Quantifying and predicting the Water-Energy-Food-Economy-Society-Environment Nexus based on Bayesian networks - A case study of China

Journal Pre-proof Quantifying and predicting the Water-Energy-Food-Economy-Society-Environment Nexus based on Bayesian networks - a case study of China

Jian Chai, Huiting Shi, Quanying Lu, Yi Hu PII:

S0959-6526(20)30313-9

DOI:

https://doi.org/10.1016/j.jclepro.2020.120266

Reference:

JCLP 120266

To appear in:

Journal of Cleaner Production

Received Date:

09 August 2019

Accepted Date:

24 January 2020

Please cite this article as: Jian Chai, Huiting Shi, Quanying Lu, Yi Hu, Quantifying and predicting the Water-Energy-Food-Economy-Society-Environment Nexus based on Bayesian networks - a case study of China, Journal of Cleaner Production (2020), https://doi.org/10.1016/j.jclepro. 2020.120266

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Journal Pre-proof Word count: 8000

Quantifying and predicting the Water-Energy-Food-EconomySociety-Environment Nexus based on Bayesian networks - a case study of China Jian Chai1, Huiting Shi1*, Quanying Lu2, Yi Hu2 1.

School of Economics and Management, Xidian University, Xi’an, 710071, China

2.

School of Economics and Management, University of Chinese Academy of Sciences, Beijing， 100190, China

Abstract The main objective of sustainable development is to ensure the current and future demand can be satisfied. Food, energy and water is the primary human demand. However, China is facing security issues of water, energy and food due to several economic, social and environmental impacts such as economic progress, population growth and environmental change. For this reason, it is important to evaluate the relationship between food, energy and water with sustainability aspects. Using Bayesian network models, we propose a quantitative analysis framework based on the Water-Energy-Food-Economy-Society-Environment Nexus. Under this framework, the causality relations between water, energy, food and economy, society, environment were studied and quantified. Additionally, the demand for water, energy, food was predicted from a perspective of systematic interaction. Different from previous studies, our research is more comprehensive, involving six subsystems. More importantly, we do research from a systematic point of view. Thirdly, the causality in the nexus was quantified. As a result, we found that water withdrawal is directly affected by population growth and energy demand, indirectly by other nodes in the nexus; energy demand is directly affected by GDP and population growth in the nexus; population growth is the only direct cause of changes in food demand. Projections show that the demand for water, energy and food in China will remain at [600,620) billion cubic meters, a growth rate of [4%, 8%) and [0%, 5%) with an average probability of 0.6772, 0.6128 and 0.7055 respectively from 2020 to 2030.

*

Corresponding author: Huiting Shi, Phone: +86 18792632518, Email: [email protected], School of

Economics and Management, Xidian University, Xi’an 710071, China

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Journal Pre-proof Keywords: Water-Energy-Food-Economy-Society-Environment nexus; Bayesian networks; Causal relationships; Quantification and prediction 1. Introduction Resources and the environment are important foundations for human survival and development. In recent years, population change together with economic growth, climate change and urbanization can cause fluctuations in the national supply and demand for water, energy and food (WEF, 2011). Thus, to achieve long-term sustainable development, a country should pay more attention to the integrated management and sustainable use of these key resources. In this paper, we take China as an example to conduct our research. It is well known that China is a country possessing abundant natural resources, but it is also the most populous country in the world, with a small amount of resources per capita. It is estimated that China's population will reach 1.44 billion by 2030, decreasing to 1.36 billion in 2050 and to 1.02 billion in 2100 (UN, 2017). In this situation, figuring out how China's future demand for key natural resources such as water, food and energy changes is critical to its sustainable development. Given that water, energy and food are tightly related, this paper considers the three resources as a system for research. The Bonn Nexus Conference in 2011 (Hoff, 2011) made the Water-Energy-Food nexus (WEF nexus) a hot topic in academia. These natural resources are interlinked with each other in the following ways (Hoff, 2011): water is essential in energy production; water extraction, distribution and treatment require energy input; energy and water are needed in food production. Fig. 1 shows the conceptual perspective of Water-Energy-Food nexus. According to Li et al. (2018), Water-Energy-Food nexus consists of two parts. One is called the core nexus which presents interactions among water, energy and food; the other is peripheral nexus that presents interdependences between water, energy, food and subsystems like society, economy and environmental. Based on the relationships among the six subsystems shown in Fig. 1, this paper aims to reveal and quantify the interaction mechanism of the Water-Energy-Food-EconomySociety-Environment Nexus, as well as predict the demand for water, energy and food under a system framework for China.

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Fig. 1. The conceptual perspective of Water-Energy-Food nexus

Much work has been done to study the Water-Energy-Food nexus (Biggs et al., 2015; Kaddoura and El Khatib, 2017; Taniguchi et al., 2017; Wichelns, 2017; Bieber et al., 2018; De Amorim et al., 2018), Water-Energy-Food-Climate (Conway et al., 2015) and Water-Energy-Food-land (Howells et al., 2013; Ringler et al., 2013) from a qualitative perspective. Specifically, Biggs et al. (2015) and Wichelns (2017) have made detailed illustrations on the concept of Water-Energy-Food nexus which help researchers to improve understanding of the system; Kaddoura and El Khatib (2017) and Dai et al. (2018) conclude the simulation tools on the nexus by reviewing existing literature. Research questions usually include: computing resource flow and its dependence (De Amorim et al., 2018), quantification of system performance (Saladini et al., 2018). Main research results include: constructing a framework for WaterEnergy-Food nexus analysis and revealing the interactions and feedback mechanism among sectors in the system (Bazilian et al., 2011; Jeswani et al., 2015; Irwin et al., 2016), simulating Water-Energy-Food nexus (Halbe et al., 2015; Giampietro et al., 2013), assessing sustainability or system risks of Water-Energy-Food nexus (De Amorim et al., 2018) and studying the Water-Energy-Food nexus from the point of view of water footprint or virtual water trade as well as putting forward relevant sustainable development methods (Mekonnen et al., 2016). Simulation tools mainly are life cycle assessment (LCA) (Al-Ansari et al., 2015), system dynamic (SD) (Halbe et al., 2015), network analysis (NA) (Duan and Chen, 2017), NexSym (MartinezHernandez et al., 2017). Different from previous studies mentioned above, this study 3

