R.S. Plant A new modelling framework for statistical cumulus dynamics
Keywords
statistical cumulus dynamics, convective plumes, macroscopic limit, cumulus parameterization
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, convective quasi-equilibrium and the macroscopic limit 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. Since the basic picture underlies most current convective parameterizations in general circulation and numerical weather prediction models, the framework provides a firm theoretical basis for investigations into improved parameterization approaches, and indeed for investigations of convective systems more generally.