An integrated modeling framework for coevolution and feedback loops of nexus across economy, ecology and food systems based on the sustainable development of water resources

Yaogeng Tan, Zengchuan Dong, Sandra M. Guzman, Xinkui Wang, Wei Yan 1. College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China 5 2. Department of Agricultural and Biological Engineering, Indian River Research and Education Center, University of Florida, Fort Pierce, FL 34945, United States. 3. School of Geographic Sciences, Xinyang Normal University, Xinyang, 464000, China Correspondence to Yaogeng Tan (170201010014@hhu.edu.cn) Abstract: Sustainable development in water resources is becoming a hot topic in recent years. The world is facing the 10 disequilibrium between the availability of resources and the increase in population with fast-growing economies and social development. This study proposes a new methodological framework of sustainable development of water resources based on the response linkages and feedback loops of economy-ecology-food (EEF) nexus. It provides a new way to identify the interconnection and coevolution process between these EEF. The multi-objective model and system dynamic (SD) model were coupled to characterize the interconnections between processes and their dynamic responses 15 to a set of scenarios. The combination of decomposition-coordination method (DC) and dynamic programming was used to find the optimal scenario based on each component of the EEF nexus. The Upper reach of Guijiang River Basin (UGRB) was presented as a case study. Results showed that the coupled multi-objective model and SD model presented in this study are able to characterize the interactions and feedback between EEF systems adequately. Most importantly, the rapid growth rate of socio-economic indexes will drive the awareness of river ecology and showed a higher sensitivity 20 under different decision preferences. The results provided in this study can provide baseline information for stakeholders and policymakers in the field of water management for a better understanding of the interactions across systems.


25
As global warming caused by climate change and growing population, the world is facing the disequilibrium between natural resources sustainability and human wellbeing (Zhang et al., 2018;Luo and Zuo, 2019;Bei et al., 2009;Yang et al., 2019). In many regions, anthropogenic activities have led to an enormous demand for natural resources, which may have a negative influence on future population development. Recently, there has been an increased interest in "sustainable development" because of its ambiguity and applicability in both local and global environments (Biggs et 30 al., 2015;Duan et al., 2019). The new targets of sustainable development aim to achieve sustainable uses of water resources, energy, and sustainable agricultural practices and promote inclusive economic development (United Nations, 2014). As the irreplaceable foundation of social development and environmental protection, water is one of the most critical natural resources and plays a vital role in socio-economic development and human production (Walter et al., 2012;Yang et al., 2018). 35 The concept of sustainable development was first presented in the World Conference on Environment and Development (WCED) (Brundtland, 1987). The goal of this conference was to discuss how to achieve a systematic development of the economy and environment, based on environmental resources protection. According to the assumption of sustainable development, the sustainable use of water resources needs population requirements, but not at the expense of finite sources of water (Lant, 2004). The core content of sustainable development of water resources is 40 https://doi.org/10.5194/hess-2020-328 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License. 3 computational modeling is often a powerful method to quantify the mutual effect of either WEF or other nexus in the 85 process of sustainable decision making. Some studies have proposed a comprehensive mathematical model for managing different resources and analyzing the inseparable interlinkages across WEF nexus over the years. The theory of Complex Adaptive System (CAS) is developed based on the systematic theory to tackle such problem as "nexus" is substantially a complex system (Holland, 1992). CAS consists of several adaptive agents that have their own goals and can change their behaviors to attain co-exist and best status by adaptive self-learning and "accumulate experiences" from external 90 changing environment. The Agent-based modeling (ABM) is also an effective approach for complex system model as each discrete and individual agent has different objectives and behaviors under different social backgrounds (Zhang et al., 2018;Macal and North, 2010). Multi-objective programming model is a promising tool to assess methodologies to achieve the goal of sustainable development as well as their subsystem nexus because adaptive process is substantially optimization among multiple objectives. For example, Li et al., (2019) developed an optimal model called Agricultural 95 Water-Energy-Food Sustainable Management (AWEFSM) to address the tradeoffs between water & land resources and energy to generate the environmentally friendly strategies and policies. Feng et al., (2016; developed a set of models considering water supply, environmental and power generation to produce a parallel development. Khan et al., (2017) addressed the impact of water management decision on water-energy-food-environment nexus on the basin scale by coupling SWAT and water system model through ABM framework. Considering systems nexus is mostly nonlinear, 100 advanced optimal programming is also used as part of the multi-objective programming. Some examples of advanced optimal programming include dynamic programming (Li et al., 2015), genetic algorithms (Chang and Chang, 2009;Bai et al.,2015), and decomposition-coordination programming (Jia et al., 2015;Tan et al., 2019). Furthermore, decision makers often need to find the optimal framework to achieve sustainable development by evaluating how each system and subsystem changes under external conditions, taking into account uncertainty in future scenarios (Wang et al., 2019). 105 According to Biggs et al., (2015) and Pahl-Wostl, (2019), the key procedure of achieving sustainable development in recent years is to develop nexus thinking, and the nexus components can include several of the following processes including water, energy, food, land, environment, ecology, economy, agriculture, etc. However, previous studies provide a limited discussion on the nexus between economy, ecology, food from a systematic perspective taking into account coevolution mechanisms to further advance into the goal of sustainable development. In this view, not only the multiple 110 processes and their mutual connections should be fully considered, but also coevolution and feedback should be investigated to further achieve sustainable development of water resources by assessing the tradeoffs across objectives.
In this study, we present a theoretical framework of water resources sustainable development based on economyecology-food (EEF) nexus, and implement model optimization to assess the tradeoffs among different scenarios to achieve the goal of each part of the EEF nexus. Then, the system dynamic (SD) model is established to evaluate the 115 endogenous dynamics and feedbacks across each objective of EEF nexus, and further evaluate the degree of sustainable development by setting up an evaluation index system based on each part of EEF nexus. The proposed integrated model is adopted to a case study in the Upper reaches of Guijiang River Basin, China. Results demonstrate how the integrated model and theoretical framework can provide useful information for the stakeholders to achieve sustainable development for water resources and provide insights for water resources management among different goals and its effect on human 120 lives.

