## 2 Data and Methods
### Ocean Wave Spectrum  
The construction of a large-scale sea surface is a significant step in the facet scattering calculation, which highly depends on the wind wave spectrum. Therefore, in order to study the facet scattering from the sea surface, it is necessary to acquire knowledge of the sea spectrum. In recent decades, many full wavenumber spectra have been proposed, of which the Donelan-Banner-Plant spectrum (D spectrum) [25], Apel spectrum (A spectrum) [26], Elfouhaily spectrum (E spectrum) [16], and the newest Hwang spectrum (H18 spectrum) [27] were used in this paper. The D spectrum considers the synthesis of DHH [28], Banner [29], and Plant [30] into a single spectral form. The A spectrum was derived from in situ measurements in the gravity wave region and from wave tank results in the gravity-capillary wave region. It addresses the consistency with observational NRCS data. The E spectrum was developed based on the unification of optical, in situ, and wave tank data, and it emphasizes the consistency with the measured mean square slopes in [31]. The H18 spectrum is a combination of the H15 spectrum [32] and the G spectrum [27]. In the high-frequency region (wavenumber \(\geq\) 4 rad/m), the H18 spectrum uses the H15. In the low-frequency region (wavenumber \(\leq\) 1 rad/m), it uses the variable spectral slope model, the G spectrum. Additionally, the spectrum in the region of 1 \(\leq\) wavenumber \(\leq\) 4 rad/m is linearly interpolated. The details of the four spectral models are presented in [16; 25; 26; 27] and will not be repeated here. Figure 1 gives the variation of D, A, E, and H18 omnidirectional spectra \(S(K)\) and curvature spectra \(B(K)=K^{3}S(K)\) with wavenumber \(k\) at wind speeds of 5 m/s, 10 m/s, and 15 m/s. It can be seen from Figure 1a-c that the omnidirectional spectra exhibit unimodal distribution features, with peaks occurring in the low wavenumber region. As wind speed increases, the peaks of spectra shift toward the low wavenumber region, and the power of each wind wave spectral component also increases in level. Figure 1e,f give the omnidirectional spectra \(S(K)\) that account for Bragg scattering for incidence angles between about 30\({}^{\circ}\) and 60\({}^{\circ}\) in the C band. From Figure 1e,f, we can know that the A spectrum's density is always the largest and the D spectrum's density is the smallest, except that the density of the A spectrum is slightly smaller than that of the E spectrum at the wind speed of 5 m/s when the wavenumber is greater than 140 rad/s. The curvature spectral densities of wind wave spectra in Figure 1h-j show a decreasing wind speed sensitivity as wind speed increases. In addition, there is a spectral peak in the capillary wave region, followed by a rapid drop-off. For a given wind speed of 15 m/s, the peak is at about 200 rad/s for the D spectrum, 700 rad/s for the A spectrum, and about 400 rad/s for the E and H18 spectra. The spectra mentioned above were used to describe wind waves, and the influence of the swell can be described by the swell spectrum, which can be expressed as follows:  
\[\mathrm{S_{swell}}\left(k_{x},k_{y}\right)=\frac{\left\langle h^{2}\right\rangle }{2\pi\sigma_{Kx}\sigma_{Ky}}\exp\left\{-\frac{1}{2}\left[\left(\frac{k_{x}-k _{xm}}{\sigma_{Kx}}\right)^{2}+\left(\frac{k_{y}-k_{ym}}{\sigma_{Ky}}\right)^ {2}\right]\right\} \tag{3}\]  
where \(\left\langle h^{2}\right\rangle\) is the root-mean-square height of the simulated swell, and its root is 1/4 of the significant wave height of swell \(H_{s}\). \(x\) is the horizontal antenna look direction (ground range direction), and \(y\) is the perpendicular horizontal direction (azimuth direction). \(k_{x}\) and \(k_{y}\) represent the wavenumber components of the wavenumber \(k\) on the range and azimuth coordinates, respectively. \(k_{xm}\) and \(k_{ym}\) denote the wavenumber at the peak of the spectrum in the range and azimuth axis direction, respectively.