Discrete ordinate method with matrix exponential for stochastic radiative transfer in broken clouds

We present a coherent treatment of the stochastic radiative transfer in an atmosphere containing clouds. Our analysis includes the derivation of an nth-order stochastic model for the solar radiation problem and arbitrary cloud statistics, as well as its particularization to broken cloud fields in general, and in particular to homogeneous three-, two- and one-dimensional broken clouds. The stochastic radiative transfer equations, which are equivalent to the Levermore–Pomraning equations, are solved by using the discrete ordinate method with matrix exponential. Using the Spherical Harmonics Discrete Ordinate Method (SHDOM) as a benchmark model, we found that the accuracy of the stochastic model, dealing with a molecular atmosphere and its underlying surface, is at least twice that of the independent pixel approximation. The stochastic model can be used to analyze the effects of cloud inhomogeneities on trace gas retrievals in the solar regime. - Highlights: • nth-order stochastic model for the solar radiation problem. • Vector stochastic model for broken clouds and a molecular atmosphere. • Solution of the stochastic transfer equation by DOME