Directory UMM :Data Elmu:jurnal:A:Agricultural Water Management:Vol45.Issue3.Aug2000:

Agricultural Water Management 45 (2000) 297±316

Crop water requirements model tested for
crops grown in Greece
M. Anadranistakisa, A. Liakatasb,*, P. Kerkidesb, S. Rizosb,
J. Gavanosisb, A. Poulovassilisb
a

Hellenic National Meteorological Service, 14 El. Venizelou , Helliniko 166 03, Athens, Greece
b
Agricultural University of Athens, 75 Iera odos, GR-118 55, Athens, Greece
Accepted 26 October 1999

Abstract
A model for estimating crop water requirements throughout crop development is presented. The
model assumes horizontal uniformity and treats the two-component system of canopy and soil
along the lines of Shuttleworth and Wallace (1985). Incorporated in the model is a 3-layer soil water
budget allowing evaluation of the soil surface and canopy resistances and time evolution of the soil
moisture in the root zone. Canopy interception is also taken into account.
Model parameterization considered mostly the crop canopy resistance, assuming neutral
atmospheric stability conditions, whereas parameterization of the aerodynamic resistances allows

for smooth transition from bare soil to a fully developed crop canopy.
The model has been validated with meteorological (temperature, relative humidity, wind speed,
net radiation ¯ux density, solar radiation ¯ux density and soil heat ¯ux density, precipitation or
irrigation) and crop (height, leaf area index and root depth) data collected from experimental ®elds
of the Agricultural University of Athens (388230 N, 238060 E). Results were veri®ed for three crops
(cotton, wheat and maize) against soil moisture pro®le changes with very satisfactory results.
Agreement between observed and estimated evapotranspiration is within 8%.
The model is sensitive to crop type and time evolution of the root zone penetration into soil while
precise determination of the minimum stomata resistance is not exclusively important.
# 2000 Elsevier Science B.V. All rights reserved.
Keywords: Aerodynamic resistance; Canopy resistance; Evapotranspiration; Water de®cit

*
Corresponding author. Tel.: ‡30-1-529-4218; fax: ‡30-1-529-4081.
E-mail addresses: anad@hnms.gr (M. Anadranistakis), liakatas@aua.gr (A. Liakatas), 1hyd2kep@aua.gr
(P. Kerkides)

0378-3774/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 3 7 7 4 ( 9 9 ) 0 0 1 0 6 - 7

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M. Anadranistakis et al. / Agricultural Water Management 45 (2000) 297±316

1. Introduction
For proper irrigation scheduling, the atmospheric demand for water vapor, the soil
characteristics and the plant specific features, i.e. the soil±plant±atmosphere continuum
as a dynamic system, should be considered. In semi-arid regions, such as Greece, rainfall
is unevenly distributed over the year. From historical records of precipitation it may be
shown that more than 80% of the mean annual precipitation falls during the months
October±February. On the other hand during the dry seasons of spring and summer the
tourist (inflow) mobility is at its peak, exercising a substantial pressure on good quality
water reserves. Irrigation is required mostly in spring and summer, thus, making water
allocation and water use efficiency a serious problem. It is, therefore, important to
develop a model to conveniently estimate actual crop water needs, which however
incorporates all influencing factors.
Although the Penman±Monteith (PM) formula is valid only for dense vegetation, one
layer models based on this formula (e.g. MORECS, described by Thompson et al., 1981)
are also applied to sparse vegetation or during the initial stages of a crop. Grant (1975)
attempted to overcome this problem by considering crop resistance (rc) as the sum of the

canopy (rsc ) and soil (rss ) resistances combined in parallel
rcÿ1 ˆ …1 ÿ B†…rsc †ÿ1 ‡ B…rss †ÿ1

(1)

The term B is a leaf area index (LAI) function, introduced to facilitate the distribution of
the available energy between the vegetation and the underlying soil. To determine the
minimum value of rc via the PM equation, detailed evapotranspiration measurements are
required on a completely wet soil.
Multi-layer models assume that each distinct layer absorbs net radiation and transfers
sensible and latent heat (Waggoner and Reifsnyder, 1968; Furniral et al., 1975; Perrier,
1976; Chen, 1984, among others). These models describe satisfactorily energy fluxes
between the canopy layers, but they give no explicit estimation of overall fluxes above the
top of the canopy, unlike the one-layer models (Lhomme, 1988). An exception to this, is
the two-layer model of Shuttleworth and Wallace (1985) (SW) developed to describe the
energy partition of sparse crops.
It is the purpose of the present work to establish a model which could lead to a better
understanding of the mechanisms of water transfer through the soil±water±crop±
atmosphere system and which could lead to an improved estimate of the actual crop water
needs. As a result, irrigation water management would be exercised in a rational and

sustainable way, affecting positively crop production, increasing therefore, the water use
efficiency.

