Precise Confidence Intervals for Annual Riverine Constituent Loads

― Based on low-frequency routine water quality monitoring ―

Abstract

A method for calculating the uncertainty of estimates of the riverine constituent loads, which comprise a major part of the material supply from the terrestrial area to the receiving waters, has not been established. In this paper, we propose the bias-corrected regression estimator that combines the Horvitz-Thompson estimator with the rating curve method as an asymptotically unbiased and precise river load estimator based on a small-size sample. In addition, confidence intervals for the proposed estimator are also proposed as a precise confidence interval. The central 95% confidence interval of annual river load by the proposed method was evaluated in terms of the bracketing probability of the true value and the width of the confidence interval, using monthly routine sampling strategy based on 173 daily water quality data sets from nine watersheds in the United States. The results demonstrate that the proposed method can provide more precise intervals, with appropriate coverage of the true loads, than the previously proposed interval based on the bootstrap-t intervals of the log-transformed Horvitz-Thompson estimator.