Use of the Lorenz Curve to Quantify Statistical Nonuniformity of Sediment Transport Rate

Abstract

The Lorenz curve and the Gini index are statistical tools that have been widely used to quantify nonuniformity in economics, ecology, and medicine, but have apparently not been previously applied in hydraulic engineering. In this work, the Lorenz curve was applied to the analysis of sediment transport data from several experiments with natural and lightweight solid particles. The distributions of instantaneous sediment transport rate data have been analyzed, leading to some interesting observations: (1) the values are quite nonuniformly distributed, with a significant proportion of zero values at the lowest sediment transport rates; and (2) the distributions of the values considering only samples with nonzero values are still quite nonuniform; yet the variability of the Gini index with the average sediment transport rate is much smaller than that obtained for the complete data samples, indicating a major role of intermittency in determining the nonuniformity of sediment transport.