Metamodeling for Groundwater Age Forecasting in the Lake Michigan Basin

Abstract

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.