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

Abstract:

A single-column modeling approach is proposed to study interaction between convection and large-scale dynamics using the quasi-geostrophic (QG) framework. Vertical motion is represented by the QG omega equation with the diabatic heating term included. 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 extratropics, where balanced adiabatic dynamics plays a larger role in inducing large-scale vertical motion. The diabatic heating term in the QG-omega equation represents the feedback from convection, coupling 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 approach is demonstrated using two representations of convection: a single- column model with a convective parameterization, 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 the convective response 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.