## 4 Test on Cosmo-SkyMed Data
### Experimental Results
This sub-ROI consists of the data input of the computational block number 5 depicted by Figure 2. Figure 12a is the long temporal series time average sub-ROI particular. Figure 12b 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 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 13a. 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 13b. Figure 11: Case study 2 magnitude SAR images. (**a**): Geolocated image with ROI footprint representation. (**b**) Particular of the ROI magnitude in the slant coordinates. Figure 10: Case study 1 experimental measurements. (**a**): Water levels observed by the ground measurement station (blue line) and by the satellite (red line). (**b**): Unwrapped phases. In the final case, it was planned to quantify the water height levels of the Tiber River as it flows through the city center of Rome. Also for this case study the experimental measurements were compared with the ground-based measuring facilities. Figure 14a shows the georeferenced SAR extended image where the ROI is visible inside the red box tagged by the yellow number 1. The geolocated SAR ROI is represented in detail in Figure 14b where the bridge is observed and contoured by the same red box. Finally, the optical representation of the _Cavour_ bridge is shown in Figure 14c. The double-bounce electromagnetic scattering effects were generated by the _Cavour_ bridge (the yellow arrow which is geolocated on the following coordinates: datum WGS-84 (EPSG); 4240, 41\({}^{\circ}\) 51\({}^{\prime}\) 36.10\({}^{\prime\prime}\) N 12\({}^{\circ}\) 28\({}^{\prime}\) 38.00\({}^{\prime\prime}\) E). The temporal trend of the river water levels is depicted in Figure 15a. In Figure 15b, the errors corresponding to the estimated values in Figure 15a are reported. In addition to the errors represented by a red line, the errors of the estimated values averaged over 5 and 10 samples are shown with a blue and a black line, respectively. As expected, it could be convenient, in the case when the data are very noisy, to exploit the smoothing effect due to averaging. Moreover, from the non-averaged errors of Figure 15b, it can be seen that some measurements are wrong but such uncompliant samples are very few; in fact, observing the trend of the average errors on 5 and 10 samples a significant drop in the error can be seen, which remains well below one meter. Figure 12: Case study 2 Sub-ROI parameters. (**a**): Sub-ROI SAR image representation in the slant coordinates. (**b**): Scattering parameters on the reference points and pixel spacing trend. Figure 13: Case study 2 experimental measurements. (**a**): Water levels observed by the ground measurement station (blue line) and by the satellite (red line). (**b**): Unwrapped phases.