Multiscale Models with Moisture and Systematic Strategies for Superparameterization

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Abstract
The accurate parameterization of moist convection presents a major challenge for the accurate prediction of weather and climate through numerical models. Superparameterization is a promising recent alternative strategy for including the effects of moist convection through explicit turbulent fluxes calculated from a cloud-resolving model. Basic scales for cloud-resolving modeling are the microscales on the order of 10 km in space on time scales on the order of 15 min, where vertical and horizontal motions are comparable and moist processes are strongly nonlinear (meso-gamma scale). In this paper, systematic multiscale asymptotic analysis is utilized to develop simplified microscale mesoscale dynamic (MMD) models for interaction between the microscales and spatiotemporal mesoscales on the order of 100 km and 2.5 h (meso-beta scale). The new MMD models lead to a systematic framework for superparameterization for numerical weather prediction (NWP) generalizing the traditional column modeling framework. The MMD formulation also provides a flexible systematic framework for devising new parameterization strategies for NWP intermediate between the two extremes of column modeling and detailed cloud-resolving modeling. It is also established here that these MMD models fit crudely into the recent systematic multiscale framework developed to explain the observed larger-scale statistical self-similarity of tropical convection, and therefore provide a systematic framework for superparameterization. Finally, it is shown that the new MMD models have the structure of a heterogeneous multiscale method so that many numerical techniques recently developed in the applied mathematics literature can be applied to this formulation.