Accuracy and precision of methods for estimating river loads

Abstract

River loads often have to be estimated from continuous discharge data but relatively infrequent sampling of sediment, solute, or pollutant concentrations. Two standard ways of doing this are to multiply mean concentration by mean discharge, and to use a rating curve to predict unmeasured concentrations. Both methods are known from previous empirical studies to underestimate true load. Statistical considerations explain these biases and yield correction factors which can be used to obtain unbiased estimates of load. Simulation experiments with normally‐distributed scatter about log‐linear trends, and sampling experiments using a natural data set, show that the corrected rating curve method has lower sampling variability than other unbiased methods based on average instantaneous load and is thus the recommended procedure when the rating plot is of the assumed form. The precision of all methods increases with sample size and decreases with increasing rating‐curve slope and scatter.

The past and future of phytoplankton in the UK's largest lake, Lough Neagh

“…The load, Lij, was corrected for bias using Ferguson (1987) yielding Lcij, that is Lcij= Lij × exp(2.651sj 2 ) where sj is the estimated standard error of equation (1) for river j. The daily, Ferguson corrected, total loading to the lake from all of the rivers was derived by equation 2:…”

Erosion thresholds and suspended sediment yields, Waipaoa River Basin, New Zealand

“…For the Mangatu the residuals were normally distributed (Kolmorgorov-Smirnov test at 5% significance level) and were constant over the range of gauged discharge, thus the rating curve was adjusted using the factor exp (s2/2) [cf. Ferguson, 1987], where s is the standard error of the LOWESS curve in natural log units. In the case of the Waipaoa River, although the residuals were normally distributed (<<5% significance level), they decreased as discharge increased (Figure 4).…”

Response of Sediment Load to Hydrological Change in the Upstream Part of the Lancang-Mekong River over the Past 50 Years

“…To reduce the statistical bias caused by the de-transformation of the variables from log space to normal space, a correction factor (CF) was proposed to multiply the resulting loads as follow [33]:…”