Application of wavelet transformation to determine wavelengths and phase velocities of gravity waves observed by lidar measurements

During the last two decades, important advances have been made in the investigation of gravity waves. However, more efforts are needed to study certain aspects of gravity waves. In the real atmosphere, gravity waves occur with different properties at different altitudes and, most often, simultaneously. In this case, when there is more than one dominant wave, the determination of gravity wave characteristics, such as the vertical wavelength and the phase velocity, is difficult. The interpretation of temperature perturbation plots versus the altitude and time as well as the application of the Fourier spectral analysis can produce errors.Exact knowledge of the wave characteristics is important both for determination of other characteristics, for example, the horizontal wave components, and for study of wave climatology. The wavelet analysis of vertical temperature profiles allows one to examine the wave's location in space. Up to now, gravity waves have been studied mainly by continuous wavelet transformation to determine dominant waves. We apply wavelet analysis to a time series of temperature profiles, observed by the ALOMAR ozone lidar at Andoya, Norway, and by the U. Bonn lidar system at ESRANGE, Sweden, both for determination of the dominant waves and for specifying the vertical wavelengths and the vertical component of the phase velocities. For this purpose, the wavelet amplitude spectra and the wavelet phase spectra are filtered and Hovmöller diagrams for dominant wavelengths are constructed. The advantage of this type of diagrams is that they give clear evidence for the localization of the dominant waves in space and time and for the development of their phase fronts.