Patterns of temporal scaling of groundwater level fluctuation

- We analyzed mono- and multi-fractal scaling for groundwater level fluctuation.
- Fractal scaling exists for groundwater level fluctuations in all aquifers.
- Fractal scaling behavior of the fluctuation for each well is site specific.
- The fractal coefficients are generally lower in the shallow wells.
- Spatial patterns of fractal scaling depend on local hydrogeological conditions.

SummaryWe studied the fractal scaling behavior of groundwater level fluctuation for various types of aquifers in Puerto Rico using the methods of (1) detrended fluctuation analysis (DFA) to examine the monofractality and (2) wavelet transform maximum modulus (WTMM) to analyze the multifractality. The DFA results show that fractals exist in groundwater fluctuations of all the aquifers with scaling patterns that are anti-persistent (1 < β < 1.5; 1.32 ± 0.12, 18 wells) or persistent (β > 1.5; 1.62 ± 0.07, 4 wells). The multifractal analysis confirmed the need to characterize these highly complex processes with multifractality, which originated from the stochastic distribution of the irregularly-shaped fluctuations. The singularity spectra of the fluctuation processes in each well were site specific. We found a general elevational effect with smaller fractal scaling coefficients in the shallower wells, except for the Northern Karst Aquifer Upper System. High spatial variability of fractal scaling of groundwater level fluctuations in the karst aquifer is due to the coupled effects of anthropogenic perturbations, precipitation, elevation and particularly the high heterogeneous hydrogeological conditions.