https://orcid.org/0000-0002-6230-5040
Abstract
The bi-level programming coupling model of uncertainty constraints and interval parameter programming is developed to optimize the allocation of water resources and conduct a comprehensive analysis of water resource carrying capacity. The model uses an uncertainty credibility number set and interval value to deal with uncertain factors, and analyses the water resources allocation of Longchuan River in central Yunnan. The competition mechanism and polynomial variation improved algorithm are used to analyze the water consumption, economic benefits and satisfaction in different planning periods when λ = 0.7, 0.8, 0.9, 1.0. The results show that the uncertain bi-level coupling model can cause changes in water allocation, pollutant discharge, system efficiency, etc., and can also effectively balance the mutual constraints between economic benefits and environmental pollution discharge, ensuring a good development trend in the planning year. The water diversion from other basins such as the Central Yunnan Water Diversion Project was transferred to Longchuan River Basin to increase the water supply, and the carrying capacity was further improved, with an increase of water resources by 25.9%. The model research has certain practical and strategic significance for maintaining the sustainable development of the ecological environment in the Longchuan River Basin
HIGHLIGHTS
A bi-level programming coupling model of uncertainty-constrained programming and interval parameter programming is established.
Competition mechanism and polynomial mutation improved algorithm is introduced.
Select typical watersheds in central Yunnan, China, and solve the optimization model.
Through the comprehensive analysis of water resources carrying capacity, the ideal evaluation results are obtained.
INTRODUCTION
Water is a precious resource for the sustainable development of the country. Global climate change and human activities directly threaten the water environment, increase the vulnerability of freshwater resources, and accelerate the contradiction between the supply and demand of water resources and also the shortage of water resources (Wang et al. 2022c). Climate change has aggravated the uneven spatio-temporal distribution of water resources and made it more difficult to allocate water resources. China's water resources are very scarce, the structure of water use is unreasonable, the water management system is not perfect, there are conflicts of interest, backward management and other issues, which have led to the increasingly prominent contradiction between supply and demand of water resources. Therefore, it is particularly important to establish an efficient water resources optimal allocation model to solve the complex water resources planning problem (Dong & Wang, 2012; Martinsen et al., 2019).
The traditional research on the optimal allocation of water resources in China mainly involves cities (Meng et al., 2020; Wei et al., 2020; Chen et al., 2021a), river basins (Han et al., 2018; Banadkooki et al., 2022; Wan et al., 2023), cross-basins (Tian et al., 2019; Kazemi et al., 2020; Sun et al., 2021) and optimal allocation of water resources based on the concept of sustainable development (Hu & Li, 2014). In the previous objective function settings, Zhang et al. (2020b) and Zhou (2022) mainly considered the minimum shortage of water resources, the maximum ecological and economic benefits as the goal, and coordinated the different water needs of various sources for residents' living, industrial production, agricultural irrigation, environmental protection, to achieve the optimal allocation of water resources between regions and basins. Kazemi et al. (2022) and Li et al. (2022a, 2022b) usually take the maximum water supply or water storage as the objective function of cross-basin water resources, and establish a multi-objective optimization model with the constraints of cross-basin project scale, multi-reservoir joint adjustment, and reasonable compensation mechanism, so that the cross-basin water resources optimization decision can be further developed. According to the research results of Hao et al. (2022) and Dou et al. (2022), the objective function is usually established under the conditions of maximum water demand, minimum water shortage, low water cost and others. In the case of the ecological environment as the key consideration, there are few studies on the setting of pollutant discharge as the objective function. For the optimal allocation model, there are many studies on the establishment of a single uncertain factor model, such as considering parameter calibration (Khosrojerdi et al., 2019), interval boundary (Bekri et al., 2015), fuzzy random (Banihabib et al., 2019) and one-way evaluation after allocation. Compared with the research on multiple uncertain factors, Chen et al. (2021b) illustrated the effectiveness of the developed multi-level model through a practical case of the Wuhan metropolitan area. Li et al. (2021) and Bi et al. (2022) established a multi-objective water resources optimal allocation model based on an improved intelligent population optimization algorithm with economic, social and ecological benefits as objective functions, strengthening the comparative evaluation research before and after planning. It is a great progress in the research of optimal allocation of water resources.
