Absorption within inhomogeneous clouds and its parameterization in general circulation models

The effect on absorption in clouds of having an inhomogeneous distribution of droplets is shown to depend on whether one replaces a homogeneous cloud by an inhomogeneous cloud that has the same mean optical thickness, or one that has the same spherical albedo. For the purposes of general circulation models (GCMs) the more appropriate comparison is between homogeneous and inhomogeneous clouds that have the same spherical albeo. so that the radiation balance of the planet with space is maintained. In this ease it is found, using Monte Carlo and independent pixel approximation calculations, that inhomogeneous clouds can absorb more than homogeneous clouds. It is also found that because of the different effects of cloud inhomogeneity on absorption and on the transmission of the direct beam the absorption efficiency of an inhomogeneous cloud may be either greater (for low and high optical depths) or lesser (for intermediate optical depths) than that for a homogeneous cloud of the same mean optical depth. This effect is relevant both to in-cloud absorption and to absorption below clouds. In order to include these effects in GCMs a simple renormalization of the single-scattering parameters of radiative transfer theory is derived that allows the effects of cloud inhomogeneities to be included in plane-parallel calculations. This renormalization method is shown to give reasonable results when compared with Monte Carlo calculations, has the appropiate limits for conservative and completely absorbing cases, and provides a simple interpretation of the effects of cloud inhomogeneities that could readily be incorporated in a GCM.