2. Model description
The SW model allows estimation of latent (lE) and sensible heat (H) fluxes separately
for vegetation (lEc , Hc) and soil (lEs , Hs). It assumes that aerodynamic mixing is
sufficient to justify the assumption of a mean flow at an average wind speed u (s mÿ1)
(Thom, 1971), that can be described by meteorological parameters like air temperature T0

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299

Fig. 1. Schematic one-dimensional description of energy distribution and the relevant resistances for relatively
sparse vegetation (according to Shuttleworth and Wallace, 1985).

(8C) and vapor pressure e0 (h Pa), while the available energy is distributed between the
soil surface and the vegetation (see Fig. 1). The aerodynamic resistance involved in
energy transfer between the vegetation elements and the mean flow is rac (s mÿ1) while
vertical transfer is controlled by two extra resistances: raa between mean flow and a

reference level and ras between soil and the mean flow level. The total latent heat flux
above the crop is described by
lE ˆ Cc PMc ‡ Cs PMs

(2)

where PMC and PMS are terms similar to those of the PM equation and they have the
form
PMc ˆ

DA ‡ …rcp D ÿ Drac As †=…raa ‡ rac †
D ‡ g…1 ‡ rsc =…raa ‡ rac ††

(3)

PMs ˆ

DA ‡ …rcp D ÿ Dras …A ÿ As ††=…raa ‡ ras †
D ‡ g…1 ‡ rss =…raa ‡ ras ††

(4)

A ˆ RN ÿ G being the ¯ux density of available energy (W mÿ2), RN the ¯ux density of
net radiation (W mÿ2), G the soil heat ¯ux density (W mÿ2), As ˆ RsN ÿ G the ¯ux
density of available energy at the soil surface (W mÿ2), RsN the ¯ux density of net
radiation at the soil surface (W mÿ2), rsc the canopy resistance (s mÿ1), rss the soil
resistance (s mÿ1), D the slope of the saturation vapor pressure curve at the mean wet bulb
temperature of the air (hPa per 8C), r the air density (kg mÿ2), cp the speci®c heat of air at
constant pressure (1010 J kgÿ1 per 8C), D the water vapor pressure de®cit at the reference
height (hPa) and g the psychrometric constant (hPa per 8C).
The coefficients Cc and Cs are functions of D, g, rac , ras , raa , rss , rsc .
The parameters remaining to be determined for the model to run are: the available
energy flux density (A), the available energy flux density at the soil (As), as well as the
aerodynamic, canopy and soil resistances. These should be coupled with parameters
describing the soil water budget. A provision for rainfall interception should also be

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M. Anadranistakis et al. / Agricultural Water Management 45 (2000) 297±316

included. This appears to be necessary for a complete mass and energy balance
description of the system taking into consideration the way irrigation water was applied.
2.1. Available energy ¯ux density
If measurements of RN and G are available, A can be determined as A ˆ RN ÿ G. Not
so straight forward is the determination of As, since no RN measurements just above soil
surface are usually available in the presence of crops. In this case one has to resort to the
use of some empirical relationships, which gives the solar radiation flux density
transmitted through a canopy. Such a relationship is proposed by Impens and Lemeur
(1969)
h
i
(5)
RsN ˆ RN exp ÿ0:622 LAI ‡ 0:055…LAI†2

Assuming that the temperature of the crop canopy elements is uniform, the exchange of
the long-wave radiation ¯ux density among them can be ignored (Denmead, 1976).
2.2. Water balance

2.2.1. Soil water
Soil water availability is fundamental in models estimating actual evapotranspiration.

In this model, it is assumed that the soil profile as a whole is characterized by identical
hydraulic properties and its water content is varying from a mean water content at field
capacity ys to a mean water content at the wilting point yw . The water table is assumed to
be at such a depth below the root zone that no significant water transport takes place from
the former to the latter.
The maximum depth (z) from which roots can extract water is subdivided into three
layers (Fig. 2). Soil evaporation is controlled via the soil resistance by the water content
of an upper soil surface layer of a thickness zg ˆ 5 cm and volumetric water content yg .
Transpiration rate is controlled via the canopy resistance by the water content of the
second soil layer X, with volumetric water content yx , which extends from the bottom of
soil surface layer to the depth where crop roots proliferate and extract soil water. The
depth of this layer (zx) is variable and increases following development of the root

Fig. 2. Schematic presentation of the root zone soil layers considered.

