Efficient data assimilation algorithm for bathymetry application

Information on the evolving state of the nearshore zone bathymetry is crucial to shoreline management, recreational safety, and naval operations. The high cost and complex logistics of using ship-based surveys for bathymetry estimation have encouraged the use of remote sensing techniques. Data assimilation methods combine the remote sensing data and nearshore hydrodynamic models to estimate the unknown bathymetry and the corresponding uncertainties. In particular, several recent efforts have combined Kalman Filter-based techniques such as ensembled-based Kalman filters with indirect video-based observations to address the bathymetry inversion problem. However, these methods often suffer from ensemble collapse and uncertainty underestimation. Here, the Compressed State Kalman Filter (CSKF) method is used to estimate the bathymetry based on observed wave celerity. In order to demonstrate the accuracy and robustness of the CSKF method, we consider twin tests with synthetic observations of wave celerity, while the bathymetry profiles are chosen based on surveys taken by the U.S. Army Corps of Engineer Field Research Facility (FRF) in Duck, NC. The first test case is a bathymetry estimation problem for a spatially smooth and temporally constant bathymetry profile. The second test case is a bathymetry estimation problem for a temporally evolving bathymetry from a smooth to a non-smooth profile. For both problems, we compare the results of CSKF with those obtained by the local ensemble transform Kalman filter (LETKF), which is a popular ensemble-based Kalman filter method.