# Study on Multi-Scale Coupled Ecological Dispatching Model Based on the Decomposition-Coordination Principle

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Generation and Evaluation of Characteristic Flow Regimes

#### 2.1.1. Base Flows

#### 2.1.2. Extreme Low Flows

#### 2.1.3. Flood Pulses and High Flow Pulses

_{T}> T

_{T}is the control section flow.

_{P}= Q

_{R}− Q

_{T}

_{P}represents the released flow from reservoirs; Q

_{R}represents the control section target flow; and Q

_{T}represents the control section flow.

#### 2.1.4. Ecological Hydraulic Parameters

#### 2.2. Construction of the Multi-Scale Coupled Ecological Dispatching Model

#### 2.2.1. The Space and Time Decomposition-Coordination Method

_{i}represents the Lagrange function of the i-th subsystem; n represents the number of subsystems; x

_{i}represents the decision vector of the i-th subsystem (in this study, it represents water released from reservoirs); f

_{i}(x

_{i}) represents the evaluation function of the i-th subsystem; $\sum _{i=1}^{n}{g}_{i}({x}_{i})}=b$ is the equality constraint between subsystems; $\sum _{i=1}^{n}{h}_{i}({x}_{i})}\ge d$ is the inequality constraint between subsystems; $\lambda $ is the equality Lagrange multiplier constraint; and $\mu $ is the inequality Kuhn-Tacker multiplier constraint.

#### 2.2.2. Coordination between Multi-Scale Subsystems

_{0}and t

_{f}are the start and finish time of subordinate subsystems, respectively (smaller scale); x

_{s}represents the subordinate subsystem decision variable; and x

_{i}is the result of superior subsystem (larger scale).

#### 2.2.3. Construction of the Subsystems

_{i}represents the Lagrange function of the i-th subsystem; ${f}_{i}({x}_{i})$ represents the evaluation function of the i-th subsystem; $\alpha $ is a 0-1 variable, which is used as a subordinate subsystem structural discrimination coefficient, 1 and 0 denote whether the i-th subsystem has a subordinate subsystem or not, respectively; ${\lambda}_{i}$ and ${\mu}_{i}$ refer to the corresponding coordination variable components of the i-th subsystem; and the other symbols are the same as those defined in Equations (4) and (5).

_{i}refers to the subsystem water supply; ${D}_{j}$ refers to the degree of change of the j-th index; M and N represent the number of superior subsystem and subordinate subsystem indicators, respectively; and the other symbols are the same as those defined in Equations (4) and (5).

#### 2.3. A Solution of the Multi-Scale Coupled Ecological Dispatching Model

#### 2.4. Description of the Study Area

^{2}. Furthermore, the stream gradient is small and the river’s ecological problems are serious. The main water conservancy projects within this area are the Xiaolangdi reservoir and the Sanmenxia reservoir; which effectively store 5.1 billion cubic meters (bcm) and 0.462 bcm of water, respectively. Annual consumptive water use in the study area is 7.5 bcm. During flood season, there are water resources to ensure the implementation of ecological operation.

- (1)
- Minimum water shortage rate:$$Min{\mathrm{f}}_{S-D}={\displaystyle \sum _{t=1}^{T}{\displaystyle \sum _{m=1}^{M}\frac{{\mathrm{D}}_{(m,t)}-{\mathrm{S}}_{D(m,t)}}{{\mathrm{D}}_{(m,t)}}}}$$
- (2)
- The minimum degree of hydrologic alteration is expressed as:$$Min{\displaystyle \sum _{i=1}^{I}{D}_{i}}={\displaystyle \sum _{L=1,2,3}\left|\frac{{N}_{i}(La)-{N}_{e}(La)}{{N}_{e}(La)}\right|}$$

- (1)
- Water level constraint:$${Z}_{\mathrm{min}}(m,t)\le Z(m,t)\le {Z}_{\mathrm{max}}(m,t)$$
- (2)
- Flow constraint:$${Q}_{O\mathrm{min}}(m,t)\le {Q}_{O}(m,t)\le {Q}_{O\mathrm{max}}(m,t)$$
- (3)
- Water balance constraint:$$V(m,t+1)=V(m,t)+{Q}_{I}(m,t)-{Q}_{O}(m,t)$$
- (4)
- Flow balance constraint:$${Q}_{I}(m+1,t)={Q}_{O}(m,t)+q(m,t)$$
- (5)
- Water supply reliability constraint:$$\begin{array}{l}reliabilit{y}_{agricultural}\ge 0.75\\ reliabilit{y}_{urban}\ge 0.95\end{array}$$

## 3. Results

^{3}/s under the premise of meeting the water supply reliability.

