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Quantification of Non-Linear Dynamics and Chaos of Ambient Particulate Matter Concentrations in Muzaffarabad City
Sharjil Saeed1, Wajid Aziz1,4, Muhammad Rafique2, Imtiaz Ahmad1, Kimberlee J. Kearfott3, Salma Batool2
1 Department of Computer Sciences and Information Technology, University of Azad Jammu and Kashmir, Muzaffarabad (AJ&K) 13100, Pakistan
2 Department of Physics University of Azad Jammu and Kashmir Muzaffarbad, 13100, Azad Kashmir, Pakistan
3 University of Michigan, Department of Nuclear Engineering and Radiological Sciences, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109-2104, USA
4 Department of Computer Science, Faculty of Computing & Information Technology, University of Jeddah, Saudi Arabia
- We have monitored particulate matters (PM1.0 and PM2.5) to investigate time series behavior.
- The results indicates PM1.0 and PM2.5 time series can be modeled using phase space reconstruction
- The positive largest Lyapunov exponent reveals a strong chaotic signature in the system.
- Hurst exponent showed persistent time series pattern.
- The mean concentration of PM2.5 was considerably higher at all measurement locations.
The present study was carried out for quantification of non-linear dynamics and chaos of ambient particulate matter (PM) concentrations in Muzaffarabad city. PM1.0 and PM2.5 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 PM1.0 concentrations. However, the mean concentration of PM2.5 was considerably higher than the standards, developed by WHO, US-EPA and European Union directives, at all six locations. For PM1.0 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 PM2.5 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 PM1.0 and PM2.5 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.
Fine particulate matter; Chaotic behavior; Hurst exponent; Time series analysis.