Modeling Entrainment and Finescale Mixing in Cumulus Clouds

Abstract

A model used to study entrainment and mixing of thermodynamic properties in the stratus-topped boundary layer has been extended to represent these processes in cumulus clouds. The new model, called the "explicit mixing parcel model" (EMPM), depicts finescale internal structure of a rising thermal in a cumulus cloud using a 1D domain. The EMPM links the conventional parcel model, which has no internal structure, and multidimensional cloud models, which resolve cloud-scale structure produced by large eddies. In the EMPM, the internal structure evolves as a consequence of a sequence of discrete entrainment events and an explicit representation of turbulent mixing based on Kerstein's linear eddy model. In this version of the EMPM, subgrid-scale (eddy) diffusion is found to be adequate for representing the effects of the smallest turbulent eddies. In addition, a simple parameterization is used to determine the local condensation or evaporation rates. If the grid size is reduced so that the Kolmogorov scale is resolved and a droplet growth model is incorporated, the EMPM can predict the local microphysical environments of individual cloud droplets. To evaluate its entrainment parameterization, the EMPM was used to predict the bulk properties of Hawaiian cumulus cloud main turrets observed by aircraft. All of the quantities required by the EMPM except for the entrained blob size were obtained from the observations. Profiles of in-cloud means and variances of thermodynamic properties calculated by the EMPM for entrained blob sizes of 50 m, 100 m, and 200 m and by a parcel model with instantaneous mixing were compared to those observed. The observed mean conserved scalar profiles are reproduced by both mixing representations, but the observed mean liquid water mixing ratio and buoyancy profiles, all of the observed variance profiles, and the observed nonbuoyancy level are better reproduced by the EMPM. For entrained blob sizes of 100 m and 200 m, undiluted cloud base air reaches the inversion base in the EMPM, as was observed. These results indicate that the EMPM's entrainment parameterization is adequate for these cloud turrets, and that the characteristic entrained blob size is about 100 m. The model results also demonstrate that the finescale structure represented by the EMPM's 1D domain can be directly compared to high-frequency aircraft measurements.