On the dynamics of midlatitude synoptic systems with intense cumulus convection

A scale analysis appropriate for midlatitude explosive cyclones is presented, including the effects of cumulus clouds. First-order equations are derived for the thermodynamic and vorticity fields. It is shown that the quasi-geostrophic form of the divergence equation is a good approximation, while the geostrophic wind approximation is no longer valid in the presence of intense convection. It is also found that diabatic heating by clouds is responsible for the enhancement of the large-scale vertical motion, which induces a divergent wind on the same order as the rotational part. Therefore, cumulus convection affects the large-scale flow through an induced secondary circulation, which manifests its effect in the thermodynamic and vorticity equations as the advection by the divergent wind component. In addition, cumulus clouds also affect the large-scale vorticity by imparting excess cloud vorticity to the environment. Interactions between cloud and large scales are also discussed in terms of the omega and potential vorticity equations. It is shown that the dominant forcing terms, i.e., diabatic heating and vortex stretching caused by cumulus clouds, tend to balance in the large-scale potential vorticity equation, and that the influence of cumulus convection appears through the smaller forcings resulting from cloud life-cycles and two nongeostrophic effects. A three-level model is used to investigate the effects of cumulus convection on baroclinic instability, with Ekman-CISK as the closure condition. It is found that the various forcing mechanisms produce different effects on the evolution and structure of the baroclinically unstable waves.