Skip to main content
Log in

Q-Weibull distribution to explain the PM2.5 air pollution concentration in Santiago de Chile

  • Regular Article - Statistical and Nonlinear Physics
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

It is shown that distribution of PM2.5 concentration recorded by eight air quality monitoring stations during 2021, covering a large part of the Santiago metropolitan region of Chile, can be explained by a q-Weibull function, which has been related in some papers to complex and non-equilibrium statistical systems. It was found that this function has an excellent fit performance on non-filtered data, which cannot be reached by other physical-statistical functions widely used to modeling air pollution distribution in the literature. Finally, relevant interpretations from the fit parameters are shown as well.

Graphic Abstract

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data availability statement

This manuscript has associated data in a data repository. [Authors’ comment: We cannot generalize the results based on what we observed during the year 2021 for the PM2.5 pollutant. It is important to note that on March 18, 2020, the “State of Constitutional Exception of Catastrophe, due to public calamity” began to apply in Chile, which was in force until March 13, 2021. It was later extended until September 2021 (Decrees 72 and 153 can be consulted on the official website of the Library of the National Congress of Chile https://www.bcn.cl), which brought a series of prevention measures, such as the closure of borders (air, land and sea), the declaration of a night curfew throughout the national territory, among other measures that affected environmental behavior in our study area (Santiago de Chile).]

References

  1. V. Leiva, M. Barros, G.A. Paula, A. Sanhueza, Generalized Birnbaum-Saunders distributions applied to air pollutant concentration. Environmetrics 19, 235–249 (2008)

    Article  MathSciNet  Google Scholar 

  2. F. Vilca, A. Sanhueza, V. Leiva, G. Christakos, An extended Birnbaum-Saunders model and its application in the study of environmental quality in Santiago. Chile. Stoch. Environ. Res. Risk Assess. 24, 771–782 (2010)

    Article  MATH  Google Scholar 

  3. Z.W. Birnbaum, S.C. Saunders, A new family of life distributions. J. Appl. Probab. 6, 319–327 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  4. Z.W. Birnbaum, S.C. Saunders, Estimation for a family of life distributions with applications to fatigue. J. Appl. Probab. 6, 328–347 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  5. B. Morel, S. Yeh, L. Cifuentes, Statistical distributions for air pollution applied to the study of the particulate problem in Santiago. Atmos. Environ. 33(16), 2575–2585 (1999)

    Article  ADS  Google Scholar 

  6. P.G. Georgopoulos, J.H. Seinfeld, Statistical distributions of air pollutant concentrations. Environ. Sci. Technol. 16(7), 401A-416A (1982)

    Article  ADS  Google Scholar 

  7. H.C. Lu, The statistical characters of PM10 concentration in Taiwan area. Atmos. Environ. 36(3), 491–502 (2002)

    Article  ADS  Google Scholar 

  8. S. Nadarajaha, S. Kotz, On the q-type distributions. Physica A 377, 465–468 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  9. G. Williams, B. Schäfer, C. Beck, Super statistical approach to air pollution statistics. Phys. Rev. Res. 2, 013019 (2020)

    Article  Google Scholar 

  10. H. He, B. Schäfer, C. Beck, Spatial heterogeneity of air pollution statistics in Europe. Sci. Rep. 12, 12215 (2022)

    Article  ADS  Google Scholar 

  11. C. Tsallis, Nonadditive entropy and nonextensive statistical mechanics—an overview after 20 years. Braz. J. Phys. 39, 337–356 (2009)

    Article  ADS  Google Scholar 

  12. S. Picoli Jr., R.S. Mendes, L.C. Malacarne, q-Exponential, Weibull, and q-Weibull distributions: an empirical analysis. Physica A 324, 678–688 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. S. Picoli Jr., R.S. Mendes, L.C. Malacarne, R.P.B. Santos, q-distributions in complex systems: a brief review. Braz. J. Phys. 39, 468–474 (2009)

