Bias and variance of some estimators of suspended sediment load

Abstract

Walling & Webb (1981) made empirical comparisons amongst a number of methods for the estimation of suspended sediment loads. This paper presents expressions for the means and variances of three of the estimates compared by Walling & Webb, on the assumption that suspended sediment concentration, c, and mean daily discharge, q, are bivariate lognormally distributed. With this assumption, not inconsistent with the literature and with data, one of the three estimates is unbiased and the other two are biassed, the bias being an exponential function of the correlation and standard deviations in the lognormal distribution. This confirms the empirical finding of Walling & Webb and supports theoretical results of Ferguson (1987) which were established without distributional assumptions. Expressions for the variances of the three estimators of suspended sediment loads also confirm the empirical result of Walling & Webb, the unbiassed estimate having variance of order 1/n whilst the biassed estimates have variances of order 1/n².