Nonlinear Bathymetry Inversion Based on Wave Property Estimation from Nearshore Video Imagery
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Video based remote sensing techniques are well suited to collect spatially resolved wave images in the surf zone with breaking waves and dynamic bathymetric changes. An advanced video-based depth inversion method is developed to remotely survey bathymetry in the surf zone. The present method involves image processing of original wave image sequences, wave property estimation based on linear feature extraction from the processed image sequences, and is combined with a nonlinear depth inversion model. The original wave image sequences are processed through video image frame differencing and directional low-pass filtering schemes to remove wave-breaking-induced foam noise having high frequencies in the surf zone. The features of individual crest trajectories are extracted from the processed and rectified image sequences, i.e. processed image cross-shore timestacks, by tracking pixels of high intensity within an interrogation window of a Radon-transform-based line-detection algorithm. The wave celerity is computed using space-time information of the extracted trajectories of individual wave crests in the cross-shore timestack domain. The presented retrieval of nearshore bathymetry from video image sequences is based on a nonlinear depth inversion using the nonlinear shallow water wave theory. The nonlinear wave amplitude dispersion effects at the breaker points are determined by combining the nonlinear shallow water celerity equation with a wave breaker criterion, thereby computing water depths iteratively from the celerity measured from the video data. The water depths estimated at the breaker points present initial bathymetric anchor points. Bathymetric profiles in the surf zone are inverted by calculating wave heights dissipated after wave breaking with a wave dissipation model and wave heights shoaled before wave breaking with a wave shoaling model. The continuous wave amplitude dispersion effects are subtracted from the measured celerity profiles, resulting in nearshore bathymetric profiles. The nonlinear depth inversion derived bathymetric estimates from nearshore imagery match the measured values with a biased mean depth error of about +0.06m in the depth range of 0.1 to 3m. In addition, the wave height estimates by the depth inversion model are comparable to the in-situ measured wave heights with a biased mean wave height error of about +0.14m. The present depth inversion method based on optical remote-sensing supports coastal management, navigation, and amphibious operations.