Application of the linear dispersion relation with respect to depth inversion and remotely sensed imagery

Remote sensing methods have been developed to estimate bathymetry through the use of a theoretical relationship between wave speed and water depth known as the linear, finite depth, dispersion equation for surface gravity waves. The authors describe a validation effort encompassing several hundred observations of wavenumber magnitude for sea-swell frequencies obtained over a wide variety of conditions to investigate possible error sources resulting from the practical application of this relationship. These wavenumber estimates were computed from pressure gauge signals using signal processing algorithms that can be equivalently applied to measurements of wave phase as imaged through remote sensors. The major goal was to determine the accuracy of the dispersion relation while attempting to minimize errors associated with sensor positioning, tidal variations, and Doppler shifts due to mean currents. For water depths outside the surf zone, the linear dispersion relation is highly accurate, with average depth estimation errors on the order of 3-9% of the observed depth. In shallower regions, nominally less than 4 m for this field site, where wave breaking is evident and nonlinear shoaling effects are more pronounced, normalized depth errors of over 50% were commonly observed with most predictions being deeper than observations. Strong correlation between these bias errors and measured wave heights emphasizes the importance of accounting for wave amplitude in the calculation of shallow water phase speeds for depth estimation. A simple depth correction is provided to allow for bathymetry estimation within the surf zone