The essence of SD modeling is to deconstruct the system and to provide a mathematical explanation of its internal interactions (Wang H. et al., 2022). Accordingly, the entire system was typically broken down into many subsystems, each of which was described separately (Dong et al., 2019). The model structure referred to the studies of Zhang et al. (2016), Li and Yang (2017), and Zhang et al. (2019). Based on the variation trend of the water supply–demand balance and the current socioeconomic status in the study region, simulations of human-water system coevolution trends were carried out. The human-water system in the study area was therefore separated into the water supply system and the water demand system, the latter being composed of water demand for domestic, agricultural, industrial, the tertiary industries, and the ecological environment. The SD model structure and causal feedback loop diagram of the human-water system in the study area are shown in Figure 3, Figure 4, respectively.

In this research, factors that directly affect human-water system were demarcated within the boundary. As for the SD model for the human-water system in the study region, the spatial boundary was the administrative division boundary of Ningxia, the time boundary was 2010–2030, and 2010–2019 was the historical period of the model used to validate the model’s authenticity. With 2020 as the datum year, the situation from 2020 to 2030 was simulated at time steps of 1 year.

The parameter values in the model were determined through four methods: (a) The parameters could be estimated based on the first-hand data (e.g., population growth rate, urbanization rate) of related statistical yearbooks, water resource bulletins, and water resource plans. (b) The parameters could be calculated using mathematical formulas according to the quantitative relations between variables in the model, such as the urban domestic sewage discharge coefficient, the rural domestic water demand quota, and the rate of treatment and reuse for wastewater and sewage. (c) The parameter values could be estimated by analyzing the mastered relevant professional knowledge, including per capita green area and quantity of livestock. (d) Statistical analysis approaches, such as the arithmetic mean method, could be used to set the parameter values based on data fitting the results with the end year unchanged, including the growth rate of industrial added value, lake wetlands area, and water demand per unit green area. For the choice of methods, the principle of the minimum simulation error was followed.

Referring to the related research of Li et al. (2018), Zhang et al. (2019), and Zhao et al. (2021), according to the quantitative relationships between variables in the SD model structure above, a total of 51 equations were involved in the model. The names and units of the main variables in the model and the SD equations, restricted by the length limit of this paper, appear in Table 1.

Vensim software is a visual modeling tool that allows you to conceptulize, document, simulate, analyze, and optimize models of dynamic systems. There are three key steps in the process of dynamic simulation using Vensim software (Wang X. et al., 2022): (1) determine the causal relationship of variables by drawing causal loop flow diagrams; (2) quantitatively describe the relationship among SD model variables by establishing mathematical equations; and (3) input the historical data of SD model variables into the Vensim software to simulate the changes of the variables under different regulation schemes.

Constructing an indicator system, or the selecting order parameters (indicators) that can characterize the information in the system, is crucial to establishing the human-water system coevolution model. Northwest China is a typical human-water system, which is coupled with many factors, including water, socioeconomic factors and ecological factors. In light of the regional characteristics of the research region, including water resource shortages, fragile ecological environments, and backward socioeconomic growth, an evaluation indicator system should therefore reflect the synergy level between the development and utilization of water resources and the socioeconomic growth as well as ecological environment protection.

For this study, a set of indicators were obtained in accordance with the principles of scientific validity, dynamics, availability, and independence. With reference to relevant literature in China and foreign countries (Kang et al., 2014; Xu et al., et al., 2016; Bao and Zou, 2018; He et al., 2018; Yang et al., 2019) and considering efficiency indicators and gross indicators, the human-water system was classified into three subsystems: socioeconomic subsystem, water resources development and utilization subsystem, and ecological environment subsystem. Through frequency statistical analysis of relevant literature, variables were then screened from the SD model of the human-water system. An evaluation indicator system of human-water system consisting of 18 evaluation indicators was initially constructed (see Table 2).

The precision of the evaluation outcomes are directly affected by the rationality of indicator weights determined in a comprehensive evaluation. In this study, the indicator weights of each subsystem of the human-water system were determined through the method of subjective weighting in combination with objective weighting. The combined weight formula is as follows (Bao and Zou, 2018):

where Zi represents the combined weight of the ith subsystem Si(i=1,2,3) (socioeconomic, water resources development and utilization, and the ecological environment subsystem). Ui stands for the weight of the ith subsystem Si(i=1,2,3) that is obtained by the entropy method, and Vi stands for the weight of the ith subsystem Si(i=1,2,3) that is obtained by the analytic hierarchy process. The entropy method and the analytic hierarchy process used to determine indicator weights were described in the discussion of relevant literature (Arief et al., 2017).

