01 Dec 2023
 | 01 Dec 2023
Status: this preprint is currently under review for the journal AMT.

Limitations in Wavelet Analysis of Non-Stationary Atmospheric Gravity Wave Signatures in Temperature Profiles

Robert Reichert, Natalie Kaifler, and Bernd Kaifler

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 and is used in a variety of research areas. In this work we use the CWT to investigate signatures of atmospheric internal gravity waves (GW) 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 shears of up to 5 ms−1 km−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 4th order Morlet wavelet, edge effects become dominant at a vertical wind shear of 3.4 ms−1 km−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 case of conservative amplitude growth, spectral leakage leads to artificially enhanced spectral power at lower altitudes. Therefore, we recommend to normalize the GW signal before the wavelet analysis and the determination of vertical wavelengths. Finally, the cascading of receiver channels which is typical for middle atmosphere lidar measurements results in an exponential saw-tooth-like pattern of measurement uncertainties as function of altitude. With the help of Monte Carlo simulations we compute a wavelet noise spectrum and determine significance levels, which enables the reliable determination of vertical wavelengths. Finally, the insights obtained from the analysis of artificial chirps are used to analyse and interpret real GW measurements from the Compact Rayleigh Autonomous Lidar in April 2018 at Río Grande, Argentina. The comparison of results of commonly used and our suggested wavelet analysis demonstrates improvements in the accuracy of determined wavelengths. For future analyses, we suggest the usage of a 4th order Morlet wavelet, the normalization of GW amplitudes before wavelet analysis, and the significance level computation based on measurement uncertainties.

Robert Reichert, Natalie Kaifler, and Bernd Kaifler

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on amt-2023-240', Anonymous Referee #1, 31 Jan 2024
    • AC1: 'Reply on RC1', Robert Reichert, 01 Feb 2024
  • RC2: 'Comment on amt-2023-240', Anonymous Referee #2, 28 Mar 2024
Robert Reichert, Natalie Kaifler, and Bernd Kaifler
Robert Reichert, Natalie Kaifler, and Bernd Kaifler


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Short summary
Imagine you want to determine how quickly the pitch of a passing ambulance’s siren changes. If the car is traveling slowly, the pitch changes only slightly, but if it is traveling fast, the pitch also changes rapidly. In a similar way, the wind in the middle atmosphere modulates the wavelength of atmospheric gravity waves. We have investigated the question of how strong the wind may be at maximum so that the change in wavelength can still be determined with the help the wavelet transformation.