## 2 Materials and Methods  
### Estimation Model for Sea Surface Roughness (SSR)  
For ASTER two-angle images, [PERSON] et al. [20] studied and established an SSR estimation model based on multi-angle SG using ASTER channel 3N and channel 3B images. The model was determined as follows:  
\[\sigma_{0}^{2}=\frac{\tan^{2}\beta_{B}-\tan^{2}\beta_{N}}{\text{Ln}\big{(} \frac{L_{pN}}{L_{pN}}\frac{R(\omega_{B})\cos\theta_{N}\cos^{4}\beta_{N}}{R( \omega_{N})\cos\theta_{B}\cos^{4}\beta_{B}}\big{)}} \tag{1}\]where \(\sigma_{0}^{2}\) is SSR, \(\theta\) is sensor viewing angle (SVA) (\(\theta_{N}\) in 3N image and \(\theta_{B}\) in 3B image), \(\phi\) is sensor azimuth angle (\(\phi_{N}\) in 3N image and \(\phi_{B}\) in 3B image), \(\theta_{0}\) is sun zenith angle, and \(\phi_{0}\) is sun azimuth angle. \(R(\omega)\) denotes the Fresnel reflection coefficient (\(R(\omega_{N})\) in 3N image and \(R(\omega_{B})\) in 3B image), and it was determined as follows:  
\[R(\omega)=\frac{1}{2}[\frac{\sin^{2}(\omega-\omega^{\prime})}{\sin^{2}(\omega +\omega^{\prime})}+\frac{\tan^{2}(\omega-\omega^{\prime})}{\tan^{2}(\omega+ \omega^{\prime})}] \tag{2}\]  
where \(\omega\) and \(\omega^{\prime}\) are the incident angle and refraction angle of the sun's rays on the inclined surface of the sea. The relationship between them is as follows:  
\[\cos(2\omega)=\cos\theta\cos\theta_{0}+\sin\theta\sin\theta_{0}\cos(\phi- \phi_{0}) \tag{3}\]  
\[\sin\omega^{\prime}=\frac{\sin\omega}{1.34} \tag{4}\]  
Here, let \(\Delta\phi\) be the relative azimuth of the sensor and the sun; it is defined as:  
\[\Delta\phi=\phi-\phi_{0} \tag{5}\]  
\(\beta\) denotes the surface tilt angle of a facet on the sea surface (\(\beta_{N}\) in 3N image and \(\beta_{B}\) in 3B image), it is defined as:  
\[\cos\beta=\frac{\cos\theta+\cos\theta_{0}}{2\cos\omega} \tag{6}\]  
\(L_{g}\) is SG radiance (\(L_{gN}\) in 3N image and \(L_{gB}\) in 3B image) according to [PERSON] (1965):  
\[L_{g}=F_{0}T\frac{R(\omega)}{4\cos\theta\cos^{4}\beta}P\big{(}Z_{x},Z_{y}\big{)} \tag{7}\]  
where \(T\) denotes the downwelling direct transmittance, according to [PERSON] and [PERSON] and [PERSON] (1998). In the open sea, the value of \(T\) is about 0.85. \(F_{0}\) denotes solar irradiance at the top of the atmosphere according to [PERSON] (1988). It can be calculated as follows:  
\[F_{0}(sday)=\overline{F}_{0}[1+0.0167\cos\big{(}\frac{2\pi(sday-3)}{365})] \tag{8}\]  
where \(sday\) is Julian Day, and \(\overline{F}_{0}\) is the average of many years of \(F_{0}\). According to the latest recommendation of the International Bureau of Weights and Measures, the value is 1367 W/m\({}^{2}\). Normalized SG radiance (\(I\)) is defined as follows:  
\[I=\frac{L_{g}}{F_{0}T}=\frac{R(\omega)}{4\cos\theta\cos^{4}\beta}P\big{(}Z_{x},Z_{y}\big{)} \tag{9}\]  
where \(P\big{(}Z_{x},Z_{y}\big{)}\) is the probability density function of the wave slope as functions of individual slope components \(Z_{x}\) and \(Z_{y}\). It is determined as follows:  
\[P\big{(}Z_{x},Z_{y}\big{)}=P(\beta)=\frac{1}{\pi\big{(}\sigma_{0}^{2}\big{)}} \exp\big{(}-\frac{\tan^{2}\beta}{\sigma_{0}^{2}}\big{)} \tag{10}\]  
According to [PERSON] et al. [PERSON] et al. (2018), when the wind speed is lower than 15 m/s, the relationship between SSR and sea surface wind speed is as follows:  
\[R(\omega)=\frac{1}{2}[\frac{\sin^{2}(\omega-\omega^{\prime})}{\sin^{2}(\omega +\omega^{\prime})}+\frac{\tan^{2}(\omega-\omega^{\prime})}{\tan^{2}(\omega+ \omega^{\prime})}] \tag{2}\]0The SVA of the ASTER 3N and 3B images selected by [PERSON] et al. (2019) were fixed values (\(\theta_{N}=0^{\circ}\) and \(\theta_{B}=27.6^{\circ}\)), and the purpose of this study was to verify whether an optimal SVA combination that has the best effect on the SSR estimation model of multi-angle SG remote sensing could be determined.