Coupling coordination development of water resources-economy-ecology system in Shanxi Province based on system dynamics

Abstract

The interaction between water resources, economy, and ecology significantly influences regional security and stability. This study developed an index system for assessing the coupling of water resources, economy, and ecology in Shanxi Province. Subsequently, a coupling coordination degree model for water resources, economy, and ecology was established to assess and analyze the coupling coordination levels. Additionally, the study employed a grey correlation analysis to investigate the impact of 21 indicators on the system’s coupling coordination. A system dynamics simulation model was then constructed to forecast various coupling coordination scenarios up to 2035. Key findings included: (1) An overall upward trend in the comprehensive evaluation index of water resources, economy, and ecology. (2) Significant developmental disparities among the eleven cities in Shanxi Province, with some cities showing a decline in 2015. (3) The economic subsystem indicators in the water resources–economy–ecology model had a 34.02% correlation, exerting a marginally greater impact on the system’s coupling coordination than other subsystems, with GDP per capita being the most influential indicator. (4) Scenario simulations predict that the highest level of coupling coordination, reaching a coupling coordination degree of 0.94, will be achieved in 2035 under Scenario 5(pursuing comprehensive development). This study elucidates the interrelationship between water resources, the economy, and the ecosystem in Shanxi Province, and proposes a programme for adjusting indicators to support future sustainable development in the region.

Introduction

Water resources are crucial for human survival, serving as the cornerstone for economic growth and ecological preservation. However, rapid economic development has led to heightened water consumption across industries, agriculture, and services, placing escalating pressure on water resources. This growth escalates water demand and leads to issues like water scarcity, pollution, and ecological damage¹. The harmonious development of water resources, economy, and ecology is crucial for regional security and stability. In response, China introduced a strategic framework in 2014 emphasizing water conservation, balanced spatial distribution, systematic management, and integrated approaches. This framework addresses the conflict between socio-economic development and ecological and environmental protection².

Coupled systems theory, a mid-to-late 20th-century development in system science, examines nonlinear large systems and offers insights into the internal mechanisms, evolutionary patterns, and the interplay between microscopic synergies and macroscopic order in complex systems³. While swift economic advancement has ushered in unparalleled material prosperity, it has concurrently precipitated concerning ecological degradation. Utilizing this theory, researchers have explored the interconnections between economic and ecological systems. Juniah et al.⁴ investigated South Sumatra, Indonesia, as their study area and determined the potential economic significance of water resources for environmental sustainability. Braat and de Groot⁵ highlighted the dependency of economic systems on ecosystem services, urging managers to make decisions for sustainable development that consider future generations’ well-being. Zuo et al.⁶ proposed addressing regional economic and ecological challenges through harmonious development approaches. Based on the coupled coordination model, the research on the triple system of water resources, economy, and ecology is expanding. Yao & An⁷ identified a complex feedback loop within the coupled water resources-economy-ecology model. Researchers have started to analyze the spatial and temporal evolution of the coordinated interactions among water resources, economic, social, ecological, and environmental systems across different regions, and to propose corresponding development strategies^8,9.

System modeling and simulation are pivotal in analyzing the coordination degree of coupled systems. For predicting coupling coordination degrees, methodologies such as the GM (1,1) grey model, autoregressive integrated moving average (ARIMA), and backpropagation (BP) neural network models are predominantly employed. Shi et al.¹⁰, Wang et al.¹¹, and Xu and Tian¹² utilized the GM (1,1) grey model to forecast the future coordinated development of various urban systems, based on historical and current trends. Wang et al.¹³ implemented an ARIMA-GM combined model to predict coupling coordination trends in the Yellow River Basin of Henan Province for 2021–2025. Jiang and He¹⁴ adopted a BP neural network to estimate the coupling coordination degree in Anhui Province’s urban systems.

Additionally, system dynamics simulation models, which combine qualitative analysis with quantitative calculations and focus on system structure and dynamics, have gained traction¹⁵. By employing system dynamics models, the evolution of the interlinked system under various scenarios can be accurately anticipated and assessed, enabling the identification of enhanced developmental pathways for the system’s key indicators. Wang¹⁶ perceives the Beijing-Tianjin-Hebei region as an integrated entity, develops a systemic dynamics model for coupled coordination, conducts policy simulations across four scenarios to explore the interplay between urbanization and ecological environment, and ultimately delineates an optimal trajectory for their coupled coordination within Beijing-Tianjin-Hebei under a holistic framework informed by simulation outcomes. Jiang et al.¹⁷ integrates dynamic simulation modeling of system dynamics with coupled coordination evaluation for achieving sustainable development of water footprint in Heilongjiang Province from a scientific perspective. Luo et al.¹⁸ used a system dynamics model to examine water supply and demand balance in Beijing. Cheng et al.¹⁹ formulated a multidimensional coupled conceptual model of social-human-ecological systems in the Three Gorges Reservoir area. They employed system dynamics to elucidate the causal feedback mechanism of the system, simulating the degree of coupled coordination from 2010 to 2030. Additionally, eight scenarios were devised to enhance the system’s coupling coordination degree by adjusting various factors.

