A Simple Model of Convective Drafts Accounting for the Perturbation Pressure Term

A simple anelastic two-column model of convective updraft accounting explicitly for the perturbation pressure term is developed. There is no vertical wind shear in the environment, and two geometries (slab or axial) are possible. A shape factor is introduced to account for transport by a nonuniform horizontal profile of the vertical velocity in the updraft and its environment. The perturbation buoyancy profile being prescribed, three parameters must be prescribed: depth and aspect ratio of the updraft and the total cell size. The model is tested for idealized buoyancy profiles and evaluated against a large-eddy simulation of daytime development of deep convection. The model behavior agrees with our understanding of the perturbation pressure within clouds. The simulated updraft quickly responds to the buoyancy field (5 min), shorter than the convection time scale, so that a steady model could be developed. Below the updraft core, a downward pressure gradient is simulated allowing the updraft to overcome a barrier of convective inhibition. This model is designed to be implemented in a convection scheme to replace classical drag formulations of the updraft model.