Abstract

The nexus of water, society, and ecology is set to become a hotspot in the coming decades. In this paper, a simple model framework is developed to describe the interactions and feedback of the three categories of components within the regional water system. Taking Huainan City in Anhui Province of China as an example, a model is established with the system dynamics method to discuss its coevolution process. The results show that the development direction of Huainan City is consistent with the planning direction. The comprehensive effectiveness of the policies for developing water-saving technologies, supporting socio-economic development and ensuring food supply could be acceptable. Moreover, the improvements of water-saving technologies for agriculture and domestic water use need to be accelerated. The support for industrial development and the restrictions on pollutant emissions need to be strengthened. Therefore, the model could help decision-makers to understand the status of the water system, modify policies and make further planning. The coevolution of the regional water system is jointly dominated by the positive feedback loop aimed at productivity and the negative one aimed at sustainability.

INTRODUCTION

Recently, the impacts of human activities on the water cycle have been growing. These are mainly caused by population growth and accelerated urbanization (Koop & van Leeuwen 2017). The subsequent problems, such as water resource use dispute, water environment pollution and water ecosystem degradation, have also become progressively prominent, forcing decision-makers to adjust their strategies to reduce the negative effects of human activities and maintain the sustainability of water resources (Savenije 2015).

Therefore, recent studies have focused on the connection between hydrological processes and human society (Kreibich et al. 2017). Since developing an interdisciplinary paradigm is necessary to deal with water-related problems, it is urgent to consider synthetically the nexus and development mode of water resources with the natural environment, organisms' habits, society, economy and politics. In this context, the Earth System Science Partnership (ESSP) proposed the water system theory (Alcamo et al. 2005), which focuses on the comprehensive issues of water and society, water and environment, water and ecology, including the connotation and composition of the water system, internal complicated connections and overall evolutionary trends.

The water system is defined as a whole consisting of the three categories of components (physical, human, and biological and biogeochemical components) with water cycles acting as a link. In studying a water system, it is necessary to apply an appropriate method to model the interconnections of coupled systems. As one of the tools to simulate the temporal variations of a complex system, the theory of system dynamics (Forrester 1987) is very consistent with that of water system theory, which emphasizes the concept of multi-state, multi-factor, and multi-variable interconnection, conversion, feedback and coevolution. In fact, the theory of system dynamics has become an important method for water resources research (Chang et al. 2015; Huang et al. 2019). Since its internal multi-factor interaction and feedback mode of operation could well reflect the concept of ‘nexus’ emphasized in the water system theory, the system dynamics method is applied to establish a complex water system model including water, society, and ecology interconnected in this study.

This paper aims to construct a conceptual framework to explore the coupled dynamics of the physical, human, and biological and biogeochemical components in a water system. A conceptual description of the three categories of components and their associations is presented. Moreover, a system dynamics model consisting of governing equations and constitutive relations is set up to simulate the coupling and coevolution of the water system in Huainan, Anhui Province, China. Finally, the process of coevolution and its dynamics in the Huainan City water system are analyzed and discussed, and the corresponding conclusions are ultimately reached.

MATERIALS AND METHODS

Study area

Huainan City, a prefecture-level city, is located in the central part of Anhui Province of China with a total area of 2,596 km2 (Figure A2 in Appendix A, available online). The city consists of six counties with a total population of 2.44 million, containing 1.12 million urban population and 1.32 million rural population in 2014. The average annual precipitation is 886.5 mm and the average annual temperature is 16.6 °C. It belongs to the Huaihe River basin, located in the middle reaches of the Huaihe River, which is its main source of water supply.

