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This paper examines the processes through which cloud heterogeneities influence solar reflection. This question is important since present methods give numerical results only for the overall radiative effect of cloud heterogeneities but cannot determine the degree to which various mechanisms are responsible for it. This study establishes a theoretical framework that defines these mechanisms and also provides a procedure to calculate their magnitude. In deriving the framework, the authors introduce a one-dimensional radiative transfer approximation, called the tilted independent pixel approximation (TIPA). TIPA uses the horizontal distribution of slant optical thicknesses along the direct solar beam to describe the radiative influence of cloud heterogeneities when horizontal transport between neighbors is not considered. The effects for horizontal transport are then attributed to two basic mechanisms: trapping and escape of radiation, when it moves to thicker and thinner cloud elements, respectively.
Várnai et al. (Wed,) studied this question.