Uncertainties of Estimates of Inertia-Gravity Energy in the Atmosphere. Part I: Intercomparison of Four Analysis Systems

This paper presents the application of the normal-mode functions to diagnose the atmospheric energy spectra in terms of balanced and inertia–gravity (IG) contributions. A set of three-dimensional orthogonal normal modes is applied to four analysis datasets from July 2007. The datasets are the operational analysis systems of NCEP and ECMWF, the NCEP–NCAR reanalyses, and the Data Assimilation Research Testbed–Community Atmospheric Model (DART–CAM), an ensemble analysis system developed at NCAR. The differences between the datasets can be considered as a measure of uncertainty of the IG contribution to the global energetics. The results show that the percentage of IG motion in the present NCEP, ECMWF, and DART–CAM analysis systems is between 1% and 2% of the total energy field. In the wave part of the flow (zonal wavenumber k ≠ 0), the IG energy contribution is between 9% and 15%. On the contrary, the NCEP–NCAR reanalyses contain more IG motion, especially in the Southern Hemisphere extratropics. Each analysis contains more energy in the eastward IG motion than in its westward counterpart. The difference is about 2%–3% of the total wave energy and it is associated with the motions projected onto the Kelvin wave in the tropics. The selected truncation parameters of the expansion (zonal, meridional, and vertical truncation) ensure that the projection provides the optimal fit to the input data on model levels. This approach is different from previous applications of the normal modes and under the linearity assumption it allows the application of the inverse projection to obtain details of circulation associated with a selected type of motion. The bulk of the IG motion is confined to the tropics. For the successful reproduction of three-dimensional circulations by the normal modes it is important that the expansion includes a number of vertical modes.