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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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Bryant J. McAvaney and William Bourke

Abstract

A one-level primitive equation spectral model has been initialized with hemispheric 500 mb geopotential height and vorticity fields using the Southern Hemisphere GARP data sets for the period 3–12 November 1969 inclusive. Experiments performed to choose values of the external parameters of the model showed that resolution up to wavenumber 15 and a mean free surface height of 5.6 km were suitable for 48 h prognoses. The distributions with respect to both latitude and planetary wavenumber in the mean square error were determined for the model prognoses. Over the mid-latitude range 30°S to 60°S and over the wavenumber range 3 to 9, 48 h prognoses proved consistently better than persistence.

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Bryant J. McAvaney, William Bourke, and Kamal Puri

Abstract

A global general circulation for mean January conditions has been conducted with a nine-level, wavenumber 15 (rhomboidal) spectral model. A semi-implicit algorithm has been used in the time integration, thereby enhancing computational economy. The simulation reproduces many qualitative aspects of the observed January climatology confirming this type of model as an attractive alternative to models using finite-difference formulations.

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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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Terry L. Hart, William Bourke, Bryant J. McAvaney, Bruce W. Forgan, and John L. McGregor

Abstract

Results are presented for perpetual January and July general circulation simulations using the Australian Bureau of Meteorology Research Centre global spectral model. Particular emphasis is placed on the impact of changes in the physical parameterizations and horizontal resolution on the modeled fields. The results include variances and eddy transports as well as zonal means and geographical distributions. Of the experiments conducted the most satisfactory results were obtained using stability-dependent vertical diffusion and a combination of the Kuo scheme for deep convection and the Tiedtke shallow convection scheme.

The simulation of the polar night region of the stratosphere in January was much more realistic than in results obtained using an earlier version of the model. The improvement is attributed to the revised radiation code, supporting the conclusions of Ramanathan et al. on the sensitivity of simulations of this region of the atmosphere to the treatment of radiative processes.

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Eric J. Pitcher, Robert C. Malone, V. Ramanathan, Maurice L. Blackmon, Kamal Puri, and William Bourke

Abstract

We describe the results of January and July simulations carded out with a nine-level spectral model, employing a rhomboidal truncation at wavenumber 15. Sea-surface temperature, sea-ice distribution and solar zenith angle are held constant in each simulation. The model includes interactive clouds and radiative processes after Ramanathan et al. (1983). Selected fields are shown which highlight the model's strengths and weaknesses.

The latitude-height distribution of the zonal wind is successfully simulated. The model captures the separation between the wintertime westerly jets in the troposphere and stratosphere and thus simulates the sign reversal in the vertical wind shear across the jet axis in the upper troposphere.

In addition to the zonal wind, we show also the zonally averaged temperature, meridional wind and vertical velocity. Regional distributions of sea-level pressure, surface air temperature, precipitation and a number of other fields defined at various pressure levels are compared in detail with observations. For the most part, the large-scale features of the observed general circulation are successfully simulated, although the sea-level pressure in the subtropics over continental regions in the wintertime is higher than observed, and the model atmosphere tends to be a few degrees colder than observed. We otter a partial explanation for this last deficiency.

There is good agreement between the model stratosphere and the actual stratosphere. Preliminary indications suggest the variability present in the model is comparable to that found in the atmosphere.

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Robert C. Malone, Eric J. Pitcher, Maurice L. Blackmon, Kamal Puri, and William Bourke

Abstract

We examine the characteristics of stationary and transient eddies in the geopotential-height field as simulated by a spectral general circulation model. The model possesses a realistic distribution of continents and oceans and realistic, but smoothed, topography. Two simulations with perpetual January and July forcing by climatological sea surface temperatures, sea ice, and insulation were extended to 1200 days, of which the final 600 days were used for the results in this study.

We find that the stationary waves are well simulated in both seasons in the Northern Hemisphere, where strong forcing by orography and land-sea thermal contrasts exists. However, in the Southern Hemisphere, where no continents are present in midlatitudes, the stationary waves have smaller amplitude than that observed in both seasons.

In both hemispheres, the transient eddies are well simulated in the winter season but are too weak in the summer season. The model fails to generate a sufficiently intense summertime midlatitude jet in either hemisphere, and this results in a low level of transient activity. The variance in the tropical troposphere is very well simulated. We examine the geographical distribution and vertical structure of the transient eddies. Fourier analysis in zonal wavenumber and temporal filtering am used to display the wavelength and frequency characteristics of the eddies.

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