## 4 Results
### Wind Field Retrieval
The results indicate that the RMSE of wind speed for all methods initially decreases and then increases with increasing wind speed. In the moderate wind speed range of 5-11 m/s, VAM3 (\(J_{NRCS+DCA}\)) exhibits the lowest RMSE. However, VAM3 (\(J_{NRCS+DCA}\)) shows a higher RMSE compared to the direct inversion method when wind speeds exceed 11 m/s. The observed discrepancy can be attributed to the inherent bias in ERA5 wind speed, which serves as the background wind speed input for VAM, particularly under high-wind-speed conditions. This specific limitation will be further examined in Section 4.3. For the wind speed deviation metric, all four methods exhibit negative biases at wind speeds greater than 7 m/s, with the negative biases being more pronounced in the three VAM approaches than the direct method, as illustrated in Figure 7c. Among these, VAM2 (\(J_{DCA}\)) exhibits the most pronounced underestimation trend, suggesting that the VAM relying solely on DCA is particularly vulnerable to the effects of background wind speed. Figure 6: Wind directions obtained from ERA5 (**a**) and those retrieved by VAM1 (\(J_{NRCS}\)) (**b**), VAM2 (\(J_{DCA}\)) (**c**), and VAM3 (\(J_{NRCS+DCA}\)) (**d**), respectively, all validated against buoy-measured wind directions. Notably, the ERA5 wind direction (**a**) serves as the external wind direction input for the direct inversion method. Figure 8a illustrates the characteristics of wind direction RMSE obtained by different retrieval methods as a function of wind speed. The results indicate that under low-wind-speed conditions (1-3 m/s), all methods display a relatively high RMSE, ranging approximately from 40\({}^{\circ}\) to 60\({}^{\circ}\). Notably, as wind speed increases, the RMSE of wind direction across all methods demonstrates a significant decreasing trend, dropping to 15\({}^{\circ}\) at a wind speed of 9 m/s and stabilizing within the wind speed range of 9-15 m/s. As wind speed continues to increase, the RMSE of all the retrieved wind directions still demonstrates a decreasing trend, although the reduction in sample size may affect the reliability of the statistical results. It is also noteworthy that VAM3 (\(J_{NRCS+DCA}\)) performs the best in the moderate wind speed range of 5-11 m/s. Regarding the bias of wind direction, the absolute deviation values for all methods remain within 4\({}^{\circ}\) across various wind speed ranges, as illustrated in Figure 8c. Figure 7: The RMSE of wind speed determined by various methods a function of wind speed (**a**), and the RMSE following the application of ERA5 wind speed correction (**b**). The bias in wind speed measurements across different methods as a function of wind speed (**c**) and the corresponding bias after ERA5 wind speed correction (**d**). Figure 9 showcases a wind field retrieved using VAM3 (\(J_{NRCS+DCA}\)) from a SAR image acquired on 30 April 2020, along the Gulf Coast, alongside the corresponding ERA5 background wind field. It can be observed that the wind field retrieved by VAM3 (\(J_{NRCS+DCA}\)) captures more dynamic characteristics. Regarding wind speed distribution, the wind speed retrieved through VAM3 (\(J_{NRCS+DCA}\)) is notably higher in the southeastern region, with the maximum wind speed approaching 11 m/s, while the background wind speed ranges from 8 to 10 m/s. Additionally, the wind speed retrieved by VAM3 (\(J_{NRCS+DCA}\)) exhibits a more significant gradient in the north-south direction, indicating a more substantial spatial variability. This gradient feature more precisely captures atmospheric dynamic processes. Regarding wind direction distribution, the background wind field shows relatively uniform and regular characteristics, with a dominant northeast-southwest direction. In contrast, the wind direction retrieved by VAM3 (\(J_{NRCS+DCA}\)) maintains a similar dominant wind direction but shows a slightly eastward shift in the southern region.