Joint Optimization of Urban Water Quantity and Quality Allocation in the Plain River Network Area

Abstract

Cities located in the plain river network area possess abundant water resources. However, due to urbanization and industrialization, there is a severe water shortage problem caused by poor water quality. To overcome this issue, a multi-objective optimal allocation model of water quantity and quality is proposed. The model considers regional water resources, economic, social, and environmental requirements and uses the NSGA-II genetic algorithm for model solution. Furthermore, to evaluate and analyze the degree of spatial equilibrium of regional water resources and how it relates to economic factors, the study uses the spatial equilibrium theory of water resources and the Gini coefficient of water resources. Jingjiang, a city in Jiangsu Province characterized by a typical plain river network area, was selected as the study area. The results of the optimal allocation of water resources in Jingjiang City show that: (1) total water consumption and chemical oxygen demand (COD) emissions for the current planning period are within their respective limits. In addition, the implementation of the water conservation program has resulted in a 5% reduction in total water shortages and a reduction of COD emissions by 1276 tons, (2) the structure of the water supply in Jingjiang City has been optimized; more than 90% of Ⅳ~V surface water is used for agriculture, and the domestic water supply is mainly from transit water, which effectively ensures that high-quality water is used in the domestic water supply, (3) the spatial equilibrium coefficient of water resources per sub-area is between 0.33 and 0.74, indicating an unbalanced or almost unbalanced level. The application of a water conservation program has resulted in the improvement of the spatial equilibrium level of water resources in each sub-area, with an overall spatial equilibrium of 0.64, indicating a more balanced level; the degree of matching of water resources with population, GDP, and land area is at the matching level, (4) according to the Gini coefficient of the distribution of water resources, the plains river network area displays a better match between water resources and economic and social factors of each water receiving area, thanks to its unique geographical location and natural conditions. This study can serve as a decision-making reference for addressing the urban water quality water shortage problem in the plain river network area.

1. Introduction

Water resources are an essential natural resource that supports human existence and facilitates sustainable economic, social, and ecological progress [1,2]. In the context of China’s rapid socio-economic growth, the discharge of industrial and agricultural wastewater has increased each year, and the total sewage discharge in the country has recently exceeded 60 billion tons, with a large proportion directly discharged into rivers and lakes without proper treatment [3,4]. Nearly 500 of the country’s more than 700 large and medium-sized rivers are subject to water pollution, and the number of rivers and lakes that meet water quality standards is decreasing, making water quality and shortage increasingly serious [5,6,7]. The deterioration of water quality in rivers and lakes exacerbates the issue of water scarcity in China [8]. With the country’s socio-economic development, population growth, and accelerated urbanization, the gap between water resource supply and demand has widened [9,10]. Moreover, water pollution has become a pressing issue, with irrational development and utilization, as well as inefficient usage of water resources, posing significant constraints on China’s socio-economic progress [11]. Ensuring a natural balance between humans and water in the future is a critical consideration for promoting social equity and economic benefits across regions with varying water resources [12]. Addressing the issue of unequal distribution of water quantity and quality in different water-use sectors at the regional level is imperative for achieving China’s socio-economic development goals [13].

Cities in the river network areas of the plains are identifiable by their low topography, dense river networks, constrained river hydrodynamics, and copious transit water [14,15]. Simultaneously, the river network in the plains area encompasses prosperous municipalities, vigorous industrial development, and a high population density, all contributing to intense competition for water resources across various industrial sectors, low comprehensive utilization of water resources, and worsening instances of water quality and supply shortages [16]. These issues have significantly hindered the region’s economic and societal growth. Therefore, optimizing the allocation of urban water resources within the plain river network area is imperative.

Water resource allocation involves the distribution of the limited water resources available in a particular region or river basin to solve the water usage conflicts that arise between different regions, generations, and users [17,18]. This process takes into account the social, economic, and ecological objectives of the river basin or region in an integrated manner [19]. The research history of water resource allocation is closely linked to the development of human society, economy, and scientific and technological advancements. In the 1980s, increasing water pollution led to water resource allocation being influenced by factors beyond just water quantity. Consequently, there was greater emphasis on analysing water quality as part of water resource allocation. In 1989, Loftis et al. [20] researched a scheduling method for lakes that integrated both water quantity and quality as targets. In 1997, Ko et al. [21] presented a comprehensive methodology that improves current approaches for integrated water quantity and quality analysis focused on revealing the practical possibility of deriving optimal integrated multi-reservoir system operational strategies that simultaneously consider downstream water quality control. In 2010, Mahjouri [22] developed a new game theory methodology for inter-basin water transfer management based on economic, equity, and environmental criteria. In order to satisfy water-quality requirements, the impacts of decreasing the instream flow in the donor basin are estimated using a water-quality simulation model, and the required treatment levels for effluents discharged into the river downstream of the water transfer point are determined. In 2020, Zhou [23] utilized digital simulation technology to develop a water allocation plan for the Yellow River. The plan considers factors such as water quantity and quality, water consumption, power generation, and water quality indicators of water functional zones. The foundation of this plan is instantaneous data information conveyance and repercussions, which ensures that both water quantity and quality are considered.

