Transient and steady-state flow models of a ground-water and lake system: Trout Lake Basin, northern Wisconsin
Most lakes in Wisconsin have are connected with the ground-water system. Ground water and lakes act as a coupled system in which ground-water flux affects lake levels, and lake levels affect ground-water levels and flux. Ground-water fluxes are difficult to measure but can be very important to the hydrology, chemistry, and biology of lakes. Numerical ground-water models are a useful method for calculating the ground-water component of lake budgets. Nevertheless, standard ground-water models are limited in their ability to model ground-water and lake systems because they assume that surface water levels are known inputs to the model. In standard practice, surface waters are commonly represented as fixed head boundary conditions. In this study, the recently developed Lake Package code was used in conjunction with MODFLOW to perform transient simulations of ground-water and lake levels and fluxes in the Trout Lake Basin in northern Wisconsin. The Lake Package calculates lake levels based on a volumetric water balance including precipitation, evaporation, surface flow, and ground-water flux. The calculated lake level is then used to calculate heads and ground-water fluxes for the subsequent time step. The modeling application reported here also uses an analytic element screening model to provide constant flux boundary conditions around the perimeter of the model. Fourteen lakes in the basin were modeled using the Lake Package. The model was calibrated to time series of lake levels in five of the lakes (1984-97), ground-water heads measured in three different years (1985, 1991, and 1997), independent estimates of average ground-water inflow rate to nine of the lakes, and base-flow estimates for 1991 through 1994. Climate sensitivity tests verified that water levels and flux in seepage lakes near ground-water divides are most sensitive to seasonal and climatic variability. Changes in ground-water inflow rate to lakes from year to year may be similar in magnitude to seasonal changes. Attempted long-term simulations (1959-83) revealed that the model is prone to instability. The source of the instability is unknown but does not appear to be in the lake stage solution.