Factors affecting the efficiency of some estimators of fluvial total phosphorus load

Abstract

The accuracy of estimating total phosphorus (TP) loads to receiving waters usually is constrained by availability of concentration data, as discharge (flow) data normally are comparatively abundant. Using 4 years of daily observations from three tributaries to the Great Lakes (Grand, Saginaw, and Sandusky Rivers), annual TP loads were tested for accuracy by five methods, including regression, ratio, and robust estimators. Monte Carlo methods were employed to simulate replicated flow‐stratified sampling of the datasets with various allocations of samples to flow strata. Each of the load calculation methods was applied to each group of simulated samples, and response was quantitated as load estimation error (computed minus “true” load). The results show the most consistently accurate estimator was Beale's stratified ratio estimator. It was, however, the only stratified estimator tested and should have been more accurate. Most accurate of the unstratified estimators was a straightforward least squares regression (log‐log) method. The response of estimation bias to flow cut point and sample allocation manipulations indicated (1) beneficial results generally (but not always) obtained from high flow weighting of sampling and (2) postsampling stratification generally may yield improved accuracy for load estimation and deserves additional research.