Diffuse reflectance of oceanic waters II Bidirectional aspects

For visible wavelengths and for most of the oceanic waters, the albedo for single scattering ( $\bar{\omega }$) is not high enough to generate within the upper layers of the ocean a completely diffuse regime, so that the upwelling radiances below the surface, as well as the water-leaving radiances, generally do not form an isotropic radiant field. The nonisotropic character and the resulting bidirectional reflectance are conveniently expressed by the Q factor, which relates a given upwelling radiance L_u(θ′, φ) to the upwelling irradiance E_u (θ′ is the nadir angle, φ is the azimuth angle, and Q = E_u/L_u); in addition the Q function is also dependent on the Sun's position. Another factor, denoted f, controls the magnitude of the global reflectance, R (= E_u/E_d, where E_d is the downwelling irradiance below the surface); f relates R to the backscattering and absorption coefficients of the water body (b_b and a, respectively), according to R = f(b_b/a). This f factor is also Sun angle dependent. By operating an azimuth-dependent Monte Carlo code, both these quantities, as well as their ratio (f/Q) have been studied as a function of the water optical characteristics, namely $\bar{\omega }$ and η; η is the ratio of the molecular scattering to the total (molecular + particles) scattering. Realistic cases (including oceanic waters, with varying chlorophyll concentrations; several wavelengths involved in the remote sensing of ocean color and variable atmospheric turbidity) have been considered. Emphasis has been put on the geometrical conditions that would be typical of a satellite-based ocean color sensor, to derive and interpret the possible variations of the signal emerging from various oceanic waters, when seen from space under various angles and solar illumination conditions.