Radiative transfer in multifractal clouds

We studied effects of the cloud inhomogeneity in subcloud scale on the reflectance, transmittance, and absorptance of two-dimensional, inhomogeneous clouds. We generated the inhomogeneous clouds as multifractal clouds with a lognormal multiplicative process. For such clouds, the information codimension C-1 is a measure of the cloud inhomogeneity. Radiative transfer through the multifractal clouds was computed with a discrete angle radiative transfer model. The average reflectance, transmittance, and absorptance of multifractal clouds with a given codimension were estimated as averages of 200 realizations. They were computed for different sets of the C-1 parameter, cloud total optical thickness, and asymmetry factor of cloud scatterers. An effective optical thickness of inhomogeneous clouds was defined empirically in the framework of a homogeneous, plane parallel cloud model. Consequently, computation of radiative flux in an inhomogeneous cloud could be transformed into that of an equivalent homogeneous, plane parallel cloud. For a two-dimensional, inhomogeneous, absorbing cloud we found that an inhomogeneous cloud absorbs generally less energy than its homogeneous counterpart. An exception was found for inhomogeneous clouds characterized by a small information codimension, a large cloud optical thickness, and a large single-scattering albedo and for which absorptance is much larger than for their homogeneous counterpart. However, this increase was less than 5% of the homogeneous cloud absorptance. The use of the effective optical thickness also enabled us to treat an inhomogeneous absorbing cloud as an equivalent homogeneous absorbing cloud and to estimate the radiative flux of the equivalent homogeneous cloud as an approximation to the one in the inhomogeneous cloud. We found no immediate need to conceive of a direct effect of the cloud inhomogeneity on the single-scattering albedo, as far as we considered this treatment as a first-order approximation. We discussed the use of the effective optical thickness in two-stream radiative approximations. We also compared our results with those based on the independent pixel approximation.