Agricultural Water Management 178 (2016) 189–200

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Agricultural Water Management
journal homepage: www.elsevier.com/locate/agwat

Improving the estimation of evaporation by the FAO-56 dual crop
coefﬁcient approach under subsurface drip irrigation
V. Phogat a,∗ , J. Šimůnek b , M.A. Skewes a , J.W. Cox a,c , M.G. McCarthy aaSouth Australian Research and Development Institute, GPO Box 397, Adelaide, SA 5001, Australia
Department of Environmental Sciences, University of California, Riverside, CA 92521, United Statesc
The University of Adelaide, PMB1, Glen Osmond, SA 5064, Australiaba r t i c l e

i n f oArticle history:
Received 8 July 2015
Received in revised form
13 September 2016
Accepted 24 September 2016
Keywords:
FAO-56 dual crop coefﬁcient
Evaporation
Subsurface drip
Evapotranspiration
Wine grapea b s t r a c t
Partitioning of evapotranspiration and estimating of irrigation contribution to evaporation play a crucialrole in managing scarce water resources and help in increasing the water productivity of crops, especiallyof sparsely vegetated plants. In this study, the FAO-56 dual crop coefﬁcient (DCC) approach for estimating
evaporation from soil under cropped conditions is adapted for subsurface drip irrigation (SDI). This new
approach involves one additional variable, the fraction of the irrigation depth contributing to evaporation(fI,Es ), which was deﬁned and integrated into the FAO-56 equations for estimating daily water balancefrom the evaporation layer (0–15 cm). Impacts of soil texture, heterogeneity, irrigation depth, design
parameters of the irrigation system on fI,Es , and the fraction of the soil surface wetted by irrigation (fw ) (andconsequently the exposed and wetted fraction (few )), were evaluated through HYDRUS-2D simulations.
The modiﬁed procedure was compared with the existing FAO-56 method for estimating components ofannual ET for wine grape under SDI.
The model simulations showed that the fI,Es fraction in a homogeneous, isotropic light-textured soil was
minimal (0.04) when SDI was placed at a depth of 25 cm. However, in medium and heavy textured soils fI,Es
was 4 times larger than in light-textured soils. The value of fw was slightly higher in ﬁne-textured (0.09)
than in medium-textured soils (0.07). In Duplex soils with two contrasting textural layers, fw (0.12–0.16)
was higher due to the presence of a heavy-textured soil layer just below the drip line. Similarly, in
Triplex soils (3 different textural layers), placing the drip line in the middle layer effectively reduced both
fI,Es and fw close to zero. In contrast, fw (0.18–0.30) and fI,Es (0.28–0.42) both increased considerably inheterogeneous soils. Both fractions (fw and fI,Es ) increased with an increase in irrigation depths, except for
fI,Es in loamy sand. The fractions were slightly lower when a drip line was placed at a depth of 10 cm (anevaporation zone) than when it was placed on the soil surface. Applying the same amount of water withdifferent discharge rates had little impact on fI,Es and fw fractions. An increase in the drip line spacing
proportionally decreased the wetted fraction on the soil surface. Annual evaporation for SDI irrigatedwine grapes at the ﬁeld study site, estimated using the existing FAO-56 procedure, was overestimatedby about 5–6% compared to using the modiﬁed procedure. However, this deviation between the two
approaches increased (18%) for heavier soil textures. It is concluded that the existing FAO-56 procedureneeds to be adjusted when used to estimate evaporation under subsurface drip irrigation. However, theimpact of the proposed modiﬁcation on evaporation needs further evaluation under other crops, soils,
and climatic conditions.
© 2016 Elsevier B.V. All rights reserved.

1. Introduction
Partitioning of ET into evaporation (Es ) and transpiration (Tp )is important for proper scheduling of irrigation for crops, espe-∗ Corresponding author.
E-mail addresses: vinod.phogat@sa.gov.au, vinphogat@gmail.com (V. Phogat).
http://dx.doi.org/10.1016/j.agwat.2016.09.022
0378-3774/© 2016 Elsevier B.V. All rights reserved.

cially under drip irrigation systems where partial wetting of thesoil surface and high system design costs increase the importanceof optimal management of the system. While Es is considered to be
an undesirable water loss, Tp is assumed to be an essential component of crop water productivity. There can be huge losses ofwater through evaporation, particularly in sparsely planted trees
and orchards, such as grapevines, where a large soil surface area
is exposed to atmospheric effects. For example, the Es /ET ratio was190

