Fractal analysis of temporal variation of air pollutant concentration by box counting

The scale-invariant behavior of air pollutant concentration (APC) time structure was investigated by applying the box counting method to APC time series. One-year series of hourly average APC observations, including O₃, CO, SO₂, NO, NO₂, and PM10 which were obtained from urban, traffic, and national park air monitoring station at Taipei (Taiwan), were transferred into a useful compact form through this method, namely, the box-dimension (D_B)-threshold (T_h) and critical scale (C_S)-threshold (T_h) plots. The validity of this approach was supported with the result that the practical implications of D_B-T_h (or C_S-T_h) plots could be interpreted in terms of traditional statistical parameters. Since the dependences of both D_B and C_S on the T_h values were closely related to the variation of APC in time, they were used to characterize the temporal distribution of APC. The analysis confirmed the existence of scale invariance in those investigated APC time series. Moreover, the D_B (C_S) was shown to be a decreasing (increasing) function of the threshold level, implying multifractal characteristics, i.e. the weak and intense regions scale differently. Some practical applications based on the box counting method were also discussed.