With population growth, the accelerating pace of urbanization and the rapid development of social economy, the human components are gradually becoming the main driving force for the evolution of the water system of Huainan City. The contradiction among the departments of water consumption is becoming increasingly sharp, thus the remaining water in the river is gradually reduced. Meanwhile, the increases of domestic sewage and agricultural and industrial waste water aggravate the deterioration of the water environment and the pressure on the aquatic ecosystem, threatening the virtuous circle of the overall water system. Although decision-makers have developed a series of policies to address these issues, the effectiveness of these policies remains to be evaluated. Therefore, in order to maintain the sustainability of the water system, it is important to establish a model to analyze and evaluate the synergistic process of the water system nexus.

Model conceptualization

Description of physical components

The water balance equation is used to describe the dynamic changes of water storage of the overall system as follows: 
formula
(1)
where dW is the amount of change of water storage of the whole water system during dt, a certain period of time. Qin is the inflow, and Pe is the net precipitation. U represents the water consumption of the entire human component. Qout is the outflow.

Description of human components

The water consumption owing to the human components is described as follows: 
formula
(2)
where Eni represents the influence of each engineering work on the water storage, such as the impact of reservoirs or water transfer projects. Du is the domestic water consumption, which is determined by policy (P), technology (T) and population (N). Iu is the industrial water consumption; Au represents the agricultural water consumption, determined by irrigated area (a), policy (P) and technology (T). Eu represents the ecological water consumption.

It is noteworthy that technology (T), policy (P), and productive forces (Pf) (Liu et al. 2014) are closely interrelated, for example, productivity and policy orientation can promote the development of technology, and the development of technology and productivity can provide more choices for policy makers.

Description of biological and biogeochemical components

For the description of biological and biogeochemical components, the focus lies in quantifying the health of the water environment and ecosystem, which are severely affected by the human components: 
formula
(3)
 
formula
(4)
where Eh represents the ecological health of the water system. Eh1 and Eh2 indicate the degree of conformity to the requirements of the ecosystem in water quantity and quality respectively, and i refers to the serial number of the indicator. One or more indicators can be selected according to the actual needs, for example, Eh1i indicates the degree of conformity in water quantity for the ith indicator; q represents the ecological water requirement, c represents the concentration of solute, and the corresponding f(q) and g(c) are the indicators that characterize their respective present situation in meeting the needs of health, and fopt(q) and gopt(c) are the corresponding most appropriate values.

In summary, the conceptual framework of the water system is shown in Figure 1.

Figure 1

Conceptual framework of regional water system.

Figure 1

Conceptual framework of regional water system.

CASE STUDY

Data

The basic data of water resources are mainly from the Water Resources Bulletin of Anhui Province (2006–2015). The series of measured data of hydrological and water quality monitoring stations are provided by Huaihe River Basin Water Resources Protection Bureau. Population, economy, sewage and other data are mainly from the Statistical Yearbook of Anhui Province (2006–2015). In addition, planning data such as water use indicators mainly come from the report of Comprehensive Planning of Water Resources of Huaihe River Basin and Shandong Peninsula, which takes 2030 as the long-term planning year, compiled by Huaihe River Water Resources Commission in 2008.

The simulation period of the model is from 2006 to 2030. Specifically, 2006 to 2014 are the historical statistics years, while 2015 to 2030 are the simulated prediction years; 2030 is the long-term planning year which will be taken as the comparison year with the basin planning data set in the report. The time step (dt) is set to 1 year. Additionally, the detailed data can be obtained through the platform of the Statistical Database of Anhui Province's Economic and Social Development.

Governing equations of physical components

Although the inflow of the mainstream may vary due to a number of factors, such as variability in precipitation, possible changes in upstream demand, and possible changes in the upstream water regulatory environment, in this case, the water resources of the water system are characterized by the average annual inflow, irrespective of the temporal variations. The statistics of water resources are mainly based on the situation of the medium year. 
formula
(5)
where Win is the inflow from the mainstream of Huaihe River, taking a constant value according to the average annual water inflow. Pe is the water resources formed by net precipitation with evaporation deducted, taking a constant value according to the statistics of water resources of the medium year, as does Wrcg, the repeated calculation of groundwater resources. The data obtained from water resources evaluation taking sub-basin as a unit would be more detailed. However, limited by the availability of data, the statistics of water resources in this study are obtained from those taking administrative region as a unit. U is water consumption in the human components. Wout is the outflow.

