A system dynamic model to quantify the impacts of water resources allocation on water–energy–food–society (WEFS) nexus

. Sustainable management of the water–energy– food (WEF) nexus remains an urgent challenge, as interactions between WEF and human sensitivity and reservoir operation in the water system are typically neglected. This study proposes a new approach for modeling the WEF nexus by incorporating human sensitivity and reservoir operation into the system. The co-evolution behaviors of the nexus across water, energy, food, and society (WEFS) were simulated using the system dynamic model. Reservoir operation was simulated to determine the water supply for energy and food systems by the Interactive River–Aquifer Simulation water resources allocation model. Shortage rates for water, energy, and food resulting from the simulations were used to qualify their impacts on the WEFS nexus through environmental awareness in society. Human sensitivity indicated by environmental awareness can then adjust the co-evolution behaviors of the WEFS nexus through feedback loops. The proposed approach was applied to the mid–lower reaches of the Hanjiang River basin in China as a case study. Results indicate that environmental awareness shows the potential to capture human sensitivity to shortages from water, energy, and food systems. Parameters related to boundary conditions


Introduction
Water, energy, and food are indispensable resources for sustainable development of society.With the growing population, urbanization, globalization, and economic development, the expected global demands for water, food, and energy in 2030 resources management by incorporating both physical and social processes.However, potential threats to WEF security exist, as few of the current studies have simultaneously considered the impacts of reservoir operation in water system on the integrated system.
Reservoirs can adjust the uneven temporal and spatial distribution of available water resources and can ensure water supply to reduce water shortage (Khare et al., 2007;Liu et al., 2019;Zeng et al., 2021;He et al., 2022).However, the available water resources are typically adopted under historical natural water flow scenarios, while reservoirs are seldom considered, or their operational rules are significantly simplified in the WEF nexus.The assessment of water supply security based on the WEF nexus should be improved.Thus, additional details regarding the reservoir operation should be incorporated into the simulation of the WEF nexus.
The water resources allocation model can simultaneously incorporate reservoir operation and water acquisition, and it has become an effective tool to quantitatively assess the impacts of reservoir operation on water supply security, as well as WEF security (Si et al., 2019;Zhou et al., 2019).Our study aims to establish a system dynamic model for the water-energy-foodsociety (WEFS) nexus and assess the impacts of reservoir operation on the WEFS nexus by integrating the water resources allocation model into the integrated system.The reminder of this paper is organized as follows: Section 2 introduces the framework for modeling the WEFS nexus and assessing the impacts of water resources allocation on the WEFS nexus.
Section 3 describes the methodologies applied in the mid-lower reaches of the Hanjiang river basin in China, which is the study area.Section 4 presents the results of the co-evolution process and the sensitivity analysis of the WEFS nexus.The impacts of water resources allocation on the WEFS nexus have also been discussed.The conclusions of this study are presented in Section 5.

Methods
System dynamic modeling (SDM) simulates the dynamics among different systems using nonlinear ordinary differential equations and dynamic feedback loops (Wolstenholme and Coyle, 1983;Swanson, 2002).SDM has become an efficient approach to facilitate the integrated analysis of sectors, processes, and interrelations among different system variables (Di Baldassarre et al., 2015;Simonovic, 2002).The SDM for assessing the WEFS nexus comprises four modules (shown in Figure 1): water system module, energy system module, food system module, and society system module.
In the water system module, socioeconomic water demand (i.e., municipal, rural, industrial, and agricultural water demand) and in-stream water demand are projected using the quota method and Tennant method (Tennant, 1976), respectively.The water demands and available water resources are further inputted into the water resources allocation model to determine the water supply and water shortage for every water use sector in each operational zone.The water supply for socioeconomic water use sectors and agricultural water shortage rates as outputs from the water system module are taken as the inputs of the energy system module and food system module to determine the energy consumption and food production, respectively.
Considering the outputs of the energy and food system modules, the energy and food shortages can be estimated by comparing the planning energy availability and target food production, respectively.The function of the society module is to capture human sensitivity to degradation in the WEF nexus (Elshafei et al., 2014).Environmental awareness is considered as the conceptual social state variable to indicate human sensitivity (Van Emmerik et al., 2014).Environmental awareness is composed of water shortage awareness, energy shortage awareness, and food shortage awareness that are determined by 100 shortages of water, energy, and food, respectively.As environmental awareness accumulates over its critical value, negative feedback on socioeconomic sectors (i.e., population, GDP, and crop area) will be triggered to constrain the increases in water demand, and further energy consumption, and food production to sustain the WEFS nexus.

Water Demand Projection
Water user comprises socioeconomic (also called off-stream) user and in-stream user.Socioeconomic water users can be classified into municipal, rural, industrial, and agricultural sectors.The quota method has been considered an efficient approach to project the annual socioeconomic water demand (Brekke et al., 2002).The amount of water demand for the socioeconomic users can be estimated using equation (1).

