2.1 HIRHAM5 regional climate model

The HIRHAM5 RCM is a hydrostatic model with 31 atmospheric layers, developed from the physics scheme of the ECHAM5 global climate model (Roeckner et al., 2003) and the numerical weather forecast model HIRLAM7 (Eerola, 2006). HIRHAM5 has been optimized to model ice sheet surface processes that are often neglected or simplified in global circulation models. For a full description we refer to Christensen et al. (2007) and Lucas-Picher et al. (2012). Here HIRHAM5 is forced at the lateral boundaries at 6-hourly intervals with relative humidity, temperature, wind vectors, and pressure from the ERA-Interim reanalysis (Dee et al., 2011). Further, daily values for sea ice concentration and sea surface temperature are also used. HIRHAM5 calculates the full surface energy balance at the surface, based on model physics as described in Lucas-Picher et al. (2012), Langen et al. (2015) and Mottram et al. (2017). HIRHAM5 also calculates the amount of snowfall, rainfall, water vapour deposition and snow sublimation that occurs at the surface. Finally, for the HIRHAM5 Antarctic simulations, we used the Antarctic domain defined in the Coordinated Regional Climate Downscaling Experiment (CORDEX) (Christensen et al., 2014) and downscaled it further to 0.11^∘ (≈12.5 km) spatial resolution with a dynamical time step of 90 s.

2.2 Subsurface model

The subsurface model was originally built on ECHAM5 physics (Roeckner et al., 2003) but has been updated to include a sophisticated albedo scheme. Following Langen et al. (2015) the shortwave albedo is computed internally and uses a linear ramping of snow albedo between 0.85 below −5 ^∘C and 0.65 at 0 ^∘C for the upper-level temperature. The albedo of bare ice is constant at 0.4. Furthermore, a transition albedo is calculated for thin snow layers on ice, based on Oerlemans and Knap (1998) with an e-folding depth of 3.2 cm for snow. Moreover, the snow and ice scheme is further developed and thereby updates the subsurface snow layers with snowfall, melt, retention of liquid water, refreezing, runoff, sublimation, and rain (Langen et al., 2015, 2017). Thereby, the subsurface model is forced with the snowfall, rainfall, evaporation, sublimation, and surface energy fluxes from HIRHAM5. These include net latent and sensible heat fluxes and downwelling shortwave and longwave radiative fluxes for 6-hourly intervals over the period 1979–2017. To reduce RCM spin-up effects, such as misrepresentation of the physical state of the atmosphere, e.g. temperature, the first year is removed from the results. Furthermore, the model has been tuned to mimic the average behaviour of the ice sheet surface at a 5–12 km scale. It cannot resolve subpixel processes. However, the small-scale features caused by surface melt translate into an increase in water content in the model. The subsurface scheme is updated hourly by interpolating the 6-hourly forcing files to 1-hourly time steps. To ensure a smooth transition between two 6-hourly files, a linear interpolation in time between the two nearest 6-hourly files is used. The horizontal resolution of the subsurface model follows the 0.11^∘ native resolution of HIRHAM5.

As the Antarctic SMB may be sensitive to the subsurface model set-up, here we use two versions of the subsurface model (Langen et al., 2017). Common for both model versions is the albedo scheme, their meltwater percolation, firn compaction, and heat diffusion schemes. Meltwater in excess of the irreducible water content (Coléou and Lesaffre, 1998) is transferred vertically from one layer to the next using a parameterization of Darcy flow developed by Hirashima et al. (2010), with hydraulic conductivity values calculated from Van Genuchten (1980) and Calonne et al. (2012) and coefficients from Hirashima et al. (2010). The impact of ice content on a layer's conductivity is described by the parameterization by Colbeck (1975). When meltwater can infiltrate into a subfreezing layer, it is refrozen and latent heat is released. Firn density is updated at each time step for compaction under each layer's overburden pressure using the parameterization by Vionnet et al. (2012).

