# Spatial Equilibrium Evaluation of the Water Resources in Tai’an City Based on the Lorenz Curve and Correlation Number

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Methods and Model Building

#### 2.1. Study Area

^{2}, accounting for 4.95% of the total area of the province. Tai’an has jurisdiction over 6 administrative regions: Taishan district, Daiyue district, Xintai city, Feicheng city, Ningyang county, and Dongping county. As shown in Figure 1, they are divided into the Yellow River and the Huaihe River basins. The basins are mainly the Dawen River system of the Yellow River basin in the north and the Sihe River system and Liangji Canal system of the Huaihe River basin in the south. The average annual precipitation of Tai’an city is 690.6 mm, which is characterized by drought in spring, flood in summer, and drought in late autumn. The annual precipitation is also more obvious, abundant, and dry alternately.

#### 2.2. Gini Coefficient Method

- (1)
- The water resource factors include the regional water resources (y
_{1}) and total water use (y_{2}), and the matching objects include the agricultural acreage (x_{1}), population (x_{2}), GDP of the secondary industry (x_{3}), GDP of the tertiary industry (x_{4}), and agricultural irrigation water consumption (x_{5}). Due to agricultural irrigation, water use is highly correlated with the total water resources, while the total water amount exhibits a less notable correlation. Hence, the matching relationships could be determined as y_{1}–x_{1}, y_{1}–x_{2}, y_{1}–x_{3}, y_{1}–x_{4}, y_{1}–x_{5}, y_{2}–x_{1}, y_{2}–x_{2}, y_{2}–x_{3}, and y_{2}–x_{4}.

- (2)
- The total amount of water resources and the total water consumption per unit of agricultural irrigation in each subregion were listed in ascending order: unit agricultural acreage, unit population, unit GDP of the secondary industry, unit GDP of the tertiary industry, and unit agricultural irrigation water consumption.
- (3)
- The proportion of matching objects (x
_{1}–x_{5}) in each subregion to those in the whole region was calculated. - (4)
- The matching primitives (y
_{1}and y_{2}) and matching objects (x_{1}–x_{5}) in each subregion were accumulated in proportion to the total region. - (5)
- The X-axis denotes the accumulative ratio of the matching objects (x
_{1}–x_{5}) in each subregion to those in the whole region, and the Y-axis denotes the accumulative ratio of the matching primitives (y_{1}and y_{2}) to draw the Lorenz curve, as shown in Figure 2. In this paper, the triangular area algorithm was used to calculate the Gini coefficient values of the water resource matching primitives and each matching object [31]:$$G={{\displaystyle \sum}}_{j=1}^{n-1}{x}_{j}{y}_{j+1}-{x}_{j+1}{y}_{j},$$_{j}denotes the unit agricultural acreage, unit population, unit GDP of the tertiary industry, unit GDP of the secondary industry, and unit agricultural irrigation water consumption in each subregion, the total water resources in water subdomain j, or the agricultural acreage, population, GDP of the secondary industry, GDP of the tertiary industry, and agricultural irrigation water use in the whole region as a proportion of the total value; y_{j}is the accumulative value of the matching primitive proportion in subregion J; and n is the number of subregions.

#### 2.3. Connection Number Method

_{ij}between the sample value of each matching relationship d

_{ij}and grade standard s

_{ijk}[37], where i = 1, 2, 3, 4, 5 denotes the serial number of the matching relationship, j = 1, 2…, n denotes the serial number of the subregion, and k = 1, 2, 3, 4, 5 is the rank.

_{ij}

_{1}, v

_{ij}

_{2}, v

_{ij}

_{3}, v

_{ij}

_{4}, and v

_{ij}

_{5}are the identity degree, difference degree, and opposition degree components of the normalized five-member relationship number, and I

_{1}, I

_{2}, and I

_{3}are the coefficients of the difference degree, with a value of [−1, 1]. The calculation method has been reported elsewhere [38,39].