In recent years, significant progress has been made in the field of water resource allocation, owing to advancements in scientific and technological domains. The goal of water resource allocation, which was previously aimed solely at achieving economic benefits, has now been expanded to include multiple objectives [24,25,26,27]. However, most research has focused on the optimal allocation of water resources from the perspective of water distribution, with fewer studies considering water quality. Additionally, further studies are also needed to determine the spatial balance of optimized water resources and how they relate to various economic factors.

In this study, Jingjiang City in Jiangsu Province, characterized by a typical plain river network area, is selected as the study area. The city is facing significant water resource challenges due to water quality problems and shortages caused by industrialization and urbanization. In order to achieve coordinated development of the urban economy, society, and ecology, a multi-objective water resources allocation model is established in Jingjiang City. The model integrates water quantity and quality to make a scientific and reasonable allocation of water resources, with the aim of maximizing the benefits to the economy, society, and environment. To ensure fair and reasonable regional water resources allocation, water resources spatial equilibrium theory and water resources Gini coefficient are used to evaluate the degree of spatial equilibrium and matching between water resources and economic factors after optimal allocation. The results of the study can provide a reference for the sustainable utilization of urban water resources and planning and management in the plains river network area.

2. Case Study

2.1. Study Area

Jingjiang City is located in the central part of Jiangsu Province, China, with a total area of 655.58 km². The region has a flat terrain and dense river network, with a Yangtze River shoreline of 52.3 km; more than 75% of the city’s total water supply is supplied by transit water mainly from the Yangtze River, making it a typical city of riverine plains and river network area. In 2018, the total water supply of Jingjiang City was 311.61 million m³, of which 311.40 million m³ was supplied by surface water sources (consisting of local surface water, transit water, and reclaimed water); 0.21 million m³ was supplied by groundwater. According to water users, agricultural water consumption is 245.51 million m³, industrial water consumption is 27.26 million m³, domestic water consumption is 36.44 million m³, and ecological environment replenishment is 2.4 million m³.

In Jinjiang City, rainfall is unevenly distributed in both space and time. Regional and prolonged heavy rainfall is rare, and local surface water resources are relatively limited, with a multi-year average of only 165 million m³. This amount is insufficient to meet the needs of local economic and social development. In 2018, the water quality compliance rate of the 12 water function zones in Jingjiang City was 87.4%, and the overall water environment quality showed a positive trend, but there is still a certain distance from full compliance with water quality standards. Therefore, given the lack of local water resources and the need to improve the quality of the water environment in Jingjiang City further, it is necessary to carry out a joint allocation of water quantity and quality for its water resources.

2.2. Data

The present study utilized data from various official sources, including the Taizhou Water Resources Bulletin spanning the years 2015 to 2020 (http://slj.taizhou.gov.cn), the Jingjiang City Master Plan from 2015 to 2030 (http://www.jingjiang.gov.cn), the Taizhou Statistical Yearbook (http://www.shujuku.org), the Jiangsu Province Water Use Quota (http://glj.jiangsu.gov.cn), and other datasets containing multiple types of data related to water resources, and the economic, social, and ecological environments. The data used in this study are sourced from official departments, ensuring their authenticity and reliability.

2.3. Forecast of Water Supply and Demand in the Planning Year

The study area of Jingjiang City, based on the current natural geography and water resource situation, was categorized into six areas, as depicted in Figure 1. The base year for the study was 2020 and the planning year was set to 2025 to align it with the national five-year plan for the economy. To account for the effects of different levels of water conservation on water demand, two scenarios were established: the basic scenario and the water conservation scenario. The basic scenario involved forecasting water demand under current water use, while the water conservation scenario aimed to optimize water conservation by improving the irrigation coefficient of farmland, reducing water abstraction per ten-thousand-yuan industrial added value, and other measures to ensure the efficient use of water resources. The water demand for domestic, industrial, agricultural, and ecological uses was calculated using the water quota forecasting method, with a guaranteed rate of p = 50%. The prediction outcomes are presented in

Table 1. Water demand of Jingjiang in the planning year (p = 50%; 10⁴ m³).

Scheme	Water Resources Zoning	Domestic Water	Agricultural Water	Industrial Water	Ecological Water	In Total
Basic scheme	Main urban area	1863	4086	1762	715	8425
	Northwest area	498	4670	542	164	5875
	Gubei area	461	2548	759	181	3949
	Jingdong area	443	3064	678	152	4336
	Yanjiang East area	286	1451	230	107	2075
	Yanjiang West area	423	3107	1114	149	4793
	In total	3974	18,926	5086	1468	29,453
Water conservation scheme	Main urban area	1736	3365	1702	664	7467
	Northwest area	469	3921	524	153	5067
	Gubei area	435	2155	733	168	3491
	Jingdong area	415	2564	655	141	3775
	Yanjiang east area	268	1226	223	99	1816
	Yanjiang west area	398	2614	1076	138	4226
	Total	3721	15,845	4913	1365	25,843

.

