Estimation of the Antarctic surface mass balance using MAR (1979-2015) and identiﬁcation of dominant processes

. The Antarctic ice sheet mass balance is a major component of the sea level budget and results from the difference of two ﬂuxes of a similar magnitude: ice ﬂow discharging in the ocean and net snow accumulation on the ice sheet surface, i.e. the surface mass balance (SMB). Separately modelling ice dynamics and surface mass balance is the only way to project future trends. In addition, mass balance studies frequently use regional climate models (RCMs) outputs as an alterna-tive to observed ﬁelds because SMB observations are particularly scarce on the ice sheet. Here we evaluate new simulations 5 of the polar RCM MAR forced by three reanalyses, ERA-Interim, JRA-55 and MERRA2, for the period 1979-2015, and we compare our (cid:58)(cid:58)(cid:58)(cid:58)(cid:58) MAR results to the last outputs of the RCM RACMO2 forced by

2 Data and methods 2.1 Regional modelling

Regional atmospheric models
For the first time, the polar-oriented regional atmospheric model MAR is applied for decades-long simulations over the whole Antarctic ice sheet.MAR atmospheric dynamics are based on the hydrostatic approximation of the primitive equations, fully described in Gallée and Schayes (1994).Prognostic equations are used to depict five water species: specific humidity, cloud droplets and ice crystals, raindrops and snow particles (Gallée, 1995).Sublimation of airborne snow particles is a direct contribution to the heat and moisture budget of the atmospheric layer in which these particles are simulated.The radiative transfer through the atmosphere is parametrised as in Morcrette (2002), with snow particles affecting the atmospheric optical depth (Gallée and Gorodetskaya, 2010).The atmospheric component is coupled to the surface scheme SISVAT (soil ice snow vegetation atmosphere transfer, De Ridder and Gallée, 1998) dealing with the energy and mass exchanges between surface, snow and atmosphere.The snow-ice part of SISVAT is based on the snow model CROCUS (Brun et al., 1992).It is a one-dimensional multilayered energy balance model which simulates meltwater refreezing, snow metamorphism and snow surface albedo depending on snow properties.We used MAR version 3.6.4,simply called MAR here-after.In this version the physical settings are the same as in MAR version 3.5.2used for Greenland (Fettweis et al., 2017), except for the adaptations detailed below.
Grid: Projection is the standard Antarctic polar stereographic (EPSG:3031).The horizontal resolution is 35 km, an intermediate resolution that results from a computation time compromise in order to run the model with multiple reanalyses and global climate model forcings over the 20th and the 21st century.The vertical discretisation is composed of 23 hybrid levels from ∼2 m to ∼17000 m above the ground.

Boundaries:
The topography is derived from the Bedmap2 surface elevation dataset (Fretwell et al., 2013).Because the Antarctic domain is about 4 times larger than the Greenland domain, the circulation has to be more strongly constrained.This is why we use a boundary relaxation of temperature and wind in the upper atmosphere starting from 400 hPa (∼6000 m above the ground) to 50 hPa (upper level), as in van de Berg and Medley (2016), whereas relaxation starts from 200 hPa in Fettweis et al. (2017).

Parameterisations:
a) The fresh :::::: surface snow density ρ s is computed as a function of 10 m wind speed ws 10 (m s −1 ) and surface temperature T s (K): with minimum-maximum values of 200-400 kg m −3 .This parameterisation was defined so that the simulated density of the first 50 cm of snow fits observations collected over the Antarctic ice sheet (see Fig. S1, with snow density database detailed in Table S1).
MAR and RACMO2 models were developed independently.We will not detail here the many physical parameterisation differences between both RCMs, but we will later highlight some of them we show having a significant impact on the modelled SMB.

Forcing reanalyses
Regional atmospheric models are forced by atmospheric fields at their lateral boundaries (pressure, wind, temperature, humidity), at the top of the troposphere (temperature, wind), as well as by sea surface conditions (sea ice concentration, sea surface temperature) every six hours.Consequently, regional atmospheric models add details and physics to the forcing model in the mid and lower troposphere and at the land or iced surface, whereas large-scale circulation patterns are driven by the forcing fields.We forced MAR with three reanalyses over Antarctica in order to evaluate the uncertainty in the simulated surface climate arising from the uncertainty in the assimilation systems: the European Centre for Medium-Range Weather Forecasts "Interim" re-analysis (here-after ERA-Interim, resolution ∼0.75°, i.e. ∼50 km at 70 °S, Dee et al., 2011), the Modern-Era Retrospective analysis for Research and Applications Version 2 (here-after MERRA2, resolution ∼0.5°, Gelaro et al., 2017), and the Japanese 55-year Reanalysis from the Japan Meteorological Agency (here-after JRA-55, resolution ∼1.25°, Kobayashi et al., 2015).
The regional atmospheric model RACMO2 is forced by ERA-Interim.We focus our study to the period 1979-2015, as reanalyses are known to be unreliable before 1979, when satellite sounding data started to be assimilated (Bromwich et al., 2007).

