Ecological Network Analysis for a Virtual Water Network

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Ecological network analysis for a virtual water network - a case study of the Heihe River Basin Delin Fang, and Bin Chen Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/es505388n • Publication Date (Web): 04 May 2015 Downloaded from http://pubs.acs.org on May 13, 2015

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Environmental Science & Technology

Ecological network analysis for a virtual water network - a case study of the Heihe River Basin Delin Fanga, Bin Chena,*,§ a

State Key Joint Laboratory of Environmental Simulation and Pollution Control, School of Environment, Beijing Normal University, Beijing 100875, P R China

1 2

ABSTRACT

3

The notions of virtual water flows provide important indicators to manifest the water

4

consumption and allocation between different sectors via product transactions. However, the

5

configuration of virtual water network (VWN) still needs further investigation to identify the

6

water interdependency among different sectors as well as the network efficiency and stability in a

7

socio-economic system. Ecological network analysis is chosen as a useful tool to examine the

8

structure and function of VWN and the interactions among its sectors. A balance analysis of

9

efficiency and redundancy is also conducted to describe the robustness ( RVWN ) of VWN. Then,

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network control analysis and network utility analysis are performed to investigate the dominant

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sectors and pathways for virtual water circulation and the mutual relationships between pairwise

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sectors. A case study of the Heihe River Basin in China shows that the balance between efficiency

13

and redundancy is situated on the left side of the robustness curve with less efficiency and higher

14

redundancy. The forestation, herding and fishing sectors and industrial sectors are found to be the

15

main controllers. The network tends to be more mutualistic and synergic, though some

16

competitive relationships that weaken the virtual water circulation still exist.

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Keywords: Network analysis, Robustness, Virtual water network, Heihe River Basin

ACS Paragon Plus Environment


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1. INTRODUCTION

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Unreasonable water circulation has escalated water exploitation and exhaustion and even

20

intensified the irrational water wastage in socio-economic systems.1,2 It is necessary to explore the

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efficient and stable management of the socio-economic water system to meet the increasing water

22

demand for the rapid economic growth, population explosion and urbanization, particularly for

23

regions or countries prone to severe droughts.3-6

24

The notion of virtual water flows has been introduced to provide a useful indicator to

25

investigate the water allocation and circulation in a socio-economic system.7-9 Allan (1993)

26

initially proposed the concept of virtual water to evaluate the total volume of water required

27

during a commodity or service production process, in order to ameliorate the water deficit

28

problem in the Middle East.10,11 The methods for the evaluation of virtual water flows can be

29

sorted into two categories including bottom-up approach based on the detailed information about

30

the water footprint calculation,7,12,13 and top-down approach based on input-output table.14-16 The

31

bottom-up method evaluates the virtual water via accounting the water used throughout the

32

production of a good and the related international trade.17-19 Because of the merits of

33

comparatively reliable data collection, this approach has been employed in several researches.20,21

34

Nevertheless, such bottom-up approach does not trace the virtual water flows through the supply

35

chain in the trade network, which is critical to allocate the responsibility to the intermediate and

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final users.14 Environmental input-output analysis (EIOA) as a top-down approach may describe

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the supply chain effects in a comprehensive perspective and distinguish the responsibilities of

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final users and promote to discover the driving forces.22,23 Furthermore, it can investigate the


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virtual water circulation through sectoral, regional, national and global supply chain to identify the

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water importer or exporter, and further to facilitate the redistribution of water.22,24-29 The

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discriminations of water scarcities in different regions can also be taken into consideration via

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EIOA.15,30-37

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There are still few studies on stability issues of the virtual water flows from the perspective

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of the systematic configuration,38,39 which should be further explored to describe the network

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structures of inner interactions and distribution of water resources throughout the socio-economic

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system. Ecological network analysis (ENA), introduced by Hannon in 1973, aims to investigate

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the interdependence of species and functional groups and determine the distribution of both direct

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and indirect ecological flows in an ecosystem, thus providing a powerful tool for investigating the

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internal structure of the virtual water flows.40 Ulanowicz introduced information theory into

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ecological network analysis and presented a uniform way to quantify system’s effective

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performance (efficiency) and reserve capacity (redundancy) with a robustness metric to signify the

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tradeoff allotment.41-44 Bodini et al employed information-based ENA to evaluate water exchanges

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between different sectors and investigate the sustainability of water resources by measuring the

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system efficiency and flexibility.45,46 Li et al. used information-based ENA to analyze the water

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system’s structures and the intensity of synthesized water use intensity and to investigate the

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sustainable systems based on the optimal balance between network efficiency and resilience with

57

consideration of complex socio-economic characters.47,48 Furthermore, Kharrazi et al. applied this

58

approach to quantify the robustness of economic resource trade flow networks including virtual

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water, oil, world commodities and so on, incorporating both intensity and extensive dimensions of



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sustainability.49 Meanwhile, Patten et al. and Finn developed a line of flow-based ecological

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network analysis,50,51 which has been successful in evaluating the direct, indirect and cycling

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flows of an ecosystem’s energy and materials and the mutual relationships between compartments

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from a whole system perspective. 52-56 The flow-based ENA, including network control analysis

64

(NCA) and network utility analysis (NUA), has also been employed in the water system analysis

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to investigate the network’s structure and function via water circulation and mutual relationship

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analyses to show the interdependence and interactions between different sectors.57-59 Yang et al.

