PNNL

Abstract

Cloud fields are stochastic scattering media due to their inhomogeneous internal structure and stochastic geometry. A radiation field transformed by such a cloud field also becomes random. This fact dictates the necessity to use statistical methods to study the cloud-radiation interaction. The ultimate goal of a statistical approach is to suggest a relatively simple and practical treatment of the stochastic radiative transfer problem and to establish the relationship between the statistical parameters of clouds and radiation. Here, we describe a new statistical treatment of solar radiative transfer in multilayer broken clouds. The term “broken clouds” means that the cloud field has stochastic geometry and deterministic optical parameters inside an individual cloud. The proposed approach is a logical development of the statistical approaches originally suggested for a single-layer broken clouds. A new statistically inhomogeneous Markovian model and the stochastic radiative transfer equation have been used to derive equations for the mean radiance of solar radiation. It is demonstrated that in extreme cases the obtained equations agree with corresponding equations previously derived for the statistically homogeneous broken clouds and the vertically inhomogeneous overcast clouds. We estimate the accuracy and robustness of the obtained equations for the mean radiance by using cloud fields provided by the stochastic Boolean model, large-eddy simulation model, satellite cloud retrievals, and radar observations. We show that the approximated equations could provide reasonable accuracy (~15%) for the ensemble-averaged, domain-averaged, and temporal-averaged radiative properties. An application of the proposed approach to the remote sensing of marine cumulus clouds is discussed.