Cheng-Cai Wang

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

Abstract 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 (DB)-threshold (Th) and critical scale (CS)-threshold (Th) plots. The validity of this approach was supported with the result that the practical implications of DB-Th (or CS-Th) plots could be interpreted in terms of traditional statistical parameters. Since the dependences of both DB and CS on the Th 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 DB (CS) 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.

Effect of Autocorrelation on Applying Central Limit Theorem to Air Pollutant Concentration Time Series

One-year of hourly average air pollutant concentration (APC) observations, including CO, NO, NO2, O3, PM10, and SO2, was used to examine the effects of autocorrelation on the assumption of Central Limit Theorem (CLT) by calculating the confidence intervals of the data that were known to be dependent. Monte Carlo sampling was used to draw random samples of various sizes from the population (1000 groups of each size), and the sample means and standard deviation of these observed means were then evaluated. Even with small sample sizes, the average of all the means in each group and the observed standard deviation of the means were found to closely approximate the means of the overall population and the standard deviation predicted by CLT, respectively. Moreover, the above consistency was closely related to the coefficient of variation of the population rather than to the degree of long-range-dependence. These results were used to interpret why the right-skewed frequency distribution observed in the mutually dependent air quality data could be accurately described using the lognormal model derived from the CLT. The link between the lognormality and multifractal characteristics in APC time series was also discussed.