Numerical Studies on a Global Barotropic Vorticity Equation Model of the Atmosphere

Samuel Y. K. Yee · Ralph Shapiro

ene 1979 · Air Force Geophysics Laboratory, Air Force Systems Command, United States Air Force

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Numerical experiments have been designed to study the suitability of certain numerical methods commonly used in the numerical modeling of the atmosphere. Specifically, we conducted experiments to address the following: (1) What effect does a Shapiro-type filter have on the results of a numerical time-integration? (2) What are the capabilities and limitations of numerical approximations such as second-order finite-difference approximations in numerical time-integrations? The Shapiro filter is found to be very effective in the removal of computation noise and is therefore useful for insuring computational stability in a long-term time-integration. For dynamically stable flows, numerical errors due to truncation and round-off are amplified by the dynamics of the stable system. Numerical methods such as second order finite-difference approximations, together with a Shapiro-type filter, are adequate in yielding approximate solutions to the modeling differential equations. For dynamically unstable flows, numerical errors are amplified as part of the dynamics of the unstable system. The use of finite-difference approximations may yield solutions which bear no resemblance whatsoever to the true solution of the differential equations. It is postulated that interactions among long wave computational modes and physical modes in a numerical model may prove to be another major obstacle in the numerical prediction of an unstable flow. (Author).