In summary, the growing body of research on coupled water resources, economy, and ecology systems, there are some gaps in existing studies. Current research in this field tends to operate in silos, focusing on regional evaluation, influencing factors, and system dynamics prediction as separate entities. In contrast, this paper integrates these three approaches into a cohesive research framework, enhancing the precision of water resources management. This paper addresses these gaps by focusing on Shanxi Province, constructed a comprehensive evaluation system for the water resources-economy-ecology coupling system in eleven cities of Shanxi Province. The main objectives of this study are as follows: (1) To evaluate and analyze the temporal and spatial dynamics of the water resources-economy-ecosystem system in Shanxi Province using a coupled coordination degree model; (2) To identify the primary obstacles affecting the system’s development; (3) Reasonably adjust the indicators to simulate the future development trend. Ultimately, this systematic study will provide a rational policy orientation to guide future development and contribute to the promotion of sustainable development in Shanxi Province.

Materials and methods

Study area

Shanxi Province, located in central China along the eastern bank of the Yellow River’s middle reaches (34°34′-40°44′N, 110°14′-114°33′E), experiences a temperate continental climate. The region, predominantly mountainous and hilly, constitutes 80% of the province’s terrain. Shanxi Province is endowed with abundant coal resources, leading to a concentration of energy-intensive industries. This industrial presence has resulted in significant environmental pollution. Additionally, the province faces a critical shortage of water resources, compounded by their uneven distribution. As part of the Yellow River Basin, Shanxi is also a major contributor to the river’s sediment load. In 2021, the province’s major rivers transferred a total of 3,451,550,000 tons of sediment, averaging an annual sediment transfer modulus of 41.3 t/km² over an area of 83,645 km². This has further exacerbated the issues of soil and water erosion. Hence, employing scientific methodologies to model and evaluate the water resources-economic-ecological system of Shanxi Province holds paramount importance in safeguarding its sustainable development. The geographical distribution of Shanxi’s eleven cities is depicted in Fig. 1.

Fig. 1

Map of the study area in Shanxi Province. Figure was generated using ARCMAP 10.8, based on the standard map (GS 2023, No. 2767), without any modifications to the boundaries of the base map.

Data sources

The data utilized to compile the Shanxi water resources–economy–ecology indicators were sourced from publications including the 2012–2022 Shanxi Statistical Yearbook(Bureau of Statistics Shanxi ,2012–2022), the Shanxi Water Resources Bulletin, as well as the 2012–2022 Shanxi Municipal Statistical Yearbooks and Water Resources Bulletins (Shanxi Water Resources Department, 2011–2021). EPS Data Platform (epsnet.com.cn). Employs interpolation techniques for data calculation in years with missing values.

Research methodology

Construction of the indicator system

This study adhered to the principles of representativeness, rationality, and data availability in constructing the evaluation index system. It integrated the realistic characteristics of water resources, economic, and ecological subsystems in Shanxi Province. The water resources subsystem considered indicators related to water supply and consumption. The economic subsystem incorporated indicators associated with population, economic, and social development. The ecological subsystem focused on indicators related to the atmospheric environment, water environment, and social environment. A total of 21 indicators were selected for this system, informed by prior research²⁰. The details of each indicator are presented in Table 1.

Table 1 Comprehensive evaluation index system integrating water resources, economy, and ecology of Shanxi Province.

Calculation of indicator weights

Once the process of selecting water resources–economy–ecology indicators has been finalized, the next step involves allocating weights to each individual indicator. There are two approaches for this task, namely subjective and objective, each with its own advantages and drawbacks. Based on this premise, some researchers have started employing a combination of weighting methods. This approach involves a blend of subjective and objective techniques to calculate indicator weights, aiming to compensate for the limitations of a single weighting method and enhance the scientific rigor of comprehensive evaluations²¹.

