A method to derive Fourier–wavelet spectra for the characterization of global-scale waves in the mesosphere and lower thermosphere and its MATLAB and Python software (fourierwavelet v1.1)

Abstract

Abstract. This paper describes a simple method for characterizing global-scale waves in the mesosphere and lower thermosphere (MLT), such as tides and traveling planetary waves, using uniformly gridded two-dimensional longitude–time data. The technique involves two steps. In the first step, the Fourier transform is performed in space (longitude), and then the 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. A Fourier–wavelet spectrum can be obtained from these wavelet coefficients, which gives the amplitude and phase of the wave as a function of time and wave period. It can be used to identify wave activity that is localized in time, similar to a wavelet spectrum, but the Fourier–wavelet spectrum can be obtained separately for eastward- and westward-propagating components and for different zonal wavenumbers. The Fourier–wavelet analysis can be easily implemented using existing Fourier and wavelet software. MATLAB and Python scripts are created and made available at https://igit.iap-kborn.de/yamazaki/fourierwavelet (last access: 18 August 2023) that compute Fourier–wavelet spectra using the wavelet software provided by Torrence and Compo (1998). Some application examples are presented using MLT data from atmospheric models.