## 2 Materials and Methods
### Methods  
#### 2.2.1 PS-InSAR Displacements  
The dataset has been analysed using the SARProZ(r) software [49; 53]. In the classical PS-InSAR technique, a target is required to be coherent in all interferograms generated with a star graph MBC [54]. A dam, as for many human-made structures, offers many artificial reflectors. For both ascending and descending datasets, a master image has been selected by minimizing the spatial and temporal decorrelations and is assumed as a reference for the estimation of a displacement time series of natural targets with 'permanent' radiometric characteristics over time. The full-graph MBC method introduces all possible connections amongst image pairs, thus using all interferograms, including those with longer temporal baseline than the ones eventually involved in the classical PS technique. The interferograms have been filtered with a Goldstein filter [55] with a fixed window size. As several interferograms were characterised by low coherence pixels, to maintain an accurate estimation of the displacements, the connections have been weighted by spatial coherence. According to [56] the temporal correlation over extra-urban areas should increase. Generally, the use of the full graph is more time demanding because it requires the analysis of n!/2(n \(-\) 2)! redundant connections (190 in this case). In addition, the size of the study area influences the processing time. In this work, the processed image is quite small (860 samples by 1120 lines), and thus, the computational time difference with the star graph is not significant. The Atmospheric Phase Screen (APS) is estimated through the \begin{table}
\begin{tabular}{c c c c c c c} \hline \multicolumn{2}{c}{**Period 1**} & \multicolumn{2}{c}{**Period 2**} & \multicolumn{2}{c}{**Period 3**} & \multicolumn{2}{c}{**Period 4**} \\ \hline \multicolumn{2}{c}{**Filling**} & \multicolumn{2}{c}{**Storing**} & \multicolumn{2}{c}{**Emptying**} & \multicolumn{2}{c}{**Filling**} \\ \hline ascending & descending & ascending & descending & ascending & descending & ascending & descending \\ \hline
05/01/15 & & & 12/03/15 & & 23/05/15 & 20/10/15 & \\  & 11/01/15 & 18/03/15 & & & 04/06/15 & 07/12/15 & \\  & 28/02/15 & & 24/03/15 & 10/06/15 & & 19/11/15 \\  & & 05/04/15 & 22/06/15 & & & 13/12/15 \\  & & 11/04/15 & & 04/07/15 & & 19/12/15 & \\  & & 17/04/15 & & & 10/07/15 & & 25/12/15 \\  & & 23/04/15 & & 16/07/15 & & 12/01/16 & \\  & & 29/04/15 & & 22/07/15 & & \\  & & 11/05/15 & 28/07/15 & & & \\  & & 09/08/15 & & & & \\  & & & 21/08/15 & & & \\  & & & & 27/08/15 & & \\  & & & 02/09/15 & & & \\  & & & 08/09/15 & & & \\  & & & 14/09/15 & & & \\  & & 26/09/15 & & & & \\  & & 08/10/15 & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: TOPSAR S-1A images. inverted residuals approach [56; 57], using the reflectivity map as a parameter for the sparse point selection. The method has been already applied to monitor dam via multi-temporal InSAR [39]. A threshold on the reflectivity (>1.8) excludes PS candidates falling on the reservoir surface. At the time of the data processing, external services, such as the Generic Atmospheric Correction Online Service for InSAR-GACOS [58; 59; 60; 61; 62] was not available. In this work, using the star graph MBC connections, the nonlinear displacements have been retrieved using a nonlinear model implemented [54] in the software. In this case, given the relatively few images comprising the time series (20 images for the ascending dataset and 11 images for the descending dataset), the window of the temporal filter has been set equal to three (images) [52]. In addition, weight in terms of spatial coherence (the mean interferometric coherence calculated as the average of a set of interferograms) has been applied during the processing involving the entire connections. The reference points in the ascending and descending tracks have a position almost coincident, close to the left bank of the dam in a stable area.