The simulations presented in this paper were created using the full energy balance model CryoGrid, which is forced by both CARRA reanalysis and AROME-ARCTIC forecasts. The workflow used is described below.

First, both the CARRA reanalysis and AROME-ARCTIC forecasts are evaluated against available observations from automatic weather stations (AWSs). Unsurprisingly, both products performed well when compared to AWSs which had been assimilated into the forcing products but had larger biases when compared to glacier AWSs which had not been assimilated. The comparison of AROME-ARCTIC and CARRA at the AWS locations were similar, albeit with larger biases and root mean square errors for AROME-ARCTIC. In addition, the consistency between the two forcings is evaluated for the overlap period (2016–2021). We found that AROME-ARCTIC is on average colder than CARRA, particularly in NW Spitsbergen where the average yearly temperature was -2 ∘C colder in AROME-ARCTIC. The full results of this analysis are described in Sect. S2 in the Supplement.

We then perform a 30-year spin-up of the CryoGrid model (described in Sect. ) for the glaciated grid points by repeating the 1991–2000 CARRA forcing to initialise the snow and ice temperature, density, and water content. The model is initialised with 47 layers of ice with a thickness between 0.1 and 1 m, totalling 20 m of glacier ice. Initially, the entire domain consists of temperate, pure glacier ice, i.e. the ice temperature of the entire column is 0 ∘C. Tests were conducted with lower initial temperatures (-5 ∘C), but it did not affect the temperature profile at the end of the spin-up. At the end of the spin-up period, the runoff, refreezing, sub-surface temperatures, and climatic mass balance reached stable values. For the non-glaciated land points, only a 2-year spin-up was used.

The energy and mass balance model CryoGrid is then used to simulate the mass balance components of both glaciers and seasonal snow from 1991–2021 using the CARRA reanalysis as forcing. The output from the CryoGrid simulations is evaluated against in situ mass balance observations and geodetic estimates. More details on the evaluation is provided later in this section.

Lastly, a second simulation with CryoGrid, this time forced by AROME-ARCTIC, is conducted from 2016 to the present. From 2016 until the summer of 2019, the AROME-ARCTIC model was initialised with too little snow over some glacier points in the ablation area, thus leading to unrealistically high surface and 2 m temperatures. To counter this effect, we use the 10 m temperature for the AROME-ARCTIC-forced simulation when unrealistically high surface temperatures occur. The AROME-ARCTIC-forced simulation is initialised from the CARRA-forced simulation at the end of 2015. Thus, the initial conditions for the 2016–2021 period are identical for the two simulations. This most likely will reduce the difference in CMB calculated using the two products compared to if different spin-ups were produced. The AROME-ARCTIC-forced CryoGrid simulations are currently automatically updated on a daily basis. In this study, we present the simulations spanning until 1 September 2022.

For the CryoGrid simulations, a fractional glacier mask is created by computing the percentage of glacier coverage in each grid point. The glacier coverage is based on the extent in the 2000s, based on the inventory of . Any points which have a fractional coverage between 10 % and 90 % are calculated with both the glaciated and non-glaciated land schemes. To calculate the average or sum of a variable for a specific region or all of Svalbard, the results are weighted based on the fractional glacier coverage.

Meteorological forcing fields of 2 m air temperature, specific humidity, incoming long- and short-wave radiation, pressure, and mass fluxes were obtained from both the Copernicus Arctic Regional ReAnalysis (CARRA) dataset and AROME-ARCTIC weather forecasts e.g..

CARRA is based on the non-hydrostatic numerical weather prediction model HARMONIE-AROME . It uses ERA5 reanalysis as boundary conditions and downscales it to a 2.5 × 2.5 km resolution over the European Arctic. The simulations are divided into two domains. Here we use the east domain, which contains Svalbard, Franz Josef Land, Novaya Zemlya, and northern Norway. CARRA currently spans the time frame from September 1990 to December 2021.