Outline of EEF nexus and its main modules
The economic, ecological and food (EEF) influences on water resources sustainability were evaluated through the development of an EEF nexus model. The framework of sustainable development is divided into three modules: economy, 125 ecology and food, and their mutual relationship are shown in Fig.1. The three modules are intercorrelated, and the EEF https://doi.org/10.5194/hess-2020-328 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License.
4 nexus motivates policymakers to analyze tradeoffs between different processes or objectives and further adjusts the optimal development mode. Arrows represent the outputs of each module, which indicates the level of impact in sustainable water development. Food and economic module attain their own target by development and controlling water resources that supply water to ensure social activities and food safety. At once it is also indispensable for ecological 130 module that maintains ecological functions, which restricts the appliance to both economic and food module. Therefore, optimal allocation is processed to take into account each module to attain sustainable development of water resources (See 2.2). Each module contains three submodules or subsystems that are interconnected based on the module goal.

Sustainable development of water resources
Economic module

Economic module
This module is used to determine the socio-economic and water interactions, including water withdrawal, usage, consumption and drainage (Luo and Zuo, 2019). It should be noted that social element is included in this module because the relationship between society and economy is usually inseparable. From the water supply perspective, it also supplies water for social (household) use. The household and industrial water demand are presented as follows: 140 where WDhou and WDindus are the annual household and industrial (including secondary and tertiary) water demand (m 3 ), N is population size, d is the days of a certain year and r is the natural growth rate, IGDP is the industrial added value (10 4  145 Yuan), qhou and qindus are the domestic and industrial water usage quota, which means daily water consumption per person (L/person/day) and water consumption of the industrial added value per 10 4 Yuan (m 3 /10 4 Yuan), respectively. The population equation presented in Eq.(1c) is a simple linear differential model called Malthusian growth model (Jørgensen and Bendoricchio, 2001;Feng et al., 2016), and GDP size is also suitable for this model. The population size changes are based on the assumption of the socio-hydrological system (See below). The objective of this module is to minimize 150 the water shortage of both human's live and industrial production, and is the necessary condition to make the maximum carrying capacity (description shown in Section 2.3.1) of population and GDP. The main variables index list is shown in Appendix A, including the model variables presented afterwards. Many researchers conceived the coevolution process of socio-hydrological system, including "Taiji-Tire model" (Liu et al., 2014), "community sensitivity model" (Elshafei et al., 2014) and "pendulum swing model" ( Van et al., 2014;155 Kandasamy et al., 2014). The social development is at the expense of sacrificing the environment, and the "pendulum model" is therefore addressed based on different development stages over the past years and adapted in Australia. Kandasamy et al., (2014) stressed that the term "pendulum swing" refers to the shift in the balance of water utilization between economic development and environmental protection. The agricultural-based society is at the beginning of the evolution, and the environmental problems have not emerged in this stage. As water resources benefit to both agricultural 160 and socio-economic development with massive government policy support and investment, the whole society's demand for resources has intensified due to the sharp growth of population as a result of increased irrigation area and agricultural productivity, and furthermore, the environment will be significantly damaged, which can be regarded as the pendulum "swings" towards the economic development. When environmental awareness is on the rise, the government will invest more in ecology, resulting in a declining population. In this case, more water is used to protect the environment, reflecting 165 that the pendulum has "swung" back to the environment.

Ecological module
(1) Ecological water demand for vegetation Ecological water demand of vegetation is used to maintain the physiological function of canopies, including photosynthesis, respiration and evapotranspiration. The method of evaluating the amount of vegetation ecological 170 demand is based on their evapotranspiration that can be treated as the water gap (Shi et al., 2016;Saxton et al., 1986): where WDveg is the vegetation water demand. ET0 is potential evapotranspiration based on the Penman-Monteith 175 equation, and the particular variables can be seen in Neitsch et al., (2011). Ks and Kc are soil moisture and canopy coefficients, respectively, which denotes the ratio of maximum water demand and potential evapotranspiration. S, Sc and Sw are the coefficient of actual, wilting and critical soil moisture, respectively. Pe is effective precipitation and is calculated based on the following (Döll and Siebert., 2002): where P is actual precipitation.
(2) River ecological demand River ecological demand is the instream water demand that is used to maintain river health and function. Its health degree can be reflected by the annual proportional flow deviation (APFD) that is used to assess the diversity of fish species (Gehrke et al., 1995). However, it is computationally unstable when the monthly streamflow is near zero (Yin et 185 al., 2010). In this study, we use the amended indicator, AAPFD, to assess the river ecological demand (Ladson and White, 1999): where Q and QN are the actual and natural streamflow. The subscript n, m and j are the total year number, mth month, and jth year. According to Ladson and White, (1999), the smaller deviation suggests the better river ecology, which is 190 reflected by smaller AAPFD, and the value of AAPFD ranges from zero to five. When the value is larger than five, the river ecosystem will be seriously damaged (Yin et al., 2010;Tan et al., 2019). Therefore, the goal of evaluating the river ecological demand is to find a suitable Q to make AAPFD minimum.
(3) Sewage water The water cycle from the socio-economic module in Fig.1 includes the water discharge as one of the outputs. This 195 water can be reused for water supply in other processes especially for socioeconomics, and make more efficient water treatment and use of recycled water. The total amount of recycled water resources is expressed by: where α and β are sewage water drainage coefficient and sewage water treatment rate, respectively. The subscript 1 and 2 is household and industrial water usage. ζ is the utilization rate of recycled water. 200

Food module
The food module is mostly related to agricultural water usage, including crop water requirements based on phenological stages and farm management including livestock production. For crops, water usage is related to crop yield. https://doi.org/10.5194/hess-2020-328 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License.
The main water supply is provided by irrigation. We use the crop coefficient method to estimate crop water demand based on the Food and Agricultural Organization report No. 56 (FAO-56) (Allen et al., 1998). For each crop, its growth 205 process can be separated into several stages that have the different potential crop water demands (Allen et al., 1998;Smilovic et al., 2016): where WP is potential crop water demand, and can also be called reference crop demand of crop i, Kc(t) is the crop 210 coefficient of stage t for a specific crop, t0 and tn is the first and last stage of the growth process of a specific crop. Wa is the irrigation water demand. The maximum crop yield is based on the hypothesis that the crop water supply (including precipitation) can meet Wp (Allen et al., 1998). According to FAO-56, crop growth is usually divided into four phenological stages: initial, development, middle and end, and corresponds to three different crop coefficients: Kc,ini, Kc,mid and Kc,end. For details, see Allen et al., (1998). For each crop, the crop yield is presented as follow (Smilovic et al.,215 2016): where Ws,t is the actual irrigation water supply for crop i at time t, Ys and Yp is the crop yield under actual and ideal condition (both irrigation water supply Ws and precipitation Pe can meet the crop water demand Wp), Ky,t is yield response factor of the crop i at time t. Due to the limitation of local water resources conditions, crop water supply is usually equal 220 to or less than crop water demand. That is, (Ws+Pe)≤Wp, and crop water supply is greatly related to crop yield. The value of Ys/Yp is also equal to or less than one, and it takes the "=" sign when the crop yield attains the maximum. In this case, the water supply also attains the maximum. For meat production, it is reflected by the production of livestock (pork and beef) and poultry (chicken, duck and goose). The calculation of water usage of livestock is the same as Eq.(1a) and here N and q are the total livestock 225 population and its corresponding water use. The production of livestock and poultry can be solved by linear regressive calculation based on local statistical yearbooks and water resources bulletin over the historical years : where YL is the production of a certain livestock (10 4 t) and WL is the actual water use of a certain livestock (10 4 m 3 ), aL and bL are primary coefficient and constant term of the stock-water production function. 230

