https://orcid.org/0009-0006-7460-567X
ABSTRACT
Water resources are essential for human survival, economic development, and ecological balance. However, they are significant contributors to greenhouse gas emissions in urban production and utilization. Despite this, research on integrating carbon reduction objectives into water resource allocation remains limited. This paper constructs a model for optimal allocation of urban water resources including unconventional water resources based on carbon emissions, and studies it in Pingliang City as an example, using NSGA-III algorithms to solve its allocation scheme. The results show that compared with the traditional configuration scheme, the proposed carbon emission reduction-based allocation model achieves cumulative carbon emission reductions of 153,000 and 267,000 metric tons for the planning period 2025–2040. Additionally, the cumulative economy can be obtained in 2025–2040 is 934,800–9,482,900 yuan and 163,141,000–16,548,700 yuan, respectively. This study can help to promote the rational utilization of urban water resources and the coordinated development of the economy, society, and environment in China, and provides a scientific basis for the sustainable development policy of water resources, which is important for realizing the goal of ‘double carbon’ in China.
HIGHLIGHTS
An optimal water resource allocation model based on carbon emission reduction was constructed.
Water resources allocation including unconventional water resources are calculated.
Allocation results can effectively reduce per capita water carbon emissions.
It can obtain carbon emission reduction economic benefits of 1.6314 million yuan.
It can provide a new idea for carbon emission reduction of urban water resources.
NOMENCLATURE
- Symbol
Parameters
the per capita carbon emissions over the years
carbon emissions per unit area over the years
the carbon emission in the m planning year
carbon emission factors for water treatment and distribution
from the source of water
the carbon emission factors of water for water use department j
the water demand of the water use department j
the water shortage of the water use department j
the carbon emission in the m planning year
the water use net benefit coefficient of the water use department j
carbon emissions from water intake systems, water supply systems, and water use systems in this area, metric ton
the net benefit of the water supply is 10 thousand yuan
the regional water shortage
regional wastewater discharge in 10 thousand m3
regional groundwater extraction in 10 thousand m3
the source of water
= 1surface water
= 2underground water
= 3recycled water
= 4rainwater
water use department
= 1domestic water department
= 2industrial water department
= 3municipal water department
= 4ecological water department
- m
planning year
- m = 1
2025
- m = 2
2030
- m = 3
2035
- m = 4
2040
the number of people in m planning year
the planned area for the n planning year
the available rainwater supply in 10 thousand m3
the water distribution relationship between the source of water i and water use departments j
the utilization rate of rainwater determined according to the construction and actual situation of the Sponge City
the reuse rate of recycled water determined according to the construction and actual situation of the Sponge City
the water distribution relationship between the source of underground water and water use departments j
the water distribution relationship between the source of rainwater and water use departments j
the available water supply of the water source i in 10 thousand
the wastewater discharge coefficient of the water use department
the amount of water distributed to water use departments j from the source of water i
the amount of water distributed to water use departments j from the source of underground water
the amount of water distributed to water use departments j from the source of rainwater
the water shortage coefficient of the water use department j
any source of water i
any water use department
INTRODUCTION
In recent years, global population expansion and urbanization have accelerated under rapid economic and social development, putting enormous pressure on water resources (Shang & Lv 2023). The extraction, treatment, and distribution of water generate large amounts of greenhouse gases, exacerbating climate change and increasing the carbon footprint of cities, making it a challenge to balance the demand for water resources with the goal of carbon reduction. Li et al. (2016) calculated the energy consumption of various links in China's water supply system at a regional scale. The results showed that the electricity consumption in the process of acquisition, treatment, transmission, and distribution of water resources, as well as wastewater treatment, accounted for approximately 4% of the total electricity consumption in the whole country that year. China has proposed the goals of carbon peaking by 2030 and carbon neutrality by 2060 (Zhao et al. 2022a). In this context, the effective allocation of water resources has become a key issue, and the introduction of carbon emission optimization targets in its optimal allocation can reconcile regional conflicts of interest, reduce carbon emissions, and help to achieve carbon neutrality (Majedi et al. 2021; Zhao et al. 2022b; Bai et al. 2024; Cui et al. 2024).