Governing equations of human components

The relevant statistics have included the impact of all water engineering works, so the variable En is not listed in the formula. During the simulation period, the government of Huainan City took the planning goal as the direction of the development of all aspects, but the various policy constraints were difficult to describe directly and quantitatively in the model. Therefore, in this case, the planning value of each target index given in the comprehensive planning report for 2030 is regarded as the system target state after considering the policy (P). In the subsection ‘Dynamics and comparisons of the target indicators’, the simulation value of each target index in 2030 will be compared with the planning value for comparative analysis: 
formula
(6)
 
formula
(7)
 
formula
(8)
 
formula
(9)
 
formula
(10)
where Du is the domestic water consumption, ur is the domestic water consumption per capita, which is determined by technology (T), and up is the public water consumption, which is a function of population (N). Iu is the industrial water consumption, uv is the water consumption per unit industrial value added, and Via is the industrial value added. Au is the agricultural water consumption, ui is the irrigation water consumption per unit area, and a is the effective irrigated area of farmland; uuni is the non-crop agricultural water consumption, including the forest, livestock and fishery water consumption. Euoff is the off-stream ecological water requirement, composed of urban environmental water consumption and rural ecological water replenishment.

According to the scope of application of the statistical model for calculation of technological change and the availability of statistical data, the calculation method of technological change in the production function improved by Tinbergen (1942) is selected in this case. In this production function, the technology (T) is only determined by time (t), and therefore the variable which is only determined by technology (T) in the calculation is also only determined by time (t).

The total population N is estimated with the logistic population model (Safuan et al. 2013): 
formula
(11)
where x0 is the population of the initial year, and r and K are the related model parameters.
The effective irrigated area (a) is determined as follows: 
formula
(12)
where a0 is the initial irrigated area, and λ is the growth rate of the irrigated area.

Governing equations of biological and biogeochemical components

This section mainly considers the influence of water quantity and quality on water environment and ecosystem health. In terms of water quantity, the degree of assurance of the instream ecological water requirement (Eh1) is taken into account: 
formula
(13)
 
formula
(14)
 
formula
(15)
where Euin is the ecological instream water requirement which supports a variety of needs, including habitat for fish and wildlife, navigation, and waste assimilation etc. The ‘Montana method’ (Orth & Maughan 1981) is used to calculate Euin according to the observed data of historical flow of the Lutaizi hydrological station located at the inlet of the study area. The remaining water resources in the river (Rr) equal the instream water resources (Wr) minus the instream water supply (Sr). Wt is the total water resources and Wunr is the water resources outside the river, including wetlands, lakes and so on. S is the total water supply, which equals the total water consumption (U), and Sunr is the water supply which does not depend on the river. Both Wunr and Sunr take a constant value according to the statistics of the medium year. Eh1 indicates whether the instream remaining water resources after deducting the instream water supply can meet instream water requirements, and it also reflects the intensity of the contradiction over water use between human society and the ecosystem.
In the aspect of water quality, policy-oriented control of the impact of chemical oxygen demand (COD) and ammonia nitrogen (NH3-N) on Huaihe River is considered in this case: 
formula
(16)
 
formula
(17)
where EmtCOD is the COD emissions in the tth year, determined by the corresponding total water consumption (U). Em0COD is the COD emissions in the initial year. Eh21 is the COD reduction rate, which represents the COD pollution status compared to the initial status. Equation (17), whose calculation principle is similar to that of Equation (16), is for calculation of NH3-N reduction rate (Eh22).