V. Phogat et al. / Agricultural Water Management 178 (2016) 189–200

found to exceed 30% in 32 out of 52 ET partitioning studies (Koolet al., 2014a). Hence, reliable estimation of Es can help in managing
the unproductive losses of irrigation water because it provides useful information for irrigation management and water use efﬁciency
improvements.
The FAO-56 dual crop coefﬁcients (DCC) approach (Allen et al.,1998) is accepted as a standard technique in the absence of measured data to calculate crop evapotranspiration demand and to
estimate Es losses, using a basal crop coefﬁcient (Kcb ) and an
evaporation coefﬁcient (Ke ). This technique is also employed toestimate potential Tp and Es in agro-hydrological modelling studies(Ramos et al., 2012; Kool et al., 2014b; Phogat et al., 2013, 2014).
The reference ET (ET0 ) is calculated using a modiﬁed PenmanMonteith equation, which incorporates a number of weather andenergy balance parameters, as described in Allen et al. (1998).
Other improvements in estimating crop evapotranspiration (ETC )are explained in subsequent publications (Allen et al., 2005a,b;
Allen and Pereira, 2009).
Surface drip (DI) and subsurface drip (SDI) irrigation are relatively recent methods of water application in irrigated agriculture.
The procedure for estimating Es and Tp by the FAO-56 DCC approachworks well for surface drip, where water is applied on the soil surface from where it spreads radially while inﬁltrating down into thesoil, in a process similar to that under sprinkler irrigation. Subsurface drip, however, applies water below the soil surface, from wherewater moves in all directions (including upwards) depending on
the soil hydraulic properties and moisture regime. The FAO-56 DCC
approach calculates Es from the evaporation zone, which in manycases is located within the top 0.10 to 0.15 m soil layer (Allen et al.,1998). Given that emitters in an SDI system may be installed below
the evaporation zone, it is clear that the fraction of applied irrigation, which moves through the evaporation zone (fI,Es ), and istherefore available to contribute towards Es , is potentially muchsmaller under SDI than under DI or sprinkler irrigation. Consequently, estimates of variables used in the FAO-56 procedure, suchas the fraction of the wetted soil surface (fw ), the fraction of thesoil surface wetted and exposed to evaporation (few ), the irrigation
depth for the fraction of the wetted soil surface (Iw ) and the irrigation depth that inﬁltrates into the soil (Ii ), will be different between
SDI and DI. For example, Cancela et al. (2015) reported fw values tobe 10 times higher for DI (0.1) than for SDI (0.01). These parameters
have a signiﬁcant impact on the estimation of evaporation for subsurface drip irrigation. Hence, there is need to modify the current
estimation procedure for the soil evaporation coefﬁcient (Ke ) for
SDI systems.
While the entire SDI system could be evaluated using processbased numerical models, rather than the simpliﬁed FAO-56 DCC
approach, such models are relatively difﬁcult to use and parameterize, and thus unlikely to be adopted by farmers. On the other hand,
the FAO-56 empirical approach Allen et al. (1998) is much simpler,
providing that its empirical parameters can be estimated, and more
widely used for practical applications. One of the objectives of thismanuscript thus is to modify the existing FAO-56 approach so that
it is applicable also for the SDI systems and show how additional
required parameters can be estimated.
The parameters of the FAO-56 approach are usually obtained
based on ﬁeld experiments. However, ﬁeld measurements of manyof these parameters, such as fI,Es for different irrigation system conﬁgurations and for different soils would be a complex and near
impossible exercise. On the other hand, there is no fundamental reason, why these coefﬁcients could not be estimated, as analternative to experimental data, using a process based model thathas been widely accepted and validated for describing particular
processes involving these parameters. The fw , few and fI,Es parameters can thus be alternatively estimated with the help of numericalmodels.

