# Simple Myths and Basic Maths About Greening Irrigation

## Abstract

Greening the economy is mostly about improving water governance and not only about putting the existing resource saving technical alternatives into practice. Focusing on the second and forgetting the first risks finishing with a highly efficient use of water services at the level of each individual user but with an unsustainable amount of water use for the entire economy. This might be happening already in many places with the modernization of irrigated agriculture, the world’s largest water user and the one offering the most promising water saving opportunities. In spite of high expectations, modern irrigation techniques seem not to be contributing to reduce water scarcity and increase drought resiliency. In fact, according to the little evidence available, in some areas they are resulting in higher water use. Building on basic economic principles this study aims to show the conditions under which this apparently paradoxical outcome, known as the Jevons’ Paradox, might appear. This basic model is expected to serve as guidance for assessing the actual outcomes of increasing irrigation efficiency and to discuss the changes in water governance that would be required for this to make a real contribution to sustainable water management.

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## Notes

1. 1.

Government subsidies for irrigation modernization are common across OECD countries, covering the totality or part of the irrigation modernization costs. This is the case for example of Australia, Austria, Mexico, the Netherlands, Portugal or Spain (OECD 2008).

2. 2.

Water withdrawal is water removed from its source for a specific use, while water use refers to the effective demand by users. The two flows are not the same because of leaks. In this paper we assume that there is no change in the transportation and delivery efficiency and we will refer directly to the technical efficiency of water use.

3. 3.

In hydrology, a water balance equation can be used to describe the flow of water in and out of a system. A general water balance equation is:

$$P= Q+ E+\varDelta S$$

Where P is precipitation, Q is runoff, E is evapotranspiration and ∆S is the change in water storage (in soil or the bedrock).

4. 4.

It should be noted, though, that after being withdrawn, water does not have the same quality nor follows the same pathway as before the withdrawal. This may have a relevant impact over economic activities downstream (Dolan et al. 2014; Wu et al. 2013).

5. 5.

There is a third possibility: neither an increase, nor a decrease, but rather no change. That is, the same amount of water is used as before; none is saved for (1) other uses or (2) the natural environment. For the purpose of rejecting irrigation efficiency increases as a water-saving measure it is enough to show that there is no change in water use, i.e. no savings.

6. 6.

The Spanish Irrigation Plan (Plan Nacional de Regadíos, PNR) 2000–2008 was a large investment effort with the aim of reducing agricultural water use. This Plan was complemented with the Shock Plan 2006. Both plans invested 7,368 M EUR to modernize 2,244,570 ha of irrigated lands and forecasted a reduction in water use of 3 662 hm3/year (MAGRAMA 2013). However, since the implementation of the PNR, water use from agriculture in these areas are far from decreasing (Gutierrez-Martin and Gomez 2011; Rodríguez-Díaz et al. 2012).

7. 7.

E measures the technical efficiency of the irrigation technology in place with, for example, typical values of 0.5 for traditional gravity, 0.7 for sprinklers and 0.9 for drip devices.

8. 8.

We also assume that this function is continuous. Non continuous functions may be of relevance for further empirical research, but it is out of the scope of this analytical paper.

9. 9.

This is the case in most of the irrigation modernization plans, such as those of Spain, Portugal, Mexico or Australia, where bulk water supply is controlled by a supplier that decides on the prices. (OECD 2008). However, this price-taking assumption is not valid if farmers are directly pumping water from an aquifer, where drawdown would influence costs and provide a counterbalancing impact on the rebound effect (Dumont et al. 2013).

10. 10.

The overall cost would still increase (to the public sector or whoever is paying the energy subsidies) and this is another drawback of this intervention.

11. 11.

Hence, irrigation efficiency is naturally higher in places where water is more productive, and irrigation modernization is perceived as a way to increase water productivity and to reduce exposure to water shortages.

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## Acknowledgments

The research leading to these results has received funding from the EU’s Seventh Framework Program (FP7/2007-2013) under grant agreements n° 265213 (EPI-WATER - Evaluating Economic Policy Instruments for Sustainable Water Management in Europe) and n° 308438 (ENHANCE - Enhancing Risk Management Partnerships for Catastrophic Natural Disasters in Europe).

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Correspondence to C. Dionisio Pérez-Blanco.