Jingjiang City relies on several sources for its water supply, including surface water, groundwater, transit water, and reclaimed water. The amount of surface water is determined using the runoff coefficient method, and the local surface water is classified into two categories based on quality, namely, Class I~III water and Class IV~V water. In order to maintain the groundwater levels, the extraction of groundwater must not exceed 0.45 million m³ in the planning year. Currently, Jingjiang City draws 250,000 m³/d of water, but as per the city’s master plan, a new water supply plant will be constructed in the planning year to expand the scale to 300,000 m³/d. Jingjiang City has eight sewage treatment plants, and their combined planned wastewater treatment capacity is 221,000 m³/d. In the planning year, the reclaimed water reuse rate is planned to be increased to 23%.

Table 2. Water supply capacity of Jingjiang in the planning year (p = 50%; 10⁴ m³).

Water Resources Zoning	Surface Water		Transit Water		Ground Water	Reclaimed Water
	Category Ⅰ~Ⅲ	Category IV~V	Piped Water	Irrigation Water
Main urban area	807	424	2770	4512	30	1051
Northwest area	803	422	2617	3308	1	39
Gubei area	552	287	1774	1551	2	171
Jingdong area	425	219	1314	2375	10	329
Yanjiang east area	260	130	756	1303	1	230
Yanjiang west area	551	287	1708	2530	0	39
In total	3399	1769	10,939	15,579	45	1859

presents the predicted outcomes of water supply at a p = 50% guarantee rate in various water resource zones of Jingjiang by 2025. The total water supply in Jingjiang is estimated to be approximately 335.90 million m³, where surface water accounts for 51.68 million m³, transit water accounts for 265.18 million m³, groundwater accounts for 0.45 million m³, and reclaimed water accounts for 1.86 million m³.

3. Methodology

3.1. Multi-Objective Optimal Allocation Model of Water Quantity and Quality

A multi-objective optimal allocation model of water quantity and quality has been developed based on the water quantity and quality requirements of various water users in the region. The primary objective of the model is to maximize the comprehensive benefits of the regional economic, social, and ecological environments while ensuring satisfaction of a range of constraints. The model is expected to provide a scientific and efficient means of allocating water resources in the region.

3.1.1. Objective Function

The objective of the joint allocation of regional water quantity and quality is to achieve the maximum comprehensive economic, social, and environmental benefits for the region. The economic objective is to maximize comprehensive economic benefits, the social objective is to minimize water shortages, and the environmental objective is to minimize COD emissions of primary pollutants in the region. The constructed objective function is as follows:

$$f(x)=\{f_1(x),f_2(x),f_3(x)\}=\left\{\begin{array}{l}\max {\displaystyle \sum _{k=1}^K{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{i=1}^I{x}_{ij}^k(b_{ij}^k-c_{ij}^k){\alpha }_{ij}^k{\beta }_{ij}^k}}}\hfill \\ \min {\displaystyle \sum _{k=1}^K{\displaystyle \sum _{j=1}^J(D_j^k-{\displaystyle \sum _{i=1}^I{x}_{ij}^k)}}}\hfill \\ \min {\displaystyle \sum _{k=1}^K{\displaystyle \sum _{j=1}^{J}0.01p_j^k{x}_{ij}^k[c_{0j}^k(1-r_1^k)+c_{1j}^k{r}_1^k-c_{1j}^k{r}_2^k]}}\hfill \end{array}\right.$$

(1)

where $b_{ij}^k$ is the water supply efficiency factor; $c_{ij}^k$ is the water supply cost factor; $x_{ij}^k$ is the amount of water supplied by source i to water user j in subarea k; ${\alpha }_{ij}^k$ is the water supply sequences of different water sources; ${\beta }_{ij}^k$ is the water equities of different water users; $D_j^k$ is the water demand of water user j in subarea k; $p_j^k$ is the sewage discharge factor of water user j in subarea k; $c_{0j}^k$ is the concentration of COD before the sewage discharged by water user j in subarea k is treated; $c_{1j}^k$ is the concentration of COD after the sewage discharged by water user j in subarea k has been treated. $r_1^k$ is the sewage treatment rate in subarea k.

3.1.2. Constraints

The regional water quantity and quality joint allocation model requires constraints such as the amount of water that water sources can supply, the amount of water demanded by water users, and the constraints on the capacity of water functional zones to accommodate pollution to be met from the perspective of water supply in terms of quality.

Constraints on water resource carrying capacity: the total water supply of each water source to different water users of each subarea shall not exceed the total available water supply of the water source.

$${\displaystyle \sum _{j=1}^J{x}_{ij}^k}\le W_i^k$$

(2)

where $W_i^k$ is the available water supply from the water source $i$ in the $k$ subarea, 10⁴ m³.

Water demand constraints for water users: the water demand of each water user shall be between the corresponding maximum and minimum water demand.

$${D_j^k}_{\min }\le {\displaystyle \sum _{j=1}^J{x}_{ij}^k}\le {D_j^k}_{\max }$$

(3)

where ${D_j^k}_{\min }$ and ${D_j^k}_{\max }$ are the minimum and actual water demand of $j$ water users in $k$ subarea respectively, 10⁴ m³.

