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The wavenumber filtering of the Kelvin waves (KWs) is performed by a multivariate projection of the ERA5 data on the horizontal structures of the KWs from linear theory and vertical structure functions (VSFs) spanning the troposphere and stratosphere. The associated equivalent depths are consistent with solutions expected for the bounded atmosphere. The zonal wavenumber spectra of the KW energy and temporal variance are shown to be continuous and red with the rotational kinetic energy being dominant over the divergent kinetic energy at zonal wavenumber  k  = 1. Spatial and temporal variance in wavenumber space is analyzed in terms of periods from linear theory. The strongest variability is found in periods of 8–12 days at  k  = 1 and VSFs with a single zero-crossing in the troposphere and a structure resembling upward propagating waves across the tropopause and higher up. Secondary maxima are associated with VSFs that have multiple zero crossings in the troposphere and small equivalent depths. A comparison of the wavenumber and wavenumber–frequency methods shows a disagreement between frequencies from the Fourier time series and linear theory. A phase-locking experiment, in which the KW phases are replaced by linear theory estimates, demonstrates that power spectra from wavenumber–frequency filtering in the troposphere are largely defined by wave phases.

Three-Dimensional Structure of the Equatorial Kelvin Wave: Vertical Structure Functions, Equivalent Depths, and Frequency and Wavenumber Spectra