Journal Pre-proof constructs causal networks based on the six subsystems shown in Fig. 1 to reveal the impact of changes in a country's peripheral nexus on the core nexus, the interdependences between water, energy, food and the impact of dynamic changes in the nexus on water, energy and food demand. Currently, there are few studies on quantification of Water-Energy-Food nexus. Valek et al. (2017) provide a quantitative study of water-energy-climate nexus to study the impact of urban water supply systems on climate for México City. Halbe et al. (2015) used the system dynamics model to quantify the system's relationships and predict future changes. Sušnik (2015) predicts the future water intake, energy consumption and food output by analyzing the correlation and causality between GDP and the three resource subsystems. Given seven GDP scenarios, future resource use can be predicted based on the GDP-resource function relationship. However, this research did not thoroughly describe the interactions of the Water-Energy-Food nexus. Sušnik (2018) proposes a quantitative analysis framework, the global Water-Energy-Food-GDP system, to describe the relationship between GDP and natural resource consumption, with 12 best-fit regression equations indicating how the subsystems of the WaterEnergy-Food-GDP nexus interact with each other. However, each equation only studies the relationship between two subsystems, without considering influences from other subsystem in the nexus. In essence, this quantitative method does not reveal the interactions among water, energy, food and GDP from system perspective. In order to improve this situation, we use one equation instead of 12 for system modeling to truly reveal the conditional correlation and its strength among subsystems in a system. Then water, energy and food demand were predicted under the proposed systematic quantitative framework. In this research, the Bayesian network (BN) model is applied to construct and quantify the causal network of this study, as well as avoid flaws in previous research described above. Bayesian network models are widely used in many fields such as economy, traffic, medical care and artificial intelligence for describing the causal relationship between variables and reasoning under uncertainty. It has been applied to forecast stock market index daily direction (Malagrino et al., 2018), construct a knowledge model of pipeline fracture in water area and predict pipeline breaks (Francis et al., 2014), predict medical costs for lung cancer patients (Wang et al., 2019), reveal the determinants of wheat yield and predict future yield in the Siberian granary (Prishchepov et al., 2019), discover the dependencies between variables in probabilistic

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Journal Pre-proof energy modeling (Bassamzadeh and Ghanem, 2017), predict the propagation of train delays (Corman and Kecman, 2018). A Bayesian network model can not only model a complex system with the simplest structure, giving a clear causal relationship between subsystems in a system, but also can reveal the strength of causality between variables and present a series of possible predictions with probability rather than a single prediction result as general methods do. Since interactions in the Water-Energy-FoodEconomy-Society-Environment nexus are highly complex with a lot of uncertainties in the future development of the social, environmental and economic subsystem (Peronne and Hornberger 2013), it is necessary to study the Water-Energy-Food-EconomySociety-Environment nexus based on Bayesian network models. In short, we try to answer the following questions by applying Bayesian networks in this paper. Firstly, what is the causal relationships in the Water-Energy-FoodEconomy-Society-Environment nexus? Secondly, how strong is the causal relationship among subsystems in the nexus? Finally, what is the future demand for water, energy and food of China? In practice, we propose a quantitative analysis framework for the Water-Energy-Food-Economy-Society-Environment nexus to reveal and quantify the causality among subsystems and predict water, energy, food demand under this framework. In this section, the research problems and its research status were described thoroughly. In section 2, we introduce the Bayesian network model in detail. In section 3, we show the data and build a Bayesian network based on the causal relationship proposed by experts in the field. Section 4 presents our results and discussions on the causal relationships and the predictions. Section 5 summaries the main conclusions. 2. Methodology 2.1 Bayesian network Bayesian network (BN) is a kind of probabilistic graphical model (PGM) for describing the relationship between variables and reasoning under uncertainty. It was invented by Judea Pearl in the 1980s and can simultaneously represent multiple probability relationships between variables in a system (Nagarajan et al., 2013). A Bayesian network consists of a directed acyclic graph (DAG) and conditional probability tables for each node in the network graph. In a directed acyclic graph G = (N, A), N represents the "node" of random variables and A represents the "arc" of probabilistic dependencies between nodes (Nagarajan et al., 2013). For example, if an arc is from node 𝑋𝑖 to 𝑋𝑗 (𝑋𝑖→𝑋𝑗), then we believe that 𝑋𝑖 is the parent node of 𝑋𝑗

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Journal Pre-proof and 𝑋𝑗 is the child node of 𝑋𝑖. P (𝑋𝑖| 𝑋𝑗) represents the conditional probability between 𝑋𝑖 and 𝑋𝑗. A Bayesian network is represented as: 𝐵 = (𝐺,𝛩), where G is a directed acyclic graph representing Bayesian network structure and 𝛩 are the parameters (conditional probability). Consider n random variables 𝑋1,𝑋2,…,𝑋𝑛, node i (1⩽ i ⩽n) belonging to G is associated to the variable 𝑋𝑖 . The joint probability distribution of Bayesian network is expressed as Eq. (1), where 𝑝𝑎𝑟𝑒𝑛𝑡𝑠(𝑋𝑖) denotes the parent nodes of 𝑋𝑖. 𝑃(𝑋𝑖|𝑝𝑎(𝑋𝑖)) is conditional probability distribution. 𝑛

