Parameterization of the Mie Extinction and Absorption Coefficients for Water Clouds

Abstract

It was found that the anomalous diffraction approximation (ADA) could be made to approximate Mie theory for absorption and extinction in water clouds by parameterizing the missing physics: 1) internal reflection/refraction, 2) photon tunneling, and 3) edge diffraction. Tunneling here refers to processes by which tangential or grazing photons beyond the physical cross section of a spherical particle may be absorbed. Contributions of the above processes to extinction and/or absorption were approximated in terms of particle size, index of refraction, and wavelength. It was found that tunneling can explain most of the difference between ADA and Mie theory for water clouds in the thermal IR. The modified ADA yielded analytical expressions for the absorption and extinction efficiencies, Qabs and Qext, which were integrated over a gamma size distribution to yield expressions for the absorption and extinction coefficients, ?abs and ?ext. These coefficients were expressed in terms of the three gamma distribution parameters, which were related to measured properties of the size distribution: liquid water content, mean, and mass-median diameter. Errors relative to Mie theory for ?abs and ?ext were generally ?10% for the effective radius range in water clouds of 5?30 ?m, for any wavelength in the solar or terrestrial spectrum. For broadband emissivities and absorptivities regarding terrestrial and solar radiation, the errors were less than 1.2% and 4%, respectively. The modified ADA dramatically reduces computation times relative to Mie theory while yielding reasonably accurate results.