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A new methodology for the diagnosis of convectively coupled equatorial waves (CCEWs) is presented. It is based on a pre-filtering of the geopotential and horizontal wind, using three-dimensional (3D) normal mode functions of the adiabatic linearized equations of a resting atmosphere, followed by a space-time spectral analysis to identify the spectral regions of coherence.The methodology permits a direct detection of various types of equatorial wave, compares the dispersion characteristics of the coupled waves with the theoretical dispersion curves and allows an identification of which vertical modes are more involved in the convection. Moreover, the proposed methodology is able to show the existence of free dry waves and moist coupled waves with a common vertical structure, which is in conformity with the effect of convective heating/cooling on the effective static stability, as deduced from the gross moist stability concept. The methodology is also sensitive to wave interactions.The methodology has been applied to the ERA-Interim horizontal wind and geopotential height fields and to the interpolated outgoing long-wave radiation (OLR) data produced by the National Oceanic and Atmospheric Administration. The results obtained provide examples of the aforementioned effects.

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An energetics formulation is here introduced that enables an explicit evaluation for the conversion rates between available potential energy and kinetic energy, the nonlinear interactions of both energy forms, and their generation and dissipation rates, in both the zonal wavenumber and vertical mode domains. The conversion rates between available potential energy and kinetic energy are further decomposed into the contributions by the rotational (Rossby) and divergent (gravity) components of the circulation field. The computed energy terms allow one to formulate a detailed energy cycle describing the flow of energy among the zonal mean and eddy components, and also among the barotropic and baroclinic components. This new energetics formulation is a development of the 3D normal-mode energetics scheme. The new formulation is applied on an assessment of the energetics of winter (December-February) circulation in the 40-yr ECMWF Re-Analysis (ERA-40), the 25-yr Japan Meteorological Agency Reanalysis (JRA-25), and the NCEP-Department of Energy Reanalysis 2 (NCEP-R2) datasets.