Cumulus Cloud Formulations for Longwave Radiation Calculations

Abstract

Longwave radiative transfer under broken cloud conditions is often treated as a problem in cloud bulk geometry, especially for cumulus clouds, because individual clouds are nearly black. However, climate models ignore cloud geometry and estimate the effects of broken cumulus clouds as the cloud amount weighted average of clear and black cloud overcast conditions (i.e., the black plate approximation). To overcome the simplicity of the black plate approximation, the authors developed a more generalized form of cloud geometrical effects on the effective cloud fraction. Following previous work, this form includes parameters that allow a more precise specification of cloud size and spatial distributions. The sensitivity of the generalized form to the variation in cloud size and spatial distributions is discussed in relation to others. Model calculations show that cloud bulk geometrical shapes, aspect ratio, size distribution, and side inclination angle are the primary factors significantly affecting the effective cloud fraction. These parameters are important at all cloud amounts with greatest sensitivity when the cloud amount is between 0.2 and 0.8. On the other hand, cloud spatial distributions do not significantly influence the effective cloud fraction when absolute cloud amount is less than 0.2 and/or when the cloud aspect ratio is less than 0.5. However, in the range of greatest sensitivity with large aspect ratio and absolute amount, model comparisons show large intermodel differences. The model discussed herein is cloud size dependent and applies most directly to small cumulus clouds (i.e., clouds small compared to the area under consideration).