## 4 Methods
### Sentinel-1  
S1 SAR images were used only to map urban and water components in addition to the optics. The other classes were mapped only with optical remote sensing due to the fact that SAR distortions in mountainous areas do not permit higher accuracy land cover mapping. Therefore, the data offered by optical remote sensing are the only data in alpine environments that are truly capable of offering consistent and reliable mapping, despite being bound to atmospheric conditions. However, due to the composite in land cover, it is possible for it to be overcome. In order to create a mask for urban areas, as first step, pairs of S1 SLC images were downloaded from the NASA ASF. In particular, to achieve interferometry with an exact repeated coverage, only images derived from the same satellite sensor in the exact acquisition mode were used (ascending or descending see Table 2). Due to the low rate of urbanization in recent years in the Aosta Valley (in terms of an increase in built-up structures), the changes in the urban footprint observed within the last couple of years can be neglected if considering the spatial resolution of the Sentinel-1 SAR sensors (deep learning was performed to refine this). Therefore, we can consider the urban footprint as a constant value for all the Sentinel-1 images acquired within a single-year time frame. The use and interpretation of SAR imagery require a series of complex pre-processing procedures, which we ran on ESA's SNAP v.8.0.0 software. Such procedures refer to the standard preprocessing commonly applied to Sentinel-1 products to derive interferometric coherence [61; 62]. The interferometry was conducted only on those images pairs which had a perpendicular baseline possibly more of 130 m within the year (in the e.g., 2020) and a temporal baseline lower than 10 days. We reported the available adopted pairs from the ASF in Table 4. \begin{table}
\begin{tabular}{l l l l} \hline \hline \multicolumn{4}{c}{**S1 Pairs Ascending Orbit**} \\ \multicolumn{4}{c}{**(Product n\({}^{c}\), Baseline, Temporal Distance in Days between the Two Acquisitions)**} \\ \hline S1A\_IW\_SLC\_1 SDV\_20200430T172 & S1B\_IW\_SLC\_1 SDV\_20200 & & \\
327\_20200430T172354\_03260\_03 BE & 506T172238\_20200506T1723 & 136 m & 5 \\ E8\_2356 & 05\_021464\_028C15\_773E & & \\ \hline S1B\_IW\_SLC\_1 SDV\_20200530T172 & S1A\_IW\_SLC\_1 SDV\_2020 & & \\
240\_20200530T172307\_021814\_02968 & 0605T172329\_20200605T172 & 152 m & 7 \\  & 0.5539 & 356\_032885\_03 CF21\_34 AB & & \\ \hline S1A\_IW\_SLC\_1 SDV\_20200804T172 & S1B\_IW\_SLC\_1 SDV\_20200 & & \\
333\_20200804T172400\_033760\_03E9B & 810T172255\_20200810T1723 & 152 m & 6 \\  & C\_E6 AD & 22\_022864\_02B66E\_1179 & & \\ \hline S1A\_IW\_SLC\_1 SDV\_20200828T172 & S1B\_IW\_SLC\_1 SDV\_20200 & & \\
334\_20200828T172401\_034110\_036F5F & 903T172253\_20200903T1723 & 162 m & 6 \\  & E\_8B79 & 20\_023214\_02C15A\_3F08 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: SAR S1 images pairs with the distance baseline and days. In particular, we adopted the approach described by the ESA guidelines available in [63; 64; 65] by introducing a variation in the type of classification. In this case, the maximum likelihood was not chosen. Instead, random forest and batch processing were created to involve all the selected pairs. It is worth noting that co-registration and terrain-shadow correction were performed in the ESA SNAP v.8.0.0 toolbox. See more detail in Figure 2.  
We used both that polarizations (VH and VV) on all the SAR input data, hence the output coherence image consisted of two separate raster files related to the different polarizations. In terms of the processing procedure, we selected only the bursts that covered our study area (the Aosta Valley autonomous region) from the original product. In addition, we computed the coherence estimation using a range window size of 10 pixels.