Model conceptualization
The framework of sustainable development theory presented in Fig.1 is of great significance by applying it in a specific region or watershed. For example, in a water system inside a watershed or a region, there are multiple water supply projects within which water users are interconnected. This system in a watershed is called a "large water resources 235 system" (Fig.2a). It is subdivided into multiple sub-watershed or subregions that are called "subsystems" (Fig.2b). In this case, reservoirs can provide not only socio-economic developments but also environmental impacts. They are constructed across the rivers to supply water for the whole region or watershed but are also most likely to cause negative impacts on the natural streamflow of rivers, which will deteriorate the instream ecological environment (Yin et al., 2010;2011;Yu et al., 2017). Therefore, reservoirs should be considered individually to target the river ecology concerns. 240 https://doi.org/10.5194/hess-2020-328 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License. To fully consider the river ecological health, the whole system is separated into subsystems that contain one individual reservoir and its several corresponding water recipient areas ( Fig.2b) as there is usually more than one reservoir in a certain region. We call these subsystems as "reservoir supply subsystem". A subsystem can be further 245 separated into the smallest unit: a reservoir and each water recipient region (or called "subarea") ( Fig.2c). In this view, the total system of sustainable development of water resources in a certain region (watershed) can be divided into several subsystems or subareas that consist of a three-level hierarchical structure. According to the theoretical framework of sustainable development of EEF presented in Section 2.1, each module has their own goals, and they can be distributed to each subarea (with the objective of food, socio-economy and vegetation) and reservoir (river ecology) (Fig.3). 250 Therefore, we can coordinate these objectives to achieve sustainable development by setting up multi-objective optimal model. (1) Economic module The objective function is presented based on each component of the EEF nexus. The goal of the economic module is aiming at increasing revenue of secondary and tertiary industries, as well as maintaining human wellbeing. It can be reflected by the minimum household and industrial shortage and is expressed by the following normalized nonlinear equation: 260 https://doi.org/10.5194/hess-2020-328 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License.
where Fecnmy is the objective function of economic module. WS and WD is total water demand (including household and industry) and supply (including reservoir and other water projects) of this module. T is the total number of the time step. Subscript k and t are the number of subarea and time step, respectively.
(2) Ecological module 265 Economic development should not be excessive because it may be at the expense of the damaging ecological environment, which is inconsistent with the concept of sustainable development. Similar to maintaining human wellbeing and increasing the revenue of industries, water resources support is also indispensable for maintaining the physiological function of vegetation and river health. The objective of the ecological module is reflected by maintaining both aspects. It should be noted that for recycled water usage, it is acted as the part of the water supply (WS) for economic module. 270 The expression of objective function for ecological module is as follows: where Feclgy is the objective function of ecological module, and 2 , , where the subscript "veg" and "riv" represents vegetation and river ecology. According to Ladson and White (1999), the value of AAPFD ranges from zero to five. Here, we divided it by 5 to normalize AAPFD and make it range from zero to one. Meanwhile, Feclgy is also normalized by getting the average of Fveg and Friv.
(3) Food module The goal of the food module is to maximize food production and is the indispensable condition of increase primary 280 industry products and maintain human wellbeing. The mathematical expression is presented as follow: where N and L are the total number of crops and livestock, respectively.

Tradeoffs between objectives
According to Eq.(6), crop production is directly related to irrigation water (FAO, 2012;Liu et al., 2002;Lyu et al., 2020), and the production of livestock is also in proportion to its water usage (see Eq. (7)). Therefore, the maximum supply of crop and livestock water demand is the most critical condition to get the maximum crop yield or meat 290 production. Therefore, the normalized objective of food module can be rewritten as: where WSfood and WDfood are the irrigation or livestock water supply & demand. Similarly, the maximum satisfaction of industrial and household water demand can get the maximum profit and revenue as well as human wellbeing, which is the same as the minimum water shortage. The same also applies to vegetation water. 295 As can be seen in objective functions, three benefits are set minimum (Eqs. (8)(9a)(11)), which may contribute to the conflict between objectives, especially ecology and economy. The tradeoffs across EEF nexus can be reflected by Pareto frontier that can describe a set of non-dominated optimal solutions that any one of these three objectives are unable to be improved unless sacrificing other objectives (Reddy and Kumar, 2007;Feng et al., 2019;Beh et al., 2015;Burke and Kendall., 2014). To overcome this problem, three major methods are used to generate Pareto frontiers: 300 evolutionary algorithms (Reddy and Kumar., 2007), ε-constraint method (Haimes et al., 1971) and weighted-sum method (Marler et al., 2009;Burke and Kendall., 2014). Considering the continuous curve of Pareto frontiers is tough to be obtained by ε-constraint method, and coverage of local optima is often prone to obtained with evolutionary algorithms (Liu et al., 2011;Burke and Kendall, 2014), the weighted-sum method is adopted in this study.
We can reclassify all the water users from each of the three modules into two categories: Instream and off-stream 305 water users (Hong et al., 2016). River ecological water demand (see Section 2.1.2) can be regarded as an instream water user and all others can be regarded as off-stream water users. Therefore, according to the objective function expressed by Eqs. (8), (9) and (11), the weighted objective function can be rewritten by: ( ) where (Fecmny+Fveg+Ffood) is off-stream water users, and Friv is the instream water users. The subscript j is the index of 310 the off-stream water users, respectively. j=1,2,3 represents socio-economic, food and vegetation water usage, which corresponds to the subscript "ecnmy", "eclgy" and "food". α and θ are weight factors and  12) is Pareto-optimal because of the positive weights and concave objectives, and the non-dominated sorting process is used to find the optimal solution of Eq.(12) because the characteristic of either concave or convex is difficult to be proven (Marler and Arora., 2009;Feng et al., 2019;315 Goicoechea et al., 1982;Zadeh, 1963). For each given combination set of α and θ, the optimal solution can be attained by decomposition and coordination (DC) principle and dynamic programming (DP) (see Section 2.2.5).
The tradeoff across objectives is reflected in the values of multiple sets of weighting factors ( ) revealing different decision makers' preferences. Considering that the contradictions also occur in off-stream water users, the balanced priority should be addressed to give consideration for each off-stream water users (Casadei et al., 2016), 320 that is, α1=α2=α3. Therefore, the tradeoff and decision preference between instream and off-stream is reflected by the different value of θ (0≤θ≤1). The larger value of θ represents more concerns about river ecology. In this study, the parameter θ is initially set as 0.5 to give an equal consideration of both instream and off-stream water usage, and different levels of θ can affect the performance of EEF nexus and are used to assess the sensibility and uncertainty of the model (see Section 3.3.5). 325 https://doi.org/10.5194/hess-2020-328 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License.

