Shallow Bathymetry from Multiple Sentinel 2 Images via the Joint Estimation of Wave Celerity and Wavelength

In this study, we present a new method called BathySent to retrieve shallow bathymetry from space that is based on the joint measurement of ocean wave celerity (c) and wavelength (λ). We developed the method to work with Sentinel 2 data, exploiting the time lag between two Sentinel 2 spectral bands, acquired quasi-simultaneously, from a single satellite dataset. Our method was based on the linear dispersion law, which related water depth to wave celerity and wavelength: when the water depth was less than about half the dominant wavelength, the wave celerity and wavelength decreased due to decreasing water depth (h) as the waves propagated towards the coast. Instead of using a best weighted $(\mathrm{c},\mathsf{\lambda })$ fit with the linear dispersion relation to retrieve h, we proposed solving the linear dispersion relation for each $(\mathrm{c},\mathsf{\lambda })$ pair to find multiple h-values within the same resolution cell. Then, we calculated the weighted averaged h-value for each resolution cell. To improve the precision of the final bathymetric map, we stacked the bathymetry values from N-different datasets acquired from the same study area on different dates. We first tested the algorithm on a set of images representing simulated ocean waves, then we applied it to a real set of Sentinel 2 data obtained of our study area, Gâvres peninsula (France, 47°,67 lat.; −3°35 lon.). A comparison with in situ bathymetry yielded good results from the synthetic images (r² = 0.9) and promising results with the Sentinel 2 images (r² = 0.7) in the 0–16 m depth zone.