The optimal allocation of water resources primarily focuses on balancing the supply and demand of water, while also ensuring water quality control. Achieving this balance requires considering multiple objectives, such as economic, social, and ecological benefits, as well as minimizing the environmental impact. This multi-dimensional challenge is typically addressed through multi-objective optimization, where different, sometimes competing, objectives are optimized simultaneously (Lu et al. 2023).With the advancement of computer technology, optimization algorithms, and artificial intelligence, these methods have increasingly been used to improve the scientific rigor and precision of water resource allocation models. Such technological advancements allow for more comprehensive and effective decision-making, addressing the complex nature of water resource management in a sustainable way. Gao et al. (2019) incorporated medium water and desalinated water into a study on water distribution and proposed an optimized allocation method for wastewater and reused water with the goal of minimizing freshwater resource consumption and energy consumption in the water supply process. In this paper, only water and energy are studied, and the relationship between water, energy, and carbon is not studied. Wang et al. (2021) proposed the improved Cuckoo algorithm (Yang & Deb 2013) and established the optimal allocation model of water resources based on the realistic ecological environment, solved the model of the Jinzhong-Changzhi water supply area, and predicted the optimal allocation results of water resources in 16 sub-areas of the Jinzhong-Changzhi water supply area at different guaranteed rates in the planning level year. While most of the studies mentioned above focus on optimizing water resource allocation based on economic, social, and environmental objectives, they often overlook the critical goal of reducing carbon emissions, which is increasingly emphasized in the context of low-carbon and sustainable development policies.
This gap is particularly critical given the significant carbon emissions associated with urban water systems (Song et al. 2022). For example, China's total water resources consumption was 599.82 × 109 m3 in 2022 and water extraction, water treatment, transmission, and distribution of China's water resources system have consumed large amounts of energy with an annual carbon emission of more than 12.01 × 109 t (Ma et al. 2022). Therefore, the research on rational allocation of water resources has gradually shifted from the traditional optimization model focusing on water supply and maximization of economic benefits to the research focusing on sustainable use of water resources, low-carbon use, and green development (Feng et al. 2023; Huang et al. 2023; Zhang et al. 2024a). Rothausen & Conway ( 2011) called for a study on urban water systems from the perspective of greenhouse gas emitters in Nature Climate Change. The emissions of greenhouse gases in urban water systems have received increasing attention from scholars. Yang et al. (2018) explored the relationship between energy, water, and carbon at the urban scale. They estimated the energy consumption, water consumption, and carbon emissions of various sectors in Shanghai and Beijing using an environmental input‒output model. Based on energy–water–carbon relations, they proposed sustainable development recommendations for different industries. However, the direct water consumption data of various economic sectors in the study are not detailed enough and are directly allocated, and the integration of sectors can also cause uncertainty. Jiang et al. (2022) advanced a chance-constrained fractional programming model for energy–water–carbon nexus systems to minimize the total system cost, where the model addressed energy-related water scarcity and carbon reduction from the power generation process. However, the current studies from the water–energy–carbon perspective mainly focus on the coupling and correlation between various factors and lack a systematic and comprehensive efficiency evaluation system, which makes it difficult to comprehensively and systematically reveal the systematic evolution law of carbon emission efficiency under complex environmental changes. Meanwhile, current research mainly focuses on the terminal consumption of factors (Wu et al. 2022; Inegbedion 2024; Su et al. 2024). However, the indirect resource consumption and carbon emission related to intermediate production or consumption are ignored, resulting in a certain deviation between the calculation and understanding of carbon emission efficiency and the actual situation. It is suggested that future studies should focus on the optimization of national space based on water–energy–carbon carrying capacity, the decoupling analysis of resource consumption and economic growth from the perspective of water–energy–carbon, the quantitative analysis of the certainty and uncertainty of the complex water–energy–carbon relationship, and the contribution of water–energy–carbon engineering measures to ‘negative emissions’, aiming to promote green and high-quality development through water–energy–carbon system collaborative management. Existing literature mostly focuses on the economic, social, and environmental objective functions of water resources allocation, and the carbon emission objective is still under-research paper, this paper takes the carbon emission objective as the research objective of optimal allocation of water resources, synergistically controlling the carbon emission and water resources allocation to promote the synergistic development of the economy, society, and ecological environment.
