Skip to main content
SpringerLink
Log in

Multifractal Characteristics in Air Pollutant Concentration Time Series

  • Published:
Water, Air, and Soil Pollution Aims and scope Submit manuscript

Abstract

One-year series of hourly average air pollutant concentration(APC) observations, including O3, CO, SO2 and NO2,were analyzed by means of statistical tools: histogram, variancemethod, and multifractal analysis, to examine the possible scale-invariant behavior and the clustering characteristics. It was found that all APC measurements exhibit the characteristicright-skewed unimodal frequency distribution and long term memory. A monodimensional fractal analysis was performed by thebox counting method. Scale invariance was found in these time series and the box dimension was shown to be a decreasing function of the threshold APC level, implying multifractal characteristics, i.e., the weak and intense regions scaledifferently. To test this hypothesis, the APC time series weretransferred into a useful compact form through the multifractalformalism, namely, the τ(q)-q and f(α)-α plots. The analysis confirmed the existence of multifractal characteristics in the investigated APC time series. It wasconcluded that the origin of both the pronounced right-skewnessand multifractal phenomena in APC time series may be interpretedin terms of the Ott (1995) proposed successive random dilution (SRD) theory and the dynamics of APC distribution process can bedescribed as a random multiplicative process.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anh, V. V., Lam, K. C., Leung, Y. and Tieng, Q. M.: 2000, ‘Multifractal Analysis of Hong Kong Air Quality Data’, Environmetrics 11, 139–149.

    Google Scholar 

  • Bencala, K. E. and Seinfeld, J. H.: 1976, ‘On Frequency Distribution of Air Pollutant Concentrations’, Atmos. Environ. 10, 941–950.

    Google Scholar 

  • Borgas, M. S.: 1992, ‘A Comparison of Intermittency Models in Turbulence’, Phys. Fluids A 4, 2055–2061.

    Google Scholar 

  • Buczkowski, S., Hildgen, P. and Cartilier, L.: 1998, ‘Measurements of Fractal Dimension by Box-counting: A Critical Analysis of Data Scatter’, Physica A 252, 23–34.

    Google Scholar 

  • Bunde, A. and Havlin, S.: 1994, Fractals in Science, Springer-Verlag, Berlin, 17 pp.

    Google Scholar 

  • Chock, D. P., Terrell, T. R. and Levitt, S. B.: 1975, ‘Time-series Analysis of Riverside, California Air Quality Data’, Atmos. Environ. 9, 978–989.

    Google Scholar 

  • Davis, A., Marshak, A., Wiscombe, W. and Cahalan, R.: 1994, ‘Multifractal Characterizations of Nonstationarity and Intermittence in Geophysical Fields: Observed, Retrieved, or Simulated’, J. Geophys. Res. 99, 8055–8072.

    Google Scholar 

  • Falconer, K.: 1990, Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons, Chichester, 288 pp.

    Google Scholar 

  • Frisch, U.: 1995, Turbulence, Cambridge University Press, Cambridge, 171 pp.

    Google Scholar 

  • Georgopoulos, P. G. and Seinfeld, J. H.: 1982, ‘Statistical Distributions of Air Pollutant Concentrations’, Environ. Sci. Technol. 16, 401A–416A.

    Google Scholar 

  • Godano, C., Alonzo, M. L. and Vilardo, G.: 1997, ‘Multifractal Approach to Time Clustering of Earthquakes. Application to Mt. Vesuvio Seismicity’, Pure Appl. Geophys. 149, 375–390.

    Google Scholar 

  • Gonzato, G., Mulargia, F. and Marzocchi, W.: 1998, ‘Practical Application of Fractal Analysis: Problems and Solutions’, Geophys. J. Int. 132, 275–282.

    Google Scholar 

  • Gutfraind, R., Sheintuch, M. and Avnir, D.: 1991, ‘Fractal and Multifractal Analysis of the Sensitivity of Catalytic Reactions to Catalyst Structure’, J. Chem. Phys. 95, 6100–6111.

    Google Scholar 

  • Hasley, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I. and Shraiman, B. I.: 1986, ‘Fractal Measures and Their Singularities: The Characterization of Strange Sets’, Phys.Rev. A 33, 1141–1152.