WD i,j
t =WQ i,j t *A i,j t /U i,j t , ( where WD i,j t is the amount of water demand for the j-th user in the i-th operational zone in the t-th year; WQ i,j t denotes the water use quota unit of water user; A i,j t is the amount of water units of water user; and U i,j t represents the utilization rate of water user.The water quota units represent the amount of water consumption per capita in municipal and rural users, the amount of water consumption per ten thousand Yuan in industrial user, and the amount of net irrigation water per unit area in agricultural user, respectively.The amount of water units represents the projected population in municipal and rural users, projected GDP in industrial user, and projected irrigated area in agricultural user. As population, GDP, crop area, and water use quota are prerequisites for water demand projection, the dynamic equations for these socioeconomic variables should be pre-determined.There are two types of methods which are popular in socioeconomic projection, Malthusian model (Bertalanffy, 1976;Malthus, 1798) and Logistic model (Law et al., 2003), which are adopted for the socioeconomic projection.The growth rate in original Malthusian model is constant (Malthus, 1798), which is not consistent with previous studies that the socioeconomic expansion in the future would slow down (He et al., 2017;Lin et al., 2016).Therefore, we used exponential terms to simulate the evolution of socioeconomic variables, which increases with decreasing rate.And feedback functions, as well as environmental carrying capacities (indicating the maximum socioeconomic size that can be carried by the system) of socioeconomic variables are adopted to constrain the evolution of these socioeconomic variables through equations ( 2)-(4) (Feng et al., 2016;Hritonenko and Yatsenko, 1999).
Socioeconomic factors in original Logistic model (Law et al., 2003) are prone to approach to their environmental carrying capacities, while the constrains among subsystems in WEFS nexus are typically neglected, which will lead over-sized socioeconomic projection.Therefore, feedback functions taken as constraints from subsystems are adopted in equation ( 5)-( 7) (Li et al., 2019;Wu et al., 2022).
)+f 1 (E)) , ( 5) where Nt, Gt, and CAt are the population, GDP, and crop area in the t-th year, respectively; Ncap, Gcap, and CAcap denote the environmental carrying capacities of population, GDP, and crop area, respectively; rP, 0, rG, 0, and rCA, 0 represent the growth rates of population, GDP, and crop area from historical observed data, respectively; rP, t, rG, t, and rCA, t are the growth rates of population, GDP, and crop area in the t-th year, respectively; κP*exp (-φPt), κG*exp (-φGt), and κCA*exp (-φCAt) are used to depict the impacts of social development on the evolution of population, GDP, and crop area, respectively; E is environmental awareness; FA is food shortage awareness; and f1, f2, and f3 represent the feedback functions.The equations for E, FA, and feedback functions are described in detail in Sections 2.4 and 2.5.
Water use quotas are also assumed to decrease with the social development owing to the expansion economy (Blanke et al., 2007;Hsiao et al., 2007).As the difficulties in saving water by technological advancement are increasing, the changing rate of water use quota is decreasing in equation ( 8) (Feng et al., 2019).
where WQ i,j t denotes the water use quota of the j-th water user in the i-th operational zone in the t-th year; rqwu, 0 and rqwu, t are the growth rates of water use quotas from historical observed data and t-th year, respectively; WQ i,j min is the minimum value of water use quotas; and κqwu*exp (-φqwut) is used to depict the water-saving effect of social development on the evolution of water use quota.

Water Resources Allocation
Based on water availability and projected water demand, available water resources can be deployed to every water use sector and in-stream water flows using a water resources allocation model.The Interactive River-Aquifer Simulation (IRAS) model is a rule-based water system simulation model developed by Cornell University (Loucks, 2002;Zeng et al., 2021;Matrosov et al., 2011).The year is divided into user-defined time step, and each time step is broken into user-defined sub-time step, based on which water resources allocation conducts.The IRAS model was adopted for water resources allocation owing to its flexibility and accuracy in water system simulations.
As water system comprises water transfer, consumption, and loss components, it is typically delineated by node network topology for the application of the water resources allocation model.Reservoir nodes and demand nodes are the most important elements in the node network topology, as they directly correspond to the processes of water supply, acquisition, and consumption.The water shortage at the demand node should first be determined based on its water demand and total water supply.The total water supply comprises natural water inflow (i.e., local water availability) and water supply from reservoir.In each sub-time step (except the first), the average natural water inflow in the previous sts-1 sub-time steps is estimated as the projected natural water inflow in the remaining sub-time steps using equation ( 9).The water shortage can then be determined by deducting the demand reduction, total real-time water inflow, and projected natural water inflow from water demand using equation (10).The total water shortage rate can then be determined using equation (11).
WE i,j sts =( 1 sts-1 WTSup i, j sts -1 sts-1 WRSup i, j sts )* (Tsts-sts+1) (sts-1) , ( 9) where ts is the current time step; Tsts denotes the total number of the sub-time steps; sts is the current sub-time step; WE i,j sts represents the projected natural water inflow for the j-th water use sector in the i-th operational zone; WTSup i, j sts is the total water supply; WRSup i, j sts is the water supply from reservoir; WD i,j ts is the water demand; fred is the demand reduction factor; WS i,j sts is the water shortage; WS i,j t and WD i,j t are the total water shortage and water demand in the t-th year, respectively; and WSR t is the total water shortage rate.
The water shortage at the demand node requires water release from the corresponding reservoir nodes according to their hydrological connections.The amount of water released from the reservoir depends on the water availability for demanddriven reservoirs and operational rules for supply-driven reservoirs, respectively.The water release for the supply-driven reservoir is linearly interpolated based on Figure 2 and equations ( 12)-( 18).Additional details on the IRAS model can be found in Matrosov et al. (2011).
q t =q min t *(1-P v )+q max where t, t1, and t2 are the current time, initial time, and end time in the period, respectively; Pt denotes the ratio of current time length to period length; , and V min e represent the maximum and minimum storages at the current time, beginning, and ending of the period, respectively; q max t , q min t , q max b , q min b , q max e , and q min e denote the maximum and minimum releases, respectively; Pv is the ratio of current storage; and qt is the current release.

Energy System Module
The energy system module focuses on the energy consumption during the water supply process for socioeconomic water users to further investigate the energy co-benefits of water resources allocation schemes (Zhao et al., 2020;Smith et al., 2016).Energy consumption for water heating and water end-use was not included in this study.Energy consumption is determined by the energy use quota and amount of water supply for the water use sectors (Smith et al., 2016).As energy use efficiency will be gradually improved with social development, the energy use quota is assumed to decrease with decreasing rate.The trajectory of the energy use is formulated in equation ( 19).The water supply for water use sectors derived from the water system module is used to estimate energy consumption using equation ( 20).The energy shortage rate will be further determined with planning energy availability using equation (21).
where EQ i,j t is the energy use quotas of the j-th water user in the i-th operational zone in the t-th year; re, 0 and re, t denote the growth rates of energy use quotas from historical observed data and the t-th year, respectively; EQ i,j min is the minimum value of energy use quotas; κe*exp(-φet) depicts the energy-saving effect of social development; ECt is the total energy consumption; WTSup i,j t is the total water supply of the j-th water user in the i-th operational zone; ESt and ESRt are the energy shortage and energy shortage rate, respectively; and PEAt is the planning energy availability.

