Future ice-sheet surface mass balance and melting in the Amundsen region, West Antarctica

We present projections of West-Antarctic surface mass balance (SMB) and surface melting to 2080-2100, under the RCP8.5 scenario and based on a regional model at 10 km resolution. Our projections are built by adding a CMIP5 (5 Coupled Model Intercomparison Project) multi-model-mean seasonal climate-change anomaly to the present-day model boundary conditions. Using an anomaly has the advantage to reduce CMIP5 model biases, and a perfect-model test reveals that our approach captures most characteristics of future changes, despite a 16-17% underestimation of projected SMB and melt rates. 5 SMB over the grounded ice sheet in the sector between Getz and Abbot increases from 336 Gt yr−1 in 1989-2009 to 455 Gt yr−1 in 2080-2100, which would reduce the global sea level changing rate by 0.33 mm yr−1. Snowfall indeed increases by 7.4 to 8.9% per ◦C of near-surface warming, due to increasing saturation water vapour pressure in warmer conditions, reduced sea-ice concentrations, and more marine air intrusion. Ice-shelf surface melt rates increase by an order of magnitude along the 21 century, mostly due to higher downward radiation 10 from increased humidity, and to reduced albedo in the presence of melting. Eastern ice shelves (Abbot, Cosgrove and Pine Island) experience significant runoff in the future, while western ice shelves (Thwaites, Crosson, Dotson and Getz) remain without runoff. This is explained by the evolution of the melt-to-snowfall ratio: below a threshold of 0.60 to 0.85, firn air is not entirely depleted by melt water, while entire depletion and runoff occur for higher ratios. This suggests that western ice shelves might remain unaffected by hydrofracturing for more than a century under RCP8.5, while eastern ice shelves have a 15 high potential for hydrofracturing before the end of this century.


Introduction
In a perfectly stable climate, the Antarctic ice sheet would have a constant mass, and the Surface Mass Balance (SMB, the sum of rainfall and snowfall minus sublimation, runoff and eroded snow) over the grounded ice sheet, i.e. 2000 to 2100 Gt yr −1 20 emission scenario. Using regional atmospheric simulations and global projections with bias corrections, Trusel et al. (2015) reported that large fractions of East and West Antarctic ice shelves could experience melt rates greater than the pre-collapse value of Larsen B by the end of the 21 st century under the warmest scenario.
Computing projections of future SMB and surface melt rates remains challenging, because of the strong natural variability at regional scales (Lenaerts et al., 2016;Donat-Magnin et al., 2020), biases in global climate models (GCMs) (Bracegirdle et al.,5 2013; Swart and Fyfe, 2012) and GCM resolutions that are too coarse to resolve the orographic processes in the relatively steep coastal area (Krinner et al., 2008;Lenaerts et al., 2012;Agosta et al., 2013). Most models that participated in the 5 th Climate Model Intercomparison Project (CMIP5 Taylor et al., 2012) overestimated the present-day Antarctic precipitation, by more than 100% in some cases (Palerme et al., 2017). These models also had a generally poor representation of the snow-pack energy balance, which is why future melt rate estimates have often been derived from simulated air temperatures rather than 10 directly provided by the models (Davies et al., 2014;Trusel et al., 2015), and most limitations remain relevant in the CMIP6 models (Mudryk et al., 2020). Recent versions of regional climate models (RCMs) with a comprehensive representation of polar processes are now able to simulate melt rates in reasonable agreement with observational estimates (Lenaerts et al., 2018;Datta et al., 2019;Donat-Magnin et al., 2020). Using this kind of RCMs to downscale projections from GCMs can significantly reduce surface biases (Fettweis et al., 2013). However, this approach is not sufficient to remove the large-scale biases inherited 15 from GCMs, and bias corrections may be needed (Trusel et al., 2015;Beaumet et al., 2019a). In this paper, we build SMB and surface melting projections at the end of the 21 st century by forcing an RCM with the 3-dimensional climate-change anomalies from a CMIP5 RCP8.5 multi-model mean, with the aim of removing a part of the CMIP model biases (see section 2).
