Influence Of Scattering On The Diffuse Attenuation Coefficient In The Asymptotic Region

Abstract

In a homogeneous ocean that both scatters and absorbs the radiance decreases with depth and the angular dependence of the radiance becomes independent of depth and of the incident distribution at the surface. In the diffusion region the asymptotic radiance distribution is only dependent on the inherent properties of the medium including the scattering phase function. Under these conditions an exact integral equation can be derived for the asymptotic radiance. A numerical calculation of the asymptotic radiance was made with Lobatto quadrature resulting in a precise estimate of the diffuse attenuation coefficient for selected values of the single scattering albedo. Calculations were made using estimated single scattering phase functions derived from scattering measurements made for a wide variety of marine and freshwater water types. A two parameter empirical expression was derived from these model calculations relating the diffuse attenuation coefficient and the single scattering albedo. Predictions are made over the entire range of single scattering albedos and are compared to those given by other investigators. The predictability of this relationship and the influence of the scattering phase function are evaluated for each of the scattering phase functions examined. Individual derived relationships are able to predict the diffusion exponent with RMS errors of less than one percent. The overall variation in determining the two parameters is approximately 3 and 18 percent using samples which varied optically from very clear waters of Sargasso Sea to the turbid waters of Lake Erie.