# Ocean Wave Inversion Based on a Ku/Ka Dual-Band Airborne Interferometric Imaging Radar Altimeter
## 3 Result
### Accuracy Analysis of Ocean Wave Inversion Results
The volumetric decorrelation was correspondingly induced by the sea surface morphology and the attenuation function of the electromagnetic wave [42; 43], and the decoherence factor \(\gamma_{v}\) could be derived as:  
\[\gamma_{v}=e^{-2\frac{2\pi\gamma_{n}B}{\pi_{1}A\tanh^{2}}} \tag{13}\]  
where \(\sigma_{h}\) is the standard deviation of the SSH and the target scene is a Gaussian random sea surface height (can better reflect the electromagnetic characteristics). Then, the payload parameters and the target scene (different SWH) were substituted into Equations (12) and (13), and the simulation results are shown in Figure 14. Due to the low orbit height of the aircraft and the small incidence angle of the antenna, the coherence of the primary and auxiliary antenna signals was ensured. According to Figure 14b, the influence of the volumetric decorrelation on the imaging was significant in the near range, and it decreased with SWH reductions (along the arrow direction). In addition, the influence caused by the volumetric decorrelation on the Ku band was less than that on the Ka band, due to the longer wavelength of the Ku band. The coherence between the master and slave SLC was further expressed as the multiplication of the decorrelation factors, as follows:  
\[\gamma=\gamma_{n}\gamma_{v} \tag{14}\]  
Figure 14: (**a**) Thermal decorrelation coefficient; (**b**) volumetric decorrelation coefficient. The coherence coefficients between the master and slave SLC for different frequency bands are illustrated in Figure 15. Here, the coefficient increased, and then decreased with the ground range, indicating that the volumetric decorrelation dominated in the near range. In addition, the coherence decreased with the ground range due to the SNR decline within the ground range. Although the echo data acquired by the DInIRA were of high quality, a large multi-look number needed to be used in the multi-look processing to achieve high accuracy of the height measurement. It was established that the interference phase difference could be approximated with the multi-look number \(WH>4\) and the coherence coefficient \(\gamma>0.2\) as:  
\[\Delta\varphi=\sqrt{\frac{1}{2 WH}}\frac{\sqrt{1-\gamma^{2}}}{\gamma} \tag{15}\]  
The simulation result of altimetric accuracy could be further calculated by substituting the calculation of Equation (15) into Equation (10). In addition, the different multi-look numbers, \(N\), were performed. As shown in Figure 16a, the altimetric accuracy was improved with an increase (along the direction of the arrow) in \(N\). The carrier parameters (\(\lambda\), \(B\), and \(\alpha\)) and the data processing parameter (\(N=80\)) were then substituted into Equation (10) for calculation, whose results (dotted line) are shown in Figure 16b. Due to the system and processing error, the theoretical altimetric accuracy was higher than the actual. Moreover, the theoretical altimetric accuracy (solid line) of the Ka band was higher than that of the Ku band when SWH = 0.7 m (according to the in situ data), and the theoretical results were generally consistent with the conclusions drawn from the field observation data. It is worth noting that the random phase noise in the Ku band remained partially residual after filtering, indicating that the Ku band was more sensitive to random noise than that of the Ka band. However, the altimetric accuracy at the far range of the Ka band was even higher than the theoretical result in the ground range of 800-1000 m, it was inferred that the distribution characteristic of the SSH was the main reason for this trend. It can be seen from Equation (10) that the inversion accuracy of this method is closely related to the SSH inversion results. In this campaign, due to the higher altimetric accuracy of the Ka band (Figure 16b), the ocean wave inversion performance of the Ka band is better than that of the Ku band. Figure 15: Theoretical correlation coefficient when SWH = 0.7 m.