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also adopted NCA and NUA to identify the quantitative control or dependency relations, describe

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the mutual relation and distinguish the beneficiary and the contributor regions/countries in the

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global virtual water network based on agricultural and livestock production trade.58

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A virtual water network (VWN), shaped by virtual water flows circulating in the

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socio-economic system, needs to maintain itself in the long term under varying conditions, which

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can be assessed in terms of the network flows between compartments.48,60-63 The tracking of

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virtual water fluxes and pathways within the system will facilitate the regulation of virtual water

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circulation and the adjustment of the sectors’ responsibilities. Moreover, the identification of

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systematic configuration is critical to keep the balance of the efficiency and redundancy of VWN.

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The efficiency of VWN represents the capacity to perform within a sufficiently organized structure

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to maintain its integrity over time. However, the most efficient flow structure, one that has no

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option for parallel pathways, sometimes puts the VWN into a brittle situation when facing with

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perturbations. For instance, with the disappearance of nodes, the VWN will show little ability to

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sustain its original function. Conversely, virtual water systems featuring more parallel circulation


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pathways, including some weaker pathways (transferring flows with less amount of virtual water),

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will have a flexible reserve as redundancy to cope with internal and external changes, though

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sacrificing efficiency.49,60,61 The whole system is dominated by relatively few strong flows with a

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multitude of weak connections providing the safety margin for efficient virtual water circulation.62

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Information-based ENA can highlight the balance between both efficiency and redundancy on a

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system level and achieve a sustainable VWN. Furthermore, the flow-based ENA method can also

87

penetrate deeply into the sector and pathway level via NCA and NUA to investigate the control

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and dependent sectors, dominant and weaker pathways, and pairwise relations.55,58,56-66 It is

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therefore useful to combine two lines of ENA with a system-based view to deepen the

90

understanding of VWN.

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This paper is organized as follows: Section 2 emphasizes the methodology, including the

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ENA model, system robustness analysis covering efficiency and redundancy facets, network

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control and utility analysis. Section 3 illustrates the analysis results of the Heihe River Basin, such

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as the calculations of system robustness, and the control and utility conditions of VWN. The last

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section offers discussion of a range of model results.

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2. MATERIALS AND METHODS

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2.1 Construction of the VWN model

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A steady state model of the VWN is developed to illustrate the inter-compartmental flows,

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mutual relationships and network configuration from the perspective of ENA. Water resources IO

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model is established based on the basic economic IO model framework via incorporating with



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statistical data about water consumption of each sectors (see Sec. 2.6 of SI). The intermediate

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input/use matrix of water resources IO model shows a clear image of virtual water trade. The

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VWN is established based on this intermediate input/use matrix, which reflects the virtual water

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trade hidden in the production transactions in the socio-economic system. A steady-state system

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meets the requirement that, for each sector of the system, the total inputs equal the total outputs

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including both inter-sector flows and boundary flows, 66 i.e.,: n

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 i 1

n

fij  y j   f ji  z j

(1)

i 1

108

In the VWN model (Fig. 1b), fij stands for the virtual water trade flows (m3 yr-1)

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originating from compartment j to compartment i, i.e., virtual water flows produced by

110

compartment i and consumed by compartment j. fij only contains direct virtual water flows

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among sectors with the direction from the production side (matrix column) to others on the

112

consumption side (matrix row). z k represents the boundary inputs of compartment k (fresh

113

water), while yk is the boundary outputs (virtual water of net exports).

114

2.2 Information-based ENA

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The indicators of information-based ENA can show a system’s efficiency and

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redundancy.49,60-62,67,68 The ascendency, which stands for VWN efficiency, shows how well

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organized these water flows are. For example, a VWN with larger water flows along fewer

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pathways will have a higher ascendency. The redundancy shows the ability of a system to

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withstand perturbations. For example, a VWN where all water flows are equally distributed along

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all pathways will have a higher redundancy. The efficiency and redundancy are mutual

121

complements of system robustness. The indicator of robustness is used to identify the balance


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between the system’s efficiency and redundancy, which is essential for a system’s vitality. Below

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is a brief explanation of this method. A more detailed description of the method is provided in the

124

Supplementary Information (SI).

