William Bourke

A multi-level spectral model. I. Formulation and hemispheric integrations

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.

An Efficient, One-Level, Primitive-Equation Spectral Model

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.

A Global Spectral Model for Simulation of the General Circulation

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.

Atmospheric General Circulation Simulations with the BMRC Global Spectral Model. The Impact of Revised Physical Parameterizations

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.

The Simulation of Stationary and Transient Geopotential-Height Eddies in January and July with a Spectral General Circulation Model

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 midlati...

Spectral Methods in Global Climate and Weather Prediction Models

Global models of atmospheric flow based on a spectral representation of the horizontal variation of dynamic variables have now become widely used in both research and operational environments. The detailed formulation of such models is discussed in the present chapter. Consideration is given to the properties of spherical harmonics, the principles of the transform method, primitive equation model formulation, model linearizations relevant to normal modes and semi-implicit time differencing, and to the current applications of spectral models in numerical weather prediction and in climate simulation.

Implications of Horizontal Resolution in Spectral Model Integrations

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.

Comparison of space and time errors in spectral numerical solutions of the global shallow-water equations

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 a...

An impact of hydrostatic extraction scheme on BMRC's global spectral model

There are two important features in geophysical fluid dynamics. One is that the atmospheric and oceanic equations of motion include the Coriolis force; another is that they describe a stratified fluid. The hydrostatic extraction scheme, or standard stratification approximation, posed by Zeng (1979), reflects the second aspect of geophysical fluid dynamics. There exist two major advantages in this scheme; accurate computation of the pressure gradient force can be obtained over steep mountain slopes, and the accumulation error in vertical finite differencing can be reduced, especially near the tropopause.Chen et al (1987) introduced the hydrostatic extraction scheme into a global spectral model, which attained preliminary success at low resolution. Zhang and Sheng et al (1990) developed and improved the hydrostatic extraction scheme in a global spectral model, in whichC0, the parameter that represents the stratification of the reference atmosphere, changes not only with height, but also with latitude. The scheme has been incorporated BMRCs global spectral model (IAPB). Four 5-day forecasts have been performed to test the IAPB with the hydrostatic extraction scheme. Objective verifications demonstrate a positive effect of the hydrostatic extration scheme on BMRCs model, particularly at upper levels, over the tropics and the Antartic region.