# Optimization Model of the Ecological Water Replenishment Scheme for Boluo Lake National Nature Reserve Based on Interval Two-Stage Stochastic Programming

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

## 3. Model Formulation

#### 3.1. Construction of the Ecological Water Replenishment Optimization Model for the Boluo Lake Wetland Based on the ITSP Method

^{2}); ${\mathrm{QT}}_{\mathrm{i}}^{\pm}$ represents the total water replenishment amount for the lake and pond (t/hm

^{2}); ${\mathrm{DEA}}_{\mathrm{ijh}}^{\pm}$ represents the area adjustment amount for the lake and pond i in the ecosystem j under scenario h (hm

^{2}); and ${\mathrm{QLT}}_{\mathrm{ih}}^{\pm}$ represents the total water transport loss for the lake and pond i under scenario h.

- (1)
- Constraints for water diversion and supplementation amount [23]:$$\left({\mathrm{AP}}_{\mathrm{i}}^{\pm}-{\mathrm{DAP}}_{\mathrm{ih}}^{\pm}\right)\times {\mathrm{QWR}}_{\mathrm{i}}^{\pm}\le {\mathrm{QAP}}_{\mathrm{ih}}^{\pm},\text{}\forall \mathrm{i},\mathrm{h}$$$$\sum}_{\mathrm{j}=3}^{4}\left({\mathrm{EA}}_{\mathrm{ij}}^{\pm}-{\mathrm{DEA}}_{\mathrm{ijh}}^{\pm}\right)\times {\mathrm{QP}}_{\mathrm{ij}}^{\pm}\le {\mathrm{QAW}}_{\mathrm{ih}}^{\pm},\forall \mathrm{i},\mathrm{h$$
- (2)
- Constraints for the water supply capacity [26]:$${\mathrm{QAI}}_{\mathrm{ih}}^{\pm}\le {\mathrm{QI}}_{\mathrm{i}}^{\pm},\forall \mathrm{i},\mathrm{h}$$$${\mathrm{QAN}}_{\mathrm{ih}}^{\pm}\le {\mathrm{QN}}_{\mathrm{i}}^{\pm},\text{}\forall \mathrm{i},\mathrm{h}$$
^{3}); ${\mathrm{QI}}_{\mathrm{i}}^{\pm}$ represents the local water in the lake and pond (m^{3}); ${\mathrm{QAN}}_{\mathrm{ih}}^{\pm}$ represents the normal supplement of the lake and pond i under scenario h (m^{3}); and ${\mathrm{QN}}_{\mathrm{i}}^{\pm}$ represents the normal supplement of the lake and pond (m^{3}). - (3)
- Constraints for the functional area [23]:$$\mathrm{A}{\mathrm{P}}_{\mathrm{i}}^{\pm}-\mathrm{D}\mathrm{A}{\mathrm{P}}_{\mathrm{i}\mathrm{h}}^{\pm}\ge 0,\forall \mathrm{i},\mathrm{h}$$$$\mathrm{E}{\mathrm{A}}_{\mathrm{i}\mathrm{j}}^{\pm}-\mathrm{D}\mathrm{E}{\mathrm{A}}_{\mathrm{i}\mathrm{j}\mathrm{h}}^{\pm}\ge 0,\forall \mathrm{i},\mathrm{h}$$$$\sum}_{\mathrm{j}=1}^{2}\mathrm{E}{\mathrm{A}}_{\mathrm{i}\mathrm{j}}^{\pm}-\mathrm{D}\mathrm{E}{\mathrm{A}}_{\mathrm{i}\mathrm{j}\mathrm{h}}^{\pm}\le \mathrm{A}{\mathrm{P}}_{\mathrm{i}}^{\pm}-\mathrm{D}\mathrm{A}{\mathrm{P}}_{\mathrm{i}\mathrm{h}}^{\pm},\forall \mathrm{i},\mathrm{h$$$$\left(\mathrm{A}{\mathrm{P}}_{\mathrm{i}}^{\pm}-\mathrm{D}\mathrm{A}{\mathrm{P}}_{\mathrm{i}\mathrm{h}}^{\pm}\right)+{\displaystyle \sum}_{\mathrm{j}=3}^{4}(\mathrm{E}{\mathrm{A}}_{\mathrm{i}\mathrm{j}}^{\pm}-\mathrm{D}\mathrm{E}{\mathrm{A}}_{\mathrm{i}\mathrm{j}\mathrm{h}}^{\pm})\le \mathrm{P}\mathrm{L}{\mathrm{A}}_{\mathrm{i}}^{\pm},\forall \mathrm{i},\mathrm{h}$$
^{2}). - (4)
- Constraints for the diversion and supplement of the water amount [24]:$$\sum}_{\mathrm{i}=1}^{5}\left[{\displaystyle \sum}_{\mathrm{j}=1}^{4}\left({\mathrm{EA}}_{\mathrm{ij}}^{\pm}-{\mathrm{DEA}}_{\mathrm{ijh}}^{\pm}\right)\times {\mathrm{QP}}_{\mathrm{ij}}^{\pm}-{\mathrm{QAI}}_{\mathrm{ih}}^{\pm}-{\mathrm{QAN}}_{\mathrm{ih}}^{\pm}\right]\le {\mathrm{QTF}}_{\mathrm{ih}}^{\pm},\forall \mathrm{h$$
