Theoretical developments on the optical properties of highly turbid waters and sea ice
Limnol. Oceanogr., 43(1), 1998, 29-33 | DOI: 10.4319/lo.1998.43.1.0029
ABSTRACT: 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 Kirks regression value, using w0 of 0.99, differed by only 2%.