Modeling the Interaction between Quasi - Geostrophic Vertical 1 Motion and Convection in a Single Column

4 A single-column modeling approach is proposed to study the interaction between convec5 tion and large-scale dynamics using the quasi-geostrophic (QG) framework. This approach 6 extends the notion of “parameterization of large-scale dynamics”, previously applied in the 7 tropics via the weak-temperature-gradient approximation and other comparable methods, 8 to the extratropics, where balanced adiabatic dynamics plays a larger role in inducing large9 scale vertical motion. The diabatic heating in an air column is resolved numerically by a 10 single-column model or a cloud-resolving model. The large-scale vertical velocity, which con11 trols vertical advection of temperature and moisture, is computed through the QG omega 12 equation including the dry adiabatic terms and the diabatic heating term. The component 13 due to diabatic heating can be thought of as geostrophic adjustment to that heating, and 14 couples the convection to the large-scale vertical motion. 15 The approach is demonstrated using two representations of convection: a single-column 16 model and linear response functions derived by Z. Kuang from a large set of cloud-resolving 17 simulations. The results are qualitatively similar in both cases. The behavior of convection 18 that is strongly coupled to large-scale dynamics is significantly different from that in the un19 coupled case. The positive feedback of the diabatic heating on the large-scale vertical motion 20 reduces the stability of the system, extends the decay time scale after initial perturbations, 21 and increases the amplitude of convective responses to transient large-scale perturbations or 22 imposed forcings. The diabatic feedback of convection on vertical motion is strongest for 23 horizontal wavelengths on the order of the Rossby deformation radius. 24