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General Circulation Models and high-resolution atmospheric regional climate models (RCMs) consistently project increasing AIS accumulation (herein defined as precipitation–sublimation) over the twenty-first century^{5, 10, 11, 12, 13, 14}. Continental-scale increases are mainly attributed to increasing precipitation due to higher atmospheric moisture concentrations in a warmer atmosphere, whereas regional patterns result mainly from the interaction between ice-sheet topography and circulation-driven changes in meridional moisture transport^{14, 15, 16}. The surface topography of the AIS leads to a spatially variable distribution of precipitation, with low precipitation rates (<50 mm yr⁻¹) over the high-elevation inner plateau and a rapid increase in precipitation towards the lower elevation coastal regions^{4, 11, 17, 18}. The projected continental-scale change in precipitation is also dominated by an increase in the coastal regions. Based on a GCM with regional zoom capacity, the mean absolute increase in precipitation over coastal areas (surface elevation <2,250 m) is projected to be three times larger than the mean increase over the inner ice sheet¹⁰. In contrast, the projected relative increase in precipitation over the twenty-first century is much more uniformly distributed and even tends to be slightly higher in the interior than in the coastal regions^{10, 13, 19}.

Despite model simulations consistently showing an increase in continental-scale accumulation with regional warming, individual estimates of the sensitivities (herein accumulation sensitivity) have a wide range, from 3.7% K⁻¹ estimated from one GCM over the twenty-first century²⁰, to 5.5% K⁻¹ derived from simulations of the historical period provided by five GCMs (ref. 5) within the Coupled Model Intercomparison Project phase 3 (CMIP3), 7% K⁻¹ based on high-resolution model simulations by the end of the twenty-first century¹¹, and 13% K⁻¹ based on simulations from 15 CMIP3 GCMs through the twenty-first century¹⁰, although the high sensitivity in the latter study may be largely due to the empirical correction factor used to adjust for resolution effects. Moreover, because high-resolution RCMs better resolve the steep coastal topography and uplift of air masses, adiabatic cooling and associated precipitation than lower-resolution global models, they often result in higher projected continental-scale precipitation changes for the same amount of warming^{10, 12}.

There are few observational data to evaluate these model simulations. Linear regression analysis of present-day observations²¹ suggests a sensitivity of 4% K⁻¹ for the Antarctic continent. However, because of the large inter-annual variability of snowfall on a continental scale⁴, long-term records are required to infer significant accumulation trends³. The analysis of a current 50-year benchmark data set has not shown a significant trend in Antarctic accumulation with time³. In combination with temperature observations, the accumulation sensitivity reaches 4.9 ± 4.9% K⁻¹, in close agreement with a GCM-derived value of 5.5 ± 0.8% K⁻¹ (ref. 5) and the early estimate by Fortuin and Oerlemans²¹. However, the simulated sensitivities are based on significant increases in accumulation rates (17 ± 4 mm century⁻¹) and temperatures that are not seen in the observational data.

Ice cores provide information about accumulation changes during the period of warming associated with the last deglaciation (~21–10 ka; Fig. 1), thus providing a unique opportunity to evaluate accumulation sensitivities independent of model simulations. At the same time, however, these records identify only local changes, and thus do not allow an assessment of the continental-scale relationship between integrated accumulation changes across the AIS and continental-mean temperatures that is critical for estimates of sea-level rise. We thus use results from a transient simulation with the coupled atmosphere–ocean Community Climate System Model version 3 (CCSM3) that spans much of the last deglaciation (22.0–14.3 ka; refs 22, 23) to derive associated continental-scale sensitivities. These results are then compared to sensitivities derived from future simulations generated by the latest generation of GCMs that contributed data to the Coupled Model Intercomparison Project phase 5 (CMIP5) based on the four Representative Concentration Pathways (RCPs) and a high-resolution future simulation by the Regional Atmospheric Climate Model 2 (RACMO2; ref. 24).

Changes in accumulation and temperature are described in comparison to a core-specific pre-industrial reference level (see Supplementary Information). Thick solid lines are derived by linear regression assuming that the intercept is zero (orange lines for ice-core data and blue lines for simulations, sensitivities are given in each panel including the 2σ uncertainty range of the sensitivities derived from the ice cores). The shaded area describes the uncertainty range of the ice-core sensitivities.

Ice-core data.

Accumulation rate data from four ice cores (EDC, EDML, Talos Dome, Vostok) are derived using the Datice methodology^{27, 28}. Accumulation rates for Law Dome are from age tie-points and an ice-flow model that simulates ice thinning from vertical strain²⁹. Accumulation rates for the WAIS Divide ice core are from annual layer counting³⁰. Temperature reconstructions are derived from isotope (δD, δ¹⁸O) records (see Supplementary Information).

CCSM3 palaeo-simulations.

The CCSM3 palaeo-simulations are described as ‘all-forcing experiment’ in ref. 22, which was driven by transient variations of orbital configurations, greenhouse gas concentrations, Atlantic meridional overturning circulation as well as quasi-transient variations of continental ice sheets since the Last Glacial Maximum.

Changes in accumulation rates derived from CMIP5 GCM data.

Relative changes in annual accumulation and absolute changes in annual near-surface air temperature are calculated with respect to a smoothed version (linear trend line) of the parallel pre-industrial control data. As data are grouped in different GCMs and scenarios, they cannot be considered as independent random variations around one single trend line. However, Fig. 3 suggests that they are well described as random variations around individual model and scenario specific trend lines. Therefore the following random effects model is fit to the data:

where ΔA_{i, j} is the relative change in integrated accumulation across the AIS (including ice shelves), ΔT_{i, j} is the absolute change in regional temperatures, ε_{i, j} describes the residual variation, and t represents the time period. Within this modelling framework, there is a multi-model mean scaling coefficient c where individual GCMs (i) and scenarios (j) specific scaling coefficients are assumed to deviate randomly from the multi-model mean. Each scenario run provides one realization of these deviations (the so called ‘random effects’), which are described by r^mod (inter-GCM deviations) and r^scen (inter-scenario deviations). All random effects are assumed to follow a normal distribution centred at zero and with standard deviations σ_mod and σ_scen, respectively.

Regional climate simulations.

To provide accumulation rates under warming conditions, we use RACMO2 simulations where lateral boundaries were prescribed by the output of the coupled global climate model HadCM3 (CMIP3 database) driven by the A1B emissions scenario. Beyond 2100, the scenario was extended to 2199 assuming constant forcing. A more detailed description of these RACMO2 model simulations is given in ref. 13.

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