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301

system. The third soil layer Y with volumetric water content yy and thickness zy, is below

the X layer and is acting as a water reservoir that supplies the X layer as the root system
grows deeper. Since the total depth (z) is fixed, zx ‡ zy ˆ z ÿ zg. For our experiments,
z ˆ 1.2 m was the maximum depth from where water is considered to be extracted by the
plants. It is a common practice to consider zx as constant (25 cm) in the stage of seedling
establishment, increasing linearly to a maximum depth, achieved at the time of maximum
leaf area index.
It is assumed that runoff is small enough to be neglected, therefore precipitation or
rainfall water entering the soil enriches surface layer first and if yg becomes equal to ys ,
any extra water is moving to the X layer. If yx becomes equal to ys , then the extra water is
moving to the Y layer. Finally if all layers reach field capacity, the extra water is lost
through deep drainage.
The following equation describes the water balance of the soil surface layer in each
time step:
DVg ˆ P ÿ I ÿ D1 ÿ 0:1Ec ÿ Es

(6)

where, DVg (mm) is the change of water content, P (mm) is the precipitation or irrigation,
I (mm) is the amount of precipitation intercepted or condensation formed on by the
canopy, D1 (mm) is the amount of water that is moving to the soil layer X, Es (mm) is the

soil evaporation and 0.1 Ec (mm) is the fraction of transpiration originated from this layer
(Noihlan and Planton, 1989).
The water balance of the layer X is described by the equation:
DVx ˆ D1 ‡ yy Dz ÿ 0:9Ec ÿ D2

(7)

where, DVx (mm) is the change of water content, 0.9 Ec is the fraction of transpiration
originated from this layer, D2 (mm) is the amount of water that is moving to the soil layer
Y and the term yy Dz expresses the water transfer from the Y layer into the X layer due to
the root system development (Dz).
The water content of the soil layer Y increases if D2 > 0.
2.3. Condensation and intercepted water
When the model estimate of Ec or Es is negative, rss or rsc is set to zero and the
calculation is performed again in order to provide an estimate of condensation at the soil
or the crop surface. Soil condensation is considered to directly enrich soil moisture, while
the interception treatment is simplified by assuming that the effective rainfall (P0 ) is the
sum of the crop condensation and the rainfall or irrigation.
A portion k of P0 is intercepted by the crop. Thus, the relations used to calculate
intercepted water (I, mm) are (Thompson et al., 1981)

I ˆ kP0

…I  Imax †

k ˆ 1 ÿ …0:5†LAI

(8)
(9)

Substantial falls of rain will completely wet the canopy and so I is constrained not to
exceed the value Imax ˆ 0.2 LAI which produces full wetting.

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The retained water forms a thin film which covers a portion of the canopy (d) and
evaporates directly, while the remainder (1 ÿ d) of the canopy continues to transpire
normally. According to Deardorff (1978) d ˆ (I/Imax)2/3.
Calculation of the evaporation rate (from the crop canopy) is performed using Eq. (3)
with rsc ˆ 0. Thus, total water loss from the crop surface is the sum: (evaporation rate)
x d ‡ (transpiration rate) x (1 ÿ d).
When the evaporative demand of the atmosphere is insufficient for all intercepted
water to be evaporated, the amount of water remaining at the end of the day is assumed to
fall on to the soil.
2.4. Aerodynamic resistance
Crop and soil are considered as a unique aerodynamic system, the characteristics of
which are expressed by the values of zero plane displacement (d ) and roughness length
(z0), given by the expressions (Ben Mehrez et al., 1992)
d ˆ 0:63sa h
z0 ˆ …1 ÿ sa †zog ‡

(10)
sa …h ÿ d†
3

(11)

where h is the crop height, zog is the roughness length of bare soil, usually taking the
value of 0.01 m (Van Bavel and Hillel, 1976), and sa is a momentum partition coef®cient
assumed to depend on LAI and, according to Shaw and Pereira (1981), given by the
expression
!


