## 3 Simulation and Analysis
### Sun Azimuth Angle  
Sun azimuth (\(\phi_{0}\)) is another important imaging geometric parameter. It varies greatly at different times of the day, different seasons of the year, and different geographical locations, such as in the Southern Hemisphere and the Northern Hemisphere. In the actual environment, it is \(0^{\circ}\leq\phi_{0}<360^{\circ}\), and \(\phi_{0}\) will also significantly impact SG. In the above simulation process, we set \(\phi_{0}=90^{\circ}\). Considering \(\phi_{0}\) in the range of \([0^{\circ},360^{\circ})\) and in steps of \(30^{\circ}\), the trend of normalized SG radiance at different SVA is simulated, as shown in Figure 9.  
According to Figure 9, the simulation results show that changes in \(\phi_{0}\) significantly impact SG radiance. Taking the peak point \(P1\) as an example, when the sun azimuth of \(P1\) is \(0^{\circ}\), the sun is in the north direction. According Equation(14), (15), (17) and (18), when SVA is negative, the sensor azimuth is about \(180^{\circ}\), the sensor takes a remote-sensing image against the sunlight, and a strong SG radiance is obtained at this time. When SVA is positive, the sensor azimuth is about \(0^{\circ}\), and the sensor takes a remote-sensing image along the sunlight, resulting in weaker SG radiance. At \(P1\), SVA is \(-20^{\circ}\) and sun zenith angle is \(20^{\circ}\). \(P1\) is the complete specular reflection point [8] when the sensor takes the image against the sun. Therefore, \(P1\) reaches the peak of SG radiance. Similarly, when the sun azimuth of \(P2\) is \(180^{\circ}\), the sun is in the south direction. When SVA is positive, the sensor azimuth is about \(0^{\circ}\), and \(P2\) is the complete specular reflection point when \(\theta=20^{\circ}\). Therefore, \(P2\) also reaches the peak of SG radiance. At other sun azimuths, complete specular reflection points do not occur under the ASTER flight orbit. However, under certain SVA, a peak of SG radiance always occurs, and as the sun azimuth changes, the peak increases or decreases according to a certain law. Considering the SG radiance threshold of 0.004, the results show that changes in the sun azimuth significantly affect the range of available SVA for the SSR estimation model. At \(\phi_{0}=0^{\circ}\), the range of available SVA is about \(-55^{\circ}\leq\theta\leq 11^{\circ}\), and at \(\phi_{0}=180^{\circ}\), the range is \(-11^{\circ}\leq\theta\leq 55^{\circ}\).  
Figure 10 shows the distribution of \(\Delta\sigma_{0}^{2}\) at different sun azimuth angles under different SVA combinations is shown in, and Figure 11 shows the statistical results of \(\rho_{10}\) and \(\rho_{20}\). According to Figure 10, the sun azimuth is also a key factor in the selection of the optimal SVA combination. The simulation results show that changes in the sun azimuth not only change the size but also the position of the optimal SVA combination range. According to Figure 11, at \(\phi_{0}=0^{\circ}\) or \(\phi_{0}=180^{\circ}\), \(\rho_{10}\) is about \(11.0\%\) and \(\rho_{20}\) is about \(12.4\%\). As the sun moves towards the east or west, \(\rho_{10}\) and \(\rho_{20}\) gradually decrease, and \(\rho_{20}\) is always about \(1.5\%\) higher than \(\rho_{10}\). At \(\phi_{0}=90^{\circ}\) or \(\phi_{0}=270^{\circ}\), \(\rho_{10}\) is about \(4.9\%\)  
Figure 9: Normalized SG radiance (\(I\)) simulated by each SVA (\(\theta\)) under different sun azimuths.  
and \(\rho_{20}\) is about 6.1%. In Figure 11, the main distributions of valley peak positions A and C correspond to the southern hemisphere region at noon in winter and the northern hemisphere region at noon in winter. The main distributions of the bottom positions B and D correspond to the mid-latitude area in the morning and afternoon, respectively. The distributions show that the SSR estimation model provides different results at different times and geographical locations.