European Journal of Agronomy 13 (2000) 125 – 153
www.elsevier.com/locate/eja
Review
Measurement and estimation of actual evapotranspiration in
the field under Mediterranean climate: a review
G. Rana a,*, N. Katerji b
a
Istituto Sperimentale Agronomico, 6ia C. Ulpiani, 5, 70125 Bari, Italy
b
INRA-Unité 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 and
semi-arid with summers characterised by high temperatures and small precipitation. Due to the scarcity of water
resources, the correct evaluation of water losses by the crops as evapotranspiration (ET) is very important in these
regions. In this paper, we initially present the most known ET measurement methods classified according to the used
approach: hydrological, micrometeorological and plant physiological. In the following, we describe the methods to
estimate ET, distinguishing the methods based on analytical approaches from the methods based on empirical
approaches. 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 coefficient
approach and soil water balance modelling approach. In the presentation of each method, we have recalled the basic
principles, underlined the time and space scale of its application and analysed its accuracy and suitability for use in
arid and semi-arid environments. A specific section is dedicated to advection. Finally, the specific problems of each
method for correct use in the Mediterranean region are underlined. In conclusion, we focus attention on the most
interesting new guidelines for research on the measurement and estimation of actual crop evapotranspiration. © 2000
Elsevier Science B.V. All rights reserved.
Keywords: Actual evapotranspiration; Direct ET measurement methods; Indirect ET measurement methods; ET modelling;
Mediterranean climate
1. Introduction
The Mediterranean climate is characterised by a
hot and dry season in summer and a mild tem* Corresponding author. Tel.: + 39-080-5475026; fax: +39080-5475023.
E-mail addresses: [email protected] (G. Rana),
[email protected] (N. Katerji).
perature associated to annual rainfall in winter.
Despite the apparent uniformity of the Mediterranean climate, a more detailed analysis shows
great differences. The dry season duration (Fig. 1)
clearly illustrates that, while the South is characterised by a long dry season, averaging \ 7
months without any precipitation, in the Northern part, the dry season is relatively limited and
1161-0301/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.
PII: S 1 1 6 1 - 0 3 0 1 ( 0 0 ) 0 0 0 7 0 - 8
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G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
Fig. 1. Duration of the dry season in the Mediterranean basin (Hamdy and Lacirignola, 1999).
does not exceed 2– 3 months. In addition, the
rainfall and temperature diagrams (Fig. 2) show
great differences between the North (autumn rainfall) and the South (winter rainfall) of the basin.
During summer, the simultaneous occurrences of
high temperatures and small precipitation causes
high evapotranspiration (Hamdy and Lacirignola,
1999). For these reasons, 75% of the available
water in the Mediterranean area is used for agricultural purposes.
Furthermore, the Mediterranean region is characterised 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
Table 1
Estimation of the percentage of irrigated soils affected by
salinity in several Mediterranean countries (Hamdy et al.,
1995)
Country
Irrigated surface (%)
Algeria
Cyprus
Egypt
Spain
Israel
Greece
Jordan
Morocco
Portugal
Syria
10–15
25
30–40
10–15
13
7
16
10–15
10–15
30–35
“
Water scarcity in the South: The water
availability in the Southern and Eastern countries of the Mediterranean basin is below the
first needs (1000 m3 per capita per year) and
prospects for the future indicate more severe
difficulties (Hamdy and Lacirignola, 1999).
“ The need to increase the irrigated surfaces because of the population increasing: The Mediterranean population increased by 67%
between 1950 and 1985.
“ Soil pollution: Nowadays, the problem of
salinity affects 7– 40% of the irrigated surface
of several Mediterranean countries (Table 1).
Therefore, accurate determination of irrigation
water supply is necessary for sustainable development and environmentally sound water management. This goal is far from achievement, in fact
the irrigation efficiency is now :45% of the
water supply and one half of this inefficiency
could be attributed to bad estimates of crops
water requirements (FAO, 1994).
About 99% of water used in agriculture is lost
by crops as evapotranspiration (ET) — it is
defined as the water loss by a vegetative unsaturated surface, under vapour form, by evaporation
from soil and transpiration from plants. Depending on the soil water conditions, a more or less
important biological control is exerted on the
water lost. In addition to this a resistance is
opposed by the canopy structure to the water
vapour transfer toward the atmosphere (Perrier,
1984; Lhomme, 1997).
127
Moreover, semi-arid and, mostly, arid climates
have a great impact on crop growth in conditioning yield and product quality. Under these
weather conditions, rainfed crops and agricultural
fields with limited water resources are often submitted to water stress. Thus, it becomes fundamental to know the exact losses of water by
evapotranspiration (i.e. actual evapotranspiration)
and the crop water status and its influence on
production.
Actual crop ET can be measured (directly or
indirectly) or estimated. For example, for research
purposes in plant eco-physiology, ET must be
precisely measured, while for farm irrigation management it can be estimated. The lower the degree
of accuracy in the estimation, the greater will be
the water waste by incorrect management of
irrigation.
In this paper, we review the most important
methods of measuring and estimating actual ET,
at plot scale (e.g. at farm level), giving, for each
method, the problems, limits and advantages for
their use in a field under the Mediterranean climate. This summary cannot be, of course, an
exhaustive and complete review of all the existing
ET methods; in fact, we will focus attention on
the most known and diffuse methods in the international research community, paying particular
attention to those used in agricultural research.
The scaling up of ET from plot scale to regional scale requires specific methods and techniques and, therefore, will not be treated in this
paper.
2. Measurement and estimation
There is a great variety of methods for measuring ET; some methods are more suitable than
others for accuracy or cost or are particularly
suitable for given space and time scales. For
several applications, ET needs to be predicted, so
it must be estimated by model.
It is convenient to discuss the methods of determining ET in considering separately the measurement and modelling aspects.
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G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
In general, a ‘measurement’ of a physical
parameter is a quantification of an attribute of the
material under investigation, directed to the answering of a specific question in an experiment
(Kempthorne and Allmaras, 1986). The quantification implies a sequence of operations or steps
that yields the resultant measurement. Conventionally, if the value of the parameter is quantified
by the use of an instrument, it is ‘directly’ measured and when it is found by means of a relationship among parameters, it is ‘indirectly’ measured
(Sette, 1977).
The methods of measuring ET should be divided into different categories, since they have
been developed to fulfil very different objectives.
One set of methods are primarily intended to
quantify the evaporation over a long period, from
weeks to months and growth season. Another set
of methods has been developed to understand the
process governing the transfer of energy and matter between the surface and atmosphere. The last
set of methods is used to study the water relations
of individual plants or part of plants. Therefore,
following Rose and Sharma (1984), it is convenient, when discussing the ET measurement, to
place the variety of methods in groups, where the
main approach or method depends on concepts
from hydrology, micrometeorology and plant
physiology, as follow:
“ ET measurement
Hydrological approaches
(1) Soil water balance
(2) Weighing lysimeters
Micrometeorological approaches
(3) Energy balance and Bowen ratio
(4) Aerodynamic method
(5) Eddy covariance
Plant physiology approaches
(6) Sap flow method
(7) Chambers system
A physical parameter can be considered as ‘estimable’ if it is expressed by a model. The objective of ET modelling can vary from the provision
of a management tool for irrigation design, to the
provision of a framework for either detailed understanding of a system or to interpret experimental results. To meet these requirements, it is more
convenient to use methods with a sound physical
basis, but often the available data only allow the
use of either empirical or statistical approaches.
Thus, to discuss the ET modelling, it is convenient
to 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 balance
modelling.