The study adopted a combined weighting method, incorporating entropy weighting (objective) and hierarchical analysis (subjective)^22,23. The entropy weighting method assigned objective weights (denoted as${w_i}$), while the hierarchical analysis method provided subjective weights (designated as ${c_i}$). ${w_i}$and ${c_i}$were then linearly combined to derive the combined weights ${Q_i}$.

$${Q_i}=a{w_i}+b{c_i}$$

(1)

where a and b are the combined weight coefficients, indicating the degree of importance of the weights. They satisfy 0 ≤ a ≤ 1, 0 ≤ b ≤ 1, and a + b = 1. In this paper, both objective and subjective weights are equally significant, with both a and b assigned a value of 0.5. The calculated values of the weights of water resources–economy–ecology indicators in Shanxi Province are illustrated in Fig. 2.

Fig. 2

Combined weights of water resources-economy-ecology indicators in Shanxi Province.

Coupling coordination degree model

The coupling coordination degree model, central to this analysis, assesses the level of coordinated development among systems. It incorporates two key concepts: coupling degree and coupling coordination degree. Coupling degree reflects the interdependence and mutual constraints between systems, indicating the structural direction of the system at critical states²⁴. Coupling coordination degree measures the extent of beneficial coupling in the interaction, indicating the quality of coordination.

The comprehensive evaluation indices for the water resources, economic, and ecological subsystems in Shanxi Province were calculated using a linear weighting method, informed by the combined weight calculation method, respectively. The specific formula and calculation details are presented below²⁵:

$${W_i}=\sum\limits_{{j=1}}^{m} {{w_j}{X^{\prime}}_{{ij}}}$$

(2)

$${E_i}=\sum\limits_{{j=1}}^{m} {{w_j}{Y^{\prime}}_{{ij}}}$$

(3)

$${N_i}=\sum\limits_{{j=1}}^{m} {{w_j}{Z^{\prime}}_{{ij}}}$$

(4)

where W_i, E_i, and N_i are the comprehensive evaluation indices of water resources, economic, and ecological subsystems, respectively, m is the number of indicators within the subsystems, w_j is the combined weight value of each subsystem’s indicator j, and ${X^{\prime}}_{{ij}}$,${Y^{\prime}}_{{ij}}$, and${Z^{\prime}}_{{ij}}$are the standardized data of indicator j for the ith year.

Based on the comprehensive evaluation indices of the subsystems, this study calculated the coupling degree and the coupling coordination degree of water resources, economy, and ecology in Shanxi Province using specific formulae²⁶:

$$C{\text{=}}\frac{{3\sqrt[3]{{{W_i}{E_i}{N_i}}}}}{{{W_i}+{E_i}+{N_i}}}$$

(5)

$$D=\sqrt {C \times T}$$

(6)

$$T=\alpha {W_i}+\beta {E_i}+\gamma {N_i}$$

(7)

where C is the coupling degree; D is the coupling coordination degree; T is the comprehensive evaluation index of the system, and $\alpha$, $\beta$, and $\gamma$ are the coefficients to be determined for each subsystem’s degree of importance. This paper assumes that the degree of importance for water resources, economy, and ecology is uniform for Shanxi Province, and therefore $\alpha {\text{=}}\beta {\text{=}}\gamma {\text{=}}1/3$.

These calculations drew upon established research to set discriminative criteria for different levels of C and D²⁷²⁸. The development stages of the water resources-economy-ecology’s coupling degree and coupling coordination degree are categorized as tabulated in Table 2.

Table 2 Grading of coupling degrees and coupling coordination degrees.

Grey correlation model

To assess the influence of each indicator on the coupling coordination degree, grey correlation analysis was employed. Originated by Professor Deng, this model quantifies the significance, magnitude, and order of variable factors within a system, effectively identifying primary and secondary factors impacting the system’s dynamic development. In this study, the water resources–economy–ecology’s coupling coordination degree of Shanxi Province served as the reference sequence, with 21 indicators as comparison sequences. The main steps in grey correlation analysis included²⁹:

• (1) Dimensionless processing of data to negate unit and magnitude biases.

