The energy-cycle analysis of the interactions between shallow and deep atmospheric convection

•Interactions between shallow and deep convection studied with energy-cycle model.•Comprehensive investigation of the nonlinear analytic model.•Possibility of periodic cycle of self-sustaining interactions by balancing stabilizing and destabilizing tendencies.•Requirements for a periodic cycle derived and implications for parameterization discussed.

Interactions between different convection modes can be investigated using an energy-cycle description under a framework of mass-flux parameterization. The present paper systematically investigates this system by taking a limit of two modes: shallow and deep convection. Shallow convection destabilizes itself as well as the other convective modes by moistening and cooling the environment, whereas deep convection stabilizes itself as well as the other modes by drying and warming the environment. As a result, shallow convection leads to a runaway growth process in its stand-alone mode, whereas deep convection simply damps out. Interaction between these two convective modes becomes a rich problem, even when it is limited to the case with no large-scale forcing, because of these opposing tendencies. Only if the two modes are coupled at a proper level can a self-sustaining system arise, exhibiting a periodic cycle. The present study establishes the conditions for self-sustaining periodic solutions. It carefully documents the behaviour of the two mode system in order to facilitate the interpretation of global model behaviours when this energy-cycle is implemented as a closure into a convection parameterization in future.