review measurement and estimation of actual

European Journal of Agronomy 13 (2000) 125–153

Review

Measurement and estimation of actual evapotranspiration inthe field under Mediterranean climate: a review

G. Rana a,*, N. Katerji b

a Istituto Sperimentale Agronomico, 6ia C. Ulpiani, 5, 70125 Bari, Italyb INRA-Unite de Bioclimatologie, 78850 Thi6er6al-Grignon, France

Received 19 February 1999; received in revised form 13 August 1999; accepted 13 May 2000

Abstract

The Mediterranean regions are submitted to a large variety of climates. In general, the environments are arid andsemi-arid with summers characterised by high temperatures and small precipitation. Due to the scarcity of waterresources, the correct evaluation of water losses by the crops as evapotranspiration (ET) is very important in theseregions. In this paper, we initially present the most known ET measurement methods classified according to the usedapproach: hydrological, micrometeorological and plant physiological. In the following, we describe the methods toestimate ET, distinguishing the methods based on analytical approaches from the methods based on empiricalapproaches. Ten methods are reviewed: soil water balance, weighing lysimeter, energy balance/Bowen ratio,aerodynamic method, eddy covariance, sap flow method, chambers system, Penman–Monteith model, crop coefficientapproach and soil water balance modelling approach. In the presentation of each method, we have recalled the basicprinciples, underlined the time and space scale of its application and analysed its accuracy and suitability for use inarid and semi-arid environments. A specific section is dedicated to advection. Finally, the specific problems of eachmethod for correct use in the Mediterranean region are underlined. In conclusion, we focus attention on the mostinteresting new guidelines for research on the measurement and estimation of actual crop evapotranspiration. © 2000Elsevier Science B.V. All rights reserved.

Keywords: Actual evapotranspiration; Direct ET measurement methods; Indirect ET measurement methods; ET modelling;Mediterranean climate

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perature associated to annual rainfall in winter.Despite the apparent uniformity of the Mediter-ranean climate, a more detailed analysis showsgreat differences. The dry season duration (Fig. 1)clearly illustrates that, while the South is charac-terised by a long dry season, averaging \7months without any precipitation, in the North-ern part, the dry season is relatively limited and

1. Introduction

The Mediterranean climate is characterised by ahot and dry season in summer and a mild tem-

* Corresponding author. Tel.: +39-080-5475026; fax: +39-080-5475023.

E-mail addresses: [email protected] (G. Rana),[email protected] (N. Katerji).

1161-0301/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.

PII: S 1161 -0301 (00 )00070 -8

G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153126

Fig. 1. Duration of the dry season in the Mediterranean basin (Hamdy and Lacirignola, 1999).

does not exceed 2–3 months. In addition, therainfall and temperature diagrams (Fig. 2) showgreat differences between the North (autumn rain-fall) and the South (winter rainfall) of the basin.During summer, the simultaneous occurrences ofhigh temperatures and small precipitation causes

high evapotranspiration (Hamdy and Lacirignola,1999). For these reasons, 75% of the availablewater in the Mediterranean area is used for agri-cultural purposes.

Furthermore, the Mediterranean region is char-acterised by:

Fig. 2. Annual pattern of air temperature and precipitation in several localities of the Mediterranean basin (Hamdy and Lacirignola,1999).

G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153 127

Table 1Estimation of the percentage of irrigated soils affected bysalinity in several Mediterranean countries (Hamdy et al.,1995)

Irrigated surface (%)Country

10–15AlgeriaCyprus 25

30–40EgyptSpain 10–15

13IsraelGreece 7

16JordanMorocco 10–15

10–15Portugal30–35Syria

Moreover, semi-arid and, mostly, arid climateshave a great impact on crop growth in condition-ing yield and product quality. Under theseweather conditions, rainfed crops and agriculturalfields with limited water resources are often sub-mitted to water stress. Thus, it becomes funda-mental to know the exact losses of water byevapotranspiration (i.e. actual evapotranspiration)and the crop water status and its influence onproduction.

Actual crop ET can be measured (directly orindirectly) or estimated. For example, for researchpurposes in plant eco-physiology, ET must beprecisely measured, while for farm irrigation man-agement it can be estimated. The lower the degreeof accuracy in the estimation, the greater will bethe water waste by incorrect management ofirrigation.

In this paper, we review the most importantmethods of measuring and estimating actual ET,at plot scale (e.g. at farm level), giving, for eachmethod, the problems, limits and advantages fortheir use in a field under the Mediterranean cli-mate. This summary cannot be, of course, anexhaustive and complete review of all the existingET methods; in fact, we will focus attention onthe most known and diffuse methods in the inter-national research community, paying particularattention to those used in agricultural research.

The scaling up of ET from plot scale to re-gional scale requires specific methods and tech-niques and, therefore, will not be treated in thispaper.

2. Measurement and estimation

There is a great variety of methods for measur-ing ET; some methods are more suitable thanothers for accuracy or cost or are particularlysuitable for given space and time scales. Forseveral applications, ET needs to be predicted, soit must be estimated by model.

It is convenient to discuss the methods of deter-mining ET in considering separately the measure-ment and modelling aspects.

� Water scarcity in the South: The wateravailability in the Southern and Eastern coun-tries of the Mediterranean basin is below thefirst needs (1000 m3 per capita per year) andprospects for the future indicate more severedifficulties (Hamdy and Lacirignola, 1999).

� The need to increase the irrigated surfaces be-cause of the population increasing: The Med-iterranean population increased by 67%between 1950 and 1985.

� Soil pollution: Nowadays, the problem ofsalinity affects 7–40% of the irrigated surfaceof several Mediterranean countries (Table 1).Therefore, accurate determination of irrigation

water supply is necessary for sustainable develop-ment and environmentally sound water manage-ment. This goal is far from achievement, in factthe irrigation efficiency is now :45% of thewater supply and one half of this inefficiencycould be attributed to bad estimates of cropswater requirements (FAO, 1994).

About 99% of water used in agriculture is lostby crops as evapotranspiration (ET) — it isdefined as the water loss by a vegetative unsatu-rated surface, under vapour form, by evaporationfrom soil and transpiration from plants. Depend-ing on the soil water conditions, a more or lessimportant biological control is exerted on thewater lost. In addition to this a resistance isopposed by the canopy structure to the watervapour transfer toward the atmosphere (Perrier,1984; Lhomme, 1997).


In general, a ‘measurement’ of a physicalparameter is a quantification of an attribute of thematerial under investigation, directed to the an-swering of a specific question in an experiment(Kempthorne and Allmaras, 1986). The quantifi-cation implies a sequence of operations or stepsthat yields the resultant measurement. Conven-tionally, if the value of the parameter is quantifiedby the use of an instrument, it is ‘directly’ mea-sured and when it is found by means of a relation-ship among parameters, it is ‘indirectly’ measured(Sette, 1977).

The methods of measuring ET should be di-vided into different categories, since they havebeen developed to fulfil very different objectives.

One set of methods are primarily intended toquantify the evaporation over a long period, fromweeks to months and growth season. Another setof methods has been developed to understand theprocess governing the transfer of energy and mat-ter between the surface and atmosphere. The lastset of methods is used to study the water relationsof individual plants or part of plants. Therefore,following Rose and Sharma (1984), it is conve-nient, when discussing the ET measurement, toplace the variety of methods in groups, where themain approach or method depends on conceptsfrom hydrology, micrometeorology and plantphysiology, as follow:� ET measurement

Hydrological approaches(1) Soil water balance(2) Weighing lysimetersMicrometeorological approaches(3) Energy balance and Bowen ratio(4) Aerodynamic method(5) Eddy covariancePlant physiology approaches(6) Sap flow method(7) Chambers system

A physical parameter can be considered as ‘es-timable’ if it is expressed by a model. The objec-tive of ET modelling can vary from the provisionof a management tool for irrigation design, to theprovision of a framework for either detailed un-derstanding of a system or to interpret experimen-tal results. To meet these requirements, it is moreconvenient to use methods with a sound physical

basis, but often the available data only allow theuse of either empirical or statistical approaches.Thus, to discuss the ET modelling, it is convenientto divide the ET models as follows:� ET estimation

Analytical approach(8) Penman–Monteith model

Empirical approach(9) Methods based on crop coefficient

approach(10) Methods based on soil water balancemodelling.