In the cross-field, the optimal allocation of water resources breaks through the research on the traditional model, combining the environmental construction, the relationship mechanism between decision-makers and managers and the optimal calculation of data. Through the complex dynamic and stable evolution strategy (Lu et al., 2022), the combination of the water environment mechanism model (Genova & Wei, 2023), and the introduction of low-carbon economic development (Wang et al., 2022a), the gaps in water resources planning and management evaluation were filled.
Considering comprehensively, the bi-level programming model is established by the connection and influence of the upper structure and the lower structure. This model uses the intelligent optimization algorithm to obtain the global optimal solution and applies it to the actual case. The establishment of this model provides a scientific basis for studying the efficient use of water resources, water environment security and promoting socio-economic development.
RESEARCH MODELS AND ALGORITHMS
Bi-level programming model
is the upper structure objective function, 
is the lower structure objective function, 
is the upper structure constraint condition, 
and is the lower structure constraint condition.According to the process of adopting the optimal solution, the upper structure influences the lower structure by setting x decision variables. The lower structure is a function of the variable y = y(x) of the upper structure, and the specific steps are as follows:
Step 1. Calculate the upper structure solution
and the lower structure solution 
, respectively.Step 2. Through the influence and relationship of the upper and lower structure objective function, the upper structure objective function critical value
and the lower structure objective function critical value 
are determined.Step 3. Solve the membership degree of the objective function of the upper and lower structure, and use the optimal membership function formula (Calvete & Galé, 2010), to solve the maximum value
of the membership function, 
which represents the satisfaction value.
Uncertainty-constrained programming model
represents the objective function decision variable; 
, 
, and 
represent function coefficients; C is the set of uncertain reliability applied to the study area when the reliability is 
, 
is the function uncertainty variable, r is the real number, and 
is set, then the constraint condition is expressed as 
. According to the research results of relevant scholars, according to the concept of credibility (Zhang et al., 2020a), the credibility value of the system function should be greater than 0.5, and each constraint satisfaction interval should be [0.5, 1].Interval parameters programming
represents the objective function decision variable; 
, 
, and 
represents function coefficients.Establishment of interval uncertainty bi-level programming optimization model
Based on the method steps of the uncertainty constraint programming model, interval parameter programming and bi-level programming, based on the bi-level programming model, the uncertainty constraint programming model and the interval parameter programming method are integrated to construct the regional water resources, social economy and ecological environment evaluation index parameters, objective function and constraint condition optimization model. The model is the interval uncertainty bi-level programming optimization model. The specific model calculation is as follows: Equations (10)–(17):
- 1.
The upper structure takes the minimum pollutant emissions as the objective function:
Constraint conditions:
- (1)Ammonium nitrogen, nitrate nitrogen, total nitrogen, total phosphorus emission constraints:(11)
- (2)Regional discharge constraints:(12)
- (3)Ecological environment water consumption constraints:where(13)
represents the amount of pollutant discharge, t; 
represents the amount of water resources allocated, 10,000 m3; h is the number of water use areas, including Nanhua County, Chuxiong City, Mouding County, Lufeng County, Yuanmou County, Yao'an County, Dayao County, Yongren County and Wuding County; k is the number of water used by the department, k = 1,2,3, which respectively represent domestic water, production water and ecological environment water; l is the number of planning years, l = 1, 2, 3…; 
represents the pollution discharge coefficient; 
indicates the discharge concentration of ammonium nitrogen, 
; similarly, 
, 
, 
represent the discharge concentration of nitrate nitrogen, total nitrogen and total phosphorus, respectively, 
; 
, 
, 
, 
represent the removal rate of each pollutant discharge index; 
indicates the total discharge amount of the pollution discharge index in the setting l planning year, t; 
indicates the total discharge amount of sewage in the planning year, million m3; 
represents the proportion coefficient of ecological environment water consumption to the allocated of water resources.
- 2.
