Bathymetric Estimation Based on Wave Refraction Patterns

Abstract

As waves enter and travel through the nearshore region, they refract and shoal as a response to gradients in the bathymetry. Many algorithms using the dispersion relationship have been developed to exploit this shoaling variation in the magnitude of the wave number, k, to allow remote sensing estimation of the underlying bathymetry. However, these methods typically ignore the refractive turning of waves as an exploitable signal. A two-step algorithm is developed to estimate bathymetry gradients from gradients in directional wave information. Local wavenumber and angle are extracted from images of surface waves using Hilbert Transform techniques. Bathymetry gradients are calculated from an augmented form of the refraction equation. Synthetic testing of the model shows that under ideal conditions, the model accurately determines two-dimensional bathymetry at wavelength scales with errors on the order of 5% of the true depth. Imagery from field data collections provides challenges for accurate data extraction of wavenumber and wave direction fields. New methods for preprocessing images using standard deviation and wavenumber filters are employed. Data extraction methods using wavelength scale least-squares fits to wrapped phase are developed and tested and show promise at this stage of the work.