use MOM (Modular Ocean Model), and the remaining five use an ocean component unique to the ensemble. Hence, there is a greater diversity of ocean components in terms of the number of unique ocean models in CMIP5. For all the CMIP6 models that use NEMO, the horizontal ocean resolution of the ORCA1 grid used is the same (roughly 1\u00b0-by-1\u00b0 of latitude, with a refinement to 1/3\u00b0 at equator), although different AOGCMs use different numbers of ocean vertical levels, which has effects on Southern Ocean OHU (Stewart and Hogg 2019). One might argue that there is a decrease in the diversity of representations of ocean processes in this ensemble of CMIP6 models, but the increasing use of common ocean components has apparently not reduced the spread of sea-level projections in response to 1pctCO2 forcing in the CMIP6 era versus CMIP5 (Fig. 4b, d). Sea-level projections from the CMIP6 ensemble were checked for similarities among models sharing a similar ocean component, but no clear correlation exists (not shown). One might therefore expect that diversity in air-sea fluxes (rather than in ocean models) causes the spread (e.g., Huber and Zanna 2017). However, the increased use of common ocean components does not necessarily mean that water properties and ocean transport processes are represented in the same way across models. NEMO and other ocean components support a potentially enormous variety of configurations through customisable combinations of different parameterisations and schemes, and spin-up procedures. Parameter choices of, for example, coefficients of vertical diffusivity and eddy mixing are important for setting OHU in the Pacific and Southern Oceans (Huber and Zanna 2017). The convergence of structure in ocean components does not directly translate into convergent representations of ocean heat uptake.\nOcean response to perturbations in individual fluxes\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-7", "text": "The CMIP5 ensemble uses ten different ocean components (ignoring version differences) among its 19 members (Table 2). In the 16 different CMIP6 AOGCMs shown, there are eight different ocean model components. In the CMIP6 ensemble, six models use a version of NEMO (Nucleus for European Modelling of the Ocean), three use POP (Parallel Ocean Program), two use MOM (Modular Ocean Model), and the remaining five use an ocean component unique to the ensemble. Hence, there is a greater diversity of ocean components in terms of the number of unique ocean models in CMIP5. For all the CMIP6 models that use NEMO, the horizontal ocean resolution of the ORCA1 grid used is the same (roughly 1\u00b0-by-1\u00b0 of latitude, with a refinement to 1/3\u00b0 at equator), although different AOGCMs use different numbers of ocean vertical levels, which has effects on Southern Ocean OHU (Stewart and Hogg 2019). One might argue that there is a decrease in the diversity of representations of ocean processes in this ensemble of CMIP6 models, but the increasing use of common ocean components has apparently not reduced the spread of sea-level projections in response to 1pctCO2 forcing in the CMIP6 era versus CMIP5 (Fig. 4b, d). Sea-level projections from the CMIP6 ensemble were checked for similarities among models sharing a similar ocean component, but no clear correlation exists (not shown). One might therefore expect that diversity in air-sea fluxes (rather than in ocean models) causes the spread (e.g., Huber and Zanna 2017). However, the increased use of common ocean components does not necessarily mean that water properties and ocean transport processes are represented in the same way across models. NEMO and other ocean components support a potentially enormous variety of configurations through customisable combinations of different parameterisations and schemes, and spin-up procedures. Parameter choices of, for example, coefficients of vertical diffusivity and eddy mixing are important for setting OHU in the Pacific and Southern Oceans (Huber and Zanna 2017). The convergence of structure in ocean components does not directly translate into convergent representations of ocean heat uptake.\nOcean response to perturbations in individual fluxes\uf0c1\nComparison of the multi model mean \u2206\u03b6 from FAF-all with the sea-level response to individual perturbations allows us to determine which features result from changes to each flux. The spatial pattern of sea-level change from the heat flux forcing (Fig. 5c) most closely matches the response to all perturbations simultaneously applied (Fig. 3c). For FAF-heat, the spatial standard deviation is 0.080 m, which is close to that of FAF-all (0.082 m). The spatial standard deviation is 0.021 m for FAF-stress and 0.018 m for FAF-water. This indicates that the heat flux contributes the most to the sea-level change in FAF-all and 1pctCO2, in agreement with previous work (Bouttes and Gregory 2014; Gregory et al. 2016). The wind stress perturbation causes part of the pattern of \u2206\u03b6, but its influence is mostly confined to the Southern Ocean (Fig. 5a). There, strengthened and poleward-shifted westerlies steepen the meridional sea-level gradient across the ACC (Frankcombe et al. 2013). The freshwater perturbation contributes the least sea-level change of the three perturbations, but it sets part of the spatial pattern of \u2206\u03b6 in the Southern and Arctic Oceans (Fig. 5e). Recall that the three key locations for which models show diverse predictions of \u2206\u03b6 in 1pctCO2 and FAF-all were the Arctic, the eastern subpolar North Atlantic and the Southern Ocean south of Australia and New Zealand (Fig. 3c, d). There is coincident diversity in the FAF-heat responses (Fig. 5d), which suggests that spread in FAF-all is due primarily to the heat flux perturbation. The dynamic sea-level responses of each AOGCM to each individually applied flux perturbation are shown in the \u201cAppendix\u201d (Fig. 13\u201316).\nFig. 5: Maps of multi model ensemble mean ocean dynamic sea-level response to individually-applied flux perturbations (left) and standard deviation across 13 AOGCMs (right) for the wind stress (FAF-stress, top), heat flux (FAF-heat, middle), and water flux (FAF-water, bottom) experiments. AOGCMs used: ACCESS-CM2, CanESM2, CanESM5, CESM2 (FAF-stress and FAF-water only), GFDL-ESM2M, GISS-E2-R-CC (FAF-stress and FAF-water only), HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0\nWind stress\uf0c1\nThe wind stress perturbation creates a gradient of \u2206\u03b6 across the Southern Ocean (Fig. 5a). The intensified Southern Ocean westerlies drive a northward positive meridional \u2206\u03b6 gradient with a zonal mean of 0.05\u20130.025 m from 75\u00b0 to 35\u00b0 S. South of 60\u00b0 S, \u2206\u03b6 diverges depending on the model (Fig. 5b). The models disagree on whether the wind stress perturbation causes negative or weakly positive depth integrated OHC change south of 60\u00b0 S (Fig. 6g), which is not yet well understood but merits further investigation. The wind stress perturbation tends to weakly warm the surface ocean, cool the shallow subsurface and warm the deeper ocean (Fig. 6d, j). Part of the discrepancy between models occurs because although this area-integrated picture is qualitatively common to models, the depth at which each OHC change inflection occurs is model-specific. In agreement with Gregory et al. (2016), while the local OHC change due to the wind stress perturbation can be large (Fig. 6a, g, j) its global integral is small; two orders of magnitude smaller than the heat flux perturbation (not shown). Other work finds that the Southern Ocean OHC response to wind stress change is sensitive to the location of the zero wind stress curl, which may be a source of some of the spread reported here (Stewart and Hogg 2019).\nFig. 6: Multi model ensemble mean integrated ocean heat content (OHC) change for FAF-stress (left), FAF-heat (middle), FAF-water (right) for 12 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, CESM2 (FAF-stress and FAF-water only), GFDL-ESM2M, GISS-E2-R-CC (FAF-stress and FAF-water only), HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0. Depth integrated OHC change (a\u2013c), area integrated OHC change (d\u2013f), zonally and depth integrated OHC change (g\u2013i), zonally integrated OHC change (j\u2013l). Dashed lines in d\u2013i indicate\u2009\u00b1\u20092 standard deviations of ensemble spread. 1 GJ\u2009=\u2009109 J, 1 ZJ\u2009=\u20091021 J, 1 EJ\u2009=\u20091018 J\nThe maps of \u2206\u03b6T, \u2206\u03b6S and \u2206\u03b6N show that the wind forced sea-level change in the Southern Ocean is almost entirely thermosteric (Fig. 7c), as suggested by Gregory et al. (2016). The perturbation causes heat to accumulate between 55\u00b0 and 30\u00b0 S while higher latitudes cool (Fig. 6a, g). This is consistent with a wind driven enhancement of the residual meridional overturning documented elsewhere (Liu et al. 2018). The halosteric change in the Southern Ocean is much smaller and opposes the thermosteric change (Fig. 7e). The wind-forced \u2206\u03b6T change is largest in the Atlantic and Indian sectors of the Southern Ocean, and the models generally agree on the pattern and magnitude of this feature, although the details of the magnitude near the South American coast are model dependent, (Fig. 7d). The non-steric component dominates the sea-level change in the Antarctic shallow shelf seas (Fig. 7g). Elsewhere, in the Pacific sector and Weddell Sea, the AOGCMs predict different magnitudes of negative \u2206\u03b6 (Fig. 7a, b) and this spread is thermosteric (Fig. 7d).", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-8", "text": "The maps of \u2206\u03b6T, \u2206\u03b6S and \u2206\u03b6N show that the wind forced sea-level change in the Southern Ocean is almost entirely thermosteric (Fig. 7c), as suggested by Gregory et al. (2016). The perturbation causes heat to accumulate between 55\u00b0 and 30\u00b0 S while higher latitudes cool (Fig. 6a, g). This is consistent with a wind driven enhancement of the residual meridional overturning documented elsewhere (Liu et al. 2018). The halosteric change in the Southern Ocean is much smaller and opposes the thermosteric change (Fig. 7e). The wind-forced \u2206\u03b6T change is largest in the Atlantic and Indian sectors of the Southern Ocean, and the models generally agree on the pattern and magnitude of this feature, although the details of the magnitude near the South American coast are model dependent, (Fig. 7d). The non-steric component dominates the sea-level change in the Antarctic shallow shelf seas (Fig. 7g). Elsewhere, in the Pacific sector and Weddell Sea, the AOGCMs predict different magnitudes of negative \u2206\u03b6 (Fig. 7a, b) and this spread is thermosteric (Fig. 7d).\nFig. 7: Multi model ensemble mean dynamic sea-level response to momentum flux forcing (a) and the standard deviation across models (b) for 13 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, CESM2, GFDL-ESM2M, GISS-E2-R-CC, HadCM3, HadGEM2-ES, HadGEM-GC31-LL, MIROC6, MPI-ESM1-2-HR, MPI-ESM-LR and MRI-ESM2-0. Multi model mean momentum flux-forced thermosteric (c), halosteric (e), and non-steric (g) contributions, and the standard deviation across models (d, f, h) where the area mean has been subtracted from (g)\nIn some models, but not all, the wind stress perturbation drives sea-level change in the Arctic East Siberian Sea and northwestern Atlantic (Fig. 5b). GISS-E2-R-CC predicts widespread, large positive \u2206\u03b6 in the Arctic, while CanESM5, MPI-ESM1-2-HR and HadCM3 predict a gradient of \u2206\u03b6 that is negative at the pole and increases southwards (Fig. 14). HadGEM3-GC31-LL shows positive \u2206\u03b6 at the pole. The other models predict near zero \u2206\u03b6 in the Arctic. The spread in the North Atlantic is due to the responses of HadGEM2-ES, MPI-ESM-LR, MPI-ESM1-2-HR and GFDL-ESM2M, which predict weakly positive \u2206\u03b6T and \u2206\u03b6S here, while the other models show \u2206\u03b6 \u2248 0 (Fig. 14).\nHeat flux\uf0c1\nThe heat flux perturbation drives the most change in sea level, both in terms of magnitude and area of effect (Fig. 5c). The perturbation causes positive OHC change over most of the ocean area (Fig. 6b) in the upper 1000 m (Fig. 6e, k). Note that even though the heat flux perturbation adds large amounts of heat to the global ocean, it is possible for the net OHC change in some locations to be weakly negative; either because of negative values of the perturbation flux or via the redistribution of heat by changing ocean transport. The models agree that the largest OHC change occurs in south of 30\u00b0 S, and the changes elsewhere are more model dependent (Fig. 6h). In the upper 300 m, the ensemble spread of the area integrated OHC change is on the order of half the mean change (Fig. 6e). This spread indicates that the strength of the mechanisms by which heat is transported away from the surface is different among models. The largest values of \u2206\u03b6 are in the North Atlantic. The most intense perturbation to the heat flux per unit area is directed here. As described earlier in Sect. 3.1, the North Atlantic redistribution feedback means that the magnitude of North Atlantic sea-level response is greater in FAF-heat and FAF-all than in 1pctCO2 experiments.\nIn general, the pattern of \u2206\u03b6 is similar across most models, and the magnitude of the change varies between models (Fig. 5). The fact that the hotspots of inter-model spread (Fig. 5d) are coincident with most of the strongest \u2206\u03b6 features reflects this. The multi-model mean map of \u2206\u03b6 (Fig. 5c) therefore reflects a pattern that is very similar to each individual model\u2019s response, rather than the mean of several very different patterns. Most models show the maximum \u2206\u03b6 between 45\u00b0 and 65\u00b0 N in the western North Atlantic (Fig. 15). All models predict the Atlantic dipole of positive \u2206\u03b6 north of 45\u00b0 N and weakly negative \u2206\u03b6 near Cape Hatteras in the western basin around 35\u00b0 N. The weak dynamic sea-level drop occurs at the center of the subtropical gyre, consistent with the decline of the dynamic sea-level gradient across the Gulf Stream. In the eastern basin off the west Saharan-African coast most models predict a \u201ctropical arm\u201d of positive \u2206\u03b6 that diminishes westward (Fig. 5c), which is weak in HadGEM2-ES and absent in GFDL-ESM2M (which shows near zero \u2206\u03b6, Fig. 15e, h). Most models predict a small region of negative \u2206\u03b6 north of Iceland. MPI-ESM-LR and MRI-ESM2-0 instead predict positive \u2206\u03b6 north of Iceland and negative/neutral \u2206\u03b6 to the south of Iceland (Fig. 15k, m). HadGEM2-ES and MPI-ESM1-2-HR exhibit regions of negative/neutral \u2206\u03b6 both south and north of Iceland (Fig. 15h, l).\nThe steric sea-level rise in the Atlantic subpolar gyre, north of 45\u00b0 N, is due predominantly to positive \u2206\u03b6S (i.e. freshening), opposed by weaker negative \u2206\u03b6T (Fig. 8c). North of 45\u00b0 N, there is positive \u2206\u03b6S and weaker negative \u2206\u03b6T,, in agreement with previous work (Bouttes et al. 2014; Saenko et al. 2015). This is consistent with a reduced northward flux of heat and salt as a result of a weakened AMOC. The models disagree on the magnitude of \u2206\u03b6, particularly to the south of Iceland (Fig. 8b) and most of this spread is due to diversity in predictions of thermosteric change, but the halosteric response is also uncertain across models (Fig. 8d, f). The sea-level change on the shelves of the subpolar North Atlantic has a strong non-steric component (Fig. 8g), consistent with an increase of on-shelf ocean mass (Yin et al. 2010).\nFig. 8: Multi model ensemble mean dynamic sea-level response to heat flux forcing (a) and the standard deviation across models (b) for 11 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR, MRI-ESM2-0. Multi model mean heat flux-forced thermosteric (c), halosteric (e), and non-steric (g) contributions, and the standard deviation across models (d, f, h) where the area mean has been subtracted from (g)", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-9", "text": "The steric sea-level rise in the Atlantic subpolar gyre, north of 45\u00b0 N, is due predominantly to positive \u2206\u03b6S (i.e. freshening), opposed by weaker negative \u2206\u03b6T (Fig. 8c). North of 45\u00b0 N, there is positive \u2206\u03b6S and weaker negative \u2206\u03b6T,, in agreement with previous work (Bouttes et al. 2014; Saenko et al. 2015). This is consistent with a reduced northward flux of heat and salt as a result of a weakened AMOC. The models disagree on the magnitude of \u2206\u03b6, particularly to the south of Iceland (Fig. 8b) and most of this spread is due to diversity in predictions of thermosteric change, but the halosteric response is also uncertain across models (Fig. 8d, f). The sea-level change on the shelves of the subpolar North Atlantic has a strong non-steric component (Fig. 8g), consistent with an increase of on-shelf ocean mass (Yin et al. 2010).\nFig. 8: Multi model ensemble mean dynamic sea-level response to heat flux forcing (a) and the standard deviation across models (b) for 11 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR, MRI-ESM2-0. Multi model mean heat flux-forced thermosteric (c), halosteric (e), and non-steric (g) contributions, and the standard deviation across models (d, f, h) where the area mean has been subtracted from (g)\nThe thermosteric and halosteric effects change sign south of 45\u00b0 N and the thermal effect dominates, but they compensate more closely, and so \u2206\u03b6 is smaller than further north. The 45\u00b0 N latitude line coincides with the divide between the North Atlantic subpolar and subtropical gyres formed by the northern boundary of the North Atlantic Current. The opposing changes either side of the divide are consistent with a change in the inter-gyre exchange of heat and salt: a warmer and saltier subtropical gyre and a cooler and fresher subpolar gyre. Further south, most models predict positive \u2206\u03b6 in the eastern basin off the West African coast (Fig. 8a). There is also considerable inter-model spread in the thermosteric and halosteric contributions (Fig. 8d, f). Interestingly, five models predict a mixture of thermo- and halosteric contributions (ACCESS-CM2, CanESM2, CanESM5, HadGEM3-GC31-LL, MPI-ESM1-2-HR), four models predict the tropical arm as being purely halosteric (HadCM3, MIROC6, MPI-ESM-LR and MRI-ESM2-0), one model predicts a purely thermosteric effect (HadGEM2-ES), and one model shows no positive \u2206\u03b6 feature here at all (GFDL-ESM2M) (not shown).\nIn the North Pacific, all models respond to the heat flux perturbation with a North\u2013South dipole in \u2206\u03b6 that changes sign around 35\u00b0 N (Fig. 8c). This meridional dipole has the opposite sign to that of the North Atlantic. In the western basin, the pattern is essentially the same across models, and its extent eastward is model dependent (Fig. 15). The dipole is mostly thermosteric (Fig. 8c), owing to a stronger accumulation of heat per unit area north of 35\u00b0 N in the region east of Newfoundland than further south (Fig. 6b). This is sea-level change is consistent with a steepening of the across-current sea-level slope, and an intensification of the Kuroshio western boundary current (Chen et al. 2019).