Limitations in wavelet analysis of non-stationary atmospheric gravity wave signatures in temperature profiles

Abstract. Continuous wavelet transform (CWT) is a commonly used mathematical tool when it comes to the time–frequency (or distance–wavenumber) analysis of non-stationary signals that is used in a variety of research areas. In this work, we use the CWT to investigate signatures of atmospheric internal gravity waves (GWs) as observed in vertical temperature profiles obtained, for instance, by lidar. The focus is laid on the determination of vertical wavelengths of dominant GWs. According to linear GW theory, these wavelengths are a function of horizontal wind speed, and hence, vertical wind shear causes shifts in the evolution of the vertical wavelength. The resulting signal fulfills the criteria of a chirp. Using complex Morlet wavelets, we apply CWT to test mountain wave signals modeling wind shear of up to 5m s-1km-1 and investigate the capabilities and limitations. We find that the sensitivity of the CWT decreases for large chirp rates, i.e., strong wind shear. For a fourth-order Morlet wavelet, edge effects become dominant at a vertical wind shear of 3.4m s-1km-1. For higher-order wavelets, edge effects dominate at even smaller values. In addition, we investigate the effect of GW amplitudes growing exponentially with altitude on the determination of vertical wavelengths. It becomes evident that in the case of conservative amplitude growth, spectral leakage leads to artificially enhanced spectral power at lower altitudes. Therefore, we recommend normalizing the GW signal before the wavelet analysis and before the determination of vertical wavelengths. Finally, the cascading of receiver channels, which is typical of middle-atmosphere lidar measurements, results in an exponential sawtooth-like pattern of measurement uncertainties as a function of altitude. With the help of Monte Carlo simulations, we compute a wavelet noise spectrum and determine significance levels, which enable the reliable determination of vertical wavelengths. Finally, the insights obtained from the analysis of artificial chirps are used to analyze and interpret real GW measurements from the Compact Rayleigh Autonomous Lidar in April 2018 in Río Grande, Argentina. Comparison of commonly used analyses and our suggested wavelet analysis demonstrate improvements in the accuracy of determined wavelengths. For future analyses, we suggest the usage of a fourth-order Morlet wavelet, normalization of GW amplitudes before wavelet analysis, and computation of the significance level based on measurement uncertainties.