A Study of Turbulence Parameterization in a Cloud Model

Abstract

A diagnostic second-order turbulence parameterization has been incorporated into a shallow anelastic three-dimensional numerical cloud model. The turbulence closure scheme for the subgrid-scale motions includes the effects of buoyancy, condensation and liquid water drag. This model has been used to study trade wind cumuli which are roughly 1200 m thick. The simulated cloud has many features in common with observed clouds (Malkus, 1954); however, the observed clouds are made up of several thermal elements instead of one as in the numerical simulation, and they persist over a much longer time period. When comparing the present model with another using deformation eddy viscosity, the following results are obtained: 1) The deformation model has a larger smoothing effect on the horizontally averaged potential temperature and water vapor mixing ratio. 2) Early in the cloud's development, the subgrid-scale kinetic energy is larger than the computed-scale kinetic energy. At the mature stage, the subgrid-scale energy is about one-half to three-quarters the magnitude of the computed-scale kinetic energy. In the deformation model the subgrid-scale turbulence is less, especially in the early stages of the cloud's history. 3) It is found that buoyancy effects can be dropped from the Reynold's stress equation without significant loss of accuracy. The results of both models are highly sensitive to changes of external parameters. This type of sensitivity is either a characteristic of clouds in general, or is a special property of the present models.