The Cumulus Parameterization Problem: Past, Present, and Future

Abstract

A review of the cumulus parameterization problem is presented with an emphasis on its conceptual aspects covering the history of the underlying ideas, major problems existing at present, and possible directions and approaches for future climate models. Since its introduction in the early 1960s, there have been decades of controversies in posing the cumulus parameterization problem. In this paper, it is suggested that confusion between budget and advection considerations is primarily responsible for the controversies. It is also pointed out that the performance of parameterization schemes can be better understood if one is not bound by their authors' justifications. The current trend in posing cumulus parameterization is away from deterministic diagnostic closures, including instantaneous adjustments, toward prognostic or nondeterministic closures, including relaxed and/or triggered adjustments. A number of questions need to be answered, however, for the merit of this trend to be fully utilized.Major practical and conceptual problems in the conventional approach of cumulus parameterization, which include artificial separations of processes and scales, are then discussed. It is rather obvious that for future climate models the scope of the problem must be drastically expanded from ''cumulus parameterization'' to ''unified cloud parameterization,'' or even to ''unified model physics.'' This is an extremely challenging task, both intellectually and computationally, and the use of multiple approaches is crucial even for a moderate success. ''Cloud-resolving convective parameterization'' or ''superparameterization'' is a promising new approach that can develop into a multiscale modeling framework (MMF). It is emphasized that the use of such a framework can unify our currently diversified modeling efforts and make verification of climate models against observations much more constructive than it is now.

Convectively Coupled Kelvin Waves in an Idealized Moist General Circulation Model

“…We use this scheme because of the simplicity in its formulation, relatively small number of parameters, and reproducibility of results. The recent review by Arakawa (2004) shows that most convection schemes can be interpreted as relaxation schemes similar to the Betts-Miller scheme, and the observations of Bretherton et al (2004) suggest a Betts-Miller-type scheme may be justified by observations as well. Further, our experiments with full GCM convection schemes suggest a wide range of sensitivities to a multitude of parameters, many of which are often undocumented in studies that use this scheme.…”

Prognostic validation of a neural network unified physics parameterization

“…Cumulus parameterizations for deep convection in particular are typically based on either 1) moist convective adjustment [Manabe and Strickler, 1964], 2) moisture convergence closure [Kuo, 1974;Tiedtke, 1989], or 3) the quasi-equilibrium hypothesis [Arakawa and Schubert, 1974;Betts, 1986;Betts and Miller, 1986]. There is a long-standing debate about the validity of these hypotheses [Emanuel et al, 1994;Arakawa, 2004], but moist convection is so complex that it is difficult to definitively prove any sort of causal relationship. Moreover, the goal of parameterization is to improve a coarse-resolution model's accuracy not to settle scientific debates.…”

Parameterizing Convective Organization to Escape the Entrainment Dilemma

“…Coarse-grid atmosphere models like General Circulation Models (GCMs) call for some parameterization of water phase changes and vertical fluxes that occur in unresolved (subgrid scale) convective drafts [Arakawa, 2004]. An appealingly physical basis for treating these effects, while respecting the relevant conservation laws, is to use a closed mathematical model of convective drafts and the associated condensate microphysics.…”