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In this study, the energy spectrum and the energy interactions of the atmospheric general circulation are analyzed, using the expansion in three dimensional normal mode functions for JRA-25 and ERA-40. The analytical solutions of the vertical structure equation are used for the expansion in the vertical direction. The problem of aliasing associated with the numerical solution is avoided by the present approach. According to the result of the energy spectrum, using the analytical vertical structure functions, it is found that the energy spectrum indicates a clear peak in the middle vertical modes, and the spectrum decreases monotonically at the higher order vertical modes. The energy interactions for lower order vertical modes are consistent with that by Tanaka and Kung (1988). It is found from the analysis of the energy interactions that there is another energy source region in the higher order vertical modes in the zonal field. It is also found from the energy flux analysis in the vertical domain that the atmospheric energy is converted from baroclinic component to barotropic component.

An Analysis of the 3-D Atmospheric Energy Spectra and Interactions Using Analytical Vertical Structure Functions and Two Reanalyses