Model coupling

The water system model constructed in this case is a coupled model, and the three involved components are internally coupled by several constitutive relations. Among them, technology (T), policy (P) and productive forces (Pf) are the key variables that make the three categories of components coupled. The most important target variable in the regional planning report is the water consumption per unit regional GDP (gross domestic product). It indicates not only the water consumption for socio-economic development, but also the degree of technological development and the effectiveness of policies. The equation for GDP is given by: 
formula
(18)
where Vag is gross agricultural output value, Vin is gross industrial output value, and Vcon and Vth are gross output value of construction industry and tertiary industry (the service industry) respectively.

RESULTS AND DISCUSSION

Model calibration and validation

The specific calculation process is as shown in Equations (5)–(18). According to the observed sequence, all dependent variables and independent variables are functionally fitted by using MATLAB. The variables determined by technology (T), such as industrial value added (Via) and off-stream ecological water requirement (Euoff), are functionally fitted with time (t). The model was calibrated using the basic variable data series from 2006 to 2014 (the constant variables and the calibrated constitutive relations are given in Appendix A), while the data in 2015 was used for validation purposes.

Since the model involves many variables, the representative part of the variables is selected for the historical test. These variables (Figure A3 in Appendix A) include (a) population, (b) domestic water consumption per capita, (c) water consumption per unit industrial value added, (d) irrigation water consumption per unit area, (e) COD emissions, (f) NH3-N emissions, (g) GDP and (h) total water consumption. The mean absolute relative errors (MARE) of variables (from (a) to (h)) during the calibration period are 0.85%, 2.40%, 6.73%, 5.43%, 4.48%, 7.43%, 6.48% and 1.95% respectively, and those during the validation period are 1.72%, 1.75%, 9.11%, 3.69%, 2.06%, 5.66%, 4.17% and 0.04% respectively. Taking all the variables into account, the overall effect of the simulation can be accepted.

Dynamics and comparisons of the target indicators

The planning report mentioned in the subsection ‘Data’ considered 2006 as the base year to predict the main indicators of the Huaihe River Basin in 2030. These indicators include water resource utilization efficiency, socio-economic development, and pollutant emission. The comparison of the target indicators can be seen in Tables 13. As shown in these tables, the trends of all target indicators are consistent with the planning.

Table 1

Comparison of planning value and simulation value of water resource utilization efficiency indicators

Water resource utilization efficiency indicatorsValue typeCurrent year (2006)Planning year (2030)
Irrigation water consumption per unit area (m3/ha) Observation (2006) and planning (2030) of the Huaihe River Basin 3,247.5 4,044.0 
Simulation of Huainan City 4,120.5 4,200.0 
Water consumption per unit industrial value added (m3/104 RMB) Observation (2006) and planning (2030) of the Huaihe River Basin 84.0 23.9 
Simulation of Huainan City 1,081.5 16.2 
Domestic water consumption per capita (L· capita−1 d−1Observation (2006) and planning (2030) of the Huaihe River Basin 118.0 131.0 
Simulation of Huainan City 98.8 135.1 
Water consumption per unit GDP (m3/104 RMB) Observation (2006) and planning (2030) of the Huaihe River Basin 224.0 57.5 
Simulation of Huainan City 726.0 57.8 
Water resource utilization efficiency indicatorsValue typeCurrent year (2006)Planning year (2030)
Irrigation water consumption per unit area (m3/ha) Observation (2006) and planning (2030) of the Huaihe River Basin 3,247.5 4,044.0 
Simulation of Huainan City 4,120.5 4,200.0 
Water consumption per unit industrial value added (m3/104 RMB) Observation (2006) and planning (2030) of the Huaihe River Basin 84.0 23.9 
Simulation of Huainan City 1,081.5 16.2 
Domestic water consumption per capita (L· capita−1 d−1Observation (2006) and planning (2030) of the Huaihe River Basin 118.0 131.0 
Simulation of Huainan City 98.8 135.1 
Water consumption per unit GDP (m3/104 RMB) Observation (2006) and planning (2030) of the Huaihe River Basin 224.0 57.5 
Simulation of Huainan City 726.0 57.8 
Table 2

