Irrigation and Drainage Systems (2005) 19: 211–221 C© Springer 2005

Irrigation reliability and the productivity of water:A proposed methodology using evapotranspirationmapping

CHRIS PERRYInstitute of Water and Environment, Cranfield University, Silsoe, Bedfordshire MK45 4DT,UK;E-mail: c.perry@cranfield.ac.uk

Abstract. Irrigation is the dominant user of water worldwide, but provision of potable water andwater for industry are higher priorities and give higher social and economic returns. Irrigationwill continue to lose water to competing sectors and the productivity of irrigation systems (sincefood demand continues to grow) remains a central issue in water management. Performanceassessment of irrigation has traditionally been difficult when based on field measurements offlows, deliveries and depths over large areas. Furthermore, performance measures have shiftedfrom narrow engineering indicators to broader productivity issues of production achieved perunit of water consumed. Remote sensing, applied to the estimation of evapotranspiration (ET)over large areas, provides analysts of irrigation systems with extraordinary new tools for theobjective assessment of consumption and production – constituting a quantum leap in the assess-ment of irrigation system performance. Awareness and utilisation of these tools is spreading,but important areas remain to be “converted” from traditional approaches that rely on an arrayof estimated parameters. The next challenge for remote sensing will be to map the frontier be-tween the reliability of the irrigation service and the productivity achieved. Reliability providesthe inducement for farmers to invest in higher productivity – to the benefit of themselves andsociety – and understanding better how the individual maximises profits within an uncertainirrigation environment can provide important guidance to managers and system designers.

Key words: remote sensing, reliability of irrigation, productivity of water

Introduction

Irrigation is the dominant user of water. Worldwide about 70% of water useis for agriculture, with a much higher figure (85%) in low and middle incomecountries, where agriculture is a major economic sector (World Bank, 1992).

But in most countries, irrigation is not the highest priority for water use:provision of potable water and water for industry give, respectively, the high-est social and financial returns. Generally, water for fisheries, navigation,power and commercial uses also take precedence over irrigation, and in manywealthy countries environmental uses are now in substantial competition with

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irrigation. Thus, paradoxically, irrigation is both the biggest user, but has tomake do with the residual water that no-one else needs.

In consequence, as populations rise and economies grow, water is trans-ferred from irrigation to other uses, and irrigation will continue to lose water tocompeting sectors. The performance of irrigation systems (since food demandcontinues to grow) remains a central issue in water management. Performance,in this context, is focused essentially on productivity: how much water is con-sumed and how much crop is produced. Society more generally also pursuesadditional objectives such as poverty alleviation and more equitable incomedistribution. These issues are not addressed here, and it is a matter for separateanalysis as to whether increasing the productivity of water will tend to im-prove or exacerbate such problems – and also a question for social scientistsand politicians as to how much production we are ready to lose to increaseequity or meet other socially desirable objectives.

Quantifying physical and productive performance of irrigation systemsthrough the development and application of indicators has been an active fieldfor many years, but the performance of the indicators has often been as difficultto assess as the performance of the irrigation systems they were applied to.

Indicators of performance: Where have we been?

Many authors have proposed indicators to measure irrigation system perfor-mance: (Bos & Nugteren, 1974; Levine, 1992; Abernethy, 1986; Seckler et al.,1988; Molden & Gates, 1990; Sakthivadivel, et al., 1993).

Some 10 years ago, the International Water Management Institute (IWMI)published a review of the indicators of irrigation performance that had beenproposed at that time (Rao, 1993). There were some 57 indicators, the vastmajority of which were to be based on measurements of physical parameters(flow rates, irrigation schedules, yields, irrigation depths, canal seepage) atfield, sub-project, project or wider scales. One of the simplest of these, RelativeWater Supply (Levine, op cit) was defined as:

Irrigation Delivery + Effective Rainfall

ETPotential + Seepage & Percolation

Measurement of these variables at various points in an irrigation system, atregular intervals, provides an indication of whether water availability exceedsor falls short of demand – an indicator of management effectiveness.