125

2.2.1 Efficiency analysis for network organization

126

The average mutual information (AMI) of a system shows the network’s capacity to perform

127

in an efficient and well-organized way to keep its integrity over the long term, which is adopted to

128

indicate the efficiency of a system from the structural perspective. AMI measures how much

129

knowing one of these variables reduces the uncertainty about the other. In a VWN, it stands for the

130

efficient end-to-end virtual water flows, which is crucial to catalyze the system’s operation and

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progression. The total system throughput of virtual water resources ( T.. ) includes the first order

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virtual water flows (m3 yr -1) transported among all sectors (only direct flows), i.e., the sum over all

133

combinations of fij . T. j stands for the flows originating from sector j, and Ti. represents the

134

 T. j  T  flows flowing into sector i. r  b j  =   and r  ai  =  i.  are the ratio of flows originating  T..   T.. 

135

from sector j to total system throughput and the ratio of flows streaming into sector i to total

136

 f  system throughput, respectively. r (ai , b j )=  ij  is the ratio of flows originating from sector j  T.. 

137

to sector i to total system throughput. AMI is defined as follows:

138

 r (ai , b j )  AMI  K  r (ai , b j ) log   r (a )r (b )  i, j j   i  fij   fijT..   K    log   T T  i , j  T..   i. . j 

139

where T..   fij , Ti.   fij , T. j   fij , and K is the scale coefficient. j

(2)

i



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The non-scaled AMI (i.e., K = 1) stands for the system’s authentic efficiency only from the

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structural perspective, which is not correlated with the size of the system, i.e., the amount of

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virtual water circulation. A VWN with high AMI value means that the flows within the network

143

are more concentrated with fewer dispersion pathways, indicating it is better organized with

144

higher efficiency. AMI scaled by T.. covers not only the intrinsic structure character of the system,

145

but also the dimension of the system. To clearly describe the diversification of the intrinsic

146

structure character, scaled AMI is not mentioned in the main text but used as gauge for system

147

efficiency in the Sec.2.2 of Supporting Information to address the size issues.

148

2.2.2 Redundancy analysis for network organization

149

The residual uncertainty stands for the unorganized part of the VWN, which is used to

150

evaluate the redundancy of the network. The high diversity and connectivity of a VWN guarantees

151

that the system will reserve diverse actions when encountered with the disruption of notes or

152

linkages. When faced with internal and external changes, the inefficient and indeterminate part of

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the virtual water flow structure is insurance for the VWN to reduce the chance of collapse (see Sec.

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2.1 of SI). The redundant pathways show the unconfirmed virtual water flows in the system,

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which provide excess options to dissipate weak throughput via various inefficient sectors. In

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information-based network analysis, the virtual water system residual uncertainty H c is defined

157

as follows:

158

  1 H c   K   r (ai , b j )  log   r (a )r (b )  i, j j   i 2  fij   fij    K    log   T T  i , j  T..   i. . j 


(3)

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Similar to AMI and ascendency, H c shows the residual uncertainty only from the authentic

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structural perspective with the scale coefficient K = 1. Redundancy displays the amount of wasted

161

“space” used to transmit certain water flows in a VWN. However, too many parallel pathways

162

make the VWN inefficient and cause some virtual water to flow along less efficient pathways. The

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scaled H c covering with system dimension conceals the intrinsic alternation of system structure,

164

so it is not chosen as the chief indicator. The explanation of scaled H c is given in Sec. 2.3 of SI.

165

2.2.3 Virtual water network robustness ( RVWN )

166

The system robustness is concerned with the balance between a system’s efficiency and

167

redundancy, measuring both how streamlined and articulated the system is and the possibility for

168

alternate flow paths, which are useful in case of internal and external changes.61,62 The virtual

169

water network robustness ( RVWN ) measurement can be derived from the indicators of efficiency

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and redundancy as follows. A relative measurement of the organized power flowing within the

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VWN, namely, the proportion of development capacity accounted for by the order degree (a, i.e.,

172

relative efficiency), is denoted by the following formula:

173

a  AMI / ( AMI  H c )

(4)

174

The RVWN depends on both the order and disorder of the system. The order part can be

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derived from the relative order (i.e., a), and the disorder part can be measured by the Boltzmann

176

formulation (i.e.,  k log(a ) ). Based on this result, the VWN interprets the balance between

177

efficiency (AMI) and redundancy ( H c ) as a single metric to show the degree of constraint and

178

degree of freedom in the system. 41,49 The RVWN is defined as follows:

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RVWN  -a log(a)

(5)



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The curve of RVWN is shown in Fig. S1 to illustrate the trade-off relationship between

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system efficiency and redundancy (see Sec. 2.2 of SI). The x axis shows the ascendency portion of

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the development capacity. If the indicator lies on the left side of the curve, the VWN is stagnant

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with less efficiency and more redundancy. If the indicator lies on the right side of the curve, the

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VWN is brittle and easily collapses in the face of internal or external changes because too much

185

efficiency sacrifices the redundancy of the VWN.

