Statistical radiative transport in one-dimensional media and its application to the terrestrial atmosphere

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Abstract
This paper describes radiative transfer through a single cloud layer that is horizontally uniform but statistically distributed in the vertical and compares the radiative transfer in such a statistical cloud to its deterministic counterpart. Specific examples of the derivation of the probability density functions of cloud reflection and transmission by single cloud layers are described for given observed statistical distributions of cloud optical depth and single scattering albedo. Numerical results of the probability density functions for cloud albedo, transmission and absorption are presented, as are the moments of these distributions. Although the computations apply to a hypothetical statistical medium that only approximate clouds in the atmosphere to a limited extent, results of this study demonstrate that radiative transfer in the statistical cloud is substantially different from that of its deterministic counterpart having the same ensemble mean properties. It is also demonstrated that the rate at which the moments of the distributions decay with order, differs for reflection and transmission in a way that is influenced by the absorption of cloud droplets and the asymmetry of droplet scattering. This result suggests that it may be difficult to infer information about the variability of transmitted solar radiation from reflection measurements.