Similar to CARRA, AROME-ARCTIC e.g. is also based on HARMONIE-AROME and provides operational forecasts at a 2.5 × 2.5 km resolution over the Barents Sea region. It uses ECMWF HRES (high-resolution) forecasts as lateral boundary conditions. The model has been operated by the Norwegian Meteorological Office since October 2015 and provides 66 h forecasts with hourly resolution every 6 h. Since this is a real-time forecast product, there are occasionally gaps in the forecast. When possible, we use the forecast initialised at 18:00 UTC, as most data are assimilated at this time. We use a 6 h lead time and extract data for 24 h at a time, thus using forecast time steps 6–30 for the simulations. This is chosen to optimise the prediction quality as well as to avoid spin-up effects. When the 18:00 UTC forecast is not available, we use longer lead times of previous forecasts to find the most recent available estimate at a given hour. In the rare case that no forecast is available for the desired period, we simply interpolate between the previous and following available time steps. Since CARRA and AROME-ARCTIC are on slightly different grids, we bilinearly interpolate the AROME-ARCTIC fields onto the CARRA grid in order for the final dataset to be consistent.

For the evaluation of the model forcing, observations from 26 automatic weather stations (AWSs) are used: 6 stations on glaciers and 20 stations on non-glaciated land (see Fig.  and Table ). The 20 stations on non-glaciated land are all operated by the Meteorological Office in Norway (MET-Norway) and have been assimilated into the CARRA and AROME-ARCTIC products. The six glacier stations, on the other hand, have not been assimilated and thus provide independent reference. The glacier stations are located on Etonbreen, operated by the University of Oslo and the Norwegian Polar Institute since 2004 (e.g. ); Kongsvegen, operated since 2007 by the Norwegian Polar Institute ; Vestfonna, operated for 2 years between 2007–2009 by Uppsala University ; and Nordenskiöldbreen and Ulvebreen, operated by Utrecht University since 2009 and 2015, respectively. The measurement interval was between 1–2 min, depending on the station. The measurement height varies between stations and during the year due to the accumulation of snow below the sensors. When available, daily mean observations of the 2 m temperature, 2 m relative humidity, 10 m wind speed, and incoming and outgoing long-wave and short-wave radiation are used for the evaluation. When wind speed is only available below 10 m, as is the case for most of the glacier stations, the wind speed at 10 m is calculated using a logarithmic wind profile (assuming neutral stratification) with a roughness length of 1 mm. The assumption of neutral stratification, however, is a limitation, potentially having a larger impact on the wind speed correction than sensor level alone. For Nordenskiöldbreen and Ulvebreen, measurements were conducted at approx 4 m above the surface, and the CARRA humidity and temperature is therefore interpolated to the measurement height by interpolation between the lowest model level (15 m) and 2 m.

The snow depth is not measured at the majority of the used stations, and we therefore do not apply any correction factor due to changes in height after snow accumulation. The uncertainty associated with ignoring this effect depends on the specific variable (temperature, humidity, wind speed) and the measurement height. These uncertainties only affect the evaluation statistics and not the model results.

Snow depths on Svalbard are modest and seldom amount to more than 1 m at most AWS sites. Assuming a snow depth of 1 m, a roughness length of snow of 1 mm, and that the wind speed can be approximated by a logarithmic profile (neutral stratification), the wind speed at 1 m above the surface is 7 % lower than the wind speed at 2 m. For wind speeds measured at 10 m, decreasing the height by 1 m only amounts to a 1 % decrease in wind speed. The wind speeds measured at the MET Norway stations and Kongsvegen, which are measured at 10 m, are therefore more robust to the effect of snow accumulation. The study by suggests a roughness length smaller than 1 mm which in turn would decrease the effect on wind speed.

It is trickier to estimate the uncertainties for temperature and relative humidity. Here, we use CARRA estimates of the temperature, pressure, wind speed, and humidity at the lowest model level (15 m) and at surface level to interpolate the temperature and specific humidity, taking into account the stability of the atmosphere. The same method and parameters are used within CARRA to calculate variables at 2 m height and are described in detail in the CARRA product user guide . The difference in temperature and humidity for all station locations is simulated for 2 m and 1 m above the surface over 2 different years (1994, a low melt year, and 2020, a high melt year). Even assuming that the snowpack lasted the full year, the yearly average deviation was <0.2 ∘C. The specific humidity at surface level was not available in CARRA, so for simplicity we assume fully saturated conditions. The yearly average difference in the results was always below 1 %.

