# Advancements for Snowmelt Monitoring by Means of Sentinel-1 SAR
## 3 Methods
### Classification Algorithm  
Change detection procedures are commonly applied for retrieving snowmelt areas from SAR backscatter images [9; 10; 11; 12; 13; 14]. This is an efficient means for reducing the impact of topography. The ratio of backscatter intensity of the SAR image with melting snow (\(\sigma_{snow}^{0}\)) _versus_ a reference image (\(\sigma_{ref}^{0}\)) of the same satellite track is computed for detecting the reduced backscatter signal of melting snow areas. Threshold-based segmentation is applied to separate snow-covered and snow-free surfaces. Preferably, the reference image is the average of multiple SAR images from dates with surfaces that are snow-free and/or covered by dry snow. Stacking multiple images reduces speckle and helps to suppress the impact of temporal variations in backscatter in the reference scenes. As a first step in the processing line, the snow image and reference images in radar geometry (Figure 1) are calibrated to radar brightness [18] and precisely co-registered to a pre-selected master image of the same track, using the orbit data and a DEM [30]. Due to the high accuracy of the S1 orbit data, geolocation at sub-pixel accuracy is achieved [20]. In the next step, the speckle-related uncertainty is reduced by applying a multichannel SAR intensity filter [31]. This filter optimally reduces speckle while preserving the intensity and spatial resolution of the individual channels. In the filtering process, \(M\) new images \(J_{k}\) are produced by linearly combining \(M\) co-registered intensity images \(I_{i}\), with \(1\ \leqslant i\ \leqslant\ M\). For intensity images with the same number of looks, \(L\), the following formulation for the filter is valid [31]:  
\[J_{k}=\ \frac{\sigma_{k}}{M}\sum_{i=1}^{M}\frac{I_{i}}{\sigma_{i}}\,\ 1\ \leqslant k\ \leqslant M \tag{1}\]  
where \(\sigma_{k}\) is the intensity in channel \(k\) of the filtered image, and \(\sigma_{i}\) is the mean intensity in the channel \(i\) of the unfiltered image. The mean intensity in the filtered images is unbiased while the loss in spatial detail is minimal. An estimate of the local mean intensity is obtained by averaging the intensity values in a local window around each pixel. We apply the filter over windows of \(7\times 7\) pixels, using the stack of multi-temporal SLC images in the two polarizations. If all pixels in a window with \(N\) pixels are spatially uncorrelated, the resulting equivalent number of looks, \(ENL\), in the filtered image is:  
\[ENL=\ \frac{M\ N\ L}{M+N-1} \tag{2}\]  
Taking into account the difference in spatial resolution of the IW mode data in LOS and azimuth, we perform block averaging over \(16\times 4\) (LOS \(\times\) azimuth) pixels of the SLC images before applying the multichannel filter. The averaged pixels have a size of about 55 m in azimuth and 58 m in ground range at 40\({}^{\circ}\) incidence angle. We estimated the equivalent number of looks by extracting the mean and variance of intensity over distributed targets with uniform surface properties extending over several hundred pixels. For the \(16\times 4\) block averaged pixels, the \(ENL\) is 26. Applying the multichannel intensity filter increases \(ENL\) significantly while maintaining the pixel size. Using one snow image and one reference image (dual channel each) we obtain after filtering \(ENL=\ 106\), and, using three reference images, \(ENL=202\). For the reference images, further speckle reduction is achieved by using averages compiled from backscatter images of multiple dates. The \(\sigma^{0}\)-ratio of the snow image _versus_ the reference image is computed separately for the \(VV\) and \(VH\) channels and transformed to a logarithmic scale (dB). The statistical analysis shows a comparatively high degree of correlation between the \(VV\) and \(VH\) ratio images, with typical values of the correlation coefficient (\(\rho\)) of \(0.85\ \leqslant\rho\leqslant 0.90\) for different study areas.