In the case of most irrigation systems in developing countries, even thesebasic data are exceptionally difficult to measure: irrigation deliveries are rarelyuniform over time or space (but an average figure is meaningless); effectiverainfall is as much a matter of opinion as scientific fact – it is common to see

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evapotranspiration (ET) specified to fractions of a millimetre, while rainfall ismeasured at best to the millimetre, and then converted to the critical “effectiverainfall” figure by a rounded factor such as 70% (and rainfall itself may varysignificantly within a large irrigation project); evapotranspiration, if computedusing the conventional Penman–Monteith approach, requires a data set that israrely available at the actual irrigation site – automatic weather stations arespreading rapidly, but usually at secure sites where ET is affected by buildingand hard surfaces; and seepage and percolation vary dramatically, dependingon prior conditions, maintenance and construction standards, at all points inthe system.

At the other end of the complexity spectrum, Molden and Gates (op cit)defined four “state variables” from which 12 performance measures weredefined, including, for example, the Structural Contribution to the EquityObjective (PES) measured as:

PES = T −1∑

T

CVR(Qd/Qs)

where T is the time period; CVR is the spatial coefficient of the region; Qd

is the actual amount delivered by the system; Qs is the amount specified fordelivery in the schedule.

Such complex performance indicators – relating to equity, reliability andproductivity present even greater challenges to field measurement, so thatrealistic estimates of the reliability of such indicators would in most cases haveshown such wide confidence intervals as to render the indicator meaningless.

It is no exaggeration to say that at the time of IWMI’s review there werefewer complete and reliably measured data sets than there were suggestedindicators. This is not surprising: it is easy to define a mathematical formulafor an indicator of performance, but the difficulties of measuring spatially andtemporally variable data were insurmountable at reasonable cost, especiallyin the conditions of many developing countries, where farm sizes are oftenless than 1 ha, overall levels of water control are poor, few calibrated struc-tures exist and even fewer are observed. Even in most developed countries,there were few complete data sets to enable assessment of irrigation systemperformance in accordance with the prescribed indicators, or to determine thescope for meeting the challenge of increasing water productivity.

An additional issue – even if the various indicators were measurable atreasonable accuracy – was interpretation: very few attempts had been madeto apply a standard set of indicators across a number of projects (Bos &Nugteren, op cit; Murray-Rust & Snellen, 1993; Merrey et al., 1994). In thelanguage of Molden et al. (1998) the indicators proposed were essentially“internal” indicators suitable for managers to check compliance with targets.These were not the same as “external” indicators that analysts might use as

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a basis for comparing the productivity of various systems, analysing whatfactors determined productivity, and hence defining appropriate managementtargets. The distinction was nicely made in Murray-Rust and Snellen’s paperbetween “doing things right” and “doing the right thing”. Few of the indicatorsproposed up to the early 1990s addressed the latter question, and few of theindicators addressing the former question were practical – in fact, it can wellbe argued that “internal” management indicators are best set at the projectlevel to address project-specific issues in a project-specific framework.

Indicators of performance: Where are we?

During the subsequent 10 years, the need for indicators of performance hasbecome increasingly pressing – especially indicators addressing the “are wedoing the right thing” question. As already noted, competition for water is in-creasing; water is being transferred from agriculture to non-agricultural uses;the need to detect and address non-beneficial uses of water is critical; andinvestments to meet such objectives are often being made in the absence ofadequate analysis. Furthermore, emphasis has shifted from technical estima-tion of “efficiency” of water delivery to a “crop per drop” perspective – lessconcerned with physical measurement of water flows in relation to targets,and more concerned with the productivity of water consumed, and the extentof non-productive consumption.

The advent of remote sensing as a tool to measure such fundamental param-eters as evapotranspiration and biomass formation has radically changed ourabilities in this area. Spatial coverage is available at the various scales needed– field, project, basin. Temporal coverage is vastly superior, at minimal cost,compared with the field measurement of data. Thus, it is now possible to con-ceive of management tools that inform system operators of the temporal andspatial pattern of water use, how productively it is being used, and where it isbeing wasted through non-beneficial evapotranspiration.

A number of parameters that had earlier been practically impossible tomeasure at the intensity needed to provide performance information could beestimated from RS data: by 2001, irrigated area; actual, reference and potentialET; and biomass formation were among a wide range of parameters assessedto be available with 80% accuracy at 95% confidence (Ede Wageningen ExpertConsultation Meeting, May 2001).