Water function zone capacity constraints: the pollutant retention capacity of each water function zone is not exceeded in the planning year by strictly controlling pollutant discharges in the region.

$${\displaystyle \sum _{k=1}^K{\displaystyle \sum _{j=1}^{J}0.01p_j^k{x}_{ij}^k}}[c_{0j}^k(1-r_1^k)+c_{1j}^k{r}_1^k-c_{1j}{r}_2^k]\le W^k$$

(4)

where $W^k$ is the water function zone capacity of the $k$ subarea, t.

Non-negative constraints on decision variables.

$$x_{ij}^k\ge 0$$

(5)

$x_{ij}^k$ is the amount of water supplied by source i to water user j in subarea k.

Water quality constraints of different water sources. Based on the standards outlined in GB 3838-2002 [28] and other relevant criteria for environmental quality, Class I~III water should be prioritized for domestic use. If there is a surplus, it can be supplied to other water users. Class IV water can be used in industry, agriculture, and the ecological environment, whereas Class V water can only be utilized for agriculture and off-channel ecological water usage due to its poor quality.

3.1.3. Model Parameter Setting

Net benefits of water supply and water distribution relationship from source to user.

Water use efficiency is measured by the economic benefits generated per unit of water resources. After reviewing relevant literature [29,30] and considering the economic and social development of the planning year, the net efficiency coefficients for industrial and agricultural water supply were determined to be 175.4 yuan/m³ and 11.2 yuan/m³, respectively. It is difficult to quantify the net benefits of domestic and ecological water supply. Considering the importance of the two relative to industrial and agricultural water use, the net benefit coefficients of domestic and ecological water supply are 300 yuan/m³ and 220 yuan/m³, respectively. Water resource allocation in Jingjiang City should follow the principles of utilizing surface water, conserving groundwater, making full use of transit water, safeguarding ecological water and water supply in terms of quality, determining the distribution relationship between water sources and water users, and realizing the joint use of multiple water sources and multiple users. The water distribution relationship is shown in

Table 3. Water distribution relationship from water sources to water users.

Water Resources	Domestic Water	Agriculture Water	Industrial Water	Ecological Water
Class Ⅰ~Ⅲ surface water	1	1	0	0
Class IV~V surface water	0	1	0	1
Piped water	1	0	1	1
Irrigation water	0	1	0	0
Ground water	0	0	1	0
Reclaimed water	0	1	1	1

, where 1 means water distribution and 0 means no water distribution.

Water supply sequence coefficient and water equity coefficient. Jingjiang City’s water supply sources are classified into four categories: surface water, transit water, groundwater, and reclaimed water. When multiple sources supply water to a user, the coefficient of the water supply sequence from each source determines the priority of that source in supplying water to the user [31]. The water equity coefficient is then used to determine the degree of priority assigned to the user in receiving water from a particular source based on their level of importance [32]. The calculation of the coefficient of water supply sequence and water use equity is based on the following formula and the results are shown in

Table 4. Values of water supply sequence coefficient and water use equity coefficient.

Coefficient	Domestic Water		Water for Agriculture				Industrial Water			Ecological Water
	Class Ⅰ~Ⅲ Surface Water	Piped Water	Class Ⅰ~Ⅲ Surface Water	Class IV~V Surface Water	Irrigation Water	Reclaimed Water	Piped Water	Ground Water	Reclaimed Water	Class IV~V Surface Water	Piped Water	Reclaimed Water
Water supply sequence	0.33	0.67	0.20	0.40	0.30	0.10	0.33	0.50	0.17	0.33	0.17	0.50
Water equity	0.67	0.40	0.33	0.67	1.00	0.10	0.67	1.00	0.30	0.33	0.20	0.33

.

$${\alpha }_{ij}^k=\frac{1+n_{i\max }^k-n_i^k}{{\displaystyle \sum _{i=1}^I(1+n_{i\max }^k-n_i^k)}}$$

(6)

$${\beta }_{ij}^k=\frac{1+m_{j\max }^k-m_j^k}{{\displaystyle \sum _{j=1}^J(1+m_{j\max }^k-m_j^k)}}$$

(7)

where $n_i^k$ is the water supply sequence number, $n_{i\max }^k$ is the maximum value of the water supply sequence number, $m_j^k$ is the water use sequence number, and $m_{j\max }^k$ is the maximum value of the water use sequence number.

Sewage discharge coefficient. During the planning year in Jingjiang City, both domestic and industrial wastewater were treated completely. The coefficient of wastewater discharge for domestic and industrial sectors was 0.85 and 0.80, respectively. The concentration of COD in the treated sewage was 120 mg/L. Based on the current agricultural production in Jingjiang City, it has been determined that the COD concentration in the return water of agricultural irrigation should be 80 mg/L, and the sewage discharge coefficient should be 0.4.

Minimum water demand of water users. It is essential to adhere to minimum water demands for domestic, industrial, agricultural, and ecological use. These minimum water demands are calculated as a percentage of the actual water demand. For domestic use, the minimum demand is set at 95% of the actual water demand, while for industrial use, it is set at 85%. For agricultural use, the minimum demand is set at 75%, and for ecological use, it is set at 90%.