In addition, observations from mass balance stakes are used for the evaluation of the CryoGrid products. When several observation points fall within one 2.5 × 2.5 km model grid, only the measurement point closest to the centre of the grid point is used. A total of 52 measurement points are used, spread over eight glaciers and ice caps (Table  and Fig. ). The stake heights are recorded once or twice a year (typically in April and September) and are converted into summer and winter mass balance estimates using snow density and snow depth data. Stake data on Austre Brøggerbreen (BRG), Midtre Lovénbreen (MLB), Kongsvegen (KNG), Holtedahlfonna (HDF), and Linnébreen (LNB) have been collected by the Norwegian Polar Institute e.g., with the oldest record dating back to 1967. The Polish Academy of Sciences have measured mass balance stakes on Hansbreen (HBR) since 1989 . The University of Oslo and the Norwegian Polar Institute started mass balance measurements on Etonbreen (ETN) on Austfonna in 2004 e.g., while Uppsala and Utrecht universities initiated stake measurements on Nordenskiöldbreen (NSB) in 2006 e.g..

Observations of runoff from glaciated catchments are sparse, but daily simulated runoff is compared to available discharge measurements from two catchments on Svalbard: Bayelva and de Geerdalen. The total area of the Bayelva catchment is 31 km2, of which 54 % is covered by glaciers. The discharge is measured using a pressure transducer and a float and wire system, which records the water level in a concrete-floored weir. The system is calibrated periodically to derive a rating curve that converts water level to discharge . The total area of the de Geerdalen catchment is 79 km2, with 10 % covered by glaciers. Discharge measurements are conducted in a narrow gorge with a stable bedrock profile using a similar system as for Bayelva . In early summer, discharge from both catchments is mainly from snowmelt, while in late summer, rainfall and glacier runoff contribute to the water flow. The monitoring at both stations is unattended, and thus the discharge data have periods with erroneous readings, mostly caused by ice or snow build-up at the sensor . However, the timing of discharge events is generally not affected.

In addition to the in situ measurements of mass balance performed by stake measurements, we use estimates of the geodetic mass balance for validation of the CryoGrid product. The geodetic mass balance is found by taking the difference between elevation data at different dates to find the change in volume. This volumetric change is then converted into mass balance by assuming a value for the bulk density. Unlike the climatic mass balance estimates provided in this study, geodetic mass balance includes frontal ablation from marine-terminating glaciers. Therefore, we only compare our results to the geodetic balance of land-terminating glaciers.

Several studies have provided estimates of the geodetic mass balance of glaciers on Svalbard (e.g. ), but here we use the estimate by , who used Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) imagery for determining the geodetic mass balance of all glaciers on Earth from 2000–2019. The results are available for all glaciers in the Randolph Glacier Inventory at a temporal resolution of 1, 2, 4, 5, 10, and 20 years. Here, we use the 5-year mass balance estimate for all land-terminating glaciers on Svalbard for model comparison (see Fig. ).

The glacier module consists of layers of pure ice with a user-defined constant ice thickness. This module has not been altered compared to the one described in . For this study, 47 layers with a thickness between 0.1 and 1 m were used, totalling 20 m of ice. Previous mass balance studies of Svalbard have used constant ice albedo values in the range of 0.3–0.4 (e.g. ) for all of Svalbard. From calibration with available mass balance observations, we found the best results using an ice albedo of 0.4. When mass is removed from the model by runoff, evaporation, or sublimation, mass is shifted up from an infinite ice reservoir below into the lowest model layer. This is done to prevent the glacier from disappearing during long spin-ups due to the lack of ice flow. The infinite reservoir is assumed to have the same temperature as the lowest model layer. If there is no snow on the surface, any excess water from rain or melt runs off instantaneously.

