Physics-based satellite-derived bathymetry (SDB) using Landsat OLI images

The estimation of depth in optically shallow waters using satellite imagery can be efficient and cost-effective. Active sensors measure the distance traveled by an emitted laser pulse propagating through the water with high precision and accuracy if the bottom peak intensity of the waveform is greater than the noise level. However, passive optical imaging of optically shallow water involves measuring the radiance after the sunlight undergoes downward attenuation on the way to the sea floor, and the reflected light is then attenuated while moving back upward to the water surface. The difficulty of satellite-derived bathymetry (SDB) arises from the fact that the measured radiance is a result of a complex association of physical elements, mainly the optical properties of the water, bottom reflectance, and depth. In this research, we attempt to apply physics-based algorithms to solve this complex problem as accurately as possible to overcome the limitation of having only a few known values from a multispectral sensor. Major analysis components are atmospheric correction, the estimation of water optical properties from optically deep water, and the optimization of bottom reflectance as well as the water depth. Specular reflection of the sky radiance from the water surface is modeled in addition to the typical atmospheric correction. The physical modeling of optically dominant components such as dissolved organic matter, phytoplankton, and suspended particulates allows the inversion of water attenuation coefficients from optically deep pixels. The atmospheric correction and water attenuation results are used in the ocean optical reflectance equation to solve for the bottom reflectance and water depth. At each stage of the solution, physics-based models and a physically valid, constrained Levenberg–Marquardt numerical optimization technique are used. The physics-based algorithm is applied to Landsat Operational Land Imager (OLI) imagery over the shallow coastal zone of Guam, Key West, and Puerto Rico. The SDB depths are compared to airborne lidar depths, and the root mean squared error (RMSE) is mostly less than 2 m over water as deep as 30 m. As the initial choice of bottom reflectance is critical, along with the bottom reflectance library, we describe a pure bottom unmixing method based on eigenvector analysis to estimate unknown site-specific bottom reflectance.