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Many Large Eddy Simulation (LES) models usethe classic Kessler parameterisation either as it is or in a modified form tomodel the process of cloud water autoconversion into precipitation. The Kesslerscheme, being linear, is particularly useful and is computationallystraightforward to implement. However, a major limitation with this scheme liesin its inability to predict different autoconversion rates for maritime andcontinental clouds. In contrast, the Berry formulation overcomes thisdifficulty, although it is cubic. Due to their different forms, it is difficultto match the two solutions to each other. In this paper we single out theprocesses of cloud conversion and accretion operating in a deep model cloud andneglect the advection terms for simplicity. This facilitates exact analyticalintegration and we are able to derive new expressions for the time of onset ofprecipitation using both the Kessler and Berry formulations. We then discuss theconditions when the two schemes are equivalent. Finally, we also criticallyexamine the process of droplet evaporation within the framework of the classicKessler scheme. We improve the existing parameterisation with an accurateestimation of the diffusional mass transport of water vapour. We thendemonstrate the overall robustness of our calculations by comparing our resultswith the experimental observations of Beard and Pruppacher, and find excellentagreement.  <b>Key words. </b>Atmospheric composition and structure ·Cloud physics and chemistry · Pollution · Meteorology and atmospheric dynamics· Precipitatio

annales geophysicae

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