• (2) Establishing reference ${x_0}$ and comparison ${x_i}$ sequences, where k represents the moment, n the sequence timeline length, and m the number of comparison sequences.

$${x_0}=\{ {x_0}(k)\vert k=1,2, \cdots \,,n\} =({x_0}(1),{x_0}(2), \cdots \,,{x_0}(n))$$

(8)

$${x_i}=\{ {x_i}(k)\vert k=1,2, \cdots \,,n\} =({x_i}(1),{x_i}(2), \cdots \,,{x_i}(n)),i=1,2, \cdots \,,m$$

(9)

• (3) Computing the correlation coefficient ${\xi _{\text{i}}}( {\text{k}})$ of the comparison sequence ${x_i}$to the reference sequence ${x_0}$ at moment k. The corresponding formula is detailed as follows:

$${\xi _i}\vert k\vert =\frac{{{{\hbox{min} }_i}{{\hbox{min} }_k}\left| {{x_0}(k) - {x_i}(k)} \right|+\rho {{\hbox{max} }_i}{{\hbox{max} }_k}\left| {{{\text{x}}_0}{\text{(}}k{\text{)}}-\left. {{x_i}{\text{(}}k{\text{)}}} \right|} \right.}}{{\left| {{x_0}(k) - {x_i}(k)} \right|+\rho {{\hbox{max} }_i}{{\hbox{max} }_k}\left| {{{\text{x}}_0}\vert k\vert -\left. {{x_i}\vert k\vert } \right|} \right.}}$$

(10)

where, for the discrimination coefficient $\rho \in \left[ {0,1} \right]$, a larger $\rho$ is related to a greater distinguishability, and$\rho$usually takes the value of 0.5. ${\hbox{min} _i}{\hbox{min} _k}\left| {{x_0}(k) - {x_i}(k)} \right|$and ${\hbox{max} _i}{\hbox{max} _k}\left| {{{\text{x}}_0}{\text{(}}k{\text{)}}-\left. {{x_i}{\text{(}}k{\text{)}}} \right|} \right.$ are the minimum and maximum differences between two levels, respectively.

• (4) Correlation calculation.

$${\Psi _i}=\frac{1}{n}\sum\limits_{{k=1}}^{n} {{\upxi _i}(k)}$$

(11)

System dynamics simulation model

System dynamics, a concept introduced by Professor Forrester in the United States, merges natural science theories with socio-economic principles. It effectively addresses high-order, nonlinear, multiple-feedback, and complex system challenges, making it an ideal approach for examining dynamic patterns in complex systems³⁰. This method simulates real system problems by modeling the dynamic interplay of system variables and feedback mechanisms. The construction of a system dynamics model involves several components: level variables (L), speed variables (S), auxiliary variables (A), and information arrows. Level variables track accumulation changes over time, while speed variables represent the pace of this accumulation, influencing the increase or decrease of level variables. Auxiliary variables serve as intermediaries in the system’s decision-making processes, and information arrows connect related variables within the system³¹.

Equation of state: Given the dynamic nature of the system, its state evolves temporally, necessitating an equation to encapsulate its state at any given moment.

$$LK=LJ+DT(IR.JK - OR.JK)$$

(12)

where, LK and LJ represent the states of variable J at moments K and J respectively, with JK indicating the time interval between these moments. DT signifies the simulation time equivalent to JK, while IR.JK and OR.JK stand as velocity variables.

Rate Equations: In the domain of system dynamics, the mathematical expressions utilized to depict the rate of change per unit time within a given system are termed as rate Eq. 

$$IR.JK - OR.JK=\frac{{L.K - L.J}}{{DT}}$$

(13)

Tabular Functions: Due to the non-linear relationships among the variables in the model, the representation of certain variables cannot be exclusively captured through algebraic combinations with other variables. Hence, it becomes imperative to visually depict the nonlinearity present in the data.

In applying system dynamics to the water resources-economy-ecology, the model encompasses water resources, population, economy, society, and environmental factors: The water resources subsystem is foundational for sustainable development, addressing water needs for living, industrial production, agriculture, and ecological stability. The economic subsystem, with GDP as a core indicator, examines the impact of economic activities and population dynamics on the overall system. The ecological subsystem, reflecting the health of the ecosystem, is crucial for the sustainability of urban and regional development and is closely linked to human production and life.

Dynamic scenario simulation within a system enables profound analysis and prediction of system behavior, particularly its responses to varying conditions. This simulation approach facilitates the comprehensive evaluation of system performance and stability across diverse scenarios, thereby enhancing system design optimization and decision-making processes. Furthermore, it serves as a valuable tool for hypothesis testing, model validation, and exploration of potential system behaviors, thereby offering robust support for system optimization and problem-solving endeavors in scientific research contexts.

