The raindrop mean free path and collision rate dependence on rainrate for three-peak equilibrium and Marshall-Palmer distributions

Using the scaling of the coalescence and breakup equation, it is shown that for equilibrium distributions, and in particular for three-peak equilibrium distributions (3PEDs), the mean free time (τ) and mean free path (λ) between raindrop collisions are both inversely proportional to the rainrate and that the total number of raindrop collisions varies with the square of the rainrate. This quantifies previous results, which showed that equilibrium is more rapidly approached for more intense rainrates. For Marshall-Palmer (MP) distributions, more collisions occur for rainrates less than approximately 40 mm h^-1 than for 3PEDs and fewer for greater rainrates because the relative number of large drops increases with rainrate. For rainrates around 50 mm h^-1, there are barely any differences in the behavior of λ and τ between MP distributions and 3PEDs. -Authors