    Google Scholar 

  • Horowitz, J. and Barakat, S.: 1979, ‘Statistical analysis of the Maximum Concentration of an Air Pollutant: Effects of Autocorrelation and Non-stationarity’, Atmos. Environ. 13, 811–818.

    Google Scholar 

  • Klement, S. and Kratky, K. W.: 1997, ‘Multifractal Analysis of Airborne Particle Count Data: The Influence of Data Preprocessing’, Aerosol Sci. Technol. 26, 12–20.

    Google Scholar 

  • Klement, S., Nittman, J., Kratky, K. W. and Actio, W. P.: 1994, ‘Multifractal Analysis of Airborne Microcontamination Particles’, Aerosol Sci. Technol. 20, 100–110.

    Google Scholar 

  • Ladoy, P., Lovejoy, S. and Schertzer, D.: 1991, ‘Extreme Variability of Climatological Data: Scaling and Intermittency’, in S. Lovejoy and D. Schertzer (eds), Non-linear Variability in Geophysics, Kluwer Academic Publishers, Norwell, MA, pp. 241–250.

    Google Scholar 

  • Lee, C. K. and Lee, S. L.: 1996, ‘Heterogeneity of Surfaces and Materials, as Reflected in Multifractal Analysis’, Heterogen. Chem. Rev. 3, 269–302.

    Google Scholar 

  • Mandelbrot, B. B.: 1982, The Fractal Geometry of Nature, Freeman, San Francisco.

    Google Scholar 

  • Meneveau, C. and Sreenivasan, K. R.: 1991, ‘The Multifractal Nature of Turbulent Energy Dissipation’, J. Fluid Mech. 224, 429–484.

    Google Scholar 

  • Olsson, J.: 1996, ‘Validity and Applicability of a Scale-independent, Multifractal Relationship for Rainfall’, Atmos. Res. 42, 53–65.

    Google Scholar 

  • Olsson, J. and Niemczynowicz, J.: 1996, ‘Multifractal Analysis of Daily Spatial Rainfall Distributions’, J. Hydrol. 187, 29–43.

    Google Scholar 

  • Olsson, J., Niemczynowicz, J. and Berndtsson, R.: 1993, ‘Fractal Analysis of High-resolution Rainfall Time Series’, J. Geophys. Res. 98, 23265–23274.

    Google Scholar 

  • Olsson, J., Niemczynowicz, J., Berndtsson, R. and Larson, M.: 1992, ‘An Analysis of the Rainfall Time Structure by Box Counting-Some Practical Implications’, J. Hydrol. 137, 261–277.

    Google Scholar 

  • Ott, W. R.: 1990, ‘A Physical Explanation of the Lognormality of Pollutant Concentrations’, J. Air and Waste Manage. Assoc. 40, 1378–1383.

    Google Scholar 

  • Ott, W. R.: 1995, Environmental Statistics and Data Analysis, Lewis, Boca Raton, 191 pp.

    Google Scholar 

  • Pfeifer, P. and Obert, M.: 1989, ‘Fractals: Basic Concepts and Terminology’, in D. Avnir (ed.), The Fractal Approach to Heterogeneous Chemistry, John Wiley & Sons, New York, pp. 11–51.

    Google Scholar 

  • Rodriguez-Iturbe, I., De Power, B. F., Sharifi, M. B. and Georgakakos, K. P.: 1989, ‘Chaos in Rainfall’, Water Resour. Res. 25, 1667–1675.

    Google Scholar 

  • Stanley, H. E. and Meakin, P.: 1988, ‘Multifractal Phenomena in Physics and Chemistry’, Nature 335, 405–409.

    Google Scholar 

  • Teverovsky, V. and Taqqu, M.: 1997, ‘Testing for Long-range Dependence in the Presence of Shifting Means or a Slowly Declining Trend, Using a Variance-type Estimator’, J. Time Ser. Anal. 18, 279–304.

    Google Scholar 

  • Vicsek, T.: 1992, Fractal Growth Phenomena, World Scientific, Singapore, 81 pp.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Environmental Engineering, Van-Nung Institute of Technology, Chungli, 320, Taiwan, ROC

    Chung-Kung Lee

Authors
  1. Chung-Kung Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chung-Kung Lee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, CK. Multifractal Characteristics in Air Pollutant Concentration Time Series. Water, Air, & Soil Pollution 135, 389–409 (2002). https://doi.org/10.1023/A:1014768632318

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014768632318

Search

Navigation