#### 2.4. Construction of the Water Resource Spatial Equilibrium Evaluation Model

- (1)
- Construction of the matching relationships. The interaction between the water resource system and economic and social system was comprehensively considered, and the matching relationship of the water resource quantity (y
_{1}–x_{1}, y_{1}–x_{2}, y_{1}–x_{3}, y_{1}–x_{4}, y_{1}–x_{5}, y_{2}–x_{1,}y_{2}–x_{2}, y_{2}–x_{3}, and y_{2}–x_{4}) was adopted as the evaluation index according to the principles of rationality, applicability, and operability [38]. A spatial equilibrium evaluation of the regional water resources was conducted. - (2)
- Calculation of the sample values d
_{ij}. The longitudinal distance between any point on the Lorenz curve corresponding to y = x (the absolute mean curve) and the same point on the abscissa can be expressed as d_{ij}(as shown in Figure 2), which can be calculated as:$${d}_{ij}={x}_{ij}-{y}_{ij},$$_{ij}is the cumulative value of the proportion of matching object i in the whole region to that in subregion j; y_{ij}is the cumulative value of the proportion of the total water resources corresponding to matching object I in subregion j; i is the serial number of the matching relationship (i = 1, 2, 3, 4, and 5 denote the cultivated land area, population, GDP of the secondary industry, GDP of the tertiary industry, and agricultural irrigation water consumption, respectively); and j is the serial number of the subregion (j = 1, 2, …, n).

- (3)
- Classification of the evaluation indicators. The closer the Lorenz curve is to the absolute mean curve, the higher the equilibrium between the matching primitives and objects, and vice versa. The length of vertical line segment S between each point on the absolute mean curve and the horizontal axis was divided into five equal grades (Ⅰ, Ⅱ, Ⅲ, Ⅳ, and Ⅴ) as the grade standard s of d
_{ij}, in which grade I is close to the absolute mean curve indicates equilibrium, grade V is far from the absolute mean curve indicates imbalance, etc. - (4)
- Calculation of the connection number of the matching relationship. With the use of the special value method [40], the coefficients of the difference degree (I
_{1}= 0.5, I_{2}= 0, and I_{3}= −0.5) and the coefficient of the opposition degree (J = −1) were considered to calculate the connection number of each matching relationship. The evaluation grades can be divided according to the standards listed in Table 4 by referring to the principle of Gini coefficient classification (60-point scale) and relevant trial results [41].

