Stochastic Analysis and Numerical Simulations of Hydraulic Head and Baseflow in Heterogeneous Media under Spatial-Temporal Random Recharge

Stochastic analysis and numerical simulations were carried out to study the temporal scaling in the time series of water table fluctuations in a one-dimensional heterogeneous aquifer under spatial-temporal random recharge. It was found in our previous study that scaling of water table fluctuations may exist and the fractal dimensions varies over space based on spectral analyses of the hourly hydraulic head (h) data observed over a four-year period at seven monitoring wells in the Walnut Creek watershed in Iowa. The estimated baseflow in the Walnut Creek and other four watersheds has temporal scaling, but there exits two distinct slopes with a break at about 30 days in the log frequency and log power spectral density plot. It was also found that the hydraulic head in an aquifer may fluctuate as a fractal in time in response to either a white-noise or a fractal recharge process, depending on how quickly the hydraulic head responds to recharge events and the physical parameters of the aquifer (i.e., transmissivity and specific yield). Numerical simulations were conducted to verify whether or not the hydraulic head and flux (baseflow) behave as fractal processes and if their fractal dimensions vary spatially, using a 1-D transient groundwater flow in heterogeneous aquifer subject to temporal and spatial random recharge (white noise in time and exponential covariance in space). The simulation results confirm the previous findings. We also derived the moment equations which were solved to obtain the mean hydraulic head and mean flux (baseflow). The spectrum for mean hydraulic heads and flux (baseflow) are plotted and analyzed to test our hypotheses and the effects of aquifer heterogeneity and spatial-temporal random recharge process on the head fluctuations and spectrum are presented and discussed.