Food System Module
The food system module focuses on estimating the amount of food production.As water is a crucial determinant for crop yield, the agricultural water shortage rate can constrain the potential crop yield (French and Schultz, 1984;Lobell et al., 2009).Owing to the technological advancements in irrigation, the amount of potential crop yield is assumed to increase with decreasing rate, as indicated by equation ( 22).With the target food production which has considered the local and exported food demands of basin, the food shortage rate can then be estimated using equations ( 23) and ( 24).
where CY i,j t is the potential crop yields of the j-th crop in the i-th operational zone in the t-th year; rpro, 0 and rpro, t are the growth rates of crop yields from historical observed data and the t-th year, respectively; κpro*exp(-φprot) depicts the impacts of social development on the evolution of crop yield; FPt denotes the total food production; CA i,j t is the crop area; WSR i,4 t represents the water shortage rate of agriculture sector; FSt and FSRt are the food shortage and food shortage rate, respectively; and TFPt is the target food production.

Society System Module
The society system module is deployed to simulate the social process of the integrated system.Environmental awareness and community sensitivity are two primary terms of social state variables in socio-hydrologic modeling that indicate the perceived level of threat to a community's quality of life (Roobavannan et al., 2018).Environmental awareness describes societal perceptions of environmental degradation within the prevailing value systems (Feng et al., 2019;Feng et al., 2016;Roobavannan et al., 2018;Van Emmerik et al., 2014).Community sensitivity indicates people's attitudes towards not only the environmental control, but also the environmental restoration (Chen et al., 2016;Elshafei et al., 2014;Roobavannan et al., 2018).As this study focuses on societal perceptions on environmental degradation, environmental awareness based on the concept described in Van Emmerik et al. ( 2014) was adopted as the social state variable.As water, energy, and food systems are considered part of the environment in this study, environmental awareness is assumed to be determined by the shortage rates of water, energy, and food.Environmental awareness accumulates when the shortage rates of water, energy, and food exceed the given critical values, but decreases otherwise.The dynamics of environmental awareness can be described by equations ( 25)-( 28).
where E, WA, EA, and FA are environmental awareness, water shortage awareness, energy shortage awareness, and food shortage awareness, respectively; WSR, ESR, and FSR denote the shortage rates of water, energy, and food, respectively; WSRcrit, ESRcrit, and FSRcrit represent the corresponding critical values of shortage rates, above which environmental deterioration can be perceived; ηW, ηE, and ηF are the perception factors describing the community's ability to identify threats of degradation; θW, θE, and θF are the auxiliary factors for environmental awareness accumulation; and ωW, ωE, and ωF denote the lapse factors that represent the decreasing rate of the shortage awareness of water, energy, and food, respectively.

Respond Links
Respond links are used to link society and water system modules through feedback.Environmental awareness increases with constant shortages in water, energy, and food.As environmental awareness accumulates above its critical value, negative feedback on socioeconomic factors is triggered (Figure 1).The growth of population, GDP, and crop area will be constrained to alleviate the stress on the integrated system.Notably, positive feedback on the expansion of crop area will be triggered to fill food shortage as food shortage awareness exceeds its critical value (Figure 1).Although food shortage awareness is part of environmental awareness, the negative feedback driven by environmental awareness on crop area can only be triggered with the prerequisite that food shortage awareness is below its threshold value, as food production should first be assured.The respond links deployed by assuming feedback functions are expressed in equations ( 29)-( 31).
where 3 Case Study

Study Area
The Hanjiang river is the longest tributary of the Yangtze river.The total area of the Hanjiang river basin is 159,000 km 2 , divided into upper and mid-lower reaches covering 95,200 and 63,800 km 2 , respectively (shown in Figure 3).The Danjiangkou reservoir is located at the upper boundary of the mid-lower reaches of the Hanjiang river basin (MLHRB) and serves as the water source for the middle route of the South-North water transfer project in China.Thus, the water availability in the MLHRB is remarkably affected by the reservoir operation.In terms of energy, as the population is large and the industry is developed in the MLHRB, the energy consumption for urban water supply is high.For agriculture, as the land is flat and fertile, MLHRB is considered an important grain-producing area, occupying one of the nine major commodity grain bases in China (i.e., Jianghan plain) (Xu et al., 2019).However, owing to population expansion, rapid urbanization, and economic development, the local demand for water, energy, and food is increasing enormously (Zeng et al., 2021;Zhang et al., 2018).The contradictions between increasing demand and limited resources will be intensified.Therefore, improving use efficiencies for water, energy and food in MLHRB is urgent (Zhang et al., 2018;Liu et al., 2019).The strictest water resources control system for water resources management policy, the total quantity control of water consumed policy, and the energy-saving and emission-reduction policy in China are implemented in the MLHRB to promote the expansion of resource-saving technology and further improve the resource use efficiencies in water, energy, and food systems.Therefore, the impacts of human activities on the WEF nexus should be assessed to sustain the collaborative development of the integrated system.
The socioeconomic data (i.e., population, GDP, and crop area) for water demand projection were collected based on administrative units, whereas the hydrological data were typically collected based on river basins.To ensure that the socioeconomic and hydrological data are consistent in operational zones, the study area was divided into 28 operational zones based on the superimposition of administrative units and sub-basins.Seventeen existing medium or large size reservoirs (the total storage volume is 37.3 billion m 3 ) were considered to regulate water flows.Based on the water connections between operational zones and river systems, the study area is shown in Figure 4, including 2 water transfer projects (the South-North and Changjiang-Hanjiang water transfer projects), 17 reservoirs, and 28 operational zones.

Data Sources
There are two main types of data: hydrological and socioeconomic data.(i.e., P = 50%, 75%, 90%, and 95% are related to the wet, normal, dry, extreme dry years), were adopted to simplify agricultural water demand series.These historical data were further used to predict the future trajectories of the WEFS nexus.

