On the application of the classic Kessler and Berry schemes in Large Eddy Simulation models with a particular emphasis on cloud autoconversion, the onset time of precipitation and droplet evaporation

Many Large Eddy Simulation (LES) models use the classic Kessler parameterisation either as it is or in a modified form to model the process of cloud water autoconversion into precipitation. The Kessler scheme, being linear, is particularly useful and is computationally straightforward to implement. However, a major limitation with this scheme lies in its inability to predict different autoconversion rates for maritime and continental clouds. In contrast, the Berry formulation overcomes this difficulty, although it is cubic. Due to their different forms, it is difficult to match the two solutions to each other. In this paper we single out the processes of cloud conversion and accretion operating in a deep model cloud and neglect the advection terms for simplicity. This facilitates exact analytical integration and we are able to derive new expressions for the time of onset of precipitation using both the Kessler and Berry formulations. We then discuss the conditions when the two schemes are equivalent. Finally, we also critically examine the process of droplet evaporation within the framework of the classic Kessler scheme. We improve the existing parameterisation with an accurate estimation of the diffusional mass transport of water vapour. We then demonstrate the overall robustness of our calculations by comparing our results with the experimental observations of Beard and Pruppacher, and find excellent agreement.