# Advancements for Snowmelt Monitoring by Means of Sentinel-1 SAR
## 3 Methods
### Classification Algorithm
This suggests that the two-dimensional feature space, spanned by the \(VV\) and \(VH\) ratio channels, can be reduced to a one-dimensional ratio image before performing the segmentation. For fusion of the two channels, we use the weighted average of the \(VV\) and \(VH\) ratio. Experimental backscatter data and theory show reduced separability of the two classes for co-polarized backscatter at low local incidence angles (below about 30\({}^{\circ}\)) [25; 29]. The separability in cross-polarized backscatter data, on the other hand, decreases only slightly towards low incidence angles. Angular trends of multitemporal backscatter ratios for Sentinel-1 data are shown in Figure 2 for wet snow areas and snow-free surfaces in three study areas. Snow masks derived from Landsat images were used to extract the \(VV\)-polarized (\(R_{vv}\)) and \(VH\)-polarized (\(R_{vh}\)) backscatter ratios for the two classes. Details on the data sets and the procedures for this analysis are presented in Sections 3.2 and 3.3. The ratios of snow-free surfaces show small angular variations, whereas the wet snow ratios change significantly. The differences between snow/snow-free classes decrease for both \(R_{vv}\) and \(R_{vh}\) from mid-range angles towards large angles. The separability between the two classes decreases significantly towards lower local incidence angles for \(R_{vv}\), and less for \(R_{vh}\). Taking into account this angular behavior, we apply the following relation for merging \(R_{vv}\) and \(R_{vh}\) ratios in order to create a combined single channel, \(R_{c}\):  
\[R_{c}=W\ R_{vh}+(1-W)\ R_{vv}. \tag{3}\]  
Figure 1: Flow chart of the algorithm for retrieval of snowmelt area from Sentinel-1 Interferometric Wide swath mode data. Figure 2: Backscatter ratio (median, Mdn, 1 st and 3 rd quartile) for S1 _VV_- and _VH_- polarized channels in dependence of the local incidence angle, \(\theta\), for areas classified as snow-free and snow-covered in Landsat images (see Section 3.2): (**a**) test site A1: Tröllaskagi; (**b**) test site A2: Ötztal Alps; (**c**) test site A3: Swiss Alps. The weight (\(W\)) varies with the local incidence angle (\(\theta\)) applying the following rule:  
\[ \begin{array}{rcl}IF&(\theta<\theta_{1})&\rightarrow&\left\{W=1.0\right\},\\ IF&(\theta_{1}&\leqslant\theta\leqslant\theta_{2})&\rightarrow&\left\{W=k \,\left[1+\,\frac{(\theta_{2}-\theta)}{(\theta_{2}-\theta_{1})}\right]\right\},\\ IF&(\theta>\theta_{2})&\rightarrow&\left\{W=k\right\}.\end{array}  \tag{4}\]  
For the data sets in this study, we use \(k=0.5\), \(\theta_{1}=20^{\circ}\), \(\theta_{2}=45^{\circ}\). This means that \(R_{vv}\) and \(R_{vth}\) have the same weight for \(\theta\geqslant 45^{\circ}\). For \(\theta<45^{\circ}\), the weight of \(R_{vv}\) decreases gradually, vanishing at \(\theta=20^{\circ}\). We limit the local incidence angles for snow mapping to the range \(15^{\circ}\leqslant\theta\leqslant 75^{\circ}\). At lower angles, the surface resolution in range decreases significantly. At higher local incidence angles, the signal-to-noise ratio for targets with low reflectivity such as wet snow is quite small. Furthermore, for steep fore-slopes and near-grazing incidence, possible errors in the DEM used for geocoding become critical. Terrain corrected geocoding is performed for the ratio image using precise orbit data. In addition, maps of the local incidence angle and masks of layover and radar shadow are generated by SAR image simulation using orbit and imaging parameters and a Digital Elevation Model as input. For the data presented in this paper we use the Digital Elevation Model over Europe (EU-DEM), which is a 3D raster data set with elevations captured at 1 arc second postings, corresponding to about 30 m [32]. For the standard snow product we are resampling the \(R_{c}\) ratio image to a 100 m grid in UTM projection. The segmentation rule (\(R_{c}<\ THR\)) for discriminating wet snow _versus_ dry snow and snow-free areas is applied to the geocoded \(R_{c}\) ratio image, using a threshold of \(THR=-2\ dB\).