Field Verification of the Relationship Between Entrainment Rate and Cumulus Cloud Diameter

Abstract

This research is concerned with the verification of an expression which relates the entrainment rate in a cumulus cloud to the diameter of that cloud, where the entrainment rate is defined as the fractional increase in cloud mass due to mixing with the environment, per unit height. A series of airplane penetrations of relatively small cumulus clouds, conducted during the summer of 1971, was used as a data base for making Stommel entrainment calculations. When a stratification of 23 cloud passes was analyzed, a strong inverse diameter dependence on the mixing rate was evident. For six cloud passes that were described as vigorously growing, well-defined, single isolated towers, the inverse relation was even stronger, and could be expressed by E=0.3/R, where E is the entrainment rate and R the radius; the expression has a correlation coefficient of 0.85. There was a strong indication that the cumulus clouds studied were best described as the end result of an evolution of a series of starting plumes, rather than as purely plume or bubble elements. Failure to find a primary cloud core beneath the main cloud cap, the evaluation of the entrainment parameter value as between bubble and plume values, and evidence of thermal-induced self-modification of the environment suggested the mixed thermal-plume nature of the cumulus clouds under study.