Suspended sediment load estimation and the problem of inadequate data sampling: a fractal view

Abstract

Suspended sediment load estimation at high resolutions is an extremely difficult task, because: (1) it depends on the availability of high-resolution water discharge and suspended sediment concentration measurements, which are often not available; (2) any errors in the measurements of these two components could significantly influence the accuracy of suspended sediment load estimation; and (3) direct measurements are very expensive. The purpose of this study is to approach this sampling problem from a new perspective of fractals (or scaling), which could provide important information on the transformation of suspended sediment load data from one scale to another. This is done by investigating the possible presence of fractal behaviour in the daily suspended sediment load data for the Mississippi River basin (at St. Louis, Missouri). The presence of fractal behaviour is investigated using five different methods, ranging from general to specific and from monofractal to multi-fractal: (1) autocorrelation function; (2) power spectrum; (3) probability distribution function; (4) box dimension; and (5) statistical moment scaling function. The results indicate the presence of multi-fractal behaviour in the suspended sediment load data, suggesting the possibility of transformation of data from one scale to another using a multi-dimensional model.