This categorisation is, of course, far from com-pletion, but can be considered a good trace in areview of ET determination.

3. Actual crop evapotranspiration measurement

The different methods for directly and indi-rectly measuring ET are based on the measure-ment of two classes of factors:1. The soil water content and the physical char-

acteristics of the evapotranspirative surface(height, plant density, canopy roughness,albedo);

2. Climatic variables: solar radiation, wind speedand thermodynamic characteristics of the at-mosphere above the canopy.

In the description of the measurement methods,we will consider as true the hypothesis of ‘conser-vative flux’, i.e. the flux density does not changewith the height above the canopy. So that, in afirst approximation, we will consider the differentfactors (belonging to both (a) and (b) classes) asconstant in the space considered (the field).

To say that the factors (a) are constant in thespace is the same as saying that evapotranspira-tive surfaces are perfectly homogeneous along thehorizontal scale. In Mediterranean regions, thishypothesis is usually far from being verified. Infact, the fields present crop types, phenologicalstages and water conditions very changeable inthe space. This induces a net discontinuity ofsurface moisture among fields and, consequently,a non-negligible effect of advection due to energyside exchange between contiguous plots.


The role of the advective regime on the mea-surement and estimation of ET will be analysed ina separate chapter at the end of the methodspresentation.

3.1. Hydrological approaches

3.1.1. Soil water balanceSoil water balance is an indirect method, in fact

ET is obtained as a residual term in the waterbalance equation. This equation is based on theprinciple of conservation of mass in one dimen-sion applied to the soil, its complete expression is:

P+I+W−ET−R−D=9 [DS ]0r (1)

where P is precipitation, I is irrigation, W iscontribution from water table upward, R is sur-face runoff, D is drainage and DS is soil waterstorage in the soil layer, where the roots are activeto supply water to the plant (r in m). All the termsare in milimeters per unit time. Soil water storagebetween two dates (i and i−1) is:

[DS ]0r = [Si−Si−1]0r (2)

with S, the soil water content.Since it is often very difficult to accurately

measure all the terms of Eq. (1), a number ofsimplifications makes this method unsuitable forprecise ET measurements. In fact, irrigation watersupply is, in principle, known and precipitationcan be measured by rain gauges, but all the otherterms need to be measured or, at least, estimated.

The soil water balance method is applicable tosmall plots (:10 m2) or to a large catchment(:10 km2); it may cover periods ranging from aweek to a year.

Often, for operational application, the soil wa-ter balance Eq. (1) is expressed in its simplifiedform:

P+I=ET9 [DS ]0r (3)

The simplifications introduced in Eq. (3) couldbe critical if applied in dry environments. In aridand semi-arid areas with very small slopes, runoffterm R could be neglected (e.g. Holmes, 1984)but, actually, it depends on the occurrence andcharacteristics of precipitation (amount, duration

and intensity) and can only be neglected for aparticular type of soil (Jensen et al., 1990), i.e.coarse (sand and loamy sand) and moderatelycoarse (sandy loam).

Drainage (D) is the most unknown of Eq. (1).Some researchers suggest that it can be neglectedin dry regions (e.g. Holmes, 1984), but actually itdepends on the soil depth, slope, permeability andsurface storage (Jensen et al., 1990; Parkes and LiYuanhua, 1996) and needs to be checked in eachparticular case (Brutsaert, 1982), depending alsoon the climate and weather (Katerji et al., 1984).In some situations it is so important that its directmeasurement can be used to estimate evapotran-spiration on a weekly or greater scale (for anextensive review see Allen et al. (1991)). More-over, Katerji et al. (1984) demonstrated that it isnot simple to establish if the water deep flow canbe neglected, in fact it can be a non-negligiblefraction of the water balance both in dry andhumid seasons and at different time scale. Ingeneral, at daily scale it can be neglected if thewater supply (P and/or I) does not exceed the soilwater capacity (Holmes, 1984; Lhomme andKaterji, 1991).

In arid regions, the terms W and DS couldshow problems of correct evaluation. In fact, ifthe soil system is closed (i.e. shallow soils or soilswith a very deep water table), W can be consid-ered negligible and DS can be easily determined.In this case, the simplified soil water balanceworks well, as shown in Fig. 3, where ET mea-sured by Eq. (3) is compared with a referencemethod (Bowen ratio). The data are relative to amaize crop grown in a Mediterranean region(Southern Italy) and soil water storage is mea-sured by TDR and the gravimetric method.

Vice versa, if the system is open (deep soils orsoils with a surfacial water table), W cannot beneglected and DS is difficult to measure exactly,so that the simplified form of the soil waterbalance does not work well. This inaccuracy waswell demonstrated by Katerji et al. (1984). In fact,they showed that during humid seasons, W andDS are of the same order, while during dry sea-sons, W can reach 30% of cumulated seasonalactual ET (Fig. 4).


Soil water content needs to be measured accu-rately and over an adequate depth. It can bemeasured by a wide number of methods (an ex-tensive review can be found in Stafford (1988) andPhene et al. (1990)). Three methods are the mostimportant: gravimetric sampling, neutron scatter-ing and electrical resistance.

The gravimetric method remains the mostwidely used, particularly by technicians and con-sultants; it is well developed at research level andalso for irrigation management purposes. It issimple to apply but it can be used only for largetime scale (weekly or greater).

Neutron probe remains a useful tool at researchlevel only and its performance has not been well-

established in arid environments. In fact, Payneand Bruck (1996), for example, stated that neu-tron probe tends to lose accuracy under the aridclimate of Sahelian Africa, mostly near the sur-face, wetting fronts and textural discontinuities;conversely, Evett and Steiner (1995) found verygood results in a wide range of situations. Fur-thermore, neutron probe poses particularlydifficult and regulatory problems in developingcountries.

Electrical resistance matrix type sensors are theleast expensive (gravimetry is cheaper) and can bereadily used for automatic irrigation control sys-tems (Phene and Howell, 1984; Phene et al., 1989,among many others), but they are not very accu-

Fig. 3. Comparison between ET measured by Bowen ratio method, soil water balance with TDR and soil water balance bygravimetric method, at daily scale, on corn grown in Southern Italy (Mastrorilli et al., 1998).


Fig. 4. Water balance component for a lucerne crop grown ina deep silt soil; (1) cumulative difference between rainfall andactual evapotranspiration since an initial date; and (2) varia-tion of the total water content in the 0–170 cm upper layer ofthe soil since the same initial date (Katerji et al., 1984).

and hourly scale.Problems can be encountered in clay soils when

the soil moisture is measured by means of probes(neutron scattering, electrical resistance or TDR).In fact, clay soils submitted to an arid climate (i.e.at low moisture content) crack where they are notadequately irrigated (e.g. Diestel, 1993); the deepcracks do not allow suitable contact between soiland probes (Haverkamp et al., 1984a,b) and thereading of the soil moisture can be affected bylarge errors (Bronswijk et al., 1995).

3.1.2. Weighing lysimetersWeighing lysimeters have been developed to

give a direct measurement of the term ET in Eq.(1). Historically, they have always been consid-ered as a suitable tool to correctly measure evapo-transpiration (Tanner, 1967; Aboukhaled et al.,1982).

In general, it is a device, a tank or container, todefine the water movement across a boundary;actually, only a ‘weighing lysimeter’ can deter-mine ET directly by the mass balance of the wateras contrasted to non-weighing lysimeter, whichindirectly determines ET by volume balance(Howell et al., 1991).

Weighing lysimeters placed in the field containssoil cultivated as the field around it, the sensor isa balance able to measure the weight variationdue to ET, often this variation is measured bymeans of an electronic sensor (i.e. load cell).Under temperate climate, they are able to mea-sure ET at a daily scale with an accuracy of\10% (Perrier et al., 1974; Klocke et al., 1985bamong others) and at an hourly scale with anaccuracy of 10–20% (Pruitt and Lourence, 1985;Allen et al., 1991).

