ORIGINAL PAPER
Estimation of actual evapotranspiration for a dripirrigatedMerlot vineyard using a threesource model
Carlos PobleteEcheverrı´a
Samuel OrtegaFarias
Received: 3 November 2008/Accepted: 30 April 2009
SpringerVerlag 2009
Abstract
A study was performed in order to evaluate thethreesource model (Clumped model) for direct estimationof actual evapotranspiration (ET
a
) and latent heat ﬂux (LE)over a dripirrigated Merlot vineyard trained on a verticalshoot positioned system (VSP) under semiarid conditions.The vineyard, with an average fractional cover of 30%, islocated in the Talca Valley, Region del Maule, Chile. Theperformance of the Clumped model was evaluated using aneddy covariance system during the 2006/2007 and 2007/ 2008 growing seasons. Results indicate that the Clumpedmodel was able to predict ET
a
with a root mean squareerror (RMSE), mean bias error (MBE), and model efﬁciency (EF) of 0.33,

0.15 mm day

1
and 74%, respectively. Also, the Clumped model simulated the daytimevariation of LE with a RMSE of 36 W m

2
, MBE of

8 W m

2
, and EF of 83%. Major disagreement (underestimated values) between observed and estimated valuesof ET
a
was found for clear days after rainfall or foggy days,but underestimated values were less than 10% of the dataanalysis. The results obtained in this study indicate thatthe Clumped model could be used to directly estimatevine water requirements for a dripirrigated vineyardtrained on a VSP. However, application of the Clumpedmodel requires a good characterization of the dripirrigatedvineyard architecture.
Keywords
Actual evapotranspiration
Clumped model
Threesource model
Merlot vineyard
Sparse canopy
Introduction
Accurate prediction of the actual evapotranspiration (ET
a
)of the vineyard is needed to estimate vine water requirements, which are used to optimize water application andgrape quality (Intrigliolo and Castel 2008; Shellie 2006;
Sivilotti et al. 2005). The direct estimation of ET
a
is complex because in many vineyards the vegetative cover of thesoil surface is usually incomplete or sparse due to the rowstructure imposed by the training systems (Yunusa et al.2004). Also, in sparse canopies such as the vineyards,aerodynamic turbulence and advection of moist air work differently from the way they do in closed canopies (Huntingford et al. 2000; Lloyd et al. 1992). Similarly, it has
been described that the degree of aerodynamic mixing insparse canopies is greater than that of closed canopies(Shuttleworth and Wallace 1985). In the particular case of
vineyards trained on a vertical shootpositioned system(VSP), bare soil often makes up the largest part of thesurface area, due to wide row spacing that increases thesoil’s contribution to the vineyard energy balance (OrtegaFarias et al. 2007). Thus, estimates of ET
a
or latent heat ﬂux(LE) from vineyards should take into account soil evaporation (
E
s
), vine canopy transpiration (
T
c
), and the interaction of ﬂuxes from these two sources (Heilman et al. 1994;Sene 1994; Trambouze et al. 1998). Additionally, for a drip
irrigated vineyard trained on a VSP, it is necessary to takeinto account two different soil evaporation sources: (1) soilunder the vine canopy, and (2) bare soil between rows.The most common and practical approach used forestimating crop evapotranspiration is the FAO56 method
Communicated by R. Evans.C. PobleteEcheverrı´a
S. OrtegaFarias (
&
)Facultad de Ciencias Agrarias, Centro de Investigacio´n yTransferencia en Riego y Agroclimatologı´a (CITRA),Universidad de Talca, Talca, Chileemail: sortega@utalca.cl
1 3
Irrig SciDOI 10.1007/s002710090183y
(Allen et al. 1998). This approach is often preferred due toits simplicity and its applicability at operational basis.However, the FAO56 method requires accurate values of crop coefﬁcients (
K
c
) which depend on climatic conditions,soil type, and the phenological stage of crops (OrtegaFarias et al. 2005). The use of standard
K
c
values obtainedfrom literature is not recommended due to the fact that it ispossible to ﬁnd differences of about 40% when these values are compared with values obtained experimentally(Rana and Katerji 2008).Recent investigations have indicated that the Clumpedmodel developed by Brenner and Incoll (1997) could beused to directly estimate ET
a
from sparse clumped canopies(Domingo et al. 1999; Were et al. 2008). The Clumped
model is based on the Penman–Monteith approach, whichconsiders that ET
a
depends on the energy balances andvapor concentration gradient controlled by surface andaerodynamic resistances (Brenner and Incoll 1997; Shuttleworth and Wallace 1985; Were et al. 2008). The
Clumped model was derived from combining the approaches of the sparsecrop model of Shuttleworth and Wallace(1985) where vegetation is assumed to be uniformly distributed over a surface, and that of Dolman (1993) whereenergy was partitioned between plant and bare soil based ontheir respective fractional covers. The Clumped model is athreesource model which considers: (1) vine canopy transpiration, (2) soil evaporation under vine canopy, and (3)soil evaporation between rows. Also the model takes intoaccount the surface and aerodynamic resistance of eachsource and it assumes that the different sources interact atmean surface ﬂow height (
z
m
) (Brenner and Incoll 1997). Inthis model, ET
a
is calculated as the sum of the Penman–Monteith equation for evaporation of each source, weightedby their fractional covers (
f
), plus a set of coefﬁcients thatrepresent the combination of these resistances. Therefore,the Clumped model differentiates the surface into vegetative and nonvegetative components, and presents a distinction between soil under vine canopy and bare soilbetween rows (Blyth 1995; Blyth et al. 1999; Brenner and
Incoll 1997; Dolman 1993; Domingo et al. 1999).
Inthisregard,Domingoetal.(1999)andWereetal.(2008)
suggested that the Clumped model could be used to directlysimulate ET
a
for a sparse clumped Retama sphaerocarpashrub. Also, recently Zhang et al. (2008), who tested theClumped model over a furrowirrigated vineyard in an ariddesert region of northwest China, obtained good results.However, the potential use of the Clumped model toestimate ET
a
over dripirrigated vineyards has not beenevaluated yet. Consequently, the objective of this study isto evaluate the Clumped model to estimate ET
a
and LEover a dripirrigated Merlot vineyard trained on a VSPunder semiarid conditions.
Materials and methods
Model descriptionThe comparison between the latent heat ﬂux values(W m