In short, while the field-level difficulties of measuring water supplies re-main, remote sensing allows us to “do the accounts”, in water consumptionterms, in ways that were unthinkable a decade ago, dramatically reshaping theway in which researchers and planners can assess systems. Suffice it to saythat in his excellent paper on water accounting Molden (1997) does not evenrefer to his own earlier and seminal work with Gates (Molden & Gates, op cit).

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We are in a new era of water management and remote sensing will be atthe heart of activities, yet some key players have still to join the club.

The FAO (AQUASTAT, 2003) has undertaken an extensive (and impor-tant) review of water withdrawal and consumption. This review is based ontraditional computations of reference ET, crop growth stage coefficients, ef-fective rainfall, etc. From these data – even though we know that our estimatesof these variables are dubious at the best of times, and particularly uncertainwhen we are assessing low-performance irrigation systems – conclusions aredrawn about the extent to which a country’s resources are utilised, how muchwater remains for further development, and how much can be “saved” bymore efficient management.

Burt et al. (2001) in assessing evaporation for irrigated agriculture inCalifornia (across multiple crops, climatic districts and technologies) basethe analysis entirely on the computations of physically based models.

Much better, and more objective, is to use standardised, direct measure-ments of the key physical parameters on which estimates of consumption andproduction can be uniformly based, thus establishing more objectively howmuch water irrigated agriculture is consuming, where, when and with whatproductivity.

Indicators of performance: What next?

The remainder of this paper sets out what the author believes is the next keyissue where remote sensing can offer insights for irrigation professionals thatcannot be obtained from conventional field measurement – insights that areat the centre of “doing the right thing”. The challenge goes beyond wateraccounting (which provides us with records of what went where and whatlevels of productivity were achieved) and addresses a component of the whyissue of variation in water productivity.

Analyses of yields (be it yield per hectare or yield per unit of water)typically show wide variations between “poor”, “average” and “good” farmerswithin the same agro-climatic and agro-economic environments. We know toothat “tail-end” farmers are often less productive than “head-end” farmers inirrigation systems. In part, this is simply because they get less water (which isdirectly reflected in lower irrigation intensity). Also, it is because their watersupply is less secure (reflected indirectly through lower yields per unit of landor water).

The literature on the relationship between yield and ET (Doorenbos &Kassam, 1979) typically defines yield to be a linear function of Potential ET,Actual ET and Potential Yield. By implication, the objective of irrigation inthis formulation is to get Actual ET as close as possible to Potential ET – andhence achieve Potential Yield.

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But Potential Yield is itself a variable whose impact is intuitively obvious.In choosing what crops to grow an irrigator makes a myriad of complextrade-offs related to his known resource availability (land, labour, machinery,money), his expectations about markets and prices and his expectations ofwater availability. Other things being equal, the farmer will be ready to investmore in a chosen crop if the availability of water is more secure: he will beready to select high yielding but water sensitive varieties, prepare the landcarefully, plant intensively and invest in high quality seeds, fertilisers andpesticides to ensure a healthier crop, thus substantially increasing PotentialYield. Conversely, if water supplies are uncertain, he will choose a drought-tolerant crop and invest little extra to try to improve on a low but secure yield –in effect, accepting a reliable Actual Yield, based on a low Potential Yield. Putanother way, farmer expectation defines Potential Yield; Actual Yield will bea fraction of Potential Yield depending on actual water availability and howit is managed. If we can improve expectations, we shift the envelope of YPOT.

This argument may seem circular: of course improving management shouldimprove reliability, leading to changes in farmer expectation over time, andfarmer actions to increase Potential Yield – a virtuous circle. But no amountof management can change the overall availability and reliability of watersupply to an irrigation project, which is a matter of hydrology and waterrights. With this boundary externally set, how can farmer expectations beimproved? In fact, there are a number of ways: first, maximising informationabout the coming irrigation season – total water available; likely periods ofsurplus/shortage. Second – and more intriguingly – an uncertain water supplywith known statistical characteristics can be partitioned into two (or more)components, each with a different level of security. Thus if 1000 units of waterare expected with 50% probability, of which 500 units are 90% likely to arrive,managers have the option to advise all the farmers to expect a share of a veryunreliable 1000 units, or to advise half the farmers to expect water with 90%certainty, while the remaining 50% will have even more extreme unreliability.Would the overall productivity of water rise under this system? In effect manywater rights systems do just this – for example, by giving higher security tosupplies to orchard crops, thus ensuring that farmers will invest to grow thesehigh value products.

