Standalone color-based bathymetry over 10 years at Duck (NC, USA) from optical satellite imagery and wave breaking analysis

Abstract

Coastal hazard forecasting and morphological modeling rely on having accurate and up-to-date nearshore bathymetry. Traditional methods (shipborne surveys, LiDAR...) provide high precision but they are expensive, complex to deploy, and only cover limited areas, leaving many coastal regions either unmapped or under surveyed. In this context, Satellite-Derived Bathymetry (SDB) provides a more accessible and scalable alternative, enabling frequent and global observations of the nearshore zone. This study applies the color-based log-band ratio method to extract nearshore bathymetry at Duck, North Carolina (USA), a highly dynamic environment with a wide range of turbidity values and wave breaking extents. The log-band ratio method is an empirical approach for estimating shallow-water depths from multispectral satellite imagery which relies on the natural attenuation of light in water column, where the ratio of two spectral bands (typically blue and green) is logarithmically related to water depth. Unlike traditional SDB approaches that require in situ bathymetry calibration, this method relies only on nearshore in situ wave height data, using satellite-detected breaking positions and breaker height-to-depth ratio as depth calibration points. Additionally, an automated approach is used to select images where the green/blue band penetrates sufficiently into the water to retrieve bathymetry (cloud, breaking, sky specular reflection, and turbidity effects) avoiding the subjectivity of traditional manual selection. The method is validated through alongshore median- and profile-based assessments, yielding a median RMSE of $\sim$60 cm. Sensitivity tests on key parameters, including the breaker height-to-depth ratio and the calibration time window, demonstrate that a constant breaker height-to-depth ratio ($\gamma$ = 0.36) provides reliable results and that a significant number of calibration points is necessary for accurate bathymetry retrieval ($\Delta T$ $>$ 2 years $\approx$ 150 images with breaking occurring). This approach retrieves instant bathymetries and allows for the extraction of bathymetry evolution over time, with 90 bathymetry maps available over the 10-year period due to the very high resolution (5-m) and 2-day revisit VEN$\mu$S satellite and the 10-m/5-day Sentinel-2 mission. The method is transferable to other optical satellites such as Landsat, although it should be applied with caution, enabling long-term nearshore bathymetry monitoring from the 1980s to the present.