Empirical projection of global sea level in 2050 driven by Antarctic and Greenland ice mass variations

Global mean sea level rise, driven by ice mass loss in Antarctic and Greenland Ice Sheets (AIS and GrIS), is a significant consequence of global warming. Although various ice sheet models have attempted to predict the ice mass balance and subsequent sea level changes, non-trivial disagreements between models exist. In this study, we employ an empirical approach to estimate the future (2050) ice mass changes for both ice sheets, assuming their historical patterns of ice dynamics would persist in the coming decades. To achieve this, we estimate decadal-scale ice discharge variations by subtracting the surface mass balance (SMB) from the observed ice mass changes and extrapolate linear trend and acceleration components of ice discharges up to 2050. We also consider future SMB data from Coupled Model Intercomparison Project phase 6 models to estimate net ice mass balance. Our estimates suggest that from 2021 to 2050, the global sea level rise due to AIS and GrIS ranges between 6–19 mm and 15–31 mm, respectively. Additionally, we investigate regional sea level variability resulting from geoid changes induced by ice mass changes in both regions, highlighting that heterogeneous sea level changes may cause more pronounced sea level rises in lower latitude regions, where major cities are located.


Introduction
Sea level rise is one of the most critical consequences of ongoing global warming.From 1993 to 2015, the global mean sea level (GMSL) increased at a rate of approximately 3.1 mm yr −1 , and has recently accelerated to about 3.5 mm yr −1 between 2005 and 2015 (Kim et al 2019).Long-term sea level change is mainly caused by sea water density change associated with ocean temperature and salinity changes, as well as water mass inflow from land to oceans (Llovel et al 2019).Water mass inflow, in particular, is a dominant contributor to GMSL rise (Chen et al 2017), accounting for about 67% of the GMSL rise during 2005-2015(Kim et al 2019)).The primary source of water mass inflow is ice mass loss from several regions, including Antarctic Ice Sheet (AIS), Greenland Ice Sheet (GrIS), mountain glaciers, and terrestrial water storage (Llovel et al 2019).Among these regions, AIS and GrIS are the main contributors to the sea level rise (Masson-Delmotte et al 2021).Therefore, it is essential to understand the future AIS and GrIS mass change to accurately project future sea level rise.
Despite efforts to estimate future changes in AIS and GrIS mass, there are significant discrepancies among results from numerical ice sheet models.For example, under the Representative Concentration Pathways (RCP) 8.5 scenario, predictions for GrIS contribution to GMSL rise range from 40 to 130 mm until 2100 (Goelzer et al 2020), and AIS predictions range from −76 to 300 mm (Seroussi et al 2020).These discrepancies appear to be associated with uncertainties in ice sheet models, which are mainly caused by differences in initial states, spatial resolutions, boundary conditions, parameterizations and climate forcings (Goelzer et al 2020, Seroussi et al 2020).
Instead of using numerical models, AIS and GrIS mass change can be projected empirically by assuming that previous trends would continue in the near future (e.g.Rignot et al 2011, Diener et al 2021).However, because the observed ice mass balance includes signals with various time scales, without correction of shorter-term (annual to decadal) variations, it is difficult to accurately recover long-term (multi-decadal or longer) components of the ice mass balance (Wouters et al 2019).Ice sheet mass balance is determined by surface mass balance (SMB) and ice discharge.SMB is an accumulation of precipitation minus meltwater runoff and sublimation (van Wessem et al 2014), while ice discharge is the flux of ice mass into oceans that is affected by many factors such as ocean circulation, basal melting, and grounding line migration (Mouginot et al 2019).Short-term fluctuations in AIS and GrIS mass balance (detrended mass balance) are typically explained by the seasonal and inter-annual variations in SMB (van den Broeke et al 2009, Shepherd et al 2020)).On the other hand, decadal and longer variability of ice mass balance is generally governed by ice discharge (Shepherd et al 2018, Kim et al 2020).Therefore, it is reasonable to project future ice discharge assuming that trends in present ice discharge would continue during the next several decades.
Recently, Ice Sheet Mass Balance Inter-Comparison Exercise 3 (IMBIE3) reported accurate monthly ice mass balance over both AIS and GrIS since 1992, by combining multiple remote sensing and numerical models (Otosaka et al 2023).In addition, the Regional Atmospheric Climate Model (RACMO) successfully depicts present-day SMB over both ice sheets (Noël et al 2018, van Wessem et al 2018).By subtracting SMB from IMBIE's ice mass balance estimates, the difference represents ice discharge.In this study, we estimate the linear trend and acceleration terms from the ice discharge time series and project future variations of ice discharge based on these terms.We consider future SMB from Coupled Model Intercomparison Project phase 6 (CMIP6) climate models and combine it with ice discharges to project future ice mass changes in both ice sheets.By summing up the mass changes in AIS and GrIS, we also calculate future sea level changes at both of global and regional scale, considering varying Earth's geopotential associated with ice mass redistribution.

