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

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.