Statistical Characterization of Grain-Size Distributions in Sandy Fluvial Systems

Abstract

Measured particle-size distributions are commonly reduced to one characteristic value (e.g., median grain diameter) that is used in sediment transport modeling and other analyses. These values are often interpolated from empirical distributions or from fitted distributions, usually assuming that observed grain-size populations are adequately represented by Gaussian or Normal distributions. In order to investigate the implications of this approach, we (1) statistically characterize grain-size distributions in samples of bed-material load, suspended load, and slackwater deposits from the sand-bedded Calamus, North Loup, and Niobrara rivers (Nebraska, USA), and (2) explore the potential impact of misfitting distributions on estimating percentile grain diameters. Although log-normal distributions are commonly used to characterize complete grain-size distributions in sedimentary systems, in this study, samples of transported sediment are best modeled with log-hyperbolic distributions, and slackwater deposits are best fitted by mixtures of distributions. Despite large overlaps in the grain sizes of bed-material-load and suspended-load samples, estimated parameters of fitted log-hyperbolic distributions show consistent differences between these samples across all rivers. Samples of bed-material load have higher modes and positive (coarse-grained) asymmetry, whereas suspended-load samples have lower modes and weaker asymmetry. Because it is has a general form, the log-hyperbolic distribution should adequately characterize unimodal grain-size samples because its parameters can yield both normal-shaped distributions as well as asymmetric distributions. In all three rivers, slackwater deposits contain the entire range of grain sizes present in suspension as well as a significant component of very fine-grained (< 0.02 mm) material that is not present in suspended-sediment samples. This suggests some degree of fractionated deposition of suspended sediment in areas of near-zero flow velocities. Ultimately, fitting parametric grain-size distributions to grain-size data can be a useful way to find effective particle-size values for use in sediment transport modeling and other studies. However, particularly with asymmetric grain-size distributions, fitting log-normal distributions to data may result in errors of estimated percentile grain sizes, which should be considered in studies relying on characteristic grain-diameter values.