Capacity of water function zone to accommodate sewage. Jingjiang City has an annual COD (Chemical Oxygen Demand) capacity of 22,960.5 tons. This refers to the maximum amount of COD that can be treated by the city’s wastewater treatment plants in a year. The COD is a commonly used parameter to measure the amount of organic pollutants in water. By treating this amount of COD, the city can ensure that the wastewater discharged into the environment meets the required standards of water quality and does not pose a threat to public health or the environment.

3.2. Model Solving

The objective function and constraints of the rational allocation model for water quantity and quality resources are extensive and non-linear, which makes it difficult to address directly. In order to solve the model, it is essential to select the appropriate optimization algorithm that can handle the complexity of the problem.

The rational allocation model for water quantity and quality resources is a complex problem that requires the appropriate optimization algorithm to solve. Among the various multi-objective optimization algorithms, NSGA-II is widely acknowledged as one of the best, as it guarantees population diversity and representativeness through non-dominated sorting and congestion distance [33]. It also employs an elite retention strategy, increasing the likelihood of preserving excellent individuals within the population [34]. Given its robustness, NSGA-II is highly suitable for addressing rational water resource allocation challenges [35]. In view of the multi-objective and non-linear characteristics of the water resource optimization model in this study, the NSGA-II algorithm was selected for the solution of the joint optimization model of water quantity and water quality. The selected algorithm functions for solving the model are as follows:

[x, fval] = gamultiobj (fitnessfcn, nvars, A, b, Aeq, beq, lb, ub, options)

(8)

where x is the decision variable; fval is the value of the function corresponding to x; fitnessfcn is the objective function of the model; nvars is the number of variables; A and b are the linear inequality constraining matrix and its constraining values, respectively; Aeq and beq are the linear equality constraining matrix and its constraining values, respectively; lb and ub are the lower and upper bounds of x, respectively; and options is the parameter setting of the algorithm. The genetic parameters set for model solving in this paper are: optimal front-end individual coefficient of 0.3, population size of 300, maximum number of evolutionary generations of 3000, number of stopping generations of 3000, and deviation from fitness function value of 1 × 10⁻⁴.

3.3. Spatial Equilibrium Assessment of Water Allocation

Water resource allocation is essentially a spatial allocation issue [36]. The spatial equilibrium assessment of water resources is to evaluate and analyze the distribution of water resources in different spaces within a region or basin and to examine the equilibrium of water resources development, utilization, and protection from a spatial perspective [37]. By assessing the spatial equilibrium of water resources, a comprehensive understanding and grasp of the water resources situation in a region or basin can be attained, providing a basis and support for formulating scientific strategies for water resources management [38]. Common quantitative indicators used for evaluating the spatial equilibrium of regional water resources are the spatial equilibrium coefficient, the spatial equilibrium degree, and the overall spatial equilibrium degree [39].

Spatial equilibrium coefficient. The spatial equilibrium coefficient represents the degree of equilibrium in the distribution of water resources across any spatial location or unit of account, and its value range is between 0 and 1. A value closer to 1 indicates a more balanced spatial distribution, while a value closer to 0 indicates a more unbalanced distribution.

$$G_{ij}=\left\{\begin{array}{ll}0\hfill & (x_{ij}<{\overline{x}}_{ij}-\Delta x_{ij1})\hfill \\ \frac{x_{ij}-{\overline{x}}_{ij}+\Delta x_{ij1}}{\Delta x_{ij1}}\hfill & ({\overline{x}}_{ij}-\Delta x_{ij1}⩽x_{ij}⩽{\overline{x}}_{ij})\hfill \\ \frac{\Delta x_{ij2}+{\overline{x}}_{ij}-x_{ij}}{\Delta x_{ij2}}\hfill & ({\overline{x}}_{ij}<x_{ij}⩽{\overline{x}}_{ij}+\Delta x_{ij2})\hfill \\ 0\hfill & (x_{ij}>{\overline{x}}_{ij}+\Delta x_{ij2})\hfill \end{array}\right.$$

(9)

where $G_{ij}$ is the spatial equilibrium coefficient of the jth computational indicator of the ith computational unit; $x_{ij}$ is the value of the jth computational indicator of the ith computational unit, and in this paper, we select domestic water, agricultural water, industrial water and ecological water as the computational indicators; ${\overline{x}}_{ij}$ is the value of the computational indicators corresponding to the spatial equilibrium coefficient of 1; $\Delta x_{ij1}$ and $\Delta x_{ij2}$ are the values according to the computational unit, and they can be the difference of the minimum value of ${\overline{x}}_{ij}$ and the maximum value of $x_{ij}$, and the value of shifted a certain distance to the left and right, respectively.

Spatial equilibrium degree. The spatial equilibrium coefficient is determined by taking a weighted average of the computational unit areas to determine spatial equilibrium across the entire region. This calculation can be performed using the following formula.

$$D_j={\displaystyle \sum _{i=1}^N(S_i{G}_{ij})}/S$$

(10)

where $D_j$ is the spatial equilibrium of the jth calculation index, S_i is the area of the ith calculation unit, S is the total area of the region, and N is the number of calculation units.

