A review of the theoretical basis for bulk mass flux convective parameterization

Abstract

Abstract. 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.

Uncertainty associated with convective wet removal of entrained aerosols in a global climate model

“…However, whether those clouds produce more precipitation relative to clouds with greater CDNC depends on moisture availability and evaporation (Stevens and Feingold, 2009), which are difficult for global models to predict (Plant, 2010). Observations have shown that convective clouds forming in regions of greater pollution, tend to have greater CDNC, which delays the onset of precipitation (Freud and Rosenfeld, 2012).…”

“…Particularly, for the case of convection, an ensemble of convective clouds at a variety of spatial scales is parameterized in each model grid box as a single entraining plume following the mass flux scheme of Tiedtke (1989). Further, the parameterization of convective precipitation (and hence wet scavenging) in global models is a notoriously challenging problem (Plant, 2010;Piriou et al, 2007;Randall et al, 2007;Arakawa, 2004). There is an ongoing need for better representation of convective cloud processes, and associated wet scavenging in global models, as our set of sensitivity simulations will indicate.…”

Simulating deep convection with a shallow convection scheme

“…The most popular method remains the use of a mass flux scheme (see e.g., Plant, 2010;Arakawa and Schubert, 1974). The latter aims to predict the vertical structure and evolution of a one-dimensional entraining-detraining plume (bulk mass flux scheme) or spectrum thereof (spectral mass flux scheme).…”

Large‐scale length and time‐scales for use with stochastic convective parametrization

“…Bulk mass flux schemes such as Gregory and Rowntree (1990)and Kain (2004) consider a single, effective cloud rather than a spectrum of clouds carrying different mass fluxes (Plant, 2010). Such schemes therefore do not yield explicit results for m. In order to compare the convective fluctuations produced by different convection schemes, it is therefore more convenient to consider fluctuations in rainfall rather than mass flux.…”

“…By definition, the cloud-base mass flux to be computed as the closure of any mass-flux parametrization is a function of the large-scale forcing (Plant, 2010). Conventionally, the local, instantaneous grid-box state is used to approximate the large-scale environment.…”