Park et al. (2023)
Title:
Future sea-level projections with a coupled atmosphere-ocean-ice-sheet model
Key Points:
Presents 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.
Exploration of potential sea-level contribution from these regions under SSP 1-1.9, 2-4.5, 5-8.5 future emission scenarios.
The model predicts ice-sheet contributions to global sea-level rise by 2150 of 0.2 ± 0.01, 0.5 ± 0.01 and 1.4 ± 0.1 m  under SSP 1-1.9, 2-4.5, 5-8.5, respectively.
Only the most substantial climate mitigation scenario SPP1-1.9 avoids a long-term sustained sea-level contribution from Greenland and Antarctica.
Keywords:
Sea-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
Corresponding author:
Jun-Young Park
Citation:
Park, 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
URL:
https://www.nature.com/articles/s41467-023-36051-9
Abstract
Climate-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 ± 0.01, 0.5 ± 0.01 and 1.4 ± 0.1 m, 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.
Introduction
Global mean sea-level (SL) has risen over the past century by about 20 cm, 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’s 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.
These 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 1.5–2.2 K and 2.6–4.1 K, 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.
Observational 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—all of which remain poorly constrained8,10.
To 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.
The simulations include an 8000-years-long coupled pre-industrial spin-up run for initialization and 10 member ensemble of simulations forced by increasing CO2 concentrations following the Shared Socioeconomic Pathway (SSP) 1–1.9, 2–4.5 and 5–8.5 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 = 0 m per (m/year)−2 and VCLIF = 0 km/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).
Results
Recent trend and interannual variability of GrIS and AIS


The simulations include an 8000-years-long coupled pre-industrial spin-up run for initialization and 10 member ensemble of simulations forced by increasing CO2 concentrations following the Shared Socioeconomic Pathway (SSP) 1–1.9, 2–4.5 and 5–8.5 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 = 0 m per (m/year)−2 and VCLIF = 0 km/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).
Results
Recent trend and interannual variability of GrIS and AIS
According to satellite observations, the GrIS and AIS have been losing mass at a rate of ~286 Gt/year in 2010–2018 CE and ~252 Gt/year in 2009–2017 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 2002–2020 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 m SLE = 3.62 × 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 2002–2020 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 (−0.075 cm/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 (−0.13 to −0.08 cm/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 (−0.04 cm/year SLE) and the forced AIS trend (−0.1 to −0.02 cm/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.
Figure 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 2002–2020 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.
Future change of global surface temperature and SL
The projected ensemble average of global surface temperature rise in 2100 CE (2150 CE) relative to the pre-industrial levels (1850–1900 CE) amounts to 1.4 ± 0.17 °C (1.2 ± 0.14 °C), 2.4 ± 0.15 °C (2.7 ± 0.16 °C) and 4.0 ± 0.15 °C (5.3 ± 0.09 °C) 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 (1995–2014 CE) the simulated end-of-century warming (2081–2100 CE) attains values of 0.3 °C for SSP1-1.9 and 2.6 °C 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.
Figure 2: Global surface temperature and sea-level (SL) projections, and their tendencies. a–d Annual anomalies (relative to the 1850–1900 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 °C/year. Different colors represent the historical (black line; period 1850–2014 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 2014–2150 CE.


