## 3 Results
### Case Validation: Kuroshio Current  
The second case study focuses on the region near the Kuroshio current, as shown in Figure 5. In Figure 5a, the wind fields derived from a Sentinel-1A SAR image over the Taiwan Strait reveal high wind activity, with peak speeds reaching 23.6 m/s. These intense winds generated significant wind waves, resulting in a maximum SWH of 4.9 m, as depicted in Figure 5b. Notably, in the southwestern offshore region of Taiwan, an area with comparatively lower wind speeds (13.3 m/s) exhibited even higher wave heights, reaching up to 5.3 m. This marked discrepancy between local wind and wave conditions suggests the presence of mixed wave fields or a dominant swell system. Such complex sea states, coupled with strong winds, pose substantial challenges for surface current retrieval, as accurately correcting for the Doppler shifts induced by high sea states is essential for isolating the contributions of ocean surface currents.  
After correcting for the non-geophysical components, the radial OSC velocity is derived from the Doppler shifts induced by the surface currents. As shown in Figure 5c, the retrieved radial OSC velocity map reveals a well-defined anticyclonic eddy in the southwestern offshore region of Taiwan, consistent with the multi-temporal drifting buoy observations (see Figure 1). The maximum radial velocity within this eddy reaches 1.4 m/s. This anticyclonic eddy originates from the Kuroshio intrusion through the Luzon Strait and is primarily driven by barotropic and baroclinic instabilities associated with the Kuroshio intrusion [41].  
At the location marked by the solid purple circle, a drifting buoy recorded a near-surface current speed of 0.56 m/s and a radial component of \(-\)0.05 m/s, which closely match the SAR-retrieved value of \(-\)0.04 m/s. Figure 5d presents the SMOC-derived radial velocities and corresponding current directions, also shown in Figure 5c. Overall, the SAR retrievals show good agreement with the SMOC data, with minor discrepancies, specifically, a slight overestimation in the southern portion of the anticyclonic eddy and an underestimation southeast of the drifting buoy location.  
Figure 4: Comparisons of SAR-retrieved radial OSC velocities with corresponding SMOC values. Colorbar represents number of data points.  
The scatter plot in Figure 6 further supports this comparison, yielding a bias of -0.06 m/s, a RMSE of 0.23 m/s, an MAE of 0.19 m/s, and a correlation coefficient of 0.92. Despite some deviations, these results demonstrate that the SAR-retrieved radial OSC velocities effectively capture the dynamic characteristics of the surface currents, even under complex oceanographic environments.  
Figure 5: (**a**) Sea surface wind field derived from a Sentinel-IA VV-polarization SAR scene acquired over the Kuroshio intrusion on 30 October 2022 at 21:52 UTC. The black arrows denote the wind directions from the ECMWF, and the colorbar represents the wind speed, in units of m/s. (**b**) The SWH simulated by the WW3 at 22:00 UTC on the same day. The black arrows denote the ECMWF wind direction, while the red arrows indicate the wave directions from the WW3. The colorbar shows the magnitude of the SWH, in units of m. (**c**) The radial OSC velocities (negative when the surface current flows toward the radar and positive when it flows away) retrieved from the SAR-measured Doppler shifts. (**d**) The radial OSC velocities from the SMOC product. The black arrows in (**c**,**d**) indicate the SMOC current directions, and the purple arrows in (**c**,**d**) represent the drifting buoy-measured current directions. The colorbars in (**c**,**d**) denote the radial OSC velocities, in units of m/s.