BLAS AND PRECISION OF PERCENTILES OF BULK GRAIN-SIZE DISTRIBUTIONS

Percentiles such as D-50 and D-84, calculated from weights retained on different sieves, are widely used to characterize grain size distribu tions (GSDs) of bulk samples of sedimentary deposits or sediment fluxe s. The sampling variability of such percentiles is not well known, and few sampling guidelines exist for reliable characterization of GSDs. We report results from computer sampling experiments on the variabilit y of sample percentiles in different-sized samples from populations wi th a log-normal GSD by weight and different sorting coefficients. Samp le sizes are scaled by the volume of a median-sized grain so that resu lts can be applied to any log-normal GSD. Sampling is random for the G SD by number that is equivalent to a specified GSD by weight. Results show important differences from standard sampling theory applicable to pebble-count GSDs. In small bulk samples all percentiles, including t he median, are underestimated (more so for smaller samples, coarser pe rcentiles and poorer sorting), and precision does not improve with the square root of sample size until fairly large sample sizes are exceed ed. Non-dimensional equations fitted by eye to the results give good a pproximations to expected bias and precision in any percentile from 50 to 95 for any given sample size and population sorting coefficient. T hey are inverted to estimate the sample size required to avoid signifi cant bias, or achieve specified precision, in any percentile of intere st given estimates of the population D-50 and sorting coefficient. Tar get sample sizes are sometimes considerably smaller, but in other circ umstances larger, than suggested by previous guidelines relating to es timation of the entire grain size distribution. Bias is likely in smal l samples of river bedload and good precision requires very large samp les of poorly sorted gravel deposits. (C) 1997 John Wiley & Sons, Ltd.