## 4 Test on Cosmo-SkyMed Data
### Experimental Results  
In Figure 8a, the SLC-ROI is reported, referring to the small patch number 1 depicted in Figure 5a,b. This ROI contains the electromagnetic representation of the bridge, used to calculate the water levels of the Po river. The detailed sub-ROI SLC image is shown in Figure 8b. This sub-ROI consists of the data input of the computational block number 5 depicted by Figure 2. Figure 9a is the long temporal series time average sub-ROI particular. Figure 9b gives the description of the scattering events related to the bridge. The purple line number 1 represents the beginning of the bridge structure. Purple line 2 shows the position of the end of the bridge, this scattering event is considered to be a stationary landmark in time. The blue line 3 represents the lowest deviation of the double-bounce scattering event with respect to the reference point, which means that the river is in flood. Line 4 represents the slightest \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**STATION** & **RIVER** & **COORDINATES (WGS-84)** & **Time of Obs.** & **Images** & **River Width** \\  & & & & **Number** & **[m]** \\ \hline Pontelagoscuro & Po & 44\({}^{\circ}\) 53\({}^{\prime}\) 18.84\({}^{\prime\prime}\) N, 11\({}^{\circ}\) 36\({}^{\prime}\) 28.89\({}^{\prime\prime}\) E & May 2009–Aug, 2018 & 106 & 340 \\ Ponte Nuovo & Tiber & 43\({}^{\circ}\) 00\({}^{\prime}\) 37.11\({}^{\prime\prime}\) N, 12\({}^{\circ}\) 25\({}^{\prime}\) 45.15\({}^{\prime\prime}\) E & Mar. 2011–Apr. 2017 & 76 & 60 \\ Ripetta & Tiber & 41\({}^{\circ}\) 54\({}^{\prime}\) 17.59\({}^{\prime\prime}\) N 12\({}^{\circ}\) 28\({}^{\prime}\) 27.84\({}^{\prime\prime}\) E & Sept. 2009–Oct. 2016 & 37 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Satellite datasets used in the analysis and corresponding river gauged stations \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Initial shifts & Coarse cross-correlation \\ Number of points & 4000 \\ Correlation threshold & 0.8 \\ Oversampling factor & 200 \\ search pixel window & 48x48 pixel \\ Points skimming (minimum points) & 30 \\ Use of DEM & Yes \\ Doppler Centr. Est. Strategy & Polynomials \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coregistration parameters  
Figure 7: Case study 3 optical representations. (**a**): georeferenced footprints of the SAR long temporal series. (**b**): ROI footprint. deviation of the double-bounce scattering event, if the pixel is represented it means that the river is dry. The variance of the double-bounce layovered backscattered echoes is strictly located inside the spatial gap contained by the blue layers 3 and 4. The temporal trend of this layover scattering line is a function of the river water level. The trend of the estimated water levels is depicted in Figure 10a. The blue line represents the water-levels measured by the CSK satellite system and the red function represents the ground truths given by the ground observation station. The unwrapped phases of the FT result are shown in Figure 10b. Figure 8: Case study 1 magnitude SAR images. (**a**): Geolocated image with ROI footprint representation. (**b**) Particular of the ROI magnitude in the slant coordinates. Figure 9: Case study 1 Sub-ROI parameters. (**a**): Sub-ROI SAR image representation in the slant coordinates. (**b**): Scattering parameters on the reference points and pixel spacing trend. Case study 2 has the objective of studying the trend of the Tiber heights in the part of the river that crosses the Umbrian region located in the Italian Central Apennines. This part of the Tiber is narrower with respect to the Po and the radar observations are a bit noisier. Considering this phenomenon, the estimation of the heights of the rivers on this section is more difficult. In Figure 11a the SLC-ROI is reported, referring to the small patch number 1 depicted in Figure 7a,b. This ROI contains the electromagnetic representation of the bridge, used to calculate the water levels of the Po river. The detailed sub-ROI SLC image is shown in Figure 11b.