  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.
