Synthesis of Entrainment and Detrainment formulations for Convection Parameterizations

Abstract:

Mixing between convective clouds and its environment, usually parameterized in terms of entrainment and detrainment, are among the most important processes that determine the strength of the climate model sensitivity. This notion has led to a renaissance of research in exploring the mechanisms of these mixing processes and, as a result, to a wide range of seemingly different parameterized formulations. In this study we are aiming to synthesize these results as to offer a solid framework for use in parameterized formulations of convection.

Detailed LES analyses in which clouds are subsampled according to their size show that entrainment rates are inversely proportional to the typical cloud radius, in accordance with original entraining plume models. These results can be shown analytically to be consistent with entrainment rate formulations of cloud ensembles that decrease inversely proportional with height, by making only mild assumptions on the shape of the associated cloud size distribution. In addition there are additional dependencies of the entrainment rates on the environmental thermodynamics such as the relative humidity and stability but these are of second order.

In contrast detrainment rates do depend to first order on the environmental thermodynamics such as relative humidity and stability. This can be understood by realizing that i) the details of the cloud size distribution do depend on these environmental factors and ii) that detrainment rates have a much stronger dependency on the shape of the cloud size distribution than entrainment rates.