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Fractional derivative models for atmospheric dispersion of pollutants

Author

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  • Goulart, A.G.O.
  • Lazo, M.J.
  • Suarez, J.M.S.
  • Moreira, D.M.

Abstract

In the present work, we investigate the potential of fractional derivatives to model atmospheric dispersion of pollutants. We propose simple fractional differential equation models for the steady state spatial distribution of concentration of a non-reactive pollutant in Planetary Boundary Layer. We solve these models and we compare the solutions with a real experiment. We found that the fractional derivative models perform far better than the traditional Gaussian model and even better than models found in the literature where it is considered that the diffusion coefficient is a function of the position in order to deal with the anomalous diffusion.

Suggested Citation

  • Goulart, A.G.O. & Lazo, M.J. & Suarez, J.M.S. & Moreira, D.M., 2017. "Fractional derivative models for atmospheric dispersion of pollutants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 9-19.
    • Handle: RePEc:eee:phsmap:v:477:y:2017:i:c:p:9-19
    DOI: 10.1016/j.physa.2017.02.022
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    Citations

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    Cited by:

    1. Miglena N. Koleva & Lubin G. Vulkov, 2023. "Numerical Solution of Fractional Models of Dispersion Contaminants in the Planetary Boundary Layer," Mathematics, MDPI, vol. 11(9), pages 1-21, April.
    2. Goulart, A.G. & Lazo, M.J. & Suarez, J.M.S., 2020. "A deformed derivative model for turbulent diffusion of contaminants in the atmosphere," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    3. Troparevsky, M.I. & Muszkats, J.P. & Seminara, S.A. & Zitto, M.E. & Piotrkowski, R., 2022. "Modeling particulate pollutants dispersed in the atmosphere using fractional turbulent diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    4. Goulart, A.G. & Lazo, M.J. & Suarez, J.M.S., 2019. "A new parameterization for the concentration flux using the fractional calculus to model the dispersion of contaminants in the Planetary Boundary Layer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 38-49.

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