\nThe lower latitudes of the Arctic around the East Siberian and Beaufort Seas show positive \u2206\u03b6 in response to the heat flux perturbation, while \u2206\u03b6 is negative at higher latitudes. The only exception to this is HadCM3 (Fig. 15), which predicts strongly negative \u2206\u03b6 everywhere in the Arctic, contributing strongly to the large inter-model spread there (Fig. 8b). The Arctic shows a strong non-steric component of \u2206\u03b6 (Fig. 8g), corresponding to a shift of mass from the highest latitudes onto the shelves. The patterns of Arctic sea-level change in 1pctCO2 and FAF-all are very similar (Fig. 3), suggesting that the coupling of sea ice to redistributed temperature rather than regular temperature in FAFMIP experiments (Sect. 2.2) does not introduce unintended effects on ocean transport. Nevertheless, the diverse representations of sea ice in AOGCMs generally remains a key source of uncertainty in the projection of future polar climate change (Meredith et al. 2019).\nThe Southern Ocean sea-level change in response to heat flux forcing is smallest at the highest latitudes (negative \u2206\u03b6), changing sign to positive \u2206\u03b6 between 40\u00b0 and 55\u00b0 S (Fig. 8a). All models predict a maximum of \u2206\u03b6 off the South African coast that extends eastward. The spatial pattern of negative \u2206\u03b6 across much of the Southern Ocean is predicted by all models. CanESM2, HadGEM3-GC31-LL, MPI-ESM-LR and GFDL-ESM2M (and to a lesser extent, HadCM3 and ACCESS-CM2) show positive \u2206\u03b6 in the sector between 130\u00b0 and 160\u00b0 E, south of Australia and New Zealand (not shown). This inter-model variation is also identifiable in the spread of sea-level responses in FAF-all (Fig. 3d) and is thermosteric (Fig. 8d).\nThe Southern Ocean \u0394\u03b6 zonal gradient in FAF-heat is the result of both thermosteric and halosteric effects (Fig. 8a, c, e). Gregory et al. (2016) pointed out that the gradient of \u0394\u03b6 across the Southern Ocean arises primarily because more heat accumulates in the mid latitudes (around 45\u00b0 S) than further south (Fig. 9a). However, if sea-level change were simply proportional to OHU, then \u0394\u03b6 would show a prominent maximum at 45\u00b0 S and decline until 25\u00b0 S. Instead, \u0394\u03b6 increases northward to about 45\u00b0 S, with only a slight decline further North (Fig. 9b, solid black line). The waters further North are warmer and therefore have greater thermal expansivity, which, in addition to the convergence of heat between 30\u201345\u00b0 S, creates a thermosteric maximum around 40\u00b0 S (Fig. 9b, red dotted line). However, at the same latitude, the changing salinity causes a halosteric effect that opposes the thermosteric effect and the meridional gradient of \u0394\u03b6 plateaus, instead of peaking at 40\u00b0 S and declining to the north (Fig. 9b, cyan dashed line). Note that the deviation between the steric sea-level change (Fig. 9b, cyan dashed line) and the dynamic change (Fig. 9b, solid black line) north of 40\u00b0 N indicates a considerable barotropic component of the change due to the redistribution of ocean mass (Lowe and Gregory 2006; Yin et al. 2010; Bouttes and Gregory 2014 and Fig. 8g).\nFig. 9: Comparison of the multi model ensemble mean zonally- and depth-integrated OHC change in response to heat flux forcing (a) and zonal mean dynamic sea-level change (b) for 11 AOGCMs, showing \u0394\u03b6 (black solid line), the thermosteric component \u0394\u03b6T (red dotted line) and the sum of thermo- and halosteric components (cyan dashed line). AOGCMs used: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR, MRI-ESM2-0\nFreshwater flux\uf0c1\nInterestingly, the sea-level response to freshwater forcing is strongly thermosteric as well as halosteric (Fig. 10c, e). The North Atlantic is sensitive to opposing, nearly compensating thermal and haline effects. The sea-level change in the Arctic is mostly halosteric, whereas the Southern Ocean shows a mostly thermosteric response. The sea-level change on the Antarctic shelves is non-steric (Fig. 10g).", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-10", "text": "Fig. 9: Comparison of the multi model ensemble mean zonally- and depth-integrated OHC change in response to heat flux forcing (a) and zonal mean dynamic sea-level change (b) for 11 AOGCMs, showing \u0394\u03b6 (black solid line), the thermosteric component \u0394\u03b6T (red dotted line) and the sum of thermo- and halosteric components (cyan dashed line). AOGCMs used: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR, MRI-ESM2-0\nFreshwater flux\uf0c1\nInterestingly, the sea-level response to freshwater forcing is strongly thermosteric as well as halosteric (Fig. 10c, e). The North Atlantic is sensitive to opposing, nearly compensating thermal and haline effects. The sea-level change in the Arctic is mostly halosteric, whereas the Southern Ocean shows a mostly thermosteric response. The sea-level change on the Antarctic shelves is non-steric (Fig. 10g).\nFig. 10: Multi model ensemble mean dynamic sea-level response to freshwater flux perturbation (a) and the standard deviation across models (b) for 13 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, CESM2, GFDL-ESM2M, GISS-E2-R-CC, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0. Multi model mean freshwater flux-forced thermosteric (c), halosteric (e), and non-steric (g) contributions, and the standard deviation across models (d, f, h) where the area mean has been subtracted from (g)\nThe locations where the models disagree on the sea-level response to freshwater forcing are not always coincident with the locations of largest sea-level change (Fig. 10a, b), particularly in the North Atlantic and the Arctic. This indicates that different models predict different features (Fig. 16), rather than all models responding with similar patterns of different magnitude. The models predict diverse patterns of sea-level change in the subpolar North Atlantic (Fig. 10b) because they disagree on the eastward extent of the sea-level change (Fig. 16). Presumably, simulated North Atlantic currents have differing sensitivities to freshwater forcing.\nThe sea-level changes closest to the Antarctic coast are predicted with some agreement across models (Fig. 10b). The inter-model spread around 50\u00b0\u201360\u00b0 S south of Australia arises due to different thermosteric responses to freshwater forcing (Fig. 10d). A poleward contraction of the ACC here would explain the positive \u0394\u03b6 (Fig. 10a) but the inter model spread suggests that not all models predict this (Figs. 10b, 16a, b, d, f, h, j).\nIn the Arctic, the freshwater forcing is widespread and positive, due to a mixture of increased river runoff and precipitation. This causes freshening, which in turn causes halosteric sea-level rise (Fig. 10e). However, the models disagree on the spatial extent of the halosteric sea-level rise (Fig. 10f).\nLinearity of sea-level responses to flux perturbations\uf0c1\nHere we explore how sea level responds to flux perturbations applied individually versus simultaneously. If the sea-level response to all perturbations is linear, then the sum of the responses when the perturbations are applied individually \u0394\u03b6sum,\n\u0394\ud835\udf01\ud835\udc60\ud835\udc62\ud835\udc5a=\u0394\ud835\udf01\ud835\udc64\ud835\udc56\ud835\udc5b\ud835\udc51+\u0394\ud835\udf01\u210e\ud835\udc52\ud835\udc4e\ud835\udc61+\u0394\ud835\udf01\ud835\udc64\ud835\udc4e\ud835\udc61\ud835\udc52\ud835\udc5f, (13)\nshould equal the response when the fluxes are applied together, \u0394\u03b6all. The differences between \u0394\u03b6sum and \u0394\u03b6all represent the nonlinear sea-level response to simultaneous flux forcing and is explored for 11 AOGCMs (Table 1, excluding CESM2 and GISS-E2-CC). The significance of nonlinear features is tested against the variability of the seven decades of FAF-passiveheat, calculated as the standard deviation of seven decadal averages, which we assume is representative of the internally generated variability in the other experiments as well. The quantity \u0394\u03b6sum\u2009\u2212\u2009\u0394\u03b6all is calculated using four independent simulations (FAF-heat, -stress, -water, -all), each with its own unforced variability. The difference \u0394\u03b6sum\u2009\u2212\u2009\u0394\u03b6all can therefore be affected by the unforced variability of four different simulations, so the standard deviation of the difference is twice the standard deviation of unforced decadal variability (from FAF-passiveheat). For a \u0394\u03b6sum\u2009\u2212\u2009\u0394\u03b6all feature to be judged significant at the 5% level, it must be larger than four times the unforced standard deviation. Locations where \u0394\u03b6sum\u2009\u2212\u2009\u0394\u03b6all is not significant are set to 0 for each model, before being averaged in Fig. 11 to reveal only significant differences. The features removed through this process are small in spatial extent and magnitude, and are particular to each model (not shown). The flux perturbations show significant nonlinear interaction in the Arctic and subpolar North Atlantic (Fig. 11a). Across the Arctic, \u0394\u03b6sum\u2009\u2212\u2009\u0394\u03b6all is negative, meaning most models predict a stronger dynamic sea-level change in FAF-all than the individual flux perturbation experiments suggest.\nFig. 11: Multi model ensemble mean nonlinear sea-level response to flux perturbations (a) and standard deviation (b) across 11 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0\nFor most of the global ocean, \u0394\u03b6sum\u2009\u2212\u2009\u0394\u03b6all is small and therefore \u0394\u03b6sum approximates the patterns of \u0394\u03b6all. However, small values of multi-model mean \u0394\u03b6sum\u2009\u2212\u2009\u0394\u03b6all are not necessarily indicative of agreement between models that the responses to perturbations sum linearly. In the western North Pacific and Southern Ocean south of Australia and New Zealand (Fig. 11b) some models show some nonlinear interactions between the flux perturbations. South of Australia and New Zealand, \u0394\u03b6wind is small, so the interaction is between the freshwater and heat fluxes. It could be that local details of the change in sea-ice cover in response to heat flux forcing are model specific, causing the momentum forcing to have different results in FAF-all versus FAF-stress where no heat perturbation is applied. More detailed investigation into each model\u2019s results is necessary to explore this.\nIn the northwest Pacific, in the Kuroshio separation region, the AOGCMs show various sensitivities to the three individual forcings (not shown). For ACCESS-CM2, GFDL-ESM2M, MIROC6 and MPI-ESM-LR, the \u0394\u03b6sum\u2009\u2212\u2009\u0394\u03b6all dipole is positive to the south and negative to the north, indicating that simultaneously applied flux perturbations do not produce the same degree of intensification of the across-current slope as when the perturbations are applied individually. For CanESM5, the dipole is reversed. For the other models there is no strong nonlinear sea-level response.\nHadGEM2-ES, MPI-ESM1-2-HR, and GFDL-ESM2M show strong nonlinear interactions between forcings in the North Atlantic, as these models are sensitive to all three perturbations here (not shown). The spread in the North Atlantic indicates that the AMOC response to the flux perturbations (and also the nonlinear interactions between them) is model-specific.\nDecomposition of ocean heat uptake\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-11", "text": "For most of the global ocean, \u0394\u03b6sum\u2009\u2212\u2009\u0394\u03b6all is small and therefore \u0394\u03b6sum approximates the patterns of \u0394\u03b6all. However, small values of multi-model mean \u0394\u03b6sum\u2009\u2212\u2009\u0394\u03b6all are not necessarily indicative of agreement between models that the responses to perturbations sum linearly. In the western North Pacific and Southern Ocean south of Australia and New Zealand (Fig. 11b) some models show some nonlinear interactions between the flux perturbations. South of Australia and New Zealand, \u0394\u03b6wind is small, so the interaction is between the freshwater and heat fluxes. It could be that local details of the change in sea-ice cover in response to heat flux forcing are model specific, causing the momentum forcing to have different results in FAF-all versus FAF-stress where no heat perturbation is applied. More detailed investigation into each model\u2019s results is necessary to explore this.\nIn the northwest Pacific, in the Kuroshio separation region, the AOGCMs show various sensitivities to the three individual forcings (not shown). For ACCESS-CM2, GFDL-ESM2M, MIROC6 and MPI-ESM-LR, the \u0394\u03b6sum\u2009\u2212\u2009\u0394\u03b6all dipole is positive to the south and negative to the north, indicating that simultaneously applied flux perturbations do not produce the same degree of intensification of the across-current slope as when the perturbations are applied individually. For CanESM5, the dipole is reversed. For the other models there is no strong nonlinear sea-level response.\nHadGEM2-ES, MPI-ESM1-2-HR, and GFDL-ESM2M show strong nonlinear interactions between forcings in the North Atlantic, as these models are sensitive to all three perturbations here (not shown). The spread in the North Atlantic indicates that the AMOC response to the flux perturbations (and also the nonlinear interactions between them) is model-specific.\nDecomposition of ocean heat uptake\uf0c1\nAs shown above, ocean dynamic sea-level change is largely thermosteric, and reflects changes in OHC. Here, we decompose the OHC change (see Sect. 2.4 and \u201cAppendix\u201d for details) of ten AOGCMs (Table 1, excluding CESM2, GISS-E2-R-CC, MIROC6) into contributions from changes in ocean transports and the uptake of the imposed perturbation. Most of the heat added to the oceans in FAF-heat is stored in the Southern Ocean, between 30\u00b0 S and 60\u00b0S (Figs. 6h, 12a), particularly in the Indo\u2013Pacific sectors. The North Atlantic shows the highest rate of heat uptake per unit area, but the small total area of the basin means its contribution the global total OHU is smaller than that of the much larger Southern Ocean (Fig. 6h). The Arctic also shows moderate rates of heat storage per unit area (Fig. 12a), but this basin stores less heat than other latitudes because of its small total area (Fig. 6h).\nFig. 12: Decomposition of depth-integrated ocean heat uptake in ten AOGCMs (ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0) in FAF-heat, left panels show the multi-model ensemble mean and right panels show the standard deviation across models for the total ocean heat uptake mean (a) and spread (b). Components of heat uptake (c, e, g) are shown as a percentage of the total (a). Passive uptake of added heat, \u0394h[\u03a6\u2212(T\u2032)], mean (c) and spread (d). Pure redistribution of unperturbed heat, \u0394h[\u03a6\u2032(T\u2212)] mean (e) and spread (f). Redistribution of added heat by the perturbed transport, \u0394h[\u03a6\u2032(T\u2032)], mean (g) and spread (h)\nIn the Southern Ocean, passive heat uptake in the Southern Ocean (Fig. 12c) is close to 100% of the total heat uptake (Fig. 12a). The OHC change due to the perturbed transport (Fig. 12e, g) is much smaller than the total passive uptake, but is locally important and strongly negative near the Ross and Weddell gyres. Further, there is relatively little spread of \u0394\u210e[\u03a6\u2212(\ud835\udc47\u2032)] across models (Fig. 12d). This means that these AOGCMs agree that heat uptake by the Southern Ocean is mostly passive, in agreement with recent findings (Bronselaer and Zanna 2020). The perturbed transport has secondary influence on heat uptake in the Southern Ocean. Both \u0394\u210e[\u03a6\u2212(\ud835\udc47\u2032)] and \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2212)] are important components in the Indian sector (Fig. 12c, e), and the spread here is not due to passive uptake (Fig. 12d). South of Australia and New Zealand, where the total OHC change differs across models (Fig. 12b) the spread comes from \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2212)] (Fig. 12f), which could suggest a model-dependent reduction of upwelling.\nOHU in the North Atlantic is characterized by positive passive heat uptake that is partially opposed by the perturbed transport (Fig. 12c, e, g). Strong negative \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2212)] and \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2032)] mean that the effect of transport change here is large, cooling the basin. Furthermore, this transport change manifests differently in different models (Fig. 12f, h). Indeed, the large spread in total heat uptake south of Iceland (Fig. 12b) results mostly from the redistribution of unperturbed temperature (Fig. 12f), with \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2032)] and \u0394\u210e[\u03a6\u2212(\ud835\udc47\u2032)] also playing smaller roles.\nModerate heat storage per unit area by the Arctic Ocean is commonly predicted across AOGCMs, but there are large differences between them (Fig. 12a, b). Here, the total OHC change has contributions from all three components: \u0394\u210e[\u03a6\u2212(\ud835\udc47\u2032)] and \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2032)] are strongly positive while \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2212)] is negative. Similarly, the spread of OHU has roots in all three components (Fig. 12d, f, h), highlighting that the mechanisms of Arctic heat uptake are highly model dependent. Since the heat flux perturbation into the Arctic is quite weak, the OHC change results from the oceanic transport of heat. Some of the added heat is brought into the basin by the unperturbed transport, (Fig. 12c). The negative values of \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2212)] (Fig. 12e), indicate reduced poleward transport of unperturbed heat, possibly due to the weakened AMOC (although reduced heat transport through the Bering Strait cannot be ruled out). The widespread positive \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2032)] in the Arctic (Fig. 12g) could be explained by the following mechanism: the heat flux perturbation causes a weakened Atlantic overturning, which causes added heat to flow northwards into the Arctic from the North Atlantic and/or North Pacific instead of being subducted and transported equatorward. Further work should explore whether such a mechanism is at work.", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-12", "text": "OHU in the North Atlantic is characterized by positive passive heat uptake that is partially opposed by the perturbed transport (Fig. 12c, e, g). Strong negative \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2212)] and \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2032)] mean that the effect of transport change here is large, cooling the basin. Furthermore, this transport change manifests differently in different models (Fig. 12f, h). Indeed, the large spread in total heat uptake south of Iceland (Fig. 12b) results mostly from the redistribution of unperturbed temperature (Fig. 12f), with \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2032)] and \u0394\u210e[\u03a6\u2212(\ud835\udc47\u2032)] also playing smaller roles.