Dynamic successive assessment of water environment carrying capacity based on a system dynamics model and an improved variable fuzzy pattern recognition method.

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Learn more: PMC Disclaimer | PMC Copyright Notice Sci Rep . 2026 Apr 10;16:16875. doi: 10.1038/s41598-026-46958-0 Dynamic successive assessment of water environment carrying capacity based on a system dynamics model and an improved variable fuzzy pattern recognition method Xinguo Sun 1, 2, ✉ , Anbang Peng 3 , Wenxin Xu 1, ✉ , Yi Shi 1 , Tianxiang Wang 4 , Wenjia Xi 1 Author information Article notes Copyright and License information 1 School of Engineering Management, Huaiyin Institute of Technology, Huai’an, 223003 Jiangsu China 2 Jiangsu Smart Factory Engineering Research Center, Huai’an, 223003 Jiangsu China 3 State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Nanjing Hydraulic Research Institute, Nanjing, 210029 China 4 Dalian University of Technology, Dalian, 116024 China ✉ Corresponding author. Received 2025 Oct 18; Accepted 2026 Mar 28; Collection date 2026. © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ . PMC Copyright notice PMCID: PMC13230757  PMID: 41963439 Abstract Water environment carrying capacity (WECC) is both a natural attribute of the water environment and a social attribute that governs regional sustainable development. Jiangsu Province, characterized by a large population and rapid economic growth, faces increasing challenges such as imbalance between water supply and demand and deteriorating water quality. Therefore, assessing WECC in this region is of great importance. Based on an analysis of water resource utilization and water quality conditions, a set of indicators for evaluating WECC was established using the Driving-Pressure-State-Impact-Response (DPSIR) framework. Grey correlation theory was applied to screen these indicators. To account for the different interpretations of index weights with respect to evaluation targets and objects, the variable fuzzy recognition method (VFPR) for water quality evaluation was enhanced by integrating the Analytic Hierarchy Process (AHP) and entropy weight method (EWM). This integration ensures that index weights reflect both objective data and expert judgment, thereby improving their rationality. The results indicate that from 2003 to 2021, WECC in Jiangsu Province declined due to rapid economic development and population growth, but gradually stabilized as economic advancement continued, highlighting a reciprocal relationship between WECC and socio-economic development. A dynamic WECC model for Jiangsu Province was developed using Vensim software and applied to scenarios designed to enhance WECC. The predicted development trends under different scenarios allowed the identification of an optimal scenario. A comprehensive evaluation of six scenarios between 2022 and 2030 suggests that maintaining the current high-speed development model would lead to a continued decline in WECC. In contrast, effective water-saving measures and strengthened sewage treatment can greatly improve water resource carrying capacity, maintaining it at a “positive carrying” level while supporting steady socio-economic growth. These findings provide valuable guidance for Jiangsu Province in enhancing its WECC and aligning socio-economic development with environmental sustainability in its top-level planning. Keywords: Water environment carrying capacity, Variable fuzzy pattern recognition model, System dynamics model, Scenario simulation, Grey correlation theory, Comprehensive weight Subject terms: Environmental sciences, Environmental social sciences, Environmental studies, Hydrology Introduction Water is an irreplaceable natural resource and a strategic economic resource. As population grows and economies expand, many regions face increasing pressure from both water scarcity and declining water environmental quality 1 . These challenges are often more pronounced in developing countries, where unequal water-resource distribution can strongly constrain further socio-economic development 2 . In this context, the concept of carrying capacity has become an important way to understand sustainability limits because it considers societal institutions, development goals, consumption patterns, and technological levels, while also accounting for how human activities affect ecosystems and how ecosystems respond 3 – 5 . Research on environmental carrying capacity has expanded to encompass resource, environmental, and ecological dimensions, and has been applied across multiple spatial scales, such as regions, watersheds, and cities, as well as across various carrying factors, including transportation, land, water resources, and tourism areas 6 – 8 . More recently, water environment carrying capacity has emerged as a direction that integrates environmental science with carrying capacity research 9 , 10 . Many researchers define water environment carrying capacity (WECC) as “the largest population and economic scale that the water environment system can support in a specific basin or region during a period while meeting its own health needs.” Others view WECC more narrowly, focusing only on the processes and capacities of aquatic systems. In general, WECC research typically involves two coupled systems: the human system and the water environment system 11 . Quantitative assessment is a core part of applied WECC research 12 – 15 . Common approaches include indicator-based evaluation systems, ecological footprint methods, multi-objective analysis, and system dynamics methods. Indicator-system methods typically compute a composite index by comparing each indicator value with a standard value, and they are widely used in WECC studies. However, different indicator-based techniques have clear tradeoffs. For example, the Vector Modulus Method is simple and intuitive but does not fully address conceptual fuzziness, vector directionality, or indicator weighting. Fuzzy Comprehensive Evaluation can handle both fuzziness and stochastic uncertainty, but its computational process may discard useful information and lead to misjudgment. Principal Component Analysis helps remove interference and identify dominant factors, yet it can be difficult to define standardized criteria for evaluation parameters. The Analytic Hierarchy Process