Parameterization of the Mie extinction and absorption coefficients for water clouds

It was found that the anomalous diffraction approximation (ADA) could be ma de 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 proc esses by which tangential or grazing photons beyond the physical cross sect ion of a spherical particle may be absorbed. Contributions of the above pro cesses to extinction and/or absorption were approximated in terms of partic le size, index of refraction, and wavelength. It was found that tunneling c an explain most of the difference between ADA and Mie theory for water clou ds in the thermal IR. The modified ADA yielded analytical expressions for the absorption and exti nction efficiencies, Q(abs) and Q(ext), which were integrated over a gamma size distribution to yield expressions for the absorption and extinction co efficients, beta(abs) and beta(ext). These coefficients were expressed in t erms of the three gamma distribution parameters, which were related to meas ured properties of the size distribution: liquid water content, mean, and m ass-median diameter. Errors relative to Mie theory for beta(abs) and beta(e xt) were generally less than or equal to 10% for the effective radius range in water clouds of 5-30 mu m, for any wavelength in the solar or terrestri al spectrum. For broadband emissivities and absorptivities regarding terres trial and solar radiation, the errors were less than 1.2%nd 4%, respectivel y. The modified ADA dramatically reduces computation times relative to Mie theory while yielding reasonably accurate results.