\nModerate heat storage per unit area by the Arctic Ocean is commonly predicted across AOGCMs, but there are large differences between them (Fig. 12a, b). Here, the total OHC change has contributions from all three components: \u0394\u210e[\u03a6\u2212(\ud835\udc47\u2032)] and \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2032)] are strongly positive while \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2212)] is negative. Similarly, the spread of OHU has roots in all three components (Fig. 12d, f, h), highlighting that the mechanisms of Arctic heat uptake are highly model dependent. Since the heat flux perturbation into the Arctic is quite weak, the OHC change results from the oceanic transport of heat. Some of the added heat is brought into the basin by the unperturbed transport, (Fig. 12c). The negative values of \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2212)] (Fig. 12e), indicate reduced poleward transport of unperturbed heat, possibly due to the weakened AMOC (although reduced heat transport through the Bering Strait cannot be ruled out). The widespread positive \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2032)] in the Arctic (Fig. 12g) could be explained by the following mechanism: the heat flux perturbation causes a weakened Atlantic overturning, which causes added heat to flow northwards into the Arctic from the North Atlantic and/or North Pacific instead of being subducted and transported equatorward. Further work should explore whether such a mechanism is at work.\nThe equatorial Atlantic shows moderate area-weighted OHU (Fig. 12a). The equatorial Atlantic OHU is mostly driven by\u0394\u210e[\u03a6\u2032(\ud835\udc47\u2212)], (Fig. 12e) and passive heat storage is important in the west, (Fig. 12c). The local heat flux perturbation is near zero (Fig. 1a) and so the heat content change here is mostly a consequence of \u03a6\u2032, rather than T\u2032. These results echo previous work, which also identify an important role of active transport change in the low latitudes (e.g. Garuba and Klinger 2018). This is one of the few locations where the redistribution of unperturbed heat has a large positive depth integral. Elsewhere in the tropics, although \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2212)] is a large component, the total heat storage per area is smaller (Fig. 12a). In the western basin, \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2032)] is weakly negative, in contrast with the eastern. This could be consistent with a weakened poleward transport of heat causing an accumulation of unperturbed and added heat, and a coincident reduced westward equatorial transport of added heat. Reduced upwelling of unperturbed temperature as a part of the weakened poleward transport of unperturbed heat could explain the accumulation of \u0394\u210e[\u03a6\u2032(\ud835\udc47\u2212)] here. Changes in the subtropical and subpolar gyre circulation (and the exchange of heat between them) as suggested by previous authors could also play a role that has not yet been explored. A complete explanation is currently lacking but warranted (Boeira Dias et al. 2020).\nDiscussion\uf0c1\nDiversity of sea-level response to common air-sea flux perturbation\uf0c1\nThe largest and most widespread features of dynamic sea-level change in response to 1pctCO2 forcing have been shown to result mostly from the change in air-sea heat flux. Further, the inter-model uncertainty of the pattern of \u0394\u03b6 results from model-specific ocean transport responses to standardized air-sea flux changes, rather than diversity in the flux changes themselves. For the most part, the spread in response to heat flux perturbation relates to different models responding with a similar pattern of sea-level change, whose magnitude differs across models. The North Atlantic hosts a large diversity of \u0394\u03b6 across models, but although the geographic pattern is different across models, the sea-level changes have similar dynamical origins. We find that the North Atlantic inter-model variance is mostly due to the redistribution of preindustrial heat being different in each model, probably in turn due to the spread in predicted weakening of the AMOC. The spread of \u0394\u03b6 also has smaller contributions from uptake of added heat by both the perturbed and unperturbed transport. Part of the spread of North Atlantic sea-level change arises because added heat penetrates into the deep ocean in deep convection sites that are geographically different among models (Bouttes et al. 2014), but this reason is found to be secondary in our analysis. Other authors pointed out that ocean heat uptake is sensitive to model-specific factors such as SST biases (He and Soden 2016), mesoscale eddy transfer (Exarchou et al. 2015; Saenko et al. 2018), stratification (Huber and Zanna 2017) and the isopycnal diffusion scheme (Exarchou et al. 2015). These factors may explain why the models that we have examined show similar horizontal patterns of heat uptake with differing magnitudes even though these models are forced with identical heat inputs.\nPrevious work has highlighted that individual models when forced with different surface fluxes can produce diverse ocean responses in terms of sea level (Bouttes and Gregory 2014) and ocean heat uptake (Huber and Zanna 2017). Indeed, the uncertainty in surface fluxes is key challenge for climate modelling. By forcing different AOGCMs with common flux perturbations the spread of sea-level projections can be more directly attributed to the diversity of ocean model formulation than in prior studies. Huber and Zanna (2017) tested the parametric uncertainty of a single a model (i.e. the sensitivity of ocean heat uptake to the choice of parameter values), finding it to be small. Parametric uncertainty is only a subset of the total uncertainty due to the different representation of ocean processes in models (Zanna et al. 2018). Therefore, while previous work shows that accurate representation of surface fluxes is essential in climate simulations, our findings add that the use of ocean models with differing structures is also a key uncertainty. Nevertheless, there is clearly still more to learn about the link between the diversity caused by differences in surface fluxes versus differing ocean models. For instance, differences in ocean model design may lead to differences in steady state properties (e.g. stratification strength, mean temperature, overturning strength etc.), which in turn affect the steady state air-sea fluxes as well as the system\u2019s sensitivity to change. On the other hand, one could argue that changes in air-sea fluxes that result from the ocean response to common flux forcing are the result of each ocean component\u2019s unique sensitivity to forcing. While previous studies and the present study have separated the spread due to ocean models and the spread due to air-sea flux change in different ways, clearly they affect each other and this connection is not yet fully understood.\nRole of individual and simultaneous flux perturbations causing key regional sea-level changes\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-13", "text": "Previous work has highlighted that individual models when forced with different surface fluxes can produce diverse ocean responses in terms of sea level (Bouttes and Gregory 2014) and ocean heat uptake (Huber and Zanna 2017). Indeed, the uncertainty in surface fluxes is key challenge for climate modelling. By forcing different AOGCMs with common flux perturbations the spread of sea-level projections can be more directly attributed to the diversity of ocean model formulation than in prior studies. Huber and Zanna (2017) tested the parametric uncertainty of a single a model (i.e. the sensitivity of ocean heat uptake to the choice of parameter values), finding it to be small. Parametric uncertainty is only a subset of the total uncertainty due to the different representation of ocean processes in models (Zanna et al. 2018). Therefore, while previous work shows that accurate representation of surface fluxes is essential in climate simulations, our findings add that the use of ocean models with differing structures is also a key uncertainty. Nevertheless, there is clearly still more to learn about the link between the diversity caused by differences in surface fluxes versus differing ocean models. For instance, differences in ocean model design may lead to differences in steady state properties (e.g. stratification strength, mean temperature, overturning strength etc.), which in turn affect the steady state air-sea fluxes as well as the system\u2019s sensitivity to change. On the other hand, one could argue that changes in air-sea fluxes that result from the ocean response to common flux forcing are the result of each ocean component\u2019s unique sensitivity to forcing. While previous studies and the present study have separated the spread due to ocean models and the spread due to air-sea flux change in different ways, clearly they affect each other and this connection is not yet fully understood.\nRole of individual and simultaneous flux perturbations causing key regional sea-level changes\uf0c1\nOne of the key features of the sea-level response to heat flux forcing was the contrast in meridional dipoles in the North Pacific and North Atlantic (Gregory et al. 2016). In the North Atlantic, the meridional dipole is positive to the north, while in the North Pacific, it is positive to the south. The opposite dipoles are consistent with recent work investigating why the Kuroshio current is predicted to strengthen in AOGCM simulations of climate change, whereas the Gulf Stream weakens (Chen et al. 2019). Those authors described how the air-sea heat flux that results from a warming climate causes stronger warming to the east of the Kuroshio than to the west, steepening the across-current density slope. In the North Atlantic, the heat flux change causes a reduction of northward salinity transport that freshens the high latitudes, reducing the across-current slope and weakening the current. This is consistent with the dynamic sea-level changes that result from FAF-heat. The thermosteric change tends to steepen the across-current slope of the Gulf Stream, but this is counteracted by the larger opposing effect of haline contraction. Our results show that the intensity and pattern of Kuroshio strengthening is similar across models, but the change in the North Atlantic is more uncertain across models (Fig. 12f). The Gulf Stream dipole, unlike the Kuroshio dipole, is likely to be affected by the AMOC weakening, and so will be different for each model. Further, Bouttes and Gregory (2014) reported that the sea-level change in the western North Pacific was caused by both the wind stress and heat flux perturbations. In our ensemble, not every model\u2019s Kuroshio and extension regions were sensitive to wind forcing.\nThe water flux perturbation shows the smallest changes of all three perturbations when applied alone, but it nevertheless has important local effects in parts of the Southern Ocean, Arctic and subpolar North Atlantic. However, the importance of the water flux change may be underestimated by considering experiments in which only one flux is varied because of nonlinear interactions between flux perturbations. Other work has described how the sea-level responses to individually applied flux perturbations combine approximately linearly (Bouttes and Gregory 2014), which we also find is true to first order. However, we have identified that the nonlinear interaction between the three forcings is model dependent, which cannot be understood from a multi-model mean perspective. Models such as GFDL-ESM2M and MRI-ESM2-0 show strong nonlinear amplification of the sea-level response in the North Atlantic when all fluxes are perturbed simultaneously. Further, other work has shown that perturbing freshwater fluxes increases the uptake of heat by the subpolar Atlantic (Garuba and Klinger 2018).\nThe Southern and Arctic Oceans host many local features of dynamic sea-level change that are model specific. Coupled models (including the ones analysed here) show markedly different sea-ice extents and sensitivities to forcing (Turner et al. 2013). It seems likely that at least some of the model spread in projections of \u2206\u03b6 stems from the fact that sea-ice thermodynamics are model specific. The Weddell Gyre and its heat budget are thought to be sensitive to regional wind forcing (Jullion et al. 2010; Saenko et al. 2015). The spread of \u2206\u03b6 and \u2206\u03b6T in response to FAF-stress in the western Weddell Gyre indicates that some models show a significant thermosteric response to intensified westerlies. Inter-model differences in Arctic dynamic sea-level change and heat uptake have very different mechanisms for each model. The diversity of Arctic climate responses forcing is not necessarily limited to the representation of the oceans, but perhaps also poor representation of ice albedo and cloud feedbacks (Karlsson and Svensson 2013), biases in the unperturbed state (Franzke et al. 2017) or other factors that have not been explored.\nThe east Atlantic \u201ctropical arm\u201d of positive \u2206\u03b6 in response to heat flux forcing is halosteric, but is not predicted by all models. The analysis of ocean heat content therefore yields little information about the cause of the feature. The feature bears strong resemblance to the tropical arm SST anomalies characteristic of the Atlantic Multidecadal Variability (Yuan et al. 2016), however, our \u2206\u03b6 feature is the result of 70 years of integration of step forcing rather than variability, and is a vertical integral signal rather than purely SST. Nevertheless, the similarity between that pattern of variability and the forced response we present suggests common driving mechanisms may be responsible. In the context of the AMV, the tropical arm is thought to arise in response to midlatitude warm SST anomalies that weaken the tropical trade winds, which reduce low cloud and dust loading, thereby warming tropical SST (Yuan et al. 2016). Observations and some models show that the tropical SST arm coincides with freshening in the upper 50 m (Kavvada et al. 2013), which is consistent with the positive \u2206\u03b6S response to FAF-heat. The origin of the freshening in our simulations is not known, and the roles of input from the subpolar Atlantic, the Mediterranean or elsewhere are not ruled out. Whether this is driven by the atmospheric response to forcing, the thermohaline circulation or a mixture of effects is not clear, but merits further investigation.\nCaveats, unmodeled processes and further outlook\uf0c1\nFAFMIP experiments were designed to provide insight into the causes of model spread in greenhouse gas-forced climate change experiments, particularly the 1pctCO2 experiment. The design aimed to mimic the magnitude of 100 years of 1pctCO2 forcing, but the North Atlantic redistribution feedback (wherein the perturbation weakens the AMOC, causing an advection-driven cooling and increasing the air-sea heat flux into the North Atlantic, see Sects. 2.2 and 3.1) causes the total heat input into the North Atlantic to be larger than the just the imposed perturbation (Gregory et al. 2016). Todd et al. (2020) investigated the strength of this unwanted feedback by forcing ocean-only models (which have no redistribution feedback) with the same heat flux perturbation as this study, and compared the ocean heat transport response with the response of coupled AOGCMs (which do have the feedback). Those authors find that the feedback causes an additional 10% AMOC weakening versus the change that occurs in fully coupled AOGCMs. The feedback affects the North Atlantic heat uptake and transport, but has limited impact elsewhere and its effect on global ocean heat uptake is smaller than the perturbation of interest. In the AOGCMs we examine, global total heat uptake is about 10% greater than the area- and time-integral of the imposed perturbation. Therefore, the forced changes in the North Atlantic presented in this work are larger than one would expect from 100 years of 1pctCO2 forcing. Nevertheless, the fact that the imposed perturbation is common to all models matters more than the precise magnitude, when investigating the sensitivity of ocean model responses to common forcing.", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-14", "text": "Caveats, unmodeled processes and further outlook\uf0c1\nFAFMIP experiments were designed to provide insight into the causes of model spread in greenhouse gas-forced climate change experiments, particularly the 1pctCO2 experiment. The design aimed to mimic the magnitude of 100 years of 1pctCO2 forcing, but the North Atlantic redistribution feedback (wherein the perturbation weakens the AMOC, causing an advection-driven cooling and increasing the air-sea heat flux into the North Atlantic, see Sects. 2.2 and 3.1) causes the total heat input into the North Atlantic to be larger than the just the imposed perturbation (Gregory et al. 2016). Todd et al. (2020) investigated the strength of this unwanted feedback by forcing ocean-only models (which have no redistribution feedback) with the same heat flux perturbation as this study, and compared the ocean heat transport response with the response of coupled AOGCMs (which do have the feedback). Those authors find that the feedback causes an additional 10% AMOC weakening versus the change that occurs in fully coupled AOGCMs. The feedback affects the North Atlantic heat uptake and transport, but has limited impact elsewhere and its effect on global ocean heat uptake is smaller than the perturbation of interest. In the AOGCMs we examine, global total heat uptake is about 10% greater than the area- and time-integral of the imposed perturbation. Therefore, the forced changes in the North Atlantic presented in this work are larger than one would expect from 100 years of 1pctCO2 forcing. Nevertheless, the fact that the imposed perturbation is common to all models matters more than the precise magnitude, when investigating the sensitivity of ocean model responses to common forcing.\nPrevious work investigating \u2018pattern scaling\u2019 has shown that the spatial structure of sea-level change remains similar across a range of magnitudes of forcing (Hawkes 2013; Perrette et al. 2013; Slangen et al. 2014; Bilbao et al. 2015). The spatial patterns of change and the underlying drivers presented here are therefore likely to be qualitatively applicable to greenhouse gas-forced experiments. Nevertheless, the sensitivity of the ocean response to different heat inputs into the North Atlantic is an open area of research, and will be further investigated in future work. Additional FAFMIP experiments, which apply heat inputs like those presented here, except with differing magnitudes in the North Atlantic, are already underway, and will be presented in future work.\nFAFMIP experiments do not account for the input of freshwater by the melting of the Greenland and Antarctic ice sheets. Over the North Atlantic area (50\u00b0\u201370\u00b0 N, 70\u00b0 W\u201330\u00b0 E), the freshwater perturbation integrates to a freshwater input of 0.007 Sv (1 Sv\u2009=\u2009106 m3 s\u22121). This is comparable in magnitude to the input of 0.006 Sv (0.00065 m year\u22121 or 0.01625 m of global mean sea-level rise) of meltwater from the Greenland Ice Sheet (GIS) over 1993\u20132018 (Frederikse et al. 2020), albeit applied for a much longer duration. Recent projections (Oppenheimer et al. 2019) of the GIS contribution to global mean sea-level rise by the year 2100 relative to 2000 across the full range of emissions scenarios are 0.063 to 0.119 m (0.00063\u20130.00119 m year\u22121), which corresponds to a freshwater input of about 0.007\u20130.013 Sv. This rough comparison suggests that the rate of addition of meltwater from the GIS alone is 1\u20131.8 times stronger than the local water flux perturbation in the North Atlantic. The water flux perturbation in the Southern Ocean (south of 45\u00b0 S) integrates to 0.115 Sv. The Antarctic Ice Sheet (AIS) loss contribution to recent historical global mean sea-level rise is smaller than that of the GIS, at 0.00032 m year\u22121 or 0.008 m over 1993\u20132018, approximately 0.003 Sv (Frederikse et al. 2020). The AIS, unlike the GIS, is dominated by marine melting (Paolo et al. 2015; Wouters et al. 2015), a coupled atmosphere-ice sheet-ocean process that cannot yet be fully interactively represented in climate models (Oppenheimer et al. 2019). As such, projections of the AIS contribution to future global mean sea level remain highly uncertain, although recent estimates of the AIS have an across-scenario range of 0.040\u20130.120 m by the year 2100 relative to 2000 (Oppenheimer et al. 2019), equivalent to 0.0004\u20130.0012 m year\u22122 or 0.004\u20130.013 Sv. The AIS contributions are therefore on the order of 0.03\u20130.1 times the perturbation imposed over the Southern Ocean. The water flux perturbation studied here was sufficient to produce features of regional sea-level change 0.05\u20130.1 m greater than the global mean in the Northwestern Atlantic and the coastal Southern Ocean. The missing GIS and AIS meltwater contributions (which are locally of a similar order to the freshwater perturbation that we imposed) could plausibly enhance the local freshwater-forced sea-level changes by an amount the order of 0.01\u20130.1 m, especially in the northwestern Atlantic. Note that this rough estimate of unmodeled meltwater contributions is not intended as a quantitative account, but instead serves to highlight a need for experiments that include these effects (Nowicki et al. 2016).