The effect of precipitation on the properties of a one-dimensional non-entraining cumulus is studied by numerically integrating the equation of motion and the equation of conservation of water substance. The initial state is taken to be the steady-state solution of the equations in the absence of precipitation. Two models of precipitation development are considered. In the first model, the cloud water is considered to change into rainwater at a prescribed rate, whenever the cloud water content exceeds a given critical value. The raindrops are assumed to have an exponential size distribution and to grow by coalescing with the cloud drops. In the second model, all the cloud water is considered to change, at a given instant, into raindrops of a given fall speed. The main conclusions are: 1) a downdraft develops in the lower levels, 2) the cloud grows vertically consequent upon the development of precipitation, and 3) the updraft and water content execute coupled oscillations.
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R. C. Srivastava (1967) studied this question.