However, the weighing lysimeter data are notalways representative of conditions of the wholefield but, in several situations, they represent onlythe ET of just one point in the field (Grebet andCuenca, 1991).

Besides the soil, height and vegetation densitydifferences between the lysimeter and outside veg-etation can severely affect ET measurements. Inthis case, both aerodynamic and radiative trans-fers to the lysimeter canopy are increasing. If thelysimeter surface and its close area are surrounded

rate in estimating actual ET in soil water deple-tion conditions (see, e.g. Bausch and Bernard,1996).

The accuracy of soil water balance stronglydepends on time and space scales of actual soilmoisture measurements (Burrough, 1989) and onthe representativeness of the soil sampling(Bertuzzi et al., 1994; Leenhard et al., 1994). Inorder to meet all these requirements for soil mois-ture measurement, the technique of time domainreflectometry (TDR) has been introduced quiterecently by Topp and Davis (1985) and Topp etal. (1994) among others. It seems that TDR isable to correctly estimate soil moisture both undertemperate (Ledieu et al., 1986; Werkhoven, 1993;Plauborg, 1995) and semi-arid climates (Mastror-illi et al., 1998). When TDR probes are used it ispossible to have a soil water balance at plot scale


by drier vegetation or bare soil, an oasis effectoccurs. Net radiation in excess of latent heat isconverted in sensible heat that is advected towardthe lysimeter, resulting in net supply of energy tothe lysimeter vegetation. All these previously de-scribed problems cause an increase of ET relativeto the surrounding crop. This overestimation ofET could be particularly important under a highradiative climate, as in the Mediterranean region.

Furthermore, environmental problems can af-fect measurements of ET with lysimeters (for areview see Allen et al. 1991). One of the mostcommon errors made is the incorrect estimationof an evaporating area of a lysimeter. In fact, thisarea is calculated by the inner dimensions of thecontainer rather than the true vegetative area,which can be greater than the lysimeter surfacewhen the vegetation from both inside and outsidethe lysimeter reaches across the rim. This errorcould be :20%.

The lysimeter rim can also influence ET mea-surements. One of the most important effects,mainly in arid environments, is the heating of themetallic rim by radiation resulting in microadvec-tion of sensible heat into the lysimeter canopy.Moreover, if the lysimeter rims are too tall rela-tive to crop, the wind is shielded and the radiativeenergy balance is modified due to the reflection ofsolar radiation by the inner wall of the rim to-ward the crop.

Under arid and semi-arid climates, problemslinked to the atmospheric evaporation demandcan worsen the performances. In fact, if the soil

inside lysimeters has deep cracks (often along theborder in contact with the soil), the water evapo-ration continues from the deepest layers, so thatlysimeter can overestimate ET in these periodsand underestimate ET in the following periods,when the water depletion inside is greater thanthat in the field, due to water stress condition ofinner plants (Jensen et al., 1990). Conversely,irrigation and rainfall infiltrate into these cracks;this, along with lack of root extraction of water,causes the soil within the lysimeters to be muchwetter than the surrounding field soil (Klocke etal., 1991).

Furthermore, the weighing lysimeter is limitedin depth in order to make possible the weighing ofthe soil–plants system; this limitation adds newproblems for its use in Mediterranean regions. Infact, it does not take into account the effects ofthe deeper water fluxes (capillary rising) on crop,which can be very important in water stress peri-ods. Moreover, in areas with deep soil, the weigh-ing lysimeter does not take into account theeffects of the total soil available on the plantgrowth. In this case, i.e. very deep soils, therepresentativeness of the lysimeter becomes a verydifficult technical problem, due to the excessiveweight of the system soil–tank–plants. In Fig. 5,three kinds of lysimeter are shown: since the totalavailable water of nearby soil is :260 mm, onlythe first one is well representative of the actualfield, but in this case the weight of the systemsoil–tank is very high (12 t).

3.2. Micrometeorological approaches

From the energetic point of view, evapotranspi-ration can be considered as the energy employedfor transporting water from inner leaves and plantorgans to the atmosphere as vapour. In this caseit is called ‘latent heat ’ (lE, with l, latent heat ofvaporisation) and it is measured as energy fluxdensity (W m−2).

We shall describe in the following sections themain methods based on physical or meteorologi-cal principles, by which the latent heat flux can bemeasured. Three techniques will be analysed: theenergy balance and Bowen ratio, the aerodynamicmethod and the eddy covariance. In general, all

Fig. 5. Three kinds of weighing lysimeter: S is surface, V isvolume, P is weight, AW is total available water (Perrier et al.,1974).


these techniques require accurate measurementsof meteorological parameters on small temporalscale (1 h or less). Due to the conservative hy-pothesis of all the flux density above the crop,they can be applied only in large flat areas withuniform vegetation. There are many situations ofpractical interest where they cannot be used,mostly in the Mediterranean regions. For exam-ple, mixed plant communities, hilly terrain andsmall plots.

Much care must be taken to analyse local andregional advection under arid conditions (Pruegeret al., 1996) and, eventually, to introduce correc-tions to the measured fluxes (see the section onadvection).

3.2.1. The energy balance and Bowen ratiomethod

The latent heat flux can be obtained from mea-surements of the energy budget of the surfacecovered with an active growing crop. In fact, lErepresents the major used part of available energydue to the radiation balance. All the energy in-volved in the evapotranspiration phenomenonmust satisfy the closure of the energy balance:

Rn−G=H+lE (4)

where we neglect advective processes and whereRn (W m−2), net radiation and G (W m−2), soilheat flux, are directly measurable by net-radiome-ters and soil heat flux plates, respectively (for anextensive review of environmental instrumenta-tion see Fritschen and Gay (1979)); and H is thesensible heat flux density (W m−2).

We define the Bowen ratio b=H/lE, so Eq.(4) can be rearranged to give

lE=Rn−G1+b

(5)

b can be measured by the ratio of the air temper-ature difference between two levels (DT) and thevapour pressure difference (De), with e (kPa) airvapour pressure, measured at the same two levels:

b=gDTDe

(6)

The Bowen ratio is an indirect method, itsaccuracy has been analysed by many authors (e.g.

Fuchs and Tanner, 1970; Sinclair et al., 1975;Revheim and Jordan, 1976) and can be estimatedto be within 10% of the measured value. TheBowen ratio method has been widely studied in avariety of field conditions and it has been provena standard very accurate method in semi-aridenvironments (e.g. Dugas et al., 1991; Frangi etal., 1996; Zhao et al., 1996) and for tall crops also(Cellier and Brunet, 1992; Rana and Katerji,1996).

As previously stated, under arid climates thecrops can experience water stress. In this case DTcan be quite high but De is very low; so that it isvery important to have highly accurate measure-ments of air vapour pressure (Angus and Watts,1984). The usual and simplest way is to use differ-ential psychrometry; to meet the requirements ofaccuracy, for continuous recording, one has tokeep the bulbs wet and clean (Fritschen and Gay,1979). Furthermore, the used thermometers haveto be well calibrated, in order to detect tempera-ture differences of 0.05–0.2°C; accuracy can besensibly improved by fluctuating the psycrometricsystem (Webb, 1960; Gay, 1988; Fritschen andSimpson, 1989).

Recently, improvements have been obtained byusing: (i) just one hygrometer that measures alter-natively the humidity of air pumped from twolevels (Cellier and Olioso, 1993); (ii) a singlecooled mirror dew point hygrometer (some suchinstruments are briefly described in Dugas et al.,(1991)); and (iii) spatial averaging systems(Bausch and Bernard, 1992). In any case, techni-cal problems remain in the hygrometers for themeasurement of air humidity in arid regions, espe-cially during water stress periods, when its value isusually very low.

