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

Crop water requirements model tested for

crops grown in Greece

M. Anadranistakis

a

, A. Liakatas

b,*

, P. Kerkides

b

, S. Rizos

b

,

J. Gavanosis

b

, A. Poulovassilis

b

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, 23806}0_{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)

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 (rc_s) and soil (rs_s) resistances combined in parallel

r_cÿ1ˆ …1ÿB†…rc_s†ÿ1‡B…r_ss†ÿ1 (1)

The termBis 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 ofrcvia 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 speedu(s mÿ1) (Thom, 1971), that can be described by meteorological parameters like air temperatureT0

(8_{C) 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 isrc_a (s mÿ1) while vertical transfer is controlled by two extra resistances: r_aa between mean flow and a reference level andrs

a between soil and the mean flow level. The total latent heat flux

above the crop is described by

lEˆCcPMc‡CsPMs (2)

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

form

density of available energy at the soil surface (W mÿ2), Rs_N the ¯ux density of net radiation at the soil surface (W mÿ2), rc

s the canopy resistance (s mÿ

1

), rs

s the soil

resistance (s mÿ1),D_{the slope of the saturation vapor pressure curve at the mean wet bulb}

temperature of the air (hPa per8_{C),rthe air density (kg m}ÿ2_),cpthe speci®c heat of air at

constant pressure (1010 J kgÿ1per8_C),Dthe water vapor pressure de®cit at the reference height (hPa) andgthe psychrometric constant (hPa per8C).

The coefficientsCcandCs are functions ofD,g,rca,ras,raa,rss,rcs.

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

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 ofRNandGare available,Acan be determined asAˆRNÿG. Not

so straight forward is the determination ofAs, since noRNmeasurements 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)

Rs_NˆRNexp ÿ0:622 LAI‡0:055…LAI†2

h i

(5)

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 capacityysto a mean water content at the wilting pointyw. 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 thicknesszgˆ5 cm and volumetric water contentyg.

Transpiration rate is controlled via the canopy resistance by the water content of the second soil layer X, with volumetric water contentyx, 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

system. The third soil layer Y with volumetric water contentyyand thicknesszy, 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‡zyˆzÿzg. For our experiments,

zˆ1.2 m was the maximum depth from where water is considered to be extracted by the plants. It is a common practice to considerzxas 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 ifygbecomes equal toys,

any extra water is moving to the X layer. Ifyxbecomes equal toys, 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:

DVgˆPÿIÿD1ÿ0:1EcÿEs (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 0.1Ec(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:

DVxˆD1‡yyDzÿ0:9EcÿD2 (7)

where,D_{Vx(mm) is the change of water content, 0.9Ec 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 termyyDzexpresses the water transfer from the Y layer into the X layer due to

the root system development (D_z).

The water content of the soil layer Y increases ifD2> 0.

2.3. Condensation and intercepted water

When the model estimate of Ec or Es is negative, rs_s or rc_s 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)

IˆkP0 …IImax† (8)

kˆ1ÿ …0:5†LAI (9)

The retained water forms a thin film which covers a portion of the canopy (d) and evaporates directly, while the remainder (1ÿd) of the canopy continues to transpire normally. According to Deardorff (1978)dˆ(I/Imax)2/3.

Calculation of the evaporation rate (from the crop canopy) is performed using Eq. (3) withr_scˆ0. Thus, total water loss from the crop surface is the sum: (evaporation rate)

xd‡(transpiration rate)x(1ÿd).

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)

dˆ0:63sah (10)

z0ˆ …1ÿsa†zog‡

sa…hÿd†

3 (11)

whereh 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), andsais a momentum partition coef®cient assumed to depend on LAI and, according to Shaw and Pereira (1981), given by the expression

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 coefficientsa, through the relationships

tˆtc‡tg (13)

tcˆsat (14)

tgˆ …1ÿsa†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,r_ac,rs_aandr_aacan be expressed as fractions of the overall aerodynamic resistance for momentum transfer in the soil-vegetation system (ra) (Anadranistakis et al., 1999)

r_acˆruÿ0

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):

Thom (1972), Legg and Long (1975) and Webb (1975) experimenting on a closed artificial crop, concluded thatucould 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 relationshipuˆ0.83u(z)sf‡(1ÿsf)u(z), whereu(z) (m sÿ1) is the wind speed at

reference height andsfis an extinction coefficient ranging from 0 (for bare soil) to 1 (for

a closed canopy). Similarly,sfmay 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,

uˆ0:83u…z†sa‡ …1ÿsa†u…z† (20)

Aerodynamic resistances parameterization allows no discontinuities during the transition from bare soil to dense vegetation. By considering that

(a) for bare soilsaˆ0 and thusuˆu…z†. From Eqs. (16)±(18) it results thatraaˆ0 and r_acbecome infinite thus stopping transpiration, whereasraˆras(the mean flow being at

the same level as the reference height)

(b) for dense vegetationsaˆ1 anduˆ0.83u(z). Correspondingly,rasbecomes infinite

and soil evaporation ceases, whereasr_aa‡r_acˆra.