This study’s system dynamics model included three subsystems: water resources, economy, and ecology. The model’s accuracy was enhanced by defining detailed parameters and relational equations to reduce uncertainty. The utilization of system dynamics to simulate the coupled water resources–economy–ecology coordinated development system in Shanxi Province was primarily divided into the following five steps³²:

• (1) Defining the simulation boundaries, base year, and simulation time for the study area.

• (2) Identifying the subsystems, variables, and causal relationships within the coupled water resources–economy–ecology system.

• (3) Using Vensim-PLE 9.3.5 to construct the flow diagram and establish the system dynamics model for the coupled system.

• (4) Conducting historical data simulations for error analysis, comparing simulation values with actual values, and calibrating parameters based on validation results.

• (5) Predicting future scenarios for the coupled water resources–economy–ecology system using the calibrated system dynamics model.

Results and analyses

Evaluation of the coupling coordination degree model

Comprehensive evaluation index analysis

The comprehensive evaluation index for the water resources-economy-ecology coupling system in Shanxi Province was calculated for the period 2011–2021. As depicted in Fig. 3, this index exhibited a fluctuating yet overall ascending trend, increasing from 0.26 in 2011 to 0.75 in 2021. Notably, the index experienced a significant decline in 2015, influenced by water resource and economic challenges, with a smaller decrease in 2019. Despite these fluctuations, the general trend was upward.

In the water resources subsystem, notable declines in the comprehensive evaluation index were observed in 2012, 2015, and 2019. These downturns were largely attributable to natural factors, specifically decreased rainfall in these years, leading to reduced total water resources. Additionally, lowered compliance rates in water functional zones and increases in water resource utilization rates, along with higher annual per capita water consumption, contributed to these index declines.

The economic subsystem’s comprehensive evaluation index showed the least marked upward trend. In 2015, Shanxi Province’s GDP saw a significant drop. The province, heavily reliant on coal-related industries constituting over 70% of its industrial value, faced challenges due to stagnation in the coal market and increased national pressure for energy conservation and emissions reduction. Despite being designated as a “national resource-based economy transformation comprehensive supporting reform pilot area” by the Chinese government in 2010, the transformative measures taken by Shanxi Province had not manifested substantial effects by 2015.

The ecological subsystem’s comprehensive evaluation index showed the most significant growth, rising from 0.16 in 2011 to 1 in 2021, with a decline only in 2017. Moreover, all the indicators within the ecological subsystem of Shanxi Province progressed in a positive direction. This improvement aligns with Shanxi Province’s post-18th CPC National Congress environmental approach. The province adopted the principle that “green water and green mountains are golden and silver mountains”, emphasizing the synergy of pollution reduction and carbon reduction, and implementing comprehensive ecological and environmental protection measures across all aspects, regions, and processes.

Fig. 3

Comprehensive evaluation indices for the water resources–economy–ecology coupling system in Shanxi Province, 2011–2021.

Analysis of the coupling coordination degree

The coupling coordination degree between water resources, economy, and ecology in Shanxi Province exhibits dynamic variation over time. By employing the coupling evaluation model, the coupling coordination degree of each city was calculated for different years, reflecting the state of water resources–economy–ecology coupling coordination in these urban areas.

As indicated in Fig. 4, from 2011 to 2021, the coupling coordination degree of each city in Shanxi Province was on an upward trajectory, with a continual improvement in coordination levels. In 2012, all 11 cities were barely coordinated. However, by 2019, all had achieved intermediate coordination. By 2021, Taiyuan and Jinzhong had advanced to quality coordinated development, and the coupling coordination degrees of the remaining cities exceeded 0.8, signifying good coordination.

Fig. 4

Coupling coordination degrees of the water resources–economy–ecology model in cities of Shanxi Province.

A more detailed micro-analysis revealed significant disparities in the development of coupling coordination across Shanxi Province, with some instability in this development. For instance, in 2021, Yuncheng City had just reached good coordination, whereas Taiyuan had already attained quality coordination. Between 2014 and 2015, cities like Yangquan, Jincheng, Shuozhou, Jinzhong, Xinzhou, and Linfen exhibited a downward trend. This variation is partly attributed to population dynamics, where all cities except Jinzhong and Taiyuan experienced population declines from 2011 to 2021. Furthermore, Taiyuan’s economic growth, driven by its equipment manufacturing (25%) and iron and steel industries (24.3%), positively impacted its water resources and ecological subsystems. This disparity underlines the necessity for cities in Shanxi Province to diversify their economies to mitigate prolonged downturns in their economic subsystems, which could destabilize the overall system and impede urban development.