SMB observations and sectors of strong SMB gradients
We use surface mass balance observations of the GLACIOCLIM-SAMBA dataset detailed in Favier et al. (2013) and updated by Wang et al. (2016).This dataset is an update of the one assembled by Vaughan et al. (1999) following the quality-control methodology defined by Magand et al. (2007).It includes 3043 reliable SMB values averaged over more than 3 years.::: We airborne-radar ::::::: method :::::::: combined :::: with ::::::: ice-core ::::::::::::: glaciochemical ::::::: analysis.: The first order feature of the Antarctic SMB is a strong coastal-inland gradient, with mean values ranging from typically greater than 500 kg m −2 yr −1 at the ice sheet margins to about 30 kg m −2 yr −1 in the dry interior plateau (Fig. 1, see also, e.g., Wang et al., 2016).We divide the sparse observation dataset (Fig. 1 -5% of MAR grid cells coverage of the ice sheet) into 10 sectors detailed in Table 1 and shown in Fig. 2. Six of them are stake transects with a stake every ∼1.5 km, which have been proven very valuable for evaluating modelled SMB (Agosta et al., 2012;Favier et al., 2013;Wang et al., 2016).The four other sectors are composed of more scattered observations covering large elevation ranges (Victoria Land, Dronning Maud Land, and Ross Ice Shelf-Mary Byrd Land).

Model-observation comparison method
RACMO2 outputs are bi-linearly interpolated to the 35×35 km MAR grid.For each SMB observation, we consider the 4 surrounding MAR grid cells, from which we eliminate ocean grid cells.We also eliminate surrounding grid cells with an  1955-2008 1753-3741 [17,18,19,20] :: [1] :::::: elevation difference with the observation greater than 200 m (missing elevation of observation is set to Bedmap2 elevation at 1 km resolution).Finally, we bi-linearly interpolate model values of the remaining grid cells at the observation location (see schematic in Fig. S2).
In a last step, we average-out the kilometre-scale variability of the observed SMB (Agosta et al., 2012) by binning point values onto grid cells.For each grid cell containing multiple observations, we average all observations contained into the grid cell weighted by the time span of observations, and in the same way we weight-average the modelled values interpolated to observation locations.This way, we obtain consistent observed and modelled averaged values on grid cells.
We discard 66 observations beginning before 1979 and spanning less than eight years.We also discard 12 observations for which the four surrounding grid cells fall in ocean, and seven observations located at specific topographic features for which none of the four surrounding grid cell has an elevation difference less than 200 m with respect to the actual location.After this, we retain 559 model-observation comparisons.are :::: from :::::: 145°W :: to ::::: 145°E :: by ::: step :: of :::: 45°.

Evaluation of the modelled SMB
The large spatial Antarctic SMB gradients, shown in Fig. 1a as modelled by MAR forced by ERA-Interim for the period 1979-2015, coincide with a strong interannual variability (Fig. 1b), expressed by a standard deviation of ∼22% of the mean SMB on average over the ice sheet (Fig. 1c).MAR SMB oscillates around the 559 observed values ::::: shows :: no ::::::::: systematic :::::: spatial 5 ::: bias : (Fig. 1d), with a mean bias of 9 : 6 : kg m −2 yr −1 (7 : 4% of the mean observed SMB)and a RMSE of 76 , ::: as :::: well :: as :: a ::::  The model-observation comparison by sectors (Fig. 2) reveals a good representation of the coast-to-plateau SMB gradients by both RCMs.MAR and RACMO2 are in good agreement despite MAR not including drifting snow processes whereas RACMO2 does, except in Ross-Mary Byrd Land and in Victoria Land where MAR simulates larger SMB than RACMO2.
Another noticeable result is that MAR forced by ERA-Interim, JRA-55 and MERRA2 give very similar results, not only at the observation locations (Fig. 2) but also at the ice sheet scale (Fig. S4, note the colour map scales compared to Fig. S9).This is why we focus on MAR forced by ERA-Interim in the following.
We find no significant differences in the SMB simulated by MAR and RACMO2 when integrated over the ice sheet or its major basins (Table 2).SMB is driven by snowfall amounts, which are more than 10 times larger than other SMB components.
Snow sublimation in RACMO2 is the sum of sublimation at the surface of the snowpack and of drifting snow sublimation, and is approximately 50 % larger than in MAR which only includes surface snow sublimation.However, surface snow sublimation alone is almost two times larger in MAR than in RACMO2 (Table 2, also shown in Fig. S5), which we investigate in the next section.Modelled surface melt is less than half of the sublimation amount, however liquid water almost entirely refreezes into the snowpack in both models (maps of modelled melt amounts are shown in Fig. S6).Temporal variability of the SMB and its components is fully driven in both RCMs by the forcing reanalyses and are therefore strongly correlated with each other (time series shown in Fig. S7).We do not elaborate on the SMB temporal variability here as this aspect will be further detailed in a forthcoming study.::
Hence, a large part of the discrepancies between modelled and observed SMB is explained by elevation curvature when wind speed is sufficiently high, which we relate to the unresolved erosion-deposition process :::::: drifting :::: snow :::::::: transport : in MAR.