AIS and GrIS mass estimates
We used ice mass balance data provided by the IMBIE3 project, which was established to reconcile ice mass balances obtained from satellite measurements for both AIS and GrIS.IMBIE3 provides monthly ice mass variations and associated uncertainties estimated from three different satellite techniques: altimetry, gravimetry, and the input-output method (Otosaka et al 2023).For AIS, we used data from January 1992 to December 2020, divided into three sub-basins based on their geographical locations: West Antarctica (WA), East Antarctica (EA), and the Antarctic Peninsula (AP).For GrIS, we used ice mass variations of the entire ice sheet for the same period.

SMB data
To separate the SMB contributions from the IMBIE3 ice mass changes, we incorporated monthly SMB data from RACMO, developed by Institute for Marine and Atmospheric research Utrecht.We used output from RACMO2.3p2, which offers improved realism in representing SMB variability compared to its predecessors (Noël et al 2015, 2019, van Wessem et al 2018).The time range of the data used in this study spanned from 1979 to 2020.The spatial resolutions of the data used in this study are 27 km (AIS) and 1 km (GrIS), respectively.The GrIS data was resampled at 10 km intervals to optimize the computational efficiency.SMB was spatially integrated over AIS (WA, EA and AP separately) and GrIS as in IMBIE3 estimates.The uncertainty of RACMO, when assessed by comparing it with in-situ measurement, is known to be 10% and 15% for the monthly SMB in AIS andGrIS, respectively (van Wessem et al 2018, Mankoff et al 2021).For example, the average yearly precipitation over the AIS was about 1980 Gton during the period from 1979 to 2020, resulting in an accuracy of about 198 Gton (0.6 mm in sea level equivalent (mmSLE)).

CMIP6 models
To project the future mass balance over AIS and GrIS, we used the latest SMB data from CMIP.CMIP was organized by the Working Group on Coupled Modeling (Eyring et al 2016), with the goal of developing and reviewing climate models.CMIP has now advanced to phase 6 (CMIP6).In addition to the RCPs in the CMIP5 project, new future pathways (Shared Socioeconomic Pathways (SSPs)) were developed by the CMIP6 project, taking into account human efforts in response to climate change.
We selected 23 CMIP6 models that offer historical simulations (1850-2014) and projections (2015) for the lowest (SSP126) and highest (SSP585) greenhouse gas emission scenarios.By incorporating these models, we aim to provide a range of plausible future projections for AIS and GrIS mass change under different emission scenarios.The list of those models is available in table S1.Each SMB model from CMIP is designed based on its unique representation of surface orography and spatial resolution.These discrepancies would be important causes of different SMB predictions among models.To reduce such potential effects, we downscaled SMB values from all models to the digital elevation model (DEM) in the RACMO model as suggested by Nowicki et al (2020) and further adjusted downscaled SMB values referenced to the RACMO DEM (text S1).
In addition to SMB dataset, we used surface temperature data from the same model to investigate the relationship between SMB and temperature trends over both ice sheets.

