Bathymetry Estimation From Single-Frame Images of Nearshore Waves

Existing methods for determining bathymetry from remotely sensed images of nearshore waves exploit only information on the magnitude of wavenumber (k = 2pi/L), ignoring spatial changes in wave direction thetas that can provide information about bathymetry gradients. These methods also require wave period information, so they can only be used when time series imagery is available. We present an algorithm where changes in direction of refracting waves are used to determine underlying bathymetry gradients based on the irrotationality of wavenumber condition. Depth dependences are explicitly introduced through the linear dispersion relationship. The final form of the model is independent of wave period so that all necessary input measurements can be derived from a single aerial snapshot taken from a plane, unmanned aerial vehicle, or satellite. Three different methods were tested for extracting wavenumber and angle from images, i.e., two based on spatial gradients of wave phase and one based on integrated travel times between sample locations (a tomographic approach). Synthetic testing using monochromatic and bichromatic waves, with and without noise, showed that while all three methods work well under ideal wave conditions, gradient methods were overly sensitive to data imperfections. The tomographic approach yielded robust wave measurements and provided confidence limits to objectively identify unusable areas. Further tests of this method using monochromatic waves on three synthetic bathymetries of increasing complexity showed a mean bathymetry bias of 0.01 m and a mean rms error of 0.17 m. While not always applicable, the model provides an alternative form of bathymetry estimation when celerity information is not available.