## 3. Results

#### 3.1. Evaluation Results of the Spatial Equilibrium of the Total Water Resources in Tai’an City

#### 3.2. Evaluation Results of the Spatial Equilibrium of the Total Water Use in Tai’an City

## 4. Discussion and Conclusions

- (1)
- The average Gini coefficients of the total water resources in Tai’an city from 2011 to 2020 were 0.21, 0.22, 0.23, 0.32, and 0.19 for the arable land area, population number, GDP of the secondary industry, GDP of the tertiary industry, and agricultural irrigation water consumption, respectively. The correlation values were 0.47, 0.30, 0.35, 0.18, and 0.46, respectively. The average Gini coefficient values of the total water use, cultivated land area, population, GDP of the secondary industry, and GDP of the tertiary industry in Tai’an from 2011 to 2020 were 0.16, 0.11, 0.17, and 0.24, and the correlation values were 0.60, 0.54, 0.55, and 0.42, respectively. In Tai’an city, the proportion of dry years from 2011 to 2020 reached 60%. Continuous drought resulted in an unbalanced spatial distribution and regional distribution of water resources and is an important reason for the difference in the equilibrium degree according to the different matching relationships [50].
- (2)
- An empirical study of the spatial equilibrium matching relationship between the total water resources and total water use in Tai’an city, cultivated land area, population number, GDP of the secondary industry, GDP of the tertiary industry, and agricultural irrigation water consumption was conducted. The results showed that the total water use–cultivated land area and total water use–population in Tai’an city from 2011 to 2020 exhibited a spatial equilibrium state. The total water resources–arable land area, total water resources–agricultural irrigation water consumption, total water use–GDP of the secondary industry, and total water use–GDP of the tertiary industry occurred in a relatively balanced state. The total water resources–population and total water resources–GDP of the secondary industry indicated a critical state. The total amount of water resources–GDP of the tertiary industry exhibited a relatively unbalanced state in space. In particular, the balance between the total water resources and the GDP of the secondary industry was poor and must be improved.
- (3)
- An uneven distribution of the total water resources in Tai’an city was obtained. River runoff in Tai’an city is mainly fed by precipitation, and the regional distribution trend of the annual runoff depth is basically consistent with that of precipitation. However, because runoff is affected by the underlying surface, the distribution of the annual runoff depth is more uneven than that of the annual precipitation. The distribution trend decreased from the eastern hilly area to the western plain area and in-creased from the eastern hilly area to the western plain area. The water resources in Tai’an city mainly stem from atmospheric precipitation. Due to the high interannual and annual variations in atmospheric precipitation, the amount of water resources also exhibits similar characteristics, resulting in large interannual fluctuations in the total amount of water resources. However, except for a small increase in 2017, the total water consumption decreased year by year and basically remained stable.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Zuo, Q.; Guo, J.; Ma, J.; Cui, G.; Yang, R.; Yu, L. Assessment of regional-scale water resources carrying capacity based on fuzzy multiple attribute decision-making and scenario simulation. J. Ecol. Indicat.
**2021**, 130, 108034. [Google Scholar] [CrossRef] - Jin, J.L.; Xu, X.G.; Cui, Y.; Zhou, R.X.; Wu, C.G.; Zhang, L.B. Water resources spatial equilibrium evaluation method based on correlation number and Lorentz curve. J. Adv. Water Sci.
**2021**, 32, 387–395. [Google Scholar] [CrossRef] - Li, F.; Wu, F.P.; Chen, L.X.; Zhao, Y.; Chen, X.N.; Shao, Z.Y. Fair and Reasonable Allocation of Trans-Boundary Water Resources Based on an Asymmetric Nash Negotiation Model from the Satisfaction Perspective: A Case Study for the Lancang–Mekong River Bain. Int. J. Environ. Res. Public Health
**2020**, 17, 7638. [Google Scholar] [CrossRef] - Wang, S.W.; Fu, L.; Peng, H.X.; Wang, J.M.; Hua, Y.A.; Gui, Z.H. Study on an Equilibrium Water Price System Based on Cooperative Game Technology. Water
**2023**, 15, 2354. [Google Scholar] [CrossRef] - Gedefaw, M.; Wang, H.; Yan, D.H.; Qin, T.L.; Wang, K.; Girma, A.; Batsuren, D.; Abiyu, A. Water Resources Allocation Systems under Irrigation Expansion and Climate Change Scenario in Awash River Basin of Ethiopia. Water
**2019**, 11, 1966. [Google Scholar] [CrossRef] [Green Version] - He, H.X.; Chen, A.Q.; Yin, M.W.; Ma, Z.Z.; You, J.J.; Xie, X.M.; Wang, Z.Z.; An, Q. Optimal Allocation Model of Water Resources Based on the Prospect Theory. Water
**2019**, 11, 1289. [Google Scholar] [CrossRef] [Green Version] - Lu, Z.X.; Wei, Y.P.; Feng, Q.; Xiao, H.L.; Cheng, G.D. Advances in social hydrology. J. Adv. Water Sci.