Ice mass balance
The mass change over the ice sheet (∆M (t)) is determined by time-integrated SMB and ice discharge: (1) SMB (t) and D (t) can be separated into long-term means during a reference period (SMB 0 and D 0 ) and anomalous components (δSMB (t) and δD (t)): By using equation (3), we can estimate the ice discharge variability (∆D) by subtracting ∆SMB from ∆M.The black and blue lines in figures 1(a) and (b) compare ∆M (from IMBIE3) and ∆SMB (from RACMO2.3p2)integrated over both ice sheets.As noted in previous studies (Seo et al 2015a, 2015b, Kim et al 2020) most of the inter-annual-to decadalvariability in ∆M over both ice sheets are explained by ∆SMB.However, some inter-annual ∆SMB variations are not apparent in ∆M because ∆M is an integrated amount of multiple geodetic datasets, including data that insensitively captures interannual SMB variability.This results in ∆D being negatively correlated with ∆SMB.Such relatively high frequency variations remained in ∆D would be a potential uncertainty source, which will be evaluated in detail later on this study.
Alternatively, observation of ∆D from satellite radar imagery (e.g.Rignot et al 2019) could be used for the future projection.However, it is well documented that ice mass change estimates from radar imagery show considerable discrepancy when compared to other methodologies (i.e.satellite gravimetry or altimetry), particularly over AIS (Shepherd et al 2018, Otosaka et al 2023), possibly due to unconstrained ice thickness at the grounding line (Morlighem et al 2020).Relying solely on ∆D from such singular method risks introducing bias into projections of future ice mass changes.Given this consideration, we opted to continue using ∆D as estimated by IMBIE ∆M and RACMO ∆SMB.
The trend and acceleration in ∆D have been mostly associated with increasing ocean temperature resulting from global climate warming, as reported in previous studies (Holland et al 2008, Joughin et al 2010, Fürst et al 2015, Selley et al 2021).Given that ∆D has shown a consistent increase over the past decades, as illustrated in figure 1, it is plausible to expect these long-term changes to persist for the next 30 years.Independent estimates from multiple satellite sensors also suggest that ∆D over both ice sheets has exhibited consistent changes dominated by linear and quadratic variabilities (Seo et al 2015a, 2015b, Rignot et al 2019, Kim et al 2020).Furthermore, future ice discharge projections for both ice sheets, as simulated by ice dynamics models, are largely characterized by these same linear and quadratic patterns (Garner et al 2021).These observation and model prediction consistently have suggested that the ongoing trend and acceleration can be used for future projections (Diener et al 2021).
The variability of ∆SMB, on the other hand, is known to be influenced by both human-induced and natural processes.The former resulting from the anthropogenic effect is associated with changes in precipitation and surface melting in response to increasing air temperature.Under the warming climate, increase in surface melting has caused SMB decrease over both ice sheets, particularly in the coastal regions of GrIS (Colosio et al 2021) and the AP (Abram et al 2013).However, compensation for the SMB reduction has occurred due to snowfall increase due to more water vapor in warmer atmosphere (Clausius-Clapeyron relation) (Mernild et al 2015, Medley andThomas 2019).The natural variations of SMB are associated with global climate oscillations.Previous studies have shown that the long-term precipitation in both ice sheets is partly modulated by periodic variabilities over the Pacific and Atlantic Oceans, such as El Nino-Southern Oscillation (Boening et al 2012, Kaitheri et al 2021, Zhang et al 2021) and/or Atlantic Multidecadal Oscillation (Auger et al 2017, Lewis et al 2017, 2019).Because those climate variabilities are unpredictable, it is not possible to assume the current trend and acceleration in ∆SMB variations would continue Table 1.Linear trends and accelerations estimated from ∆M and −∆D over AIS and GrIS.The 1σ uncertainties were also presented.