Among available numerical models, HYDRUS-2D (Šimůnek
et al., 2008) has been extensively used in evaluating the impact ofvarious irrigation system designs (e.g. Skaggs et al., 2010; Phogat
et al., 2012; Naglic et al., 2014) and in solving other water balance and solute transport problems for surface (e.g. Phogat et al.,2013, 2014; Elmaloglou et al., 2013; Li et al., 2015) and subsurface (e.g. Cote et al., 2003; Lazarovitch et al., 2005; Singh et al.,2006; Kandelous et al., 2012; El-Nesr et al., 2014) drip systems.
Provenzano (2007) and Kandelous and Šimůnek (2010) tested thismodel for modelling water distribution around the subsurface dripper with variable drip line placements and drip discharges, andcompared the dimensions of the wetted zone in laboratory and ﬁeld
conditions involving soils of varied textures. Similarly, Skaggs et al.
(2004) showed that HYDRUS-2D simulations matched well a uniform wetted pattern along a SDI drip line with a dripper distance of
30 cm in the ﬁeld. According to the ISI’s Web of Science (Šimůnek
et al., 2016), HYDRUS-2D model has been successfully used to simulate drip/trickle irrigation in more than 80 peer-reviewed journal
manuscripts. It is thus very likely that a calibrated HYDRUS model
can provide reliable results as a surrogate to ﬁeld experimental
data. Therefore, HYDRUS-2D can be employed to estimate fI,Es and
fw for different soil textures, soil horizon heterogeneity, and for
different irrigation system designs.
The objectives of this investigation were (a) to compute thepotential fraction of the irrigation depth entering the evaporation
zone (fI,Es ) and wetted soil surface fraction (fw ) (and from this the
exposed and wetted fraction, few ) for ﬁeld soil using HYDRUS-2D,(b) to simulate the impact of soil type, soil heterogeneities, anddrip designs on fw and fI,Es for SDI in hypothetical scenarios, and(c) to compare the seasonal ET components (Tp , Es and ETC ) of thewine grapes estimated by the original and the modiﬁed FAO-56
DCC approaches for two seasons (2010–11 and 2011–12) for ﬁeld
conditions and for other hypothetical uniform soils. The modiﬁed
FAO-56 DCC approach incorporates fI,Es fraction in the existing FAO56 procedure for the estimation of evaporation component for SDI
conditions. This modiﬁcation in FAO-56 DCC is discussed in moredetails in the following sections.
The ﬁeld estimated values of daily transpiration (Tp ) and evaporation (Es ) by modiﬁed FAO-56 approach were used as inputs
to HYDRUS-2D in a companion paper (Phogat et al., 2016, underreview) which describes the calibration and validation of HYDRUS2D and the estimation of actual ET components under ﬁeld
conditions for SDI-irrigated wine grapes. The improved FAO-56
procedure could be helpful in providing better estimates of evaporation losses, and could result in improved irrigation scheduling,
irrigation efﬁciency, and water productivity under SDI systems.

2. Materials and methods
2.1. FAO 56: background
The FAO 56 DCC procedure (Allen et al., 1998) utilizes weather
data to estimate ET for a reference crop (ET0 ) and then multiplies
this estimate by a crop coefﬁcient (Kc ), which adjusts ET0 for a
speciﬁc crop. The reference crop generally represents a clipped,
well-watered grass. The potential crop ET (ETC ) may differ fromthe reference ET (ET0 ) as the ground cover, canopy properties, andaerodynamic resistance of a particular crop are different from thereference crop. This procedure has two approaches: i) the single
Kc approach, which integrates differences in evaporation and transpiration between ﬁeld crops and the reference crop into a single
crop coefﬁcient (Kc ); ii) the dual crop coefﬁcient approach, which
separates the crop coefﬁcient into two coefﬁcients: a basal crop
coefﬁcient (Kcb ) responsible for transpiration, and a soil evapora-

V. Phogat et al. / Agricultural Water Management 178 (2016) 189–200

tion coefﬁcient (Ke ), i.e., Kc = Kcb + Ke . The equations for estimating
ETC under both approaches are:
ET C = K c∗ ET0(1)

ET C = (K cb + K e )∗ ET0(2)

The calculation of ETC using these two approaches has been standardized by Allen et al. (1998) and discussed at length by theseauthors (Allen et al., 2005a,b; Allen and Pereira, 2009). Only thepertinent equations for the dual crop coefﬁcient approach and themodiﬁcation thereof are described here.
The evaporation coefﬁcient (Ke ) expresses the evaporation component of ETC . It attains a maximum value immediately following
precipitation or full cover irrigation, e.g., sprinkler irrigation, andbecomes minimal or zero when the soil surface is dry. However,the crop coefﬁcient (Kc = Kcb + Ke ) never exceeds a maximum value(Kcmax ), which is estimated from the relative humidity, wind speed
and crop height as:
Kc max = max
−45)]



3



, Kcb + 0.05

De,i = De,i−1 − (Pi − ROi ) −(3)

where RHmin represents the mean values of daily minimum relative
humidity during the mid- or late season growth stage (%), u2 isthe mean value of daily wind speed at 2 m height during the midor late season growth stage (m/s) and ht is the mean plant height
during the mid- or late season stage (m). Kc max represents an upper
limit on evaporation and transpiration from the cropped surface,and reﬂects natural constraints on available energy. It ranges fromabout 1.05 to 1.3 when using the grass reference ET0 (Allen et al.,2005a).
However, most of the time the evaporation component of Kc (Ke )is reduced below its potential level due to the reduced availabilityof water for evaporation from the soil. Under these conditions Ke isestimated as:
Ke = Kr (Kcmax − Kcb ) ≤ few Kcmax(4)where Kr is the soil evaporation reduction coefﬁcient and its value
ranges from 0 to 1 and few is the exposed and wetted soil fraction(0.01-1).
When the soil surface is very wet, as happens during precipitation events, Kr = 1 (stage 1 evaporation; Ritchie, 1972). However, a
few days after a precipitation event, evaporation is reduced below
its potential rate (Kcmax −Kcb ) and Kr is less than 1, which represents
stage 2 of evaporation (Ritchie, 1972). During stage 2 evaporation,
Kr , is evaluated as:
Kr =TEW − De,i-1
0 ≤ De,i-1 ≤ TEW
TEW -REWTEW = 1000 fc − 0.5wp ZeE
Ii+ i + Tew,i + DPe,i
fw
few