On the other hand, there are limitations in the multi-objective optimization research methods for water allocation. The multi-objective optimization algorithms used in the current research (Verma et al. 2021; Akter et al. 2024; Yang et al. 2024), such as simulated annealing algorithm, particle swarm optimization algorithm, artificial neural network, artificial immunity algorithm, NSGA-II, grey wolf optimization algorithm, and MOEA/D, among them, simulated annealing algorithm, grey wolf optimization algorithm, and artificial neural network are only capable of generating a single objective, and they are not suitable for multi-objective optimization scenarios. The NSGA-II algorithm is more suitable for optimization problems with less than 3 objectives, while NSGA-III and MOEA/D algorithms are suitable for multi-dimensional objectives (Deb et al. 2002; Li et al. 2014). It should be noted that the MOEA/D algorithm produces different results for different decomposition methods of the objective function, which needs to be adjusted according to the specific problem, and the parameter setting is more complicated and cumbersome, which will affect the convergence of the algorithm if it is not set correctly. The NSGA-III algorithm introduces the reference point mechanism, which effectively improves the uniformity and convergence of the solution set and maintains the diversity of the solutions better, so the NSGA-III algorithm is chosen in this paper. In this paper, the NSGA-III algorithm is used to solve the multi-objective function. Yuan et al. (2023) researched and designed a dynamic, seasonally adapted, multi-objective, multi-temporal water resource allocation system, which coordinates economic efficiency, fairness, and utilization efficiency, and adopted the NSGA-III algorithm in an effort to simulate the optimal water resources equilibrium solution when facing three different sub-risks, namely, high, medium, and low.
In the context of the ‘dual carbon’ goals, this paper incorporates carbon emissions into the objective function and includes recycled water and rainwater as part of the water resources for integrated optimal allocation. An optimization model for water resource allocation is developed with objectives including carbon emissions, economic benefits, social benefits, wastewater discharge, and groundwater extraction. Using Pingliang City as a case study, the allocation scheme is solved with the NSGA-III algorithm in MATLAB R2022b. This approach not only provides a scientific framework for the efficient allocation of urban water resources but also contributes significantly to achieving the ‘dual carbon’ targets. It offers valuable insights into sustainable water management practices and can serve as a reference for optimizing urban water resource planning in line with broader environmental and societal goals.
CONSTRUCTION OF THE MODEL
Model framework
The flow chart of NSGA-III.
Multi-objective water resources optimal allocation model.
Sensitivity analyses based on parameter configurations may have a significant impact on the quality of Pareto frontiers. Literature studies (Zitzler et al. 2000; Rosenthal & Borschbach 2014; Tanabe & Oyama 2017) have shown that population size and crossover rate have a significant impact on the quality of the Pareto frontiers, especially in terms of convergence speed, diversity, and stability. Too small a population may lead to insufficient diversity, which can trap the algorithm in local optimization, resulting in a narrow and discontinuous Pareto frontier. In contrast, larger populations are better aligned with the distribution of reference points, thus ensuring greater stability. However, this comes at the cost of slower convergence. Too high a crossover rate may lead to premature convergence to a suboptimal Pareto frontier, while too low a crossover rate may hinder the population's ability to efficiently explore the solution space, which may lead to an incomplete or globally suboptimal Pareto frontier. Therefore, many studies have chosen parameter values directly based on empirical evidence. In this paper, we also directly refer to the previously determined values, taking the population size to be 100, crossover rate to be 0.9, mutation rate to be 0.01, and the number of evolutionary generations to be 200 (Wang et al. 2022; Shirajuddin et al. 2023).