Evolution of the coupling coordination degree in Shanxi Province

Figure 5 illustrates the evolution of the coupling coordination degree in Shanxi Province. From 2011 to 2015, growth in the coupled system’s coordination degree was slow and even declined in 2015. However, from 2016 to 2021, there was a rapid increase. The overall water resources-economy-ecology coupling coordination degree in Shanxi Province showed an upward trend over the decade, rising from 0.5008 to 0.8531, eventually reaching a level of good coordination.

Fig. 5

Coupling coordination degrees of the water resources–economy–ecology model in Shanxi Province, 2011–2021.

Correlation analysis

This section examined the influence of internal indicators on the coupling coordination degree by conducting grey correlation analysis. The analysis focused on 21 evaluation indicators of the water resources-economy-ecology in Shanxi Province over 11 years. Using the coupling coordination degree as the reference sequence, the correlation coefficient and degree of each evaluation indicator were studied, with the discrimination coefficient set at 0.50 in the grey correlation analysis. The calculated correlation coefficients are presented in Table 3.

Table 3 Correlation coefficient calculations for indicators across years.

Based on the correlation coefficients from Table 3, the correlation degree of each indicator was computed as detailed in Table 4. The correlation degree values ranged from 0.59 to 1.0, with higher values indicating a stronger correlation with the reference sequence (coupling coordination degree) and, hence, a higher degree of impact. Notably, GDP per capita (indicator 9) exhibited the highest correlation at 0.939, followed by urbanization rate (indicator 14) with a correlation of 0.816. Conversely, water consumption of CNY 10,000 GDP (indicator 11) and ammonia nitrogen emission (indicator 18) showed lower correlations of 0.624 and 0.592, respectively.

Table 4 Correlation calculation results.

The results of subsystem correlation degrees, depicted in Fig. 6, revealed that the correlation degree proportion of water resources subsystem indicators in Shanxi Province was 33.75%, economic subsystem indicators at 34.02%, and ecological subsystem indicators at 32.24%. These findings suggest that economic subsystem indicators are the most significant factors influencing the coupled and coordinated development in Shanxi Province. Meanwhile, the water resources and environmental system indicators have comparably significant impacts on the coupling coordination degree.

Fig. 6

Results of subsystem correlation degrees of 21 indicators in Shanxi Province: (a) Water resources; (b) Economy; (c) Ecology.

Prediction of coupling coordination degrees

This study developed a water resources–economy–ecology dynamics model for Shanxi Province, incorporating the feedback mechanisms and causal links between systems and indicators. This model approached the problem from a dynamic development perspective. It encompassed all eleven cities in Shanxi Province, spanning a simulation period from 2011 to 2035. This period was divided into an 11-year historical validation phase (2011–2021) and a 14-year prediction and simulation phase (2022–2035), with yearly time steps.

Subsystem indicators were categorized into level variables, auxiliary variables, and speed variables, with their interconnections qualitatively and quantitatively represented through information arrows and numerical equations.

In the water resources subsystem, total water use and population were level variables. Incremental water supply was a speed variable, with average annual rainfall, per capita domestic water consumption, and water functional zone compliance rates acting as constants and auxiliary variables.

The economic subsystem employed irrigated area as a level variable, GDP growth rate as a primary speed variable, and auxiliary variables like GDP per capita, secondary production proportion, water consumption of CNY 10,000 GDP, and per capita grain output to reflect economic and social development in Shanxi Province.

For the ecological subsystem, urban greening area and ecological water use were level variables. Auxiliary variables included the annual average concentration of inhalable particles, SO₂ and ammonia nitrogen emissions, sewage treatment rate, and greening coverage rate of built-up areas, depicting the ecological environment status from atmospheric, water, and social perspectives.

The system dynamics flow diagram of Shanxi Province’s coupled water resources-economy-ecology system is illustrated in Fig. 7.

Fig. 7

The dynamics flow diagram of water resources–economy–ecology system in Shanxi Province.

Validation of the model accuracy

Given that system dynamics simulates real-world social systems, model accuracy is crucial for its effectiveness³³. Before proceeding with prediction simulations, the model’s validity and accuracy were tested through error analysis. Representative variables from each subsystem were selected for this purpose. As shown in Table 5, the errors for most indicators remained within 10%, an acceptable range, except for the air compliance rate, which exceeded this threshold in certain years. These findings suggest that the model operates effectively, accurately reflecting real-world scenarios and laying a solid foundation for future dynamic forecasts.

