Application of Sparse Sensing for Stream Nutrient Monitoring Programs

Abstract. Existing stream nutrient (i.e., nitrogen or phosphorus) monitoring approaches often exhibit low sampling frequency and associated high uncertainty due to financial and maintenance constraints. Data-driven Sparse Sensing (DSS) offers an alternative approach to estimate concentration data at high resolution using fewer measurements. DSS transforms stream data from training locations into a reduced-dimension space and identifies optimal sampling times. These optimal measurements are used to reconstruct high-resolution concentration data at target locations. In this study, we used the DSS framework to estimate stream nutrient concentrations and loads (nitrate nitrite as NOx and total phosphorus as TP) across the US Midwest region, with additional analyses in other hydrologic regions to examine regional variability in optimal sampling times. The modeling approach was designed to address key issues in nutrient monitoring programs, including determining the required size and length of training data and establishing data selection procedures. The base model predicted NOx and TP concentrations and loads with good accuracy (NSE > 0.5, load error < ±4 % for NOx; NSE >0.45, load error < ±10 % for TP) using only 40–60 samples per year (~10–15 % of total measurements). Optimal sampling times were concentrated in spring and early summer in the Midwest but varied across regions. Findings indicated that DSS requires only 2–3 years of training data from either 10–15 regional monitoring locations (NOx and TP) or the target location itself (NOx). This study demonstrates that DSS can be integrated into nutrient monitoring programs to generate high-resolution stream data, estimate loads, and support resource-efficient management decisions.