3.2.2. The aerodynamic methodIf we assume that a flux density can be related

to the gradient of the concentration in the atmo-spheric surface layer (ASL), the latent heat flux bythe aerodynamic technique can be determined di-rectly by means of the scaling factors u* and q*,with q specific air humidity (kg kg−1), (see e.g.Grant, 1975; Saugier and Ripley, 1978):

lE= −lru*q* (7)


here r is density of air (kg m−3) and the frictionvelocity u* (m s−1) is derived from the windprofile measurement:

u*=ku

ln�z−d

z0

�−Cm

(8)

where k=0.41 is the von Karman constant, d (m)is the zero plane displacement height, z0 (m) is theroughness length of the surface and Cm is thestability correction function for momentum trans-port. q* is determined similarly from the humidityprofile measurement:

q*=k(q−q0)

ln�z−d

z0

�−C6

(9)

where q0 is the air humidity extrapolated at z=d+z0 and C6 is the correction function for latentheat transport.

The calculation of stability functions is made byiterative processes (e.g. Pieri and Fuchs, 1990);users who did not take stability corrections intoaccount have been criticised (Tanner, 1963; Per-rier et al., 1974). The problem of taking intoaccount the atmospheric stability is particularlyimportant in arid environments. In fact, the cou-pling of dry soil and rapid warming or cooling upof air at contact with the earth surface (vegetationor bare soil) leads to extreme conditions of strongstability and instability, with sudden passage froma regime to the opposite one.

The major difficulty with this technique is thecorrect measurement of the vapour pressure atdifferent heights above the crop. For this reasonlE can be derived indirectly by the energy balanceEq. (4) if the sensible heat flux is determined bythe flux-gradient relation:

H= −rcpu*T* (10)

where T* is deduced by the air temperatureprofile:

T*=k(T−T0)

lnz−d

z0

−Ch

(11)

where T0 is the temperature extrapolated at z=d+z0 and Ch is the correction function for theheat transport.

Under this form, the main advantage of theaerodynamic technique consists in avoiding hu-midity measurements. Nevertheless, the accuracydepends on the number of measurement levels ofwind speed and temperature profiles. In fact, Eq.(8) and Eq. (11) require at least three or fourlevels (Webb, 1965), but accuracy is improvedwhen several levels are used (Legg et al., 1981;Wieringa, 1993). When the stability correctionfunctions of Dyer and Hicks (1970) and Paulson(1970) are used, this method gives good results(Grant, 1975; Pieri and Fuchs, 1990).

A simplified version of the method has beenproposed by Itier (1980, 1981) and Riou (1982),based on the measurement of Du and DT, i.e.wind speed and temperature at two levels only.This method was successfully used to measureactual evapotranspiration of soybean grown in aregion of Southern Italy (Rana et al., 1990).

The aerodynamic method does not work withenough accuracy on tall crops, neither in its com-plete form (Garratt, 1978; Thom et al., 1975) norin its simplified form (Rana and Katerji, 1996).Correction for making this method applicable fortall crops was attempted by Cellier and Brunet(1992).

3.2.3. The eddy co6arianceThe transport of scalar (vapour, heat, CO2) and

vectorial amounts (i.e. momentum) in the lowatmosphere in contact with the canopies is mostlygoverned by air turbulence. The first completescientific contributions to this topic were given byDyer (1961) and Hicks (1970); for extensive de-tails of the theory see, for example, Stull (1988).

When certain assumptions are valid, theory pre-dicts that fluxes from the surface can be measuredcorrelating the vertical wind fluctuations from themean (w %) with the fluctuations from the mean inconcentration of the transported admixture. Sothat for latent heat, we can write the followingcovariance of vertical wind speed (m s−1) andvapour density (q % in g m−3):

lE=lw %q % (12)

By making measurements of the instantaneousfluctuations of vertical wind speed w % and ofhumidity q % at sufficient frequency to obtain the


contribution from all the significant sizes of eddyand summing their product over an hourly timescale (from 15 min to 1 h), Eq. (12) gives directlythe actual crop evapotranspiration.

A representative fetch is required; fetch toheight ratios of 100 are usually considered ade-quate but longer fetches are desirable (Wieringa,1993). The distribution of eddy size contributingto vertical transport creates a range of frequenciesimportant to eddy correlation measurements (fora brief review of the method requirements, seeTanner et al. (1985)). The sensors must suffi-ciently respond to measure the frequencies at thehigh end of the range, while covariance averagingtime must be long enough to include frequenciesat the low end (Kaimal et al., 1972; McBean,1972).

To measure ET directly by this method, verticalwind fluctuations have to be measured and ac-quired contemporary to the vapour density. Thefirst one can be measured by sonic anemometer,the second by fast response hygrometer; bothhave to be acquired at a typical frequency of10–20 Hz. The Krypton-type fast hygrometersperform well in the field, but they are expensiveand very delicate, so they need particular mainte-nance. In fact, the commercial fast hygrometerscan be severely damaged if moistened, thereforethey can only be installed during the day period,which makes it difficult to use this instrumentcontinuously for a period longer than a few days.Furthermore, errors in eddy covariance methodcan be due not only to possible deviations fromthe theoretical assumptions, but also to problemsof the sensors configuration and meteorologicalcharacteristics (Foken and Wichura, 1996).

One important hypothesis to be verified is thattime series must be stationary at the scale of theaveraging period, which requires some kind ofdetrending of the original turbulent signals, likelinear detrending or more complex high-passfiltering (Kaimal and Finningan, 1994).

Other known problems are due to the geometri-cal configuration of the sensors. A distortion ofthe flow can be caused by the sensor arrangementof the anemometer itself and other sensors. Thespatial separation between the sonic anemometerand the hygrometer can cause lack of covariance

between the wind speed and the humidity fluctua-tions. In fact, the typical distance between themeasuring path of the vertical wind fluctuationand the hygrometer is 30–40 cm, this spacing actslike a lower-pass filtering process on the measuredsignals and must be corrected (Foken andWichura, 1996).

An important aspect to be considered is thedensity correction (Webb et al., 1980), this correc-tion is particularly important in semi-arid envi-ronments, in fact it is proportional to the sensibleheat flux and may be quite large for high Bowenratio (Villalobos, 1997).

To avoid some of the above problems linked tothe humidity fluctuations measurements, lE canbe obtained indirectly as residue of the energybudget Eq. (4) if the sensible heat flux is expressedby:

H=rcpw %T % (13)

where cp (J kg−1 C−1) is the specific heat anddensity of air. The wind speed and temperaturefluctuations are measured by means of sonicanemometer and fast response thermometer,respectively.

Despite problems linked to the correct manage-ment of the sensors and data remain, this methodhas very good performances both at hourly anddaily scale, also in semi-arid environments. In Fig.6, the comparison between ET measured by thismethod and Bowen ratio method, at daily scale, isshown for a tall crop (sweet sorghum) grown inSouthern Italy.

In conclusion, the use of eddy covariance forlatent or sensible heat flux is still a useful toolonly at research level, even if the recent develop-ment of robust sensors could permit in the futureits practical application in arid regions.

3.3. Plant physiology approaches

Plant physiology methods either measure waterloss from a whole plant or a group of plants.These may include methods such as tracer tech-nique and porometry but here, only the mostdiffuse methods will be analysed: the sap flowmethod and the chambers system.


Fig. 6. Comparison between ET measured by eddy covariancefor sensible heat flux and ET measured by Bowen ratiomethod, at daily scale, on sweet sorghum grown in SouthernItaly (Rana and Katerji, 1996).

stem from the heater element. The difference be-tween the heat input and these losses is assumedto be dissipated by convection with the sap flowup the stem and may be directly related to waterflow (Kjelgaard et al., 1997). The mass flow rate F(g t−1) is expressed by the relationship:

F=Qh−Qv−Qr

cw·dT(14)

where Qh is input heat, Qv is vertical conductiveheat, Qr is radial heat loss to environment, cw (Jg−1 K−1) is specific heat of water and dT is thetemperature difference between the upstream anddownstream thermocouples. With the commercialinstrumentation, the mass flow rate per plant canbe measured at hourly scale.

