Measures for Describing the Size Distribution of Sediments

TLDR

Numerous measures describe sediment grain‑size distribution, yet quartile‑based parameters are less significant than those grounded in rigorous statistics, and the lack of standardization hampers cross‑locality comparisons. The study recommends five graphic‑analogue parameters that approximate the commonly used statistical moment measures. These parameters are computed from five percentile diameters (phi 5, phi 16, phi 50, phi 84, phi 95) of the cumulative size‑frequency curve, encompassing mean/median, standard deviation, kurtosis, and two skewness metrics, allowing reconstruction of the curve. Applying these graphic parameters enhances reported data value, often eliminating the need for full mechanical analysis, and although correlation with moment measures weakens with increasing skewness, the first three moments can still be estimated with comparable accuracy across many distributions.

Abstract

Numerous measures are used in the literature to describe the grain-size distribution of sediments. Consideration of these measures indicates that parameters computed from quartiles may not be as significant as those based on more rigorous statistical concepts. In addition, the lack of standardization of descriptive measures has resulted in limited application of the findings from one locality to another. The use of five parameters that serve as approximate graphic analogies to the moment measures commonly employed in statistics is recommended. The parameters are computed from five percentile diameters obtained from the cumulative size-frequency curve of a sediment. They include the mean (or median) diameter, standard deviation, kurtosis, and two measures of skewness, the second measure being sensitive to skew properties of the tails of the sediment distribution. If the five descriptive measures are listed for a sediment, it is possible to compute the five percentile diameters on which they are based (phi 5 , phi 16 , phi 50 , phi 84 , and phi 95 ), and hence five significant points on the cumulative carve of the sediment. This increases the value of the data listed for a sediment in a report, and in many cases eliminates the necessity of including the complete mechanical analysis of the sediment. The degree of correlation of the graphic parameters to the corresponding moment measures decreases as the distribution becomes more skew. However, for a fairly wide range of distributions, the first three moment measures can be ascertained from the graphic parameters with about the same degree of accuracy as is obtained by computing rough moment measures.