A One-dimensional Cumulus Model Including Pressure Perturbations

Abstract

A model for shallow cumulus convection is formulated in which the vertical momentum equation and horizontal divergence equation are combined to produce a diagnostic equation for the perturbation pressure field. These equations, together with the first law of thermodynamics and equation of continuity of water substance, are averaged horizontally over the cloud area (a cylinder of constant radius). The resulting set can be integrated in time to study the life cycle of a nonprecipitating cumulus initiated by release of a small buoyant element. The results indicate that the perturbation pressure field plays an essential role by reducing the extremely sharp gradients in velocity near the cloud top, which are common to most other one-dimensional models. Inclusion of the pressure field also makes it possible to predict the radial scale at which the maximum cloud growth rate will occur.