The micro-engineering problems of the heatemitters and detectors discussed by Cohen et al.(1981) were recently overcome by Kjelgaard et al.(1997), by using constant heat input instead ofvariable heat input and using surface-mountedthermocouples instead of the inserted ones. Thesegauges do not disturb the plant root medium butthere is still biometric difficulty in extrapolatingfrom one or more plants to the canopy. Further-more, in spite of the fact that the heat balancemethod is more dependent upon the sap flow ratethan upon stem anatomy (Zhang and Kirkham,1995), at low flow rates (often the case in asemi-arid and arid environment when the cropsare under water stress) important differences wereobserved between the sap flow determined by thegauges and plant water losses observed by a refer-ence method (Kjelgaard et al., 1997). The bestresults are obtained at a daily scale, mostly ontrees.

For the sap flow method it is necessary do ascaling up of the transpiration measurement fromplant to field scale. This is possible only if thecanopy structure and the spatial variability of theplants characteristics (density, height, LAI) areprecisely known.

Recently, Grime and Sinclair (1999) reportedsources of error for the constant power stem heatbalance method when commercial gauges areused. Their analysis demonstrated that measure-ment errors in determining the diurnal pattern oftranspiration could be due to the heat storage in

3.3.1. Sap flow methodSap flow is closely linked to plant transpiration

by means of simple accurate models; sap flow canbe measured by two basic methods: (i) heat pulseand (ii) heat balance.

In heat pulse method, applied by Cohen et al.(1988) in herbaceous plants, sap flow is estimatedby measuring heat velocity, stem area and xylemconductive area. This method seems to be inaccu-rate at a low transpiration rate (Cohen et al.,1993); moreover, it needs calibration for everycrop species.

Therefore, the most popular sap flow method isbased on the heat balance method. It is based onthe concepts proposed by Cermak et al. (1973),Sakuratani (1981), Granier (1985) and Steinberget al., (1990). The plant transpiration can beestimated by determining the sap mass flow; thisis done using gauges that are attached to orinserted in the plant stem. For the heat balancemethod, a heater element is placed around theplant stem to provide energy to the system. Ther-mocouples are used to determine how much heatis lost by conduction up, down and radially in the


the stem and the pattern of ambient temperature.Moreover, the determining of the sheath conduc-tance by the night-time sap flow measurement canbe affected by error due to the stem variationduring the season.

These errors are highly dependent on operatingconditions and can be minimised by followingappropriate recommendations.

Problems linked to the death of the fresh tissuesaround the heated area, due to silicone applica-tion, can be minimised by reducing the period ofcontinuous measurement to 1–2 weeks (Wiltshireet al., 1995).

The sap flow method approaches only transpi-ration measurements, neglecting soil evaporation.Nevertheless, under the Mediterranean climateevaporation from soil can be a very importantfraction (up to 20% of total evapotranspiration)of the soil–plant–atmosphere water budget (Brut-saert, 1982; Klocke et al., 1985a,b).

3.3.2. Chambers system methodThe chambers to rapidly measure ET were de-

scribed for the first time by Reicosky and Peters(1977). They consist of aluminium conduits cov-ered with Mylar, polyetilene or other plastic orglass films; the air within the chamber was mixedcontinuously with strategically located fans. Thefirst version was portable (by means of a tractor,for example) and ET rate was calculated by apsychrometer before the chamber was lowered onthe plot and 1 min later, as latent heat storage.The volume of the chamber can be easily adaptedto a herbaceous field crop and the accuracy was:10%, compared with weighing lysimeters (Rei-cosky et al., 1983).

This system was used by Reicosky (1985) tomeasure, on a daily scale, ET on several differenttreatments more easily than the weighing lysime-ter, but it is not suitable for long term ET mea-surements. Furthermore, more serious errors maybe introduced if chamber results were extrapo-lated over time as well as spatially (Livingstonand Hutchinson, 1994).

Under a semi-arid climate, Dugas et al. (1991)demonstrated that portable chambers, equippedwith an infrared analyser (BINOS, Inficon Ley-bold-Heraeus, NY) for measuring vapour density

differences in differential mode, are not represen-tative of the field, particularly on its margins,where ET measurements were affected by sur-rounding conditions. Furthermore, the last im-proved version of portable chambers can be veryexpensive, due to the high costs for key compo-nents (data acquisition system and infra-redanalyser) and accurate chamber manufacturingthat may require some heavy engineering.

Recent developments of portable chamber sys-tems can be found in Wagner and Reicosky(1996); here the equipment also provides CO2

measurements, but its complexity and costs limitits use for research to a small temporal scale.

The chambers are also suitable for researchstudies on orchard crops (Katerji et al., 1994).The most serious problems of almost all chambersare related to the modification of the microclimateduring the measurement period. First, the solarradiation balance, since the chambers were de-signed for simultaneous measurement of bothCO2 and water vapour exchanges (Denmead,1984). These dual requirements are not often com-patible because wall materials are usually selectedfor high transmission in the short wavelengths,neglecting the long-wave exchange (:20% of theincoming short-wave radiation). Second, the airtemperature: its rapid increase inside the cham-bers could alter the biological control of leavestranspiration process. Finally, the wind speed:inside the chamber it could be strongly reducedwith direct consequences on ET measurementaccuracy.

4. Actual crop evapotranspiration modelling

Actual ET can be estimated by means of moreor less complex models: the accuracy of ET esti-mation is proportional to the degree of empiri-cism in the used model or sub-models. Thus, wecan categorise the ET estimation into three groupsof methods:1. Methods based on analytical modelling of

evapotranspiration;2. Methods in which actual crop ET is deducted

from the evapotranspiration of a referencesurface;


3. Methods based on a soil water balancemodelling.

4.1. ET analytical models

One-dimensional equations based on aerody-namic theory and energy balance — for thisreason called combination models (Penman, 1948;Monteith, 1965, 1973) — have proved very usefulin the actual crop ET estimation, because theytake into account both the canopy properties andmeteorological conditions (Szeicz and Long, 1969;Black et al., 1970; Szeicz et al., 1973).

The most widely used form of the combinationequation, called Penman-Monteith equation, canbe expressed under the form (Allen et al., 1989):

lE=DA+rcpVPD/ra

D+g(1+rc/ra)(15)

In Eq. (15) we can distinguish weather non-para-metric and parametric variables:� weather non-parametric variables: A=Rn−G

(W m−2) is available energy, D (kPa C−1), isthe slope of the saturation vapour pressureversus temperature function, VPD (kPa) is airvapour pressure deficit and g (kPa C−1) is thepsychrometric constant;

� parametric variables: ra (s m−1) is the aerody-namic resistance and rc (s m−1) is the bulkcanopy resistance.All the terms have to be accurately evaluated

(Allen, 1996). While the non-parametric data arestandard measurable climatic variables, the para-metric data are not directly measurable and theyneed to be modelled. Indeed, the first one (ra) isthe aerial boundary layer resistance and describesthe role of the interface between canopy andatmosphere in the water vapour transfer; the sec-ond one (rc) is the resistance that the canopyopposes to the diffusion of water vapour frominner leaves toward the atmosphere and it isinfluenced by biological, climatological and agro-nomical variables. This model is applied to thewhole plant community as if it were a single ‘bigleaf’ located at the height of virtual momentumabsorption (Thom, 1975).

The degree of empiricism of the Penman–Mon-teith equation (and consequently its success)

mainly depends on the accuracy of the estimationof the canopy resistance (Beven, 1979).

Rana and Katerji (1998) demonstrated that,under a semi-arid climate, the canopy resistanceplays the major role, so that its modelling is themost critical point of the Penman–Monteithmodel to estimate actual crop ET under the Med-iterranean climate. In particular, their sensitivityanalysis on Penman–Monteith model showedthat: (i) in well-watered conditions, rc modelling issensible to Rn variations in the case of low crops(i.e. reference grass) and it is sensible to vapourpressure deficit variations, both in the case ofmedium (Fig. 7) and tall crops (Fig. 8); (ii) inwater stress conditions, rc modelling is sensible tothe actual crop water status (Figs. 7 and 8).

