# Development of an Interdisciplinary Prediction System Combining Sediment Transport Simulation and Ensemble Method

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Governing Equation of SRH-2D

#### 2.2. Ensemble Method

#### 2.3. Multiple Parameters Combination

- Manning’s coefficient:

- 2.
- Time step:

- 3.
- Sediment formula:

- 4.
- Adaptation length:

## 3. Application

## 4. Results and Discussion

#### 4.1. Performance of Bed Elevation Hindcasting

#### 4.2. Performance of Sediment Concentration Hindcasting

#### 4.3. Determination of Ensemble Size

## 5. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${C}_{t}$ | model constant and the default value = 0.7 is used in this study |

$d$ | average particle size. |

${d}_{50}$ | median diameter (m) |

$D$ | average water depth |

${E}_{base}$ | the RMSE obtained from the single model |

${E}_{t\mathrm{arg}et}$ | the RMSE obtained from the multiple parameters combination averaging |

$g$ | acceleration of gravity |

$h$ | water depth |

$k$ | turbulent kinetic energy |

${K}_{s}$ | bed load constants |

${K}_{r}$ | bed load constants |

$n$ | manning’s coefficient |

${p}_{k}$ | volume of particle distribution in active layer fraction and $\sum _{k}{p}_{ak}=1$ |

${p}_{ak}^{\ast}$ | volume of particle distribution in sub-surface fraction |

${q}_{b}$ | erosion rate potential |

${q}_{t}$ | unit sediment discharge (ton/m) |

$Q$ | the observed value |

$\widehat{Q}$ | the hindcast value |

$\overline{\widehat{Q}}$ | the means of hindcast value |

$R$ | hydraulic radius (m) |

$S$ | energy slope |

${T}_{xx}$, ${T}_{xy}$, ${T}_{yy}$ | depth-averaged stresses due to turbulence and dispersion |

$t$ | time |

$U$ | depth-averaged velocity in $x$-direction |

${U}_{\ast}$ | bed frictional velocity |

$V$ | depth-averaged velocity in $y$-direction |

${V}_{S}$ | average velocity |

$x$ | $x$-direction in Cartesian coordinate |

$y$ | $y$-direction in Cartesian coordinate |

$z$ | water surface elevation |

$z$ | bed elevation |

$\rho $ | water density |

${\rho}_{s}$ | sediment density |

${\tau}_{b}$ | bed shear stress |

${\tau}_{bx}$ | bed shear stresses in $x$-direction |

${\tau}_{by}$ | bed shear stresses in $y$-direction |

${\tau}_{g}$ | particle shear stress; |

$\upsilon $ | kinematic viscosity of water |

${\upsilon}_{t}$ | eddy viscosity |

${\delta}_{a}$ | active layer thickness, which is the sensitive parameter in sedimentation simulation |

${\delta}_{b}$ | sub-surface layer thickness |

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**Figure 3.**Simulation performance obtained from (

**a**) individual member; (

**b**) different ensemble sizes in Beigang River.

**Figure 5.**Comparison of the measurement and the simulation obtained from different ensemble sizes of (

**a**–

**c**) in Beigang River.

**Figure 6.**Comparison of prediction and observation obtained from different ensemble sizes in Dahan River, (

**a**) Parker; (

**b**) MPM.

**Figure 7.**Simulation performance obtained from different ensemble sizes in Dahan River, (

**a**) Parker; (

**b**) MPM.

**Figure 9.**Performance of (

**a**) cross-section elevation; (

**b**) sediment concentration; (

**c**) bed elevation by different ensemble sizes.

Term | Manning’s Coefficient | Time Step | Sediment Formula | Adaptation Length |
---|---|---|---|---|

Range | 0.015–0.050 | 0.5–2.5 (s) | MPM (1948), and Parker (1990) | 1 to 5 times river width |

Region | Event Duration (h) | Initial Condition | Target |
---|---|---|---|

Beigang | 2000–2007 typhoons | 2000 bed elevation | Cross-section variation |

Dahan | 2012–2013 typhoons | 2012 bed elevation | Sediment concentration, river bed elevation |

Region | Beigang River | ||
---|---|---|---|

RMSE(m) | CC | NS | |

single | 2.393 | 0.529 | 0.170 |

20 | 2.320 | 0.547 | 0.219 |

40 | 2.321 | 0.548 | 0.220 |

60 | 2.311 | 0.548 | 0.226 |

80 | 2.309 | 0.549 | 0.227 |

100 | 2.300 | 0.549 | 0.233 |

Region | Parker (1990) | MPM (2006) | ||||
---|---|---|---|---|---|---|

RMSE(m) | CC | NS | RMSE(m) | CC | NS | |

single | 3118 | 0.934 | 0.173 | 5215 | 0.946 | 0.032 |

20 | 2060 | 0.951 | 0.639 | 3642 | 0.958 | 0.045 |

40 | 1907 | 0.956 | 0.691 | 3442 | 0.959 | 0.062 |

60 | 1894 | 0.959 | 0.69 | 3290 | 0.963 | 0.079 |

80 | 1838 | 0.961 | 0.713 | 3169 | 0.962 | 0.145 |

100 | 1785 | 0.963 | 0.73 | 3070 | 0.963 | 0.198 |

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**MDPI and ACS Style**

Ho, H.-C.; Chiang, Y.-M.; Lin, C.-C.; Lee, H.-Y.; Huang, C.-C. Development of an Interdisciplinary Prediction System Combining Sediment Transport Simulation and Ensemble Method. *Water* **2021**, *13*, 2588.
https://doi.org/10.3390/w13182588

**AMA Style**

Ho H-C, Chiang Y-M, Lin C-C, Lee H-Y, Huang C-C. Development of an Interdisciplinary Prediction System Combining Sediment Transport Simulation and Ensemble Method. *Water*. 2021; 13(18):2588.
https://doi.org/10.3390/w13182588

**Chicago/Turabian Style**

Ho, Hao-Che, Yen-Ming Chiang, Che-Chi Lin, Hong-Yuan Lee, and Cheng-Chia Huang. 2021. "Development of an Interdisciplinary Prediction System Combining Sediment Transport Simulation and Ensemble Method" *Water* 13, no. 18: 2588.
https://doi.org/10.3390/w13182588