The Finite-Amplitude Nature of Tropical Cyclogenesis

We have constructed a simple, balanced, axisymmetric model as a means of understanding the existence of the threshold amplitude for tropical cyclogenesis discovered by Rotunno and Emanuel. The model is similar to Ooyama's but is phrased in Schubert and Hack's potential radius coordinates. The essential difference between this and other balanced models lies in the representation of convective clouds. In the present model the cumulus updraft mass flux depends simply and directly on the buoyancy (on angular momentum surfaces) of lifted subcloud-layer air and is not explicitly constrained by moisture convergence. The downdraft mass flux is equal to the updraft flux multiplied by (1−ε), where ε is the precipitation efficiency. The complete spectrum of convective clouds in nature is here represented by two extremes: deep clouds with a precipitation efficiency of one, and shallow, nonprecipitating clouds. The former stabilize the atmosphere both by heating the free atmosphere and drying out the subcloud layer, whereas the shallow clouds stabilize only through drying of the subcloud layer. The two cloud types may coexist. In the crude vertical structure of the model, shallow clouds have the same thermodynamic effect as precipitation-induced downdrafts. Model runs without shallow clouds but with precipitation-induced downdrafts produce the same qualitative features as the runs with shallow clouds. The existence of low-precipitation-efficiency clouds is crucial to the model hurricane development. When a weak vortex is placed in contact with the sea surface, the enhanced surface fluxes together with adiabatic cooling induced by Ekman pumping destabilize the atmosphere. The initial convective clouds that form have relatively low precipitation efficiency and thus only partially compensate for the adiabatic cooling associated with the Ekman pumping. They do, however, import low θe air into the subcloud layer. The vortex core therefore cools and the vortex decays. Only when the anomalous surface fluxes are strong enough, and /or the middle troposphere humid enough does the subcloud layer θe increase, and with it the temperature of the core and the amplitude of the cyclone. The low-precipitation-efficiency clouds play a dual role, however. Once amplification begins, these clouds continue to dominate the convection outside the eyewall, keeping the boundary layer θe relatively low. Without low-precipitation-efficiency clouds, large heating occurs in the outer region and the vortex expands and weakens.