0:5
…LAI†2
(12)
exp ÿ
sa ˆ 1 ÿ
8
0:5 ‡ LAI
It is obvious that in the case of a complete canopy (LAI > 4), sa  1 and this leads
to the well-known expressions d ˆ 0.63 h and z0 ˆ (h ÿ d)/3 (Ben Mehrez et al.,
1992).
According to Taconet et al. (1986), momentum absorption may take place partly by the
canopy and partly by the soil, depending on the value of the coefficient sa, through the
relationships
t ˆ t c ‡ tg

(13)

tc ˆ sa t

(14)

tg ˆ …1 ÿ sa †t

(15)

t being the momentum ¯ux density, subscripts c and g denoting canopy and soil,
respectively.
Assuming that the aerodynamic resistances to sensible and latent heat transfer are
equal to the resistance for momentum transfer, rac , ras and raa can be expressed as fractions
of the overall aerodynamic resistance for momentum transfer in the soil-vegetation
system (ra) (Anadranistakis et al., 1999)

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303

rac ˆ

ru ÿ 0
u
u
ra
ˆ
ˆ
2
tc
sa u sa u…z†

(16)

raa ˆ

ru…z† ÿ ru u…z† ÿ u u…z† ÿ u
ˆ
ˆ
ra
t
u2
u…z†

(17)

ras ˆ

ru ÿ 0
u
u
ra
ˆ
ˆ
tg
…1 ÿ sa †u2 …1 ÿ sa †u…z†

(18)

u* being the friction velocity (u2 ˆ t/r) and u(z) the wind speed at reference level. ra is
affected by the atmospheric stability conditions and may be expressed as to include the
extra resistance that stems from the fact that the level of sensible and latent heat exchange
(z00 ) is lower than that of momentum exchange (z0) (Thom and Oliver, 1977):



1
zÿd
zÿd
ln
ra ˆ 2
ÿ CM ln 0 ÿ CH
(19)
k u…z†
z0
z0
where z00 ˆ z0/7 (Garratt, 1978) and CM ˆ CH ˆ 0 for neutral stability conditions.
Thom (1972), Legg and Long (1975) and Webb (1975) experimenting on a closed
artificial crop, concluded that u could be considered equal to 1/3 of the wind speed at the
top of the canopy. Extending the above results to sparse crops, Deardorff (1978) proposed
the relationship u ˆ 0.83 u(z) sf ‡ (1 ÿ sf) u(z), where u(z) (m sÿ1) is the wind speed at
reference height and sf is an extinction coefficient ranging from 0 (for bare soil) to 1 (for
a closed canopy). Similarly, sf may be replaced by the momentum distribution coefficient
sa, which covers the same range of values and depends on LAI, satisfying the gradual
transition from bare soil to a fully developed canopy. Therefore,
u ˆ 0:83u…z†sa ‡ …1 ÿ sa †u…z†

(20)

Aerodynamic resistances parameterization allows no discontinuities during the transition
from bare soil to dense vegetation. By considering that
(a) for bare soil sa ˆ 0 and thus u ˆ u…z†. From Eqs. (16)±(18) it results that raa ˆ 0 and
rac become infinite thus stopping transpiration, whereas ra ˆ ras (the mean flow being at
the same level as the reference height)
(b) for dense vegetation sa ˆ 1 and u ˆ 0.83 u(z). Correspondingly, ras becomes infinite
and soil evaporation ceases, whereas raa ‡ rac ˆ ra .
(c) for incomplete canopies, ra comes from the parallel connection of ras and rac , serially
connected with raa …ra ˆ ‰…rac †ÿ1 ‡ …ras †ÿ1 Šÿ1 ‡ raa †.
2.5. Canopy resistance
The canopy resistance (rsc ) depends upon atmospheric factors and upon available soil
water. Assuming that rs is the stomatal resistance (rsmin being its minimum value), rsc is
given by
rsc ˆ

rsmin f1 …Rs †
f2 …yx †LAI2

(21)

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M. Anadranistakis et al. / Agricultural Water Management 45 (2000) 297±316

