Results of a Monte Carlo investigation of the diffuse attenuation coefficient

Abstract

There has been a large effort to relate the apparent optical properties of ocean water to the inherent optical properties, which are the absorption coefficient a, the scattering coefficient b, and the scattering phase function rho(theta). The diffuse attenuation coefficient kdiff' has most often been considered an apparent optical property. However, kdiff' can be considered a quasi-inherent property kdiff' when defined as a steady-state light distribution attenuation coefficient. The Honey-Wilson research empirically relates kdiff' to a and b. The Honey-Wilson relation most likely applies to a limited range of water types because it does not include dependence on rho(theta). A series of Monte Carlo simulations were initiated to calculate kdiff' in an unstratified water column. The calculations, which reflected open ocean water types, used ranges of the single-scattering albedo omega(0) and the mean forward-scattering angle theta(m) for two analytic phase functions with different shapes. It was found that kdiff' is nearly independent of the shape of rho(theta) and can be easily parameterized in terms of a, b, and theta(m) for 0.11 <or= theta(m) <or= 0.48 rad and 0.5 <or= omega(0) <or= 0.95. kdiff' is an asymptotic quantity; that is, a steady-state distribution is reached only after many scattering lengths.