# Evaluation of Water Resources Carrying Capacity of Zhangye City Based on Combined Weights and TOPSIS Modeling

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Application Example

#### 2.1. Overview of the Study Area

^{3}, of which the living water consumption of the city is CNY 1998 billion. The annual total water consumption is 1.998 billion m

^{3}. Among this water consumption, the domestic water consumption is 0.46 billion m

^{3}, the industrial water consumption is 0.19 billion m

^{3}, the agricultural water consumption is 1.775 billion m

^{3}, the ecological water consumption is 158 million m

^{3}, the annual average precipitation is 182.40 mm, decreasing from the southeast to the northwest, the Chemical Oxygen Demand (COD) is 2.90 million ton, and the ammonia nitrogen discharge is 0.12 million ton.

#### 2.2. Data Sources

## 3. Research Method

#### 3.1. Construction of Water Resources Carrying Capacity Index System

#### 3.1.1. Construction of Water Resources Carrying Capacity Index System

#### 3.1.2. Status Evaluation Level Is Determined

#### 3.2. Determination of Weights

#### 3.2.1. AHP Method for Determining Weights

- (1)
- Construct a judgment matrix A containing 12 indicators $\mathrm{A}=({{\mathrm{a}}_{\mathrm{i}\mathrm{j}})}_{\mathrm{m}\times \mathrm{n}}$.${\mathrm{a}}_{\mathrm{i}\mathrm{j}}$ representing the factors ${\mathrm{a}}_{\mathrm{i}}$ relative to the ${\mathrm{a}}_{\mathrm{j}}$ importance values (i, j = 1, 2, ……, n), with values ranging from 1 to 9.
- (2)
- Calculate the importance ranking. According to the judgment matrix, the weights are derived and normalized, and then sorted by the importance of each evaluation indicator according to the numerical value, i.e., the weights of each indicator ${\mathsf{\omega}}_{\mathrm{j}}$ utilize the formula $\mathrm{A}{\mathsf{\omega}}_{\mathrm{j}}={\mathsf{\lambda}}_{\mathrm{m}\mathrm{a}\mathrm{x}}{\mathsf{\omega}}_{\mathrm{j}}$ to find the maximum characteristic root of A ${\mathsf{\lambda}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$.
- (3)
- Consistency test. In order to verify that the resulting weights are within the allowed range, the formula $\mathrm{C}\mathrm{R}=\mathrm{C}\mathrm{I}/\mathrm{R}\mathrm{I}$ Consistency test is performed. When CR < 0.1 or ${\mathsf{\lambda}}_{\mathrm{m}\mathrm{a}\mathrm{x}}=\mathrm{n}$, CI = 0, the consistency requirement is satisfied. Otherwise, the judgment matrix should be adjusted.