\nGravitational, rotational and deformational (GRD) processes associated with ice mass loss to the oceans, which typically impose a negative feedback on sea-level rise by elevating retreating glaciers away from marine heat, are also not accounted for in this study. However, the magnitude of these effects is too small to reduce the rate of AIS melting over the twenty-first century sea-level rise, and become more important after the year 2250 (Larour et al. 2019; Oppenheimer et al. 2019). More generally though, GRD processes are vital in the determination of local relative sea-level change through the 21st Century and beyond (Mitrovica et al. 2011; Oppenheimer et al. 2019). The complex interaction between atmosphere\u2013ocean-ice sheet-GRD processes makes it difficult to speculate about the net effects of all processes, and highlights a need to interactively simulate all such elements of the system.\nEchoing findings from the previous generation of coupled atmosphere\u2013ocean climate models, the regions showing the largest dynamic sea-level changes at the end of the twenty-first century also show the largest inter-model uncertainty (Church et al. 2013, Figs., 3, 4). Regions with both large projected changes and large uncertainty are the northwestern Atlantic, the Arctic, parts of the Southern Ocean and the northwest Pacific. This uncertainty highlights an ongoing need to better understand the reasons for diverse predictions of ocean transport change in these regions. This inter-model spread cannot presently be readily reduced by excluding models, since it is not trivial to determine the relative robustness of each AOGCM projection. Accordingly, the upper and lower limits of future sea-level scenarios should be constructed with the consideration that the dynamic sea level in these regions could be larger or smaller than the multi-model ensemble mean suggests. There is an increasing understanding that the diversity of cloud feedbacks is an important cause of the variations of climate sensitivity across different AOGCMs (Zelinka et al. 2020). Establishing realistic representations of cloud feedbacks in AOGCMs is therefore a key step to reduce the spread future climate and sea-level projections. Regarding ocean components, Lyu et al. (2020) have recently attributed the spread of sea-level projections to biases in model mean states, and so the reduction of such biases remains an important goal for climate projection.\nConclusions\uf0c1\nThis work documents how FAFMIP experiments are useful tools to derive a new understanding of the drivers of dynamic sea-level change in idealized greenhouse gas forcing experiments. Notably, these latest FAFMIP results show that:\nMost of the spread of predictions of dynamic sea-level change in response to idealised greenhouse gas forcing by AOGCMs can be reproduced by forcing models with common air-sea flux perturbations. These findings show that the diverse representation of the ocean component in climate models is a key uncertainty in sea-level projection under greenhouse gas forcing.\nThe increased air-sea heat flux associated with greenhouse gas forced climate change sets the broad spatial pattern of dynamic sea-level change. The dynamic sea-level changes that result from the changing freshwater flux and wind stress have important effects locally but are smaller contributors to the global change.\nThe main effect of the wind-stress change is to rearrange the distribution of heat in the Southern Ocean, which steepens the meridional sea-level gradient.\nThe sea-level response to the change in surface freshwater flux is mostly confined to the Arctic and the Southern Ocean south of Australia and New Zealand, although models disagree on whether North Atlantic is affected significantly.\nThe Southern Ocean absorbs a large portion of the added heat perturbation, where models agree that most of this heat is taken up like a passive tracer, without strongly affecting the local transport.", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "63dd50a3dfc4-15", "text": "Conclusions\uf0c1\nThis work documents how FAFMIP experiments are useful tools to derive a new understanding of the drivers of dynamic sea-level change in idealized greenhouse gas forcing experiments. Notably, these latest FAFMIP results show that:\nMost of the spread of predictions of dynamic sea-level change in response to idealised greenhouse gas forcing by AOGCMs can be reproduced by forcing models with common air-sea flux perturbations. These findings show that the diverse representation of the ocean component in climate models is a key uncertainty in sea-level projection under greenhouse gas forcing.\nThe increased air-sea heat flux associated with greenhouse gas forced climate change sets the broad spatial pattern of dynamic sea-level change. The dynamic sea-level changes that result from the changing freshwater flux and wind stress have important effects locally but are smaller contributors to the global change.\nThe main effect of the wind-stress change is to rearrange the distribution of heat in the Southern Ocean, which steepens the meridional sea-level gradient.\nThe sea-level response to the change in surface freshwater flux is mostly confined to the Arctic and the Southern Ocean south of Australia and New Zealand, although models disagree on whether North Atlantic is affected significantly.\nThe Southern Ocean absorbs a large portion of the added heat perturbation, where models agree that most of this heat is taken up like a passive tracer, without strongly affecting the local transport.\nThe flux perturbations create nonlinear dynamic sea-level responses when applied simultaneously, especially in the Arctic and the North Atlantic, but the details are different across models.\nFAFMIP simulations provide new avenues to probe the sea-level response to greenhouse gas forcing, and ocean heat-content change generally. The results presented here represent a step highlighting where AOGCMs give diverse predictions of sea-level change because of their different ocean models. Many details of local processes that cause the sea-level changes described here remain to be fully explored. We have highlighted that a key source of spread of AOGCM predictions of sea-level change in the North Atlantic is because the change of local transport is highly model dependent; subsequent work should uncover what characteristics of ocean models cause this. AOGCMs give diverse predictions about Arctic heat uptake, owing to the interaction between passive and active heat uptake processes that call for more detailed examination. Further process-based analysis of FAFMIP simulations will shed new light on the key areas of uncertainty highlighted here.", "source": "https://sealeveldocs.readthedocs.io/en/latest/couldrey21.html"}
{"id": "cf8deb22c40d-0", "text": "Kopp et al. (2014)\uf0c1\nTitle:\nProbabilistic 21st and 22nd century sea-level projections at a global network of tide-gauge sites\nKey Points:\nRates of local sea-level rise differs from rate of global sea-level rise\nDifferences arise from land motion, ocean dynamics, and Antarctic mass balance\nLocal sea-level rise can dramatically increase flood probabilities\nCorresponding author:\nRobert E. Kopp\nCitation:\nKopp, R. E., R. M. Horton, C. M. Little, J. X. Mitrovica, M. Oppenheimer, D. J. Rasmussen, B. H. Strauss, and C. Tebaldi (2014), Probabilistic 21st and 22nd century sea-level projections at a global network of tide-gauge sites, Earth\u2019s Future, 2, 383 \u2013 406, doi:10.1002/2014EF000239.\nURL:\nhttps://agupubs.onlinelibrary.wiley.com/doi/10.1002/2014EF000239\nAbstract\uf0c1\nSea-level rise due to both climate change and non-climatic factors threatens coastal settlements, infrastructure, and ecosystems. Projections of mean global sea-level (GSL) rise provide insufficient information to plan adaptive responses; local decisions require local projections that accommodate different risk tolerances and time frames and that can be linked to storm surge projections. Here we present a global set of local sea-level (LSL) projections to inform decisions on timescales ranging from the coming decades through the 22nd century. We provide complete probability distributions, informed by a combination of expert community assessment, expert elicitation, and process modeling. Between the years 2000 and 2100, we project a very likely (90% probability) GSL rise of 0.5 to 1.2 m under representative concentration pathway (RCP) 8.5, 0.4 to 0.9 m under RCP 4.5, and 0.3 to 0.8 m under RCP 2.6. Site-to-site differences in LSL projections are due to varying non-climatic background uplift or subsidence, oceanographic effects, and spatially variable responses of the geoid and the lithosphere to shrinking land ice. The Antarctic ice sheet (AIS) constitutes a growing share of variance in GSL and LSL projections. In the global average and at many locations, it is the dominant source of variance in late 21st century projections, though at some sites oceanographic processes contribute the largest share throughout the century. LSL rise dramatically reshapes flood risk, greatly increasing the expected number of \u201c1-in-10\u201d and \u201c1-in-100\u201d year events.\nIntroduction\uf0c1\nSea-level rise figures prominently among the consequences of climate change. It impacts settlements and ecosystems both through permanent inundation of the lowest-lying areas and by increasing the frequency and/or severity of storm surge over a much larger region. In Miami-Dade County, Florida, for example, a uniform 90-cm sea-level rise would permanently inundate the residences of about 5% of the county\u2019s population, about the same fraction currently threatened by the storm tide of a 1-in-100 year flood event [Tebaldi et al., 2012]. A 1-in-100 year flood on top of such a sea-level rise would, assuming geographically uniform flooding, expose an additional 35% of the population (Climate Central, Surging Seas, 2013, retrieved from SurgingSeas.org, updated November 2013).\nThe future rate of mean global sea-level (GSL) rise will be controlled primarily by the thermal expansion of ocean water and by mass loss from glaciers, ice caps, and ice sheets [Church et al., 2013]. Changes in land water storage, through groundwater depletion and reservoir impoundment, may have influenced twentieth-century sea-level change [Gregory et al., 2013] but are expected to be relatively minor contributors compared to other factors in the current century [Church et al., 2013].\nLocal sea-level (LSL) change can differ significantly from GSL rise [Milne et al., 2009; Stammer et al., 2013], so for adaptation planning and risk management, localized assessments are critical. The spatial variability of LSL change arises from: (1) non-uniform changes in ocean dynamics, heat content, and salinity [Levermann et al., 2005; Yin et al., 2009], (2) perturbations in the Earth\u2019s gravitational \ufb01eld and crustal height (together known as static-equilibrium effects) associated with the redistribution of mass between the cryosphere and the ocean [Kopp et al., 2010; Mitrovica et al., 2011], (3) glacial isostatic adjustment (GIA) [Farrell and Clark, 1976], and (4) vertical land motion due to tectonics, local groundwater, and hydrocarbon withdrawal, and natural sediment compaction and transport [e.g., Miller et al., 2013].\nMost past assessments of LSL change have focused on specific regions, such as the Netherlands [Katsman et al., 2011], the U.S. Paci\ufb01c coast [National Research Council, 2012], New York City [Horton et al., 2011; New York City Panel on Climate Change, 2013], and New Jersey [Miller et al., 2013]. Slangen et al. [2012], Slangen et al. [2014], Perrette et al. [2013], and Church et al. [2013] [AR5] have produced global projections of LSL using Coupled Model Intercomparsion Project (CMIP) projections [Taylor et al., 2012] for thermal expansion and ocean dynamics, along with estimates of net land ice changes, their associated static-equilibrium e\ufb00ects and GIA.\nHere we expand upon past efforts to project LSL globally. First, we present a complete probability distribution. This is critical for planning purposes; the likely (67% probability) ranges presented in AR5 and many other previous efforts provide no information about the highest 17% of outcomes, which may well be key to risk management. Second, we indicatively extend our projections to 2200, in order to inform both decision-making regarding long-term infrastructure investment decisions and their longer term land use consequences, and also greenhouse gas mitigation decisions in the context of long-term sea-level rise commitments [Levermann et al., 2013]. Finally, using a Gaussian process model [Kopp, 2013] of historical tide-gauge data [Holgate et al., 2013], we include probabilistic estimates of local non-climatic factors.\nWe first present our framework and projections for selected locations (projections for all tide-gauge locations are included in the Supporting Information), then assess the effects of sea-level rise on coastal flooding risk at these locations. Throughout, we seek to employ transparent assumptions and an easily replicable methodology that is useful for risk assessment and can be readily updated with new information.\nMethods\uf0c1\nLSL projections require the projection and aggregation of the individual components of sea-level change [e.g., Milne et al., 2009] at each site of interest. Here, we project three ice sheet components (the Greenland Ice Sheet, GIS; the West Antarctic ice sheet, WAIS; and the East Antarctic ice sheet, EAIS); glacier and ice cap (GIC) surface mass balance (SMB); global mean thermal expansion and regional ocean steric and ocean dynamic effects (which we collectively call oceanographic processes); land water storage; and long-term, local, non-climatic sea-level change due to factors such as GIA, sediment compaction, and tectonics. In our base case, we allow correlations, derived from the SMB model, between different mountain glaciers but otherwise assume that, conditional upon a global radiative forcing pathway, the components are independent of one another. To calculate GSL and LSL probability distributions, we employ 10,000 Latin hypercube samples from time-dependent probability distributions of cumulative sea-level rise contributions for each of the individual components. The sources of information used to develop these distributions are described below and summarized in Figure 1.\nFigure 1: Logical \ufb02ow of sources of information used in local sea-level projections. GCMs, global climate models; GIC, glaciers and ice caps; SMB: surface mass balance.\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/kopp14.html"}
{"id": "cf8deb22c40d-1", "text": "We first present our framework and projections for selected locations (projections for all tide-gauge locations are included in the Supporting Information), then assess the effects of sea-level rise on coastal flooding risk at these locations. Throughout, we seek to employ transparent assumptions and an easily replicable methodology that is useful for risk assessment and can be readily updated with new information.\nMethods\uf0c1\nLSL projections require the projection and aggregation of the individual components of sea-level change [e.g., Milne et al., 2009] at each site of interest. Here, we project three ice sheet components (the Greenland Ice Sheet, GIS; the West Antarctic ice sheet, WAIS; and the East Antarctic ice sheet, EAIS); glacier and ice cap (GIC) surface mass balance (SMB); global mean thermal expansion and regional ocean steric and ocean dynamic effects (which we collectively call oceanographic processes); land water storage; and long-term, local, non-climatic sea-level change due to factors such as GIA, sediment compaction, and tectonics. In our base case, we allow correlations, derived from the SMB model, between different mountain glaciers but otherwise assume that, conditional upon a global radiative forcing pathway, the components are independent of one another. To calculate GSL and LSL probability distributions, we employ 10,000 Latin hypercube samples from time-dependent probability distributions of cumulative sea-level rise contributions for each of the individual components. The sources of information used to develop these distributions are described below and summarized in Figure 1.\nFigure 1: Logical \ufb02ow of sources of information used in local sea-level projections. GCMs, global climate models; GIC, glaciers and ice caps; SMB: surface mass balance.\uf0c1\nWe construct separate projections for three representative concentration pathways (RCPs): RCP 2.6, RCP 4.5, and RCP 8.5 [Meinshausen et al., 2011], which correspond respectively to likely global mean temperature increases in 2081 \u2013 2100 of 1.9-2.3\u02daC, 2.0-3.6\u02daC, and 3.2-5.4\u02daC above 1850-1900 levels [Intergovernmental Panel on Climate Change, 2013]. We do not consider RCP 6.0, as 21st-century sea-level rise projections for this pathway are nearly identical to those for RCP 4.5, and few CMIP Phase 5 (CMIP5) model runs for RCP 6.0 extend beyond 2100 [Taylor et al., 2012]. The RCPs do not represent socioeconomic scenarios but can be compared to emissions in no-policy socioeconomic projections such as the Shared Socioeconomic Pathways (SSPs) [O\u2019Neill et al., 2014]. Radiative forcing in RCP 6.0 in the second half of the century is comparable to that in the lowest emissions SSP (SSP 1), while RCP 8.5 is above four of the SSPs but below the highest-emission SSP [Riahi, 2013]. Thus, RCP 8.5 can be viewed as corresponding to high-end business-as-usual emissions and RCP 4.5 as a moderate mitigation policy scenario. RCP 2.6 requires net-negative global emissions in the last quarter of the 21st century, implying a combination of intensive greenhouse gas mitigation and at least modest active carbon dioxide removal.\nIce Sheets\uf0c1\nOur projections of 21st-century changes in mass balance of GIS and the Antarctic ice sheet (AIS) are generated by combining the projections of AR5 and the expert elicitation of Bamber and Aspinall [2013] [BA13]. AR5 is used to characterize median and likely ranges of sea-level change, while BA13 is used to calibrate the shape of the tails (Supporting Information Figure S1 and Table S1).\nFigure S1:  Exceedance probabilities for GIS (left) and AIS (right) mass loss between 2000 and 2100 in RCP 8.5, in meters equivalent sea level. Green curves are derived from Bamber and Aspinall [2013], blue curves from the median and likely range of AR5, and red curves are a hybrid based on the green curves but shifted and scaled to match the median and likely range of AR5.