We focus on the Amundsen Sea sector, where potential future melt-induced hydrofracturing and associated loss of ice-shelf buttressing could have large effects on the stability of the West Antarctic ice sheet and therefore on sea level rise (Pattyn 20 et al., 2019). Currently the Amundsen sector accounts for 60% of the total Antarctic mass loss . While oceanic melting is currently the dominant process causing mass loss (Thoma et al., 2008;Turner et al., 2017;Jenkins, 2016;Jenkins et al., 2018), surface air temperature is expected to increase (Bracegirdle et al., 2008), and whether the ice shelves of the Amundsen sectors will respond with the same hydrofracturing mechanism as in the Antarctic Peninsula remains an open question. Contrasting behaviours were indeed projected for individual ice shelves in previous studies at relatively coarse reso-25 lution (Kuipers Munneke et al., 2014;Trusel et al., 2015). In the following, we describe our general methodology (section 2), then we describe future projections in section 3, with a particular focus on SMB over the grounded ice sheet (relevant for sea level) and melting over the ice shelves (relevant for hydrofracturing). We also thoroughly discuss the impact of modelling and methodological biases in our projections, and we propose an extrapolation of our results to other scenarios and time horizons (section 4). 2 Method 2.1 Regional atmosphere and firn model Our projections of the West Antarctic surface climate for the end of the 21 st century are based on version 3.9.3 of the MAR regional atmospheric model (Gallée and Schayes, 1994;Agosta et al., 2019). Our regional configuration is centred on the Amundsen Sea sector, covers 2800×2400 km, and was developed by Donat-Magnin et al. (2020). The horizontal resolution is 5 10 km and and we use 24 vertical sigma levels located from approximately 1 m above the ground to 0.1 hPa. The topography is derived from BEDMAP2 (Fretwell et al., 2013) and the drainage basins used for averages are those defined by Mouginot et al. (2017).
The radiative scheme and cloud properties are the same as in Datta et al. (2019) and the surface scheme, including snow density and roughness, are the same as in Agosta et al. (2019). The atmosphere is coupled to the SISVAT surface scheme (Soil 10 Ice Snow Vegetation Atmosphere Transfer, Gallée and Duynkerke, 1997;, which here is a 30-layer snow/firn model representing the first 20 m with refined resolution at the surface. It includes prognostic equations for temperature, mass, water content and snow properties (dendricity, sphericity and grain size). SISVAT and the atmosphere are coupled through exchanges of mass fluxes as well as radiative and turbulent heat fluxes.
Surface albedo depends on the evolving snow properties and on the solar zenithal angle (Tedesco et al., 2016). As in Agosta In case of surface melting or rainfall, liquid water percolates downward into the next firn layers, with a water retention of 10% of the porosity in each successive layer. The firn layers are fully permeable until they reach a close-off density of 830 kg m −3 .
To account for possible cracks in ice lenses and moulins, the part of available water that is transmitted downward to the next layer decreases as a linear function of firn density, from 100% transmitted at the close-off density to zero at 900 kg m −3 and For the future, we calculate the climate-change absolute anomaly from a CMIP5 multi-model mean (MMM), and we add it to the 6-hourly ERA-interim variables used to drive MAR, i.e. sea surface temperature (SST), sea ice cover (SIC), and 3dimensional wind velocity, air temperature and specific humidity. Considering all these anomalies together allows keeping the consistency of linear relationships, such as the geostrophic and thermal wind balances, although it does not necessarily conserve non-linear relationships. This type of method was previously referred to as "anomaly nesting" (Misra and Kanamitsu, 2004), or 5 "pseudo global warming" (e.g., Kimura and Kitoh, 2007) although this term was often used for more simple temperature and humidity perturbation methods (e.g. Schär et al., 1996). The MMM anomaly is defined as the mean difference between 1989- ESM-LR, MPI-ESM-MR, MRI-CGCM3, NorESM1-ME, NorESM1-M, bcc-csm1-1, inmcm4. We take the first available ensemble member for each model (i.e. "r1i1p1" or "r2i1p1" if not available). The anomaly is calculated separately for each calendar month, meaning that we apply an anomaly that includes a seasonal cycle. Monthly anomalies are linearly interpolated to avoid discontinuity of 6-hourly boundary conditions. In the future simulation, we do not modify greenhouse gases concen- 15 trations in our regional domain, which is expected to have a minor effect because the dominant effect of global increase in greenhouse gases concentrations on our regional simulations comes from changes in sea surface and sea ice forcing as well as through increased humidity and temperature at the lateral boundaries (Krinner et al., 2014;Bull et al., 2020).
