Xin Gao , Xuan Wang, Hongbin Shi

School of Urban-rural Planning and Landscape Architecture, Xuchang University, Henan 46100, China


Received: October 31, 2019
Revised: May 1, 2019
Accepted: May 10, 2019

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Cite this article:

Gao, X., Wang, X. and Shi, H. (2019). Multifractal Cascade Analysis on the Nature of Air Pollutants Concentration Time Series over China. Aerosol Air Qual. Res. 19: 2100-2114.


  • Statistical and spectral analysis of the air pollution data are performed.
  • The underlying physical meanings of multifractal parameters are explored.
  • The random multiplicative cascade models are applied in the air pollution fields.


 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 αβ, binomial, and uniform models, can effectively recover extreme values.

Keywords: Cascade; Multifractal; Air pollutant; Time series; Downscaling.

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