20th‐Century Antarctic Sea Level Mitigation Driven by Uncertain East Antarctic Accumulation History

Increasing snow accumulation over the Antarctic Ice Sheet may mitigate future sea level rise. However, current estimates of mitigation potential are poorly constrained due to limited records of past variability. We present an annually resolved reconstruction of Antarctic snow accumulation from 1801 to 2000 CE, employing a paleoclimate data assimilation methodology to integrate ice core records with a multi‐model ensemble of climate simulations. Our reconstruction correlates well with instrumental reanalysis, and we find that Antarctic accumulation rates increased over the 20th‐century, resulting in a modest amount (∼1 mm) of sea level mitigation. Mitigation is primarily driven by an accelerating trend since around 1970. Our results contrast with previous mitigation estimates of ∼10–12 mm; this discrepancy is due to poorly constrained baseline estimates of 19th‐century accumulation in East Antarctica. Our reconstruction suggests that the uncertainty of future sea level mitigation from increasing Antarctic accumulation has been underestimated.


Introduction
Projections of future sea level contribution from the Antarctic Ice Sheet (AIS) are highly uncertain, with existing studies disagreeing on the sign of the contribution (Edwards et al., 2021;Payne et al., 2021;Seroussi et al., 2020;Siahaan et al., 2022).The Antarctic contribution to global mean sea level change is primarily driven by two competing processes: a positive contribution (raising sea level) from ocean-driven ice mass loss at the margins of the ice sheet and a negative contribution (lowering sea level) from increased snow accumulation at the surface.In response to warming temperatures over Antarctica, both ice-shelf basal melting (Golledge et al., 2019;Levermann et al., 2020) and snow accumulation (Frieler et al., 2015;Lenaerts et al., 2016) are projected to increase.However, studies of the Antarctic temperature-accumulation relationship have indicated a wide range in sensitivity (e.g., Fudge et al., 2016), and that general circulation models may be overestimating the increased snowfall due to warming (Nicola et al., 2023).
Since the late 20th-century, Antarctica has undergone both significant warming (Nicolas & Bromwich, 2014;Steig et al., 2009) and ice sheet mass loss (Rignot et al., 2019;Shepherd et al., 2018).However, 20th-century Antarctic accumulation trends, and their impact on global mean sea level, remain poorly understood.Satellite observations of ice sheet mass change span only recent decades (e.g., Pritchard et al., 2009;Smith et al., 2020); furthermore, instrumental reanalysis products are unreliable prior to the satellite era (Schneider & Fogt, 2018).Ice core records can be used to infer past accumulation, but are spatially restricted point measurements that must be extrapolated across Antarctica to gain insight relevant to global sea level change.Reconstructions that combine ice core data with dynamically consistent spatial interpolation are limited in number, and different methodologies yield conflicting results: either an insignificant 20th-century Antarctic accumulation trend (Frezzotti et al., 2013;Monaghan et al., 2006) or a significant accumulation increase contributing to sea level mitigation (Dalaiden et al., 2020;Medley & Thomas, 2019;Thomas et al., 2017;Wang & Xiao, 2023).
Paleoclimate data assimilation is a powerful framework for generating spatially complete climate reconstructions from geographically sparse proxy data sets.Combining both spatial information from climate models and temporal information from proxy records, this approach offers greater versatility than alternate statistical methods, improves compatibility with the physics of the climate system, and provides a robust framework for uncertainty quantification (Hakim et al., 2016;Klein et al., 2019).To our knowledge, only one study (Dalaiden et al., 2020) has employed a data assimilation methodology to reconstruct Antarctic accumulation; alternate studies have instead relied on extrapolation of spatial covariance structures within instrumental reanalyzes (Medley & Thomas, 2019;Monaghan et al., 2006;Wang & Xiao, 2023) or construction of regional ice core composites (Frezzotti et al., 2013;Thomas et al., 2017).
The Last Millennium Reanalysis, a well-established data assimilation framework with robust capabilities for reconstructing a wide range of climatic variables (Hakim et al., 2016;Tardif et al., 2019), has previously been adapted for polar reconstructions through incorporation of ice core records from Antarctica (O'Connor et al., 2021) and Greenland (Badgeley et al., 2020).Here, we incorporate a set of 120 ice core accumulation and water isotope records from Antarctica.We reconstruct spatially complete and annually resolved accumulation variability over the AIS from 1801 to 2000 CE, and the equivalent contribution to global mean sea level.

