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FREDERICK G. SHUMAN

Abstract

Two methods of solving the balance equation are outlined. Both methods have been used successfully on a daily operational basis at the Joint Numerical Weather Prediction Unit for a period of more than a year. Solutions were on the operational grid of 30 × 34 points spaced at 381-km. intervals.

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FREDERICK G. SHUMAN

Abstract

A method is developed for the design of finite-difference smoothing and filtering operators which meet pre-determined specifications, and which are applicable to automatic computing machinery. The general technique is to build complicated operators from the simplest types. The necessity for smoothing predicted fields of stream functions before inverting the balance equation for heights of isobaric surfaces is brought out.

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FREDERICK G. SHUMAN

Abstract

The physical inconsistency of geostrophic flow and small surface pressure tendencies is discussed. The frequently disastrous consequences in conventional geostrophic barotropic predictions are numerically identified by comparisons with experimental “semi-geostrophic” barotropic predictions from which the inconsistency has been removed. Effects of the inconsistency of the geostrophic wind field with the equations of motion are also quantitatively isolated by comparisons of semi-geostrophic predictions with predictions made with wind fields which satisfy the balance equation. It is concluded that the principal fault of the conventional geostrophic approximation lies in the violation of the continuity equation. Its lack of the dynamic effects expressed in the equations of motion seems also significant, but is less important.

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FREDERICK G. SHUMAN and LLOYD W. VANDERMAN

Abstract

A primitive-equation free-surface barotropic model was designed for the tropical belt. By the use of Shuman's difference system, experiments were made to test the effect of both approximate and correct boundary conditions on the forecast fields. Results are shown in the figures. With the correct boundary conditions a successful forecast was calculated without smoothing to 100 days.

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FREDERICK G. SHUMAN and JOHN D. STACKPOLE

Abstract

Numerical experimentation with various finite difference formulations of a particular set of differential equations incorporating a map scale factor indicates that the stability of the calculations is as dependent upon the manner in which the map factor is introduced as the form in which the dynamic terms of the equations are written.

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ANDRÉ J. ROBERT, FREDERICK G. SHUMAN, and JOSEPH P. GERRITY JR.

Abstract

A rather general theory of nonlinear computational stability is reported. Instability is caused by both spatial and temporal high frequencies that, if not present initially, will appear from nonlinear interactions. It appears that through simple remedies relative stability, if not perfect stability, can be achieved.

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