Region Variable
Linear trend (Gton yr −1 ) in the future.Therefore, simply extrapolating ∆M, including the contribution of ∆SMB, would lead to significant error resulting from uncertainties in natural variability.
Figure 1 shows the importance of ∆M separation into ∆SMB and −∆D for the future projections.For example, in GrIS, ∆M clearly shows apparent acceleration of ice mass loss in 2003.If such patterns continue, significant ice mass loss would be expected.However, the abrupt increase of ice mass loss was due to the similar increase of ∆SMB and thus after correction of SMB, −∆D shows rather steady variations.
We compared the linear trends and accelerations estimated from ∆M and −∆D over both ice sheets (table 1).A regression function f (t) = a 0 + a 1 t + 1 2 a 2 t 2 was used to estimate the long-term variations.For AIS, the linear trend and acceleration of −∆D were found to be 12%-26% smaller than those of ∆M.For GrIS, the differences are more pronounced, with −∆D showing about 34% smaller in linear trend and about 50% smaller acceleration than ∆M.
Uncertainties (1σ) in trends and accelerations were estimated for each component, considering three potential sources of error.First, the random error emerges from inaccuracies in ∆M and ∆SMB estimates.We generated ten thousand zero-mean Gaussian random realizations, corresponding to the error of each variable (sections 2.1.1 and 2.1.2),and linear trends and accelerations were estimated for each realization.The standard deviations of linear trends and accelerations from ten thousand realizations were treated as random errors.The second uncertainty source, regression error, stems from residuals in the regression fit.Uncorrected ∆SMB in ∆D would be the main source of this uncertainty as shown in figure 1.We followed the approach recommended by Williams et al (2014), taking into account the correlated nature of errors presented in the ice mass change time-series.We used the Hector software package (Bos et al 2013) for error estimation, selecting the general Gauss Markov model, consistent with findings from King and Watson (2022).Finally, the systematic error can be arisen from inaccuracies in SMB 0 , used for calculating ∆SMB in equation ( 2).We considered this error as the standard error of the mean (= σ √ n , where n = 30 represents the number of years, and σ is standard deviation) of the annual SMB errors.The annual SMB errors were obtained as 10% of the AIS annual SMB and 15% of the GrIS SMB, as described in section 2.1.2,for the 1979-2008 period.
We determined total errors (table 1) from the root-sum-squares of the three error sources, under the assumption that they are not correlated each other.It is worth noting that the confidence intervals for −∆D (= ∆M − ∆SMB) are larger than those for ∆M because −∆D includes errors from both ∆SMB and ∆M.The magnitudes of three relevant error sources are provided in tables S2 and S3.Notably, the systematic error stands out as the predominant uncertainty source, accounting for about 36.6 Gton yr −1 for AIS ∆SMB and about 28.4 Gton yr −1 for GrIS ∆SMB.

Future projection
We estimated the future ice mass change of AIS and GrIS using an empirical approach based on CMIP6 SMB models and the extrapolation of −∆D obtained from IMBIE3 ∆M minus RACMO ∆SMB.To do this, we first extrapolated the time series of −∆D up to 2050 over both ice sheets using two long-term components presented in table 1.We refer to −∆D proj for the projection of −∆D.We also estimated the uncertainty of −∆D proj by extrapolating the upper and lower bounds of confidence intervals shown in table 1, assuming that the errors during the observational period would be propagated in the same way in the future.For SMB projections (∆SMB proj ), we calculated the ensemble mean of the 23 CMIP6 SMB models for each scenario (2021-2050) and historical simulation .∆SMB proj was estimated from the difference between means of SMB projections and historical simulation.
Two primary error sources were considered for ∆SMB proj .The first was the variance attributable to inconsistencies across individual models.We quantified this as the standard error of the mean, σ √ n , in which n is the number of models and σ is standard deviation of the model's estimates.The second source of error was systematic in nature, introduced by the subtraction of the historical SMB mean in our projection calculation.We determined this error as the standard error of the mean across the 23 historical simulations.
The future ice mass changes were calculated by summing up −∆D proj and ∆SMB proj , with the uncertainties of the projections estimated by a root-sumsquare of −∆D proj and ∆SMB proj errors.