2
) obtained by the eddy covariance system (LE
ec
)and those simulated by the Clumped model (LE
c
) wasrealized at 30min time intervals. 30min values of latentheat ﬂux were converted to daily actual evapotranspirationusing the following expression:ET
a
¼
P
ii
¼
1
LE
ec
kq
w
1
:
8
ð
1
Þ
where ET
a
is the actual evapotranspiration from vineyard(mm day

1
), 1.8 a conversion factor,
k
the latent heat of vaporization (MJ kg

1
),
q
w
the density of water(1,000 kg m

3
), LE
ec
is the latent heat ﬂux obtained byeddy covariance (W m

2
),
i
the number of measurementsin the daylight time period (25 measurements from 8:00 to20:00 hours).The Clumped model computes LE as the sum of vinecanopy transpiration, evaporation from soil under the vinecanopy, and evaporation from soil between rows weightedby their fractional covers (
f
) (Brenner and Incoll 1997):LE
c
¼
f C
c
PM
c
þ
C
s
PM
s
ð Þ þ
1
f
ð Þ
C
bs
PM
bs
ð
2
Þ
where LE
c
is the latent heat ﬂux computed by theClumped model (W m

2
). PM
c
, PM
s
and PM
bs
arePenman–Monteith type combination equations for estimating the canopy transpiration, evaporation from soilunder vine canopy, and bare soil between rows (all inW m

2
), respectively.
C
c
is the canopy resistance coefﬁcient,
C
s
the soil resistance coefﬁcient under plant, and
C
bs
the soil resistance coefﬁcient between rows (alldimensionless).The values of PM
c
, PM
s
, PM
bs
and
C
c
,
C
s
, and
C
bs
arecomputed by the following equations:PM
c
¼
D
A
þ
q
C
p
D
D
r
ca
A
s
r
aa
þ
r
ca
h i
D
þ
c
1
þ
r
cs
r
aa
þ
r
ca
h i
ð
3
Þ
PM
s
¼
D
A
þ
q
C
p
D
D
r
sa
A
c
r
aa
þ
r
sa
h i
D
þ
c
1
þ
r
ss
r
aa
þ
r
sa
h i
ð
4
Þ
PM
bs
¼
D
A
þ
q
C
p
Dr
aa
þ
r
bsa
h i
D
þ
c
1
þ
r
bss
r
aa
þ
r
bsa
h i
ð
5
Þ
C
c
¼
R
bs
R
s
R
c
þ
R
a
ð Þ
R
s
R
c
R
bs
þð
1
f
Þ
R
s
R
c
R
a
ð Þþ
f R
bs
R
s
R
a
ð Þþ
f R
bs
R
c
R
a
ð Þð
6
Þ
Irrig Sci
1 3
C
s
¼
R
bs
R
c
R
s
þ
R
a
ð Þ
R
s
R
c
R
bs
þ ð
1
f
Þ
R
s
R
c
R
a
ð Þ þ
f R
bs
R
s
R
a
ð Þ þ
f R
bs
R
c
R
a
ð Þð
7
Þ
C
bs
¼
R
s
R
c
R
bs
þ
R
a
ð Þ
R
s
R
c
R
bs
þð
1
f
Þ
R
s
R
c
R
a
ð Þþ
f R
bs
R
s
R
a
ð Þþ
f R
bs
R
c
R
a
ð Þð
8
Þ
where
A
is the total energy available above the vineyard(W m

