First-order estimation of stochastic parameters of a sediment transport model

Abstract

First-order approximation techniques for estimating stochastic parameters of a sediment transport model are presented. The non-homogeneous compound Poisson model of Shen-Todorovic eliminating certain idealized assumptions to describe the movement of sediment in natural streams is a revision of the earlier homogeneous model of Einstein-Hubbell-Sayre. However, the complexity of the non-homogeneous model and the difficulty in determining the model parameters has limited its application. The proposed approximation techniques employ the first-order Taylor expansions, with respect to a selected temporal or spatial point by a finite difference, of the cumulative probability distribution function (CDF) of particle displacements. The first-order expansions are divided by the original CDF for further simplification. The simplified forward- and backwardexpansions are numerically solved as a system to evaluate the parameter at the specified point. The non-homogeneous parameters are pursued with successive applications of this procedure to various points. An example of sediment infiltration into the gravel column is provided showing the procedures of parameter estimation and the verification of results. Temporal and spatial variations of the parameters are also discussed.