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