Constraints
The model constraints include the connection of subsystems, the water balance equation, and the upper and lower limits. The details are found in Supplementary material S1 in Appendix B.

model solution
The EEF model of water resources sustainability is a compound system that is classified into multiple hieratical 330 structures (Fig.3). Therefore, the model solution of this structure should be solved by systematical analysis techniques, such as Dantzig-wolfe decomposition technique (Deeb and Shahidehpour, 1990), Generalized Bender Decomposition (Rabiee and Parniani., 2013), aggregation-decomposition (AD) (Tan et al., 2017) and decomposition-coordination (DC) (Li et al., 2015;Jia et al., 2015). Considering DC method can reduce the system dimension to save computing time, and optimization order among each subsystem is arbitrary, this study uses DC method to solve this sophisticated model. The 335 total procedure of both DC and DP is provided in Supplementary materials S2 in Appendix B.

Coevolution mechanism for each component of EEF nexus
Water resources provide the resources support for agriculture (food module), industry (economy module) and environment (ecology module). These components can, respectively, provide the crops and meat to ensure food security, 340 making profit, and make human and nature co-exist harmoniously. The mutual relations among the three components of an EEF nexus determines the coevolution process (Feng et al., 2016). According to the framework of EEF nexus presented in section 2.1, the coevolution and responses of EEF nexus is shown in Fig.4. As shown in Fig.4, the socioeconomic development, along with the population and GDP size, will undoubtedly increase (Biggs et al., 2015;Duan et al., 2019), which will be reflected in an increase in water demand (I). However, the 345 ecosystem will be damaged due to the volume of water that is going to supply those increased population needs (II). Therefore, the optimization model presented in this study can provide information to coordinate the nexus between systems, provide a water allocation scheme based on each module's water requirements, and maintain the ecological health of rivers and freshwater sources (III). The population and GDP growth rate are unable to increase infinitely because regional water resources are usually unable to carry a continuously exponential growing population size and 350 GDP. We call this term as "carrying capacity" that is used to describe the rate of socioeconomical development under certain water resources conditions Wu et al., 2018). It is determined by the amount of actual water supply and allocation in a certain year. The carrying capacity can reflect the development status of a region and can inversely affect the predicted socioeconomic indexes (IV). It can give references for policymakers for urban comprehensive planning and can influence the process of coevolution and feedback of EEF nexus (V). In this study, we 355 use the concept of "overload index" to illustrate the relationship between carrying capacity and predicted economic index (mainly for population and GDP) and is expressed as follow: where OI, PI, CI is the overload index, predicted economic indicator and carrying economic indicator (i.e. carrying capacity). The overload index can be classified into five levels based on the value of OI and shown in Table 1. This 360 feedback loop indicated that the rapid growth of the economy would deteriorate ecological health because the limited water resources in a certain area cannot afford the increasing socio-economy. Additionally, ecological health is an indispensable element of sustainable development. It will further decrease the carrying capacity, and the socio-economy will, therefore, be negatively influenced, stimulating the policymakers to readjust the scale of socio-economy. Another feedback of the EEF nexus is reflected by the ecology-food nexus. Agricultural water is the largest water consumer and is deeply affected by rainfall and potential evapotranspiration. According to Allen et al., (1998), more evapotranspiration will cause more agricultural water demand (VII), and water supply pressure from water projects will 370 increase subsequently. However, if the rainfall increases, there will be less water supply pressure. Otherwise, the increased water supply from reservoirs will alternate the natural flow, which will deteriorate the river's ecological health and drive the optimal model to adjust the water allocation scheme (VII-II-III). Afterward, the agricultural water supply will affect food production (VI), which is similar to the effect that economy-ecology nexus reflects. However, the socioeconomical changes would also indirectly affect the food system and more than just rainfall and evapotranspiration, i.e., 375 the changes of economic concern will also drive the optimal model described in this study and further influences the food production (I-II-III-VI). Besides crop production, stock farming is another source of food for meat production and is also affected by this economy-ecology linkage. It should be noted that as food system is the indispensable component for human lives, the food production will directly affect the changes of carrying population (VIII) and subsequently affects the feedback loop of economy-ecology (I-II-III), further starting the new loop of whole EEF nexus. 380 From Fig.4, we can see that each component EEF nexus interacts mutually and are reciprocal causation. They are interconnected by the changes in water supply and demand system. To reflect the complicated and detailed relationships and feedbacks based on Fig.4, system dynamic model (SD) (Forrester and Warfield., 1971) is presented in this study. It is a well-established system simulation method for visualizing, understanding and analyzing complicated dynamic feedback systems that exhibit nonlinear, multi-feedback and time-varying properties . It can embody 385 the framework of the detailed EEF nexus modules and can be seen as the detail and extension of the general framework of sustainable development (Fig.1). The detailed mutual relationships of each variable are shown in Supplementary materials S3 in Appendix B.

