## 4 Results and Discussion
### SAR Dataset Results
From Figure 5a, the higher contribution (mean = 1.34 m/s; std = 0.96 m/s, Table 3) seems clearly to derive from the uncertainty of the SSW direction, while the one (mean = 0.61 m/s; std = 0.27 m/s, Table 3) associated with the NRCS uncertainty is demonstrated to be meaningful as well. The lower contribution (mean = 0.11 m/s; std = 0.04 m/s, Table 3) is linked to the uncertainty of the incidence angle. These contributions, which depend also on the actual true state, shown in Figure 5b, represent on average about the 59.81% (\(\pm\) 15.26%), 34.63% (\(\pm\) 14.63%) and 6.65% (\(\pm\) 3.47%) \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**CMOD5.N**} & \multicolumn{4}{c}{**CMOD7**} \\ \cline{2-7}  & **5 km** & **10 km** & **15 km** & **5 km** & **10 km** & **15 km** \\ \hline mean\(\forall_{\text{l}}\ldots\text{N\_ROI}\)(E1\_ROI\({}_{\text{l}}\)) (m/s) 1 & 0.61 & 0.59 & 0.67 & 0.57 & 0.55 & 0.63 \\  & (34.63\%) & (45.43\%) & (50.66\%) & (34.52\%) & (45.23\%) & (51.03\%) \\ \hline std\(\forall_{\text{l}}\ldots\text{N\_ROI}\)(E1\_ROI\({}_{\text{l}}\)) (m/s) 1 & 0.27 & 0.28 & 0.31 & 0.25 & 0.26 & 0.29 \\  & (14.63\%) & (13.78\%) & (12.08\%) & (14.89\%) & (14.02\%) & (12.39\%) \\ \hline mean\(\forall_{\text{l}}\ldots\text{N\_ROI}\)(E2\_ROI\({}_{\text{l}}\)) (m/s) 1 & 0.11 & 0.19 & 0.28 & 0.11 & 0.18 & 0.26 \\  & (6.65\%) & (14.99\%) & (22.03\%) & (6.87\%) & (15.20\%) & (22.30\%) \\ \hline std\(\forall_{\text{l}}\ldots\text{N\_ROI}\)(E2\_ROI\({}_{\text{l}}\)) (m/s) 1 & 0.04 & 0.08 & 0.11 & 0.04 & 0.08 & 0.11 \\  & (3.47\%) & (5.96\%) & (7.66\%) & (3.77\%) & (6.13\%) & (7.86\%) \\ \hline mean\(\forall_{\text{l}}\ldots\text{N\_ROI}\)(E3\_ROI\({}_{\text{l}}\)) (m/s) 1 & 1.34 & 0.62 & 0.42 & 1.29 & 0.59 & 0.39 \\  & (59.81\%) & (41.38\%) & (29.23\%) & (59.91\%) & (41.63\%) & (29.18\%) \\ \hline std\(\forall_{\text{l}}\ldots\text{N\_ROI}\)(E3\_ROI\({}_{\text{l}}\)) (m/s) 1 & 0.96 & 0.41 & 0.27 & 0.96 & 0.39 & 0.26 \\  & (15.26\%) & (14.68\%) & (12.49\%) & (15.26\%) & (14.86\%) & (12.63\%) \\ \hline \hline \end{tabular}  
* Ek\(\_\)ROI\({}_{\text{l}}\) represents the GMF-derived SSW speed uncertainty (m/s) within the i-th ROI, where k = 1, k = 2 and k = 3 means (\(\sigma_{0}\),\(\theta\),\(\varphi\),\(\Delta\theta\)), (\(\varphi\),\(\Delta\theta\)) and (\(\varphi_{0}\),\(\theta\),\(\Delta\varphi\)), respectively.  
\end{table} 
Table 3: Statistics (in (m/s)) and ratio (in (%)) about the contribution, due to the true state (\(\sigma_{0}\),\(\theta\),\(\varphi\)) and a single uncertainty among the ones regarding the NRCS (\(\Delta\sigma_{0}\)) (E1), the incidence angle (\(\Delta\theta\)) (E2) and the MS LG-Mod SSW (relative) direction (\(\Delta\varphi\)) (E3), to the total SAR SSW speed uncertainty (m/s) for all ROIs, at various dimensions and for two different applied GMFs. of the total SSW speed uncertainty, as reported previously in Table 3. Looking at the trends in Figure 5b, an inverse correlation between the two dominant contributions due to the SSW direction and the NRCS uncertainty could be noticed. The reason could be that, when the directional content within a ROI rises, the SSW direction uncertainty decreases, and consequently the corresponding contribution to the total SAR SSW speed uncertainty decreases as well. At the same time, a growing ROI directional content corresponds to an increase of the NRCS uncertainty, together with its contribution to the total SAR SSW speed uncertainty itself. Figure 6 shows, as sample spatial distributions, the NRCS \(\sigma_{0}\) (a), the incidence angle \(\theta\) (\(\lx@math@degree\)) (c), the MS LG-Mod SSW direction \(\varphi\) (\(\lx@math@degree\)) (e), and the CMOD5.N-derived SSW speed W (m/s) (g), with their related uncertainties \(\Delta\sigma_{0}\) (b), \(\Delta\theta\) (\(\lx@math@degree\)) (d), \(\Delta\varphi\) (\(\lx@math@degree\)) (f) and \(\Delta\text{W}_{\text{max}}\) (m/s) (h), respectively.