Comparative numerical integration of simple atmospheric models on a spherical grid

Abstract

The non-divergent barotropic model, the two-layer quasi-geostrophic baroclinic model, and the two-layer balanced baroclinic model of variable static stability are integrated in parallel on a spherical grid with comparable boundary and initial conditions for the case of 00 GCT,3 7 December 1957. The integrations of the barotropic and quasigeostrophic models show the expected accuracy decay to 72 hr, characterized by excessive momentum transport into the jet and an overall failure to predict significant baroclinic development. The balanced model displays an initially similar behavior, although the vertical motions are about twice those of the quasi-geostrophic case. Beyond 12 hr the balanced model's vertical motions become excessively cellular and of increased magnitude, and a progressively serious distortion of the solutions takes place by 24 hr. The energy transformations of the variable-stability model indicate a disturbance evolution significantly different from that of the quasi-geostrophic model, although beyond 12 hr these transformations are themselves seriously influenced by the computed vertical motions. A number of recommendations for further tests are made, of which the improvement of the finite-difference schemes is probably the most important.DOI: 10.1111/j.2153-3490.1963.tb01404.x