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 ρ(θ). The diffuse attenuation coefficient k diff has most often been considered an apparent optical property. However, k diff can be considered a quasi-inherent property k diff′ when defined as a steady-state light distribution attenuation coefficient. The Honey–Wilson research empirically relates k diff 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 ρ(θ). A series of Monte Carlo simulations were initiated to calculate k diff′ in an unstratified water column. The calculations, which reflected open ocean water types, used ranges of the single-scattering albedo ω0 and the mean forward-scattering angle θm for two analytic phase functions with different shapes. It was found that k diff′ is nearly independent of the shape of ρ(θ) and can be easily parameterized in terms of a, b, and θm for 0.11 ≤ θm ≤ 0.48 rad and 0.5 ≤ ω0 ≤ 0.95. k diff′ is an asymptotic quantity; that is, a steady-state distribution is reached only after many scattering lengths.
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