# Evaluation and Optimization of Hydrological Connectivity Based on Graph Theory: A Case Study in Dongliao River Basin, China

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, accounting for 8% of the total land area of Jilin Province. The DRB spans ~2.5° longitudes and ~1.5° latitudes (123°18′52″–125°47′4″ E and 42°36′46″–44°9′28″ N). The administrative area covers 9 counties (cities and districts) comprising 90 townships. The area is located in the upper reaches of the DRB system and has no transit water. Owing to climate change, precipitation in the area is persistently low, resulting in a resource-based water shortage. The per capita water resource in the basin is 495 m

^{3}, which is 31% of the provincial average and 23% of the national average. Moreover, the water resource development and utilization rates are much higher than the internationally accepted 40% threshold. The basin system includes the three main rivers (Dongliao River, Zhaosutai River, and Tiaozi River), each of which has numerous tributaries. The topography of the DRB is generally gentle, with ~2/3 of the area having a slope of <5°, gradually decreasing from east to west; the highest elevation is 650 m and the average elevation is 328 m. The DRB in Jilin Province is in the transition zone from mixed coniferous and broad forests to grasslands and has the characteristics of forest vegetation. The average annual temperature ranges from 4.4 to 8.1 °C, with an average multi-year temperature of 6.3 °C and an average multi-year precipitation of 547.47 mm. The top three areas of land-use in the basin are 70.58% arable land, 14.12% forest land, and 8.82% construction land. All counties (cities) are important commercial grain-production bases in Jilin Province.

#### 2.2. Data Sources

#### 2.3. Hydrological Connectivity Assessment Based on Graph Theory

_{i}] (i = 1,......, n) and water hydrological links E = [(uv)] (u, v ∈ N, with the symbol [uv] denoting the link between point u and point v). The bipartite graph G can be uniquely specified by an n × n adjacency matrix A(G) describing specific relationships between nodes, which is the basis for computing the connectivity index.

_{i}and a

_{j}are attributes of nodes i and j, respectively (e.g., drainage areas separated by transport paths); nl

_{ij}is the number of links in the shortest path between nodes i and j, respectively; A

_{L}is the maximum landscape attribute (e.g., the total area of the catchment).

#### 2.4. Basin Hydrological Connectivity Optimization Model

_{i}is the cumulative cost of the i-th raster cell to the target and is the minimum resistance accumulated in the pathway from the raster cell at that location to the source; D

_{i}is the cumulative number of pixels in the pathway from a raster cell i in space to the target at minimum cost; F

_{i}is the cumulative cost of the resistance of a raster cell i at the surface.

^{2}were selected and graded into targets based on the functional importance of water ecology. Finally, five levels of optimization targets were obtained. The grading of basin optimization targets is listed in Table 2.

#### 2.5. Spatial Autocorrelation of Hydrological Connectivity Barriers

_{i}is the hydrological resistance value; ω

_{ij}is the spatial weight value; n equals the total number of elements; and s

^{2}is the aggregation of all spatial weights. Global Moran index values are distributed in [−1, 1], with [0, 1] indicating a positive correlation between geographical entities, [−1, 0] indicating a negative relationship, and 0 indicating no relationship. The higher the absolute value, the higher the degree of spatial autocorrelation.

#### 2.6. Barycenter Migration Model

_{t}and Y

_{t}are the latitude and longitude of a certain class of centers. In the space of class t: C

_{ti}is the area of the i-th connectivity barriers in t level; X

_{i}and Y

_{i}are the latitude and longitude of the i patch, respectively; p is the total number of fragments in a certain class of space in year t. The distance of the center of gravity shift of hydrological connectivity resistance is calculated by the following equation:

_{t}and Y

_{t}denote the longitude and latitude at the sampling point at optimization level t, respectively; X

_{t}′ and Y

_{t}′ denote the longitude and latitude at the sampling point at optimization level t′, respectively.

## 3. Results and Discussion

#### 3.1. Basin Hydrological Connectivity Evaluation

#### 3.2. Basin Hydrological Connectivity Optimization

#### 3.3. Evolution of the Center of Gravity for Different Optimization Levels

#### 3.4. Spatial Evolutionary Features

#### 3.5. Connectivity Program

## 4. Conclusions and Future Suggestions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Structure of hydrological connectivity in the Dongliao River Basin (DRB). River, the original water system is generalized as a river network link; link-edge, an edge node in the river network node, connected to only one link; link-center, a non-edge node in the river network node, connected to multiple links in the whole network.

**Figure 4.**Introduction to the three connectivity indices. (

**a**) with larger $\mathsf{\beta}$, $\mathsf{\gamma}$ and IIC; (

**b**) with smaller $\mathsf{\beta},\mathsf{\gamma}$ and IIC.

**Figure 6.**Slope and independent presence of water bodies in the Dongliao River Basin (DRB). Independent presence of water bodies occurs in areas where the slope is relatively small in relation to the surrounding area, a demonstration of the 7 objectives of 1 level of optimization.

**Figure 7.**Spatial distribution of impediments and superimposed resistance cost for hydrological connectivity in the Dongliao River Basin (DRB).

**Figure 8.**Optimization results for hydrological connectivity (water flow obstruction and additional pathways) at all levels in the Dongliao River Basin (DRB).

