# Performance Analysis of Ocean Surface Topography
## 3 OST Altimetry Results and Analysis of InIRA
### Altimetric Precision Estimation  
According to the altimetric sensitivity analysis in Section 2.3, a 10-cm height change causes a mere 0.001\(-\)0.01 rad phase change for InIRA. The phase change is too small compared to the dynamic phase range, which is between [-\(\pi\), \(\pi\)]. Moreover, the phase noise level is too high for OST-associated phase change to emerge on Figure 7c.  
Phases in the black box in Figure 7c are multi-looked to lower the phase noise level; the phase dynamic range decreases significantly and the OST associated phases finally emerges on the 1-km grid, as shown in Figure 8.  
The altimetric precision on a 1-km and 5-km grid are estimated by calculating the RMSE of the phase in the same ground-range bin. The simulated altimetric precision is also presented to compare with the estimated results (the SWH is set to be 1.8 m according to the meteorological data during the image acquisition), as shown in Figure 9a. Since the altimetric precision within 7\({}^{\circ}\)-8\({}^{\circ}\) incidence range is too large, the precision axis is on logarithmic scale to present the curves more clearly. Throughout the entire swath, the estimated precision on a 5-km grid (the magenta solid line) is higher than that of a 1-km grid (the red solid line) due to larger multi-look number. The estimated precision is lower than the simulated results (the dashed lines), and to analyze the reason for this difference, the precision difference curves within 1\({}^{\circ}\)-7\({}^{\circ}\) incidence range are shown in Figure 9b. Due to the random error  
Figure 8: Multi-look interferometric phase on a 1-km grid. Phases in the blue box corresponds to the internal wave area.  
Figure 7: (**a**) Intensity image in slant-range direction without antenna pattern correction; (**b**) coregistered phase of two SAR complex images; (**c**) relative phase after flat-earth phase removal; (**d**) coherence between two SAR complex images. The azimuth and slant-range directions are indicated by arrows.  
suppression by multi-looking, the precision difference on a 5-km grid is lower than that of a 1-km grid. However, a considerable residual difference still exits and, apart from the fact that the OST changes slightly in the area, the residual difference is mainly caused by the residual calibration error and data processing induced error. Most of these are systematic errors and cannot be further removed by multi-looking (within the 4\({}^{\circ}\)-5\({}^{\circ}\) incidence range, the difference is almost the same as the 1-km curve, which indicates that the precision difference is mainly from systematic errors).  
In Figure 8, phases in the blue box are much lower than the surrounding phases. This anomaly causes the estimated precision drops sharply and deviates notably from the simulated precision when the incidence is above \(\sim\)7\({}^{\circ}\), as shown in Figure 9a. According to Figure 7a, ocean internal waves happen to exist in this area. In Figure 10, by comparing the intensity, coherence and phase images of the interval waves, we deduce that the altimetric precision decline is caused by the modulation of internal waves on ocean surface roughness. In the far range, the modulated area appears darker than the surrounding area, which indicates the decline of the SNR. As the SNR decreases, so does the coherence of the modulated area. The coherence decline increases the phase noise and worsens the altimetric precision.