The j (j = 1, 2, ……, nth) order parameter of the subsystem Si was set as xij (ni being the number of order parameters of the ith subsystem). The degree of order of the subsystem Si was then calculated according to Eq. (2) (Liu et al., 2014), using the principle of membership degree from fuzzy mathematics. A larger order parameter indicated a better type (Liu et al., 2017). Next, the degree of order was calculated according to Eq. (3) (Bao and Zou, 2018). The smaller the order parameter, the better the type. The degree of order was calculated according to Eq. (4) (Bao and Zou, 2018).

In Eq. (2), μi is the degree of order of the ith subsystem; λj is the weight coefficient of the order parameter xij, denoting the role of the jth objective in ensuring the orderly operation of the subsystem; μij(xij) is the degree of order of the jth order parameter of the ith subsystem, usually h1=0,h2=0.3,h3=0.6,h4=0.8,h5=1; and c1j,c2j,c3j,c4j,c5j is the threshold of the order parameter xij(cnj≤xij≤cn+1,j,n=1,…,5).

The indicator (order parameter) values of the subsystems of the human-water system coevolution model from 2020 to 2030 were acquired from the simulation results of the SD model for the human-water system. It was emphasized that human-water system coevolution is a dynamic process in this study. The degree of order of subsystems and the synergy index of the whole system were relative values, and the thresholds were selected according to the extreme values of indicators.

The overall degree of order of the system depended on both the synergetic orderliness in subsystems and the degree of synergy between subsystems; that is, it depended on the comprehensive performance of the synergy index. Therefore, simulating the human-water system coevolution situation referred to studying the synergy indexes of the three relevant subsystems in different periods. Following are the formulas employed to calculate the synergy index (Liu et al., 2014):

In Eqs (5) and (6), ES and RS are the information entropy and synergy indexes of the system, respectively; μi is the degree of order of subsystems; and Emax=lnn is the maximum information entropy, meaning that the system is in its most chaotic and disordered state. The dynamic change of RS can identify the coevolution and development directions of the system: a larger number for RS suggests a larger synergy index, signifying a higher degree of coevolution of the system, while a smaller number for RS indicates a smaller synergy index, implying a lower degree of coevolution of the system, on the basis of which the coevolution situation of the human-water system is simulated.

The status continuation scheme was employed to model the coevolution trends of the human-water system under the current social development pattern, to facilitate comparisons with the other schemes. The parameter values of control variables therefore remained unaltered.

Aside from the benchmark control variable parameters, the supplementary water capacity of the unit lake wetlands area was included as the major control variables of the environmentally friendly scheme. This scheme design is mainly based on the current socioeconomic growth situation and Plan’s requirements of “improving ecological water, guaranteeing domestic water, and saving production water.”

On the basis of the benchmark control variable parameters, this study takes the growth rate of industrial added value and the growth rate of tertiary industry as the main control variables of the industrial structures adjustment scheme. This scheme design is mainly based on the Plan’s requirements of “taking water resources carrying capacity as the boundary of socioeconomic growth, restricting the operation of cities, industries, land and population within the boundary, conducting industrial structures adjustment, and building a high-end, green, intelligent and integrated modern industrial system.”

Along with the benchmark control variable parameters, the water effective utilization coefficient for farmland irrigation, the proportion of high-efficiency water-saving irrigation areas, the water quota for industrial added value, and the rate of treatment and reuse for wastewater and sewage were taken as major control variables of the water conservation and pollution prevention scheme. This scheme design is mainly based on the goal requirements stated in the Plan that declared that “by 2025, the water effective utilization coefficient for farmland irrigation will rise to 0.6 in the whole region, the proportion of high-efficiency water-saving irrigation areas will be increased to 55%, water quota for industrial added value will drop to 29 m³, the urban treatment rate of wastewater and sewage will be 100%, and the reuse rate of reclaimed water will be 50%.”

Taking into account the benchmark control variable parameters, the control variables of the comprehensive optimization scheme were designed by integrating all control variables in the environmentally friendly scheme, the industrial structure adjustment scheme, and the water conservation and pollution control scheme, which were the same as those in the three schemes previously mentioned.

Eight key variables were used to verify the validity of the model (including total population, GDP, and industrial added value) in 2010–2019 in the SD model (see Table 3). By comparing the simulated data to the historical data, the relative error of the variables was determined. According to the results, all eight key variables of the model had relative errors less than 10%, indicating a good simulation effect. Therefore, the model could be used to simulate the coevolution trends of the human-water system in Ningxia.

The supply to demand ratio of water was the target of the sensitivity analysis in this study. The sensitivity analysis function in Vensim software was used to test the sensitivity of each parameter. The sensitivity test interval for each parameter was set to increase or decrease by 50%, or an interval value was set based on future development potential. The effect of the changes in each parameter value in the sensitive range on the supply to demand ratio of water was observed. By comparing the sensitive band, the wider the sensitive zone is, the larger the area is, which means that the parameter has a greater influence on the water supply and demand ratio. Finally, 7 parameters with a greater influence on the water supply and demand ratio are identified, which also indicates that the parameters have a strong influence on the model behavior. Table 4 and Figure 5 illustrate the sensitivity analysis interval settings and selected parameters, respectively.