combines qualitative and quantitative reasoning which is relatively easy to apply, but the use of judgment-matrix validation and adjustment can be highly subjective, which limits its methodological robustness 16 . More broadly, indicator system approaches often reflect the coordination between water environment conditions and human activities rather than WECC in a strict sense. Their outputs are typically dimensionless indices, and they often fail to capture feedback effects between the water environment and socio-economic factors 17 , 18 . System dynamics (SD) offers a complementary perspective because it is designed for dynamic simulation of complex systems with nonlinear relationships, multiple feedback loops, and time-varying behavior, which makes it suitable for evaluating and predicting WECC 19 , 20 . At the same time, SD models typically have limited ability to represent spatial heterogeneity within subsystems. Prior studies have therefore coupled SD with other tools (e.g., hierarchical analysis, entropy weighting, and multi-objective linear empowerment function) to enable a more comprehensive quantitative and qualitative evaluation of WECC 21 – 23 . Beyond SD, the ecological footprint method is also used in WECC and water ecological carrying capacity research because it is operational and uses standardized representation methods. However, it tends to emphasize regional ecological sustainability while paying less attention to broader sustainable development needs, inclduing economic, social, and technological aspects. Multi-objective comprehensive analysis can integrate multiple objectives (e.g., society, economy, population, and environment) to search for an overall optimal solution, but solving multi-objective nonlinear programming problems can be challenging in practice 24 . To enable a dynamic and continuous assessment of Jiangsu Province’s WECC from both objective and subjective perspectives, this study first analyzes local conditions related to water-resource development, utilization, and water quality. Based on this analysis, an initial indicator system for WECC evaluation is constructed using the Driving-Pressure-State-Impact-Response (DPSIR) framework. Grey correlation theory is then used to screen candidate indicators and determine their weights, while variable fuzzy set theory is applied to calculate Jiangsu’s annual WECC. Finally, an SD model of Jiangsu’s WECC is built in Vensim to explore WECC development trends under different improvement scenarios and to identify an optimal management strategy. The remainder of this paper is organized as follows: Section " Study area and data " introduces the study area and datasets; Section " Methodology " presents the SD model and evaluation framework; Section " Results and discussion " provides results and discussion; and Section " Conclusion " concludes the study. Study area and data Study area Jiangsu Province is located on the eastern coast of China, extending from 116°18′ to 121°57′E, and 30°45′ to 35°20′N. The Yangtze River and the Huaihe River cross the province from south to north, while the Beijing–Hangzhou Grand Canal runs through its central area, creating a dense and highly connected river–canal network (Fig. 1 ). Mean annual precipitation ranges from 800 to 1100 mm, corresponding to an average total precipitation of 102.06 billion m 3 . Between 2011 and 2024, Jiangsu’s annual water resources averaged 40.38 billion m 3 , with a per-capita availability of only 494 m 3 . Both precipitation and surface water runoff increase from north to south, and their distribution is strongly uneven. By the end of 2024, the province’s permanent population reached 85.26 million, which is 7.94% higher than in 2011, and its GDP grew by 181.98%. Fig. 1. Open in a new tab River network and major lakes in Jiangsu Province. Since 2021, water environmental quality in Jiangsu has shown steady and notable improvement. The proportion of national monitoring sections meeting or exceeding Class III water quality standards has reached a record high in recent years, and water quality in key river basins has continued to improve. Taihu Lake, in particular, has achieved a historic breakthrough in water quality. These accomplishments demonstrate Jiangsu’s commitment to ecological conservation and green development while maintaining sustained economic growth. By 2026, Jiangsu aims for further improvements in surface water quality and the elimination of water bodies classified as worse than Class V. Despite the progress, substantial spatial disparities remain. Some regions still face limited water environmental capacity, and pressures associated with water quality consumption of water resources require continued attention.Figure was created by one of the authors using ArcGIS Desktop 10.6 (Esri, USA), which was obtained from the official website " https://www.esri.com/zh-cn/home ". Data Data on water resources and water environment were obtained from the Jiangsu Province Water Resources Bulletin and the Jiangsu Province Environmental Bulletin. Economic, population, and urbanization data were sourced from the China Statistical Yearbook, while other relevant information was collected from the National Economic and Social Development Bulletins and the water resources bulletins of various cities. Methodology This study proposes a method for evaluating WECC by integrating a modified VFPR method with a SD model (Fig. 2 ). First, a comprehensive evaluation system is constructed based on the DPSIR framework, and the grey correlation method is applied to optimize and screen the indicator system. Second, to account for both the subjective importance and objective information of each indicator, the traditional weights in the variable fuzzy model are replaced with integrated weights. The hierarchical analysis (AHP) method is used to determine the subjective importance of each indicator, while the entropy weight method calculates their objective weights. Finally, a system dynamics model is developed for WECC evaluation and applied to Jiangsu Province. The improved model supports dynamic integrated evaluation and scenario simulation of water environment carrying capacity, and the Monte Carlo method is used to assess the impact of random errors on the evaluation results. Fig. 2. Open in a new tab Research methodology flowchart. WECC indicator system