Results and Discussion
The SDM was applied to the MLHRB.Specifically, water availability from 1956 to 2016 was adopted as the future water availability, while dynamic water demand was projected in water system module, both of which were inputted into water resources allocation model.As the water resources allocation model in the water system module took a monthly time step in the study (and the sub-time step was the default value: 1 day), the annual water supply and water shortage were first 315 determined before being outputted to the energy system and food system modules, respectively.The annual shortage rates of water, energy, and food were then used to determine environmental awareness and further the feedback.Table 1 lists the initial settings of the external variables for the integrated system.The co-evolutionary behaviors of the WEFS nexus were analyzed as follows: (1) the system dynamic model was calibrated using observed data, (2) co-evolution of the WEFS nexus was then interpreted and analyzed, (3) the impacts of environmental awareness feedback and water resources allocation on 320 the WEFS nexus were discussed, and (4) sensitivity analysis for WEFS nexus was tested.a ECC indicates the environmental carrying capacity.b As the primary source of water supply for agricultural use in the study area is surface water, rather than groundwater, the energy consumption in the water supply process for agricultural water use is negligible, and the energy use quota for agricultural water use is set as 0.

Model Calibration
As some parameters are adopted as auxiliary parameters, which are not equipped with exactly physical definitions, there is no independent empirical data to calibrate them.Therefore, by reviewing previous studies (Feng et al., 2019;Feng et al., 2016;Van Emmerik et al., 2014) and expert knowledge, we evaluated the order of magnitudes and rational boundaries for these parameters.An initial parameter sensitivity analysis was then adopted to screen out the insensitive parameter, which provided distinguishing 13 insensitive and 21 sensitive parameters.As the insensitive parameters are not able to remarkably alter the system, the empirical values in previous studies (Feng et al., 2019;Feng et al., 2016) were adopted.The sensitive parameters in the model were then calibrated based on the observed data, and the calibrated values are presented in Table S2 in supplementary file.The Nash-Sutcliffe Efficiency (NSE) coefficient and percentage bias (PBIAS) (Krause et al., 2005;Nash and Sutcliffe, 1970) were used to calibrate the model.When the NSE was >0.7 and absolute value of PBIAS was <15%, the modeling performance was considered reliable.The simulated state variables, including annual water demand, energy consumption, food production, population, GDP, and crop area, were compared with their observed values during 2010-  Substantial studies indicate that environmental awareness is considered as an important factor in modelling socioeconomic decisions and policies for water, energy and food systems (Li et al., 2019;Li et al., 2021;Lian et al., 2018;Rockson et al., 2013;Xiong et al., 2016).For instance, Xiong et al. (2016) investigated the evolution newspaper coverage of water issues in was the primary target of China before 2000.With the conflict between water demand and supply being intensified, concerns about water security arisen in the newspaper since 2000, which indicated that environmental awareness towards water shortage emerged.Related policies (e.g., the strictest water resources control system for water resources management policy in China) were thereby implemented to constrain the over-speed socioeconomic expansion and further ensure water security.

As shown in
Therefore, the established model still has potential to simulate the co-evolution of WEFS nexus.

Co-evolution of WEFS Nexus
The calibrated system dynamic model was used to examine the properties of the integrated system by simulating the coevolution of state variables in the WEFS nexus.

375
Based on the trajectory of environmental awareness, the co-evolution processes of water demand and energy consumption in Malthusian model were divided into four phases: expansion, contraction, recession, and recovery, which was consistent with the results in Feng et al. (2016) and Elshafei et al. (2014).. Food production was divided into five phases based on the trajectory of food shortage awareness: accelerating expansion, natural expansion, contraction, recession, and recovery.The four phases in the co-evolution process for water demand and energy consumption can be interpreted as follows.
With environmental awareness below its critical value, the negative feedback on socioeconomic sectors is not triggered, and water demand, as well as energy consumption, increases rapidly, which is defined as expansion phase (2010-2032).In the beginning of co-evolution, the water and energy demands can be satisfied by water and energy availability.The shortage rates of water and energy were typically below their critical values (Figure 5 (h)), and thus, shortage awareness of water and energy remained at a low level as shown in Figure 5 (i).Despite food shortage struck the system in the beginning, the shortage rate of which was 0.153 and more than its critical value 0.05, the environmental awareness led by food shortage awareness was still within its critical value 8.0.Therefore, environmental awareness feedback wasn't triggered to constrain socioeconomic sectors, and water demand, as well as energy consumption, thereby keeps increasing.
As environmental awareness exceeds its critical value, negative feedback on socioeconomic sectors is triggered, and water demand and energy consumption is constrained, which is defined as contraction phase ( 2033 As environmental awareness accumulates to the maximum value, water demand, and energy consumption decrease significantly, which is defined as recession phase (2040-2045).Environmental awareness feedback indeed constrained water demand and energy consumption, which decreased but still exceeded local water and energy carrying capacities.Therefore, as the shortage rates of water and energy remained exceeding their critical values (Figure 5 (h)), environmental awareness continued accumulating and reached the maximum value of 13.2 at the end of the recession phase, thereby decreasing water demand and energy consumption.
As environmental awareness gradually decreases below its critical value, water demand and energy consumption decrease slightly and then tend to stabilize, which is defined as recovery phase .With continuous decline of socioeconomic sectors, water demand and energy consumption gradually decreased within their carrying capacities.The shortage rates of water and energy have then decreased to below their critical values since 2047, resulting in the decreases in water shortage awareness and energy shortage awareness (Figure 5 (h) and (i)).As the environmental awareness decreased below its critical value, negative feedback was removed, and the integrated system tended to stabilize.
The co-evolution process of food production can be interpreted in the similar way.It's worth noting that the accelerating expansion phase (2010-2022) is unique for food production.As the food production cannot satisfy the target value in the beginning of co-evolution, food shortage emerged and led the increase of food shortage awareness (Figure 5 (h), and (i)).
With food shortage awareness increasing over its critical value, positive feedback on crop area was triggered, and further accelerated the increase of food production.
For Logistic model, socioeconomic sectors kept increasing in the initial phase.The rapid socioeconomic expansion was slowed down until the negative feedback driven by environmental awareness was triggered.With the increasing environmental awareness, socioeconomic recession was followed.Since the decreasing socioeconomic sectors were much lower than their environmental capacities and feedback driven by environmental awareness was weakening, the variables turned to increase again to approach to their environmental capacities, and rolled in cycles.
One of the major differences between results of Malthusian model and Logistic model is that state variable evolution in logistic model fluctuates remarkably and performs periodicity.However, it's worth noting that the socioeconomic expansion in the future will slow down and tend to stabilization (He et al., 2017;Lin et al., 2016), the growth rate of which will thereby decrease as time goes.Moreover, the economic development in the study area is also expected to gradually grow and then remains stable according to the Integrated Water Resources Planning of Hanjiang River Basin (CWRC, 2016).As the periodic fluctuation for WEFS nexus evolution through Logistic model is not consistent with the slowed socioeconomic expansion in foreseeable future and cannot fitly satisfy the planning in the study area, Logistic model is not adopted.
Malthusian model can fitly meet the demand mentioned above, which is thereby applied for further analysis on WEFS nexus in our study.

