### 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.

Original language | English |
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Pages (from-to) | 359-375 |

Number of pages | 17 |

Journal | Stochastic Hydrology and Hydraulics |

Volume | 12 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1998 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Environmental Engineering
- Environmental Chemistry
- Modelling and Simulation
- Water Science and Technology
- Safety, Risk, Reliability and Quality
- Environmental Science(all)
- Ocean Engineering
- Mechanical Engineering

### Cite this

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*Stochastic Hydrology and Hydraulics*, vol. 12, no. 6, pp. 359-375. https://doi.org/10.1007/s004770050025

**Higher-order approximation techniques for estimating stochastic parameter of a sediment transport model.** / Wu, F. C.; Wang, Chi-Kuei.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Higher-order approximation techniques for estimating stochastic parameter of a sediment transport model

AU - Wu, F. C.

AU - Wang, Chi-Kuei

PY - 1998/1/1

Y1 - 1998/1/1

N2 - 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.

AB - 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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U2 - 10.1007/s004770050025

DO - 10.1007/s004770050025

M3 - Article

VL - 12

SP - 359

EP - 375

JO - Stochastic Environmental Research and Risk Assessment

JF - Stochastic Environmental Research and Risk Assessment

SN - 1436-3240

IS - 6

ER -