𝑃(𝑋1,𝑋2,…,𝑋𝑛) = ∏𝑖 = 1𝑃(𝑋𝑖|𝑝𝑎𝑟𝑒𝑛𝑡𝑠(𝑋𝑖))

(1)

Bayesian networks not only allow discrete random variables but also enable continuous type of data, even incomplete data sets. Discrete Bayesian network refers to the network structure in which the node variables are discrete and Continuous Bayesian network (or Gaussian Bayesian networks) refers to the structure in which the node variables are continuous (Nagarajan et al., 2013). The biggest difference between the two models is that the data in discrete Bayesian networks are discretized which can cause some information loss, but the model does not specify a specific distribution type. While a continuous Bayesian network assumes that the dependencies between variables is linear relationship and the joint probability distribution of all random variables is multivariate normal distribution. Considering the strictness of the Gaussian Bayesian networks assumption, we choose discrete Bayesian networks to do our research. 2.2 Learning and Inference of Bayesian networks As was pointed by Nagarajan et al. (2013), the task of fitting a Bayesian network is usually called learning which consists of structure learning and parameter learning. Structure learning identify the graph structure of a Bayesian network while parameter learning gives the joint probability distribution of the variables on a Bayesian network structure. In general, there are 3 different ways to construct a Bayesian network. (1) The nodes, structures and parameters of Bayesian networks are determined by domainspecific knowledge. (2) The nodes are determined by the knowledge of experts, while the structure and parameters are learned from data. (3) The nodes and structures are determined by domain expert knowledge, while the parameters are learned from data. In this paper, the third method is applied in our research. Probabilistic reasoning also called conditional probabilistic query is to calculate the edge distribution and conditional distribution after structure learning and parameter learning. The state of query variables can be inferred given the state of a set of evidential variables. Bayes theorem is used to compute the distribution, as shown in Eq. (2):

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Journal Pre-proof 𝑃(𝑄│𝐸) =

𝑃(𝑄,𝐸) 𝑃(𝐸)

(2)

where Q is query variable and E is evidential variable. There are different types of probabilistic reasoning, including diagnostic reasoning from result to cause, predictive reasoning from cause to result (Type of reasoning in this paper), and causal association reasoning with the same result but different reasons (Korb and Nicholson, 2010). Reasoning methods include precise reasoning and approximate reasoning. We take logic sampling algorithm (a kind of approximate reasoning) for prediction in this article. R packages that can be used to deal with Bayesian networks are bnlearn, catnet, deal, pcalg, gRbase and gRain (Nagarajan et al., 2013). In this paper, we chose package bnlearn to conduct our models. A Bayesian network model is a probabilistic knowledge representation and reasoning model which can represent complex systems with the simplest structure, giving a clear causal relationship between subsystems in a system. This causal relationship between two nodes is uncertain and can reflect the conditional dependencies between variables. In addition, Bayesian networks can simultaneously represent a multitude of probabilistic relationships between variables in a system with one equation called the joint probability distribution, and do not have to distinguish between independent and dependent variables which is different from traditional statistical models are of the form y=f(x). Research processes of our work are presented in Fig. 2.

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Fig. 2. The chart of research processes

3. Materials and Modeling 3.1 Variables and Data Based on the Document Analysis method and the conceptual framework of the Water-Energy-Food-Economy-Society-Environment nexus shown in Fig.1, this paper selects nine variables as representative indicators of economic, social, environmental, water, energy, and food subsystems (see Table 1 for details) to establish our Bayesian network structure. Applying Document Analysis method means each indicator chosen in our research was based on the in-depth analysis of previous studies similar to this research topic. And the causal relationships between indicators were also proved to be strong by them. Table 1 Variables for studying the Water-Energy-Food-Economy-Society-Environment nexus Subsystem name

Indicators

References

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Total national GDP (J)

Sušnik (2018)

Social

Total national population (S)

Wicaksono & Kang, 2018

Environmental

Annual rainfall (H)

Taniguchi et al., 2017

Total water stock (W1)

Wicaksono & Kang, 2018

Total national water withdrawal (W2)

Sušnik (2018)

Total national energy consumption (E1)

Wicaksono & Kang, 2018

Total national energy production (E2)

Wicaksono & Kang, 2018

Total national crop production (F2)

Sušnik (2018)

Total national crop consumption (F1)

Wicaksono & Kang, 2018

Water

Energy

Food

Annual data from 1978 to 2018 was obtained from the China Statistical Yearbook. For food demand (F1), there are 4.17% missing data (in percentage of total data) and Regression Imputation method was used for filling. Since the total population is closely related to food consumption, we use the relationship between them to estimate the missing value of F1. Since GDP, total population, energy consumption, energy production, food consumption and food production all showed obvious growth trends, hence we take their discretized growth rates to build Bayesian network models. The annual rainfall, water resources stock and water intake indicators are directly discretized. Usually, there are many discretization criteria can be used to discretize our data (Prishchepov et al., 2019). Here we take equal width intervals. Taking into account the characteristics of historical data and the size of our sample data, we divide the evidence variable in each model into three states and disperse the query variables into more than three states. Actually, the more discrete the query variables are, the more accurate the prediction results will be. However, this will be at the expense of estimating more parameters which makes the model unstable when the sample size is not large enough. Therefore, we should maintain a balance between the number of parameters and the sample size. Discretization results are shown in Table 2 and Table 3. Table 2 Discretization results of evidence variables Variable