Ice sheet mass projections and global sea level changes
Our estimates of ice mass changes (∆M proj ) for AIS and GrIS are shown in green lines of figure 2. Using the SMB models based on the SSP126 scenario, we estimate that the ice mass of AIS (figure 2(a)) and GrIS (figure 2(b)) would be decreased by −4707 ± 2453 Gton (13.1 ± 6.8 mmSLE) and −8225 ± 2716 Gton (22.9 ± 7.6 mmSLE), respectively, from 2021 to 2050.Similar results are found when using the SMB models based on the SSP585 scenario, with estimated loss of −4653 ± 2455 Gton (12.9 ± 6.8 mmSLE) for AIS (figure 2(b)) and −8366 ± 2754 Gton (23.3 ± 7.7 mmSLE) for GrIS (figure 2(d)).The combined projections suggest a total ice loss of about −12 932 Gton (SSP126) and −13 019 Gton (SSP585) by 2050, corresponding to a GMSL rise of about 36 mm (21-51 mm, table 2).The projections from the trend and acceleration components of IMBIE ∆M (table 1) are also plotted as black lines in figure 2, and these show larger ice mass losses in both regions during 2021-2050.This highlights the importance of considering −∆D proj and ∆SMB proj separately for future ice mass projections.
The sixth assessment report (AR6) from the Intergovernmental Panel on Climate Change suggested comprehensive estimates of sea level rise from numerical model predictions of ice mass loss from both ice sheets (Garner et al 2021).The estimated contribution from the two ice sheets between 2020 and 2050 were about −5.8-71.7 cm (SSP126) or −6.6-82.5 cm (SSP585) to GMSL rise.In comparison, our results project a contribution of about 2.1-5.1 cm to GMSL rise for both emission scenarios during the same period.This places our projections at the lower bound of the AR6 predictions.
The contributions of −∆D proj and ∆SMB proj are also shown as red and blue lines in figure 2. For AIS, −∆D proj is the dominant factor in total ice mass loss in 2050.Specifically, ice mass loss in AIS associated with −∆D proj is estimated to be about −4834 Gton, similar to ∆M proj .∆SMB proj is predicted to slightly increase in both SSP126 (figure 2(a)) and SSP585 (figure 2(b)) scenarios.This increase, slightly more substantial under SSP585 (about +180 Gton, figure 2(b)) than SSP126 (about +127 Gton, figure 2(a)), is attributed to the larger snowfall than meltwater runoff and evaporation (figure S3) due to climate warming.Concurrently, the surface temperatures from the same CMIP6 models exhibit a rise rate over three times higher in SSP585 compared to SSP126 (figure S4).This discrepancy elucidates why ∆SMB proj under SSP585 is larger than under SSP126.
Ice discharge is also projected to play a significant role in the mass loss of GrIS in 2050 (figures 2(c) and (d)).The estimated decrease in −∆D proj for GrIS is about −8559 Gton, which is larger than that of AIS (−4834 Gton).Both scenarios exhibit a moderate increase in ∆SMB proj , similar to AIS (figures 2(c) and (d)).The increase in ∆SMB proj is explained by an increase in snowfall, surpassing surface melting (figure S3).