#### 3.2.2. Entropy Weighting Method for Determining Weights

- (1)
- Take j indicators in year i and form an initial data matrix $\mathrm{A}=({{\mathrm{Z}}_{\mathrm{i}\mathrm{j}})}_{\mathrm{m}\times \mathrm{n}}$ (i= 1, 2, …, m; j=1, 2, …, n), where ${\mathrm{Z}}_{\mathrm{i}\mathrm{j}}$ is the value of the jth indicator in the ith year; the raw data corresponding to the 12 indicators are organized to form the initial matrix.
- (2)
- Normalization of the indicators to form a normalization matrix ${\mathrm{R}}_{\mathrm{i}\mathrm{j}}$, according to Equations (1) and (2).Positive indicators:$${\mathrm{R}}_{\mathrm{i}\mathrm{j}}=\frac{{\mathrm{Z}}_{\mathrm{i}\mathrm{j}}-\mathrm{m}\mathrm{i}\mathrm{n}({\mathrm{Z}}_{1\mathrm{j}},{\mathrm{Z}}_{2\mathrm{j}},\dots {\mathrm{Z}}_{\mathrm{m}\mathrm{j}})}{\mathrm{max}\left({\mathrm{Z}}_{1\mathrm{j}},{\mathrm{Z}}_{2\mathrm{j}},\dots {\mathrm{Z}}_{\mathrm{m}\mathrm{j}}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left({\mathrm{Z}}_{1\mathrm{j}},{\mathrm{Z}}_{2\mathrm{j}},\dots {\mathrm{Z}}_{\mathrm{m}\mathrm{j}}\right)}+1$$Negative indicators:$${\mathrm{R}}_{\mathrm{i}\mathrm{j}}=\frac{\mathrm{min}\left({\mathrm{Z}}_{1\mathrm{j}},{\mathrm{Z}}_{2\mathrm{j}},\dots {\mathrm{Z}}_{\mathrm{m}\mathrm{j}}\right)-{\mathrm{Z}}_{\mathrm{i}\mathrm{j}}}{\mathrm{max}\left({\mathrm{Z}}_{1\mathrm{j}},{\mathrm{Z}}_{2\mathrm{j}},\dots {\mathrm{Z}}_{\mathrm{m}\mathrm{j}}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left({\mathrm{Z}}_{1\mathrm{j}},{\mathrm{Z}}_{2\mathrm{j}},\dots {\mathrm{Z}}_{\mathrm{m}\mathrm{j}}\right)}+1$$
- (3)
- Perform entropy value calculation according to Formula (3), where ${\mathrm{B}}_{\mathrm{j}}$ is the entropy value of the jth evaluation index.$${\mathrm{B}}_{\mathrm{j}}=-\frac{1}{\mathrm{lnm}}{\sum}_{\mathrm{j}=1}^{\mathrm{m}}\frac{{\mathrm{R}}_{\mathrm{i}\mathrm{j}}}{\sum _{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{R}}_{\mathrm{i}\mathrm{j}}}\mathrm{ln}(\frac{{\mathrm{R}}_{\mathrm{i}\mathrm{j}}}{\sum _{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{R}}_{\mathrm{i}\mathrm{j}}})$$

#### 3.2.3. Determination of Composite Weights

#### 3.3. Evaluation of Water Resource Carrying Capacity Based on TOPSIS Modeling

- (1)
- With N objects to be evaluated and M evaluation indicators, forming the original data matrix and processing matrix, we have the matrix $\mathrm{U}$, $\mathrm{U}={\left({\mathrm{u}}_{\mathrm{i}\mathrm{j}}\right)}_{\mathrm{n}\times \mathrm{m}}$.
- (2)
- To normalize the matrix $\mathrm{U}$ Normalized according to Equation (6), we obtain the quantile normalized decision matrix $\mathrm{A}$:$$\mathrm{A}={\left({\mathrm{a}}_{\mathrm{i}\mathrm{j}}\right)}_{\mathrm{n}\times \mathrm{m}}(\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{h}.)\mathrm{g}\mathrm{e}\mathrm{n}\mathrm{u}\mathrm{s}\phantom{\rule{0ex}{0ex}}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{m}\mathrm{e}\left(\mathrm{o}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{e}\right){\mathrm{A}}_{\mathrm{i}\mathrm{j}}=\frac{{\mathrm{u}}_{\mathrm{i}\mathrm{j}}}{\sqrt{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{u}}_{\mathrm{i}\mathrm{j}}^{2}}}$$
- (3)