Description

Discretization

J

GDP growth rate

<10%: low; 10%~20%: medium; ≥ 20%: high

S

Population growth rate

<0.5%: low; 0.5%~1%: medium; ≥ 1%: high

H

Annual rainfall

<6000: less; 6000~6500: moderate; ≥ 6500: adequate

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Energy consumption growth rate

<5%: low; 5%~10%: medium; ≥ 10%: high

E2

Energy production growth rate

<0%: negative; 0%~10%: low; ≥ 10%: high

F1

Food demand growth rate

<0%: negative; 0%~5%: low; ≥ 5%: high

F2

Food production growth rate

<0%: negative; 0%~5%: low; ≥ 5%: high

W1

Water resources stock

<2700: less;2700~2900: moderate; ≥ 2900: adequate

W2

Water intake

<570: less; 570~600: moderate; ≥ 600: massive

Note: The unit of H, W1 and W2 are billion cubic meters.

Table 3 Discretization results of query variables Prediction

Node states

node W2

E1

F1

w1

w2

w3

w4

[540,560)

[560,580)

[580,600)

[600,620)

e1

e2

e3

(-∞, 0%)

[0%, 4%)

f1 (-∞, 0%)

-

-

e4

e5

e6

[4%, 8%)

[8%, 12%)

[12%, 16%)

[12%, ∞)

f2

f3

f4

[0%, 5%)

[5%,10%)

[10%, ∞)

-

-

Note: The unit of water withdrawal is billion cubic meters

3.2 Analysis of casual relationships between subsystems The six subsystems presented in Fig. 1 are key aspects of a country's sustainable development. To understand the operation of the nexus, it is necessary to clearly understand the characteristics of each subsystem and its relationship with other subsystems. -Economic Subsystem: Economic subsystem is one of the peripheral factors of the Water-Energy-Food-Economy-Society-Environment

nexus

and

contains

many

evaluation indicators like GDP, price, unemployment. However, to simplify the network structure, we choose annual GDP as the representative index of this subsystem to analyze the influence of economy on water, energy and food in the construction of Bayesian networks (Sušnik, 2018). The economic subsystem can affect the demand of resource to a certain extent. It has been confirmed that GDP growth is the reason why China’s energy demand has increased over the past three decades (Liu et al., 2017). -Social Subsystem: Social subsystem also has an impact on water, energy and food. We choose the total population as a representative indicator of this subsystem. In recent 10

Journal Pre-proof years, the growth of the world population and the advancement of urbanization have accelerated the demand for water, energy, food (De Beurs and Henebry, 2004). As far as China is concerned, the size of its population has a direct impact on the country's demand for water, energy and food. That is to say, the change of population is the reason why the demand of the three kinds of natural resources fluctuates. -Environmental Subsystem: Environmental subsystem has the most direct relationship with water, energy and food. During the last few years, climate change and environmental pollution have exerted huge influences on the supply and demand of water, energy, food. Here we choose annual rainfall as a representative indicator for the subsystem (Taniguchi et al., 2017). Obviously, rainfall will exert influences on food production and water storage in that year (Lissner et al., 2014). -Water subsystem: In this research, total national water withdrawal instead of water consumption was chosen as demand indicator to measure the pressure on available water resources. According to Sušnik (2018), water intake is generally higher than water consumption. For instance, some energy production processes extract large amounts of water, but consume relatively little. In addition, we choose the water stock as a supply indicator for this subsystem. Agriculture, industry, energy and residential life are the main water demand sectors, of which agriculture is the sector with the largest water demand (Karatayev et al., 2017). Specifically, processes of energy production from both traditional and emerging sources are often highly dependent on water supply such as: resource extraction, cooling system and processing of fossil fuels (Cai et al., 2018; Mekonnen et al., 2015). -Energy Subsystem: Energy consumption and primary energy production were chosen respectively as demand and supply indicator to build Bayesian networks. Energy subsystem is the source of operational power for the entire system. For example, China's high-speed economic growth is natural resources (especially energy)-driven (Liu et al., 2017); residents can't do without energy for cooking and traveling (Hoff, 2011); the extraction, purification, transportation and other processes of water resources depend on energy (De Beurs and Henebry, 2004; Cai et al., 2018); finally, agricultural mechanization and crop fertilization, irrigation also require a lot of energy (Wicaksono & Kang, 2018). -Food subsystem: In this paper, food represents main crops in the agricultural subsystem such as rice, wheat, corn, beans and potatoes. We take crop yields as total national food production and crop consumption as total national food demand.

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Journal Pre-proof Obviously, agricultural subsystem also has a direct impact on the water and energy. For example, fertilizers (energy) and pesticides required for food production have a direct causal relationship with the pollution of water resources and the reduction of water supply (Cai et al., 2018; Wicaksono & Kang, 2018). In addition, food as a production input of biomass energy will have a direct impact on the supply of energy (Yang et al., 2009; Wicaksono & Kang, 2018). However, considering the unrestricted limits of data, these two causal relationships are not taken into account in the topology of the Bayesian network (indicated by dashed lines in Fig. 3). The causal relationship based on expert knowledge between the subsystems discussed above is shown in Table 4. The Bayesian network topology presenting the Water-Energy-Food-Economy-Society-Environment nexus can be seen in Fig. 3. Table 4 Summary of causal relationships in the nexus Subsystem

Links

Explanation

J→WEF

J→E1

GDP → energy consumption

S→W2

population → water withdrawal

S→E1

population → energy consumption

S→F1

population → crop consumption

H→W1

Annual rainfall → water stock

Taniguchi et al., 2017;

