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A Spectral Cumulus Parameterization for Use in Numerical Models of the Tropical Atmosphere

James J. HackIBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598

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Wayne H. SchubertDepartment of Atmospheric Science, Colorado State University, Fort Collins, CO 80523

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Pedro L. Silva DiasInstituto Astronomico e Geofisico, Universdade de São Paulo, São Paulo, Brazil

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Abstract

The spectral cumulus parameterization theory of Arakawa and Schubert is presented in the convective flux form as opposed to the original detrainment form. This flux form is more convenient for use in numerical prediction models. The equations are grouped into one of three categories that are members of a control flow diagram: feedback, static control, and dynamic control. The dynamic control, which determines the cloud base mass flux distribution, is formulated as an optimization problem. This allows quasi-equilibrium to be satisfied as closely as possible while maintaining the necessary nonnegativity constraint on the cloud base mass flux.

Results of two applications of the parameterization are shown. The first illustrates the dependence of the predicted cloud mass flux distribution on the vertical profile of the large-scale vertical motion field. According to the assumption of quasi-equilibrium of the cloud work function, the mass flux associated with deep clouds is controlled by large-scale vertical motion in the middle and upper troposphere, not just by vertical motion at the top of the mixed layer. The second application shows the evolution of the mass flux distribution during the simulated intensification of a tropical vortex using an axisymmetric primitive equation model. A similar sensitivity of deep convection to the development of upper level vertical motion is also observed. These examples demonstrate the inherent potential of this spectral approach for helping to establish a better understanding of the physical nature of the interaction of organized cumulus convection with the large-scale fields not available in more conventional empirical parameterization methods.

Abstract

The spectral cumulus parameterization theory of Arakawa and Schubert is presented in the convective flux form as opposed to the original detrainment form. This flux form is more convenient for use in numerical prediction models. The equations are grouped into one of three categories that are members of a control flow diagram: feedback, static control, and dynamic control. The dynamic control, which determines the cloud base mass flux distribution, is formulated as an optimization problem. This allows quasi-equilibrium to be satisfied as closely as possible while maintaining the necessary nonnegativity constraint on the cloud base mass flux.

Results of two applications of the parameterization are shown. The first illustrates the dependence of the predicted cloud mass flux distribution on the vertical profile of the large-scale vertical motion field. According to the assumption of quasi-equilibrium of the cloud work function, the mass flux associated with deep clouds is controlled by large-scale vertical motion in the middle and upper troposphere, not just by vertical motion at the top of the mixed layer. The second application shows the evolution of the mass flux distribution during the simulated intensification of a tropical vortex using an axisymmetric primitive equation model. A similar sensitivity of deep convection to the development of upper level vertical motion is also observed. These examples demonstrate the inherent potential of this spectral approach for helping to establish a better understanding of the physical nature of the interaction of organized cumulus convection with the large-scale fields not available in more conventional empirical parameterization methods.

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