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Abstract A generalized framework for cumulus parameterization applicable to any horizontal resolution between those typically used in general circulation and cloud-resolving models is presented. It is pointed out that the key parameter in the generalization is σ, which is the fractional area covered by convective updrafts in the grid cell. Practically all conventional cumulus parameterizations assume σ ≪ 1, at least implicitly, using the gridpoint values of the thermodynamic variables to define the thermal structure of the cloud environment. The proposed framework, called “unified parameterization,” eliminates this assumption from the beginning, allowing a smooth transition to an explicit simulation of cloud-scale processes as the resolution increases. If clouds and the environment are horizontally homogeneous with a top-hat profile, as is widely assumed in the conventional parameterizations, it is shown that the σ dependence of the eddy transport is through a simple quadratic function. Together with a properly chosen closure, the unified parameterization determines σ for each realization of grid-scale processes. The parameterization can also provide a framework for including stochastic parameterization. The remaining issues include parameterization of the in-cloud eddy transport because of the inhomogeneous structure of clouds.
Arakawa et al. (Fri,) studied this question.