Methods
We use offline paleoclimate data assimilation to produce our accumulation reconstructions.Specifically, we apply the ensemble Kalman filter methodology employed by the Last Millennium Reanalysis framework (Hakim et al., 2016;Tardif et al., 2019; more details in Text S4 of Supporting Information S1).Spatial completeness in the final reconstructions is provided by the climate model "prior" ensemble; priors consist of base model states drawn from historical climate simulations, which supply a geographic covariance structure.We construct a multi-model ensemble ("MME") prior, which amalgamates randomly drawn samples from nine separate CMIP5 Last Millennium (850-1850 CE) climate model simulations (Taylor et al., 2012).We run additional reconstructions with the nine individual Last Millennium simulations; we also test one "postindustrial" (1850-2005 CE) prior (Table S1 in Supporting Information S1; more details in Text S2 of Supporting Information S1).
To convert the "prior" base climate state into the "posterior" final state estimate, we use an ensemble Kalman filter to assimilate novel information from proxy records.In total, we incorporate 120 ice core records (Figures S1 and S2 in Supporting Information S1, more details in Text S1 of Supporting Information S1), including 62 water isotope records (Stenni et al., 2017) and 58 accumulation records (Thomas et al., 2017).A forward model maps the prior state estimate to proxy space, relying on linear regression to the GISS Surface Temperature Analysis (Hansen et al., 2010; more details in Text S3 of Supporting Information S1); to qualify our results, we note that this approach is sensitive to both the observed and modeled temperature-accumulation relationship.Finally, we produce the posterior state estimate: A 250-member ensemble of annually resolved gridded accumulation anomalies from 1801 to 2000.As accumulation in Antarctica is dominated by precipitation (Dalaiden et al., 2021), we assume the two to be equivalent.The anomaly reference period used is the 1951-1980 mean.
To determine sector-wide accumulation trends, we spatially integrate gridded accumulation over the Antarctic drainage basins defined by Zwally et al. (2012), excluding ice shelves.We convert reconstructed accumulation into the equivalent contribution to global mean sea level by following Medley and Thomas (2019) in integrating the annual accumulation time series relative to the 19th-century mean (more details in Text S5 of Supporting Information S1).

Skill Validation
We analyze the spatial skill of accumulation reconstructions through comparison with ERA5 instrumental reanalysis between 1981 and 2000 CE.In general, highest skill is found around the West Antarctic Ice Sheet (WAIS), Antarctic Peninsula (AP), and Wilkes Land; the lowest skill is found around Dronning Maud Land (DML) and the interior East Antarctic Plateau.The MME demonstrates the highest skill of the tested priors, with the greatest improvements occurring in the low-skill, low accumulation regions of the East Antarctic Plateau (Figures S3 and S4 in Supporting Information S1; Table S1 in Supporting Information S1).This is consistent with a previous finding that multi-model ensembles improve climate reconstruction skill for regions with high uncertainty that are far from proxy sites (Parsons et al., 2021).We present the MME reconstruction from now onwards.
The MME displays high skill (p < 0.05; CE > 0) over most of West Antarctica (Figure 1); a spatially weighted average for WAIS gives r = 0.67 and CE = 0.33.Skill in East Antarctica is more variable, with much of the East Antarctic Plateau and DML exhibiting a lack of skill (p > 0.05; CE < 0; Figure 1).Nevertheless, spatially averaged metrics for the East Antarctic Ice Sheet (EAIS) show reasonable skill, with a positive CE (0.17) and a near-significant correlation (r = 0.43; p = 0.06).A previous evaluation of precipitation reconstruction potential found skill to be broadly correlated with high accumulation rates (an indicator of higher-quality proxy records) and geographic proximity to proxy sites (Steiger et al., 2017).This relationship holds in our reconstruction; higher skill in WAIS likely reflects denser proxy coverage and higher accumulation rates.

