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On fractal nature of groundwater level fluctuations due to rainfall process

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  • Joelson, Maminirina
  • Golder, Jacques
  • Beltrame, Philippe
  • Néel, Marie-Christine
  • Di Pietro, Liliana

Abstract

Hourly resolution time series of groundwater level fluctuations are analyzed after removing the seasonal cycle. It is found that fluctuations of groundwater levels have fractal scaling and a persistent behavior. We show also that groundwater level fluctuations exhibit non-Gaussian heavy tailed probability distribution that is well fitted by the Lévy stable distribution. Implications of the present results on the groundwater system modeling as a fractional Lévy motion and the connection with the anomalous diffusion inside the soil are discussed.

Suggested Citation

  • Joelson, Maminirina & Golder, Jacques & Beltrame, Philippe & Néel, Marie-Christine & Di Pietro, Liliana, 2016. "On fractal nature of groundwater level fluctuations due to rainfall process," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 103-115.
    • Handle: RePEc:eee:chsofr:v:82:y:2016:i:c:p:103-115
    DOI: 10.1016/j.chaos.2015.11.010
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    References listed on IDEAS

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    1. Metzler, Ralf & Chechkin, Aleksei V. & Gonchar, Vsevolod Yu. & Klafter, Joseph, 2007. "Some fundamental aspects of Lévy flights," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 129-142.
    2. Weron, Rafał, 2002. "Estimating long-range dependence: finite sample properties and confidence intervals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 285-299.
    3. Shang, Pengjian & Kamae, Santi, 2005. "Fractal nature of time series in the sediment transport phenomenon," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 997-1007.
    4. Melvin J. Hinich, 1982. "Testing For Gaussianity And Linearity Of A Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(3), pages 169-176, May.
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    Cited by:

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    2. Burnecki, Krzysztof & Sikora, Grzegorz, 2017. "Identification and validation of stable ARFIMA processes with application to UMTS data," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 456-466.

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