^{3}). - (5)
- Constraints for water diversion and the supplementation order [24]:$${\mathrm{QAW}}_{\mathrm{ih}}^{\pm}=\left\{\begin{array}{c}\left({\mathrm{QAI}}_{\mathrm{ih}}^{\pm}-{\mathrm{QLI}}_{\mathrm{ih}}^{\pm}\right)+\left({\mathrm{QAN}}_{\mathrm{ih}}^{\pm}-{\mathrm{QLN}}_{\mathrm{ih}}^{\pm}\right)+\left({\mathrm{QAF}}_{\mathrm{ih}}^{\pm}-{\mathrm{QLF}}_{\mathrm{ih}}^{\pm}\right)-{\mathrm{QAP}}_{\mathrm{ih}}^{\pm}\\ \mathrm{if}{\mathrm{AP}}_{\mathrm{i}}^{\pm}-{\mathrm{DAP}}_{\mathrm{ih}}^{\pm}\ge {\mathrm{AP}}_{\mathrm{imin}}^{\pm}\\ 0,\mathrm{if}{\mathrm{AP}}_{\mathrm{i}}^{\pm}-{\mathrm{DAP}}_{\mathrm{ih}}^{\pm}\le {\mathrm{AP}}_{\mathrm{imin}}^{\pm}\mathrm{or}{\mathrm{Y}}_{\mathrm{i}3},{\mathrm{Y}}_{\mathrm{i}4}=0\end{array},\forall \mathrm{i},\mathrm{h}\right.$$$$\left({\mathrm{EA}}_{\mathrm{i}4}^{\pm}-{\mathrm{DEA}}_{\mathrm{i}4\mathrm{h}}^{\pm}\right)\times {\mathrm{QP}}_{\mathrm{i}4}^{\pm}=\left\{\begin{array}{c}{\mathrm{QAW}}_{\mathrm{ih}}^{\pm}-\left({\mathrm{EA}}_{\mathrm{i}3}^{\pm}-{\mathrm{DEA}}_{\mathrm{i}3\mathrm{h}}^{\pm}\right)\times {\mathrm{QP}}_{\mathrm{i}3}^{\pm}\\ \mathrm{if}{\mathrm{EA}}_{\mathrm{i}3}^{\pm}-{\mathrm{DEA}}_{\mathrm{i}3\mathrm{h}}^{\pm}\ge {\mathrm{EA}}_{\mathrm{mini}3}^{\pm}\mathrm{and}{\mathrm{Y}}_{\mathrm{i}4}=1\\ 0,\mathrm{if}{\mathrm{EA}}_{\mathrm{i}3}^{\pm}-{\mathrm{DEA}}_{\mathrm{i}3\mathrm{h}}^{\pm}\le {\mathrm{EA}}_{\mathrm{mini}3}^{\pm}\mathrm{and}{\mathrm{Y}}_{\mathrm{i}4}=0\end{array}\right.,\forall \mathrm{i},\mathrm{h}$$
^{3}); ${\mathrm{QLN}}_{\mathrm{ih}}^{\pm}$ represents the loss of water transport for the normal supplement of the lake and pond i under scenario h (m^{3}); ${\mathrm{QLF}}_{\mathrm{ih}}^{\pm}$ represents the loss of water transport for the flood diversion and supplement of the lake and pond i under scenario h (m^{3}); ${\mathrm{Y}}_{\mathrm{i}3}$ denotes the presence or absence of the reed wetland in the lake and pond i; ${\mathrm{Y}}_{\mathrm{i}4}$ denotes the presence or absence of marsh wetland in the lake and pond i; Y = 0 denotes that the type of wetland is present; and Y = 1 denotes that there is no such type of wetland. - (6)
- Constraints for the ecological value:$${\mathrm{TEBE}}_{\mathrm{kh}}^{\pm}={\displaystyle \sum}_{\mathrm{i}=1}^{5}{\displaystyle \sum}_{\mathrm{j}=1}^{4}{\mathrm{EBW}}_{\mathrm{jk}}^{\pm}\times \left({\mathrm{EA}}_{\mathrm{ij}}^{\pm}-{\mathrm{DEA}}_{\mathrm{ijh}}^{\pm}\right)$$$${\mathrm{TEBE}}_{\mathrm{kh}}^{\pm}\ge {\mathrm{TEB}}_{\mathrm{k}}^{\pm}$$
^{4}CNY); ${\mathrm{EBW}}_{\mathrm{jk}}^{\pm}$ represents the ecological value compensation of the ecosystem j (10^{4}CNY); and ${\mathrm{EBW}}_{\mathrm{jk}}^{\pm}$ represents the total ecological value of the index system of the project scheme (10^{4}CNY). - (7)
- The non-negative constraint:$$\mathrm{Q}\mathrm{A}{\mathrm{I}}_{\mathrm{i}\mathrm{h}}^{\pm},\mathrm{Q}\mathrm{A}{\mathrm{N}}_{\mathrm{i}\mathrm{h}}^{\pm},\mathrm{Q}\mathrm{A}{\mathrm{F}}_{\mathrm{i}\mathrm{h}}^{\pm},\mathrm{Q}\mathrm{A}{\mathrm{W}}_{\mathrm{i}\mathrm{h}}^{\pm},\mathrm{Q}\mathrm{A}{\mathrm{P}}_{\mathrm{i}\mathrm{h}}^{\pm}\ge 0$$

