**4. Discussion**

#### *4.1. Uncertainty Analysis and Limitations*

All presented data on AAR and mass balances include uncertainties. It is difficult to quantitatively assess the respective error per observation technique. The assessment of annual AAR is usually more subject to uncertainties. For a glacier-wide estimate of AAR, peaks above the glacier or airplane observations are beneficial to prevent misclassification of recent and perennial firn. For very small accumulation areas left after a strong ablation summer, correct assessments depend on accumulation stakes and direct observations. This is especially the case for a strong negative year in terms of mass balance subsequent to a rather less negative year. Extrapolation for the whole glacier area and interpolation in between observations is challenging.

The introduced two-step thresholding based on wet snow scenes (Section 2.2.4) does include some local uncertainties. We observed areas that showed *γ*0 values below the respective threshold, which certainly were snow free in late August and September (Figure 7f). Such areas usually were present on HEF and GPF and, for both glaciers, limited to the glacier tongue regions. It appears from comparing images with and without applied correction for systematic backscatter offsets (Section 2.2.3) that these areas deviate strongly from median *γ*0 (Figure 4). The applied backscatter enhancement was

probably not sufficient to correct for these deviations. In general, rough surfaces like bare glacier ice increase the reflected backscatter [38] for SAR data due to enhanced diffusive scattering. We can only speculate about the reasons of this amplification of the decline in *γ*0. Although the applied DEM does not indicate layover and shadowing for those areas, we assume that the steep topography has some effects, especially because the DEM used for SAR processing was generated up to more than ten years prior to acquisition dates and the glacier surface lowered significantly within this time period.

In general, the presented RMS deviations of WSCAF to results from optical remote sensing imagery are below 10%. However, sample sizes for comparison are low. We only found four optical scenes, which were recorded shortly prior or after an S1 data acquisition. For the three analyzed AOIs, the calculated RMS values represent not very resilient statistical values. An accuracy of below 10% is encouraging, however, considering the fact that conventional methods rely on data interand extrapolation or are hampered by cloud coverage. Since for three consecutive years only very few optical scenes were available during the ablation periods, SAR data offer a significant progress in determination of annual and seasonal transient snowlines and, consequently, AAR. Six days of overpass rates enabled already almost complete coverage for the ablation seasons 2017 and 2018 with a high temporal resolution.

In addition, such a high temporal resolution demonstrates difficulties in data interpretation by simple thresholding. The sensitivity of WSCAF results on deviations in thresholds is in most cases very low. Derived uncertainty ranges are at ±2%, which corresponds to the sizes of data markers in Figures 5 and 6. However, some errorbars cross the set 50% WSCAF criterion for different thresholding and, consequently, sensitivity analysis are performed over more than 1 dB. Especially for GPF with its flat plateau above 3100 m a.s.l., fluctuation in thresholding occurs more frequently. In most cases, sensitivity increases shortly after a recent new snow event. New snow has two different effects on WSCAF classification from SAR data. If the recent new snow coverage experiences melt, the WSCAF will significantly increase. In addition, dry new snow increases volume scattering from the surface, and, consequently, resulting backscatter values of former wet surfaces may reach above the set threshold values. Hence, determined WSCAF decreases. Such occurrences can be observed for instance at the end of each GY or shortly after 01 October. Here, WSCAFs reduce to roughly 0%. Disregarding this effect would result in misclassification of minimal wet snow extents per ablation season. The applied criterion for the search of minimal extents in wet snow each year seems to work properly to neglect such dry snow covered minimum in WSCAF.

Since large large threshold sensitivities—displayed via errorbars—can be related to new snow events or WSCAFs at about 50%, such values are prone to errors and uncertainties. For comparison with optical remote sensing data or for determination of annual AAR values, we recommend focusing on SAR data being insensitive to threshold variations. For S1 data with six days return cycles, this would reduce seasonal coverage by one (2017) to four (2018) scenes for VF and limit the temporal coverage for GPF to only half of the previously analyzed scenes.

#### *4.2. Discrimination of Wet Snow and Firn*

Not only do dielectric permittivities change backscatter emissivity of surfaces, but surface roughness as well (e.g., [38]). Wet snow and wet firn have similar dielectric permittivities, if the volumetric liquid water content (*θw*) is equal and impurities are negligible (s = snow, f = firn, *ρs* = 360 kg/m3, *θw* = 0.04, *ρf* = 500 kg/m3; *s* = 2.8, *f* = 3.2). Concave furrows as a result of melt and sublimation processes on the snow surface increase with continuing ablation, especially, for the inner Alpine dry regions with intensified sublimation observed here. According to the Rayleigh criterion, surfaces are considered as rough for SAR data, if *h* > *λ*/8*cosδ* [39] with *h* the height of the surface features, *δ* the given incidence angles and *λ* the wavelength of the respective platform. This leads to a roughness sensitivity of roughly *h* > 8 mm for C-band data. For soil surfaces, [40,41] found that SAR backscatter increases are most sensitive to changes in surface roughness of 0 < *Zs* ≤ 0.4 with *Zs* = *<sup>s</sup>*2/*l*, the roughness parameter where *s* is the root mean square of surface height *h* and *l* the