Adding an anomaly is relatively simple, but requires a specific calculation for two variables. First, specific humidity is set to zero in the rare cases where applying the CMIP5 anomaly would produce unphysical negative values. Second, sea-ice 20 concentration (SIC) anomalies are applied through an iterative process, which is needed because some locations have non-zero SIC on some days, and zero SIC on other days. As negative SIC values are unphysical, applying a negative climatological SIC anomaly to all days (but keeping days with zero SIC unchanged) does not conserve the applied CMIP5 anomaly. To circumvent this issue, we apply the anomaly through 20 iterations: we start applying the CMIP5-MMM anomaly to the days and locations with SIC greater than zero (for negative anomaly) and smaller than 100% (for positive anomaly), and after each iteration, we 25 calculate the residual SIC that would be needed to reach the original CMIP5-MMM SIC anomaly, and we add it to the applied climatological anomaly. The effect of this sea-ice anomaly correction is briefly described in section 4. Alternative sea-ice correction methods were evaluated by Beaumet et al. (2019b), but here we prefer to stay as close as possible to the simple anomaly method used for the other variables.
As discussed by Knutti et al. (2010), the MMM is often considered as the "best" estimate for future climate because indi-30 vidual model biases are partly cancelled in the MMM, although an equal weight for all the models does not account for the fact that models are not independent from each other because of the same operating centres, common history, shared physical parameterisations and numerical methods (Knutti et al., 2017;Herger et al., 2018). Given that the CMIP model biases are largely stationary even under strong climate changes (Krinner and Flanner, 2018), our method is also expected to remove a part of the biases in individual model projections. This method has previously been used in various regional studies (e.g. Sato et al.,35 https://doi.org/10.5194/tc-2020-113 Preprint. Discussion started: 1 July 2020 c Author(s) 2020. CC BY 4.0 License. 2007;Knutson et al., 2008;Michaelis et al., 2017;Dutheil et al., 2019) but, to our knowledge, never in Antarctica. Krinner et al. (2008Krinner et al. ( , 2014 and Beaumet et al. (2019a) used anomalies in global simulations with a stretched grid over Antarctica, but this only involved anomalies in sea surface conditions.
All the simulation years are run in parallel with a 12-year spin up for each simulated year, which is sufficient to obtain a steady runoff in the future simulation over all ice shelves except Abbot (see Discussion). When not stated otherwise, the 5 present-day period represents 1988-2017. The future period corresponds to the 1988-2017 period to which was added the CMIP5-MMM anomaly (2080-2100 minus 1989-2009) and therefore represents something like 2079-2108 (with the interannual variability of 1988-2017). While our CMIP5-MMM anomaly is only based on 21 years, we decided to run our regional simulations over 30 years, which provides more statistical significance given that surface melt rates and SMB exhibit high interannual variability in this region (Scott et al., 2019;Donat-Magnin et al., 2020). Retrospectively, it would have been better 10 to use the same 30-year time window for CMIP5 and for our MAR simulations. We now briefly describe the CMIP5-MMM anomalies applied to ERA-interim. The troposphere is warmed relatively uniformly from the surface to ∼300 hPa (Fig. 1a). There is a clear seasonal cycle in the low-troposphere anomalies, with stronger warming in winter than in summer. This is related to stronger changes in winter sea-ice cover compared to summer (solid lines in Fig. 2), because present-day summers are already relatively sea-ice free and, as such, sea-ice cover cannot decrease much 15 further. As expected from the radiative effects of greenhouse gases, the stratosphere tends to cool in response to increased anthropogenic emissions of greenhouse gases (e.g. Seidel et al., 2011). There is also a clear seasonal cycle in the lower stratosphere (∼100 hPa), with future warming in spring and summer and cooling in the other seasons, which is related to seasonal effects of ozone recovery (Perlwitz et al., 2008). Specific humidity increases as the troposphere warms ( Fig. 1b) for the present-day (blue) and future (dark-red) simulations.