Sustainable development degree (SDD) assessment
The EEF nexus is a complex system with all ecological, economic and food systems, or modules as we called in 390 this study, affecting water resources. A proper EEF balance provides resource support to achieve sustainable development. Therefore, the three modules should be considered to evaluate the sustainable development degree. We selected the indicators listed in Table 2 based on the three modules and are used to evaluate the impact of sustainable development. The property (+, -) of indicators denotes positive and negative indicators, respectively. The positive (negative) 395 indicators mean they have positive (negative) impacts on the corresponding module and were termed as a development (constraint) index . Considering the ranges of indicators listed in Table 2 are different, they should be normalized before evaluation. The positive and negative indicators normalization is shown by Eq.(14a) and (14b). where xij and yij is the original and normalized indicator j in sample i, and m is the total number of samples. Then, the entropy weight method is adopted to calculate SDD, which calculates the information entropy of indicators that reflects their relative change degree on the whole system (Wang et al., 2019). The information entropy of indicator j in sample i is expressed by: where n is the total number of indicators in a certain module. The SDD is calculated based on the coupling coordination degree (Sun and Cui, 2018) that reflects the degree of 410 coordination of various factors or subsystems. In this study, SDD is calculated based on the coordination of three modules (EEF) and expressed by:  where ECNMY(t), ECLGY(t) and FOOD(t) are the coordination degree of economy, ecology and food module, respectively. P, Q, R is the total indicator number in economy, ecology and food module.

Research framework
Based on the framework of sustainable development of water resources and the above methodology, the achievement of sustainability of water resources is solved by coupling multiple objective optimal model and SD model 420 of EEF nexus in the whole process in this research. According to the outline of the EEF nexus, reservoirs are of relatively high robustness for ecological module, while rainfall and evapotranspiration are also indispensable for crop yield equation of food module and development level of socio-economy is also of great significance in economic module. Hence, they should be clarified before implementing the EEF nexus model. The development level of socio-economy is reflected by the population size and GDP. The observed monthly historical streamflow data, precipitation and 425 temperature can be regarded as the ensemble of reservoir inflow predictions, areal precipitation and potential evapotranspiration in the near future, respectively (Feng et al., 2019). That is, for a certain year in the future, streamflow data of historical decades can be treated as all the possible reservoir inflows, while precipitation and temperature data of the same time scale can be utilized as the input of crop yield equation for all possible hydrological frequencies. It should be noted that reservoir construction would change the natural streamflow regime and the statistics after construction 430 would be inconsistent with those before construction. Therefore, the streamflow data period after construction should be "restored" to keep consistent with those before construction. The details of restoring methods can be found in Deng et al., (2015). All the optimization results, including water supply and demand, food production, objective functions, can https://doi.org/10.5194/hess-2020-328 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License.
16 be obtained to reflect the operational decisions for average level within a particular year. The whole research procedure is shown as follows: 435 First, initialize the EEF nexus model. The parameter of the model includes reservoir storage, the water recession rate from previous sub-area, initial streamflow release from reservoir(s), hydrological data (rainfall and evapotranspiration), recycled water usage rate and predicted socio-economic index for each horizon year (initial parameter settings are shown in Table 3).
Second, start the optimal model within each horizon year by using the decomposition-coordination principle and 440 dynamic programming. If the optimal water allocation scheme for each year is generated, go to the next step. Otherwise, repeat this step (Section 2.2). Finally, the optimal solution is used to drive the system dynamic model and simulate the trajectories of corresponding variables of EEF nexus (including objective functions in the optimal model, streamflow water, carrying capacity, food production) and evaluate the coordinative degree of each module and SDD (Section 2.3). 445

A brief description of study area
Guijiang River Basin (GRB) is one of the most imperative branch basins of the Xijiang River Basin (XRB) in South China. XRB belongs to the typical karst area and is the second-largest river basin in China in terms of total runoff and also the third largest river basin in terms of total area. The names of the mainstream of XRB are Nanpan River, Hongshui 450 River, and Xijiang River in the upper, middle and lower stream, respectively. Yujiang, Liujiang and Guijiang are the main branch river of XRB (see Fig.5). The upper reach of Guijiang River Basin (UGRB) (24°6'~25°55'N, 110°~111°20'E) is selected as a case study as it represents the highly conflicts between socioeconomic growth and ecological protection in karst areas. Furthermore, reservoirs are widely constructed in UGRB to supply water for socioeconomy but are likely to deteriorate the river ecological health by alternating natural flow (Yin et al., 2010;2011). 455 UGRB is also a karst area with a total area of 13,131 km 2 , with a total population of about three million people. Also, UGRB has a total crop planting area of about 2,400 km 2 , a total vegetation area of about 3,700 km 2 , and yearly average precipitation of about 1600mm. UGRB is located in Guilin City and refers to eight administrative regions (or counties). Seven reservoirs are constructed in UGRB to provide water resources support for maintaining the development of socioeconomy. The detailed parameters of seven reservoirs and their three-level hieratical structure including subareas are 460 found in Supplementary material S4 in Appendix B. Guilin city is both heavy industrial city and national major tourist city, and the population and economic development will keep rapidly increasing in the near future. It will exacerbate the conflicts between social development, food safety and environmental protection especially for that of river ecological environment, resulting in severe ecological deterioration of the lower Guijiang River basin and even lower XRB. Therefore, how to achieve coordination and sustainable development in UGRB between these aspects is becoming a 465 challenging problem in upcoming years and is necessary to be solved.

Datasets and parameter initialization
Datasets of the case study include socio-economic, water use, land use, meteorological and hydrological data. The 470 major source of socio-economic data, including population and GDP, are the statistical yearbooks of both Guilin City and Guangxi autonomous region from 2005-2014 (http://data.cnki.net). The Municipal Government of Guilin City (MGGC) predicted population and GDP till 2040, along with per capita water use that is from the water industry standard of the People's Republic of China, to predict the water demand of economic module (Venkatesan et al., 2011). The growth rate is based on these predictions and shown in Table 3. The sharply increased rate occurred in the second stage, which 475 corresponds to the era that "heavy government policy support and investment" and "population grow rapidly" as what Kandasamy et al. (2014) stressed in "pendulum model" (see Section 2.1.1). The growth rate from 2031 to 2040 is lower compared with that from 2021 to 2030, which corresponding to the era of "remediation and emergence of the environmental customer" as stated in Kandasamy et al., (2014). Water use data include historical water usage and total water amount found in Guilin water resources bulletin (2005~2014). Land use data contain the spatial distribution of 480 crops and vegetations with a resolution of 1km×1km that can be found in the Resource and Environment Data Cloud Platform, China Academy of Sciences (REDCP-CAS) (http://www.resdc.cn). Meteorological data from 1956 to 2013, including daily average wind speed, sunshine duration, maximum and minimum temperature, relative humidity and precipitation, are found in meteorological stations (http://data.cma.cn) and are used to calculate ET0 and effective precipitation that is the main input of crop production equation. The hydrological data from 1958 to 2013 include the 485 monthly inflow of each reservoir and can be found in hydrological stations. All the initialized parameters are list in Table  3, and the total index of the data sources can be found in Supplementary materials S5 in Appendix B.