(7)

where De,i- 1 is the cumulative depth of evaporation following complete wetting from the exposed and wetted fraction of the topsoil
at the end of day i-1 (mm), De,i is the cumulative depth of evaporation (depletion) following complete wetting at the end of day i(mm), Pi is precipitation on day i (mm), ROi represents precipitation runoff from the soil surface on day i (mm), which depends on
soil surface conditions and intensity and amount of precipitation.
However, for relatively ﬂat land and sandy soils RO can be assumed
to be negligible (Allen et al., 1998), and this is conﬁrmed by observations at the ﬁeld site. Ii is the irrigation depth that inﬁltrates into
the soil on day i (mm), Ei represents evaporation on day i (i.e., Ei = Ke
ETo) (mm), Tew,i is the depth of transpiration from the exposed andwetted fraction of the soil surface layer on day i (mm), which isassumed to be negligible for deep rooted crops (Allen et al., 1998;
Allen, 2000), DPe,i is the deep percolation loss from the topsoil layer
on day i when the soil water content exceeds ﬁeld capacity (mm).
The variable fw represents the fraction of the soil surface wettedby irrigation (0.01–1) and the variable few is the exposed and wetted
soil fraction (0.01–1), derived directly from fw and crop cover (fc ).
Drip irrigation applies water to only a small fraction of the soil surface, hence the calculation of evaporation coefﬁcient (Ke ) for drip
irrigation (both surface and subsurface) requires calculation of thedaily water balance for the fraction of the soil surface, which is bothwetted and exposed to sunlight (few ).

(5)

where TEW is total evaporable water (mm) and REW represents
readily evaporable water (mm). De,i-1 in Eq. (5) is the cumulative
depth of evaporation from the soil surface layer at the end of day
i-1 (mm), which is estimated by a daily water balance describedin Allen et al. (1998), and reproduced as Eq. (7) below. The TEW isestimated as:there are contrasting reports in the literature about Ze for different soils, especially for stage 2 evaporation (Ritchie, 1972). Chanzy
and Bruckler (1993) considered Ze equal to 0.05 m for evaporation
measurement from loam, silt clay loam and clay soils. Further complicating the issue, Burt et al. (2005) reported that the Kr values
obtained by FAO-56 with Ze = 0.1 m were similar to those measured
by Chanzy and Bruckler (1993). Allen et al. (2005b) used a Ze of
0.15 m for sand, attempting to account for deeper drying depths
in the relatively hot climate of Imperial Valley. Torres and Calera(2010) observed that soil evaporation continues even below the0.15 m soil depth and reported the maximum evaporation depth
to be 0.2 m for sandy loam to loam soils. Hence, there is no clear
understanding in the literature about the maximum depth of soil
contributing to evaporation. Since, we deal with a range of soils andheterogeneity conditions in this study, we use a common value of0.15 m to have a ﬁxed volume of soil for all scenarios. The dailywater balance in the top soil layer is estimated according to Allenet al. (1998, Eq. 77), as:

1.2 + [0.04 (u2 − 2) − 0.004 (RHmin

 ht 0.3  

191

(6)

where  fc is the water content at ﬁeld capacity (mm),  wp represents
the water content at a wilting point (mm) and Ze is the evaporating depth (m), or the soil depth from which evaporation draws
water, taken as 0.15 m. This is the upper limit of Ze reported inAllen et al. (1998). The evaporating depth is reported to vary withthe texture of the soil, being smaller (0.1 m) in coarse soils andlarger (0.15m) in heavy textured soils Allen et al. (1998). However,

2.2. Proposed modiﬁcation of FAO-56
Eq. (7) reﬂects irrigation applied to the soil surface and inﬁltrating through the surface layer, as illustrated in Fig. 1A (fromAllen et al., 1998). Under subsurface drip irrigation (SDI), irrigation water does not inﬁltrate (Ii ) through the soil surface, but isapplied at a speciﬁed depth in the soil and, consequently, moves inall directions depending upon the soil hydraulic properties (Fig. 1B).
Therefore, only a fraction of the irrigation depth (Ii ) travels towards
the evaporation zone (deﬁned as the top 0.10 to 0.15 m soil depth
in Allen et al., 1998) due to capillary action, which depends on thesoil type, soil heterogeneity, the initial water content, the hydraulicgradient acting on the soil surface, irrigation depths, root water
uptake, the dripper discharge rate, and a burial depth of the drip
line. Hence, there is a need to deﬁne the fraction of the irrigation
depth that is exposed to evaporation (fI,Es ) under SDI. Incorporating

192

V. Phogat et al. / Agricultural Water Management 178 (2016) 189–200

Fig. 1. Water balance of soil surface layer, as presented in FAO-56 (Eq.(7)) (from Allen et al., 1998) (A), and modiﬁed for SDI (Eq. (8)) (B).

