## 3 Results
### Effect of Non-Gaussianity on NRCS Simulation
Additionally, the NRCS from the non-Gaussian surface predicted by the modified TSM is in good agreement with that of the Sentinel-1 data as a function of incidence angle and wind speed in the upwind direction under HH polarization. This phenomenon arises because the simulation results of the conventional TSM based on the A spectrum always underestimate the scattering of Sentinel-1 owing to the neglect of wave breaking under HH polarization, and the positive correction introduced by the modified TSM in the upwind direction compensates for this underestimation to a certain extent. Furthermore, in the downwind direction under VV polarization, the NRCS calculated by the modified TSM based on the Tayfun ocean surface also performs better than the others because the TSM based on the A spectrum slightly overestimates the backscatter of Sentinel-1 data, and the negative correction introduced by the modified TSM compensates for some of the overestimation. The average NRCSs simulated based on the conventional TSM + Gaussian sea surface, conventional TSM + Tayfun sea surface, and modified TSM + Tayfun sea surface and their comparison with the reference data as functions of the wind direction at the wind speed of 10 m/s and incidence angle of 32\({}^{\circ}\) under VV and HH polarizations are shown in Figure 10. This figure shows that the simulated NRCS based on the conventional TSM + Gaussian sea surface is almost the same as that based on the conventional TSM + Tayfun sea surface over the wind direction range of 0\({}^{\circ}\)-360\({}^{\circ}\). The modified TSM can simulate the upwind/downwind asymmetry of backscatter, which cannot be described by the conventional TSM. The modified TSM achieves this by introducing a positive correction in the upwind direction (0\({}^{\circ}\)) and a negative correction in the downwind direction (180\({}^{\circ}\)) using the complementary term proportional to the sea surface bispectrum. Moreover, the  
Figure 7: Comparison of a Gaussian sea surface and Tayfun sea surface at 10 m/s wind speed and 32\({}^{\circ}\) incidence angle in the upwind direction. **(a)** Pdfs for surface elevations; **(b)** profiles of surface elevations; **(c)** pdfs for slopes along range direction. Blue solid curve, Gaussian sea surface; red dashed curve, non-Gaussian sea surface constructed by Tayfun model. minimum of the modified-TSM-simulated NRCS deviates from the crosswind direction (90\({}^{\circ}\)/270\({}^{\circ}\)) and moves to the downwind direction. All these changes diminish the gap between the predicted NRCS and the measured NRCS. The upwind-downwind asymmetries predicted based on the conventional TSM + Gaussian sea surface, the conventional TSM + Tayfun sea surface, and the modified TSM + Tayfun sea surface and their comparison with the reference data as functions of the incidence angle at the wind speed of 10 m/s under VV and HH polarizations are shown in Figure 11a,b, and those as a function of wind speed at the incidence angle of 32\({}^{\circ}\) under VV and HH polarizations are shown in Figure 11c,d. The upwind-downwind asymmetry cannot be predicted by the conventional TSM based on either the Gaussian or the Tayfun sea surface, indicating that the construction of the Tayfun sea surface cannot explain the upwind-downwind asymmetry of sea surface scattering. The differences between the upwind and downwind NRCSs simulated by the modified TSM are in good agreement with the measurement data and the NRCSs predicted by the empirical model at the incidence angle of 30\({}^{\circ}\)-50\({}^{\circ}\) and a wind speed of 3 m/s-16 m/s under VV and HH polarizations, which is consistent with [36]. Figure 8: The simulated average NRCSs based on the conventional TSM + Gaussian sea surface, conventional TSM + Tayfun sea surface, and modified TSM + Tayfun sea surface and their comparison with the reference data at a 10 m/s wind speed as functions of the incidence angle **(a,b)** in the upwind direction under VV and HH polarizations and **(c,d)** in the downwind direction under VV and HH polarizations.