Metamodeling and mapping of nitrate flux in the unsaturated zone and groundwater, Wisconsin, USA

Nitrate contamination of groundwater in agricultural areas poses a major challenge to the sustainability of water resources. Aquifer vulnerability models are useful tools that can help resource managers identify areas of concern, but quantifying nitrogen (N) inputs in such models is challenging, especially at large spatial scales. We sought to improve regional nitrate (NO3−) input functions by characterizing unsaturated zone NO3− transport to groundwater through use of surrogate, machine-learning metamodels of a process-based N flux model. The metamodels used boosted regression trees (BRTs) to relate mappable landscape variables to parameters and outputs of a previous “vertical flux method” (VFM) applied at sampled wells in the Fox, Wolf, and Peshtigo (FWP) river basins in northeastern Wisconsin. In this context, the metamodels upscaled the VFM results throughout the region, and the VFM parameters and outputs are the metamodel response variables. The study area encompassed the domain of a detailed numerical model that provided additional predictor variables, including groundwater recharge, to the metamodels. We used a statistical learning framework to test a range of model complexities to identify suitable hyperparameters of the six BRT metamodels corresponding to each response variable of interest: NO3− source concentration factor (which determines the local NO3− input concentration); unsaturated zone travel time; NO3− concentration at the water table in 1980, 2000, and 2020 (three separate metamodels); and NO3− “extinction depth”, the eventual steady state depth of the NO3− front. The final metamodels were trained to 129 wells within the active numerical flow model area, and considered 58 mappable predictor variables compiled in a geographic information system (GIS). These metamodels had training and cross-validation testing R2 values of 0.52 - 0.86 and 0.22 - 0.38, respectively, and predictions were compiled as maps of the above response variables. Testing performance was reasonable, considering that we limited the metamodel predictor variables to mappable factors as opposed to using all available VFM input variables. Relationships between metamodel predictor variables and mapped outputs were generally consistent with expectations, e.g. with greater source concentrations and NO3− at the groundwater table in areas of intensive crop use and well drained soils. Shorter unsaturated zone travel times in poorly drained areas likely indicated preferential flow through clay soils, and a tendency for fine grained deposits to collocate with areas of shallower water table. Numerical estimates of groundwater recharge were important in the metamodels and may have been a proxy for N input and redox conditions in the northern FWP, which had shallow predicted NO3− extinction depth. The metamodel results provide proof-of-concept for regional characterization of unsaturated zone NO3− transport processes in a statistical framework based on readily mappable GIS input variables.