Climate Dynamics

, Volume 43, Issue 5–6, pp 1339–1356 | Cite as

An introduction to combined Fourier–wavelet transform and its application to convectively coupled equatorial waves

  • Kazuyoshi Kikuchi


Convectively coupled equatorial waves (CCEWs) are major sources of tropical day-to-day variability. The majority of CCEWs-related studies for the past decade or so have based their analyses, in one form or another, on the Fourier-based space–time spectral analysis method developed by Wheeler and Kiladis (WK). Like other atmospheric and oceanic phenomena, however, CCEWs exhibit pronounced nonstationarity, which the conventional Fourier-based method has difficulty elucidating. The purpose of this study is to introduce an analysis method that is able to describe the time-varying spectral features of CCEWs. The method is based on a transform, referred to as the combined Fourier–wavelet transform (CFWT), defined as a combination of the Fourier transform in space (longitude) and wavelet transform in time, providing an instantaneous space–time spectrum at any given time. The elaboration made on how to display the CFWT spectrum in a manner analogous to the conventional method (i.e., as a function of zonal wavenumber and frequency) and how to estimate the background noise spectrum renders the method more practically feasible. As a practical example, this study analyzes 3-hourly cloud archive user service (CLAUS) cloudiness data for 23 years. The CFWT and WK methods exhibit a remarkable level of agreement in the distributions of climatological-mean space–time spectra over a wide range of space–time scales ranging in time from several hours to several tens of days, indicating the instantaneous CFWT spectrum provides a reasonable snapshot. The usefulness of the capability to localize space–time spectra in time is demonstrated through examinations of the annual cycle, interannual variability, and a case study.


Convectively coupled equatorial waves Tropical convection Wavelet Annual cycle Interannual variability 



This research was supported by NSF Grant AGS-1005599 and by the Global Research Laboratory (GRL) Program from the Ministry of Education, Science, and Technology (MEST), Korea. Additional support was provided by the JAMSTEC through its sponsorship of research activities at the IPRC. These results were obtained using the CLAUS archive held at the British Atmospheric Data Centre, produced using ISCCP source data distributed by the NASA Langley Data Center. The author acknowledges the use of the 1D WT program provided by C. Torrence and G. Compo, which is available at URL: to develop the CFWT code and of a package provided by CCSM AMWG to compute Fourier-based zonal wavenumber-frequency power spectrum. The Niño3.4 index, based on OISST.v2 product, was obtained from the U.S. Weather Service’s Climate Prediction Center Web site at NOAA_OI_SST_V2 data provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their Web site at The author thanks Dr. Yasunaga for his comments on how to estimate the background power spectrum, Dr. George N. Kiladis for helpful comments on an earlier version of the manuscript, and anonymous reviewers for their suggestions and comments.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.International Pacific Research Center, School of Ocean and Earth Science and TechnologyUniversity of Hawaii at MānoaHonoluluUSA

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