2
),
A
s
the available energy of soil under vinecanopy (W m

2
),
A
c
the available energy of vine canopy(W m

2
),
D
the slope of the vapor pressure versustemperature curve (kPa
C

1
),
C
p is the speciﬁc heatcapacity of the air at constant pressure (1,013 J kg

1
C

1
),
q
the air density (kg m

3
),
c
the psychrometric constant(kPa
C

1
),
D
the water vapor deﬁcit of the air at thereference height (
z
r
) (kPa),
r
ac
the aerodynamic resistanceof the vine from the leaf surface to mean surface ﬂowheight (
z
m
) (s m

1
),
r
aa
is the aerodynamic resistancebetween
z
m
and
z
r
(s m

1
),
r
abs
the aerodynamic resistancebetween the bare soil surface between rows and
z
m
(s m

1
),
r
as
the aerodynamic resistance between the soilunder vine canopy and
z
m
(s m

1
),
r
sc
the canopy resistance(s m

1
),
r
ss
the soil surface resistance under vine canopy(s m

1
), and
r
sbs
is the soil surface resistance between rows(s m

1
). The values of
R
c
,
R
s
,
R
a
, and
R
bs
are estimated asfollows:
R
c
¼
D
þ
c
ð Þ
r
ca
þ
c
r
cs
ð
9
Þ
R
s
¼
D
þ
c
ð Þ
r
sa
þ
c
r
ss
ð
10
Þ
R
a
¼
D
þ
c
ð Þ
r
aa
ð
11
Þ
R
bs
¼
D
þ
c
ð Þ
r
bsa
þ
c
r
bss
ð
12
Þ
The values of
A
,
A
c
, and
A
s
are computed using thefollowing expressions:
A
¼
Rn
G
avg
ð
13
Þ
A
c
¼
Rn
Rn
s
ð
14
Þ
A
s
¼
Rn
s
G
uv
ð
15
Þ
where Rn is the net radiation from the vineyard (W m

2
),
G
avg
the average soil heat ﬂux (W m

2
),
G
uv
the soil heatﬂux under the vine canopy (W m

2
), and Rn
s
the netradiation under the vine canopy (W m

2
), which can becalculated using Beer’s law as follows:Rn
s
¼
Rnexp
CLAI
ð
16
Þ
where LAI is leaf area index (m
2
m

2
), and
C
theextinction coefﬁcient of the canopy for net radiation(dimensionless). The values of canopy resistance (
r
sc
) of avineyard with hipostomatous leaves are computed asfollows (Laﬂeur and Rouse 1990):
r
cs
¼
r
st
LAI
¼
1
g
s
LAI
ð
17
Þ
where
r
st
is the mean stomatal resistance (s m

1
),
g
s
themean stomatal conductance. Using the Shuttleworth andGurney (1990) approach, values of
r
ac
are estimated by thefollowing expressions:
r
ca
¼
r
b
LAI
ð
18
Þ
r
b
¼
n
a
wu
h
0
:
5
1
e
n
2
ð Þ
1
ð
19
Þ
u
h
¼
u
k
ln
h
d z
o
ð
20
Þ
u
¼
ku
r
ln
ð
z
r
d
Þ
z
o
h i
ð
21
Þ
z
o
¼
z
0
o
þ
0
:
3
h c
d
LAI
ð Þ
0
:
5
ð
22
Þ
d
¼
1
:
1
h
ln 1
þ
c
d
LAI
ð Þ
0
:
25
ð
23
Þ
where
r
b
is the mean boundary layer resistance of hipostomatous leaf per unit surface area of vegetation (s m

1
);
n
*the attenuation coefﬁcient for wind speed (dimensionless),
n
the eddy diffusivity decay coefﬁcient (dimensionless),
w
the average leaf width (m),
a
constant (Choudhury andMonteith 1988),
u
h
the wind speed at the top of the canopyaverage height (m s

1
),
d
the displacement height (m),
h
the height of the vine canopy (m),
k
the von Karman’sconstant (dimensionless),
z
o
the roughness length (m),
u
*the friction velocity (m s

