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Earth System Dynamics An interactive open-access journal of the European Geosciences Union

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Earth Syst. Dynam., 8, 931-949, 2017
https://doi.org/10.5194/esd-8-931-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
24 Oct 2017
Fractal scaling analysis of groundwater dynamics in confined aquifers
Tongbi Tu1, Ali Ercan1,2, and M. Levent Kavvas1,2 1J. Amorocho Hydraulics Laboratory, Dept. of Civil and Environmental Engineering, University of California, Davis, CA 95616, USA
2Hydrologic Research Laboratory, Dept. of Civil and Environmental Engineering, University of California, Davis, CA 95616, USA
Abstract. Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

Citation: Tu, T., Ercan, A., and Kavvas, M. L.: Fractal scaling analysis of groundwater dynamics in confined aquifers, Earth Syst. Dynam., 8, 931-949, https://doi.org/10.5194/esd-8-931-2017, 2017.
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Short summary
Groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior, and the underlying distribution exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics. The estimated Hurst exponent is highly dependent on the length and the specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist.
Groundwater level fluctuations in confined aquifer wells with long observations exhibit...
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