Cumulus Entrainment and Cloud Droplet Spectra: A Numerical Model within a Two-Dimensional Dynamical Framework

Abstract

A simple numerical model designed to predict the evolution of cloud droplet spectra with special emphasis on the role of entrainment is developed for a case of nonprecipitating cloud. The model assumes that the cloud water mixing ratio at any grid location is equal to that predicted by a cloud model using bulk microphysics; that is, supersaturation/undersaturation inside cloud is neglected. Locally, only undiluted droplet concentrations are assumed to exist; any average dilution of cloud droplet concentration observed over a grid volume is interpreted as an effect of internal structure within the grid, with undiluted cloudy patches coexisting with those that are cloud free. Activation of cloud condensation nuclei is assumed to always produce the same initial spectrum of cloud droplets. Further condensational growth of this initial spectrum produces a set of base functions that are used to represent droplet spectral evolution. The microphysical model, combined with the two-dimensional cloud model using bulk microphysics, is applied to an idealized case of small cumulus. It is shown that, within the current framework, entrainment usually leads to fresh activation of cloud droplets and results in multimodal spectra in actively growing cells. Both broad and narrow cloud droplet spectra are predicted in old, highly diluted cells at cloud periphery. These results are discussed in the context of both observational and theoretical studies of droplet spectral evolution.