**Figure 10.**Center-of-gravity migration in the Dongliao River Basin (DRB) for each resistance area at different optimization levels.

**Figure 11.**Global Moran index and scatter plots of water flow obstruction for optimization results from level 1 to level 5 for the Dongliao River Basin (DRB).

**Figure 12.**Results of the Local indicators of spatial association (LISA) clustered clustering of water flow obstruction for different levels of optimization the Dongliao River Basin (DRB).

Component Factors | Total Weights | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Terrain factor | Threshold | 0 to 2.22 | 2.23 to 4.45 | 4.46 to 6.68 | 6.69 to 9.16 | 9.17 to 11.88 | 11.89 to 15.35 | 15.36 to 20.55 | 20.56 to 29.96 | 29.96 to 63.15 | 0.61 |

Resistance weights | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | ||

Hydrological factors | Threshold | −1 to −0.61 | −0.62 to −0.56 | −0.55 to −0.50 | −0.49 to −0.41 | −0.40 to −0.30 | −0.29 to −0.13 | −0.12 to 0.19 | 0.20 to 0.66 | 0.67 to 1 | 0.24 |

Resistance weights | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | ||

Human activities | Threshold | Farmland | Woodland | Grassland | Water | Bare land | Construction land | / | 0.15 | ||

Resistance weights | 6 | 7 | 4 | 1 | 3 | 8 | / |

Priority Level | Water Surface Area (10,000 m^{2}) | Number |
---|---|---|

1 | 600–200 | 7 |

2 | 200–50 | 14 |

3 | 50–20 | 24 |

4 | 2–5 | 62 |

5 | 5–1 | 123 |

**Table 3.**Post-optimization indicators of hydrological connectivity in the Dongliao River Basin (DRB).

Optimization Goals | Δm | Δn | β | Δβ(%) | γ | Δγ(%) | IIC | ΔIIC(%) | |
---|---|---|---|---|---|---|---|---|---|

Level 1 optimization | 7 | 14 | 14 | 0.9184 | 0.3387 | 0.3078 | 0.3259 | 5.1639 | 1.8963 |

Level 2 optimization | 14 | 27 | 27 | 0.9284 | 1.4312 | 0.3110 | 1.3690 | 5.2623 | 3.8379 |

Level 3 optimization | 24 | 46 | 47 | 0.9381 | 2.4910 | 0.3141 | 2.3794 | 5.386 | 6.2788 |

Level 4 optimization | 62 | 118 | 119 | 0.9492 | 3.7037 | 0.3175 | 3.4876 | 6.603 | 30.2932 |

Level 5 optimization | 123 | 224 | 230 | 0.9563 | 4.4794 | 0.3196 | 4.1721 | 7.6371 | 50.6985 |

SiP | LiaoY | GongZl | Total | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

TieD | TieX | LiS | ShuangL | YiT | XiA | LongS | DongF | DongL | ||||

Scenario 1 | Number of paths | 0 | 0 | 0 | 5 | 1 | 0 | 0 | 0 | 0 | 1 | 7;48,346 |

Path length (m) | 0 | 0 | 0 | 40,702 | 6145 | 0 | 0 | 0 | 0 | 1499 | ||

Total | 6;46,847 | 0 | 1;1499 | |||||||||

Scenario 2 | Number of paths | 3 | 1 | 5 | 17 | 22 | 0 | 2 | 32 | 13 | 12 | 107;33,7030 |

Path length (m) | 8803 | 1410 | 9344 | 94,014 | 69,020 | 0 | 4387 | 68,245 | 37,804 | 44,003 | ||

Total | 48;182,591 | 47;110,436 | 12;44,003 | |||||||||

Scenario 3 | Number of paths | 10 | 5 | 15 | 27 | 41 | 3 | 6 | 55 | 25 | 43 | 230;574,749 |

Path length (m) | 28,291 | 6764 | 34,144 | 101,069 | 115,102 | 5486 | 10,299 | 107,747 | 63,487 | 102,360 | ||

Total | 98;285,370 | 89;187,019 | 43;102,360 |

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**MDPI and ACS Style**

Tian, N.; Zhang, Y.; Li, J.; Du, W.; Liu, X.; Jiang, H.; Bian, H. Evaluation and Optimization of Hydrological Connectivity Based on Graph Theory: A Case Study in Dongliao River Basin, China. *Water* **2022**, *14*, 3958.
https://doi.org/10.3390/w14233958

**AMA Style**

Tian N, Zhang Y, Li J, Du W, Liu X, Jiang H, Bian H. Evaluation and Optimization of Hydrological Connectivity Based on Graph Theory: A Case Study in Dongliao River Basin, China. *Water*. 2022; 14(23):3958.
https://doi.org/10.3390/w14233958

**Chicago/Turabian Style**

Tian, Naixu, Yue Zhang, Jianwei Li, Walian Du, Xingpeng Liu, Haibo Jiang, and Hongfeng Bian. 2022. "Evaluation and Optimization of Hydrological Connectivity Based on Graph Theory: A Case Study in Dongliao River Basin, China" *Water* 14, no. 23: 3958.
https://doi.org/10.3390/w14233958