A Comparison of Continuous and Stochastic Methods for Modeling Rain Drop Growth in Clouds

TL;DR

This paper compares continuous and stochastic models for raindrop growth in clouds, finding that the stochastic approach provides more realistic and faster growth rate predictions, especially for larger drops.

Contribution

It introduces and compares a numerical continuous model and a Monte Carlo stochastic model for raindrop growth, highlighting the improved realism of the stochastic method.

Findings

Stochastic model predicts faster droplet growth for larger drops.

Continuous model underestimates growth rates.

Stochastic approach aligns better with observed raindrop development.

Abstract

Two models for raindrop growth in clouds are developed and compared. A continuous accretion model is solved numerically for drop growth from 20-50 microns, using a polynomial approximation to the collection kernel, and is shown to underestimate growth rates. A Monte Carlo simulation for stochastic growth is also implemented to demonstrate discrete drop growth. The approach models the effect of decreased average time between captures as the drop size increases. It is found that the stochastic model yields a more realistic growth rate, especially for larger drop sizes. It is concluded that the stochastic model showed faster droplet accumulation and hence shorter times for drop growth.