Temporal Scaling Analytical Method to Identify Multi-Fractionality in Groundwater Head Fluctuations

Natural dynamics such as groundwater head fluctuations may exhibit multi-fractionality, likely caused by multi-scale aquifer heterogeneity and other controlling factors, whose statistics requires efficient quantification methods. As a scaling exponent, the Hurst exponent can describe the temporal correlation or multifractal behavior in groundwater level fluctuation processes. However, the scaling behavior may change with time under natural conditions, likely due to the non-stationary evolution of internal and external conditions, which cannot be characterized by traditional methods using a single or several scaling exponents for the complex features of the overall process. This methods note quantifies the multi-fractionality using the timescale local Hurst exponent (TS-LHE) and then proposes a systematic statistical method to analyze groundwater head fluctuations. Time series of daily groundwater level fluctuations from three wells located in the lower Mississippi valley are analyzed, after removing the seasonal cycle, which leads to transient TS-LHE, implying multi-fractionality and multifractal-scaling behavior that changes with time and location. Therefore, the temporal scaling analysis proposed here may provide useful and quantitative information to understand the nature of dynamic hydrologic systems.