# Research on Optimal Allocation of Water Resources in Handan City Based on the Refined Water Resource Allocation Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}and 2.150 billion m

^{3}, respectively, and the water shortage rate is 11.72% and 22.11%, respectively. The water shortage is mainly in agriculture. In 2035, the allocated water volumes in normal and dry years will be 2.504 billion m

^{3}and 2.33 billion m

^{3}, respectively, and the water shortage rates will be 4.50% and 21.84%, respectively. After optimized allocation, the water supply structure was significantly improved. The proportion of groundwater supply will decrease at each planning level year, and the water supply of external water transfer and unconventional water will increase. This research can provide technical reference to the Handan development scheme depending on water resources in the future, as well as the optimal allocation of water resources in other cities in the Beijing–Tianjin–Hebei Region.

## 1. Introduction

## 2. Overview and Data Sources of the Study Area

#### 2.1. Overview of the Study Area

^{3}, and the per capita water resources were 118 m

^{3}(1980–2016), which is at a low level nationwide and is considered a resource-based water shortage. The region is also dominated by traditional high-energy-consuming industries and high-water-consuming agriculture, and the added value of six high-energy-consuming industries such as ferrous metal smelting, non-ferrous metal smelting, and electric power and heat production accounts for more than 50% of the industries above the designated size. The development and utilization of the total amount of water resources were at a high level. Due to the dependence on a large number of over-extracted groundwater resources in recent decades to maintain domestic and production water, some parts of the eastern plain have experienced problems such as groundwater level decline, surface settlement, and scrapping of machine wells.

#### 2.2. Data Sources

## 3. Forecast of Water Supply and Demand in the Planning Year

^{8}m

^{3}and 29.40 × 10

^{8}m

^{3}in normal and dry years, respectively (see Figure 2 for water demand of different industries in different districts and counties). The total water demand in normal and dry years in 2035 will be 26.21 × 10

^{8}m

^{3}and 29.81 × 10

^{8}m

^{3}, respectively; water demand of different industries in each district and county is shown in Figure 3.

^{8}m

^{3}and 20.99 × 10

^{8}m

^{3}, respectively. In 2035, the available water supply in normal and dry years will be 25.02 × 10

^{8}m

^{3}and 23.31 × 10

^{8}m

^{3}, respectively. Figure 4 reflects the proportion of available water supply of each water source under different scenarios in 2025 and 2035. Due to the prominent phenomenon of rain-fed agriculture in the region, agricultural water shortage is essentially normal, and 2020 was a dry year, making the current regional water supply predicted under the flat dry scenario in different planning years lower than the total water demand.

## 4. The Water Resources Optimal Allocation

#### 4.1. Regional Model Construction

#### 4.1.1. Objective Function

#### 4.1.2. Constraints

#### 4.2. Construction of Regional Water Supply and Consumption Network

#### 4.3. Model Parameter Adjustment

_{f}and K

_{y}of the total objective function were set to be 10. In terms of the optimization algorithm, the NSGAII- S algorithm was adopted, and the water quantity distributed by each water source to each water user was taken as the decision variable. Set optimization simulation parameters: the population size was 100, the gene length was 0, the crossover probability was 0.32, the mutation probability was 0.04, and the maximum number of runs was 1500.

#### 4.4. Verification of Simulation Results

## 5. Results and Analysis of Water Resource Allocation

#### 5.1. Optimization Analysis of Water Resource Allocation

^{8}m

^{3}< allocated water volume ≤ 3.00 × 10

^{8}m

^{3}): Wu’an, Daming, Weixian, Linzhang, Yongnian. The second grade (1.00 × 10

^{8}m

^{3}< allocated water volume ≤ 1.80 × 10

^{8}m

^{3}): Hanshan, Congtai, Quzhou, Jize, Feixiang, Shexian, Guantao. The third grade (0.25 × 10

^{8}m

^{3}< allocated water volume ≤ 1.00 × 10

^{8}m

^{3}): Fuxing, Fengfeng, Qiuxian, Guangping, Cheng’an, Cixian. It can be seen that the water resource allocation in Handan City has a relatively significant spatial difference, and this distribution difference was similar in different planning level years and different scenarios.

