STATISTICAL CHARACTERISTICS OF SOME ESTIMATORS OF SEDIMENT AND NUTRIENT LOADINGS

This paper explores some of the statistical characteristics of estimators of sediment load which require the integration over time of the product of a concentration (c) with a discharge (q). Using a bivariate lognormal distribution for the discrete variables (ci, qi), (i = 1, …, n), approximate confidence intervals are calculated for an unbiassed estimator of sediment yield, and the exact sampling distribution of the estimator is obtained by numerical integration of a Fourier transform. This permits an investigation of the rapidity with which the estimator tends to normality. Provided the data sequences are serially independent, the same technique can be used to obtain the distribution of an estimator without the assumption of bivariate lognormality. Some characteristics of an “extrapolation” estimate of sediment yield are derived, in which power law regression is used to estimate concentration from discharge when measurements of the latter are more plentiful than the former. Subject to model assumptions, the extrapolation estimate is found to underestimate the true sediment load, although its variance is smaller; this confirms results obtained by other workers who use empirical sampling and alternative theoretical approaches. Copyright 1990 by the American Geophysical Union.