A Scale Analysis of Deep Moist Convection and Some Related Numerical Calculations

Abstract

A scale analysis valid for deep moist convection is carried out. The approximate equations of motion are anelastic with the time scale set by the Brunt- Väisälä frequency. A new assumption is that the base state potential temperature is a slowly varying function of the vertical coordinate. It is this assumption that eliminates the energetic inconsistency discussed by Wilhelmson and Ogura (1972) for a non-isentropic base state. Another key result is that the dynamic pressure is an order of magnitude smaller than the first-order temperature and potential temperature. In agreement with observations, the kinetic energy is found to be an order of magnitude smaller than the first-order thermodynamic energy. A set of six numerical simulations representing moderately deep moist convection is carried out. The base state is an idealized maritime tropical sounding with no vertical wind shear. The first calculation (Run A) shows the growth and dissipation of a typical shower cloud. The remaining calculations have small changes in either initial conditions or model equations from Run A. These calculations indicate the sensitivity of the present model to different approximations and give additional evidence for the validity of the scale analysis.