## 2 Data and Methods
### Facet Scattering Model  
In this paper, the TSM was used to calculate the facet scattering of the sea surface. Under the assumption that the ocean surface consists of small-scale roughness superimposed on a large-scale surface, TSM combines the Bragg scattering from the small-scale roughness, whose wavelengths are in the order of the electromagnetic wave, and the local tilting and hydrodynamic modulations due to the longer underlying waves. It can be expressed as follows:  
\[\sigma_{pp}^{s}\left(\theta^{\prime}\right)=16\pi k_{i}^{4}\cos^{4}\theta^{ \prime}G_{pp}S(K_{B},\varphi) \tag{8}\]  
where \(\theta^{\prime}\) is the local incidence angle of each tilting facet related to the inclination of the large-scale sea surface. The subscript \(pp\) indicates the VV or HH polarization state, \(k_{i}\) is the radar wavenumber, and \(G_{pp}\) is the VV or HH scattering coefficient. \(K_{B}=2k_{i}\)sin\(\theta\) is the Bragg resonance wavenumber, and \(\theta\) is the incidence angle. However, the conventional TSM cannot describe the upwind-downwind asymmetry of microwave backscatter from the ocean surface. Because the simulated NRCSs based on conventional TSM are 180 degrees symmetric in the azimuth direction, we developed a modified TSM by adding a backscattering correction term proportional to the bispectrum function into the conventional model. The NRCS for each individual facet of the surface can be given as follows:  
\[\sigma_{pp}^{0}\left(\theta^{\prime}\right)=\sigma_{pp}^{s}\left(\theta^{ \prime}\right)+\sigma_{pp}^{c}\left(\theta^{\prime}\right) \tag{9}\]  
where \(\sigma^{c}\) is the complementary term to consider the third-order statistics of the sea surface. According to [36], \(\sigma^{c}\) can be expressed as follows:  
\[\sigma_{pp}^{c}\left(\theta^{\prime}\right)=-{k_{i}}^{5}\cos^{3}\theta^{ \prime}B_{a}\left(K_{B},\varphi\right)\left[4\left|f_{pp}\right|^{2}+1.5\text {Re}\left[f_{pp}\cdot F_{pp}\right]+0.125\big{|}F_{pp}\big{|}^{2}\right] \tag{10}\]where \(f_{pp}\) and \(F_{pp}\) are the polarization-dependent coefficients, and \(B_{a}\) is the imaginary part of the bispectrum. \(B_{a}\) can be written as follows:  
\[B_{a}(K_{B},\varphi)=-\frac{K_{B}s_{0}^{6}\big{(}6-K_{B}{}^{2}s_{0}^{2}\cos^{2} \varphi\big{)}\cos\varphi}{16}\exp\left(-\frac{K_{B}{}^{2}s_{0}^{2}}{4}\right) \tag{11}\]  
where \(s_{0}\) is the skewness parameter, which can be expressed as follows [37]:  
\[s_{0}=\zeta\xi\frac{\sigma_{R}}{(U_{12.5}-A/B)^{1/3}U_{12.5}^{1/2}} \tag{12}\]  
\[\xi=\frac{(6/B)^{1/3}}{\sqrt{0.5C}} \tag{13}\]  
where \(A\) = 5.0 \(\times\) 10\({}^{-2}\), \(B\) = 42 \(\times\) 10\({}^{-3}\), and \(C\) = 5.1 \(\times\) 10\({}^{-3}\). \(A\) and \(B\) are the coefficients in the relation between skewness coefficients and wind speed proposed by [PERSON] [32,38]. \(C\) is the coefficient in the expression of the total slope variance as a function of the wind speed. \(U_{12.5}\) denotes the wind speed at a height of 12.5 m above the sea surface, and \(\sigma_{R}{}^{2}\) is the vertical variance of a small-scale wave, which can then be evaluated from the following:  
\[\delta=k_{i}\sigma_{R} \tag{14}\]  
\[\delta=0.205\log_{10}u_{*}-0.0125 \tag{15}\]  
where \(u_{*}\) is the wind friction velocity. \(\zeta\) is an undetermined parameter and can be estimated by minimizing the difference between the upwind-downwind asymmetry predicted by the modified TSM and that provided by CMD05.n. \(\zeta\) is mainly related to the wind speed, and the dependence of \(\zeta\) on the incidence angle is small [36]. Additionally, the estimated \(\zeta\) values under different spectra are almost the same, with the difference being within 0.01 dB. Figure 3 shows the variations of \(\zeta\) with wind speed based on the A spectrum and the cosine spreading function under VV and HH polarizations at an incidence angle of 32\({}^{\circ}\). We can see from Figure 3 that for a given incidence angle, \(\zeta\) is a nonlinear monotonically increasing function of wind speed, and the increasing rate speeds up gradually.