Modeling the Interaction between Quasi-Geostrophic Vertical Motion and Convection in a Single Column

A single-column modeling approach is proposed to study interaction between convection and large-scale dynamics using the quasi-geostrophic (QG) framework. This approach extends the notion of "parameterization of large-scale dynamics", previously applied in the tropics using the weak temperature gradient approximation and other comparable methods, to the subtropics and extratropics, where balanced adiabatic dynamics plays a larger role in inducing large-scale vertical motion. Vertical motion is represented by the QG omega equation with the diabatic heating term included. The diabatic (convective) heating in an air column is calculated numerically by a single-column model or a cloud-resolving model. Vertical advection of temperature and moisture by omega associated with geostrophic adjustment to convective heating is computed through the diabatic heating term in the QG omega equation, and is applied on the air column interactively. The convective-heating-induced omega thus represents a feedback from convection and couples the convection and large-scale vertical motion. The strength of the coupling depends on the characteristic wavelength of the large-scale disturbances, a free parameter in the system.

This modeling approach is demonstrated using two representations of convection: a single-column model and linear response functions derived by Z. Kuang from a large set of cloud-resolving simulations. The results are qualitatively similar in both cases, though the linear response functions allow for a more thorough analysis of the system dynamics. The behavior of convection that is strongly coupled to large-scale vertical motion is significantly different from that in the uncoupled case in which large-scale dynamics is not present. The positive feedback of the diabatic heating on the large-scale vertical motion reduces the stability of the system, extends the decay time scale after initial perturbations, and increases the amplitude of convective responses to transient large-scale perturbations or imposed forcings. The diabatic feedback of convection on vertical motion is strongest for horizontal wavelengths roughly between 2000 km and 1000 km.