Comparison of Three Evapotranspiration Models to Bowen

8/3/2019 Comparison of Three Evapotranspiration Models to Bowen

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Comparison of three evapotranspiration models to Bowen

ratio-energy balance method for a vineyard in an arid

desert region of northwest China

Baozhong Zhang a, Shaozhong Kang a,*, Fusheng Li b, Lu Zhang c

aCenter for Agricultural Water Research in China, China Agricultural University, Beijing 100083, Chinab Agricultural College, Guangxi University, Nanning 530005, ChinacCSIRO Land and Water, GPO Box 1666, Canberra, ACT 2601, Australia

1. Introduction

Grapevines are important for local economy in the arid region

of northwest China since the region has abundant sunlight

resource and is suitable for vine industry. In recent years,

horticulture has been becoming an important industry for

local economy. For example, the region produces high quality

grape fruits. However, limited water resources affect the

sustainability of vine production in the region (Du et al., 2005).

In the arid region, deep groundwater has been extracted for

irrigation to maintain agricultural production. With develop-

ment of irrigated agriculture and rapid population growth in

the region, over-exploration of water resources has led to

serious environmental degradations, e.g. gradually falling of

groundwater table, shrinking of vegetation areas, soil salini-

zation and desertification (Kang et al., 2004). Thus manage-

ment of irrigation to increase water use efficiency of vine crop

is important for sustainable economic development and

a g r i c u l t u r a l a n d f o r e s t m e t e o r o l o g y 1 4 8 ( 2 0 0 8 ) 1 6 2 9 1 6 4 0

a r t i c l e i n f o

Article history:

Received 26 November 2007

Received in revised form

8 April 2008

Accepted 19 May 2008

Keywords:

Bowen ratio-energy balance

Clumping model

Evapotranspiration

PenmanMonteith model

ShuttleWallace model

Vineyard

a b s t r a c t

The accurate determination of vineyard evapotranspiration (ET) in the arid desert region of

northwest China is important for allocating irrigation water and improving water use

efficiency. Taken a vineyard at theShiyang river basin of theHexi corridor of Gansu Province

as an example, this study evaluated the applicability of the Bowen ratio-energy balance

(BREB) method in the arid desert region of northwest China, simulated the variation of

vineyard ET by PenmanMonteith (PM), ShuttleWallace (SW) and Clumping (C) models in

thisregionand compared the estimated ETby the threemodels with the measured ETby the

BREB. Results indicated that the BREB could provide the accurate measurement of vineyard

ET from the arid desert region when the Bowen ratio instrument with higher accuracy was

correctly installed. Generally, thevariationof theestimatedET from PM, SWand C modelswere similar to that of the measured ET by the BREB method. However, the PM model

overestimated the ET significantly; the estimated ET from the SW and C models, especially

from the C model was approximately equal to the measured ET by the BREB. After a rainfall,

the performances of the SW and C models were also good. Therefore, among the three

models, the C model was the optimal model in simulating the vineyard ET in the arid region

of northwest China. However, after a frost, the C model significantly overestimated the

evapotranspiration because the canopy resistance did not fully reflect the dramatic

decrease of grapevine transpiration.

# 2008 Elsevier B.V. All rights reserved.

* Corresponding author. Fax: +86 10 62737611.E-mail address: [email protected] (S. Kang).

a v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a g r f o r m e t

0168-1923/$ see front matter # 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.agrformet.2008.05.016
mailto:[email protected]://dx.doi.org/10.1016/j.agrformet.2008.05.016http://dx.doi.org/10.1016/j.agrformet.2008.05.016mailto:[email protected]


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accurate determination of vineyard evapotranspiration (ET)

will provide scientific basis for such strategies.

The Bowen ratio-energy balance (BREB) is a micrometeor-

ological method for estimating evapotranspiration that has

been widely used in a variety of field conditions. However, the

application of BREB system to estimate ET in fruit trees is still

not clear because of the following assumptions. (1) The closure

ofthe energy balance is forced (Brotzge and Crawford, 2003). (2)Eddy diffusivity of vapor(Kw) is equal to Eddy diffusivity of heat

(Kh) (Angus and Watts, 1984) and during the nighttime,

advection, and high wind speed, the assumption is disputed.

But, in general, the BREB method has high measurement

accuracy when adopting the reasonable set of criteria for

selecting between reliable and unreliable measure values

(Azevedo et al., 2003; Cellier and Brunet, 1992; Dugas et al.,

1991). Spittlehouse and Black (1979, 1980) and Federer (1970)

analyzed the applicability of BREB method to forest evapo-

transpiration. There are also some reports on the estimation of

vineyard evapotranspiration over the whole growing season

using the BREB method (Ham et al., 1991; Ham and Heilman,

1991; Spano et al., 2000; Yunusa et al., 2004) and they indicatethatBREB has goodperformances in estimating the fruit treeET.