Results: projections
In this section, we present SMB and surface melting projections derived from ERA-interim and the CMIP5-MMM-RCP8.5 anomaly. We simply refer to the corresponding simulations as "present" and "future" in the following. We also investigate the causes for these changes and we discuss possible consequences for potential ice-shelf hydrofracturing and sea level rise.

5
The future SMB is increased by 30 to 40%, keeping a very similar pattern to present day ( Fig. 3a,b), i.e. mostly controlled by the steep slopes and local topographic features near the ice-sheet margin. Considering the grounded part (which matters for sea level rise) of all the drainage basins from Getz to Abbot (boundaries indicated in Fig. 3a), SMB increases from 336 Gt yr −1 presently to 455 Gt yr −1 at the end of the 21 st century (Tab. 1). As previously reported by Ligtenberg et al. (2013), increasing snowfall explains most of the SMB changes. Projected sublimation slightly decreases in all basins, while rainfall slightly 10 increases, but both components remain two orders of magnitude smaller than snowfall. Runoff is projected to remain negligible over the grounded ice sheet in this sector.  Table 1. SMB and its components over the grounded part of individual glacial drainage basins, for present day (regular) and future (bold).
The results are here provided in Gt yr −1 , i.e. integrated over the drainage basins to be directly convertible into a rate of sea level rise. SMB is the sum of snowfall and rainfall minus sublimation and runoff. The bottom row shows the relative increase in snowfall per degree of air warming at 2 m above ground level (see eq. 1).

SMB component Abbot Cosgrove Pine Island Thwaites Crosson Dotson Getz
( We now briefly analyse possible causes for increased SMB in a warmer climate. In the following, the relative increase A in a variable V (saturation water vapour pressure or snowfall) per degrees of warming is calculated by integrating: which has the advantage to give A values that are relatively independent of the chosen (T 2 − T 1 ) temperature interval given the approximate exponential relationship expected for the variables under consideration.

5
The saturation water vapour pressure increases with air temperature, at a rate of 7.1 ± 0.1 % • C −1 in the 0-10 • C range (Clausius-Clapeyron relation). In our simulations, near surface warming reaches 3.4 to 3.7 • C for the various basins, which is very close to the RCP8.5 MMM global warming value (Collins et al., 2013). The corresponding increase in snowfall over the grounded ice sheet represents +7.4 to +8.9% • C −1 (bottom row of Tab. 1), which is higher than the theoretical Clausius-Clapeyron rate. This indicates that other factors may contribute to increasing snowfall in the Amundsen sector.
To further understand the mechanism for increased snowfall, we now consider projections for the four seasons separately (Fig. 4). The strongest increase in SMB occurs in MAM (followed by JJA), which corresponds to the season with largest changes in sea-ice concentrations in the vicinity of the ice-sheet margin (see dashed lines in Fig. 2). While  refers to the maximum saturation water vapour pressure, we suggest that decreasing coastal sea-ice cover makes surface air masses closer to their saturation level, as previously suggested by Gallée (1996) and Kittel et al. (2018). This mechanism is also consistent with the modelling results of Wang et al. (2020) who find that precipitation over the coastal Amundsen region mostly comes from evaporation occurring all the way from the Tropical Pacific to the Amundsen Sea. Another possible contributor to increased snowfall is the changing low-troposphere circulation, which shows a cyclonic anomaly in MAM, 10 favouring humidity transport towards the ice sheet (Fig. 5). As warming at the height where precipitation is formed is relevant for Clausius-Clapeyron, a stronger warming far above the surface than in its vicinity could also contribute to explain this stronger sensitivity, although Fig. 1a suggests slightly stronger near-surface warming.

Ice-shelf surface melting and runoff
We have shown that runoff plays no significant role in the simulated SMB over the grounded ice sheet and therefore on sea 15 level projections. However, surface melting and subsequent runoff may lead to meltwater ponding over ice shelves and trigger hydrofracturing. In this section, we therefore focus on surface melting and runoff projections over the seven major ice shelves from Getz to Abbot. In this paper, we do not investigate supra-glacial hydrology and hydrofracture mechanics in details, we simply consider the presence of widespread runoff as an indicator for potential hydrofracturing.
