Estimating constituent loads

Water Resources Research
By: , and 



Several recent articles have called attention to the problem of retransformation bias, which can arise when log linear regression models are used to estimate sediment or other constituent loads. In some cases the bias can lead to underestimation of constituent loads by as much as 50%, and several procedures have been suggested for reducing or eliminating it. However, some of the procedures recommended for reducing the bias can actually increase it. This paper compares the bias and variance of three procedures that can be used with log linear regression models: the traditional rating curve estimator, a modified rating curve method, and a minimum variance unbiased estimator (MVUE). Analytical derivations of the bias and efficiency of all three estimators are presented. It is shown that for many conditions the traditional and the modified estimator can provide satisfactory estimates. However, other conditions exist where they have substantial bias and a large mean square error. These conditions commonly occur when sample sizes are small, or when loads are estimated during high-flow conditions. The MVUE, however, is unbiased and always performs nearly as well or better than the rating curve estimator or the modified estimator provided that the hypothesis of the log linear model is correct. Since an efficient unbiased estimator is available, there seems to be no reason to employ biased estimators.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title Estimating constituent loads
Series title Water Resources Research
DOI 10.1029/WR025i005p00937
Volume 25
Issue 5
Year Published 1989
Language English
Publisher American Geophysical Union
Description 6 p.
First page 937
Last page 942