Since measurement of ET is limited by temporal and spatial

factors, mathematical modelling of evapotranspiration is an

important tool to answer many of the important questions

basedontheestimatesoverlargecatchmentareasandlongtime

scales (Domingo et al., 1999). Among many models of evapo-

transpiration thathave beendeveloped,the bestknown models

are the single-layer PenmanMonteith (PM) model (Monteith

and Unsworth, 1990; Ortega-Farias et al., 2004, 2006; Rana et al.,

1997a,b), and the two-layer ShuttleWallace (SW) model

(Farahani and Ahuja, 1996; Nichols, 1992; Sene, 1994; Shuttle-

worth and Wallace, 1985; Teh et al., 2001; Wallace et al., 1990 ).

The PM model cannot distinguish between soil evapora-tion andplant transpiration, andtreatsthe land surface as one

homogeneous layer (Monteith, 1965). Its simplicity makes the

model widelyused andmany studies have shown that the PM

model is accurate to describe evapotranspiration in densely

vegetated canopies (Monteith and Unsworth, 1990). But such

models may be inappropriate for partially or sparsely

vegetated canopies because it does not sufficiently consider

the differences between vegetation and soil, especially on

sparsely vegetated canopies (Mo, 1998), and the source/sinks

of fluxes may occur at significantly separated heights

(Farahani and Bausch, 1995). However, other studies have

argued that the PM model with a variable surface canopy

resistance (rc) can be a good tool to estimate ET directly forsparsely vegetated canopies under different soil water con-

ditions (Ortega-Farias et al., 2004, 2006; Rana et al., 1997a,b).

Because there is argument about whetherthe PM model is

appropriate for sparsely vegetated canopies or not and the

model cannot distinguish between soil evaporation and plant

transpiration, Shuttleworth and Wallace (1985) developed a

two-layer model (SW model) to estimate soil evaporation and

transpiration separately. The soil evaporation included in the

SWmodel improves the prediction of ET when leaf area index

is low. The SW model has been proved particularly useful for

row crops and clumping crops (Farahani and Bausch, 1995;

Farahani and Ahuja, 1996; Nichols, 1992; Sene, 1994; Stannard,

1993; Teh et al., 2001; Wallace et al., 1990 ).

Although many results have shown that the SW model is

better than the PM model when applied in sparsely vegetated

canopies, there also are many hypotheses and disadvantages

for the SW model. Thus the sparse-crop model of Shuttle-

worth and Wallace (1985) has been extended to several multi-

layer modelsin some cases,for example, a Clumping (C)model

(Brenner and Incoll, 1997; Domingo et al., 1999; Guo, 1999;

Tourula and Heikinheino, 1998). The C model overcomes thelimitation of uniformlydistributed vegetation over a surface in

the SW model (Brenner and Incoll, 1997), however, it is

simpler compared with other multi-species canopies or soils

models such as that reported by Gu et al. (1999). The C model

partitions energy among vegetation and soil based on

fractional vegetative cover (f) and its theory is more reason-

able compared with those of single- andtwo- layer models. But

the multi-layer models require a large number of parameters

and determination of these parameters is difficult, leading to

increased model error. Moreover, the calculation of evapo-

transpiration using the modelsis inevitably complicated.Thus

the multi-layer models are not easy to apply in estimating ET

(Zhang et al., 2001). Brenner and Incoll (1997) showed the Cmodel slightly improved the estimated ET in a dry valley in

Spain whencompared to the SW model. Domingoet al. (1999)

gave more detailed description of the radiation balance in

modifying the C model, then the model improved the

agreement between predicted and observed ET by the BREB,

but the modified C model needs more parameters in energy

flows within sparse vegetation. Thus the applicability of C

model to the arid desert regions of northwest China needs to

be verified.

As stated above, although there are many reported studies

on the Bowen ratio-energy balance, PenmanMonteith, Shut-

tleworthWallace andClumping models, a fewworks reported

in the literature on the BREB and the three evapotranspirationmodels for the arid desert region ofnorthwestChina.Thusit is

important to study the applicability of the Bowen ratio-energy

balance and three evapotranspiration models in the arid

desert region of northwest China.

The objectives of this study were to evaluate the applic-

ability of the BREB and the three evapotranspiration models

for estimating ET in the arid desert region of northwest China,

and to determine the limit of three models and the optimal

model to establish the irrigation scheduling for local vineyard.

