Statistical Effects in the Evolution of a Distribution of Cloud Droplets by Coalescence

Abstract

Several years ago Telford pointed out that the simplest coalescence model, in which a small group of droplets grew with unit collection efficiency by collecting droplets of half their volume, did not remain bimodal but that the statistical fluctuations in the discrete coalescence events caused many sizes to be evolved from the original two. A few droplets per million grew much more rapidly than the average; Telford was thereby able to shorten considerably the time necessary for rain formation in warm clouds. Results have been obtained by numerical solution of the integro-differential equation which describes the time variation of a droplet distribution. Hocking's collection efficiencies were used. The computations show that Telford's mechanism is equally, if not more, effective when the initial distribution is continuous.