Objective functions
Water resource optimization allocation aims to enable urban social development, economic progress, and ecological civilization to achieve harmonious and sustainable development at both time and space dimensions through the rational distribution of limited water resources to maximize the overall interests of the system (Figure 2). Under the ‘double carbon’ background, the introduction of carbon emission optimization targets in the process of water resources allocation optimization can not only effectively reduce carbon emission but also play a strong role in demonstrating carbon emission reduction. This paper takes Pingliang City as an example and constructs a water resources allocation optimization model with carbon emissions, economic benefits, social benefits, wastewater discharge, and groundwater extraction as objectives (Si-feng & Bing 2024).
- (1) Carbon emission objective (Wu et al. 2021; Zhang et al. 2024b): To minimize carbon emissions from water intake systems, water supply systems, and water use systems in this area.where(1)
refers to carbon emissions from water intake systems, water supply systems, and water use systems in this area, metric ton; i refers to the source of water; 
= 1 refers to surface water; 
= 2 refers to underground water; 
= 3 refers to recycled water; 
= 4 refers to rainwater; j refers to water use department; 
= 1 refers to domestic water department; 
= 2 refers to industrial water department; 
= 3 refers to municipal water department; 
= 4 refers to ecological water department; 
refers to the amount of water distributed to water use departments
from the source of water i, in 10 thousand m3; 
refers to the water distribution relationship between the source of water i and water use departments
; 
refers to carbon emission factors for water treatment and distribution i from the source of water, in kgCO2/m3; 
refers to the carbon emission factors of water for water use department j, in kgCO2/m3. - (2) Economic benefit objective (Velasco et al. 2017): To maximize the net benefit of the regional water supply.where(2)
refers to the net benefit of the water supply in 10 thousand yuan; 
refers to the water use net benefit coefficient of the water use department j, 10 thousand yuan/10 thousand m3; the remaining symbols are the same as above. - (3) Social benefit objective (Velasco et al. 2017): To minimize regional water shortages.(3)
where(4)
refers to the regional water shortage, 10 thousand m3; 
refers to the water shortage of water use department j, in 10 thousand m3; 
is the water demand of water use department j, in 10 thousand m3; 
refers to the water shortage coefficient of water use department j; the remaining symbols are the same as above. - (4) Environmental objective (Naghdi et al. 2021): The environmental objective is represented by wastewater discharge. The objective is to minimize the main wastewater discharge in the region.where(5)
refers to regional wastewater discharge in 10 thousand m3; 
refers to the wastewater discharge coefficient of the water use department j, in %; the remaining symbols are the same as above. - (5) Groundwater extraction objective (Naghdi et al. 2021): To minimize regional groundwater extraction.where(6)
refers to regional groundwater extraction in 10 thousand m3; the remaining symbols are the same as above.
Constrained conditions
The objective function is subject to the constraints of the problem, which, as mentioned, express the physical, technical, economic, environmental, or regulatory restrictions of the problem. The optimal solution values will provide the minimum or maximum result of the objective function, having met all the constraints of the problem (Garcia & Alamanos 2022). The constraints in this article are for the relationship between the decision variables and the constraints related to water resources, and the variables of the objective function can be established only if the actual conditions of water resources are satisfied. Therefore certain constraints need to be set.
