Parameterization of the Vertical Transport of Momentum by Cumulus Clouds. Part I: Theory

Abstract

A scheme is developed to parameterize the vertical transport of momentum by cumulus clouds, in which the effect of a cloud-induced pressure field is included. In addition, a new form for momentum exchange between clouds and their environment is used. The scheme incorporates a simple cloud model which includes both updraft and downdraft and specifies the cloud dynamic fields to enable us to determine the mean pressure gradient force across the clouds. It is shown that in a typical environment with vertical wind shear, the pressure gradient force is along the direction of the wind shear. The equation governing cloud mean momentum together with the diagnostic equation for cloud-induced pressure field is solved by iteration to evaluate quantitatively the horizontal pressure gradient force across the cloud and determine the cloud mean momentum. Application of the parameterization scheme to GATE convective events will be presented in Part II of this paper.