186

2.3 Network control analysis (NCA)

187

Network control analysis (NCA) is adapted to evaluate the dominance of one sector over

188

another via pairwise environs. The distributed control matrix is defined to explain the influence of

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one sector exerted on another within the overall system configuration, which is featured by the

190

integral flow. 55,56,56,69 The integral flow matrix is defined as N and N’, which includes both the

191

direct and indirect flows through the system:66

192

N  [nij ]  (I  G)1 N'  [nij1 ]  (I  G' )1

193

where G  [ gij ] , gij  fij / T. j ; G'  [ gij' ] , and gij'  fij / Ti. . Based on this equation, the control

194

difference matrix (CD) and dimensionless control ratio matrix (CR) can be defined to facilitate

195

the explanation of pairwise individual comparisons of the fractional transfer water values

196

considering both the direct and indirect effects:56

197

CD  [cdij ]  [nij  n ji ]

(7)

198

nij  n ji  ] nij  n ji  0, crij  [ max(nij , n ji ) CR  [crij ]   n  n  0, cr  0 ji ij  ij

(8)

199

where cdij and crij indicate the control influence of compartment j on compartment i via the


(6)

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integral system flows. If the CD value is positive, it stands for the control intensity; otherwise, it

201

shows the dependent intensity. CR is a non-dimensional matrix with a value between 0 and 1. If

202

the value is closer to 1, this pairwise relationship has a definite direction; otherwise, the control

203

pairwise relationship is weaker. Accordingly, the stronger or weaker control relations will be

204

reflected on the pathways. Thus, if the crij is closer to 1, the pairwise pathway can be defined as

205

a stronger pathway with definite direction. On the contrary, if the value is closer to 0, the pathway

206

can be described as a weaker pathway with uncertain directions as the two directions have

207

relatively equal strength. Furthermore, the mean value of positive crij (μ = Mean ( crij ), crij >0))

208

and standard deviation of positive crij (σ = Standard Deviation ( crij ), crij >0)) can be used to

209

identify the control power condition of the system.

210

Because the magnitude of the control difference values are additive, the sector magnitude of

211

control weighing can be evaluated by summing the rows of the CD matrix.56 The system control

212

vector matrix (SC) can thus be given as follows:

213

SC  [sc j ]  [ cdkj ]

n

(9)

k 1

214

where the subscript j represents the specific donor compartment. If the value of sc j is positive,

215

the focal sector j controls the system; otherwise, it is controlled by the system. Supported by the

216

NCA, the dominant sectors and strong linkages along with the dependent sectors and weaker

217

linkages can be identified.

218

2.4 Network utility analysis (NUA)

219

Network utility analysis (NUA) is used to evaluate the mutual relationships between different

220

sectors in the VWN. The mutual benefit between compartments is evaluated via a matrix of



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mutualism.70,71 The direct mutualism evaluates the direct relationship between compartments with

222

a direct utility matrix D:

223

D  dij   [

224

where dij is the inter-compartmental flow utility and Ti is the sum of flows in or out of sector i

225

when the system is at steady state. The integral mutualism considers both direct and indirect

226

effects encompassing the integral effects hidden in the system, interpreted via the integral utility

227

matrix U:

228

U  D0  D1  D2 

229

where D0 stands for the initial flows, D1 for the direct utility relation, and Dn for the direct

230

utility relationships realized by the extended flow pathways.

fij  f ji Ti

]

(10)

 Dn 

 (I - D)1

(11)

231

The relationships between different economic sectors can be identified through the

232

positive/negative signs of the mutualism index. In terms of the two opposite directions, there are

233

always two signs for each pair of compartments in the D and U matrices. The sign matrix of D and

234

U, i.e., SignD and SignU, facilitates the interpretation of the inner relationships between pair

235

compartments. In the two sign combinations of pair sectors, (+,+) stands for a mutualistic

236

relationship, (+,–) for an exploitative relationship, (–,+) for an exploited relationship, and (–,–) for

237

a competitive relationship (more information is shown in Sec. 2.4 of SI).70 Because U matrix

238

shows the integrated mutual relationships including both direct and indirect influences, only U

239

matrix is chosen to exhibit the system mutual utility condition.

240 241

From a systematic perspective, the network mutualism index (NM) and network synergism index (SI) can be used to determine the fitness of the current VWN:65,70


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NM  SignU () / SignU ()

243

SI   uij

n

(12)

n

(13)

j 1 i 1

244

where the NM is the ratio of the number of positive signs over the number of negative signs in U.