#### 3.2. Model Parameters

## 4. Results, Analysis and Discussion

#### 4.1. Analysis of the Ecological Water Replenishment Variation in the Boluo Lake Wetland Water Replenishment Project Based on the ITSP Method

#### 4.1.1. Ecological Water Replenishment Configuration Scheme for the Boluo Lake Wetland Water Replenishment Project Based on the ITSP Method

#### 4.1.2. Variation in the Flood Diversion Volume of the Water Replenishment Project for the Boluo Lake Wetland Based on the ITSP Method

#### 4.2. Analysis of the Ecological Water Replenishment Variation in the Boluo Lake Wetland Water Replenishment Project Based on the ITSP Method

^{4}hm

^{2}, accounting for an increase of (2300.00%, 1987.59%), as compared to the initial area. While the lower limits of the reed wetland area and the marsh wetland area were lower than those of the corresponding initial areas, the upper limits were increased by 700.00% and 716.00%, respectively. In the Boluo Lake, the largest after the optimization was the area of fish ponds, with a value of (2.94, 8.00) × 10

^{4}hm

^{2}, which was an increase of (326.76%, 515.35%) compared to the initial area. In the Boluo Lake region, except for the crab ponds, the other three functional regions greatly exhibited increased upper and lower limits of their respective areas. In Mobopao, except for the crab pond area that remained unchanged, the other three functional regions exhibited decreased lower limits of their respective areas compared to the initial area, while the upper limits of their areas increased significantly by 449.72%, 700.00%, and 700.00%, respectively. In Yuanbaowapao, no change occurred in the lower limits of the fish pond area and crab pond area after the optimization. The lower limits of two areas, the reed wetland, and the marsh wetland, were reduced compared to the respective initial areas, and the upper limits of three functional regions, except for the fish pond, were increased substantially by 100.00%, 860.00%, and 700.00%, respectively. In Aobaotupao, the reed wetland had the largest restoration area, with a value of (0.48, 1.58) × 10

^{4}hm

^{2}, which accounted for an increase of (1500.00%, 2538.46%) compared to the initial area. The lower limit of the fish pond area remained unchanged compared to the original scheme, while the lower limit of the crab pond and marsh wetland areas was reduced; whereas, the upper limits of all three functional areas were increased significantly by 100.00%, 479.64%, and 710.67%, respectively. Overall, the marsh wetlands that present the highest ecological service value were observed to have a decrease in the lower limit of their area in all ecosystem types, with the exception of the Boluo Lake region, which was mainly because soak pond water and reed wetland water were prioritized for the ecological water replenishment to achieve the best restoration of the ecological functions. In comparison to the original scheme, the overall functional area optimized using the ITSP method was greatly increased, indicating that the ecological water replenishment was effective in restoring the wetland area.