Regional sea level variability
It has been expected that sea level variations associated with AIS and GrIS ice mass loss were not uniform due to the self-attraction and loading (SAL) effect (Farrell and Clark 1976).Previous studies showed observational evidence of such regional sea level variations based on GRACE gravity data (Hsu and Velicogna 2017, Jeon et al 2021).Unique spatial pattern of regional sea level variations has been referred to sea level fingerprint (SLF).To understand future sea level, we estimated the SLF resulting from future AIS and GrIS ice mass loss estimated here.For AIS, we further estimated ice mass loss in three regions separately: West Antarctica (WA), East Antarctica (EA) and Antarctic Peninsula (AP) (figure S5).For GrIS, the projected ice mass was distributed uniformly across its entire basin.Consequently, it is important to note that the SLF for areas adjacent to GrIS, such  Using the estimated ice mass, we calculated initial estimates of SLF, according to Farrell and Clark (1976).Changes in ice sheet mass and resulting sea level variations also affect Earth's rotational axis orientation by altering in rotational inertia, which results in a shift in centrifugal force that redistributes the sea level.We account for this effect, known as the rotational feedback (Munk andMacDonald 1960, Adhikari et al 2019), in our final SLF estimation.The implementation of SLF from the projected ice mass changes is described in more detail in text S2 of the supporting information.
Figures 3(a) and (b) show SLFs resulting from the mass changes of AIS and GrIS, as estimated based on the SSP585 SMB scenario.Similar results are observed in estimates based on the SSP126 SMB scenario (figure S6).Although the ice mass change in both regions is expected to cause the global sea level rise (about 13 mm from AIS and 23 mm from GrIS) (section 3.1), regional sea level anomalies from both ice sheets are very different due to SAL effect.
The sea level anomalies resulting from the combined effect of ice mass loss in AIS and GrIS are shown in figure 3(c).While sea level drops are expected in the oceans near GrIS and WA, most of the low-and mid-latitude regions are expected to experience larger sea level rises than GMSL (shown in green lines).We selected five major cities (London, Singapore, Incheon, Sydney, and New York) located along coasts and estimated sea level rise projection (figure 3(d)).We also separated the sea level rise due to AIS and GrIS to understand the relative contribution of both ice sheets.Of the five cities, London and New York were estimated to experience lower sea level rises (about 17 mm and 29 mm, respectively) than GMSL.A higher contribution from GrIS than AIS is expected for most cities, except for London, which is adjacent to GrIS.Sea level rise in Sydney was estimated to about 35 mm similar to GMSL.In contrast, Singapore and Incheon, located far from the two ice sheets, are predicted to experience sea level rises greater than GMSL (about 39 mm and 40 mm, respectively), with higher contribution from GrIS than AIS.These results support previous studies indicating that equatorial Asian coastal cities are vulnerable to future sea level rise and potential flooding events

Summary and discussions
We used an empirical approach to project the ice mass loss of AIS and GrIS from 2021 to 2050, based on the assumption that the long-term variations of ice discharge over the past 30 years would continue in the next 30 years.However, the similar assumption was not applied for SMB variables, as their long-term variations are contaminated by natural, periodic variability.Instead, we relied on the ensemble mean of the CMIP6 model outputs for future SMB predictions.Our estimates suggest that both AIS and GrIS would experience a similar amount of ice mass loss, corresponding to a GMSL rise of 6-19 mm and 15-31 mm, respectively, by 2050, with most of the ice loss attributed to ice discharge.Taken together, the GMSL rise due to the mass loss from both ice sheet is 21-51 mm.This projection lies at the lower bound of predictions from AR6.The sea level rise due to the mass loss of the two ice sheets is expected to be particularly pronounced in lower latitude regions due to the SAL effect.