    Article  ADS  Google Scholar 

  14. P. Rosin, E. Rammler, The laws governing the fineness of powdered coal. J. Inst. Fuel 7, 29 (1933)

    Google Scholar 

  15. Z. Fang, B.R. Patterson, M.E. Turner, Modeling particle size distributions by the Weibull distribution function. Mater. Charact. 31(3), 177–182 (1993)

    Article  Google Scholar 

  16. M. Jonasz, G.R. Fournier, The particle size distribution, in Light Scattering by Particles in Water. ed. by M. Jonasz, G.R. Fournier (Academic Press, New York, 2007), pp.267–445

    Chapter  Google Scholar 

  17. W.K. Brown, K.H. Wohletz, Derivation of the Weibull distribution based on physical principles and its connection to the Rosin-Rammler and lognormal distributions. J. Appl. Phys. 78, 2758 (1995)

    Article  ADS  Google Scholar 

  18. U.M.S. Costa, V.N. Freire, L.C. Malacarne, R.S. Mendes, S. Picoli Jr., E.A. de Vasconcelos, E.F. da Silva, An improved description of the dielectric breakdown in oxides based on a generalized Weibull distribution. Physica A 361, 209–215 (2006)

    Article  ADS  Google Scholar 

  19. E. Koo, C.M. Tam, W.L. Chang, Statistical analysis of meteorological and SO2 data. In Proceedings, Annual Meeting, Air Pollution Control Association, vol. 5, p. 8 (1984)

  20. J.A. Taylor, R.W. Simpson, A.J. Jakeman, A hybrid model for predicting the distribution of pollutants dispersed from line sources. Sci. Total Environ. 46(1–4), 191–213 (1985)

  21. A.J. Taylor, R.W. Jakeman, Simpson, Modeling distributions of air pollutant concentrations—I. Identification of statistical models. Atmos. Environ. 20(9), 1781–1789 (1986)

    Article  ADS  Google Scholar 

  22. R. Ganguly, B.M. Broderick, Performance evaluation and sensitivity analysis of the general finite line source model for CO concentrations adjacent to motorways: A note. Transport. Res. Part D 13, 198–205 (2008)

    Article  Google Scholar 

  23. M.Y. Nasir, N.A. Ghazali, M.I.Z. Mokhtar, N. Suhaimi, Fitting statistical distributions functions on ozone concentration data at coastal areas. Malay. J. Anal. Sci. 20(3), 551–559 (2016)

    Article  Google Scholar 

  24. S.D. Dubey, Compound gamma, beta and F distributions. Metrika 16, 27–31 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  25. N.L. Johnson, S. Kotz, N. Balakrishnan, in Continuous Univariate Distributions, vol. 1. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. Wiley, New York (1994)

  26. A. Pelliccioni, I. Ventrone, U. Poll, L. Lepore, M. Angelon, Use of the Weibull distribution parameters to characterize the atmospheric pollution monitoring. Trans. Ecol. Environ. (1997). https://doi.org/10.2495/AIR970471

  27. K. Briggs, C. Beck, Modelling train delays with q-exponential functions. Physica A 378, 498 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  28. A.I. Aguirre-Salado, H. Vaquera-Huerta, C.A. Aguirre-Salado, S. Reyes-Mora, A.D. Olvera-Cervantes, G.A. Lancho-Romero, C. Soubervielle-Montalvo, Developing a hierarchical model for the spatial analysis of PM10 pollution extremes in the Mexico City metropolitan area. Int. J. Environ. Res. Public Health 14(7), 734 (2017)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ewin Sánchez.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sánchez, E. Q-Weibull distribution to explain the PM2.5 air pollution concentration in Santiago de Chile. Eur. Phys. J. B 96, 108 (2023). https://doi.org/10.1140/epjb/s10051-023-00576-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-023-00576-1

Navigation