ACP Atmospheric Chemistry and Physics ACP Atmos. Chem. Phys. 1680-7324 Copernicus Publications Göttingen, Germany 10.5194/acp-10-3529-2010 A review of the theoretical basis for bulk mass flux convective parameterization Plant R. S. 1 Department of Meteorology, University of Reading, Earley Gate, P.O. Box 243, Reading, RG6 6BB, UK 16 04 2010 10 8 3529 3544 Copyright: © 2010 R. S. Plant 2010 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://acp.copernicus.org/articles/10/3529/2010/acp-10-3529-2010.html The full text article is available as a PDF file from https://acp.copernicus.org/articles/10/3529/2010/acp-10-3529-2010.pdf

Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function, the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterizations that use a parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.

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