The PSR (Pressure State Response) model is a framework for evaluating environmental systems. In this model, “Pressure” refers to the consumption of resources and environmental degradation caused by human activities, which exerts pressure on the environment. “State” represents the condition of the natural environment, including the quality and quantity of various resources. “Response” denotes the actions taken by society to promote sustainable development and mitigate environmental pressures. The PSR model was first proposed by the OECD to assess the global environment status 25 . Its core idea is that human activities impose pressures on natural resources and the environment, altering the environmental state and resource conditions, and that society responds through environmental, economic, and other policies to reduce these pressures and maintain environmental sustainability 26 . The WECC can be considered a complex "human-water-economy" system, which is regulated through continuous interactions and feedbacks, aligning with the principles of the PSR model. The DPSIR (Driving Force-Pressure-State-Impact-Response) model extends both the DSR (Driving Force-State-Response) and PSR frameworks by incorporating the feedback of water environmental conditions on human society. This allows it to capture the interactive relationships between human activities and aquatic ecosystems comprehensively. The DPSIR model has been widely applied in watershed ecological security assessments. In recent years, it has also been increasingly used in studies of WECC. Therefore, selecting an indicator system based on the DPSIR framework enables an objective quantification of the actual WECC. The DPSIR model provides a comprehensive framework for assessing WECC by examining its subsystems from five perspectives: driving, pressure, state, impact, and response (Fig. 3 ). By integrating interactions among the regional environment, economic development, resources, and human activities, the model facilitates the construction of a robust and systematic indicator system. This model is particularly useful for exploring system orderliness and causal relationships. The development of a well-structured indicator system is fundamental to WECC research. Based on the DPSIR framework, relevant literature, and theoretical analysis, a comprehensive indicator system is constructed, as summarized in Table 1 . Fig. 3. Open in a new tab DPSIR framework for Water Environment Carrying Capacity (WECC). Table 1. Candidate indicators system for WECC. Candidate indicators system Subsystems Indicators Impact(I) Exploitation and utilization ratio of water resources (%, X1) Water resources per capita (m 3 /PER, X2) Driving(D) Surface water environmental quality (compliance rate%, X3) Total population (10 4 people, X4) Urbanization rate (%, X5) Per capita Gross Domestic Product (GDP) (Yuan/PER, X6) Pressure(P) Water consumption per capita (m 3 /PER, X7) Domestic sewage discharge (10 8 ton, X8) Domestic wastewater COD emissions (10 4 ton, X9) Value added in industry (CNY 10 8 , X10) Production of water demand (10 8 m 3 , X11) Water consumption intensity of industrial output (m 3 /10 4 Yuan, X12) Industrial wastewater discharge (10 4 ton, X13) Industrial wastewater COD emissions (10 4 ton, X14) State(S) Cultivated land area(1,000 hectares, X15) Irrigation estimates coverage rate (%, X16) Water consumption per unit of irrigation area (m 3 , X17) Water consumption intensity of GDP (m 3 /10 4 Yuan, X18) GDP growth rate (%, X19) Response(R) Industrial wastewater discharge rate up to standard (%, X20) The ratio of investment in water environmental pollution control to GDP (%, X21) Open in a new tab Indicator System screening based on gray correlation theory Since its establishment in 1982, grey system theory has been widely applied across social, economic, scientific, technological, agricultural, industrial, and ecological fields. Grey correlation analysis forms the foundation of grey system-based analysis, prediction, and decision-making 27 . The central concept of grey correlation theory is that the closeness of the relationship between sequences can be determined by the similarity of the geometric shapes of their curves: the more similar the curves, the higher the correlation between the corresponding sequences. Equations. ( 1 ) and ( 2 ) are used to calculate the grey correlation screening index. 1 2 Here, (0, 1) is a distinguishing coefficient; (X 0 , X i ) is grey relational grade between X 0 and X i , with i = 1, 2, …, m; ( x 0 ( k ), and x i ( k )) is correlation coefficient at point k . The resulting , i = 1, 2, …, m is referred to as Deng’s correlational degree. The screening order and indicator weights are determined according to the ranking of these correlation degrees. Water resources development and water environment quality are key drivers of social and economic development. Accordingly, the characterization indicators (Exploitation and utilization Ratio of Water Resources,X 1 ; Water Resources per Capita, X 2 ; and Surface Water Environmental Quality, X 3 ) are used as reference series to calculate the relevant factors and their corresponding correlation coefficients R, as shown in Equation ( 3 ). 3 Based on the relational degree matrix and considering the association of each indicator with the three reference sequences, the comprehensive correlation coefficient is calculated using Equation ( 4 ). 4 VFPR model of WECC Variable fuzzy set (VFS) theory suggests that under co-dimensionality, objective phenomena can exhibit fuzziness during intermediate transitions 28 . This aligns with the inherent ambiguity in categorizing WECC. Variable fuzzy sets include approaches such as optimization, recognition, and clustering, along with various improved models. Since WECC evaluation is based on grade standards, it can be formulated as an identification of membership degrees. Using variable fuzzy recognition thus reflects the fuzziness of WECC and avoids the singularity of traditional evaluation models. However, traditional models may not accurately capture the impact of sample information when indicators exceed standard limits. This study employs a modified VFPR model combined with an AHP-E model to conduct dynamic successive assessments of WECC. Equation ( 5 ) calculates the synthetic relative membership degree for sample i belonging to standard h , with four variants corresponding to different choices of parameters a and p . 