The two model versions differ in the management of the layers within the model. The first model version developed by Langen et al. (2017) has 32 subsurface layers with a fixed predefined mass, expressed in metres of water equivalent (m w.e.), given by $D_N=D_{\mathrm{1}}{\mathit{\lambda }}^{N-\mathrm{1}}$, where N is the given layer and D₁=0.065 m w.e. This fixed model implies an Eulerian framework, meaning that when snowfall occurs at the surface, it is added to the first layer, and an equal mass from that layer is shifted to the underlying layer. The same goes for each layer in the model column. The same procedure is followed when mass is removed from the top layer due to runoff or sublimation. Then each layer takes from their underlying neighbour an amount of snow/firn equivalent to the mass lost at the surface. The temperature and density of the layers are updated as the average between the snow or firn that is received by the layer, and what remains there. In the following we refer to this model version as the Fixed model.

The second model version uses a Lagrangian framework for the layer evolution developed by Vandecrux et al. (2018, 2020a, b). Layers evolve through a splitting and merging dynamic based on a number of weighted criteria. This dynamical model, henceforth referred to as the Dyn model, has 64 subsurface layers, the number of which are fixed during the simulation. When snowfall occurs at the surface, it is first stored in a “fresh snow bucket”. When this snow bucket reaches 0.065 m w.e., its content is added as a new layer at the surface of the subsurface scheme, and two layers need to be merged elsewhere in the model column. The layer merging scheme assesses how likely a layer is to be merged with its underlying neighbour based on seven criteria: the layers' difference in temperature, density, grain size, water content, ice content, depth, and the thickness of the layers. The first five criteria make it preferable to merge layers with small differences. The sixth criterion makes it preferable to merge deep layers rather than shallow layers. In this case the shallow layer limit is set to 5 m w.e.; this criterion carries twice the weight of the first five. The final criterion says that no layer can be thicker than a maximum thickness, in this case 10 m w.e.; this is set to avoid the deepest layers continuing to grow. A weighted average of the criteria, where the first five are weighted equally, while the depth and thickness criteria are weighted double and triple respectively, is used by the model to determine which layers should be merged. When surface sublimation or runoff occurs, it is taken from the snow bucket and then from the top layer. When a layer decreases in thickness and its mass reaches 0.065 m w.e., then it is merged with the underlying layer, and another layer can be split in two elsewhere in the model column. The splitting routine is based on two criteria: thickness of the layer where thick layers are more likely to split and shallowness where shallow layers are more likely to split. The two criteria are weighted $\mathrm{60}/\mathrm{40}$. However, the minimum thickness of any layer is always 0.065 m w.e. to avoid numerical instability. The bottom of the lowest model layer is assumed to exchange mass and energy with an infinite layer of ice with a temperature, like in the Fixed model (Langen et al., 2015), calculated from climatological mean of the HIRHAM5 2 m temperature.

Another difference between the two model versions is that the dynamic-layer model simultaneously melts the snow and ice content of the top layer while the Fixed-layer model melts the snow content first and then the ice content of the top layer. This update aims at preventing the top layer from becoming only ice and a barrier to meltwater infiltration. Furthermore, the Dyn model's runoff is routed downstream using Darcy's law and the local surface slope, whereas the Fixed model follows Zuo and Oerlemans (1996), and excess water in a layer cannot be transferred to the underlying neighbour. Both the Fixed and Dyn versions require a fresh snow density value when adding snowfall at the surface. We here use the Antarctic parameterization from Kaspers et al. (2004), who use local climatological means of skin temperature, 10 m wind speed, and accumulation rates; here the means from HIRHAM5 have been used.

2.3 Experimental set-up

The Fixed model was initialized with a firn column with uniform density of 330 kg m⁻³ and a temperature at the bottom of the firn pack given by the climatological mean of the HIRHAM5 2 m temperature. Spin-up was performed by repeating a decade (1980–1989) multiple times. The state of the subsurface at the end of each decade was used as the initial state for the next iteration. There were no appreciable shifts in the Antarctic climate from 1980–2019 (Medley et al., 2020), so the 1980s can be used as a representative decade for spinning up the subsurface. The Fixed subsurface scheme was spun up over 25 iterations (250 years). Afterwards, the actual experiment ran from 1979–2017. To limit computing time, the dynamical model was initialized with the last spin-up from the Fixed model and extrapolated to the 64 layers of the Dyn model. From then, additional spin-ups (1980–1989) ensured that the dynamical splitting and merging of layers had time to evolve throughout the firn pack. Two spin-up experiments have been carried out for the Dyn model: one that uses 3 decades of additional spin-up (Dyn03), resulting in a total of 280 spin-up years (250 from the fixed model and 30 years in the dynamical model), and one that uses 15 decades of spin-up (Dyn15), resulting in a total of 400 spin-up years.

