The validity of a simple statistical model for estimating fluvial constituent loads: An Empirical study involving nutrient loads entering Chesapeake Bay

We consider the appropriateness of “rating curves” and other log linear models to estimate the fluvial transport of nutrients. Split-sample studies using data from tributaries to the Chesapeake Bay reveal that a minimum variance unbiased estimator (MVUE), based on a simple log linear model, provides satisfactory load estimates, even in some cases where the model exhibited significant lack of fit. For total nitrogen (TN) the average difference between the MVUE estimates and the observed loads ranges from −8% to + 2% at the four sites. The corresponding range for total phosphorus (TP) is −6% to +5%. None of these differences is statistically significant. The observed variability of the MVUE load estimates for TN and TP, which ranges from 7% to 25% depending on the case, is accurately predicted by statistical theory.