2. Materials and methods

2.1. Experimental site and measurements

The experiment was conducted during the periods of April

October, 2005 and 2006 at the Experimental Station for Water-

saving in Agriculture and Ecology in the Shiyang river basin of

China Agricultural University, located in Wuwei, Gansu

Province, in the border of Tenger Desert (N 3785202000, E

10285005000, altitude 1581 m). The site is in a typical continental

temperate climate zone. It is rich in sunlight resource with a

mean annual sunshine duration over 3000 h, mean annual

temperature of 8 8C, annual accumulated temperature (>0 8C)

of 3550 8C and frost-free days of 150 days. However, the region

is limited in water resources with a mean annual precipitation



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of 164 mm, and mean annual evaporation from a free water

surface is 2000 mm. Average groundwater table varied

between 25 and 30 m below the ground surface. Soil is light

sandy loam texture, with a mean dry bulk density of 1.43 g/

cm3, mean porosity of 52%, mean volumetric soil water

content at field capacity of 0.37 cm3/cm3 and mean volumetric

soil water content at wilting point of 0.12 cm3/cm3 at the 0

100 cm layers.Measurements were made in a vineyard in the Experi-

mental Station and the grapevines were planted in 2000, with

row spacing of 290 cm and plant spacing of 180 cm. The trellis

for grape vine was 1.5 m in height. Grapevine roots are mainly

distributed at the 4060 cm soil layers, with the deepest roots

at the about 100 cm layers. The maximumallowable soil water

depletion was 250 mm. The experimental vineyard was

furrow-irrigated five times in 2005 and four times in 2006

over the whole growing stage for both years according to the

local vineyard irrigation, i.e. with irrigation amount of 15 mm

for the first two irrigation dates, 20 mm for other irrigation

dates in 2005, and irrigation amount of 41.7 mm for each

irrigation date in 2006, respectively.The Bowen ratio instrument (Campbell Scientific Inc., USA)

was installed in a grape-plant row near the south side of

central vineyard and there was about 110 m of fetch in the up

wind direction (northwest) during the experimentation. The

net radiation (Rn) was measured by net radiometer (model

Q7.1) mounted at 1.0 m above the vegetation surface. The soil

heat flux (G) was measured at two points, in the ditch and

ridge, by heat flux plates (model HFP01) inserted at 80 mm

below the ground surface and was calculated from heat

storage above 80 mm. Heat storage was calculated from soil

temperature measured as an average of temperatures at 20

and 60 mm depths. Temperature and humidity were mea-

sured using two integrated temperaturehumidity probesinside radiation-shielded (model HMP45C). The heights of the

two fixed measurements were 0.5 and 1.9 m above the

vegetation surface. All data were collected by a data-logger

(model CR23X) every 5 s and 10 min averages were calculated

and stored. Measurements were made continuously during

the period of 7 May15October in 2005 and 1 May7 October in

2006.

Soil moisture measurements were made at the center of

the experimental filed using portable device (Diviner 2000,

Sentek Pty. Ltd., Australia). Diviner 2000 consists of a probe

and hand-held data logger and utilizes frequency domain

reflectometry (FDR) to measure soil water throughout the

profile. Ninety-six and thirty-six PVC access tubes were evenlyinstalled in the experimental site in 2005 and 2006. Measure-

ments were made at 0.1 m intervals with maximal soil depth

of 1.0 m every third day in 2005 or every day in 2006. The

frequency of the soil moisture measurements was increased

to hourly interval after each irrigation and rainfall. The

gravimetric sampling technique and steel rings was used to

calibrate the Diviner 2000 display unit.

Leaf stomatal resistance was measured every 5 days with

LCI portable photosynthesis system (ADC BioScientific Ltd.,

England) and the frequency of the leaf stomatal resistance

measurements was increased to daily interval after each

irrigation. Leaf area index was measured every 15 days using

AccuPAR LP-80 (Decagon Devices Inc., USA). Fractional

vegetative cover (f) was estimated by measuring the dimen-

sion of canopy every 15 days. And the solar radiation,

precipitation, maximum and minimum air temperature,

relative humidity and wind speed were measured with a

standard automatic weather station near the experimental

vineyard.

2.2. Bowen ratio-energy balance method

The latent heat flux can be estimated by Bowen ratio-energy

balance method as follows:

lET Rn G

1 b(1)

where lET is the latent heat flux (W/m2), l the heat of water

vaporization (J/kg), ET the evapotranspiration (mm), Rn thenet

radiation (W/m2), and G is the ground heat flux (W/m2). The

Bowen ratio (b) is defined as follows:

b gDT

De(2)

where DTand De are the temperature (8C) and vapor pressure

(kPa) difference between the two measurement levels, respec-

tively, gthe psychrometric constant (kPa/8C). Then thevegeta-

tion evapotranspiration can be calculated from Eqs. (1) and (2).

The accuracy of the calculated values of latent and sensible

heat fluxes depends on theaccuracy of the Bowen ratio (b) and

the situations in which the BREB fails or causes inconsistent

results have been analyzed (Angus and Watts, 1984; Perez

et al., 1999). In the paper, the set of criteria for selecting

between reliable and unreliable values promoted by Perez

et al. (1999) was adopted.

