A numerical study of precipitation development in cumulus clouds with the use of an Eulerian one-dimensional cloud model which consists of the vertical equation of motion, the mass continuity equation, the thermodynamic equation and the parameterized cloud microphysics for liquid and solid water substances is presented. Especially the differences between warm cumulus and ice-bearing cumulus clouds are investigated. Condensed water substance is classified into three components, cloud droplets (cloud water), raindrops (precipitation water) and frozen raindrops (solid water).
The parameterized liquid phase processes include condensation of w ater vapour, autoconversion of cloud droplets to raindrops, collection of cloud droplets by raindrops and evaporation of cloud droplets and raindrops. The ice phase processes include heterogeneous glaciation of raindrops, riming, sublimation of water vapour, melting of frozen raindrops, evaporation of frozen raindrops and evaporation of melting frozen raindrops.
The main results obtained are as follows: 1) The model presented here simulates fairly well some qualitative characteristics of ice-bearing cumulus clouds as observed by Byers and Braham (1949) and others, Especially the inclusion of the time and temperature dependent glaciation process results in a more realistic simulation of the phase change of water substance.2) In warm cumulus the maximum rain intensity appears only once, whereas in ice-bearing cumulus cloud a secondary maximum rain intensity is observed when the major glaciation occurs in a relatively warmer supercooled temperature region. Although the stimulation of cloud growth is expected by including the ice phase in the model, the maximum rain intensity, the total amount of rainfall at the ground surface and the precipitation efficiency are all larger in magnitude in warm cumulus than in ice-bearing cumulus cloud. These results are qualitatively not inconsistent with the work by Koenig and Murray (1976) and their caution, explained in the article, is borne out by the results of our present study.3) According to the sensitivity analyses of the model for various atmospheric conditions, there may be optimum values of lapse rate of temperature and surface temperature for the occurrence of the most intense rainfall and the largest amount of total rainfall under a given humidity distribution. A cumulus cloud with a larger horizontal size causes stronger rain intensity and a larger amount of rainfall.4) Cloud physical processes exert great influence on the development of cumulus clouds. Generally speaking, a cumulus cloud with cloud physical parameters with a sense of faster production of precipitation water causes earlier initiation of the maximum rain intensity and the lifetime of such a cloud is shorter and the precipitation efficiency is larger but the maximum rain intensity is rather affected by the thermodynamic structure of the environmental atmosphere. Limitations of the model are also discussed.
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