## 4 Results and Discussion
### SAR Dataset Results  
Table 3 reports statistics (in (m/s)) about the contribution to the total SAR SSW speed uncertainty (m/s) (E = \(\Delta\text{W}_{\text{max}}\)), due to the true state (\(\sigma_{0}\),\(\rho\),\(\varphi\)), along with a single uncertainty term 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), evaluated for all the ROIs, at various dimensions and for two applied GMFs. The ratio of each non-additive contribution to the total SSW speed uncertainty and the total SSW speed uncertainty itself (i.e., 100 \(\times\) Ei/E (%), i = 1, 2, 3) is also reported in the table. It is interesting to note that:  
* For each ROI size adopted, the CMOD5.N and the CMOD7 produce a similar ratio, for both mean and standard deviation, and for each contribution (i.e., E1, E2 and E3). * For each GMF applied, the ratio of both mean and standard deviation for each contribution depends on the ROI dimension. In particular, focusing on the ratio of the mean values, with an increasing ROI dimension, both the contributions E1 and E2, strictly due to the NRCS (\(\Delta\sigma_{0}\)) and the incidence angle (\(\Delta\theta\)) uncertainty, respectively, increases; on the other hand, the contribution E3, strictly due to the MS LG-Mod SSW relative direction uncertainty (\(\Delta\varphi\)), decreases. For example (Table 3),  
Figure 4: The CMOD5.N-derived SAR SSW speed uncertainty \(\Delta\text{W}_{\text{max}}\) (m/s), due to both the fixed true state (W,\(\theta\),\(\varphi\)) = (15 m/s, 37.5\({}^{\circ}\), 175\({}^{\circ}\)) and the varying triplet of uncertainties (\(\Delta\sigma_{0}\),\(\Delta\theta\),\(\Delta\varphi\)), respectively in the range [0, 0.005] (\(y\) axis), [0\({}^{\circ}\), 0.2\({}^{\circ}\)] (with a step of 0.1\({}^{\circ}\)) (\(z\) axis) and [0\({}^{\circ}\), 90\({}^{\circ}\)] (\(x\) axis). for our S-1 dataset, the results for the CMOD7 application show that the contribution E1 varies from 34.5% (at 5 km) to 51.0% (at 15 km), the contribution E2 changes from 6.9% (at 5 km) to 22.3% (at 15 km), and the contribution E3 decreases from 59.9% (at 5 km) to 29.2% (at 15 km). Therefore, with an increasing ROI dimension, the terms E1 and E2 weigh more, while the term E3 counts less, exactly at the same time that the uncertainty of the NCRS and the incidence angle worsen, and the uncertainty of the wind direction becomes more precise and accurate (Table 1). However, the combination of these concurrent factors basically produces a better estimation of the SAR SSW speed uncertainty for a greater ROI dimension (Table 2). Independently from the ROI dimension, both E1 and E3 are particularly significant, and consequently the uncertainty of both NRCS (\(\Delta\sigma_{0}\)) and the SSW direction (\(\Delta\varphi\)) must be taken into account in the estimation of the SAR SSW speed uncertainty. On the contrary, E2 and the effect of incidence angle uncertainty (\(\Delta\theta\)) may be ignored, especially for smaller ROI dimensions. The previous results can be visualised in Figure 5 for the case of 5 km ROI dimension and the CMOD5.N GMF. Figure 5a plots in black the total amount of CMOD5.N-derived SAR SSW speed uncertainty derived considering the three uncertainties (\(\Delta\sigma_{0}\),\(\Delta\theta\),\(\Delta\varphi\)) and the true state (\(\sigma_{0}\),\(\theta\),\(\varphi\)) within each ROI. The value of SSW speed uncertainty components is obtained instead from the true state itself and, in turn, a single uncertainty term among the ones regarding the NRCS, incidence angle and MS LG-Mod SSW relative direction are reported in green, blue and red, respectively. Figure 5b shows, with the same colours, the ratio of each contribution with the total SSW speed uncertainty (i.e., 100 \(\times\) Ei/E (%), i = 1, 2, 3), for the same ROIs and the CMOD5.N.