2.3. Soil water balance

Soil water balance is an indirect method for estimating

evapotranspiration and it is based on the principle of

conservation of mass:

P I W ET R D DS (3)

where P is the precipitation (mm), I the irrigation (mm), Wthe

contribution from water table upward (mm), ET the actual

evapotranspiration (mm), R the surface runoff (mm), D the

drainage (mm)and DS is the change in soil waterstorage (mm)

and can be calculated as

DS St2 St1 (4)

with S(t1) and S(t2) are the soil water content at time t1 (mm)

and t2 (mm), respectively.

In our study, firstly, water cannot be flooded from the ditch

because the flow rate of furrow in the vineyard is not greater.

Secondly, the experimental site was flat and the precipitation

was not intensive. Furthermore, segregation belt was built

between the vineyard and the surrounding area, so the runoff

could be negligible. And the drainage (D) could also be

neglected according to the data of soil water content in the

profile after irrigation (Fig. 1) and there is a layer of

impermeable clay below about 100 cm. Contribution from

water table upward (W) was considered negligible because the

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water table was over 25 m deep. The soil water balance Eq. (3)

can be simplified:

P I ET DS (5)

Evapotranspiration can be calculated from Eq. (5) once

precipitation, irrigation, and soil moisture are known.

2.4. Evapotranspiration model

2.4.1. PenmanMonteith model

The PenmanMonteith (PM) model can be expressed as(Monteith, 1965)

lET DRn G rCpD=ra

D g1 rc=ra(6)

where D is the slope of the saturation vapor pressure curve

(kPa/8C), r the air density (kg/m3), Cp thespecific heat of dry air

at constant pressure (J/(kg K)), D thewater vapor deficit(kPa), rathe aerodynamic resistance (s/m) and rc is the surface canopy

resistance (s/m).

The surface canopy resistance rc, which depends on

climate factors and available soil water, can be expressed as

follows ( Jarvis, 1976):

rc rSTmin

LAIeQ

i FiXi(7)

where rSTmin is the minimal stomatal resistance of individual

leaves under optimal conditions (taken as 146 s/m). LAIe is the

effective LAI and equals to actual LAI for LAI 2, LAI/2 for

LAI ! 4, and 2 for intermediate values of LAI. Xi is a specific

environmental variable, and Fi(Xi) is the stress function ofXi,

with 0 Fi(Xi) 1. Ignoring the concentration of CO2, the

remaining environmental stress functions are as follows (Jar-

vis, 1976):

F1S S

1100

1100 a1

S a1 (8)

F2T T TLTH T

TH a2=a2TL

a2 TLTH a2THa2=a2TL

(9)

F3D ea3 D (10)

F4u

1 u! uFu uW

uF uW uF < u< uW0 u uW

8>: (11)

where S is the incoming photosynthetically active radiation

flux (W/m2), T the air temperature (K), uF is the soil water

content at field capacity (cm3/cm3), uW the soil moisture con-

tent at wilting point (cm3/cm3), and uis the actual soil moist-

ure content in the root-zone (cm3/cm3). TH and TL are the

upper and lower temperature limits outside of which tran-

spiration is assumed to cease (8C) and are set at values of

40 and 0 8C (Harris et al., 2004). The a1, a2 and a3, derived by

multi-variate optimization, are 57.67, 25.78 and 9.65, respec-

tively.

The aerodynamic resistance ra can be expressedas (Perrier,1975a,b)

ra lnz d=hc d lnz d=z0

k2u(12)

where k is Karman constant (0.40), z the reference height (m),

hc is mean crop height (m), d the zero plane displacement (m),

u the wind speed at the reference height (m/s), and z0 is the

roughness length of the crop relative to momentum transfer

(m).

Roughness length (z0) and zero plane displacement (d) are

defined as functions of crop height and leaf area index (LAI)

(Brenner and Incoll, 1997), given by

d 1:1hc ln1 X0:25 (13)

z0 z00 0:3hcX

0:5 0


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Cpsw 1

1 RpswRasw=RsswR

psw Rasw

(19)

Rssw D grsa gr

ss (20)

Rpsw D grpa gr

ps (21)

Ra

sw D gra

a (22)

where lE is the latent heat flux of evaporation from the soil

surface (W/m2), lT the latent heat of transpiration from

canopy (W/m2), rps the canopy resistance (s/m), rpa the aero-

dynamic resistance of the canopy to in-canopy flow (s/m), rssthe soil surface resistance (s/m), raa and r

sa the aerodynamic

resistances from the reference height to in-canopy heat

exchange plane height and from there to the soil surface (s/

m), respectively,Asw and Assw arethe total available energy and

the available energy to the soil (W/m2), respectively, which are

defined as follows:

Asw Rn G (23)

Assw Rsnsw G (24)

where Rsnsw is net radiation fluxes into the soil surface

(W/m2).