\uf0c1\nTable S1: Ice sheet mass loss in sensitivity cases (cm equivalent sea level, RCP 8.5 in 2100)\ncm\nGIS\nAIS\n50\n17-83\n5-95\n0.5-99.5\n99.9\n50\n17-83\n5-95\n0.5-99.5\n99.9\nDefault\n14\n8-25\n5-39\n3-70\n<95\n4\n-8-15\n-11-33\n-14-91\n<155\nAR5\n14\n8-25\n5-39\n3-68\n<95\n4\n-8-15\n-16-23\n-26-35\n<40\nBA\n14\n10-21\n9-29\n7-48\n<65\n14\n2-41\n-2-84\n-4-220\n<375\nAlt. Corr.\n14\n8-25\n5-39\n3-70\n<95\n4\n-8-15\n-12-33\n-14-85\n<185\nAR5 separately assesses AIS and GIS mass balance changes driven by SMB and ice sheet dynamics. For ice sheet dynamics, AR5 determined that there was insufficient knowledge to differentiate between RCP 2.6 and 4.5 (and 8.5 for AIS). Projections of total ice sheet mass loss \u2013 given as a likely cumulative sea-level rise contribution \u2013 are thus partially scenario-independent. BA13 probed more deeply into the tail of ice sheet mass loss projections, inquiring into the 5th-95th percentile ranges of GIS, EAIS, and WAIS. However, BA13 does not differentiate between SMB and ice sheet dynamics or between RCPs.\nWe reconcile the projections as described in the Supporting Information. For AIS, the reconciled RCP 8.5 projections (median/likely/very likely [90% probability] of 4/\u22128 to 15/\u221211 to 33 cm) are significantly reduced in range relative to BA13 (median/likely/very likely of 13/2 to 41/\u22122 to 83 cm); for GIS, the reconciled projections are almost identical to those based directly on AR5 and have a likely range (8 \u2013 25 cm) close to the very likely range estimated from BA13 (9-29 cm) (Supporting Information Table S1).\nIce sheet mass balance changes do not cause globally uniform sea-level rise. To account for the differing patterns of static-equilibrium sea-level rise caused by land ice mass loss, we apply sea-level fingerprints, calculated after Mitrovica et al. [2011] (Supporting Information Figure S2). These \ufb01ngerprints assume mass loss from each ice sheet is uniform; in most regions, the error introduced by this assumption is minimal [Mitrovica et al., 2011].\nFigure S2: Static equilibrium sea-level fingerprints employed for (a) GIS, (b) EAIS, (c) WAIS, and (d) median glaciers and ice cap mass loss. Units are meters of local sea level change per meter global sea level change.\uf0c1\nGlacier and Ice Caps\uf0c1\nFor each RCP, we generate mass balance projections for 17 different source regions of glaciers and ice caps (described in the Supporting Information). For each source region, we employ a multivariate t-distribution of ice mass change with a mean and covariance estimated from the process model results of Marzeion et al. [2012]. Each source region has a distinct static-equilibrium sea-level fingerprint, calculated in the same fashion as for ice sheet mass loss (Supporting Information Figure S2).\nThe projections based on Marzeion et al. [2012] are modestly narrower and have a slightly higher median than those of AR5: a likely range of 9-15 cm from non-Antarctic glaciers by 2100 for RCP 2.6 (vs. 4-16 cm for AR5) and 14-21 cm for RCP 8.5 (vs. 9-23 cm for AR5). We opt for the Marzeion et al. [2012] projections because of the availability of disaggregated output representing projections based on a suite of global climate models (GCMs) for each source region.\nOceanographic Processes\uf0c1\nProjections of changes in GSL due to thermal expansion and in LSL due to regional steric and dynamic effects are based upon the CMIP5 GCMs. In particular, we employ a t-distribution with the mean and covariance of a multi-model ensemble constructed from the CMIP5 archive (Supporting Information Figures S3 and S4, Table S2). Values used are 19-year running averages. For each model, we use a single realization. The sea-level change at each tide-gauge location is assumed to be represented by the nearest ocean grid cell value of each GCM.", "source": "https://sealeveldocs.readthedocs.io/en/latest/kopp14.html"}
{"id": "cf8deb22c40d-2", "text": "Figure S2: Static equilibrium sea-level fingerprints employed for (a) GIS, (b) EAIS, (c) WAIS, and (d) median glaciers and ice cap mass loss. Units are meters of local sea level change per meter global sea level change.\uf0c1\nGlacier and Ice Caps\uf0c1\nFor each RCP, we generate mass balance projections for 17 different source regions of glaciers and ice caps (described in the Supporting Information). For each source region, we employ a multivariate t-distribution of ice mass change with a mean and covariance estimated from the process model results of Marzeion et al. [2012]. Each source region has a distinct static-equilibrium sea-level fingerprint, calculated in the same fashion as for ice sheet mass loss (Supporting Information Figure S2).\nThe projections based on Marzeion et al. [2012] are modestly narrower and have a slightly higher median than those of AR5: a likely range of 9-15 cm from non-Antarctic glaciers by 2100 for RCP 2.6 (vs. 4-16 cm for AR5) and 14-21 cm for RCP 8.5 (vs. 9-23 cm for AR5). We opt for the Marzeion et al. [2012] projections because of the availability of disaggregated output representing projections based on a suite of global climate models (GCMs) for each source region.\nOceanographic Processes\uf0c1\nProjections of changes in GSL due to thermal expansion and in LSL due to regional steric and dynamic effects are based upon the CMIP5 GCMs. In particular, we employ a t-distribution with the mean and covariance of a multi-model ensemble constructed from the CMIP5 archive (Supporting Information Figures S3 and S4, Table S2). Values used are 19-year running averages. For each model, we use a single realization. The sea-level change at each tide-gauge location is assumed to be represented by the nearest ocean grid cell value of each GCM.\nFigure S3: CMIP5 thermal expansion projections (left) and after smoothing and drift correction (right). Black = GSL curve of Church and White [2011]. Dashed = mean/max/min of GSL with glacier and ice cap projections removed.\uf0c1\nFigure S4: Map of (top) median and (middle) width of likely range of ocean dynamic contribution to sea-level rise between 2000 and 2100 for RCP 8.5 (not including the contribution of global mean thermal expansion). (Bottom) Number of model projections retained at each site in RCP 8.5.\uf0c1\nTable S2: CMIP5 models used for thermal expansion and oceanographic processes\nThe horizontal resolution of the CMIP5 ocean models is ~1 degree. In these coarse-resolution models, sea level at the coast may differ from the open ocean due to local biases driven by unresolved processes (e.g., coastal currents) and bathymetry [Holt et al., 2009] or via the influence of small-scale processes (e.g., eddies) on larger-scale steric and dynamic changes [Penduff et al., 2010, 2011]. Although there is some evidence that climate-forced trends in sea level are not sensitive to resolution [Penduff et al., 2011; Suzuki et al., 2005], higher-resolution coastal modeling is required to determine whether the probabilities estimated at the GCM grid scale are significantly changed by sub-grid processes.\nGCM projections exhibit a range of late nineteenth-century sea-level behavior largely attributable to model drift. Uncorrected GCM-based estimates of the rate of mean global sea-level change from 1861 to 1900 range from \u22120.4 to +1.1 mm/yr. To correct for global-mean model drift, we apply a linear correction term to each model. The linear correction adjusts the rate of GSL rise over 1861-1900 to match a rate of thermal expansion estimated by removing the multi-model average of GIC mass loss from Marzeion et al. [2012] from the GSL curve of Church and White [2011]. After correction, the rate of thermal expansion over 1861\u20131900 is 0.3 \u00b1 0.9 (2\u03c3) mm/yr (Supporting Information Figure S3).\nConsistent with AR5\u2019s judgment that the 5th-95th percentile of CMIP5 output represents a likely (67% probability) range for global mean thermal expansion, we multiply the standard deviation of the t-distribution for oceanographic processes by 1.7.\nLand Water Storage\uf0c1\nFollowing the approach of Rahmstorf et al. [2012], we estimate GSL change due to changes in water storage on land based upon the relationship between such changes and population (Supporting Information Figure S5). For changes in reservoir storage, we use the historical cumulative impoundment estimate of Chao et al. [2008]. We assume that reservoir construction is a sigmoidal function of population:\n\\[I = a \\times \\mathrm{erf}\\left(\\frac{{P(t) - b}}{{c}}\\right) + I_0\\]\nwhere I is impoundment expressed in mm equivalent sea level (esl), P(t) is world population as a function of time, and the remaining variables are constants. The results imply a maximum additional impoundment of 6 mm (esl) on top of the current 30 mm; based on the discrepancy between the \u201cnominal\u201d and \u201cactual\u201d impoundment estimated by Chao et al. [2008], we conservatively allow a 2\u03c3 error in this estimate of \u00b150 %.\nFor the rate of groundwater depletion, we fit the estimates of Wada et al. [2012] and Konikow [2011] as linear functions of population, forced through the origin. The estimate of Wada et al. [2012] is based on fluxes estimated from a global hydrological model of groundwater recharge and a global database of groundwater abstraction, while that of Konikow [2011] uses a range of approaches depending on the data available for each aquifer. We take the mean and standard deviation of the two slopes estimated (0.06 \u00b1 0.02 mm/yr/billion people) and allow an additional 2 error of \u00b150%, a level based upon the errors estimated by the authors of the two impoundment studies. In our main calculation, we do not include the water resource assessment model-based estimate of Pokhrel et al. [2012], which is about a factor of three higher than the other two estimates; we include this estimate in a sensitivity case.\nWe employ population projections derived from United Nations Department of Economics and Social A\ufb00airs [2014]. We treat population as distributed following a triangular distribution, with the median, minimum, and maximum values corresponding to the middle, low, and high U.N. scenarios (10.9, 6.8, and 16.6 billion people in 2100, respectively). For scenarios in which population declines, we allow some reduction in impoundment, but do not allow impoundment to decrease below its year 2000 level.\nGlacial Isostatic Adjustment, Tectonics, and Other Non-Climatic Local Effects\uf0c1\nGIA, tectonics, and other non-climatic local effects that can be approximated as linear trends over the twentieth century are assumed to continue unchanged in the 21st and 22nd centuries. This is a good assumption for GIA, but imperfect for other processes. Tectonic processes can operate unsteadily, and a linear trend estimated from the historical record may be inaccurate. LSL rise related to fluid withdrawal is subject to engineering, resource depletion, market factors and policy controls, and might either increase or decrease in the future relative to historical levels. In addition, the trend estimates can encompass slow ocean dynamic changes that are close to constant over the historical record but could change in the future. Nonetheless, for a global analysis, assuming the continuation of observed historical changes offers the best currently feasible approach.\nWe estimate historical rates using a spatiotemporal Gaussian process model akin to that employed by Kopp [2013]. Sea level as recorded in the tide-gauge records (Permanent Service for Mean Sea Level, Tide-gauge data, retrieved from http://www.psmsl.org/data/obtaining/, accessed January 2014) is represented as the sum of three Gaussian processes: (1) a globally uniform process, (2) a regionally varying, temporally linear process, and (3) a regionally varying, temporally autocorrelated non-linear process. We allow for spatial non-stationarity in the Gaussian process prior by optimizing the hyperparameters separately for each of 15 regions (Supporting Information Table S4 and Figure S6). The posterior estimate of the second (linear) process at each site is used for forward projections. Mathematical details are provided in the Supporting Information.\nTable S4: Optimized model hyperparameters by region\nFigure S6: Tide gauge sites and regions used in background rate calculation.\uf0c1\nPost-2100 Projections\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/kopp14.html"}
{"id": "cf8deb22c40d-3", "text": "Glacial Isostatic Adjustment, Tectonics, and Other Non-Climatic Local Effects\uf0c1\nGIA, tectonics, and other non-climatic local effects that can be approximated as linear trends over the twentieth century are assumed to continue unchanged in the 21st and 22nd centuries. This is a good assumption for GIA, but imperfect for other processes. Tectonic processes can operate unsteadily, and a linear trend estimated from the historical record may be inaccurate. LSL rise related to fluid withdrawal is subject to engineering, resource depletion, market factors and policy controls, and might either increase or decrease in the future relative to historical levels. In addition, the trend estimates can encompass slow ocean dynamic changes that are close to constant over the historical record but could change in the future. Nonetheless, for a global analysis, assuming the continuation of observed historical changes offers the best currently feasible approach.\nWe estimate historical rates using a spatiotemporal Gaussian process model akin to that employed by Kopp [2013]. Sea level as recorded in the tide-gauge records (Permanent Service for Mean Sea Level, Tide-gauge data, retrieved from http://www.psmsl.org/data/obtaining/, accessed January 2014) is represented as the sum of three Gaussian processes: (1) a globally uniform process, (2) a regionally varying, temporally linear process, and (3) a regionally varying, temporally autocorrelated non-linear process. We allow for spatial non-stationarity in the Gaussian process prior by optimizing the hyperparameters separately for each of 15 regions (Supporting Information Table S4 and Figure S6). The posterior estimate of the second (linear) process at each site is used for forward projections. Mathematical details are provided in the Supporting Information.\nTable S4: Optimized model hyperparameters by region\nFigure S6: Tide gauge sites and regions used in background rate calculation.\uf0c1\nPost-2100 Projections\uf0c1\nIndicative post-2100 projections are developed according to the methods described in the previous sections. For ice sheet mass balance, we continue the constant 21st century acceleration. For non-climatic factors that are approximated as linear in the 21st century, we continue the constant 21st century rate. For land water storage, we extend the population projections using the 22nd century growth rates of United Nations Department of Economics and Social A\ufb00airs [2004] and use the same relationships of impoundment and groundwater depletion to population as in the 21st century (Supporting Information Figure S5). The number of GCM-based model results for GIC and oceanographic processes drops significantly beyond 2100 (Supporting Information Table S2), leading in these terms to a modest discontinuity and a reduction in variance in these terms at the start of the 22nd century (Supporting Information Figure S7). Acknowledging the limitations of these assumptions, we present post-2100 projections in tables rounded to the nearest decimeter.\nFlood Probabilities\uf0c1\nTo examine the implications of our projections for coastal flooding, we combine Latin hypercube samples from the sea-level distribution for an illustrative subset of sites with maximum-likelihood generalized Pareto distributions (GPDs) estimated from observed storm tides after Tebaldi et al. [2012], updated to use the full historic record of hourly water levels available at each location. Hourly data for non-U.S. sites are from the University of Hawaii Sea Level Center (retrieved from uhslc.soest.hawaii.edu, May 2014). The estimated GPDs do not take into account any future changes in storm frequency, intensity, or track [e.g., Knutson et al., 2010], so projected future flood probabilities should be viewed primarily as an illustration.\nUsing the maximum-likelihood GPDs, we compute return levels corresponding to a set of representative return periods (e.g., the 1-in-10 or 1-in-100 year flood events). For each decade of each realization of LSL change, we then add the projected sea-level change and re-estimate a GPD. The result for each realization is a trajectory of probabilities over time for each of the original return levels. For example, for the 10-year event, the initial probability at 2000 is 10% per year and increases over time as sea-level rises. Cumulatively summing each decade\u2019s expectation through the century, we compute the expected number of the original events by 2100. Under stationary sea levels, there would be one expected 1-in-100 year event and ten expected 1-in-10 year events between 2001 and 2100.\nSea-Level Projections\uf0c1\nMean Global Sea-Level Projections\uf0c1\nThe cumulative 21st century GSL contribution of each component is shown in Figure 2 (for RCP 8.5) and in Table 1 and Supporting Information Figure S7 (for all RCPs). In the 21st century, thermal expansion and GIC provide the largest contributions to the median outcome and have narrower uncertainty ranges than the ice sheet contributions. AIS has the broadest uncertainty range, extending from a small negative contribution to sea level (presumably due to warming-induced increased snow accumulation) to a large positive contribution (requiring a substantial and/or widespread dynamic change).\nFigure 2: Projections of cumulative contributions of (a) the Greenland ice sheet, (b) the Antarctic ice sheet, (c) thermal expansion, and (d) glaciers to sea-level rise in RCP 8.5. Heavy = median, light = 67% range, dashed = 5th \u2013 95th percentile; dotted = 0.5th-99.5th percentiles.\uf0c1\nTable 1: GSL Projections. TE: Thermal expansion, LWS: Land water storage, H14: Horton et al. [2014], J12: Jevrejeva et al. [2012], S12: Schaeffer et al. [2012]. All values are cm above 2000 CE baseline except for AR5, which is above a 1986\u20132005 baseline.\nRCP 8.5\nRCP 4.5\nRCP 2.6\ncm\n50\n17-83\n5-95\n0.5-99.5\n99.9\n50\n17-83\n5-95\n0.5-99.5\n99.9\n50\n17-83\n5-95\n0.5-99.5\n99.9\n2100 - Components\nGIC\n18\n14-21\n11-24\n7-29\n<30\n13\n10-17\n7-19\n3-23\n<25\n12\n9-15\n7-17\n3-20\n<25\nGIS\n14\n8-25\n5-39\n3-70\n<95\n9\n4-15\n2-23\n0-40\n<55\n6\n4-12\n3-17\n2-31\n<45\nAIS\n4\n-8 to 15\n-11 to 33\n-14 to 91\n<155\n5\n-5 to 16\n-9 to 33\n-11 to 88\n<150\n6\n-4 to 17\n-8 to 35\n-10 to 93\n<155\nTE\n37\n28-46\n22-52\n12-62\n<65\n26\n18-34\n13-40\n4-48\n<55\n19\n13-26\n8-31\n1-38\n<40\nLWS\n5\n3-7\n2-8\n-0 to 11\n<11\n5\n3-7\n2-8\n-0 to 11\n<11\n5\n3-7\n2-8\n-0 to 11\n<11\nTotal\n79\n62-100\n52-121\n39-176\n<245\n59\n45-77\n36-93\n24-147\n<215\n50\n37-65\n29-82\n19-141\n<210\nProjections by year\n2030\n14\n12-17\n11-18\n8-21\n<25\n14\n12-16\n10-18\n8-20\n<20\n14\n12-16\n10-18\n8-20\n<20\n2050\n29\n24-34\n21-38\n16-49\n<60\n26\n21-31\n18-35\n14-44\n<55\n25\n21-29\n18-33\n14-43\n<55\n2100\n79\n62-100\n52-121\n39-176\n<245\n59\n45-77\n36-93\n24-147\n<215\n50\n37-65\n29-82\n19-141\n<210\n2150\n130\n100-180\n80-230\n60-370\n<540\n90\n60-130\n40-170\n20-310\n<480\n70\n50-110\n30-150\n20-290\n<460\n2200\n200\n130-280\n100-370\n60-630\n<950\n130\n70-200\n40-270\n10-520\n<830\n100\n50-160", "source": "https://sealeveldocs.readthedocs.io/en/latest/kopp14.html"}