- (1) Constraints on water supply (Musa 2021): The sum of the water supply from the water source i to all water users is less than or equal to the available water supply of that water source.where(7)
refers to the available water supply of the water source
in 10 thousand m3; the remaining symbols are the same as above. - (2) Constraints on water demand (Musa 2021): The total water supply to the water use department j from all water sources is not more than 1.1 times the water demand of this water use department and not less than 0.9 times.where(8)
refers to the water demand of the water use department j; the remaining symbols are the same as above. - (3) Constraints on the reuse rate of recycled water: The water production rate of the sewage treatment plant is 0.8. The reuse rate of urban recycled water shall not be less than that determined according to the construction and actual situation of Sponge City.where(9)
refers to the reuse rate of recycled water determined according to the construction and actual situation of the Sponge City, in percent; - (4) Constraints on the utilization rate of rainwater: The utilization rate of urban rainwater is not less than the utilization rate of recycled water determined according to the construction and actual situation of Sponge City.where(10)
refers to the available rainwater supply in 10 thousand m3; 
refers to the utilization rate of rainwater determined according to the construction and actual situation of the Sponge City, in %; the remaining symbols are the same as above. - (5) Nonnegative constraints (Si-feng & Bing 2024): The water supply to water use departments i and j from the source of water is nonnegative.(11)
Determination of model parameters
Water use net benefit coefficient
According to references (Li et al. 2015; Wang et al. 2016; Liu et al. 2022), the net benefit coefficients of water use departments are determined. The domestic water net benefit coefficient is equal to the Gross Domestic Product (GDP) of Kongtong District, Pingliang City divided by the comprehensive domestic water consumption. The industrial water net benefit coefficient is the reciprocal of ten thousand yuan of industrial water consumption. Considering that the environment is closely related to residents' lives, the environmental water net benefit coefficient is consistent with the domestic water net benefit coefficient. The net benefit coefficient of ecological water replenishment is taken as half of the environmental water consumption, as shown in Table 1.
Net benefits of domestic, industrial, environmental, and ecological water use
| Planning year | Domestic water (10 thousand yuan/10 thousand m3) | Industry (10 thousand yuan/10 thousand m3) | Municipal (10 thousand yuan/10 thousand m3) | Ecological water replenishment (10 thousand yuan/10 thousand yuan m3) |
|---|---|---|---|---|
| 2025 | 650 | 275 | 650 | 325 |
| 2030 | 700 | 355 | 700 | 350 |
| 2035 | 750 | 414 | 750 | 375 |
| 2040 | 800 | 482 | 800 | 400 |
| Planning year | Domestic water (10 thousand yuan/10 thousand m3) | Industry (10 thousand yuan/10 thousand m3) | Municipal (10 thousand yuan/10 thousand m3) | Ecological water replenishment (10 thousand yuan/10 thousand yuan m3) |
|---|---|---|---|---|
| 2025 | 650 | 275 | 650 | 325 |
| 2030 | 700 | 355 | 700 | 350 |
| 2035 | 750 | 414 | 750 | 375 |
| 2040 | 800 | 482 | 800 | 400 |
Water distribution relation
= 1; no filling represents no water distribution, 
= 0. 
Water distribution relationship diagram.
Water scarcity coefficient
Based on industry demand and the social benefits generated by unilateral water use, the corresponding water scarcity weights are distributed to various industries to minimize regional water scarcity and achieve coordinated development of the regional economy (Zhang et al. 2022). The water scarcity coefficients in domestic, industry, municipal administration, and ecology are 0.4, 0.3, 0.2, and 0.1, respectively (Wang et al. 2016).
Sewage discharge coefficient
The pollutant discharge coefficient in the research area is determined according to the Code of Urban Wastewater Engineering Planning (GB 50318-2017). Considering the actual development of the research area, the domestic sewage discharge coefficient 
is 0.85, and the industrial sewage discharge coefficient 
is 0.70. In this paper, only domestic and industrial sewage discharge are considered, rather than environmental and ecological water discharge.
Carbon emission factor
Carbon emissions from different water sources in the process of water treatment and distribution mainly include carbon emissions from the water intake system and water supply system. The water intake system mainly draws water from rivers, lakes, reservoirs, and groundwater sources through power facilities such as pumps, while the water supply system includes water transportation, water treatment, and water distribution. On the basis of the estimation of carbon emissions of the water intake system and water supply system from different water sources (Rothausen & Conway 2011; Plappally & Lienhard V 2012; Xiang & Jia 2019), the carbon emission factors of different water sources in the process of water treatment and distribution are obtained, as shown in Table 2.