4.1.1. Methods of determining canopy resistanceOne of the most diffuse methods of estimating

rc is that proposed by Szeicz and Long (1969), inwhich canopy resistance can be determined as afunction of daily mean stomatal resistance of thesingle leaves (rs) and leaf area index of the leaveseffective in transpiration (LAIeff). These authorsassumed that only the surfacial layer of thecanopy participates effectively to the transpira-tion. Usually, such a canopy resistance is assumedto be half the full crop LAI:

rc=rs

LAIeff

(16)

This equation is suggested to be used for refer-ence crop ET (Allen et al., 1989) and it is alsoused, under light different form, for field crop ET(Steiner et al., 1991; Stannard, 1993; Howell et al.,1995).

Since the spatial and temporal variability of thesoil water status (and, consequently, of the plantwater status) is very high and the microclimate towhich they are exposed is very different (Den-mead, 1984), to obtain sufficiently accuratecanopy resistance values by means of this method,it is necessary to realise a great number of mea-surements of stomatal resistance in a brief intervaltime.

Furthermore, from the theoretical and practicalpoint of view, the problems of scaling-up thecanopy resistance from leaf to canopy is not


completely solved (Jarvis and McNaughton, 1986;Baldocchi, 1989; Baldocchi et al., 1991; Raupach,1995); particularly in semi-arid environments (Ste-duto et al., 1997).

An improvement of this estimating method hasbeen proposed by Monteith (1965) and tested andapplied by Katerji and Perrier (1985). In thismethod, the canopy was divided into layers andcanopy resistance was estimated starting fromstomatal resistance measured layer by layer andweighted with the LAI of each layer. The expres-sion of the canopy conductance (gc=1/rc) isgiven, in this case, by the relationship:

gc=%i

gci·LAIi (17)

where gciis the stomatal conductance measured

on the leaves belonging to the layer characterisedby LAIi. Usually i is equal to 2 or 3, following the

crop growth: an example is given in Table 2 foran alfalfa crop divided into three layers. Thisapproach is difficult and hard to carry out, givingrc values not always accurate. Nevertheless, theestimation of field crop ET can be acceptable, atleast for well-watered crops (Katerji and Perrier,1985).

The most complete model of rc should have thefollowing general form (Stewart, 1988, 1989; Itier,1996):

rc= f(LAI, Rg, VPD, T, crop water status) (18)

where Rg is global radiation.Actually, the better way to evaluate the crop

water status is by means of measurements of leafwater potential (Cf) or root-sources abscisic acid(ABA) (Zhang et al. 1987; Zhang and Davies,1989). As previously stated, the plant water statusvaries almost instantaneously, so that to have

Fig. 7. The sensitivity coefficients as function of predawn leaf water potential (PLWP, MPa) for grain sorghum; A is availableenergy, ra is aerodynamic resistance, rc is canopy resistance and VPD is vapour pressure deficit (Rana and Katerji, 1998).


Fig. 8. The sensitivity coefficients as function of predawn leaf water potential (PLWP, MPa) for sweet sorghum; for symbols see Fig.7 (Rana and Katerji, 1998).

acceptable accuracy of the actual crop waterstatus, a great number of Cf or ABA measure-ments has to be carried out during the entire day.Hence, this method is not suitable for practicalapplication in a field.

In order to avoid the problem of a large num-

ber of punctual measurements, a number of mod-els as expressed by the general relationship Eq.(18), have been developed for dry conditions. Forexample, Hatfield (1985) modelled rc in the func-tion of global radiation and available soil waterby means of an experimental function. Fuchs et

Table 2Variability of stomatal resistance on the two sides of the leaf in an alfalfa canopya

Stomatal resistance and S.E. (s m−1)Canopy layer LAI and S.E. Canopy conductance (mm s−1)I

Lower sideUpper side

Top 117929 115929 1.7590.35 30.21Medium 1999702 5599196 2.190.42 14.3

104493653 1.50.8590.1712009420Bottom

46.04.7Canopy

a The resulting canopy resistance is 22 s m−1 (Saugier and Katerji, 1991).


al. (1987) stated that rc can be modelled by meansof photosynthetic active radiation (PAR) and soilmoisture deficit, but this model is only valid formild to medium stress. Again, regressive experi-mental functions were used by Jarvis (1976) tomodel rc in the function of LAI, Rg, VPD, T andsoil water potential. Unfortunately, all these func-tions need to be locally calibrated per crop and,often, they need also a time calibration, i.e. theyare not valid for the whole growth season (Stew-art, 1988).

An original approach to take into account thecrop water status to estimate ET by means ofPenman–Monteith model was presented by Ranaet al. (1997b), in which rc is modelled as a func-tion of ‘predawn leaf water potential’, Cb. Thisparameter represents the crop water status and itdoes not need to be measured instantaneously,but just once a day. The application of such amodel in semi-arid environments gives quite goodresults. Such rc model is valid for crops growingunder semi-arid climate (i.e. also for crops underwater stress) and needs to be calibrated only ‘percrop’ so that it can be generalised (Rana et al.,1997c). It is possible to use the transpirable soilwater as input of the model instead of Cb, but inthis case the model looses its generality and mustbe locally calibrated (Rana et al., 1997a).

4.2. ET empirical models

By these methods, the water consumption ofcrops is estimated as a fraction of the referenceevapotranspiration (ET0):

ET=Kc ·ET0 (19)

where Kc is the experimentally derived crop coeffi-cient and ET0 is the maximum evapotranspira-tion; the latter can be evaluated (i) on a referencecrop or (ii) on free water in a pan. The accuracyof such an estimation depends on:� the reference chosen (grass meadow or free

water in a standard pan);� the method used to evaluate reference ET

(measurement or modelling);� the method used to evaluate the crop coeffi-

cient Kc.

Moreover, the data necessary for the determi-nation of reference evapotranspiration ET0 areusually collected in standard agrometeorologicalstations. These stations are usually installed to berepresentative of the catchment, i.e. an area ofseveral squared kilometres in extension.

4.2.1. ET0 reference crop determinationIn this case, ET0 is the water consumed by a

standard crop. In order to make procedures andresults comparable world-wide, a well adaptedvariety of clipped grass has been chosen. It mustbe 8–16 cm high, actively growing and in well-wa-tered conditions, subjected to the same weather asthe crop whose water consumption is to be esti-mated. ET0 can be again measured (e.g. by meansof a weighing lysimeter) or estimated. Thereforethe comments and observations made for actualcrop ET are still valid for ET0 determination. Inthe following, we analysed the more used modelsof ET0.

A semi-empirical approach to estimate ET0 wasproposed by Penman (1956) as:

ET0=DRn+gEA

D+g(20)

where

EA= f(u)(e−e*) (21)

and

f(u)=1+0.54 u2 (22)

with u2, wind speed measured 2 m above the soilsurface.

The empiricism of this formula is into the windfunction f(u). Actually, this function is just alinear regression adjustment to take into accountthe differences between estimated and observedET0 for grass grown in the UK. Therefore, it is apseudo exchange coefficient, which is supposed totake into account the ET grass regulation. Thisobservation explains why it is necessary to adaptthe function f(u) to each site, in order to correctlyapply the Penman formula in the Mediterraneanregions. Furthermore, it is clear that the windfunction decreases going from North towardSouth (Fig. 9) and these results point out thedependence of canopy resistance on the vapour


pressure deficit, which increases going from Northto South Europe (Choisnel, 1988).

Today the most used and suggested method toevaluate reference ET is based on the Penman–Monteith model, therefore, having the same prob-lems encountered in actual crop ET estimationregarding rc modelling.

Rana et al. (1994) proposed an ET0 estimatedby means of the Penman–Monteith model, inwhich canopy resistance is analytically modelled.This model was tested in Mediterranean regions,but it is valid in humid environments too. Theydemonstrated that rc varies with the climate and itis sensitive to any agronomic practice (irrigationdate, grass cutting, phytopathological situation);in Fig. 10 hourly rc values are shown before andafter grass cutting and irrigation.

