Parameterization for cloud longwave scattering for use in atmospheric models

A parameterization for the scattering of thermal infrared (longwave) radiation by clouds has been developed based on discrete-ordinate multiple-scattering calculations. The effect of backscattering is folded into the emission of an atmospheric layer and the absorption between levels by scaling the cloud optical thickness. The scaling is a function of the single-scattering albedo and asymmetry factor. For wide ranges of cloud particle size, optical thickness, height, and atmospheric conditions, flux errors induced by the parameterization are small. They are <4 W m(-2) (2%) in the upward flux at the top of the atmosphere and <2 W m(-2) (1%) in the downward flux at the surface. Compared to the case that scattering by clouds is neglected, the flux errors are more than a factor of 2 smaller. The maximum error in cooling rate is approximate to 8%, which occurs at the top of clouds, as well as at the base of high clouds where the difference between the cloud and surface temperatures is large. With the scaling approximation, radiative transfer equations for a cloudy atmosphere are identical with those for a clear atmosphere, and the difficulties in applying a multiple-scattering algorithm to a partly cloudy atmosphere (assuming homogeneous clouds) are avoided. The computational efficiency is practically the same as that for a clear atmosphere. The parameterization represents a significant reduction in one source of the errors involved in the calculation of longwave cooling in cloudy atmospheres.