Multifractal Cascade Analysis on the Nature of Air Pollutants Concentration Time Series over China

Xin Gao,Xuan Wang,Hongbin Shi

doi:10.4209/aaqr.2018.10.0364

Abstract

ABSTRACT This study investigates the temporal multifractal cascade behaviors of air pollution in major cities of China by using 1-year data of the hourly time series of six pollutants (PM2.5, PM10, CO, NO2, O3, and SO2) and the air quality index (AQI) as model inputs. Given that the air pollution time series generally exhibit positive skewness with a heavy tail, a stable distribution with four parameters, such as Levy α-stable distribution, reasonably fits the frequency distributions of the data over the entire range. The periodicity and nonstationarity shared by the series are also spectrally analyzed, and all of the pollutants display a daily and semi-daily cycle as well as two dynamical regimes with a cut-off scale around 11 days. Using universal multifractal analysis, the two parameters (α and C1) in an air pollution system are measured, and their underlying significance is also addressed via analogues of the Monte Carlo simulation data. Moreover, self-organizing criticality analysis on the data of the air pollution index (API) indicates first-order multifractal phase transitions, with an estimated interval of the order of the moment (qD) that varies between 1.95 and 2.98. Finally, downscaled performances of multifractal cascade models are numerically evaluated, demonstrating that log-normal and log-Poisson models, but not α, β, binomial, and uniform models, can effectively recover extreme values.

Highlights

Air pollution has become one of the most concerning environmental problems in the world because of its significant negative impacts on human health and restrictions on national development
This study investigates the temporal multifractal cascade behaviors of air pollution in major cities of China by using 1-year data of the hourly time series of six pollutants (PM2.5, PM10, CO, NO2, O3, and SO2) and the air quality index (AQI) as model inputs
The Statistical Features of the Air Pollution Time Series The possible divergence of high moments for statistical quantities about heavy-tailed random variables indicates the inefficiency and instability on the estimation or analysis by using traditional probability theory, and a new probabilistic model will be adopted to characterize the statistical distributions of the air pollutants

Summary

Introduction

Air pollution has become one of the most concerning environmental problems in the world because of its significant negative impacts on human health and restrictions on national development. With the heavy dependence on the fluctuations of a variety of meteorological and emission variables, air pollutant concentrations randomly and irregularly varied with regard to time and space. Knowledge of the structure of the time series of the concentrations of major air pollutants is needed in order to make pollution prevention policies and better understand dynamical mechanisms governing their temporal variabilities (Xepapadeas, 1992; Liu et al, 2003; Esposito et al, 2016). Time series of air pollution data measured at any location usually distributes as a strong right-skewed unimodal shape (Georgopoulos and Seinfeld, 1982).

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Conclusion