## 4 Results and Discussion
### Contribution of Different Parameters to SAR SSW Speed Uncertainty  
The uncertainty in SAR SSW speed obtained through a GMF inversion procedure depends on several parameters. In particular, the uncertainty \(\Delta\)W\({}_{\max}\) is mainly affected by both the triplet of uncertainties (\(\Delta\)\(\sigma_{0}\),\(\Delta\)\(\Theta\),\(\Delta\)\(\varphi\)) (bullet i, Section 3) and the true state triplet (\(\sigma_{0}\),\(\theta\),\(\varphi\)) (bullet ii, Section 3). Figures 3 and 4 highlight the relevance of all combining parameters. Figure 3a shows, for a fixed triplet of uncertainties (\(\Delta\)\(\sigma_{0}\),\(\Delta\)\(\varphi\)) = (0.005,0.1\({}^{\circ}\),10\({}^{\circ}\)), the total CMD5.N-derived SAR SSW speed uncertainty \(\Delta\)W\({}_{\max}\) (m/s) plotted as a function of the varying true state (W,\(\theta\),\(\varphi\)), where \(\varphi\) is from 0\({}^{\circ}\) (upwind) to 180\({}^{\circ}\) (downwind) (\(x\) axis), W is between 5 and 25 m/s (\(y\) axis), and \(\theta\) is 29\({}^{\circ}\), 37.5\({}^{\circ}\), and 46\({}^{\circ}\) (\(z\) axis). Note that the SSW speed W is reported on the \(y\) axis rather than the sigma nontight \(\sigma_{0}\) with the aim to allow for an intuitive understanding of the true state. Secondly, the SSW directions \(\varphi\) from 180\({}^{\circ}\) to 360\({}^{\circ}\) are not plotted since the CMOD models, like CMOD5.N, are symmetric with respect to the direction \(\varphi\) = 180\({}^{\circ}\), once the wind speed W and the incidence angle \(\theta\) have been fixed. Finally, the values on the \(z\) axis cover the range of incidence angles \(\theta\) for Sentinel-1 acquisitions. The contribution to \(\Delta\)W\({}_{\max}\) obtained considering each single uncertainty, i.e., the one derived from the NRCS (\(\Delta\)\(\sigma_{0}\) = 0.005), the incidence angle (\(\Delta\)\(\theta\) = 0.1\({}^{\circ}\)) and the MS LG-Mod SSW (relative) direction (\(\Delta\)\(\varphi\) = 10\({}^{\circ}\)), with the same true state (W,\(\theta\),\(\varphi\)), is shown in Figure 3b-d, respectively. From Figure 3b, the fixed uncertainty \(\Delta\)  
Figure 3: The total C-band MODel 5.N (CMOD5.N)-derived SAR SSW speed uncertainty \(\Delta\)W\({}_{\max}\) (m/s), due to both the fixed triplet of uncertainties (\(\Delta\)\(\sigma_{0}\),\(\Delta\)\(\Theta\),\(\Delta\)\(\varphi\)) = (0.005,0.1\({}^{\circ}\),10\({}^{\circ}\)) and the varying true state (W,\(\theta\),\(\varphi\)) (**a**). The contribution to this uncertainty only due to a single uncertainty among the ones regarding NRCS (\(\Delta\)\(\sigma_{0}\) = 0.005) (**b**), incidence angle (\(\Delta\)\(\theta\) = 0.1\({}^{\circ}\)) (**c**), and MS LG-Mod SSW (relative) direction (\(\Delta\)\(\varphi\) = 10\({}^{\circ}\)) (**d**), with the same true state (W,\(\theta\),\(\varphi\)). The wind speed uncertainty is computed for the wind direction \(\varphi\) from 0\({}^{\circ}\) (upwind) to 180\({}^{\circ}\) (downwind) (\(x\) axis), the wind speed W between 5 and 25 m/s (\(y\) axis), and the incidence angle \(\theta\) of 29\({}^{\circ}\), 37.5\({}^{\circ}\), and 46\({}^{\circ}\) (\(z\) axis). weights more for lower wind speeds, and especially for higher incidence angles. The wind direction that is more affected by this single uncertainty is the crosswind direction. When the only uncertainty \(\Delta\theta\) is considered, as shown in Figure 3c, the SSW speed uncertainty decreases with increasing incidence angles and increasing wind speeds as well, with the upwind direction that represents the worst-case estimation. When the only uncertainty \(\Delta\varphi\) is applied, Figure 3d shows again the decreasing SSW speed uncertainty with increasing incidence angles and wind speeds, with a worst-case estimation for a direction around the middle of the range [0\({}^{\circ}\), 45\({}^{\circ}\)]. When these three contributions are all applied, their effects combine together in a complex way to provide the total SSW speed uncertainty, as reported in Figure 3a.