Bathymetry Determination Based on Abundant Wavenumbers Estimated from the Local Phase Gradient of X-Band Radar Images

A phase gradient (PG)-based algorithm is proposed in this study to determine coastal bathymetry from X-band radar images. Although local wavenumbers with the same spatial resolution of the wave field can be obtained from the wave field using the PG method, only a single wavenumber result can be extracted from each location theoretically. Due to the influence of unavoidable noise on the wave field image, single wavenumber estimation often shows high uncertainty. This study combines a bandpass filter and directional pass filter to produce different nearly monocomponent wave fields from X-band radar images and then estimates more wavenumbers from these wave fields using the PG method. However, the distributions of wavenumbers in higher-frequency bins still show high variance because the strength of wave signals is weak. We confirmed that the uncertain wavenumber–frequency pairs can be improved using the Kalman filter and are more consistent with the dispersion relation curve. To decrease the influence of inaccurate wavenumbers, we also use the strength of the wave signals as the weights for the least-squares fit. Although the depth errors from shallow-water areas are still unavoidable, we can remove the inaccurate depth estimation from shallow-water areas according to the coefficients of determination of the fitting. In summary, the algorithm proposed in this study can obtain a bathymetry map with high spatial resolution. In contrast to the depth result estimated using a single wavenumber of each frequency bin, we confirm that more wavenumbers from each of the frequency bins are helpful in fitting the dispersion relation curve and obtaining a more reliable depth result.