245

SI assesses the magnitude of the positive and negative relationships of a system. If the positive

246

signs are in the dominant position, (i.e., NM > 1 and SI > 0), the system is mutualistic. If not, some

247

negative or problematic pathways should be modified or mitigated.58,65

248

2.5 Study site and data

249

The Heihe River Basin is the second largest inland river basin in the arid region of northwest

250

China, covering an area of approximately 128,000 km2 with an altitude of 4300 m and annual

251

normal runoff of 1.58×109 m3. The location of the Heihe River Basin is illustrated in Fig. 1a. With

252

rapid socio-economic development and increasing population density, the unreasonable water

253

utilization structure in the middle regions of the Heihe River Basin leads to an extensive

254

exploitation of water resources. The Ganzhou District, which is chosen as a case study, is one of

255

the most developed regions in the middle region of the Heihe River Basin, with intensive

256

agricultural activities as the main economic contributor. The VWN is established on EIOA model

257

based on the data from Gansu Statistical Yearbook 2012, Zhangye Statistical Yearbook 2012 and

258

the work of Zhang (more information about data sources are shown in Sec. 2.6 of SI).72-74 In this

259

paper, the VWN of the Ganzhou District is aggregated into six economic sectors, each of which

260

consists of a block of sectors with similar water use habits, to manifest the virtual water

261

circulation (see Fig. 1b). This aggregation of sectors allows us to distinguish the pairwise

262

relationship between similar sectors as a block and the other remaining blocks, without having to



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aggregate more than is required by the available data. 30 The sectors include (1) Farming (Far), (2)

264

Livestock (Liv), (3) Forestation, Herding and Fishing and related activities (FHF), (4) Industrial

265

(Ind), (5) Construction (Con) and (6) Services (Ser). The investigation time ranges from 2002 to

266

2010.

z1

y1

1 Far f61 z6

y6

f12 f16

f34

f62 6 Ser

f65 f64

2 Liv f24

f32

f23

f41 f14 f53

5 Con

z5

y2

f42

f36 f46

y5

z2

f21

f26 f63

f56

f43

f54

3 FHF f43

f45

f34

y3

z3

4 Ind y4

z4

267 268

(a)

(b)

269 270

Fig. 1 Virtual water network model for Ganzhou District in the Heihe River Basin.

271

Notes: fij : Virtual water flows from j to i. yk : Boundary outputs for k. zk : Boundary inputs for

272 273

k.

274

3. RESULTS

275

3.1 Calculation of RVWN

276

3.1.1 Average Mutual Information (AMI)

(a) Study site, (b) Virtual water network model

277

The results of AMI representing the system efficiency are shown in Fig. S3. The AMI reaches

278

a peak value of 0.053 in 2007, implying that the virtual water flows are highly concentrated with


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279

clear directions and the system efficiency is at its highest; however, in 2002, the AMI value is at its

280

lowest with a value of 0.031 because the virtual water flows are relatively evenly distributed,

281

providing less room for specialization and indicating that the flow distribution along the pathways

282

between different sectors influences the AMI of the VWN. The results of scaled AMI are shown in

283

Sec. 3.2 of SI.

284

3.1.2 Residual uncertainty ( H c )

285

The values of H c representing the redundancy during 2002-2010 (see Fig. S5) range

286

between 0.2 and 0.4; H c declines to its lowest value in 2005 and increases to its highest value of

287

0.391 in 2008. The even distribution of virtual water flows means the network system has more

288

options to deliver water flows, which improves the system’s capacity to keep stable when faced

289

with internal or external changes. The results of scaled H c are shown in Sec. 3.3 of SI.

290

3.1.3 Degree of order (a) and RVWN

0.4 0.35 0.3

RVWN

0.25 0.2 0.15 0.1 0.05 0

291 292

Redundancy 0

0.1

0.2

0.3

Efficiency 0.4

0.5

0.6

0.7

0.8

0.9

a Fig. 2 The relationship between a and RVWN in the VWN


1


Page 16 of 35

293 294

The calculation results of a are shown in Fig. S7, which is affected by the combination of

295

AMI and H c . The relationship between a and RVWN is depicted in Fig. 2. From 2005 to 2007, the

296

VWN has the highest a and RVWN values, indicating that the VWN is well organized with more

297

regularity and orderliness compared with the VWN in other phases. All of the RVWN dots are

298

scattered on the left side of the robustness curve, demonstrating that the VWN is characterized by

299

higher redundancy and lower efficiency.

300

3.2 NCA for the VWN

Control and Dependence Intensity

8.0E-5

Far Liv FHF Ind Con Ser

6.0E-5 4.0E-5 2.0E-5 0.0 -2.0E-5 -4.0E-5 -6.0E-5 2002

2003

2004

2005

2006

2007

2008

2009

2010

Year

301 302 303 304 305

Notes: Dots above the horizon line (the dotted line) mean the sector is the controller of the system;

306

The system control or dependence intensity of each sector is shown in Fig. 3 based on the

307

results of the SC matrix. Before 2008, the control intensity of each sector is spread in a large scale,

308

while the distribution trend significantly converges afterward. This observation indicates that the

Fig. 3 The system control or dependence intensity of each sector otherwise, the sector is dominated by other sectors.


Page 17 of 35


309

control powers of all of the sectors are comparatively equally distributed, and the system is not

310

controlled by single or minor sectors.

311

From 2002 to 2004, Ind is the largest controller of the VWN. However, the situation changes

312

from 2005 to 2007, when the dominant sector became FHF. From 2008 to 2010, Ind becomes the

313

controller again. As for the dependents, the value of Con is always below the horizon line in a

314

large scale, especially from 2002 to 2007, which indicates that Con is the major dependent in the

315

VWN. The variation curves of FHF, Ind and Ser shows sudden changes from 2005 to 2007.

