## 3 Methodology
### FDS GMF Development
#### 3.3.1 ECMWF Reanalysis Data  
The matchup NWP data, used to train the empirical FDS GMF, are the 10-m referenced sea surface wind speed reanalysis data provided by the ECMWF. In this study, we used the ERA-Interim dataset of the ECMWF reanalysis to conduct a 2-month global sea surface wind speed retrieval from 1 July 2019 to 1 September 2019. The ERA-Interim reanalysis dataset used has an interpolated spatial dimension of 0.125\({}^{\circ}\) longitude/latitude and 3-h increments of temporal resolution. Finally, the matchup volume of the NBRCSs was 12,632,225 with alignment criteria of 1 h and the nearest longitude/latitude grid. The matchup maximum wind was up to 40.8 m/s. After the 3-dB beam-width antenna pattern screening, the scatter density plot was obtained between the NBRCS and ECMWF reanalysis winds, as shown in Figure 3a. The wind speeds range from 0.5 to 40.8 m/s. A significant power function relationship between the ECMWF reanalysis winds and NBRCS extracted from DDMs can be inferred. Therefore, the empirical FDS GMF was developed based on this relationship. As shown in Figure 3a, 16.86% of the NBRCSs from 0 to 20 correspond to the moderate wind speeds of 5 to 15 m/s, indicating that a large amount of NBRCSs will correspond to this wind speed range. Consequently, the wind speeds above 15 m/s will be underrated by these extra data. Accordingly, a quality control method is necessary to screen out the low NBRCSs that relate to the low and moderate wind speeds mentioned above. Therefore, after the antenna pattern gains control of a 3-dB beam-width and SNR of 4-dB quality control, 80% of the data were employed as the training set; the remaining 20% was used to validate the model accuracy. The scatter density plot after quality control of the antenna pattern and SNR is shown in Figure 3b. Notably, by setting up the filters of the antenna gain control and SNR threshold, the NBRCS ambiguity problem of moderate wind speeds between 5 and 15 m/s can be largely mitigated from the rate of 16.86% to 1.59%, which effectively improves the performance of the empirical GMF. Next, we further developed the empirical FDS GMF based on the NBRCS (\(\sigma_{0}\)), wind speed (\(U_{10}\)), and elevation angle (\(\theta_{ele}\)). Here, the elevation angle is the angle between the horizontal plane and the line extending from the spacecraft to the specular point. First, we built a lookup table (LUT) for the elevation angle. It is known that the common sea Fresnel coefficient varies as the elevation angle increases. The elevation angle of 28\({}^{\circ}\) is the inflection point at which the left-handed circle polarization takes a larger portion compared with the right-handed circle polarization. Thus, the elevation angle is divided into 63 bins, and the bin center is incremented by 1\({}^{\circ}\) from 28\({}^{\circ}\) to 90\({}^{\circ}\) with a 1\({}^{\circ}\) bin width. Therefore, all the DDMs and auxiliary information within each elevation bin compute the optimal coefficients of the power function (\(U_{10}=A\sigma_{0}^{B}+C\)), as shown in Figure 4. The coefficients of the power functions of different elevation angles then fill the 2-D LUT. Figure 4 presents examples of the empirical GMF that correspond to elevation angles of 35-84\({}^{\circ}\), indicating that the elevation angle has a greater influence on the wind speed. Figure 4: Examples of empirical GMFs of BF-1B channel 2 at elevation angles of 35–84\({}^{\circ}\). The FDS GMF trained by the ECMWF reanalysis follow the power function form. The red curves are the best-fit functions of the corresponding elevation angles. The coefficients of the power functions are presented in the text boxes. Figure 3: Scatter density plots of normalized bistatic radar cross section (NBRCS) against ECMWF reanalysis data. The colors show the amount of matchup pairs in the density bins. The \(x\)-axis is the BF-1 A/B NBRCS and the \(y\)-axis is the ECMWF reanalysis wind speeds. The high-density pair locations are shown by the warmer colors.