4.1. Differences in Mass Balance Assessment Approaches
The latest published work on Austre Grønfjordbreen mass balance [
15] provides data measured by the glaciological method since 2004 and modeled using the empirical temperature approach. The latest published work on Austre Grønfjordbreen mass balance [
15] provides data since 2004 as measured by the glaciological method and by modeling using the empirical temperature approach originally suggested by Krenke and Khodakov [
37], in which the argument is the average summer air temperature with the parabolic dependence of the exponent of 3.25. (
Figure 11).
Regarding the mass balance values obtained by the glaciological method in different studies, the discrepancy may be caused by several factors: the approach used to interpolate mass balance over the entire glacier area, the values of ice and snow density that is used for calculating accumulation and ablation into a water equivalent and averaging the winter mass balance value over several years, accounting for glacier area change. In [
15], calculation of mass balance was carried out for four altitude zones. Surface ablation values were averaged in each altitude zone based on the stakes data. The density of ice was taken to be equal to 0.88 kg m
−3. The snow accumulation was also averaged for each altitude zone, and four values were used for the entire period of mass balance record. All the values of net mass balance were calculated assuming that the balance year ends on 15 August. In this study we accounted for the glacier area decrease in each altitude zone, while in [
15], it was considered constant. The glacier area recession was 15% in 2014–2020, and when such a change is not taken into account, a difference in mass balance calculation of 0.55 m w.e. a
–1 is obtained.
The model and reconstruction results were calibrated according to the stake measurements. Thus, the glaciological and modeled mass balances are in agreement for the calibration period. The reconstructed values of annual mass balance from 2014 to 2019 by day-degree method are 0.02 m w.e. a–1 more negative than what was estimated using the glaciological methods. If using the DDFs = 6.0 and 2.0 mm °C−1 d−1 for ice and snow, correspondingly, the geodetic balance is less negative than reconstructed by the DDF model. The mean difference is 0.33 and 0.10 m w.e. a–1 for 2008–2013 and 2013–2017, respectively. Therefore to make a better fit with geodetic results for 2008–2013, we calibrated DDFs again and used DDFice = 5.0 mm °C−1 d−1 and DDFsnow = 2.0 mm °C−1 d−1 (the mean difference is 0.01 m w.e. a–1).
The mean mass balance differences between the geodetic and energy-balance approaches for the periods 2013–2017 and 2008–2013 are 0.22 m w.e. a–1 and 0.16 m w.e. a–1, respectively. We assume that a more accurate result can be reached using a more complex energy-balance model, compared to a DDF-approach using one set of parameters for the entire period of reconstruction. The DDF-approach requires the regular calibration of parameters and comparison with other methods, but it is useful as an approximation, and such meteorological parameters as temperature and precipitation are still more accessible for calculation.
4.2. Comparison with the Other Olaciers of the Archipelago
According to various authors cited in the IPCC report from 2006 to 2015, annual loss of Svalbard glaciers ranges from −250 ± 160 to −400 ± 230 kg m
–2 y
–1 [
5]. The latest relevant review of the mass balance of Svalbard glaciers was carried out by Schuler et al. [
10,
38]. In particular, in this paper the comparison of several Svalbard-wide estimates of annual glacier mass balance using different methods is given. Summarizing the available data on the mass balance of Svalbard, authors in [
10] estimated that Svalbard loses annually −7 ± 4 Gt (2000–2019) (the climatic mass balance) and −8 ± 6 Gt as the total mass balance.
Here we present the results of mass balance reconstruction of Austre Grønfjordbreen in comparison with 11 other glaciers of the archipelago. The most continuous mass balance series longer than 20 years exist for Austre Brøggerbreen, Midtre Lovénbreen, Kongsvegen Hansbreen and Waldemarbreen (
Table 6).
The observed and reconstructed annual mass balance of Austre Grønfjordbreen from 2006 to 2020 is shown in
Figure 12a, together with measured annual mass balances for 11 Svalbard glaciers for the same period. The cumulative curves for the entire monitoring period of all these glaciers are shown in
Figure 12b.