The factor f1(Rs) accounts for the in¯uence of solar radiation ¯ux density (Rs) on rsc .
According to Dickinson (1984) and Dickinson et al. (1986), f1(Rs) ˆ (1 ‡ f0 )/(f0 ‡ (rsmin/
r smax)) and f 0 ˆ (0.55 Rs/RL )(2/LAI), where the maximum stomatal resistance
rsmax ˆ 3000 s mÿ1 (Norman, 1979) and RL ˆ 100 W mÿ2 is a threshold radiation
value above which the stomata open. The term 2/LAI expresses the shading between leaves, while the factor 0.55 represents the PAR portion of solar radiation ¯ux
density.
The function f2(yx ) takes into account the effect of water stress on the canopy
resistance and plays a key role in the determination of rsc , especially in xerothermic
climatic conditions. Decrease of the X layer soil moisture (yx) causes closing of the
stomata and, therefore, rsc increases (Gollan et al., 1986). It is usually assumed that the
reaction of stomata begins as soon as the available soil water falls below its maximum
available value (ys ÿ yw)zx. For example Thompson et al. (1981) and Noihlan and
Planton (1989) assume that stomatal closure begins when soil water falls below a
relatively high critical fraction of its maximum value (0.6 or 0.75, respectively) under
low evaporative demand. Under high evaporative demand, it is possible that the soil
hydraulic properties and the hydraulic head gradients may acquire values preventing
sufficient water supply of roots and, therefore, stomata closing may begin at even
higher fractions of (ys ÿ yw)zx (Anadranistakis et al., 1997b). Contrary to this, even a
low soil water content of the root zone may sufficiently supply the roots with water,
without resulting in stomatal closure, when evaporative demand is low. Doorenbos
et al., (1986) suggest critical fractions ranging for different crops between 0.125 and
0.7, for an atmospheric demand varying from 2 to 10 mm dayÿ1. Poulovassilis et al.,
(1994, 1995) found for wheat that, under high evaporative demand (larger than
6.5 mm dayÿ1) the critical fraction could be as high as 0.95. Their observations are in
close agreement with the results of Denmead and Shaw (1962). Denmead and Shaw
(DS), having conducted experiments with maize grown in containers, determined the
critical values of the soil moisture (yc), in relation to the atmospheric demand (Emax),
below which actual evapotranspiration becomes lower than Emax. The soil used was
yolo silty loam with ys ˆ 0.36 cm3 cmÿ3 and yw ˆ 0.22 cm3 cmÿ2. Transforming the
critical soil moisture values (yc) obtained, to values of the coefficient c (c ˆ (yc ÿ yw)/
(ys ÿ yw)) the experimental results of DS may be expressed by a second degree
polynomial
c ˆ 0:01‰9:5 ÿ 1:4Emax ‡ 2:2…Emax †2 Š Emax  6:5 mm dayÿ1
c ˆ 0:95
Emax > 6:5 mm dayÿ1

(22)

In the absence of other similar results, Eq. (22) is the best option available for
determining c.
From Eq. (21), f2(wx) could, thus, be modified according to Noihlan and Planton
(1989) as:
yx > cys
f2 …yx † ˆ 1
…yx ÿ yw †
yw < yx  cys
f2 …yx † ˆ
…cys ÿ yw †
f2 …yx † ˆ 0
yx  y w

(23)

M. Anadranistakis et al. / Agricultural Water Management 45 (2000) 297±316

305

2.6. Soil resistance
This is assumed to depend strongly on yg according to the relationship
s
f …yg †
rss ˆ rsmin

(24)

s
rsmin

where
is the minimum soil surface resistance, which corresponds to soil moisture at
®eld capacity and its value is assumed equal to 100 s mÿ1 (Szeicz et al., 1969; Thompson
et al., 1981). For a dry soil rss may reach the value of 10 000 s mÿ1 (Fuchs and Tanner,
1967; Wallace et al., 1981).
According to Thompson et al. (1981)
 
ys
ÿ 1:5
(25)
f …yg † ˆ 2:5
yg
3. Experimentation and model Implementation
The model described above has been validated with data collected from the
experimental fields of the Agricultural University of Athens (388230 N, 238060 E and
110 m altitude). Irrigated maize, cotton and (normally) rain-fed wheat crops were planted
in three level 500 m  200 m (with 150±250 m fetch) plots.
Measurements related to atmospheric, plant and soil water characteristics were
conducted. In the center of each plot meteorological parameters were logged every 10 s
and the respective hourly values were stored. Weathertronics instruments measuring air
temperature (T), relative humidity (RH) and wind speed (u) at 2 m above the top of the
canopy on a mast of adjustable height, as well as net radiation flux density RN and solar
radiation flux density Rs above the canopy and soil heat flux density G at the soil surface
were used. Two such heat plates were placed at a few millimeter below the soil surface.
Precipitation and irrigation water applied were also recorded.
Next to each set of meteorological sensors, a pit 2 m  2 m  2 m was excavated.
Through one of its exposed vertical sides, 10 tensiometers 1 m long were inserted at
various depths into the soil with a small inclination to the horizontal. Also inserted at the
same depths were calibrated Bouyoucos blocks for following soil water pressure
changes at large negative values. Neutron probe access tubes 2 m long, one for each pit,
were installed in front of the vertical rows of tensiometers and blocks, 1.6 m from the pit
side. The neutron probe used was calibrated in situ by comparing its water content
readings with those determined on soil samples, extracted during installation of the
access tubes, as well as on undisturbed soil samples collected regularly during the
experiment. Neutron probe measurements were normally taken on a weekly basis but
more frequently when large water content changes occurred following rain or irrigation.
The water content of the upper soil layer (0±0.2 m) was determined gravimetrically on
small undisturbed soil samples extracted. Comparison of the difference in soil water
content is determined by the neutron probe before and after irrigation with the irrigation
water applied (by big gun sprinkler) was the final check of the neutron probe
calibration.