Recently, Todorovic (1997) proposed a variablecanopy resistance, both at hourly and daily scale,modelled in the function of standard meteorologi-cal parameters. It was shown that ET0 calculatedby the Penman–Monteith model with such a re-sistance works well under different climates.

Several authors proposed an ET0 Penman–Monteith formula using constant value of rc (Al-len et al., 1989). Steduto et al. (1996) tested suchET0 estimates with constant rc in several Mediter-ranean regions. Their results demonstrated thatthis approach does not have good performancesin all the experimental sites.

Other simpler methods to estimate referencecrop ET are based on statistical–empirical formu-las (an exhaustive review of these methods can befound in Jensen et al. (1990)). These methods can

Fig. 9. Comparison among four f(u) wind functions in the Penman equation: Penman is f(u)=0.26(1+0.54 u); Businger isf(u)=0.37 u ; Doorenbos and Pruitt is f(u)=0.27(1+0.86 u); Seguin is f(u)=0.37 u0.88; Losavio et al. is f(u)=0.12 u0.67 (Losavioet al., 1992).


Fig. 10. Canopy resistance during a day for a reference grassgrown in Southern Italy, (a) before and after grass cutting and(b) before and after irrigation (Rana et al., 1994).

4.2.2. The reference ET0 calculated by the pane6aporation

Pan evaporation data can be used to estimatereference ET, using a simple proportionalrelationship:

ET0=Kp·Epan (23)

where Kp is dependent on the type of pan in-volved, the pan environment in relation to nearbysurfaces and the climate. Doorenbos and Pruitt(1977) provided detailed guidelines for using pandata to estimate reference ET0. In the case of apan surrounded by short green grass, Kp rangesbetween 0.4 and 0.85. In semi-arid environmentsits mean value is :0.7 (Jensen et al., 1990). Thevalue of Kp to be adopted is strongly dependenton the upwind fetch and on the local advection.

An attempt to model the pan coefficient, Kp hasbeen made by Perrier and Hallaire (1979a,b), onthe basis of experimental pan data measured in ahumid–tropical area (Baldy, 1978). They ex-pressed Kp in the function of climatic variablesand a coefficient b, the ratio between the ex-change coefficient of the pan and the wind func-tion f(u) of the Penman’s formula, as

Kp=1+a(1−RH)

1+ab(1−RH)(24)

with RH relative air humidity and a a coefficient,function of air temperature, net radiation andwind speed. This latter coefficient is dependent on

be used very easily from a practical point of view,above all in rural lands. However, their empiri-cism may lead to very inaccurate estimations, asclearly shown by Ibrahim (1996), in arid environ-ments (Table 3).

Table 3Seasonal reference evapotranspiration (ET0) in 3 years and average percent deviation from the mean value in the north central areaof the Nile delta region (Egypt) (Ibrahim, 1996).

Percent deviation from mean valueMethod Average seasonal ET0 (cm)Seasonal ET0

1979 1980 1981

(a) Blaney–Criddle 61.8163.2 60.31 61.71 −4.3766.78 63.20 66.82 65.60 +1.66(b) Radiation

(c) Modified Penman −5.1361.2260.2460.6062.8281.9782.92 +27.0381.3581.64(d) Rijtema

49.73 48.00 49.96(e) Thornthwaite −22.5952.1686.75 80.50(f) Jensen and Haise 79.41 82.08 +27.20

54.1456.75 −17.28(g) Evaporation pan 53.3849.24−6.5960.2863.47 58.45(h) Turc 58.93

66.62Average 63.78 63.17 64.53


Fig. 11. Theoretical curves of pan coefficient Kp in function ofrelative air humidity (a=0.8), b=2 is for humid seasons,b=2.5 is for medium seasons and b=3 is for dry seasons(Perrier and Hallaire, 1979b).

4.2.3. The crop coefficient Kc

The crop coefficient represents an integration ofthe effects that distinguish the crop from thereference ET; many such Kc are reported in theliterature (e.g. Doorenbos and Pruitt, 1977; Allenet al., 1998) usually derived from soil water bal-ance experiments.

Crop coefficient can be improved for estimatingthe effects of evaporation from wet soil on Kc ona daily basis (Wright, 1982). In this case, the cropcoefficient can be expressed by the equation:

Kc=Ks·Kcb+Ke (25)

where Ks is a stress reduction coefficient (0}1).Kcb is the basal crop coefficient (0}1.4) andrepresents the ratio of ET and ET0 under condi-tions when the soil surface is dry, but where thesoil water content of the root zone is adequate tosustain full plant transpiration; Ke is a soil waterevaporation coefficient (0}1.4). It can be experi-mentally calculated in the function of soil waterstorage, DS and depends on the amount of soilavailable to the plants’ roots. In fact, in open soilsystems, when the conditions are favourable forroot system development, Ks is almost constant,also when soil humidity decreases considerably,because of an appreciable contribution of thenon-rooted soil layer to the water balance. Inclosed soil systems (pots, for example) Ks is vari-able following the soil humidity and it begins todecrease appreciably for values of soil water re-serve :60–70% of available soil water to transpi-ration. This Ks behaviour is reported in Fig. 12, inwhich the ratio of actual to potential ET of awell-irrigated corn crop is reported in the functionof the available soil water, for the above men-tioned two conditions (open and closed soils).

In order to avoid the difficulties linked to theavailable soil water conditions, it is possible toevaluate Ks by means of the predawn leaf waterpotential, Cb. Itier et al. (1992) demonstrated thatthis relationship (and Ks as a consequence) hasgeneral validity, since it does not depend on thesoil type and site.

The methods to estimate crop coefficients andreference ET have been recently modified by Allenet al. (1994a), Allen et al. (1994b) and Allen et al.(1996).

the site climate and can be considered constantand =0.8 in arid environment. Fig. 11 shows thecoefficient Kp in the function of RH for threevalues of b (b=2, humid seasons; b=2.5, inter-mediate seasons; b=3, dry seasons).

Fig. 12. Relative evapotranspiration (actual ET/maximum ET)in function of available soil water for a corn crop grown in aclosed soil system (pots) and in open soil system (a deep fieldwith favourable environmental conditions) (Tardieu andKaterji, 1991).


The crop coefficient plays an essential role inpractice (Pereira et al., 1999) and it has beenwidely used to estimate actual ET for irrigationscheduling purposes. However, it can be subjectto serious criticism regarding the meaning and theuse of crop coefficient. Besides obvious variationsamong different crops, empirical crop coefficientswere shown to be affected by crop developmentand weather conditions (De Bruin, 1987). Fur-thermore, Stanghellini et al. (1990) demonstratedthat no coefficients should be expected to varyaccording to the conditions of both climate andcrop stage under which they are derived. More-over, these researchers stated that the crop re-quirements based on a same value of the cropcoefficient do not have the same accuracy fordifferent months, different seasons, and, above allat different sites. This inaccuracy of the Kc ap-proach can be found in the discrepancies betweenlocal calculated Kc and crop coefficients reportedin literature (e.g. Rana et al., 1990; Vasic et al.,1996).

4.2.4. Soil water balance modellingAn exhaustive survey of the most diffuse mod-

els for soil water balance can be found in de Jongand Bootsma (1995) and Leenhardt et al. (1995).

Two classes of models are generally retained forthe simulation of soil water balance: (i) mechanis-tic models and (ii) analogue (or water reservoirs)models.

In the mechanistic approach, the water flux inthe soil is controlled by the existence of soil waterpotential gradients, by means of Darcy’s law andcontinuity principle. The equations are usuallysolved by different methods, all involving thesplitting of the soil in more or less small layers (deJong, 1981; Feddes et al., 1988). The difficulties inthe application of these models are linked to (i)the accuracy of the used pedo-transfer functionsfor estimating the water transfer and (ii) the pro-cedures used for estimating the boundary condi-tions of the soil–plant–atmosphere system.

