## Interferometry processing
#### 4.2.1 Water Mask  
The calibration process was done following the [67] approach. Additionally, the normalized difference polarization index (NDPI) and the cross ratio (CR) were calculated to examine water and humid areas. Four S1 stacks were created defining the GRD Sigma0 dB product, considering the ascending and descending modes for the VV and VH bands used in the NDPI and CR computations (see Table 1 in the materials section). In places where SAR geometrical distortion often impacts a portion of the imagery taken in the ascending or descending mode, these stacks of bands were finally trimmed using an aspect layer recovered by the 10 m DTM VDA. The angle of view and the aspect layer were taken into consideration beginning with the ancillary and metadata files during the clipping to exclude areas affected by significant distortions in both the ascending and descending mode as described by [38]. In order to fill the gaps left in each stack by the removal of the sections that were severely impacted by the distortions, the stacks were finally mosaicked. In the case of both the distortions, we evaluated those portions with a higher incidence angle in accordance with [38; 62]. SAGA GIS was used for this task. The finished stack was then uploaded into the GEE to produce an annual SAR synthetic composite in order to compute the NDPI and CR. As indicated earlier, the SAR composite was employed to map the water component more accurately. To assess the water area components, the following SAR bands and indexes (Table 5) were adopted after a pre-processing phase and the creation of a composite to reduce the SAR distortions. NDPI and CR has been calculated as follows:  
NDPI Normalized Difference Polarization Index [68]  
\[\mathrm{NDPI}=\frac{\mathrm{VH-VV}}{\mathrm{VH+VV}}\]  
CR Cross ratio [68]  
\[\mathrm{CR}\;=\frac{\mathrm{VH}}{\mathrm{VV}}\]  
As demonstrated by [69] in a complex morphological context, the SAT approach was more effective than the Otsu thresholding method. Therefore, these bands were included to map surface water areas through a robust stepwise automatic thresholding (SAT) approach [69]. The SAT approach consisted of the following steps. (1) SAR data was pre-processed to create a backscattering coefficient that was georeferenced with high resolution LiDAR-derived DEM (in this case the Aosta Valley DEM with 2 m step resampled at 10 m). (2) SAT for relief displacement and de-speckle filtering was used to reduce noise \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**S1 GRD**} \\ \hline
**ID** & **Bands/Index** & **Description** \\ \hline
1 & “VV & Single co-polarization, vertical transmit/vertical receive \\
2 & “VH” & Dual-band cross-polarization, vertical \\  & & transmit/horizontal receive \\
3 & “VV\_STD” & Standard deviation single co-polarization, vertical \\  & & transmit/vertical receive \\
4 & “VH\_STD” & Standard deviation dual-band cross-polarization, vertical transmit/horizontal receive \\
5 & “NDPI” & Normalized Difference Polarization Index \\
6 & “NDPI\_STD” & Standard deviation Normalized Difference Polarization \\
7 & “CR” & Index \\
8 & “CR\_STD” & Cross ratio \\ \hline \hline \end{tabular}
\end{table} 
Table 5: SAR Sentinel-1 GRD bands in water mapping. in the data. (3) The conversion to dB was performed in the SNAP vers.8.0.0. In fact, the strength of the radar signal reflected from a unit area on the corresponding point in the scene determined the pixel value of the SAR image. The backscatter coefficient \(\beta 0\) was calibrated and employed to convert the values from the digital number to the reflectivity of the surface objects. The target's radar cross-section per surface unit with regard to the local incidence angle was parameter \(\beta 0\). After that, all SAR data were transformed from raw data to power units (decibels-dB). The de-speckle filter was used to eliminate the salt and pepper noise while keeping the edges and the textural structures prior to the data analysis due to the speckle effect created by the coherent radiation used by radar systems.