A Study of Cloud Mixing and Evolution Using PDF Methods. Part I: Cloud Front Propagation and Evaporation

Abstract

The evolution of mean relative humidity (RH) is studied in an isobaric system of clear and cloudy air mixed by an incompressible velocity field. A constant droplet radius assumption is employed that implies a simple dependence of the mixing time scale, τ_eddy, and the reaction (evaporation) time scale, τ_react, on the specifics of the droplet size spectrum. A dilemma is found in the RH e-folding time, τ_efold, predicted by two common microphysical schemes: models that resolve supersaturation and ignore subgrid correlations, which gives τ_efold ∼ τ_react, and PDF schemes that assume instantaneous evaporation and predict τ_efold ∼ τ_eddy. The resolution of this dilemma, Magnussen and Hjertager’s eddy dissipation concept (EDC) model τ_efold ∼ max(τ_eddy, τ_react), is revealed in the results of 1D eddy diffusivity simulations and a new probability density function (PDF) approach to cloud mixing and evolution in which evaporation is explicitly resolved and the shape of the PDF is not specified a priori. The EDC model is shown to exactly solve the nonturbulent problem of spurious production of cloud-edge supersaturations described by Stevens et al. and produce good results in the more general turbulent case.