Stream Nutrient Load and Concentration Estimation From Minimal Measurements

High‐resolution measurements of nutrients in rivers are vital to assess water quality and catchment material balances. Yet, such measurements are often cost‐prohibitive. To improve sampling efficiency, data‐driven sparse sensing (DSS) is proposed to recover high‐resolution nutrient time‐series from sparse flow and concentration measurements. DSS leverages dimension‐reduction to identify basis functions that optimally represent available data, and analyzes these basis functions to identify optimal times and locations for future measurements. A model trained on high‐resolution flow and concentration measurements from few locations accurately reconstructed nutrient concentration time‐series and annual loads at target sites spanning the Midwest region of the US. Optimal sampling times occurred in spring, while sampling locations were distributed across catchment area and flow. Sparse measurements (20–80 per year) at optimal sampling times and locations were sufficient to accurately estimate nutrient concentrations and loads (error <±2% for NOx; <±9% for total phosphorus). DSS promises to enable cost‐effective water quality monitoring.