Stochastic and Self-Organisation Patterns in a 17-Year PM10 Time Series in Athens, Greece

Dimitrios Nikolopoulos; Aftab Alam; Ermioni Petraki; Michail Papoutsidakis; Panayiotis Yannakopoulos; Konstantinos P Moustris

doi:10.3390/e23030307

Stochastic and Self-Organisation Patterns in a 17-Year PM₁₀ Time Series in Athens, Greece

Entropy (Basel). 2021 Mar 5;23(3):307. doi: 10.3390/e23030307.

Authors

Dimitrios Nikolopoulos¹, Aftab Alam², Ermioni Petraki³, Michail Papoutsidakis¹, Panayiotis Yannakopoulos³, Konstantinos P Moustris⁴

Affiliations

¹ Department of Industrial Design and Production Engineering, University of West Attica, GR-12244 Aigaleo, Greece.
² Centre for Earthquake Studies, National Centre for Physics, Islamabad 44000, Pakistan.
³ Department of Informatics and Computer Engineering, University of West Attica, GR-12233 Aigaleo, Greece.
⁴ Department of Mechanical Engineering, University of West Attica, Petrou Ralli & Thivon 250, GR-12244 Aigaleo, Greece.

Abstract

This paper utilises statistical and entropy methods for the investigation of a 17-year PM₁₀ time series recorded from five stations in Athens, Greece, in order to delineate existing stochastic and self-organisation trends. Stochastic patterns are analysed via lumping and sliding, in windows of various lengths. Decreasing trends are found between Windows 1 and 3500-4000, for all stations. Self-organisation is studied through Boltzmann and Tsallis entropy via sliding and symbolic dynamics in selected parts. Several values are below -2 (Boltzmann entropy) and 1.18 (Tsallis entropy) over the Boltzmann constant. A published method is utilised to locate areas for which the PM₁₀ system is out of stochastic behaviour and, simultaneously, exhibits critical self-organised tendencies. Sixty-six two-month windows are found for various dates. From these, nine are common to at least three different stations. Combining previous publications, two areas are non-stochastic and exhibit, simultaneously, fractal, long-memory and self-organisation patterns through a combination of 15 different fractal and SOC analysis techniques. In these areas, block-entropy (range 0.650-2.924) is significantly lower compared to the remaining areas of non-stochastic but self-organisation trends. It is the first time to utilise entropy analysis for PM₁₀ series and, importantly, in combination with results from previously published fractal methods.

Keywords: Boltzmann entropy; PM10; Statistical analysis; Tsallis entropy; air pollution.