#### 4.3. Analysis of the Change in the Ecological Service Value of the Boluo Lake Wetland Water Replenishment Project Based on the ITSP Method

^{6}CNY) > microclimate adjustment (141.24, 162.71) × 10

^{6}CNY) > fish (125.56, 147.72) × 10

^{6}CNY) > pollution absorption capacity (80.25, 92.45) × 10

^{6}CNY) > crab (46.33, 54.50) × 10

^{6}CNY) > tourist development (29.69, 34.21) × 10

^{6}CNY) > volume of flood water mobilized (28.89, 33.28) × 10

^{6}CNY) > oxygen release (18.50, 21.36) × 10

^{6}CNY) > biodiversity maintenance (10.43, 12.02) × 10

^{6}CNY) > urban landscape (8.03, 9.24) × 10

^{6}CNY) > reed (5.47, 6.32) × 10

^{6}CNY) > natural landscape (3.21, 3.70) × 10

^{6}CNY) > scientific culture (2.01, 2.31) × 10

^{6}CNY) > carbon sequestration (1.90, 2.19) × 10

^{6}CNY) > water supply (0.00, 0.00) × 10

^{6}CNY).In this sequence, the top two indicators, namely plant adsorption, and microclimate adjustment, as well as the fourth indicator, i.e., pollution absorption capacity, are all indicators of the environmental regulation of the ecosystem, which suggests that the ecological water replenishment project in the present study focused on environmental benefits. The two indicators capable of generating direct economic value, namely fish and crab, are in the third and fifth place, respectively, indicating that the ecological water replenishment project in the present study does not just focus on the ecological benefits, and rather completely utilizes the local economic benefits while focusing on the ecological benefits alongside. With the exception of the three ecological service functions of fish, crab, and water supply, which remained unchanged compared to the recommended scheme for the project, the upper and lower limits of the ecological service values of the other ecological service functions were improved. In comparison to the ecological service value in the recommended scheme for the project, the largest improvement was observed in the carbon sequestration, with a value of (23.90%, 21.58%), while the upper and lower limits of the ecological service value of the remaining ecological service functions were increased by over 15%. This indicates that compared to the recommended scheme for the project, the ITSP method optimization scheme obtained a higher ecological service value while ensuring the restoration of the ecosystem functions.

#### 4.4. Evaluation of the Feasibility of the Ecological Water Replenishment Optimization Model Based on the ITSP Method for the Boluo Lake Wetland Water Replenishment Project

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Comparison between the recommended scheme for the project and the ITSP-based model optimization scheme for the ecological water replenishment project of each lake in the Boluo Lake Wetland National Nature Reserve. (I = 1 to 5 represent the Toudaogang Reservoir, Boluo Lake, Mobopao, Yuanbaowapao, and Aobaotupao, respectively).

**Figure 3.**The extent of change in the area of the functional areas for each land type in the different study areas compared to the area in the recommended scheme for the project. (I = 1 to 5 represent the Toudaogang Reservoir, Boluo Lake, Mobopao, Yuanbaowapao, and Aobaotupao, respectively; J = 1 to 4 represent fish ponds, crab ponds, reed wetlands, and marsh wetlands, respectively).

**Figure 4.**The value of ecological services and the magnitude of change under the different indicator systems.

**Table 1.**Ecological water replenishment for each lake bubble in the Boluo Lake Wetland National Nature Reserve.

Name of Lake Bubble | Total Water Replenishment (10^{4} m^{3}) | ||
---|---|---|---|

Original Scheme | ITSP Model | Range of Variation | |

Toudaogang Reservoir | 651.46 | (562.40, 692.94) | (−13.67%, 6.37%) |

Boluo Lake | 5289.64 | (697.50, 6476.21) | (−86.81%, 22.43%) |

Mobopao | 768.72 | (41.60, 698.60) | (−94.59%, −9.12%) |

Yuanbaowapao | 546.50 | (0.00, 138.90) | (−100.00%, −74.58%) |

Aobaotupao | 1211.64 | (234.40, 1798.29) | (−80.65%, 48.42%) |

**Table 2.**Flood diversion volumes for each of the lake bubbles in the Boluo Lake under different scenarios.

Name of Lake Bubble | Flood Diversion Volume (10^{4} m^{3}) | |||
---|---|---|---|---|