{"id": "cf8deb22c40d-4", "text": "4\n-8 to 15\n-11 to 33\n-14 to 91\n<155\n5\n-5 to 16\n-9 to 33\n-11 to 88\n<150\n6\n-4 to 17\n-8 to 35\n-10 to 93\n<155\nTE\n37\n28-46\n22-52\n12-62\n<65\n26\n18-34\n13-40\n4-48\n<55\n19\n13-26\n8-31\n1-38\n<40\nLWS\n5\n3-7\n2-8\n-0 to 11\n<11\n5\n3-7\n2-8\n-0 to 11\n<11\n5\n3-7\n2-8\n-0 to 11\n<11\nTotal\n79\n62-100\n52-121\n39-176\n<245\n59\n45-77\n36-93\n24-147\n<215\n50\n37-65\n29-82\n19-141\n<210\nProjections by year\n2030\n14\n12-17\n11-18\n8-21\n<25\n14\n12-16\n10-18\n8-20\n<20\n14\n12-16\n10-18\n8-20\n<20\n2050\n29\n24-34\n21-38\n16-49\n<60\n26\n21-31\n18-35\n14-44\n<55\n25\n21-29\n18-33\n14-43\n<55\n2100\n79\n62-100\n52-121\n39-176\n<245\n59\n45-77\n36-93\n24-147\n<215\n50\n37-65\n29-82\n19-141\n<210\n2150\n130\n100-180\n80-230\n60-370\n<540\n90\n60-130\n40-170\n20-310\n<480\n70\n50-110\n30-150\n20-290\n<460\n2200\n200\n130-280\n100-370\n60-630\n<950\n130\n70-200\n40-270\n10-520\n<830\n100\n50-160\n30-240\n10-500\n<810\nOther projections for 2100\nAR5\n73\n53\u201397\n52\n35\u201370\n43\n28\u201360\nH14\n70\u2013120\n50\u2013150\n40\u201360\n25-70\nJ12\n110\n81\u2013165\n75\n52\u2013110\n57\n36\u201383\nS12\n90\n64\u2013121\n75\n52\u201396\nFigure S7: Projections of (a) Greenland ice sheet, (b) Antarctic ice sheet, (c) thermal expansion, and (d) glacier contributions to sea-level rise in RCP 8.5 (red), RCP 4.5 (blue) and RCP 2.6 (green). Heavy = median, dashed = 67% range.\uf0c1\nAdding samples from the component distributions together indicates a likely GSL rise (Figure 3 and Table 1) in RCP 8.5 of 0.6 \u2013 1.0 m by 2100, with a very likely range of 0.5 \u2013 1.2 m and a virtually certain (99% probability) range of 0.4 \u2013 1.8 m. The right-skewed \u201cfat tail\u201d of the projections arises from the ice sheet components. Even in the low-emissions RCP 2.6 pathway, sea-level rise by 2100 very likely exceeds the 32 cm that would be projected from a simple linear continuation of the 1993 \u2013 2009 rate [Church and White, 2011].\nFigure 3: Projections of GSL rise for the three RCPs. Heavy = median, dashed = 5th \u2013 95th percentile, dotted = 0.5th \u2013 99.5th percentiles.\uf0c1\nThrough the middle of the current century, GSL rise is nearly indistinguishable between the three forcing pathways (Figure 3 and Table 1). Only in the second half of the century do differences of >6 cm begin to emerge in either the median or the tails of the projections. By 2100, median projections reach 0.8 m for RCP 8.5, 0.6 m for RCP 4.5 and 0.5 m for RCP 2.6. By 2200, upper tail outcomes are clearly higher in the high-forcing pathway, yet there remains significant overlap in the ranges of all three pathways, with likely GSL rise by 2200 of 1.3 \u2013 2.8 m in RCP 8.5 and 0.5 \u2013 1.6 m in RCP 2.6. The overlap between RCPs is due in significant part to the large and scenario-independent uncertainty of AIS dynamics, even as the thermal expansion, GIC and, to a lesser extent, GIS contributions begin to differentiate (Supporting Information Figure S7).\nThe importance of different components to the GSL uncertainty varies with time. While in 2020 about two-thirds of the total variance in GSL is due to uncertainty in projections of thermal expansion, by 2050 in RCP 8.5 changes in ice sheet volume are responsible for more than half the variance and changes in thermal expansion for only about one-third. By 2100, AIS alone is responsible for half the variance, with an additional 30% due to GIS uncertainty and only 15% due to uncertainty in thermal expansion (Figure 4). Because the uncertainty in AIS mass loss is largely scenario-independent, its dominant contribution to variance holds across RCPs; indeed, it is even more dominant in lower emissions pathways where the contributions from other sources are smaller and more strongly constrained (Supporting Information Figure S8).\nFigure 4: Sources of variance in raw (a, c) and fractional terms (b, d), globally (a \u2013 b) and at New York City (c \u2013 d) in RCP 8.5. AIS: Antarctic ice sheet, GIS: Greenland ice sheet, TE: thermal expansion, Ocean: oceanographic processes, GIC: glaciers and ice caps, LWS: land water storage, Bkgd: local background effects.\uf0c1\nFigure S8: Sources of variance in raw (left) and fractional terms (right), for a range of sites under RCP 2.6.\uf0c1\nComparison With Other Global Projections\uf0c1\nBy construction, our likely projections of GSL in 2100 are close to those of AR5 (Table 1), though differ slightly (e.g., in RCP 8.5 in 2100, 0.6 \u2013 1.0 m vs. AR5\u2019s 0.5 \u2013 1.0 m) due to: (1) the drift correction to a possibly non-zero (0.3 \u00b1 0.9 mm/yr) background thermal expansion, (2) the use of Marzeion et al. [2012] for GIC, and (3) the use of a year 2000 as opposed to 1985 \u2013 2005 baseline. AR5 projections of GSL rise are lower than those from other sources, such as semi-empirical models [Rahmstorf , 2007; Schae\ufb00er et al., 2012; Vermeer and Rahmstorf , 2009] and expert surveys [Horton et al., 2014]. However, AR5 only projects likely ranges; higher magnitudes of ice loss are implied if less likely outcomes are considered [Little et al., 2013a].\nBy using plausible information to complement the AR5 analysis, we project a very likely GSL rise in 2100 of 0.4 \u2013 0.9 m for RCP 4.5, which compares to the 90% probability semi-empirical projections of 0.5 \u2013 1.1 m [Jevrejeva et al., 2012] and 0.6 \u2013 1.2 m [Schaeffer et al., 2012]. The widths of the semi-empirical very likely ranges are similar to those of our projections, with the entire distribution shifted to higher values. The 95th percentiles of these two semi-empirical projections resemble the 98th and 99th percentiles of our projection, respectively.", "source": "https://sealeveldocs.readthedocs.io/en/latest/kopp14.html"}
{"id": "cf8deb22c40d-5", "text": "Figure S8: Sources of variance in raw (left) and fractional terms (right), for a range of sites under RCP 2.6.\uf0c1\nComparison With Other Global Projections\uf0c1\nBy construction, our likely projections of GSL in 2100 are close to those of AR5 (Table 1), though differ slightly (e.g., in RCP 8.5 in 2100, 0.6 \u2013 1.0 m vs. AR5\u2019s 0.5 \u2013 1.0 m) due to: (1) the drift correction to a possibly non-zero (0.3 \u00b1 0.9 mm/yr) background thermal expansion, (2) the use of Marzeion et al. [2012] for GIC, and (3) the use of a year 2000 as opposed to 1985 \u2013 2005 baseline. AR5 projections of GSL rise are lower than those from other sources, such as semi-empirical models [Rahmstorf , 2007; Schae\ufb00er et al., 2012; Vermeer and Rahmstorf , 2009] and expert surveys [Horton et al., 2014]. However, AR5 only projects likely ranges; higher magnitudes of ice loss are implied if less likely outcomes are considered [Little et al., 2013a].\nBy using plausible information to complement the AR5 analysis, we project a very likely GSL rise in 2100 of 0.4 \u2013 0.9 m for RCP 4.5, which compares to the 90% probability semi-empirical projections of 0.5 \u2013 1.1 m [Jevrejeva et al., 2012] and 0.6 \u2013 1.2 m [Schaeffer et al., 2012]. The widths of the semi-empirical very likely ranges are similar to those of our projections, with the entire distribution shifted to higher values. The 95th percentiles of these two semi-empirical projections resemble the 98th and 99th percentiles of our projection, respectively.\nHorton et al. [2014] conducted a survey of 90 experts with a substantial published record in sea-level research. Their survey found likely/very likely sea-level rise by 2100 of 0.7 \u2013 1.2/0.5 \u2013 1.5 m under RCP 8.5 and 0.4 \u2013 0.6/0.3 \u2013 0.7 m under RCP 2.6. Our projections for RCP 2.6 are similar to those of the surveyed experts, with a slightly fatter upper tail, while the experts\u2019 responses for RCP 8.5 are considerably fatter-tailed than our projections. The surveyed experts\u2019 83rd and 95th percentiles correspond to our 95th and 99th percentiles, respectively. Although Horton et al. [2014] did not probe the reasons why their surveyed experts different from AR5, we suggest it may be related to expectations about the behavior of Antarctica. As noted previously, high-end estimates of Antarctic mass loss from the expert elicitation of BA13 are higher than would be expected from the likely range of AR5 projections; our reconciled ice sheet projections significantly lower this contribution. (See also the sensitivity tests in section 4 for comparison.)\nOur 99.9th percentile estimate for 2100 under RCP 8.5, 2.5 m, is consistent with other estimates of the maximum physically possible rate of sea-level rise in the 21st century [e.g., Miller et al., 2013]. It is higher than the 2.0 m estimate of Pfeffer et al. [2008], which corresponds to our 99.7th percentile. Comparing the individual contribution to Pfeffer et al.\u2019s high-end projection shows that their projected GIC mass loss (55 cm) exceeds our highest projected value (32 cm), while their projections of GIS and AIS mass loss (53 and 62 cm, respectively) correspond to our 98th and 99th percentiles. Their projection of thermal expansion (30 cm) includes no uncertainty and corresponds to our 22nd percentile [cf., Sriver et al., 2012]. They do not include changes in sea-level rise resulting from changes in land water storage. As noted previously, the tail of the sea-level rise projections is dominated by the uncertainty in AIS mass loss, which is lower in Pfeffer et al. [2008] than in either our projections or BA13.\nLocal Sea-Level Projections: Patterns\uf0c1\nFigure 5 displays the median LSL projections for RCP 8.5 in 2100 and the projection uncertainty, as reflected by the difference between the 17th and 83rd percentile levels. In Figure 6, we illustrate the relationship between LSL and GSL using three indices: (1) the median value of R, which we define as the ratio of LSL change driven by land ice and oceanographic components to GSL change driven by those same components (Figure 6a), (2) the uncertainty in R, reflected in Figure 6b by the difference between its 17th and 83rd percentile levels, and (3) the magnitude and uncertainty of background, non-climatic LSL change (Figure 6c). For sites where R is close to 1 and exhibits little uncertainty, GSL projections with adjustment for local land motion provide a reasonable estimate of LSL; for other sites, more detailed projections, such as those in this article, are necessary.\nFigure 5: (a) Median projection and (b) width of likely range of local sea-level rise (m) in 2100 under RCP 8.5.\uf0c1\nFigure 6: (a) Median ratio R of climatically driven LSL change to climatically driven GSL exchange (i.e., excluding land water storage and local land motion) in RCP 8.5 in 2100; (b) width of the 17th \u2013 83rd percentile range of R; (c) mean estimates of background rate of sea-level rise due to GIA, tectonics, and other local factors (mm/yr). Open circles in bottom indicate sites where 2 $sigma$ range spans zero.\uf0c1\nThe median value of R (Figure 6a) is within 5 % of unity at about a quarter of tide-gauge sites, with higher values in much of Oceania, the Indian Ocean, and southern Africa resulting from the static-equilibrium effects of land ice mass loss. R generally declines toward higher latitudes due to static-equilibrium effects, but with values elevated in northeastern North America and to a lesser extent the North and Baltic Seas by oceanographic processes. This pattern \u2014 with sea-level rise dampened near land ice and enhanced far from it and in the northwestern North Atlantic \u2014 resembles that found by previous studies [Kopp et al., 2010; Perrette et al., 2013; Slangen et al., 2012, 2014]. Uncertainty in R (Figure 6b) is also relatively small (likely range width of < 30 %) in the inhabited southern hemisphere and low-latitude northern hemisphere, with the range increasing northwards due to both the sensitivity of static-equilibrium effects to the particular distribution of shrinking land ice reservoirs and \u2014 especially in northeastern North America, the Baltic Sea, and the Russian Arctic \u2014 uncertainty in oceanographic processes (Supporting Information Figure S4).\nAdded on top of the climatically driven factors reflected in R are the global effects of land water storage (not shown in Figure 6) and the effects of local land motion (Figure 6c). Moderately high rates of land subsidence can be associated with GIA, as in the northeastern United States (e.g., 1.3 \u00b1 0.2 mm/yr at New York City), while more extreme rates generally include contributions from fluid withdrawal, delta processes, and/or tectonics. Subsidence driven by fluid withdrawal and delta processes is high at sites such as Bangkok, Thailand (background rate of 11.9 \u00b1 1.1 mm/yr at the Fort Phracula Chomklao tide gauge), Grand Isle, Louisiana (7.2 \u00b1 0.5 mm/yr), Manila, the Philippines (background rate of 4.9 \u00b1 0.6 mm/yr), and Kolkata, India (5.1 \u00b1 1.0 mm/yr). Episodic tectonic factors play an important role in both subsidence and uplift in Japan, where average background rates can range from \u2212 5.2 \u00b1 0.7 mm/yr at Onahama to 18.0 \u00b1 1.6 mm/yr at Toba. At high latitudes, GIA-related uplift gives rise to high background rates of sea-level fall, as can be seen in places like Juneau, Alaska, (\u2212 14.9 \u00b1 0.5 mm/yr), and Ratan, Sweden (\u2212 9.3 \u00b1 0.2 mm/yr). While some previous global projections have used physical models to incorporate GIA [e.g., Slangen et al., 2012, 2014], the current projections are to our knowledge the first to employ observationally based rates.\nLocal Sea-Level Projections: Examples\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/kopp14.html"}
{"id": "cf8deb22c40d-6", "text": "Added on top of the climatically driven factors reflected in R are the global effects of land water storage (not shown in Figure 6) and the effects of local land motion (Figure 6c). Moderately high rates of land subsidence can be associated with GIA, as in the northeastern United States (e.g., 1.3 \u00b1 0.2 mm/yr at New York City), while more extreme rates generally include contributions from fluid withdrawal, delta processes, and/or tectonics. Subsidence driven by fluid withdrawal and delta processes is high at sites such as Bangkok, Thailand (background rate of 11.9 \u00b1 1.1 mm/yr at the Fort Phracula Chomklao tide gauge), Grand Isle, Louisiana (7.2 \u00b1 0.5 mm/yr), Manila, the Philippines (background rate of 4.9 \u00b1 0.6 mm/yr), and Kolkata, India (5.1 \u00b1 1.0 mm/yr). Episodic tectonic factors play an important role in both subsidence and uplift in Japan, where average background rates can range from \u2212 5.2 \u00b1 0.7 mm/yr at Onahama to 18.0 \u00b1 1.6 mm/yr at Toba. At high latitudes, GIA-related uplift gives rise to high background rates of sea-level fall, as can be seen in places like Juneau, Alaska, (\u2212 14.9 \u00b1 0.5 mm/yr), and Ratan, Sweden (\u2212 9.3 \u00b1 0.2 mm/yr). While some previous global projections have used physical models to incorporate GIA [e.g., Slangen et al., 2012, 2014], the current projections are to our knowledge the first to employ observationally based rates.\nLocal Sea-Level Projections: Examples\uf0c1\nTo illustrate the importance of local factors for sea-level rise projections, we consider several sites along the coasts of the United States where different factors dominate LSL change (Tables 2 and 3). While we focus on projections for RCP 8.5 as a way of highlighting the differences between GSL and LSL, similar considerations apply to other RCPs, which are shown in the tables.\nTable 2: LSL Projections for New York, NY, USA (Bkgd: 1.31 \u00b1 0.18 mm/yr), Sewell\u2019s Point, VA, USA (Bkgd: 2.45 \u00b1 0.29 mm/yr), Key West, FL, USA (Bkgd: 0.46 \u00b1 0.41 mm/yy), Galveston, TX, USA (Bkgd: 4.56 \u00b1 0.27 mm/yr), San Francisco, CA, USA (Bkgd: \u2212 0.08 \u00b1 0.18 mm/yr), Juneau, AK, USA (Bkgd: \u2212 14.91 \u00b1 0.53 mm/yr), Honolulu, HI, USA (Bkgd: \u2212 0.20 \u00b1 0.39 mm/yr), Cuxhaven, Germany (Bkgd: 1.00 \u00b1 0.17 mm/yr), Stockholm, Sweden (Bkgd: \u2212 5.01 \u00b1 0.12 mm/yr), Kushimoto, Japan (Bkgd: 1.46 \u00b1 0.80 mm/yr), Valparaiso, Chile (Bkgd: \u2212 2.47 \u00b1 0.79 mm/yr) in RCP 8.5, RCP 4.5 and RCP 2.6 emission scenarios.\nTable 3: Components of LSL rise in 2100 for New York, NY, USA, Sewell\u2019s Point, VA, USA, Key West, FL, USA, Galveston, TX, USA, San Francisco, CA, USA, Juneau, AK, USA, Honolulu, HI, USA, Cuxhaven, Germany, Stockholm, Sweden, Kushimoto, Japan, Valparaiso, Chile in RCP 8.5, RCP 4.5 and RCP 2.6 emission scenarios.\nNew York City experiences greater-than-global sea-level rise under almost all plausible projections, with a likely range of 0.7 \u2013 1.3 m by 2100 under RCP 8.5. Three factors enhance sea-level rise at New York. First, due to its location on the subsiding peripheral bulge of the former Laurentide Ice Sheet, the site experiences GIA-related sea-level rise of 1.3 \u00b1 0.2 mm/yr. Second, the rotational effects of WAIS mass loss increase\nthe region\u2019s sea-level response to WAIS mass loss by about 20% [Mitrovica et al., 2009]. Third, as noted\nin earlier papers [Kopp et al., 2010; Yin et al., 2009; Yin and Goddard, 2013], changes in the Gulf Stream may result in dynamic sea-level rise in the mid-Atlantic United States. This enhancement can be seen by examining the difference between oceanographic sea-level rise at New York and the global average, which has a median of 14 cm and a likely range of \u22126 to +35 cm. These three effects are partially counteracted by the \u223c55 % reduction in the sea-level response due to GIS mass loss, associated with the gravitationally induced migration of water away from of this relatively proximal ice mass. Indeed, the climatic factors that amplify and reduce LSL rise relative to GSL rise are nearly balanced in the median projection (R = 1.03, with a likely range of 0.73 \u2013 1.30), with GIA effects pushing local rise to levels that exceed the global rise.\nSewell\u2019s Point in Norfolk, VA, is projected to experience higher-than-global mean sea-level rise due to the same factors as New York City: subsidence due to GIA, enhanced influence of WAIS mass loss, and exposure to changes in the Gulf Stream. Being located farther south along the U.S. East Coast, Norfolk experiences somewhat smaller ocean dynamic changes (median and likely ocean dynamic sea-level rise increment of 9 cm and \u22128 to 26 cm) but greater sea-level rise due to GIS mass loss (experiencing about \u223c45 % less sea-level rise than the global mean). Its R value (1.00, likely range of 0.75 \u2013 1.22) is similar to New York City. However, whereas New York City sits upon bedrock, Norfolk is located on the soft sediments of the Coastal Plain [Miller et al., 2013]. As a consequence, it is exposed to sea-level rise due to both natural sediment compaction and compaction caused by groundwater withdrawal, which increases the background non-climatic rate of sea-level rise to 2.5 \u00b1 0.3 mm/yr. Accordingly, the likely range of LSL rise for RCP 8.5 in 2100 is 0.8 \u2013 1.3 m.\nSea-level rise at Key West, Florida, is closer to the global mean, with a likely range in RCP 8.5 by 2100 of 0.6 \u2013 1.1 m (median R = 1.00, likely range of 0.83 \u2013 1.15, background rise of 0.5 \u00b1 0.4 mm/yr). By contrast, the deltaic western Gulf of Mexico coastline experiences some of the fastest rates of sea-level rise in the world as a result of groundwater withdrawal and hydrocarbon production [Kolker et al., 2011; White and Tremblay, 1995]. At Galveston, Texas, a background subsidence rate of 4.6 \u00b1 0.3 mm/yr drives a likely range of sea-level rise by 2100 in RCP 8.5 of 1.0 \u2013 1.5 m. Because the uncertainty in subsidence rate is small relative to other sources of uncertainty, this causes a shift in the range rather than a broadening of overall uncertainty, as occurs at New York City (reflected in a likely R of 0.78 \u2013 1.13, which is narrower than at New York City).\nThe Paci\ufb01c Coast of the contiguous United States is subject to considerable short length-scale sea-level rise variability due to tectonics, as can be seen by comparing the background non-climatic rate of sea-level rise at Los Angeles (\u2212 1.1 \u00b1 0.3 mm/yr) and nearby Santa Monica (\u2212 0.6 \u00b1 0.3 mm/yr). In general, sea-level rise on this coast is close to the global average, with a likely range in 2100 under RCP 8.5 at San Francisco of 0.6 \u2013 1.0 m (median R = 0.96, likely 0.84 \u2013 1.08, background rate of \u2212 0.1 \u00b1 0.2 mm/yr). The slightly lower-than-global projection is a result of smaller Greenland and GIC contributions due to proximity to these land ice reservoirs, though counterbalanced by enhanced sea-level rise from AIS mass loss. Ocean dynamic factors are projected to play a minimal role.", "source": "https://sealeveldocs.readthedocs.io/en/latest/kopp14.html"}