On average over the seven major ice shelves from Getz to Abbot, surface melt rates are projected to increase by one order 20 of magnitude, and melt occurrence is projected to increase from typically a week per year to 1-2 months per year (Tab. 2). As previously noticed by Kuipers Munneke et al. (2014) and Trusel et al. (2015), we find an exponential dependency of melt rates to 2 m air temperatures (not shown), with a much stronger dependency on temperature than SMB (Clausius-Clapeyron). In terms of seasonality, future melt rates are strongly increased in summer (DJF) over all the ice shelves, while Abbot, Cosgrove and Pine Island also experience significantly more melting in fall and spring (Fig. 6).

25
Rainfall is also projected to increase (Tab. 2), but represents a relatively small fraction of surface melting (less than 15% for all the ice shelves). Future surface melting and rainfall entirely refreeze in the firn for all the ice shelves from Getz to Thwaites, which leads to no runoff in the future. In contrast, Abbot, Cosgrove and Pine Island produce some runoff, although most surface melting and rainfall also refreeze in the firn.
The contrast between western (Getz to Thwaites) and eastern (Pine Island to Abbot) ice shelves can be explained by vari-30 ations of the melt-to-snowfall ratio, which we now explain from simple considerations. First of all, if surface melt water percolates into snow layers that are below the freezing point, it partly refreezes, which releases latent heat and warms the snow layers. Therefore, the melt-to-snowfall ratio must typically exceed a few hundredth to bring the snow to 0 • C and allow the existence of liquid water in snow. To generate runoff, melt rates also need to be sufficiently high to significantly deplete air in 10 https://doi.org/10.5194/tc-2020-113 Preprint. Discussion started: 1 July 2020 c Author(s) 2020. CC BY 4.0 License.  snow or firn. Based on a simple model, Pfeffer et al. (1991) estimated that surface melting would lead to maximum snow-air depletion for melt-to-snowfall ratios greater than approximately 0.7, considering fresh-snow and close-off densities of 300 and 830 kg m −3 respectively, and snow at −15 • C . This 0.7 ratio was the sum of 0.06 required to warm the snow to 0 • C , and 0.64 needed for complete snow-air depletion (see their Appendix). This shows that in the presence of relatively fresh snow, large melt-to-snowfall ratios are needed to produce runoff, mostly because large melt rates are needed to fill the porosity brought by 5 snowfall.
Going back to our simulations, we note the importance of the melt-to-snowfall ratio for the runoff produced by MAR over the ice shelves, with episodic runoff for annual melt-to-snowfall ratios as low as 0.25, and a very high probability of runoff for annual melt-to-snowfall ratios greater than ∼0.85. (Fig. 7). The ratio allowing runoff exhibits some variability due to varying snow characteristics and a more complex firn model than in Pfeffer et al. (1991), but on average, runoff becomes more likely The existence of such a threshold explains the runoff variations across the ice shelves (middle row of Tab. 2): Abbot, Cosgrove and Pine Island have relatively high future melt rates (∼500 mm w. e. yr −1 ) but Abbot receives much higher snowfall, which explains that surface melting produces less runoff than over Cosgrove and Pine Island; the four other ice shelves experience both relatively high snowfall and weak melt rates, which explains the absence of runoff in a warmer climate. Concerning Pine Island, it should be noted that high melt rates are concentrated on its north-eastern flank (Figs. 3,6), so potential hydrofrac-5 turing may be limited to that part, which is not the most important in terms of ice sheet dynamics and instability (e.g. Favier et al., 2014).