Table 5 Simulation accuracy tests for system indicators, 2011–2021 (relative error in %).

Scenario modeling and prediction

This study utilized historical data trends from 2011 to 2021 and aligned with the goals in Outline of the Fourteenth Five-Year Plan for the National Economic and Social Development and the Long-Range Objectives Through the Year 2035 for Shanxi Province. The forecasting period extended from 2022 to 2035. Based on the correlation analysis of indicator variables, the model’s auxiliary variable parameters were adjusted according to indicator importance. Adjustments included modifying the GDP growth rate and population growth rate to regulate GDP per capita. Outline of the 2035 Shanxi Province Plan, envisioned for achievement by 2035 are a target urbanization rate of 68% and a full-scale sewage treatment rate of 100%. Furthermore, given the variability of water resources, for analytical calculations, the water resources spanning from 2022 to 2035 are considered as multi-year average water resources. Consequently, five development scenarios were established: maintaining the status quo, focusing on water conservation, prioritizing economic development, emphasizing environmental protection, and pursuing comprehensive development. The adjustments to variable parameters for each scenario are detailed in Table 6.

Table 6 Variable parameter adjustment.

Using Vensim-PLE 9.3.5 software, the system dynamics model simulated these five scenarios. The simulation predicted the values of each indicator in the coupled water resources-economy–ecology evaluation index system of Shanxi Province for 2022–2035. The calculated coupling coordination degrees are depicted in Fig. 8.

Fig. 8

Variation of coupling coordination degrees under different scenarios.

The projections showed varying outcomes for each scenario:

Scenario 1 (maintaining the status quo): The coupling coordination degree gradually increases from 0.45 to 0.88, reaching good coordination by 2035. However, the overall growth rate in coordination is modest.

Scenario 2 (focusing on water conservation): By reducing total and industrial water use, ammonia nitrogen emissions and pollution are lowered. The coupling coordination degree is projected to reach 0.91 in 2035, second only to the comprehensive development scenario.

Scenario 3 (prioritizing economic development): This scenario involves slowing population growth and boosting GDP growth, aiming for rapid urban economic progress. The system’s coupling coordination degree is expected to rise from 0.44 to 0.88, reaching a good coordination state and matching the status quo scenario by 2035.

Scenario 4 (emphasizing environmental protection): Prioritizing ecological protection, this scenario increases ecological water use and urban greening rates while reducing SO₂ emissions and concentration of inhalable particles. The coupling coordination degree under this scenario is anticipated to reach 0.90 in 2035, surpassing the status quo.

Scenario 5 (pursuing comprehensive development): This approach integrates factors from all scenarios, balancing water resources, economic development, and ecological protection. It is predicted to result in the highest coupling coordination degree, rising from 0.44 to 0.94 by 2035, indicating high-quality coordinated development.

Discussion

Methodological discussion

• (1) The coupling coordination degree model is vital in evaluating multi-system coupling. However, there is no standard method for calculating the weights of system index data, leading to varied approaches. Some researchers, like Zhao & Liu³⁴ and Gu et al.³⁵, have used a single weighting approach, i.e., the entropy weighting method. Others, like Wu et al.³⁶, have combined methods like the G1 assignment and entropy weighting to construct the combined weight of the coupled water resources–economy–ecology system of the Tarim River Basin. Our study adopted a mix of the hierarchical analysis method and entropy weighting, which balances subjective decision-making with objective data representation.

• (2) Accurate forecasting is crucial for guiding regions towards quality development. The dynamic nature of the coupled water resources-economy-ecology system in Shanxi Province, characterized by continuous exchanges of materials, information, and energy, necessitates a robust system dynamics model. Hu et al.³⁷ and Wu et al.³⁸ previously developed a system dynamics simulation model, focusing solely on predicting indicators through simulation. In contrast, this paper enhances the simulation by incorporating a coupling evaluation, thereby enriching the predictive capability of the model. Li et al.³⁹ constructed five scenarios based on key influencing factors for simulation, advocating for water conservation, the establishment of a multi-faceted water recharge system, and prudent population control as pivotal strategies to realize high-quality development in the Xiongan New Area. Yang et al.⁴⁰ conducted an analysis of 275 prefecture-level cities in China, revealing that advancements in industrial structure, expansion of drainage infrastructure, and the implementation of centralized wastewater treatment policies significantly improved water resource management and economic efficiency. In conclusion, this paper expands upon previous similar studies by incorporating additional treatments, thereby making the analysis richer and more comprehensive. It provides a detailed discussion of scenario simulation and prediction indicator adjustments, offering valuable insights for studying regional policy directions.

