The atmospheric Kelvin wave has been widely studied due to its importance in atmospheric dynamics. Since a long-term climatological study is absent in the literature, we have employed the two-dimensional fast Fourier transform (2D-FFT) method for the 40-year long-term reanalysis of the dataset, ERA-Interim, to investigate the properties of Kelvin waves with wavenumbers 1 (E1) and 2 (E2) at 6–24 days wave periods over the equatorial region of ±10° latitude between a 15 and 45 km altitude during

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... he period 1979–2019. The spatio-temporal variations of the E1 and E2 wave amplitudes were compared to the information of stratospheric quasi-biennial oscillation (QBO), and the wave amplitudes were found to have an inter-QBO cycle variation that was related to sea surface temperature and convections, as well as an intra-QBO cycle variation that was caused by interactions between the waves and stratospheric mean flows. Also, the E1 waves with 6–10 day periods and the E2 waves with 6 days period were observed to penetrate the westerly regime of QBO, which has a thickness less than the vertical wavelengths of those waves, and the waves could further propagate upward to higher altitudes. In a case study of the period 2006–2013, the wave amplitudes showed a good correlation with the Niño 3.4 index, outgoing longwave radiation (OLR), and precipitation during 2006–2013, though this was not the case for the full time series. The present paper is the first report on the 40-year climatology of Kelvin waves, and the morphology of Kelvin waves will help us diagnose the anomalies of wave activity and QBO in the future.