H→F2

Annual rainfall → crop production

Lissner et al., 2014;

W2→E2

water withdrawal → energy production

W2→F2

water withdrawal → crop production

E1→F2

energy consumption→ crop production

E1→W2

energy consumption → water intake

S→WEF

H→WEF

W-E-F

References Liu et al., 2017 ; Sušnik (2018) Yoshikawa et al., 2014 ; Alcamo et al., 2007 De Beurs & Henebry, 2004; Hoff, 2011 Li et al., 2018 ; De Beurs & Henebry, 2004

Cai et al., 2018; Sušnik (2018) Mekonnen et al., 2015 ; Sušnik (2018) Wicaksono & Kang, 2018; Sušnik (2018) De Beurs & Henebry, 2004; Cai et al., 2018

3.3 Establishment of Bayesian network topology Model of the Water-Energy-Food-Economy-Society-Environment nexus was

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Journal Pre-proof built based on expert knowledge discussed above, which reflects the scientific understanding of the nexus in this filed. It can be seen that Fig. 3 clearly describes the causal relationships in the nexus. In this structure, nodes represent the selected variables of the six subsystems. Directed edges show the causality between nodes. The joint probability distribution containing all nodes is expressed as Eq. (3), which reveals the causality among water, energy, food, economy, social and environment. 𝑃(𝐽,𝑆,𝐻,𝑊1,𝑊2,𝐸1,𝐸2,𝐹1,𝐹2) = 𝑃(𝐽)𝑃(𝑆)𝑃(𝐻)𝑃(𝑊1│𝐻)𝑃(𝐸1|𝐽,𝑆)𝑃(𝐹1|𝑆)𝑃(𝑊2|𝑆,𝐸1)𝑃(𝐸2|𝑊2)𝑃 (𝐹2|𝐻,𝑊2,𝐸1) (3)

Fig. 3. Bayesian network topology Note: the full line in the figure refers to the causal relationship we want to quantify, and the dash line in the figure refers to the causal relationship not considered in this study.

4. Results and Discussions 4.1 Results and discussions of causality quantification The parameter learning can be performed after the Bayesian network structure is obtained. The results are shown in Fig. 4. As mentioned above, the Bayesian network topology with conditional probability tables can show how states and the probabilities of a node propagate to its child node as well as the strength of causality between nodes. Accurate conditional probability distribution tables and probability propagation paths help to clearly understand the causal relationships between subsystems in the WaterEnergy-Food-Economy-Society-Environment nexus and predict demands based on the 13

Journal Pre-proof dynamic evolution of events. Obviously, there are strong causal relationships between subsystems in the nexus as shown in Fig. 4. In this section, we mainly focus on the quantitative causality in the network to reveal the specific impact of the changing trends of J, S, H, W, E and F on W2, E1 and F1, F2. (1) Node W2 was analyzed at first. As shown in Fig. 4, node W2 represents the annual water withdrawal, and its parent nodes are population (S) and energy consumption (E1). The directed edges S → W2 and E1 → W2 indicate that the increase in population and energy consumption is the reason for the change in water withdrawal. It can be seen from the conditional probability distribution table of W2 in Fig. 4 that when the population and energy demand grow at a high speed (S=high; E1=high), the probability of taking a large amount of water (W2=massive) is 0.938, and the probability of taking moderate water (W2=moderate) is 0.045, and the probability of taking less water (W2 =less) is 0.017. Therefore, we draw a conclusion that when population is growing at a rate of more than 1% and energy is growing at a rate of more than 10%, China's water intake will remain at [600, ∞) billion cubic meters, considering that 0.938 is much larger than 0.045 and 0.017. Similarly, we can analyze the effect of other different scenarios of S and E1 on the change of W2 according to Table P (W2) in Fig. 4.

Fig. 4. Quantized Bayesian network structure. Table A.1 and A.2 show the conditional probability distribution of E1 and F2 respectively in appendix.

In conclusion, W2 is directly affected by nodes S and E1, and indirectly by other nodes in the nexus. When (S, E1)=(high, high) or (S, E1)=(medium, low) or (S, 14

Journal Pre-proof E1)=(low, medium), W2=massive. When (S, E1)=(medium, medium) or (S, E1)=(low, high) or (S, E1)=(low, low), W2=moderate. When (S, E1)=(high, medium) or (S, E1)=(high, low) or (S, E1)=(medium, high), W2=less. The conditional probability of 0.965, 0.757 and 0.978 show a strong causal relationship between the three states of W2 and (S, E1). That is to say, W2=massive is mainly due to (S, E1)=(low, medium) with a probability of 0.965. W2=moderate is mainly caused by (S, E1)=(medium, medium) with a probability of 0.757. W2=less is mainly due to (S, E1)=(medium, high) with a probability of 0.978. The above conclusions are consistent with China's reality that the total amount of population and energy demand were small in the early days, even though the growth rate was relatively large, resulting in less water intake. (2) From Fig. 4, we can conclude that E1 is directly affected by nodes J and S. Table A.1 shows the conditional probability relationship between node E1 and its parent nodes J and S. Specifically, When (J, S)=(high, high) or (J, S)=(high, medium) or (J, S)=(medium, low), E1=medium. When (J, S)=(high, low) or (J, S)=(medium, high) or (J, S)=(medium, medium) or (J, S)=(low, high) or (J, S)=(low, medium) or (J, S)=(low, low), E1=low. The conditional probability of 0.364, 0.926 and 0.941 show a strong causality between the three states of E1 and (J, S). That is to say, E1=high is mainly due to (J, S)=(high, low) with a probability of 0.364. E1=medium is mainly caused by (J, S)=(high, medium) with a probability of 0.926. E1=low is mainly due to (J, S)=(low, low) with a probability of 0.941. (3) According to Table P (F1) in Fig. 4, conclusions can be drawn that population (S) is the only direct cause of changes in food demand. When the population grows at a high speed (S=high), the growth rate of food demand is also high (F1=high) with a probability of 0.688. When the population grows at a medium or low speed (S=medium/low), the growth rate of food demand is low (F1=low) with a probability of 0.611 or 0.719. (4) From Fig. 4, we can conclude that F2 is directly affected by nodes H, W2 and E1, and indirectly by other nodes in the nexus. Table A.2 shows the conditional probability relationship between node F2 and its parent nodes H, W2 and E1. The conditional probability of 0.994, 0.996 and 0.984 show a strong causality between the three states of F2 and (H, W2, E1). In other words, F2=high is mainly due to (H, W2, E1)=(less, massive, medium) with a probability of 0.994. F2=low is mainly because of (H, W2, E1)=(moderate, massive, low) with a probability of 0.996. F2=negative is mainly due to (H, W2, E1)=(less, massive, high) with a probability of 0.984.