This categorisation is, of course, far from completion, but can be considered a good trace in a
review of ET determination.
3. Actual crop evapotranspiration measurement
The different methods for directly and indirectly measuring ET are based on the measurement of two classes of factors:
1. The soil water content and the physical characteristics of the evapotranspirative surface
(height, plant density, canopy roughness,
albedo);
2. Climatic variables: solar radiation, wind speed
and thermodynamic characteristics of the atmosphere above the canopy.
In the description of the measurement methods,
we will consider as true the hypothesis of ‘conservative flux’, i.e. the flux density does not change
with the height above the canopy. So that, in a
first approximation, we will consider the different
factors (belonging to both (a) and (b) classes) as
constant in the space considered (the field).
To say that the factors (a) are constant in the
space is the same as saying that evapotranspirative surfaces are perfectly homogeneous along the
horizontal scale. In Mediterranean regions, this
hypothesis is usually far from being verified. In
fact, the fields present crop types, phenological
stages and water conditions very changeable in
the space. This induces a net discontinuity of
surface moisture among fields and, consequently,
a non-negligible effect of advection due to energy
side exchange between contiguous plots.
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
The role of the advective regime on the measurement and estimation of ET will be analysed in
a separate chapter at the end of the methods
presentation.
3.1. Hydrological approaches
3.1.1. Soil water balance
Soil water balance is an indirect method, in fact
ET is obtained as a residual term in the water
balance equation. This equation is based on the
principle of conservation of mass in one dimension applied to the soil, its complete expression is:
P + I + W− ET− R− D = 9 [DS]r0
(1)
where P is precipitation, I is irrigation, W is
contribution from water table upward, R is surface runoff, D is drainage and DS is soil water
storage in the soil layer, where the roots are active
to supply water to the plant (r in m). All the terms
are in milimeters per unit time. Soil water storage
between two dates (i and i −1) is:
[DS]r0 = [Si −Si − 1]r0
(2)
with S, the soil water content.
Since it is often very difficult to accurately
measure all the terms of Eq. (1), a number of
simplifications makes this method unsuitable for
precise ET measurements. In fact, irrigation water
supply is, in principle, known and precipitation
can be measured by rain gauges, but all the other
terms need to be measured or, at least, estimated.
The soil water balance method is applicable to
small plots (:10 m2) or to a large catchment
( : 10 km2); it may cover periods ranging from a
week to a year.
Often, for operational application, the soil water balance Eq. (1) is expressed in its simplified
form:
P +I = ET9 [DS]r0
(3)
The simplifications introduced in Eq. (3) could
be critical if applied in dry environments. In arid
and semi-arid areas with very small slopes, runoff
term R could be neglected (e.g. Holmes, 1984)
but, actually, it depends on the occurrence and
characteristics of precipitation (amount, duration
129
and intensity) and can only be neglected for a
particular type of soil (Jensen et al., 1990), i.e.
coarse (sand and loamy sand) and moderately
coarse (sandy loam).
Drainage (D) is the most unknown of Eq. (1).
Some researchers suggest that it can be neglected
in dry regions (e.g. Holmes, 1984), but actually it
depends on the soil depth, slope, permeability and
surface storage (Jensen et al., 1990; Parkes and Li
Yuanhua, 1996) and needs to be checked in each
particular case (Brutsaert, 1982), depending also
on the climate and weather (Katerji et al., 1984).
In some situations it is so important that its direct
measurement can be used to estimate evapotranspiration on a weekly or greater scale (for an
extensive review see Allen et al. (1991)). Moreover, Katerji et al. (1984) demonstrated that it is
not simple to establish if the water deep flow can
be neglected, in fact it can be a non-negligible
fraction of the water balance both in dry and
humid seasons and at different time scale. In
general, at daily scale it can be neglected if the
water supply (P and/or I) does not exceed the soil
water capacity (Holmes, 1984; Lhomme and
Katerji, 1991).
In arid regions, the terms W and DS could
show problems of correct evaluation. In fact, if
the soil system is closed (i.e. shallow soils or soils
with a very deep water table), W can be considered negligible and DS can be easily determined.
In this case, the simplified soil water balance
works well, as shown in Fig. 3, where ET measured by Eq. (3) is compared with a reference
method (Bowen ratio). The data are relative to a
maize crop grown in a Mediterranean region
(Southern Italy) and soil water storage is measured by TDR and the gravimetric method.
Vice versa, if the system is open (deep soils or
soils with a surfacial water table), W cannot be
neglected and DS is difficult to measure exactly,
so that the simplified form of the soil water
balance does not work well. This inaccuracy was
well demonstrated by Katerji et al. (1984). In fact,
they showed that during humid seasons, W and
DS are of the same order, while during dry seasons, W can reach 30% of cumulated seasonal
actual ET (Fig. 4).
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G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
Soil water content needs to be measured accurately and over an adequate depth. It can be
measured by a wide number of methods (an extensive review can be found in Stafford (1988) and
Phene et al. (1990)). Three methods are the most
important: gravimetric sampling, neutron scattering and electrical resistance.
The gravimetric method remains the most
widely used, particularly by technicians and consultants; it is well developed at research level and
also for irrigation management purposes. It is
simple to apply but it can be used only for large
time scale (weekly or greater).
Neutron probe remains a useful tool at research
level only and its performance has not been well-
established in arid environments. In fact, Payne
and Bruck (1996), for example, stated that neutron probe tends to lose accuracy under the arid
climate of Sahelian Africa, mostly near the surface, wetting fronts and textural discontinuities;
conversely, Evett and Steiner (1995) found very
good results in a wide range of situations. Furthermore, neutron probe poses particularly
difficult and regulatory problems in developing
countries.
Electrical resistance matrix type sensors are the
least expensive (gravimetry is cheaper) and can be
readily used for automatic irrigation control systems (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 by
gravimetric method, at daily scale, on corn grown in Southern Italy (Mastrorilli et al., 1998).
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
131
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 not
adequately irrigated (e.g. Diestel, 1993); the deep
cracks do not allow suitable contact between soil
and probes (Haverkamp et al., 1984a,b) and the
reading of the soil moisture can be affected by
large errors (Bronswijk et al., 1995).
Fig. 4. Water balance component for a lucerne crop grown in
a deep silt soil; (1) cumulative difference between rainfall and
actual evapotranspiration since an initial date; and (2) variation of the total water content in the 0–170 cm upper layer of
the soil since the same initial date (Katerji et al., 1984).
rate in estimating actual ET in soil water depletion conditions (see, e.g. Bausch and Bernard,
1996).
The accuracy of soil water balance strongly
depends on time and space scales of actual soil
moisture measurements (Burrough, 1989) and on
the representativeness of the soil sampling
(Bertuzzi et al., 1994; Leenhard et al., 1994). In
order to meet all these requirements for soil moisture measurement, the technique of time domain
reflectometry (TDR) has been introduced quite
recently by Topp and Davis (1985) and Topp et
al. (1994) among others. It seems that TDR is
able to correctly estimate soil moisture both under
temperate (Ledieu et al., 1986; Werkhoven, 1993;
Plauborg, 1995) and semi-arid climates (Mastrorilli et al., 1998). When TDR probes are used it is
possible to have a soil water balance at plot scale
3.1.2. Weighing lysimeters
Weighing lysimeters have been developed to
give a direct measurement of the term ET in Eq.
(1). Historically, they have always been considered as a suitable tool to correctly measure evapotranspiration (Tanner, 1967; Aboukhaled et al.,
1982).
