The grain size distribution function of suspended load in the lower Yellow River

Abstract

The log-normal distribution function (LNDF) and Weibull cumulative density function (WCDF) represent two prevalent approaches for characterizing sediment grain size distributions. This study analyzes annual average suspended load grain size data (standardized to equivalent settling diameters) from seven hydrological stations in the lower Yellow River (LYR) spanning 1962-2020, employing various distribution functions for grain size fitting. Results demonstrate that the Weibull probability density function (WPDF) offers significant advantages over both LNDF and WCDF in terms of fitting accuracy, parameter stability, simplicity, and practical applicability for characterizing suspended load grain size distributions in the LYR. Based on these findings, universal formulas were developed for the suspended load grain size distribution across the seven stations and the entire lower reaches, yielding determination coefficients (R²) exceeding 0.9. These formulas can be applied to estimate suspended load grain size in data-scarce cross-sections. The existence of such universal formulas suggests that interannual fluctuations in suspended load grain size in the LYR are constrained within a limited range, suggesting that sediment grain size may represent an inherent property of the river channel. This limited variability may be attributed to the fact that sediments in the LYR are primarily derived from a relatively fixed source region—the Loess Plateau. The observed stability over an extended period also offers valuable insights into the fundamental properties of river systems and their long-term behavior.

Keywords

grain size / lognormal distribution / suspended load / the lower Yellow River (LYR) / Weibull cumulative density function (WCDF) / Weibull probability density function (WPDF)

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