Applying wavelet transforms to analyse aircraft‐measured turbulence and turbulent fluxes in the atmospheric boundary layer over eastern Siberia

The wavelet spectral method was applied to aircraft‐based measurements of atmospheric turbulence obtained during joint Russian–Japanese research on the atmospheric boundary layer near Yakutsk (eastern Siberia) in April–June 2000. Practical ways to apply Fourier and wavelet methods for aircraft‐based turbulence data are described. Comparisons between Fourier and wavelet transform results are shown and they demonstrate, in conjunction with theoretical and experimental restrictions, that the Fourier transform method is not useful for studying non‐homogeneous turbulence. The wavelet method is free from many disadvantages of Fourier analysis and can yield more informative results. Comparison of Fourier and Morlet wavelet spectra showed good agreement at high frequencies (small scales). The quality of the wavelet transform and corresponding software was estimated by comparing the original data with restored data constructed with an inverse wavelet transform. A Haar wavelet basis was inappropriate for the turbulence data; the ‘mother’ wavelet function recommended in this study is the Morlet wavelet. Good agreement was also shown between variances and covariances estimated with different mathematical techniques, i.e. through non‐orthogonal wavelet spectra and through eddy correlation methods.