Higher-order approximation techniques for estimating stochastic parameter of a sediment transport model

Higher-order approximation techniques for estimating stochastic parameter o f the non-homogeneous Poisson (NHP) model are presented. The NHP model is c haracterized by a two-parameter cumulative probability distribution functio n (CDF) of sediment displacement. Those two parameters are the temporal and spatial intensity functions, physically representing the inverse of the av erage rest period and step length of sediment particles, respectively. Diff iculty of estimating the parameters has, however, restricted the applicatio ns of the NHP model. The approximation techniques are proposed to address s uch problem. The basic idea of the method is to approximate a model involvi ng stochastic parameters by Taylor series expansion. The expansion preserve s certain higher-order terms of interest. Using the experimental (laborator y or held) data, one can determine the model parameters through a system of equations that are simplified by the approximation technique. The paramete rs so determined are used to predict the cumulative distribution of sedimen t displacement. The second-order approximation leads to a significant reduc tion of the CDF error (of the order of 47%) compared to the first-order app roximation. Error analysis is performed to evaluate the accuracy of the fir st- and second-order approximations with respect to the experimental data. The higher-order approximations provide better estimations of the sediment transport and deposition that are critical factors for such environment as spawning gravel-bed.