A comparison of four techniques for separating different time scales in atmospheric variables

In this paper, four methods for spectrally decomposing time series of atmospheric variables are compared. Two of these methods have been previously applied to the analysis of time series of atmospheric variables, while the others are being applied for the first time. This paper focuses on the practical applications of time scale separation techniques rather than on an in-depth comparison of the mathematical features of the filtering techniques. The performance of the above filtering methods is illustrated and evaluated using both simulated and observed ozone time series data. The adaptive window Fourier transform filter is shown to extract fluctuations of known frequency as cleanly as the Morlet wavelet and, therefore, is a useful new tool for time–frequency analyses of atmospheric variables. Simulation results indicate that all four of these filters provide qualitatively similar results when used to extract the energy in five frequency bands of particular interest in time series of atmospheric variables. However, differences can exist when different filters are used to study the temporal variations of the extracted components. In addition, it is shown that all filters are able to capture the year-to-year fluctuations in the magnitudes of individual components. Such analysis can be used to discern the time scales that cause long-term changes in pollutant concentrations. As no single filter performs best in separating the various time scales, great care has to be taken to match the filter characteristics with the objectives of a given analysis.