Quantification of Non-Linear Dynamics and Chaos of Ambient Particulate Matter Concentrations in Muzaffarabad City

ABSTRACT

The present study was carried out for quantification of non-linear dynamics and chaos of ambient particulate matter (PM) concentrations in Muzaffarabad city. PM_1.0 and PM_2.5 concentrations were monitored at six different locations for a continuous 6 h period. The linear behavior of the acquired time series data was analyzed using descriptive statistics. Specifically, the chaotic temporal behavior of the PM concentration was analyzed using phase space reconstruction, the Hurst exponent, and the largest Lyapunov exponent. The average mutual function was used to calculate proper time delay, while the false nearest neighbor method was used to calculate the proper embedding dimension for the phase space reconstruction. No health-protective quantitative standard exists for PM_1.0 concentrations. However, the mean concentration of PM_2.5 was considerably higher than the standards, developed by WHO, US-EPA and European Union directives, at all six locations. For PM_1.0 minimum, 293 ± 149 µg m^–3, and maximum, 544 ± 490 µg m^–3, values were recorded at CMH Chowk and Chehla Bridge locations respectively. For PM_2.5 minimum, 394 ± 262 µg m^–3 and maximum, 633 ± 426 µg m^–3, values were recorded at CMH Chowk and at old secretariat respectively. The results indicates PM_1.0 and PM_2.5 concentration time series can be modeled using phase space reconstruction by properly selecting the embedding parameters. The positive largest Lyapunov exponent reveals a strong chaotic signature in the system dynamics for both particulate sizes. Furthermore, Hurst exponent for both particulates was close to 1, showing highly persistent time series pattern.