Single-parameter effective dynamics of warm cloud precipitation

TL;DR

This paper develops an analytical framework for understanding warm cloud precipitation dynamics, revealing that a single non-dimensional parameter governs cloud evolution and linking initial conditions to observable cloud properties.

Contribution

It introduces a simplified model separating mass-conserving and fallout regimes, showing that cloud evolution depends primarily on a single parameter, and derives analytical formulas for cloud and rain water evolution.

Findings

Cloud observables collapse as a function of the parameter μ.

An unexpected relationship between cloud water and accumulated rain.

Fallout can be modeled with a constant bulk fall speed.

Abstract

Cloud observables such as precipitation efficiency and cloud lifetime are key quantities in weather and climate, but understanding their quantitative connection to initial conditions such as initial cloud water mass or droplet size remains challenging. Here we study the evolution of cloud droplets with a bin microphysics scheme, modeling both gravitational coagulation as well as fallout, and develop analytical formulae to describe the evolution of bulk cloud and rain water. We separate the dynamics into a mass-conserving and fallout-dominated regime, which reveals that the overall dynamics are governed by a single non-dimensional parameter $\mu$, the ratio of accretion and sedimentation time scales. Cloud observables from the simulations accordingly collapse as a function of $\mu$. We also find an unexpected relationship between cloud water and accumulated rain, and that fallout can be modeled with a bulk fall speed which is constant in time despite an evolving raindrop distribution.