Comparison of planning value and simulation value of socio-economic development indicators

Socio-economic development indicatorsValue typeCurrent year (2006)Planning year (2030)Variation
Population (104 capita) Observation (2006) and planning (2030) of the Huaihe River Basin 16,287.0 19,170.0 17.7% 
Simulation of Huainan City 235.8 270.7 14.8% 
Gross domestic product (108 RMB) Observation (2006) and planning (2030) of the Huaihe River Basin 15,192.0 77,384.0 409.4% 
Simulation of Huainan City 274.3 1,395.3 408.7% 
Industrial value added (108 RMB) Observation (2006) and planning (2030) of the Huaihe River Basin 6,876.0 31,651.0 360.3% 
Simulation of Huainan City 127.2 533.3 319.3% 
Effective irrigation area of farmland (103 ha) Observation (2006) and planning (2030) of the Huaihe River Basin 16,246.0 17,064.0 5.0% 
Simulation of Huainan City 103.1 107.0 3.8% 
Socio-economic development indicatorsValue typeCurrent year (2006)Planning year (2030)Variation
Population (104 capita) Observation (2006) and planning (2030) of the Huaihe River Basin 16,287.0 19,170.0 17.7% 
Simulation of Huainan City 235.8 270.7 14.8% 
Gross domestic product (108 RMB) Observation (2006) and planning (2030) of the Huaihe River Basin 15,192.0 77,384.0 409.4% 
Simulation of Huainan City 274.3 1,395.3 408.7% 
Industrial value added (108 RMB) Observation (2006) and planning (2030) of the Huaihe River Basin 6,876.0 31,651.0 360.3% 
Simulation of Huainan City 127.2 533.3 319.3% 
Effective irrigation area of farmland (103 ha) Observation (2006) and planning (2030) of the Huaihe River Basin 16,246.0 17,064.0 5.0% 
Simulation of Huainan City 103.1 107.0 3.8% 
Table 3

Comparison of planning value and simulation value of pollutant emission indicators

Pollutant emission indicatorsValue typeCurrent year (2006)Planning year (2030)Reduction rate
COD emissions (ton) Observation (2006) and planning (2030) of the Huaihe River Basin 872,941.0 200,776.4 −77.0% 
Simulation of Huainan City 7,313.5 2,073.0 −71.7% 
NH3-N emissions (ton) Observation (2006) and planning (2030) of the Huaihe River Basin 97,824.0 13,695.4 −86.0% 
Simulation of Huainan City 1,643.8 359.2 −78.1% 
Pollutant emission indicatorsValue typeCurrent year (2006)Planning year (2030)Reduction rate
COD emissions (ton) Observation (2006) and planning (2030) of the Huaihe River Basin 872,941.0 200,776.4 −77.0% 
Simulation of Huainan City 7,313.5 2,073.0 −71.7% 
NH3-N emissions (ton) Observation (2006) and planning (2030) of the Huaihe River Basin 97,824.0 13,695.4 −86.0% 
Simulation of Huainan City 1,643.8 359.2 −78.1% 

The indicators of water resource utilization efficiency can reflect the level of water use, water saving, economy and science and technology development during a certain period. In 2006, the irrigation water consumption per unit area in Huainan City was much higher than the average level in the Huaihe River Basin. Although the gap would be smaller in 2030, the simulated value for Huainan City is still higher than the average level of the river basin planning. This indicates that the improvement of agricultural water-saving technologies in Huainan City needs to be accelerated. The same would be true for water-saving technologies of domestic water use through the analysis of domestic water consumption per capita. In contrast, the effectiveness of the policies for the improvement of industrial water-saving technologies is encouraging. Moreover, the comprehensive effectiveness of the policies for the improvement of water-saving technologies would be acceptable through the analysis of water consumption per unit GDP, which would be reduced to being nearly identical in the planning year (2030) from more than three times in 2006.

