## 4 Results and Discussion
### Assessment of SAR SSW Direction and Speed Uncertainty as Proxy of Accuracy  
To evaluate the results of SAR-derived SSW direction and speed uncertainty, the former derived from the MS LG-Mod algorithm and the latter from the proposed methodology and here applied to the S-1 dataset, wind data from the global ECMWF model were exploited. As all the examined ROIs are located on \"open waters\" in the Atlantic European northwest shelf, the ECMWF model data may be considered for comparisons. The first comparison is made by means of SSW direction and speed values obtained by the MS LG-Mod and the GMF-based inversion (i.e., \(\varphi\) and W, respectively) and the wind estimates from the ECMWF (i.e., \(\varphi_{\rm ECMWF}\) and \(W_{\rm ECMWF}\), respectively), thus providing summary statistics, such as the R\({}^{2}\), the RMSE and the MBE. Figure 8a illustrates the scatterplot of the MS LG-Mod SSW direction (\(y\) axis) and the ECMWF model direction (\(x\) axis), for all the 5 km by 5 km ROIs (N ROI = 11,902). The values of R\({}^{2}\) (=0.94), RMSE (=14.36\({}^{\circ}\)) and MBE (=5.10\({}^{\circ}\)) reveal a quite good agreement between the SAR-based technique (in the case of wind rows visibility) and the global NWP model (when applied to open waters) in wind direction estimation. Similar plots and results (R\({}^{2}\) = 0.97; RMSE = 11.53\({}^{\circ}\); MBE = 5.19\({}^{\circ}\) and R\({}^{2}\) = 0.98; RMSE = 10.63\({}^{\circ}\); MBE = 5.15\({}^{\circ}\)) were obtained for all the 10 km and 15 km square ROIs, respectively. Figure 8b reports instead the scatterplot of the SAR SSW speed (\(y\) axis) and the ECMWF model speed (\(x\) axis), for the same ROIs and the CMOD5.N. Statistics obtained from the comparison  
Figure 7: Contribution to the total CMOD5.N-derived SAR SSW speed uncertainty \(\Delta\)W\({}_{\rm max}\) (m/s) (shown in Figure 6h), due to the true state (\(\sigma_{0}\),\(\theta\),\(\varphi\)) and a single uncertainty term among the ones regarding the NRCS (\(\Delta\sigma_{0}\)) (**a**), the incidence angle (\(\Delta\theta\)) (**b**), and the MS LG-Mod SSW (relative) direction (\(\Delta\varphi\)) (**c**). All maps are obtained at 5 km by 5 km from a Sentinel-1 IW image, ascending, VV-polarised, acquired on 16 th May 2018 at 17:33:28 UTC. Estimated SSW vectors are superimposed. between the SAR-derived SSW speed and the ECMWF one (R\({}^{2}\) = 0.53; RMSE = 3.20 m/s; MBE = 1.98 m/s, and R\({}^{2}\) = 0.53; RMSE = 2.76 m/s; MBE = 1.50 m/s for CMOD5.N and CMOD7, respectively) show less agreement in wind speed estimation compared to wind direction estimation, for both applied GMFs. This fact is true also for the 10 km (R\({}^{2}\) = 0.56; RMSE = 2.99 m/s; MBE = 1.88 m/s, and R\({}^{2}\) = 0.56; RMSE = 2.56 m/s; MBE = 1.41 m/s for CMOD5.N and CMOD7, respectively) and the 15 km (R\({}^{2}\) = 0.57; RMSE = 2.96 m/s; MBE = 1.89 m/s, and R\({}^{2}\) = 0.57; RMSE = 2.52 m/s; MBE = 1.41 m/s for CMOD5.N and CMOD7, respectively) processing results. Another evaluation is based on the RMSE values computed as the root mean square of the SAR-derived SSW direction and speed uncertainty (i.e., \(\Delta\varphi\) and \(\Delta W_{\text{max}}\), respectively), on the one hand, and the absolute difference between the SAR-derived SSW direction and speed estimates and the ECMWF ones (i.e., \(\mid\varphi-\varphi_{\text{ECMWF}}\mid\) and \(\mid\)W-\(W_{\text{ECMWF}}\mid\), respectively), on the other hand. Figure 8: (**a**) Scatterplot of the MS LG-Mod SSW direction (\(y\) axis) and the European Centre for Medium-Range Weather Forecasts (ECMWF) model 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 = 0.99. (**b**) Scatterplot of the SAR SSW speed (\(y\) axis) and the ECMWF model speed (\(x\) axis), for the same ROIs and the CMOD5.N. Cyan dashed line shows the regression line with a slope A = 1.14. Both black dashed lines represent the reference line with a slope of 1. Table 4 summaries these comparison results.