Our analysis employed the ensemble mean of all 23 CMIP6 models, assuming that averaging a larger number of models would provide a more robust future estimate.However, the SMB predictions for high-latitude regions, such as AIS and GrIS, often exhibit limitations in their accuracy.For example, SMB from CMIP does not account for the existence of bare ice over GrIS and frequently underestimates summer melt due to a lack of melt-albedo feedback (Holube et al 2022).The AIS's SMB projections also display pronounced model variability, largely due to differences in each model's climate sensitivity (Kittel et al 2021).Such limits have led to a rigorous effort to identify the most precise models (Roussel et al 2020).
Barthel et al (2020) established a protocol with the CMIP5 ensemble to identify standout models, some of which have been incorporated into the Ice Sheet Model Intercomparison Project phase 6 (Seroussi et al 2020).Following this methodology, we further selected six optimal models from the available 23 CMIP6 models for both AIS and GrIS.These selected models exhibited minimal deviations from the RACMO SMB outputs and ensured a wide projection range, aiming to deliver robust and diversified future projections for AIS and GrIS mass changes.The detailed methodologies for the optimal model selection are described in text S3.For GrIS, the projections using the six selected models were almost identical compared to those from 23 models, but with a roughly doubled uncertainty (figures S8(c) and (d)).For AIS, the six models projected a distinct increasing trend, which excessively compensate for the decrease in −∆D proj , leading to the estimation that there would be negligible ice mass loss from AIS in the future (figures S8(a) and (b)).The combined sea level rise projection ranges from 0.1 to 5.0 cm (table S4), which shows a D Lee et al difference from our main results, yet still falls within the future sea level rise projection range suggested by AR6.This demonstrates that our results highly depend on the choice of SMB model particularly for AIS, thus highlighting the importance of improving the performance of modeled SMB to refine the accuracy of projections.
Our empirical projection based on temporal extrapolation of ice discharge is independent of SSP scenario and does not account for the sensitivity of future climate changes to ice discharge.Implicitly, this approach presumes that the contribution of various positive and negative feedback mechanisms, which have caused imbalance in Antarctic and Greenland ice discharge over the past three decades, will persist at the same magnitude in the future.Moreover, by treating ice discharge as an independent of SMB, we risk overlooking the potential interplay between these factors (Winkelmann et al 2012), which could introduce an additional bias into our estimates.However, despite the potential for various mechanisms to either accelerate (Weertman 1974, DeConto and Pollard 2016, Schmidt et al 2023)  In such conditions, our results based on recent observations, although simple, may provide meaningful statistical insight for the near future.However, caution should be exercised when extrapolating our results to longer timescales due to the uncertain potential impacts of various mechanisms that could either suppress or enhance ice discharge acceleration.To advance our understanding of the AIS and GrIS response to ongoing climate change and to better guide mitigation efforts, future studies should address and integrate these complexities.