In general, it is a device, a tank or container, to
define the water movement across a boundary;
actually, only a ‘weighing lysimeter’ can determine ET directly by the mass balance of the water
as contrasted to non-weighing lysimeter, which
indirectly determines ET by volume balance
(Howell et al., 1991).
Weighing lysimeters placed in the field contains
soil cultivated as the field around it, the sensor is
a balance able to measure the weight variation
due to ET, often this variation is measured by
means of an electronic sensor (i.e. load cell).
Under temperate climate, they are able to measure ET at a daily scale with an accuracy of
\10% (Perrier et al., 1974; Klocke et al., 1985b
among others) and at an hourly scale with an
accuracy of 10–20% (Pruitt and Lourence, 1985;
Allen et al., 1991).
However, the weighing lysimeter data are not
always representative of conditions of the whole
field but, in several situations, they represent only
the ET of just one point in the field (Grebet and
Cuenca, 1991).
Besides the soil, height and vegetation density
differences between the lysimeter and outside vegetation can severely affect ET measurements. In
this case, both aerodynamic and radiative transfers to the lysimeter canopy are increasing. If the
lysimeter surface and its close area are surrounded
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G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
by drier vegetation or bare soil, an oasis effect
occurs. Net radiation in excess of latent heat is
converted in sensible heat that is advected toward
the lysimeter, resulting in net supply of energy to
the lysimeter vegetation. All these previously described problems cause an increase of ET relative
to the surrounding crop. This overestimation of
ET could be particularly important under a high
radiative climate, as in the Mediterranean region.
Furthermore, environmental problems can affect measurements of ET with lysimeters (for a
review see Allen et al. 1991). One of the most
common errors made is the incorrect estimation
of an evaporating area of a lysimeter. In fact, this
area is calculated by the inner dimensions of the
container rather than the true vegetative area,
which can be greater than the lysimeter surface
when the vegetation from both inside and outside
the lysimeter reaches across the rim. This error
could be : 20%.
The lysimeter rim can also influence ET measurements. One of the most important effects,
mainly in arid environments, is the heating of the
metallic rim by radiation resulting in microadvection of sensible heat into the lysimeter canopy.
Moreover, if the lysimeter rims are too tall relative to crop, the wind is shielded and the radiative
energy balance is modified due to the reflection of
solar radiation by the inner wall of the rim toward the crop.
Under arid and semi-arid climates, problems
linked to the atmospheric evaporation demand
can worsen the performances. In fact, if the soil
inside lysimeters has deep cracks (often along the
border in contact with the soil), the water evaporation continues from the deepest layers, so that
lysimeter can overestimate ET in these periods
and underestimate ET in the following periods,
when the water depletion inside is greater than
that in the field, due to water stress condition of
inner 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 much
wetter than the surrounding field soil (Klocke et
al., 1991).
Furthermore, the weighing lysimeter is limited
in depth in order to make possible the weighing of
the soil–plants system; this limitation adds new
problems for its use in Mediterranean regions. In
fact, it does not take into account the effects of
the deeper water fluxes (capillary rising) on crop,
which can be very important in water stress periods. Moreover, in areas with deep soil, the weighing lysimeter does not take into account the
effects of the total soil available on the plant
growth. In this case, i.e. very deep soils, the
representativeness of the lysimeter becomes a very
difficult technical problem, due to the excessive
weight of the system soil–tank–plants. In Fig. 5,
three kinds of lysimeter are shown: since the total
available water of nearby soil is : 260 mm, only
the first one is well representative of the actual
field, but in this case the weight of the system
soil–tank is very high (12 t).
3.2. Micrometeorological approaches
Fig. 5. Three kinds of weighing lysimeter: S is surface, V is
volume, P is weight, AW is total available water (Perrier et al.,
1974).
From the energetic point of view, evapotranspiration can be considered as the energy employed
for transporting water from inner leaves and plant
organs to the atmosphere as vapour. In this case
it is called ‘latent heat ’ (lE, with l, latent heat of
vaporisation) and it is measured as energy flux
density (W m − 2).
We shall describe in the following sections the
main methods based on physical or meteorological principles, by which the latent heat flux can be
measured. Three techniques will be analysed: the
energy balance and Bowen ratio, the aerodynamic
method and the eddy covariance. In general, all
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
these techniques require accurate measurements
of meteorological parameters on small temporal
scale (1 h or less). Due to the conservative hypothesis of all the flux density above the crop,
they can be applied only in large flat areas with
uniform vegetation. There are many situations of
practical interest where they cannot be used,
mostly in the Mediterranean regions. For example, mixed plant communities, hilly terrain and
small plots.
Much care must be taken to analyse local and
regional advection under arid conditions (Prueger
et al., 1996) and, eventually, to introduce corrections to the measured fluxes (see the section on
advection).
3.2.1. The energy balance and Bowen ratio
method
The latent heat flux can be obtained from measurements of the energy budget of the surface
covered with an active growing crop. In fact, lE
represents the major used part of available energy
due to the radiation balance. All the energy involved in the evapotranspiration phenomenon
must satisfy the closure of the energy balance:
Rn − G= H+ lE
(4)
where we neglect advective processes and where
Rn (W m − 2), net radiation and G (W m − 2), soil
heat flux, are directly measurable by net-radiometers and soil heat flux plates, respectively (for an
extensive review of environmental instrumentation see Fritschen and Gay (1979)); and H is the
sensible heat flux density (W m − 2).
We define the Bowen ratio b =H/lE, so Eq.
(4) can be rearranged to give
lE=
Rn − G
1 +b
DT
De
Fuchs and Tanner, 1970; Sinclair et al., 1975;
Revheim and Jordan, 1976) and can be estimated
to be within 10% of the measured value. The
Bowen ratio method has been widely studied in a
variety of field conditions and it has been proven
a standard very accurate method in semi-arid
environments (e.g. Dugas et al., 1991; Frangi et
al., 1996; Zhao et al., 1996) and for tall crops also
(Cellier and Brunet, 1992; Rana and Katerji,
1996).
As previously stated, under arid climates the
crops can experience water stress. In this case DT
can be quite high but De is very low; so that it is
very important to have highly accurate measurements of air vapour pressure (Angus and Watts,
1984). The usual and simplest way is to use differential psychrometry; to meet the requirements of
accuracy, for continuous recording, one has to
keep the bulbs wet and clean (Fritschen and Gay,
1979). Furthermore, the used thermometers have
to be well calibrated, in order to detect temperature differences of 0.05–0.2°C; accuracy can be
sensibly improved by fluctuating the psycrometric
system (Webb, 1960; Gay, 1988; Fritschen and
Simpson, 1989).
Recently, improvements have been obtained by
using: (i) just one hygrometer that measures alternatively the humidity of air pumped from two
levels (Cellier and Olioso, 1993); (ii) a single
cooled mirror dew point hygrometer (some such
instruments are briefly described in Dugas et al.,
(1991)); and (iii) spatial averaging systems
(Bausch and Bernard, 1992). In any case, technical problems remain in the hygrometers for the
measurement of air humidity in arid regions, especially during water stress periods, when its value is
usually very low.
(5)
b can be measured by the ratio of the air temperature difference between two levels (DT) and the
vapour pressure difference (De), with e (kPa) air
vapour pressure, measured at the same two levels:
b= g
133
(6)
The Bowen ratio is an indirect method, its
accuracy has been analysed by many authors (e.g.