In the analogue approach, the soil is treated asa collection of water reservoirs, filled by rainfallor irrigation and emptied by evapotranspirationand drainage. They can be based on the twofollowing principles (Lhomme and Katerji, 1991):1. determination of soil water storage DS as

function of the soil and roots depth (e.g.Lhomme and Eldin, 1985; Brisson et al., 1992)

2. the split of soil water in readily transpirablesoil water (RTSW) and total TSW (e.g.Freteaud et al., 1987). The stress coefficient Ks

is supposed to be approximately =1 in theRTSW range, then it decreases as the waterreserve is in the TSW range.

In a previous paragraph we have analysed thedifficulties in determining the soil water storageand the evolution of Ks in function of DS, partic-ularly under a Mediterranean climate. Effectively,Ben Nouna (1995) showed that, in semi-arid re-gions with closed system soils, the water reservoirapproach can be very useful in estimating actualET only if very accurate measurements of DS canbe realised (Fig. 13).

5. ET evaluation in advection regime

All the previously presented methods to mea-sure and/or estimate actual crop ET are based on

Fig. 13. Comparison between ET estimated by a water reser-voir model as proposed by Lhomme and Katerji (1991) andET estimated by water balance with DS measured by TDR ona daily scale (Ben Nouna, 1995).


a fundamental critical hypothesis that the consid-ered systems were conservative, i.e. the profiles ofair temperature, water vapour concentration andwind speed are constant along the horizontal axeX (e.g. Itier and Perrier, 1976; Stull, 1988).

In the Mediterranean regions, the scarcity ofavailable water resources leads to irrigated landsin a selective way, with the creation of areascharacterised by strong discontinuity of water va-pour concentration at surface level, also for simi-lar crops. The air thermodynamic characteristicsare strongly influenced by the surface conditions,so that the air passing from a dry field toward anirrigated field is cooled as well as its humidityincreases. Hence, near the boundary of the irri-gated field, ET rapidly increases, then slowly de-creases along the wind direction following thethermodynamic characteristics of the air coupledwith the vegetation surface.

In general, the latent heat flux density measuredor estimated in one point of the plot is, actually,the sum of two terms: (i) a term translating theequilibrium between the evaporative demand ofthe air determined by the Penman model and cropwater conditions; (ii) an additional flux, more orless important, depending on the lateral transferof energy by advection. From an energetic pointof view, latent best flux depends on the modifica-tions of the vapour and thermal characteristics ofthe air passing through the considered surface.

The theoretical studies on local advection(Philip 1959; Taylor, 1970; Itier and Perrier, 1976;Itier et al., 1994) showed that the advective flux(Fa) depends on: (i) the fetch F (m); (ii) theroughness length of the crop, z0 (m); (iii) the windspeed through the friction velocity u* (m s−1);and (iv) the temperature difference between thedry and irrigated fields, DT (°C).

From the operational point of view such asituation in which an advection regime is verifiedleads to two main consequences:1. In order to have a correct representativeness

of ET, it is necessary to correct a posteriori theevapotranspiration measured by means ofweighing lysimeters, soil water balance, sapflow method and chambers system methodwhen the fetch is not large enough to avoid

advection effects. A possible simple correctionwas proposed by Itier et al. (1978) as:

Fa=360·u* ·DT 6z0/F (26)

This correction can be of 1–2 mm per day fortemperature differences between dry and irri-gated field of 5–10°C (Itier et al., 1978).

2. The micrometeorological methods must be ap-plied in order to make the measurements in-side the equilibrium fully adapted boundarylayer. The fetch value assuring an acceptableadapted layer for micrometeorological is re-ported by Wieringa, (1993) as:

F$2z0�10z

z0

�ln

10zz0

−1�n

(27)

where z is the height of the top sensor.Regarding the Bowen ratio method, it is well

known that it can underestimate ET under strongregional advective conditions (Blad and Rosen-berg, 1974). This implies an extensive fetch in theupwind direction for the air flowing over thesurface of at least 100 times the maximum heightof measurements, but Heilman et al. (1989)demonstrated that the Bowen ratio method can besuccessfully applied up to fetch-to-height ratios aslow as 20:1.

6. Conclusions

In Mediterranean areas submitted to arid andsemi-arid climates, ET ranges over a large intervaldepending on water regimes (irrigated or non-irri-gated fields). Among the other weather variables,air temperature and humidity experience a largegap between night and day and between winterand summer; the wind is very variable movingfrom the coast to internal areas. So that, in gen-eral, we can state that all the weather variablesrange in a very large interval of values. Moreover,the variation in one parameter immediately influ-ences all the other variables that are mutuallylinked. These facts make difficult to correctlyevaluate the crop actual evapotranspiration.

In this review, we have presented the mostimportant methods of measuring and modellingactual evapotranspiration in arid and semi-arid


Table 4Classification by space and time of ET methods to measure or model actual evapotranspiration, adapted by Stewart (1984)

Hour Day MonthMinute Growth season Year

Catchment -----------Crop coefficient method-----------

Uniform area ------------Crop coefficient method----------—Micrometeorological method-----------Soil water balance---------

------------Soil water balance with TDR------------------Penman–Monteith model---------------

Group of plants -------Weighting lysimeter; chambers system----------------Sap flow--------

--------Sap flow-------Plant

environments. Some methods are more suitablethan others in terms of convenience, accuracy orcost for the measurement of ET at a particularspatial and over a particular time scale. In Table4 the classification of the presented ET methods byspace and time scale is shown.

We tried to give, for each method, the advantagesand disadvantages for their use in the Mediter-ranean regions; the summary of this analysis for themeasurement methods is reported in Table 5.

In summary, two major observations arepossible:

Table 5Summary of the advantages and disadvantages of the ET measurement methods

DisadvantagesAdvantagesMeasurementmethod

Soil water balance Large spatial variabilitySoil moisture simple to be evaluated withgravimetric method Difficult to be applied when the drainage andNot expensive if the gravimetric method is used capillary rising are important

Difficult to measure soil moisture in cracked soilsDirect method FixedWeighing lysimeter

Difficult maintenanceIt could be not representative of the plot areaExpensiveDifficult to have correct measurement of the wetSimple sensors to be installedEnergy balance/temperature if psychrometers are usedSuitable also for tall cropsBowen ratioThe sensors need to be inverted to reduce biasIt can be also used when the fetch is 20:1Difficult maintenanceNot very expensive if psychrometers are used

Aerodynamic It needs to be corrected for the stabilitySimple sensors to be installedNot suitable for tall cropsIt does not need humidity measurements

Not very expensiveDelicate sensorsEddy covariance Direct method with fast hygrometerDifficult software for data acquisitionHygrometer very delicate expensiveDifficult scaling-upSuitable for small plotsSap flow

It takes into account the variability among plants The gauges need to be deplaced every 1–2 weeksThe soil evaporation is neglected

Chambers method It modifies the microclimateSuitable for small plotsDifficult scaling-upIt can be used also for detecting emissions of

different gases


1. The ET measurement methods are based onconcepts which can be critical under semi-aridand arid environments for several reasons: (i)representativeness (the weighing lysimeter, forexample); (ii) instrumentation (air humiditysensors for example); (iii) microclimate (advec-tion regime); and (iv) hypothesis of applicabil-ity (the simplified aerodynamic method forexample). Thus, in order to establish the de-gree of accuracy of the obtained ET measure-ment and the validity of a method, it isnecessary to consider all these parameters.

2. The estimation methods based on an analyti-cal approach could be very accurate but, usu-ally, they are not practical enough. The moreoperational estimation methods (crop coeffi-cient approach, ET0 calculation, water balancemodelling) can be generally affected by verylarge errors.

Nowadays, a new research trend is being devel-oped in order to integrate these two approachesof actual evapotranspiration estimation. Thesenew models tend to introduce into the analyticalapproach an acceptable degree of empiricism (Al-len et al., 1989; Rana et al., 1994; Pereira et al.,1999). We think that such methods should beaccepted and encouraged in the future, since theseapproaches can greatly improve the water man-agement at farm level, one of the greatest prob-lems of the Mediterranean countries.

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