Patterns of temporal scaling of groundwater level fluctuation

Abstract

SUMMARY We 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 multi-fractal 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.

Fractal scaling analysis of groundwater dynamics in confined aquifers

“…They analyzed 4 years of continuous hourly data from seven wells and found that groundwater level fluctuations are likely to follow fractional Brownian motion (fBm) and that temporal scaling crossovers exist in the fluctuations. These findings were later confirmed by Little and Bloomfield (2010), Rakhshandehroo and Amiri (2012), and Yu et al (2016) with the application of DFA to hourly or 15 min interval data for up to 5 years from 7 wells, daily data for 6 years from 2 wells, and daily data from 22 wells that have more than 2500 records, respectively. Rakhshandehroo and Amiri (2012) further utilized MF-DFA to evaluate the multifractality of groundwater level fluctuations and concluded that the extent of multifractality in groundwater level fluctuations is stronger than that in river runoff.…”

“…Consequently, groundwater level fluctuations are often nonstationary, rendering variabilities over different spatial and temporal scales and resulting in no dependence on single representative spatial and temporal scales. Therefore, groundwater level fluctuations are often characterized as scale-free processes and modeled as fractional Brownian motion (Hardstone et al, 2012;Yu et al, 2016). Although not necessarily totally random, groundwater level fluctuations may demonstrate long-range dependence through time, implying…”

“…Tu et al: Fractal scaling analysis of groundwater dynamics in confined aquifers a power-law relationship over a variety of timescales, which can be represented by fractals (Yu et al, 2016).…”

“…Temporal fractal scaling analysis of groundwater dynamics can be essential to a better understanding of the modeling of hydrological processes by considering temporal correlations and scaling cascading issues, since groundwater closely links to surface water in hydrological modeling and hydrological models are built upon certain temporal and spatial scales (Blöschl and Sivapalan, 1995;Yu et al, 2016). Hence, fractal scaling analysis of groundwater level fluctuations can guide more representative modeling in hydrological models and in coupled land-atmosphere models.…”

“…In fact, groundwater dynamics were found to provide a positive feedback to the memory of land surface hydrological processes in climate systems, and enhanced knowledge of fractal behavior in subsurface hydrological processes can help improve weather forecast and climate prediction on different temporal scales (Lo and Famiglietti, 2010). Furthermore, fractal scaling analysis of groundwater level fluctuations may help investigate extreme events and anthropogenic forcing in Earth systems (Yu et al, 2016).…”