# Performance Analysis of Ocean Surface Topography
## 4 Discussion  
The modulation of internal waves on ocean surface roughness leads to a sharp decline in altimetric precision. However, the modulation effect seems to be quite different between the near and far range of the image. Classical SAR ocean imaging theory presumes that under 20\({}^{\circ}\)-60\({}^{\circ}\) incidence, the SAR received signal is mainly from Bragg scattering. When the modulated area gets smoother,  
Figure 10: (**a**) Intensity (**b**) coherence and (**c**) phase image of the internal wave area.  
Figure 9: (**a**) Altimetric precision of the estimated and simulated results and (**b**) precision difference between the estimated and simulated results on a 1-km and 5-km grid, respectively.  
the backscattered signal will decrease and the internal waves will appear as dark stripes, which coincides with the situation that occurred in the far range. While different from conventional SAR, the near-nadir incidence of InIRA determines its received signals are mainly from specular reflection, so internal waves are supposed to be bright stripes, which coincides with the near range situation, and a similar phenomenon observed by satellite altimeter has also been reported in [25]. Obviously, there is an intensity boundary around -5\({}^{\circ}\) incidence, as shown in Figure 11a.  
The intensity boundary phenomenon also happens around the area where the ocean surface is covered by oil slick, as shown in Figure 11b. In the near range, the slicks look brighter than the surrounding area, while darker in the far range. Since the modulation of oil slick also makes the ocean surface smoother, so the intensity boundary can be explained by the same reason as of the internal waves\({}^{\prime}\).  
Considering the near-nadir incidence of InIRA, the intensity boundary can be explained as follows.  
In the near range, the incidence is almost vertical, meanwhile, a small surface slope induced by ocean waves also exists, as shown in Figure 12. When radar signals illuminate the ocean surface, most of the signals will reflect straight back into the receiver. Since under the modulation of internal waves or oil slick, the ocean surface get smoother, so reflected signals from modulated ocean area become stronger. This makes the internal waves or oil slick appear brighter than the surrounding area.  
In the far range, the incidence increases, however, the surface slope does not increase since it is largely dominated by the local sea state. Though most of the radar signals are also specular-reflected, only few of them can head back into the receiver. It gets even worse around the modulated area since the backscattered signal also decreases because of the smoother surface roughness. This makes the internal waves or oil slick appear darker than the surrounding area.  
Figure 11: Intensity boundary phenomenon of (**a**) internal waves (as shown in the red boxes); (**b**) oil slick.  
Figure 12: Schematic diagram of the intensity boundary phenomenon.  
The position where the intensity boundary locates is determined by ocean wave slope, and the ocean wave slope is dominated by the local sea state. So future near-nadir InSAR should consider this phenomenon while designing the incidence range. Our future work will derive the relationship between the intensity boundary and sea state from the statistics of the acquired data.