316

During this period, FHF becomes the dominant controller. Meanwhile, Ind loses its position of

317

major controller in the VWN, as it is before and after this period. Ser turns into a dependent that

318

received virtual water from other sectors, and then becomes a controller again from 2008 to 2010.

319

The change tendencies of the dependence of Con and Liv are similar, where the dependence

320

intensity on other sectors declines. Far’s dependence strength declines from 2002 to 2007, and it

321

becomes a controller from 2008 to 2009. μ = 0.704

σ = 0.266

μ = 0.763

σ = 0.253 1

Far

0.9

Far

0.8 Liv

0.7 0.6

FHF

0.8 Liv FHF

0.6

Ind

0.4

0.5 Ind

0.4 0.3

Con

Con 0.2 0.1

Ser Far

Liv

FHF

Ind

Con

Ser

0.2 Ser Far

Liv

FHF

Ind

(b) 2003,2004

(a) 2002


Con

Ser

0


μ = 0.887

σ = 0.166

Page 18 of 35

μ = 0.808

σ = 0.231

1

Far

Far

0.9 0.8

0.8

Liv

Liv

0.7 FHF

0.6

FHF

Ind

0.4

Ind

0.6 0.5 0.4 0.3

Con

Con

0.2

0.2

0.1

Ser

Ser Far

Liv

FHF

Ind

Con

(c) 2005,2006,2007

Ser

0

Far

Liv

FHF

Ind

Con

Ser

0

(d) 2008,2009,2010

322 323 324 325 326

Notes: The control/dependence relationships between sectors are presented from the production

327

Fig. 4 shows the control ratio condition of each sector. In 2002, Ind and Ser are the two main

328

dominators of the system. Liv and Con depend on other virtual water suppliers (i.e., Far, FHF, Ind

329

and Ser). From 2003 to 2004, FHF is the major virtual water resources supplier, and every control

330

power on other sectors is above 80%. Liv still significantly depends on other sectors, which are all

331

above 50%. During the stage from 2005 to 2007, this situation is intensified. The control power of

332

FHF on others is above 95% on average. The reliance of Liv on other sectors is nearly 99%,

333

indicating that the virtual water resources of Liv seriously rely on imports from others and rarely

334

exports to other sectors. From 2008 to 2010, the system’s control state changes obviously so that

335

Ind became the major controller, and FHF and Con become the largest dependents with average

336

values above 80%.

Fig. 4 Pairwise control relationship between each sector of the VWN derived from the results of the control ratio matrix (CR) side (matrix column) to others on the consumption side (matrix row).

337

In addition to the dominant sectors, the stronger and weaker pathways can also be identified.

338

Strong linkages exist between the following pairwise sectors: Far – Liv, FHF – Liv, Ser – Liv,

339

FHF – Con and Ind – Con. The pairwise relationship with control intensity lower than 50% can be


Page 19 of 35


340

defined as weaker control relation. The weaker pathways include Liv – Con, Ind – Ser and Ser –

341

Con.

342

Regarding the statistic indicators in Fig. 4, it can be seen that the system’s control strength

343

from 2005 to 2007 is the most powerful with an average control ratio value (μ) of 0.887.

344

Furthermore, the standard deviation value of the control ratio (σ) is comparatively lower,

345

indicating that the control power is more centralized to such a high level.

346

3.3 NUA for the VWN Far

+

Liv

+ -

+

FHF

+ -

- +

+

Ind

- +

- +

- +

+

Con

- -

- -

+ -

+ -

+

Ser

- +

- +

- +

- -

- +

+

Far

Liv

FHF

Ind

Con

Ser

NM = 1.00 SI = 5.68

Far

+

Liv

+ -

FHF - +

- +

+

Ind

- +

- +

+ -

+

Con

- -

- -

+ -

+ -

+

Ser

- +

- +

+ -

+ -

- +

+

Far

Liv

FHF

Ind

Con

Ser

(a) 2002

(b) 2003,2004

Far

+

Liv

+ -

+

FHF

+ +

+ +

+

Ind

- +

- +

+ -

+

Con

+ -

+ -

+ -

- -

+

Ser

- +

- +

+ -

- +

- -

+

Far

Liv

FHF

Ind

Con

Ser

NM = 1.40 SI = 5.91

(c) 2005,2006,2007

347 348 349 350 351 352 353

NM = 1.12 SI = 5.48

+

Far

+

Liv

+ -

NM = 1.12 SI = 6.07

+

FHF + -

- -

+

Ind

- +

- +

- +

+

Con

+ +

- -

+ -

+ -

+

Ser

- -

- +

- +

+ -

+ -

+

Far

Liv

FHF

Ind

Con

Ser

(d) 2008,2009,2010

+ + Mutualistic relation

- + Exploited relation

+ - Exploitation relation

- - Competition relation

Fig. 5 Integral mutual relationship for the VWN Notes: The integral utility relationships between sectors are presented from the production side (matrix column) to others on the consumption side (matrix row). The block with dark blue shadow means that the mutual relationship of these two sectors differs from the one of the previous phase. NM (network mutualism index): ratio of the number of positive signs over the number of negative signs in utility matrix. SI (network synergism index): summation of all elements of the utility



354

matrix to assess the magnitude of the positive and negative relationships of a system.