**2016**, 27, 772–783. [Google Scholar] [CrossRef] - Kahil, M.T.; Dinar, A.; Albiac, J. Modeling water scarcity and droughts for policy adaptation to climate change in arid and semiarid regions. J. Hydrol.
**2015**, 522, 95–109. [Google Scholar] [CrossRef] [Green Version] - Guo, L.D.; Xia, Z.Q.; Wang, Z.J. The aral sea and the balkhash lake change and the environment effect comparison. Adv. Water Sci.
**2011**, 22, 764–770. [Google Scholar] - MQureshi, E.; Whitte, S.M.; Mainuddin, M.; Marvanek, S.; Elmahdi, A. A biophysical and economic model of agriculture and water in the Murray-Darling basin, Australia. Environ. Model. Softw.
**2013**, 41, 98–106. [Google Scholar] [CrossRef] - Jin, J.L.; Li, J.Q.; Wu, C.G.; He, J.; Guo, X.N.; Zhang, H.Y.; Chen, M.L.; Chen, L. Research progress on spatial equilibrium of water resources. J. North China Univ. Water Resour. Electr. Power (Nat. Sci. Ed.)
**2019**, 40, 47–60. [Google Scholar] [CrossRef] - Guo, X.N.; Li, J.Q.; Li, Y.L.; He, J.; Jin, J.L. Evaluation and control measures of water resources spatial equilibrium in Beijing-Tianjin-Hebei region. J. Water Resour. Prot.
**2022**, 38, 62–66+81. [Google Scholar] - Zhou, S.; Huang, Y.; Wei, Y.; Wang, G. Socio-hydrological water balance for water allocation between human and envi-ronmental purposes in catchments. Hydrol. Earth Syst. Sci.
**2015**, 19, 3715–3726. [Google Scholar] [CrossRef] [Green Version] - Zhang, L.B.; Yu, H.Y.; Jin, J.L.; Hu, Y.N.; Cui, Y.; Wu, C.G. Evaluation and optimal control of water resources spatial equilibrium in large irrigation area based on correlation number. J. Hydraul. Eng.
**2021**, 52, 1011–1023. [Google Scholar] [CrossRef] - Jin, J.L.; Xu, X.G.; Zhou, R.X.; Cui, Y.; Ning, S.W.; Zhou, Y.L.; Wu, C.G. Water resources spatial equilibrium evaluation method based on correlation number and coupling coordination degree. J. Water Resour. Prot.
**2021**, 37, 387–395. [Google Scholar] [CrossRef] - Xia, F.; Chen, Y.; Dou, M.; Han, Y.P. Calculation method and application of water resources spatial equilibrium coefficient. J. Water Resour. Prot.
**2020**, 36, 52–57. [Google Scholar] [CrossRef] - Yang, Y.F.; Wang, H.R.; Wang, C.; Zhang, Y.Y. Coupling Variable Fuzzy Sets and Gini Coefficient to Evaluate the Spatial Equilibrium of Water Resources. J. Water Resour.
**2022**, 49, 292–300. [Google Scholar] [CrossRef] - Yang, Y.F.; Gong, S.X.; Wang, H.G.; Zhao, Z.Y.; Yang, B. Construction and application of a spatial equilibrium evaluation model for water resources. J. Prog. Water Sci.
**2021**, 32, 33–44. [Google Scholar] [CrossRef] - Liang, X.; Li, J.; Guo, G.; Li, S.; Gong, Q. Urban water resource utilization efficiency based on SBM-undesirable–Gini coefficient–kernel density in Gansu Province, China. Environ. Dev. Sustain.
**2022**, 18, 1–20. [Google Scholar] [CrossRef] - Liu, H.; Jia, Y.; Niu, C.; Gan, Y. Spatial Pattern Analysis of Regional Water Use Profile Based on the Gini Coefficient and Location Quotient. J. Am. Water Resour. Assoc.
**2019**, 55, 1349–1366. [Google Scholar] [CrossRef] - Wang, X.; Chen, Y.; Li, Z.; Fang, G.; Wang, F.; Hao, H. Water resources management and dynamic changes in water politics in the transboundary river basins of Central Asia. Hydrol. Earth Syst. Sci.
**2021**, 25, 3281–3299. [Google Scholar] [CrossRef] - Correa-Parra, J.; Vergara-Perucich, J.F.; Aguirre-Nuñez, C. Water Privatization and Inequality: Gini Coefficient for Water Resources in Chile. Water
**2020**, 12, 3369. [Google Scholar] [CrossRef] - Zhou, R.X.; Jin, J.L.; Cui, Y.; Ning, S.W.; Zhou, L.G.; Zhang, L.B.; Wu, C.G.; Zhou, Y.L. Spatial Equilibrium Evaluation of Regional Water Resources Carrying Capacity Based on Dynamic Weight Method and Dagum Gini Coefficient. Front. Earth Sci.
**2022**, 9, 790349. [Google Scholar] [CrossRef] - Gunasekara, N.K.; Kazama, S.; Yamazaki, D.; Oki, T. Water Conflict Risk due to Water Resource Availability and Unequal Distribution. Water Resour Manag.
**2014**, 28, 169–184. [Google Scholar] [CrossRef] - Kazama, S.; Sarukkalige, P.R.; Ekkawatpanit, C.; Sawamoto, M. Evaluation of the inequality of water resources. Proc. ICE Water Manag.
**2013**, 166, 303–314. [Google Scholar] [CrossRef] - Masaki, Y.; Hanasaki, N.; Takahashi, K.; Hijioka, Y. Global-scale analysis on future changes in flow regimes using Gini and Lorenz asymmetry coefficients. Water Resour. Res.
