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Observations and theory of convectively coupled equatorial waves suggest that they can be categorized into two distinct groups. Moisture modes are waves whose thermodynamics are governed by moisture fluctuations. The thermodynamics of the gravity wave group, on the other hand, are rooted in buoyancy (temperature) fluctuations. On the basis of scale analysis, it is found that a simple nondimensional parameter—akin to the Rossby number—can explain the processes that lead to the existence of these two groups. This parameter, defined as N mode , indicates that moisture modes arise when anomalous convection lasts sufficiently long so that dry gravity waves eliminate the temperature anomalies in the convective region, satisfying weak temperature gradient (WTG) balance. This process causes moisture anomalies to dominate the distribution of moist enthalpy (or moist static energy), and hence the evolution of the wave. Conversely, convectively coupled gravity waves arise when anomalous convection eliminates the moisture anomalies more rapidly than dry gravity waves can adjust the troposphere toward WTG balance, causing temperature to govern the moist enthalpy distribution and evolution. Spectral analysis of reanalysis data indicates that slowly propagating waves ( c p ~ 3 m s −1 ) are likely to be moisture modes while fast waves ( c p ~ 30 m s −1 ) exhibit gravity wave behavior, with “mixed moisture–gravity” waves existing in between. While these findings are obtained from a highly idealized framework, it is hypothesized that they can be extended to understand simulations of convectively coupled waves in GCMs and the thermodynamics of more complex phenomena. 

A new diagnostic framework is developed and applied to ERA-Interim to quantitatively assess vertical velocity (omega) profiles in the wavenumber–frequency domain. Two quantities are defined with the first two EOF–PC pairs of omega profiles in the tropical ocean: a top-heaviness ratio and a tilt ratio. The top-heaviness and tilt ratios are defined, respectively, as the cospectrum and quadrature spectrum of PC1 and PC2 divided by the power spectrum of PC1. They represent how top-heavy an omega profile is at the convective maximum, and how much tilt omega profiles contain in the spatiotemporal evolution of a wave. The top-heaviness ratio reveals that omega profiles become more top-heavy as the time scale (spatial scale) becomes longer (larger). The MJO has the most top-heavy profile while the eastward inertio-gravity (EIG) and westward inertio-gravity (WIG) waves have the most bottom-heavy profiles. The tilt ratio reveals that the Kelvin, WIG, EIG, and mixed Rossby–gravity (MRG) waves, categorized as convectively coupled gravity waves, have significant tilt in the omega profiles, while the equatorial Rossby (ER) wave and MJO, categorized as slow-moving moisture modes, have less tilt. The gross moist stability (GMS), cloud–radiation feedback, and effective GMS were also computed for each wave. The MJO with the most top-heavy omega profile exhibits high GMS, but has negative effective GMS due to strong cloud–radiation feedbacks. Similarly, the ER wave also exhibits negative effective GMS with a top-heavy omega profile. These results may indicate that top-heavy omega profiles build up more moist static energy via strong cloud–radiation feedbacks, and as a result, are more preferable for the moisture mode instability.