## 3 Results
### The Influence of Directional Wave Spectra on NRCS Simulation at Different Azimuth Angles
As can be seen from Figure 9, the use of different wave spectra has little effect on the prediction of azimuthal fluctuation of the modified TSM, though it results in rather different performance under different wind speeds and incidence angles. To some extent, the directional spreading function affects the azimuthal fluctuation of the scattering simulated by the modified TSM. Different directional spreading functions yield different azimuth fluctuations. Additionally, the relative undulating patterns produced by different spreading functions are rather different at different wind speeds, whereas they are mostly similar at different incidence angles. Figure 9: Predictions of the modified TSM using A + Cosine, A + Sech, A + Gaussian, AH18 + Cosine, AH18 + Sech, and AH18 + Gaussian, and their comparisons with CMOD5.n and the ASCAT measurements. (**a–c**) At incidence angle of 30\({}^{\circ}\) under wind speeds of 3 m/s, 9 m/s, and 16 m/s. (**d–f**) At incidence angle of 50\({}^{\circ}\) under wind speeds of 3 m/s, 9 m/s, and 16 m/s. At a low wind speed, the Sech spreading function yields larger NRCS in the upwind/downwind directions (0\({}^{\circ}\)/180\({}^{\circ}\)) and smaller NRCS in the crosswind directions (90\({}^{\circ}\)/270\({}^{\circ}\)) than the Cosine and Gaussian spreading functions. That is, the NRCS estimated with the Sech spreading function has slightly greater ups and downs with wind direction. At a lower incidence angle, the Cosine and Gaussian spreading functions are in better agreement with CMOD5.n and the ASCAT data. At a higher incidence angle, the Sech spreading function achieves a similar up and down pattern to the CMOD5.n, while the Cosine and Gaussian spreading functions, which have slightly weaker ups and downs with wind direction, are in better agreement with the ASCAT data. At a moderate wind speed, the Cosine and Sech spreading functions, which yield almost the same results, have better performance at lower incidence angles compared with CMOD5.n and the ASCAT data. However, at a higher incidence angle, the Gaussian spreading function, which produces the largest ups and downs, performs better. At a high wind speed, the Cosine spreading function is in better agreement with CMOD5.n at lower incidence angles. However, the Gaussian spreading function achieves a similar up and down pattern to the ASCAT data. At a higher incidence angle, the Sech spreading function achieves a similar up and down pattern to CMOD5.n. Meanwhile, the Cosine and Gaussian spreading functions are in better agreement with the ASCAT data. As can be seen, the optimum spreading function is different when the wind speed and incidence angle are different. In general, the Gaussian spreading function has better performance in predicting the azimuthal fluctuation of scattering, except that the Cosine and Sech spreading functions work better at a moderate wind speed when the incidence angle is low. The most important azimuth behavior of ocean radar backscatter is the upwind-downwind asymmetry. The upwind-downwind asymmetry estimated with different directional wave spectra is different. Figure 10 shows the differences between the NRCSs in upwind and downwind directions calculated by the modified TSM with A + Cosine, A + Sech, A + Gaussian, AH18 + Cosine, AH18 + Sech, and AH18 + Gaussian input, and the results of ASCAT and CMOD5.n ((a)-(c)) as functions of incidence angle at wind speeds of 3 m/s, 9 m/s and 16 m/s, and ((d)-(f)) as functions of wind speed at incidence angles of 30\({}^{\circ}\), 40\({}^{\circ}\), and 50\({}^{\circ}\). At low winds, the computed upwind-downwind differences using the six wave directional spectra are lower than the ASCAT data and CMOD5.n, but they show a similar increasing trend with the incidence angle increasing from 30\({}^{\circ}\) to 50\({}^{\circ}\).