355

Fig. 5 shows the integral relationships (in the integral utility sign matrix, SignU) between

356

pairwise social-economic sectors in the VWN. In 2002, there are only two types of relationships,

357

exploitative and competitive. The competitive relationships account for 25% of the total

358

relationships, including the pairwise sectors of Far – Con, Liv – Con, and Ind – Ser, which

359

indicates that the Con water requirement puts stress on the irrigation and livestock water supply

360

and the local industrialization sacrifices the public services’ water supply. The Ind and Ser sectors

361

are the largest contributors during the water trade interactions, as they are under the exploitation of

362

4 other sectors. Liv is the largest water beneficiary because it exploits the Far, FHF, Ind and Ser

363

sectors. From 2003 to 2004, four relationships change. One competitive relationship changes to an

364

exploitative relationship (Ind – Ser). The directions of three exploitative relationships shift, which

365

are all correlated with FHF, including Far – FHF, FHF – Ind, and FHF – Ser. Afterward, FHF

366

become the largest contributor as it is exploited by every other sector, while Far and Liv turns into

367

the major exploiters of the FHF, Ind, Con and Ser sectors. From 2005 to 2007, a mutualistic

368

relationship occurs in the pairwise relations of Far – FHF and Liv – FHF, indicating that the inner

369

relationships among the three agricultural sectors are prone to the synergism. Two competitive

370

relationships change to exploitative relationships (Far – Con, Liv – Con), and two exploitative

371

relationships alter to competitive relationships (Ind – Con, Con – Ser). All of them are correlated

372

with Con as the largest exploiter. The largest contributor is FHF, as it owns positive utility

373

relationships with all other sectors, transferring virtual water to the other sectors. From 2008 to

374

2010, Liv is the most competitive one, as it competes with FHF and Con and is exploited by Far,

375

Ind and Ser. Ind delivers profits through water transactions to other sectors, as it is the contributor


Page 20 of 35

Page 21 of 35


376

to other five sectors. During the whole period (2002–2010), two pairwise relationships

377

continuously change, i.e., FHF – Far ((+,–) → (–,+) → (+,+) → (+,–)) and Ser – Ind ((–,–) → (+,–)

378

→ (–,+) → (+,–)).

379

The exploitative relationship is the dominating one among the pairwise relations throughout

380

the study period, with proportions above 67.7% and as high as 83.3%. The competitive

381

relationship always exists, indicating that the virtual water transaction structure of VWN inclines

382

to a relationship of competition between sectors.

383

4. DISCUSSION

384

Unlike fresh water management strategies, which mainly focus on the efficiency of the target

385

production processes of water utilization, the VWN provides an integral view via the link of

386

virtual water flows with different socio-economic activities. ENA is a powerful tool considering

387

its detailed pathway-focused analysis based on the network configuration and nodes’ interactions.

388

It uncovers the indirect flows and influences hidden in the network systems from a whole

389

systematic perspective, which contributes greatly to the formation of a system’s structure and

390

function. Different from the accounting methods that only focus on the efficiency aspect, ENA can

391

evaluate the stability of the whole system from the balance between efficiency and redundancy,

392

which is vital for the system’s stability long-term sustainability. In addition, the anatomy of the

393

network can be characterized by NCA and NUA based on how the virtual water flows are

394

distributed within a network at the sectoral and pathway levels. The network’s control and

395

dependence intensity and the mutual relationships between pairwise sectors display another facet

396

of the VWN that might be helpful to water resources management, i.e., it uncovers the dominators



397

and dependents along with the beneficiaries and contributors of the system. As such, ENA

398

highlights the pathways of flows and interactions between sectors, thus manifesting the

399

sector-level dynamics and system-wide conditions for reasonable water resources allocation in the

400

VWN.

401

The case study of Ganzhou District in the Heihe River Basin based on ENA shows that, the

402

agricultural sector is the major local economic sector with high-intensity water consumption. The

403

current policies for water management emphasize the control of the total amount of water

404

consumption in this region, ignoring the balance between efficiency and redundancy for virtual

405

water circulation within the socio-economic system. Although the total fresh water consumption

406

declines (see Sec. 3.1 of SI), the efficiency of VWN is still low. Compared to the previous studies

407

(see Sec. 2.2 of SI),49,60,61 it can be seen that the robustness of VWN remains on the left-side of the

408

ideal robustness curve, implying that the VWN has a higher redundancy level due to stable

409

circulation among various sectors but lower system efficiency, which is contrary to the intuition

410

that human-designed networks should be more efficient. This occurs because except for the

411

freshwater flowing through specific supply chains, the water hidden in the products or services is

412

circulating within diverse sectors with more exchanges along various pathways, which results in

413

higher redundancy.