If snowfall is added to the model, a snow module is added on top of the glacier ice or firn (see Fig. ). If the snow survives on the glacier surface for more than 1 year, the snow layer is moved to a firn scheme. The snow and firn schemes have the same model physics for this application, but newly fallen snow will not be mixed with a firn layer. These modules have been specifically added to the model for this study. The snow and firn modules follow a slightly altered CROCUS snow scheme as described in . Some of the main differences to the snow schemes presented in are

additional output variables, including refreezing, internal accumulation, CMB, and SMB;

Figure  shows the average yearly temperature and precipitation in CARRA over 1991–2021, as well as significant trends (p<0.05) in both variables. The average temperature over Svalbard land areas is -7.9 ∘C, with the highest average annual temperatures over low-elevation non-glaciated land (up to -2.0 ∘C) and the lowest temperatures over high-elevation glacier points (down to -12.8 ∘C). There is a significant positive trend in the temperature at all points (p<0.05), with an average trend of 1.4 ∘C per decade (p<0.01). The largest trends are in the east of Svalbard (up to 2.4 ∘C per decade), while the lowest trend is along the west coast (down to 1.0 ∘C per decade).

The average precipitation over Svalbard is 0.62 mw.e.yr-1. There is a small but significant trend in the average yearly precipitation of 0.05 mw.e. per decade (p<0.01). There is a larger trend in the precipitation over glacier-covered points (0.06 mw.e. per decade) than non-glacier-covered points (0.03 mw.e. per decade). Although there is no significant trend for all areas of Svalbard, there is a positive trend over e.g. Austfonna, Vestfonna, and northern Spitsbergen. The largest trend is over NE Austfonna of 0.17 mw.e. per decade. Over the investigated period, on average 90 % of the precipitation fell as snowfall. There is a significant decreasing trend in the ratio between snow and rain, with the percentage of precipitation falling as snow decreased by -2.0 % per decade (p=0.01). For glacier-covered points, 95 % of the precipitation falls as snow, with a significant decreasing trend of -1.3 % per decade (p=0.02). Over non-glacier-covered points, however, 85 % of the precipitation falls as snow, with a significant decreasing trend of -2.8 % per decade (p=0.01).

In this section, it is investigated if AROME-ARCTIC simulations can be used to extend the CARRA-forced simulations and provide almost real-time estimates of the conditions of glaciers on Svalbard.

Figure a–b show the average difference between the CARRA-forced and AROME-ARCTIC-forced CMB and runoff over the 2016–2021 period. For most regions, the CMB (Fig. a) simulated using AROME-ARCTIC closely matches that of CARRA, although with large deviations for Nordenskiöldland. For the other regions, the average difference between the CARRA and AROME-ARCTIC estimates is <0.10 mw.e.yr-1, while for Nordenskiöldland it is 0.41 mw.e.yr-1.

Averaged over the whole domain, the annual CMB is similar in the two simulations but with a more negative CMB when using AROME-ARCTIC of about -0.1 mw.e.yr-1 from 2016–2017 and a more positive CMB when using AROME-ARCTIC in 2019–2021 of approximately 0.1 mw.e.yr-1. Generally, the AROME-ARCTIC simulations contain slightly lower winter CMBs, with an average difference of -0.04 mw.e.yr-1. The summer CMB is more variable, but generally the values in the AROME-ARCTIC simulations are less negative than CARRA (by -0.05 mw.e.yr-1 on average).

The glacier runoff (Fig. b) is generally higher in the AROME-ARCTIC-forced simulations for SW Spitsbergen and Barentsøya–Edgeøya and lower for Kvitøya and Nordenskiöldland. The average difference (AROME-ARCTIC – CARRA) from 2016–2021 is -0.03 mw.e.yr-1, ranging between 0.10 and -0.13 mw.e.yr-1 for individual years. The runoff from seasonal snow on non-glaciated land is also similar overall, with the average value from AROME-ARCTIC only slightly larger than CARRA by 0.008 mw.e.yr-1. Interestingly, although the glacier runoff is lower in the AROME-ARCTIC simulations for Nordenskiöldland, the runoff from seasonal snow is not. This indicates that the difference between the CARRA and AROME-ARCTIC runoff estimates is not due to differences in precipitation.

Thus, AROME-ARCTIC forcing generally produces results for the mass balance and runoff of Svalbard that are similar, within 0.2 mw.e.yr-1 for both variables, to those simulated using CARRA forcing. This indicates that AROME-ARCTIC can be used to create near-real-time estimates of the climatic mass balance of Svalbard, although the uncertainties may be larger than generated by the CARRA-forced simulations. However, for simulations of Nordenskiöldland, one should be aware that large differences exist compared to CARRA.

