Linear depth inversion sensitivity to wave viewing angle using synthetic optical video

Abstract

The accuracy of bathymetry estimated by optical implementations of remotely sensed depth inversion algorithms is in part related to the presence of optical wave signal in the images, which depend nonlinearly on the water surface slope. The signal to noise ratio in video images of waves decreases under large azimuthal angles between the camera and wave propagation direction, which can result in poor bathymetry estimation. We quantified errors in depth estimation by analysing the sensitivity of the optical implementation of cBathy v1.1, a widely applied algorithm for depth inversion in coastal regions, to wave viewing angle using synthetic tests. We found relative root mean square errors between 0.02 and 0.08 when the azimuthal angle between the camera look direction and wave approach was less than 75°. However, for higher azimuthal angles, the wave signal was dominated by short wavelengths in the optical images leading to larger depth errors (relative root mean square error = 0.2). We also investigated the sensitivity of the initial guess of the wave direction in the nonlinear solution used by the cBathy v1.1 algorithm to estimate water depth. Observed water depth errors caused by wave viewing angle or initial guess of the wave direction are shown in part to be related to errors in the estimates of frequency and wavenumber. The synthetic methodology and the results of the sensitivity analysis can be generalized to test the accuracy of depth estimation in shore-based video monitoring systems, to design future fixed camera coastal video monitoring stations or to drive the choice of the better viewing angles using small Unmanned Aerial Systems (sUAS) using the Matlab Toolbox we developed.