3.2.2. The aerodynamic method
If we assume that a flux density can be related
to the gradient of the concentration in the atmospheric surface layer (ASL), the latent heat flux by
the aerodynamic technique can be determined directly 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)
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
134
here r is density of air (kg m − 3) and the friction
velocity u* (m s − 1) is derived from the wind
profile measurement:
ku
(8)
z−d
ln
−Cm
z0
where k= 0.41 is the von Karman constant, d (m)
is the zero plane displacement height, z0 (m) is the
roughness length of the surface and Cm is the
stability correction function for momentum transport. q* is determined similarly from the humidity
profile measurement:
u*=
k(q−q0)
(9)
z−d
ln
−C6
z0
where q0 is the air humidity extrapolated at z =
d + z0 and C6 is the correction function for latent
heat transport.
The calculation of stability functions is made by
iterative processes (e.g. Pieri and Fuchs, 1990);
users who did not take stability corrections into
account have been criticised (Tanner, 1963; Perrier et al., 1974). The problem of taking into
account the atmospheric stability is particularly
important in arid environments. In fact, the coupling of dry soil and rapid warming or cooling up
of air at contact with the earth surface (vegetation
or bare soil) leads to extreme conditions of strong
stability and instability, with sudden passage from
a regime to the opposite one.
The major difficulty with this technique is the
correct measurement of the vapour pressure at
different heights above the crop. For this reason
lE can be derived indirectly by the energy balance
Eq. (4) if the sensible heat flux is determined by
the flux-gradient relation:
q* =
H = −rcpu*T*
(10)
where T* is deduced by the air temperature
profile:
k(T −T0)
(11)
z− d
ln
− Ch
z0
where T0 is the temperature extrapolated at z=
d + z0 and Ch is the correction function for the
heat transport.
T* =
Under this form, the main advantage of the
aerodynamic technique consists in avoiding humidity measurements. Nevertheless, the accuracy
depends on the number of measurement levels of
wind speed and temperature profiles. In fact, Eq.
(8) and Eq. (11) require at least three or four
levels (Webb, 1965), but accuracy is improved
when several levels are used (Legg et al., 1981;
Wieringa, 1993). When the stability correction
functions 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 been
proposed 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 measure
actual evapotranspiration of soybean grown in a
region of Southern Italy (Rana et al., 1990).
The aerodynamic method does not work with
enough accuracy on tall crops, neither in its complete form (Garratt, 1978; Thom et al., 1975) nor
in its simplified form (Rana and Katerji, 1996).
Correction for making this method applicable for
tall crops was attempted by Cellier and Brunet
(1992).
3.2.3. The eddy co6ariance
The transport of scalar (vapour, heat, CO2) and
vectorial amounts (i.e. momentum) in the low
atmosphere in contact with the canopies is mostly
governed by air turbulence. The first complete
scientific contributions to this topic were given by
Dyer (1961) and Hicks (1970); for extensive details of the theory see, for example, Stull (1988).
When certain assumptions are valid, theory predicts that fluxes from the surface can be measured
correlating the vertical wind fluctuations from the
mean (w%) with the fluctuations from the mean in
concentration of the transported admixture. So
that for latent heat, we can write the following
covariance of vertical wind speed (m s − 1) and
vapour density (q% in g m − 3):
lE= lw%q%
(12)
By making measurements of the instantaneous
fluctuations of vertical wind speed w% and of
humidity q% at sufficient frequency to obtain the
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
contribution from all the significant sizes of eddy
and summing their product over an hourly time
scale (from 15 min to 1 h), Eq. (12) gives directly
the actual crop evapotranspiration.
A representative fetch is required; fetch to
height ratios of 100 are usually considered adequate but longer fetches are desirable (Wieringa,
1993). The distribution of eddy size contributing
to vertical transport creates a range of frequencies
important to eddy correlation measurements (for
a brief review of the method requirements, see
Tanner et al. (1985)). The sensors must sufficiently respond to measure the frequencies at the
high end of the range, while covariance averaging
time must be long enough to include frequencies
at the low end (Kaimal et al., 1972; McBean,
1972).
To measure ET directly by this method, vertical
wind fluctuations have to be measured and acquired contemporary to the vapour density. The
first one can be measured by sonic anemometer,
the second by fast response hygrometer; both
have to be acquired at a typical frequency of
10 – 20 Hz. The Krypton-type fast hygrometers
perform well in the field, but they are expensive
and very delicate, so they need particular maintenance. In fact, the commercial fast hygrometers
can be severely damaged if moistened, therefore
they can only be installed during the day period,
which makes it difficult to use this instrument
continuously for a period longer than a few days.
Furthermore, errors in eddy covariance method
can be due not only to possible deviations from
the theoretical assumptions, but also to problems
of the sensors configuration and meteorological
characteristics (Foken and Wichura, 1996).
One important hypothesis to be verified is that
time series must be stationary at the scale of the
averaging period, which requires some kind of
detrending of the original turbulent signals, like
linear detrending or more complex high-pass
filtering (Kaimal and Finningan, 1994).
Other known problems are due to the geometrical configuration of the sensors. A distortion of
the flow can be caused by the sensor arrangement
of the anemometer itself and other sensors. The
spatial separation between the sonic anemometer
and the hygrometer can cause lack of covariance
135
between the wind speed and the humidity fluctuations. In fact, the typical distance between the
measuring path of the vertical wind fluctuation
and the hygrometer is 30–40 cm, this spacing acts
like a lower-pass filtering process on the measured
signals and must be corrected (Foken and
Wichura, 1996).
An important aspect to be considered is the
density correction (Webb et al., 1980), this correction is particularly important in semi-arid environments, in fact it is proportional to the sensible
heat flux and may be quite large for high Bowen
ratio (Villalobos, 1997).
To avoid some of the above problems linked to
the humidity fluctuations measurements, lE can
be obtained indirectly as residue of the energy
budget Eq. (4) if the sensible heat flux is expressed
by:
H= rcpw%T%
(13)
where cp (J kg − 1 C − 1) is the specific heat and
density of air. The wind speed and temperature
fluctuations are measured by means of sonic
anemometer and fast response thermometer,
respectively.
Despite problems linked to the correct management of the sensors and data remain, this method
has very good performances both at hourly and
daily scale, also in semi-arid environments. In Fig.
6, the comparison between ET measured by this
method and Bowen ratio method, at daily scale, is
shown for a tall crop (sweet sorghum) grown in
Southern Italy.
In conclusion, the use of eddy covariance for
latent or sensible heat flux is still a useful tool
only at research level, even if the recent development of robust sensors could permit in the future
its practical application in arid regions.
3.3. Plant physiology approaches
Plant physiology methods either measure water
loss from a whole plant or a group of plants.
These may include methods such as tracer technique and porometry but here, only the most
diffuse methods will be analysed: the sap flow
method and the chambers system.
136
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
stem from the heater element. The difference between the heat input and these losses is assumed
to be dissipated by convection with the sap flow
up the stem and may be directly related to water
flow (Kjelgaard et al., 1997). The mass flow rate F
(g t − 1) is expressed by the relationship:
F=
Fig. 6. Comparison between ET measured by eddy covariance
for sensible heat flux and ET measured by Bowen ratio
method, at daily scale, on sweet sorghum grown in Southern
Italy (Rana and Katerji, 1996).
3.3.1. Sap flow method
Sap flow is closely linked to plant transpiration
by means of simple accurate models; sap flow can
be measured by two basic methods: (i) heat pulse
and (ii) heat balance.
In heat pulse method, applied by Cohen et al.