Impacts of Environmental Awareness Feedback and Water Resources Allocation on WEFS Nexus
To determine the potential impacts of environmental awareness feedback and water resources allocation on the WEFS nexus, four scenarios were set, the description of which is provided in Table 3.The Ecrit and FAcrit under scenario Ⅱ were set as 10,000 to ensure that the feedback cannot be triggered in the study, and the WSRcrit in scenarios Ⅲ and Ⅳ were set as 0.15 to avoid the explosion of water shortage awareness.The other parameters in scenarios II, III, and IV were consistent with the calibrated values of scenario I, as listed in Table S2.Scenarios I and II and scenarios III and IV were used to investigate the impacts of environmental awareness feedback and water resources allocation on the WEFS nexus, respectively.The average annual values of water demand, energy consumption, food production, and shortage rates for water, energy, and food are listed in Table 4. Figure 6 shows the trajectories of key state variables of the integrated system, including water demand; energy consumption; food production; shortage rates for water, energy, and food; awareness of water shortage, energy shortage, and food shortage; and environmental awareness.

WEFS Nexus Response to Environmental Awareness Feedback
Environmental awareness indicates societal perceptions of resources shortages and is the driving factor of feedback on socioeconomic sectors.Both the average annual water demand and energy consumption increased from 16.94 billion m 3 and 1,710 million t under scenario Ⅰ to 17.66 billion m 3 and 1,930 million t under scenario Ⅱ, respectively, as environmental awareness feedback was removed, whereas the food production decreased slightly, from 6,519 million t to 6,248 million t.
Specifically, owing to high food shortage in the accelerating expansion phase of food production, the positive feedback on crop area was triggered by food shortage awareness to accelerate the increase in crop area.Food production was thus evidently larger when feedback was considered in Figure 6 (c).Food shortage was then alleviated, and the average shortage rate decreased from 1.74% to 1.07%.The increasing crop area meanwhile led to an increase in agricultural water demand (Figure 6 (a)).However, as the increasing water demand remained within the carrying capacity, little difference in the water shortage rate existed between scenarios I and II (i.e., 7.03% and 7.44%, respectively).As the water supply was efficiently ensured, the impacts on urban water supply and the corresponding energy consumption were negligible.As water demand and energy consumption increased rapidly in the expansion phase, environmental awareness increased remarkably owing to the constant water and energy shortages, as shown in Figure 6 (d) and (f).Negative feedback was triggered to constrain the socioeconomic expansion.Compared with scenario Ⅱ, water demand and energy consumption decreased remarkably under scenario Ⅰ.The stress on water and energy supplies was thus relieved, particularly for the energy system, the shortage rate of which decreased from 17.16% to 5.80%.Therefore, environmental awareness can efficiently capture resources shortages and regulate the pace of socioeconomic expansion through feedback, which can maintain the integrated system from constant resources shortages to sustain the concordant development of the WEFS nexus.

WEFS Nexus Response to Water Resources Allocation
Water is considered the major driving factor for the WEFS nexus.Rational water resources management plays an important role in the sustainable development of the WEFS nexus.Water resources allocation can regulate the water flow by reservoir operation, which is considered one of the most effective tools for water resources management.Based on the Integrated Water Resources Planning of Hanjiang River Basin (CWRC, 2016), domesticity and ecology water uses should be ensured first.The priorities for water use from high to low are municipal and rural domesticity, in-stream ecology, and industrial and agricultural sectors, respectively.The average annual water demand, supply, and shortage under scenarios III and IV are listed in Table 5.Despite the increase in water demand from 14,359 to 17,286 million m 3 under scenario Ⅲ, the water supply also increased from 12,077 to 16,042 million m 3 .The total water shortage rate decreased from 15.89% to 7.20% owing to rational water resources allocation.As more available water resources can be stored in the flood season and then released in the dry season through reservoir operation, the uneven temporal and spatial distributions of available water resources were remarkably relieved, thereby increasing the water supply insurance.For water use sectors, water shortages were primarily found in industrial and agricultural sectors (719 and 399 million m 3 , respectively), and other sectors can be satisfied under scenario Ⅲ.
Water shortage became more serious under scenario IV, as the water shortage rates of these five sectors increased significantly in Table 5, from 0.24%, 0.23%, 11.05%, 6.21%, and 3.29% to 8.67%, 8.69%, 21.26%, 15.80%, and 12.34%, respectively.To analyze the spatial distribution of water shortage rates, Figure 7 shows the water shortage rate in each operational zone under scenarios III and IV.The water shortage rates of the study area under scenario Ⅳ were evidently higher than those under scenario Ⅲ, particularly for the operational zones located at the basin boundaries (e.g., operational zones Z1, Z2, Z8, Z12, Z13, Z21 and so on).As the boundary zones are far away from the mainstream of the Hanjiang river and their local water availability is unevenly distributed, the regulating capacity of the water system is limited and is not sufficiently strong to ensure the water supply.For the co-evolution of WEFS nexus, a remarkable decrease in the average annual water demand and energy consumption was observed as water resources allocation was removed from 17.29 billion m 3 and 1,761 million t under scenario Ⅲ to 14.36 billion m 3 and 884 million t under scenario Ⅳ, while the food production also decreased slightly from 6,638 million t to 6,344 million t.Under scenario Ⅳ without considering water resources allocation, the average water shortage rate was 15.89%, exceeding the critical value.Water shortage awareness continued to accumulate (Figure 6 (g)).As the water supply could not be effectively ensured and remained at a low level, the energy consumption for urban water supply was small and always within its planning value.No energy shortage awareness was accumulated at the beginning of the co-evolution shown in Figure 6 (g).Meanwhile, as agricultural water demand cannot be ensured, food production was also lowered (Figure 6 (c)).
Higher food shortages then led to higher food shortage awareness (Figure 6 (e), and (g)).Thus, positive feedback to increase crop area was strengthened.As observed in Figure 6 (a) and (c), the water demand increased slightly and food production increased rapidly.As environmental awareness accumulated over its critical value in 2015 and continued to increase, negative feedback to constrain the socioeconomic expansion was triggered and continued to strengthen.The energy consumption thereby continued to decrease in Figure 6 (b), accounting for the significant decrease in the energy shortage rate (i.e., from 8.25% to 0).Environmental awareness increased and reached the maximum value of 21.6 in 2032 owing to the constant water shortage.With the strong negative feedback, the water demand and food production decreased remarkably and remained at a low level, as shown in Figure 6 (a) and (c), which accounts for the increasing food shortage rate (i.e., from 1.08% to 3.08%).
With water resources allocation taken into account, water shortage was significantly alleviated under scenario Ⅳ, as discussed in the water resources allocation results (from 15.89% scenario Ⅳ to 7.20% under scenario Ⅲ).The water shortage rate remained below its critical value in the entire co-evolution process (Figure 6 (e)).Thus, there was no accumulation of water shortage awareness shown in Figure 6 (g).Energy consumption continued to increase as the water supply was ensured.Environmental awareness accumulation was primarily due to energy shortage.
Overall, water resources allocation can effectively alleviate water shortage to decrease water shortage awareness by increasing the water supply.The increase in environmental awareness is primarily due to the constant high-level energy shortage rate.Therefore, planning energy availability is the primary boundary condition for sustainable development of the WEFS nexus when water resources allocation is considered.Under the scenario without considering water resources allocation, the risk of water shortage is high.Water shortage awareness continues to accumulate and remains at a high level under scenario Ⅳ, which further contributes to high-level environmental awareness.The energy consumption and food production will be decreased by negative feedback.Water availability becomes the vital resource constraining the concordant development of the WEFS nexus.