The radiation reaching the soil surface can be calculated

using Beers law as follows:

Rsnsw Rn expC LAI (25)

where C is the extinction coefficient of light attenuation, 0.68

for fully grown plant (Sene, 1994). And the extinction coeffi-

cient is 0 for bare soil and 0.24 for the experimental vineyardby the linear interpolation when the vegetative cover of vine-

yard is 0.35.

2.4.2.1. Canopy resistance. The canopy resistance rps is related

to environmental variables ( Jarvis, 1976):

rps rSTmin

LAIeQ

i FiXi(26)

where the parameters are computed in Eqs. (8)(11).

2.4.2.2. Aerodynamic resistances. The aerodynamic resis-

tances raa and rsa are calculated from the vertical wind profile

at the field and the eddy diffusion coefficient. Above thecanopy height, the eddy diffusion coefficient (K) is given by

K kuz d (27)

where u* is the friction velocity (m/s).

Beneaththe canopyheight, the exponential decrease of the

eddy diffusion coefficient (K) through the canopy is given as

follows:

K Kh exp n 1 z

n

h i(28)

where Kh is the eddy diffusion coefficient at the top of canopy

(m2/s), and n is the extinction coefficient of the eddy diffusion.

Brutsaert (1982) indicated that n = 2.5 when hc < 1 m; n = 4.25

when hc > 10 m. In our study, n = 2.6 by the linearinterpolation

when hc is 1.5 m. Kh is determined as follows:

Kh kuhc d (29)

The aerodynamic resistances raa and rsa are obtained by

integrating the eddy diffusion coefficients from the soil

surface to the level of the preferred sink of momentum inthe canopy, and from there to the reference height ( Shuttle-

worth and Gurney, 1990), as follows:

raa 1

Kuln

z d

hc d

hcnKh

exp n 1 z0 d

hc

1

(30)

rsa hc expn

nKhexp

nz00hc

exp n

z0 d

hc

(31)

The bulk boundary layer resistance of canopy is calculated

as (Shuttleworth and Wallace, 1985)

rpa rb

2LAI(32)

where rb is the mean boundary layer resistance (s/m),taken for

50 s/m (Brisson et al., 1998).

2.4.2.3. Soil surface resistance. The soil surface resistance (rss)

is the resistance to water vapor movement from the interior to

the surface of the soil, and is assumed to depend strongly on

the water content of an upper soil surface layer (us). The soil

surface resistance was calculated as (Anadranistakis et al.,

2000)

rss rssmin fus (33)

where rssmin is the minimum soil surface resistance, which

corresponds to soil moisture at field capacity and its value isassumed equal to 100 s/m (Camillo and Gurney, 1986; Thomp-

son et al., 1981), us is the watercontentof an upper soil surface

layer (cm3/cm3).

According to Thompson et al. (1981), f(us) is approximately

expressed as follows:

fus 2:5uF

us

1:5 (34)

2.4.3. Clumping model

The Clumping (C) model, based on SW model, separates the

soil surface into fractional areas inside and outside the

influence of the canopy. This model can be expressed asfollows (Brenner and Incoll, 1997):

lET lEs lEbs lT

fCsc PMsc C

pc PM

pc 1 fC

bsc PM

bsc (35)

where lEs is the latent heat of evaporation from soil under the

plant (W/m2), lEbs the latent heat of evaporation from bare soil

(W/m2), f is the fractional vegetative cover and is about 0.35

over the whole growing season. The terms used in Eq. (35) are

expressed as

PMpc DAc rCpD Dr

pa A

sc=r

aa r

pa

D g1 rps=raa r

pa

(36)



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PMsc DAc rCpD DrsaA

pc =r

aa r

sa

D g1 rss=raa r

sa

(37)

PMbsc DAbsc rCpD=r

aa r

bsa

D g1 rbss =raa r

bsa

(38)

Csc Rbsc R

pc R

sc R

ac=R

scR

pc R

bsc 1 fR

scR

pc R

ac fR

bsc R

scR

ac

fRbsc Rpc Rac (39)

Cpc Rbsc R

scR

pc R

ac =R

scR

pc R

bsc 1 fR

scR

pc R

ac fR

bsc R

scR

ac

fRbsc Rpc R

ac (40)

Cbsc RscR

pc R

bsc R

ac =R

scR

pc R

bsc 1 fR

scR

pc R

ac fR

bsc R

scR

ac

fRbsc Rpc R

ac (41)

Rsc D grsa gr

ss (42)

Rp

c D grp

a grp

s (43)

Rbsc D grbsa gr

bss (44)

Rac D graa (45)

where Ac, Apc , Asc and A

bsc are energy available to evapotran-

spiration, to the plant, to soil under shrub andbare soil (W/m2),

respectively, rbsa the eddy diffusion resistances from in-canopy

heat exchange plane height to the soil surface (s/m), rbss the soil

surface resistance of bare soil (s/m).

