Spatiotemporal Wavelet Transform and the Multiscale Behavior of the Madden–Julian Oscillation*

Abstract

Abstract Meteorological and geophysical phenomena involve multiple-scale processes. Here the spatiotemporal wavelet transform (STWT) is applied to detect significant, nonstationary, wave propagation signals from a time–space domain. One of the major advantages of the STWT is the capability to localize the wave properties in both space and time, which facilitates the study of interactions among multiple-scale disturbances by providing relevant information about energy concentration at a given time and space. The global wavelet spectrum (scalogram) of the STWT, which gives an integrated view of the spectrum as wavenumber and frequency, provides a lucid picture of the spectral power distribution that is consistent with the result obtained from the Fourier-based space–time power spectrum. The STWT has also the capability of reconstruction and thus can be used as a spatiotemporal wave filter. The STWT analysis is applied to analyze the multiscale structure of the Madden–Julian oscillation (MJO) studied by Nakazawa. All types of convectively coupled equatorial waves were identified. The analysis results reveal the structural differences between the MJO and Kelvin waves and their different relationships with the embedded westward propagating inertio-gravity (WIG) waves: for the Kelvin wave the enhanced activity of the WIG waves coincides with the most active convective area, whereas for the MJO the enhanced WIG waves occur to the east of the MJO convective center. In addition, the WIG waves in the MJO have shorter wavelengths and periods, but those in the Kelvin waves have longer wavelengths and periods. This difference may hold a key to understanding the propagation speed difference between the MJO and Kelvin waves. The possible “upscale feedback” of the WIG waves on the MJO and Kelvin waves is also discussed.