{"id": "cf8deb22c40d-7", "text": "Sea-level rise at Key West, Florida, is closer to the global mean, with a likely range in RCP 8.5 by 2100 of 0.6 \u2013 1.1 m (median R = 1.00, likely range of 0.83 \u2013 1.15, background rise of 0.5 \u00b1 0.4 mm/yr). By contrast, the deltaic western Gulf of Mexico coastline experiences some of the fastest rates of sea-level rise in the world as a result of groundwater withdrawal and hydrocarbon production [Kolker et al., 2011; White and Tremblay, 1995]. At Galveston, Texas, a background subsidence rate of 4.6 \u00b1 0.3 mm/yr drives a likely range of sea-level rise by 2100 in RCP 8.5 of 1.0 \u2013 1.5 m. Because the uncertainty in subsidence rate is small relative to other sources of uncertainty, this causes a shift in the range rather than a broadening of overall uncertainty, as occurs at New York City (reflected in a likely R of 0.78 \u2013 1.13, which is narrower than at New York City).\nThe Paci\ufb01c Coast of the contiguous United States is subject to considerable short length-scale sea-level rise variability due to tectonics, as can be seen by comparing the background non-climatic rate of sea-level rise at Los Angeles (\u2212 1.1 \u00b1 0.3 mm/yr) and nearby Santa Monica (\u2212 0.6 \u00b1 0.3 mm/yr). In general, sea-level rise on this coast is close to the global average, with a likely range in 2100 under RCP 8.5 at San Francisco of 0.6 \u2013 1.0 m (median R = 0.96, likely 0.84 \u2013 1.08, background rate of \u2212 0.1 \u00b1 0.2 mm/yr). The slightly lower-than-global projection is a result of smaller Greenland and GIC contributions due to proximity to these land ice reservoirs, though counterbalanced by enhanced sea-level rise from AIS mass loss. Ocean dynamic factors are projected to play a minimal role.\nFarther north, the proximity of historic and modern glaciers controls LSL projections. At Juneau, predicted sea-level rise is dominated by a glacio-isostatic sea-level fall of 14.9 \u00b1 0.5 mm/yr, interpreted as resulting primarily from the ongoing response to post-Little Ice Age glacial mass loss, with a secondary contribution from post-Last Glacial Maximum GIA [Larsen et al., 2005]. Moreover, shrinking glaciers in Alaska and western Canada cause about 2.4 mm of LSL fall at Juneau for every mm of global sea-level rise, which reduces the overall magnitude of sea-level rise caused by projected glacial mass loss (median R = 0.71, likely 0.59 \u2013 0.83). As a consequence, under RCP 8.5 Juneau is likely to experience a sea level fall of 0.7 \u2013 1.1 m by 2100.\nHawai\u2018i and other central Paci\ufb01c islands experience significantly greater-than-average sea-level rise resulting from land ice mass loss (20% enhancement for GIS, EAIS, and the median combination of shrinking glaciers, and 30% for WAIS, giving rise to median R = 1.13 and likely 0.98 \u2013 1.26). The likely range of sea-level rise at Honolulu, Hawai\u2018i, is slightly higher than the global mean (0.6 \u2013 1.1 m in 2100 under RCP 8.5, with a background rate of \u2212 0.2 \u00b1 0.4 mm/yr). The amplification relative to the global mean is more apparent in the tail of the projections, where ice sheet mass loss contributions constitute a larger proportion of the sea-level rise. As a consequence, the tail of sea-level rise is fatter at Hawai\u2018i than globally, with a 95th percentile in RCP 8.5 of 1.4 m (compared to GSL of 1.2 m) and a 99.5th percentile of 2.1 m (compared to GSL of 1.8 m).\nA similar range of behaviors is seen outside the United States. At Cuxhaven, on the German North Sea coast, a slightly higher-than-global likely range of 0.6 \u2013 1.1 m arises from a background subsidence rate of 1.0 \u00b1 0.2 mm/yr. Because of its relative proximity to Greenland, Cuxhaven is less exposed to climatically driven sea-level rise than average (median R = 0.89, likely 0.62 \u2013 1.15); unlike sites in eastern North America that are similarly close to Greenland, it does not experience a countervailing oceanographic sea-level rise. The city of Stockholm, Sweden, like Juneau, is experiencing a strong GIA-related uplift of \u22125.0 \u00b1 0.1 mm/yr, leading to a likely sea-level rise of \u22120.4 to +0.8 m. Being farther from a large, actively shrinking glacier, however, Stockholm is in the median more exposed than Juneau to climatically driven sea-level change (median R = 0.83, likely 0.41 \u2013 1.20).\nLike Honolulu, the town of Kushimoto, in Wakayama Prefacture, Japan, is in the far-\ufb01eld of the major ice sheets and most major glaciers. It is also exposed to a likely ocean dynamic sea-level rise of \u22125 to +18 cm in 2100. Together, these factors lead to a median R = 1.14, likely 0.98 \u2013 1.28. Kushimoto also is experiencing tectonic subsidence, leading to a likely sea-level rise in 2100 of 0.8 \u2013 1.3 m.\nThe city of Valparaiso, on the Chilean Paci\ufb01c coast, is experiencing tectonic uplift of 2.5 \u00b1 0.8 and exposed to a likely ocean dynamic sea-level fall of \u22122 to 9 cm. Although it experiences about 30% less-than-global sea-level rise due to WAIS mass loss, it experiences a larger-than-average response to GIS, EAIS, and most glaciers; accordingly its overall sensitivity to sea-level rise is close to the global average (median R = 0.99, likely 0.90 \u2013 1.08). All these factors together yield a likely 2100 sea-level rise 0.4 \u2013 0.8 m.\nVariance and Sensitivity Assessment\uf0c1\nAs shown in the previous section, LSL rise is controlled by different factors \u2014 both climatic and non-climatic \u2014 at different locations and intervals over the next two centuries. The analysis also reveals that the adopted risk tolerance (choice of exceedance probability) influences the importance of different components. Median outcomes will vary regionally, driven strongly by varying levels of subsidence and, in certain regions, oceanographic processes. High-end (low-probability) outcomes are driven, globally and in most locations, by uncertainty in the ice sheet contribution, with the Antarctic signal becoming dominant in the highest end of the tail, particularly later in the century (Figure 4 and Supporting Information Figures S8 and S9). This contribution varies less by location.\nFigure S9: Sources of variance in raw (left) and fractional terms (right), for a range of sites under RCP 8.5.\uf0c1\nTo test the robustness of our results, we examine three alternate assumptions regarding ice sheet mass loss and two alternative assumptions regarding the robustness of GCM projections (Supporting Information Tables S1 and S3):\nAR: using a lognormal fit to the AR5 median and likely ranges of ice sheet mass balance (GIS almost unchanged from reconciled projections; for AIS, very likely range of \u221215 to 23 cm in RCP 8.5 by 2100)\nBA: using a lognormal fit to the BA13 median and very likely projections of ice sheet mass balance (GIS: median 14 cm and very likely 9 \u2013 29 cm; AIS: median 14 cm, very likely \u22122 to 83 cm)\nAlt. Corr.: assuming positive correlations of 0.7 between WAIS and GIS and a negative correlation of \u22120.2 between EAIS and the other two ice sheets, following the main projections of Bamber and Aspinall [2013]\nHigh GCM Confidence: assuming the very likely ranges estimated by the GCMs for oceanographic changes are very likely rather than likely ranges.\nReduced degrees of freedom (DOF): Assuming the GCMs collectively provide only six independent estimates of GIC and oceanographic change, due to non-independence of models.\nHigher groundwater depletion (GWD): The ratio of groundwater depletion to population is treated as a triangular distribution, with the minimum, median, and maximum estimated respectively from Konikow [2011], Wada et al. [2012] and Pokhrel et al. [2012].\nTable S1: Ice sheet mass loss in sensitivity cases (cm equivalent sea level, RCP 8.5 in 2100)", "source": "https://sealeveldocs.readthedocs.io/en/latest/kopp14.html"}
{"id": "cf8deb22c40d-8", "text": "Figure S9: Sources of variance in raw (left) and fractional terms (right), for a range of sites under RCP 8.5.\uf0c1\nTo test the robustness of our results, we examine three alternate assumptions regarding ice sheet mass loss and two alternative assumptions regarding the robustness of GCM projections (Supporting Information Tables S1 and S3):\nAR: using a lognormal fit to the AR5 median and likely ranges of ice sheet mass balance (GIS almost unchanged from reconciled projections; for AIS, very likely range of \u221215 to 23 cm in RCP 8.5 by 2100)\nBA: using a lognormal fit to the BA13 median and very likely projections of ice sheet mass balance (GIS: median 14 cm and very likely 9 \u2013 29 cm; AIS: median 14 cm, very likely \u22122 to 83 cm)\nAlt. Corr.: assuming positive correlations of 0.7 between WAIS and GIS and a negative correlation of \u22120.2 between EAIS and the other two ice sheets, following the main projections of Bamber and Aspinall [2013]\nHigh GCM Confidence: assuming the very likely ranges estimated by the GCMs for oceanographic changes are very likely rather than likely ranges.\nReduced degrees of freedom (DOF): Assuming the GCMs collectively provide only six independent estimates of GIC and oceanographic change, due to non-independence of models.\nHigher groundwater depletion (GWD): The ratio of groundwater depletion to population is treated as a triangular distribution, with the minimum, median, and maximum estimated respectively from Konikow [2011], Wada et al. [2012] and Pokhrel et al. [2012].\nTable S1: Ice sheet mass loss in sensitivity cases (cm equivalent sea level, RCP 8.5 in 2100)\nTable S3: Sensitivity tests (cm, RCP 8.5 in 2100) for GSL and LSL in set of locations.\nAt a global level and at most locations, the two alternative characterizations of ice sheet mass changes have the largest effects, with the median sea-level rise under RCP 8.5 in 2100 varying between 79 cm under default assumptions and case AR and 91 cm under case BA. The effect is larger in the tails, with 99.5th percentile projections of 140 cm under AR, 176 cm under default assumptions, 187 cm under Alt. Corr., and 300 cm under BA. Varying the confidence in GCMs, by contrast, has little global effect. Although the per-capita rate of groundwater depletion estimated from Pokhrel et al. [2012] is about three times that of the Wada et al. [2012], the overall effect of the Higher GWD assumption is small due to the magnitude of other uncertainties; this case experiences 3 cm extra GSL rise at the 5th percentile, 4 cm at the median, and 6 cm at the 99.5th percentile.\nWhile all LSL projections are sensitive to assumptions about ice sheet behavior, some are sensitive to assumptions about confidence in GCM output. Due to the wide range of projections in the CMIP5 ensemble at New York City [Yin, 2012], the 99.5th percentile projections are 212 cm under default assumptions, 205 cm under High GCM Confidence, and 232 cm under Reduced DOF. Even at New York City, however, GCM uncertainty remains secondary to ice sheet uncertainty; the 99.5th percentile is 178 cm under AR, 212 cm under Alt. Corr., and 359 cm under BA. Moreover, the significance of GCM uncertainty can be quite small: at the sites discussed above, the difference between the 99.5th percentiles of the High GCM Con\ufb01dence and Reduced DOF cases under RCP 8.5 in 2100 is 27 cm at New York, 19 cm at Sewell\u2019s Point, 12 cm at Cuxhaven, 9 cm at Galveston, and 6 cm or less at Honolulu, Juneau, Key West, Kushimoto, San Francisco, and Valparaiso. A large difference (55 cm) at Stockholm may reflect differences between GCMs in the representation of the semi-closed Baltic Sea.\nThese sensitivity analyses are not exhaustive. There remains a need for improved ice sheet models to allow robust projections of the ice sheet component without heavy reliance upon expert elicitation. However, the development of such models is hindered by the limited consensus on the magnitude of positive and negative feedbacks on ice loss, such as those involving (a) temperature and snow albedo [Picard et al., 2012], (b) forest \ufb01res and snow albedo [Keegan et al., 2014], (c) snowfall and ice sheet discharge [Winkelmann et al., 2012], (d) grounding line retreat [Joughin et al., 2014; Rignot et al., 2014; Schoof , 2007],(e) static-equilibrium sea-level and grounding line retreat [Gomez et al., 2010, 2012, 2013], (f ) meltwater, ocean temperature, sea ice, and snowfall [Bintanja et al., 2013], and (g) ice-cliff collapse [Bassis and Walker, 2012; Pollard and DeConto, 2013]. The wide range of projections and underlying uncertainties in continental-scale model projections pose challenges for interpreting the likelihood of their results [Bindschadler et al., 2013]. It is possible, however, that incomplete information could be better integrated in a probabilistic framework [Little et al., 2013a, 2013b].\nFurthermore, structural errors in models of other sea level components remain probable. These errors (e.g., a systematic bias caused by a missing process and/or feedback) may have a large impact on tails. Here, we do not attempt to perform a systematic analysis. However, we believe that this framework may be used to effectively allow for these possibilities to be considered. The subjective judgment applied in formulating these distributions is explicit and may be revisited over time.\nImplications for Coastal Flooding\uf0c1\nSince our projections provide full probability distributions, they can be combined with extreme value distributions to estimate the expected number of years in which flooding exceeds a given elevation, integrated over a given interval of time. Note that this is different from the expected number of flood events in a single year; the question here is not, \u201cwhat is the probability of a flood of at least height X, given the projected sea-level change in 2050?\u201d but, \u201cin how many years between 2000 and 2050 do we expect floods of at least height X, given the projected pathway of sea level change?\u201d Table 4 shows the expected number of years under each RCP with current \u201c1-in-10 year\u201d (10% probability per year) and \u201c1-in-100 year\u201d (1% probability per year) flood events for a selection of sites over 2001 \u2013 2030, 2001 \u2013 2050, and 2001 \u2013 2100. Figure 7 shows the expected fraction of years with at least one event at the New York City, Key West, Cuxhaven, and Kushimoto tide gauges for a range of heights and the same periods of time under RCP 8.5; additional tide gauges and RCPs are shown in Supporting Information Figure S10.\nTable 4: Expected number of years with flood events of a given height under different RCPs. Heights for U.S. sites are with respect to the local mean higher high water datum for the 1983\u20132001 epoch. Heights for non-U.S. sites are with respect to the local mean sea level datum for the 1983\u20132001 epoch.\nFigure 7: Expected fraction of years with flooding at tide gauges in excess of a given height under stationary sea level (black) and RCP 8.5 over 2001 \u2013 2030 (blue), 2050 (green) and 2100 (red). Grey vertical lines indicate the current 1-in-10 and 1-in-100 year flood levels. Heights are relative to mean higher high water for U.S. sites and mean sea level for non-U.S. sites.\uf0c1\nFigure S10. Expected fraction of years with flooding at tide gauges in excess of a given height under stationary sea level (solid black), RCP 2.6 (dot-dashed), RCP 4.5 (dashed) and RCP 8.5 (solid), over 2001 to 2030 (blue), 2050 (green) and 2100 (red). Grey vertical lines indicate the current 1-in-10 and 1-in-100 year flood levels. Heights are relative to mean higher high water for U.S. sites and mean sea level for non-U.S. sites.\uf0c1", "source": "https://sealeveldocs.readthedocs.io/en/latest/kopp14.html"}
{"id": "cf8deb22c40d-9", "text": "Table 4: Expected number of years with flood events of a given height under different RCPs. Heights for U.S. sites are with respect to the local mean higher high water datum for the 1983\u20132001 epoch. Heights for non-U.S. sites are with respect to the local mean sea level datum for the 1983\u20132001 epoch.\nFigure 7: Expected fraction of years with flooding at tide gauges in excess of a given height under stationary sea level (black) and RCP 8.5 over 2001 \u2013 2030 (blue), 2050 (green) and 2100 (red). Grey vertical lines indicate the current 1-in-10 and 1-in-100 year flood levels. Heights are relative to mean higher high water for U.S. sites and mean sea level for non-U.S. sites.\uf0c1\nFigure S10. Expected fraction of years with flooding at tide gauges in excess of a given height under stationary sea level (solid black), RCP 2.6 (dot-dashed), RCP 4.5 (dashed) and RCP 8.5 (solid), over 2001 to 2030 (blue), 2050 (green) and 2100 (red). Grey vertical lines indicate the current 1-in-10 and 1-in-100 year flood levels. Heights are relative to mean higher high water for U.S. sites and mean sea level for non-U.S. sites.\uf0c1\nAt seven of the nine sites considered (New York, Sewell\u2019s Point, Key West, Galveston, San Francisco, Kushimoto, and Valparaiso, though not Cuxhaven or Stockholm), the expected number of years with current 1-in-10 year flood events, integrated over the 21st century, is under all RCPs at least five times larger than the 10 that would be predicted without sea-level rise. At the same seven sites, the expected number of years in the 21st century with current 1-in-100 year flood events is at least four times higher under RCP 2.6 and at least 8 times higher under RCP 8.5 than the 1 that would be expected without sea-level rise.\nThe increase in expected flood events is influenced both by the magnitude of projected LSL rise and by the range of past flood events. The latter is reflected in the difference between the 1-in-10 year and 1-in-100 year flood elevations, which will be larger at tide gauges that have experienced more extreme flood events. New York City and Cuxhaven are projected to experience fairly high sea-level rise (likely 0.7 to 1.3 m and 0.6 to 1.1 m by 2100 under RCP 8.5, respectively) but have also historically experienced large flood events, with the 1-in-100 year flood level about 70 cm higher than the 1-in-10 year flood level. Under RCP 8.5, these two sites respectively expect nine and four 1-in-100 year floods over the 21st century \u2014 the same as would be expected for 1-in-11 year and 1-in-25 year events without sea-level rise.