A Global General Circulation Model of the Atmosphere Based on the Semi-Spectral Method

Abstract

A new type of global general circulation model has been developed consisting of a finite difference representation in a single meridional-height plane, with the zonal variance of the atmospheric fields being treated by truncated Fourier series. The manipulation of the nonlinear terms of the equations was effected by using the so-called spectral-grid transform technique. Maintenance of stability in the model required the application of a filter designed by Shapiro which removed 2-grid-interval waves in the meridional grid from each of the variables. Stable integration of the model was achieved over a 100-day test. The model was initiated from somewhat unrealistic, but particularly convenient, conditions generated by a zonally symmetric model corresponding to the mean term of the Fourier series. For the first 90 days of the integration the series was truncated at wavenumber 6, but this was increased to 10 for the last 10 days. Although the final results were not entirely realistic because some aspects of the initial conditions still persisted, primarily in the stratosphere, when the experiment was prematurely terminated, many features of the real atmosphere were reproduced. In particular the initial single Hadley cell was transformed into the conventional 3-cell structure of the troposphere, a subtropical jet stream evolved, and fairly realistic synoptic disturbances were obtained. However further integration with higher wavenumbers is needed to fully assess the potential of this approach. Compared to conventional grid-point models, the principal advantage of the semi-spectral model is the improved accuracy of the differentiations in the zonal direction. In addition no problems were encountered in the polar regions of the model. This model is easy to understand and to use and is also particularly flexible, being readily convertible into hemispheric or channel models.