Coalescence and collision-induced breakup of water drops are the two basic drop-interaction processes governing warm-rain development. In this work, recently derived model results are used to construct a parameterization of drop-spectrum evolution as an initial Marshall-Palmer-type drop distribution undergoes the effects of coalescence and breakup. The parameterization, as developed so far, is designed to represent with accuracy only the large-drop portion of the spectrum. The initial distributions are of the form of N = N0e−AD where Λ and N0 are constants, and D denotes raindrop diameter (mm). During its evolution, the large-drop portion of the spectrum maintains exponential form, approaching an equilibrium with Λ=3.6 mm−1. Analysis pertaining to the parameterization has led to the discovery that initial spectra with Λ>3.6 mm−1 rapidly just to a quasi-stationary state before slowly approaching the true equilibrium.
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Philip S. Brown (1987) studied this question.