THEORETICAL DEVELOPMENTS ON THE OPTICAL-PROPERTIES OF HIGHLY TURBID WATERS AND SEA-ICE

The photon diffusion equation is derived in a direct manner from the r adiative transfer equation and is shown to be an asymptotic equation t hat can be directly related to asymptotic radiative transfer theory. D iffusion theory predicts that the asymptotic diffuse attenuation coeff icient, K-infinity, is related to the beam attenuation coefficient, c, the albedo, omega(0), and the asymmetry parameter, g, of the scatteri ng phase function by K-infinity = c root 3[1 - omega(0) - g(omega(0) - omega(0)(2))]. Kirk has previously published a K relationship based e ntirely on Monte Carlo radiative transfer simulations that can be expr essed in the form K-infinity = c root 1 - 2 omega(0) + omega(0)(2) + G (omega(0) - omega(0)(2)), where G is a regression parameter Equating t hese two results gives G = 3(1 - g) + 2(1/omega(0) - 1), showing expli citly, as Kirk found numerically, how G is a function of omega(0) and g. These results are expected to be valid for highly turbid water wher e omega(0) > 0.95. Comparison of the analytical expression for G with Kirk's regression value, using omega(0) of 0.99, differed by only 2%.