Reconstructed Accumulation Trends
During the 19th-century, we find no significant trend across any Antarctic sector.However, we find a clear positive trend in Antarctic snow accumulation over the 20th-century.AIS-wide accumulation increased by 0.4 ± 0.1 Gt yr 2 from 1901 to 2000, accelerating to 1.1 ± 0.6 Gt yr 2 after 1957 (Figure 2a).This trend was principally driven by a late-century acceleration (Figure 2g) in AP and WAIS (Figures 2b and 2d).We find a positive trend in eastern WAIS that dominates a slight negative trend in western WAIS (Figure 2g); this "see-saw" pattern, characteristic of the Amundsen Sea Low, is also found in the reconstructions of MT19, Dalaiden et al. (2020;"D20"), and Wang and Xiao (2023;"WX23").
We find no significant trend in EAIS across any evaluated time period (Figure 2c), although we do find a localized late-century negative trend in coastal DML (Figure 2g).The lack of significant trends in EAIS stands in contrast to  the estimates from MT19, D20, and WX23, all of whom find a statistically significant increase in EAIS accumulation from 1801 to 2000 (Table S3 in Supporting Information S1).

Sea Level Mitigation
We find that 20th-century AIS sea level mitigation due to snow accumulation (Figure 3a) was insignificant (1.2 ± 3.5 mm), and that WAIS (1.7 ± 1.0 mm) was the only Antarctic sector to definitively mitigate sea level rise (Table 1).We find no significant mitigation from EAIS ( 0.3 ± 1.9 mm) or AP ( 0.2 ± 0.5 mm).Examination of a more restricted interval  reveals a significant trend.In our reconstruction, AIS mitigated sea level rise from 1970 to 2000 (0.7 ± 0.3 mm dec 1 , with a total mitigation of 2.2 ± 0.8 mm), comparably driven by both WAIS (0.3 ± 0.1 mm dec 1 ) and EAIS (0.3 ± 0.1 mm dec 1 ); this is a shift from the 1901-1970 period, where we find no significant AIS mitigation trend (Table 1).
Our estimate of 20th-century AIS sea level mitigation is an order of magnitude lower than the values found by MT19 (∼10 mm) and WX23 (∼12 mm), with no overlap between our confidence intervals (Figure 3b).Despite this, we find strong agreement with their estimates of sea level mitigation from WAIS (∼2-3 mm) and AP (∼0 mm).Thus, the discrepancy comes from EAIS.Both MT19 and WX23 find EAIS to have dominated (∼8 mm) the overall AIS mitigation contribution, while we find the contribution of EAIS to be insignificant (Figure 3b).This discrepancy stems from different estimates of the 19th-century baseline used to calculate 20thcentury mitigation, which we discuss in the following section.

