# Ocean Wave Inversion Based on a Ku/Ka Dual-Band Airborne Interferometric Imaging Radar Altimeter
## 3 Result
### Verification Based on In situ Data  
With reference to Table 2, the WPD inversion results for the wind waves were consistent with the environmental wind direction (EWD, according to the mobile weather station), verifying the inversion accuracy of the OWS in part. The raw data of the in situ GNSS buoy needed to be further processed for validation. The post-processing kinematic (PPK) method has been accordingly demonstrated to be an efficient technique for extracting GNSS data [37]. Thus, the PPK method was finally adopted to retrieve the 5 Hz SSH from the data acquired by the GNSS buoy. To compare it with the inversion results of the OWPs based on the echo data, the 1D SSH inversed by the buoy data used the same reference surface (viz. the WGS-84 reference ellipsoid). The inversion results of the 1-D SSH are shown in Figure 12a. The height sequence collected by the GNSS buoy mainly contained the low frequency signals (related to the tides) and the high-frequency signals (related to the wave-induced SSH). In order to suppress the influence of the noise signals, high-frequency ocean waves signals and the boat-related signals on the ocean wave inversion, a low-pass filter was utilized (cut-off interval was set to 25 s). In addition, the influence of the long-period signals was decreased using a Butterworth high-pass filter. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Data**} & \multirow{2}{*}{**EWD/\({}^{\circ}\)**} & \multicolumn{2}{c}{**WPD/\({}^{\circ}\)**} \\ \cline{3-4}  & & **Main Swell** & **Main Wind Wave** \\ \hline Mobile weather & & & \\ station & Southeast & - & - \\ Ku band & - & \(\sim\)105 & \(\sim\)80 \\ Ka band & - & \(\sim\)105 & \(\sim\)80 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Inversion results of WPD based on OWS and wind direction. Figure 11: Inversion results of OWS in: (**a**) The Ku band; (**b**) the Ka band. Due to the complex environmental conditions of the sea surface, the collected data during 1 h (16:00-17:00) around the DInIRA imaging time was selected for validation purposes. As shown in Figure 12a, the selected time interval is indicated by the blue rectangle box, and the part with the red rectangle box is related to the towing of the ship. The 1D relative height of the sea surface was further obtained after tidal correction, and the 1D frequency spectra \(S_{buoy}(f)\) were calculated using the fast Fourier transform (FFT). The 1D OWS are accordingly obtained using the following equation [36]:  
\[S_{buoy}(k)=\frac{\sqrt{g/k}S_{buoy}(f)}{4\pi} \tag{7}\]  
The 1D OWS inversed by the GNSS buoy data are depicted in Figure 12b. It was inferred that the two main wave patterns (wind waves and swell waves) existed in the GNSS area. The main wave number of the swells was \(\sim\)0.1 rad/m, and that of the wind waves was \(\sim\)0.28 rad/m, corresponding to the \(\sim\)59.16 m and \(\sim\)23.01 m wavelengths, respectively. The SWH was further achieved by integrating the 1D OWS [28]:  
\[\text{SWH}=4.005\times\sqrt{\int\ S_{buoy}(k)dk} \tag{8}\]  
In order to better compare with in situ buoy data, the 2D wavenumber spectra were converted to 1D wavenumber spectra using the following equation [36]:  
\[S(k)=\int_{-\pi}^{\pi}S(k\cos\varphi,k\sin\varphi)kd\varphi \tag{9}\]  
where \(S(k\cos\varphi,k\sin\varphi)\) denotes the 2D wavenumber spectra, and \(\varphi\) is the angle with respect to the positive direction of the \(k_{x}\) axis. The conversion results are shown in Figure 12b, and it can be seen that the 1D spectrum inversion results of the Ka band are closer to the I -situ GNSS data than those of Ku band.