5 Here, u hi is the combined relative superiority of the decision set i ; h is the rank; a i is the lower limit of the level of a decision i ; b i is the upper limit of the level of a decision i ; s hj is the relative attribute of the standardized indicator value j for level h; m is the total number of indicators; ω j is the indicator weight from the AHP-E model; a is the model optimization criterion parameter. p is the distance parameter, each taking values of 1 or 2. Weighting method of WECC In traditional variable fuzzy models, indicator weights are typically determined through pairwise comparisons, which are strongly influenced by human judgment and can be interpreted in two layers. The first layer reflects the impact of indicators on the evaluation object, capturing both the magnitude of individual indicators and their interrelationships, and is ideally derived from objective data. The second layer represents the impact of indicators on evaluation objectives, reflecting the relative importance of each indicator, and is usually obtained through subjective judgment. To address these two aspects, the entropy weight method 29 , 30 is used to determine the quantitative weight of indicator values W 1i , while the Analytic Hierarchy Process 31 – 33 is used to determine the importance weight W 2i . The final comprehensive weight is obtained by combining these two weights through multiplication and subsequent normalization. The AHP-E based weighting process is as follows: Constructing the judgment matrix The importance of each indicator is quantified using the 1-9 scale method. For m indicators in the criterion layer, n(n-1)/2 pairwise comparisons are conducted to consstruct an m×m AHP judgment matrix A. 6 Normalization and weight calculation Matrix A is normalized according to Equation ( 7 ). The weight w i of the i-th factor is calculated as in Equation ( 8 ). The maximum eigenvalue corresponding to the eigenvector w is calculated based on A=λmax, as shown in Equation ( 9 ). 7 8 9 Consistency check The consistency index ( CI ) and the consistency ratio ( CR ) are calculated using Equation ( 10 ): 10 where RI is the random consistency index depending on n . If RC <0.10, the judgment matrix is considered consistent; otherwise, the comparison values C ij should be revised and the matrix reconstructed. For the entropy weighting, given m evaluation indicators and n evaluation objects, the original data matrix R=(rij) m×n is constructed. The entropy H i of the i-th indicator is defined by Equations ( 11 - 12 ): 11 12 where P ij is the proportion of the j-th object’s value in the i-th index. To avoid undefined values when P ij =0, it is set that P ij lnP ij = 0. The entropy weight W 2i is then calculated using Equation ( 13 ). 13 Finally, the quantitative weight W 1i and the importance weight W 2i are combined by multiplication and normalization to obtain the composite weight W i of each indicator, as shown in Equation ( 14 ). The level characteristic value of the samples is calculated using Equation ( 15 ). 14 15 Construction of the SD model The SD model is well-suited for simulating WECC under multiple scenarios due to its ability to represent nonlinear processes, dynamic accumulation, and feedback mechanisms. The SD model includes three types of variables: state variables, which describe the current system state and accumulated information; rate variables, which directly affect the state variables and represent their rates of change; and auxiliary variables, which provide environmental parameters, process data, or numerical inputs, typically represented using lookup tables 34 , 35 . The relationships among these variables are formulated as Equations ( 16 )-( 18 ). State variables (Level) represent real-world accumulations, such as population, pollution stocks, or mechanical stress, and are mathematically formulated using finite difference equations as follows: 16 where R 1 (t) and R 2 (t) denote the inflow and outflow rates, respectively. Rates serve as the governing factors that determine changes in the state variables, with their standard mathematical expressions given in Equation ( 17 ). 17 Auxiliary variables capture specific environmental parameters, process data, test functions, or numerical inputs to the system, and are typically represented by table functions (lookup tables), with their canonical mathematical formulation defined in Equation ( 18 ). 18 Based on socio-economic conditions and the watershed WECC indicator system, the SD model subdivides the system into six subsystems: population, economic, water resource demand, water resource supply, water environment, and water pollution and management. For Jiangsu Province, these are further aggregated into social, economic, water resource, and environmental subsystems. The feedback loops of the system are illustrated in Fig. 4 , and the overall model flowchart is shown in Fig. 5 . Model parameters and key equations are detailed in Table 5 . The simulation period spans 2011-2030 with an annual time step; data from 2011-2021 are used for parameter calibration, while data from 2022-2030 are used for scenario simulation. Fig. 4. Open in a new tab The feedback loops of the water environment and economy-society-environment system. Fig. 5. Open in a new tab Relationship diagram of WECC. Table 5. The system parameters and key equations. Name Unit Equations GDP 10 8 yuan = Value added of agriculture+Value added of industry+Value added of services Value added in agriculture 10 8 yuan = INTEG(Value added of agriculture×Growth rate of agricultural value added, Initial value of agricultural value added) Growth rate of agricultural value added / =WITHLOOKUP(Time,([(2011,0.09668)-(2030,1)],(2011,0.09668),(2012,0.09846),(2013,-0.01513),(2014,-0.00232),(2015,0.01551),(2016,-0.10388),(2017,0.06646),(2018,0.05406),(2019,0.1028),(2020,0.0387),(2021,0.09429),(2030,0.09))) Agricultural water demand 10 8 m 3 =Water consumption of 10,000 yuan of agricultural value added×Value added in agriculture/10000 Water consumption of 10,000 yuan of agricultural value added / =WITHLOOKUP(Time,([(2011,494.88)-(2030,1000)],(2011,494.88),(2012,448.43),(2013,393.1),(2014,403.78),(2015,393.38),(2016,366.47),(2017,402.88),(2018,362.79),(2019,324.86),(2020,277.57),(2021,240.92),(2022,227.65),(2030,200))) Value