Sensitivity Analysis for WEFS Nexus
As is discussed above, both environmental awareness feedback and water resources allocation are of great significance to WEFS nexus, the sensitivity analysis of which is conducted to help managers to identify the important parameters and rational water resources allocation schemes for the integrated system.
As environmental awareness feedback is dominated by the critical values and boundary conditions of the WEFS nexus, seven parameters were selected for sensitivity analysis (i.e., parameter 1~7 in Table 6).For water resources allocation, different reservoir operation schemes were adopted by adjusting water release from reservoir.Specifically, a multiplier for water release was added as a parameter to demonstrate the ratio to water release in scenario I (i.e., parameter 8 in Table 6).
Each parameter was varied by the given increment, with the other parameters remaining unchanged.The maximum and minimum values, as well as the increments for the seven parameters, are listed in Table 6.Parameter sensitivity analysis was then conducted by analyzing the trajectories of environmental awareness, water demand, energy consumption, and food production, as shown in Figures 8, 9, 10, and 11.

Sensitivity Analysis of Environmental Awareness Feedback on WEFS Nexus
The variations in the parameters 1~7 can evidently change the trajectory of environmental awareness shown in Figure 8.The socioeconomic sectors including water demand, energy consumption, and food production were then changed by feedback driven by environmental awareness (Figure 9, 10, and 11), indicating that WEFS nexus is sensitive to the seven parameters.
Specifically, the sensitive responses to parameters WSRcrit, ESRcrit, PEA, and Ecrit primarily occurred in the contraction and recession phases of the co-evolution process for WEFS nexus.As demands from water and energy systems can always be ensured by abundant resources availability in the expansion phase, limited water and energy shortages were observed.
Environmental awareness accumulated primarily from food shortage awareness but remained below its critical value (Figure 5 (i)).As the feedback due to environmental awareness was not sufficiently strong, the impacts on the co-evolution of WEFS nexus were negligible and were considered as the insensitivity.However, with social development, water demand and energy consumption continued to grow and increase over the local carrying capability, leading an increase in environmental As the agricultural water use was directly drawn from river system, the energy use quota during water supply was small and negligible.Energy consumption was thus not sensitive to FSRcrit, FAcrit, and TFP as shown in Figure 10.Therefore, constraining FSRcrit, FAcrit, and TFP is an effective way to increase food production by advancing and strengthening the feedback driven by food shortage awareness, which accounts for the sensitive responses of environmental awareness, water demand, and food production in expansion phase.
Simultaneously, it's worth noting that although constraining WSRcrit, ESRcrit, PEA, and Ecrit can maintain the integrated system from constant water shortage and energy shortage, the over-constrained condition can also sharply increase environmental awareness (Figure 8 (a), (b), (d), and (e)).Environmental awareness feedback was remarkably advanced, which shortened the expansion phase and led to violent degradation of socioeconomic sectors (indicated by drastic decreases of water demand, energy consumption and food production in Figure 9, 10, and 11, respectively).The sustainability of WEFS nexus was seriously challenged.Similarly, despite food production can be effectively increased by constraining FSRcrit, FAcrit, and TFP, the over-constrained condition will cause a considerable increase in water demand, as shown in Figure 9 (c), (e), and (f), which will further put stress on the water supply.Moreover, the regulating capacity of the local system should also be considered during parameter selection.For example, there was an abrupt decrease when WSRcrit was set to 0.05, as shown in Figure 9 (a), Figure 10 (a), and Figure 11 (a).Violent socioeconomic degradation dominated by environmental awareness feedback was triggered to decrease environmental awareness, indicating that the WSRcrit was over-constrained and exceeded the regulating capacity of the local water system.Therefore, a rational parameter setting should be based on the sustainability of long-term co-evolution for socioeconomic sectors and the regulating capacity of the local system, which is of great significance for sustaining the stability of the WEFS nexus.
As each shortage is experienced by different users with different connections to basin development dynamics (e.g., shortages from water, energy, and food are aggregated into environmental awareness, despite the food which is planned to be exported is considered in target food production), it's necessary to discuss the contributions to environmental awareness from water, energy, and food systems.Therefore, three weight factors were assigned to shortage awareness of water, energy, and food in equation ( 32) to adjust the over-estimated or under-estimated environmental awareness due to discordant scales.For instance, considering the target food production comprises inner food demand and exported food, the environmental awareness within the basin is over-estimated, and the weight factor for food shortage awareness can be set lower than 1.0 as a reduction factor to decrease current food shortage awareness.Sensitivity analysis was then conducted.Each weight factor was varied by given increment, while the other two weight factors were set to 1.0 as reference.The results are presented in Figure S1, S2, S3, and S4 in supplementary file.
where wf1, wf2, and wf3 are the weight factors for water, energy, and food shortage awareness, respectively.
WEFS nexus is sensitive to shortage awareness weight factors.Specifically, weight factors for water and energy shortage awareness can remarkably impact the recession phases of water demand, energy consumption, and food production.Lower weight factor can delay environmental awareness accumulation, and thus extend the contraction phase.However, more violent socioeconomic deterioration was also accompanied in the later recession phase, which consequently led the slightly smaller socioeconomic size in recovery phase.Weight factor for food shortage awareness can effectively dominate the whole evolution of water demand, and energy consumption.Lower weight factor indicated that smaller food shortage awareness can be accumulated.Feedback to increase crop area was thereby weakened.Both agriculture water demand and food production were decreased.As energy use quota for agricultural water supply is negligible, little response of energy consumption can be found.