The projected ensemble average of global surface temperature rise in 2100 CE (2150 CE) relative to the pre-industrial levels (1850–1900 CE) amounts to 1.4 ± 0.17 °C (1.2 ± 0.14 °C), 2.4 ± 0.15 °C (2.7 ± 0.16 °C) and 4.0 ± 0.15 °C (5.3 ± 0.09 °C) 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 (1995–2014 CE) the simulated end-of-century warming (2081–2100 CE) attains values of 0.3 °C for SSP1-1.9 and 2.6 °C 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.
Figure 2: Global surface temperature and sea-level (SL) projections, and their tendencies. a–d Annual anomalies (relative to the 1850–1900 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 °C/year. Different colors represent the historical (black line; period 1850–2014 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 2014–2150 CE.
Higher 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 ± 1, 18 ± 0.9 and 23 ± 1.6 cm and the AIS adds 3 ± 0.8, 7 ± 1.4, and 15 ± 1.5 cm 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 ± 0.9, 24 ± 1.3, 39 ± 2 (19 ± 1.4, 48 ± 1.4, 136 ± 6.2) 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 m 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–h) 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°C warming (above the pre-industrial level) target emphasized by the Paris agreement41 is insufficient to prevent accelerated SL rise over the next century [42].
Ice loss from GrIS and AIS
In our model simulations, future warming leads to an increase in snow accumulation and ice thickness in the central part of GrIS (Fig. 3c–e, Fig. 4a) and West Antarctica (Fig. 3f–h, Fig. 4e). However, the negative mass balance terms together are considerably larger (Fig. 4b–d, f–h), leading to a net projected 80-year mass loss for the different scenarios of 14 ± 1.5, 20 ± 0.9 and 25 ± 1.5 cm SLE for GrIS and 46 ± 6, 94 ± 8 and 152 ± 8 cm 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° × 3° 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.
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 1850–1860 CE mean ice thickness (grayscale colormap) and 400 m Arctic Ocean (AO) temperature (red-yellow colormap); d 2090–2100 CE change in SSP5-8.5 scenario of GrIS ice thickness with respect to 1850–1860 CE and change in mean AO subsurface temperature; e same as d, but for period 2140–2150 CE; f, g same as c–e, but for AIS with 400 m 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.


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 1850–1860 CE mean ice thickness (grayscale colormap) and 400 m Arctic Ocean (AO) temperature (red-yellow colormap); d 2090–2100 CE change in SSP5-8.5 scenario of GrIS ice thickness with respect to 1850–1860 CE and change in mean AO subsurface temperature; e same as d, but for period 2140–2150 CE; f, g same as c–e, but for AIS with 400 m 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.
Figure 4: Individual mass balance terms for Greenland ice-sheet (GrIS) and Antarctic ice-sheet (AIS). 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 historical (black line; period 1850–2014 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 2014–2150 CE.
According 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 cm/year SLE by 2080 CE (corresponding to a freshwater flux into the ocean of ~0.34 Sv; 1 Sv = 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–h) – each component with their individual temporal contributions to the total freshwater and SL effect.
In 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 ± 0.3 cm/year SLE by 2150 CE (Fig. 4b)—a ~30-fold increase compared to the recent observed interannual rates of GrIS mass loss (Supplementary Fig. S3a).
Ice-sheet/climate feedbacks in Southern Hemisphere
To 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 °C 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 °C 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 cm/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.
Figure 5: Climate-ice-sheet feedbacks in Southern Hemisphere. a–c Annual anomalies (relative to the 1850–1900 CE mean) of (a) the Southern Ocean (SO) surface salinity, (b) 400 m subsurface Southern Ocean (SSO) temperature and (c) surface air temperature averaged between 60°S and 90°S. d is the SO sea-ice area averaged between 60°S and 90°S. 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 2014–2150 CE.
When 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).
Sensitivity of subsurface Southern Ocean warming


Figure 5: Climate-ice-sheet feedbacks in Southern Hemisphere. a–c Annual anomalies (relative to the 1850–1900 CE mean) of (a) the Southern Ocean (SO) surface salinity, (b) 400 m subsurface Southern Ocean (SSO) temperature and (c) surface air temperature averaged between 60°S and 90°S. d is the SO sea-ice area averaged between 60°S and 90°S. 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 2014–2150 CE.
When 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).
Sensitivity of subsurface Southern Ocean warming
To 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
T^{IM} = 2 × (T^{LC} - T^{LC}_{1850}) + T^{LC}_{1850} (1)
where T^{LC} is the 400 m 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–h) relative to SSP5-8.5 (Fig. 6a–d). This is most evident in Ross ice-shelf which vanishes completely by 2100 CE, leading to an integrated freshwater input of 2 ± 0.35 m SLE total AIS mass by 2100 CE (Fig. 6p) and de facto SL rise of 0.5 ± 0.04 m (Fig. 6o). Ice calving is the largest term in the mass balance over AIS (Fig. 4e–h). However, as the shelf retreat accelerates mainly due to the basal melting, the role of ice calving term diminishes (Supplementary Fig. S6g, h).
Figure 6: Transections of the Antarctic Ross ice-shelf, and global temperature and SL. a–l Transects of Antarctic Ross-ice-shelf simulated in (a–d) SSP5-8.5, (e–h) Re_SSP5-8.5_2xSOTA and (i–l) Re_SSP5-8.5_2xSOTA_MWOFF experiments in 1850, 1950, 2015 and 2100 CE. Dashed lines indicate grounding lines. m–p Time series of annual anomalies (relative to the 1850–1900 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–l are shown in Supplementary Fig. S9 as a red line.
The result of increased Antarctic meltwater fluxes by enhanced SSO warming concurs with our previous discussion of a global warming slowdown by 0.4 °C, relative to a simulation without such coupling (Fig. 6n red and blue lines). However, this sensitivity experiment increases SL by an additional 3 cm SL rise (Fig. 6o). Not unexpectedly, SSO warming does not show any significant influence on the GrIS (Supplementary Fig. S6a–d).
Discussion
Here 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.
In our high-end emission scenario, the GrIS and AIS each contribute about 60–70 cm 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 °C 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 °C (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 cm/year shortly before 2300 CE (Supplementary Fig. S7g). The Antarctic SL contribution for SSP2-4.5 fluctuates between 0.2 and 0.3 cm/year from 2200–2500 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 m by 2500 CE. In contrast, the aggressive greenhouse gas reduction scenario SSP1-1.9 with temperatures leveling off at less than 1.5 °C (Supplementary Fig. S7a, e) is sufficient to prevent substantial ice-loss in Antarctica (Supplementary Fig. S7h) over the next centuries.
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).