Overall spatial equilibrium degree. The overall spatial equilibrium degree can be used to indicate the distribution of water resources in a region. The overall spatial balance of water resources is calculated by weighting and summing the spatial balances of the calculated indicators, ranging from 0 to 1. The closer the value is to 1, the more balanced the distribution of water resources is throughout the region, whereas the closer it is to 0, the more unbalanced it is. The formula for this calculation is as follows.

$$D={\displaystyle \sum _{i=1}^M{D}_j{\alpha }_j}$$

(11)

where D is the overall spatial balance degree of water resources; α_j is the weight coefficient of the calculation index j, ${\alpha }_1+{\alpha }_2+\cdots +{\alpha }_j=1$; it is assumed that the weights of the calculated indicators are equal; and M is the number of calculation indexes.

According to the above quantification method of water resources spatial equilibrium, when the spatial equilibrium coefficient is 1, the spatial equilibrium level of water resources is the highest. When the spatial balance coefficient is 0, the spatial equilibrium level of water resources is the lowest. Therefore, in order to visually express the degree of spatial equilibrium of water resources, and based on the results of existing research [40,41], seven spatial equilibrium levels are set up in order with the interval of 0.2, as shown in

Table 5. Classification of water resource spatial equilibrium grades.

Serial Number	Spatial Balance Degree	Spatial Balance Level
1	[0, 0.2)	Unbalance
2	[0.2, 0.4)	Close to unbalance
3	[0.4, 0.6)	Less balance
4	[0.6, 0.8)	Basic balance
5	[0.8, 1.0]	Balance

.

3.4. Gini Coefficient of Water Distribution

The demand for regional water resources is closely tied to population and economic factors, requiring a proportional allocation of water resources to match population and GDP [42]. The Gini coefficient is employed to quantify how well regional water resources correspond to economic factors [43]. The Gini coefficient measures the distribution imbalance of water resources in a region, which can indicate the fairness of that distribution [44]. A low Gini coefficient for the distribution of water resources indicates an even distribution throughout the region, with minimal differences in water availability between regions; conversely, a high Gini coefficient indicates an unequal distribution of water resources within the region [45]. The Gini coefficient formula for water distribution calculation is presented below.

$$G=\left|1-{\displaystyle \sum _{i=1}^n(x_i-x_{i-1})(y_i+y_{i+1})}\right|$$

(12)

where X_i represents the cumulative percentage of water resources in a region and y_i represents the cumulative percentage of economic development factors. Following international practice, the Gini coefficient of 0.4 serves as the “warning line” for wealth distribution, which is also used in this study. The Gini coefficient of 0.2 or lower indicates a high degree of matching between the distribution of water resources and economic development factors. A Gini coefficient between 0.2 and 0.3 suggests a relatively matched situation; a “critical match” between 0.3 and 0.4, a “mismatch” is indicated by a Gini coefficient between 0.4 and 0.5; a “deep mismatch” is indicated by a coefficient above 0.5 (

Table 6. Gini Coefficient Evaluation Rating Criteria.

Gini Coefficient	[0, 0.2)	[0.2, 0.3)	[0.3, 0.4)	[0.4, 0.5)	[0.5, 1.0]
Rating Levels	match	relative match	critical match	mismatch	deep mismatch

).

4. Results and Analysis of Water Allocation

4.1. Water Allocation Results

To obtain the optimal allocation model solution, the gamultiobj function is called to solve the model. The subjective and objective weights are then calculated using the hierarchy process method [46] and entropy weight method [47]. The economic benefits, social benefits, and ecological and environmental benefits of the goal are assigned an integrated weight coefficient value of 0.31, 0.28, and 0.41, respectively. The solution set is multiplied by the integrated weights of the indicators and summed up to obtain the comprehensive benefits of each program. Finally, the solution with the largest comprehensive benefits is selected as the final configuration program. The results of the water allocation for the planning year in Jingjiang City are shown in

Table 7. Water resource allocation results of Jingjiang City in the planning year (10⁴ m³).

Scheme	Water Resources Zoning	Domestic Water		Water for Agriculture				Industrial Water			Ecological Water			In Total
		Class Ⅰ~Ⅲ Surface Water	Piped Water	Class Ⅰ~Ⅲ Surface Water	Class IV~V Surface Water	Irrigation Water	Reclaimed Water	Piped Water	Ground Water	Reclaimed Water	Class IV~V Surface Water	Piped Water	Reclaimed Water
Basic scheme	Main urban area	96	1681	710	422	2913	1	1089	30	407	2	1	643	7993
	Northwest area	13	485	777	407	2738	0	462	1	5	15	108	34	5044
	Gubei area	0	461	552	281	914	4	637	2	7	6	1	160	3024
	Jingdong area	11	432	341	202	1998	0	377	10	194	17	1	135	3717
	Yanjiang East area	46	240	138	122	1188	3	100	1	129	4	6	97	2074
	Yanjiang West area	2	421	549	272	1489	1	949	0	3	15	92	35	3828
	In total	168	3720	3066	1707	11,239	10	3613	44	745	59	208	1103	25,680
Water conservation scheme	Main urban area	3	1712	804	424	2109	4	1020	30	457	0	38	590	7191
	Northwest area	7	462	726	156	2800	32	447	1	5	83	61	3	4782
	Gubei area	2	433	549	240	938	33	585	2	45	47	28	93	2995
	Jingdong area	11	404	379	54	1940	5	429	10	204	16	5	120	3577
	Yanjiang East area	7	261	25	13	1187	1	72	1	147	10	6	82	1812
	Yanjiang West area	10	388	470	260	1532	5	920	0	1	27	78	33	3724
	In total	40	3660	2954	1147	10,506	79	3473	44	858	182	216	921	24,082

.

