heoretical developments on the optical properties of highly turbid waters and sea ice
Maffione, Robert A.
Limnol. Oceangr. 43:29-33

The photon diffusion equation is derived in a direct manner from the radiative transfer equation and is shown to be an asymptotic equation that can be directly related to asymptotic radiative transfer theory. Diffusion theory predicts that the asymptotic diffuse attenuation coefficient, K, is related to the beam attenuation coefficient, c, the single scattering albedo, w₀, and the asymmetry parameter, g, of the scattering phase function by [equatio ommitted]. Kirk has previously published a K relationship based entirely on Monte Carlo radiative transfer simulations that can be expressed in the form K = [equation omitted], where G is a regression parameter. Equating these two results gives G = 3( 1 - g) + 2(1/w₀ - l), showing explicitly, as Kirk found numerically, how G is a function of w₀ and g. These results are expected to be valid for highly turbid water where w₀ > 0.95. Comparison of the analytical expression for G with Kirk’s regression value, using w₀ of 0.99, differed by only 2%.