All three model simulations (summarized in Table 1) provide outputs of monthly and yearly means of all 3D variables (density, grain size, firn temperature, and ice/water/firn content) and daily 2D fields (SMB, runoff, superimposed ice, melt, albedo, ground heat flux, refreezing, diagnosed snow depth (which is an estimate based on the snow concentration in each layer), and net shortwave and net longwave radiation) of the surface variables. Furthermore daily columns for specified coordinates interpolated to the nearest grid cell have been retrieved for comparison of in situ measurements. For the two simulations with dynamical layer thickness, the daily 3D fields are interpolated into a fixed grid, with the same number of layers, so time averages could be calculated.

Table 1Model overview and main differences.

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Figure 1Mean SMB from 1980 to 2017 in mm yr⁻¹ of w.e. (a) The mean of the model mean; note the nonlinear colour bar. (b) West AIS where the δSMB has the largest differences between model versions (model minus ensemble mean).

2.4 Regional drivers and mass balance

The SAM is characterized in Fogt and Bromwich (2006) as the zonal pressure anomalies in the high southern latitudes having opposite sign to those of the midlatitudes. The SAM drives the westerly winds around Antarctica, but the stream oscillates north–south. The SAM can have three phases: positive, neutral, or negative, where positive creates a higher pressure over the midlatitudes and lower pressure over Antarctica and thus moves the westerly winds closer to Antarctica. A negative SAM creates a lower pressure over the midlatitudes and a higher pressure over Antarctica, moving the westerly winds north. When neutral there is no pressure difference anomaly. To investigate how the phase of SAM affects the SMB, monthly SAM data, as calculated by Marshall (2018), have been used. From 1980–2017, 261 months showed a positive SAM (SAM+), 193 months showed a negative SAM (SAM−), and 2 months were neutral. The SAM data are given as one monthly number, i.e. one number for the entire Antarctic domain. To see whether there is a link between SAM and SMB, the monthly SMB values were divided into two groups: SAM+ and SAM−. Then the mean SMB for all months with SAM+ was subtracted from the mean SMB for the entire period and likewise for SAM−. To examine whether there was a statistically robust difference in the δSMB signals, we performed a bootstrapping analysis, using 1200 random resamplings without replacement of the SAM data, to see whether the δSMB signals could be replicated randomly and if it could be produced randomly whether the signal would not be robust. Statistically robustness has been defined as δSMB values falling outside the 5th–95th percentile range. In order to maintain the seasonal variability in the SMB, the SAM data were shuffled in sets of 12 – in this way the order of the months was maintained and thus the seasonal cycle retained. Then confidence intervals were determined as the 5th and 95th percentiles of the distribution of the resampled δSMB values.

Observing the mass balance can be helpful to assess the spatial patterns of SMB and evaluate the modelled results. Mass balance can be derived from gravimetric measurements from space. Here GRACE/GRACE-FO mass loss time series data were computed for the period 2002–2020, using a mascon approach based on CSR R6 level-2 data, complete to harmonic degree 96 (Forsberg et al., 2017). The lowest-degree terms were substituted with satellite laser ranging data and glacial isostatic adjustment corrections from the model of Whitehouse et al. (2012). From Eq. (1) we know that MB should be equal to SMB minus discharge (SMB − D). So to evaluate our SMB model performance, GRACE and SMB − D have been plotted. The discharge values were derived from two studies: Gardner et al. (2018) and Rignot et al. (2019). Gardner et al. (2018) gave values from 2008 and 2015; here we took the mean value and used D_Gardner over the period. Rignot et al. (2019) have derived decadal mean discharge values from 1999–2010 and 2010–2017; for D_Rignot the relevant discharge values were used. The SMB value used here is for the grounded AIS only, and since the modelled SMB values are quite similar over the grounded AIS, it is only shown here for the Dyn15 simulation.

Figure 2Integrated precipitation (a), SMB (b), melt (c), refreezing (d), and runoff (e) all in Gt yr⁻¹. Panel (f) shows the runoff to melt fraction. For the three model simulations, for the entire AIS with ice shelves (ToAIS), and for the GAIS. Note different values on the y axis.