We now briefly analyse the causes for increased melting in a warmer climate. All along the future melting season, less energy is lost by the ice-shelf surface through net longwave radiation (Fig. 8b), which is a consequence of higher downward longwave radiation, as expected in the presence of higher specific humidity, only partly compensated by higher upward longwave radiation emitted by a warmer snow surface in the future (Fig. 8a,b). In the future, more energy is also received by the snow surface through shortwave radiative fluxes over the melting season (Fig. 8c), which is explained by a melt-albedo feedback, i.e. a decreased ice-shelf albedo as a result of more melting (Fig. 8e). These changes are partly compensated by 13 https://doi.org/10.5194/tc-2020-113 Preprint. Discussion started: 1 July 2020 c Author(s) 2020. CC BY 4.0 License. less shortwave radiation received by the snow surface (negative anomaly of the downward component in Fig. 8a), which is explained by a moderate increase in summer cloudiness (not shown) in the future. Changes in sensible and latent heat fluxes are less important than changes in radiative forcing, but they compensate a part of the increased net longwave and shortwave radiations (Fig. 8a,d). This may be related to a thicker planetary boundary layer in the future (Fig. 8f), i.e. reduced near-surface temperature and humidity vertical gradients, similar to the difference between summer and winter (Fig. 8d,f).

4 Discussion
We first discuss some limitations of our modelling and methodological approaches and their impacts on our projections. Then, we discuss the possibility to extrapolate our results to other climate perturbations.

Modelling and methodological limitations
We first assess the ability of our projection method to capture the future climatology in a similar way as Yoshikane et al.
(2012), i.e. running a perfect-model test (i.e. assuming that the future is perfectly known by considering that a given projection is true). To do so, we now consider a single model, namely ACCESS-1.3 (Bi et al., 2013;Lewis and Karoly, 2014), which reproduces remarkably well the present-day climate over Antarctica (Agosta et al., 2015;Naughten et al., 2018;Barthel et al., 5 2020). We first run MAR forced by ACCESS-1.3 over 1989-2009 and 2080-2100 under the RCP8.5 scenario, and we consider 2080-2100 from this run as the true future. Then, we calculate the seasonal climatological anomaly and add it to the presentday interannual forcing, i.e. following the methodology described in the previous section but using present-day ACCESS-1.3 and its future anomalies instead of ERA-interim and the CMIP5 MMM anomaly. The future based on the absolute anomaly method is referred to as projected future in this section, and it is compared to the true future (from the direct downscaling 10 of ACCESS-1.3). The fidelity of our projection method is assessed by comparing the difference between the projected future and the true future (i.e., the projection bias) to the true climate change signal (true future minus present). We can see that our iterative sea-ice correction (see section 2) is effective, reducing the SIC projection bias from 14% to 0.3% of the climate-change anomaly in SON, and from 40% to 20% of the climate-change anomaly in DJF (Fig. 9a).  Over the ice sheet, the near-surface projection biases are 0.6 • C in JJA and 0.2 • C in DJF, which is relatively small compared to a warming signal of 3.5 • C and 3.0 • C for these two seasons respectively (Fig. 9b). Looking at the peak melt rate in January ( Fig. 9c), we find that the projection bias represents 17% of the climate-change signal, vs 34% if no iterative method is used for sea ice. The annual SMB projection bias represents 16% of the projected increase, vs 32% if no iterative method is used for sea ice (Fig. 9d). In terms of spatial pattern, the climate change signal remains significantly larger than the projection bias 5 at most locations (Fig. 10a,b). The melt projection bias is positive at most melting locations, with a bias consistently smaller than the climate change signal (Fig. 10c,d).
To summarise our assessment of our projection method, it has the advantage to start from a present-day state that is not affected by present-day biases in CMIP5 models and to be applicable to a multi-model-mean projection, which is expected 17 https://doi.org/10.5194/tc-2020-113 Preprint. Discussion started: 1 July 2020 c Author(s) 2020. CC BY 4.0 License. to remove a part of the CMIP5 model biases. The counterpart of these advantages are biases in the projection itself. These biases are estimated to remain below 20% based on our perfect-model approach. A part of these biases may be related to the imperfect method used to apply the sea-ice anomaly. Using iterative absolute anomalies typically removes half of the projection biases compared to a simple absolute anomaly, but the bias is not completely removed in summer, and more iterations or a refined method may be needed in our approach. Alternative approaches to build future sea-ice concentrations were proposed 5 by Beaumet et al. (2019b), and some of them may be more effective at removing projection biases, although their approaches produced biases of similar magnitude as our iterative absolute anomaly method (their Fig. 5). Another possible cause for our projection biases is the fact that we assume unchanged interannual variability with respect to the mean in the projected future, while the true future experiences a different variability. Changes in interannual variability or extreme events may indeed affect non-linear processes (e.g., melt rates vary exponentially with temperatures) even if the mean is the same in the true future and 10 the projected future. Notwithstanding these limitations, we consider that our methodology has some advantages and should be used for projections together with other existing methods.

