Model evaluation

The SMB product is evaluated using 1611 local (in situ) annual balance measurements from 101 sites (Fig. 1a) collected in the ablation and accumulation zones of Svalbard glaciers over the period 1967–2015 (see “Methods” section; Supplementary Fig. 2a). Good agreement with the SMB product is found (R2 = 0.63), with a small positive bias of 5 mm w.e. yr−1 (water equivalent). Note that significant deviations (RMSE) of up to 440 mm w.e. yr−1 remain locally (Supplementary Fig. 2a). Unlike the downscaled SMB product, stake measurements in the accumulation zone do not include internal accumulation from the refreezing of melt and rain (see “Methods” section). Ignoring internal accumulation when comparing the model to stake measurements located in the accumulation zone leads to a small RMSE increase of  ~50 mm w.e. yr−1. We estimate an uncertainty in total Svalbard SMB of 1.6 Gt yr−1 (~25%) for the period 1958–2018 (see “Methods” section). Using data from the moderate resolution imaging spectroradiometer (MODIS) satellite over 2000–2018, we also evaluate the modelled bare ice area, i.e. the part of the ablation zone where bare ice is exposed after the seasonal snow has melted (Supplementary Fig. 2b). To that end, we divide Svalbard into six sectors (Fig. 1a) namely Northwest (NW), Northeast (NE), Vestfonna (VF), AF, Barentsøya and Edgeøya (BE), and South Spitsbergen (SS). With 93% of the variance explained and an average negative bias of 90 km2, modelled and observed bare ice area compare very well (Supplementary Fig. 2b).

We assume that solid ice discharge estimate for 2000–2006 (D = 6.8 ± 1.8 Gt yr−1)13 is valid for the whole study period (1958–2018). In line with Dunse et al. (2015)20, we increase solid ice discharge by 4.2 ± 1.6 Gt yr−1 from 2012 onwards, following the surge of a major AF outlet glacier. Combining this with the downscaled SMB product, we reconstruct the mass change of Svalbard glaciers over the last six decades (Fig. 2). The modelled mass change is obtained by integrating both SMB and D in time starting from zero in 1958. Our reconstruction agrees very well with remote-sensing records from GRACE (2002–2016)10 and ICESat/CryoSat-2 altimetry (2003–2018) with R2 = 0.93 and 0.98, respectively (Supplementary Fig. 2c). Not only the recent mass trends but also the seasonal and interannual variabilities are accurately reproduced. Supplementary Table 1 compares our results to other mass change estimates derived from geodetic techniques1,11, GRACE5,6,7,8,10, SMB models including a positive degree day25, two energy balance models26,27, two regional climate models21,22, and in situ measurements12.

Fig. 2: Cumulative mass change of Svalbard glaciers and contribution to sea level rise.

Time series of monthly cumulative modelled SMB, measured cumulative solid ice discharge (D)11,12 and reconstructed cumulative mass balance (MB = SMB−D) for the period 1958–2018. Observed mass change derived from GRACE (2002–2016), ICESat (2003–2009) and CryoSat-2 (2010–2018) are also shown. For clarity, GRACE data are shown with a positive offset of 100 Gt. The right y-axis translates Svalbard cumulative mass balance into global sea level rise equivalent. Supplementary Fig. 2c zooms in on the satellite period (2003–2018).

Recent mass loss onset

Our reconstruction shows that Svalbard glaciers remained in approximate balance (SMB ≈ D) until the mid-1980s (Fig. 2), i.e. the surface mass gain compensates the dynamic mass loss from calving13. Net mass loss starts around 1985, primarily due to a persistent SMB decrease, reinforced from 2012 onwards by enhanced ice discharge20, but with a mass loss pause between 2005 and 2012. Our reconstruction suggests that Svalbard has lost  ~350 Gt of ice since 1985, contributing  ~1 mm to global sea level rise (Fig. 2). Both remote-sensing data and our reconstruction show that Svalbard glaciers have experienced mass loss since the mid-1980s, including the pause between 2005 and 2012. Understanding the drivers of the pronounced post-1985 mass loss variability requires investigating spatial and temporal fluctuations in individual SMB components.

