## 5 Discussion and Performance Assessment  
This section provides comments on the experimental results observed in the three case studies. The experimental results show that the implemented algorithm is quite robust, although sometimes it fails to provide a reliable estimate. This is because there is a temporal misalignment from the actual SAR observation that occurs in Italy either early in the morning or late in the evening compared to the measurement of the instrument located in the immediate vicinity of the bridges. This time misalignment is also found to be many hours.  
In Figure 16, the scatterplot is reported for each case study, representing the comparison between the water levels estimated by satellite and those observed by the in-situ station. For the Po and the Tiber in Rome (Figure 16 left and right) the water levels overlap the bisector line, as also indicated by the linear regression (red line). In the case of Tiber at Ponte Nuovo (Figure 16 center) the simulated water levels underestimate the ground-based observations up to 2 m, whereas they overestimate the higher water levels. Therefore, the red line does not lie upon the bisector line as the other two cases.  
The worst performance are obtained for the Ponte Nuovo case study (as shown at the center of Figure 16). It is worth noticing that this case study has to be selected to provide an example of a difficult scene to analyze. This difficulty can be attributed to the width of the river that in this region is quite narrow (60 m as shown in Table 1) and is greatly contaminated by the surrounding vegetation. These characteristics can affect the satellite measurements and represent a good testbed for the proposed algorithm which, despite everything, would provide still reliable results as shown in the  
Figure 14: (**a**): Case study 3 ROI. (**b**): ROI footprint. (**c**): Cavour bridge optical image.  
Figure 15: Case study 3 results. (**a**): Ground-station data (red) and satellite observations (blue), versus pixels. (**b**): Water level errors versus time. Blue: CSK versus true. Red: CSK versus true (5 observations average). Black: CSK versus true (10 observations average).  
figure. A possible solution to improve the performance of the algorithm could be the installation of corner reflectors in the scene to mitigate the effect of the noise introduced in the radar measurements.  
In order to quantify the performances of the analysis, four indicators are calculated:  
* the Pearson correlation coefficient (R),
* the Nash-Sutcliffe efficiency (NS) [27],
* the root-mean square error (RMSE), expressed in [m],
* the related root-mean square error (RRMSE), defined as the ratio between the RMSE and the mean of the observed water levels.  
Table 3 shows the performances for the three case studies comparing the water levels estimated by the procedure and those observed by in-situ stations. As deduced by the scatterplots, best results are obtained for case study one and three, with coefficient of correlation greater than 0.88 and NS greater than 0.77.  
Lower performances are obtained for case two with NS smaller than zero and RRMSE of 39%. However, if we calculate the performance considering the linear regression as shown in Figure 16 (center), the performances improve (NS = 0.43; RMSE = 0.51; RRMSE = 0.29). This means that the procedure can fail in terms of absolute values but can be a support to evaluate a variability of the water level if no other measurements are available, as for example in ungauged basins.  
In the first case study, the value of the RMSE is quite high (0.91 m) comparing to the other two cases but the RRMSE is the lowest. This is due to the fact that the RMSE is an absolute figure of merit that is not related to a specific value as, on the contrary, the RRMSE. In fact, for the case 1, the water levels range from 6 to 15 m, whereas a narrower range characterizes the other two cases.