The application of an analytic element model to investigate groundwater-lake interactions at Pretty Lake, Wisconsin

Pretty Lake is a 64 acre, sandy-bottomed groundwater flow-through lake that has a history of hydrologic disturbance. Residents and regulators require a better understanding of lake-groundwater interaction to develop measures to protect the lake's hydrologic system and water quality. A groundwater flow model was constructed as a tool to synthesize field data collected at the site, delineate recharge areas that supply groundwater to the lake, and predict die effect of dredging an adjacent drainage ditch. The one layer, two-dimensional steady-state areal model used analytic element (AE) methods because they are quick to apply and include sophisticated simulation of groundwater-surface water interaction. The model calibrated well to groundwater heads (mean absolute difference = 0.05 m), lake stage (within 0.05 m) and ditch fluxes (mean absolute difference = 0.0023 m³·s⁻¹). Model results showed that a single 1000 m wide recharge area supplies all the groundwater inflow to the lake. In addition, the model predicted that dredging an adjacent ditch by 3.0 m would lower the lake level by 0.31 m. The analytic element model was verified using a widely accepted finite-difference (FD) code; differences were less than ±0.015 m near die lake area and reached a maximum of 0.08 m at far corners of the FD grid. These differences are likely a result of die nodal interpolation inherent to FD techniques and error associated with applying a discrete boundary to die AE infinite aquifer. Although developed recently, AE methods have great potential to aid characterizations of groundwater-lake systems.