The Pressure Perturbation and the Numerical Modeling of a Cloud

Abstract

The adaptation of the deep convection equations of Ogura and Phillips to moist convection results in an implicit relationship between temperature, potential temperature, pressure, and saturation vapor pressure. Typically, the pressure is treated as a known function of height to eliminate this condition. The effect of this approximation is investigated by numerically integrating the primitive equations in two-dimensional Cartesian coordinates. The model includes precipitation, and the equations are integrated for the life cycle of a strong cumulus cell. The result indicates that the non-dimensional pressure perturbation is notably an order smaller than scale analysis indicates it might be and that the deviation from the environmental pressure can be ignored in determining the saturation vapor pressure. This is partly because the pressure diagnostic equation acts to smooth out the pressure distribution.