• (3) Our study highlights the complementarity of the water resources, economy, and ecology systems in Shanxi Province. For instance, at the municipal level, Taiyuan’s economic subsystem successfully transitioned from energy-centric to diversified development, positively influencing both water resources and ecological subsystems. At the provincial level, scenarios focusing on water conservation and environmental protection show greater coordinated development than the status quo scenario. This comprehensive approach is essential for sustainable development. By conducting a comprehensive scenario analysis for the future development of Shanxi Province, the emphasis will be placed on advancing the conservation and efficient utilization of water resources. Specific measures include stringent management of water usage, reducing water consumption for domestic purposes, minimizing wastewater discharge, and enhancing the recycling of water resources. Strategies aimed at diminishing agricultural land usage, fostering water-efficient agricultural practices, enhancing urban industrial and domestic water conservation initiatives, and systematically phasing out water-intensive and inefficient technologies and equipment, are instrumental in the comprehensive adoption of water usage measures. Additionally, Shanxi Province abounds in coal resources, efforts will be made to boost investments in green industries, reduce coal consumption, and thereby curtail industrial pollution emissions. Whilst effective population control measures are also imperative to mitigate resource scarcity and alleviate environmental strain.

Limitations and future research directions

(1) In the context of indicator construction, a predominant practice involves borrowing indicators from analogous studies. Consequently, the selection process is inherently subjective, and the limited number of indicators within the system may result in disparate indicators exhibiting similar orientations. Moving forward, principal component analysis or correlation analysis can be employed to screen indicators and further enhance the indicator system.

(2) The system dynamics model developed in this study is constrained by its system boundary, focusing solely on the closed system comprising water resources, economy, and ecology within Shanxi Province. This confinement restricts the model’s capacity to capture interactions with external systems, such as energy subsystems. Future iterations will incorporate these additional subsystems to enhance the simulation model’s comprehensiveness.

(3) In this investigation, the coupling coordination outcomes between the current situation evaluation and simulation prediction exhibit a lack of coherence due to disparate evaluation years and divergent extreme values during indicator standardization. This incongruity results in a progression from low to high coupling coordination between the historical validation period and the simulation prediction period. To enhance the consistency of the evaluation process in subsequent analyses, integrating present and forthcoming data for standardized computations could establish a cohesive link between current state results and future simulations.

Conclusions

• (1) The comprehensive evaluation index of the water resources-economy-ecology in Shanxi Province had generally trended upwards. However, the water resources subsystem showed significant sensitivity to natural conditions, with notable decreases in 2012, 2015, and 2019. The economic subsystem exhibited the smallest average growth, with overall stability except for a downturn in 2015. The ecological subsystem’s comprehensive evaluation index consistently increased, especially after 2017.

• (2) The coupling coordination degree among water resources, economy, and ecology in Shanxi Province and its cities improved over time. By 2021, the coupling coordination degree exceeded 0.8, indicative of good coordination. However, disparities in development among different cities in Shanxi Province were notable, suggesting the need for tailored strategies to promote safe, coupled, and coordinated development.

• (3) Analysis of 21 indicators within Shanxi Province’s water resources–economy–ecology revealed the highest correlation with GDP per capita and the lowest with ammonia nitrogen emissions. The indicators’ correlation contribution was distributed among the three subsystems, with 33.75% from water resources, 34.02% from economy, and 32.24% from the ecological subsystem.

• (4) The system dynamics model’s scenario analysis for 2022–2035 indicates an increasing trend in coupling coordination across all five scenarios. The comprehensive development scenario exhibits the highest coupling coordination degree, while the economic development scenario shows the lowest. Notably, the comprehensive development scenario is projected to achieve a high-quality coordinated development level with a coupling coordination degree of 0.94 by 2035.

This study endeavors to elucidate the dynamic interplay among indicators within the integrated system of regional water resources, economy, and ecology, aiming to foster high-quality and coordinated development within the system. Through this, we aim to offer insights into realizing sustainable development within the region and discerning policy trajectories concerning indicator factors. The model employed in this investigation demonstrates suitability for analyzing unified multi-system planning, applicability extends to global regional, national, provincial, and watershed scales, promoting the sustainable development of regional systems through comprehensive consideration of water resources, economic factors, and ecological dynamics.