Calibration of basal melt on past ice discharge lowers projections of Antarctica’s sea level contribution

Antarctic mass loss is the largest contributor to uncertainties in sea level projections on centennial timescales. In this study the contribution of Antarctica’s ice discharge to future sea level changes is computed with ocean thermal forcing from 14 earth system models and linear response functions from 16 ice sheet models for three greenhouse gas emission scenarios. Different than in previous studies, basal melt was calibrated on observed Antarctic ice discharge rather than on basal melt itself with an iterative approach. For each model combination, a linear and quadratic melt dependency were calibrated both 5 regionally (in five Antarctic sectors) and at the continental scale. Projections using all model combinations show that the variation in basal melt computation methods affect the projected sea level more than the scenario variations (SSP1-2.6 to SSP5-8.5). After calibration, a high number of model pairs still underestimated ice discharge in hindcasts over 1979-2017. Therefore top 10% best-performing model combinations were selected for each method. A comparison between these model selections shows that the quadratic melt parameterisation with Antarctic-wide calibration performs best in reproducing past ice 10 discharge. We conclude that calibration of basal melt on past ice discharge combined with model selection makes projections of Antarctic ice discharge (more) consistent with observations over the past four decades. Moreover, calibration of basal melt on past ice discharge results in lower basal melt sensitivities and thus lower projections of Antarctica’s sea level contribution than estimates of previous multi-model studies.


Ocean forcing
The ocean forcing consists of annual mean simulated subsurface ocean temperatures by CMIP6 ESMs. The ocean temperatures are taken from the historical experiment  and the Shared Socioeconomic Pathways (SSP) SSP1-2.6, SSP2-4.5 and SSP5-8.5 (2015SSP5-8.5 ( -2100. Only models that have data available at the Earth System Grid Federation (ESGF) data server for the 95 historical experiment and all three SSP scenarios (at the time of study) are considered. In addition, models should provide data for the full period (1850-2100) without any data gaps since the computation of the delayed ice sheet response requires a continuous time series. Table 1 summarises which models have been taken into account. Table 1. CMIP6 models that have been evaluated. For each region the subsurface ocean temperature bias (in K) compared to the GREP reanalysis is indicated over the period 1993-2018, including years 2015-2018 for the SSP2-4.5 scenario. The 'drift correction' column indicates whether the piControl experiment was used for model drift correction or the historical experiment.    SSP2-4.5 (2015SSP2-4.5 ( -2018 for this visualisation. Note that the tick distances of the vertical axis are the same for all regions, but the ranges are different.

Basal melt parameterisation
Warming of ocean water above the freezing point temperature in ice shelf cavities induces basal melt of the corresponding ice shelves. CMIP6 models, however, typically do not represent ice shelf cavities and the related thermal and dynamical properties.
Coastal ocean temperatures should therefore be translated into these cavities. This can be done by using a parameterisation that relates the far-field (coastal) ocean temperature to basal melt. Most of the simple basal melt parameterisations assume a relation 125 with thermal forcing. Our method employs a linear and quadratic melt relation with thermal forcing (Table 3). The quadratic relation was suggested to outperform a linear relation (Favier et al., 2019), but we will apply both so that we can compare our results with the linear relation used in Levermann et al. (2020). The linear relation is defined as: It assumes a constant heat exchange, independent on the local stratification and circulation. The quadratic relation is defined 130 as: where m is the basal melt and γ is the calibration parameter. The quadratic relation assumes that the heat exchange scales with the buoyancy-driven cavity circulation and that this scales linearly with the large-scale temperature gradient. The values of the physical constants ρ sw , c po , ρ i and L i are given in Table 4. The freezing-melting point temperature T f underneath ice shelves 135 Table 3. Abbreviations for basal melt parameterisation and calibration methods. Two different basal melt parameterisation methods were employed: linear and quadratic. Each parameterisation has been calibrated Antarctic wide and regionally. Unbounded means that γ has zero as lower limit and no upper limit for at least 95% of the ESM-RF combinations. Bounded means that the Levermann et al. (2020)  is computed from the ocean salinity S o and the depth of the ice shelf base z b : See Table 4 for the values of the physical constants. Favier et al. take T o and T f either as local or nonlocal values, where nonlocal is the product of local and nonlocal (averaged over the entire ice draft of a given sector) thermal forcing. In the current study, a purely nonlocal forcing is applied, similar to DeConto and Pollard (2016) and Levermann et al. (2020). The values of 140 T o are computed as averages over the five (far-field) oceanic sectors, around the depth of the ice shelf base (see Table 2). Since most CMIP6 models do not resolve cavities, the far-field ocean temperature is taken. The underlying assumption is that the ocean temperature remains constant while it is advected into the cavity. Also note that the ocean sectors are somewhat wider than the continental shelf, consistent with Levermann et al. (2020). The advantage of a wider region is that it allows for more assimilated observations in the reanalysis product that is used for the bias adjustment of ocean temperature (the continental 145 shelf region is only sparsely sampled). Furthermore, the resolution of most CMIP6 models is not high enough to resolve the ocean circulation on the continental shelf, including the Antarctic Slope Current (Thompson et al., 2018). The computation of T f is based on a constant salinity value for each oceanic sector, which is computed from the far-field salinity climatology of the reanalysis data. The resulting values of T f are approximately -1.6 • C in each sector.
Note that the melt is positive if the ocean temperature exceeds the freezing-melting point temperature and negative (i.e. water 150 is refreezing) otherwise. The change in basal melt anomaly is defined as the difference in basal melt between time t and the baseline time period, 1850-1930. This period was chosen since it is long enough to reduce the impact of natural variability on the baseline but short enough so that it doesn't include the trends due to anthropogenic forcing.
Basal melt anomalies in linear parameterisations do not depend on the mean temperature, only on the anomaly. In contrast, basal melt computed from the quadratic parameterisation depend on the mean temperature as well. As a consequence, biases 155 in ocean temperature will influence the estimated magnitude of basal melt changes. Ocean temperatures were therefore bias- It should be noted that γ has a different order of magnitude in the linear and quadratic parameterisation and is not directly comparable.