2.4.3.1. Available energy. The incoming radiation (Rn) is

divided into the radiation absorbed by the plant (Rpn) and theradiation absorbed by the soil (Rsn). If the energy stored in the

plant is assumed to be negligible, then:

Rsnc Rn eC LAI= f (46)

Rpnc Rn Rsnc (47)

Asc Rsnc G

s (48)

Absc Rn Gbs (49)

Apc Rpnc (50)

where Rpnc and Rsnc are the radiation absorbed by the plant and

the radiation absorbed by the soil (W/m2), respectively, Gs and

Gbs the ground heat flux under plant and bare soil (W/m2),

respectively, C is the extinctioncoefficient of light attenuation,

0.68 for fully grown plant (Sene, 1994).

2.4.3.2. Resistance for clumping model. The Clumping (C)

model, based on the SW model, newly introduces the

resistance of the bare soil surface (rbss ) and the aerodynamic

resistance between the bare soil surface and the mean surface

flow height (rbsa ).The resistance ofthe bare soilsurface (rbss )can

be calculated using Eqs. (33) and (34), but in which soil water

content is the water content of bare soil surface. The

aerodynamic resistance between the bare soil surface and

the mean surface flow height (rbsa ) can be calculated by

assuming that the bare soil surface is totally unaffected by

adjacent vegetation so that its aerodynamic resistance equals

rba, which is defined by

rba lnzm=z00

2

k2

um

(51)

where zm is the mean surface flow height (m), which is

assumed 0.75hc (Brenner and Incoll, 1997), and um is the wind

speed at zm (m/s).

Actual aerodynamic resistance (rbsa ) varies between rba and

rsa. Since the form of the functional relationship of this change

is not known, rbsa varied linearly between rba and r

sa as fvaries

from 0 to 1 (Brenner and Incoll, 1997). Moreover, the

calculation of other resistance is similar to those of SW

model.

2.5. Evaluation of model performance

In this study, we decided to use four statistics following

recommendations by Legates and McCabe (1999) and they

are: the modified coefficient of efficiency (E1), the modified

index of agreement (d1), mean absolute error (MAE) and the

mean ( P) between the methods. The modified coefficient (E1)

is defined as

E1 1:0

PNi1 jQi PijPNi1 jQi Qj

(52)

where Qi is observed value, Q the mean observed value, Pimodeled value. The modified index of agreement (d1) is given

by

d1 1:0

PNi1 jQi PijPN

i1jQi Qj jPi Qj(53)

3. Results and discussion

3.1. Micro-climate parameters and reference

evapotranspiration

Mostly days of the growing season were observed with daily

values of Rs and Rn between 3.5029.90 MJ/(m2 d) and 1.5817.96 MJ/(m2 d), and the ratio of Rn 0.410.80 (Fig. 2a).

Atmospheric conditions at the vineyard were very dry

and hot where average values of Ta, D and u were between

6.8 and 25.1 8C, 0.14 and 2.16 kPa and 0.13 and 2.40 m/s,

respectively (Fig. 2b, c and d). The maximum ratio of Rn was

measured in July and August, July and August were also the

months with the frequent precipitation, about 127 mm. The

maximum diurnal D and Ta were 4.754 kPa and 36.3 8C.

Reference evapotranspiration (ET0), estimated by the Pen-

manMonteith equation (Allen et al., 1998), during the whole

growing season was 499 mm. Monthly reference ET0 was

highest in June with 123 mm while reference ET0 appeared to

be lowest in September with 59 mm (Fig. 2e).



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3.2. Comparison of evapotranspiration measured by the

Bowen ratio-energy balance and soil water balance methods

Daily average evapotranspiration (ET) calculated over 7-day

periods using the soil water balance method (ETWB) was

compared with the corresponding daily average ET measured

by the Bowen ratio-energy balance method (ETBREB) as shown

in Fig. 3. The regression equation between ETBREB and ETWBwas ETBREB = 0.9817ETWB (R

2 = 0.7664). The regression was not

statistically different from line 1:1 and the root mean squared

error (RMSE) between the two methods was 0.37 mm per day,

indicating a good agreement between the estimated ET by the

two methods. During the whole growing season, the LAI was

02 m2/m2 and f was about 0.35, thus the measured ETvariation by the BREB method could be used as the standard

value to judge theestimated daily ET from thePM, SW and C

models. However, these results did not fully mean that the

BREB method was going to work properly on a 30-min periods,

because (1) this study did not take into account the effect of

shade of rows during the course of the day (Spano et al., 2000).