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3.1 Evaluation against observations

Koenig and Montgomery (2019) have, in the SumUp dataset, collected accumulation rates over Antarctica. Here we evaluated the modelled SMB values against the SumUp accumulations assuming that over most of the AIS accumulation is nearly equivalent to SMB. The SumUp dataset has yearly measurements for some locations and mean values for longer periods for other locations. To make it consistent, we computed the yearly mean at each location, shown in Fig. 3a, and compared it with the nearest grid cell in the ensemble mean for the period from 1980 to 2017. If there was more than one measurement in one grid cell, an average was used (Fig. 3b). Lastly, we computed the change between the observations and the ensemble mean in percent (Fig. 3c). In total 2221 measurements have been used, located in 251 different grid cells. The SumUp accumulation dataset has areas with a high concentration of measurements, like Marie Byrd Land, Dronning Maud Land, and Dome Charlie; however, in East Antarctica there are larger areas that are not represented in the SumUp dataset. The accumulation ranges from near 0 to 100 mm w.e. yr⁻¹ at the South Pole, Dronning Maud Land, and Dome Charlie and up towards 1000 mm w.e. yr⁻¹ in Marie Byrd Land and the coast of Dronning Maud Land. Figure 3b shows the difference between the model ensemble mean and the in situ observations where it is seen that there are some large numerical differences in Marie Byrd Land and near the coast in Dronning Maud Land. Figure 3c displays the difference in percent for the δSMB; it shows that only three of the 251 grid cell comparisons have a difference greater than ±100 %. Furthermore half of the 251 comparison points fit within ±13 %.

Modelled firn densities are evaluated using the SumUp dataset (Koenig and Montgomery, 2019). When disregarding firn cores shallower than 2 m, there were 139 density profiles left (Fig. 4). All the references for the firn profiles can be found in the reference list. These profiles vary in depth, from a few metres to 100 m, but the majority are drilled to 10 m depth. Knowing the coring date, we compare it to the modelled density of the nearest grid cell on the same date. Before the inter-comparison, the modelled and observed density profiles were interpolated to the same vertical resolution (if the model resolution is higher than the core resolution, the model is interpolated to fit the core resolution and vice versa). In the SumUp dataset 96 profiles had the exact date given, and seven SumUp profiles only had year and month given. Here the modelled mean density of the given month was compared. Finally 36 cores had only the year given; in these cases the modelled mean density of January was compared, as we assume they were most likely collected in the middle of the standard Antarctic summer field season. To evaluate the model performance we calculate mean difference (MD) and standard deviation (SD) between the modelled and observed firn densities. A statistical comparison of the mean difference and 1 standard deviation between the firn cores and the modelled densities is given in Table 3 for the three simulations. Summed up over the AIS, all simulations overestimate the densities below 550 kg m⁻³ and underestimate the densities above 550 kg m⁻³. It is seen that the Fixed version outperforms Dyn03 and Dyn15 for densities below 550 kg m⁻³. Conversely, Dyn03 and Dyn15 outperform the Fixed version for densities above 550 kg m⁻³. All three simulations show the best statistics for higher densities. The agreement with the in situ cores also varies spatially (Fig. 5). Generally the spatial density bias is consistent between the models.

Figure 4The white colour shows the GAIS, and the grey colours show the locations of ice shelves. The spatial distribution of observations are shown with light brown triangles for borehole temperatures and magenta circles for the location of the density profiles. The grounded basins are derived from Zwally et al. (2012) and outlined by black lines.

Figure 5The density bias between simulations and the observations (model minus core). The outer ring represents densities less than 550 kg m⁻³, and the inner circle represents densities greater than 550 kg m⁻³. Panel (a) is the Fixed model, (b) is Dyn03, and (c) is Dyn15. Each panel shows the entire AIS with three dashed black boxes. Each box outlines a zoom-in area: from east to west the Dronning Maud Land, Filchner–Ronne ice shelf, and Marie Byrd Land. All panels have the same colour bar.

Table 3Mean difference between the modelled and observed firn densities (model – core) and standard deviation of the modelled densities above and below 550 kg m⁻³. In total 139 cores were used; see Fig. 4 for locations.