For the status continuation scheme, the supply to demand ratio of water would drop from 1.02 in 2020 to 0.81 in 2030 (Figure 7A), and only 81% of the water demand would be met by the water supply system in the region, resulting in a water deficit of 1.602 billion m³ (Figure 7B). The proportion of agricultural water use would decline from 86% in 2020 to 80% in 2030 (Figure 7C), which is still higher than the national level of 61% in 2020. In 2030, the tertiary industry and the ecological environments will, respectively, contribute only 2 and 3% of the total water use (Figures 7E,F), with agricultural water use dominating the water use structure. Due to the imbalance between water supply and demand, unreasonable water use structure, and a low rate of treatment and reuse for wastewater and sewage(Figure 7G), the socioeconomic growth and environmental protection would not be balanced through the human-water system. The synergy index of the human-water system would drop from 0.39 in 2020 to 0.35 in 2030 (Figure 6), worsening the human-water relationship.

For the environmentally friendly scheme, the environmental water use would rise by 234 million m³ from 2020 to 2030 (Figure 7F), and its proportion would rise from 4% in 2020 to 6% in 2030. However, the increase in ecological water use would intensify the load on the water supply. The supply to demand ratio of water would drop to 0.8 (Figure 7A), which is lower than that in the status continuation scheme, with a water shortage of 1.786 billion m³ (Figure 7B). In 2020–2024, the synergy index of the human-water system would rise from 0.39 in 2020 to 0.47 in 2024 as a result of the increase in environmental water use (Figure 6). In 2025–2030, the supply to demand ratio of water would continuously drop, enlarging the gap between supply and demand, and with these fluctuations the synergy index of the human-water system would decline. These occurrences would indicate that the human-water relationship cannot be improved simply by increasing the environmental water use.

For the industrial structures adjustment scheme, the supply to demand ratio of water would drop to 0.85 by 2030 (Figure 7A), which would decrease slowly compared to that decrease in the status continuation scheme, easing the contradiction between supply and demand. However, the gap between supply and demand would still be 1.232 billion m³ (Figure 7B). Compared to the status continuation scheme, the growth rate of added value of tertiary industry would be higher (Figure 7I). The synergy index of the human-water system would increase from 0.39 in 2019 to 0.45 in 2030 (Figure 6). The human-water relationship would, therefore, be slightly improved.

For the water conservation and pollution prevention scheme, the supply to demand ratio of water would see a sharp increase from 2020 to 2030, bringing supply and demand into balance (Figure 7A). The agricultural water demand would drop to 5.841 billion m³ by 2030, a fall of 60 million m³ from the demand in 2020 (Figure 7C). The sewage treatment and reuse would increase by 294 million m³ (Figure 7G), an increase much bigger than that of the status continuation scheme. As the supply to demand ratio of water rose, the increases in the added value of industry and the added value of tertiary industry exceeded those of the status continuation scheme (Figures 7H,I). The synergy index of the human-water system would rise from 0.39 in 2019 to 0.67 in 2030 (Figure 6). Given that increasing the environmental water use was not considered, room for improving the human-water relationship would remain.

For the comprehensive optimization scheme, the supply to demand ratio of water would always be larger than 1 from 2020–2030 (Figure 7A), bringing supply and demand into balance. By 2030, the proportion of agricultural water use would drop to 77%, a fall of 9 percentage points compared with that in 2019 (Figure 7C), and the fall would be larger than that in single regulation schemes. The proportion of industrial water use would increase to 10%, and the increase would be smaller than that in single regulation scheme (Figure 7D). The tertiary industrial water use would rise to 3% in 2030 from 1% in 2020, a larger increase than that in single regulation schemes (Figure 7E). The proportion of environmental water use would increase from 4% in 2020 to 7% in 2030, a larger increase than that in single regulation schemes (Figure 7F). The treatment and reuse for wastewater and sewage would rise by 309 million m³, which is a higher growth rate than that in single regulation schemes (Figure 7G). The growth in the added value of tertiary industry was projected to be larger than that in single regulation schemes (Figure 7I). The synergy index of the human-water system would increase to 0.81, an increase larger than that in single regulation schemes (Figure 6), indicating that the human-water relationship would be optimized and regulated.

With a complex structure, the human-water system involves many variables. Additionally, the structure of supply and demand for water will be influenced by such factors as climate change, water pricing, and water transfer policies. Hence, the model proposed in this study should be refined to provide a better fit with policy requirements. The human-water relationship involves economics, water resources, hydrology and other disciplines, so an optimization model that couples the SD model and multi-objective planning model or hydrological model could be further adapted to optimize the distribution of water resources across social, economic, and ecological systems, thus optimizing human-water relationship.

Having compared and analyzed the simulation results of the five schemes previously mentioned, the following actions can be taken to improve the human-water relationship.