0.5

θ (cm3cm-3)

0.4

Experimental
Fitted

0.3
0.2
0.1
0
1

10

100
1000
Suction h (cm)10000

100000

1

10

100

10000

1000001000

1.0E+00

K (m s-1)

1.0E-03

Fitted

1.0E-06
1.0E-09
1.0E-12

impact of SDI on fw . In terms of the evaporation term, the only
impact of SDI is on few , which is derived from fw . Consequently
there is no need to modify the evaporation term of Eq. (8), rather
just to account for the impact of SDI on fw , and therefore on few .
However, it should be noted that fw is assumed to be equal to 1 forrainfall (Allen et al., 1998).
Allen et al. (2005a,b) proposed an extension of evaporation
estimation involving separate prediction of contribution from precipitation and from the wetted and exposed fraction. In such casethe proposed modiﬁcation for SDI conditions would be associated with the irrigation term only. The modiﬁed equation for
the extended procedure would be similar to the above equation(Eq. (8)), while all other variables would remain similar to those
explained in Allen et al. (2005a,b). However, for the comparisonof the existing and modiﬁed procedures for the estimation of ET
components, we use an earlier version (Allen et al., 1998) due to its
wider acceptability even under partially wetting irrigation conditions (Flumignan et al., 2011; Fandiño et al., 2012; Paço et al., 2012;
Martins et al., 2013; Cancela et al., 2015).

1.0E-15

2.3. Estimation of the fI,Es and fw fractions for the ﬁeld site

1.0E-18
Fig. 2. Measured and ﬁtted (van Genuchten, 1980) relationships between volumetric water content () and pressure head (h); and a predicted relationship between
hydraulic conductivity (K) and pressure head (h) for the 0–15 cm soil layer.

this consideration into FAO-56, Eq. (7) can be modiﬁed for SDI as
follows:
De,i = De,i−1 − (Pi − ROi ) −Ii × fI,Es
E+ i + Tew,i + DPe,i
few
fw

(8)

where Ii is the applied irrigation depth (mm) and fI,Es represents
the fraction of the irrigation depth that moves to the evaporation
zone. Hence, fI,Es represents the fraction of the irrigation depth thatis exposed to evaporation in the evaporation zone, and is 1 for all
above ground irrigation systems, but ranges from 0 to 1 for SDI. This
fraction will also impact the fraction of the soil surface wetted byirrigation (fw ), and therefore the fraction exposed and wetted (few ).
All of the above fractions are depicted in Fig. 1B.
SDI impacts evaporation as described in Eq. (8) in two ways, atthe irrigation input term (Ii /fw ) and at the evaporation term (Ei /few ).
The impact on the irrigation input term is in the proportional reﬁlling of the evaporation zone by irrigation, and thus a fractional term
(fI,Es ) has been introduced to account for this, in addition to the

In this investigation HYDRUS-2D was employed to computethe potential fI,Es and fw for SDI in a vertical spatial domain of
335 × 100 cm. This domain was adopted based on the vine spacing in a ﬁeld experiment conducted with Chardonnay wine grapes
under subsurface drip (SDI) in the Markaranka vineyard (34.08◦ S
and 139.87◦ E), located near Waikerie in South Australia. Moredetails about the experimental layout, irrigation design, and water
applications are given in Section 2.5 below and in Phogat et al.
(2016, under review), in which the HYDRUS-2D model was calibrated and validated for two consecutive wine grape seasons. The
same soil hydraulic and drip design parameters as in the ﬁeld experiment are used in this study to compute fw and fI,Es for SDI.
The soil hydraulic parameters for the experimental site were
estimated from measured values of the water content-pressure
head relationship. Water content-pressure head relations were
measured using a tension plate (for pressure heads larger than−100 cm) and on a pressure plate (for pressures heads smaller than−100 cm down to −15,000 cm) apparatus on undisturbed soil coresamples (Ford, 1997) taken at different depths (0–15, 15–30, 30–60
and 60–100 cm) at 4 locations within the trial site, and averaged
between the 4 locations for each depth to represent the entire ﬁeld
site. The van Genuchten-Mualem constitutive relationship (vanV. Phogat et al. / Agricultural Water Management 178 (2016) 189–200

193

Fig. 3. Computational domain, spatial discretization and distribution of different soil horizons used for HYDRUS-2D simulation of the ﬁeld site.

