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WILLIAM BOURKE

Abstract

A one-level, global, spectral model using the primitive equations is formulated in terms of a concise form of the prognostic equations for vorticity and divergence. The model integration incorporates a grid transform technique to evaluate nonlinear terms; the computational efficiency of the model is found to be far superior to that of an equivalent model based on the traditional interaction coefficients. The transform model, in integrations of 116 days, satisfies principles of conservation of energy, angular momentum, and square potential vorticity to a high degree.

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William Bourke

Abstract

The formulation of a multi-level spectral model suitable for simulation of atmospheric flow on a hemispheric or global scale is presented. The derived primitive equations are employed together with spectral-grid transform procedures in the multi-level domain. An efficient semi-implicit time integration scheme is detailed and results of numerical integrations initialized from analytic fields and Southern Hemisphere data sets are presented.

A simple initializing device of divergence dissipation is suggested and shown to be most effective in eliminating spurious large-scale inertia-gravity oscillations.

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Kamal Puri
and
William Bourke

Abstract

Free surface and non-divergent spectral models have been integrated using varying resolutions with both analytic and meteorological initial fields. The results have been interpreted in terms of convergence of solutions. Both types of integrations show that convergent solutions are obtained over a period of a few days provided that sufficient resolution is used. Energy, enstrophy, and error distributions with planetary wavenumber also indicate crucial differences between the highest and lowest resolution integrations.

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Michael J. Naughton
,
Gerald L. Browning
, and
William Bourke

Abstract

The convergence of spectral model numerical solutions of the global shallow-water equations is examined as a function of the time step and the spectral truncation. The contributions to the errors due to the spatial and temporal discretizations are separately identified and compared. Numerical convergence experiments are performed with the inviscid equations from smooth (Rossby-Haurwitz wave) and observed (R45 atmospheric analysis) initial conditions, and also with the diffusive shallow-water equations. Results are compared with the forced inviscid shallow-water equations case studied by Browning et at. Reduction of the time discretization error by the removal of fast waves from the solution using initialization is shown. The effects of forcing and diffusion on the convergence are discussed. Time truncation errors are found to dominate when a feature is large scale and well resolved; spatial truncation errors dominate-for small-scale features and also for large scales after the small scales have affected them. Possible implications of these results for global atmospheric modeling are discussed.

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