The Optimal Balance in a Low-Order Atmospheric Model

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  • 1 Division of Meteorology, Department of Geography, University of Alberta, Edmonton, Alberta, Canada
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Abstract

The Baer-Tribbia scheme leads to a divergent series in locating the slow manifold of Lorenz's model. The optimal asymptotic approximation is used to “sum” the divergent series. The method gives reasonable approximations to the full solutions of the model and provides the optimal balance relations. The “imbalance,” which is the difference between the actual flow and the optimal balance state, is found to consist of nearly monochromatic inertial-gravity waves. However, the optimal asymptotic approximation fails to give a reasonable estimate of the level of inertial-gravity wave activity from the Rossby modes. The reason may be that the numerical experiments are undertaken at moderate Rossby numbers, whereas the notion of an optimal expansion strictly applies only in the limit of the small Rossby number.

Abstract

The Baer-Tribbia scheme leads to a divergent series in locating the slow manifold of Lorenz's model. The optimal asymptotic approximation is used to “sum” the divergent series. The method gives reasonable approximations to the full solutions of the model and provides the optimal balance relations. The “imbalance,” which is the difference between the actual flow and the optimal balance state, is found to consist of nearly monochromatic inertial-gravity waves. However, the optimal asymptotic approximation fails to give a reasonable estimate of the level of inertial-gravity wave activity from the Rossby modes. The reason may be that the numerical experiments are undertaken at moderate Rossby numbers, whereas the notion of an optimal expansion strictly applies only in the limit of the small Rossby number.

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