Results and discussion
The proposed theoretical model is implemented in this case study to acquire the coevolution mechanism and https://doi.org/10.5194/hess-2020-328 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License.
18 response link of the EEF nexus. Time scale is divided into three stages: 2016~2020, 2021~2030 and 2031~2040, which 490 correspond to different states of the "pendulum model" addressed by Kandasamy et al. (2014). The proposed study area is also an integrated water resources system with seven reservoirs and eight subareas and can be separated into several subsystems based on section 2.2.1. The detailed conceptualization model of UGRB is presented in Supplementary material S4.

SD model calibration and validation
The historical data was used in the model for calibration and validation by comparing simulated and historical results. Some parameters, including sewage water treatment rate, water drainage coefficient, the utilization rate of recycled water, should be calibrated before validation and is also shown in Table 3. The yearly comparison of simulated and historical household & industrial, agricultural and off-stream vegetation water use is shown in Table 4. They are 500 corresponding to the economic, food and ecology module of EEF nexus model. We can see that simulation results of the SD model are well matched with the actual values, with the relative error of less than ±5%, indicating that the proposed model is reliable and can simulate the future coevolution process.

Coevolution process of EEF nexus 505
The coevolution trajectories of population, GDP, water supply & demand, streamflow and objective function (Fecnmy, Feclgy, Ffood) (based on Eq.(8),(9),(10)) referring to each component of the EEF nexus is shown in Fig.6. As can be seen in Fig.6, the coevolution process of all the items shows the characteristics of different stages. Finally, the (quasi-)stable state is converged, i.e., the variations of each variable are small or close to zero. It happens because the rate of external changes in the last stage (i.e., economic indexes) is much lower than in the previous stage, which decreases the internal 510 changes (i.e., Streamflow water and three objective functions) and finally the stable status of the whole system is achieved. In the first stage, the growth rate is relatively low and is based on the historical data, and the growth rate of Fecnmy, Feclgy and Ffood is also slow. When entering the second stage, the economic growth will increase sharply to ensure the local economic development, and water demand is also increasing. However, according to the achievement of sustainable development based on the optimal model, ecological concerns should not be neglected. Therefore, the 515 increase of river streamflow will also happen driven by the optimal model to maintain the river ecological health, https://doi.org/10.5194/hess-2020-328 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License. 20 consequently reducing the total water supply and increasing the water shortage of water users (Fig.6c). As Ffood and Fecnmy can reflect the water shortage of the corresponding water users, their value will also increase sharply ( Fig.6e and  6g) due to the rapid increase of socio-economic indexes. When entering the last stage, the development of socio-economy will tend to stable, and the increasing speed of Ffood and Fecnmy will decrease compared with that in the second stage. It 520 is easy to understand because the relatively stable development of socio-economy does not need too much increased streamflow water (the increase rate of streamflow water is also closed to a relatively stable state), and both changing rates of water supply and demand tend to be stable consequently (Fig.6c).
We can also see that the water supply system competes for the instream ecological system. As shown in Fig.6, especially in stage 2, increased streamflow is accompanied by increased Fecnmy and Ffood ( Fig.6e and 6g), reflecting the 525 decreased satisfaction degree of the water supply of socio-economy and agriculture, thereby revealing the competition use of instream and off-stream water uses. The trade-off between instream and off-stream water users can be obtained by the optimal model to solve for the best coordination status between them by adjusting economic development modes and balance the priority of each water users. It should be noted that the ecological objective (Feclgy) is in a relatively stable status in all stages compared with other objectives (Fig.6f). This is because the ecological module contains not 530 only river streamflow but also vegetation. The booming economy drives the optimal model to focus more on river ecological health (Friv) and there are limited water resources for off-stream water users including vegetation. The dual effect of increasing streamflow water and decreasing water for vegetation makes the Feclgy relatively stable. However, the optimal model takes the effect that the optimal allocation scheme is obtained by shifting streamflow water because instream and off-stream water use is intrinsically conflicted with each other, and should be coordinated by adjusting 535 different weights of each component (see section 3.3.5). Fig.7 illustrated the loop of economy-ecology feedback. As demonstrated in Fig.7, the response linkage of carrying 540 capacity and overload index involves the changes of economic indexes, water supply & demand and streamflow water (Feng et al., 2019). In the beginning, the economy is still increasing slowly, and the increasing rate of water demand is also slow. The population and GDP are near the carrying capacity in this stage (i.e., the value of OI is near 1). In the following stage, both increasing population and GDP intensify the water demand ( Fig.7a and b). To satisfy socioeconomic development demands, water supply of economic module has also increased. However, according to the 545 coevolution of the whole system obtained by optimal model, there will be a higher concern of the river ecological system https://doi.org/10.5194/hess-2020-328 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License. 22 (Fig.6c, Fig.7c). In this view, the feedback linkage will take effect as that the growing rate of water supply of household and industry (Fig.7d) will fail to catch the rate of water demand (Fig.7b) and therefore contributes to the increase of water shortage, which is in accordance with the performance shown in Fig.6e. The increasing water shortage will generate the gap between carrying capacity (Fig.7e) and predicted economic indexes (Fig.7a). Then, the overload index 550 will further increase, consequently affecting the socio-economic development. It will force the local policymakers to readjust the regional development level and influence the population and GDP, indicating a new round of feedback. In this view, we can see that the rapid growth of economy in the second stage will activate the protection mechanism of river ecology by increasing the streamflow, and the rest water is unable to support the increasing economic development.

