Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution

A spectral model of the inherent optical properties (absorption and scattering coefficients a and b, respectively) of oceanic case 1 waters with varying chlorophyll concentrations C is operated. It provides the initial conditions for Monte Carlo simulations aimed at examining the diffuse reflectance directly beneath the surface R and its variations with the solar zenith angle ζ. In most oceanic waters, molecular scattering is not negligible, and molecular backscattering may largely exceed backscattering. The variable contributions (depending on C and wavelength) of water molecules and particles in the scattering process result in considerable variations in the shape of the volume-scattering function. R(ζ) is sensitive to this shape. From the simulations, R (which increases as ζ increases) appears to be linearly related to cos ζ, with a slope that is strongly dependent on η_b, the ratio of molecular backscattering to particle backscattering. The value of the single-scattering albedo $(\overline{\omega }=b/a+b)$ has a negligible influence on the R(ζ) function provided that $\overline{\omega }<0.8$, a condition that is always fulfilled when dealing with oceanic case 1 waters. Practical formulas for R(ζ) are proposed. They include the influence of the diffuse sky radiation. The history of each photon and the number of collisions it experiences before exiting have been recorded. These histories and also a probabilistic approach allow the variations of R with cos ζ, η_b, and $\overline{\omega }$ to be understood.