A Hybrid Statistical-Mechanistic Model for Forecasting Groundwater Quality in the Great Lakes Basin

Unsaturated zone travel time (UT) and fraction of applied nitrogen leaching (nitrogen leaching concentration factor, FCN) to groundwater are two important factors that affect groundwater quality. The goal of this study was to map these and other related factors to unsampled areas across the Great Lakes Basin region by integrating landscape variables such as landuse and soil type with a process model. The "vertical flux method" (VFM) is a process model that estimates sampled groundwater tracer concentrations (CFCs, tritium, helium) based on groundwater and well parameters such as recharge, reaction rates, and sample depth. We developed a "hybrid" statistical approach that estimates UT and FCN by combining the VFM with a nonlinear regression to link adjustable VFM parameters (recharge, reaction rates) to readily available landscape variables. The composite hybrid model features (1) estimation of the VFM parameters with a separate nonlinear regression model comprising landscape variables followed by (2) a forward run of the VFM model to estimate groundwater tracer concentrations. Model 1 regression parameters were estimated with PEST (model-independent parameter estimation and uncertainty analysis software) using finite-difference approximation and singular-value decomposition, based on model 2 outputs and sampled groundwater tracers including oxygen, nitrate, CFCs, tritium, and helium. Preliminary runs of the hybrid, composite model reduced the PEST objective function by approximately 90 percent. Parameter identifiability was computed as a measure of the ability to resolve each model 1 landscape regression coefficient based on the available tracer data. Landscape regression coefficients related to recharge and the nitrogen leaching concentration factor had the highest identifiabilities in general, while mobile water content and the oxygen concentration at which denitrification begins had the lowest. Individual landscape regression coefficients' identifiabilities were variable among each VFM parameter regression. The current work displays the feasibility of the hybrid model and the potential for improved regional parameter estimates and increased understanding of their relationship to landscape variables.