Release of Potential Instability: Part I. A Sequential Plume Model within a Hydrostatic Primitive Equation Model

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Abstract
The release of potential instability by large-scale lifting and the subsequent interaction of cumulus convection and the hydrostatic mesoscale flow in a most complex scale-interaction process. This process is an essential part of tropical weather but it is also important in extratropical cyclones through the formation of mesoscale rainbands that contribute much of the precipitation. The purpose of this paper is to qualitatively and quantitatively clarify the potential instability release process within a framework that will permit calculation of convective/mesoscale interactions. The approach is to use an extension of the Lagrangian form of the one-dimensional cumulus model to provide values of convective-scale changes to a hydrostatic primitive equation model. This cumulus sub-routine locates the base of the convection, computes the cumulus plume that will build, accounts for the environmental subsidence, and mixes the subsided environment with the cumulus plume after rainout. These plumes build sequentially when the subroutine is called every 20 min at each column in the hydrostatic model. The convection model is explained in some detail along with its behavior within the hydrostatic model. The use of this scheme for convective adjustment is contrasted with other schemes; it is emphasized that this scheme is more generally applicable and includes the temporal evolution of mesoscale convective disturbances through consumption of pre-existing potential instability as well as the resupply of warm moist air (fuel). Examples of convective/mesoscale interaction will he presented in Part II along with examples of the sensitivity of the results to variations in initial conditions and numerical coefficients.

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