Area-average solar radiative transfer in three-dimensionally inhomogeneous clouds: The Independently Scattering Cloudlet Model

A new conceptual and computational basis is described for renormalizing the single-scatter and extinction properties (optical depth, single-scatter albedo, and scattering phase function or asymmetry parameter) of a three-dimensionally inhomogeneous cloud volume or layer so as to describe a radiatively equivalent homogeneous volume or layer. The renormalization may allow area-averaged fluxes and intensities to be efficiently computed for some inhomogeneous cloud fields using standard homogeneous (e.g., plane parallel) radiative transfer codes. In the Independently Scattering Cloudlet (ISC) model, macroscopic "cloudlets" distributed randomly throughout a volume are treated as discrete scatterers, analogous to individual cloud droplets but with modified single-scatter properties due to internal multiple scattering. If a volume encompasses only cloudlets that are optically thin, the renormalized single-scatter properties for the volume revert to the intrinsic values and the homogeneous case is recovered. Although the ISC approach is based on a highly idealized, and therefore unrealistic, geometric model of inhomogeneous cloud structure, comparisons with accurate Monte Carlo flux calculations for more realistic random structures reveal surprising accuracy in its reproduction of the relationship between area-averaged albedo, direct transmittance, diffuse transmittance, and in-cloud absorptance. In particular, it describes the approximate functional dependence of these characteristics on the intrinsic single-scatter albedo when all other parameters are held constant. Moreover, it reproduces the relationship between renormalized single-scatter albedo and renormalized optical thickness derived independently, via a perturbative analysis, by other authors. Finally, the ISC model offers a reasonably intuitive physical interpretation of how cloud inhomogeneities influence area-averaged solar radiative transfer, including the significant enhancement of in-cloud absorption under certain conditions.