The objective function of the lower structure is to maximize social and economic benefits:
Constraint conditions:
- (1)Water supply capacity constraints in water area:(15)
- (2)Domestic water constraints in water area:(16)
- (3)Constraints on water consumption per 10,000 yuan of industrial output value:(17)
represents socio-economic benefits, 10,000 yuan; 
represents water supply benefit coefficient, yuan/m3; 
represents water price, yuan/m3; 
represents the water cost coefficient, yuan/m3; 
represents the total amount of water supply, t; 
represents the total urban population, 10,000 people; 
represents urban domestic water consumption, m3/d, 
represents gross industrial production, 10,000 yuan; 
and 
represent the upper and lower limits of water consumption per 10,000 yuan of industrial output value, m3/10,000 yuan.
Model algorithm solution
There are various model algorithms employed to solve many engineering problems (Deb et al., 2002; Reyes-Sierra & Coello, 2006; Yang & Deb, 2014; Wang et al. 2022b; Zhao et al., 2022), among them, the solution of single-objective optimization algorithm is a scalar, and the solution of multi-objective optimization algorithm is a vector. The size of the vector cannot be compared by simple magnitude. Therefore, based on the original algorithm of the sparrow search algorithm (Li et al. 2022a), the algorithm-solving process is improved, the competition mechanism (Zeng et al., 2021) and polynomial mutation (Wen et al., 2021) is introduced, and the non-dominated vector sorting is used for size comparison.
Individual competition reference of population.
Among them, 
is an exponential distribution, and the larger the index value, the closer the mutant individual is to the previous generation. According to multiple checks and references to relevant literature, the value of 
is set to 20, and the improved algorithm has the ability to obtain the optimal solution. u is the upper limit of sparrow position, 
is the lower limit of sparrow position, 
and 
are random numbers in the range of [0, 1].
Model ideas
The research of the water resources optimization coupling model is carried out on the basis of basic theory and system analysis. The effective use of water resources supports the sustainable development of the social economy and is also an important part. Based on the study of water resources, population, economy and environment in the region, the results of optimal allocation of water resources are obtained through carrying capacity evaluation and supply and demand balance analysis.
In the process of water resources allocation, we should not only aggregate environmental, economic and social factors into a single-objective function to form a bi-level programming model, but also integrate uncertain constraint programming and interval parameter programming into the model framework. Considering that the environmental impact in the process of water resources utilization (especially the emission of ammonium nitrogen, nitrate nitrogen, total nitrogen and total phosphorus) has become a restrictive factor for the effective utilization of water resources, the minimum target of pollutant emission in the process of water resources allocation and utilization is taken as the upper structure of the model. At the same time, considering that the distribution of water resources allocation income is the focus of maintaining social stability and promoting the coordinated development of river basins, the goal of maximizing the social and economic benefits of water resources allocation is introduced as the lower structure of the model. However, in the process of water resource allocation, the minimum discharge of pollutants and the maximization of social and economic benefits are used as the objective functions, and the results of water resource allocation often conflict with each other. In order to cope with the conflict of interests between different decision-makers, in the process of uncertainty bi-level programming, the upper structure model should fully consider the decision of the lower structure, and then adjust and optimize its own allocation plan. According to its own development needs, the optimal decision-making scheme is made, the global optimal solution is obtained, and the carrying capacity of water resources in the basin is analyzed, including the balance of supply and demand of water resources and the evaluation of the development trend of carrying capacity.
Model construction idea diagram.
CASE ANALYSIS
Overview of the study area
Location of the Longchuan River and water resources zoning of the basin comprehensive planning.
Location of the Longchuan River and water resources zoning of the basin comprehensive planning.
Generalized network of the water resources system in the Longchuan River Basin.
The multi-year average precipitation in the Longchuan River Basin is 876.2 mm, the multi-year average evaporation is 1,160.1–2,226.8 mm, and the multi-year average temperature is 14.8–21.5 °C. The highest monthly average temperature appears in June when the temperature is 20.9 °C, the lowest monthly average temperature appears in January when the temperature is 8.2 °C, the extreme maximum temperature is 32.4 °C, the extreme minimum temperature is –4.8 °C, the multi-year average relative humidity is 57–75%, the multi-year average sunshine is 2,177–2,593 h, the multi-year average wind speed is 1.5–3.3 m/s, and the average maximum wind speed is 21.0 m/s (wind direction NE).
