# Distributed-Framework Basin Modeling System: Ⅲ. Hydraulic Modeling System

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Plain River HFU

#### 2.1.1. River Network Component Generalization

#### 2.1.2. One-Dimensional River Flow Simulation

^{2}/s) from the surrounding surfaces; Q is the flow rate of the cross-section (m

^{3}/s); A is the flow area (m

^{2}); B is the flow width (m); z is the water depth (m); V

_{x}is the velocity of lateral flow along the main river, which was zero in this study; K is the conveyance coefficient, which indicates the actual river convey capacity; $\alpha $ is the momentum correction coefficient, which describes the velocity distribution along the cross-section. The momentum correction coefficient can be calculated with $\alpha =\frac{A}{{K}^{2}}{{\displaystyle \sum}}_{j=1}^{m}\frac{{K}_{j}^{2}}{{A}_{j}}$ when the friction slopes are the same for the main channel and overbank area; m is the number of the main-channel and overbank-area regions; ${A}_{j}$ and ${K}_{j}$ are the flow area and conveyance of the jth flow region; A and K are the sum of A

_{j}and K

_{j}, respectively. $\alpha =1$ when the flow is limited in the main channel.

_{2}− 1, L

_{2}− 2, L

_{2}− 3, …, L

_{1}.

_{1}+ 1, L

_{1}+ 2, L

_{1}+ 3, …, L

_{2}.

#### 2.1.3. Two-Dimensional River Flow Simulation

- (1)
- The discretization of continuity Equation (Equation (11))

- (2)
- The discretization of momentum Equation (Equation (12))

- (3)
- Solving the continuity and momentum matrix with boundary condition

#### 2.1.4. Flow Simulation in River Intersections

#### 2.1.5. Flow Simulation in a Loop River

#### 2.1.6. Flow Simulation for a River Network

#### 2.2. Lakes and Reservoir’s HFU

#### 2.2.1. Zero-Dimensional Flow Simulation in Lakes

#### 2.2.2. Two-Dimensional Flow Simulation in Lakes

- (1)
- The first step:

- (2)
- The second step:

#### 2.3. Hydraulic Engineering Structure’s HFU

^{2}/s) is the gravity acceleration coefficient, which equals 9.81.

^{3}/s) and ${Q}_{s}$ (m

^{3}/s) are the flow through the weir at the free outfall and submerge conditions, respectively; ${\delta}_{f}$, ${\beta}_{f}$, and ${\delta}_{s}$ are discretization coefficients that can be solved with the known boundary condition by the iteration method.

#### 2.4. Case Test of DF-RMS

#### 2.4.1. Basic Information on the Study Area

#### 2.4.2. Model Conceptualization for the Study Area

^{2}storage area. The effects of wind stress should be considered to establish the full two-dimensional simulation model. The Hongze unit was divided into a total of 6174 computing cells with a cell size of 500 m.

## 3. Results and Discussion

## 4. Summary and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Boundary-fitted transformation and discretization of $\left(x,y\right)$ (

**a**) and $\left(\mathsf{\xi},\text{}\mathsf{\eta}\right)$ (

**b**) space.

**Figure 7.**(

**a**) Schematic of the study area and (

**b**) boundary condition sites and generalized information.

**Figure 8.**Simulated and observed water surface elevations with calibrated and validated model of two stations in 1982 and 1991: (

**a**,

**c**) for Bengbu station; (

**b**,

**d**) for Wujiadu station.

**Figure 9.**Simulated and observed flow rates with calibrated and validated model of two stations in 1982 and 1991: (

**a**) for Xiaoliuxiang; (

**b**,

**c**) for Sanhe Gate station.

Name | X-Resolution (m) | Y-Resolution (m) | Number of Simulation Node |
---|---|---|---|

