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THE PREDICTION OF GENERAL QUASI-GEOSTROPHIC MOTIONS

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  • 1 Institute for Advanced Study
  • | 2 U. S. Weather Bureau
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Abstract

Methods are presented for the numerical integration of several rather general approximations to the quasi-geostrophic equations of motion. The choice of the vertical grid interval involved in these approximations is justified by scale considerations. Three of the approximations involve the integration of non-linear partial differential equations of elliptic type, and the method of solution used is described in some detail because of its quite general applicability.

The results of the integrations for each version are presented and compared with those obtained earlier from simple versions. The principle conclusion is that the prediction error is not eliminated by a more refined treatment of the quasi-geostrophic equations, but is at least partly inherent in the geostrophic formulation itself. The retention of terms that are neglected in the first-order geostrophic approximation changes the aspect of the error but does not eliminate it.

Abstract

Methods are presented for the numerical integration of several rather general approximations to the quasi-geostrophic equations of motion. The choice of the vertical grid interval involved in these approximations is justified by scale considerations. Three of the approximations involve the integration of non-linear partial differential equations of elliptic type, and the method of solution used is described in some detail because of its quite general applicability.

The results of the integrations for each version are presented and compared with those obtained earlier from simple versions. The principle conclusion is that the prediction error is not eliminated by a more refined treatment of the quasi-geostrophic equations, but is at least partly inherent in the geostrophic formulation itself. The retention of terms that are neglected in the first-order geostrophic approximation changes the aspect of the error but does not eliminate it.

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