(1988) in herbaceous plants, sap flow is estimated
by measuring heat velocity, stem area and xylem
conductive area. This method seems to be inaccurate at a low transpiration rate (Cohen et al.,
1993); moreover, it needs calibration for every
crop species.
Therefore, the most popular sap flow method is
based on the heat balance method. It is based on
the concepts proposed by Cermak et al. (1973),
Sakuratani (1981), Granier (1985) and Steinberg
et al., (1990). The plant transpiration can be
estimated by determining the sap mass flow; this
is done using gauges that are attached to or
inserted in the plant stem. For the heat balance
method, a heater element is placed around the
plant stem to provide energy to the system. Thermocouples are used to determine how much heat
is lost by conduction up, down and radially in the
Qh − Qv − Qr
cw·dT
(14)
where Qh is input heat, Qv is vertical conductive
heat, Qr is radial heat loss to environment, cw (J
g − 1 K − 1) is specific heat of water and dT is the
temperature difference between the upstream and
downstream thermocouples. With the commercial
instrumentation, the mass flow rate per plant can
be measured at hourly scale.
The micro-engineering problems of the heat
emitters and detectors discussed by Cohen et al.
(1981) were recently overcome by Kjelgaard et al.
(1997), by using constant heat input instead of
variable heat input and using surface-mounted
thermocouples instead of the inserted ones. These
gauges do not disturb the plant root medium but
there is still biometric difficulty in extrapolating
from one or more plants to the canopy. Furthermore, in spite of the fact that the heat balance
method is more dependent upon the sap flow rate
than upon stem anatomy (Zhang and Kirkham,
1995), at low flow rates (often the case in a
semi-arid and arid environment when the crops
are under water stress) important differences were
observed between the sap flow determined by the
gauges and plant water losses observed by a reference method (Kjelgaard et al., 1997). The best
results are obtained at a daily scale, mostly on
trees.
For the sap flow method it is necessary do a
scaling up of the transpiration measurement from
plant to field scale. This is possible only if the
canopy structure and the spatial variability of the
plants characteristics (density, height, LAI) are
precisely known.
Recently, Grime and Sinclair (1999) reported
sources of error for the constant power stem heat
balance method when commercial gauges are
used. Their analysis demonstrated that measurement errors in determining the diurnal pattern of
transpiration could be due to the heat storage in
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
the stem and the pattern of ambient temperature.
Moreover, the determining of the sheath conductance by the night-time sap flow measurement can
be affected by error due to the stem variation
during the season.
These errors are highly dependent on operating
conditions and can be minimised by following
appropriate recommendations.
Problems linked to the death of the fresh tissues
around the heated area, due to silicone application, can be minimised by reducing the period of
continuous measurement to 1 – 2 weeks (Wiltshire
et al., 1995).
The sap flow method approaches only transpiration measurements, neglecting soil evaporation.
Nevertheless, under the Mediterranean climate
evaporation from soil can be a very important
fraction (up to 20% of total evapotranspiration)
of the soil–plant–atmosphere water budget (Brutsaert, 1982; Klocke et al., 1985a,b).
3.3.2. Chambers system method
The chambers to rapidly measure ET were described for the first time by Reicosky and Peters
(1977). They consist of aluminium conduits covered with Mylar, polyetilene or other plastic or
glass films; the air within the chamber was mixed
continuously with strategically located fans. The
first version was portable (by means of a tractor,
for example) and ET rate was calculated by a
psychrometer before the chamber was lowered on
the plot and 1 min later, as latent heat storage.
The volume of the chamber can be easily adapted
to a herbaceous field crop and the accuracy was
: 10%, compared with weighing lysimeters (Reicosky et al., 1983).
This system was used by Reicosky (1985) to
measure, on a daily scale, ET on several different
treatments more easily than the weighing lysimeter, but it is not suitable for long term ET measurements. Furthermore, more serious errors may
be introduced if chamber results were extrapolated over time as well as spatially (Livingston
and Hutchinson, 1994).
Under a semi-arid climate, Dugas et al. (1991)
demonstrated that portable chambers, equipped
with an infrared analyser (BINOS, Inficon Leybold-Heraeus, NY) for measuring vapour density
137
differences in differential mode, are not representative of the field, particularly on its margins,
where ET measurements were affected by surrounding conditions. Furthermore, the last improved version of portable chambers can be very
expensive, due to the high costs for key components (data acquisition system and infra-red
analyser) and accurate chamber manufacturing
that may require some heavy engineering.
Recent developments of portable chamber systems can be found in Wagner and Reicosky
(1996); here the equipment also provides CO2
measurements, but its complexity and costs limit
its use for research to a small temporal scale.
The chambers are also suitable for research
studies on orchard crops (Katerji et al., 1994).
The most serious problems of almost all chambers
are related to the modification of the microclimate
during the measurement period. First, the solar
radiation balance, since the chambers were designed for simultaneous measurement of both
CO2 and water vapour exchanges (Denmead,
1984). These dual requirements are not often compatible because wall materials are usually selected
for high transmission in the short wavelengths,
neglecting the long-wave exchange (: 20% of the
incoming short-wave radiation). Second, the air
temperature: its rapid increase inside the chambers could alter the biological control of leaves
transpiration process. Finally, the wind speed:
inside the chamber it could be strongly reduced
with direct consequences on ET measurement
accuracy.
4. Actual crop evapotranspiration modelling
Actual ET can be estimated by means of more
or less complex models: the accuracy of ET estimation is proportional to the degree of empiricism in the used model or sub-models. Thus, we
can categorise the ET estimation into three groups
of methods:
1. Methods based on analytical modelling of
evapotranspiration;
2. Methods in which actual crop ET is deducted
from the evapotranspiration of a reference
surface;
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
138
3. Methods based on a soil water balance
modelling.
4.1. ET analytical models
One-dimensional equations based on aerodynamic theory and energy balance — for this
reason called combination models (Penman, 1948;
Monteith, 1965, 1973) — have proved very useful
in the actual crop ET estimation, because they
take into account both the canopy properties and
meteorological conditions (Szeicz and Long, 1969;
Black et al., 1970; Szeicz et al., 1973).
The most widely used form of the combination
equation, called Penman-Monteith equation, can
be 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-parametric and parametric variables:
“ weather non-parametric variables: A = Rn −G
(W m − 2) is available energy, D (kPa C − 1), is
the slope of the saturation vapour pressure
versus temperature function, VPD (kPa) is air
vapour pressure deficit and g (kPa C − 1) is the
psychrometric constant;
“ parametric variables: ra (s m − 1) is the aerodynamic resistance and rc (s m − 1) is the bulk
canopy resistance.
All the terms have to be accurately evaluated
(Allen, 1996). While the non-parametric data are
standard measurable climatic variables, the parametric data are not directly measurable and they
need to be modelled. Indeed, the first one (ra) is
the aerial boundary layer resistance and describes
the role of the interface between canopy and
atmosphere in the water vapour transfer; the second one (rc) is the resistance that the canopy
opposes to the diffusion of water vapour from
inner leaves toward the atmosphere and it is
influenced by biological, climatological and agronomical variables. This model is applied to the
whole plant community as if it were a single ‘big
leaf’ located at the height of virtual momentum
absorption (Thom, 1975).
The degree of empiricism of the Penman – Monteith equation (and consequently its success)
mainly depends on the accuracy of the estimation
of the canopy resistance (Beven, 1979).