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Linear response functions (RFs) from LARMIP-2 will be used to compute the cumulative sea level contribution ∆S (in meters) due to a change in basal melt for each of the five sectors: LARMIP-2 provides RFs of 16 ice sheet models. Combined with the 14 ESMs (Table 1) The linear basal melt parameterisation has been calibrated in two ways: with bounded and unbounded γ values (Table 3).  The calibration is applied regionally and Antarctic-wide (Table 3). For each ESM-RF pair, the γ parameter with the best 180 fit (lowest RMSE) is selected for each of the five sectors in an iterative approach (Fig. 1). For the regional calibration the summed Antarctic response is the sum of the regionally calibrated contributions with five basin-specific γ values. In addition, the calibration is performed with the same γ value in each region, resulting in Antarctic-wide calibrated γ values.

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Basal melt is computed from subsurface ocean temperature time series (Fig. 1). The temperature time series are shown in For the quadratic parameterisation, a similar comparison was made with the γ values applied in ISMIP6 . Also for the quadratic paramerisation, our median Antarctic-wide calibrated γ (calibrated on four decades of observed ice discharge) sits at the lower end of the γ range of the Antarctic mean calibration (blue shading in Fig To summarise, a comparison of the γ values in our study and γ equivalents in LARMIP-2 (Levermann et al., 2020) and ISMIP6  suggests that calibration on past ice discharge rather than on basal melt observations results in relatively low γ values for the Antarctic-wide calibration. The Amundsen and Peninsula sector are more consistent with the high end of the γ ranges applied in LARMIP-2 and the Antarctic mean calibration of ISMIP6, while the other sectors (EAIS, 220 Ross, Amundsen) are more consistent with the lower end of those γ ranges.

Hindcasts of Antarctic sea level contribution
Hindcasts of the Antarctic dynamic contribution to sea level rise are made to assess how well Rignot ice discharge could be reproduced after calibration over the period 1979-2017. The total Antarctic sea level response is based on the summed contribution over the five sectors using the six calibrated basal melt computation methods (Table 3). and Pine Island Glacier (PIGL) calibration, respectively. For PIGL the 95% bound is 4.71 × 10 5 , which is outside the scale of the vertical axis. Figure 6 shows the hindcasts of all combinations of CMIP6 models and LARMIP-2 linear response functions using the calibrated γ values (Fig. 5). Each panel represents a basal melt computation method, as specified on top (Table 3). First, we evaluate the magnitude of the modelled sea level contributions. Most ESM-RF pairs are not able to capture the magnitude of the summed Antarctic sea level contribution. For each method, the sea level contribution is underestimated by the median response. This underestimation can be largely attributed to the high number of γ values that were set to zero in the calibration The median values of the bounded hindcasts (right panels) are closer to observations. This is because the calibrated γ value is greater than zero for each ESM-RF pair. Counter-intuitively at first notice, the linear bounded hindcasts (right panels) have a higher intermodel spread than the unbounded hindcasts. The bounded γ values, however, provide less freedom to restrict 235 the historical response of individual ESM-RF pairs to observations, explaining the higher intermodel spread in the sea level contribution. Hindcasts of regional sea level contributions are further discussed in Appendix A.