Discussion and conclusion
In our study, we evaluate new estimates of the Antarctic SMB obtained with the polar RCM MAR run for the first time for decades-long simulations at the scale of the whole Antarctic ice sheet.We use model settings comparable to previous MAR simulations over Greenland (Fettweis et al., 2017) but with a specific upper atmosphere relaxation and new fresh :::::: surface snow density and roughness length parameterisations.We present the dynamical downscaling of ERA-Interim, JRA-55 and MERRA2 with MAR for the satellite era  where we can rely on reanalyses products.Remarkably, MAR forced by those three reanalyses give similar spatial and temporal SMB patterns.We also compare MAR with the latest simulations of the RCM RACMO2 forced by ERA-Interim (van Wessem et al., 2017) ::::::::::::::::::::: (van Wessem et al., 2018).We find no significant differences between MAR and RACMO2 SMB when integrated on the AIS and its major basins (Table 2).least 1300 m above the ground for comparison with CloudSat products, but ideally at all model levels below 1500 m above the ground to be able to compute sublimation of precipitation in the low-level atmospheric layers.This was not the case for MAR and RACMO2 outputs used in this study, but it will become a standard output in forthcoming MAR simulations.
We expect that accounting for drifting snow in MAR will lead to significant improvements in describing the Antarctic SMB and surface climate, as it will enable (1) a quantification of the drifting snow sublimation mass sink, (2) a more realistic representation of relative humidity and temperature in the boundary layer, and (3) an explicit modelling of near-zero accumulation areas (wind glaze areas) and of the redistribution of snow ::: the :::::: drifting ::::: snow :::::::: transport : from crests to valleys.Exploring the impact of horizontal and vertical model resolution on drifting snow estimates and on sublimation of precipitation in katabatic channels will also be of importance as those processes are related to the shape of the ice sheet ::: and :: to ::: the :::::::: advection ::: of :::::::::: precipitation :: in ::: the :::::::::: atmospheric :::::: layers.

Figure 2 .
Figure 2. Modelled vs. observed SMB for sectors and transects as detailed in Table1.RACMO2 outputs are bi-linearly interpolated to the MAR grid.SMB values are first averaged on MAR grid cells (Sec.2.2.2) then along chosen grid direction (Fig.S2) or by elevation bins.Distance along transect starts at the coast.Uncertainty of observed SMB (grey shaded area) is the standard deviation of observations contained in each grid cell (sub-grid variability), estimated as a function of the mean observed SMB (see Fig.S3).Despite SMB values corresponding to grid cell averages, we display one marker for each observation, with the x axis corresponding to the observation location along transect or elevation.Markers with white faces are for bins containing less than 10 observations and black faces for bins containing more than 10 observations.Magenta bands mark grid cells where more than 15 % of precipitation sublimates in the katabatic layers according toGrazioli et al. (2017).

Figure 3 .
Figure 3.For each transect, we show (top) annual mean 10 m wind speed, (middle) curvature of elevation and (bottom) difference in SMB between models and observation.Blue lines and colour shading are for MAR(ERA-Interim) outputs and red lines are for RACMO2(ERA-Interim) outputs.Values are computed as in Fig. 2. For Law Dome-Wilkes Land, MAR SMB is shifted by −30 kg m −2 yr −1 .

Table 1 .
Sectors extracted from the GLACIOCLIM-SAMBA database.

Table 2 .
(Shepherd et al., 2018)B on average for 1979-2015 ± one standard deviation of annual values, in Gt yr −1 .Antarctic Ice sheet (AIS) and basins geometry are based on Rignot basins(Shepherd et al., 2018).RACMO2 is bi-linearly interpolated on MAR grid and the same mask is applied to both models, with area given for this mask.SMB is computed as follows: MAR SMB = Snowfall + Rainfall − Surface snow sublimation − Run-off; RACMO2 SMB = Snowfall + Rainfall -Surface snow sublimation -Drifting snow sublimation -