Variational Analysis and the Slow Manifold

Norman A. Phillips NOAA, National Meteorological Center, Washington, DC 20233

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Simon W. Chang Naval Research Laboratory, Washington, D.C.

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Abstract

The principles of variational analysis are reviewed in a symbolic manner, with emphasis on the error introduced by a failure to use an exact constraint. A technique to approximate a nonlinear exact constraint is suggested, with the object of avoiding error magnification in regions of good data, in the process of analyzing slow mode amplitudes for nonlinear mode initialization. The technique amounts to subtractingall fast modes from the data fields that form the input to the variational analysis. The analysis procedure is then focused on only the analysis of slow mode fields. These general considerations are demonstrated by computations with the vortex model of Tribbia, and show how nonlinear mode techniques can improve initial analyses in a more significant way than the mere elimination of noise. A review of the relative merits and weaknesses of optimum interpolation and variational analysis suggests a logical way to use both techniques in an operational analysis system.

Abstract

The principles of variational analysis are reviewed in a symbolic manner, with emphasis on the error introduced by a failure to use an exact constraint. A technique to approximate a nonlinear exact constraint is suggested, with the object of avoiding error magnification in regions of good data, in the process of analyzing slow mode amplitudes for nonlinear mode initialization. The technique amounts to subtractingall fast modes from the data fields that form the input to the variational analysis. The analysis procedure is then focused on only the analysis of slow mode fields. These general considerations are demonstrated by computations with the vortex model of Tribbia, and show how nonlinear mode techniques can improve initial analyses in a more significant way than the mere elimination of noise. A review of the relative merits and weaknesses of optimum interpolation and variational analysis suggests a logical way to use both techniques in an operational analysis system.

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