Rana and Katerji (1998) demonstrated that,
under a semi-arid climate, the canopy resistance
plays the major role, so that its modelling is the
most critical point of the Penman–Monteith
model to estimate actual crop ET under the Mediterranean climate. In particular, their sensitivity
analysis on Penman–Monteith model showed
that: (i) in well-watered conditions, rc modelling is
sensible to Rn variations in the case of low crops
(i.e. reference grass) and it is sensible to vapour
pressure deficit variations, both in the case of
medium (Fig. 7) and tall crops (Fig. 8); (ii) in
water stress conditions, rc modelling is sensible to
the actual crop water status (Figs. 7 and 8).
4.1.1. Methods of determining canopy resistance
One of the most diffuse methods of estimating
rc is that proposed by Szeicz and Long (1969), in
which canopy resistance can be determined as a
function of daily mean stomatal resistance of the
single leaves (rs) and leaf area index of the leaves
effective in transpiration (LAIeff). These authors
assumed that only the surfacial layer of the
canopy participates effectively to the transpiration. Usually, such a canopy resistance is assumed
to be half the full crop LAI:
rc =
rs
LAIeff
(16)
This equation is suggested to be used for reference crop ET (Allen et al., 1989) and it is also
used, 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 the
soil water status (and, consequently, of the plant
water status) is very high and the microclimate to
which they are exposed is very different (Denmead, 1984), to obtain sufficiently accurate
canopy resistance values by means of this method,
it is necessary to realise a great number of measurements of stomatal resistance in a brief interval
time.
Furthermore, from the theoretical and practical
point of view, the problems of scaling-up the
canopy resistance from leaf to canopy is not
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
completely solved (Jarvis and McNaughton, 1986;
Baldocchi, 1989; Baldocchi et al., 1991; Raupach,
1995); particularly in semi-arid environments (Steduto et al., 1997).
An improvement of this estimating method has
been proposed by Monteith (1965) and tested and
applied by Katerji and Perrier (1985). In this
method, the canopy was divided into layers and
canopy resistance was estimated starting from
stomatal resistance measured layer by layer and
weighted with the LAI of each layer. The expression of the canopy conductance (gc =1/rc) is
given, in this case, by the relationship:
gc = %gci ·LAIi
(17)
i
where gci is the stomatal conductance measured
on the leaves belonging to the layer characterised
by LAIi. Usually i is equal to 2 or 3, following the
139
crop growth: an example is given in Table 2 for
an alfalfa crop divided into three layers. This
approach is difficult and hard to carry out, giving
rc values not always accurate. Nevertheless, the
estimation of field crop ET can be acceptable, at
least for well-watered crops (Katerji and Perrier,
1985).
The most complete model of rc should have the
following 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 leaf
water potential (Cf) or root-sources abscisic acid
(ABA) (Zhang et al. 1987; Zhang and Davies,
1989). As previously stated, the plant water status
varies 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 available
energy, ra is aerodynamic resistance, rc is canopy resistance and VPD is vapour pressure deficit (Rana and Katerji, 1998).
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
140
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 water
status, a great number of Cf or ABA measurements has to be carried out during the entire day.
Hence, this method is not suitable for practical
application in a field.
In order to avoid the problem of a large num-
ber of punctual measurements, a number of models as expressed by the general relationship Eq.
(18), have been developed for dry conditions. For
example, Hatfield (1985) modelled rc in the function of global radiation and available soil water
by means of an experimental function. Fuchs et
Table 2
Variability of stomatal resistance on the two sides of the leaf in an alfalfa canopya
I
Canopy layer
1
2
3
Top
Medium
Bottom
Canopy
a
Stomatal resistance and S.E. (s m−1)
Upper side
Lower side
1179 29
1999 70
1044 9365
1159 29
5599 196
1200 9 420
LAI and S.E.
Canopy conductance (mm s−1)
1.75 90.35
2.1 9 0.42
0.85 9 0.17
30.2
14.3
1.5
4.7
46.0
The resulting canopy resistance is 22 s m−1 (Saugier and Katerji, 1991).
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
141
al. (1987) stated that rc can be modelled by means
of photosynthetic active radiation (PAR) and soil
moisture deficit, but this model is only valid for
mild to medium stress. Again, regressive experimental functions were used by Jarvis (1976) to
model rc in the function of LAI, Rg, VPD, T and
soil water potential. Unfortunately, all these functions need to be locally calibrated per crop and,
often, they need also a time calibration, i.e. they
are not valid for the whole growth season (Stewart, 1988).
An original approach to take into account the
crop water status to estimate ET by means of
Penman–Monteith model was presented by Rana
et al. (1997b), in which rc is modelled as a function of ‘predawn leaf water potential’, Cb. This
parameter represents the crop water status and it
does not need to be measured instantaneously,
but just once a day. The application of such a
model in semi-arid environments gives quite good
results. Such rc model is valid for crops growing
under semi-arid climate (i.e. also for crops under
water stress) and needs to be calibrated only ‘per
crop’ so that it can be generalised (Rana et al.,
1997c). It is possible to use the transpirable soil
water as input of the model instead of Cb, but in
this case the model looses its generality and must
be locally calibrated (Rana et al., 1997a).
Moreover, the data necessary for the determination of reference evapotranspiration ET0 are
usually collected in standard agrometeorological
stations. These stations are usually installed to be
representative of the catchment, i.e. an area of
several squared kilometres in extension.
4.2. ET empirical models
and
By these methods, the water consumption of
crops is estimated as a fraction of the reference
evapotranspiration (ET0):
ET=Kc ·ET0
(19)
where Kc is the experimentally derived crop coefficient and ET0 is the maximum evapotranspiration; the latter can be evaluated (i) on a reference
crop or (ii) on free water in a pan. The accuracy
of 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 coefficient Kc.
4.2.1. ET0 reference crop determination
In this case, ET0 is the water consumed by a
standard crop. In order to make procedures and
results comparable world-wide, a well adapted
variety of clipped grass has been chosen. It must
be 8–16 cm high, actively growing and in well-watered conditions, subjected to the same weather as
the crop whose water consumption is to be estimated. ET0 can be again measured (e.g. by means
of a weighing lysimeter) or estimated. Therefore
the comments and observations made for actual
crop ET are still valid for ET0 determination. In
the following, we analysed the more used models
of ET0.
A semi-empirical approach to estimate ET0 was
proposed by Penman (1956) as:
DRn + gEA
D+ g
(20)
EA=f(u)(e −e*)
(21)
ET0 =
where
f(u)=1 +0.54 u2
(22)
with u2, wind speed measured 2 m above the soil
surface.
The empiricism of this formula is into the wind
function f(u). Actually, this function is just a
linear regression adjustment to take into account
the differences between estimated and observed
ET0 for grass grown in the UK. Therefore, it is a
pseudo exchange coefficient, which is supposed to
take into account the ET grass regulation. This
observation explains why it is necessary to adapt
the function f(u) to each site, in order to correctly
apply the Penman formula in the Mediterranean
regions. Furthermore, it is clear that the wind
function decreases going from North toward
South (Fig. 9) and these results point out the
dependence of canopy resistance on the vapour
142
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
pressure deficit, which increases going from North
to South Europe (Choisnel, 1988).
Today the most used and suggested method to
evaluate reference ET is based on the Penman –
Monteith model, therefore, having the same problems encountered in actual crop ET estimation
regarding rc modelling.
Rana et al. (1994) proposed an ET0 estimated
by means of the Penman – Monteith model, in
which canopy resistance is analytically modelled.
This model was tested in Mediterranean regions,
but it is valid in humid environments too. They
demonstrated that rc varies with the climate and it
is sensitive to any agronomic practice (irrigation
date, grass cutting, phytopathological situation);
in Fig. 10 hourly rc values are shown before and
after grass cutting and irrigation.