The Recommended Scheme for Project | ITSP Model | |||

H = 1 | H = 2 | H = 3 | ||

Toudaogang Reservoir | 0.00 | (0.00, 335.63) | (0.00, 335.63) | (0.00, 335.63) |

Boluo Lake | 621.00 | (0.00, 0.00) | (0.00, 0.00) | (0.00, 0.00) |

Mobopao | 295.00 | (0.00, 431.10) | (0.00, 478.80) | (0.00, 12.60) |

Yuanbaowapao | 2.00 | (0.00, 289.80) | (0.00, 289.80) | (0.00, 56.70) |

Aobaotupao | 14.00 | (0.00, 910.70) | (0.00, 910.70) | (0.00, 910.70) |

Total | 932.00 | (0.00, 1967.23) | (0.00, 2014.93) | (0.00, 1315.63) |

Name of Lake Bubble | Functional Area | Area of Functional Areas (10^{4} hm^{2}) | ||
---|---|---|---|---|

Original Scheme | The Recommended Scheme for Project | ITSP Model | ||

Toudaogang Reservoir | Fish pond | (0.03, 0.05) | 0.40 | (0.72, 1.04) |

Crab pond | (0.00, 0.00) | 0.00 | (0.00, 0.68) | |

Reed wetland | (0.06, 0.12) | 1.00 | (0.00, 0.96) | |

Marsh wetland | (0.02, 0.04) | 0.34 | (0.00, 0.33) | |

Boluo Lake | Fish pond | (0.69, 1.30) | 10.84 | (2.94, 8.00) |

Crab pond | (0.00, 0.00) | 0.00 | (0.00, 0.00) | |

Reed wetland | (0.26, 0.48) | 4.00 | (2.07, 3.84) | |

Marsh wetland | (0.13, 0.24) | 2.00 | (1.92, 2.77) | |

Mobopao | Fish pond | (0.07, 0.13) | 0.00 | (0.00, 0.71) |

Crab pond | (0.00, 0.00) | 1.07 | (0.00, 0.00) | |

Reed wetland | (0.03, 0.06) | 0.50 | (0.00, 0.48) | |

Marsh wetland | (0.06, 0.12) | 1.00 | (0.00, 0.96) | |

Yuanbaowapao | Fish pond | (0.00, 0.00) | 0.00 | (0.00, 0.00) |

Crab pond | (0.00, 0.00) | 0.00 | (0.00, 1.14) | |

Reed wetland | (0.01, 0.01) | 0.10 | (0.00, 0.10) | |

Marsh wetland | (0.03, 0.06) | 0.50 | (0.00, 0.48) | |

Aobaotupao | Fish pond | (0.00, 0.00) | 0.00 | (0.00, 2.68) |

Crab pond | (0.20, 0.37) | 3.05 | (0.00, 2.14) | |

Reed wetland | (0.03, 0.06) | 0.50 | (0.48, 1.58) | |

Marsh wetland | (0.05, 0.09) | 0.76 | (0.00, 0.73) |

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**MDPI and ACS Style**

Huang, J.; Zhao, L.; Sun, S. Optimization Model of the Ecological Water Replenishment Scheme for Boluo Lake National Nature Reserve Based on Interval Two-Stage Stochastic Programming. *Water* **2021**, *13*, 1007.
https://doi.org/10.3390/w13081007

**AMA Style**

Huang J, Zhao L, Sun S. Optimization Model of the Ecological Water Replenishment Scheme for Boluo Lake National Nature Reserve Based on Interval Two-Stage Stochastic Programming. *Water*. 2021; 13(8):1007.
https://doi.org/10.3390/w13081007

**Chicago/Turabian Style**

Huang, Jin, Lei Zhao, and Shijun Sun. 2021. "Optimization Model of the Ecological Water Replenishment Scheme for Boluo Lake National Nature Reserve Based on Interval Two-Stage Stochastic Programming" *Water* 13, no. 8: 1007.
https://doi.org/10.3390/w13081007