**2014**, 50, 4054–4078. [Google Scholar] [CrossRef] - Kazemi, M.; Bozorg-Haddad, O.; Fallah-Mehdipour, E.; Loáiciga, H.A. Inter-basin hydropolitics for optimal water resources allocation. Environ. Monit. Assess.
**2020**, 192, 478. [Google Scholar] [CrossRef] - Zhang, J.; Li, Y.; Liu, C.; Qu, Z.; Li, F.; Yang, Z.; Jiang, L.; Fu, J. Application of Set Pair Analysis in a Comprehensive Evaluation of Water Resource Assets: A Case Study of Wuhan City, China. Water
**2019**, 11, 1718. [Google Scholar] [CrossRef] [Green Version] - Niu, C.; Chang, J.X.; Wang, Y.M.; Shi, X.G.; Wang, X.B.; Guo, A.J.; Jin, W.T.; Zhou, S. A Water Resource Equilibrium Regulation Model Under Water Resource Utilization Conflict: A Case Study in the Yellow River Basin. J. Water Resour. Res.
**2022**, 58, e2021WR030779. [Google Scholar] [CrossRef] - Gong, H.E. Gini Coefficient and its practical application. J. Mark. Demogr. Anal.
**2002**, 8, 35–40. [Google Scholar] - Chen, L.S.; Huang, Q. An exact calculation method for Gini coefficient and its application in China. J. Discret. Math. Sci. Cryptogr.
**2018**, 21, 1353–1363. [Google Scholar] [CrossRef] - Chen, J.D.; Pu, M.; Hou, W.X. The trend of the Gini coefficient of China (1978–2010). J. Chin. Econ. Bus. Stud.
**2019**, 17, 213–214. [Google Scholar] [CrossRef] - Zhao, K.Q. Set pair analysis and preliminary application. J. Nat. Explor.
**1994**, 7, 67–72. [Google Scholar] - Jin, J.L.; Chen, L.; Chen, M.L.; Li, J.Q.; Zhang, L.B.; Dong, T. Water resources carrying capacity evaluation method based on set pair analysis and risk matrix. Yangtze River
**2018**, 49, 35–41. [Google Scholar] [CrossRef] - Ye, L.C. Calculation method for Gini coefficient. J. China Stat.
**2003**, 256, 60. [Google Scholar] - Jin, J.L.; Zhang, H.Y.; Chen, M.L.; Cui, Y.; Ning, S.W. Evaluation and diagnosis of agricultural drought vulnerability based on grey correlation degree and correlation number coupling. J. Catastrophol.
**2019**, 34, 1–7. [Google Scholar] [CrossRef] - Jin, J.L.; Shen, S.X.; Li, J.Q.; Cui, Y.; Wu, C.G. Evaluation and diagnostic analysis method of regional water resources carrying capacity based on correlation number. J. North China Univ. Water Resour. Electr. Power (Nat. Sci. Ed.)
**2018**, 39, 1–9. [Google Scholar] - Jin, J.L.; Wu, K.Y.; Wei, Y.M. Watershed water security evaluation model based on correlation number. J. Hydraul. Eng.
**2008**, 379, 401–409. [Google Scholar] [CrossRef] - Chen, S.Y. Variable Fuzzy Set Theory and Method for Water Resources and flood Control System Engineering; Dalian University of Technology: Dalian, China, 2003. [Google Scholar]
- Yang, Q.Q. Intelligent Modeling Method of Regional Water and Soil Resources Matching Analysis and Its Application. Ph.D. Thesis, Hefei University of Technology, Hefei, China, 2016. [Google Scholar]
- Wu, D.M. Gini coefficient theory and empirical analysis. J. Econ. Restruct.
**2002**, 115, 37–40. [Google Scholar] - Tai’an Statistics Bureau. Tai’an Statistical Yearbook; Tai’an Statistics Bureau: Tai’an, China, 2012–2021. [Google Scholar]
- Tai’an Water Resources Bureau. Tai’an Water Resources Bulletin; Tai’an Water Resources Bureau: Tai’an, China, 2011–2020. [Google Scholar]
- Tai’an City People’s Government. Main Data Bulletin of the Third Land Survey of Tai’an City; Tai’an City People’s Government: Tai’an, China, 2022. [Google Scholar]
- Tai’an City Statistics Bureau. Administrative Division; Tai’an City Statistics Bureau: Tai’an, China, 2022. [Google Scholar]
- Jahandideh-Tehrani, M.; Bozorg Haddad, O.; Loáiciga, H.A. Hydropower Reservoir Management Under Climate Change: The Karoon Reservoir System. Water Resour Manag.
**2015**, 29, 749–770. [Google Scholar] [CrossRef] - Li, M.S.; Yang, X.H.; Wu, F.F.; Babuna, P. Spatial equilibrium-based multi-objective optimal allocation of regional water resources. J. Hydrol. Reg. Stud.
**2022**, 44, 101219. [Google Scholar] [CrossRef] - Molla, D.D.; Tegaye, T.A.; Fletcher, C.G. Simulated surface and shallow groundwater resources in the Abaya-Chamo Lake basin, Ethiopia using a spatially-distributed water balance model. J. Hydrol. Reg. Stud.
**2019**, 24, 100615. [Google Scholar] [CrossRef] - Bian, D.; Yang, X.; Xiang, W.; Sun, B.; Chen, Y.; Babuna, P.; Li, M.; Yuan, Z. A new model to evaluate water resource spatial equilibrium based on the game theory coupling weight method and the coupling coordination degree. J. Clean. Prod.
**2022**, 366, 132907. [Google Scholar] [CrossRef] - Yao, L.M.; Xu, Z.W.; Chen, X.D. Sustainable water allocation strategies under various climate scenarios: A case study in China. J. Hydrol.
**2019**, 574, 529–543. [Google Scholar] [CrossRef]