1
),
u
r
the wind speed at
z
r
(m s

1
),
c
d
the drag coefﬁcient (dimensionless),
z
0
o
is theroughness length of the bare soil (m).The values of
r
aa
and
r
as
are estimated by the followingexpressions:
r
aa
¼
1
ku
ln
z
r
d h
d
þ
hnK
h
e
n
1
Z
0
þ
d
p
ð Þ
h
1
ð
24
Þ
r
sa
¼
he
n
nK
h
e
nz
0
0
h
e
n
ð
Z
0
þ
d
p
h
!
ð
25
Þ
K
h
¼
ku
ð
h
d
Þ ð
26
Þ
where
d
p
is the zero plane displacement height (m) (takenas 0.63 h),
Z
0
the zero roughness length of the surface (m)(taken as 0.13 h) and
K
h
the diffusivity at the top of thecanopy (m
2
s

1
). The values of aerodynamic resistance(
r
abs
) between the bare soil surface and
z
m
can be calculatedassuming a linear variation between
r
ab
and
r
as
with f changing from 0 to 1 (Brenner and Incoll 1997; Villagarciaet al. 2007):
Irrig Sci
1 3
r
bsa
¼
fr
sa
þ ð
1
f
Þ
r
ba
ð
27
Þ
r
ba
¼
ln
z
m
z
0
0
2
k
2
u
m
ð
28
Þ
where
r
ab
is the aerodynamic resistance of bare soil totallyunaffected by vegetation (s m

1
), and
u
m
is wind speed at
z
m
. Figure 1 shows a diagram of resistance network used inthe Clumped model including the different heights (
z
=
0,
z
m
and
z
r
) and
f
value. Finally, the constant input parameters used to test the Clumped model are indicated inTable 1.Study siteData used to test the Clumped model were collected from adripirrigated Merlot vineyard located in the Talca Valley,Region del Maule, Chile (35
8
25
0
LS; 71
8
32
0
LW; 125 mabove sea level) during 2006/2007 (season 1) and 2007/ 2008 (season 2) growing seasons. The climate of the studyarea is Mediterranean semiarid with an average dailytemperature of 17.1
C and an average annual rainfall of 679 mm. The summer period is usually dry and hot (2.2%of annual rainfall) while the spring is wet (16% of annualrainfall). The soil at the vineyard is classiﬁed as Talcaseries (Fine family, mixed, thermic Ultic Haploxeralfs)with a clay loam texture and average bulk density of 1.5 g cm

3
. For the effective rooting depth (0–60 cm), theaverage volumetric soil water content at ﬁeld capacity(
h
FC
) and wilting point (
h
WP
) were 0.36 and 0.22 m
3
m

3
,respectively. The vineyard plot (4.25 ha) used for themeteorological and micrometeorological measurementswas mostly homogeneous and ﬂat. Also, the vineyard plotis surrounded by other vineyard plots with the same conditions. The soil surface was maintained free of cover cropduring the study periods (Fig. 1).The vineyard was irrigated daily using 4 L h

