## 3 Results and Discussion
### Case-Study I: Lakes
It can be noticed that the reflected power from water roughly increases linearly with the incident angle (the satellite elevation). It can also be noticed that although we did not set a cut-off for the elevation angle, the useful measurements i.e., the measurements from water, were for angles greater than 30 degrees in our data collection. Measurements from satellites with less then 30\({}^{\circ}\) simply did not fall on the lakes during this data collection, and thus did not show significant reflections. Figure 5: Comparison of the peak-to-noise-floor separation of the reflected signal for (**a**) data set (1), and (**b**) data set (2), when the sensor crossed the lakes on the different passes: north to south (**top**), south to north (**middle**), and west to east (**bottom**). The previous results and discussion prove the possibility of detecting the presence of water using our low cost, software radio GNSS-R sensor. They also prove that the edges of water are well detected. In the following sub-sections, we are investigating the collected data to extract information about the area of the detected water surfaces. Then, we are analyzing the benefit of multi-GNSS for GNSS-R, by investigating the improvement in water surface area estimation when multi-GNSS are considered. Figure 6: GNSS signals specular reflection points superimposed into an orthophotomap. The colorgrades indicate the measured reflected power \(\alpha_{mean}\). Water Surface Area Estimation and Benefit of Multi-GNSS  
Figure 8 reports the lines of specular points for which the value of \(\alpha_{mean}\) exceeded 6 dB. Here, we superimposed the specular points into the orthophotomap of the upper lake and we linked the extreme points in order to form a polygon. This roughly creates an estimation of the water surface using GNSS-R. This particular encircled area is 0.822 km\({}^{2}\). It is marginally smaller than the true surface of the lake which is approximately 0.89 km\({}^{2}\) as reported in [57]. This estimate of the surface water area is about 7.5% less than the true area. But, since we are processing only the reflected GPS signals, the accuracy of such an estimate could be enhanced by taking advantage of multi-GNSS signals. In order to investigate the improvement introduced by Galileo, GLONASS and BeiDou signals, we simulated a realistic flight trajectory and evaluated the increase in the number of specular points on the Northern lake. Figure 9a reports the sensor trajectory we choose for the simulation. It passes the Northern lake roughly in the middle, both on the north-south and west-east directions. We calculated the lines of specular points for the satellites belonging to the various constellations. We evaluated this trajectory at 100 and 200 m heights above the Earth surface, which are typical values for small UAV flights. The reason for simulating two heights is to ensure that the simulated height of the flight is not biasing the results we obtain, due to the fact that we are measuring a specific lake area; since the flight height should be proportional to the size of the targeted water body. Figure 9b-e show samples of the results, with clear enhancement in the number of specular points lines when constellations are added. Here we report the results of the 200 m flight height above the Northern lake only. The advantages of considering multi-GNSS reflectometry were also quantified in terms of the accuracy of the estimation of the surface area of the Northern lake, evaluated as the  
Figure 8: Estimation of the Northern Avigliana lake surface area using GNSS-R. The red dotted lines represent the estimated boundary of the lake from the GNSS signals reflected from the water surface. Figure 7: The reflected power from the lake \(\alpha_{mean}\) VS. satellite elevation. ratio between the estimated area and the true area. Figure 9f reports the estimation accuracy versus the number of visible satellites, which improves when adding more GNSS signals.