The Longchuan River length of 272.5 km was selected for the annual water quality evaluation. Among them, rivers with Classes II–III water quality account for 27.7%, rivers with Class IV water quality account for 50.7%, and rivers with Class V and inferior V water quality account for 21.6%. In the wet season, rivers with Class II-III water quality account for 27.7%, and rivers with water quality Class V and inferior V account for 72.3%. In the dry season, rivers with Classes II–III water quality account for 70.1%, rivers with Class IV water quality account for 8.3%, and rivers with Class V and inferior V water quality account for 21.6%. In the Longchuan River Basin, the pollutants in the mainstream mainly come from chemical substances and heavy metal pollution. In the tributaries, the water quality of the Zidian River and Xijing River reached Class II, and the water quality of the Qingling River reached Classes II–III. Due to the small number of factories, mines and other enterprises, and human activities having little impact, the water quality of the tributaries is relatively good, which can basically meet the requirements of water supply along the river.
Evaluation index analysis
According to the design principles of the index system, follow the scientific, practical, feasible, representative, and policy relevance, and include the main influencing factors in the system as much as possible. Preliminary selection of 16 index factors affecting water resources–social economy–ecological environment in the Longchuan River Basin. Specific indicators are shown in Table 1.
Evaluation index and weight of water resources in the Longchuan River Basin.
| Index system | Specific indicators | Indicator symbol | Index weight |
|---|---|---|---|
| Water resources system | Water resources per unit area of watershed | X1 | 0.059 |
| Per capita water resources | X2 | 0.061 | |
| Water Transfer Per Unit Area Outside Watershed | X3 | 0.091 | |
| Water consumption of 10,000 yuan industrial output value | X4 | 0.046 | |
| Ecological environment water consumption per capita | X5 | 0.038 | |
| Per capita water storage capacity | X6 | 0.083 | |
| Social and economic systems | Per capita GDP | X7 | 0.062 |
| GDP per water | X8 | 0.057 | |
| Urbanization rate | X9 | 0.089 | |
| Effective irrigation area | X10 | 0.079 | |
| Ecological and environmental systems |  | X11 | 0.059 |
 | X12 | 0.067 | |
 | X13 | 0.061 | |
 | X14 | 0.071 | |
| Ratio of man-made sewage discharge to river runoff | X15 | 0.040 | |
| soil erosion rate | X16 | 0.037 |
| Index system | Specific indicators | Indicator symbol | Index weight |
|---|---|---|---|
| Water resources system | Water resources per unit area of watershed | X1 | 0.059 |
| Per capita water resources | X2 | 0.061 | |
| Water Transfer Per Unit Area Outside Watershed | X3 | 0.091 | |
| Water consumption of 10,000 yuan industrial output value | X4 | 0.046 | |
| Ecological environment water consumption per capita | X5 | 0.038 | |
| Per capita water storage capacity | X6 | 0.083 | |
| Social and economic systems | Per capita GDP | X7 | 0.062 |
| GDP per water | X8 | 0.057 | |
| Urbanization rate | X9 | 0.089 | |
| Effective irrigation area | X10 | 0.079 | |
| Ecological and environmental systems | | X11 | 0.059 |
| | X12 | 0.067 | |
| | X13 | 0.061 | |
| | X14 | 0.071 | |
| Ratio of man-made sewage discharge to river runoff | X15 | 0.040 | |
| soil erosion rate | X16 | 0.037 |
Data analysis
Considering the intersection and complexity of the comprehensive system of water resources–society–economy–ecological environment and other comprehensive systems, referring to factors such as ecological environment compensation mechanism, taking the comprehensiveness, dynamic and static, comparability of basic data as the principle, setting the minimum pollutant discharge and maximum economic benefit as the upper and lower structure objective functions, selecting 2000, 2004, 2010, and 2020 as the current status year as the basis, 2025, 2030, and 2035 as the planning year. Nanhua County, Chuxiong City, Mouding County, Lufeng County, Yuanmou County, Yao'an County, Dayao County, Yongren County, and Wuding County in typical plateau areas are determined as water-using areas. The current annual water supply and consumption data of the living, production and ecological conditions in these nine regions mainly come from the Water Resources Bulletin, Environmental Bulletin and Statistical Yearbook, which are used as input and output in the coupling model. Missing data were obtained by interpolation and fitting through theoretical analysis and linear analysis.