Ablation zone expansion and firn line retreat

Figure 3a shows time series of individual SMB components covering the period 1958–2018. The ice caps of Svalbard experience average summer melt (1958–1984 average of 28.7 Gt yr−1, Supplementary Table 2) that exceeds annual total precipitation (23.0 Gt yr−1 including rain and snow) by 25%. This proves that retention of surface meltwater in the firn through refreezing is crucial to sustain these ice caps. The refreezing capacity is defined as the fraction of liquid water (melt and rain) that is retained in the firn. Before 1985, the refreezing capacity was 54%, reducing meltwater runoff (16.3 Gt yr−1) and resulting in a positive SMB (6.3 ± 1.6 Gt yr−1; Fig. 3a). This surface mass gain was almost exactly offset by solid ice discharge (6.8 ± 1.8 Gt yr−1)13.

Fig. 3: Ablation zone expansion and reduced refreezing capacity.

a Time series of annual SMB and components including surface melt, runoff, total precipitation, and refreezing for the period 1958–2018. b Time series of annual ELA for the whole of Svalbard (black) and individual sectors (Fig. 1a, orange band). c Time series showing the modelled ablation zone area, the modelled and observed (MODIS) bare ice area as a fraction of the total Svalbard land ice area (%). d Time series of annual refreezing capacity for the whole of Svalbard (black) and individual sectors (cyan band). Dashed lines show averages for the periods 1958–1984 and 1985–2018. The grey shade highlights the period 2005–2012 when Svalbard SMB temporarily returned to the pre-1985 SMB conditions. Dashed grey lines represent the 2005–2012 mean conditions.

Following a modest atmospheric warming (+0.5 °C; 1985–2018 minus 1958–1984), the average equilibrium line altitude (ELA; local SMB = 0) moved upwards by  ~100 m, from  ~350  to  ~450 m a.s.l. (Fig. 3b). The orange band in Fig. 3b spans the six regional ELA values, the change ranging from +80 m in SS to +130 m in the NE sectors (Supplementary Tables 2 and 3). The ELA increase caused a rapid retreat of the firn line, as shown by the post-1985 growth of the bare ice zone (+75%; Fig. 3c) in good agreement with MODIS records (see “Methods” section). As a result, the ablation zone expanded from 27% to 44% of the total glacier area (Fig. 3c). While total precipitation did not significantly change after 1985 (−1%), surface melt increased by 24%, exceeding accumulation by 58%, while the refreezing capacity declined from 54% (1958–1984) to 41% (1985–2018; Fig. 3d). The blue band in Fig. 3d spans the six individual regions that underwent a simultaneous and similar decline in refreezing capacity, ranging from 22% in NW to 36% in BE sectors, respectively (Supplementary Tables 2 and 3). Consequently, SMB became predominantly negative (−2.6 ± 1.6 Gt yr−1), initiating the post-1985 mass loss of Svalbard glaciers. We conclude that all regions in Svalbard experienced rapid ablation zone expansion and reduced firn refreezing capacity, resulting in strongly increased meltwater runoff (+55%), driving the post-1985 glacial mass loss (MB = −10.2 ± 3.4 Gt yr−1; Supplementary Table 3).


Compared to other Arctic ice masses23,24, Svalbard glaciers have a low elevation and are relatively flat with a marked hypsometry peak at  ~450 m a.s.l. (Fig. 1b). Before 1985, the ELA was at 350 ± 60 m a.s.l., well below the hypsometry peak (Figs. 1, 3b and Supplementary Fig. 3a). In this period, 70% of the total glacier area was covered with extensive firn zones, in which most meltwater and rain were refrozen. This kept the SMB positive, as runoff remained smaller than snow accumulation (Fig. 3a). Following a modest atmospheric warming after 1985, the ELA moved upward by  ~100 m to 440 ± 80 m a.s.l. (Fig. 3b and Supplementary Fig. 3b), nearly coinciding with the hypsometry peak (Supplementary Fig. 3d). This rapidly expanded the ablation zone, exposing large areas to increased melt. The subsequent firn line retreat strongly reduced the fraction of melt that refreezes above the pre-1985 ELA (Fig. 3d), enhancing runoff 75% faster than melt (+8.9 vs. +6.7 Gt yr−1). Supplementary Fig. 4a shows the ELA change across Svalbard as a result of the post-1985 warming (R = 0.82; Fig. 4a). The ablation zone extent increases non-linearly with the upward migration of the ELA (Fig. 4b), reflecting the proximity of the hypsometry peak (Fig. 3b, c). The size of the ablation zone in turn governs meltwater production (Fig. 4c), since most of the melt is produced over low-lying marginal glaciers exposing dark bare ice (Supplementary Fig. 4b). In the absence of refreezing, the low albedo of exposed ice increases melt through enhanced absorption of incoming solar radiation, in turn driving the runoff increase. Most remarkably, increased melt triggers a pronounced non-linear decrease in refreezing capacity (Fig. 4d), as (i) the firn line retreat strongly reduces the firn area hence limiting meltwater retention, and (ii) meltwater fills the pore space of the remaining firn through refreezing. These mechanisms could likely be reinforced by increased rainfall episodes in a warmer climate, further reducing firn refreezing capacity30.

