## 4 Results and Discussion
### Assessment of SAR SSW Direction and Speed Uncertainty as Proxy of Accuracy
From an overall point of view, there can be seen the same trends for the two different computations (namely, \"SAR uncertainty\" and \" ISAR-ECMWF I \" in the table), showing a decreasing (bettering) of RMSE values with an increasing ROI dimension. These findings are shared by estimations regarding both SSW direction and speed. However, the \"SAR uncertainty\" RMSE values exhibit an under-estimation with respect to the \" ISAR-ECMWF I \" evaluation. The final evaluation relies on the direct comparison between the SAR-derived SSW direction and speed uncertainty (i.e., \(\Delta\varphi\) and \(\Delta\text{W}_{\text{max}}\), respectively) and the absolute difference of the SAR-derived SSW direction and speed estimates with the corresponding ECMWF ones (i.e., \(\mid\varphi\)-\(\varphi_{\text{ECMWF}}\mid\) and \(\mid\text{W-W}_{\text{ECMWF}}\mid\), respectively). Figure 9 illustrates two binned scatterplots: (a) the MS LG-Mod SSW direction uncertainty, \(\Delta\varphi\) (\(\circ\)), (\(y\) axis) plotted as a function of the absolute difference between the MS LG-Mod SSW direction and the ECMWF wind direction (\(x\) axis), for all the 5 km by 5 km ROIs (N_ROI = 11,902); and (b) the SAR SSW speed uncertainty, \(\Delta\text{W}_{\text{max}}\) (m/s), (\(y\) axis) plotted as a function of the absolute difference between the SAR SSW speed and the ECMWF wind speed (\(x\) axis), for the same ROIs and the applied GMF CMOD5.N. For each bin (1 m/s and 5\(\circ\) for wind speed and direction uncertainty, respectively), the number of samples in the bin (N) and the aggregate statistics, m (mean) and s (standard deviation), are provided (unless N is too small, i.e., less than 1/100 of N_ROI). Table 5 collects these further comparison results obtained for all ROIs, at various dimensions and with two different GMFs applied (for wind speed retrievals). The values of R\({}^{2}\) indicate a high correlation between the uncertainty derived from the two different computations, i.e., the one obtained only from SAR estimations and the other from the comparison SAR vs. ECMWF. The values of A (slope) and B (intercept) in a linear regression model show again (as in Table 4) an under-estimation of the SAR uncertainty with respect to the ISAR-ECMWF I uncertainty. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**MS LG-Mod**} & \multicolumn{3}{c}{**CMOD5.N (m/s)**} & \multicolumn{3}{c}{**CMOD7 (m/s)**} \\ \cline{2-10}  & & **5 km** & **10 km** & **15 km** & **5 km** & **10 km** & **15 km** & **5 km** & **10 km** & **15 km** \\ \hline R\({}^{2}\) & 0.96 & 0.94 & 0.96 & 0.97 & 0.99 & 0.91 & 0.96  
To achieve an accurate assessment of results, it should be recalled that:  
* Although ERA5 wind data are gathered in this work in \"open water\" condition and assumed as reference for comparisons, these global NWP model data are doubtless affected by their own uncertainties, e.g., with a wind speed RMSE ranging from 1.25 to 1.5 m/s in the Dutch North Sea [47]. * SSW direction and the related uncertainty are provided by the MS LG-Mod algorithm as a directional mean and a measure of the directional content within each WVC [40]. However, the directionality of patterns in a cell may be sometimes affected by other local phenomena, even after a careful human eye selection of regions characterised by wind rows. In addition, as well known, the direction extracted by wind rows is not exactly aligned to the actual local wind direction [33], also depending on the phenomena causing the wind rows themselves. Figure 9: (a) 5\({}^{\circ}\)-binned scatterplot of the MS LG-Mod SSW direction uncertainty, \(\Delta\varphi\) (\({}^{\circ}\)), (\(y\) axis) vs. the absolute difference between the MS LG-Mod SSW direction and the ECMWF wind direction (\(x\) axis), for all the 5 km by 5 km ROIs (N_ROI = 11,902). Red dashed line shows the regression line with a slope A = 0.15.