The mass balance of all these glaciers was negative or close to zero for 2006–2018. In general, Austre Grønfjordbreen mass balance repeats the mass balance of other glaciers but is the most negative one with the mean value of reconstructed annual mass balance of −1.44 m w.e. a
–1. The western part of the archipelago is mostly influenced by the warm West Spitsbergen Current. The temperature depends on winter time sea ice; the southwest of Svalbard generally remains ice-free due to poleward heat transport through the current [
41,
42]. The series of mass balance observations of two glaciers (Irenebreen and Waldemarbreen) are the most negative besides for Austre Grønfjordbreen (–0.99 and −1.16 m w.e.a
–1, respectively). These glaciers are also situated on the west coast with a relatively small area. The glaciers of the same size class that are located slightly to the North (Austre Brøggerbreen, Austre Lovénbreen, Midtre Lovénbreen) have less negative mass balance (−0.60, −0.51 and −0.48 m w.e. a
–1, respectively). Less negative mass balances are found for larger glaciers, such as Kongsvegen, Etonbreen, Nordenskiöldbreen and Hansbreen (−0.09, −0.05, −0.07 and −0.31 m w.e. a
–1, respectively). Etonbreen is an outlet from the Austfonna ice cap, and its mass balance is close to zero. Schuler et al. [
10] conclude that small glaciers experience more negative surface mass balances because they lose mass faster than large glaciers due to their hypsometric distributions of area with elevation.
All cumulative curves show the steady negative trend over the past 16 years. Over the period from 2006 to 2020, the cumulative mass balance of Austre Grønfjordbreen according to our modelling results was −21.62 m w.e. This is in agreement with the cumulative mass balances of glaciers in southern and central Spitsbergen rather than glaciers in the northwest of Svalbard concerning both small and large sized glaciers [
10].
According to multi-temporal digital inventory of Svalbard glaciers by Nuth [
6] and the original glacier inventory of Svalbard by Hagen [
43], which followed the identification and parameter definitions outlined in the World Glacier Inventory [
44], the largest relative area changes between the periods of these two inventories occurred in Nordenskiöld Land area. The results from [
22] showed that the reduction of valley glaciers of Nordenskiöld Land is inversely proportional to their size. The elevation range is an important factor since it is directly related to the ablation. At higher altitudes, an increase of solid precipitation amount is usually observed if not taking into account orographic factors and precipitation distribution that can be complex. This increase can somewhat compensate the summer melting. However, the equilibrium line altitude (ELA) on Austre Grønfjordbreen is above the highest point of the glacier now.
The process of mass balance evolution varies in terms of the climatic regime and local meteorological conditions. The simulations made by Van Pelt et al. [
42] for 2012–2016 include a long-term mean distribution of air temperature on Svalbard. The area nearby Austre Grønfjordbreen experienced relatively high temperature rates during the simulation period. At the given simulation based on the reanalysis the precipitation rate was minimal, and at the same time snow onset started relatively late and the disappearance was relatively early. The snow depth was minimal, but the rate of rainfall was relatively high [
42], and these factors negatively affected glacier mass.
Available long-term mass balance observations on Svalbard show the impact of regional climatic aspects as well as the hypsometric differences. Austre Grønfjordbreen mass balance is the lowest among other observed glaciers due to a combination of factors: low elevation range, location on the western part of Central Spitsbergen and a small area with the absence of an accumulation zone.
4.3. Degree-Day Factors Variations
Temperature and precipitation are not the only factors affecting the glacier mass balance, though the role of air temperature is explained by the fact that it is a universal characteristic of almost all components of the heat balance [
37]. In fact, the overall mass change is determined mainly by the energy balance at the glacier surface. Thus, as a simplification,
DDFs physically parameterize energy balance components that have an influence on melting. Individual energy components that provide energy for melting vary in space and time, and thus
DDF meanings are different for individual glaciers [
29], and therefore the degree-day approach does not accurately represent the spatial variability of melt over the entire glacier surface. Reported values of degree-day factors of glaciers and snow-covered basins can be found in [
28,
29]. At the same time, the
DDFs used at a century timescale and that remained stable until the mid of 1970s have decreased by 7% per decade [
45]; therefore,
DDFs must be used with caution and only for reconstructing changes over short periods of time.
