Higher-order approximation techniques for estimating stochastic parameter of a sediment transport model |
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| Authors: | F-C Wu C-K Wang |
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| Institution: | (1) Department of Agricultural Engineering and Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan, 10617, Republic of China, TW;(2) Department of Agricultural Engineering, National Taiwan University, Taipei, Taiwan, 10617, Republic of China, TW |
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| Abstract: | Higher-order approximation techniques for estimating stochastic parameter of the non-homogeneous Poisson (NHP) model are
presented. The NHP model is characterized by a two-parameter cumulative probability distribution function (CDF) of sediment
displacement. Those two parameters are the temporal and spatial intensity functions, physically representing the inverse of
the average rest period and step length of sediment particles, respectively. Difficulty of estimating the parameters has,
however, restricted the applications of the NHP model. The approximation techniques are proposed to address such problem.
The basic idea of the method is to approximate a model involving stochastic parameters by Taylor series expansion. The expansion
preserves certain higher-order terms of interest. Using the experimental (laboratory or field) data, one can determine the
model parameters through a system of equations that are simplified by the approximation technique. The parameters so determined
are used to predict the cumulative distribution of sediment displacement. The second-order approximation leads to a significant
reduction of the CDF error (of the order of 47%) compared to the first-order approximation. Error analysis is performed to
evaluate the accuracy of the first- 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. |
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| Keywords: | : Non-homogeneous Poisson model parameter estimation approximation technique Taylor series cumulative probability distribution function intensity function error analysis |
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