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 <i>a</i>, the scattering coefficient <i>b</i>, and the scattering phase function ρ(θ). The diffuse attenuation coefficient <i>k</i><sub>diff</sub> has most often been considered an apparent optical property. However, <i>k</i><sub>diff</sub> can be considered a quasi-inherent property <i>k</i><sub>diff</sub>′ when defined as a steady-state light distribution attenuation coefficient. The Honey–Wilson research empirically relates <i>k</i><sub>diff</sub> to <i>a</i> and <i>b</i>. The Honey–Wilson relation most likely applies to a limited range of water types because it does not include dependence on ρ(θ). A series of Monte Carlo simulations were initiated to calculate <i>k</i><sub>diff</sub>′ in an unstratified water column. The calculations, which reflected open ocean water types, used ranges of the single-scattering albedo ω<sub>0</sub> and the mean forward-scattering angle θ<sub><i>m</i></sub> for two analytic phase functions with different shapes. It was found that <i>k</i><sub>diff</sub>′ is nearly independent of the shape of ρ(θ) and can be easily parameterized in terms of <i>a</i>, <i>b</i>, and θ<sub><i>m</i></sub> for 0.11 ≤ θ<sub><i>m</i></sub> ≤ 0.48 rad and 0.5 ≤ ω<sub>0</sub> ≤ 0.95. <i>k</i><sub>diff</sub>′ is an asymptotic quantity; that is, a steady-state distribution is reached only after many scattering lengths.
© 1999 Optical Society of America
Brian M. Concannon and Jon P. Davis, "Results of a Monte Carlo Investigation of the Diffuse Attenuation Coefficient," Appl. Opt. 38, 5104-5107 (1999)