- (4)
- Calculate the distance of each evaluation object to the optimal solution according to Equations (7) and (8) ${\mathrm{B}}_{\mathrm{i}}^{+}$ and the distance to the worst solution ${\mathrm{B}}_{\mathrm{i}}^{-}$ and normalize to determine the relative closeness of each evaluation object to the optimal solution, i.e., the closeness degree ${\mathrm{T}}_{\mathrm{i}}$, the larger the value, the closer to the optimal solution. For ${\mathrm{T}}_{\mathrm{i}}$, the larger the value, the closer it is to the optimal solution. For ${\mathrm{T}}_{\mathrm{i}}$, the value is between 0 and 1, and the closer to 1, the closer the level is to the optimal solution, and vice versa.$${\mathrm{B}}_{\mathrm{i}}^{+}=\sqrt{{\sum}_{\mathrm{j}=1}^{\mathrm{m}}{[\mathsf{\omega}}_{\mathrm{j}}^{\u2033}({\mathrm{A}}_{\mathrm{j}}^{+}-{\mathrm{A}}_{\mathrm{i}\mathrm{j}}{\left)\right]}^{2}}$$$${\mathrm{B}}_{\mathrm{i}}^{-}=\sqrt{{\sum}_{\mathrm{j}=1}^{\mathrm{m}}{[\mathsf{\omega}}_{\mathrm{j}}^{\u2033}({\mathrm{A}}_{\mathrm{j}}^{-}-{\mathrm{A}}_{\mathrm{i}\mathrm{j}}{\left)\right]}^{2}}$$

#### 3.4. Calculation of Barrier Degree Factor

#### 3.5. Water Resources Carrying Capacity Evaluation Flow Chart

## 4. Analysis of Results

#### 4.1. Combination Weight

^{3}of farmland irrigation is the smallest, which is 0.036. In general, the comprehensive weight is closer to reality, which improves the shortcomings of the AHP and entropy weight methods so as to avoid the problem that the evaluation results are divorced from the actual situation.

#### 4.2. Analysis of Evaluation Results of Each Subsystem of Water Resources Carrying Capacity

_{i}. The calculation results are shown in Figure 3.

#### 4.2.1. Overall Analysis

^{3}in 2010 to 2412 million m

^{3}in 2014; the rapid development of industry and agriculture leads to the high water consumption level in agriculture and industry, such as industrial value added from CNY 5.540 billion in 2010 to CNY 8.523 billion in 2014, and the water consumption of agricultural irrigation has been at a high level from 2010 to 2014. It can be seen that the combined effect of the above reasons has a large impediment to the environmental carrying capacity of water resources, resulting in Zhangye City, where the environmental carrying capacity of water resources has shown a clear downward trend. The environmental carrying capacity of water resources has been gradually increasing since 2014, and the carrying capacity index in 2020 reached 0.615, which is more than double that in 2014. Analyzing the reasons in depth, the achievement is, on the one hand, due to the innovation of the water-saving technology model, which improves the utilization efficiency of agricultural water. For example, in 2010, the General Office of Gansu Provincial People’s Government issued the document “Gansu Provincial People’s Government on the Issuance of Gansu Provincial Hexi and Along the Yellow Main Irrigation Areas of High-efficient Farmland Water Saving Technology Promotion Support Measures and Gansu Provincial Hexi and Along the Yellow Main Irrigation Areas of High-efficient Farmland Water Saving Technology Promotion Three-Year Plan”; in 2013, Gansu Provincial Department of Agriculture and Animal Husbandry, and another four departments and offices jointly issued the document “On the issuance of the province’s 2013 high-efficiency farmland water-saving technology promotion plan notice”. Technology Promotion Plan” document, Zhangye City, provided a demonstration and promotion of membrane drip irrigation and another three high-efficiency farmland water-saving technologies, so that, in Zhangye City, the amount of water used for farmland irrigation can achieve a substantial reduction in the usage of water resources of Zhangye City, significantly improving the environmental carrying capacity of water resources in Zhangye City.

