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

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 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 re, and droplet absorptances differ? When albedos are equalized by altering ℒ (fixed re), absorptance differences are generally within ±5%, but values of ℒ for the IPA exceed those for the PPH model often by much more than 20%, depending on ℒ and the extent of inhomogeneity. On the other hand, alteration of re, (fixed ℒ) requires that the IPA use smaller values of re than the PPR model. Therefore, since droplet single-scattering albedos increase with decreasing re, IPA absorptances are generally 5%–50% less than PPH absorptances, depending on ℒ and the extent of inhomogeneity. The overall implications are that by representing subgrid variability of marine boundary layer clouds in GCMs i) ℒ will increase, ii) re will decrease, and iii) there will probably he slightly less solar absorption by clouds relative to current values. Moreover, the magnitude of absorptance differences depend in part on the number of spectral bands J used to resolve the solar spectrum. In general, differences for J = 4 and J = 24 are approximately equivalent but for J<4, as in most GCMs, absorptance differences between the gamma IPA and PPH models are exaggerated and often of the wrong sign relative to those for J = 24.