Sensitivity Analysis of Water Resources Allocation Schemes on WEFS Nexus
The WEFS nexus in the study area was evidently constrained under water resources allocation schemes with smaller water release from reservoir.The decreasing water supply directly increased water shortage, the average annual shortage rate of which increased from 6.41% to 8.01%.The rapid increase of water shortage awareness then accelerated environmental awareness accumulation and further the feedback shown in Figure 8 (h).As the negative feedback on socioeconomic sectors was strengthened, water demand decreased rapidly in recession phase (Figure 9 (h)).Water supply was thereby decreased with decreasing water demand, which accounts for the decreasing energy consumption during water supply process shown in Figure 10 (h).For food system, decreasing water release notably altered the stability of food production evolution (Figure 11 (h)).Higher water shortage rate led smaller food production and further larger food shortage awareness.Feedback driven by food shortage awareness was strengthened to increase crop area.Food production thereby increased in expansion phase.
However, increasing crop area was accompanied by increasing agricultural water demand, which brought increases of water shortage and environmental awareness.With stronger environmental awareness feedback, food production in recession phase thereby decreased rapidly.
shortage and socioeconomic variables including water demand, energy consumption, and food production were considered.
Operational zones were classified into four types as shown in Figure 12  As environmental awareness feedback on population, GDP, and crop area was conducted in the entire study area, the water demand variations in Z1, Z8, Z9, and Z13 were similar, and all of them were small (Figure 13  Sanliping reservoir (shown in Figure 3).The regulating capacity of water project was strong enough to cover most part of water demand.Therefore, the increasing water release remarkably relived water shortage (water shortage rate decreased from 12.56% to 4.20%), particularly in industrial and agricultural users, as shown in Figure 13 (e).Energy consumption during water supply process thus increased, and food production also increased owing to the decreasing agricultural water shortage rate.Response of Z8 to water resources allocation schemes was similar to Z1.The difference was that local reservoirs in Z8 can provide limited regulating capacity, which can only cover part of water demand.Water shortage was effectively alleviated, but still considerable (water shortage rates were always more than 18% shown in Figure 13(d)).Z13 was far away from the mainstream and there was no local reservoir.The regulating capacity of water project was so weak that no response to water resources allocation schemes was observed.Water was always the key resource constraining the development of Z13 (Figure 13 (d)).
It's worth noting that it doesn't mean more water release from reservoir can always promote the development of the integrated system.As shown in Figure 13 (e), and (f), remarkable decreases of water shortage were no longer observed, since reservoir release multiplier was more than 1.2.As excessive water release may decrease reservoir storage in dry season, even more water shortages were found, as shown in Figure 13 (e), and (f), which further constrained socioeconomic expansion (Figure 13 (b), and (c)).Therefore, regulating capacity of water project is an important factor to ensure the stability of water system to sustain WEFS nexus.In the area equipped with strong regulating capacity of water project, water demand can always be covered and the integrated system is not sensitive to varied water release from reservoir.While in the area with certain regulating capacity of water project but can not totally cover the water demand, regulating the water release from reservoir by rational water resources allocation schemes can effectively ensure water supply and thereby contributes to the sustainable development of the integrated system.

Conclusions
The sustainable management of the WEF nexus remains an urgent challenge, as human sensitivity and reservoir operation are seldom considered in recent studies.This study used environmental awareness to capture human sensitivity and simultaneously incorporated reservoir operation in the form of water resources allocation model (i.e., IRAS model) into water system to develop a system dynamic model for the WEFS nexus.The proposed approach was applied to the MLHRB in China.The conclusions drawn from the study are as follows.
The proposed approach provides a valid analytical tool for exploring the long-term co-evolution of the nexus across the water, energy, food, and society systems.Environmental awareness in the society system shows potential to capture human sensitivity to shortages from water, energy, and food systems.The feedback driven by environmental awareness can regulate the pace of socioeconomic expansion to maintain the integrated system from constant resources shortages, which contributes to the sustainability of the WEFS nexus.The co-evolution of water demand, energy consumption, and food production can be divided into expansion (accelerating and natural expansion for food production), contraction, recession, and recovery

Figure 1 .
Figure 1.Structure of WEFS nexus model and its feedbacks.
Respond links are driven by environmental awareness and food shortage awareness.The terms of feedback functions are based on the studies of Feng et al. (2019) and Van Emmerik et al. (2014), which have been established to have good performance and suitability, as they have been successfully applied to simulate the human response to environmental degradation in the Murrumbidgee river basin (Australia) and Hehuang region (China).

