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 (μ̄) is a simple quantity that describes the angular distribution of radiance at a given point. A model of the rate of vertical change of μ̄ 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 μ̄ throughout the water column is well approximated by a single exponential function. The dependense of the parameter Pr, which describes the rate of change of μ̄ with optical depth, on the single-scattering albedo ω0, is well approximated by a quadratic function. By applying a linearization technique to the Prvs. ω0relationships, we identified the contributions of absorption and scattering to Pr. Our results indicate that scattering is the more important process, contributing > 50 to Prfor typical situations when ω0> 0.1. Absorption dominates Prwhen ω0< 0.1, which occurs only in very clear oceanic water at long wavelengths (> 650nm). 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 Pr. Using spectral bio-optical models with several Chl concentrations, we also examined the rate of change μ̄ with geometric depth Pzfor 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 Pzwith varying Chl concentration.