A Numerical Simulation of Warm Cumulus Clouds: Part I. Parameterized vs Non-Parameterized Microphysics

Abstract

A time-dependent, one-dimensional model of the life cycle of an isolated warm cumulus cloud is presented that combines the vertical equation of motion, the equation of mass continuity, the first law of thermodynamics, and the equations of continuity of water vapor and liquid hydrometeors. The dynamic interaction between the cloud and its environment is modeled by two entrainment terms: turbulent entrainment representing lateral mixing at the side boundaries of the cloud, and dynamic entrainment representing the systematic inflow or outflow of air required to satisfy mass continuity. The formation and growth of drops by condensation, stochastic coalescence, and droplet breakup are modeled in detail for 67 logarithmically-spaced Eulerian size classes covering a range of particle sizes from 2 to 4040 ?m in radius. The numerical method of simulating microphysical processes was investigated 1) by systematically reducing the number of mass classes used to represent the hydrometeor size spectrum and 2) by replacing the rigorous formulation of the microphysical processes by a set of parameterized expressions. Calculations with the model gave results which were in good agreement with observations of the dynamical and microphysical properties of warm maritime cumuli. The formation and development of the tropical rain shower was particularly well simulated. Reasonable model predictions were obtained when as few as 45 logarithmically-spaced mass classes were used to characterize the hydrometeor size spectrum. When fewer mass classes or parameterized microphysical techniques were used, the model results were significantly different.