Uncertainties of estimates of inertia-gravity energy in the atmosphere. Part II: Large-scale equatorial waves

This paper analyzes the spectra and spatiotemporal features of the large-scale inertia-gravity (IG) circulations in four analysis systems in the tropics. Of special interest is the Kelvin wave (KW), which represents between 7% and 25% of the total IG wave (zonal wavenumber k≠0) energy. The mixed Rossby-gravity (MRG) mode comprises between 4% and 15% of the IG wave energy. At the longest scales, the KW spectra are fitted by a 2⁵/3 law while the MRG energy spectrum appears flat. At shorter scales both modes follow a 23 law. Energy spectra of the total IG wave motion at long zonal scales (zonal wavenumber smaller than 7) have slopes close to 21. The average circulation associated with KW is characterized by reverse flows in the upper and lower troposphere consistent with the ideas behind simple tropical models. The inverse projection is used to quantify the role of Kelvin and MRG waves in current analysis systems in the upper troposphere over the Indian Ocean. At these levels, easterlies between 10°S and 30°N are represented by the KW to a significant degree while the cross-equatorial flow toward the descending branch of the Hadley cell at 10°S is associated with the MRG waves. The transient structure of equatorial waves is presented in the space of normal modes defined by the zonal wavenumbers, meridional Hough functions, and the vertical eigenfunctions. The difference in the depth of the model domain in DART-CAM and NCEP-NCAR on one hand and ECMWF and NCEP on the other appears to be one reason for different wave propagation properties. In the latter case the vertical energy propagation is diagnosed by filtering the propagating KW modes back to physical space. The results agree with the linear theory of vertically propagating equatorial waves.