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).
In 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 mm 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.
Whereas 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 km in Antarctica and ~5.6°, 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 cm/year SLE over the next ~100 years (Fig. 4f–h), is a first order process that needs to be included in future SL assessments.
Methods
The 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.
LOVECLIM earth system model
The 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° × 5.6° 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° × 3° 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.
PSUIM ice-sheet/shelf model
The 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° latitude and 0.5° longitude is used in the Northern Hemisphere and a stereographic grid is adopted for Antarctica with a resolution of 20 km.
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 = 1.0, CREVLIQ = 100 m per (m/year)−2 and VCLIF = 3 km/year5. Here we use a value of OCFAC = 1.5, 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 1996–2016 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.
Climate-ice-sheet model coupling (LOVECLIP)
A 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 (“chunks”) [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.


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 = 1.0, CREVLIQ = 100 m per (m/year)−2 and VCLIF = 3 km/year5. Here we use a value of OCFAC = 1.5, 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 1996–2016 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.
Climate-ice-sheet model coupling (LOVECLIP)
A 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 (“chunks”) [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.
LOVECLIM’s 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.
Spin-up and initial conditions
The 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.
Statistics of forced and unforced ice-sheet mass balance
To compare whether the observed ice-sheet mass balance estimated from the Gravity Recovery and Climate Experiment (GRACE)33 for the period 2002–2020 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 −1.5 cm for GrIS and −4 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).
Scenario simulations
To 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 “likely range” 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).
To 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 = 0 m per (m/year)−2 and VCLIF = 0 km/year) with and without meltwater flux coupling (experiments SSP5-8.5_HFCMOFF and SSP5-8.5_MWHFCMOFF) (Supplementary Figs. S4, S5).
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.
Supplementary information
Figure S1: Coupling algorithm. This schematic shows how the LOVECLIP is coupled and exchanges variables and boundary conditions between LOVECLIM and PSUIM.
Figure 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.
Figure 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.


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.
Supplementary information
Figure S1: Coupling algorithm. This schematic shows how the LOVECLIP is coupled and exchanges variables and boundary conditions between LOVECLIM and PSUIM.
Figure 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.
Figure 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.
Figure S4: Global surface temperature and sea-level (SL) projections, and their tendencies. (a-d) annual anomalies (relative to the 1850–1900 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 °C/year. Different colors represent the SSP5-8.5 with historical (black line; period 1850– 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 2014–2150 CE. The sudden drops seen in (f and g) are due to the changes in parameters associated with hydrofracturing and ice-cliff failure.
Figure 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 1850–2150 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 2014–2150 CE.
Figure 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).
Figure S7: Long-term Global surface temperature and sea-level (SL) projections, and their tendencies. (a-d) annual anomalies (relative to the 1850–1900 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 °C/year. Different colors represent the historical (black line; period 1850–2014 CE), and SSP1-1.9 (blue line) and SSP2-4.5 (pink line) simulations during the period 2014–2500 CE.
Figure 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. ∆temperature 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.
Figure S9: Transection of Ross ice-shelf. The red line in this map indicates the location of Ross ice-shelf transection shown in figure 6.
Figure 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.
Figure 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.
Table 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.


