## Data and Data Preparation
### Digital Elevation Models  
Elevation information is essential in ASMAG for two purposes: (1) For topographic correction of illumination effects, and (2) to derive elevation bands to determine the SLA. In this study, we follow the recommendation of [PERSON] et al., (2016) [39] and use a DEM from 2000 for the full time series. This reduces biases due to nonlinear changes in glacier extent and may include periods of larger and smaller glaciers. We use the Shuttle Radar Topography Mission (SRTM) 1 arc second global DEM (30 m resolution) from the year 2000 (downloaded from [[http://earthexplorer.usgs.gov/](http://earthexplorer.usgs.gov/)]([http://earthexplorer.usgs.gov/](http://earthexplorer.usgs.gov/))) which was acquired in about the middle of the investigated period. Hence, for constantly shrinking glaciers the DEM elevations (and derived SLA values) underestimate glacier surfaces at the start of the record and overestimate them at the end. The SRTM DEM is referenced to the Earth Gravitational Model 1996 (EGM96) with a reported mean vertical accuracy of \(\pm\)16 m [40,41]. As in other regions, only small gaps of glaciers were found in the SRTM DEM (3.15 km\({}^{2}\), \(\sim\)0.8%) (Figure 1) [41]. These gaps were filled with co-registered (see details in Table 3) ASTER Global Digital Elevation Model version 2 (ASTER GDEM V2) data that were also downloaded from Earth Explorer. The ASTER GDEM V2 provides averaged elevation values from 2000-2012 and is available with a 1 arc second (30 m) cell size in geographic coordinates referenced to the EGM96 datum. The vertical accuracy is given as 17 m at a 95% confidence level [42]. For the remainder of the paper, the void-filled SRTM DEM is named reference DEM. All SLA values calculated in this study refer to the reference DEM and represent geoidal heights, so that they can be compared to field measurements of the ELA. To determine trends in surface elevation over Hintereisferner, we used a national DEM (swissstopo DHM25 level 1) from 1992 and a 30 m version of the TanDEM-X DEM that was acquired between 2010 and 2014) [43]. The former DEM is derived from topographic maps (scale 1:50,000) and elevation values refer to the Swiss projection with a local geoid (CH1903) and a user-defined datum. The TanDEM-X DEM is made available by DLR and provided in geographic coordinates with a horizontal resolution of 12 and 30 m. The reported absolute vertical accuracies are \(<\)10 m. The vertical datum is WGS84-G1150, i.e., heights are ellipsoidal heights. Within this study, only the TanDEM-X DEM and the ASTER GDEM V2 were co-registered to the SRTM DEM using the method described by [PERSON] and [PERSON] (2011) [44] because the swissstopo DEM already showed elevation differences of less than 1 m for stable terrain (AZ: -0.65m, standard deviation \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Space craft** & **Sensor/Operation Time** & **Image Bands** & \
\begin{tabular}{c} **Spatial Resolution** \\ **Optica/Thermal [m]** \\ \end{tabular} &
\begin{tabular}{c} **Radiometric** \\ **Resolution [bit]** \\ \end{tabular} & **Scene Count** \\ \hline Landsat 4 & TM (1982–1993) & 7 & 30/120 & 8 & 2 \\ Landsat 5 & MSS (1984–2013) & 4 & 60/none & 8 & 1 \\ Landsat 5 & TM (1984–2013) & 7 & 30/120 & 8 & 39 \\ Landsat 7 & ETM SLC on (1999–2003) & 9 & 30/60 & 8 & 4 \\ Landsat 7 & ETM SLC off (2003–2016) & 9 & 30/80 & 8 & 13 \\ Landsat 8 & OLI TIRS (2013–2016) & 11 & 30/100 & 12 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Landsat sensor characteristics and dataset overview. \begin{table}
\begin{tabular}{l r r} \hline \hline
**Coreg. Parameters** & **TanDEM-X [m]** & **ASTER GDEM V2 [m]** \\ \hline \hline \(\overline{d}\overline{h}\) before & \(-\)57.8 & 10.8 \\ STD before & 10.4 & 13.07 \\ \(\Delta\)X & \(-\)31.7 & \(-\)32.5 \\ \(\Delta\)Y & \(-\)11 & \(-\)8 \\ \(\Delta\)Z & \(-\)54.5 & \(-\)7.5 \\ \(\overline{d}\overline{h}\) after & 0.02 & \(-\)0.06 \\ STD after & 6.47 & 10.22 \\ \hline \hline \end{tabular}
\end{table}