## 3 Results and Discussions  
### DCA Correction  
Figure 3 displays a SAR image acquired in the Gulf of Maine on 10 August 2019, by S-1A. In Figure 2(a), the NRCS acquired by VV polarization is depicted, while Figure 2(b) illustrates the estimated Doppler centroid frequency. This image is collected by the ascending  
Figure 2: Flowchart of DCA correction and inversion of wind and current velocity as well as the validation. orbit with the satellite flying from the south to the north, and a detrend pattern of NRCS is clear from the left (near-range) to the right (far-range) of this plot. It exhibits a complex ocean scene, particularly close to the land. For instance, dark spots corresponding to low radar backscatter are observed in the upper left corner of the image, possibly due to an oil spill or a low-wind area. A cluster of bright targets is observed near the Grand Manan Island at longitude of 67.5\({}^{\circ}\) W and latitude of 44.5\({}^{\circ}\) N. In addition to NRCS, the Doppler centroid annotated in the S-1 level-2 product is given in Figure 3b. The value of the Doppler centroid over the sea surface differs from that over the land. A couple of outlier patterns are clear, including the periodic band along the flight direction and the non-zero values over the land. Figure 4a presents the predicted (geometric) Doppler frequency. After subtracting the predicted Doppler frequency from the SAR-estimated Doppler frequency, the outliers possibly caused by environmental factors still persist. To mitigate the impact, we initially employ the 3\(\sigma\) method to identify and eliminate these anomalies along both the azimuth and range directions for each swath. The 3\(\sigma\) method, as defined in Equation (4), flags a pixel as an outlier when its value deviates from the median by more than three standard deviations (with the median and standard deviation calculated in either the range or azimuth directions). For each pixel in the image domain, it is considered as an outlier if satisfying the following condition:  
\[|x-\hat{x}_{ra}|>3\sigma_{ra}\;or\;|x-\hat{x}_{az}|>3\sigma_{az} \tag{4}\]  
where '\(x\)' denotes the SAR-estimated Doppler centroid, \(\hat{x}\) is the median value, and '\(\sigma\)' is the standard deviation along the range or azimut direction, respectively. The Doppler centroid values of the outlier pixels are replaced by the average over the surrounding 25 \(\times\) 25 pixels. Figure 4b exhibits the Doppler centroid anomaly after the removal of outliers. The undulating pattern observed in each sub-strip in Figure 4b, known as a burst, is called \(f_{sca}\), and it exhibits distinct periodic changes in the azimuthal direction. There are currently two methods: (1) removing trend signals in the spatial domain; (2) removing them in the frequency domain through Fourier transform [23]. This study uses the first method. Each sub-strip is first averaged in the range direction (the solid blue line in Figure 5a), and the trend in the azimuth signal is removed by fitting and subtracting a third-order polynomial (the dashed blue line in Figure 5a), and a periodically changing signal is then obtained (the solid black line in Figure 5a). We assume that this is the scallop signal, and then have it removed from \(f_{sca}\) for each sub-swath. Figure 5b shows the Doppler centroid anomaly after scalloping correction. Notably, since 24 June 2020, the S-1 Instrument Processing Facility version 3.30 (IPF) incorporates an azimuth scalloping correction, resulting in a threefold reduction in modulation [24]. We have checked that the  
Figure 3: Map of an SAR image acquired over the Gulf of Maine on 10 August 2019 for **(a)** NRCS at VV polarization and **(b)** SAR-estimated Doppler centroid. products collected after this IPF mostly have a subtle scalloping effect. Nevertheless, the above mentioned algorithm is consistently implemented for all products despite the fact that this procedure might have a negligible impact on the scalloping removal.