Fig. 4: Sensitivity of Svalbard refreezing capacity to atmospheric warming.

Scatter plots showing Svalbard-wide correlations between a June–July–August 2 m air temperature anomaly (1985–2018 minus 1958–1984) and ELA. b ELA and ablation zone area, c ablation zone area and surface melt, and d melt and firn refreezing capacity. Statistics include number of records (N), correlation (R), and fitting parameters (ac). e Post-1985 change in refreezing capacity (%; 1985–2018 minus 1958–1984). ELA for the period 1985–2018 is also shown as a black line.

Regionally, the upward migration of the ELA is largest in the northernmost sectors, e.g. NE (+130 m) and AF (+120 m), compared to southern sectors with an average of +85 m (Supplementary Tables 2 and 3). As a result, the ablation zone also grew fastest in the north, e.g. NE (+73%), VF (+91%), and notably AF (+137%; Supplementary Fig. 4a) compared to southern sectors (+48% on average; Supplementary Tables 2 and 3). For the northern sectors, this resulted in a 66–71% runoff increase after 1985, i.e. well above the Svalbard average (+55%; Supplementary Tables 2 and 3). These three northernmost sectors exhibit a stronger response to atmospheric warming because of a pronounced decline in refreezing capacity across their accumulation zones (-40% locally; Fig. 4d, e), increasing runoff at all elevations (Supplementary Fig. 4b). These results are in line with the study of Van Pelt et al. (2019) (see their Fig. 9d)27. Since it has the largest accumulation zone, the strongest sensitivity to atmospheric warming is found for AF ice cap (AF sector), containing a third (~2500 km3)16 of the total ice volume in the archipelago. In contrast, for regions with smaller accumulation zones (NW and SS) or that had already lost most of their refreezing capacity before 1985 (BE; Supplementary Table 2), the runoff increase is restricted to the margins (Supplementary Fig. 4b), and primarily driven by ablation zone expansion rather than loss of refreezing capacity (Fig. 4c).

The fact that the ELA now fluctuates around the hypsometry maximum makes Svalbard glaciers highly sensitive to changes in atmospheric temperature. During warm summers, the ablation zone now covers more than half of the surface area of most ice caps (Fig. 3c). In the warm summer of 2013, the ablation zone even covered 77% of the land ice area (Fig. 5b), almost twice the post-1985 average (44%; Supplementary Table 3). This pronounced expansion stems from the fact that in 2013 the ELA moved to 590 m a.s.l., i.e. above the hypsometry peak (Supplementary Fig. 3d). Consequently, the refreezing capacity dropped to 28% (2013), more than doubling runoff compared to previous years (47 Gt yr−1; Fig. 3a). We conclude that the post-1985 decline in refreezing capacity will persist under continued warming: a temporary return to pre-1985 SMB values in the period 2005–2012 (Figs. 3a and 5a) did not lead to the recovery of the refreezing capacity (Fig. 3d). At the current mass loss rate (19.4 ± 3.4 Gt yr−1 for 2013–2018), Svalbard glaciers would completely melt within the next 400 years.

Fig. 5: Ablation zone expansion in summer 2013.

a SMB average for the period 2005–2012, with SMB conditions similar to 1958–1984. b SMB for year 2013 highlighting how fast the ablation zone expands when the ELA migrates well above the hypsometry maximum (~450 m a.s.l.). From the thickest to the thinnest, black lines outline the ELA for periods 1958–1984, 1985–2018 (a and b) and year 2013 (b only).

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