(c) for incomplete canopies,racomes from the parallel connection ofrs_aandrc_a, serially

connected withr_aa…raˆ ‰…r_ac†ÿ1‡ …rs_a†ÿ1Šÿ1‡ra_a†.

2.5. Canopy resistance

The canopy resistance (r_sc) depends upon atmospheric factors and upon available soil water. Assuming thatrsis the stomatal resistance (rsminbeing its minimum value),rcs is

given by

r_scˆrsminf1…Rs†

f2…yx†LAI2

The factorf1(Rs) accounts for the in¯uence of solar radiation ¯ux density (Rs) onrc_s.

According to Dickinson (1984) and Dickinson et al. (1986),f1(Rs)ˆ(1‡f0)/(f0‡(rsmin/

rsmax)) and f0ˆ(0.55Rs/RL)(2/LAI), where the maximum stomatal resistance

rsmaxˆ3000 s mÿ1 (Norman, 1979) and RLˆ100 W mÿ2 is a threshold radiation

value above which the stomata open. The term 2/LAI expresses the shading bet-ween 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 r_sc, especially in xerothermic climatic conditions. Decrease of the X layer soil moisture (yx) causes closing of the

stomata and, therefore,rc_s 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 (ysÿyw)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 (ysÿyw)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 ysˆ0.36 cm3cmÿ3and ywˆ0.22 cm3cmÿ2. Transforming the

critical soil moisture values (yc) obtained, to values of the coefficientc(cˆ(ycÿyw)/

(ysÿyw)) the experimental results of DS may be expressed by a second degree

polynomial

cˆ0:01‰9:5ÿ1:4Emax‡2:2…Emax†2Š Emax6:5 mm dayÿ1 cˆ0:95 Emax>6:5 mm dayÿ1

(22)

In the absence of other similar results, Eq. (22) is the best option available for determiningc.

From Eq. (21), f2(wx) could, thus, be modified according to Noihlan and Planton

2.6. Soil resistance

This is assumed to depend strongly onygaccording to the relationship

r_ssˆr_smins f…yg† (24)

wherer_smins 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 soilrs_s may reach the value of 10 000 s mÿ1(Fuchs and Tanner,

The model described above has been validated with data collected from the experimental fields of the Agricultural University of Athens (388₂₃0_{N, 23}8₀₆0_{E and}

110 m altitude). Irrigated maize, cotton and (normally) rain-fed wheat crops were planted in three level 500 m200 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 densityRNand solar

radiation flux densityRsabove the canopy and soil heat flux densityGat 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.

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 (C_MˆC_{Hˆ0 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 (yxˆyy) 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 depthzxof the soil layer X. It

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 (LAIˆ0±0.2) it could be assumed thatzxremains approximately constant and equal to 0.25 m. After that and until

the complete ground coverage (LAIˆ2.8),zxwas considered as linearly increasing with

time (days after planting), until it reached the valuezxˆ0.6 m. Finally, during the rapid

growth of plants until the end of flowering,zxwas considered as linearly increasing too,

but with a different slope until its maximum valuezxˆ1.2 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)ˆ1 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 evapotran-spiration 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%.

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 (LAIˆ1) 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 meanzxequal 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

rsminˆ190 s mÿ 1

.

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%. 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).

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.

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 LAIˆ1.75) 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 (LAIˆ5) due to reduced soil moisture, in disagreement with the common assumption in evapotranspira-tion 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 ofrsminˆ85 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 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.

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 (rˆ0.97 with interceptaˆ0.38 and slopebˆ0.92) 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 valueyc, 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 constantycˆ0.75ys(Thompson et al., 1981) or a varying (as a function ofEmax)yc

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 (ycˆ0.75) (dot line) and varying (dashed line) critical soil moisture values.

(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 onrsminand the pattern of root development, another two

runs of the model were executed (cotton crop) by considering:

(a)rsminˆ68 s mÿ1or rsminˆ102 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 mÿ

1

) 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 torsmin, 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

f2(yx) on rc_s, which is certainly more important than rsmin. Similar results, which

fingerprint at the relative influence of soil moisture on evapotranspiration, through the termf2(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, whereasRNcan be estimated as a function

of solar radiation and atmospheric humidity (Linacre, 1968) andGcan be expressed as a fraction ofRN(Anadranistakis et al., 1997a)

6. Conclusions

Results, have shown that the agreement between measured and estimated evapo-transpiration, 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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