Effect of temporally correlated recharge on fluctuations of groundwater levels

Abstract

The effect of temporally correlated groundwater recharge, R(t), on fluctuations of the hydraulic head, h(t), was investigated with theoretical analyses and numerical simulations. Under an exponentially correlated recharge (ECR) process, analytical solutions for the hydraulic head covariance, C hh, and variance, σh2, were derived with a linear reservoir model. It was found that Chh and σh2 are time-dependent or nonstationary and reduce to those derived in a previous study for a white noise recharge (WNR) when the correlation timescale of the recharge process approaches zero. It is also found that σh2 for ECR is proportional to t2, while that for WNR is proportional to t for a substantial period of time, indicating that h(t) under ECR may vary as a smooth curve with no fractal characteristics (D = 1.0), while h(t) under WNR fluctuates as a Brownian motion (D = 1.5). The theoretical findings were verified by numerical simulations: The power spectra of the simulated heads with a one-dimensional transient groundwater flow model under ECR were shown to have distinct slopes in the log-log plot with D = 1.02. It was emphasized that the effect of temporal correlation in groundwater recharge is to dampen the fluctuations of the head and base flow and that daily groundwater recharge rates may have little temporal correlation in the hydrogeological conditions similar to the Walnut Creek site. Copyright 2006 by the American Geophysical Union.