15

Journal Pre-proof Changes in annual rainfall (H), water withdrawals (W2) and energy consumption (E1) are direct and major causes of fluctuations in the growth rate of food production (F2) while other nodes are indirect causes. Specifically, when rainfall, water withdrawal and the growth rate of energy demand is (-∞, 6000), [600, ∞) and [5%, 10%) respectively, the food production will increase at the rate of (5%, ∞). When rainfall, water withdrawal and the growth rate of energy demand is [6000, 6500), [600, ∞) and (-∞, 5%) respectively, the food production will increase at the rate of [0%, 5%). When rainfall, water withdrawal and the growth rate of energy demand is (-∞, 6000), [600, ∞) and (10%, ∞) respectively, the food production will increase at the rate of (-∞, 0%). 4.2 Results and discussions of demand predictions The inference mechanism of the Bayesian network model can be described as: when new information about a random variable (evidence) becomes available, it is propagated through the network by updating the posterior probabilities (beliefs) of the relevant nodes. Surprisingly, even if not all evidence variables are observed, we can still obtain reliable predictions for the target variable. However, most traditional forecasting methods cannot do this. In this paper, we select one node (China's future population growth rate) to conditionally reason the future values of water withdrawal, energy demand and food demand. According to the projections by UN (2017), China's population growth rate from 2020 to 2025 is 0.2% and from 2025 to 2030 is 0.03%. Based on the Bayesian network structure proposed by Section 3, we constructed three different Bayesian network models using three group of data sets (with different evidence variables and query variables) to predict the demand for water, energy and food respectively. The forecast results are presented as follows. Model 1: Water withdrawal forecasting Evidence variables: J, S, H, E1, E2, F1, F2, W1 (with 3 states) Query variables: W2 (with 4 states) Prediction Input: China's population growth rate from 2020 to 2030. Prediction Output: Prediction results for future water demand as shown in Table A.3 and Fig. 5.

16

Journal Pre-proof

Fig. 5. Prediction results of water withdrawal from 2020 to 2030

The results in Table A.3 show China's demand for water in the next ten years will remain at [540, 560) with an average probability of 0.0353, at [560, 580) with an average probability of 0.0326, at [580, 600) with an average probability of 0.2548 and at [600, 620) billion cubic meters with an average probability of 0.6772. This can also be clearly seen from Fig. 5. In short, when the total population grows at a low rate, China's demand for water will remain at [600, 620) billion cubic meters with an average probability of 0.6772 from 2020 to 2030. Table A.3 shows that the prediction result of ARIMA model is a value of [600, 620), which also indicates that Bayesian network model is accurate when predicting water demand, from a systematic perspective. Model 2: Energy demand forecasting Evidence variables: J, S, H, E2, F1, F2, W1, W2 (with 3 states) Query variables: E1 (with 6 states) Prediction Input: China's population growth rate from 2020 to 2030. Prediction Output: Prediction results for future energy demand as shown in Table A.4 and Fig. 6.

17

Journal Pre-proof Fig. 6. Prediction results of energy demand growth rate from 2020 to 2030

The results in Table A.4 show that the demand for primary energy in China from 2020 to 2030 will grow at a rate of (-∞,0%) with an average probability of 0.0408, at a rate of [0%,4%) with an average probability of 0.2195, at a rate of [4%,8%) with an average probability of 0.6128, at a rate of [8%,12%) with an average probability of 0.0395, at a rate of [12%,16%) with an average probability of 0.0440, at a rate of [16%, +∞) with an average probability of 0.0431. This can also be seen from Fig. 6. If the energy demand of the previous year is known, the range of demand for the next year can be obtained based on the predicted growth rate. It can be seen that in Table A.4 that all the prediction values of ARIMA model fall into the range of [4%,8%). So, we come to a conclusion that when the total population grows at a low rate, China's demand for energy will grow at a rate of [4%,8%) with an average probability of 0.6128 from 2020 to 2030. Model 3: Food demand forecasting Evidence variables: J, S, H, E1, E2, F2, W1, W2 (with 3 states) Query variables: F1 (with 4 states) Prediction Input: China's population growth rate from 2020 to 2030. Prediction Output: Predictions for future food demand growth rate as shown in Table A.5 and Fig. 7.

