Approaches for modeling lake-ground water interactions have evolved significantly from early simulations that used fixed lake stages specified as constant head to sophisticated LAK packages for MODFLOW. Although model input can be complex, the LAK package capabilities and output are superior to methods that rely on a fixed lake stage and compare well to other simple methods where lake stage can be calculated. Regardless of the approach, guidelines presented here for model grid size, location of three-dimensional flow, and extent of vertical capture can facilitate the construction of appropriately detailed models that simulate important lake-ground water interactions without adding unnecessary complexity. In addition to MODFLOW approaches, lake simulation has been formulated in terms of analytic elements. The analytic element lake package had acceptable agreement with a published LAKI problem, even though there were differences in the total lake conductance and number of layers used in the two models. The grid size used in the original LAKI problem, however, violated a grid size guideline presented in this paper. Grid sensitivity analyses demonstrated that an appreciable discrepancy in the distribution of stream and lake flux was related to the large grid size used in the original LAKI problem. This artifact is expected regardless of MODFLOW LAK package used. When the grid size was reduced, a finite-difference formulation approached the analytic element results. These insights and guidelines can help ensure that the proper lake simulation tool is being selected and applied.

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In a typical ground water flow model, lakes are represented by specified head nodes requiring that lake levels be known a priori. To remove this limitation, previous researchers assigned high hydraulic conductivity (K) values to nodes that represent a lake, under the assumption that the simulated head at the nodes in the high-K zone accurately reflects lake level. The solution should also produce a constant water level across the lake. We developed a model of a simple hypothetical ground water/lake system to test whether solutions using high-K lake nodes are sensitive to the value of K selected to represent the lake. Results show that the larger the contrast between the K of the aquifer and the K of the lake nodes, the smaller the error tolerance required for the solution to converge. For our test problem, a contrast of three orders of magnitude produced a head difference across the lake of 0.005 m under a regional gradient of the order of 10(-3) m/m, while a contrast of four orders of magnitude produced a head difference of 0.001 m. The high-K method was then used to simulate lake levels in Pretty Lake, Wisconsin. Results for both the hypothetical system and the application to Pretty Lake compared favorably with results using a lake package developed for MODFLOW (Merritt and Konikow 2000). While our results demonstrate that the high-K method accurately simulates lake levels, this method has more cumbersome postprocessing and longer run times than the same problem simulated using the lake package.

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Numerical models were constructed for simulation of groundwater flow in the Menomonee Valley Brownfield, in Milwaukee, Wisconsin. An understanding of groundwater flow is necessary to develop an efficient program to sample ground water for contaminants. Models were constructed in a stepwise fashion, beginning with a regional, single-layer, analytic-element model (GFLOW code) that provided boundary conditions for a local, eight layer, finite-difference model (MODFLOW code) centered on the Menomonee Valley Brownfield. The primary source of ground water to the models is recharge over the model domains; primary sinks for ground water within the models are surface-water features and the Milwaukee Metropolitan Sewerage District Inline Storage System (ISS). Calibration targets were hydraulic heads, surfacewater fluxes, vertical gradients, and groundwater infiltration to the ISS. Simulation of groundwater flow by use of the MODFLOW model indicates that about 73 percent of recharge within the MODFLOW domain circulates to the ISS and 27 percent discharges to gaining surface-water bodies. In addition, infiltration to the ISS comes from the following sources: 36 percent from recharge within the model domain, 45 percent from lateral flow into the domain, 15 percent from Lake Michigan, and 4 percent from other surface-water bodies. Particle tracking reveals that the median traveltime from the recharge point to surface-water features is 8 years; the median time to the ISS is 255 years. The traveltimes to the ISS are least over the northern part of the valley, where dolomite is near the land surface. The distribution of traveltimes in the MODFLOW simulation is greatly influenced by the effective porosity values assigned to the various lithologies.