Quantifying the lucky droplet model for rainfall

TL;DR

This paper uses large deviation theory to estimate the timescale for rain formation from ice-free clouds, focusing on the rare 'lucky' droplets that grow rapidly through collisions.

Contribution

It introduces a novel application of large deviation theory to quantify the probability and timescale of rapid droplet growth leading to rainfall.

Findings

Estimated rain onset timescales as a function of collision rates

Identified the growth pattern of 'lucky' droplets with evenly spaced initial collisions

Provided insights into the rapid formation of raindrops in ice-free clouds

Abstract

It is difficult to explain rainfall from ice-free clouds, because the timescale for the onset of rain showers is shorter than the mean time for collisions between microscopic water droplets. It has been suggested that raindrops are produced from very rare ' lucky' droplets, which undergo a large number of collisions on a timescale which is short compared to the mean time for a the first collision. This work uses large deviation theory to develop estimates for the timescale for the onset of a rain shower, as a function of the collision rate coefficients. The growth history of the fast-growing droplets which do become raindrops is discussed. It is shown that their first few collisions are always approximately equally spaced in time, regardless of how the mean time for typical droplets varies as a function of the number of collisions.