Source of Disagreement With Previous Mitigation Estimates
To our knowledge, only two previous Antarctic accumulation reconstructions (MT19 and WX23) have quantified the equivalent impact on sea level rise; both of these studies utilize similar methodologies, following Monaghan et al. (2006).Our estimate of 20th-century sea level mitigation (∼1 mm) is substantially smaller than that of MT19 (∼10 mm) and WX23 (∼12 mm).Nevertheless, we agree with both reconstructions on numerous points: (a) a significant 1901-2000 AIS accumulation increase (∼0.4-0.6 Gt yr 2 ); (b) similar 20th-century spatial trends, including a positive trend in AP and eastern WAIS, and a negative trend in western WAIS (Figures 2e-2g); and (c) similar 1901-2000 sea level mitigation from WAIS (∼2-3 mm) and AP (∼0 mm).Thus, the large discrepancy in 20th-century sea level mitigation comes from EAIS.
All three reconstructions find an insignificant 1901-2000 EAIS accumulation trend (∼0.0-0.1 Gt yr 2 ), despite the disagreement over 20th-century EAIS sea level mitigation.The discrepancy between our reconstruction and those of MT19 and WX23 is instead due to different 19th-century baseline values used to calculate 20th-century mitigation.All three studies obtain a baseline value by taking the 19th-century mean of their own accumulation reconstruction; sea level mitigation is calculated by integrating the 20th-century accumulation time series relative to this value.While we find no significant EAIS accumulation trend from 1801 to 1900, both MT19 and WX23 find a significant accumulation increase during this period.Relative to the 20th-century time series, our 19thcentury baseline is higher.If we decrease our baseline value to match that of MT19 (by 29 Gt yr 1 ), we obtain 20th-century mitigation values (AIS: 9.2 ± 3.5 mm; EAIS: 7.7 ± 1.9 mm) that agree closely with MT19 and WX23.Thus, the observed disagreement is dominated by uncertainty in 19th-century EAIS accumulation.
Both MT19 and WX23 use the kriging-like interpolation method of Monaghan et al. (2006) to generate spatially complete estimates of past accumulation trend.Agreement between the two reconstructions is therefore unsurprising.Their disagreement with our reconstruction over the 19th-century EAIS trend is due to methodological differences, as we all use a similar proxy network.Where proxy records for a given spatial region have high variance and disagree with one another, as is the case across EAIS (Thomas et al., 2017), our reconstruction will default to no trend.By contrast, the method of MT19 and WX23 relies on extrapolation of satellite-era  covariance between proxy records and climate indices, assuming that observed relationships during a period of increasing Antarctic accumulation are constant.
Our data assimilation-based reconstruction contributes methodological diversity to the limited set of 20th-century Antarctic sea level mitigation estimates.Both our and previous approaches demonstrate skill in WAIS, where a high-quality, spatially well-distributed proxy network is available; neither method demonstrates significant skill in EAIS.Thus, the disagreement in 19th-century AIS accumulation is due to uncertainties in the EAIS proxy record, which is highly variable, geographically sparse, and agrees poorly with external climate estimates (Thomas et al., 2017).The lack of overlapping EAIS uncertainties between our reconstruction and MT19 suggests that both approaches underestimate the true uncertainty of accumulation histories in data-sparse regions.This lack of skill in EAIS precludes a confident estimate of total 20th-century sea level mitigation from AIS.

Late 20th-Century Mitigation and Comparison With Dynamic Ice Loss
We find significant AIS-wide sea level mitigation from 1970 onwards (Table 1).The decadal trend in sea level mitigation shows a consistent increase after 1960, ultimately becoming positive (95% confidence) from 1970 onwards.This late 20th-century trend reflects a significant mitigation of sea level rise, distinct from the previous 160 years of the reconstruction.While MT19 find AIS to mitigate sea level rise throughout the 20th-century, they note a doubling of the mitigation rate after 1979.Indeed, the accelerating overall AIS accumulation trend (Figure 2a) suggests that the AIS continued to mitigate sea level rise into the 21st-century; this is supported by instrumental reanalyzes, including ERA5 and MERRA-2 (Gelaro et al., 2017), which show a positive Antarctic precipitation trend from the late 20th-century into the present.Increasing snow accumulation over WAIS since the late 20th-century has been attributed to anthropogenic causes (Dalaiden et al., 2022), and increased snow accumulation on the AIS will likely continue to mitigate sea level rise into the future (e.g., Lenaerts et al., 2016).
We note strong spatial similarities between our 1957-2000 reconstruction (Figure 2g) and the 1957-2000 reconstruction of MT19, where the Southern Annular Mode (SAM)-congruent P -E trend is the dominant principal component (see Figure 1d of Medley and Thomas ( 2019)); these include a "see-saw" pattern over WAIS, a