#### 5.2. Analysis of the Water Shortage Rate

#### 5.2.1. Analysis of the Regional Water Shortage Rate

#### 5.2.2. Analysis of the Industry Water Shortage Rate

^{8}m

^{3}and 7.22 × 10

^{8}m

^{3}in normal and dry years, respectively, and the agricultural water shortage rates will be 17.39% and 39.37%, respectively, as shown in Figure 13. Except for Shexian, all other districts and counties will have agricultural water use gaps to varying degrees. The agricultural water use gap in Fuxing and Wu’an will be the largest; in a normal year, the water shortage rates will be 80.72% and 70.39%, respectively, and this will increase to 84.50% and 72.76% in a dry year, respectively. This is followed by Congtai, Qiuxian, Hanshan, and Cheng’an. In a normal water year, the water shortage rates will be 53.86%, 51.53%, 46.33%, and 31.62%, respectively. In a dry year, the water shortage rates will increase to 67.31%, 63.90%, 64.87%, and 54.38%, respectively. The agricultural water use in nine districts and counties will have obvious gaps in dry years, such as in Yongnian and Jize. The water shortage rates will increase from about 10% in a normal year to 20–60%. In Linzhang in particular, the agricultural water shortage rate will be 0.03% in a normal year and 32.75% in a dry year. The gap of agricultural water use in Fengfeng will be relatively small, with a water shortage rate of 0.77% in a normal water year and 9.03% in a dry year.

^{8}m

^{3}and 5.96 × 10

^{8}m

^{3}, respectively; and the agricultural water shortage rate will be 8.59% and 32.49%, respectively, as shown in Figure 14. In a normal year, the agricultural water shortage in Fuxing, Wu’an, Qiuxian, and Cheng’an will be large, with water shortage rates of 37.59%, 27.00%, 44.45%, and 34.81%, respectively. The agricultural water shortage of other districts and counties will be relatively small, below 3%. In dry years, the agricultural water shortage rate in Hanshan and Yongnian will be the largest at 86.74% and 81.78%, respectively. The next will be Congtai, Fuxing, Wu’an, Qiuxian, Jize, Cheng’an, and Cixian, with water shortage rates ranging from 25% to 65%. The water shortage rates of other districts and counties will be between 10% and 20%. To sum up, agricultural water shortage will still be serious in dry years.

