A new modelling framework for statistical cumulus dynamics

TL;DR

This paper introduces a novel, explicit time-dependent and stochastic modelling framework for atmospheric convective systems, representing them as collections of plumes with probabilistic rules, extending previous models.

Contribution

It removes simplifying assumptions of prior models by incorporating explicit time dependence and stochasticity, enabling more realistic simulations of cumulus dynamics.

Findings

Framework encompasses previous models as special cases

Allows extensions beyond traditional limits

Demonstrates flexibility in modeling plume interactions

Abstract

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time-dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits.