Effects of Cloud Heterogeneities on Shortwave Radiation: Comparison of Cloud-Top Variability and Internal Heterogeneity

Abstract

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. Using the proposed framework, the study examines the shortwave radiative effects of cloud-top height and cloud volume extinction coefficient variations. It is shown and explained that identical variations in cloud optical thickness can cause much stronger heterogeneity effects if they are due to variations in geometrical cloud thickness rather than in volume extinction coefficient. The differences in albedo can exceed 0.05, and the relative differences in reflectance toward the zenith can be greater than 25% for overhead sun and 50% for oblique sun. The paper also explains a previously observed phenomenon: it shows that the trapping of upwelling radiation causes the zenith reflectance of heterogeneous clouds to increase with decreasing solar elevation.