added of industry 10 8 yuan = INTEG(Value added of industry×Growth rate of value added in industry, Initial value of industry value added) Growth rate of value added in industry =WITHLOOKUP(Time,([(2011,0.06679)-(2030,1)],(2011,0.06679),(2012,0.05417),(2013,0.01699),(2014,-0.0417),(2015,0.06048),(2016,0.03862),(2017,0.01223),(2018,-0.15229),(2019,0),(2020,0.2035),(2021,0.04191),(2030,0.09))) Industrial water demand 10 8 m 3 =Water consumption of 10,000 yuan of industrial added value×Value added of industry/10000 Water consumption of 10,000 yuan of agricultural value added / =WITHLOOKUP(Time,([(2011,494.88)-(2030,1000)],(2011,494.88),(2012,448.43),(2013,393.1),(2014,403.78),(2015,393.38),(2016,366.47),(2017,402.88),(2018,362.79),(2019,324.86),(2020,277.57),(2021,240.92),(2022,227.65),(2030,200))) Industrial wastewater discharge 10 8 ton =Industrial wastewater discharge factor×Industrial water demand Industrial wastewater discharge factor / =WITHLOOKUP(Time,([(2011,0.525)-(2030,1)],(2012,0.528),(2013,0.537),(2014,0.55),(2015,0.601),(2016,0.574),(2017,0.544),(2018,0.559),(2019,0.542),(2020,0.538),(2021,0.535),(2022,0.561),(2030,0.5))) Value added of services 10 8 yuan = INTEG(Value added of services×Growth rate of value added in services, Initial value of services value added) Growth rate of value added in services / =WITHLOOKUP(Time,([(2011,0.10628)-(2030,1)],(2011,0.10628),(2012,0.0697),(2013,0.09184),(2014,0.09296),(2015,0.11193),(2016,0.12908),(2017,0.10586),(2018,0.08157),(2019,0.04118),(2020,0.06766),(2021,0.04567),(2030,0.09))) Total population 10 4 people = INTEG(Total population×Population growth rate, Initial value of population) population growth rate / =WITHLOOKUP(Time,([(2011,0.06679)-(2030,1)],(2012,0.05417),(2013,0.01699),(2014,-0.0417),(2015,0.06048),(2016,0.03862),(2017,0.01223),(2018,-0.15229),(2019,0),(2020,0.2035),(2021,0.04191),(2030,0.09))) Population growth rate =WITHLOOKUP(Time,([(2011,0.00649)-(2030,1)],(2011,0.00649),(2012,0.00617),(2013,0.00695),(2014,0.00555),(2015,0.00606),(2016,0.00669),(2017,0.00479),(2018,0.00476),(2019,-0.04742),(2020,0.02987),(2021,-0.00376),(2030,0.04))) Domestic water demand 10 8 m 3 =Urban population×Per capita urban domestic water consumption/10000 Domestic sewage discharge 10 8 ton =Domestic sewage discharge factor×Domestic water demand Domestic sewage discharge factor / =WITHLOOKUP(Time,([(2011,0.656),-(2030,1)],(2011,0.656),(2012,0.738),(2013,0.738),(2014,0.726),(2015,0.719),(2016,0.63),(2017,0.531),(2018,0.498),(2019,0.49),(2020,0.471),(2021,0.442),(2022,0.428),(2030,0.38) )) Total water demand 10 8 m 3 =Production water demand+Ecological water demand+Domestic water demand Production water demand 10 8 m 3 =Agricultural water demand+Industrial water demand+Water demand in the service sector Total water supply 10 8 m 3 =Surface water+Underground water+Water reuse+Interregional water transfer Amount of Water Pollution 10 8 ton =Industrial wastewater discharge+Domestic sewage discharge+Sewage discharges from the service sector Total effluent COD discharge 10 4 ton =Industrial wastewater COD emissions+Domestic wastewater COD emissions Open in a new tab Three scenarios are considered in the model to explore the potential development of the watershed water ecological carrying capacity. These scenarios collectively allow the exploration of system responses under varying management strategies and development pathways. The status quo scenario assumes that the watershed maintains its current development trajectory, with all model parameters remaining unchanged, providing a baseline for comparison with other scenarios. The efficient water conservation scenario emphasizes improving water use efficiency and reducing overall water consumption. Under this scenario, the total water supply in Jiangsu is projected at 56.0 billion m 3 in 2015, 58.0 billion m 3 in 2020 and 60.0billion m 3 in 2030. In line with provincial and national initiatives, Jiangsu has actively promoted the construction of water-saving society pilot projects, with a total of 7 national-level and 11 provincial-level projects completed. Therefore, the water consumption per 10,000 CNY of industrial added value is set at 30m 3 , and that of agricultural added value at 400m 3 in 2030. The strict sewage treatment scenario focuses on enhancing environmental protection, controlling pollution, and improving overall water quality. This scenario assumes an increase in wastewater treatment capacity, maintaining minimum effluent discharge and chemical oxygen demand (COD) coefficients, with treatment capacity increased by 50% in 2025 and 80% in 2030. Furthermore, the scenario incorporates assumptions on socio-economic development, with high and low growth rates for primary, secondary, and tertiary industries set at 9% and 3%, respectively, and population natural growth rates assumed to be 4% and 0.5%. Results and discussion Selection results of evaluation indicators The correlation matrix R is first computed to assess the relationships among all candidate indicators. The matrix is shown below. 19 Based on this matrix,, the comprehensive correlation coefficients are as follows: 20 The ranking results show that the index most strongly associated with the comprehensive correlation degree of the three reference series is the irrigation estimate coverage rate, followed by total population, water consumption per unit of irrigation area, urbanization rate, industrial wastewater discharge rate up to standard, cultivated land area, water consumption per capita, domestic sewage discharge, production water demand, industrial wastewater discharge. The indicator system and corresponding standards are presented in Table 2 . Table 2. Indicator system and corresponding standards for WECC. Candidate indicators system Grades Indicators 1 2 3 4 5 Exploitation and utilization ratio of water resources (%, Y1) 0.1 0.4 0.5 0.6 0.65 Water resources per capita (m 3 /PER, Y2) 200 400 600 800 900 Surface water environmental quality (compliance rate%, Y3) 1 0.8 0.6 0.4 0.2 Total population (10 4 people, Y4) 7000 7500 8000 8500 9000 Urbanization rate (%, Y5) 0.4 0.5 0.6 0.7 0.8 Water consumption per capita (m 3 /PER, Y6) 200 400 600 800 850 Domestic sewage discharge (10 8 ton, Y7) 15 20 30 40 50 Production water demand (10 8 m 3 , Y8) 150 180 