#### 5.3. Optimized Configuration of the Water Supply Structure

## 6. Conclusions

- (1)
- The total water demand of Handan in 2025 was estimated to be 2.54 billion m
^{3}and 2.94 billion m^{3}in normal and dry years, respectively. The simulated allocation water volumes of the model were 2.24 billion m^{3}and 2.10 billion m^{3}, respectively. The water deficient rates were 11.69% and 28.61%, respectively. In 2035, the total water demand in normal and dry years was estimated to be 2.62 billion m^{3}and 2.98 billion m^{3}, respectively, and the model simulated allocation water was 2.50 billion m^{3}and 2.33 billion m^{3}, respectively. The water shortage rates were 4.54% and 21.80%, respectively, being significantly improved compared with that in 2025. - (2)
- The water allocation in different planning years and different normal and dry years can essentially meet the domestic, industry, and ecology water demand, but the agricultural water shortage will be serious. In 2025, the agricultural water shortage in normal and dry years will be 250 million m
^{3}and 720 million m^{3}, respectively. The agricultural water shortage will be alleviated in 2035, and the agricultural water shortage will be reduced to 99 million m^{3}and 596 million m^{3}in normal and dry years, respectively. - (3)
- The regional groundwater as the water supply source will account for 32.16% and 35.86%, respectively, in the normal and dry years in 2025, and 32.10% and 32.51%, respectively, in 2035. Although will decrease slightly, the groundwater will still play a major role in the regional water supply source in the future. With the further development of ecological civilization construction and comprehensive treatment of groundwater, its proportion will gradually decline, while the water supply of external water transfer and unconventional water will increase. This will mainly be because of the construction of key supporting projects of the South to North Water Transfer Project and the transformation of enterprise water resources to recycling.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Wang, H.; Wang, J.; Liu, J.H.; Mei, C. Analysis of urban water cycle evolution and countermeasures. J. Hydraul. Eng.
**2021**, 52, 3–11. [Google Scholar] [CrossRef] - Wang, H.; You, J.J. Progress of water resources allocation during the past 30 years in China. J. Hydraul. Eng.
**2016**, 47, 265–271+282. [Google Scholar] [CrossRef] - Liu, M.Y.; Zhang, L.; Luan, Q.H.; Xu, D.; Liu, B. Application of artificial fish swarm algorithm in optimal allocation of water resources in Hejian County. Hydro.-Sci. Eng.
**2021**, 3, 74–83. [Google Scholar] - Zeng, M.; Wang, F.; Zhang, Y.P.; Yu, S. Research on of the optimal allocation of water resources in Guangdong Province based on fish swarm algorithm. J. Northwest Univ. Nat. Sci. Ed.
**2020**, 50, 733–741. [Google Scholar] [CrossRef] - Shan, B.Y.; Guo, P.; Zhang, F.; Guo, S. A multi-objective optimization model solving method based on genetic algorithm and scheme evaluatio. J. China Agric. Univ.
**2019**, 24, 157–165. [Google Scholar] [CrossRef] - Fang, G.H.; Guo, Y.X.; Wen, X.; Huang, X. Application of improved multi-objective quantum genetic algorithm on water resources optimal operation of Jiangsu Section of South-to-North Water Transfer East Route Project. Water Resour. Prot.
**2018**, 34, 34–41. [Google Scholar] - Li, X.D.; Sha, J.X.; Liu, B.; Yan, Z.H.; Li, S.; Zhou, W.K. Optimal allocation of water resources based on whale optimization algorithm. China Rural Water Hydropower
**2018**, 4, 40–45,49. [Google Scholar] - Ji, N.Y.; Yang, K.; Chen, J.; Yang, J. Research on optimal allocation model of regional water resources based on IABC-PSO algorithm. Yangtze River
**2021**, 52, 49–57,87. [Google Scholar] - Zhu, S.F.; Li, Z.X. Research on Optimal Allocation of Water Resources based on Improved NSGA-II Algorithm in Jinzhong City. China Rural Water Hydropower
**2020**, 34, 1–18. [Google Scholar] - Sha, J.X. Application of improved NSGA-Ⅱ in optimal allocation of water resources in Xingtai city. Water Resour. Power
**2018**, 36, 21–25. [Google Scholar] - Wang, H.; Gao, Z.H.; Sun, C.; Zhang, J.; Li, T. Water Resource Allocation for Irrigation Optimized using the NSGA-ⅡModel: Theory and Application. J. Irrig. Drain.
**2021**, 40, 118–124. [Google Scholar] - Mallawaarachchi, T.; Auricht, C.; Loch, A.; Adamson, D.; Quiggin, J. Water allocation in Australia’s Murray–Darling Basin: Managing change under heightened uncertainty. Econ. Anal. Policy
**2020**, 66, 345–369. [Google Scholar] [CrossRef] - Cheng, K.; Wei, S.; Ren, Y.T.; Fu, Q. Optimal allocation of agricultural water resources under the background of China’s agricultural water price reform-a case study of Heilongjiang province. Appl. Math. Model.
**2021**, 97, 636–649. [Google Scholar] [CrossRef] - Liu, D.; Guo, S.; Shao, Q.; Liu, P.; Xiong, L.; Wang, L.; Hong, X.; Xu, Y.; Wang, Z. Assessing the effects of adaptation measures on optimal water resources allocation under varied water availability conditions. J. Hydrol.
**2018**, 556, 759–774. [Google Scholar] [CrossRef] - Feng, J.H. Optimal allocation of regional water resources based on multi-objective dynamic equilibrium strategy. Appl. Math. Model.
**2021**, 90, 1183–1203. [Google Scholar] [CrossRef] - Gao, L.M.; Chen, H.W.; Li, F.L. Quantity/quality-dual-control-based optimal allocation of water resources in the typical water-shortage area of North China. South-North Water Transf. Water Sci. Technol.
**2020**, 18, 70–78. [Google Scholar] [CrossRef] - Zeng, X.T.; Zhang, S.J.; Feng, J.; Huang, G.H.; Li, Y.P.; Zhang, P.; Chen, J.P.; Li, K.L. A multi-reservoir based water-hydroenergy management model for identifying the risk horizon of regional resources-energy policy under uncertainties. Energy Convers. Manag.
**2017**, 143, 66–84. [Google Scholar] [CrossRef] - Zhuang, X.W.; Li, Y.P.; Huang, G.H.; Zeng, X.T. An inexact joint-probabilistic programming method for risk assessment in water resources allocation. Stoch. Environ. Res. Risk Assess.
**2015**, 29, 1287–1301. [Google Scholar] [CrossRef] - Sang, X.F.; Wang, H.; Wang, J.H.; Zhao, Y.; Zhou, Z. Water resources comprehensive allocation and simulation model (WAS), part Ⅰ: Theory and development. J. Hydraul. Eng.
**2018**, 49, 1259–1451. [Google Scholar] [CrossRef] - Sang, X.F.; Zhao, Y.; Zhai, Z.L.; Chang, H. Water resources comprehensive allocation and simulation model (WAS), part Ⅱ: Application. J. Hydraul. Eng.
**2019**, 50, 201–208. [Google Scholar] [CrossRef] - Chang, H.Y. Development and Improvement of WAS Model and Application of Water Resources Allocation in Beijing-Tianjin-Hebei Region. Master’s Thesis, China Institute of Water Resources & Hydropower Research, Beijing, China, 2019. [Google Scholar]
- Cao, Y.Q.; Li, L.H. Simulation analysis of water resources in Beijing based on integrated comprehensive water simulation and allocation model. Adv. Sci. Technol. Water Resour.
**2021**, 41, 25–31. [Google Scholar] - Du, L.J.; Chen, G.F.; Liu, C.S.; Wang, X.; Liu, J.; Wang, H. GWAS model-based optimal allocation of water resources in irrigation district. Water Resour. Hydropower Eng.
**2020**, 51, 26–35. [Google Scholar] - Luan, Q.H.; Gao, H.Y.; Liu, H.L.; He, L.; Ma, J.; Wang, C. Optimal allocation of water resources in Wu’an County based on GWAS model. Water Resour. Prot.
**2022**. [Google Scholar] - Ma, J.; Duan, N.; Lv, R.L.; Luan, Q.H.; Wang, Q. Health evaluation methods of water-cycle and related applications: A case study on Handan city. Sci. Technol. Eng.
**2021**, 21, 14372–14378. [Google Scholar] - Huo, H.S. Handan Statistical Yearbook (2020); China Statistics Press: Beijing, China, 2020; pp. 33–316.
- Guo, J.P.; Wang, X.H.; Li, C.Y.; Yan, X.T.; Liu, H.L. Handan Water Resources Bulletin (2020); Handan Water Resources Management Center: Handan, China, 2021; pp. 1–43. [Google Scholar]

