Assessing uncertainty in annual nitrogen, phosphorus, and suspended sediment load estimates in three agricultural...

Accurate estimation of constituent loads is important for studies of ecosystem mass balance or total maximum daily loads. In response, there has been an effort to develop methods to increase both accuracy and precision of constituent load estimates. The relationship between constituent concentration and stream discharge is often complicated, potentially leading to high uncertainty in load estimates for certain constituents, especially at longer-term (annual) scales. We used the loadflex R package to compare uncertainty in annual load estimates from concentration vs. discharge relationships in constituents of interest in agricultural systems, including ammonium as nitrogen (NH₄-N), nitrate as nitrogen (NO₃-N), soluble reactive phosphorus (SRP), and suspended sediments (SS). We predicted that uncertainty would be greatest in NO₃-N and SS due to complex relationships between constituent concentration and discharge. We also predicted lower uncertainty with a composite method compared to regression or interpolation methods. Contrary to predictions, we observed the lowest uncertainty in annual NO₃-N load estimates (relative error 1.5-23%); however, uncertainty was greatest in SS load estimates, consistent with predictions (relative error 19-96%). For all constituents, we also generally observed reductions in uncertainty by up to 34% using the composite method compared to regression and interpolation approaches, as predicted. These results highlight differences in uncertainty among different constituents and will aid in model selection for future studies requiring accurate and precise estimates of constituent load.