#### 4.2.2. Analysis of Water Resources Development and Utilization Subsystems

^{3}, which was 5.72% higher than the 2.882 billion m

^{3}in 2013, and the total amount of regional water resources increased from 3.042 billion m

^{3}to 3.182 billion m

^{3}, and the amount of underground water resources was 125 million m

^{3}(minus duplicates), a decrease of 0.35 billion m

^{3}from 160 million m

^{3}in 2013, a decrease of more than 20%. Although the problem of overexploitation of groundwater has been managed, the overall supply of water resources in the region is still in a disadvantageous position, which also reduces the amount of water resources in Zhangye City according to the Ministry of Water Resources’ “Heihe River Water Allocation Program” of Zhangye City’s discharged water volume. Four of the water resources development and utilization subsystems in 2019 indicators have all increased compared to the previous year, and the water resources carrying condition has significantly improved, indicating that the management measures formulated by Zhangye City in recent years in terms of water resources development and utilization have played a role.

#### 4.2.3. Economic and Social Subsystem Analysis

^{3}in 2015 to 0.19 billion m

^{3}, which is attributed to the development of industry in Zhangye City and the commitment to promote agricultural and industrial water-saving measures to build a water-saving society in a comprehensive way, which is consistent with the conclusion of Wang Yan [47].

#### 4.2.4. Ecological Subsystem Analysis

^{3}to 158 million m

^{3}in 2020, and the ecological water use rate average obstacle ranked sixth, which indicates that the ecological water use percentage still needs to be increased in order for the water resources carrying capacity to be further improved.

#### 4.3. Obstacle Degree Analysis of Water Resources Carrying Capacity Evaluation Index

## 5. Conclusions

- (1)
- The combinatorial weight method combines subjective cognition and objective laws of data, making combinatorial weights more scientific and reasonable.
- (2)
- The evaluation results show that the water resources carrying capacity from 2010 to 2014 is generally stable on the macro level, but from the micro level, the water resources carrying capacity has a certain fluctuation and shows an increasing trend year by year. The closeness value of water resources carrying capacity in Zhangye City is between 0.273 and 0.561, and the grade of water resources carrying capacity is in grades III and IV. From 2014 to 2020 (except 2020), the water resources carrying capacity of Zhangye City showed an increasing trend year by year, and the closeness value of the water resources carrying capacity was between 0.297 and 0.615. The water resources carrying capacity level was still at grade III and grade IV, belonging to the medium or below medium level, indicating that the overall water resources carrying capacity of the region was weak and needed to be further improved.
- (3)
- From 2010 to 2020, the carrying capacity of water resource development and utilization in Zhangye City fluctuates greatly; the carrying capacity of economic and social society is basically synchronized with the carrying capacity of water resources; and the carrying capacity of the ecological environment increases the most. The steady improvement of economic and social conditions is the main factor for the improvement of the comprehensive carrying capacity of water resources in Zhangye City, and the impact of the ecological environment is also an important factor influencing the carrying capacity of water resources in Zhangye City.
- (4)
- The six indicators of per capita water consumption, surface water resources per unit area, per capita water resource possession, underground water resources per unit area, urbanization rate, and ecological water use rate are the main obstacles to the water resources carrying capacity of Zhangye City, of which the most influential are the indicators of surface water resources per unit area and per capita water consumption, and the main criterion layer of the water resources carrying capacity of Zhangye City is the water resources exploitation and utilization criterion layer.
- (5)
- Zhangye City should strengthen water resources management, optimize the water use structure of various industries, vigorously promote the whole society to save water, implement precise policies, fine-tune the water use process, improve the water utilization rate, scientifically carry out ecological protection and restoration projects, rationally carry out ecological water replenishment, and gradually eliminate environmental risks so as to further improve the water resources carrying capacity of the region.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Temporal variation of water resources carrying capacity in Zhangye city from 2010 to 2020.

