Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field

The average cosine of the underwater light field (i) is a simple quantity that describes the angular distribution of radiance at a given point. A model of the rate of vertical change of ji in the ocean was developed in order to examine the influences of light absorption and scattering. We made calculations of radiative transfer based on invariant imbedding theory assuming an optically homogeneous ocean with a typical scattering phase function and the simple boundary conditions of the sun overhead in a black sky and a flat ocean surface. Under such conditions, the decrease of ji throughout the water column is well approximated by a single exponential function. The dependence of the parameter P7, which describes the rate of change of ji with optical depth, on the single-scattering albedo wo, is well approximated by a quadratic function. By applying a linearization technique to the P, vs. w. relationship, we identified the contributions of absorption and scattering to P,. Our results indicate that scattering is the more important process, contributing >50% to P, for typical situations when w. > 0.1. Absorption dominates P, when w. 6 50 nm). Our analysis of the effect of scattering phase function shows that the scattering into the middle angles, approximately between 20” and 45”, largely determines the magnitude of P,. Using spectral bio-optical models with several Chl concentrations, we also examined the rate of change in ji with geometric depth P, for various water types with realistic values of the absorption and scattering coefficients. This analysis shows large variations in both the magnitude and the spectral behavior of P, with varying Chl concentration. The average cosine of the light field (fi) is a simple and convenient quantity that describes the angular distribution of the underwater radiance at a given point. This quantity is defined as