Estimating uncertainty in ambient and saturation nutrient uptake metrics from nutrient pulse releases in stream ecosystems

Nutrient spiraling is an important ecosystem process characterizing nutrient transport and uptake in streams. Various nutrient addition methods are used to estimate uptake metrics; however, uncertainty in the metrics is not often evaluated. A method was developed to quantify uncertainty in ambient and saturation nutrient uptake metrics estimated from saturating pulse nutrient additions (Tracer Additions for Spiraling Curve Characterization; TASCC). Using a Monte Carlo (MC) approach, the 95% confidence interval (CI) was estimated for ambient uptake lengths (S_w-amb) and maximum areal uptake rates (Umax) based on 100,000 datasets generated from each of four nitrogen and five phosphorous TASCC experiments conducted seasonally in a forest stream in eastern Tennessee, U.S.A. Uncertainty estimates from the MC approach were compared to the CIs estimated from ordinary least squares (OLS) and non-linear least squares (NLS) models used to calculate S_w-amb and Umax, respectively, from the TASCC method. The CIs for S_w-amb and U_max were large, but were not consistently larger using the MC method. Despite the large CIs, significant differences (based on non-overlapping CIs) in nutrient metrics among seasons were found with more significant differences using the OLS/NLS vs. the MC method. We suggest that the MC approach is a robust way to estimate uncertainty, as the calculation of S_w-amb and U_max violates assumptions of OLS/NLS while the MC approach is free of these assumptions. The MC approach can be applied to other ecosystem metrics that are calculated from multiple parameters, providing a more robust estimate of these metrics and their associated uncertainties.