## 6 Discussion
### Results Obtained from ASMAG
#### 6.2.2 Digital Elevation Model  
A systematic bias is introduced by using the reference DEM from 2000 for the full study period, as this is neither representative of the glacier surface from 1985 nor of recent times. Assuming a more or less constant surface lowering with time introduces a bias, in particular in rapidly down-wasting glacier parts at lower elevations. We have thus investigated this effect on HEF as this glacier is covered in a 1992 DEM from swissotopo and a DEM from the TanDEM-X mission (acquired around 2013). Figure 10 shows elevation profiles extracted along a centre line from all three DEMs (DEM 1992, SRTM DEM, TanDEM-X), revealing increasing differences towards lower elevations. When averaging differences in four elevation bins, the obtained values in the lowest interval (2500-2600 m) are about 64 m higher in 1992 and about 60 m lower with TanDEM-X (Table 5). Such systematic differences have to be considered when interpreting the time series depicted in Figure 7. Strictly, only the SLA values derived around the year 2000 are unbiased. With DEMs from three points in time available it would be possible to apply elevation dependent correction factors of surface elevation for each year. However, multiple DEMs are not yet generally available for most regions, so here we have only investigated the theoretical effect of neglecting such changes. In the above calculation of differences (that compares an optical DEM to C- and X-Band radar DEMs) we have not corrected elevation differences due to radar penetration [(67; 68)] as they are about an order of magnitude smaller. In effect, SLAs before 2000 have to be corrected by up to +64 m and lowered to max -60 m after 2000. Such a correction would bring values from the first period closer to the measurements but would move those from the second period further away. Nevertheless, most of the SLA values derived in this work stem from around 3000 m (see Figure 7) where the elevation difference are less prominent. In flat and smooth terrain the vertical accuracy of the DEM is often much higher than in steep rugged terrain [(69)]. As glacier surfaces are comparably flat (see Figure 1 for mean slope values per glacier) and smooth (30 m cell size) it can be assumed that the reported vertical accuracy of the SRTM DEM (\(\pm 16\) m) is not exceeded over glaciers. Still remaining differences can be due to radar penetration (as shown by [(70)]) or local artefacts. The systematic differences due to general surface lowering, \begin{table}
\begin{tabular}{c c c c c} \hline  & **2500–2600 (m)** & **2600–2700 (m)** & **2700–2800 (m)** & **2800–2900 (m)** \\ \hline \(\overline{dt}\) 1992–2000 [m] & 64 & 54 & 40 & 32 \\ \(\overline{dt}\) 2013–2000 [m] & –60 & –48 & –32 & –21 \\ \hline \end{tabular}
\end{table} 
Table 5: Mean elevation differences for the listed elevation intervals for HEF from the DEM 1992, the SRTM DEM (2000) and the TanDEM-X DEM (2013). Figure 10: (**a**) Surface elevation for the lower part of HEF as shown in the image. (**b**) Elevation values are derived from three DEMs for a manually digitized centre line. so that the landscape below might partly shine through. Whereas thin ice clouds can be detected over ice and snow by their higher SWIR reflectance [21], the cloud tops of optically thick water clouds (cumulus) might be detected by their lower thermal infrared (TIR) emission (i.e., they are cooler). However, for the optically thin boundaries of a cloud the difference to the reduced TIR emission over ice and snow might be small so that cloud parts might remain over glaciers and be classified as snow by ASMAG. Moreover, the (static) band thresholds for the cloud cover mapping procedure are currently calibrated for only one scene per Landsat type, so that the calculated percentages of cloud cover above a glacier are not always reliable. This could be improved in future versions of ASMAG, preferably in a scene-dependent manner. Shadows from clouds and cast shadows from steep topography cause problems for the Ekstrand correction.