Socio-economic development indicators include the total population, GDP, industrial value added, and effective irrigated area of farmland. Since the planning values were set for the entire Huaihe River Basin, the simulated values and the planning values would be compared in the form of the increase or decrease of socio-economic indicators from 2006 to 2030. As shown in Table 2, the variation of GDP in Huainan City from 2006 to 2030 is roughly identical to the planning in the Huaihe River Basin. This indicates that the integrated effectiveness of the policies for supporting social and economic development is sufficiently satisfactory. However, the effectiveness of the policies for supporting industrial development might need to be improved. Moreover, although the increase of the effective irrigation area of Huainan City is smaller than that of the Huaihe River Basin, the same is true for population growth. In the river basin planning, it was planned to use a 5.0% increase in the effective irrigated area to ensure the food supply for a 17.7% population growth. The corresponding ratio in Huainan City ranges from 3.8% to 14.8%, which means that the effectiveness of the policies ensuring food supply could be acceptable.

The main pollutant emissions targets are the key indicators reflecting the pressure on the water environment. According to Table 3, emissions of both pollutants show a drastic downward trend. Based on the comparison, it can be inferred that stricter controls of both pollutant emissions are needed.

Coevolution of the nexus

The coevolution of water consumption, output value, water consumption per unit output value, and pollutant emissions reduction rate are shown in Figure 2(a)2(d).

Figure 2

Coevolution of the nexus of the Huainan City water system.

Figure 2

Coevolution of the nexus of the Huainan City water system.

In the study area, the current policy guidance is to support various industries to transform their mode of economic growth and adopt advanced techniques to improve the efficiency of resource utilization. As the overall water consumption per unit output value decreases, water use efficiency gradually increases. The most critical influence on the total water consumption is the industrial water consumption, which declines significantly with technological advance. This is mainly due to industrial structure changing significantly during the simulation period. In the 1980s, water resources management in Huainan City focused on meeting the water demand for production. Many industrial enterprises had no metering facilities, no water quotas, and no water-saving measures, and industrial circulating water discharged once, causing serious waste of water resources. In 2001, the industrial water reuse rate of Huainan City was only 35%.

At the beginning of the 21st century, various industrial water-saving measures were implemented and industrial water use efficiency improved. On the basis of the planning report, these measures included developing industries with high water use efficiency, transforming water use processes and promotion, strengthening industrial cooling water saving, strengthening enterprise water management, and upgrading equipment and water distribution networks. The annual water plan prepared by Huainan City has clearly stipulated that the quota of water use plans for enterprises with low industrial water repetition rate should not be increased, and the quotas of water use plans for those severely wasting water and violating water-saving regulations should be deducted. In addition, according to the planning report, major water-consuming industries, such as thermal power generation, petroleum and petrochemical, steel, textile, chemical and food, are the key objects for water-saving transformation in the production process. The water-saving measures include reducing water withdrawal, improving wastewater treatment and reuse, and utilizing seawater reclaimed water and mine water if available. The principal water-consuming industries in Huainan City are thermal power and mining. Due to the lack of detailed water utilization information for thermal power and mining in Huainan City, its evolution could not be simulated in this study. However, the availability of this detailed information might contribute to further research into the evolution process of industrial water consumption.

The agricultural water consumption also shows a downward trend under the influence of both technology and irrigated area, while the domestic water consumption gradually increases under the synergy of technological improvement and population growth. This is mainly due to the relatively stable agricultural industrial structure and the gradually maturing water-saving irrigation technology in the study area. The rate of decrease of water consumption per unit area has gradually stabilized. As the population grows, the demand for grain increases and the irrigated area increases accordingly. Consequently, the agricultural water consumption gradually tends to decline steadily. Overall, the speed of industrial water-saving technological innovation is faster than that of agriculture. This could be considered as a positive feedback loop, in which resources of water, land and human are combined to generate wealth which can promote technological advance. Technological innovation can further improve the efficiency of resource utilization, and is also conducive to environmental pollution control with policy guidance. Liu et al. (2014) also explained such a positive feedback cycle with the concept of productive force.

