**3. Results**

#### *3.1. Wet Snow Covered Area Extent*

Figures 5 and 6 display the seasonality of backscatter distributions being above or below the thresholds. For all four observed accumulation seasons (winter periods), snow surface conditions are constantly dry and, hence, WSCAFs are at about zero. Since we determined no changes during periods from January until early April in 2015 and 2016, we minimized data acquisition for this period for the remaining years. From late April to May, the snow surface is starting to becoming wet and reaches towards average WSCAFs in June of 80–90%. June 2015 is an exception, when only 60–70% are reached. However, we could only analyze a single June scene in 2015, which was recorded at the very beginning

of the month. After the launch of S1B in spring 2016 and the following commissioning phase, C-band data were available with six days return cycles beginning in late September 2016. The ablation seasons 2017 and 2018 provide a much more detailed view on temporal and spatial changes of WSCAF for all AOIs. WSCAF recession during the ablation season after June is usually very rapid with interruptions by new snow events (Figure 6). New snow events during the ablation season can have a large effect on B [35] due to the short term increase in albedo up to values of 0.9. In summer 2017, two snow fall events can be directly related to sharp increases in WSCAF for all three AOIs. It is possible to detect a peak in WSCAFs for 15 July 2017 for all three AOIs, while respective amplitudes are different. VF decreases after 1 July 2017 from about 80% WSCAF to below 20%, the same occurs for HEF, whereas GPF remains at 60%. The corresponding snow fall events were recorded for 6 and 7 July. However, no increase in WSCAF as a consequence of this recent new snow is recognizable for the subsequent SAR analysis on 9 July 2017. Temperatures remained low and, hence, this recent snow was not affected by melt. Shortly before the following SAR image, snow melt changed *γ*0 resulting in a local peak of derived WSCAF. The next peak in WSCAF observed at 20 August 2017 is related to new snow as well. Again, amplitudes are significantly larger for GPF in comparison with VF and HEF. In summer 2018, WSCAFs decrease to very low values for VF and HEF with only slight interruptions. Solely, the new snow event in late August this summer has a remarkable effect on WSCAFs for those two AOIs. GPF, however, is characterized by two additional peaks in July and mid August. At the Ultrasonic location on VF, no snow fall could be recognized. At least for mid August, we noticed a liquid precipitation event at lower elevations, while higher glacier regions received new snow. The mostly northerly exposed GPF, which has a large flat plateau above 3100 m a.s.l., results in a WSCAF increase to above 30% for this SAR scene.

The applied two-step approach has an effect on sensitivity displayed through errorbars. Large errorbars can—in most cases—be attributed to recent new snow precipitations (Figures 5 and 6). After a snow fall event, the area extent of wet snow change across the criterion of 50% for the application of the *β*2, which, as a consequence, can have a strong effect on determined WSCAFs. This is regularly the case for GPF.

For comparison with optical remote sensing data, four SAR scenes were available, which fulfill the requirements of a temporal offset of maximum ±4 days. The root mean square (RMS) deviation for the four periods for VF and GPF and only two periods for HEF (due to cloud coverage) results in 8.5% difference. This deviation is insensitive to subtraction of standard deviations from *β*1 and *β*2 (RMS deviation of 7.8%) but increases to a RMS deviations of 18.1% when applying the higher threshold range. Unfortunately, a new snow event during the night of 14 to 15 August 2018 above roughly 3200 m a.s.l. had a significant influence on the SAR detected WSCAF at 15 August in the morning. This new snow was already melted before the acquisition of optical imagery the subsequent morning. Discarding this SAR value from RMS analysis leads to deviations of only 4.9% with an sensitivity range of 4.7–13.5%

We used changes in snow/ice height measured at the lower glacier tongue of VF as a proxy to assess ice melt progress until the end of the respective GY. For all three analysed ablation seasons, the depicted annual minimum in snowline from SAR data was before the respective end of the GY. To relate ablation progress, we compare ice heights for these dates with 30 September each year. In 2016, the ice surface lowered by −27 cm from 12 September until 30 September (to −2.66 m). The subsequent year, the offset in ice surface reduced to 19 cm for an even longer time span (26 August–30 September) with an annual ablation of −3.1 m at the end of the GY. Finally, in 2018, we observed a surface lowering of 28 cm for only ten days between SAR minimum and end of GY ( −4.53 m). All surface height values are related to the start of the respective GY, which is set to a surface height of 0.0 m. No annual mass balance assessment for GPF are conducted so far.

Offsets to estimates from field investigations are presented in Table 4. RMS deviation result in 8.2% for HEF and VF for a sample size of five.

**Figure 5.** Wet snow covered area fraction for Sentinel-1 (S1) series per area of interest (AOI) Vernagtferner (VF) (**a**), Hintereisferner (HEF) (**b**), Gepatschferner (GPF) (**c**) and results for the new snow index (**d**) from January 2015–October 2016. Black rectangles display S1 scenes with error bars for uncertainties in thresholds, red circles show field data determined accumulation area ratio (AAR) and green diamonds display results for the normalized difference snow index (NDSI) from Landsat images and snow classification results from Sentinel-2 data. Field data for the AOI GPF in (**c**) were only acquired for Kesselwandferner.

