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

Category: Air Pollution Modeling

Accepted Manuscripts
DOI: 10.4209/aaqr.2018.10.0364

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Xin Gao , Xuan Wang, Hongbin Shi

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


  • 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 the time series of air pollution in major cities of China, taking one-year data of hourly time series of six pollutants (PM2.5, PM10, CO, NO2, O3 ,SO2) and Air Quality Index (AQI) as model inputs. Considering the right-skewness with heavy tail widely existed in an air pollution time series, the stable distribution with four parameters is used to fit the frequency distributions of all the data, and the result shows that it can give well fittings over the whole range like the log-normal model. The shared periodicity and nonstaionarity are also investigated based on spectral analysis, and the usual cycles such as daily and semi-daily cycles and two dynamical regimes with a crossover at approximately 11 days are widely found in all the pollution series. In the universal multifractal analysis, the underlying significances of the two parameters in air pollution system are addressed by means of the analogues of simulation data. Moreover, an evidence of first order multifractal phase transitions is found through self-organizing criticality analysis on the data of Air Pollution Index (API), which can provide an available estimation interval of the moment order qD varying between 1.95 and 2.98. Finally, downscaling performances of the multifractal cascade models are numerically investigated with the aim to explore the potential applications in the air pollution field, which demonstrate that log-normal and log-Poisson models, but not α, β, binomial and uniform models, can effectively recover the extreme values.


Cascade Multifractal Air pollutant Time series Downscaling

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