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M. Anadranistakis et al. / Agricultural Water Management 45 (2000) 297±316

Moisture characteristics were determined in the laboratory on several disturbed and
undisturbed soil samples subjected to pressures ranging from 1/3 atm (33 kPa) to 15 atm
(1500 kPa) in pressure plate and membrane apparatuses. The volumetric water content
determined on undisturbed samples of the top soil layer at 1/3 atm (moisture content at
field capacity) was close to 35% while that at 15 atm (moisture content at the wilting
point) was close to 15%. Dry bulk densities were determined in the laboratory where
porosities and hydraulic conductivities at saturation, mechanical and chemical analyses
were also performed.
Field capacity was also determined in the field after irrigation and it was found that it
did not differ significantly from its laboratory value. In some cases, moisture
characteristics were obtained also in the field by correlating pressure values recorded
by the tensiometers and Bouyoucos blocks with the moisture contents of undisturbed soil
samples.
Using the soil moisture characteristics determined in the laboratory and in situ, soil
water content could be estimated (besides measurements with the neutron probe) by
recording changes of the soil water pressure heads. On the other hand, the hydraulic head
profiles and gradients and corresponding soil water flow directions, as well as the water
content profiles and their changes could be closely followed.
Throughout the growing period of all crops, phenological observations were taken and
the green leaf area index (LAI) was evaluated on a weekly basis from the leaves of 1.0 m
row plants with help of a leaf area meter. Also measured weekly were the plant height (h),
as well as the root depth on the soil profile of a pit between rows. Fertilizer and irrigation
water applications, as well as pesticide control followed the normal practice of the area
farming.
Neutral atmospheric stability was considered (CM ˆ CH ˆ 0 in Eq. (19)) for model
implementation, on a 1 h time step. Initial values of soil moisture in the top layer (yg) as
well as of layers X and Y (yx ˆ yy) were obtained from corresponding soil moisture
profiles. The overall error, by which moisture changes in the soil profile were followed,
was as less than 2%.
Results are presented separately for each crop.

4. Results
4.1. Maize
Maize (Zea mays) was sown on 9 July, the first leaf appeared on 17 July, fruit
formation began on 5 September, and the crop was harvested on 3 November 1994.
Maximum values of LAI and crop height were 6 and 2.95 m, respectively.
During the whole growing period six irrigations were applied resulting in a cumulative
water supply of 359 mm while during the same period cumulative precipitation reached
129 mm, allowing root zone (0±1.2 m) total soil water content (calculated by the soil
moisture profiles integration) to remain close to 300 mm (Fig. 3).
The study of the time evolution of the soil moisture profiles revealed the gradual in
depth expansion of the root zone and the increase of the depth zx of the soil layer X. It

M. Anadranistakis et al. / Agricultural Water Management 45 (2000) 297±316

307

Fig. 3. Time variation of LAI and root zone water content, as well as dates and amounts of rainfall or irrigation
on the maize crop.

was found that the rate of increase of the root zone was closely associated with the rate of
increase of LAI. Thus, during the period of emergence (LAI ˆ 0±0.2) it could be
assumed that zx remains approximately constant and equal to 0.25 m. After that and until
the complete ground coverage (LAI ˆ 2.8), zx was considered as linearly increasing with
time (days after planting), until it reached the value zx ˆ 0.6 m. Finally, during the rapid
growth of plants until the end of flowering, zx was considered as linearly increasing too,
but with a different slope until its maximum value zx ˆ 1.2 m.
During the time interval 10±31 October 1994, soil moisture was very close to field
capacity due to successive rainfall events following irrigation with 75 mm (Fig. 3).
Therefore, the effect of soil moisture on the stomatal resistance (rs) was negligible in this
period and, thus, it was assumed that f2(yx) ˆ 1 and evapotranspiration rates were
maximum. This proved to be very convenient in estimating the minimum stomatal
resistance (rsmin), which was found to be 165 s mÿ1, thus bringing into coincidence model
evapotranspiration estimate to the actual measurement of that same period.
In Fig. 4 mean values as well as the cumulative evapotranspiration calculated through
the model are compared with those derived from the soil moisture profile changes. There
is a good agreement throughout the period except for the mean values at the ends of
August and September, where the difference between measured and calculated
evapotranspiration is, respectively, 0.8 and 0.7 mm dayÿ1. The cumulative evapotranspiration of 446.2 mm, predicted by the model, when compared to the measured one of
434.6 mm represents a relative error of less than 3%.