With the rapid development of the social economy, in the next 20 years, the amount of water resources in the Longchuan River Basin has changed, which is reflected in the changes in multi-year average total water demand, supply and shortage. The predicted values of 2025, 2030, and 2035 are shown in Table 2.
The balance between supply and demand of water resources in the Longchuan River Basin.
| Year | The first supply demand balance | The second supply demand balance | The third supply demand balance | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Water supply | Water need | Water scarcity | Water supply | Water need | Water scarcity | Water supply | Water need | Water scarcity | |
| 2025 | 6.26 | 11.29 | 5.03 | 7.55 | 10.51 | 2.96 | 10.2 | 10.51 | 0.31 |
| 2030 | 6.67 | 12.36 | 5.69 | 7.25 | 11.27 | 4.02 | 11.04 | 11.27 | 0.23 |
| 2035 | 7.09 | 12.93 | 5.84 | 7.96 | 12.26 | 4.3 | 11.35 | 11.7 | 0.35 |
| Year | The first supply demand balance | The second supply demand balance | The third supply demand balance | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Water supply | Water need | Water scarcity | Water supply | Water need | Water scarcity | Water supply | Water need | Water scarcity | |
| 2025 | 6.26 | 11.29 | 5.03 | 7.55 | 10.51 | 2.96 | 10.2 | 10.51 | 0.31 |
| 2030 | 6.67 | 12.36 | 5.69 | 7.25 | 11.27 | 4.02 | 11.04 | 11.27 | 0.23 |
| 2035 | 7.09 | 12.93 | 5.84 | 7.96 | 12.26 | 4.3 | 11.35 | 11.7 | 0.35 |
RESULTS AND DISCUSSION
Analysis of water use department under different credibility
The proportion of different water departments in different credibility levels during the planning period.
The proportion of different water departments in different credibility levels during the planning period.
Analysis of pollutant discharge
, 
, 
and 
showed no significant difference between months and months throughout the year (P > 0.05). Compared with the corresponding mean values of water quality parameters, in the second quarter of the year, 
reached the water quality II standard, 
was within the standard value range, 
was greater than the water quality standard, and 
reached the water quality III standard; in the third quarter, 
reached the surface environmental quality class II standard, 
and 
had no change, and 
also rose to the surface water quality class II standard. In general, the total amount of discharge increases significantly as the planning period moves forward, indicating that the total allocation of water resources during the planning period is also increasing; from the perspective of credibility, the allocation of water resources becomes smaller as the value of the credibility increases, which leads to a decrease in the discharge of pollutants. It can be seen from Figures 6 and 7, from the perspective of water use in the basin, that the amount of water resources allocated to domestic water and production water produces higher pollutant emissions, mainly nitrogen, phosphorus and other nutrients, mainly related to farmland, engineering construction and other affected areas. 
Emissions of pollutants in different planning periods under different credibility levels in the lower structure. (a) Emissions of various pollutants in different planning periods and (b) emissions of pollutants with different credibility in different planning periods.
Emissions of pollutants in different planning periods under different credibility levels in the lower structure. (a) Emissions of various pollutants in different planning periods and (b) emissions of pollutants with different credibility in different planning periods.
Emissions of pollutants in different planning periods under different credibility levels in superstructure. (a) Emissions of various pollutants in different planning periods and (b) emissions of pollutants with different credibility levels in different planning periods.
Emissions of pollutants in different planning periods under different credibility levels in superstructure. (a) Emissions of various pollutants in different planning periods and (b) emissions of pollutants with different credibility levels in different planning periods.