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Over the Filchner–Ronne ice shelf, in Dronning Maud Land and in Marie Byrd Land the distribution of profiles are quite dense; these areas are marked with boxes (Fig. 5). All simulations overestimate the density of firn over the Filchner–Ronne ice shelf. Of the 36 cores on the Filchner–Ronne ice shelf, only two have underestimated densities in the simulations. The rest of the cores have overestimated densities from 2.5 and up to 200 kg m⁻³. In general all three simulations have the largest biases in this region. If the cores on the Filchner–Ronne were not included in the statistics, the mean deviation for densities below 550 kg m⁻³ would be between 36–38 kg m⁻³; for densities above 550 kg m⁻³ the mean deviation would not change much. Mottram et al. (2021) show that the HIRHAM5 model estimates higher precipitation over the Filchner–Ronne ice shelf than other RCMs, and the overestimate in density may therefore relate to overestimated precipitation in this area, which is compliant with our Fig. 3. However, as they also note, the lack of continuous SMB observations makes it difficult to be certain if and by how much precipitation is overestimated in this region. It could also be due to an overestimation for melt and refreezing over the ice shelf.

In Dronning Maud Land there are 30 cores with a very small bias. The majority of the core densities agree within ±25 kg m⁻³, apart from three cores near the coast that are overestimated by 100 kg m⁻³ in all three simulations.

Marie Byrd Land shows a general pattern of underestimated densities in 37 cores in all simulations. However, Dyn03 and Dyn15 have lower biases compared to the Fixed. In Dyn03 and Dyn15, four cores were underestimated by more than 25 kg m⁻³, compared to five cores in the Fixed model. Both Dyn03 and Dyn15 have six cores where the mean deviations are between 0 and 2.5 kg m⁻³ for densities less than 550 kg m⁻³, but they underestimate densities greater than 550 kg m⁻³, with a mean deviation between 10 and 25 kg m⁻³.

Figure 6Examples of density profiles. In each of the four subfigures, the left-hand plot shows the firn core in black and the modelled density from Fixed, Dyn03, and Dyn15 in red, blue, and green. The right-hand plot shows the difference. The cores are (a) BER02C90_02 taken in 1990 (Wagenbach et al., 1994), (b) DML03C98_09 taken in 1998 (Oerter et al., 2000), (c) FRI14C90_336 taken in 1990 (Graf and Oerter, 2006), and (d) Site 11 taken in 2013 (Morris et al., 2017).

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For the Ross ice shelf cores and near the South Pole, the Fixed simulation overestimates most of the cores, some of them by 50 to 100 kg m⁻³ for densities less than 550 kg m⁻³ and more than 100 kg m⁻³ for densities greater than 550 kg m⁻³. However, for Dyn03 and Dyn15 we also observe an overestimation of most cores, but only six of them are overestimated by more than 25 kg m⁻³.

Figure 6 shows 4 of the 139 firn cores: core BER02C90_02 (Wagenbach et al., 1994) (Fig. 6a), core DML03C98_09 (Oerter et al., 2000) (Fig. 6b), core FRI14C90_336 (Graf and Oerter, 2006) (Fig. 6c), and core Site 11 (Morris et al., 2017) (Fig. 6d). These four cores are selected because they are located in different regions of the AIS, and, furthermore, they show different examples of under-/overestimations of modelled densities. The Fixed simulation fit quite well (±20 kg m⁻³) with the core taken on Berkner Island (Fig. 6a), whereas Dyn03 and Dyn15 show a larger bias mainly at the surface and the top 3 m of the firnpack. The core from Dronning Maud Land (Fig. 6b) has a high vertical resolution; the deeper the cores go, the smaller the biases become. Cores FRI14C90_336 and Site 11 are taken on the Ronne ice shelf and in Marie Byrd Land respectively. The model densities in FRI14C90_336 are overestimated below 1 m depth, and the mean bias is 200 kg m⁻³. At Site 11 all simulations underestimate the density; however below 2 m depth, the underestimation is nearly constant with a mean bias of −20 kg m⁻³.

