Evaluating sampling efficiency when estimating sediment source contributions to suspended sediment in rivers by fingerprinting

A general method is proposed which measures the increase in uncertainty when sampling effort is reduced in sediment fingerprinting. The method gives quantitative measures of how reduced sampling of material in one of the source areas, and/or of suspended sediment in streams, increases the uncertainties in the proportions of sediment contributed from the sources. Because the proportions of sediment contributed by the source areas must add to one, standard errors of the estimated proportions cannot be used as the usual measures of uncertainty: the paper uses instead the volume of the joint 95% confidence region for the estimated proportions. The paper shows how the uncertainty in this volume changes as numbers of suspended sediment samples, and the numbers of samples collected from cropped fields, are reduced by successive steps from 24 (20, in the case of cropped fields) to 16, 12, 8, 4 and 2 samples. As expected, uncertainty increases rapidly as the number of samples - whether of suspended sediment or from cropped fields - is reduced drastically. The pattern of increasing uncertainty is similar both for reductions in suspended sediment sampling, and for reduced sampling from cropped areas. When the number of suspended sediment samples, and the number of samples from cropped fields, are reduced to the same values, the increase in uncertainty from fewer suspended sediment samples was always slightly greater than the increased uncertainty from the reduced sampling of cropped areas, although this finding took no account of differences in the costs of field sampling and laboratory analysis. Copyright (c) 2016 John Wiley & Sons, Ltd.