## 4 Results
### Analysis of Intra-Pass Noise  
This subsection analyzes the noise in WL\({}_{i}\) observations within each satellite pass, which is the statistics of a series of consecutive independent samples during a single pass over the target. Figure 10 compares the performance of the presented WL\({}_{i}\) filter in the Itoiz Reservoir with the mean and the median by displaying the error with respect to the WL\({}_{t}\) of the in situ station. The top panel shows the water level error (WL\({}_{i}\)E) obtained from all FFSAR measurements, and the panel below shows, for each date, the mean and the standard deviation as error bars. The third and fourth panels show, for each date, the median and the filtered WL\({}_{i}\) from FFSAR-derived measurements. Figure 10 shows that the distribution of FFSAR measurements can contain outliers with WL\({}_{i}\)Es larger than a few meters, thereby making the mean an unsuitable approach, due to its sensitivity to the  
Figure 9: The data in this figure include all the passes of S6 over the target locations where the in situ water level was inside the satellite window of observation. The top panel shows, for FFSAR and UFSAR, the distribution of nadir (NM) and across-track (AM) measurements. The middle and bottom panel show a classification of the water level errors (WL\({}_{i}\)Es) from all FFSAR and UFSAR-OCOG measurements in five error groups.  
presence of outliers. In contrast, the median, which is less sensitive to outliers, generally achieved WL\({}_{u}\)Es below 10 cm. However, when the distribution of measurements is sparse and presents multiple peaks, as shown in Figure 5, the median might not be able to select an accurate WL\({}_{a}\). Such sparse distribution can occur due to the presence of several bright off-nadir scatterers within the radar's footprint. This problem is tackled by the presented filter, which looks for the WL\({}_{i}\) cluster with the highest density instead of the WL\({}_{i}\) that falls in the middle of an ordered sequence of measurements, as the median does.  
Figure 11 displays the WL\({}_{i}\)E of all FFSAR measurements in Yesa Reservoir, limited to those with an in situ WL\({}_{t}\) within the satellite's window. Each pixel represents a measurement, with black pixels indicating errors equal to or greater than 100 cm. The figure illustrates that the majority of measurements had WL\({}_{i}\)Es well below 20 cm. However, it also reveals the presence of large errors scattered across the water mask, suggesting that corrupted measurements can originate from any location within it, not just at its edges. This observation underscores that intra-pass noise can arise from various points inside the water mask, contributing to the overall measurement uncertainty. Additionally, Figure 11 depicts the variability in the number of waveforms and the latitude range obtained from each satellite pass, influenced by the satellite's drift from the nominal track and the shape of the water mask.  
Figure 10: Water level error (WL\({}_{i}\)E) in the Itoiz Reservoir calculated as the difference between the FFSAR-derived WL\({}_{i}\) and the WL\({}_{t}\) of the in situ station. The top panel presents the WL\({}_{i}\)Es of all FFSAR measurements for each pass. The second panel presents the mean and the standard deviation as error bars. The third and fourth panels present the median and filtered WL\({}_{i}\)E. The gap in observations at the middle of the time series is due to an incorrect position of the satellite’s range window.