The values of economic, social, and ecological benefits under the basic and water conservation scenarios for Jingjiang City in the planning year are shown in

Table 8. Target values under different scenarios for the planning level year in Jingjiang City.

Scheme	Net Benefits of Water Supply/(Million Yuan)	Water Shortages/%	COD Emission/t
Basic scheme	241.4	12	14,098.5
Water conservation scheme	232.7	7	12,821.8

. Notably, the total amount of water used under both schemes did not exceed the control target of 400 million m³, while the total amount of COD discharged was managed within the allowable limits of sewage holding capacity. This observation indicates that the allocation scheme was reasonable and feasible. Although the net benefit of water supply under the water conservation scenario was lower by 870 million yuan when compared to the basic scenario, the water shortage rate and COD emission were 5% and 1276 tons lower, respectively, than the basic scenario. Furthermore, the water shortage rate in Jingjiang City under the water conservation scenario decreased to 7%, thereby demonstrating the positive effects of enhanced water conservation levels in addressing water shortages in the city.

Table 9. COD emission of each sub-area in different schemes s(t).

Scheme	Main Urban Area	Northwest Area	Jingdong Area	Jingdong Area	Yanjiang East Area	Yanjiang West Area
Basic scheme	4555.3	2447.5	1963.7	1908.9	882.5	2340.6
Water conservation scheme	4144.2	2287.6	1882.4	1540.0	814.5	2153.1

presents the COD emission of each sub-area under each program. The data reveals that the COD emission associated with the water conservation program is comparatively lower than the basic program. The largest COD emission is observed in the main urban area due to its large population and rapid industrialization. Both domestic sewage and industrial wastewater contribute to this emission. Effective measures such as improving water conservation and controlling pollutant discharge can significantly enhance the regional water environment in the planning year.

4.2. Analysis of Water Supply Structure

The structure of water supply and water use in the receiving areas for different water use scenarios in the planning level year is shown in Figure 2.

From the perspective of water supply, both the basic and water conservation scenarios depict a similar water supply structure in each receiving area. Surface water, transit water, groundwater, and reclaimed water provide 19.5%, 73.1%, 0.17%, and 7.2% of the water supply, respectively, in the basic scenario. The overall water supply in the water conservation scenario is reduced compared to the basic scenario. Transit water is the primary source of water in both scenarios, accounting for more than 70% of all water supplies. Groundwater supply accounts for the smallest proportion, and the water supply is within the range of groundwater extraction. Reclaimed water is mainly used for water supply for industry and the ecological environment in all sub-areas, and the water supply quantity is mainly determined by the annual sewage treatment capacity in the planning year. The allocation results reveal that IV~V surface water is predominantly used for agricultural irrigation and ecological water, with more than 90% of IV~V surface water being used for agricultural water, which effectively ensures high-quality water is used for domestic water.

From the perspective of water demand, water usage in the basic program for the planning year is distributed as follows: 15.14% for domestic purposes, 62.39% for agricultural purposes, 17.14% for industrial purposes, and 5.33% for ecological purposes. Although the proportion of water used for agriculture drops to 60% in the water conservation program, it remains the sector with the highest usage of water. The main urban area receives the largest water allocation among all the water-receiving areas. This is because it serves as a crucial spatial carrier for the production, living, and ecological functions of Jingjiang City and is the primary center of urban function agglomeration.

4.3. Analysis of Spatial Equilibrium of Water Resources

The spatial balance coefficients for water usage in each area were calculated using the spatial balance quantification method, which is outlined in Formulas (9)–(11). The overall spatial balance of water resources in the planning year was also calculated.

Table 10. Spatial equalization coefficients of different scenarios for the planning year in Jingjiang City.

Scheme	Water Resources Zoning	Spatial Equalization Coefficients				Overall Spatial Equalization
		Domestic Water	Water for Agriculture	Industrial Water	Ecological Water
Basic scheme	Main urban area	0.25	0.31	0.47	0.30	0.33
	Northwest area	0.70	0.37	0.67	0.65	0.60
	Gubei area	0.63	0.63	0.89	0.69	0.71
	Jingdong area	0.59	0.95	0.81	0.62	0.74
	Yanjiang East area	0.28	0.51	0.37	0.39	0.39
	Yanjiang West area	0.55	0.87	0.85	0.57	0.71
Water conservation scheme	Main urban area	0.43	0.63	0.49	0.38	0.48
	Northwest area	0.76	0.45	0.70	0.66	0.64
	Gubei area	0.70	0.67	0.96	0.76	0.78
	Jingdong area	0.67	0.97	0.86	0.64	0.79
	Yanjiang East area	0.44	0.50	0.41	0.45	0.45
	Yanjiang West area	0.65	0.93	0.77	0.63	0.74

presents the results of these calculations based on the water allocation outcomes obtained during the planning year.

