## Interferometry processing
### Training Set and Validation Set Definition  
In order to better understand the spatial extent distribution of each class and determine the ideal number of training areas for each class in the training set, a K-means unsupervised classification with 15 classes was conducted after constructing the initial input dataset. Regarding the last criteria, there needed to be enough training pixels for each spectral class to enable accurate estimations of the components of the covariance matrix and the class conditional mean vector. The covariance matrix for an N-dimensional multispectral space was symmetric and has a size of N*N. Therefore, it required an estimation from the training data for 1/2N (N + 1) unique elements. It took at least N (N + 1) independent samples to keep the matrix from being singular. The good news was that each N-dimensional pixel vector contained N samples (one for each waveband). As a result, only (N + 1) independent training pixels were necessary. Since it was challenging to guarantee the independence of the pixels, more than the minimum amount was chosen. [37; 70] advocate for using as many as 100 N training pixels per class, with 10 N being the lowest practical number. Therefore, a minimum of 250 polygons (containing a minimum of 5 pixels) were computed for this categorization, taking only the spectral bands and relative indices without the standard deviation (see Figure 3). The object-based segmentation (OBS) approach was performed using the mean shift algorithm available on the Orfeo Toolbox software v.8.0.0 [71, 72]. The OBS algorithms aimed at minimizing the spectral heterogeneity of the polygons by comparing the relative spectral properties of the neighboring pixels. The resulting segmentation vector layer (SVL) was generated according to a previously defined minimum mapping unit of 300 m\({}^{2}\). In particular, the segmentation was performed with reference to the S2 bands performing a bilinear resampling on those without a native 10 GSD. Then, the images were segmented based on an internally homogeneous spectral response. The segments were then vectorized to generate the corresponding vector layer. During the segmentation, the required parameters were set to the values shown in Table 6. The SEG was then used to explore the internal features other than the spectral signatures, such as the recurrent radiometric patterns (texture) and the shape. Some of these polygons were then randomly extracted and others were created by analyzing the signatures of the entire stack to define the training areas, including GTDP. As previously mentioned, the regions of interests (ROI) per each class were defined mostly on the field and partially by applying both a segmentation and a spectral signature-photo interpretation phase. Figure 3 depicts the distribution of the ROIs in the study area. Each ROI per class had a number of polygons up to 250. An overall of 4300 ROIs were \begin{table}
\begin{tabular}{c c} \hline _Segmentation Parameter_ & _Settings_ \\ \hline Spatial radius & 3 pixels \\ Range radius & 100 DN \\ Mode convergence threshold & 0.1 \\ Maximum numerous of iterations & 200 \\ Minimum region size & 3 pixels \\ \hline \end{tabular}
\end{table} 
Table 6: Segmentation settings in SAGA GIS. Figure 3: ROIs considering both the training and validation sets. defined and 70% of them were adopted as the training set 30% as the validation set. In the developed EO local service, the ROI detection and the relative changes through time were performed by coupling a self-developed semi-automatic technique. The fact that the technique required a manual check in case of an anomaly was linked to the reason that a simple probabilistic approach such as those developed in Dynamic World by Google did not permit the mapping of the real changes that happen with a high degree of accuracy, especially in alpine areas. In the first phase a pixel-based analysis into each of the ROIs were performed in the GEE by analyzing the variance of each of the \(S\)2 bands.