The Plume Model of the Mass–Flux Convective Parameterization Schemes

The general circulation models are used for climate predictions and weather forecasting, resolving governing prognostic equations at resolutions at which the convection is typically unresolved. As convection is responsible for important feedback in the climate system and is associated with severe weather events, the climate and weather models must estimate the convection as a function of the resolved mean state of the atmosphere. This procedure is called convective parameterization, and the specific approach in which this task is achieved depends on the specific parameterization scheme employed by the general circulation model. However, almost all of the modern parameterization schemes are based on the same theoretical framework. Although state-of-the-art parameterization schemes still struggle to model convective transport and fractions of convective clouds accurately, limited attempts to change the fundamental theoretical bases have been made in recent years. The aim of this article is to discuss the theoretical bases under which the plume model is introduced in the mass-flux convective parameterization schemes and how these bases have changed in recent years as an attempt to change some of the current problems of the mass-flux parameterizations. This review examines the evolution of the plume model underlying mass–flux convection parameterizations. The discussion focuses on five key topics: (i) the interpretation of convective plumes as representations of cloud ensembles, (ii) entrainment and detrainment assumptions, (iii) prognostic formulations and convective memory, (iv) unified formulations for shallow and deep convection, and (v) challenges associated with convection in the gray zone. The review argues that many recent developments can be interpreted as relaxations of assumptions originally associated with the steady-state plume framework, and discusses the implications of these relaxations for the physical interpretation of mass–flux parameterizations.