System benefit analysis
. Under different credibility conditions, the satisfaction value decreases with the increase of credibility. The value of credibility 
is divided into 0.7, 0.8, 0.9, and 1.0. The smaller the value is, the lower the credibility condition of the system is, so as to obtain higher satisfaction, and the overall satisfaction range is [0.69,0.72], which balances the relationship between the upper and lower structures. In addition, in different planning periods, with different reliability values selected, the obtained system benefit intervals are [616.73,756.93], [489.98, 628.18], [329.06, 469.32], [218.48, 310.37] billion yuan. The development trend of system benefit is opposite to the value of credibility, the higher the credibility, the lower the benefit. When 
= 0.7, the maximum advantages of system benefits can be fully utilized, thereby reducing the risk of system constraints. Otherwise, the opposite is true. Considering comprehensively, it is particularly important to balance system benefit, satisfaction and reliability under the dual effect of uncertainty constraint programming and interval parameter programming. The calculation results of the system benefit and satisfaction value are shown in Figures 8 and 9. 
Comparison of system benefit and satisfaction value results of the lower structure system.
Comparison of system benefit and satisfaction value results of the lower structure system.
Comparison of system benefit and satisfaction value results of the upper structure system.
Comparison of system benefit and satisfaction value results of the upper structure system.
Compared with the results of single-layer model
The upper structure and the lower structure are used as objective functions to establish two single-level objective programming optimization models. That is, the uncertain water resources single-level planning model with the minimum pollutant emission and the uncertain water resources single-layer planning model with the maximum social and economic benefits. The two single-level programming models are compared with the uncertain bi-level programming model, and the results are shown in Table 3. The upper structure model only considers the watershed environment. The optimal solutions of the model optimization have the lowest pollutant emissions and system benefits, and the water supply of the water sector is also allocated according to the minimum demand. The lower structure model is from the perspective of social and economic benefits. The final optimization results are distributed according to the maximum economic benefits and the highest supply and demand requirements of the water sector. At the same time, it brings environmental pollution and leads to an increase in pollutant emissions. The uncertainty bi-level programming optimization model takes into account the requirements of environmental pollutant discharge and socio-economic system benefits. The results can provide reasonable water resources allocation schemes, economic allocation schemes, environmental governance schemes and water supply and demand requirements for different decision-making management departments and water use departments. In general, the upper structure model reflects the optimization of the water environment; the lower structure model reflects the promotion of economic and social development in the basin; the bi-level programming model provides the best solution results in both environmental and economic aspects.
Comparison of system benefits and total pollutant emissions between single-level and bi-level models.
| λ = 0.7 | λ = 0.8 | λ = 0.9 | λ = 1.0 | |||||
|---|---|---|---|---|---|---|---|---|
| Different credibility Numerical value | Upper limit | Lower limit | Upper limit | Lower limit | Upper limit | Lower limit | Upper limit | Lower limit |
| A single-level programming model with the goal of minimizing pollutant emissions | ||||||||
| System benefits (billion yuan) | 687.39 | 597.88 | 621.54 | 553.61 | 599.12 | 500.93 | 563.75 | 486.54 |
| Total amount of pollutant discharged (million tons) | 3.96 | 3.87 | 3.89 | 3.84 | 3.85 | 3.83 | 3.82 | 3.80 |
| A single-level programming model aiming at maximizing social and economic benefits | ||||||||
| System benefits (billion yuan) | 758.73 | 740.22 | 741.92 | 727.78 | 729.62 | 719.46 | 711.06 | 698.96 |
| Total amount of pollutant discharged (million tons) | 4.16 | 4.13 | 4.14 | 4.10 | 4.11 | 4.08 | 4.09 | 4.05 |
| Uncertainty bi-level programming model | ||||||||
| System benefits (billion yuan) | 709.06 | 668.05 | 682.73 | 643.695 | 669.57 | 612.15 | 635.43 | 582.55 |
| Total amount of pollutant discharged (million tons) | 4.06 | 4.00 | 4.02 | 3.97 | 3.98 | 3.95 | 3.96 | 3.91 |
| λ = 0.7 | λ = 0.8 | λ = 0.9 | λ = 1.0 | |||||
|---|---|---|---|---|---|---|---|---|
| Different credibility Numerical value | Upper limit | Lower limit | Upper limit | Lower limit | Upper limit | Lower limit | Upper limit | Lower limit |
| A single-level programming model with the goal of minimizing pollutant emissions | ||||||||
| System benefits (billion yuan) | 687.39 | 597.88 | 621.54 | 553.61 | 599.12 | 500.93 | 563.75 | 486.54 |
| Total amount of pollutant discharged (million tons) | 3.96 | 3.87 | 3.89 | 3.84 | 3.85 | 3.83 | 3.82 | 3.80 |
| A single-level programming model aiming at maximizing social and economic benefits | ||||||||
| System benefits (billion yuan) | 758.73 | 740.22 | 741.92 | 727.78 | 729.62 | 719.46 | 711.06 | 698.96 |
| Total amount of pollutant discharged (million tons) | 4.16 | 4.13 | 4.14 | 4.10 | 4.11 | 4.08 | 4.09 | 4.05 |
| Uncertainty bi-level programming model | ||||||||
| System benefits (billion yuan) | 709.06 | 668.05 | 682.73 | 643.695 | 669.57 | 612.15 | 635.43 | 582.55 |
| Total amount of pollutant discharged (million tons) | 4.06 | 4.00 | 4.02 | 3.97 | 3.98 | 3.95 | 3.96 | 3.91 |
Comprehensive evaluation of carrying capacity
Comprehensive evaluation results of influencing factors.