In sum, understanding the relationship between reliability and productivityhas important implications for the productivity of water in agriculture, andhence the water required to meet specific levels of production, and the de-sign and management of irrigation systems: while the FAO 33 (Doorenbos &Kassam) and other models can estimate the ex post impact of a 10% shortfallin water availability at a certain time and for a given crop and treatment –we currently have no basis for predicting what the ex ante impact on farmerchoice of (say) a 20% chance of a 50% shortfall will be.

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The analysis presented below holds for any relationship between yield andET – whether linear, quadratic or other. Most of the literature shows linear re-lationships. In FAO 33, for example, we see various sets of linear relationshipsbetween yield and ET – but the slopes of those relationships vary significantlybetween crop growth stages. For convenience here it is assumed that the rela-tionship is curvilinear rather than piece-wise linear (i.e. that the crop switchesinstantly between stages from one slope to another). More recent informationfrom remote sensing data in China confirms the likelihood that the relationshipis in fact curvilinear (Bastiaanssen, 2003, personal communication).

Figure 1 shows a relationship between yield and total ET for various pro-duction strategies for a typical field crop, ranging from a low potential yield,low-input crop to a high potential yield, high-input crop. The relationship isthat proposed by Hargreaves (1997) and actually referred to the relationshipbetween yield and moisture availability. It is assumed for the purpose of thisanalysis to hold also for the relationship between ET and actual yield for aspecific crop technology, and is conveniently clearly specified as:

Yield = 0.8 × ET + 1.3 × ET2 − 1.1 × ET3

The Hargreaves relationship is pleasing to an economist in its demonstrationof varying marginal returns, and different optima for returns to water andreturns to land. The expression (which was derived from a large volume ofdata for field crops) evaluates to unity for yield when ET is also at unity (thatis, Potential Yield is achieved at Potential ET).

We may thus evaluate a “family” of yield/ET outcomes for the same cropunder different conditions of husbandry as shown in Figure 1. The top curve

Figure 1. Yield vs. ET for a range of crop husbandry conditions.

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represents the Yield/ET frontier for a crop planted at high density, with highyield potential and all necessary nutrient and other chemical support. Thelower curves represent the potential frontier for a range of lower input options– though the total seasonal ET for a fully matured crop is essentially constant.The range of yields presented (with a factor of five between the highest andlowest) is not extreme: wheat yields within Europe varied from 1.5 t/ha (Por-tugal) to 8.6 t/ha (The Netherlands) in 1995 (CIMMYT, 2003). Clearly, thefarmers in these populations are following different strategies for a variety ofreasons – but both operate within the European Common Agricultural Policy,so that significant aspects of their decision framework are common.

Focusing now on irrigation as a key variable in determining farmer strategy,we can note from Figure 1 that for a given quantity of ET (say 0.5 potential),yield can range from about 0.1 of potential to 0.6 of potential. Why wouldany farmer choose a low yield strategy when the ratio of productivity for afixed level of ET (or water consumption) is so high?

If we convert our indicator from yield to net value by assuming the fol-lowing cost data, the issue becomes clear (Table 1):

Table 1. Assumed yield, cost and income data for low and high potential yields.

Low yield crop High yield crop

Potential yield 1 unit/ha 5 units/ha

Fixed cost (seed, fertiliser, pesticide) 0.2 units 3 units

Variable cost (harvesting) 0.1 units × yield 0.1 units × yield

Net income at maximum yield/ha 1 − 0.2 − 0.1 = 0.7 units 5 − 3 − 0.5 = 1.5 units

While the potential net income from the high yield crop is more thandouble the income from the low yield crop, the low yield crop gives a betteroutcome (higher profit, or lower loss) for any level of ET lower than about0.65 (see Figure 2).

