Assessing uncertainty in annual nitrogen, phosphorus, and suspended sediment load estimates in three agricultural streams using a 21-year dataset


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.

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We are especially grateful for the assistance from Hueston Woods State Park personnel for allowing us to install and operate gauging stations within the park and for their cooperation throughout the study period. We also thank the many students and research associates at Miami University who participated in data collection and analysis over the 21 years, especially Annie Bowling, Alan Christian, Janelle Duncan, Jenifer Headworth, Lesley Knoll, Elizabeth Mette, Peter Levi, and Tera Ratliff. We thank M. Gonzalez, T. Willimson, A. Rock, T. Fisher, and M. Barrett for their helpful comments, and two anonymous reviewers for improvements to this manuscript. Concentration and discharge data for Four Mile Creek, Little Four Mile Creek, and Marshall’s Branch for 1994–2008 are publicly available in Ecological Archives E094-085-D1. Concentration and discharge data for 2009–2014 are available at request of the corresponding author.

Funding information

This research was supported mainly by National Science Foundation awards 9318452, 9726877, 0235755, 0743192, and 1255159 (the latter three awards are from the Long-term Research in Environmental Biology (LTREB) program). Additional support was provided by the Ohio Department of Natural Resources (Division of Parks and Division of Wildlife) and the Miami Valley Resource Conservation and Development District.

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Correspondence to Patrick T. Kelly.

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Kelly, P.T., Vanni, M.J. & Renwick, W.H. Assessing uncertainty in annual nitrogen, phosphorus, and suspended sediment load estimates in three agricultural streams using a 21-year dataset. Environ Monit Assess 190, 91 (2018).

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  • Stream load
  • Loadflex
  • Uncertainty
  • Composite method
  • Nitrate
  • Suspended sediments