Bathymetry in the nearshore changes continuously under energetic interactions with shoaling and breaking waves. A large storm can bring about significant changes of the nearshore bathymetry on a time scale of an hour. Nearshore bathymetry is required to describe depth-induced wave changes and large-scale fluid motions. The evolution of nearshore bathymetry will be predicted based on current bathymetry and nearshore hydrodynamics. Depth inversion methods by remote-sensing have been developed to cover a large span of spatial and temporal scales, substituting conventional labor-and-time intensive in-situ bathymetry survey methods. However, earlier depth inversion methods have limitations at estimating bathymetry accurately in the surf zone because of image noise due to foam induced by wave breaking in the surf zone.

Video based remote sensing techniques are well-suited to collect spatially resolved wave images in the surf zone with breaking waves. Herein, an advanced video-based depth inversion method is developed to remotely survey bathymetry in the surf zone. Optical wave image sequences in time, captured in the nearshore by video cameras mounted on top of a high building, are used. 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 use of a nonlinear depth inversion model.

The original wave image sequences are processed through video image frame differencing and directional low-pass image filtering (i.e. an elliptic Butterworth filter) to remove the noise arising from foam in the surf zone and characterized by high frequencies in the video imagery. The processed image sequences are rectified into the real world coordinates to generate cross-shore image timestacks which collect time-series of pixel intensity at a one dimensional array along a cross-shore transect in the rectified image sequences. The extraction of individual wave crest features are conducted in the processed cross-shore image timestacks having a two dimensional space-time domain. The features of individual crest trajectories are extracted by tracking pixels of high intensity values within an interrogation sub-window of a Radon-transform-based line-detection algorithm. The wave phase celerity is computed using space-time information of the individual wave crest trajectories extracted in the cross-shore timestack domain.

The computed nearshore bathymetry from video image sequences is based on a nonlinear depth inversion using the nonlinear shallow water wave equation theory. The present nonlinear depth inversion method consists of 3 model components: wave breaker model, wave dissipation model, wave shoaling model. The nonlinear wave amplitude dispersion effects at the breaker points are determined by the wave breaker model, i.e. combining the approximate nonlinear shallow water wave equation-based celerity equation with a wave breaker criterion, thereby computing water depths iteratively from the celerity derived 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 after wave breaking with the wave dissipation model and wave heights shoaled before wave breaking with the 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.