Over the past decade, guided by the environment-friendly mode for social development, the city has vigorously promoted resource conservation and pollution control to restore the various functions of ecosystems. In order to ensure the sustainable development of water resources and ecosystems, relevant policies for the discharge control indicators of the main sections of the mainstream of the Huaihe River have been formulated. Considering that the prefecture-level administrative region is an important unit of social–economic development and water resources management, it is significant to further formulate policies and regulations to restrict the discharge of the export sections of the prefecture-level cities, which would be conducive to the further development of the model. As seen in Figure 2(e), under the guidance of the relevant policies and depending on economic development and technological progress, the utilization rate of water resources has been decreasing year by year. Figure 2(f) indicates the degree of assurance for the instream ecological water requirement under the condition of the dry year, that is, the ratio of ecological water requirement to remaining instream water resources for different descriptions of flows. During the simulation period, the degree of assurance gradually increases with the decrease of water resource utilization rate, but the overall improvement degree is relatively small. This indicates that the recovery of various functions of ecosystems in the water system of Huainan City is relatively slow under the negative feedback loop dominated by a restorative force, which is consistent with the observation of Feng et al. (2016) on water supply, power generation and environment systems. They suggested that the degradation of ecosystems takes years and the recovery process could take decades. Furthermore, the current monitoring of ecosystems in various regions of China is still in its initial stage, and the basic data related to ecosystem function is relatively scarce, but its progress might be gradually accelerated. In order to more accurately formulate policies for the restoration of ecosystem functions, it is necessary to explore in future studies the linkages and feedback between water quantity, water quality and ecological indicators describing ecosystem state, such as biomass, density and diversity index.

CONCLUSION

This paper presents a water system model framework that describes the physical, human, and biological and biogeochemical components and their nexus. The coevolution of the nexus for Huainan City was simulated with a system dynamics model. By comparing the simulation results with the river basin planning, it is possible to test whether the development of the water system is consistent with the development direction and rate of government planning. The main driving factors for the evolution of the water system could be regarded as the sum of the positive feedback loop aimed at improving social productivity and the negative one aimed at ensuring the sustainability of natural resources. Among them, the technology and policy in the human components determine the utilization efficiency of resources and the speed of recovery of ecosystem functions, so both of them dominate the coevolution under the synergies of the two cycles.

Finally, the proposed water system model here possesses the ability to simulate the population growth, technological innovation and wealth accumulation mode. Therefore, the authors suppose this model framework can be used to simulate the coevolution of various coupled water systems. Against the background of different climates, political forms and economic developments, the model framework could be expanded according to specific research needs and used to study the interaction and feedback of the three categories of components in the water system. It is worth noting that with the increasing attention paid to the water demand contradiction between social–economic development and the ecosystems, the process of water resources management reform would continue to accelerate. More detailed regulations on water quantity and water quality in administrative districts at all levels would be gradually promulgated, and the collection and transmission of information on water resources and ecosystems would gradually be automated. Therefore, future studies should take these evolutions into account and adjust the model according to more detailed relevant data to improve the applicability of the model, which makes the collection and availability of data more critical.

ACKNOWLEDGEMENTS

This work was supported by the National Key Research and Development Program (during the 13th Five-year Plan) under Grant No. 2016YFC0401301, National Natural Science Foundation of China (Grant No. 41890823 and Grant No. 51809239), Ministry of Science and Technology, PRC, and the Major Science and Technology Program for Water Pollution Control and Treatment (No. 2017ZX07602-003).

SUPPLEMENTARY DATA

The Supplementary Data for this paper are available online at http://dx.doi.org/10.2166/ws.2019.121.

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Revue de l'Institut International de Statistique/Review of the International Statistical Institute
10
(
1–2
),
37
48
.

Supplementary data