## 4 Test on Cosmo-SkyMed Data
### Case Studies and In-Situ Observations  
The processed data belong to the persistent Earth observation mission called MAPITALY procured by the Italian Space Agency (ASI). This mission performs the interferometric observation of the whole Italian territory with a revisiting time of about 10 days. For the analysis, three datasets of CSK images were considered based on three study areas. The results estimated from satellite data were validated by comparison with the ground observations of water level recorded in a consistent period with respect to the satellite images. In particular, three gauged stations along two Italian rivers were considered--Pontelagoscuro along the Po River, Ponte Nuovo and Ripetta along the Tiber River.  
The first case study observes the Po River located on the Northern Italy at the Pontelagoscuro station. Figure 5a shows the georeferenced representation of the SAR long temporal series. Inside  
Figure 4: Results of simulated data. (**a**): reflectivity profile. (**b**): Unwrapped phases. (**c**): water-levels estimated results (pixels).  
the SAR acquisition footprints there is a small red box with a yellow marker inside, geolocated on the following coordinates: datum WGS-84 (EPSG): 4240, 44\({}^{\circ}\) 53\({}^{\prime}\) 16.66\({}^{\prime\prime}\) N 11\({}^{\circ}\) 36\({}^{\prime}\) 29.42\({}^{\prime\prime}\) E. This box is tagged in yellow with the number 1. This ROI-footprint is represented in detail in Figure 5b where the bridge is observed by an optical image and contoured by the same red box. The ground water levels are registered by the Agenzia Interregionale del Filume Po.  
The second data-set is measured over the Tiber river located in Central Italy. Figure 6a represents some footprints of the SAR observations. Inside the SAR acquisition footprints there is a small red box with a green marker inside, geolocated on the following coordinates--datum WGS-84 (EPSG): 4240, 43\({}^{\circ}\) 00\({}^{\prime}\) 37.84\({}^{\prime\prime}\) N 12\({}^{\circ}\) 25\({}^{\prime}\) 44.89\({}^{\prime\prime}\) E. This box is tagged in yellow with the number 1. This ROI-footprint is represented in detail in Figure 6b where the bridge is observed by an optical image and contoured by the same red box. The observed water levels are registered by the Servizio Idrografico of the Umbria Region.  
The last case study is composed of satellite observations concentrated on the city of Rome. The optical representation of the environment where the river water level has been estimated is reported in Figure 7a. The picture also reports the footprints of the long temporal series of the interferometric SAR observations. The measurements are focused on the Cavour bridge where the optical representation of the infrastructure is reported in Figure 7b. The data are registered by the Agenzia Regionale Protezione Civile of the Lazio Region.  
Figure 5: Case study 1 optical representations. (**a**): georeferenced footprints of the SAR long temporal series. (**b**): region of interest (ROI) footprint.  
Figure 6: Case study 2 optical representations. (**a**): georeferenced footprints of the SAR long temporal series. (**b**): ROI footprint.  
The number of processed images for study areas and the period of analysis is specified in Table 1. The number of images varies from 27 images for the study area at Rome and 106 for Pontelagoscuro station. The period of images is different, ranging from 2 to 9 years. For all the experiments, we set the cross-correlation window size to \(128\times 128\) pixels and the oversampling factor to 64 in both the range and azimuth directions. This value was found to be an optimal pixel dilation level. All the coregistration parameters are reported in Table 2.