## Appendix

### The Efficiency Elasticity of Water Use (∈ W,E )

According to Eq. (7):

$$\frac{dW}{dE}=-\left(\frac{W}{E}+\frac{\frac{\partial F\left( E W\right)}{\partial \left( E W\right)}}{\frac{\partial^2 F\left( E W\right)}{\partial {\left( E W\right)}^2}{E}^2}-\frac{\frac{\partial c(E)}{\partial E}}{\frac{\partial^2 F\left( E W\right)}{\partial {\left( E W\right)}^2}{E}^2}\right)$$

Which, after multiplying both sides by $$\frac{E}{W}$$, results in:

$$\frac{dW}{dE}\frac{E}{W}={\mathit{\in}}_{W, E}=-1+\frac{\frac{\partial F\left( E W\right)}{\partial \left( E W\right)}}{\frac{\partial^2 F\left( E W\right)}{\partial {\left( E W\right)}^2} EW}-\frac{\frac{\partial c(E)}{\partial E}}{\frac{\partial^2 F\left( E W\right)}{\partial {\left( E W\right)}^2} EW}$$

Now we transform the previous equation as follows in order to represent the efficiency elasticity of water use ( W,E ) as a function of the efficiency elasticity of the water application cost ( c,E ) and the efficiency elasticity of the marginal productivity of water consumption $$\left(\frac{{\mathit{\in}}_{\partial F(EW)}}{\partial (EW)}, E\right)$$. First we make some simple transformations:

$${\mathit{\in}}_{W, E}=-1+\frac{1}{\frac{\frac{\partial^2 F\left( E W\right)}{\partial {\left( E W\right)}^2} EW}{\frac{\partial F\left( E W\right)}{\partial \left( E W\right)}}}-\left(\frac{\frac{\partial c(E)}{\partial E}\frac{E}{c(E)}}{\frac{\frac{\partial^2 F\left( E W\right)}{\partial {\left( E W\right)}^2} EW}{\frac{\partial F\left( E W\right)}{\partial \left( E W\right)}}}\right)\left(\frac{1}{\frac{\partial F\left( E W\right)}{\partial \left( E W\right)}\frac{E}{c(E)}}\right)$$

Using the chain rule we obtain:

$${\mathit{\in}}_{W, E}=-1+\frac{1}{\frac{\partial \frac{\partial F\left( E W\right)}{\partial \left( E W\right)}}{\partial E}\frac{E}{\frac{\partial F\left( E W\right)}{\partial \left( E W\right)}}}-\left(\frac{\frac{\partial c(E)}{\partial E}\frac{E}{c(E)}}{\frac{\partial \frac{\partial F\left( E W\right)}{\partial \left( E W\right)}}{\partial E}\frac{E}{\frac{\partial F\left( E W\right)}{\partial \left( E W\right)}}}\right)\left(\frac{1}{\frac{\partial F\left( E W\right)}{\partial \left( E W\right)}\frac{E}{c(E)}}\right)$$

Using Eq. (4) $$\left(\frac{\partial F\left( E W\right)}{\partial \left( E W\right)}=\frac{P+ c(E)}{E}\right)$$ and operating, we obtain:

$${\mathit{\in}}_{W, E}=-1+\frac{1}{\frac{\partial \frac{\partial F\left( E W\right)}{\partial \left( E W\right)}}{\partial E}\frac{E}{\frac{\partial F\left( E W\right)}{\partial \left( E W\right)}}}-\left(\frac{\frac{\partial c(E)}{\partial E}\frac{E}{c(E)}}{\frac{\partial \frac{\partial F\left( E W\right)}{\partial \left( E W\right)}}{\partial E}\frac{E}{\frac{\partial F\left( E W\right)}{\partial \left( E W\right)}}}\right)\left(\frac{c(E)}{P+ c(E)}\right)$$

Which, alternatively, can be expressed as Eq. (8):

$${\mathit{\in}}_{W, E}=-1+\frac{1}{\frac{{\mathit{\in}}_{\partial F\left( E W\right)}}{\partial \left( E W\right)}, E}-\left(\frac{{\mathit{\in}}_{c, E}}{\frac{{\mathit{\in}}_{\partial F\left( E W\right)}}{\partial \left( E W\right)}, E}\right)\left(\frac{c(E)}{P+ c(E)}\right)$$

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Gómez, C.M., Pérez-Blanco, C.D. Simple Myths and Basic Maths About Greening Irrigation. Water Resour Manage 28, 4035–4044 (2014). https://doi.org/10.1007/s11269-014-0725-9

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