Carbon emission factors of different water sources and water use departments
| Water sources or water use departments | Water sources (kgCO2/m3) | Water use departments (kgCO2/m3) | ||||||
|---|---|---|---|---|---|---|---|---|
| Surface water | Groundwater | Recycled water | Rainwater | Domestic | Industrial | Municipal | Ecological | |
| Carbon emission factors | 0.946 | 1.907 | 1.45 | 2.353 | 7.684 | 0.323 | 0.052 | 0.035 |
| Water sources or water use departments | Water sources (kgCO2/m3) | Water use departments (kgCO2/m3) | ||||||
|---|---|---|---|---|---|---|---|---|
| Surface water | Groundwater | Recycled water | Rainwater | Domestic | Industrial | Municipal | Ecological | |
| Carbon emission factors | 0.946 | 1.907 | 1.45 | 2.353 | 7.684 | 0.323 | 0.052 | 0.035 |
The urban water system is the core of carbon emissions from water resources. Some studies have shown that the carbon emissions in the terminal water use process dominate the overall carbon emissions of the urban water system, far more than carbon emissions in water intake and supply processes. On the basis of the estimation of carbon emissions of different water use departments (Zhou et al. 2019), the carbon emission factors of different water use departments are obtained, as shown in Table 1.
Reuse rate of recycled water
According to the construction plan and actual development of Sponge City in Pingliang City, the reuse rate of sewage water 
in 2025, 2030, 2035, and 2040 will be 40, 50, 55, and 60%, respectively.
Utilization rate of rainwater
According to the construction plan and actual development of Sponge City in Pingliang City, the utilization rate of rainwater 
in 2025, 2030, 2035, and 2040 will be 6, 10, 12, and 15%, respectively.
CASE STUDY
Overview of the study area
Pingliang City is situated in the ecologically fragile Loess Plateau region. Its economic development faces prominent challenges, including intensive exploitation of mineral resources, inadequate environmental protection infrastructure, and a significant dependance on traditional industrial pathways. Notably, the coal and power industries account for over 80% of the added value of above-scale industries, indicating a lagging construction of a green industrial system. Meanwhile, the region confronts issues such as low-level intensive management of water resources, low utilization rate of non-conventional water sources, weak social awareness of water conservation, and limited total available water resources.
Schematic map of the study area.
In summary, To achieve efficient utilization of limited surface water resources, rational development of groundwater, and full exploitation of non-conventional water resources, it is urgent to conduct a study on the optimal allocation of water resources in the region. This research will provide scientific and theoretical support for water resources planning and management in Pingliang's central urban area.
Data acquisition and analysis
The water sources in the central urban area of Pingliang are mainly divided into surface water, groundwater, recycled water, and rainwater, and the main water use departments include domestic, industrial, municipal, and ecological. According to water resource data in 2010–2020, the water demand and supply in the planning years (2025, 2030, 2035, and 2040) are predicted using the quota method when the guaranteed rate P = 75%. The specific predicted results of the available water supply and water demand in various planning years are shown in Tables 3 and 4. These tables show that when surface water and groundwater are provided for total water consumption in the central urban area of Pingliang, the water shortage problem occurs in each planning year, and the water shortage rates are 16.07, 22.21, 25.23, and 27.81%, respectively. When surface water, groundwater, recycled water, and rainwater are supplied for total water consumption in the central urban area of Pingliang, no water scarcity occurs in various planning years.