Planning Years | Scenarios | Water Demand (10^{8} m^{3}) | Allocated Water Volume (10^{8} m^{3}) | Water Shortage Rate (%) |
---|---|---|---|---|

2025 | 50% | 25.40 | 22.43 | 11.69 |

75% | 29.40 | 20.99 | 28.61 | |

2035 | 50% | 26.21 | 25.02 | 4.54 |

75% | 29.81 | 23.31 | 21.80 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ma, J.; Liu, H.; Wu, W.; Zhang, Y.; Dong, S. Research on Optimal Allocation of Water Resources in Handan City Based on the Refined Water Resource Allocation Model. *Water* **2023**, *15*, 154.
https://doi.org/10.3390/w15010154

**AMA Style**

Ma J, Liu H, Wu W, Zhang Y, Dong S. Research on Optimal Allocation of Water Resources in Handan City Based on the Refined Water Resource Allocation Model. *Water*. 2023; 15(1):154.
https://doi.org/10.3390/w15010154

**Chicago/Turabian Style**

Ma, Jing, Hongliang Liu, Wenfeng Wu, Yinqin Zhang, and Sen Dong. 2023. "Research on Optimal Allocation of Water Resources in Handan City Based on the Refined Water Resource Allocation Model" *Water* 15, no. 1: 154.
https://doi.org/10.3390/w15010154