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

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doi:10.5194/esd-2017-27
© Author(s) 2017. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
04 Apr 2017
Review status
This discussion paper is under review for the journal Earth System Dynamics (ESD).
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 hydro-climatic 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 of 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, which can model both the long-memory behavior as well as 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. Discuss., doi:10.5194/esd-2017-27, in review, 2017.
Tongbi Tu et al.
Tongbi Tu et al.
Tongbi Tu et al.

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Short summary
Groundwater level fluctuations of 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 closely 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 of confined aquifer wells with long observations exhibit...
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