Geophysical Research Letters
10.1029/2023GL106991 positive trend over AP, and a negative trend over coastal DML.Medley and Thomas (2019) determine that spatial accumulation variability is dominated by dynamic change, in the form of an anthropogenically forced (Arblaster & Meehl, 2006;Fogt & Marshall, 2020) positive trend in the SAM.Our results are consistent with this finding.Furthermore, existing SAM reconstructions (King et al., 2023;O'Connor et al., 2021) have found the modern anthropogenically driven trend to begin in the mid-to-late 20th-century, occurring near-contemporaneously with the positive accumulation trend in our reconstruction.
While AIS accumulation mitigated sea level rise during the late 20th-century, this assessment does not account for contemporaneous mass loss.We find that increasing accumulation mitigated 59% of the sea level rise caused by dynamic ice loss from 1979 to 1999 (Rignot et al., 2019).From 1979 to 1989, we find cumulative mass gain of 36 ± 9 Gt yr 1 ; for the same period, Rignot et al. (2019) find mass loss of 52 ± 7 Gt yr 1 .Likewise, from 1989 to 1999, we find mass gain to increase by 41 ± 9 Gt yr 1 , while Rignot et al. (2019) find mass loss to increase by 79 ± 11 Gt yr 1 .The regions with the greatest increases in accumulation, such as AP and Amundsen Sea Coast, were those that saw the greatest increases in dynamic ice loss (Gardner et al., 2018).While increased accumulation directly mitigates sea level rise through ice sheet mass gain, it can also indirectly raise sea level by enhancing ice dynamic flux (Frieler et al., 2015), although modern dynamic ice loss appears driven by oceanic forcing of outlet glaciers (Smith et al., 2020).While Antarctic accumulation had a mitigating effect on the contribution to sea level rise, it likely did not keep pace with contemporaneous late 20th-century mass loss.

Outlook
Numerous limitations in the proxy record impede our understanding of past EAIS accumulation.Spatial and temporal proxy coverage is sparse: the majority of records are located in a limited area around central DML (Figure S1 in Supporting Information S1), and many records do not span the full reconstruction period (Figure S2 in Supporting Information S1).Furthermore, low accumulation rates across much of EAIS preclude accurate identification of annual layers, leading to lower-quality records.Thomas et al. (2017) conclude that existing records from the East Antarctic Plateau may not be representative of true regional trends, as the regional ice core composite shows poor agreement with modeled SMB from RACMO2 (van Wessem et al., 2018).
EAIS is the dominant contributor to Antarctic accumulation, accounting for approximately 70% of net annual accumulation over AIS (Mottram et al., 2021).Thus, uncertainty in EAIS accumulation has significant implications for future sea level change.Antarctic sea level projections for the 21st-century consistently show a regional disparity, with WAIS losing mass and EAIS gaining mass; EAIS is thus predicted to be a principal mitigator of future sea level rise (Payne et al., 2021;Seroussi et al., 2020;Siahaan et al., 2022).However, observational estimates of Antarctic mass change have indicated substantial uncertainty around the EAIS contribution, in part due to short and varying observational timescales.Shepherd et al. (2018) find an insignificant EAIS mass gain trend of 5 ± 46 Gt yr 1 from 1992 to 2017; alternate studies have found EAIS to be either gaining (Smith et al., 2020;Zwally et al., 2015) or losing (Rignot et al., 2019) mass.
The large disagreement between our EAIS reconstruction and those of MT19 and WX23, all of which use similar input data and dynamically consistent spatial interpolation methods, highlights the need for better constraints on EAIS accumulation history and climate sensitivity, as well as improvements in methodology.To gain a better understanding of temporal trends in EAIS accumulation, greater spatial diversity of EAIS ice core sites is necessary.In particular, we note the high uncertainty in our reconstruction around Wilkes Land (Figure S5 in Supporting Information S1), likely due to a dearth of existing ice cores (Figure S1 in Supporting Information S1).
An investigation of optimal EAIS drilling sites (Vance et al., 2016) identified specific locations where highresolution records, geographically complementary to existing sites, can likely be obtained.As ice core records yield information for a large geographic area, higher accumulation coastal cores can provide insight into the low accumulation-rate interior.To address the 19th-century baseline issue, high-frequency ice penetrating radar, which images the upper ∼100 m, can be used to infer multi-decadal accumulation rates (e.g., Le Meur et al., 2018), with greatly improved spatial coverage compared to ice cores.Extending ice cores to the present would allow analysis that is contemporaneous with satellite observations of Antarctic mass change (e.g., Shepherd et al., 2018;Smith et al., 2020).Higher quality temperature and accumulation histories, and a data assimilation approach that does not rely on the temperature-accumulation relationship, are also necessary to assess the sensitivity of accumulation to temperature change (e.g., Nicola et al., 2023).Direct assimilation of accumulation records (e.g., Dalaiden et al., 2021) has the advantage of being independent of biases in temperature-accumulation sensitivity but also has a variety of challenges that lead to lower skill, particularly in East Antarctica (Text S5 in Supporting Information S1; Table S2 in Supporting Information S1).Understanding the relative strengths of reconstructions using both the temperature-accumulation relationship and direct assimilation will be an important extension of our current work.While internally consistent estimation of the error covariance matrix is a notable challenge, it can be estimated by quantifying the spatial representativeness of ice core accumulation records and would open up significant opportunities to examine the temperature-accumulation relationship over time (e.g., Badgeley et al., 2020).Moreover, additional records will help constrain the sensitivity of Antarctic accumulation to future warming and the amount of sea level mitigation.