Performances of feedback loops and response linkages
It further contributes to the overload of the water resources system, which even restricts the socio-economy instead. In 555 the last stage, the continuous increase of the overload index stimulates the policymakers to alleviate the increase rate of population and GDP ( Fig.7a and f). It forces the relatively slower increase rate of streamflow water and there will be more water space for socio-economic development. Although the water shortage is increasing, its rate is lower than that in the second stage. The carrying capacity will be able to catch the predicted economic index if the stable or slower growth rate continues. The overload index is also decreased and the whole system tends to be stable. 560 Another performance is the ecology-food response linkage and is shown in Fig.8. It not only illustrated the linkage between food and ecological water usage but also demonstrated the coevolution of ecology components of both instream (river ecology) and off-stream (vegetation) aspects. We can see from Fig.8 that the increased streamflow water 565 is the driving force of ecology-food response. However, the increasing streamflow water was driven by the rapidly increasing socio-economic scale. The optimal model is used to achieve the goal of sustainable development to balance the need of different users, especially that of instream and off-stream. The increased streamflow has two effects in ecology-food response linkage. First, the variable Friv describes the ecological health of a certain river. According to Eq.
(3) and Eq.(9c), the higher value of streamflow water indicates the lower value of Friv, which indicates that the river 570 ecology is getting better. Second, the increasing streamflow water restricts the water supply of all off-stream water users, including agricultural and vegetation water (Fig.8b). Irrigation and vegetation water use is the largest off-stream water consumer, and their increased water shortage was also driven by increased streamflow water (Fig.8d). It should be noted that the food module includes not only crops but also livestock. Livestock breeding will inevitably increase to https://doi.org/10.5194/hess-2020-328 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License.
24 make more production value of primary industry, and there will consequently be more water demand for livestock. 575 The dual effect of increased streamflow water and decreased vegetation water makes the stable change of Feclgy (Fig.8e), indicating that the ecological aspect of UGRB is maintaining a good status. According to Eq.(6), crop yield is strongly affected by the satisfaction degree of irrigation water, and the increased water shortage of crop water will, 580 therefore, indicate the decrease of crop yields (Fig.8f). In contrast, the decreased water shortage of livestock could induce an increase in meat production. The detailed changes of crop yield and meat production are presented in Fig.9.
We can see from Fig.9 that a relatively large proportion of food production is from crop yield. Although meat production is increasing, it accounts for relatively less proportion, and thereby the total food production will first decrease and then tend to be stable in the last stage (Fig.9c). Besides, the decreased food production is driven by the increased streamflow 585 water that also caused an increasing overload index (Fig.7f) especially in the second stage. Thus, we can infer that the decreased food production may also indirectly increase overload index, and is verified by the demonstration of https://doi.org/10.5194/hess-2020-328 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License. 25 comparison between Fig.9c and Fig.7f in the second stage. Simultaneously, it is clear that the relatively stable changing rate of food production occurred in the last stage (Fig.9c), accompanied by the decreased overload index in the same period (Fig.7f). This is the economy-food response linkage that takes effect as the higher socioeconomic growing rate 590 will have an adverse effect on food safety, further affecting the carrying capacity. Therefore, the linkage of economyfood, economy-ecology and ecology-food were all presented, which indicated that the three components interact and respond with each other.

Assessment of coordinative degree of each subsystem and SDD
The calculation result of SDD of EEF nexus and coordination degree of economy (ECNMY), ecology (ECLGY) and food is demonstrated in Fig.10. We can see that the variation of the four variables is also showing the state characteristics. The ECNMY in the first stage is increasing, but it had an either decreasing (UGRB, Guilin urban area, Lingui, etc.) or stable (Xing'an, Yangshuo) trend in the second stage, indicating the coordinative status of socio-economy 600 is not good caused by the excessive growth rate of economy. The decreased coordinative status of economy subsystem also influences other subsystems and the SDD of total EEF nexus, reflected by the decrease of ECLGY, FOOD, and further SDD. Fortunately, the decreasing rate of ECLGY is smoother compared with that of FOOD, indicating the performance of ecology of UGRB is relative well compared with socioeconomics and agriculture. This performance could be due to the dual effect of increasing streamflow water, sewage and recycled water treatment, and decreasing 605 vegetation irrigation. The same was true for other administrative regions of UGRB. Moreover, for the whole basin, the value of ECNMY in the later period of the second stage (about 2028~2030) is even lower than FOOD and ECLGY, From the perspective of administrative regions, it is more obvious in Guilin urban area, Pingle and Lipu counties. It happens because the economic-stressed stage has been last almost ten years in 2030, which is similar to the "pendulum model" that takes the effect that the pendulum "swing" towards the economic-stressed system (See 2.1.1). As socio-economic 610 index increases sharply and continuously, the ecological protection mechanism will also be continuously triggered to increase the overload index, resulting in both ECNMY and SDD reached the minimum. When it comes to the third stage, the value of ECNMY increases, indicating the coordination of the economic subsystem is improving. It revealed the decreasing of overload index and the increasing carrying capacity, due to the relatively slower increasing rate of water demand of economic module. The increasing value of ECNMY even promotes 615 the coordinative degree of ecology and food, and the value of SDD is consequently increased, revealing that the stable economic growth will promote the sustainable development of EEF nexus. The good phenomenon of the last stage happens because the relatively slow growth rate of water demand for the economic module will generate more water for food and ecology, and the increasing sewage and recycled water treatment rate will provide relatively more water for users. The coevolution process is based on the assumption of the "pendulum model" presented by Van et al., (2014) and 620 Kandasamy et al., (2014), where the environmental awareness has raised, and stable population rate occurred in the last era. The result presented in this study is similar to the findings in Van et al., (2014) and Kandasamy et al., (2014). Furthermore, we can speculate that in the 2040s, the pendulum of ULRB will also "swung" back to the stage of protective