210 240 270 Industrial wastewater discharge (10 4 ton, Y9) 10 15 20 25 30 Cultivated land area (1,000 hectares, Y10) 4000 4200 4400 4600 4900 Irrigation estimates coverage rate (%, Y11) 0.75 0.8 0.85 0.9 1 Water consumption per unit of irrigation area (m 3 , Y12) 350 380 410 440 480 Industrial wastewater discharge rate up to standard (%, Y13) 1 0.8 0.6 0.4 0.2 Open in a new tab Results of the indicator system weights Water quality indicators contribute differently to changes in overall water conditions. Their relative importance needs to be evaluated by considering both expert judgment and the inherent complexity and systematic nature of water quality assessment. To quantify the importance of each indicator, a weighting analysis was conducted. The analytic hierarchy process is widely used because it simplifies the comparison of multiple factors into pairwise judgments across several hierarchical levels. Five Experts in water resources, environmental science, economics and government administration were invited to develop the judgment matrix for the indicator system. The weights of each indicator calculated using the analytic hierarchy process and the entropy weight method are presented in Table 3 . Table 3. Weight of each indicator. Weight of indicators Weighting methodology WESCC WEPCC WERCC Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y13 Equal weighting 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 Entropy weight 0.037 0.061 0.102 0.119 0.101 0.100 0.064 0.105 0.087 0.060 0.048 0.075 0.041 AHP 0.116 0.092 0.292 0.018 0.018 0.036 0.027 0.036 0.036 0.023 0.021 0.034 0.250 AHP-E 0.060 0.079 0.417 0.031 0.026 0.051 0.024 0.054 0.044 0.020 0.014 0.036 0.146 PCA 0.068 0.071 0.084 0.081 0.080 0.065 0.082 0.075 0.092 0.075 0.090 0.063 0.073 Grey correlation 0.078 0.079 0.079 0.074 0.074 0.07 0.079 0.078 0.078 0.077 0.077 0.077 0.079 Open in a new tab The variable fuzzy identification method operates by transforming indicator eigenvalues into affiliation degrees corresponding to each evaluation level. It then calculates the level distance of individual indicators, determines the level affiliation of each evaluation sample based on the indicator weights, and finally computes the level eigenvalues to identify the evaluation level of each sample. Results of the VFPR model The evaluation results (Fig. 6 ) show that the WECC of Jiangsu Province remained between Grade 2 and Grade 3 and was consistently close to Grade 3, with a long-term average value of 2.98., This indicates that the WECC was at a middle-lower level. From 2003 to 2008, the WECC was relatively low due to rapid population growth and accelerated economic development. The time series further shows that from 2009 to 2021, as water conservation measures strengthened and efforts to control water pollution increased, the carrying capacity of the water environment continued to improve. Although the total population, GDP, and urbanization level increased during this period, both water consumption and sewage discharge declined, leading to a substantial improvement in surface water quality. As a result, the WECC experienced a notable improvement, shifting from approximately 3.5 before 2009 to around 2.5 in the subsequent years. To verify the reliability of the model, the results were compared with those obtained from the fuzzy comprehensive assessment (FCA) method (Fig. 5 ). The two methods showed consistent trends in WECC levels, demonstrating the validity of the proposed model. Fig. 6. Open in a new tab The WECC evaluation results of Jiangsu Province. Results of the SD model Four representative variables, including total population, GDP, total water demand, and amount of water pollution, were selected for the historical test. The results are shown in Table 4 and Fig. 7 . The relative error of each variable, as well as the average relative error, is less than 5%, indicating that the model performs well and can accurately reflect the actual situation. The SD model was evaluated using three methods: the intuitive test, the historicity test, and the sensitivity test. The intuitive test examines the definitions of the variables, the internal logical relationships within the system, the boundary conditions, the equations used for variable calculations, and the consistency of unit conversions. The “Check Model” and “Check Units” functions in Vensim 10.0.1 software were used to verify the model structure and unit consistency. The results showed that both the model structure and units were valid. Table 4. Validation of SD model simulation errors. Time Total Population (10,000 Capita) GDP (100 million) Total water demand (10 8 m 3 ) Amount of water pollution (10 4 Ton) Historical data Simulated data Error (%) Historical data Simulated data Error (%) Historical data Simulated data Error (%) Historical data Simulated data Error (%) 2011 8023 8013 -0.12 49110 49087 -0.05 552.1 552.2 0.02 59.1 59.2 0.17 2012 8120 8109 -0.14 54058 54048 -0.02 552.5 552.2 -0.05 59.9 59.8 -0.17 2013 8192 8199 0.09 59162 59146 -0.03 576.4 576.7 0.05 59.2 59.4 0.34 2014 8281 8267 -0.17 65088 65077 -0.02 591.3 590.8 -0.08 60.1 60.02 -0.13 2015 8315 8227 -1.06 70117 70123 0.01 574.5 573.3 -0.21 62 61.9 -0.16 2016 8381 8391 0.12 77389 77395 0.01 577.3 577.4 0.02 61.6 61.5 -0.16 2017 8423 8435 0.14 85870 85859 -0.01 591.3 591.4 0.02 48.9 48.7 -0.41 2018 8446 8451 0.06 92596 92578 -0.02 591.7 592.1 0.07 48.8 48.9 0.20 2019 8469 8472 0.04 99632 99646 0.01 618.9 619.1 0.03 59.7 59.8 0.17 2020 8477 8488 0.13 102719 102738 0.02 571.8 572 0.04 48.2 48.4 0.41 2021 8505 8512 0.08 116364 116378 0.01 567.5 568.3 0.14 48.6 48.8 0.41 Open in a new tab Fig. 7. Open in a new tab Calibration results of the SD model parameters. Since the SD model is an abstraction of the real world under certain conditions, it is necessary to evaluate its validity and sensitivity before running simulations in Vensim 10.0.1 to ensure the reliability of the results. To verify the model’s validity, each variable was simulated for the period 2011-2021, and the simulation results were compared with historical data. A relative error of less than 10% indicates that the model simulation is sufficiently accurate and effective. In Fig. 8 , the status quo continuation scenario under the high-speed mode requires the most water. By 2030, the total water demand under the three high-speed