Fig. 7. Prediction results of food demand growth rate from 2020 to 2030

It can be seen from Table A.5 that China's demand for food in the next ten years will remain a growth rate of (-∞, 0%) with an average probability of 0.2532, of [0%, 5%) with an average probability of 0.7055, of [5%,10%) with an average probability of 0.0202, of [10%, ∞) with an average probability of 0.0210. Fig. 7 also shows the 18

Journal Pre-proof forecast results of food demand from 2020 to 2030. If the food demand for the previous year is known, the range of demand for the next year can be determined based on the projected growth rate. To sum up, when the total population grows at a low rate, China's demand for food will remain a growth rate of [0%, 5%) with an average probability of 0.7055. The prediction results of ARIMA model in Table A.5 that are consistent with those of Bayesian network model also confirms our conclusion. 5. Conclusions China is facing security issues of water, energy and food due to several economic, social and environmental impacts such as economic progress, population growth and environmental change. However, to achieve sustainable development, it is crucial to ensure the current and future demand can be satisfied. For this reason, it is important to evaluate the relationship between food, energy and water with sustainability aspects. In this research, we propose a quantitative analysis framework based on Bayesian network model for the Water-Energy-Food-Economy-Society-Environment nexus to reveal and quantify the causality among subsystems and predict water, energy, food demand under this framework. There are four main contributions in this paper. First of all, we clearly show the causal relationship between subsystems and the strength of this causal relationship. Secondly, unlike previous studies, for the first time, we have predicted the demand for water, energy and food under the system framework. Thirdly, our research results have an important contribution to China's integrated resource management and sustainable development. Fourthly, our study provides a reference for other researchers for those who are committed to complex system modeling. Main conclusions are stated as follows: (1) The increase in population (S) and energy demand (E1) is the direct reason for changes in water withdrawal (W2) and other variables in the nexus are indirect causes. When S grows at a rate of less than 0.5% and E1 increases at a speed of [5%, 10%), W2 is [600, ∞) billion cubic meters. When S grows at a rate of [0.5%, 1%) and E1 increases at a rate of [5%, 10%), W2 is [570, 600) billion cubic meters. When S grows at a rate of [0.5%, 1%) and E1 increases at a rate of [10%, ∞), W2 is (-∞, 570) billion cubic meters. (2) Fluctuations in GDP (J) and population growth rates (S) will lead to changes in energy demand (E1). When J and S growth rates are [20%, ∞) and (-∞, 0.5%) respectively, E1 will increase at a rate of [10%, ∞). When J and S growth rates are [20%, ∞) and [0.5%, 1%), E1 will increase at a speed of [5%, 10%). When J and S

19

Journal Pre-proof growth rates are (-∞, 10%) and (-∞, 0.5%), E1 will increase at a rate of (-∞, 5%). (3) Population (S) is the only direct cause of changes in food demand (F1). Specifically, When the population grows at a rate greater than 1%, the growth rate of food demand is more than 5%. When the population grows at a rate of (-∞, 1%), the growth rate of food demand is (0%, 5%). (4) The low population growth rate in the future will lead to the following changes in China's resource demand: the demand for water remains at [600, 620) billion cubic meters with an average probability of 0.6772; the demand for energy grows at a rate of [4%,8%) with an average probability of 0.6128; the demand for food remains a growth rate of [0%, 5%) with an average probability of 0.7055 from 2020 to 2030. There are two limitations in this study. On one hand, the relationship between subsystems of the Water-Energy-Food-Economy-Society-Environment nexus is not static, but dynamic. Our research has not capture the dynamic of system. On the other hand, the prediction result is an interval, not a specific value, which is not accurate enough. Therefore, in the future research, we intend to use the Dynamic Bayesian Network model to show the dynamic causal relationship between the subsystems. More importantly, we will try to narrow the prediction interval as much as possible to make the results more accurate. On this basis, we will add indicators to analyze the impact of changes in economic, social and environmental factors on water, energy and food supply. Acknowledgements We are very grateful to the editors and reviewers for their contributions to this study. This work is supported by the National Natural Science Foundation of China (NSFC) (71874133), the Annual Basic Scientific Research Project of Xidian University (2019), and the Seed Foundation of Innovation Practice for Graduate Students in Xi'dian University. Appendix The conditional probability P (E1|S, J) is calculated, and the results are shown in table A.1. Table A.1 Conditional probability distribution table of E1 P(E1) J

S

high

medium

low

high high

high medium

0.159 0.032

0.838 0.926

0.003 0.042

20

Journal Pre-proof high medium medium medium low low low

low high medium low high medium low

0.364 0.003 0.329 0.010 0.011 0.003 0.033

0.278 0.395 0.232 0.661 0.344 0.169 0.026

0.602 0.602 0.439 0.329 0.645 0.828 0.941

The conditional probability P (F2|E1, H, W2) is calculated, and the results are shown in table A.2. Table A.2 Conditional probability distribution table of F2 P(F2) H

W2

E1

high

low

negative

adequate adequate adequate adequate adequate adequate adequate adequate adequate moderate moderate moderate moderate moderate moderate moderate moderate moderate less less less less less less less less less

massive massive massive moderate moderate moderate less less less massive massive massive moderate moderate moderate less less less massive massive massive moderate moderate moderate less less less

high medium low high medium low high medium low high medium low high medium low high medium low high medium low high medium low high medium low

0.333 0.018 0.004 0.500 0.013 0.358 0.329 0.465 0.345 0.395 0.275 0.000 0.313 0.003 0.358 0.000 0.006 0.479 0.016 0.994 0.008 0.355 0.004 0.005 0.984 0.408 0.504

0.396 0.973 0.540 0.333 0.982 0.331 0.379 0.523 0.650 0.303 0.369 0.996 0.312 0.308 0.282 0.515 0.990 0.003 0.000 0.000 0.983 0.286 0.988 0.345 0.006 0.188 0.494