**Figure 2.**Diagram of the water resource spatial equilibrium evaluation model based on the connection number and Lorenz curve. (I–V indicates the level classification of evaluation indicators in the following paragraphs.)

**Figure 5.**Evaluation results of the spatial equilibrium of the total water resources. ((

**a**–

**e**) represents the evaluation results of total water resources, cultivated land area, population, GDP of secondary industry, GDP of tertiary industry and water consumption of agricultural irrigation respectively.)

**Figure 6.**Evaluation results of the spatial balance of the total water use. ((

**a**–

**d**) represents the evaluation results of total water use, cultivated land area, population, GDP of secondary industry and GDP of tertiary industry respectively.)

Water Resource Factor | Matching Factor | Gini Coefficient Matching Relationship | |
---|---|---|---|

Water resources (w) | Agricultural acreage (1) | Water resources and cultivated land area | Gw1 |

Population (2) | Water resources and population | Gw2 | |

GDP of the secondary industry (3) | Water resources and GDP of the secondary industry | Gw3 | |

GDP of the tertiary industry (4) | Water resources and GDP of the tertiary industry | Gw4 | |

Water consumption for agricultural irrigation (5) | Total water resources and agricultural irrigation water consumption | Gw5 | |

Water use (u) | Agricultural acreage (1) | Water use and cultivated land area | Gu1 |

Population (2) | Water use and population | Gu2 | |

GDP of the secondary industry (3) | Water use and GDP of the secondary industry | Gu3 | |

GDP of the tertiary industry (4) | Water use and GDP of the tertiary industry | Gu4 |

Gini coefficient | Less than 0.2 | 0.2–0.3 | 0.3–0.4 | 0.4–0.5 | Greater than 0.5 |

Evaluation results | Absolute balance | Comparative balance | Relative balance | Comparative inequality | Absolute inequality |

Water Resource Factor | Matching Factor | Connection Number Matching Relationship | |
---|---|---|---|

Water resources (w) | Agricultural acreage (1) | Water resources and cultivated land area | uw1 |

Population (2) | Water resources and population | uw2 | |

GDP of the secondary industry (3) | Water resources and GDP of the secondary industry | uw3 | |

GDP of the tertiary industry (4) | Water resources and GDP of the tertiary industry | uw4 | |

Water consumption for agricultural irrigation (5) | Total water resources and agricultural irrigation water consumption | uw5 | |

Water use (u) | Agricultural acreage (1) | Water use and cultivated land area | uu1 |

Population (2) | Water use and population | uu2 | |

GDP of the secondary industry (3) | Connection number of water use and GDP of the secondary industry | uu3 |

**Table 4.**Evaluation grade of the matching relationship between the Gini coefficient and connection number.

Gini coefficient | [0, 0.2) | [0.2, 0.3) | [0.3, 0.4) | [0.4, 0.5) | [0.5, 1.0) |

Evaluation results | High match | Comparative match | Relative matching | Comparative mismatch | High mismatch |

Connection number | [−1.00, −0.05] | (−0.05, 0.20] | (0.20, 0.38] | (0.38, 0.58] | (0.58, 1.00] |

