22 Dec 2022
 | 22 Dec 2022

A two-step method to derive combined Fourier-wavelet spectra from space-time data for studying planetary-scale waves, and its Matlab and Python software (cfw v1.0)

Yosuke Yamazaki

Abstract. The combined Fourier-wavelet (CFW) transform is a useful technique to characterize planetary-scale waves, such as tides and traveling planetary waves in the Earth's atmosphere. A CFW spectrum, presented in a time versus period diagram, can be used to identify wave activity that is localized in time, similar to a wavelet spectrum. A CFW spectrum can be obtained for each of eastward- and westward-propagating wave components with different zonal wavenumbers. This paper introduces an easy-to-implement method to derive CFW spectra in two steps. In the first step, the Fourier transform is performed in space (longitude), and time series of the space Fourier coefficients are derived. In the second step, the wavelet transform is performed on these time series, and wavelet coefficients are derived. It is shown that the CFW transform can be easily derived from these wavelet coefficients. The results suggest that existing Fourier and wavelet software can be utilized to derive CFW spectra. Matlab and Python scripts are created and made available at that compute CFW spectra using the wavelet software provided by Torrence and Compo (1998). Some application examples are presented using longitude-time data from atmospheric and geomagnetic-field models.

Yosuke Yamazaki

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2022-1275', Jun-Ichi Yano, 30 Dec 2022
  • RC2: 'Comment on egusphere-2022-1275', Anonymous Referee #2, 15 May 2023

Yosuke Yamazaki

Model code and software

CFW Software for Matlab and Python Yosuke Yamazaki

Matlab and Python software for computing combined Fourier-wavelet spectra: cfw v1.0 Yosuke Yamazaki

Yosuke Yamazaki


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Short summary
The Earth's atmosphere can support various types of planetary-scale waves. Some waves propagate eastward and others westward, and they can have different zonal wavenumbers. The combined Fourier-wavelet (CFW) analysis is a useful technique for identifying different components of planetary-scale waves and their temporal variability. This paper introduces an easy-to-implement method to derive CFW spectra from 2-D space-time data. Application examples are presented using atmospheric models.