Figure 1 .
Figure 1.Ice mass balance over AIS (a) and GrIS (b).The black lines represent ∆M from IMBIE3, and blue lines are ∆SMB from RACMO2.3p2.The red lines show the difference between ∆M and ∆SMB, representing −∆D.The red dashed lines show quadratic polynomial fits.The uncertainties of ∆M are provided by IMBIE3 data center.The uncertainties of ∆SMB were estimated by root-sum-square of SMB error (section 2.1.2) as used in the previous study (Selley et al 2021).The uncertainties of −∆D were calculated as root-sum-square of ∆M and ∆SMB errors assuming that they are not correlated each other.Seasonal cycles are removed for all graphs.

Figure 2 .
Figure 2. Ice mass change projections for AIS (a)-(b) and GrIS (c)-(d) up to 2050.Red lines depict ice discharge projections, and blue lines represent SMB projections for SSP126 (a), (c) and SSP585 (b), (d) scenarios.Green lines are net mass change estimated by combining SMB and ice discharge projections.Black lines indicate temporal extrapolation of IMBIE3 ice mass estimates using their long-term components.

Figure 3 .
Figure 3. Sea level projection in 2050 resulting from mass loss from AIS (a) and GrIS (b) as calculated using the future projection based on SSP585 SMB scenario.(c) Combined effects of ice mass contributions from both ice sheets.Green lines indicate contour lines of global mean sea level change (GMSL).(d) The projected sea level changes in major cities (denoted by cyan stars in (a)-(c)) due to the mass loss from the two ice sheets, with GMSL included for comparison.
or decelerate (Gomez et al 2015, Yoon et al 2022) future ice discharge from ice sheets, the feedback mechanisms associated with these processes are likely to manifest over centuries rather than the immediate decades ahead.This is due to the delayed effect of transmission through oceanic and atmospheric circulation and the intrinsic response time of ice dynamics (Winkelmann et al 2012, Timmermann and Hellmer 2013, Naughten et al 2021).It has also been posited that a range of unidentified drivers, differing behavior of individual glaciers, and imprecise feedback mechanisms, along with boundary conditions, contribute to considerable uncertainties in future projections derived from ice dynamics models (Pattyn and Morlighem 2020), irrespective of the climate change scenario (Lowry et al 2021).
35 303-20 Morlighem M et al 2020 Deep glacial troughs and stablizing ridges unveiled beneath the margin of the Antarctic ice sheet Nat.Geosci.13 132-7 Mouginot J, Rignot E, Bjørk A A, van den Broeke M, Millan R, Morlighem M, Noël B, Scheuchl B and Wood M 2019 Forty-six years of Greenland ice sheet mass balance from 1972 to 2018 Proc.Natl Acad.Sci.116 9239 Munk W H and MacDonald G J F 1960 Continentality and the gravitational field of the Earth J. Geophys.Res.65 2169-72 Naughten K A, Rydt J D, Rosier S H, Jenkins A, Holland P R and Ridley J K 2021 Two-timescale response of a large Antarctic ice shelf to climate change Nat.Commun.12 1991 Noël B et al 2018 Modelling the climate and surface mass balance of polar ice sheets using RACMO2-part 1: Greenland (1958-2016) Cryosphere 12 811-31 Noël B, van de Berg W J, Lhermitte S and van den Broeke M R 2019 Rapid ablation zone expansion amplifies north Greenland mass loss Sci.Adv. 5 eaaw0123 Noël B, van de Berg W J, van Meijgaard E, Kuipers Munneke P, van de Wal R S W and van den Broeke M R 2015 Evaluation of the updated regional climate model RACMO2.3:summer snowfall impact on the Greenland ice sheet Cryosphere 9 1831-44 Nowicki S et al 2020 Experimental protocol for sea level projections from ISMIP6 stand-alone ice sheet models Cryosphere 14 2331-68 Otosaka I et al 2023 Mass balance of the Greenland and Antarctic ice sheets from 1992 to 2020 Earth Syst.Sci.Data 15 1597-616 Pattyn F and Morlighem M 2020 The uncertain future of the Antarctic ice sheet Science 367 1331-5 Perrette M, Landerer F, Riva R, Frieler K and Meinshausen M 2013 A scaling approach to project regional sea level rise and its uncertainties Earth Syst.Dyn. 4 11-29 Rignot E, Mouginot J, Scheuchl B, van den Broeke M, van Wessem M J and Morlighem M 2019 Four decades of Antarctic ice sheet mass balance from 1979-2017 Proc.Natl Acad.Sci.116 1095-103 Rignot E, Velicogna I, van den Broeke M R, Monaghan A and Lenaerts J 2011 Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise Geophys.Res.Lett.38 L05503 Roussel M-L, Lemonnier F, Genthon C and Krinner G 2020 Brief communication: evaluating Antarctic precipitation in ERA5 and CMIP6 against CloudSat observations Cryosphere 14 2715-27 Schmidt B E et al 2023 Heterogeneous melting near the Thwaites Glacier grounding line Nature 614 471-8 Selley H L et al 2021 Widespread increase in dynamic imbalance in the Getz region of Antarctica from 1994 to 2018 Nat.Commun.12 1133 Seo K-W, Waliser D E, Lee C-K, Tian B, Scambos T, Kim B M, van Angelen J H and van den Broeke M R 2015b Accelerated mass loss from Greenland ice sheet: links to atmospheric circulation in the North Atlantic Glob.Planet.Change 128 61-71 Seo K-W, Wilson C R, Scambos T, Kim B-M, Waliser D E, Tian B, Kim B-H and Eom J 2015a Surface mass balance

Table 2 .
Projections of global sea level rise until 2050.The 1σ uncertainties were also presented.
et al 2021 Greenland ice sheet mass balance from 1840 through next week Earth Syst.Sci.Data 13 5001-25 Masson-Delmotte V, Z. P, Pirani A, Connors S L, Péan C and Berger S 2021 IPCC, 2021: climate change 2021: the physical science basis Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge University Press) Medley B and Thomas E R 2019 Increased snowfall over the Antarctic ice sheet mitigated twentieth-century sea-level rise Nat.Clim.Change 9 34-39 Mernild S H, Hanna E, McConnell J R, Sigl M, Beckerman A P, Yde J C, Cappelen J, Malmros J K and Steffen K 2015 Greenland precipitation trends in a long-term instrumental climate context (1890-2012): evaluation of coastal and ice core records Int.J. Climatol.