\nStockholm has experienced fairly few large flood events, with the 1-in-100 year flood level only about 20 cm higher than the 1-in-10 year flood level, but also has a low projected sea-level rise (likely \u20130.2 to 0.5 m). As a consequence, it also expects nine 1-in-100 year floods over the 21st century under RCP 8.5. Key West, by contrast, has a projected sea-level rise similar to Cuxhaven but has not experienced as many large flood events. The 1-in-100 year flood level there is only about 23 cm higher than the 1-in-10 year flood level. Accordingly, it is expected to experience 48 years over the 21st century with a 1-in-100 year flood event, about the same as would be expected for a 1-in-2 year event without sea-level rise\nThe most extreme case among the nine sites considered is Kushimoto, which both has a large projected sea-level rise (likely 0.8 \u2013 1.3 m by 2100) and has experienced few large flood events, with the 1-in-100 year flood level just 10 cm higher than the 1-in-10 year flood level. Over the course of the 21st century, under all RCPs, Kushimoto is expected to experience more than 60 years with flooding exceeding the current 1-in-100 year flood level.\nSea-level rise allowances [Hunter et al., 2013] quantify the amount by which a structure needs to be raised so that its current flood probability remains unchanged. For example, the U.S. National Flood Insurance Program\u2019s Special Flood Hazard Areas are de\ufb01ned as areas with a 1% per year flood probability [National Flood Insurance Program, 2013]. A corresponding sea-level rise allowance would indicate the height above the current 1-in-100 year flood zone that would maintain an average 1% per year flood probability over the period of interest. Note that, because the allowance is with respect to flood risk integrated over time, its magnitude is less than that of the sea-level change expected by the end of the period of interest. At New York City, a project with a 2001\u20132030 lifetime, such as a house with a 30-year mortgage, would need to be elevated by 17 cm above the no-sea-level-rise 1-in-100 year flood zone to maintain a 1% per year flood probability. An infrastructure project with a 2001\u20132050 lifetime would need to be raised 26 cm, while a project with a 2001\u20132100 life time would need to be elevated by 52\u201369 cm, depending on the emissions trajectory (Figure 7).\nCautions\uf0c1\nIn addition to highlighting the sensitivities and research needs noted in section 4, we raise several cautions in interpreting our projections.\nFirst, in the near-term, internal variability in sea-level rise [e.g., Bromirski et al., 2011] makes estimation of precise timing of LSL change difficult. Most sites experience interannual variability with a 2 sigma ($sigma$) range of about 4 \u2013 10 cm [Hay et al., 2013; Kopp et al., 2010]. At the illustrative sites we consider, the difference between the 17th and 83rd percentile projections exceeds the decimeter level between 2030 and 2050. Until this threshold is reached, year-to-year variability will be comparable to the uncertainty in projections.\nSecond, as previously noted, historically estimated background rates of local, non-climatic processes may not continue unchanged. For example, while we project 72 \u00b1 5 cm of 21st century sea-level rise due to non-climatic factors at Grand Isle, Louisiana, changes in fluid withdrawal could reduce the projection [Blum and Roberts, 2012].\nThird, our background rate estimates are the result of an algorithm applied to a global database of tide-gauge data, with different sites having been subjected to different degrees of quality control. Some tide-gauge sites may have experienced datum shifts or other local sources of errors not identified by the analysis. We recommend that users of projections for practical applications in specific regions scrutinize local tide-gauge records for such effects.\nFourth, our flood probability estimates should be viewed indicatively. They are based on hourly tide-gauge records that may be of insufficient length to capture accurately the statistics of rare flood events. They do not account for projected changes in tropical or extratropical cyclone climatology, such as the expectation that Category 4 and 5 hurricanes may become more frequent in the North Atlantic [e.g., Bender et al., 2010] and perhaps globally [Emanuel, 2013]. They are developed for specific tide-gauge locations where flood risk is likely indicative of, but not identical to, risk for the wider vicinity, due to variation in local topography and hydrodynamics. Nonetheless, they do highlight the inadequacy of flood risk assessments based on historic flood probabilities for guiding long-term decisions in the face of ongoing sea-level rise.\nConclusions\uf0c1\nAssessments of climate change risk, whether in the context of evaluation of economic costs or the planning of resilient coastal communities and ecosystem reserves, require projections of sea-level changes that characterize not just likely sea-level changes but also tail risk. Moreover, these projections must estimate sea-level change at specific locations, not just at the global mean. They must also cover a range of timescales relevant for planning purposes, from the 30-year time scale of a typical U.S. mortgage, to the > 50 year lifetime of long-lived infrastructure projects, to the > 1 century lifetime of the development effects of infrastructure investments. In this article, we synthesize several lines of information, including model projections, formal expert elicitation, and expert assessment as embodied in the Intergovernmental Panel on Climate Change\u2019s Fifth Assessment Report, to generate projections that fulfill all three desiderata.", "source": "https://sealeveldocs.readthedocs.io/en/latest/kopp14.html"}
{"id": "cf8deb22c40d-10", "text": "Third, our background rate estimates are the result of an algorithm applied to a global database of tide-gauge data, with different sites having been subjected to different degrees of quality control. Some tide-gauge sites may have experienced datum shifts or other local sources of errors not identified by the analysis. We recommend that users of projections for practical applications in specific regions scrutinize local tide-gauge records for such effects.\nFourth, our flood probability estimates should be viewed indicatively. They are based on hourly tide-gauge records that may be of insufficient length to capture accurately the statistics of rare flood events. They do not account for projected changes in tropical or extratropical cyclone climatology, such as the expectation that Category 4 and 5 hurricanes may become more frequent in the North Atlantic [e.g., Bender et al., 2010] and perhaps globally [Emanuel, 2013]. They are developed for specific tide-gauge locations where flood risk is likely indicative of, but not identical to, risk for the wider vicinity, due to variation in local topography and hydrodynamics. Nonetheless, they do highlight the inadequacy of flood risk assessments based on historic flood probabilities for guiding long-term decisions in the face of ongoing sea-level rise.\nConclusions\uf0c1\nAssessments of climate change risk, whether in the context of evaluation of economic costs or the planning of resilient coastal communities and ecosystem reserves, require projections of sea-level changes that characterize not just likely sea-level changes but also tail risk. Moreover, these projections must estimate sea-level change at specific locations, not just at the global mean. They must also cover a range of timescales relevant for planning purposes, from the 30-year time scale of a typical U.S. mortgage, to the > 50 year lifetime of long-lived infrastructure projects, to the > 1 century lifetime of the development effects of infrastructure investments. In this article, we synthesize several lines of information, including model projections, formal expert elicitation, and expert assessment as embodied in the Intergovernmental Panel on Climate Change\u2019s Fifth Assessment Report, to generate projections that fulfill all three desiderata.\nUnder RCP 8.5, we project a very likely mean global sea-level rise of 0.5 \u2013 1.2 m by 2100 and 1.0 \u2013 3.7 m by 2200, which under the strong emissions mitigation of RCP 2.6 is lowered to 0.3 \u2013 0.8 m by 2100 and 0.3 \u2013 2.4 m by 2200. Local sea-level rise projections differ from the global mean due to differing background rates of non-climatic sea-level change, spatially variable responses to different land ice reservoirs due to static-equilibrium effects, and spatially variable ocean steric and dynamic changes. Static-equilibrium effects lead to a tendency for greater-than-global sea-level rise in the central and western Paci\ufb01c Ocean. Mid-latitude and high-latitude sites in North America and Europe are generally less exposed to climatically driven sea-level change, with the exception of northeastern North America, which has potential for a high oceanographic sea-level contribution. At most sites, by the end of the century, uncertainty is due primarily to uncertainty in AIS mass loss, though oceanographic uncertainty is also a major term at sites where oceanographic processes may make a significant contribution to sea-level rise.\nProbabilistic projections of future local sea-level rise pathways can be combined with statistical or hydrodynamic flood projections to estimate flood probabilities that more accurately assess the risks relevant to structures and populations. Projected sea-level rise can dramatically change estimated risks; at the Battery in New York City, for example, we project over the 21st century an expected nine years with \u201c1-in-100 year\u201d\u2019 flood events under RCP 8.5 and four under RCP 2.6. Such projections, especially if improved or augmented by more detailed storm and flood models that include factors such as changes in tropical and extratropical cyclone climatology and by hydrodynamic models of overland flooding, can guide insurance, land use planning, and other forms of coastal climate change risk management.\nSupplementary methods\uf0c1\nIce sheet mass loss\uf0c1\nTo reconcile the AR5 and BA13 projections of ice sheet mass loss, we first fit log-normal distributions to the rates of ice mass change in 2100 for AR5 and BA13. Assuming linear increases in ice loss rates from the levels of 2000\u20132011 [Shepherd et al., 2012], we calculate a distribution of cumulative ice sheet mass loss at each time point. We then shift the BA13-derived projections by a constant, so that their medians agree with those of the AR5-derived projections. Since BA13 separates WAIS and EAIS while AR5 does not, we approximate the median \u2018AR5\u2019 WAIS contribution by scaling the AR5 median AIS estimate by the ratio of the median BA13 WAIS projection to the median BA13 AIS projection. Finally, we apply a multiplier to the difference from the median so that the derived distribution matches the 67% probability AR5 range. We use separate multipliers for outcomes above and below the median projections. For example, for RCP 8.5 in 2100, we decrease the RCP 8.5 projections for AIS by 10 cm (from 14 cm to 4 cm), then multiply positive deviations from the median by 0.4 and negative deviations by 1.0. We use the same scale factors for WAIS and for total AIS. The resulting distributions are shown in Table S1 and Figure S1.\nGlacier and ice caps\uf0c1\nWe project mass loss for seventeen glacier and ice cap source regions: Alaska, Western Canada and the United States, Ellesmere Island, Ban Island, the Greenland periphery, Iceland, Svalbard, Scandinavia, Kamchatka, Novaya Zemlya, the Alps, the Caucasus, the northern Himalayas, the southern Himalayas, the low latitude Andes, Patagonia, and New Zealand. (Following AR5, Antarctic peripheral glaciers and ice caps are included in the calculation of AIS mass loss.)\nOceanographic processes\uf0c1\nThe \u2018zostoga\u2019 or (for the GFDL models) \u2018zosga\u2019 variables were used for GSL, while for LSL the global term was added to the local dynamic sea level anomaly, given by the difference between \u2018zos\u2019 and the global mean of \u2018zos\u2019.\nTo account for identifiable problems with specific models (for example, the way some models, such as MIROC-ESM, handle inland seas), we remove on a site-by-site basis projections that have an amplitude in 2100 more than ten times the median local amplitude. In cases where the standard deviation of projections in 2100 (after removal of the extreme outliers identified by the median amplitude) is greater than 20 cm, we also remove models that deviate from the mean by more than three standard deviations. Finally, to account for discrepancies in the accounting of sea surface height where there is sea ice coverage, we exclude MIROC and GISS models at latitudes greater than 50 degrees. Figure S4 shows the median and likely range of the projected ocean dynamic contribution to RCP 8.5 in 2100 (excluding the effects of global mean thermal expansion), as well as the number of models contributing to the assessment at each site after the removal of outliers.\nGaussian process model for tide gauge data\uf0c1\nThe Gaussian process prior for sea level has a mean given by the GIA projections of the ICE-5G VM2-90 model [Peltier , 2004] and a covariance given by the covariance function $k(r_1,t_1,r_2,t_2)$. The covariance is the sum of three terms: one representing GSL change ($k_{global}$), one representing linear local and regional sea-level changes ($k_{linear}$), and one representing non-linear local and regional sea-level changes ($k_{nonlin}$). The covariance function is given by\n$$ k(r_1,t_1,r_2,t_2) = k_{global}(t_1,t_2) + k_{linear}(r_1,t_1,r_2,t_2) + k_{linear}(r_1,t_1,r_2,t_2) + k_{nonlin}(r_1,t_1,r_2,t_2) $$ (S1)\n$$ k_{global}(t_1,t_2) = theta^2_1 t_1 t_2 + theta^2_2 C(| t_2-t_1 | /theta_3,theta_4) $$ (S2)\n$$ k_{linear}(r_1,t_1,r_2,t_2) = theta^2_5 t_1 t_2 times (theta_7 delta_{r1,r2} + (1 - theta_7) times D(alpha(r_1, r_2)/theta_6)) + delta_{r1,r2} theta^2_Delta $$ (S3)\n$$ k_{nonlin}(r_1,t_1,r_2,t_2) = theta^2_8 C( | t_2 - t_1 | /theta_9,theta_{10}) times (theta_{11}delta_{r1,r2} + (1 - theta_{11}) times D(alpha(r_1, r_2)/theta_{12})) $$ (S4)", "source": "https://sealeveldocs.readthedocs.io/en/latest/kopp14.html"}
{"id": "cf8deb22c40d-11", "text": "Gaussian process model for tide gauge data\uf0c1\nThe Gaussian process prior for sea level has a mean given by the GIA projections of the ICE-5G VM2-90 model [Peltier , 2004] and a covariance given by the covariance function $k(r_1,t_1,r_2,t_2)$. The covariance is the sum of three terms: one representing GSL change ($k_{global}$), one representing linear local and regional sea-level changes ($k_{linear}$), and one representing non-linear local and regional sea-level changes ($k_{nonlin}$). The covariance function is given by\n$$ k(r_1,t_1,r_2,t_2) = k_{global}(t_1,t_2) + k_{linear}(r_1,t_1,r_2,t_2) + k_{linear}(r_1,t_1,r_2,t_2) + k_{nonlin}(r_1,t_1,r_2,t_2) $$ (S1)\n$$ k_{global}(t_1,t_2) = theta^2_1 t_1 t_2 + theta^2_2 C(| t_2-t_1 | /theta_3,theta_4) $$ (S2)\n$$ k_{linear}(r_1,t_1,r_2,t_2) = theta^2_5 t_1 t_2 times (theta_7 delta_{r1,r2} + (1 - theta_7) times D(alpha(r_1, r_2)/theta_6)) + delta_{r1,r2} theta^2_Delta $$ (S3)\n$$ k_{nonlin}(r_1,t_1,r_2,t_2) = theta^2_8 C( | t_2 - t_1 | /theta_9,theta_{10}) times (theta_{11}delta_{r1,r2} + (1 - theta_{11}) times D(alpha(r_1, r_2)/theta_{12})) $$ (S4)\n$$ theta_Delta = 50 sqrt{theta^2_1 + theta^2_5} $$ (S5)\n$$ C(r,v) = frac{2^{1-v}}{Gamma(v)} (sqrt{2v}r)^v K_v (sqrt{2v}r) $$ (S6)\n$$ D(r) = (1 + sqrt{5}r + 5r^2 / 3) times exp{(-sqrt{5}r)} $$ (S7)\nwhere $theta_i$ are hyperparameters, $C$ is a Mat\u00e9rn covariance function with smoothness parameter $v$, $Gamma$ is the gamma function, $K_v$ is a modified Bessel function of the second kind, $D$ is a twice-differentiable Mat\u00e9rn covariance function with smoothness parameter $v = 5/2$, $delta_{i,j}$ is the Kroneker delta function (equal to 1 if $i = j$ and 0 otherwise), and $alpha(r_1,r_2)$ is the angular distance between points $r_1$ and $r_2$ [Rasmussen and Williams, 2006]. The product terms $(t_1t_2)$ represent linear deviations from the prior mean; the times $t_i$ are measured with respect to the year 2005 CE.\nThe hyperparameters reflect prior estimates of: the amplitude of the rate of linear GSL change ($theta_1$), the amplitude of non-linear GSL change ($theta_2$), the timescale of non-linear GSL change ($theta_3$), the smoothness of non-linear GSL change ($theta_4$), the amplitude of the rate of linear LSL change ($theta_5$), the spatial scale of regionally-coherent linear LSL change ($theta_6$), the fraction of linear LSL change that is not regionally coherent ($theta_7 in [0, 1]$), the amplitude of non-linear LSL change ($theta_8$), the timescale of non-linear LSL change ($theta_9$), the smoothness of non-linear LSL change ($theta_{10}$), the fraction of non-linear LSL change that is not regionally coherent ($theta_{11} in [0, 1]$), the spatial scale of regionally-coherent non-linear LSL change ($theta_{12}$), and the amplitude of datum offsets between tide gauges ($theta_{Delta}$).\nThe regions for hyperparameter tuning (Table S4, Figure S6) are defined using the coastlines defined by the Permanent Service for Mean Sea Level (PSMSL) [Holgate et al., 2013] (Permanent Service for Mean Sea Level, Tide gauge data, retrieved from http://www.psmsl.org/data/obtaining/, accessed January 2014). There is limited overlap between regions; for prediction in areas where regions overlap, the prediction from the region with more data is used.\nFor each region, we first optimize the hyperparameters of $k_{global}$ to maximize the likelihood of the GSL curve of Church and White [2011]. Then, we optimize the hyperparameters through a four step process: first optimizing assuming no spatial correlation ($theta_7,theta_{11} = 1$), then optimizing the spatial correlation of the background linear term, then re-optimizing assuming no spatial correlation in the non-linear terms ($theta_{11} = 1$), then finally optimizing the spatial correlation of the Mat\u00e9rn terms. For the hyperparameter optimization, we only consider the longest half of all tide gauges in a region provided that there are more than five tide gauges in the region; otherwise (as occurs in the Antarctic and Iceland/Svalbard regions), we include any tide gauge with a record length of at least 15 years.\nWithin each region, we estimate the regional and local linear rates using the optimized model for that region, applied to the tide gauge data from the region and the GSL curve of Church and White [2011]. We then fit the regional field of linear rates with a Gaussian process having mean 0 and covariance function\n$$ theta_5^2 t_1 t_2 times (theta_7^2 D (alpha(r_1,r_2)/theta_6^{prime}) + (1 - theta_7)^2 D (alpha(r_1,r_2)/theta_6)) $$,\noptimizing $theta_6^{prime}$ under the constraint that $theta_6^{prime} < theta_6$. This additional step allows for spatial continuity in rates at a finer length scale than $theta_6$. 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{"id": "cf8deb22c40d-13", "text": "Horton, B. P., S. Rahmstorf, S. E. Engelhart, and A. C. Kemp (2014), Expert assessment of sea-level rise by AD 2100 and AD 2300, Quat. Sci. Rev., 84, 1 \u2013 6, doi:10.1016/j.quascirev.2013.11.002.\nHorton, R. M., V. Gornitz, D. A. Bader, A. C. Ruane, R. Goldberg, and C. Rosenzweig (2011), Climate hazard assessment for stakeholder adaptation planning in New York City, J. Appl. Meteorol. Climatol., 50(11), 2247 \u2013 2266, doi:10.1175/2011JAMC2521.1.\nHunter, J., J. Church, N. White, and X. Zhang (2013), Towards a global regionally varying allowance for sea-level rise, Ocean Eng., 71, 17 \u2013 27, doi:10.1016/j.oceaneng.2012.12.041.\nIntergovernmental Panel on Climate Change (2013), Summary for policy makers, in Climate Change 2013: The Physical Science Basis, edited by T. F. Stocker, D. Qin, G.-K. Plattner, M. Tignor, S. K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex, and P. Midgley, pp. 3 \u2013 29, Cambridge Univ. Press, Cambridge, U. 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