Vertical Normal Mode Transforms: Theory and Application

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Abstract
The separation of the vertical structure of the, solutions of the primitive (hydrostatic) meteorological equations is formalized as a vertical normal-mode transform. The transform is implemented for arbitrary static stability profiles by the Rayleigh-Ritz method, which is based on a variational formulation closely connected with energetics. With polynomial basis functions the order of accuracy is exponential. When vertical transforms of observed fields are computed, energy may be aliased onto the wrong vertical modes; this aliasing may be reduced substantially by a careful choice of sampling levels. The spectral distributions of observed tropical forcings of the wind and mass fields are presented.

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