A Parameterization for Computing Grid-Averaged Solar Fluxes for Inhomogeneous Marine Boundary Layer Clouds. Part I: Methodology and Homogeneous Biases

Abstract

Abstract A method of computing grid-averaged solar radiative fluxes for horizontally inhomogeneous marine boundary layer cloud fields is presented. Its underlying assumptions are as follows: i) the independent pixel approximation (IPA) is applicable and ii) for regions the size of general circulation model (GCM) grid cells, frequency distributions of cloud optical depth τ can be approximated by gamma distribution functions. Equations are furnished for albedo and transmittance that, when applied to judiciously chosen spectral bands, require about three to four times as much CPU time as plane-parallel, homogeneous (PPH) two-stream approximations, which are ubiquitous to GCMs. This is not a hindrance, as two-stream solutions command typically less than 1% of a GCM's CPU consumption. This method, referred to as the gamma IPA, requires estimates of the mean and variance of τ for each applicable grid cell. Biases associated with PPH models are assessed assuming that cloud properties in GCMs are tuned to yield a...