scenarios exceeds that of the low-speed mode by 20 billion m 3 . Without water-saving measures, total water demand is projected to reach 77.1 billion m 3 in 2025 and 110.3 billion m 3 in 2030. Implementing water-saving measures can effectively mitigate the rapid increase in water consumption driven by population growth and economic development. In the status quo continuation scenario under the high-speed mode, sewage discharge increases the most, reaching 5.855 billion tons in 2025 and 7.440 billion tons in 2030. This indicates that without water-saving and pollution control measures, sewage discharge will rise substantially during periods of rapid economic growth. Under the efficient water-saving mode (Scenario 1), sewage discharge is projected to reach 5.353 billion tons in 2025 and 5.992 billion tons in 2030. Under the strict pollution control mode (Scenario 2), it is expected to decline to 4.878 billion tons in 2025 and 4.701 billion tons in 2030.These results demonstrate that even under conditions of rapid economic and population growth, efficient water-saving and strict pollution control can keep the water environment within its carrying capacity. Fig. 8. Open in a new tab Simulation results of key WECC indicators under different scenarios. Fig. 9 shows that if the current high-speed development model continues, the WECC will remain at a relatively low level, declining from 2.30 to 2.40. This is because Jiangsu Province already maintains a leading level of water resource management. By 2022, surface water quality in the province improved to a superior level, with all inferior V-class water bodies eliminated and the proportion of national monitoring sections meeting or exceeding standards reaching a historical high. Nonetheless, from a sustainable development perspective and considering the public’s high expectations for environmental quality, it remains important to further enhance the carrying capacity of the water environment. Simulation results for Scenario 1 and Scenario 2 indicate that effective water-saving measures and strengthened sewage treatment can significantly increase the water environment’s carrying capacity and maintain it at a “positive carrying” level, while supporting steady economic and social growth. With ongoing socio-economic development, water demand and pollution are expected to increase, placing additional pressure on watershed ecosystems and exacerbating conflicts between development and ecological protection. Based on simulations of six scenarios, water-saving emerges as an important approach not only to reduce pollution and improve water quality but also to enhance social and environmental benefits. Therefore, it is urgent to strengthen water-saving measures, promote water-saving standards, establish a water-saving system, and cultivate residents’ awareness of water conservation. Sewage treatment is also crucial for protecting water resources and improving the ecological environment. This can be achieved by developing and introducing new technologies, enhancing regional sewage treatment, and encouraging market-oriented approaches to sewage management. Fig. 9. Open in a new tab Projected WECC values under different scenarios. To further enhance Jiangsu Province’s water environment carrying capacity, comprehensive strategies should be implemented across development, utilization, management, and scientific planning. In terms of water resource development and utilization, the province should make full use of its abundant transit water resources, strengthen water conservancy infrastructure, and ensure adequate water supply to support ongoing industrialization and urbanization. In agriculture, water-saving irrigation techniques, including channel seepage prevention, sprinkler irrigation, and micro-irrigation, should be promoted to improve irrigation efficiency and reduce water consumption per unit area. For the industrial sector, it is important to limit high water-intensive industries, upgrade production processes and water-saving technologies, and lower water consumption per unit of industrial output. Establishing industrial water quotas, formulating water-saving plans, increasing water reuse rates, and promoting centralized water supply within industrial parks are also essential measures. In the domestic sector, strengthening the construction of water-saving facilities, enhancing public outreach, and fostering greater awareness of household water conservation are necessary. Pollution control and ecological restoration should focus on both improving the quality of water bodies and addressing the sources of wastewater discharge. Strict implementation of domestic sewage and industrial wastewater treatment standards must be ensured. At the management level, institutional innovations should be advanced to develop mechanisms for water conservation, water use regulation, and water pollution control that integrate economic incentives with regulatory measures. Uncertainty analysis There are both model and data uncertainties in the prediction of WECC assessments. Many uncertainties exist in the assessment of WECC. In terms of model uncertainty, the uncertainty is analyzed by comparing two models: variable fuzzy identification and fuzzy comprehensive evaluation. Concerning the uncertainty of the weights of the indicator system, the uncertainty was analyzed by comparing different weight calculation methods (Fig. 10 and Table 6 ). The results show that there is a significant trend difference between subjective weight and objective weight results from 2003 to 2021. The objective weighting method considers that the importance of these indicators in the process of determining the regional WECC is similar, but the Water resources per capita, Surface water environmental quality, and Industrial wastewater discharge rate up to standard directly determines the size of the WECC. Therefore, this paper comprehensively considers the two layers of indicator weights, composite weights are utilized instead of the weights in the traditional variable fuzzy model. That is, the use of AHP method from the perspective of the system, to determine the importance of the indicators of the weight, the use of entropy weight method comprehensive consideration of the correlation between the indicators, to determine the quantitative value of the indicators of the weight. However, with