Temporal scaling of hydraulic head and river base flow and its implication for groundwater recharge

Abstract

[1] Spectral analyses were conducted for hourly hydraulic head (h) data observed over a 4-year period at seven monitoring wells in the Walnut Creek watershed, Iowa. The log power spectral density of the hydraulic head fluctuations versus log frequency ( f ) at all seven wells is shown to have a distinct slope or fractal dimension (D), indicating temporal scaling in the time series of water level fluctuations. The fractal dimension of the time series varies from well to well, and the spectrum for the average h over all seven wells has a fractal dimension of 1.46 and Hurst coefficient of 0.54. The log power spectral density of estimated base flow in the Walnut Creek and four other watersheds versus log f is shown to have two distinct slopes with a break in scaling at about 30 days. It is shown that the groundwater recharge process in a basin can be estimated from a head spectrum based on existing theoretical results. Hydraulic head in an aquifer may fluctuate as a fractal in time in response to either a white noise or fractal recharge process, depending on physical parameters (i.e., transmissivity and specific yield) of the aquifer. The recharge process at the Walnut Creek watershed is shown to have a white noise spectrum based on the observed head spectrum.

Effect of temporally correlated recharge on fluctuations of groundwater levels

“…Most relevantly to the current study, they found that daily recharge rates at the Walnut Creek watershed may be a white noise process. The findings of Zhang and Schilling [2004] were further verified by Zhang and Li [2005] with nonstationary spectral analyses and numerical simulations. They showed that temporal scaling may indeed exist in h(t) which fluctuates as a fractional Brownian motion in most aquifers.…”

“…For example, at our Walnut Creek site, a/S Y = 1.12 Â 10 À4 where a = 3T/L 2 [Gelhar and Wilson, 1974] and thus t 0 = 0.112 when t = 1000 days. This may explain why the Hurst coefficient calculated from the heads observed during a period of four years (1460 days) at the Walnut Creek site is 0.53 [Zhang and Schilling, 2004] (very close to 0.5) and confirm that the recharge in the Walnut Creek aquifer is a nearly white noise process with little temporal correlation. In the following numerical simulations under ECR, we will verify the theoretical results and show that the head fluctuates much more smoothly with H % 1.0 or D % 1.0.…”

“…These slopes are substantially larger than those for WNR [Zhang and Li, 2005, Figure 7]. The values of and corresponding fractal dimension (D = (5 À )/2) and Hurst coefficient (H = 2 À D) [Turcotte, 1992;Carr, 1995] of the simulated h(t) are listed in Table 1 along with those estimated from the simulated h(t) with WNR [Zhang and Li, 2005] and those based on the observed h(t) at the Walnut Creek site [Zhang and Schilling, 2004]. For the case simulated in this study under ECR, the values of , D, and H at the four well locations are 2.95, 1.02, and 0.98, respectively, while those obtained under WNR are 1.84, 1.58, and 0.42, respectively.…”

“…[12] We adopt the one-dimensional transient equation used by Zhang and Li [2005] to approximate groundwater flow in an unconfined aquifer along a hillslope from a groundwater divide to a creek, similar to the setting at the Walnut Creek Watershed [Zhang and Schilling, 2004, Figure 1], i.e.,…”

“…One may obtain valuable information about groundwater recharge and discharge by studying fluctuations of water levels in monitoring wells. Recently, Zhang and Schilling [2004] analyzed the hourly water level fluctuations in seven wells along a transect at the Walnut Creek watershed, Iowa from January 1996 to March 2000 and found that the hydraulic head, h(t), in an aquifer may fluctuate as a temporal fractal in response to either a white noise or a fractal recharge process, depending on how quickly the aquifer responds to a recharge event and on the physical parameters of the aquifer (i.e., transmissivity and specific yield). Most relevantly to the current study, they found that daily recharge rates at the Walnut Creek watershed may be a white noise process.…”