PARAMETERIZATIONS FOR CLOUD OVERLAPPING AND SHORTWAVE SINGLE-SCATTERING PROPERTIES FOR USE IN GENERAL-CIRCULATION AND CLOUD ENSEMBLE MODELS

Parameterizations for cloud single-scattering properties and the scali ng of optical thickness in a partial cloudiness condition have been de veloped for use in atmospheric models. Cloud optical properties are pa rameterized for four broad bands in the solar (or shortwave) spectrum; one in the ultraviolet and visible region and three in the infrared r egion. The extinction coefficient, single-scattering albedo, and asymm etry factor are parameterized separately for ice and water clouds. Bas ed on high spectral-resolution calculations, the effective single-scat tering coalbedo of a broad band is determined such that errors in the fluxes at the top of the atmosphere and at the surface are minimized. This parameterization introduces errors of a few percent in the absorp tion of shortwave radiation in the atmosphere and at the surface. Scal ing of the optical thickness is based on the maximum-random cloud-over lapping approximation, The atmosphere is divided into three height gro ups separated approximately by the 400- and 700-mb levels. Clouds are assumed maximally overlapped within each height group and randomly ove rlapped among different groups. The scaling is applied only to the max imally overlapped cloud layers in individual height groups. The scalin g as a function of the optical thickness, cloud amount, and the solar zenith angle is derived from detailed calculations and empirically adj usted to minimize errors in the fluxes at the top of the atmosphere an d at the surface. Different scaling is used for direct and diffuse rad iation. Except for a large solar zenith angle, the error in fluxes int roduced by the scaling is only a few percent. In terms of absolute err or, it is within a few watts per square meter.