Fangqiu Lake | 500 | 500 | 326 |

Linbei section | 500 | 500 | 111 |

Huayuan Lake | 500 | 500 | 920 |

Xiangfu section | 500 | 500 | 184 |

Pancunwa | 500 | 500 | 570 |

Yantan | 500 | 500 | 63 |

Hatan | 500 | 500 | 44 |

Chenggenwei | 500 | 500 | 52 |

Hongze Lake | 500 | 500 | 6174 |

Total | - | - | 8444 |

Location | Station Name | Z_{psi} (m) | Z_{pob} (m) | R^{2} | ∆Z_{p} (m) |
---|---|---|---|---|---|

Input boundary | Bengbu | 21.49 ^{1} (22.11) ^{2} | 21.47 (22.2) | 0.998 (0.997) | 0.02 (‒0.09) |

Sihong | 16.05 (15.19) | 16.05 (15.11) | −(‒) | 0 (0.08) | |

Tuanjiezha | 18.79 (16.57) | 18.75 (16.67) | 0.955 (‒) | 0.04 (‒0.10) | |

Internal part | Wujiadu | 21.13 (21.75) | 21.12 (21.81) | 0.996 (0.997) | 0.01 (‒0.06) |

Mohekou | 20.46 (21.08) | 20.42 (‒) | 0.996 (−) | 0.04 (−) | |

Linhuaiguan | 20.05 (20.68) | 20.01 (20.64) | 0.995 (0.995) | 0.04 (0.04) | |

Wuhe | 18.29 (18.93) | 18.31 (18.88) | 0.994 (0.994) | ‒0.02 (0.05) | |

Fushan | 17.4 (18.07) | 17.39 (17.98) | 0.993 (0.995) | 0.01 (0.09) | |

Xiaoliuxiang | 17.13 (17.79) | 17.13 (17.74) | 0.994 (0.995) | 0 (0.05) | |

Huayuanzui | 15.75 (16.60) | 15.73 (16.64) | 0.991 (0.987) | 0.02 (‒0.04) | |

Xuyi | 14.58 (15.38) | 14.63 (15.38) | 0.977 (0.99) | ‒0.05 (0) | |

Xinhetou | 13.36 (14.42) | 13.74 (14.42) | 0.67 (0.81) | ‒0.38 (0) | |

Laozishan | 13.31 (14.18) | 13.29 (14.23) | 0.915 (0.981) | 0.02 (‒0.05) | |

Linhuaitou | 12.91 (14.08) | 12.93 (14.04) | 0.935 (0.984) | ‒0.02 (0.04) | |

Shangzui | 12.88 (14.05) | 12.74 (13.95) | 0.906 (0.947) | 0.14 (0.10) | |

Output boundary | Gaoliangjian | 12.88 (14.06) | 12.77 (14.02) | 0.944 (0.981) | 0.11 (0.04) |

^{1}The calibration results for the year 1982;

^{2}the validation results for the year 1991. Z

_{psi}(m) is the simulated peak water elevation, Z

_{pob}(m) is the observed peak water elevation, R

^{2}is the determination coefficient of simulated and observed results, ∆Z

_{p}(m) is the difference between the simulated and observed water elevation, ∆Z

_{p}= Z

_{psi}− Z

_{pob}.

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**MDPI and ACS Style**

Li, X.; Wang, C.; Chen, G.; Fang, X.; Zhang, P.; Hua, W.
Distributed-Framework Basin Modeling System: Ⅲ. Hydraulic Modeling System. *Water* **2021**, *13*, 649.
https://doi.org/10.3390/w13050649

**AMA Style**

Li X, Wang C, Chen G, Fang X, Zhang P, Hua W.
Distributed-Framework Basin Modeling System: Ⅲ. Hydraulic Modeling System. *Water*. 2021; 13(5):649.
https://doi.org/10.3390/w13050649

**Chicago/Turabian Style**

Li, Xiaoning, Chuanhai Wang, Gang Chen, Xing Fang, Pingnan Zhang, and Wenjuan Hua.
2021. "Distributed-Framework Basin Modeling System: Ⅲ. Hydraulic Modeling System" *Water* 13, no. 5: 649.
https://doi.org/10.3390/w13050649