Review PapersEvaluating fractal behavior in groundwater level fluctuations time series

SummaryIn this study, fractal and multifractal self-affinity in two datasets (d1 and d2) of groundwater level fluctuations time series, each having more than 2000 data points, were evaluated. Variation method, power spectrum, and Detrended Fluctuation Analysis (DFA) were used to estimate fluctuation exponent of the datasets. Multifractal detrended fluctuation analysis (MF-DFA) was used to evaluate multifractal behavior of d1 and d2. Results obtained in this study were compared to two other natural self-affine time series; turbulent open channel flow and river runoff. It was shown that a relatively high (and almost identical) level of multifractality exists in both datasets. The multifractality was postulated to be due to different long-range correlations for small and large fluctuations in the series. Minimum number of data points required to get a stable fractal dimension for groundwater level fluctuation time series (∼1500) was found to be much smaller than that for velocity variations in an open channel (∼2500). Comparing λ exponents of several river runoff time series (0.55 < λ < 0.95) to estimated λ for d1 and d2 (∼1.37), it was concluded that river runoff time series are likely to follow fractional Gaussian noise (fGn) characteristics while groundwater level fluctuation time series may be of fractional Brownian motion (fBm) type. The multifractal cascade model which explained multifractal behavior in river runoff time series also explained that of d1 and d2. However, the range of singularities is wider in d1 and d2 than that for river runoffs.