Vol. 9, issue 01, article # 2Pomraning G.S. Effective radiative transfer properties for partially cloudy atmospheres. // Atmospheric and oceanic optics. 1996. V. 9. No. 01. P. 7–16.
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In this paper, we suggest a relatively simple radiation treatment of the broken cloud field problem. The underlying equations are based upon a Markovian model, which treats this radiative transfer problem by a stochastic formalism. Specifically, the partially cloudy atmosphere is treated as a two-component (clouds and clear sky) mixture, which is described by a set of two coupled deterministic equations for the ensemble-averaged intensity. For Markovian statistics, these equations are exact in a purely absorbing mixture, and are reasonably accurate and very robust in the general case including scattering. This description can also be modified to account for non-Marcovian statistics. We show that in two different asymptotic limits this set of two coupled equations can be renormalized to a single radiative transfer equation, involving effective atmospheric properties. These two limits correspond to a nearly transparent atmosphere and small correlation length mixing statistics. General spatial dependences of cloud and clear sky properties, as well as inhomogeneous and anisotropic statistics, are allowed in the formalism.