Palmer et al. (2020)
Title:
Exploring the Drivers of Global and Local Sea-Level Change Over the 21st Century and Beyond
Key Points:
We 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
Analysis 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
The 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
Corresponding author:
Palmer
Citation:
Palmer, 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‐Level Change Over the 21st Century and Beyond. Earth’s Future, 8(9). doi:10.1029/2019ef001413
URL:
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2019EF001413
Abstract
We 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 ( > 50%) 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.
Introduction
The IPCC Special Report on Oceans and Cryosphere in a Changing Climate (SROCC) estimates that global-mean sea level (GMSL) increased by 0.16 ± 0.05 m over the period 1902–2015 (IPCC, 2019). Furthermore, GMSL rise is accelerating: The estimated rate for 2006–2015 (3.6 mm yr − 1) is about 2.5 times the rate for 1901–1990 (1.4 mm yr − 1) 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.
A 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).
The 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.
First, 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 “GRD” has been introduced by Gregory et al. (2019). Previously these effects have been referred to as the “sea-level equation” or “(gravitational) fingerprints,” for example.
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 “fingerprints” 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.
The 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—a 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.


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 “fingerprints” 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.
The 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—a 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.
Since the publication of AR5 several studies have highlighted the need for more comprehensive information on potential future sea-level change “tail risk” 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.
An 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 “H +  + ” 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).
The 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.
Data
Tide Gauge Data
The 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.
Figure 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.
Satellite Altimeter Data
The 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 1993–2015 and provides monthly mean values for GMSL and two-dimensional fields on a ¼ × ¼° 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.
CMIP5 Data
The 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.
The 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).
Our 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).


CMIP5 Data
The 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.
The 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).
Our 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).
At 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  +  zos) and global-mean thermosteric sea-level change (zostoga) across the CMIP5 ensemble at each tide gauge location.
The 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.
Figure 2: Projections of sterodynamic sea level change for the period 2081–2100 relative to the 1986–2005 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).
GRD Estimates
Changes 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’s 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.
The 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.
Figure 3: Estimates of the combined effect of mass changes on Earth’s 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.
The 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).


Figure 3: Estimates of the combined effect of mass changes on Earth’s 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.
The 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).
Computing the standard deviations across the three GRD estimates shows that differences are largest in the regions of ice/water mass loss (Figures 3d–3f, 3j, and 3k), corresponding to the negative value regions seen in the mean GRD patterns (Figures 3a–3c and 3g–3i). 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.
Glacial Isostatic Adjustment
Similar 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’s 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’s 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).
We 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 2004–2005. This final GIA estimate is identical to that used by Slangen et al. (2014). All three GIA data sets are provided on a 1  ×  1° latitude-longitude grid.
There 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).
Methods
Global-Mean Sea-Level Projections
The 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 “global thermal expansion” and is the only term that does not constitute a change in ocean mass following Gregory et al. (2019).
For 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).
Note 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.


Methods
Global-Mean Sea-Level Projections
The 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 “global thermal expansion” and is the only term that does not constitute a change in ocean mass following Gregory et al. (2019).
For 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).
Note 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.
While 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, “shelf models” with time delay). All percentiles are reproduced to within ±0.01 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).
We 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.
Table 1: The Methods Used for Each Component of Global-Mean Sea Level (GMSL) Change According to Time Horizon
Sea-level component     21st century method     Extended 2300 method
Global 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 × 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).
Antarctica: 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–S) T(t), where A is the time-mean snowfall accumulation during 1985–2005, P  = 5.1 ± 1.5% °C −1 is the rate of increase of snowfall with Antarctic warming, R  = 1.1 ± 0.2 is the ratio of Antarctic to global warming, and S is a number in the range 0.00–0.035 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).
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 λ. The parameters L and λ are scenario-dependent; for instance, RCP2.6 has L  =  56 mm and λ  =  0.92, RCP8.5 91 mm and 0.86. The 2100 rate is held constant between 2100 and 2300.
Greenland: 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 1.00–1.15 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  =  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.
Greenland: 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 0.020–0.085 m for RCP8.5 and 0.014–0.063 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.