Numerical studies on a global barotropic vorticity equation model of the atmosphere
Abstract
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 Shapirotype filter have on the results of a numerical timeintegration? (2) What are the capabilities and limitations of numerical approximations such as secondorder finitedifference approximations in numerical timeintegrations? 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 longterm timeintegration. For dynamically stable flows, numerical errors due to truncation and roundoff are amplified by the dynamics of the stable system. Numerical methods such as second order finitedifference approximations, together with a Shapirotype 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 finitedifference 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.
 Publication:

Final Report Air Force Geophysics Lab
 Pub Date:
 December 1979
 Bibcode:
 1979afgl.rept.....Y
 Keywords:

 Atmospheric Models;
 Barotropic Flow;
 Mathematical Models;
 Numerical Integration;
 Energy Transfer;
 Finite Difference Theory;
 Flow Distribution;
 Kinetic Energy;
 Vortices;
 Geophysics