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.
The series of manuals on techniques describes procedures for planning and executing specialized work in water-resources investigations. The material is grouped under major subject headings called "books" and further subdivided into sections and chapters. Section A of Book 3 is on surface water. The unit of publication, the chapter, is limited to a narrow field of subject matter. This format permits flexibility in revision and publication as the need arises. Chapter Al8 deals with the application of dye and gas tracers for the measurement of stream reaeration coefficients. Provisional drafts of chapters are distributed to field offices of the U.S.
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