Recently, Todorovic (1997) proposed a variable
canopy resistance, both at hourly and daily scale,
modelled in the function of standard meteorological parameters. It was shown that ET0 calculated
by the Penman–Monteith model with such a resistance works well under different climates.
Several authors proposed an ET0 Penman–
Monteith formula using constant value of rc (Allen et al., 1989). Steduto et al. (1996) tested such
ET0 estimates with constant rc in several Mediterranean regions. Their results demonstrated that
this approach does not have good performances
in all the experimental sites.
Other simpler methods to estimate reference
crop ET are based on statistical–empirical formulas (an exhaustive review of these methods can be
found 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 is
f(u) = 0.37 u; Doorenbos and Pruitt is f(u)= 0.27(1+ 0.86 u); Seguin is f(u) =0.37 u 0.88; Losavio et al. is f(u) =0.12 u 0.67 (Losavio
et al., 1992).
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
143
4.2.2. The reference ET0 calculated by the pan
e6aporation
Pan evaporation data can be used to estimate
reference ET, using a simple proportional
relationship:
ET0 = Kp·Epan
Fig. 10. Canopy resistance during a day for a reference grass
grown in Southern Italy, (a) before and after grass cutting and
(b) before and after irrigation (Rana et al., 1994).
be used very easily from a practical point of view,
above all in rural lands. However, their empiricism may lead to very inaccurate estimations, as
clearly shown by Ibrahim (1996), in arid environments (Table 3).
(23)
where Kp is dependent on the type of pan involved, the pan environment in relation to nearby
surfaces and the climate. Doorenbos and Pruitt
(1977) provided detailed guidelines for using pan
data to estimate reference ET0. In the case of a
pan surrounded by short green grass, Kp ranges
between 0.4 and 0.85. In semi-arid environments
its mean value is : 0.7 (Jensen et al., 1990). The
value of Kp to be adopted is strongly dependent
on the upwind fetch and on the local advection.
An attempt to model the pan coefficient, Kp has
been made by Perrier and Hallaire (1979a,b), on
the basis of experimental pan data measured in a
humid–tropical area (Baldy, 1978). They expressed Kp in the function of climatic variables
and a coefficient b, the ratio between the exchange coefficient of the pan and the wind function 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 and
wind speed. This latter coefficient is dependent on
Table 3
Seasonal reference evapotranspiration (ET0) in 3 years and average percent deviation from the mean value in the north central area
of the Nile delta region (Egypt) (Ibrahim, 1996).
Method
Seasonal ET0
Average seasonal ET0 (cm)
Percent deviation from mean value
−4.37
+1.66
−5.13
+27.03
−22.59
+27.20
−17.28
−6.59
1979
1980
1981
(a) Blaney–Criddle
(b) Radiation
(c) Modified Penman
(d) Rijtema
(e) Thornthwaite
(f) Jensen and Haise
(g) Evaporation pan
(h) Turc
63.2
66.78
62.82
81.64
52.16
86.75
56.75
63.47
61.81
63.20
60.60
81.35
49.73
80.50
54.14
58.93
60.31
66.82
60.24
82.92
48.00
79.41
49.24
58.45
61.71
65.60
61.22
81.97
49.96
82.08
53.38
60.28
Average
66.62
63.78
63.17
64.53
144
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4.2.3. The crop coefficient Kc
The crop coefficient represents an integration of
the effects that distinguish the crop from the
reference ET; many such Kc are reported in the
literature (e.g. Doorenbos and Pruitt, 1977; Allen
et al., 1998) usually derived from soil water balance experiments.
Crop coefficient can be improved for estimating
the effects of evaporation from wet soil on Kc on
a daily basis (Wright, 1982). In this case, the crop
coefficient can be expressed by the equation:
Kc = Ks·Kcb + Ke
Fig. 11. Theoretical curves of pan coefficient Kp in function of
relative 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).
the site climate and can be considered constant
and = 0.8 in arid environment. Fig. 11 shows the
coefficient Kp in the function of RH for three
values of b (b = 2, humid seasons; b =2.5, intermediate 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 a
closed soil system (pots) and in open soil system (a deep field
with favourable environmental conditions) (Tardieu and
Katerji, 1991).
(25)
where Ks is a stress reduction coefficient (0} 1).
Kcb is the basal crop coefficient (0} 1.4) and
represents the ratio of ET and ET0 under conditions when the soil surface is dry, but where the
soil water content of the root zone is adequate to
sustain full plant transpiration; Ke is a soil water
evaporation coefficient (0} 1.4). It can be experimentally calculated in the function of soil water
storage, DS and depends on the amount of soil
available to the plants’ roots. In fact, in open soil
systems, when the conditions are favourable for
root system development, Ks is almost constant,
also when soil humidity decreases considerably,
because of an appreciable contribution of the
non-rooted soil layer to the water balance. In
closed soil systems (pots, for example) Ks is variable following the soil humidity and it begins to
decrease appreciably for values of soil water reserve :60–70% of available soil water to transpiration. This Ks behaviour is reported in Fig. 12, in
which the ratio of actual to potential ET of a
well-irrigated corn crop is reported in the function
of the available soil water, for the above mentioned two conditions (open and closed soils).
In order to avoid the difficulties linked to the
available soil water conditions, it is possible to
evaluate Ks by means of the predawn leaf water
potential, Cb. Itier et al. (1992) demonstrated that
this relationship (and Ks as a consequence) has
general validity, since it does not depend on the
soil type and site.
The methods to estimate crop coefficients and
reference ET have been recently modified by Allen
et al. (1994a), Allen et al. (1994b) and Allen et al.
(1996).
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
The crop coefficient plays an essential role in
practice (Pereira et al., 1999) and it has been
widely used to estimate actual ET for irrigation
scheduling purposes. However, it can be subject
to serious criticism regarding the meaning and the
use of crop coefficient. Besides obvious variations
among different crops, empirical crop coefficients
were shown to be affected by crop development
and weather conditions (De Bruin, 1987). Furthermore, Stanghellini et al. (1990) demonstrated
that no coefficients should be expected to vary
according to the conditions of both climate and
crop stage under which they are derived. Moreover, these researchers stated that the crop requirements based on a same value of the crop
coefficient do not have the same accuracy for
different months, different seasons, and, above all
at different sites. This inaccuracy of the Kc approach can be found in the discrepancies between
local calculated Kc and crop coefficients reported
in literature (e.g. Rana et al., 1990; Vasic et al.,
1996).
Fig. 13. Comparison between ET estimated by a water reservoir model as proposed by Lhomme and Katerji (1991) and
ET estimated by water balance with DS measured by TDR on
a daily scale (Ben Nouna, 1995).
145
4.2.4. Soil water balance modelling
An exhaustive survey of the most diffuse models for soil water balance can be found in de Jong
and Bootsma (1995) and Leenhardt et al. (1995).
Two classes of models are generally retained for
the simulation of soil water balance: (i) mechanistic models and (ii) analogue (or water reservoirs)
models.
In the mechanistic approach, the water flux in
the soil is controlled by the existence of soil water
potential gradients, by means of Darcy’s law and
continuity principle. The equations are usually
solved by different methods, all involving the
splitting of the soil in more or less small layers (de
Jong, 1981; Feddes et al., 1988). The difficulties in
the application of these models are linked to (i)
the accuracy of the used pedo-transfer functions
for estimating the water transfer and (ii) the procedures used for estimating the boundary conditions of the soil–plant–atmosphere system.
