Optimal Transport for Assessing Nitrate Source-Pathway Connectivity

Excessive nitrate threatens a wide range of water resources, aquatic habitats, and sensitive infrastructure. Despite this problem, tracing a nutrient from its eventual fate back to its origin remains an elusive challenge due to heterogeneity in how nutrient sources and hydrologic pathways are connected. Typically, this problem is underdetermined (i.e., too many unknowns, not enough equations) and cannot be solved with existing methodologies. The theory of optimal transport allows for the solution of underdetermined systems, and here we construct a novel formulation for its use in water quality modeling. Our objective was to develop an optimal transport modeling framework—coupled to Bayesian source unmixing, loadograph pathway separation, and geospatial connectivity analysis—to apportion nitrate loading from three sources (soil, fertilizer, and manure) across three pathways (quick, intermediate, and slow), resulting in nine possible source-pathway couplings (soil-quick, soil-intermediate, …, manure-slow). We apply this model to a 30 month elemental (NO₃⁻) and isotopic (δ¹⁵N and δ¹⁸O) nitrate data set from a karst watershed in Kentucky, USA. Modeling results indicate that—of the nine possible source-pathway couplings—nearly 60% of nitrate export is facilitated by just three: fertilizer-quick (16.4%), manure-intermediate (15.4%), and soil-slow (27.2%). Further, we reinforce the need to explicitly consider heterogeneity in source-pathway connectivity as homogeneous assumptions lead to erroneous inferences. The applicability of the model, its input requirements, and transferability to other sites is discussed. Lastly, we simulated two land management scenarios (field buffers and septic repair) and demonstrate how optimal transport can be used to test nutrient reduction strategies.