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

First-order approximation techniques for estimating stochastic parameters o f a sediment transport model are presented. The non-homogeneous compound Po isson model of Shen-Todorovic eliminating certain idealized assumptions to describe the movement of sediment in natural streams is a revision of the e arlier homogeneous model of Einstein-Hubbell-Sayre. However, the complexity of the non-homogeneous model and the difficulty in determining the model p arameters has limited its application. The proposed approximation technique s employ the first-order Taylor expansions, with respect to a selected temp oral or spatial point by a finite difference, of the cumulative probability distribution function (CDF) of particle displacements. The first-order exp ansions are divided by the original CDF for further simplification. The sim plified forward- and backward-expansions are numerically solved as a system to evaluate the parameter at the specified point. The non-homogeneous para meters are pursued with successive applications of this procedure to variou s points. An example of sediment infiltration into the gravel column is pro vided showing the procedures of parameter estimation and the verification o f results. Temporal and spatial variations of the parameters are also discu ssed.