Genuchten, 1980) was ﬁtted to measured soil water retention data
and used to predict the unsaturated hydraulic conductivity function. Resulting -h and K-h relationships are depicted in Fig. 2 for
the 0–15 cm soil depth.
The saturated hydraulic conductivity (Ks) and bulk density werealso measured on the undisturbed soil cores following standard
procedures (Klute, 1986). Estimated values of soil hydraulic parameters for different depths at the ﬁeld site are given in Table 1
and were utilized as input parameters in HYDRUS-2D. Trenching or ripping activities associated with installation of SDI induce
mixing of the soil directly above the drip line. Hence, averagevalues of hydraulic parameters of the two upper layers (0–15 cm
and 15–30 cm) were considered for that region (30 cm × 30 cm) torepresent the ﬁeld conditions. The computational domain and its
spatial discretization, as well as the distribution of soil horizons at
the ﬁeld site are shown in Fig. 3. Although the soil type description
for all layers below the depth of 15 cm is the same (loamy sand),different hydraulic parameters were estimated based on laboratory measurements on undisturbed core samples. More details on
parameterization, initial and boundary conditions, calibration andvalidation of HYDRUS-2D are given in Phogat et al. (2016 underreview).
The transport domain was divided into two regions for massbalance calculations, the ﬁrst region representing the evaporation
zone extended from the soil surface to 15 cm (0–15 cm) soil depth,
and the second region representing the remainder of the rootzone
extended from 15 cm to 100 cm soil depth. The initial water content varied, based on measurements taken at the ﬁeld site using
calibrated Theta probes, from 0.05 cm3 cm−3 at the soil surface to0.17 cm3 cm−3 at the bottom of the proﬁle. These water contents
match with the measured values from the soil cores. Since the goalof simulations was to assess the internal distribution of irrigationwater within the two soil regions, a single irrigation applicationof 5 mm (approximately equal to the average amount of irrigationin the ﬁeld experiment) was simulated, and the volume of water
entering the evaporation zone was observed 24 h after the irrigation. Irrigation lasted for 4.1875 h, and the remaining time allowed
for redistribution of the water applied. A similar procedure wasadopted by Skaggs et al. (2004) and Kandelous and Šimůnek (2010)
to examine the wetting front pattern under SDI in sandy loam andclay loam soils, respectively.
The irrigation system design is described in Section 2.5 below
and in Phogat et al. (2016 under review). The difference between
the initial and ﬁnal volumes of water (after 24 h) in the ﬁrst region(0–15 cm) is the amount of irrigation water that entered into theevaporation zone, which was then expressed as a fraction of thewater applied. Hence, fI,Es was estimated as the potential contribution of a single irrigation to the evaporation zone (0–15 cm soil
depth). The simulated spatial extent of changes in water content(wetted length) was observed at the same time at the soil surface. The wetted length decreased from the bottom (at the 15 cm
depth) to the top (at the soil surface, 0 cm) of the evaporation zone
in a semi-circular fashion. Thus, the potential fraction of the soil
surface wetted by irrigation (fw ) was estimated by dividing thewetted length with the distance between drip lines (or plant row
spacing). Field measurements of Skaggs et al. (2004) indicate thatclosely placed drippers (30–40 cm) produce a continuously wetted
soil surface of a uniform width above the drip tape. However, an
exact surface area wetted by individual drippers may need to be
estimated in other situations.

2.4. Impact of soil texture, soil heterogeneity, irrigation depth,and drip design parameters on the fw and fI,Es fractions
Using the same computational domain and drip design parameters (drip line depth, emitter discharge, and spacing) as used forexperimental conditions, the potential fw and fI,Es fractions were
estimated in the same way as described above for different uniform soil textures by changing the soil hydraulic parameters in
the domain. Similarly, the impact of soil heterogeneity was evaluated by changing the soil hydraulic properties and layering within
the domain. We evaluated the impact of two (Duplex) and three(Triplex) distinct layers of varied textures in the soil proﬁle. A soil
containing two distinct horizons of contrasting textures is known asa Duplex soil (Chittleborough, 1992). In the simulation, a loamy or
sandy topsoil (0–30 cm) abruptly overlying much heavier textured
subsoil (30–100 cm) was modelled. Such soils represent between
half and two-thirds of the agricultural land in Australia (Tennant
et al., 1992). Similarly Triplex soils show 3 distinct soil texturallayers (0–15, 15–30, 30–100 cm) in the soil proﬁle. The hydraulicparameters for these uniform soils and different heterogeneous layers in Duplex and Triplex soils were adapted from the HYDRUS
database and are shown in Table 1. These parameters have beenused in many similar studies (e.g. Assoluine, 2002; Cote et al., 2003;
Gärdenäs et al., 2005; Lazarovitch et al., 2009; El-Nesr et al., 2014)
evaluating water movement and solute transport problems for drip
irrigation systems. Two combinations of Duplex (sandy loam-clay
loam and sandy loam-clay, respectively, in 0–30 and 30–100 cm soil
depths) and Triplex (loamy sand-sandy loam-clay loam and loamy
sand-sandy loam-clay, respectively, in 0–15, 15–30 and 30–100 cm

