Uncertainty in nitrate load calculations evaluated using Monte Carlo simulations based on in-situ nitrate sensors in two Danish headwater streams

• HF sensors used to measure NO3-N in two Danish headwater streams over two years • Monte Carlo assessments of NO3-N loads to explore the uncertainty of grab sampling. • Load uncertainty of infrequent sampling strategies was high for monthly loads. • Periods with high RBI (e.g., storm events) significantly increased uncertainty in NO3-N load estimates. This study used high-frequency (HF) nitrate-nitrogen (NO3-N) sensor data to explore the uncertainty of calculating NO3-N loads in two headwater streams (Horndrup and Lyby-Grønning) with infrequent sample collection. Accurate annual and monthly N load estimates are crucial for cost-efficient management of N in catchments and for correct calibration and validation of catchment models like SWAT. Ultraviolet (UV) NO3-N sensors were installed in the two agricultural headwater streams for two hydrological years (June 2021 to May 2023) to measure NO3-N concentrations every minute. The cleaned dataset was used to investigate NO3-N load estimates using a Monte Carlo approach, with 1000 simulations for five infrequent sampling strategies: daily, weekly, fortnightly, 18 annual samples, and monthly samples. Bias (Flux Bias Statistic), precision (standard deviation), and total uncertainty (RMSE) were calculated for the annual and monthly NO3-N loads. Richards-Baker Flashiness Index (RBI) was used to explore the influence of hydrology on differences between HF and infrequent sampling. The sampling strategy needed to meet a bias and achieve RMSE <2 %, 5 %, and 10 % for monthly loads was explored. The uncertainty of the load estimates increased with fewer grab samples. The bias and RMSE of the annual load estimates from the five strategies were <±7.7 % and <10.3 %, respectively. Monthly NO3-N loads had higher uncertainties, with average bias and RMSE of ±4 % and 15 % (max. −13 % and 28 %) in Horndrup Stream and ±7 % and 27 % (max. 89 % and 194 %) in Lyby-Grønning Stream. In Horndrup Stream, a significant negative linear relationship between the bias of monthly NO3-N loads and RBI indicated higher underestimation with more storm events. In Lyby-Grønning Stream, precision decreased with higher RBI.