Figure c–d show the cumulative CMB and glacier runoff for the 2021/22 glaciological year simulated with AROME-ARCTIC forcing compared to the span in simulations from the 1991–2021 CARRA-forced simulations. The mean of the CARRA-forced simulations from 1991–2021 is shown with a dashed black line, while the minimum and maximum years are shown in grey. In order to better compare the CARRA- and AROME-ARCTIC-forced simulations, the AROME-ARCTIC-forced estimates are shown with an uncertainty, given as 2 standard deviations of the differences between the CARRA- and AROME-ARCTIC-forced simulations from 2016/17–2020/21. In other words, this uncertainty indicates what the CMB would most likely have been if CARRA had been used as forcing as opposed to AROME-ARCTIC for these simulations.

During the winter months, there is generally little difference between the simulations with the difference forcings, and we can therefore have a high confidence in the AROME-ARCTIC results. During the summer, however, larger differences arise between the different products, which accumulate over the melt season. Based on the 2016/17–2020/21 simulations, the estimated standard error in both the CMB and runoff is 0.12 mw.e.yr-1 by the end of the mass balance year.

Based on AROME-ARCTIC, 2021/22 is a record negative mass balance year for Svalbard, with a CMB of -0.86 mw.e.yr-1. There is a highly negative mass balance in all regions on Svalbard. The runoff from glaciers is also the highest over the simulation period at 1.6 mw.e.yr-1 (58 Gtyr-1).

The datasets presented in this paper only account for the climatic mass balance and therefore do not include e.g. the mass loss from frontal ablation. However, by comparing the climatic mass balance estimate to the estimates of total mass balance from e.g. geodetic methods, one can reach a rough estimate of the mass loss due to calving. Similar to the model validation, we use the estimates from but now include tidewater glaciers in the comparison. By subtracting the CARRA-forced simulated climatic mass balance from the geodetic estimate, we can get an estimate of the calving rate. These estimated calving rates are from 0 to -0.19 myr-1 in the early 2000s (2000–2004), followed by an increase in 2005–2009 with possible values between -0.15 and -0.67 myr-1. These numbers are consistent with the estimate by of -0.18 myr-1 from 2000–2006. In the first half of the 2010s, the calving rate is between 0 and -0.43 myr-1, while in the latter half it is between 0 and -0.5 myr-1. The large range in calving rates reflects the uncertainty in the geodetic estimate. The calving after 2010 is likely increased due to the surge of Basin 3, the largest outlet basin of the Austfonna ice cap, which significantly increased the calving from the ice cap e.g..

Several sources of uncertainty are introduced through the creation of the glacier mass balance dataset in this study. The sources of these uncertainties are comprised of the model physics, the initial model state, atmospheric forcing, glacier extent, and topographic simplification. It is, however, difficult to quantify the contribution of each individual source. This section discusses these sources of uncertainty.

Several other studies have previously quantified the Svalbard-wide mass balance and runoff. Direct comparison between our results and other studies is in some cases hampered by differences in time period, areal coverage, and the type of mass balance calculated (e.g. estimates from gravimetry or geodetic methods will estimate the total mass balance, including frontal ablation).

Here, we only compare against studies which calculate either the climatic or surface mass balance and those which have published results within our simulation period of 1991–2020. When available, we compare simulated average 2 m temperature, yearly precipitation, climatic mass balance, and runoff (Table  and Fig. ).

The climatic mass balance simulated in this study is similar to estimates from other studies. The CMB in this study is slightly less negative than that simulated by , which could partly be due to the higher precipitation in this study. There are larger differences between our CMB and the estimates by and , where our simulated CMB is higher by 0.22 and 0.05 mw.e.yr-1, respectively. In the case of , this is partly due to a big difference between the estimates for 2013, where the CMB estimated by is strongly negative. A more negative mass balance is consistent with the higher average 2 m temperatures used for their simulations. On the other hand, our simulations have a more negative CMB than those simulated by . This is likely related to the much lower precipitation in our simulations. When comparing the estimates of specific runoff, our results are consistent with . The precipitation, CMB, and runoff values in this study are consistent with those of .

The temporal evolution of each of the CMB studies is plotted against our results in Fig. . The temporal pattern is similar for all the estimates, with high inter-model correlations between 0.8 and 0.9.