So, there were potential errors in the measurement ofG on 30-

min period. However, on daily basis,these errorswere notvery

important because daily cumulative values ofG always were

close to zero. (2) Overestimation could be counterbalanced by

underestimation during daytime or the nighttime. It could

have important errors in the estimation of vineyard ET on 30-

min time intervals, especially under advection conditions.Some reports also showed that most of the cases in which the

BREB method fails appear in the evening, during the night and

in the early morning or under advection condition (Unland

et al., 1996; Perez et al., 1999; Rana and Katerji, 2000 ). The

errors on 30-min period of BREB will be discussed based on

eddy covariance and heat pulse method in our further study.

Although the BREB method may have errors in the estimation

of vineyard ET on 30-min intervals, the reliable measured ET

by BREB could be provided adopting the certain criteria for

rejecting inaccurate data (Perez et al., 1999). Therefore, the

measured ET variation by the BREB method was still used as

the standard value to judge the estimated ET from the

evapotranspiration models. Many related studies also showed

Fig. 2 Daily value of solar radiation (Rs), net radiation (Rn),

air temperature (Ta), vapor pressure deficit (D), wind speed

(u) and reference evapotranspiration (ET0 ) under different

rainfall and irrigation conditions during the growing

period in 2006.

Fig. 3 Comparison of average daily evapotranspiration

(ET) estimated by the Bowen ratio-energy balance and soil

water balance methods.*, data from 10 May to 6 October

2005;*, data from 19 May to 7 October 2006. ETBREB,

measured evapotranspiration by the Bowen ratio-energy

balance method, ETWB, measured evapotranspiration bysoil water balance method.



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9/12

was far greater than the canopy resistance, which resulted in

the partition proportion of soil surface available energy into

the latent heat flux lower than that of canopy available energy

into the latent heat flux. However, the canopy resistance

model does not sufficiently reflect the change of leaf and soil

water condition and energy partition, leading to lower canopy

resistance, therefore, all available energy intothe canopy in P

M model will overestimate the evapotranspiration. (3) The

vegetation cover of vineyard is very low, not meeting the

assumptions of the PM model.However, some studies indicated the PM model under-

estimated ET in the early stage of crop, but the performance of

thePM model was good in thevigorousstage (Kato et al., 2004).

Suchdifference may also result fromthe canopy resistance and

soil water status. In theexperimentofKato et al. (2004), a sparse

canopy with full irrigation resulted in higher soil water content

and lower soil surface resistance, generally lower than the

canopy resistance. But in our experiment, because the furrow-

irrigated vineyard of arid desert oasis reduced the area of wet

soil, soil surface resistance (about 800 s/m of dry soil) was

generally higher than the canopy resistance (about 300 s/m

during the day), which resulted in ET difference from the result

ofKatoetal.(2004). Stannard(1993) alsoindicatedthatwhenthesurface canopy resistance was much greater than the soil

surface resistance, the PM model severely underestimatedthe

evapotranspiration. Therefore, when the PM model is applied

to some specific crops and places, the relationshipbetween the

canopy resistance in the model and environmental variables

and the value of canopy resistance will vary (Jarvis, 1976). For

sparsely vegetated canopies, the surface canopy resistance will

also include the effect of soil evaporation (Shuttleworth and

Wallace, 1985).

Since soil surface resistancewas newly introducedin the S

W and C models, thus the two models could better reflect the

actual soil evaporation. The estimates of evapotranspiration

from the SW and C models were better than that from the PM (Figs. 4 and 5 and Table 1). The slopes of regression equation

was 1.22, with MAE of 38.69 W/m2, E1 of 0.460 and d1 of 0.751,

indicating that the estimated ET by the SW model was

slightly greater than the measured ET. The estimates of

evapotranspiration from the C model were in good agreement

with the measurements,and the slopes of regression equation

between the estimated ET from the C model and themeasured

ETby the BREBmethodwas 0.99, with MAE of31.78 W/m2, E1 of

0.556 andd1 of 0.779. Therefore,the estimated ET from the SW

and C models, especially from the C model agreed well with

the measured ET.

The estimates of evapotranspiration from the SW and C

models agreed well with the measurements mainly because

these models acknowledged the differences between soil

evaporation and plant transpiration (0.57 and 0.54 of T/ET by

SW and C models, respectively). Some studies also indicated

that in the sparsely vegetated canopies, the SW and C model

estimates evapotranspiration well (Brenner and Incoll, 1997;

Domingo et al., 1999; Farahani and Bausch, 1995; Farahani and

Ahuja, 1996; Stannard, 1993; Teh et al., 2001). However, there

still existed the differencebetween the estimates from the two

models and the BREB measurements. Such difference may

result from the effect of canopy resistance and soil surfaceresistanceand theinaccurate estimates of energy components

in the vegetation and soil. The reasons for the inaccurate

estimates of energy components are that: (1) the SW and C

models do not include the difference of the reflectivity and

long-wave radiation between soils and canopy. Brenner and

Incoll (1997) indicated that the maximal difference of long-

wave radiation between the canopy and bare soil was about

100 W/m2. (2) The canopyintercept model forsolar radiationis

simpler because the diurnal variation of shallow time andarea

of vineyard soil surface is not included (Zhang et al., 2001).

