Spectral Representation of Three-Dimensional Global Data by Expansion in Normal Mode Functions

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  • 1 National Center for Atmospheric Research,2 Boulder, CO 80307
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Abstract

To represent atmospheric data spectrally in three indices (zonal wavenumber, and meridional and vertical modal indices), we propose to use three-dimensional normal mode functions (NMF's) to express the wind and mass fields simultaneously. The NMF's are constructed from the eigensolutions of a global primitive equation model and they are orthogonal functions. The vertical parts are obtained from the solutions of the vertical structure equation with the equivalent height as the eigenvalue. The vertical modal index is associated with a different value of the equivalent height. The horizontal parts of NMF's are Hough harmonics with zonal wavenumber and meridional modal index as two-dimensional scalings. The expansion of global data in terms of NMF's permits the partition of energy into two distinct kinds of motions-gravity-inertia modes and rotational modes of Rossby/Haurwitz type. Both kinds of motion are also partitioned into different vertical modes. Results of the spectral distribution of atmospheric energy, obtained by expanding in the NMF's hemispherical data of the National Meteorological Center, are presented. Information obtained will be useful to select proper horizontal and vertical computational resolutions for representation of atmospheric data.

Abstract

To represent atmospheric data spectrally in three indices (zonal wavenumber, and meridional and vertical modal indices), we propose to use three-dimensional normal mode functions (NMF's) to express the wind and mass fields simultaneously. The NMF's are constructed from the eigensolutions of a global primitive equation model and they are orthogonal functions. The vertical parts are obtained from the solutions of the vertical structure equation with the equivalent height as the eigenvalue. The vertical modal index is associated with a different value of the equivalent height. The horizontal parts of NMF's are Hough harmonics with zonal wavenumber and meridional modal index as two-dimensional scalings. The expansion of global data in terms of NMF's permits the partition of energy into two distinct kinds of motions-gravity-inertia modes and rotational modes of Rossby/Haurwitz type. Both kinds of motion are also partitioned into different vertical modes. Results of the spectral distribution of atmospheric energy, obtained by expanding in the NMF's hemispherical data of the National Meteorological Center, are presented. Information obtained will be useful to select proper horizontal and vertical computational resolutions for representation of atmospheric data.

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