1
drippersspaced at intervals of 1.5 m. The Merlot vines were plantedin 1999 in North–South rows, 2.5 m apart, with 1.5 mwithinrow spacing and were trained on a vertical shootpositioned system (VSP) with the main wire 1 m above thesoil surface. The shoots were maintained on a verticalplane by three wires, the highest one was located 2 mabove the soil surface. The average vine trunk diameterswere 0.117 m (
±
0.08 m) for the ﬁrst season and 0.129 m(
±
0.01 m) for the second season.Field measurementsThe irrigation management of the Merlot vineyard wasdone using a maximum allowed depletion (MAD) of 29%(174 mm). In this regard, the volumetric soil water content(
h
) at the rooting depth (0.6 m) (
h
rd
) was monitored weeklyin 12 sampling points distributed inside the vineyard usinga portable TDR unit (TRASE, Soil Moisture Corp., SantaBarbara, CA, USA). Also,
h
of the upper soil layer(0.08 m) was measured both under the vine canopy (
h
uv
)and in the soil between rows (
h
bs
) using a Theta Probe(ML2x, DeltaT Devices, Cambridge, England). Values of
h
were measured in four sampling points for each
h
uv
and
h
bs
. Additionally, the intercomparison indicated that differences between TDR and Theta Probe sensors were lessthan 0.4%.Vine water status was evaluated weekly using the midday stem water potential (
w
x
) measured by a pressurechamber (PMS 600, PMS Instrument Company, Corvallis,OR, USA).
w
x
was measured on 12 young fully expandedleaves (two leaves per vine), wrapped in aluminum foil,and encased in plastic bags at least 2 h before measurement(Chone et al. 2001). Also, the stomatal conductance (
g
s
)was measured ten times during each season on 16 youngfully expanded leaves (four leaves per vine) in their naturalorientation around midday (from 11:00 to 14:00 hours) bya portable gasexchange system (LI6400, LICOR Inc.,Lincoln, NE, USA).The leaf area index (LAI) was estimated using the following equation (Johnson et al. 2003; OrtegaFarias et al.2007):LA
shoot
¼
634
:
86
þ
3543
:
92
ð
SL)
ð
29
Þ
LAI
¼
P
j
1
LA
shoot
A
v
ð
30
Þ
where LA
shoot
is the total leaf area per shoot (m
2
),
A
v
thevine area (m
2
), SL the shoot length (m), and
j
the total
Fig. 1
Schematic representation of resistance network and heightsused in the Clumped modelIrrig Sci
1 3
shoot number per vine. The total shoot length per vine wasmeasured once a week on four representative vines duringeach seasons. Thirty vines were totally defoliated todevelop Eq. 29 and total leaf area per shoot was calculatedby a digital image analysis of the leaves.The average fractional cover (
f
) for the vineyard wasestimated ten times during each season by measuring theprojected area occupied by the vine (shaded area at midday) over 64 vines. The average height of the vineyard (
h
)and the reference height (
z
r
) were 2.1 and 4.7 m, respectively. Also, the mean surface ﬂow height (
z
m
) was 1.6 m(
z
m
=
0.76
h
) (Brenner and Incoll 1997).Measurements of meteorological variables and energybalance components were made from November 2006 [dayof year (DOY) 319] to April 2007 (DOY 93) and December2007 (DOY 345) to March 2008 (DOY 62). The air temperature (
T
a
) and relative humidity (RH) were monitored at
z
r
and
z
m
using two Vaisala probes (HMP45C and HMP3C,Campbell Scientiﬁc Inc., Logan, Utah, USA). The windspeed (
u
) and wind direction (wd) were measured at thesame height by two cup anemometers and two wind vanes(YOUNG, 031015, Michigan, USA), respectively. Thesolar radiation (Rs) was measured with a Silicon Pyranometer (LI200X, Campbell Scientiﬁc Inc., Logan, UT,USA) and precipitation (pp) was measured with a pluviometer (RGB1, Campbell Scientiﬁc Inc., Logan, UT, USA)both at
z
r
. The net radiation over the vineyard (Rn
avg
) wasmeasured at
z
r
by a fourway net radiometer, which consists of two pyranometers (CM3) and two pyrgeometers(CG3) (CNR1, Kipp&Zonen Inc., Delft, Netherlands). Allmeteorological variables were recorded every 10 s by a
Table 1
List of constants used in the clumped modelSymbol Name Value Units Source
n
Eddy diffusivity decay coefﬁcient 2.5 Dimensionless Shuttleworth and Wallace (1985)
n
* Attenuation coefﬁcient for wind speed 2.5 Dimensionless Choudhury and Monteith (1988)
r
st
Mean stomatal resistance 201 s m

1
Measured in season 1
r
st
Mean stomatal resistance 204 s m

1
Measured in season 2
h
Height of the canopy 2.1 m Measured
f
Fractional vegetative cover 0.3 Dimensionless Measured
a
Constant in Eq. 18 0.01 Dimensionless Choudhury and Monteith (1988)
k
Von Karman’s constant 0.41 Dimensionless Shuttleworth and Wallace (1985)cd Drag coefﬁcient 0.07 Dimensionless Shuttleworth and Gurney (1990)
C
Extinction coefﬁcient 0.38 Dimensionless Measured
r
ss
Resistance of the soil under vine 20 s m

1
Brenner and Incoll (1997)
r
sbs
Resistance of the bare soil surface 2,000 s m

1
Shuttleworth and Wallace (1985)
z
m
Mean surface ﬂow height 1.60 m Brenner and Incoll (1997)
w
Mean width of the leaf 0.018 m Measured
z
r
Reference height 5.0 m Measured
z
0
o
Roughness length of bare soil 0.01 m Sene (1994)
d
p
Zero plane displacement 1.32 m Shuttleworth and Wallace (1985)
d
Displacement height 0.80 m Brenner and Incoll (1997)
z
o
Roughness length 0.12 m Brenner and Incoll (1997)
Z
o
Zero roughness length 0.27 m Shuttleworth and Wallace (1985)
Fig. 2
Aerial photography of the study site and eddy covariancetowerIrrig Sci
1 3