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Water for food:
The global virtual water trade network
ENAC /
EDCE
Auteur(e)s
Samir Suweis1
Encadrement Prof. A. Rinaldo1
2010
1
Laboratory of Ecohydrology (ECHO)
What is Virtual water ?
We might not be aware, but the food production is by far the most freshwater-consuming process (90% of the total world
water resources! [1]). Figure 1 shows estimations on the volume of water needed to produce some ordinary food and drink
products [1,2].
Figure 1
Virtual water is defined as the amount of water used in the entire production process of a given commodity [3].
We calculated the virtual water content (VWC) of 5 unprocessed crops (barley, corn, rice, soy, and wheat) and 3 livestock
products (beef, chicken, and pork) for each nation by water withdrawal source using the H08 global hydrological model at
a spatial scale of 0.5o x 0.5o [4]. VWC of crops is defined as the evapotranspiration during a cropping period divided by the
crop yield. The VWC of unprocessed livestock products is proportional to the the water consumption per head during the
livestock life cycle.
Due to population growth, economic development and climate change, recurrent or ephemeral water shortages are a
crucial global challenge, in particular because of their impacts on food production.
The global
Figure 2
Figure 3
Virtual
water
trade
network (GVWTN)
Data on international food trade from the year 2000 and concerning the 184 nations under study,
have been obtained from FAO [5]. Combining the H08 model outputs with the food trade we
calculate VW flows among nations and the weighted GVWTN is built. By analyzing the network
we can identify VW importer and exporter (Fig. 2-3). VW water flows can be also aggregated from
country scale continental scale [6] (Fig. 4).
Mathematical Box
The network is described by a
matrix W, whose elements wij
represent the VW traded from
country i to node j; aij=ϴ(wij) is
1 if i is linked to j, 0 otherwise.
The network is characterized by
the following node’s properties:
The main results of the network analysis are:
• high heterogeneity of the volumes of traded VW: only 4% of
the total links accounts for 80% of the total flow volume;
• nodes with high degree tend to provide connectivity to nodes
Figure 4
with low degrees, but typically with small fluxes;
• The average clustering coefficient is very high and the graph exhibits a small-world network
behavior [7], providing a quantitative measure of the globalization of water resources.
ModelLing: controls of the GVWTN
Figure 5
We have developed a model that allows a concise description of the GVWTN. Our findings
show that the topological and weighted features of the network can be determined,
respectively, by two external characteristics of each node: namely, the gross domestic product
(GDP) and the (average) yearly rainfall [mm/yr] on agricultural area [km2] (RAA
[mm·km2/yr]). In the literature this type of control variables are known as fitness variables.
P>(x) is the probability of having a value ≥ x
Figure 6
They measure the relative importance of the vertices in the GVWTN. GDP and RAA are
assumed to be good candidates to explain the structure of the GVWTN. In fact the country
GDP is closely related to its trade activity, while volumes of VW traded depend on the amount
of crops and meat produced in that country, that in turn depends on the RAA. A good
agreement between data and model results proves these facts (see figures 5 and 6).
Mathematical Box
The fitness network-building
algorithm consists in: a) we
connect every couple of distinct
vertices, i-j with a probability
p(xi; xj) = σxixj /(1 +σxixj); b) we
assign to each link between i and
j a weight wij with value given by
q(yi; yj) =η yiyj . The parameters
of the model are σ and η and
they are determined by the
conditions: Σi,j p(xi; xj)=L and
Σi,j q(yi; yj)=Φ, where L is the
total number of edges and Φ the
total flux. x and y are the
normalized GDP and RAA.
Future Scenarios
Figure 7
Our theoretical framework is suitable to investigate future scenarios of the GVWTN structure. We estimate the annual rainfall for
2030-2050 from the A2 socio-economic scenario of the World Climate Research Program [8]. Then by using published
projections of the GDP and RAA [9], we build the fitness functions p(xTi; xTj) and q(yTi ; yTj ), where xT and yT are the projections
of the fitness variables at year T = 2030. All climate change scenarios yield a decrease in rainfall at a global scale, but the total
arable land is predicted to increase around 1%, thereby leading to an increase of the total RAA. We find that the nations with
larger strength benefit from these changes in RAA.
Figure 7 summarizes the results of the structure of the GVWTN under the driest climate change scenario (in green; the black line
instead refers to the year 2000). These results suggest that these economic and climatic future scenarios will likely enhance the
globalization of water resources, giving to water-rich countries even more inroad for reaching poorly connected nodes. At the
same time, the observed rich-gets-richer phenomenon will intensify the reliance of most of the nations on the few VW hubs.
References
[1] Hoekstra, A., and A. K. Chapagain, Globalization of Water, (2008) [2] Kekeritz, T., The Virtual Water Project, http://virtualwater.eu/ [3] Allan, T., Alloc. and Manag. 2, 13–26, (1993)
[4] Hanasaki, N., T. Inuzuka, S. Kanae, and T. Oki, J. Hydrol., 384 (3-4), 232–244, (2010) [5] FAO, Food trade data, www.faostat.fao.org , (2000) [6] Konar, M. et al., Water Resour. Res., 47, (2011)
[7] Suewis, S. et al., Geophys. Res. Lett., 38, L10403, (2011) [8] Meehl,G.A., Bull. Amer. Met. Soc., 88, 1383–1394 , (2007) [9] FAO, World agriculture: towards 2030/2050, (2000).