| Year | 2000 | 2004 | 2010 | 2020 | 2025 | 2030 | 2035 |
|---|---|---|---|---|---|---|---|
| P* | −2.551 | −2.048 | −0.566 | 2.270 | 2.545 | 2.811 | 3.040 |
| P | −2.361 | −1.933 | −0.541 | 2.978 | 3.321 | 3.541 | 3.977 |
| Year | 2000 | 2004 | 2010 | 2020 | 2025 | 2030 | 2035 |
|---|---|---|---|---|---|---|---|
| P* | −2.551 | −2.048 | −0.566 | 2.270 | 2.545 | 2.811 | 3.040 |
| P | −2.361 | −1.933 | −0.541 | 2.978 | 3.321 | 3.541 | 3.977 |
Note: P* indicates a water diversion scenario without external basins, P indicates a water diversion scenario with external basins.
Comparison of comprehensive evaluation results of water resources carrying capacity in the Longchuanjiang River Basin.
Comparison of comprehensive evaluation results of water resources carrying capacity in the Longchuanjiang River Basin.
Without external basin water diversion scenario
In the absence of water diversion from external basins, the carrying capacity of water resources tends to slow down from 2020, and the development trend gradually reaches the ultimate carrying capacity state, which indicates that the potential of water resources development is relatively small. The ratio of the total water supply of Longchuan River Basin in 2000 to that in 2004 was 1:1.08, and the amount of water transferred from the external basin was 0.15 billion m3, accounting for 0.27% of the total water supply, a very small proportion. The current situation mainly relies on regional self-owned water source projects to meet the water demand of the region, mainly water storage projects, followed by water diversion projects. The water supply structure model is basically the same, and the water allocation for living, production and agriculture has increased by 0.081 billion m3, 15.9 million m3, and 19.1 million m3. Among them, the effective irrigated area reached 978,000 mu in 2004. Compared with the effective irrigated area in 2000, the agricultural water consumption decreased by 2.6%, indicating that it is impossible to rely on the existing water source projects to balance the annual water demand, and it is necessary to increase the utilization of water resources and increase the water supply to ensure the needs of social and economic development.
Since the economy of the Longchuan River Basin is relatively developed in central Yunnan, the water use efficiency is relatively high, and the utilization of water conservancy projects is high, indicating that the utilization of water resources has brought a greater degree of development to the economy. If the original water resources are maintained, it will lag behind the economic development of this region in the future.