## 4. Discussion

## 5. Conclusions

^{3}/s can reduce the degree of hydrologic alteration from 86% to 53% in the downstream Yellow River. Model optimization results were compared with results of the POF approach. The comparison showed that further reduction in hydrologic alteration is possible, but further research is needed to determine which method is more suitable for accomplishing this task.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) Large-scale model optimization processes; (

**b**) Small-scale model optimization processes.

Length/cm | Suitable Flow Velocity/(m/s) | Critical Flow Velocity/(m/s) | |
---|---|---|---|

Gymnocypris eckloni herzenstein | 20–25 | 0.3–0.8 | 1.00 |

25–35 | 0.3–0.8 | 1.10 |

Characteristic Flow Regimes | Descriptive Parameters | Hierarchy of Model |
---|---|---|

Base Flows | Magnitude of base flows | Large-scale |

Extreme Low Flows | Magnitude, frequency, duration, and timing of extremely low flows | Small-scale |

Flood Pulses and High Flow Pulses | The magnitude, frequency, duration, and timing of flood and high flow pulses | Small-scale |

Ecological Hydraulic Parameters | The hydraulic parameters for specific species in different growth cycles | Small-scale |

Index | Current Scheduling | POF Approach | Optimization Model | Ecosystem Influences [38] |
---|---|---|---|---|

Magnitude of monthly discharge conditions | 0.81 | 0.67 (0.62–0.71) | 0.60 (0.55–0.63) | To meet the habitat needs of aquatic organisms, the needs of plants for soil moisture content, the water needs of terrestrial organisms with high reliability, the migration needs of carnivores, and the influences of water temperature and oxygen content. |

Magnitude and duration of annual extreme discharge conditions | 0.72 | 0.88 (0.80–0.95) | 0.41 (0.40–0.42) | To meet the needs of vegetation expansion, river topography and natural habitat construction, nutrient exchange in rivers and flood detention areas, distribution of plant communities in lakes, and ponds and flood detention areas. |

Timing of annual extreme discharge conditions | 0.99 | 1.22 (0.88–1.44) | 0.27 (0.25–0.29) | To meet the migration of fish spawning, the cycle of life reproduction, biological breeding habitat conditions, and species evolution needs. |

Frequency and duration of high/low flow pulses | 0.83 | 0.71 (0.68–0.7) | 0.70 (0.69–0.72) | To generate the frequency and magnitude of soil moisture stress for plants. |

Rate/frequency of hydrograph changes | 0.71 | 1.12 (0.99–1.20) | 0.67 (0.65–0.69) | To meet the drought of plants, the trapping of organics on the island and in the flood detention area, and the drying stress of low-speed organisms. |

Suitable ecological velocity | 0.29 | 0.40 (0.38–0.42) | 0.46 (0.43–0.49) | To meet the appropriate velocity requirements of fish. |

Whether Considering Characteristic Flow Requirements | Whether Introducing Small-Scale Model | Hydrologic Alteration | Agricultural Water Supply Reliability | Urban Water Supply Reliability |
---|---|---|---|---|

Yes | Yes | 53% | More than 75% | More than 95% |

Yes | No | ≥53% | ||

No | Yes | 87% | More than 90% | |

No | No | ≥87% |

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**MDPI and ACS Style**

Zhou, T.; Dong, Z.; Wang, W.; Shi, R.; Gao, X.; Huang, Z.
Study on Multi-Scale Coupled Ecological Dispatching Model Based on the Decomposition-Coordination Principle. *Water* **2019**, *11*, 1443.
https://doi.org/10.3390/w11071443

**AMA Style**

Zhou T, Dong Z, Wang W, Shi R, Gao X, Huang Z.
Study on Multi-Scale Coupled Ecological Dispatching Model Based on the Decomposition-Coordination Principle. *Water*. 2019; 11(7):1443.
https://doi.org/10.3390/w11071443

**Chicago/Turabian Style**

Zhou, Tao, Zengchuan Dong, Wenzhuo Wang, Rensheng Shi, Xiaoqi Gao, and Zhihong Huang.
2019. "Study on Multi-Scale Coupled Ecological Dispatching Model Based on the Decomposition-Coordination Principle" *Water* 11, no. 7: 1443.
https://doi.org/10.3390/w11071443