Fractal Fluctuations of Groundwater Levels: Detrended Fluctuation Analysis

Groundwater system is a complex dynamic system characterized by nonstationary input (recharge), output (baseflow), and response (groundwater levels). A new method, Detrended Fluctuation Analysis (DFA), which has been used to analyze biological time series during the last decade and is more robust than spectral analysis, is applied to quantify scaling properties of the observed nonstationary groundwater levels, streamflow, and baseflow. With the results obtained with DFA, we further verify that fluctuations of groundwater levels may indeed be a fractional Brownian motion and that fractal scaling may be universal since fluctuations of groundwater levels are affected by various processes of different time scales. We also found that there may exist at least two crossovers in fractal scaling of groundwater level fluctuations: one between a few days to 10 days and the other between a few months to a year. Variations of groundwater levels are persistent at small time scales (less than a few to 10 days), anti-persistent at intermediate time scales (between 10 days and a few months), and 1/f noises at large time scale (more than a few months). In general, temporal correlation decreases as time scale increases and increases from rainfalls to streamflow, to groundwater, and to baseflow due to the dampening effect by the land surface, soils, and aquifers.