Selection of ESM-RF pairs
From the previous analyses we can conclude that for all basal melt computation methods most ESM-RF pairs are not able to capture the magnitude of the observed Antarctic sea level response to a reasonable extent. This makes them less trust-240 worthy for future projections of the sea level response. Therefore, the calibration on ice discharge is combined with a model selection step in which ESM-RF pairs are selected that capture the summed Antarctic response. ESM-RF pairs are ranked based on their ability to simulate the magnitude of the observed Antarctic ice discharge over the 1979-2017 period. To compare the performance between the different methods, for each method the top 10% best-ranking ESM-RF pairs are selected. By taking the top 10%, the same number of pairs (22) is selected for each method. The best models are defined as the ESM-245 RF combinations with the lowest RMSE compared to observed ice discharge over the full period. Figure Table A1. The LBR method has the highest mean RMSE due to the wide spread between individual model 250 combinations as explained in Sect. 3.2.
Although the model selection reproduces the summed Antarctic sea level response quite accurately, the acceleration in the observations is not well simulated (Fig. 7). On average, the selected models overestimate Antarctic discharge before around 2010 and underestimate it thereafter. Furthermore, for individual regions the response is not always well captured (see e.g. Figures A1 and A2 for the QUA and QUR method, respectively). The spread in individual regions is higher for the Antarctic-255 wide calibration than for the regional calibration. Antarctic-wide calibration leads to regional responses that are overestimated in some regions and underestimated in others (Fig. A1) since the same γ is used for each region. Differences between Antarcticwide and regional calibration are greatest for the Amundsen region, which is the most important contributing region to the summed Antarctic response over the hindcasting period. The Amundsen and Peninsula contributions are underestimated by the selected models for the Antarctic-wide calibration. The EAIS response is reasonably well reproduced. The responses of the 260 Ross and Weddell region are slightly overestimated. The errors in the individual regions compensate each other, resulting in a summed Antarctic response that is well captured. For the regional calibration, the responses in individual regions are better captured and more restricted (Fig. A2).

Projections
In this section, projections of the summed Antarctic sea level contribution are presented. The projections comprise the 21st 265 century. Computations start in the year 1850 so that the delayed contribution of basal melt is included in the future sea level response. We assess two metrics: the cumulative magnitude and the rate of the sea level response. The cumulative magnitude of the sea level response is used to compare differences over the 21st century. The sea level response rate at the end of the 21st century is indicative of differences in committed sea level rise beyond 2100.   ESM-RF combinations and the bottom panels the top 10% selections. Not surprisingly a higher emission scenerio leads to a higher sea level contribution. Absolute differences between the basal melt computation methods become more explicit for the 275 higher emission scenarios, but relative differences (ratio of highest to lowest) are comparable. For the full model suite, the basal melt computation method affects the relative uncertainty in median sea level contribution more than the SSP scenarios (Table 5).
When the calibration bounds are not considered (unbounded calibrations only), the impact of the basal melt computation reduces. Then the influence of basal melt computation on variation in projected sea level is similar to the influence of scenarios.

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The basal melt computation can be subdivided into calibration and parameterisation steps. The calibration step is the most distinctive feature of the basal melt computation in terms of the projected magnitude of the sea level contribution. Antarcticwide calibration results in higher projections than regional calibration. Bounded calibration gives higher values than unbounded calibration (comparison for the linear parameterisation only). The effect of the parameterisation is smallest (comparison for the unbounded calibration only).