Total water availability for the planning year
| Planning year | Surface water (10 thousand m3) | Groundwater (10 thousand m3) | Recycled water (10 thousand m3) | Rainwater (10 thousand m3) | Total available water supply (10 thousand m3) |
|---|---|---|---|---|---|
| 2025 | 730 | 1,760 | 1,591.55 | 735.88 | 4,817.43 |
| 2030 | 730 | 1,760 | 1,727.71 | 735.88 | 4,953.59 |
| 2035 | 730 | 1,760 | 1,801.53 | 735.88 | 5,027.41 |
| 2040 | 730 | 1,760 | 1,865.61 | 735.88 | 5,091.49 |
| Planning year | Surface water (10 thousand m3) | Groundwater (10 thousand m3) | Recycled water (10 thousand m3) | Rainwater (10 thousand m3) | Total available water supply (10 thousand m3) |
|---|---|---|---|---|---|
| 2025 | 730 | 1,760 | 1,591.55 | 735.88 | 4,817.43 |
| 2030 | 730 | 1,760 | 1,727.71 | 735.88 | 4,953.59 |
| 2035 | 730 | 1,760 | 1,801.53 | 735.88 | 5,027.41 |
| 2040 | 730 | 1,760 | 1,865.61 | 735.88 | 5,091.49 |
Total water consumption in the planning year
| Planning year | Domestic (10 thousand m3) | Industrial (10 thousand m3) | Municipal (10 thousand m3) | Ecological (10 thousand m3) | Total water demand (10 thousand m3) |
|---|---|---|---|---|---|
| 2025 | 1,237.35 | 1,339.50 | 176.96 | 213.00 | 2,966.81 |
| 2030 | 1,502.41 | 1,260.79 | 224.52 | 213.00 | 3,200.72 |
| 2035 | 1,664.73 | 1,195.44 | 257.23 | 213.00 | 3,330.40 |
| 2040 | 1,810.25 | 1,133.23 | 292.61 | 213.00 | 3,449.09 |
| Planning year | Domestic (10 thousand m3) | Industrial (10 thousand m3) | Municipal (10 thousand m3) | Ecological (10 thousand m3) | Total water demand (10 thousand m3) |
|---|---|---|---|---|---|
| 2025 | 1,237.35 | 1,339.50 | 176.96 | 213.00 | 2,966.81 |
| 2030 | 1,502.41 | 1,260.79 | 224.52 | 213.00 | 3,200.72 |
| 2035 | 1,664.73 | 1,195.44 | 257.23 | 213.00 | 3,330.40 |
| 2040 | 1,810.25 | 1,133.23 | 292.61 | 213.00 | 3,449.09 |
RESULTS AND ANALYSIS
Optimization scheme determination
The optimal allocation scheme of water resources in 2025 with a guaranteed rate of P = 75%.
The optimal allocation scheme of water resources in 2025 with a guaranteed rate of P = 75%.
Optimized allocation result
Schematic diagram of the relationship between supply and demand of water supply sources and water-using sectors in the planning year (10 thousand m3).
Schematic diagram of the relationship between supply and demand of water supply sources and water-using sectors in the planning year (10 thousand m3).
Total carbon emissions
Total carbon emissions in the central urban area of Pingliang in 2011–2020 and various planning years.
Total carbon emissions in the central urban area of Pingliang in 2011–2020 and various planning years.
Carbon emissions per unit water volume
Carbon emissions per unit water volume, carbon emissions per unit water supply, and per unit water consumption in the central urban area of Pingliang in 2011–2020 and planning years.
Carbon emissions per unit water volume, carbon emissions per unit water supply, and per unit water consumption in the central urban area of Pingliang in 2011–2020 and planning years.
Carbon emissions per capita
refers to the carbon emission in the m planning year, t, m = 1 is 2025, m = 2 is 2030, m = 3 is 2035, and m = 4 is 2040; A refers to the per capita carbon emissions over the years, t/person; 
refers to the number of people in m planning year, people. 
Carbon emissions and carbon reduction rate of water resources in the planning year calculated by per capita.
Carbon emissions and carbon reduction rate of water resources in the planning year calculated by per capita.
Carbon emissions per unit area
refers to the carbon emission in the m planning year, t; B refers to carbon emissions per unit area over the years, 
; 
and refers to the planned area for the n planning year. 
Carbon emissions and carbon reduction rate of water resources in the planning year calculated per unit area.
Carbon emissions and carbon reduction rate of water resources in the planning year calculated per unit area.
