## 3 Results
### Determination of the Modified TSM  
The values of the empirical parameter \(\zeta\) in the modified TSM are estimated by minimizing the upwind-downwind asymmetry predicted by the modified TSM and that given by CMOD5.n. Figure 4 shows the estimations of \(\zeta\) as functions of incidence angle at wind speeds of 3 m/s, 9 m/s, and 16 m/s under different directional wave spectra of D + Cosine, D + Cech, D + Gaussian, A + Cosine, A + Sech, A + Gaussian, E + Cosine, E + Sech, E + Gaussian, H18 + Cosine, H18 + Sech, and H18 + Gaussian. Figure 4 indicates that the \(\zeta\) does not exhibit any dependence on incidence angle when the wind speed is low (3 m/s) for all the directional wave spectra. The value of \(\zeta\) remains at 0.01 over the 30\({}^{\circ}\)-50\({}^{\circ}\) incidence angle range for the D spectrum, and remains at 0.02 for the A, E, and H18 spectra. At moderate wind speed (9 m/s), different wave spectra yield rather different \(\zeta\) behaviors with incidence angle, while that produced by different spreading functions is similar. The \(\zeta\) estimated with the E spectrum is the most sensitive to the incidence angle, followed by the H18 spectrum, and the values of \(\zeta\) based on the D and A spectra are independent of the incidence angle. The \(\zeta\) value based on the D and A spectra remains at 0.16 and 0.18, respectively. The \(\zeta\) values calculated with the E and H18 spectra fluctuate up and down with the incidence angle, and the fluctuations are within 0.03 when the incidence angle increases from 30\({}^{\circ}\) to 50\({}^{\circ}\). At high wind speed (16 m/s), the estimations of \(\zeta\) with different directional wave spectra all show a stronger dependence on incidence angle. They generally first increase and then decrease with the increase in the incidence angle. The \(\zeta\) values do not fluctuate more than 0.1 over the 30\({}^{\circ}\)-50\({}^{\circ}\) incidence angle range. Additionally, the \(\zeta\) estimated with the A spectrum is the largest, followed by that estimated with the E spectrum; the \(\zeta\) values estimated with the D and H18 spectra are the smallest. It is worth noting that one peak occurs in each curve for the E and H18 spectra at a moderate wind speed in Figure 4d-f, and for all spectra at a high wind speed in Figure 4g-i. This phenomenon occurs because the \(\zeta\) is determined by the level of upwind-downwind difference, and the difference in the upwind and downwind NRCSs calculated by CMOD5.n created a peak value near low incidence angles (see Figure 10b,c). Figure 5 shows the variation in \(\zeta\) with wind speed at incidence angles of 30\({}^{\circ}\), 40\({}^{\circ}\), and 50\({}^{\circ}\). As shown, the value of \(\zeta\) increases roughly from 0.02 to 0.90 when the wind speed increases from 3 m/s to 16 m/s. For a certain incidence angle, \(\zeta\) increases with wind speed and the increasing rate gradually accelerates. These results are different from those shown in Figure 1 of [23], where \(\zeta\) increases linearly from 0.03 to 0.21 as the wind speed increases from 2 m/s to 20 m/s. The \(\zeta\) values in [23] are obtained based on the airborne measurements under large incidence angles of 60\({}^{\circ}\)-80\({}^{\circ}\). In addition, the estimated \(\zeta\) values under different spreading functions are almost the same for a given wave spectrum over the wind speed range of 3-16 m/s. The \(\zeta\) values estimated based on different wave spectra for a given spreading function are somewhat different at higher wind speeds, where the \(\zeta\) value of A spectrum is always larger than others. The \(\zeta\) values obtained based on the D, E, and H18 spectra are almost the same, except for the high incidence angle (50\({}^{\circ}\)), where the \(\zeta\) of the E spectrum is larger than that of the D and H18 spectra. What deserves special mention is that the sensitivity of \(\zeta\) to wind speed is much stronger than its sensitivity to incidence angle.