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M. Anadranistakis et al. / Agricultural Water Management 45 (2000) 297±316

Fig. 4. Mean and cumulative values of maize actual evapotranspiration, calculated by the model (dot line) and
derived from the soil moisture pro®le (solid line).

4.2. Wheat
Wheat (Triticum aestivum) was sown on 9 December 1992 and harvested on 2 July
1993. Crop growth became noticeable from 1 March 1993 (LAI ˆ 1) and LAI reached its
maximum value (6.2) when the crop height was 0.7 m. During the whole period of
cultivation, precipitation totaled 205 mm and supplementary irrigation of 25 mm was
applied at the end of April 1993, allowing root zone (0±1.2 m) soil water content
(calculated by integrating soil moisture profiles) to vary between 200 and 400 mm
(Fig. 5).
Soil moisture profiles in winter showed that the soil depth from which roots were
extracting water varied from 0.3 to 0.6 m, allowing the assumption of a mean zx equal to
0.45 m. Later on, a linear extension of the root zone was considered until (mid of April)
the roots became longest (1.2 m) when plant coverage was maximum.
As there was lack of meteorological data for a short period of time, the study of wheat
development had to be conducted in two periods, the first between 19 January and 31
March 1993 and the second from 15 April until 15 June 1993. During the first part of
March, soil moisture was close to field capacity allowing estimation of
rsmin ˆ 190 s mÿ1.
In Fig. 6 mean values as well as the cumulative evapotranspiration calculated through
the model are compared with those derived from the soil moisture profile changes. An
underestimation is observed during almost the entire period of crop development but, at
the end, a total overestimation of 22 mm is equivalent to a relative error of 8%.

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309

Fig. 5. Time variation of LAI and root zone water content, as well as dates and amounts of rainfall or irrigation
on the wheat crop.

Fig. 6. Mean and cumulative values of wheat actual evapotranspiration, calculated by the model (dot line) and
derived from the soil moisture pro®le (solid line).

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M. Anadranistakis et al. / Agricultural Water Management 45 (2000) 297±316

Fig. 7. Time variation of LAI and root zone water content, as well as dates and amounts of rainfall or irrigation
on the cotton crop.

Deviations between measured and estimated values are larger in shorter (approximately
weekly) periods, becoming maximum (1.25 mm dayÿ1) at the beginning of March (when
there were some snowfalls).
4.3. Cotton
Study of the 1992 cotton (Gossypium hirsutum) refers to the period from 7 July (when
LAI ˆ 1.75) until 12 October when cotton was harvested. LAI attained a maximum value
of 5 while the maximum crop height was 0.9 m. Three irrigations of a total of 164 mm
were applied allowing root zone (0±1.2 m) soil water content (calculated by integrating
soil moisture profiles) to remain close to 200 mm (Fig. 7).
By studying the soil moisture profiles it may be deduced that the depth from which
water was extracted reached its maximum value (1.2 m) towards the end of September,
much later than the time (end of July) of maximum crop development (LAI ˆ 5) due to
reduced soil moisture, in disagreement with the common assumption in evapotranspiration estimating models that root depth increases linearly up to the maximum plant
coverage of the soil and then it remains constant. During the period 10±20 August 1992,
soil moisture retained quite high values, due to 76 mm of irrigation, allowing
determination of rsmin ˆ 85 s mÿ1, in agreement with Stanhill (1976).
In Fig. 8 mean values as well as the cumulative evapotranspiration calculated through
the model are compared with those derived from the soil moisture profile. A slight

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311

Fig. 8. Mean and cumulative values of cotton actual evapotranspiration, calculated by the model (dot line) and
derived from the soil moisture pro®le (solid line).

underestimation is noticeable towards the end of the growing period. Final estimate of
339 mm compared with measured 341 mm, shows a relative error of less than 1%.

