A PARAMETERIZATION FOR COMPUTING GRID-AVERAGED SOLAR FLUXES FOR INHOMOGENEOUS MARINE BOUNDARY-LAYER CLOUDS .2. VALIDATION USING SATELLITE DATA

The independent pixel approximation (IPA) is one of the simplest metho ds of computing solar radiative fluxes for inhomogeneous clouds. It cl aims that if p(tau) is a normalized probability density function for c loud optical depth tau and R(pp)(tau) is plane-parallel, homogeneous ( PPH) albedo, mean cloud albedo can be approximated by integrating p(ta u)R(pp)(tau) over all tau. The purpose of this study is to assess the ability of the gamma distribution function to represent p(tau) for mar ine boundary layer clouds and to examine the accuracy of the ensuing g amma IPA albedos. In a separate study, pixel values of tau were inferr ed from high spatial resolution Landsat imagery of marine boundary lay er clouds. The present study utilizes 45 images, each measuring (58 km )(2). For each image, a density function p(obs)(tau) is estimated, and , using the mean <(tau)over bar> and variance of tau, a corresponding truncated gamma distribution function p(gamma)(tau) is defined. For a diverse range of clouds, p(gamma)(tau) usually approximate p(obs)(tau) well. The best results are for overcast stratocumulus and small, brok en cumulus, while the worst results are for streets of moderately thic k cumulus observed at relatively large solar zenith angles. After both p(obs)(tau) and corresponding p(gamma)(tau) are filtered through the IPA; however, resulting solar zenith angle dependent and spherical alb edos often agree to well within 5%, regardless of cloud type. Furtherm ore, disparities between IPA albedos using p(obs)(7) and p(gamma)(tau) are roughly 10 times smaller than disparities between IPA albedos usi ng p(obs)(tau) and corresponding PPH albedos [R(pp)(<(tau)over bar>)]. 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 pa rameterization, dependent on cloud fraction, is furnished that may ena ble the gamma IPA to be used in GCMs.