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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Aquitards protect underlying aquifers from contaminants and limit recharge to those aquifers. Understanding the mechanisms and quantity of ground water flow across aquitards to underlying aquifers is essential for ground water planning and assessment. We present results of laboratory testing for shale hydraulic conductivities, a methodology for determining the vertical hydraulic conductivity (K(v)) of aquitards at regional scales and demonstrate the importance of discrete flow pathways across aquitards. A regional shale aquitard in southeastern Wisconsin, the Maquoketa Formation, was studied to define the role that an aquitard plays in a regional ground water flow system. Calibration of a regional ground water flow model for southeastern Wisconsin using both predevelopment steady-state and transient targets suggested that the regional K(v) of the Maquoketa Formation is 1.8 x 10(-11) m/s. The core-scale measurements of the K(v) of the Maquoketa Formation range from 1.8 x 10(-14) to 4.1 x 10(-12) m/s. Flow through some additional pathways in the shale, potential fractures or open boreholes, can explain the apparent increase of the regional-scale K(v). Based on well logs, erosional windows or high-conductivity zones seem unlikely pathways. Fractures cutting through the entire thickness of the shale spaced 5 km apart with an aperture of 50 microns could provide enough flow across the aquitard to match that provided by an equivalent bulk K(v) of 1.8 x 10(-11) m/s. In a similar fashion, only 50 wells of 0.1 m radius open to aquifers above and below the shale and evenly spaced 10 km apart across southeastern Wisconsin can match the model K(v).

Groundwater age is an important indicator of groundwater susceptibility to anthropogenic contamination and a key input to statistical models for forecasting water quality. Numerical models can provide estimates of groundwater age, enabling interpretation of measured age tracers. However, to extend to national‐scale groundwater systems where numerical models are not routinely available, a more efficient metamodeling approach can provide a less precise but widely applicable estimate of groundwater age, trained to make forecasts based on predictor variables that can be measured independent of numerical models. We trained gradient‐boosted regression tree statistical metamodels to MODFLOW/MODPATH‐derived groundwater age estimates in five inset models in the Lake Michigan Basin, USA. Using high‐throughput computing, we explored an exhaustive range of tuning parameters and tested metamodels through cross validation, a 20% holdout, and a round robin approach among the five inset models withholding each inset model from training and testing on the held‐out inset model. Forecast skill—measured by Nash Sutcliffe efficiency—was high for age‐related responses in the 20% hold‐out case (ranging from 0.73 to 0.84). The round robin analysis provided the opportunity to explore extending to unmodeled areas and a greater range of skill indicated the need to evaluate when it is appropriate to apply a metamodel from one region to another. We further explored the ramifications of metamodel simplification achieved through removing predictor variables based on their estimated importance. We found that similar metamodel performance was achievable with a fraction of the candidate set of predictor variables with well construction variables being most important.

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