The intricacies of identifying equatorial waves

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 β$$ \beta $$‐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. Equatorial waves dominate synoptic‐ to planetary‐scale variability in the Tropics from the daily to the subseasonal time‐scale. This paper is the first to systematically compare the most widely used methods that have been developed to isolate equatorial waves from satellite or model data. The graphic displays the dispersion relation of the linear wave solutions of the rotating shallow‐