414

The stronger control pathways are identified based on NCA as Far – Liv, Ser – Liv and FHF

415

– Con, indicating that there are clear water flow directions from Farming to Livestock, Services to

416

Livestock, and Forestation, Herding and Fishing to Construction sectors. The weaker pathways,

417

including Ind – Ser and Ser – Con, mean that the water flows between the pairwise sectors are not


Page 22 of 35

Page 23 of 35


418

totally controlled by one side, i.e., the virtual water flow directions from the Industry to Services

419

and Services to Construction sectors are not obvious. From the sectoral perspective, the

420

controlling effects of Ind as the largest controller of Far and Liv are notable, indicating that the

421

agricultural activities need great inputs from industrial products associated with huge water

422

consumption, e.g., farm machinery or irrigation systems. Although the farming sector is the largest

423

water consumer in this region, the major controller is industrial sector instead of farming sector.

424

This is because that most of the agricultural products are exported to other regions instead of

425

consumed in local area, while the industrial products are usually consumed locally to support

426

economic production activities, which is critical for the local virtual water circulation. Although

427

farming sector consumes large amount of water resources directly, it still exploits water resources

428

from local industry sector indirectly. From the network perspective, it is significant to improve

429

water utilization efficiencies of both agricultural and industrial sectors because agricultural sector

430

is the main direct consumer while industry sector contributes virtual water to agricultural activities

431

in an indirect manner.

432

The NUA results show that the NM indicator (positive/negative signs) in the matrix during

433

the study period is higher than or equal to 1, implying that the system has more positive utility

434

relationships and is in a better mutualism shape. In particular, the NM reaches its highest value

435

from 2005 to 2007, indicating that the system is under the most mutualistic conditions. Although

436

the NM declined from 2008 to 2010, the SI indicator reaches its highest value, demonstrating that

437

the system has an increasing synergism. Moreover, the diagonal elements of SignU are all positive,

438

showing that all of the sectors have an active utility impact on each other. However, it should be



439

noted that although the system shows a good performance of mutualism and synergism, there are

440

still some competitive relationships that may cause potential risk for the water security in the

441

current configuration of VWN.

442

There are various water management policies aiming to mitigate the contradiction between

443

water supply and water demand in the Heihe River Basin, which are mainly about the reduction of

444

total water inputs.13,15,75 This study aims to add an accurate investigation of virtual water flow

445

network, which uses ecological network analysis to cover both direct and indirect flows and

446

describe the water system structure and sectoral characteristics via virtual water transaction. The

447

results show that the efficiency of VWN is still low, indicating that it needs more virtual water

448

flows to pass through stronger pathways with higher virtual water intensity. It can be seen from

449

NCA and NUA that Con – Liv, Ser – Ind and Ser – Con are weaker pathways with unclear

450

pairwise relations, i.e., Con – Liv: (–,–) → (+,–) → (–,–), Ser – Ind: (–,–) → (+,–) → (–,+)

451

→ (+,–), Ser – Con: (–,+) → (–,–) → (+,–). Thus, strengthening the virtual water trade between

452

Con – Liv, Ser – Ind and Ser – Con might improve the VWN structure and promote the systematic

453

efficiency. Meanwhile, from the sectoral perspective, farming sector is the major direct water user

454

and imports net virtual water from industry sector indirectly. The indirect water consumption

455

correlated with industrial activities should therefore be considered to coordinately reduce the

456

virtual water consumption of farming activities, e.g., improving the production technology of local

457

industries or importing industrial products from other regions outside the Heihe River Basin.

458 ACKNOWLEDGEMENTS


Page 24 of 35

Page 25 of 35


This work was supported by the Fund for Creative Research Groups of the National Natural Science Foundation of China (No. 51121003), Major Research Plan of the National Natural Science Foundation of China (No. 91325302), National Natural Science Foundation of China (No. 41271543), and Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20130003110027).

ASSOCIATED CONTENT Supporting Information Available The explanatory details of ENA methodology and calculation details of VWN are presented in the Supporting Information. This information is available free of charge via the Internet at http://pubs.acs.org/.

459

AUTHOR INFORMATION 460

Corresponding author

461

**Tel.: +86−10−58807368; fax: +86−10−58807368; e−mail: [email protected] (Bin Chen).

462

Affiliation: State Key Joint Laboratory of Environmental Simulation and Pollution Control,

463

School of Environment, Beijing Normal University, Beijing 100875, China

464 465

Author Contributions

466 467 468

§Both authors have equal contribution as the first author.

469

The authors declare no competing financial interest.

Notes

470



471

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Ecological Network Analysis for a Virtual Water Network

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