In the analogue approach, the soil is treated as
a collection of water reservoirs, filled by rainfall
or irrigation and emptied by evapotranspiration
and drainage. They can be based on the two
following 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 transpirable
soil water (RTSW) and total TSW (e.g.
Fréteaud et al., 1987). The stress coefficient Ks
is supposed to be approximately = 1 in the
RTSW range, then it decreases as the water
reserve is in the TSW range.
In a previous paragraph we have analysed the
difficulties in determining the soil water storage
and the evolution of Ks in function of DS, particularly under a Mediterranean climate. Effectively,
Ben Nouna (1995) showed that, in semi-arid regions with closed system soils, the water reservoir
approach can be very useful in estimating actual
ET only if very accurate measurements of DS can
be realised (Fig. 13).
5. ET evaluation in advection regime
All the previously presented methods to measure and/or estimate actual crop ET are based on
146
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
a fundamental critical hypothesis that the considered systems were conservative, i.e. the profiles of
air temperature, water vapour concentration and
wind speed are constant along the horizontal axe
X (e.g. Itier and Perrier, 1976; Stull, 1988).
In the Mediterranean regions, the scarcity of
available water resources leads to irrigated lands
in a selective way, with the creation of areas
characterised by strong discontinuity of water vapour concentration at surface level, also for similar crops. The air thermodynamic characteristics
are strongly influenced by the surface conditions,
so that the air passing from a dry field toward an
irrigated field is cooled as well as its humidity
increases. Hence, near the boundary of the irrigated field, ET rapidly increases, then slowly decreases along the wind direction following the
thermodynamic characteristics of the air coupled
with the vegetation surface.
In general, the latent heat flux density measured
or estimated in one point of the plot is, actually,
the sum of two terms: (i) a term translating the
equilibrium between the evaporative demand of
the air determined by the Penman model and crop
water conditions; (ii) an additional flux, more or
less important, depending on the lateral transfer
of energy by advection. From an energetic point
of view, latent best flux depends on the modifications of the vapour and thermal characteristics of
the 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) the
roughness length of the crop, z0 (m); (iii) the wind
speed through the friction velocity u* (m s − 1);
and (iv) the temperature difference between the
dry and irrigated fields, DT (°C).
From the operational point of view such a
situation in which an advection regime is verified
leads to two main consequences:
1. In order to have a correct representativeness
of ET, it is necessary to correct a posteriori the
evapotranspiration measured by means of
weighing lysimeters, soil water balance, sap
flow method and chambers system method
when the fetch is not large enough to avoid
advection effects. A possible simple correction
was proposed by Itier et al. (1978) as:
6
Fa = 360·u*·DT z
0/F
(26)
This correction can be of 1–2 mm per day for
temperature differences between dry and irrigated field of 5–10°C (Itier et al., 1978).
2. The micrometeorological methods must be applied in order to make the measurements inside the equilibrium fully adapted boundary
layer. The fetch value assuring an acceptable
adapted layer for micrometeorological is reported by Wieringa, (1993) as:
F$ 2z0
10z
10z
ln
−1
z0
z0
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 strong
regional advective conditions (Blad and Rosenberg, 1974). This implies an extensive fetch in the
upwind direction for the air flowing over the
surface of at least 100 times the maximum height
of measurements, but Heilman et al. (1989)
demonstrated that the Bowen ratio method can be
successfully applied up to fetch-to-height ratios as
low as 20:1.
6. Conclusions
In Mediterranean areas submitted to arid and
semi-arid climates, ET ranges over a large interval
depending on water regimes (irrigated or non-irrigated fields). Among the other weather variables,
air temperature and humidity experience a large
gap between night and day and between winter
and summer; the wind is very variable moving
from the coast to internal areas. So that, in general, we can state that all the weather variables
range in a very large interval of values. Moreover,
the variation in one parameter immediately influences all the other variables that are mutually
linked. These facts make difficult to correctly
evaluate the crop actual evapotranspiration.
In this review, we have presented the most
important methods of measuring and modelling
actual evapotranspiration in arid and semi-arid
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
147
Table 4
Classification by space and time of ET methods to measure or model actual evapotranspiration, adapted by Stewart (1984)
Minute
Hour
Day
Month
Catchment
Uniform area
Growth season
Year
-----------Crop coefficient method----------—Micrometeorological method--
------------Crop coefficient method------------------Soil water balance--------------------Soil water balance with TDR-----------------Penman–Monteith model---------------
Group of plants
-------Weighting lysimeter; chambers system---------------Sap flow--------
Plant
--------Sap flow-------
environments. Some methods are more suitable
than others in terms of convenience, accuracy or
cost for the measurement of ET at a particular
spatial and over a particular time scale. In Table
4 the classification of the presented ET methods by
space and time scale is shown.
We tried to give, for each method, the advantages
and disadvantages for their use in the Mediterranean regions; the summary of this analysis for the
measurement methods is reported in Table 5.
In summary, two major observations are
possible:
Table 5
Summary of the advantages and disadvantages of the ET measurement methods
Measurement
method
Advantages
Disadvantages
Soil water balance
Soil moisture simple to be evaluated with
gravimetric method
Not expensive if the gravimetric method is used
Large spatial variability
Difficult to be applied when the drainage and
capillary rising are important
Difficult to measure soil moisture in cracked soils
Fixed
Difficult maintenance
It could be not representative of the plot area
Expensive
Difficult to have correct measurement of the wet
temperature if psychrometers are used
The sensors need to be inverted to reduce bias
Difficult maintenance
It needs to be corrected for the stability
Not suitable for tall crops
Weighing lysimeter Direct method
Energy balance/
Bowen ratio
Aerodynamic
Eddy covariance
Simple sensors to be installed
Suitable also for tall crops
It can be also used when the fetch is 20:1
Not very expensive if psychrometers are used
Simple sensors to be installed
It does not need humidity measurements
Not very expensive
Direct method with fast hygrometer
Sap flow
Suitable for small plots
It takes into account the variability among plants
Chambers method
Suitable for small plots
It can be used also for detecting emissions of
different gases
Delicate sensors
Difficult software for data acquisition
Hygrometer very delicate expensive
Difficult scaling-up
The gauges need to be deplaced every 1–2 weeks
The soil evaporation is neglected
It modifies the microclimate
Difficult scaling-up
148
G. Rana, N. Katerji / Europ. J. Agronomy 13 (2000) 125–153
1. The ET measurement methods are based on
concepts which can be critical under semi-arid
and arid environments for several reasons: (i)
representativeness (the weighing lysimeter, for
example); (ii) instrumentation (air humidity
sensors for example); (iii) microclimate (advection regime); and (iv) hypothesis of applicability (the simplified aerodynamic method for
example). Thus, in order to establish the degree of accuracy of the obtained ET measurement and the validity of a method, it is
necessary to consider all these parameters.
2. The estimation methods based on an analytical approach could be very accurate but, usually, they are not practical enough. The more
operational estimation methods (crop coefficient approach, ET0 calculation, water balance
modelling) can be generally affected by very
large errors.
Nowadays, a new research trend is being developed in order to integrate these two approaches
of actual evapotranspiration estimation. These
new models tend to introduce into the analytical
approach an acceptable degree of empiricism (Allen et al., 1989; Rana et al., 1994; Pereira et al.,
1999). We think that such methods should be
accepted and encouraged in the future, since these
approaches can greatly improve the water management at farm level, one of the greatest problems of the Mediterranean countries.
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