The influence of the bottom albedo on the diffuse reflectance of a flat, homogeneous ocean is computed as a function of bottom depth and albedo for three oceanic scattering phase functions and several values of ω0. The results show that the bottom can have a large effect on the reflectivity, especially for small optical depths. When combined with the observed optical properties of clear natural water, the calculations are shown to be in good agreement with the observed dependence of in-water nadir radiance spectra, with depth. The apparent independence of the reflectance on the mode of illumination observed earlier for the infinitely deep ocean is found to be invalid for a shallow ocean. The effect of departures of the bottom law of diffuse reflectance from Lambertian is investigated and shown to be considerable in some cases.
Howard R. Gordon and Otis B. Brown, "Influence of Bottom Depth and Albedo on the Diffuse Reflectance of a Flat Homogeneous Ocean," Appl. Opt. 13, 2153-2159 (1974)