A PARAMETERIZATION FOR COMPUTING GRID-AVERAGED SOLAR FLUXES FOR INHOMOGENEOUS MARINE BOUNDARY-LAYER CLOUDS .1. METHODOLOGY AND HOMOGENEOUS BIASES

method of computing grid-averaged solar radiative fluxes for horizonta lly inhomogeneous marine boundary layer cloud fields is presented. Its underlying assumptions are as follows: i) the independent pixel appro ximation (IPA) is applicable and ii) for regions the size of general c irculation model (GCM) grid cells, frequency distributions of cloud op tical depth tau can be approximated by gamma distribution functions. E quations are furnished for albedo and transmittance that, when applied to judiciously chosen spectral bands, require about three to four tim es as much CPU time as plane-parallel, homogeneous (PPH) two-stream ap proximations, which are ubiquitous to GCMs. This is not a hindrance, a s two-stream solutions command typically less than 1% of a GCM's CPU c onsumption. This method, referred to as the gamma IPA, requires estima tes of the mean and variance of tau for each applicable grid cell. Bia ses associated with PPH models are assessed assuming that cloud proper ties in GCMs are tuned to yield albedos that agree with those inferred from satellite data. Thus, it is pertinent to ask: when cloud albedos for the gamma IPA and PPH models are forced to be equal, how do their cloud liquid water paths L, droplet effective radii r(e), and droplet absorptances differ? When albedos are equalized by altering L (fixed r(e)), absorptance differences are generally within +/-5%, but values of L for the IPA exceed those for the PPH model often by much more tha n 20%, depending on L and the extent of inhomogeneity. On the other ha nd, alteration of r(e) (fixed L) requires that the IPA use smaller val ues of r(e) than the PPH model. Therefore, since droplet single-scatte ring albedos increase with decreasing r(e), IPA absorptances are gener ally 5%-50% less than PPH absorptances, depending on dl and the extent of inhomogeneity. The overall implications are that by representing s ubgrid variability of marine boundary layer clouds in GCMs i) dl will increase, ii) r(e) will decrease, and iii) there will probably be slig htly less solar absorption by clouds relative to current values. Moreo ver, the magnitude of absorptance differences depend in part on the nu mber of spectral bands J used to resolve the solar spectrum. In genera l, differences for J = 4 and J = 24 are approximately equivalent but f or J < 4, as in most GCMs, absorptance differences between the gamma T PA and PPH models are exaggerated and often of the wrong sign relative to those for J = 24.