Interactions between Shallow and Deep Convection under a Finite Departure from Convective Quasi Equilibrium

The present paper presents a simple theory for the transformation of nonprecipitating, shallow convection into precipitating, deep convective clouds. Tomake the pertinent point amuch idealized system is considered, consisting only of shallow and deep convection without large-scale forcing. The transformation is described by an explicit coupling between these two types of convection. Shallow convection moistens and cools the atmosphere, whereas deep convection dries and warms the atmosphere, leading to destabilization and stabilization, respectively. Consequently, in their own stand-alonemodes, shallow convection perpetually grows, whereas deep convection simply damps: the former never reaches equilibrium, and the latter is never spontaneously generated. Coupling themodes together is the only way to reconcile these undesirable separate tendencies, so that the convective system as a whole can remain in a stable periodic state under this idealized setting. Such coupling is a key missing element in current global atmospheric models. The energy cycle description used herein is fully consistent with the original formulation byArakawa and Schubert, and is suitable for direct implementation into models using a mass flux parameterization. The coupling would alleviate current problems with the representation of these two types of convection in numerical models. The present theory also provides a pertinent framework for analyzing large-eddy simulations and cloud-resolving modeling.