In the past two decades there has been extensive research into the nature of atmospheric convection and scale interactions in cumulus regimes. A major goal of these efforts has been to advance the state of the art in cumulus parameterization. This paper reviews the cumulus parameterization problem in terms of fundamental principles, goals and dynamics constraints as they apply to parameterization in mesoscale and large scale numerical models. Several popular current schemes are discussed in terms of their relationships to these overall aspects of the problem.

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