Optimal Transport for Assessing Nitrate Source‐Pathway Connectivity

Abstract

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 (NO 3 −) and isotopic (δ 15 N and δ 18 O) 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.

Nitrate Hysteresis as a Tool for Revealing Storm‐Event Dynamics and Improving Water Quality Model Performance

“…Prior work in this basin, using water isotopes (δ 2 𝐴𝐴 HH 2 O and δ 1 8 𝐴𝐴 OH 2 O ) and rainfall-discharge cross-covariance analysis, also showed that spring discharge responds to rainfall input on the same day that it occurs . Further, high-resolution sampling of storms events in the basin for nitrate stable isotopes (δ 1 5 𝐴𝐴 NNO 3 and δ 1 8 𝐴𝐴 ONO 3 ) showed that maximum nitrate concentration lags peak spring discharge and likely originates from the soil and epikarst zones (Husic et al, 2020). Other studies also corroborate the idea that the greatest nitrate concentrations may be reflective of a soil-nitrate pool that becomes highly connected to the epikarst during wet conditions (Zhang et al, 2020).…”

“…Prior work in this basin, using water isotopes ( δ 2 $${\mathrm{H}}_{{\mathrm{H}}_{2}\mathrm{O}}$$ and δ 18 $${\mathrm{O}}_{{\mathrm{H}}_{2}\mathrm{O}}$$) and rainfall‐discharge cross‐covariance analysis, also showed that spring discharge responds to rainfall input on the same day that it occurs (Husic, Fox, Adams, Backus, et al., 2019; Husic, Fox, Adams, Ford, et al., 2019). Further, high‐resolution sampling of storms events in the basin for nitrate stable isotopes ( δ 15 $${\mathrm{N}}_{{\mathrm{N}\mathrm{O}}_{3}}$$ and δ 18 $${\mathrm{O}}_{{\mathrm{N}\mathrm{O}}_{3}}$$) showed that maximum nitrate concentration lags peak spring discharge (Husic, Fox, Adams, Ford, et al., 2019) and likely originates from the soil and epikarst zones (Husic et al., 2020). Other studies also corroborate the idea that the greatest nitrate concentrations may be reflective of a soil‐nitrate pool that becomes highly connected to the epikarst during wet conditions (Zhang et al., 2020).…”

Degree of Anthropogenic Land Disturbance Controls Fluvial Sediment Hysteresis

“…Recent radioisotope tracing of sediment in Johnson County supports this idea as bank sediment constitutes, on average, 59% (Kill Creek) to 73% (Indian Creek) of the fluvial sediment load . This bank material is mobilized using runoff from impervious surfaces and construction sites − and is then routed to the mainstream corridor by way of dense urban roadway drainage (2–3 times greater roadway density than in rural basins, Table ), where sediment connectivity remains elevated. , …”

“…45 This bank material is mobilized using runoff from impervious surfaces and construction sites 46−48 and is then routed to the mainstream corridor by way of dense urban roadway drainage (2−3 times greater roadway density than in rural basins, Table 1), where sediment connectivity remains elevated. 44,49 Wastewater treatment facility discharge, which is greatest in the studied urban watersheds, provides a constant source of water to keep material entrained and sediment transport capacity high. 50,51 For example, in the most-urban Indian Creek, where plant discharges are 7 times greater than in any of the other watersheds (Table 1), permitted discharge constitutes up to an average of 80% of streamflow (Figure S5), providing significant energy for transport.…”

Predicting Potential Climate Change Impacts on Groundwater Nitrate Pollution and Risk in an Intensely Cultivated Area of South Asia

“…The occurrence of elevated nitrate concentrations (GW NO 3 ) in groundwater is a persistent concern in numerous countries around the globe, especially in shallow aquifers beneath highly agrarian areas − and soils offering higher permeability . Elevated nitrate above the permissible limit of 45 mg/L is a major groundwater problem in agrarian South Asia as well as in India. − Although different natural and human practices like deposition from the atmosphere, , crop nitrogen fixation, use of animal manure, sewage application in agriculture, , and faulty urban sewages , are argued to contribute to nitrate concentrations, the excess use of chemical fertilizers is perceived as the primary source of high GW NO 3 . , Studies were conducted to limit nitrate leaching from the source by controlling fertilizer applications, − tracking nitrate movement pathways, − and developing treatment strategies including biological methods. − Despite these studies, encounters with high concentrations of GW NO 3 in the global aquifers are still a persistent concern to policymakers …”