different expectations of the WECC, indicator system weights of the WECC at different stages of development should change dynamically. Fig. 10. Open in a new tab WECC assessment results under different indicator weights. Table 6. WECC evaluation results under different weight methods. Year Wweighting methods equal weighting entropy weighting AHP AHP-E PCA Grey correlation 2003 2.867 2.809 3.141 3.463 2.864 2.872 2004 2.848 2.862 2.996 3.327 2.846 2.843 2005 3.107 3.125 3.163 3.522 3.090 3.108 2006 3.108 3.167 3.132 3.494 3.085 3.106 2007 3.194 3.246 3.219 3.599 3.171 3.193 2008 3.105 3.153 3.093 3.439 3.088 3.101 2009 3.088 3.105 2.949 3.177 3.063 3.083 2010 3.110 3.128 2.860 3.045 3.093 3.103 2011 3.175 3.179 2.890 3.051 3.160 3.170 2012 3.158 3.174 2.847 3.021 3.153 3.151 2013 3.197 3.260 2.854 3.029 3.179 3.189 2014 3.251 3.345 2.857 3.034 3.238 3.241 2015 3.270 3.329 2.791 2.894 3.268 3.263 2016 3.327 3.351 2.672 2.620 3.309 3.320 2017 3.176 3.251 2.501 2.451 3.157 3.160 2018 3.174 3.241 2.452 2.374 3.151 3.158 2019 3.237 3.300 2.467 2.419 3.211 3.221 2020 3.167 3.197 2.501 2.410 3.144 3.153 2021 3.148 3.190 2.449 2.331 3.132 3.134 Open in a new tab Random errors are inevitable in the process of sample collection, calculation, storage, and testing for various evaluation indicators of WECC. The Monte Carlo method, also known as the statistical experiment method or random simulation method, is a numerical method that solves engineering, physics, mathematics, and other problems by artificially generating and utilizing random numbers and randomly sampling random processes and variables. It is particularly suitable for stochastic problems. The Monte Carlo method is used for a sensitivity analysis and the model parameters are as follows: the average μ is Xij ; standard deviations σ are 0.1 Xij , 0.3 Xij , 0.5 Xij respectively to analyze influence of different degree of deviation; running times N is 1200. We then use Monte Carlo simulation to generate flood samples and evaluates them with the variable fuzzy identification model based on integrated weights, thereby analyzing how the indicator uncertainty affects WECC results. The simulation results indicate that as data uncertainty increases, the uncertainty in model outputs also rises. However, all results remain within the 95% confidence interval, as illustrated in Fig. 11 and Table 7 . Fig. 11. Open in a new tab Impact of data uncertainty on the assessment of WECC. Table 7. Data uncertainty simulation results. Year σ Are 0.1 X ij σ Are 0.3 X ij σ Are 0.5 X ij Mean Confidence interval Mean Confidence interval Mean Confidence interval 2003 3.462 3.394 3.530 3.460 3.262 3.658 3.454 3.099 3.809 2004 3.328 3.263 3.393 3.328 3.122 3.534 3.325 2.997 3.653 2005 3.523 3.454 3.593 3.524 3.316 3.732 3.516 3.169 3.864 2006 3.495 3.427 3.563 3.491 3.285 3.696 3.498 3.154 3.843 2007 3.600 3.531 3.669 3.596 3.386 3.807 3.598 3.241 3.955 2008 3.437 3.369 3.505 3.435 3.234 3.636 3.431 3.088 3.774 2009 3.177 3.116 3.239 3.176 2.995 3.358 3.174 2.865 3.483 2010 3.045 2.986 3.103 3.044 2.870 3.219 3.049 2.742 3.356 2011 3.049 2.989 3.109 3.048 2.869 3.227 3.049 2.740 3.358 2012 3.022 2.965 3.079 3.021 2.842 3.200 3.029 2.725 3.332 2013 3.030 2.973 3.086 3.035 2.857 3.213 3.017 2.720 3.315 2014 3.033 2.975 3.091 3.036 2.864 3.208 3.032 2.737 3.326 2015 2.894 2.838 2.950 2.896 2.722 3.070 2.893 2.603 3.183 2016 2.620 2.570 2.669 2.621 2.471 2.771 2.617 2.374 2.860 2017 2.452 2.402 2.501 2.452 2.310 2.594 2.452 2.211 2.693 2018 2.375 2.327 2.422 2.371 2.240 2.502 2.376 2.137 2.615 2019 2.419 2.374 2.464 2.421 2.284 2.558 2.423 2.189 2.656 2020 2.411 2.363 2.459 2.415 2.279 2.551 2.401 2.158 2.643 2021 2.331 2.284 2.378 2.328 2.191 2.465 2.331 2.102 2.560 Open in a new tab Conclusion In this study, the DPSIR framework and grey correlation theory were used to construct a comprehensive WECC evaluation indicator system. The modification of VFPR model parameters based on extreme case tests addressed a key limitation of the traditional model, which cannot accurately reflect the impact of sample index changes when the indicators exceed standard ranges. Furthermore, a SD model of WECC was developed to simulate the WECC index of Jiangsu Province under different scenarios. Simulation results indicate that population growth as well as economic and social development place pressure on the carrying capacity while driving improvements in water environment quality. Under the conventional high-growth scenario, the carrying capacity of the water environment is projected to continue declining.. In contrast, scenarios emphasizing water conservation and wastewater treatment exhibit an inverted U-shaped trajectory in carrying capacity, suggesting initial improvement followed by stabilization. The coordinated development scenario, which integrates economic growth, water resource management, and environmental protection, is conducive to the sustainable development of both the ecological environment and socioeconomic systems, achieving a balance among social, economic, and environmental benefits. Future research could focus on exploring the spatial and temporal evolution of WECC from the perspective of underlying physical mechanisms. See Tables 5 , 6 , 7 . Author contributions All authors contributed to the study’s conception and design. Data curation, data collection, and formal analysis were performed by T.W., X.S.,Y.S.; the first draft of the manuscript was written by X.S.; writing—review, and editing were performed by Wenxin Xu., A.P., Wenjia Xi. All authors have read and agreed to the published version of the manuscript. Funding The study is supported by the Ministry of Education of Humanities and Social Science project (Grant no. 23YJC630154), Basic Research Program of Jiangsu (Grant no. BK20241976, BK20230723, BK20251104), Natural Science Research Project of Jiangsu Province Colleges and Universities (Grant no. 23KJB560002). Data availability Data is provided within the supplementary information files. Declarations Competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Footnotes Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Contributor Information Xinguo Sun, Email: sunxinguo48144562@hyit.edu.cn. Wenxin Xu, Email: 2015301580222@whu.edu.cn. References 1. Dai, D., Sun, M., Lv, X. & Lei, K. 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