## 3 Results
### The Influence of Directional Wave Spectra on NRCS Simulation at Different Azimuth Angles
The AH18 spectrum yields larger upwind-downwind NRCS differences than the A spectrum, which is more consistent with the reference data, while the results produced by the Cosine, Sech, and Gaussian directional spreading functions are almost the same over the whole incidence angle range of 30\({}^{\circ}\)-50\({}^{\circ}\). At moderate winds, different wave spectra yield rather different incidence angle dependences of the upwind-downwind differences. The AH18 spectrum produces a faster increasing trend at lower incidence angles and a faster decreasing trend at higher incidence angles. The transition angle is about 37\({}^{\circ}\) for all the three spreading functions. By comparison, the A spectrum yields a much slower increasing and decreasing trend, and a larger transition angle that is approximately within 46\({}^{\circ}\)-48\({}^{\circ}\). The upwind-downwind difference estimated with the Cosine spreading function is the largest, followed by the Sech one, and the Gaussian one is the smallest. The best agreement with CMOD5.n is obtained by the AH18 + Gaussian at lower incidence angles, while at higher incidence angles it is the A + Gaussian. The ASCAT data are close to the AH18 spectrum with all three spreading functions when the incidence angle <44\({}^{\circ}\), but in good agreement with the A + Gaussian at incidence angles larger than 44\({}^{\circ}\). At high winds, the upwind-downwind differences first increase then decrease with the incidence angle increasing, and the transition angle is approximately 37\({}^{\circ}\). All the six directional wave spectra yield rather good results, expect that the simulations based on the AH18 + Cosine and AH18 + Gaussian underestimate the results of CMOD5.n over the incidence angles of 30\({}^{\circ}\)-50\({}^{\circ}\). In general, the A spectrum + Sech achieves the best agreement with CMOD5.n. However, the resultspredicted by the CMOD5.n and modified model are in poor agreement with the ASCAT data at a high wind speed. That might be because the amount of ASCAT data is insufficient at a high wind speed, and the upwind-downwind NRCS differences calculated by the ASCAT data are not accurate enough. At an incidence angle of 30\({}^{\circ}\), the A spectrum and the AH18 spectrum yield slightly different behaviors of the upwind-downwind differences with wind speed, while that produced by the different spreading functions is rather similar. All the six wave directional spectra yield an increasing trend as wind speed changes from 3 m/s to 16 m/s, which is not consistent with the slightly decreasing trend seen in CMOD5.n when the wind speed is less than 7 m/s. The discrepancies at low wind speeds could be attributed to the uncertainties in the bispectrum, which become greater with decreasing wind speeds. In general, the A + Gaussian performs better than the others over the wind speed range from 3 m/s to 16 m/s compared with CMOD5.n. Compared with the ASCAT data, all the six directional wave spectra and CMOD5.n underestimate the upwind-downwind differences at wind  
Figure 10: Upwind–downwind asymmetry predicted by the modified TSM with different wave directional spectra input, and their comparison with the ASCAT and CMOD5.n. (**a–c**) As a function of incidence angle at wind speeds of 3 m/s, 9 m/s, and 16 m/s. (**d–f**) As a function of wind speed at incidence angles of 30\({}^{\circ}\), 40\({}^{\circ}\), and 50\({}^{\circ}\). speeds lower than 10 m/s. At an incidence angle of 40\({}^{\circ}\), the AH18 spectrum, regardless of the spreading function used, yields a different trend with wind speed compared to CMOD5.n at wind speeds of 3 m/s-16 m/s, and so does the A + Cosine. Overall, the upwind-downwind differences estimated with the A + Gaussian show the best agreement with CMOD5.n for different wind speeds. The AH18 + Sech performs better when the wind speed is lower than 10 m/s compared with the ASCAT data. At an incidence angle of 50\({}^{\circ}\), none of the six directional wave spectra yield the decreasing trend seen in CMOD5.n with wind speed at wind speeds less than about 6 m/s.