# Ocean Wave Inversion Based on a Ku/Ka Dual-Band Airborne Interferometric Imaging Radar Altimeter
## 3 Result
### Accuracy Analysis of Ocean Wave Inversion Results  
For the InIRA system, the altimetric accuracy could be calculated by:  
\[\Delta h=\frac{\lambda r_{1}\sin\theta}{2\pi B\cos(\theta-\alpha)}\Delta\phi \tag{10}\]  
where \(\Delta h\) stands for the relative height change and \(\Delta\phi\) corresponds to the phase change. Therefore, a smaller incidence angle, a longer baseline, a shorter radar wavelength, and more accurate phase difference could significantly improve the altimetric accuracy. Since the phase was limited to [\(-\pi\),\(\pi\)], a sizeable relative height (\(\sim\)6 m at near range) change led to phase ambiguity (wrapping) [38]. The altimetric ambiguity was further determined as the relative height change corresponding to the 2\(\pi\) phase change, and was calculated by:  
\[h_{2\pi}=\frac{\lambda r_{1}\sin\theta}{B\cos(\theta-\alpha)} \tag{11}\]  
The DInIRA parameters configured in this campaign were substituted into Equation (11), whose results are shown in Figure 13a, where the buoy area (viz. the inversion experiment area of the ocean waves) is indicated by the blue box. Although the Ka-band wavelength was shorter than that of the Ku band, the altimetric ambiguity could also change from 5 m (near range) to 28 m (far range) due to its short length of the baseline (0.34 m). As the SSH change was usually within a few meters, the processing procedure of the phase unwrapping could be avoided, to a large extent, with the parameter configuration of the DInIRA. However, excessive altimetric ambiguity could also bring challenges to the design of the DInIRA system. According to Figure 13b, the corresponding phase change decreased from 0.058 rad (near range) to 0.013 rad (far range) in the Ka band for a relative height change of 5 cm. The stringent requirement for phase sensitivity also required that the thermal noise of the system was limited to a certain level, and that the data processing was highly precise. As compared with the Ka band, the Ku band possessed more stringent requirements for limiting the random errors, such as the thermal noise in the near range. Figure 13: (a) Altimetric ambiguity of DInIRA; (b) Altimetric sensitivity of DInIRA corresponds to a 5 cm height change. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Data**} & \multirow{2}{*}{**SWH/m**} & \multirow{2}{*}{**Bias/m**} & \multicolumn{5}{c}{**MWW/m**} \\ \cline{3-6}  & & & **Swell** & **Bias/m** & **Wind Waves** & **Bias/m** \\ \hline GNSS & & & & & & \\ buoy & 0.69 & - & 62.83 & - & 22.44 & - \\ Ku band & 1.07 & 0.38 & 46.08 & 16.75 & 20.12 & 2.32 \\ Ka band & 0.96 & 0.27 & 59.16 & 3.67 & 23.01 & 0.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Inversion results of SWH and MWW. An essential prerequisite for high-accuracy inversion of the SSH is a high coherence between the signals acquired by the primary and auxiliary antennas. The decorrelation factors [39; 40] mainly include thermal, doppler, baseline, volumetric, time, and data processing. The doppler and baseline decorrelation can be removed by prefiltering in azimuth and range directions, respectively. The time decorrelation only needs to be considered in multi-pass measurement systems. Due to the high imaging quality of the airborne DInIRA, the height measurement error (after registration and multi-look fliting) caused by data processing decorrelation was only on the order of millimeters, and therefore, could be disregarded. Thermal decorrelation was mainly induced by the InIRA system thermal noise [41]. Thermal noise influenced the phase error the most, and the decoherence factor \(\gamma_{n}\) caused by the thermal noise could be derived as:  
\[\gamma_{n}=\sqrt{\frac{SNR_{1}SNR_{2}}{(1+SNR_{1})(1+SNR_{2})}} \tag{12}\]  
where \(SNR_{1}\) and \(SNR_{2}\) denote the SNR of the master and the slave SLC, respectively. Of note, the SNRs of the master and slave images were estimated from the echo data.