José M. Castanheira

Equatorial Kelvin waves (KWs) are associated with a variety of equatorial atmospheric phenomena, namely, tropical convection, cloud and precipitation variability, tropical cyclogenesis, the onset of monsoon season over Africa and India, and even the quasi‐biennial oscillation and the Madden–Julian oscillation. As such, if operational forecasts are to improve near the Tropics, it is important that they correctly represent KWs. This article aims at developing a novel methodology for identifying KWs in real‐time operational forecasts at specific longitudes using only the meridional structures of the solutions to the free Laplace tidal equations, known as Hough vector functions. The main advantages of this newly proposed methodology are that (a) it can identify KWs at a specific longitude and (b) very low computational cost is needed to apply it to real‐time operational forecasts. The application of the method to 2015–2017 European Centre for Medium‐range Weather Forecasts (ECMWF) analysis and operational forecast data reveals a systematic bias in the representation of KWs by the ECMWF operational forecast model.

Equatorial waves are essential features of the tropical atmosphere dynamics, and their diagnosis is relevant for both operational and climate analysis. Here, we present a method for the identification of equatorial waves using the multivariate spatial structures of the eigensolutions of the linearized shallow‐water equations over the sphere, named Hough function vectors. The method does not require any a priori space–time filtering to separate westward‐ and eastward‐moving waves, and it can be applied to instantaneous or daily circulation fields. The wave types (Kelvin, Rossby, mixed Rossby–gravity, inertio‐gravity) are unambiguously identified by the intrinsic dynamical relationship between the horizontal wind components and geopotential fields represented in the multivariate meridional structures of the Hough function vectors. Both free and convectively coupled equatorial waves can be diagnosed. Moreover, different time filterings can be applied a posteriori, depending on the purposes of the analysis. This article is written as a proof of concept, and direct comparisons are made with results of other methods recently reviewed in a work published in this journal.