PIG
We now discuss the consequences of the aforementioned model and methodological biases for future runoff and potential hydrofracturing. Our projection method produces an underestimation of both snowfall and melt rates in the future by 16-17%.
Adding these errors to both snowfall and melting values in Tab. 2 would keep the melt-to-snowfall ratio unchanged. As such, the We now discuss another critical aspect of firn modelling, which is the spin-up duration. Our approach has consisted of running a present and a future 30-year snapshot, which means that the future firn has not experienced transient changes throughout 25 the 21 st century. Instead, we have run a 12-year spin up under future conditions for every simulated year of the future experiment (the years are run in parallel). We now consider runoff in DJF 1998 with climate anomalies on top, which is the summer with highest melt rates in our projection and is preceded by a decade of relatively high melt rates (Donat-Magnin et al., 2020). We consider that the spin up duration is sufficiently long if the DJF-1998 runoff reaches a steady state for spin-up durations shorter than 12 years. Whatever the spin-up duration, there is no significant runoff at the surface of Getz, Dotson,

30
Crosson and Thwaites (Fig. 11), which is expected due to the low melt-to-snowfall ratio (see previous section). For Pine Island and Cosgrove, an approximate steady state seems to be reached after 6-7 years, although runoff at Cosgrove still experiences fluctuations of ±10%. In contrast, the runoff over Abbot is still drifting after 12 years of spin up. This is likely related to the relatively weak but non-zero runoff associated with a melt-to-snowfall ratio close to the critical threshold, which probably means that the firn is still slowly filling up after 12 years. Expanding the spin-up duration much further under constant 2080-

Extrapolation to other climate perturbations
While CMIP5-MMM-RCP8.5 at the end of the 21 st century is meaningful, it is also interesting to estimate the likelihood of 5 widespread ice-shelf runoff further in the future or following alternative emission scenarios. To do so, we evaluate the melt-tosnowfall ratio for a given additional warming or cooling, assuming that snowfall (SNF) and melt rates (MLT) evolve following simple relationships with temperature. Such relationships can be obtained from the literature. The snowfall (SNF) dependency to temperature can be obtained by the Magnus empirical fit of the Clausisus-Clapeyron relationship (Koutsoyiannis, 2012), here further simplified by linearizing the term of the exponential around 0 • C . The melt rate (MLT) has also an exponential 10 dependency to near surface temperature, with an empirical expression derived by Trusel et al. (2015) from a numerical model 20 https://doi.org/10.5194/tc-2020-113 Preprint. Discussion started: 1 July 2020 c Author(s) 2020. CC BY 4.0 License. applied to the entire Antarctic ice sheet. For a given ice shelf (is), this yields: where ∆T represents warming with respect to present-day ) and ∆T p is the CMIP5-MMM-RCP8.5 warming analysed in this study (2080-2100 minus 1989-2009). The two first lines of (2) are obtained by using the simulated future values on individual ice shelves at ∆T = ∆T p , i.e. SNF is,p and MLT is,p . The third line gives the melt-to-snowfall ratio of a 5 given ice shelf (R is ).
While the expressions in (2) have the advantage to be theoretically valid for general Antarctic conditions, local fits based on our simulations are also meaningful. Another expression can be derived assuming the same exponential form as (2) but with a coefficient in the exponential calculated as the average of the seven values calculated for individual ice shelves: This second method gives a stronger sensitivity to warming than (2). Recalculating an exponential fit for melt rates in a similar way as Trusel et al. (2015) also gives a stronger sensitivity (not shown), which can be a specificity of either the Amundsen region or our model configuration.