Thus, if a farmer is not confident that the irrigation service will providemore that 65% of full irrigation requirement, he will in this example switchfrom the high to the low yield potential option.

Clearly, a farmer faced with progressively less reliable supplies will optfor a cropping strategy closer to the low income option of Figure 2 – an optionwhich provides a much higher probability of a positive outcome for the farmer,and the guarantee of a less-bad negative outcome. Intiuitively this is obvious,and it is exactly what we observe in subsistence rainfed environments. Thequestion is how to characterise the relationship between declining reliability ofsupply and declining Potential Yield so as to choose design and managementoptions that increase total productivity.

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Figure 2. Income vs. ET for low and high yield crop options.

Mapping the reliability/productivity frontier through remotesensing – a research challenge

It is broadly estimated that some 300 Mha may eventually be irrigated, ofwhich 270 Mha are already developed. Irrigation development in global termsis over (though some significant “local” schemes, such as Narmada riverdevelopment in India and the Three Gorges and South-North Transfer inChina, remain), and the future of irrigation “development” consists of makingexisting facilities more productive, often with less water than they have today.

Returning now to Figure 1, we see first that the potential production gain tosociety from a farmer choosing the “high yield” strategy is a yield incrementof 400% over the “low yield” strategy, an increment which exceeds the impactof irrigation itself in many circumstances. In Figure 2 we see that the incomegain to the farmer is 100% – much lower though still substantial. The keypoint is that society is the major beneficiary of a farmer’s choice to invest ina high-input strategy.

Second, it is interesting that the “investment” to make that productivityjump is funded by the farmer – he trusts the irrigation system and invests inhigh yielding seeds, improved land preparation, fertilisers, pesticides, weed-ing and so on – safe in the knowledge that water at least will not limit his

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production. This is induced investment, knowledgably targeted and not at acost to the taxpayer. It has exceptionally high returns. But we know nothingbeyond the intuitive map presented here about the actual relationship betweendegree of unreliability and the farmer response; we do not in truth even knowwhat the key parameters might be in the definition – variation from target cu-mulative volume? Critical depletion of soil moisture? What parameters shoulda system manager use to minimise reliability impacts on farmer investmentsin productivity?

Remote sensing offers the potential to address the problem: spatial mon-itoring of seasonal trends in ET can provide indices of reliability. Remotesensing allows us to plot, at the pixel level, the progress of ET, crop growthand the productivity of land and water through the crop season. Thus we canconceive of computing (for a sample of plots of a specific crop) the path oftranspiration over time, and the ultimate productivity of water. For a crop re-ceiving fully adequate irrigation, we would expect the evaporative fraction tobe close to unity for the entire season, highest overall productivity of land andquite high productivity of water. Where irrigation is reliable, but less wateris available than might potentially be utilised (land being plentiful in relationto water) we might expect to observe a consistent pattern of reduced evap-orative fraction in the range where yield falls less than water consumption,and overall observe a somewhat lower productivity of land, and the maximumproductivity thereof.

Where we observe random reductions in evaporative fraction, we expectto observe (as a result of the farmer’s risk aversion and lower levels of inputs)significantly lower levels of land and water productivity. Quantifying the re-lationship between the degree of random reduction in the evaporative fractionand the overall productivity of land and water will open the way to clarifyingthe nature of the relationship between the unreliability of irrigation and theproductivity of water.

Such patterns, and far more insightful ones that will be developed asdata accumulates, can be related to final yields and converted to water pro-ductivity statistics – eventually tracing the frontier between reliability andproductivity.

Measurement will be difficult: we have to observe many farmers experi-encing various levels of unreliability, and somehow quantify the results intopatterns that can help us design and manage systems better – by reducingunreliability to the extent possible.

Practical outcomes include:

• Better understanding of the extent to which complex irrigation schedules,designed to meet precise needs of water sensitive crops should be pursuedat the cost of potential degradation in reliability.

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• Insights into whether erratic inflows into dams are better released as lowervolumes at higher reliability – saving unexpected peaks for later use asreliable, controlled supplies in a subsequent season.

These and other analyses can guide those designing the management strategiesfor the improved irrigation facilities that will feed and clothe future genera-tions – a small challenge, with a potentially huge reward.

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