Sensitivity analysis of decision preferences considering weight uncertainty
In the current study, the optimal decisions over the years were obtained by optimal model. Each water user is set equal to take into account each stakeholder to fully achieve the sustainable development. However, due to the internal conditions of different regions and preferences of policymakers, the weight of each component is usually different and 630 difficult to be determined since the equal weight for each water users for sustainable development may not applicable in every regions or watersheds, which is one of the most important sources of uncertainties. Since the most contradictory among water users is the conflict between instream river ecology and off-stream water users (Homa et al., 2005;Yin et al., 2010;Shiau and Wu, 2013;Rheinheimer et al., 2016), the uncertainty is mainly embedded in different values of θ (See Eq.(12c)) that reflects the priority of streamflow water, which is also the main variables of coevolution process. The 635 results of uncertainty and sensitivity analysis is shown in Fig.11. According to Eq.(12), the more value of θ is, the more concern of instream water uses. As demonstrated in Fig.11, 640 the coordination degree of each component and their sustainable development (SDD) shows the different sensibilities from stage perspective, especially that of ECNMY(t), FOOD(t) and SDD. We can see that these three variables under the different value of θ in the first two stages are sensitive, but they converge to a similar trend in the last stage. That is, the difference of these variables under different value of θ in the last stage is small compared with that in the second stage, indicating that the decision preference is sensitive to θ when the growth rate of socio-economic index is 645 exceptionally high, while the trajectories of these valuables are insensitive to θ when the growth rate of population size and GDP are relatively stable.
When it comes to ECLGY(t), it shows no apparent sensitivities because the ecological module contains river and vegetation ecology that belong to the instream and off-stream water use category. However, the different weight of streamflow water θ gives the guideline for ecological stakeholders. The higher value of θ indicates a lower value of 650 vegetation weight (α3) (See Eq.(12)) as they are of different categories (instream and off-stream) and conflict with each other. Although they both belong to ecological water usage, they also should be coordinated through different weighting factors (θ and α3). The deeper concern of streamflow water should be attracted (with a higher value of θ of 2/3) in 2020s to increase ECLGY as off-stream water users are increasing dramatically. In comparison, off-stream water demands tend to be stable in 2030s and vegetation concern can be moderately increased (with a lower value of θ of 1/2) to increase the 655 value of ECLGY. However, the shallow value of θ (1/3 or 1/4) cannot perform the best for ecological module as streamflow water cannot be allocated to an extremely low weight. The balance of both ecological water usage is still needed. In addition, of all these four assessment variables, the trend in the second stage is decreasing while it is increasing in the last stage, showing that the relatively stable growth of socio-economy promotes the coordination of each component and the sustainable development among EEF nexus, instead of dramatical growth. 660 As different values of θ can influence the performance of EEF nexus especially in the second stage in which higher sensitivity shows, the result can also give a reference to policymakers for tradeoffs of more than just ecological stakeholders. We can see that in the stage on which the higher emphasis of the economy was put (2020s), if the ecological awareness was still neglected (θ=1/3 or 1/4), there will be less coordination degree of economy (ECNMY) and food (FOOD) as well as SDD (Fig.11a,b and d). Therefore, the tradeoffs between instream and off-stream water usage should 665 be fulfilled to achieve the coordination and sustainable development, i.e., in the stage to which the economic aspect is paid high attention, the weight of river ecology should be inversely set higher in the objective function of the optimal model to achieve the relative equilibrium between instream and off-stream water uses. To prove, we can see that the performance of ECNMY(t), FOOD(t) and SDD is better under θ=2/3 or 1/2 compared with the condition when θ=1/3 or 1/4. But the performance of coordination and sustainable development would no longer be that sensitive when the 670 economic growth rate is stable. The preference of θ also influences the objective functions of the EEF nexus model. As can be seen from Fig.11e~11g, a higher value of θ results in lower Fecnmy and Ffood and higher Feclgy, indicating the smaller water shortage of economic and food modules and less awareness of ecology, and vice versa. However, only by evaluating the objective functions is too one-sided to reveal the interaction of EEF nexus and cannot give a comprehensive reference for water 675 resources management. It should still be couple with the coordination degree and SDD to give the reference for policymakers on the full scale.

Conclusion
In this study, we incorporated the coevolution process between EEF nexus systems by coupling a theoretical framework with a system dynamic model. The coevolution model contributes to explore the dynamic changes of each 680 system as well as the status of sustainable development of water resources within the EEF nexus framework. The multiple objective model is used to obtain the optimal water allocation scheme of each system, while system dynamic model is used to explore the dynamic coevolution process and response linkages, as well as sustainable development degrees across these components. The coupled model was applied in the upper reaches of Guijiang River Basin, China, and the sensitivity and uncertainty analysis are also conducted to better understand the model performance. The following 685 conclusions can be drawn from this study: (1) The coupling models can efficiently reveal the water allocation scheme, coevolution process, optimal decisions and tradeoffs under the changing external conditions. The feedback loops and response linkages (including economyecology, economy-food and ecology-food) can be mathematically expressed, providing a powerful tool for better understanding the constitutive linkages and properties of EEF nexus. 690 (2) The changes of socio-economic indexes will result in the shifting in behaviors of the optimal water allocation scheme, i.e., the rapid socioeconomic development will raise the awareness of environmental protection, reflected by the increasing of reservoir streamflow, and further influences the dynamic performances and coevolution of other components. The excessive socioeconomical development will trigger the ecological protection mechanism, further increasing water shortage, and decreasing food production. Furthermore, these changes will increase the population 695 vulnerability and overload index, which will also vulnerable to sustainable development degree, and ultimately have a https://doi.org/10.5194/hess-2020-328 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License. 29 bad impact on the coupled system instead. Once the socioeconomical growth rate is stable, the coordination and sustainable development degree of the whole system will be improved.
(3) Sensitivity and uncertainty analysis revealed that different preferences can influence the coevolution process and the status of coordination and sustainable development. Its performance is sensitive to the awareness of reservoir 700 streamflow when the growth rate of socio-economy is extremely high. In this case, more emphasis of streamflow should be put on to improve the coordination of each component and sustainable development across the subsystems. The coordination and sustainable development degree are insensitive to the reservoir streamflow under the lower growth rate of socio-economy. The proposed model is adopted in a case study in a typical karst area in South China, and the results present in this 705 study can give powerful references for decision makers to identify the coordinated management and assess comprehensive plans. The theoretical framework and methodology presented in this study are suitable for any other watersheds and regions that contain reservoirs, especially for areas with prominent conflicts between multiple water users. Although this study attempts to present a new framework of economy-ecology-food nexus, there is still room for improvement. For example, sustainable development also contains energy, land use, climate change and other aspects, 710 which consequently increases the dimension of the model and more complicated approaches might be introduced to obtain the optimal solutions. Moreover, the sources of uncertainties not only contain the conflicts between instream and off-stream water usages but also the usages within off-stream, probably reflected by the different structures of industries, which will also be our further works of the future research.