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V. Phogat et al. / Agricultural Water Management 178 (2016) 189–200

Table 1
Soil hydraulic parameters for the van Genuchten-Mualem function (van Genuchten, 1980) and the bulk density for different soil layers in a) ﬁeld site soil, b) uniform soils,
and c) heterogeneous soils.
Depths (cm)Soil texture

Soil hydraulic parameters

Bulk density(g cm−3 )r (cm3 cm−3 )s (cm3 cm−3 )␣ (cm−1 )nKs (cm d−1 )la) Field site soil (measured)
0–15
Sand
15–30
Loamy sandLoamy sand
30–60
Loamy sand
60–100

0.04
0.04
0.05
0.05

0.41
0.39
0.38
0.37

0.03
0.03
0.04
0.04

2.09
2.29
1.70
1.62

561.60216.00259.20172.80

0.52
0.56
0.41
0.38

1.50
1.57
1.41
1.44

b) Uniform soils (from literature)
0–100
Loamy sand
0–100
Loam
0–100
Clay loam

0.057
0.078
0.095

0.41
0.43
0.41

0.124
0.036
0.019

2.28
1.56
1.31

350.2
24.96
6.24

0.5
0.5
0.5

–
–
–

c) Heterogeneous soils: i) Duplex (from literature)
Sandy loam
0.065
0–30
Clay loam
0.095
30–100

0.41
0.41

0.075
0.019

1.89
1.31

106.1
6.24

0.5
0.5

–
–

Heterogeneous soils: ii) Triplex (from literature)
Loamy sand
0.057
0–15
Sandy loam
0.065
15–30
0.068
30–100
Clay

0.41
0.41
0.38

0.124
0.075
0.008

2.28
1.89
1.09

350.2
106.1
4.8

0.5
0.5
0.5

–
–
–

soil depths) were studied. Initial water contents were assumed tovary between air dry at the soil surface and ﬁeld capacity at thebottom of the domain in all these simulations.
The impact of different irrigation depths (5, 7.5, 10, 12.5 and15 cm) and SDI design parameters, i.e., different discharge rates(1.6, 2, 2.5, 3 and 4 L h−1 ), different drip line depths (0, 10, 15, 20,
25 cm soil depth), and drip line spacings (100, 200 and 300 cm),on the evaporation fraction (fI,Es ) and the wetted fraction (fw ) was
also evaluated in different uniform soil textures in the same verticalspatial domain shown in Fig. 3, by changing the corresponding irrigation depth, discharge rate, and emitter placement. Soil hydraulicproperties for uniform soil textures (loamy sand, loam and clayloam) are shown in Table 1. Initial water contents for these simulations were also assumed to vary between air dry at the soil surface
and ﬁeld capacity at the bottom of the domain.
2.5. Comparison of ET components estimated by the original andmodiﬁed FAO-56 procedures
The original and modiﬁed FAO-56 procedures were used toestimate annual ET components for the experimental ﬁeld site in
the SDI irrigated Chardonnay wine grape vineyard at Markaranka(34.08◦ S and 139.87◦ E), based on 2010–11 and 2011–12 climate
data. The vineyard was planted in November 2004 at a vine spacing of 2.5 m and row spacing of 3.35 m. The SDI drip lines wereplaced 25 cm deep and 25 cm away from the vine row. The irrigation system consisted of a pressure compensated drip system(Toro Drip-In® Rootguard® ) with emitters at a spacing of 40 cm
with a discharge rate of 1.6 L h−1 . The soils at the site are predominately light textured, ranging from sand to loamy sand, withthe sand content varying from 84 to 91% and small fractions ofclay (9–13%) and silt (0–3%). Weather data were collected at an
automated weather station located at Qualco, 4 km from the experimental site. The climate is characterized as dry, with warm to hotsummers and mild winters. Total rainfall during the two experimental periods from 22 September 2010 to 30 June 2011 and from 7
September 2011 to 30 June 2012 was 338 mm and 236 mm, respectively. Grass reference evapotranspiration (ET0 ) estimated using the
FAO Penman-Monteith equation (Allen et al., 1998) during 2010–11
and 2011–12 growing seasons was 904 mm and 1055 mm, respectively. Mild frost conditions occurred during the winter months.
Local soil and climate parameters used to estimate Es , Tp and
ETC for wine grapes for two seasons following the FAO-56 DCC

