Estimating uncertainty in streamflow and solute fluxes at the Hubbard Brook Experimental Forest, New Hampshire, USA

Stream fluxes are commonly reported without a complete accounting for uncertainty in the estimates, which makes it difficult to evaluate the significance of findings or to identify where to direct efforts to improve monitoring programs. At the Hubbard Brook Experimental Forest in the White Mountains of New Hampshire, USA, stream flow has been monitored continuously and solute concentrations have been sampled approximately weekly in small, gaged headwater streams since 1963, yet comprehensive uncertainty analyses have not been reported. We propagated uncertainty in the stage height–discharge relationship, watershed area, analytical chemistry, the concentration–discharge relationship used to interpolate solute concentrations, and the streamflow gap-filling procedure to estimate uncertainty for both streamflow and solute fluxes for a recent 6-year period (2013–2018) using a Monte Carlo approach. As a percentage of solute fluxes, uncertainty was highest for NH₄⁺ (34%), total dissolved nitrogen (8.8%), NO₃⁻ (8.1%), and K⁺ (7.4%), and lowest for dissolved organic carbon (3.7%), SO₄²⁻ (4.0%), and Mg²⁺ (4.4%). In units of flux, uncertainties were highest for solutes in highest concentration (Si, DOC, SO₄²⁻, and Na⁺) and lowest for those lowest in concentration (H⁺ and NH₄⁺). Laboratory analysis of solute concentration was a greater source of uncertainty than streamflow for solute flux, with the exception of DOC. Our results suggest that uncertainty in solute fluxes could be reduced with more precise measurements of solute concentrations. Additionally, more discharge measurements during high flows are needed to better characterize the stage-discharge relationship. Quantifying uncertainty in streamflow and element export is important because it allows for determination of significance of differences in fluxes, which can be used to assess watershed response to disturbance and environmental change.