Based on the data presented in Figure 3a–d, it is evident that the water resource balance in Jingjiang City is not optimal. The spatial balance coefficient for water resources in each receiving area ranges from 0.33 to 0.74 under the basic program, with an overall balance degree of 0.57, which is quite close to an unbalanced state. The implementation of the water conservation program has resulted in an improvement in the spatial balance level of each receiving area, leading to an overall balance degree of 0.64, a more balanced level. However, the main urban area and the Jingdong area along the river still exhibit poor spatial balance levels, which are close to an unbalanced state. The measures adopted under the water conservation program, such as enhancing water resource utilization efficiency, optimizing water resource allocation structure, strengthening water resource management, and raising public awareness of water conservation, have significantly promoted the balanced spatial distribution of limited water resources.

4.4. Analysis of Gini Coefficient

Table 11. Gini coefficient of water resources distribution in the planning year.

Scheme	Population	GDP	Land Area
Basic scheme	0.22	0.17	0.15
Water conservation scheme	0.19	0.15	0.14

displays the Gini coefficient of water resource distribution in Jingjiang City, calculated using Formula (12). This coefficient indicates the degree to which water resources correspond with various economic factors and is measured according to the standard of Gini coefficient grade.

According to Table 11, the effective allocation of water resources in Jingjiang City is favorable and corresponds well with various economic factors. The Gini coefficient for water resources and GDP is 0.17, while for land area is 0.15, indicating a favorable matching grade. The population of each water-receiving area has a relative matching grade of 0.22. The water conservation program has improved the alignment between water resources and economic factors in each area, bringing it to a matching grade. The program has also helped to reduce the disparity in water resource distribution, playing an essential role in reducing the Gini coefficient of water distribution.

5. Conclusions

The paper presents a multi-objective optimal allocation model of water quantity and quality in the plain river network area that aims to maximize net benefit, minimize total water shortage, and reduce COD emissions while satisfying various constraints. The NSGA-II algorithm is utilized to solve the allocation problem under the basic and conservation schemes. Based on maximizing the comprehensive benefit to the regional economic, social, and ecological environments, the optimal allocation of water resources in Jingjiang City was achieved in the planning year. The main conclusions are as follows:

(1)

Total water consumption and chemical oxygen demand (COD) emissions for the current planning period are within their respective limits. In addition, the implementation of the water conservation program has resulted in a 5% reduction in total water shortage and a reduction of 1276 tons of COD emissions. These results highlight the importance of increasing water conservation efforts to mitigate water scarcity and reduce COD emissions in the region. In addition, the optimization of the water supply infrastructure in Jingjiang City has proven to be an important step in ensuring the quality of the water supply. More than 90% of the surface water classified as Grade IV to V is used for agricultural purposes, while the domestic water supply relies mainly on transit water, which effectively ensures quality water is used in domestic water supplies.

(2)

This paper presents the concept of spatial equilibrium of water resources and the Gini coefficient of water resource distribution, which can be utilized to gauge the level of regional water resource equilibrium and its compatibility with different economic factors following allocation. Based on the analysis, the spatial equilibrium coefficient of water resources per sub-area is between 0.33 and 0.74, indicating an unbalanced or almost unbalanced level. However, the application of a water conservation program has resulted in the improvement of the spatial equilibrium level of water resources in each sub-area, with an overall spatial equilibrium of 0.64, indicating a more balanced level. In light of the Gini coefficient of water resource distribution, the plains river network area displays a better match between water resources and economic and social factors of each water receiving area, thanks to its unique geographical location and natural conditions.

(3)

The allocation of water resources in Jingjiang City is based on the upper and lower limits of water demand among users, which does not entirely fulfill the water requirements of individual users, leading to a significant supply and demand contradiction. To promote sustainable economic and social development in the city, a series of recommended actions have been proposed. These include incorporating water supply in city planning, optimizing industrial layout, vigorously developing the recycling economy, increasing the penetration rate of water-saving appliances and the amount of recycled water, enhancing water conservation awareness among residents, and continuously improving water resource utilization efficiency. Additionally, it is suggested to enhance the remediation of river outfalls and surface source pollution management, increase water reuse, restore river channels, and implement water and ecological restoration projects for comprehensive water environment management and sustainable use of water resources.

6. Limitation

Taking the city of Jingjiang as a case study, this paper presents a preliminary exploration and research on the theory, methodology, and modeling of the joint allocation of regional water quantity and quality. However, due to the complexity of the problem under study, there are still areas that require further improvement in the theory and methodology of the paper.

(1)

The optimization of water resources involves various factors, including precipitation and climate, which can affect the results of the allocation process. This paper does not consider the impact of these uncertain factors on the allocation optimization, and future research in this area can improve the accuracy of the optimization results.

(2)

Although the model proposed in this paper has been applied in Jingjiang City, it has not yet been used to manage real water resources. In the future, the theory and methodology can be introduced into the management of real water resources, such as water allocation, optimization, and scheduling, to expand the scope of application and the practicality of the methodology.