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  • Author or Editor: James J. Hack x
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James J. Hack
and
Wayne H. Schubert

Abstract

Under certain circumstances a large fraction of the energy generated by the release of latent heat in a tropical cyclone cab be partitioned to gravity-inertia wave motion rather than to balanced flow. In this way most of the generated energy is radiated away to the far field. If a primitive equation tropical cyclone model is to successfully simulate this process, its lateral boundary condition must be able to transmit the gravity-inertia wave energy generated in the interior of the model. Most present models seem deficient in this regard. As an improvement we explore the possibility of using a cylindrical, pure gravity wave radiation condition. Since there is a wide range of gravity wave phase velocities in a stratified atmosphere, it is necessary to apply the radiation condition vertical mode by vertical mode rather than level by level. The usefulness of this radiation condition and several other conditions in present use is tested both by a reflectivity analysis and by simple numerical time integrations.

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James J. Hack
,
Wayne H. Schubert
, and
Pedro L. Silva Dias

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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