Evaluation results | V (disequilibrium) | IV (comparative disequilibrium) | III (critical) | II (comparative equilibrium) | I (equilibrium) |

Gini Coefficients | Results of Gini Coefficient Evaluation in Different Years | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | |

Gw1 | 0.294 | 0.237 | 0.307 | 0.109 | 0.102 | 0.207 | 0.140 | 0.168 | 0.259 | 0.249 |

Gw2 | 0.270 | 0.199 | 0.242 | 0.144 | 0.142 | 0.218 | 0.152 | 0.245 | 0.358 | 0.185 |

Gw3 | 0.258 | 0.215 | 0.194 | 0.190 | 0.192 | 0.243 | 0.152 | 0.191 | 0.312 | 0.310 |

Gw4 | 0.333 | 0.296 | 0.296 | 0.307 | 0.308 | 0.348 | 0.268 | 0.331 | 0.396 | 0.307 |

Gw5 | 0.275 | 0.202 | 0.267 | 0.114 | 0.097 | 0.206 | 0.169 | 0.154 | 0.311 | 0.153 |

Gu1 | 0.189 | 0.193 | 0.159 | 0.109 | 0.160 | 0.129 | 0.140 | 0.153 | 0.174 | 0.162 |

Gu2 | 0.088 | 0.058 | 0.097 | 0.144 | 0.089 | 0.090 | 0.089 | 0.217 | 0.086 | 0.116 |

Gu3 | 0.181 | 0.163 | 0.134 | 0.190 | 0.095 | 0.108 | 0.107 | 0.261 | 0.228 | 0.236 |

Gu4 | 0.211 | 0.196 | 0.232 | 0.245 | 0.232 | 0.237 | 0.239 | 0.359 | 0.212 | 0.234 |

Connection Number | Results of Connection Number Evaluation in Different Years | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | |

uw1 | 0.323 | 0.490 | 0.249 | 0.627 | 0.625 | 0.425 | 0.698 | 0.569 | 0.441 | 0.400 |

uw2 | 0.171 | 0.328 | 0.213 | 0.407 | 0.424 | 0.384 | 0.364 | 0.284 | 0.079 | 0.354 |

uw3 | 0.194 | 0.383 | 0.340 | 0.414 | 0.424 | 0.416 | 0.424 | 0.342 | 0.233 | 0.287 |

uw4 | 0.075 | 0.185 | 0.134 | 0.305 | 0.293 | 0.266 | 0.336 | 0.206 | 0.045 | 0.090 |

uw5 | 0.293 | 0.470 | 0.350 | 0.531 | 0.620 | 0.393 | 0.553 | 0.610 | 0.291 | 0.490 |

uu1 | 0.569 | 0.569 | 0.601 | 0.627 | 0.617 | 0.637 | 0.615 | 0.627 | 0.557 | 0.567 |

uu2 | 0.632 | 0.589 | 0.555 | 0.407 | 0.555 | 0.563 | 0.522 | 0.482 | 0.550 | 0.506 |

uu3 | 0.579 | 0.587 | 0.626 | 0.414 | 0.621 | 0.636 | 0.614 | 0.448 | 0.493 | 0.488 |

uu4 | 0.454 | 0.516 | 0.421 | 0.402 | 0.428 | 0.428 | 0.420 | 0.260 | 0.452 | 0.425 |

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## Share and Cite

**MDPI and ACS Style**

Lou, Y.; Qiu, Q.; Zhang, M.; Feng, Z.; Dong, J.
Spatial Equilibrium Evaluation of the Water Resources in Tai’an City Based on the Lorenz Curve and Correlation Number. *Water* **2023**, *15*, 2617.
https://doi.org/10.3390/w15142617

**AMA Style**

Lou Y, Qiu Q, Zhang M, Feng Z, Dong J.
Spatial Equilibrium Evaluation of the Water Resources in Tai’an City Based on the Lorenz Curve and Correlation Number. *Water*. 2023; 15(14):2617.
https://doi.org/10.3390/w15142617

**Chicago/Turabian Style**

Lou, Yanqian, Qingtai Qiu, Mingtai Zhang, Zhonglun Feng, and Jie Dong.
2023. "Spatial Equilibrium Evaluation of the Water Resources in Tai’an City Based on the Lorenz Curve and Correlation Number" *Water* 15, no. 14: 2617.
https://doi.org/10.3390/w15142617