## 4 Results and Discussion
### SAR Dataset Results
All maps are obtained at 5 km by 5 km and refer to a 65 km by 65 km region in the Atlantic European northwest shelf, which was cropped from the VV-polarised, ascending, Sentinel-l IW image acquired on 16 th May 2018 at 17:33:28 UTC. Estimated SSW vectors are superimposed in each image of the figure. SSW directions derive from MS LG-Mod, while speeds are from the proposed methodology. SSW vectors are referred to the range-azimuth geometry using the true heading parameter of the S-1 image. According to average results obtained for the CMOD5.N and the 5 km ROI dimension  
Figure 5: The total CMOD5.N-derived SAR SSW speed uncertainty \(\Delta\text{W}_{\text{max}}\) (m/s) (purple), derived considering the three uncertainties (\(\Delta\sigma_{0}\),\(\Delta\theta\),\(\Delta\varphi\)) and the true state (\(\sigma_{0}\),\(\theta\),\(\varphi\)), and the contribution to this uncertainty due to the true state (\(\sigma_{0}\),\(\theta\),\(\varphi\)) and a single uncertainty among the ones regarding the NRCS (\(\Delta\sigma_{0}\)) (green), the incidence angle (\(\Delta\theta\)) (blue) and the MS LG-Mod SSW (relative) direction (\(\Delta\varphi\)) (red) (**a**). The corresponding ratio with reference to the total SSW speed uncertainty shown, in the range [0, 100] (%), with the same colours (**b**). Values are obtained for all the 5 km-ROIs. (Table 3, first column), the contribution \(\Delta\)W\({}_{3}\) due to the SSW direction uncertainty (\(\Delta\varphi\), Figure 6f) is the one that weighs the most, for such conditions, in the total SAR SSW speed uncertainty (\(\Delta\)W\({}_{\text{max}}\), Figure 6h). The spatial variability in Figure 6f and h can suggest a kind of correlation between \(\Delta\varphi\) and \(\Delta\)W\({}_{\text{max}}\), respectively. Figure 7 illustrates the contribution to the total CMD5.N-derived SAR SSW speed uncertainty \(\Delta\)W\({}_{\text{max}}\) (m/s) (Figure 6h), due to the true state (\(\sigma_{0}\),\(\theta\),\(\varphi\)), and only a single uncertainty term among the ones regarding the NRCS (\(\Delta\)\(\sigma_{0}\)) (a), the incidence angle (\(\Delta\theta\)  
Figure 6: SAR NRCS \(\sigma_{0}\) (**a**), incidence angle \(\theta\) (\({}^{\circ}\)) (**c**), MS LG-Mod SSW direction \(\varphi\) (\({}^{\circ}\)) (**e**) and CMD5.N-derived SSW speed W (m/s) (**g**), with their uncertainties \(\Delta\)\(\sigma_{0}\) (**b**), \(\Delta\)\(\theta\) (\({}^{\circ}\)) (**d**), \(\Delta\)\(\varphi\) (\({}^{\circ}\)) (**f**) and \(\Delta\)W\({}_{\text{max}}\) (m/s) (**h**), respectively. 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. (b), and the MS LG-Mod SSW (relative) direction (\(\Delta\varphi\)) (c). Again, all maps are obtained at 5 km by 5 km from the same S-1 IW crop image used for Figure 6. According to results shown in Figure 5, as well as to statistics reported in the first column of Table 3 (regarding the case of CMOD5.N and the 5 km ROI dimension), Figure 7a-c confirm respectively that the higher contribution to the total SSW speed uncertainty derives from the uncertainty of the SSW direction, the intermediate one is associated with the NRCS uncertainty, while the lower one is linked to the uncertainty of the incidence angle. The correlation between \(\Delta\)W\({}_{\rm max}\) (Figure 6h) and \(\Delta\)W\({}_{3}\) (Figure 7c) is quite clear.