The modelled subsurface temperatures are evaluated against observed 10 m firn temperature measurements from 49 boreholes (van den Broeke, 2008) (see Fig. 4 for the locations). Most of the temperatures were taken in the 1980s and 1990s; however only the year or decade is known for when these were taken. Therefore they are compared with the modelled mean 10 m firn temperature from 1980–2000. We evaluated the model performance using the root-mean-square difference (RMSD), mean difference (MD), and coefficient of determination (R²). Subsurface temperatures are only sparsely available in Antarctica. The measured 10 m firn temperatures are compared with the modelled mean 10 m firn temperature of the nearest grid cell (Fig. 7). The red, blue, and green lines are the regression lines of first order, for Fixed, Dyn03, and Dyn15; they have an R² of 0.98, 0.97, and 0.98, respectively. It is assumed that the in situ temperatures are true, so the errors are in the modelled temperatures. For temperatures below −30 ^∘C the three simulations are in agreement, but in warmer firn temperatures > −30 ^∘C, the agreement becomes worse. The mean deviation of the three model simulations is listed Table 4.

Table 4Mean deviation, root-mean-square deviation, and coefficient of determination, for the modelled and observed 10 m temperature.

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Figure 7The dots are 10 m temperature from boreholes vs. mean model 10 m temperature. The solid lines are the regression lines of first order, and the grey dashed line shows the diagonal.

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4.1 Satellite gravimetric mass balance

Over the AP there is a large disagreement between SMB − D_Gardner and SMB − D_Rignot, the mean discharge values differ by 90 Gt yr⁻¹, with D_Rignot being the largest. This results in opposite trends of SMB − D. SMB − D_Gardner shows a mass gain of around 600 Gt, and SMB − D_Rignot shows approximate mass loss of 1150 Gt over the period, whereas GRACE has a mass loss of around 400 Gt for the period (Fig. 8a). There are times when the variability between GRACE and the two SMB-D graphs follows each other, e.g. local peak around year 2006, 2011, and 2017. Since the discharge is plotted as a constant, this variability originates from the SMB model, most likely precipitation. This means that the D_Gardner value is too small, D_Rignot values are too large, or the SMB magnitude is too low or high depending on which discharge is used. As the resolution of GRACE is quite coarse, it can add to the uncertainties over the AP, because of narrow topography. Over the grounded West AIS the trend of GRACE, SMB − D_Rignot, and SMB − D_Gardner agrees. They all see a mass loss, of around 2000, 2150, and 1700 Gt, respectively, for the overlapping period (Fig. 8b). The discharge values from the two studies differ only by 2 Gt yr⁻¹ from 2002 to 2010 but by 50 Gt yr⁻¹ from 2010 to 2017, with D_Gardner being the lowest. GRACE measures a smaller mass loss in the beginning of the period, and then around 2009 the GRACE mass loss increases. Both Gardner et al. (2018) and Rignot et al. (2019) have found an increasing discharge in West Antarctica. However due to the limited temporal resolution from Gardner et al. (2018), the discharge is assumed constant, resulting in an equal offset in SMB − D from 2002–2009, but then diverging results from 2010. This shows that in areas where there are large changes in the dynamic mass loss, discharge values with a higher temporal resolution are needed.

Figure 9SMBa (monthly values minus mean values) in months for SAM− (a) and SAM+ (b), for each basin. The vertical dashed lines split the basins into areas. Starting from the left, we show basins towards the Weddell Sea, Dronning Maud Land, eastern coast, Ross Sea, western coast/Amundsen Sea, and Bellingshausen Sea. The thin bars are the 5th and 95th percentiles, for the bootstrapping analysis with 1200 runs. Locations of the basins can be seen in Fig. 4. In basins where the SMBa values fall outside the percentiles, there is a robust relationship between the SMB and SAM.

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Over the East GAIS the agreement between GRACE and SMB − D_Gardner is remarkably good. Between 2009 and 2011 large snowfall events were observed in Dronning Maud Land (Boening et al., 2012; Lenaerts et al., 2013) (basins 5–8 in Fig. 4). These snowfall events led to rapid mass gain, which is seen in both GRACE and SMB − D_Gardner, especially in 2009–2010 (Fig. 8c). This mass gain is less pronounced in SMB − D_Rignot because it estimates an overall mass loss for the period. In the SMB signal there are yearly variabilities; however, these variabilities are larger in the GRACE data compared to SMB − D. For the entire GAIS GRACE detects a mass loss of 900 Gt, SMB − D_Gardner shows a mass gain of 500 Gt, and SMB − D_Gardner shows a mass loss of 4000 Gt, for the overlapping period 2002–2017. The majority of that difference between GRACE and SMB − D_Gardner can be attributed to the AP. The difference between GRACE and SMB − D_Rignot arises from the AP and East GAIS.