With external basin water diversion scenario
In 2000, the development and utilization of water resources in the Longchuan River Basin reached 34.6%. The development of water resources was based on the principle of restricting the excessive growth of water use and combining quota management with total volume control. Water use efficiency was given priority, and the water supply capacity of projects was supplemented. In 2020, the development and utilization of water resources reached 56.4%, exceeding the internationally recognized 40% reasonable development level. In the case of without water diversion from the external basin, the total amount of water consumption is strictly limited, considering from the perspective of water saving measures, water allocation mainly tends to focus on water use efficiency. In 2030, the development and utilization of water resources will drop to the same level as in 2010, due to the construction of water diversion in central Yunnan and the construction of key small and medium-sized water source projects in this area. The water supply in the external basin will increase from 183 million m3 in 2020 to 315.7 million m3 in 2030, an increase of 297.4 million m3. The amount of water transferred has accounted for 35.0% of the total water supply in the basin, the irrigation area has increased by 49,800 mu, and the utilization coefficient of irrigation water is 0.70–0.71. During this 10-year period, the added value ratio of domestic water, production water and ecological water reaches 1:5.73:0.12, so the increased amount of water diversion and allocation is 0.434 million m3, 248.8 million m3 and 0.052 million m3. Production of water accounts for the main part of the water diversion, and under the condition of ensuring the production of water, it promotes social economy and drives the overall rise of water resources in the basin.
According to the comprehensive development trend of Figure 9, it can be seen that the carrying capacity of water resources is gradually increasing, with a score of 3.541. Compared with the scenario without water diversion from external basins, the comprehensive evaluation value of water resources carrying capacity is increased by 0.73, an increase of 25.9%, which shows that the carrying capacity of water resources has been improved on the basis of the basin limit. The Central Yunnan water diversion projects are in line with the goal of focusing on cities and towns, taking into account the water demand for agriculture and the ecological environment, improving the ecological environment, human activities and economic development methods, and providing a guarantee for the protection of water resources in the Longchuan River Basin.
CONCLUSIONS
Uncertainty-constrained programming and interval parameter programming are introduced into the bi-level programming model to propose an optimal uncertainty water resource coupling model. The new bi-level model is applied to nine water use areas in the Longchuan River Basin, and the water resources optimization study was carried out in the three planning periods of 2025, 2030, and 2035. The results showed that:
- (1)
The bi-level programming optimization model with interval uncertainty can reflect the characteristics and interaction effects of multi-level and multi-objective in complex water resources systems. In this study, the model was introduced into the water resource allocation system of typical river basins in the Yunnan plateau region, uncertainty-constrained planning and interval parameters was integrated into the model, which not only solves the problem of strong directivity of a single aspect in the single-level planning model, but also improves the accuracy and reliability of the bi-level programming model in dealing with the multi-objective complex relationship of water resources.
- (2)
The model uses the sparrow search algorithm, introduces competition mechanism and polynomial variation, and obtains the optimal solution after improvement, to obtain the optimization results of pollutant discharge, system benefit and satisfaction.
- (3)
The bi-level programming model is often used to solve the multi-objective optimization problem. From the perspective of the integrity of the model, the constraints and connections between the upper structure, the lower structure and the regional water use departments are solved. At the same time, the bi-level programming model also has the function of comparing the economic benefits and satisfaction of the system in water resources allocation, and can provide practical solutions for the harmonious development of the region in the future.
- (4)
The comparison and analysis of the optimization results with the single-level planning model show that the bi-level planning model comprehensively considers the pollutant discharge targets in the environment, and regional, social and economic development goals, and takes into account the two-way results of the single-level planning model under different credibility levels, which is more advantageous than the single directionality of the two single-level planning models, and can provide a practical plan for the harmonious development of the region in the future.
- (5)
The carrying capacity evaluation method can explain the development trend of regional water resources in detail. The comprehensive evaluation results show that the implementation of a cross-regional water diversion project has a certain role in promoting the sustainable and harmonious development of water resources-social economy-ecological environment and other comprehensive systems in the Longchuan River Basin.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge the financial support from the General Program of the National Natural Science Foundation of China (No. 11972144) and High-level talents and innovative teams in Yunnan Province (No. 2018HC024).
DATA AVAILABILITY STATEMENT
All relevant data are available from an online repository or repositories: Yunnan Statistical Yearbook: http://stats.yn.gov.cn/tjsj/tjnj/; Yunnan Water Resources Bulletin: http://wcb.yn.gov.cn/html/shuiziyuangongbao/; Yunnan Soil and Water Conservation Bulletin: http://wcb.yn.gov.cn/html/shuitubaochigongbao/.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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