The extrapolations corresponding to (2) and (3)  scenario, but given the large snowfall spatial variability around Antarctica and across the Amundsen region, we believe that the melt-to-snowfall ratio is a better indicator of potential ice-shelf collapse than a uniform melt-rate threshold. and under alternative scenarios (RCP2.6 and RCP4.5). This warming is derived from Collins et al. (2013, their Tab. 12.2), assuming that the regional warming remains equal to global warming (supported by our results as well as Collins et al., 2013). The black horizontal lines indicate three indicative thresholds for widespread runoff: the future 0.60 ratio simulated at Abbot in 2080-2100 (which is the minimum ratio for which we detect significant runoff), the 0.70 ratio estimated by Pfeffer et al. (1991), and the 0.85 ratio for which more than 50% of the grid points experience runoff (Fig. 7). The warming range for which the extrapolations cross the 0.60 and 0.85 thresholds are indicated by the horizontal color bars at the bottom.
In this study, we have presented future projections of SMB and surface melting at the end of the 21 st century under the RCP8.5 scenario, based on the MAR regional atmospheric model at 10 km resolution. The climate change anomaly is calculated from the seasonal climatology of a CMIP5 multi-model mean, and added to the ERA-interim reanalysis which is used for presentday boundary conditions. The use of an anomaly has the advantage to start from a present state with small biases compared 5 to observations, and is expected to reduce future biases as most CMIP5 biases were shown to be stationary. Besides, the use of a multi-model mean is expected to cancel the biases that are not common to a majority of models. An important caveat of this method is that we assume unchanged interannual variability with respect to the mean. A perfect-model test indicates that our approach captures future changes in most variables, despite an underestimation of SMB and melt rate changes by 17% on average.

10
Considering the drainage basins of the seven major ice shelves from Getz to Abbot, and only for the grounded parts of the ice sheet, we find that SMB increases from 336 Gt yr −1 to 455 Gt yr −1 throughout the 21 st century, which would reduce the global sea level changing rate by 0.33 mm yr −1 . Even in the future climate, SMB over the grounded ice sheet remains nearly equivalent to snowfall in this region. Snowfall increases by 7.4 to 8.9% per • C of near-surface air warming, which is similar to global warming in this region. This sensitivity is slightly larger than previous estimates for the whole ice sheet (Palerme et al.,15 2017; Lenaerts et al., 2016;Ligtenberg et al., 2013, and references therein), and larger than predicted by Clausius-Clapeyron (increase in saturation vapour pressure by 7 to 7.5% • C −1 ). This may be explained by a decreased sea-ice cover along the ice-sheet margin, which helps near-surface air masses to reach their water vapour saturation. Changes in local circulation in autumn, and associated advection of marine air, may also favour higher SMB in the future.
Then, we have analysed future surface melting and runoff at the surface of ice shelves because they can lead to hydrofrac-20 turing and ice-shelf collapse. At the surface of the seven major ice shelves between Getz and Abbot, future melt rates are increased by an order of magnitude compared to present day, and the average number of melt days per year in the future exceeds 30 for most ice shelves. However, most melt water refreezes in the firn, even in the future run, as previously found by Kuipers Munneke et al. (2014) and Ligtenberg et al. (2013). Hence, significant amounts of runoff (produced after warming of the snowpack and depletion of the firn air content by melt water) are only found over Abbot, Cosgrove and Pine Island 25 ice shelves at the end of the 21 st century. All the ice shelves from Thwaites to Getz are projected to remain nearly runofffree throughout the 21 st century. The melt-to-snowfall ratio explains regional contrasts in our projections, and runoff becomes significant if this ratio exceeds 0.60 to 0.85. Based on the melt and snowfall dependencies to near-surface warming, we have extrapolated our projections further in time and for other scenarios. Although uncertain, this suggests that most ice shelves could remain runoff-free by 2100 under RCP2.6 and RCP4.5, to the exception of Cosgrove. Under RCP8.5, the ice shelves 30 from Thwaites to Getz may only experience widespread runoff in the second half of the 22 nd century, and possibly the 23 rd century in the case of Crosson. These results suggest that for Getz, Dotson, Crosson and Thwaites, ice-shelf collapse is unlikely to be triggered by hydrofracturing before the 22 nd century. Nonetheless, it does not mean that these ice shelves will not collapse