Data integration across scales to estimate subsurface nitrate fluxes in agricultural areas

Estimation of nitrate and water fluxes through unsaturated zones and aquifers in agricultural areas involves extrapolation of local-scale data across complex hydrogeochemical landscapes. Nitrate fate and transport in the subsurface has been characterized directly or indirectly at field to sub-regional scales using measurements of dissolved gases and age tracers in groundwater wells. Accurate extrapolation of such information across watersheds is a central goal for holistic management of agricultural nutrients. This presentation gives an overview of a decade of research on numerical and mathematical techniques to characterize subsurface nitrate fluxes from field to regional scale with emphasis on recent advancements in a data integration framework for large regions such as central eastern Wisconsin, and the Great Lakes basin. Calibrated numerical models established the relevance and scale-dependency of typical local-scale parameters for processes such as recharge and nitrate reduction as they are represented at larger scales. The key processes identified by the numerical models were integrated into the "vertical flux method" (VFM), which is a data integration framework combining parameter estimation and mathematical models of the key processes. In applications at field scales, the method reliably reproduces vertical profiles of agricultural chemicals and age tracers. At greater scales, with sparser age-tracers and dissolved gas analyses, Tikhonov regularization was needed for convergence of the parameter estimation procedure. An application of the regularized VFM in Central Wisconsin achieved a close match between observed and estimated concentrations of nitrate and tracers and provided proof of concept for a regionalized VFM. VFM estimates of parameters and predictions at the locations of wells were extrapolated using machine learning applied to the VFM results in combination with landscape parameters such as land-use and hydrogeochemical properties. In the most recent study of the Great Lakes Basin, a hybrid statistical-mechanistic VFM has been developed that does not require Tikhonov regularization, but rather uses non-linear regression to link the landscape variables to the VFM parameters, and calibrates the regression parameters rather than the VFM parameters to achieve direct estimation of processes across the entire region.