Brenner and Incoll (1997) assumed that the fractional shadow

area only corresponds to the vegetative cover when the sun

wasdirectly overhand. At other timesfwill be larger, thus onlyfusedin theC model istoo simpler todescribebaresoil surface

area, which also lead to the errors in the estimates of energy

components. (3) The interaction of different energy compo-

nents will affect energy flux greatly. Ham and Heilman (1991)

indicated that about 1/3 of the sensible heat flux is used for

cotton transpiration. Heilman et al. (1994) also had similar

result forgrape vine in Texas,USA. Therefore, the predicted ET

for the SW and C model has some differences from the

measured value by the BREB method.

Among the PM,SW and C models, the estimatedET bythe

C model coincided closely with the BREB measurements,

which could be suitable for estimating the vineyard ET in the

region. Furthermore, the model can separate the evaporationfrom soil and the transpiration from plants, thus the models

could be used to study the water use of grapevines.

3.3.2. Comparison of diurnal estimated and measured

evapotranspiration after a rainfall

The effect of rainfall on diurnal evapotranspiration was

simulated by the three models (Fig. 6). Fig. 6 shows that the

SW and C models tended to follow the general trend of

measured ET whereas the PM model underestimated the

midday ET. Because the only computational mechanisms the

PM model used to increase ET after a rainfall were a slightly

increased value of net radiation and a decreased value of

canopy resistance due to a decreased value ofD. However, the

Table 1 Correlation between the estimated evapotranspiration of vineyard by three models over 30-min period and themeasured evapotranspiration by Bowen ratio-energy balance during the growing period in 2006

Model Regressive equation E1 d1 MAE Q P

PM lETPM = 1.29lETBREB 0.205 0.686 56.95 61.69 100.88

SW lETSW = 1.22lETBREB 0.460 0.751 38.69 61.69 90.38

C lETC = 0.99lETBREB 0.556 0.779 31.78 61.69 73.65

lETPM, lETSW and lETC are the respective estimated evapotranspiration of vineyard from PM, SW and C models, lETBREB is the measuredevapotranspiration by the Bowen ratio-energy balance. E1 is the modified coefficient of efficiency; d1 is the modified index of agreement; MAE is

the mean absolute error, Q is the mean oflET measured by the BREB, and P is the mean oflET estimated from three models.



10/12

decreased value of D also decreased the aerodynamic term,

which tended to decrease ET (Stannard, 1993). The SW and C

models explicitly accounted for bare soil evaporation after a

rainfall, thus the performances of the SW and C models were

better.

3.3.3. Comparison of diurnal estimated and measured

evapotranspiration after a frost

The diurnal patterns of estimated ET from the PM, SW and C

modelsand measured ET bythe BREBmethod, aftera frost, are

shown in Fig. 7. It can be seen that although the C model

generally performed well, its performance after a frost varied.

The C model (including the PM and SW models) severelyoverestimated the measure value of evapotranspiration.

Because after a frost, plants might suffer chill injury,

characterized by destruction of the plants membrane and

cell framework, which inhibited or destroyed enzyme activa-

tion (Li et al., 2003), the actual value of stomata resistance was

virtually significantly increased and the transpiration

decreased. However, the model value of stomata resistance

did not fully reflect the change of grapevine stomata

resistance, which will underestimate stomata resistance

and overestimate ET value of grapevine in our study.

4. Conclusions

In summary, the following conclusions can be drawn from thisstudy:

(1) The Bowen ratio-energy balance method could provide

accurate estimates of vineyard ET from the arid desert

region when the Bowen ratio instrument was appropri-

ately installed on the corresponding equilibrium layer to

the evapotranspiration surface to avoid the possible heat

circulation between the studied area and adjacent dry

environment area.

(2) Generally, the diurnal variation of the estimated ET by the

PM, SW and C models was similar to those measured by

the BREB method. The estimated ET from the SW and Cmodels, especially from the C model agreed well with the

measured ET by the BREB, but the PM model significantly

overestimated the ET. After a rainfall, the soil was wet, the

performances of the SW and C models were also good.

Therefore, among the three models, the C model was the

optimal model in simulating the vineyard ET in the arid

region of northwest China.

(3) Although the C model performed well after a rainfall, it

significantly overestimated the ET after a frost because the

canopy resistance did not fully reflect the dramatic

decrease of grapevine transpiration.

Acknowledgements

We are grateful for the grant support from financial support

from the Chinese National Natural Science Fund (50679081,

50528909), the National High-Tech 863 Project of China

(2006AA100203) and PCSIRT (IRT0657).

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Comparison of Three Evapotranspiration Models to Bowen