A Rational Approach to Cumulus Parameterization

Deep atmospheric convection is treated parametrically in global weather and climate models. The division of labor between explicit and parameterized calculations is traditionally based on the horizontal scale of grid cells. This becomes problematic when the grid size decreases to the scale of convection. An alternative division of labor computes the balanced part of the flow explicitly and parameterizes the unbalanced part of the flow. (``Balance'' refers to a dynamical condition in rotating fluids relating the winds to thermodynamic variables. The simplest case is geostrophic balance in which the horizontal pressure gradient in the fluid balances the Coriolis force.) The advantage of this approach is that balanced dynamics is robust, with far fewer degrees of freedom than convection, and represents the actual large-scale flow with reasonable fidelity. The challenge is then to understand how the balanced flow controls the unbalanced flow, i.e., convection and related circulations, and conversely, how the unbalanced flow affects the balanced component. We discuss recent progress in this program based on numerical modeling and observation of deep convection in tropical weather systems over the ocean.