Diffise reflectance of oceanic shallow waters: Influence of water depth and bottom albedo

We used simplifying assumptions to derive analytical formulae expressing the reflectance of shallow waters as a function of observation depth and of bottom depth and albedo. These formulae also involve two apparent optical properties of the water body: a mean diffise attenuation coefficient and a hypothetical reflectance which would be observed if the bottom was infinitely deep. The validity of these approximate formulae was tested by comparing their outputs with accurate solutions of the radiative transfer obtained under the same boundary conditions by Monte Carlo simulations. These approximations were also checked by comparing the reflectance spectra for varying bottom depths and compositions determined in coastal lagoons with those predicted by the formulae. These predictions were based on separate determinations of the spectral albedos of typical materials covering the floor, such as coral sand and various green or brown algae. The simple analytical expressions are accurate enough for most practical applications and also allow quantitative discussion of the limitations of remote-sensing techniques for bottom recognition and bathymetry. As early as 1944, Duntley used a spectrograph mounted in a glass-bottomed boat or flown in an airplane to analyze radiances emerging from the ocean and shallow waters. He evidenced the influence of the water depth on the spectral composition of the upward flux (Duntley 1963). Using a Monte Carlo technique, Plass and Kattawar (1972) calculated the radiative field in the atmosphere+cean system and in particular examined the dependence of the upward flux on the albedo of the ocean floor. Gordon and Brown (1974) studied the diffuse reflectance of a shallow ocean using Monte Carlo simulations and a probabilistic approach. Gordon and Brown provided an analysis based on photon history of the light field as modified by the presence of a reflecting bottom. In, addition, Ackleson and Klemas (1986) developed a two-flow model that simulated the light field within a canopy of bottom-adhering plants. A single scattering approximation for irradiance reflectance was also