The view that convectively coupled Kelvin waves and the Madden–Julian oscillation (MJO) are distinct modes is tested by regressing data from the Climate Forecast System Reanalysis against satellite outgoing longwave radiation data filtered for particular zonal wavenumbers and frequencies by wavelet analysis. Results confirm that nearly dry Kelvin waves have horizontal structures consistent with their equatorial beta-plane shallow-water-theory counterparts, with westerly winds collocated with the lower-tropospheric ridge, while the MJO and signals along Kelvin wave dispersion curves at low shallow-water-model equivalent depths are characterized by geopotential troughs extending westward from the region of lower-tropospheric easterly wind anomalies through the region of lower-tropospheric westerly winds collocated with deep convection. Results show that as equivalent depth decreases from that of the dry waves (concomitant with intensification of the associated convection), the ridge in the westerlies and the trough in the easterlies shift westward. The analysis therefore demonstrates a continuous field of intermediate structures between the two extremes, suggesting that Kelvin waves and the MJO are not dynamically distinct modes. Instead, signals consistent with Kelvin waves become more consistent with the MJO as the associated convection intensifies. This result depends little on zonal scale. Further analysis also shows how activity in synoptic-scale Kelvin waves characterized by particular phase speeds evolves with the planetary-scale MJO.

Equatorial waves (EWs) are synoptic‐ to planetary‐scale propagating disturbances at low latitudes with periods from a few days to several weeks. Here, this term includes Kelvin waves, equatorial Rossby waves, mixed Rossby–gravity waves, and inertio‐gravity waves, which are well described by linear wave theory, but it also other tropical disturbances such as easterly waves and the intraseasonal Madden–Julian Oscillation with more complex dynamics. EWs can couple with deep convection, leading to a substantial modulation of clouds and rainfall. EWs are amongst the dynamic features of the troposphere with the longest intrinsic predictability, and models are beginning to forecast them with an exploitable level of skill. Most of the methods developed to identify and objectively isolate EWs in observations and model fields rely on (or at least refer to) the adiabatic, frictionless linearized primitive equations on the sphere or the shallow‐water system on the equatorial ‐plane. Common ingredients to these methods are zonal wave‐number–frequency filtering (Fourier or wavelet) and/or projections onto predefined empirical or theoretical dynamical patterns. This paper gives an overview of six different methods to isolate EWs and their structures, discusses the underlying assumptions, evaluates the applicability to different problems, and provides a systematic comparison based on a case study (February 20–May 20, 2009) and a climatological analysis (2001–2018). In addition, the influence of different input fields (e.g., winds, geopotential, outgoing long‐wave radiation, rainfall) is investigated. Based on the results, we generally recommend employing a combination of wave‐number–frequency filtering and spatial‐projection methods (and of different input fields) to check for robustness of the identified signal. In cases of disagreement, one needs to carefully investigate which assumptions made for the individual methods are most probably not fulfilled. This will help in choosing an approach optimally suited to a given problem at hand and avoid misinterpretation of the results.

Wave‐number‐frequency power spectrum analysis has been used as a primary tool to detect the ranges of wave numbers and frequencies about which observed convectively coupled equatorial waves are active. Previous works have suggested that activity in these waves clusters between roughly 12 and 60 m equivalent depths because spectral peaks normalized by dividing by a smoothed spectral background follow those ranges. Through a combination of wave‐number‐frequency power spectrum analysis, filtering and linear regression, this work shows that the traditional approach generates confusion because it conflates different, sometimes conflicting, signals from around the world that contribute to the same parts of the spectrum. Results also suggest that the traditional method leads us to ignore substantial power associated with variability structurally consistent with observed Kelvin waves but that occurs at lower frequencies. Wave signals at these frequencies are stronger than but similar to Kelvin wave signals coincident with the Kelvin peak in the normalized spectrum. Results suggest that the wave signal itself has red properties, possibly because more strongly convectively coupled waves propagate more slowly. The slower, more intense wave signals outside of the standard band would impact tangible weather signals and should not be ignored in operations. Instead, results support the view that disturbances labelled as Kelvin waves form a continuum with the Madden–Julian Oscillation (MJO) and suggest that the whole region of the spectrum from the broadly recognized Kelvin band to the MJO should be considered together.

This study corrects the hypsometric equation by restoring the nontraditional terms to relax the hydrostatic approximation. The nontraditional terms include one Coriolis term and two metric terms in the vertical momentum equation. The hypsometric equations with and without the nontraditional correction are used to calculate the geopotential height of pressure levels using more than 300,000 selected tropical rawinsonde profiles. With westerlies between two pressure levels, the thickness of the layer increases, which reduces the upward pressure gradient forces to balance the upward nontraditional Coriolis forces; the opposite is true for easterlies. Hence, zonal winds are negatively correlated with traditional geopotential height biases aloft. At 500 hPa, for example, traditional geopotential height error in the tropical troposphere is on the order of at least 0.5 m, which is considerable with respect to geopotential height variability in tropical large‐scale flow, on the order of 10 to 15 m.