| description abstract | The Independent Pixel approximation (IPA) is one of the simplest methods of computing solar radiative fluxes for inhomogencous clouds. It claims that if p(τ) is a normalized probability density function for cloud optical depth τ and Rpp(τ) is plane-parallel, homogeneous (PPH) albedo, mean cloud albedo can be approximated by integrating p(τ)Rpp(τ) over all τ. The purpose of this study is to assess the ability of the gamma distribution function to represent p(τ) for marine boundary layer clouds and to examine the accuracy of the ensuing gamma IPA albedos. In a separate study, pixel values of τ were inferred from high spatial resolution Landsat imagery of marine boundary layer clouds. The present study utilizes 45 images, each measuring (58 km)2. For each image, a density function pobs(τ) is estimated, and, using the mean τ? and variance of τ, a corresponding truncated gamma distribution function p?(τ) is defined. For a diverse range of clouds, p?(τ) usually approximate pobs(τ) well. The best results are for overcast stratocumulus and small, broken cumulus, while the worst results are for streets of moderately thick cumulus observed at relatively large solar zenith angles. After both pobs(τ) and corresponding pobs(τ) are filtered through the IPA; however, resulting solar zenith angle dependent and spherical albedos often agree to well within 5%, regardless of cloud type. Furthermore, disparities between IPA albedos using pobs(τ) and p?(τ) are roughly 10 times smaller than disparities between IPA albedos using pobs(τ) and corresponding PPH albedos [Rpp(τ?)].Thus, for marine boundary layer clouds, the gamma IPA can be expected to remove most of the PPH bias currently present in GCMs. A simple parameterization, dependent on cloud fraction, is furnished that may enable the gamma IPA to be used in GCMs. | |
