A Parametric Model of Cumulus Convection

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Abstract
The interaction of cumulus convection with larger scale systems is perhaps the most fundamental problem confronting meteorology today. The main obstacle to the clarification of this problem, however, is the lack of understanding of the dynamics of individual cumulus clouds and of the processes by which they impart heat and mass to their surroundings. As a tool in the investigation of these subjects, a one-dimensional, time-dependent model has been developed. Although the model is fundamentally one-dimensional, the clouds are assumed to consist of two regions—a protected core and an exposed surrounding shell. The entire depth of the cloud is numerically simulated for each of these mutually interacting regions. The mixing between cloud and environment is parameterized in the model in terms of the turbulence intensity of the interior and exterior of the cloud. In this way, the commonly used but physically invalid assumption of similarity is avoided. Additional equations have been introduced in the model to predict the turbulence level of the cloud at all times. The internal circulation of the clouds and the attending redistribution of mass between levels is parameterized in the model in terms of the one-dimensional velocity field of the core. Laboratory and theoretical information about spherical vortices is used in the parameterization. Results of a typical cloud simulation are presented. The model has shown to be successful in simulating the entire life cycle of cumulus clouds subject to different initial conditions. Although a strict comparison with particular real cases has not been attempted, the computed values for the different variables compare reasonably well with the values commonly observed for tropical clouds. In addition, the model has proven successful in avoiding the unrealistic large radii developed in the early stages of those clouds that were simulated with previous one-dimensional models.

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