Target Level | Standardized Layer | Indicator Layer | Unit (of Measure) | Formula | Indicator Polarity |
---|---|---|---|---|---|

Water carrying capacity (A) | Water Resources Development and Utilization (B_{1}) | Surface water resources per unit area (C_{1}) | million m^{3}·km^{−2} | Regional surface water resources/regional area | greater than zero |

Groundwater resources per unit area (C_{2}) | million m^{3}·km^{−2} | Volume of regional groundwater resources (net of duplicates)/area of region | greater than zero | ||

Water resources per capita (C_{3}) | m^{3}/people | Regional water resources (net of duplicates)/total number of people living in the region | greater than zero | ||

Precipitation (C_{4}) | mm | Annual precipitation in the region | greater than zero | ||

Economic and social (B_{2}) | Urbanization rate (C_{5}) | % | Urban resident population/total resident population of the area | turn one’s back on | |

Per capita water use (C_{6}) | m^{3}/person | Water consumption/total resident population of the region | turn one’s back on | ||

Water consumption of GDP (C_{7}) | m^{3}/million | Total regional water use/regional GDP | turn one’s back on | ||

Average acre-foot water use for agricultural irrigation (C_{8}) | m^{3}/mu | Agricultural irrigation water consumption/cultivated land area | turn one’s back on | ||

Water consumption per CNY 10,000 of industrial added value (C_{9}) | m^{3}/million | Industrial water consumption/industrial value added | turn one’s back on | ||

Ecology (B_{3}) | Chemical Oxygen Demand (C_{10}) | million t | statistical data | turn one’s back on | |

Ammonia emissions (C_{11}) | million t | statistical data | turn one’s back on | ||

Ecological water use rate (C_{12}) | % | Ecosystem water use/total water resources | greater than zero |

**Table 2.**Grading criteria for indicators for evaluating the state of water resources carrying capacity.

Rating | Class I | Class II | Class III | Class IV | Class V |
---|---|---|---|---|---|

C_{1}: Surface water resources per unit area/(10,000 m^{3}·km^{−2} ) | ≥25 | [20, 25] | [15, 20] | [10, 15] | <10 |

C_{2}: Groundwater resources per unit area/(10,000 m^{3}·km^{−2}) | ≥7 | [6, 7) | [5, 6] | [4, 5) | <4 |

C_{3}: Per capita water availability/(m^{3}/person) | ≥2000 | [1700, 2000] | [1000, 1700] | [500, 1000) | <500 |

C_{4}: Average annual precipitation/(mm) | ≥800 | [600, 800] | [400, 600] | [200, 400] | <200 |

C_{5}: Urbanization rate/(%) | <40 | [40, 45] | [45, 50] | [50, 55] | ≥55 |

C_{6}: Per capita water consumption (m^{3}/person) | <200 | [200, 300] | [300, 400] | [400, 500] | ≥500 |

C_{7}: GDP water use (m^{3}/million dollars) | <200 | [200, 400] | [400, 600] | [600, 800] | ≥800 |

C_{8}: Average acreage water use for agricultural irrigation (m^{3}/mu) | <300 | [300, 400] | [400, 500] | [500, 600] | ≥600 |

C_{9}: Water consumption per CNY 10,000 of industrial added value (m^{3}/10,000 CNY) | <15 | [15, 50] | [50, 100] | [100, 200] | ≥200 |

C_{10}: Chemical Oxygen Demand (million tons) | <1 | [1, 3) | [3, 5) | [5, 10] | ≥10 |

C_{11}: Ammonia nitrogen emissions (million tons) | <0.1 | [0.1, 0.3) | [0.3, 0.5) | [0.5, 1) | ≥1 |

C_{12}: Ecological water use rate (%) | ≥5 | [3, 5) | [2, 3) | [1, 2) | <1 |

Evaluation Indicators | AHP Weighting | Entropy Weight | Portfolio Weighting |
---|---|---|---|

