Vertical Velocity Profiles in Convectively Coupled Equatorial Waves and MJO: New Diagnoses of Vertical Velocity Profiles in the Wavenumber-Frequency Domain

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 inertiogravity (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.