0.271 0.009 0.456 0.167 0.005 0.311 0.291 0.011 0.005 0.302 0.356 0.004 0.375 0.689 0.360 0.485 0.004 0.518 0.984 0.006 0.009 0.359 0.007 0.650 0.009 0.403 0.001

The conditional probability P(W2|S) is calculated which can be seen in table A.3. Table A.3 Prediction results of water withdrawal from 2020 to 2030 w1

w2

w3 21

w4

ARIMA

Journal Pre-proof

2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030

[540,560)

[560,580)

[580,600)

[600,620)

Prediction

0.0324 0.0359 0.0290 0.0395 0.0369 0.0415 0.0345 0.0352 0.0288 0.0396 0.0355

0.0287 0.0332 0.0372 0.0329 0.0397 0.0245 0.0354 0.0342 0.0288 0.0348 0.0288

0.2703 0.2758 0.2454 0.2436 0.2405 0.2497 0.2404 0.2434 0.2683 0.2677 0.2574

0.6685 0.6549 0.6881 0.6839 0.6827 0.6843 0.6897 0.6872 0.6740 0.6579 0.6782

606.3 607.8 605.5 606.2 608.3 604.6 605.7 610.3 606.9 607.3 609.4

Note: The unit of water withdrawal is billion cubic meters The conditional probability P(E1|S) is calculated which are shown in table A.4. Table A.4 Prediction results of energy demand growth rate from 2020 to 2030 e1 (-∞,0%)

e2 [0%,4%)

e3 [4%,8%)

e4 [8%,12%)

e5 [12%,16%)

[16%,∞)

ARIMA Prediction

0.0325 0.0458 0.0363 0.0400 0.0472 0.0360 0.0434 0.0350 0.0485 0.0419 0.0427

0.2157 0.2188 0.2200 0.2135 0.2225 0.2085 0.2035 0.2155 0.2493 0.2316 0.2156

0.6157 0.6145 0.6227 0.6310 0.6117 0.6237 0.6181 0.6197 0.5878 0.5824 0.6133

0.0433 0.0402 0.0451 0.0333 0.0404 0.0369 0.0443 0.0405 0.0291 0.0457 0.0353

0.0315 0.0346 0.0432 0.0428 0.0375 0.0464 0.0501 0.0414 0.0465 0.0648 0.0455

0.0610 0.0458 0.0324 0.0390 0.0404 0.0483 0.0405 0.0478 0.0387 0.0333 0.0474

4.77% 4.70% 4.63% 4.56% 4.50% 4.44% 4.38% 4.32% 4.27% 4.22% 4.17%

2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030

e6

The conditional probability P(F1|S) is calculated which are shown in table A.5. Table A.5 Prediction results of food demand growth rate from 2020 to 2030

2020 2021 2022 2023 2024 2025 2026 2027 2028 2029

f1 (-∞, 0%)

f2 [0%, 5%)

f3 [5%,10%)

f4 [10%, ∞)

ARIMA Prediction

0.2466 0.2475 0.2611 0.2585 0.2551 0.2546 0.2678 0.2427 0.2429 0.2701

0.7060 0.7169 0.6883 0.7026 0.7098 0.7074 0.6885 0.7129 0.7211 0.6849

0.0245 0.0147 0.0281 0.0174 0.0189 0.0212 0.0209 0.0183 0.0170 0.0225

0.0226 0.0207 0.0223 0.0213 0.0160 0.0167 0.0228 0.0260 0.0189 0.0225

2.0% 1.96% 1.92% 1.89% 1.85% 1.82% 1.79% 1.76% 1.73% 1.70%

22

Journal Pre-proof 2030

0.2386

0.7222

0.0182

0.0209

1.67%

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Journal Pre-proof 123. doi:10.1016/j.envsci.2016.12.018. Wicaksono, A., & Kang, D., 2018. Nationwide simulation of water, energy, and food nexus: Case study in South Korea and Indonesia. Journal of Hydro-Environment Research. doi:10.1016/j.jher.2018.10.003. WEF. World Economic Forum Water Initiative (2011). Water security: the water– food–energy–climate nexus. Washington, DC: Island Press. Yang, H., Zhou, Y., & Liu, J., 2009. Land and water requirements of biofuel and implications for food supply and the environment in China. Energy Policy, 37(5), 1876–1885. doi:10.1016/j.enpol.2009.01.035. Yoshikawa, S., Cho, J., Yamada, H.G., Hanasaki, N., Kanae, S., 2014. An assessment of global net irrigation water requirements from various water supply sources to sustain irrigation: rivers and reservoirs (1960–2050). Hydrol. Earth Syst. Sci. 18, 4289–4310. doi:10.5194 /hess-18-4289-2014.

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Journal Pre-proof Author Contribution Section

Jian Chai: Conceptualization, Funding acquisition, Supervision, Project administration Huiting Shi: Data curation, Methodology, Software, Formal analysis, Roles/Writing original draft, Validation, Visualization Quanying Lu: Investigation, Writing - review & editing, Resources Yi Hu: Investigation, Writing - review & editing

Journal Pre-proof Declaration of Interests

We declare that we have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. There's no conflict of interest exits in the submission of this manuscript.

Journal Pre-proof 1. Integrated resource management is crucial for national sustainable development. 2. Proposing a quantitative analysis framework based on Bayesian networks. 3. Water intake is directly affected by population growth and energy demand. 4. GDP and population are direct causes of changes in energy demand in the nexus. 5. Population is the only direct cause of changes in food demand in the nexus.

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