Scaling characteristics in ozone concentration time series (OCTS)

Abstract

One-year series of hourly average ozone observations, which were obtained from urban and national park air monitoring stations at Taipei (Taiwan), were analyzed by means of descriptive statistics and fractal methods to examine the scaling structures of ozone concentrations. It was found that all ozone measurements exhibited the characteristic right-skewed frequency distribution, cyclic pattern, and long-term memory. A mono-fractal analysis was performed by transferring the ozone concentration time series (OCTS) into a useful compact form, namely, the box-dimension ( D B)–threshold ( T h) and critical scale ( C S)–threshold ( T h) plots. Scale invariance was found in these time series and the box dimension was shown to be a decreasing function of the threshold ozone level, implying the existence of multifractal characteristics. To test this hypothesis, the OCTS were transferred into the multifractal spectra, namely, the τ( q)– q plots. The analysis confirmed the existence of multifractal characteristics in the investigated OCTS. A simple two-scale Cantor set with unequal scales and weights was then used to fit the calculated τ( q)– q plots. This model fitted remarkably well the entire spectrum of scaling exponents for the examined OCTS. Because the existence of chaos behavior in OCTS has been reported in the literature, the possibility of a chaotic multifractal approach for OCTS characterization was discussed.