C_{1} | 0.232 | 0.089 | 0.161 |

C_{6} | 0.205 | 0.08 | 0.142 |

C_{2} | 0.115 | 0.098 | 0.106 |

C_{5} | 0.098 | 0.086 | 0.092 |

C_{12} | 0.083 | 0.082 | 0.083 |

C_{10} | 0.069 | 0.076 | 0.073 |

C_{3} | 0.055 | 0.082 | 0.068 |

C_{11} | 0.049 | 0.086 | 0.067 |

C_{9} | 0.034 | 0.097 | 0.066 |

C_{7} | 0.023 | 0.098 | 0.061 |

C_{4} | 0.023 | 0.067 | 0.045 |

C_{8} | 0.014 | 0.059 | 0.036 |

**Table 4.**Barrier degree of water resources carrying capacity evaluation indicators in Zhangye City, 2010–2020.

Vintages | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{12} |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2010 | 18.09 | 11.44 | 7.71 | 4.89 | 6.39 | 15.79 | 8.45 | 4.99 | 9.14 | 1.83 | 3.37 | 7.92 |

2011 | 16.77 | 10.86 | 7.12 | 4.90 | 5.96 | 14.70 | 6.63 | 4.29 | 7.03 | 8.28 | 6.97 | 6.48 |

2012 | 16.52 | 11.34 | 7.16 | 4.61 | 6.57 | 14.32 | 6.20 | 4.41 | 6.94 | 7.67 | 7.69 | 6.55 |

2013 | 16.93 | 10.94 | 7.16 | 4.94 | 7.16 | 16.71 | 5.68 | 3.73 | 6.26 | 7.44 | 7.17 | 5.88 |

2014 | 16.24 | 11.75 | 6.89 | 4.49 | 7.63 | 17.12 | 5.45 | 3.97 | 6.17 | 7.25 | 6.40 | 6.66 |

2015 | 16.36 | 11.40 | 6.90 | 4.50 | 8.47 | 16.69 | 5.39 | 4.14 | 5.69 | 7.30 | 6.19 | 6.96 |

2016 | 15.92 | 13.72 | 6.78 | 5.03 | 9.35 | 14.04 | 5.19 | 3.54 | 5.66 | 7.27 | 6.17 | 7.32 |

2017 | 16.73 | 12.68 | 7.06 | 4.71 | 10.75 | 12.47 | 5.36 | 3.40 | 5.68 | 7.23 | 5.97 | 7.96 |

2018 | 19.46 | 11.76 | 8.12 | 5.32 | 11.27 | 11.20 | 4.99 | 2.43 | 5.58 | 7.10 | 5.45 | 7.31 |

2019 | 19.41 | 9.82 | 7.99 | 4.90 | 12.64 | 10.57 | 5.09 | 2.75 | 5.55 | 7.29 | 5.89 | 8.07 |

2020 | 20.84 | 12.25 | 8.65 | 5.72 | 13.15 | 8.64 | 4.87 | 2.08 | 4.94 | 6.60 | 5.30 | 6.96 |

average value | 17.57 | 11.63 | 7.41 | 4.91 | 9.03 | 13.84 | 5.75 | 3.61 | 6.24 | 6.84 | 6.05 | 7.10 |

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## Share and Cite

**MDPI and ACS Style**

Yang, M.; Qu, D.; Shen, Y.; Yang, S.; Liu, B.; Lu, W.
Evaluation of Water Resources Carrying Capacity of Zhangye City Based on Combined Weights and TOPSIS Modeling. *Water* **2023**, *15*, 4229.
https://doi.org/10.3390/w15244229

**AMA Style**

Yang M, Qu D, Shen Y, Yang S, Liu B, Lu W.
Evaluation of Water Resources Carrying Capacity of Zhangye City Based on Combined Weights and TOPSIS Modeling. *Water*. 2023; 15(24):4229.
https://doi.org/10.3390/w15244229

**Chicago/Turabian Style**

Yang, Mingyue, Deye Qu, Yue Shen, Shanquan Yang, Bin Liu, and Wenjing Lu.
2023. "Evaluation of Water Resources Carrying Capacity of Zhangye City Based on Combined Weights and TOPSIS Modeling" *Water* 15, no. 24: 4229.
https://doi.org/10.3390/w15244229