Conclusion
We employ a paleoclimate data assimilation methodology to integrate ice core records with climate model simulations, thereby producing an annually resolved reconstruction of Antarctic snow accumulation from 1801 to 2000 CE.We demonstrate good reconstruction skill in WAIS and AP where a high-quality array of ice core records exists; in EAIS, the reconstruction skill is not significant, likely due to the sparsity of high-quality ice core records.We find that Antarctic accumulation rates increased in the 20th-century, primarily driven by a latecentury acceleration in West Antarctica.We find modest sea level mitigation of ∼1 mm in the 20th-century, which contrasts with the much larger estimates of ∼10-12 mm found by Medley and Thomas (2019) and Wang and Xiao (2023).As all three studies agree on mitigation from WAIS and AP, the discrepancy is dominated by different estimates of mean 19th-century accumulation in EAIS.Our results suggest that uncertainty in 20thcentury Antarctic sea level mitigation is substantial, indicating the need for better constraints on East Antarctic accumulation history and climate sensitivity.Additional ice cores, selected for high accumulation rates to preserve robust annual variation and with a targeted spatial distribution, would allow for more confident reconstruction and would place firmer constraints on future changes in sea level.

Figure 1 .
Figure 1.(a) Correlation and (b) coefficient of efficiency between the multi-model ensemble accumulation reconstruction and ERA5 annual precipitation output for the period 1981-2000 CE.Correlation values with p < 0.05 are designated with stippling; positive CE values indicate reconstruction skillfulness.

Figure 2 .
Figure 2. (a-d) Temporal and (e-g) spatial trends in Antarctic accumulation, over the 19th and 20th centuries.Annually resolved accumulation anomalies in (a-d) are shown relative to the 19th-century mean, and represent a spatial integration over the given Antarctic sector.Trendline uncertainties and shaded bounds designate the 95% confidence interval (±2σ).

Figure 3 .
Figure 3. (a) Temporally cumulative sea level mitigation from each Antarctic sector for the period 1901-2000, with the regional 19th-century mean used as the baseline value.Shaded bounds represent the 95% confidence interval for Antarctic Ice Sheet mitigation, accounting for both uncertainty in the 1901-2000 mitigation distribution (±2σ) and the standard error (±2σ M ) of the 19th-century mean.(b) Total 20th-century sea level mitigation for each Antarctic sector, with uncertainties shown; our estimates multi-model ensemble are compared to those from Medley and Thomas (2019; "MT19").

Table 1
Cumulative Estimates and Trends in 20th-Century Sea Level Mitigation for Each Antarctic Sector, With Uncertainties Representing the 95% Confidence Interval Note.Significant values and trends are bolded.