correlation length. For reasonable *s* and *l* values, we derive *Zs* as displayed in Figure 9. It is obvious that backscatter increases are caused by increases in *s* between 0 cm to about 7 cm for correlation lengths observed in the field. An increase in surface roughness up to 7 cm can usually be observed for transitions from seasonal snow to firn (see Figure A1). For the short in situ transect separating firn and wet snow recorded the same day as a SAR acquisition, we found sufficient agreemen<sup>t</sup> of 3–4 pixels. However, the difference of the thresholds separating firn and snow is close to the given resolution limits of S1 data.

**Figure 9.** Numerical simulation of variations of the roughness parameter *Zs* with changes in roughness height *s* and correlation length *l*.

#### *4.3. SAR Data for Application in Seasonal Mass Balance Estimates*

It remains debatable to which degree field assessments of AAR are accurate. Usually, no continuous snowline data are available for field assessments. Accumulation area ratios for alpine glaciers are commonly estimated according to elevation ranges and stake readings. However, without a long-term time series of direct measurements, no reliable AAR to B relationship can be established.

The long time series of mass balance observations for HEF and VF with data distributions from 0% to almost 100% in AAR enable for deriving a resilient formulation for the AAR to B correlation. Inserting SAR based annual AAR in a linear fit results in average offsets of 200–300 mm w.e. This is above given uncertainty ranges for systematic errors of direct mass balance measurements and above the uncertainty of the linear approximation for each glacier. Two limiting factors reduce accuracy of such an approach: (i) for both time series, the linear relationship resulted in average errors larger than 100 mm w.e. (RMS deviation VF 212 mm w.e., HEF 154 mm w.e.); and (ii) the date of SAR acquisition is crucial. The approach by Dyurgerov et al. [37] with a generalized relationship over 99 glaciers is not sufficient for the rather flat and southerly exposed VF to accurately determine B just from AAR observations. For HEF, as a more typical valley glacier, this generalized approximation provides better estimates on B for the three observed GYs. Reducing the globally derived glacier relationship of B and AAR to the geographical region of the Eastern Alps provides larger deviations for HEF and decreases the offset for VF. However, data used in [37] have a temporal extent until early 2000. Including the strong ablation seasons within the last decade most likely will influence the derived relationship of AAR and B.

Observation of the temporal evolution of the transient snowline with SAR data is reliably possible with the presented algorithm for the glaciers of the Rofental, Austria. Single scenes are very difficult to interpret, since the respective acquisition can be biased by recent new snow precipitation. However, data interpretation benefit from time series of SAR observations with high temporal resolution and thus misinterpretation due to new snow events is limited. In addition, the applied criteria for the search of annual minimum reliably exclude scenes covered by recent dry snow.

Whether the proposed two-step approach for discriminating wet snow and firn is applicable for other areas in various latitudes or climatological regions remains unknown. For glaciers outside middle latitudes without pronounced seasonality (e.g., high latitudes and very high altitudes), remote sensing data only provide snapshots depending on the time of acquisition and prevailing weather conditions. The derived data on WSCAF for such geographical regions has no or limited significance on ablation progress. As a first step for each region, *γ*0 values for wet snow conditions have to be analyzed for all acquired orbits and polarization channels. In case sufficient amounts of SAR scenes fully covered by wet snow are available, the processing routines as described here can be implemented into automatic data analysis resulting in an output of just WSCAF per acquisition.

However, such data analysis does not directly lead to surface mass balance per glacier area. The relationship of annual AAR to B is usually significantly different for each glacier and relies on individual topography, elevation range and aspect. Empirical approaches such as the one proposed by Drolon et al. [42] are less influenced by individual glacier topographies and do not need long-term data series. However, [42] focuses rather on large scale accuracies than on individual glaciers and use optical satellite data with the named restrictions on visibility. In addition, presented uncertainties on annual mass balance values are rather large.

Other SAR platforms using X- or L-band sensors are most likely applicable for such an analysis as well (see [43]). Again, for proposed workflow described here, it is prerequisite that wet snow scenes can be used to derive threshold values and to apply topographic corrections. The main disadvantage for those platforms is the temporal resolution with return cycles of more than 10 days. For instance, over several years of ALOS-PALSAR-1 and 2 data, we could only acquire three June scenes for the region analyzed here.