5. Discussion
The scatterplot of mean values of measured (using the soil moisture profiles) and
estimated by the model evapotranspiration are presented for all crops in Fig. 9. In the
same figure, the perfect prediction line is also shown. Agreement between estimated and
measured values is very good (r ˆ 0.97 with intercept a ˆ 0.38 and slope b ˆ 0.92) in the
whole range of evapotranspiration values, with the maximum deviation observed around
the value of 3 mm dayÿ1. Similar are the conclusions when taking into account the root
mean square error (RMSE) and the mean absolute error (MAE), being, respectively, 0.48
and 0.33 mm dayÿ1.
Considering the atmosphere as neutrally stable does not create significant errors when
evapotranspiration estimation is made on approximately a weekly basis (Anadranistakis
et al., 1999).
Model sensitivity was checked in terms of crop canopy resistance parameterization.
Prior to this, however, the parameterization of the critical value yc, below which f2(yx)
starts becoming effective, was tested. In Fig. 10 the cumulative values of (maize crop)
evapotranspiration measured (soil moisture profiles) and estimated by considering either
a constant yc ˆ 0.75 ys (Thompson et al., 1981) or a varying (as a function of Emax) yc

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Fig. 9. Scatterplot of mean measured (using the soil moisture pro®les) evapotranspiration versus calculated by
the model for all crops studied. The perfect prediction line is also shown.

Fig. 10. Cumulative maize evapotranspiration obtained from the soil moisture pro®le (solid line) and estimated
by considering constant (yc ˆ 0.75) (dot line) and varying (dashed line) critical soil moisture values.

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313

(Doorenbos et al., 1986), are presented. An overestimation, apparent already from the
beginning of the period, becomes at the end of the period 60 and 73 mm, respectively, for
the two proposals about yc, showing that, under a high evaporative demand of the
atmosphere (as the case is in Greece during the summer), both proposals are not very
good, contrary to the parameterization suggested by Denmead and Shaw (1962).
To test the model sensitivity on rsmin and the pattern of root development, another two
runs of the model were executed (cotton crop) by considering:
(a) rsmin ˆ 68 s mÿ1 or rsmin ˆ 102 s mÿ1 (i.e., values by 20% smaller or larger than
the `actual' value imposed by the model) and the observed rate of root development.
(b) the actual rsmin value (85 s mÿ1) and a linear increase of root depth up to the
maximum LAI (Fig. 11).
Although all final evapotranspiration values are practically equal (maximum deviation
of 5 mm), probably due to the low soil moisture combined with the high evaporative
demand of the atmosphere resulting in severe soil water depletion under all cases, the
intermediate values differ significantly only when a linear root development pattern up to
the maximum LAI is considered (maximum deviation of 35 mm) showing that the model
is not very sensitive to rsmin, but it is rather sensitive to the pattern of root development.
The sensitivity to the rate of root development is attributable to the influence of the term

Fig. 11. Cumulative cotton evapotranspiration obtained from the soil moisture pro®les (solid line) and estimated
by considering (a) the observed rate of root development and the minimum stomatal resistance rsmin ˆ 68 s mÿ1
(upper dot line) or 102 s mÿ1 (lower dot line) (b) a linear increase of root depth up to the maximum LAI and
rsmin ˆ 85 s mÿ1 (dashed line).

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f2(yx) on rsc , which is certainly more important than rsmin. Similar results, which
fingerprint at the relative influence of soil moisture on evapotranspiration, through the
term f2(yx), were reported also by other workers, such as Franks et al. (1997).
Most of the physical parameters required to run the model (T, RH, u) are usually
measured by a standard meteorological station, whereas RN can be estimated as a function
of solar radiation and atmospheric humidity (Linacre, 1968) and G can be expressed as a
fraction of RN (Anadranistakis et al., 1997a)

6. Conclusions
Results, have shown that the agreement between measured and estimated evapotranspiration, in parts of or the whole growing period, is satisfactory, their difference not
exceeding 8%. Therefore, the model applied maybe a reliable tool in irrigation planning
in Greece for estimating crop water needs.
As the most influential factor of evapotranspiration of crops grown in Greece is the soil
water availability, model parameterization considered mainly the crop canopy resistance.
Precise determination of the minimum stomatal resistance is not exclusively important,
but in estimating the canopy resistance the soil-moisture depended term (f2(yx)) and the
rate of increase of the soil depth, from which water is extracted by the root system, seem
to be important. The model is sensitive to crop type and time evolution of the root zone
penetration into the soil.
The usual considerations of soil water depletion (Thompson et al., 1981; Doorenbos
et al., 1986) and root development pattern (linear up to the maximum LAI) are not
applicable under high evaporative demand and drought conditions both common in a
Greek summer.

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