# Ocean Wave Inversion Based on a Ku/Ka Dual-Band Airborne Interferometric Imaging Radar Altimeter
## 2 Method
### Ocean Wave Inversion
In order to improve the accuracy of ocean wave inversion, the random phase errors (which can impact the SSH inversion) in the interferometric phase diagrams needed to be suppressed. Since the sea surface was relatively stable and its interference phase was uniformly distributed, the multi-look filtering algorithm could ensure the original geometry of the sea surface even in the area of unexpected phase changes. Similarly, [PERSON] et al., (2016) [35] proposed a relationship between the standard deviation of the phase noise and the multi-look numbers, establishing that the phase noise could be moderated by adding to the multi-look numbers. However, an excessive multi-look  
Figure 7: Coherence coefficient map in: (**a**) The Ku band; (**b**) the Ka band. Interference phase diagram in: (**c**) The Ku band; (**d**) the Ka band. number could distort the SSH. Moreover, [PERSON] et al., (2021) [36], in a more systematic study on the selection of multi-look numbers, suggested that an inappropriate multi-look number could cause additional random phase errors and even partly suppress the inversion of wind waves. In addition to random phase noise, an additional phase introduced by the scattering of the sea surface objects, the distribution of the flat earth phase, and the ground distance resolution, accordingly, needed to be further considered when filtering the interference phases. In this paper, a 40 \(\times\) 2 multi-look window was chosen for filtering with the mean filtering algorithm, and the results are illustrated in Figure 8a. The phase filtering significantly downgraded the effect of the random phase noise for further experiments. The flat-earth phase also needed to be removed for extracting the elevation phase (closely related to the ocean waves). In this paper, the flat-earth phase was thus removed based on the orbital data of the inertial navigation system in the plane. The interferometric phase diagram (viz. the Ka band) is shown in Figure 8a. As well, Figure 8b displays the elevation phase after removing the flat-earth effect, and the upper right part of Figure 8b represents the selected local area (i.e., the buoy area), and the ocean wave profiles, which can be clearly distinguished. The selected area is utilized for the inversion of the ocean waves. The inversion results of the SSH in the Ku and Ka bands are shown in Figure 9. Given the incidence angle configuration, the swath of the Ka band (\(\sim\)800 m) was wider than that of Ku band (\(\sim\)700 m). In addition, the inversion results of the far range performed relatively worse as compared with the near range, due to the lower SNR. The phase error caused by the low SNR still existed after filtering, and therefore, these areas were avoided as much as possible when selecting the crossover ones. In this paper, we selected the buoy areas in the SSH inversion results of the Ku (in black box) and Ka bands (in red box) for further experiments, respectively. Noteworthy, the Ka band was more sensitive to the sea surface geometry than the Ku band, whose differences are described in Section 4. To draw a distinction with the field instrument data, the SSH inversion results of the GNSS buoy (viz. the boxed area in Figure 9) were cropped for validation. The original SSH inversed by the DInIRA at the GNSS buoy area (grid resolution of 0.3 m \(\times\) 0.3 m) is presented in Figure 10b,d. It was generally accepted that the signals with the wavelengths less than 3 m in the ocean were primarily noise signals, and that the long-period signals (might be associated with the geoid signal) could affect the inversion of ocean waves. These signals could be removed by using a band-pass filter (cut-off wavelength was set to 3-150 m). Finally, the wavelengths of 3-150 m were further retained after filtering, and the residual signals in the data were mainly the ocean waves. The results after band pass filtering are depicted in Figure 10a,c, and then exploited to retrieve the ocean waves.