Simulation of the shallow aquifer in the vicinity of Silver Lake, Washington County, Wisconsin, using analytic elements

Shallow ground-water flow in the vicinity of Silver Lake, Washington County, Wisconsin, was investigated to develop an understanding of the hydrology of the shallow aquifer, define a water balance for the lake, delineate ground-water recharge areas for the lake, and to estimate solute flux toward the lake. A single-layer, steady-state, analytic-element model was used to simulate shallow ground-water flow. Regional model parameters include a recharge rate of 4 inches per year, hydraulic conductivity of 50 feet per day and a model base of 800 feet above sea level. A model inhomogeneity was added to represent deviations from these regional values for an area roughly coincident with the Kettle Moraine Area that trends through the study area. Model calibration was accomplished by varying the regional parameter values and those of the inhomogeneity through trial-and-error to determine a best-fit match between simulated and measured values for head and streamflow targets. There was no change to the regional parameter values as a result of calibration, however, the calibrated values for the inhomogeneity are: recharge rate of 12 inches per year, hydraulic conductivity of 20 feet per day, and a model base of 900 feet. These changes represent a four- to five-fold reduction in transmissivity within the inhomogeneity as compared to the regional model.

A Silver Lake water budget was defined using both published hydrologic data and simulations using the calibrated model. Model simulations show that 1.08 cubic feet per second of ground water enters Silver Lake on the upgradient (primarily western) side and 0.08 cubic feet per second recharges to ground water on the downgradient (primarily eastern) side. Net precipitation (precipitation minus evaporation) on the lake is 0.04 cubic feet per second. Collectively, these water-budget terms provide a residual value of 1.04 cubic feet per second flow to Silver Creek at the north end of Silver Lake, which is a very good match to the range of measured flow (0.7 to 5.2 cubic feet per second). Ground-water recharge areas for Silver Lake are largely on the western side of the lake. The recharge area for the northern two-thirds of Silver Lake is west toward Big Cedar Lake. Assuming a porosity of 20 percent, model results indicate that the 50-year time-of-travel for recharge to Silver Lake does not extend to Big Cedar Lake. The recharge area for the southern one-third of Silver Lake is west toward Little Cedar Lake. Model results indicate that time of travel for recharge to Silver Lake from Little Cedar Lake is about 15 to 20 years. For travel times greater than 15 or 20 years, the ground-water recharge area for Little Cedar Lake and inflow from Big Cedar Lake also should be considered recharge affecting Silver Lake. Solute flux toward Silver Lake was calculated based on simulated ground-water flux and measured concentrations in the upgradient piezometers and observation wells.