An evaluation of methods for estimating decadal stream loads

Effective management of water resources requires accurate information on the mass, or load of water-quality constituents transported from upstream watersheds to downstream receiving waters. Despite this need, no single method has been shown to consistently provide accurate load estimates among different water-quality constituents, sampling sites, and sampling regimes. We evaluate the accuracy of several load estimation methods across a broad range of sampling and environmental conditions. This analysis uses random sub-samples drawn from temporally-dense data sets of total nitrogen, total phosphorus, nitrate, and suspended-sediment concentration, and includes measurements of specific conductance which was used as a surrogate for dissolved solids concentration. Methods considered include linear interpolation and ratio estimators, regression-based methods historically employed by the U.S. Geological Survey, and newer flexible techniques including Weighted Regressions on Time, Season, and Discharge (WRTDS) and a generalized non-linear additive model. No single method is identified to have the greatest accuracy across all constituents, sites, and sampling scenarios. Most methods provide accurate estimates of specific conductance (used as a surrogate for total dissolved solids or specific major ions) and total nitrogen – lower accuracy is observed for the estimation of nitrate, total phosphorus and suspended sediment loads. Methods that allow for flexibility in the relation between concentration and flow conditions, specifically Beale’s ratio estimator and WRTDS, exhibit greater estimation accuracy and lower bias. Evaluation of methods across simulated sampling scenarios indicate that (1) high-flow sampling is necessary to produce accurate load estimates, (2) extrapolation of sample data through time or across more extreme flow conditions reduces load estimate accuracy, and (3) WRTDS and methods that use a Kalman filter or smoothing to correct for departures between individual modeled and observed values benefit most from more frequent water-quality sampling.