## 3 Results
### Effect of Swell on NRCS Simulation
Figure 16: The profile of NRCS in the range direction based on the same parameters in Figure 15. (**a**) Incidence angle is 35\({}^{\circ}\), wind speed is 13 m/s, wind direction is 240\({}^{\circ}\) relative to range direction, VV polarization, significant wave height of swell is 4 m, swell wavelength is 200 m, and direction of the dominant wave is 180\({}^{\circ}\) relative to range direction; (**b**) incidence angle is 44\({}^{\circ}\), wind speed is 7.4 m/s, wind direction is 91\({}^{\circ}\) relative to range direction, HH polarization, significant wave height of swell is 4 m, swell wavelength is 196 m, and direction of the dominant wave is 191\({}^{\circ}\) relative to range direction. wave information such as wind direction and wavelength is contained in the scattering image. In comparison, the dominant wave wavelength and dominant wave direction of the simulation with swell are in good agreement with the Sentinel-1 data, with errors of \(\pm\)0.1 m and \(\pm\)0.5\({}^{\circ}\), respectively. Moreover, the introduction of swell diminishes the gap between the spectral density of the simulation and the measurement. Figure 17: The scattering images corresponding to ID 1 of (**a**) the Sentinel-1 data, (**b**) simulation based on modified TSM + Tayfun sea surface without swell, (**c**) the area enclosed by red solid line in (**b**), and (**d**) simulation based on modified TSM + Tayfun sea surface with swell. Figure 18: The scattering image spectra corresponding to ID 1 of (**a**) the Sentinel-1 data, (**b**) simulation based on modified TSM + Tayfun sea surface without swell, and (**c**) simulation based on modified TSM + Tayfun sea surface with swell. Figure 19 shows the scattering images corresponding to ID 2. This figure shows that the patterns of the scattering image of the wind wave sea surface at moderate wind speed (e.g., 7.1 m/s) are clearer than those at a low wind speed (e.g., 4.7 m/s) because the wavelength of wind waves increases with the wind speed. The direction of the stripes in the simulated scattering image without swell is similar to that of the Sentinel-1 data because the direction of the wind wave propagation is similar to that of swell in this example. The patterns of the Sentinel-1 data are well simulated by the simulation with swell. Figure 20 presents the image spectra of the scattering image corresponding to ID 2. The wavelengths and directions of the dominant waves obtained from the scattering image spectra in Figure 20 are listed in Table 3. The level of the simulated spectrum based on the wind wave sea surface at a moderate wind speed was determined to be larger than that at a low wind speed, but a large difference remains between the simulated spectral density and the measurement, and the introduction of swell diminishes the gap. As expected, the wavelength and direction of the dominant waves simulated using the sea surface with swell are almost the same as those of the Sentinel-1 data. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Ocean Surface** & \
\begin{tabular}{c} **Wavelength of the** \\ **Dominant Wave (m)** \\ \end{tabular} &
\begin{tabular}{c} **Direction of the Dominant Wave** \\ **(degree)** \\ \end{tabular} \\ \hline Sentinel-1 data & 171.5 & 149.0 \\ Sea surface without swell & 19.4 & 227.4 \\ Sea surface with swell & 171.5 & 149.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The wavelength and direction of dominant wave obtained from the scattering image spectra in Figure 18.  
Figure 19: Similar to Figure 17 but corresponding to ID 2. As highlighted above, the scattering image patterns and scattering image spectra of Sentinel-1 data can be successfully simulated by the modified TSM based on the Tayfun ocean surface with swell at various sea states. In [46], it is also proved that the textural features in simulated SAR images based on swell are in good agreement with those of the RADARSAT-2 SAR image.