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Second, the variation in the response rates is assessed at the end of the 21st century (Table 6). These are important for sea level differences beyond 2100. The response rate is computed by a linear regression on the sea level response over the period 2081-2100. The difference between the lowest and highest basal melt method shows that the influence of the basal melt computation method on the response rate is equal to or greater than the effect of the emission scenario. By considering unbounded calibration methods only, the influence of the scenarios dominates over the basal melt computation method. The basal melt 290 Table 5. Relative uncertainty in the dynamic Antarctic contribution to sea level rise in 2100 compared to 1995-2014. Relative differences were assessed by the variation factor, which is specified as the sea level contribution associated with variations in a specific source variable.
If the source variable varies from value A to value B, we quantify the impact of this variable on the sea level contribution by the variation factor B/A (following Hinkel et al. 2021 Figure 9. Same as Fig. 8 but for the sea level response rates over the period 2080-2100. computation can be subdivided into calibration and parameterisation parts. The calibration step is the most distinctive feature in the basal melt computation. Antarctic-wide calibration results in higher projections than regional calibration. Bounded calibration gives higher values than unbounded calibration (comparison for the linear parameterisation only). The effect of the parameterisation is smallest; The quadratic parameterisation provides higher estimates of future sea level rise rates than the linear parameterisation (comparison for the unbounded calibration only). We conclude that sea level variations associated with basal melt computation methods are equal or greater than variations between different pathways of future greenhouse gas emission scenarios. Within the basal melt computation methods, the calibration step is more important than the parameterisation type for the contribution of Antarctic ice discharge to sea level up to and beyond 2100.

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In Sect. 3.3 the top 10% best ESM-RF pairs were selected based on their performance in reproducing observed Antarctic ice discharge over four decades. Figure 10 presents the projections of these selections. For each scenario, the top 10% selection shows on average a 20-28 mm higher median cumulative sea level response than the full model suite (Fig. 8). This can be partly attributed to the fact that the selection does not include models with a γ of zero for the regions that contribute most (Amundsen, EAIS) to the sea level increase. Averaged over all basal melt computation methods, SSP5-8.5 has a median cumulative increase 305 of 110 mm compared to 78 mm in SSP1-2.6. Furthermore, the different basal melt computation methods give more similar results for the selection than for the full model suite (Table 5). In contrast to the full model suite, for the selection there is no clear relation between the basal melt computation method and the response magnitude within an emission scenario. For the top 10% selection the influence on the response magnitude of the basal melt computation method is thus equal to or smaller than the effect of the emission scenario.

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The top 10% selection shows on average 0.2-0.5 mm yr −1 higher sea level rates than the full model suite (Fig. 9). SSP5-8.5 has a median response rate that is about twice as large as the rate of SSP1-2.6. As for the cumulative contribution, the rates of the selected ESM-RF combinations are more equal between different basal melt computation methods for the model selection than for the full model suite (Table 6). For the top 10% selection the influence on the response rate of the basal melt computation method is smaller than the effect of the emission scenario. Different than for the full model suite, the selection consistently 315 shows higher sea level rates for the Antarctic-wide calibration than for the regional calibration. This can be explained by the higher contributions (higher γ) of the Ross and Weddell sectors, which show a clear warming trend in the subsurface ocean ( Fig. 4). Other aspects (bounded vs unbounded calibration, quadratic vs linear parameterization) do not have a noticeable effect on the response rate of the top 10% selection.
For the top 10% of each basal melt computation method, the quadratic parameterisation combined with an Antarctic-320 wide calibration (QUA) resulted in the best estimate of Antarctic discharge over almost four decades (lowest overall RMSE) (Sect. 3.2). If reproducing the past is good indicator for making future projections, this basal melt computation method (QUA) will arguably provide the best estimate for the sea level contribution of Antarctic discharge over the coming century. We compared our best estimate with the emulated ISMIP6 and LARMIP-2 studies as presented in IPCC AR6 (Table 7). The cumulative sea level response is equal or smaller in magnitude than emulated ISMIP6 estimates across all scenarios (depending on the basal 325 melt computation method). Compared to LARMIP-2, the response is smaller. The differences with ISMIP6 and LARMIP-2 can be mainly attributed to the calibration on past ice discharge, which resulted in less sensitive basal melt parameterisations (Fig. 5).

