Normalized gross moist stability in cyclogenesis

Radiation and surface fluxes of latent and sensible heat together constitute a source of entropy which, in the steady state, equals the lateral export of entropy from a convecting region. We define the ratio of entropy export to the laterally imported water vapor in a convecting region as the normalized gross moist stability (NGMS). Closely related to Neelin and Held's gross moist stability, NGMS directly relates the thermodynamic forcing to precipitation rate in the steady state, and thus makes a useful tool for understanding the control of precipitation by the environment.

Using a cumulus ensemble model in the context of the weak temperature gradient approximation, we are able to determine numerically the value of NGMS and the corresponding precipitation as a function of entropy forcing in different environmental conditions. In general, a decrease in NGMS corresponds to an increase in rainfall and vice-versa. The decrease in NGMS may be related to an increase in moisture import or to a decrease in moist entropy export. The latter is strongly influenced by the level of nondivergence of the convection since the lower this level, the less low-entropy mid-level air enters into the convecting region. The difference between exported and imported entropy is decreased, resulting in a lower value of NGMS. These conditions also correspond to an increase in precipitation efficiency.

We investigate these effects in the context of tropical cyclogenesis by modeling convection in environments which favor spin-up. Specifically, using our cumulus ensemble model with weak temperature gradient boundary conditions, we impose perturbations to radiative convective equilibrium profiles of potential temperature or humidity to reflect atmospheric stabilization or moisturization, respectively, characteristic of cyclogenesis. It is not surprising that moisturizing the lower troposphere results in a larger precipitation rate and correspondingly lower value of NGMS. However, we found that stabilizing the atmospheric profile by imposing a warming in the upper troposphere and a cooling in the lower troposphere (as typically occurs in tropical waves) also results in a lowering of NGMS with an increase in precipitation. Calculation of the NGMS in effect provides a way to determine quantitatively the precipitation efficiency which Emanuel found to be so important in his simple model of tropical cyclogenesis.