Temporal scaling of hydraulic head fluctuations: Nonstationary spectral analyses and numerical simulations

Abstract

Temporal scaling of the hydraulic head time series, h(t), was found in a previous analysis of hourly measured head data. This issue is further investigated in this paper with nonstationary spectral analyses and numerical simulations. The results show that temporal scaling may indeed exist in h(t), which fluctuates like a fractional Brownian motion in most aquifers. On the basis of a linear reservoir model with a white noise recharge input, we show that the variance and covariance of h(t) are functions of time: The head variance increases with time and approaches a constant limit as time progresses, while the covariance decreases with the separation time interval for a fixed time and approaches the typical exponential covariance as time increases. The spectra of the simulated h(t) using a one‐dimensional transient groundwater flow model with a white noise recharge in both homogeneous and heterogeneous aquifers are shown to be proportional to f‐β, where f is frequency and β ∼ 1.84 (or H = 0.42). Heterogeneity in the hydraulic conductivity may affect the fractal dimension of h(t) in highly permeable aquifers but not in the low permeable aquifer simulated in this study.