Modelling uncertainties
Here we assess the role of CMIP6 ESMs and LARMIP-2 ice sheet models in projection uncertainties by comparing the median 330 projected sea level contributions for the basal melt computation method with the best performance in the hindcasts (QUA). Fig.   11 shows the projected Antarctic sea level contribution for each individual CMIP6 model as computed with the QUA method.
The spread for each CMIP6 model is determined by the linear response functions. Noticeably, the differences between the scenarios are small compared to the the differences between individual CMIP6 models. The median sea level contribution for SSP1-2.6 (SSP5-8.5) varies from 0 mm (0 mm) for CAS-ESM2-0 to 174 (254) mm for MPI-ESM1-2-LR. This difference can 335 be attributed to the difference between CMIP6 models. Similar to Fig. 11, Fig. 12 shows the projected Antarctic sea level contribution for each individual ice sheet model (RF).
Here, the spread is determined by the CMIP6 models. Clearly, the spread between RFs is smaller than between CMIP6 models.
Furthermore, the RF spread is also greater than the scenario-induced spread. The sea level contribution for SSP1-2.6 (SSP5-8.5) varies from 6 mm (10 mm) for GRIS-LSC to 86 mm (127 mm) for ISSM-JPL, pointing at a difference that can be attributed to 340 ice sheet models of 80 mm (117) mm, influencing the sea level contribution by a factor 12.7 (14.3).
In this study, calibrated projections of Antarctica's dynamic sea level contribution were made that are consistent with four decades of past ice discharge in observations. Calibration was applied on the basal melt parameterisation. The contribution of Antarctica's ice discharge to sea level changes is computed with state-of-the-art ESMs from Coupled Model Intercomparison Project Phase 6 (CMIP6) and linear response functions from LARMIP-2 ice sheet models. The major strength of this method is that multiple climate and ice sheet models can be combined to assess the full range of modelling uncertainties. A drawback of the method is that non-linearities between thermal forcing and ice sheet mass loss, related to ice sheet instabilities are not considered because we use the Linear Response Functions framework. Our results show that the models that we used, even the top 10%, are not able to represent the acceleration present in the observations (Fig. 7), with overestimation of mass loss 350 before 2010 and underestimation thereafter. This could be explained by ice sheet/ocean feedbacks that are not represented in the models. One reason to introduce the quadratic parameterisation was to account for some positive feedback between ice melt and ocean forcing. However the feedback between surface freshening due to melt water and basal ice shelf melt is not explicitly simulated. Recent studies suggest that this feedback is positive (Bronselaer et al., 2018;Golledge et al., 2019;Sadai et al., 2020), which could explain the inability of our models to represent the observed acceleration. It should also be noted that The likeliest explanation would be that the models predict a warming while the observed discharge decreased over the observation period (or vice versa). This could be caused either by the importance of natural variability in the observations or by the inability of the ESMs to simulate temperature trends around Antarctica. Furthermore, the observed ice discharge trend could be close to zero (for the Weddell sector). Another explanation is that the water inside the ice shelf 365 cavities is blocked from the water in the coastal region outside the cavities due to density gradients. This contradicts the assumption in this study that water from the open ocean can freely access the ice shelf cavities. It is questionable whether the situation during the calibration period is representative for the future. In the future model projections (Fig. 4), especially for SSP5-8.5, all coastal regions, especially the Weddell and Ross sectors, experience a warming signal. As the open ocean outside the cavities warms, it could be expected that this warming will at a certain moment also be transported inside the cavities, 370 and contribute there to basal melt and ice discharge. New calibration will then lead to γ values that are greater than zero.
This means that calibrated γ values that link open ocean subsurface temperatures outside cavities to basal melt underneath ice shelves could be climate-state dependent. It should also be noted that we calibrated the basal melt parameterisation based on basal melt anomalies and not on absolute basal melt. This is because that allows us to better represent observed melt but the Table 7. Projected dynamic contributions to sea level in meters from the Antarctic ice sheet in 2100 relative to 1995-2014. The numbers for LARMIP-2, ISMIP6 and SMB are obtained from the IPCC AR6 report (Fox-Kemper et al., 2021). Note that for the ISMIP6 estimate surface mass balance contributions are removed as our study only accounts for ice discharge. QUA and LBA are shown as the best-performing method in reproducing hindcasts (QUA) and the method that is most comparable to the LARMIP-2 experiment, but calibrated on past ice discharge (LBA) (Fig. 7).
. ice shelf cavities are not (fully) represented, leading to deficiencies in the process representation (Mathiot et al., 2017).

Scenario
In this study, an Antarctic-wide and regional calibration of the basal melt parameterisation have been applied. Arguably, the regional parameterisation is more physically correct since individual regions might respond differently to similar forcing due to differences in ice and ocean dynamics and ice geometries. However, for the Ross, Weddell and Peninsula regions, 50-84% of the ESM-RF combinations have a calibrated γ equal to zero, resulting in no sea level contribution in future projections. For 380 these regions, regional calibration leads to lower median contributions than Antarctic-wide calibration. A possible reason is that these regions have no clear ocean temperature trend over the period 1850-2018 (and thus small thermal forcing) and relatively small changes in ice discharge during the calibration period. Calibrating on the Antarctic-wide response gives a less accurate reproduction of the historical mass loss in these regions, but arguably a better prediction of future mass loss (when the ocean is warming in these regions). Also, it should be noted that the quadratic parameterisation does introduce some regional difference ity range should be revised downward to be consistent with past ice discharge. Here, it should also be noted that LARMIP-2 overestimates the mass loss observations of Shepherd et al. (2018). The same argument applies to the ISMIP6 γ-values. Similar to LARMIP-2, calibration shows that γ values in the lower bound of the Antarctic mean range applied in ISMIP6 are more consistent with four decades of past Antarctic ice discharge (Fig. 5). Consistent with the higher melt sensitivity the projected sea level contributions are therefore higher in LARMIP-2 and ISMIP6.

