On wavelet techniques in atmospheric sciences

Wavelet analysis has been formalized extensively due to the efforts of mathematicians, physicists and engineers in the last two decades. It has generated a tremendous interest in these communities both in theoretical and applied areas, in such a way that wavelet analysis is also considered now as a nucleus of shared aspirations and ideas. Initially applied to seismic signal studies in geophysics in the 1980s, wavelet techniques have been explored in the atmospheric sciences since the pioneer applications in turbulence studies. If one decides to apply the wavelet analysis to a given signal, it is worthwhile to assess the actual need of the technique itself and the best way to perform it. In atmospheric signal applications, two main directions have been followed: the singularity and the variance analysis. In this paper, the potential uses of this tool supported by some recently published works in the field of atmospheric sciences are discussed. Therefore, initially the characteristics and main properties of the wavelet analysis are presented, focusing on those that are mostly used in the analysis of atmospheric signals. Continuous and discrete wavelet transforms are also discussed, as well as the scalograms and the variance analysis. Finally, some examples of wavelet analysis applied to a wide range of atmospheric science phenomena are presented.