4.2 Circulation effects on SMB and the Southern Annular Mode

We observe a robust (outside the 5th–95th percentile range) relationship between SMB and SAM in 13 out of the 27 basins (Fig. 9a and b). For each phase of the SAM, SMB anomalies (SMBa) are defined as the SMB in months with a SAM− or SAM+ monthly mean minus SMB over the full period. The SMBa for SAM−, when the westerlies are further away from the Antarctic continent, shows magnitudes well outside the percentiles for all model simulations. Basins 2 and 3 that have outlets to the Filchner–Ronne ice shelf (EAIS); basin 4 in Dronning Maud Land (EAIS); basin 7 in Enderby Land (EAIS); basins 9, 10, and 12 surrounding the Amery ice shelf (EAIS); basins 17, 18, and 19 with an outlet into Ross ice shelf; basin 20 in Marie Byrd Land (WAIS); and basins 24 and 25 located on the windward side of the AP are particularly affected by SAM−. For SAM+, when the westerlies are closer to the continent the SMBa magnitudes are generally smaller and have an opposite sign; however we see the same pattern in the same basins as for SAM−. A SAM+ phase results in a relatively low pressure over the AIS compared to the midlatitudes, and we see a negative SMBa in 16 of 27 basins, namely 6, 9–13, 15–23, and 26 (Fig. 9b). Marshall et al. (2017) reported a similar signal for precipitation, which confirms our results since precipitation is the main driver of SMB. Basin 26 shows a negative SMBa, and basin 27 has a slightly positive SMBa, which is due to the steep orography on the windward side of the AP creating a shadowing effect on the leeward side of the AP. For SAM− the SMBa signal is opposite, and the mean magnitude of the signal is 26 % larger in all basins (Fig. 9a). During months of SAM+ the average SAM index is 1.45. Figure 9 shows that basins 1–5, 7, 14, 24–25, and 27 have SMB anomalies (SMBa) of the same sign as the SAM: SMB is 0.28 Gt per month higher than average in the case of SAM+ and 0.39 Gt per month lower than average in the case of SAM−. Those basins are mostly located in the east, Ross, and Amundsen Sea sectors. Contrastingly, basins 6, 8–13, 15–23, and 26 have SMB 0.32 Gt per month below average in months of SAM+ and 0.43 Gt per month above average in months of SAM−. These basins are mostly located in the Weddell Sea, Dronning Maud Land, and Bellingshausen sectors. For months with SAM− the average SAM index is −1.36. We can see that for SAM of similar absolute magnitude, SAM− has a stronger impact on SMB over the GAIS.

In both positive and negative SAM events basins 24 and 25 on the windward side of the AP show strong correlation between the SAM index and SMB magnitude also reported by Marshall et al. (2017). So even though the AP is narrow (50 to 300 km across) the SAM plays an important role. Comparing with Vannitsem et al. (2019), we see agreement in large parts of West Antarctica. However, it is difficult to compare in East Antarctica because we use basins, and most of them go far inland, whereas Vannitsem et al. (2019) defined narrow coastal regions and one large plateau region.

From 1980 to 2017 the SAM has become more positive (Fogt and Marshall, 2020), this positive trend in the SAM is attributed to stratospheric ozone depletion (Thompson et al., 2011; Fogt et al., 2017). If this trend continues the basins on the leeward side of the AP will see a smaller mass gain in the future, which could accelerate the collapse of the Larsen ice shelf. This is also seen in basins 9, 10, 11, and 12 surrounding the Amery ice shelf and basin 21 where Thwaites glacier is located. Not all of the above-mentioned basins show δSMB signals that are statistically robust (i.e. the signals are within the 5th or 95th percentiles), but if the trend in the positive SAM continues, it might become an important factor in the future (Fogt and Marshall, 2020).

It is thus important to take the SAM phases into account when investigating the SMB at a regional scale. Furthermore it is extremely important that global circulation models resolve the SAM realistically if future climate projections are to be used with confidence to make projections of sea level rise from Antarctica.