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A short assessment was made on the role of CMIP6 ESMs and LARMIP-2 ice sheet models in projection uncertainties by comparing the median projected sea level contributions for the basal melt computation method with the best performance in the hindcasts (QUA) (Sect. 3.4.3). This assessment shows that modelling uncertainties, especially those related to ocean temperature evolution from ESMs, are a greater source of uncertainty in Antarctic mass loss projections than the emission scenarios and the basal melt computation method. These large intermodel differences in ESMs as well as RFs explain why 415 model selection is essential to make future projections more consistent with observations of past ice discharge.
The projected Antarctic discharge shows a clear sensitivity to the emission scenario. Limiting emissions to scenario SSP1-2.6 compared to , would lead to about 30% reduction in the median projected sea level contribution of Antarctic 430 discharge in 2100. The delayed feedback of ice discharge to increasing ocean temperatures (as modelled by the linear response functions) implies that the associated sea level contribution only becomes scenario-dependent after around 2050.
For the full model suite, the basal melt computation method has a greater impact on the projected sea level contribution than the emission scenario. Across all scenarios, the median Antarctic ice loss is two times higher for the highest method than for the lowest method. Bounded calibration leads to higher median projections than unbounded calibration since all γ 435 values are greater than zero due to the lower bound. Calibrating on the summed Antarctic response leads to higher projections than calibration per region. This can be explained by regions with a small or negative past contribution to sea level that have  The top 10% selection gives 20-28 mm higher median projections than the full model suite. This difference can be partly attributed to the unbounded basal melt computation methods, which include γ values equal to zero for the full model suite.
After selection, the top 10% γ values are greater than zero for the dominant contributing regions (Amundsen, EAIS), resulting in higher estimates. For the bounded methods, there is no significant difference between the full model selection and top 10%.
This study shows that calibration of the basal melt parameterisation on past ice discharge provides a way to constrain 445 historical and future evolution of Antarctic basal melt to observations. This leads to reduced spread in the projections of the sea level contribution of Antarctica's ice discharge from basal melt over the 21st century. Moreover, this calibration shows that the two main studies on which the IPCC AR6 Antarctic sea level contributions are based (ISMIP6 and LARMIP-2) use basal melt sensitivities that are higher than the calibrated values that we found. If these studies would have calibrated their basal melt computations on past observations of ice discharge, this would have resulted in lower projections of Antarctica's sea level 450 contribution.
This is due to the parabolic shape of the observed ice discharge over the observational period (Fig. A2). For the Weddell region, the cumulative ice discharge is close to zero, resulting in the relatively small calibrated γ values. For the Ross region, the Rignot ice discharge even shows a declining sea level contribution over the reanalysis period, which could not even be reproduced by 465 the best fitting CMIP6 models (Fig. A2). Figure 3 consistently shows no decline in the median ocean temperature of the CMIP6 models over the historical period, pointing at a deficiency in ocean forcing for the Ross region. In the Ross region negative γ values would give a better fit for many ESM-RF pairs, but this would be physically incorrect since this would suggest that warmer temperatures lead to less basal melt and vice versa. As a consequence, a high percentage of the ESM-RF pairs has a γ with a value of zero in the Ross region. For the Peninsula, about half of the models has a γ value of zero. Consistently, most 470 CMIP6 models do not simulate a positive temperature trend in this region over the historical period (Fig. 3), also pointing at a deficiency in the ocean forcing. For the Amundsen and EAIS regions, most models have positive calibrated γ values, consistent with the positive sea level contribution in these regions and simulated ocean warming trend over the historical period.
Author contributions. EvdL, SD and DLB designed the study. DLB downloaded the CMIP6 data from the ESGF node and wrote the code to read it. EvdL performed the computations and prepared the manuscript with contributions from all co-authors.   Figure A2. Same as Fig. A1, but for the QUR method.