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Virtual Water

March 4, 2013

Readers of this blog will likely remember virtual memory, the savior of personal computing in the days before abundant and inexpensive memory chips. Virtual memory allowed magnetic disk storage to be a seamless extension of a computer's working memory space. Virtual memory worked adequately, until memory usage became so great that thrashing occurred. It was easy to diagnose this problem, since hard disk drives in those days made a lot of noise.

Wikipedia has a list of the many things described as virtual. These include virtual ground, beloved of analog circuit designers like me,[1] virtual reality; and virtual colonoscopy, which is very close to what a Star Trek version of this examination might be, but still not as thorough as the real thing.

There are a few virtual items in physics, including virtual work, which, surprisingly, doesn't concern Wally. The Dilbert character, Wally, bears a close resemblance to one of my undergraduate physics professors. In his defense, my professor did quite a bit of "real" work, he supervised my independent study, and he further facilitated my entré into graduate school. There's also the interesting concept of virtual particles.

Virtual particles exist because of the inherent uncertainty of quantum mechanics, succinctly expressed by the Heisenberg uncertainty principle
σp σxh/4π

in which σp and σx are the standard deviations of momentum and position, and h is Planck's constant. The time (T)-energy (E) equivalent of this formula (usually expressed as ΔE ΔT ≥ h/4π, although this is a simplification) reveals the magical property that particles can come into existence for short periods of time out of nothingness. "Real" particles can interact with each other through an exchange of of a virtual particle. These interactions can be pictured in Feynman diagrams, an example of which is shown in the figure.

Feynman diagram for exchange of momentum between two particles.

Feynman diagram for exchange of momentum k between particles with initial momenta, p1 and p2.

In the case of electrons interacting electromagnetically, the momentum transfer is effected by a virtual photon, shown by the dashed line.

(Via Wikimedia Commons))

Empty space is not that empty, as Paul Dirac theorized. It can be visualized as a background of pairs of virtual electrons and virtual positrons, eponymously named the Dirac sea. The Dirac sea explains some strange properties of the vacuum, such as vacuum polarization.

Now that we've summarized the more technical virtual objects, it's time to get to a currently important topic in a world becoming increasingly starved of potable water; namely, the concept of virtual water. Virtual water is water used in the growth, harvesting and packaging of food, or the manufacture of commodities.

Virtual water is important, since it depletes water resources, and it's most important when these items are shipped outside of a country; that is, the country is exporting its water, often without realizing it. Such water export has currency, since we may be facing the prospect of peak water as a complement to peak oil. I reviewed some of the world's water problems in a previous article (The Water Equivalent of Energy, June 1, 2010).

It's projected that 1.8 billion people will face water scarcity by 2025, at which time two thirds of the world's population may be subjected to water stress.[2] China, which has polluted about seventy percent of its water supply, is likely to run out of fresh water by 2030.[3] The 2030 Water Resources Group states that competing demands for water resources may lead to an estimated 40 percent supply shortage by 2030.[4]

Global water distribution

Water, water,
every where,
Nor any drop to drink.

(A portion of figure 4.1, slightly modified, from ref. 2.)

The concept of virtual water was invented in 1993 by John Anthony Allan, a professor at King's College London. His focus at that time was on the arid and semi-arid Middle East, and he suggested that countries there could "import" water by importing food.

As an extreme example, about 1,600 cubic meters of water are needed on average to produce a metric ton of wheat. It takes gallons of water to produce an integrated circuit. Israel exports a lot of water when it exports citrus fruits to Europe. Water deficient countries would save considerable water by importing meat, since livestock are fed grain with considerable virtual water content.

Physicists from the University of Padua have teamed with environmental scientists from the École Polytechnique Fédérale de Lausanne in a paper on virtual water recently posted on arXiv.[5] Their paper is an analysis of the global water imbalance and a caution about export policy and the food trade.

Figure caption

Dependency of countries on local and virtual water from data for the years 1996-2005. The political situation in the former Soviet Union during that time made analysis of that data more difficult. (Figure 1 of ref. 5.)

The primary point of the analysis is that water-rich countries will likely reduce their export of virtual water in the future, leaving water-poor countries at risk. The authors propose the following mitigating scenarios.[5]
(1) Cooperative interactions among nations whereby water rich countries maintain a tiny fraction of their food production available for export.
(2) Changes in consumption patterns.
(3) A positive feedback between demographic growth and technological innovations.

The first two points are political solutions, whereas the last point is a call for more R&D. I place more faith in the R&D solution than politics.

Net flow of virtual water between selected countries

Go with the flow.

Net flow of virtual water between selected countries

(Figure 2, modified, from ref. 5.)


  1. Dev Gualtieri, "Driven Shield Enables Large-Area Capacitive Sensor," Electronic Design, Jan. 15, 2013.
  2. Russell Arthurton, et al., Chapter 4 - "Water" from Global Environmental Outlook - GEO4 environment for development, United Nations Environment Programme, 2007 (23.5 MB PDF file).
  3. Cherian Thomas, Unni Krishnan and Sophie Leung, "China-India Water Shortage Means Coca-Cola Joins Intel in Fight," Bloomberg Online (May 26, 2010).
  4. Charting our water future, 2030 Water Resources Group, 2009.
  5. Samir Suweis, Andrea Rinaldo, Amos Maritan and Paolo D'Odorico, "Virtual water controlled demographic growth of nations," arXiv Preprint Server, January 29, 2013.

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