The Representation of Convection in Mesoscale Models. Part I: Scheme Fabrication and Calibration

Abstract

Currently, there is no adequate cumulus parameterization suitable for use in mesoscale models having horizontal resolutions between 5 and 50 kilometers. Based on the similarity of the temporal and spatial evolution of the vertical variances between a CCOPE supercell and a generic tropical squall line as explicitly simulated by the Regional Atmospheric Modeling System developed at Colorado State University, a convective parameterization scheme is developed that represents microscale turbulence with a modified second-order closure scheme and cumulus draft-scale eddies with a convective adjustment scheme. The microscale turbulence scheme is based upon the Mellor and Yamada 2.5-level closure modified to predict solely on w? w? and includes Zeman and Lumley's formulation for the buoyancy-driven mixed layer to close the pressure term and the eddy transport term. If deep convection is indicated, the microscale turbulence scheme includes contributions from cumulus draft-scale fluxes determined from a cloud model and uses different length scales to represent the planetary boundary-layer eddies and the in-cloud eddies. The cumulus draft-scale tendencies of heat, moisture, and hydrometeors are specified by a mesoscale compensation term and a convective adjustment term. The convective adjustment term is the difference between a cloud model-derived properly and its environmental value, and is modulated by a time scale determined through a moist static energy balance. The mesoscale compensation term is a product of the vertical gradient of the appropriate scalar and a convective velocity equal to (w? w?)½. The cloud model is calibrated and generalized by comparisons with conditionally sampled data from the two explicitly simulated storms. One unique feature of this approach is that the parameterization is not simply a local grid column scheme; w? w? is transported by the turbulence as well as the mean horizontal and vertical winds. Thus, the scheme responds to shear and is more global in nature than current cumulus parameterizations, and maintains a memory of previous convective activity. Furthermore, the scheme provides explicit cumulus source functions for all hydrometeor species. Results from a simple two-dimensional simulation of deep cumulus indicate the satisfactory performance of this scheme. Part II of this paper will compare explicit simulations of two- and three-dimensional Florida sea-breeze convection with parameterized simulations on various coarser grids.