Effects of cloud heterogeneities on shortwave radiation: Comparison of cloud-top variability and internal heterogeneity

This paper examines the processes through which cloud heterogeneities influ ence solar reflection. This question is important since present methods giv e numerical results only for the overall radiative effect of cloud heteroge neities but cannot determine the degree to which various mechanisms are res ponsible for it. This study establishes a theoretical framework that define s these mechanisms and also provides a procedure to calculate their magnitu de. In deriving the framework, the authors introduce a one-dimensional radi ative transfer approximation, called the tilted independent pixel approxima tion (TIPA). TIPA uses the horizontal distribution of slant optical thickne sses along the direct solar beam to describe the radiative influence of clo ud heterogeneities when horizontal transport between neighbors is not consi dered. The effects for horizontal transport are then attributed to two basi c mechanisms: trapping and escape of radiation, when it moves to thicker an d thinner cloud elements, respectively. Using the proposed framework, the study examines the shortwave radiative ef fects of cloud-top height and cloud volume extinction coefficient variation s. It is shown and explained that identical variations in cloud optical thi ckness can cause much stronger heterogeneity effects if they are due to var iations in geometrical cloud thickness rather than in volume extinction coe fficient. The differences in albedo can exceed 0.05, and the relative diffe rences in reflectance toward the zenith can be greater than 25% for overhea d sun and 50% for oblique sun. The paper also explains a previously observe d phenomenon: it shows that the trapping of upwelling radiation causes the zenith reflectance of heterogeneous clouds to increase with decreasing sola r elevation.