For Svalbard, a variability of degree-day factors for snow and ice has been overviewed by Möller and Kohler [
12]. The degree-day factors for snow are in the range of 3 −24 mm C
–1 d
–1, and 9–13.8 mm C
–1 d
–1 for ice [
12]. On Kongsvegen, the 21 year stake record results in a
DDF of 3.0 mm C
−1 d
−1 for snow and 3.5 mm C
−1 d
−1 for ice [
46]. On Kronebreen, the
DDF for snow is 3.1 mm C
−1 d
−1 and 4.7 mm C
−1 a
−1 for ice [
46]. Hence, our calibration results of 5.0 and 6.0 mm C
−1 d
−1 for ice and 2.0 mm C
–1 d
–1 for snow surfaces are reasonable and are in good accordance with the previously reported
DDFs for Svalbard.
4.4. Sensitivity Tests
Assessment of glacier mass-balance sensitivity to climate change enables interpretation of the glacier–climate interaction. Surface mass balance sensitivity to air temperature, solar radiation, precipitation and topographical variables is necessary to calibrate/validate the numerical models used to simulate the evolution of glaciers [
47].
The mass-balance sensitivity of Austre Grønfjordbreen to climatic fluctuation was assessed over the period 2014–2019. The average annual mass balance was recalculated by re-running the degree-day model with the same parameters, but assuming a 1 °C increase in temperature or a 10% change in precipitation throughout the balance year. Mass-balance sensitivity to air temperature (dMB/dT) and precipitation (dMB/dP) was calculated as the difference between the modelled values.
The calculated mass-balance sensitivity to air temperature is −1.04 m w.e °C −1, which corresponds to the highest sensitivity on Svalbard among the assessed by temperature-index model.
Sensitivity values of net mass balance to temperature change (1 °C increase) assessed by the degree-day approach for Austre Brøggerbreen, Midtre Lovénbreen, Kongsvegen and Hansbreen are −0.49, −0.48, −0.69 and −0.49 (m w.e. a
–1), respectively [
48].
The same sensitivity test was also conducted for precipitation. Calculated mass balance sensitivity to precipitation for Austre Grønfjordbreen is 0.10 m w.e. for a 10% change. For both Midtre Lovénbreen and Kongsvegen, the sensitivity for 10% change in precipitation is 0.05 (m w.e. a
–1), and a 31% increase of snow precipitation is needed to compensate for the net mass loss induced by an air temperature increase of +1°C [
48].
In a number of papers on Svalbard glaciers, the mass balance sensitivity to changes in air temperature and the amount of precipitation is estimated using energy balance models [
35,
36,
49,
50]. For example Van Pelt et al. [
49] assessed the sensitivity for Nordenskiöldbreen as 0.10 m w.e. for a 10% change in precipitation and −0.36 m w.e for a 1 °C increase in temperature. A 1 °C temperature change can be offset by a 32% change in precipitation of a similar sign in cases of seasonally uniform perturbations [
49]. For Midtre Lovénbreen, Kongsvegen and Holtedahfonna, the mass balance will change by 0.13; 0.12; 0.13 (m w.e. a
–1), respectively, in case of 10% precipitation change and the rise of 1 °C will lead to mass balance decrease of −0.83, −0.69 and −0.55 (m w.e. a
–1), respectively [
36].
In order to assess the precipitation amount that is needed to offset the mass loss due to a 1 °C rise, we adjusted the model several times until the increased melting could be covered by the adjusted precipitation, while the other model parameters were kept unchanged. The result showed that a two-fold increase in precipitation could compensate the increased mass loss due to air temperature rise.