Benefits from carbon emission reduction
Transaction details of different carbon markets in China.
Calculation of carbon reduction benefits in terms of per capita carbon emissions.
Calculation of carbon reduction benefits in terms of per capita carbon emissions.
Calculation of carbon reduction benefits in terms of carbon emissions per unit area.
Calculation of carbon reduction benefits in terms of carbon emissions per unit area.
CONCLUSIONS
Under the background of ‘double carbon’, this paper incorporates carbon emission and unconventional water resources into the optimal allocation of water resources, constructs a water resources allocation optimization model with carbon emissions, economic benefits, social benefits, wastewater discharge, and groundwater extraction as the objectives, and conducts a study on Pingliang City as an example, which is solved by NSGA-III algorithm. The optimized allocation results indicate that with the continuous increase in water consumption, the total carbon emissions in the planning years (2025, 2030, 2035, and 2040) are continuously increasing, namely, to 150,600, 173,900, 187,500, and 202,400 t, respectively. Carbon emission per unit of water in the planning years is also on an increasing trend, which is mainly due to the fact that carbon emission per unit of water consumption is continuously increasing while carbon emission per unit of water supply remains constant. Carbon emissions per capita and per unit area are both lower than the historical average. In the traditional allocation plan, carbon emissions for the planning years are estimated by averaging the per capita carbon emissions over previous years. The optimized allocation plan, however, achieves carbon emission reductions of 39,300, 34,700, 32,700, and 29,100 metric tons in 2025, 2030, 2035, and 2040, with corresponding carbon reduction rates of 20.69, 16.54, 14.85, and 12.55%. The cumulative carbon emission reduction over the period from 2025 to 2040 is 153,000 metric tons. Similarly, when carbon emissions are estimated based on the average carbon emissions per unit area over previous years, the optimized allocation plan results in reductions of 58,200, 56,600, 69,100, and 76,000 metric tons in the planning years, with carbon reduction rates of 27.89, 24.55, 26.93, and 27.30%, respectively. The cumulative carbon emission reduction in this case is 267,000 metric tons from 2025 to 2040. According to price estimation in China's carbon trading market, the carbon emission reduction benefits are calculated from the perspectives of per capita carbon emission and carbon emission per unit area, and the cumulative economic benefits in 2025–2040 are estimated to be 934,800–9,482,900 and 1,631,400–16,548,700 yuan, respectively. The results show that this optimized allocation of water resources can reduce carbon emissions to a certain extent, providing a scientific basis for the optimized allocation of urban water resources and playing an important role in promoting China's realization of the ‘double carbon’ goal. Future research could focus on further refining allocation models by incorporating additional factors such as climate change projections and regional disparities in water availability.
There exist several limitations in our work. First, there are certain operational differences in water systems across different cities. The carbon emission coefficients referenced in this study were determined based on data from other regions without in-depth field investigations and statistical analysis, which may have impacted the accuracy of the research. Second, most parameters adopted in this paper are static indicators lacking dynamic data support, resulting in limitations in the comprehensiveness, explanatory power, and practical application value of the study. For future research, we recommend prioritizing the development of dynamic models to quantify carbon-water synergy benefits under various scenarios and establishing an integrated sponge city information platform with carbon management capabilities. This platform should achieve unified functions including stormwater warning, resource allocation, and carbon emission monitoring.
ACKNOWLEDGEMENTS
The authors are thankful to Professor Wei Bigui from Lanzhou Jiaotong University for providing the platform necessary to complete this research. The authors are also grateful to the anonymous reviewers for their efforts that helped sharpen and focus the work for greater visibility.
AUTHOR CONTRIBUTION STATEMENT
All authors listed have significantly contributed to the development and the writing of this article.
FUNDING STATEMENT
This research was funded by the National Natural Science Foundations of China (Nos: 52060014), Department of Education of Gansu Province: Major cultivation project of scientific research innovation platform in university (2024CXPT-14) and Longxi County Science and Technology Program Funding (LXBYY004).
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.
