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Novel Data Assimilation Algorithm for Nearshore Bathymetry

It can be expensive and difficult to collect direct bathymetry data for nearshore regions, especially in high-energy locations where there are temporally and spatially varying bathymetric features like sandbars. As a result, there has been increasing interest in remote assessment techniques for estimating bathymetry. Recent efforts have combined Kalman filter–based techniques with indirect video-based observations for bathymetry inversion. Here, we estimate nearshore bathymetry by utilizing observed wave celerity and wave height, which are related to bathymetry through phase-averaged wave dynamics. We present a modified compressed-state Kalman filter (CSKF) method, a fast and scalable Kalman filter method for linear and nonlinear problems with large numbers of unknowns and measurements, and apply it to two nearshore bathymetry estimation problems. To illustrate the robustness and accuracy of our method, we compare its performance with that of two ensemble-based approaches on twin bathymetry estimation problems with profiles based on surveys taken by the U.S. Army Corps of Engineer Field Research Facility (FRF) in Duck, North Carolina. We first consider an estimation problem for a temporally constant bathymetry profile. Then we estimate bathymetry as it evolves in time. Our results indicate that the CSKF method is more accurate and robust than the ensemble-based methods with the same computational cost. The superior performance is due to the optimal low-rank representation of the covariance matrices.