Accuracy of Nearshore Bathymetry Inverted From ${X}$ -Band Radar and Optical Video Data

Abstract

Shore-based remote sensing platforms are increasingly used to frequently (~daily) obtain bathymetric information of large (~km $^{2}$ ) nearshore regions over many years. With recorded wave frequency $\Omega $ and wavenumber $k$ (and hence wave phase speed $c = \Omega /k$ ), bed elevation $z_{b}$ can be derived using a model that relates $\Omega $ and $k$ to water depth. However, the accuracy of $z_{b}$ as a function of the sensor and the method of $\Omega -k$ retrieval is not well known, especially not under low-period waves. Here, we assess the accuracy of $z_{b}$ , based on two sensors with their own method of phase speed retrieval, in a dynamic, kilometer-scale environment (Sand Engine, The Netherlands). Bias in $z_{b}$ is systematic. A fast Fourier transform (FFT) method on ${X}$ -band radar imagery produced $z_{b}$ too shallow by 1.0 m for $-15~\text {m} \leq z_{b} \leq -9$ m, and too deep by 2.3 m for $z_{b}\geq -6$ m. A cross-spectral method on optical video imagery produced $z_{b}$ too shallow by 0.59 m for $-10~\text {m} \leq z_{b} \leq -5$ m, and too deep by 0.92 m for $z_{b}\geq -1$ m. Intermediate depths had negligible bias, −0.02 m for the radar-FFT approach and −0.01 m for the video-CS approach. The collapse of the FFT method in shallow water may be explained by the inhomogeneity of the wave field in the 960 m $\times960$ m analysis windows. A shoreward limit of the FFT method is proposed that depends on $z_{b}$ in the analysis windows.