**Figure 6.** Wet snow covered area fraction for Sentinel-1 (S1) series per area of interest (AOI) Vernagtferner (VF) (**a**), Hintereisferner (HEF) (**b**), Gepatschferner (GPF) (**c**) and results for the new snow index (**d**) from January 2017–October 2018. Black rectangles display S1 scenes with error bars for uncertainties in thresholds, red circles show field data determined accumulation area ratio (AAR) and green diamonds display results for the normalized difference snow index (NDSI) from Landsat images and snow classification results from Sentinel-2 data. Field data for the AOI GPF in (**c**) were only acquired for Kesselwandferner.



#### *3.2. Discriminating Firn and Wet Snow*

Only reliable discriminations between wet snow and firn enable derivation of annual AAR for various glaciers. We analyze for accuracies in wet snow–firn discrimination by a short in situ GPS transect for the transient snowline on VF. For this 303 m long transect discriminating firn from wet snow, we determined an average offset for the SAR-derived transient snowline of 35 m and for optical data this offset decreases to 19 m. In addition, 35 m correspond to about 3–4 pixels for a 10 m × 10 m SAR resolution. The respective S2 data providing optical data has the same ground resolution. However, optical data have been recorded four days prior to ground truth and S1 data. Apart from the short 300 m in situ line, qualitatively, we demonstrate agreemen<sup>t</sup> of optical data with SAR data in Figure 7. It is inevitable that disagreement between optical data and SAR data occur, but, in general, this overview confirms the 3–4 pixel accuracy determined for the in situ data.

#### *3.3. From Minimum Wet Snow Extent to Mass Balances*

For Vernagtferner and Hintereisferner, long-term summer and winter mass balance series exist (VF: 1964/65–2016/17; HEF: 1952/53–2017/18; [21,22]) (e.g., [36]). We plotted relationships of AAR and mass balance (B) for VF and HEF in Figure 8. It is clearly visible that a linear fit matches the relation between B and AAR adequately. Coefficients of determination (R2) are high reaching *R*<sup>2</sup> = 0.93 for HEF with a sample size of 66 years and a range of 0% to above 80% in AAR. The *R*<sup>2</sup> = 0.90 for VF is slightly lower with a lower sample size of 53 years and a higher range from 0% to more than 90% in AAR. Calculated RMS deviations to the linear approximation for both glaciers are at 212 mm w.e. for VF and 154 mm w.e. for HEF.

Such long-term mass balance series with reliable relationships of AAR and B enable direct conversion from SAR determined annual AAR to B (Figure 8, Table 5). Deviations to observed B values from field data are highly variable from +435 mm w.e. to −73 mm w.e. for VF and from +248 mm w.e. to −241 mm w.e. for HEF using S1 data. In absolute deviations, those numbers average to 254 mm w.e. for VF and 231 mm w.e. for HEF. Such average offsets are above the given accuracy ranges of the linear approximation (in RMS deviation); however, sample numbers are very low.

Instead of an individually derived linear relationship for each single glacier, Dyurgerov et al. [37] used 99 index glaciers and came up with an average relationship for AAR and B. We included results from this average formula in Table 5 and Figure 8, together with a relationship derived from just Eastern Alpine glaciers (11 glaciers with B and AAR values) listed in [37]. For both glacier areas and most observation years, offsets in mass balance values surpass the given uncertainty range for direct measurements with the glaciological method significantly. Dyurgerov's approximation result in an average absolute offset for VF of 797 mm w.e.. However, the rather typically shaped valley glacier area of HEF matches the general approach by Dyurgerov significantly better. Average absolute offsets sum up to 190 mm w.e.. An approximation established just for Eastern Alpine glaciers does not decrease offsets. Calculated average absolute deviations are 377 mm w.e. for VF and 367 mm w.e. for HEF. The sample number for the Eastern Alps is very low with just 11 glaciers; however, the *R*<sup>2</sup> of the linear approximation reaches 0.79 and the RMS deviation for the 11 glaciers results in 179 mm w.e.

**Figure 7.** Comparison of Sentinel-2 (S2) optical data showing firn and snow patches with Sentinel-1 (S1) derived wet snow covered area fraction maps for all areas of interest (AOIs) and for each AOI respectively. The color coding is constantly displaying derived firn (red) and wet snow (blue) areas for all presented S1 data. S2 imagery was recorded on 16 September 2018 and S1 data on 20 September 2018. S2 imagery (**a**), S1 analysis presenting all three AOIs (**b**), zoom for AOI Vernagtferner with optical (**c**) and S1 data (**d**), zoom for AOI Hintereisferner with optical (**e**) and S1 data (**f**), zoom for a fraction of AOI Gepatschferner with optical (**g**) and S1 data (**h**). Coordinates are given in UTM with datum WGS 1984. All maps are aligned equally.

**Figure 8.** Mass balance (B) versus accumulation area ratio (AAR) distribution for 53 years of records for Vernagtferner (VF) (**a**) and 66 years of records for Hintereisferner (**b**) (HEF). Black circles indicate results from the linear approximation by Dyurgerov et al. [37]. Correlation coefficients and formulation for the linear fit are presented.

**Table 5.** Annual mass balance (B) estimates from field data and annual minimum accumulation area ratios (AAR) determined from Sentinel-1 (S1) scenes. For conversion from accumulation area ratio (AAR) to B, we used the formulations of the linear fit for Vernagtferner (VF) and Hintereisferner (HEF) displayed in Figure 8, Dyurgerov's average relationship [37] (Dyu) for all glaciers and specified just for the Eastern Alps (Dyu EAlps). All mass balance values are presented in millimeter water equivalent (mm w.e.).