Figure 3 .
Figure 3. Location of mid-lower reaches of Hanjiang river basin.

Figure 4 .
Figure 4. Sketch of the water system for the mid-lower reaches of Hanjiang river basin.
Figure 5 shows the trajectories of population; GDP; crop area; water demand; energy consumption; food production; shortage rates for water, energy, and food; awareness for water shortage, energy shortage, and food shortage; and environmental awareness during 2010-2070.

Figure 5 .
Figure 5. Trajectories of state variables in WEFS nexus: (a) population; (b) GDP; (c) crop area; (d) percentage variations 370 -2039).Although quotas for water use and energy use decreased (Figure 5 (d)) with technological advancement, water demand and energy consumption kept lowly increasing owing to the continuous socioeconomic expansion (Figure 5 (a), (b), and (c)).Shortage rates of water and energy remained over their critical values (Figure 5 (h), and (i)), leading the increases of water shortage awareness and energy shortage awareness, and further environmental awareness.Consequently, environmental awareness exceeded its critical value in 2033 and continued to increase.Negative feedback on socioeconomic sectors was triggered and strengthened.Water demand and energy consumption gradually increased with decreasing rate and reached their maximum values of 19.2 billion m 3 and 1,916 million kw*h, respectively, at the end of the contraction phase.

Figure 6 .
Figure 6.Trajectories of state variables in WEFS nexus under scenario Ⅰ , Ⅱ , Ⅲ , and Ⅳ : (a) water demand; (b) energy consumption; (c) food production; (d) and (e) shortage rates of water, energy, and food; (f) and (g) water shortage awareness, energy shortage awareness, food shortage awareness, and environmental awareness.

Figure 7 .
Figure 7. Distribution of water shortage rates.

Figure 9 .
Figure 9. Trajectories of water demand with varied parameters.

Figure 10 .
Figure 10.Trajectories of energy consumption with varied parameters.

Figure 11 .
Figure 11.Trajectories of food production with varied parameters.
awareness.Negative feedback on socioeconomic sectors was then triggered.WSRcrit and ESRcrit are the critical values that determine the awareness of water and energy shortages to accumulate, and PEA indicates the amount of planning energy availability, which directly determines the energy shortage.The environmental awareness accumulation can be thereby accelerated by constraining WSRcrit, ESRcrit, and PEA (Figure 8 (a), (b), and (d)).Ecrit is the threshold for the negative feedback triggering driven by environmental awareness.A lower Ecrit means community is more sensitive to resources shortage and feedback is easier to trigger (Figure 8 (g)).Therefore, environmental awareness feedback to constrain socioeconomic expansion can be advanced and strengthened by lowering WSRcrit, ESRcrit, PEA, and Ecrit, accounting for the sensitive response of WEFS nexus in contraction and recession phases.FSRcrit, TFP, and FAcrit performed sensitivity during the entire co-evolution process for WEFS nexus.As food shortages were considerable in the accelerating expansion phase, food shortage awareness increased rapidly, driving the feedback to increase crop area.TFP can directly determine food shortage, and FSRcrit and FAcrit determine thresholds for food shortage awareness accumulation and feedback triggering by food shortage awareness, respectively.Positive feedback on crop area to increase food production can thus be advanced and strengthened by constraining FSRcrit, TFP, and FAcrit (Figure 8 (c), (e), and (f)).The crop area then continued increasing until environmental awareness feedback was triggered, resulting in the increases in food production (Figure 11 (c), (e), and (f)) and water demand from agricultural sector (Figure 9 (c), (e), and (f)).

Figure 12 .
Figure 12.Spatial distribution of A, B, C, and D types of operational zones.

Figure 13 .
Figure 13.Socioeconomic variables with varied reservoir release multiplier in Z9, Z1, Z8, and Z13: (a) changing rates of water demand; (b) changing rates of energy consumption; (c) changing rate of food production; (d) water shortage rates; (e) water shortage rates of water users in Z1 (user 1, 2, 3, 4, and 5 are related to municipal, rural, in-stream ecology, industrial, and agricultural users); (f) water shortage rates of water users in Z8.
(a)), which indicated that water supply was the primary factor affecting the integrated system.No water shortage was observed in Z9 under different water resources allocation schemes (Figure13 (d)), and the energy consumption, and food production also exhibited insensitivity shown in Figure13(b), and (c).As Z9 located along the main stream of Hanjiang river, the regulating capacity of water project was strong due to Danjiangkou reservoir (whose total storage is 33,910 million m 3 ).Despite of the reduction of water release, the water demand can always be ensured, and the energy consumption, and food production thereby remained stability.Water shortage rate in Z1 decreased evidently with the increase of water release (Figure13 (d)), and the energy consumption, and food production further increased remarkably, as shown in Figure13(b), and (c).Z1 located at the boundary of study area, the water supply of which mainly depended on

Figure 2. Water release rule for supply-driven reservoir.
Ecrit and FAcrit are the critical values for environmental awareness and food shortage awareness, respectively; δ rp E , δ rg E , and δ ra E denote the factors describing feedback capability from environmental awareness; δ ra F is the factor describing feedback capability from food shortage awareness; ζ 1 , ζ 2 , and ζ 3 E represent the auxiliary factors for feedback functions driven by environmental awareness; and ζ 3 F is the auxiliary factor for feedback functions driven by food shortage awareness.

Table 1 Model initial condition setup.
Table 2, the NSEs range from 0.74 to 0.97, and the corresponding PBIASs are from -4.2% to 5.2%, indicating that both Malthusian model and Logistic model can effectively fit the observed data of WEFS nexus.

Table 2 NSE and PBIAS of state variables. Model Indicator Water demand Energy consumption Food production Population GDP Crop area
Hepburn et al. (2010)t the observed data can only cover the initial phase of WEFS nexus co-evolution.The environmental awareness stays at a low level and the feedback is not triggered, which indicates that feedback driven by high-level environmental awareness hasn't been calibrated yet.However, as environmental awareness is a subjective variable, there are no empirical data to calibrate it, which requires more evidences to show adaptive human response to environmental awareness.Hepburn et al. (2010)have reviewed studies on environmentally related human behavioral economics.