Prioritizing Irrigation‐System Upgrades to Maximize Improvements to Agricultural Drain‐Network Water Quality: A Graph‐Theoretic Approach

We develop and demonstrate an approach to optimally prioritize fields for irrigation‐system upgrades to improve agricultural‐drain discharge water quality. The approach accounts for the attenuation of pollutants transported along complex drain networks from fields to drain‐network outlets. The approach produces a Pareto‐optimal cost curve of irrigation‐system upgrade combinations that compromise between maximizing the reduction of drain‐outlet loads and minimizing upgrade implementation costs. The approach utilizes a graph‐theoretic data structure to organize drain‐network data, route drain‐network flow paths, and formulate objectives and constraints for multi‐objective optimization. Due to the linearity of the objective functions and constraints, Pareto‐optimal solutions are obtained along the cost curve by prioritizing fields by decreasing load‐reduction/cost ratio (pollutant load‐reduction per cost). Multi‐objective optimization will identify additional Pareto‐optimal solutions along the cost curve providing additional compromises. The approach allows for a computationally efficient prioritization, providing a level of complexity that is able to incorporate commonly available data. The cost curve is highly sensitive to the pollutant attenuation coefficient, with higher attenuation coefficients resulting in low sensitivity of load reduction to cost. While the focus of this work is on irrigation‐system upgrades, there are other conservation actions and/or land‐use change scenarios that this method could also prioritize. Analyses of this nature could prove valuable in improving the allocation of limited conservation funding and/or developing cost‐effective water quality trading programs. We demonstrate the approach on a collection of drain networks around Grand View, Idaho, USA with the objective to reduce total phosphorus loads to the Snake River. Plain Language Summary Upgrading agricultural irrigation systems can improve water quality by reducing nutrient and sediment pollution entering adjacent waterways. For example, upgrading from flooding of fields to sprinkler irrigation results in significantly less water leaving fields, resulting in less nutrient and sediment pollution. However, the benefits and costs associated with irrigation‐system upgrades on individual fields depend on many variables, such as crop type, slope, soil type, etc. In this study, we develop an approach that considers these variables to prioritize irrigation upgrades that maximize