approach are given in Table 2. Tabulated crop coefﬁcients forthe initial (Kcbini ), mid (Kcbmid ) and late (Kcbend ) seasons for wine
grapes (Table 2) were taken from Allen and Pereira (2009) for a
mid-density vineyard (Fceff = 0.5). However, Kcbmid and Kcbend were
adjusted depending on the prevailing minimum relative humidity,
average wind speed and plant height as described in Allen et al.
(1998). The adjusted values are given in Table 2.
The soils and irrigation water had salinity below threshold levels, hence osmotic stress due to salinity was not considered. Total
available water (TAW) was estimated from the type of soil in eachhorizon (Table 1) and rooting depth (Zr ) (Table 2). The initial waterdeﬁcit was estimated from measured water content data from thedifferent soil layers (0–15, 15–30, 30–60, 60–100 cm) of the rootzone. The ﬁeld capacity ( fc ) values for different layers are given in
Table 2. The residual water content ( r , Table 1) was assumed asmoisture content at wilting point ( wp ) for the calculation of TAW
which is a common approximation (van Genuchten, 1980). The  fc  wp for different layers falls within the range reported in FAO-56(Allen et al., 1998) for these soils. The readily available water (RAW)in the Zr was estimated as per the equation given in FAO-56 (Allenet al., 1998):
RAW = pTAW

(9)where, p is the average fraction of TAW that can be depleted fromthe root zone before moisture stress. It was estimated daily following a numerical approximation (Allen et al., 1998) adjusting p fordaily ETC :p = pTable22 + 0.04 (5 − ETC )(10)

where, pTable 22 value (0.45) for wine grape was taken from Allenet al. (1998). The estimated values of p during 2010–11 and2011–12 varied from 0.33–0.64 and 0.35–0.65, respectively.
The readily evaporable water (REW) was shown to vary from 8
to 9 mm for the ﬁeld soils (Stevens et al., 2012). Evaporation takes
place from the exposed and wetted soil surface (few , Eqs. (4), (7) and(8)) in drip irrigation systems, where only a fraction of the soil surface is wetted by irrigation application. Nonetheless, for orchards(e.g., wine grape) where fw is exposed to large evaporative energy(Bonachela et al., 2001) and signiﬁcant ventilation (Allen et al.,2005a), few = fw . However, for rainfall the effective surface exposedto evaporation (few ) is set equal 1-fc (Allen et al., 2005a), where, fc
is the fraction of the soil surface shaded by the crop. Therefore, theV. Phogat et al. / Agricultural Water Management 178 (2016) 189–200

195

Table 2
Values of different parameters used to estimate daily transpiration (Tp ) and daily evaporation (Es ) for wine grape for the ﬁeld site following the original and modiﬁed FAO-56
DCC approaches.
Parameter

Value

Parameter

Value

Lini a,c
Ldev a,c
Lmid a,c
Llate a,c
 fc (0–15 cm)c
 fc (15–30 cm)c
 fc (30–60 cm)c
 fc (60–100 cm) c
fw , SDIe
fw , RaincfI,Es b,e
RAW (mm)c
TAW (mm)c
TEW (mm)c
REW (mm)c

15
30
100
90
0.09
0.10
0.11
0.12
0.22
1
0.42
34
60
12
8

Plant height h (m)cRooting depth Zr (m)a,c
Vineyard density (Fceff )a,c
Evaporable depth Ze (m)a,d
Mid-season Min RH (%) (2010−11)c
Mid-season Min RH (%) (2011−12)a,c
Av. Wind speed (m/s) (2010−11)c
Av. Wind speed (m/s) (2011−12)a,c
Kcb ini d
Kcbmid dKcbend d
Kcb midadj (2010−11)c
Kcb midadj (2011−12)a,c
Kcb endadj (2010−11)c
Kcb endadj (2011−12)a,c

1.5
1.0
0.5
0.15
27.0
23.0
3.65
3.88
0.20
0.65
0.5
0.76
0.78
0.61
0.63

a

Also used in uniform soils (loamy sand, loam and clay loam).
Used only in the modiﬁed FAO-56 approach.
cMeasured or estimated at ﬁeld site.
dTaken from literature.
e
Simulated using Hydrus-2D.
bdaily few fraction during the crop season was estimated dependingon the irrigation or rainfall event as outlined in Allen et al. (1998):

few = min(1 − fc , fw )(11)

where, fc is the fraction of the soil surface shaded by the crop. The
variation of fc during the vine growth was observed to vary from0.01 to 50%. The maximum fraction of ground cover was attained
during the mid-season of vine growth. The experimental area was
kept weed free by adopting proper weed control operations during the experimental period, to minimise water losses throughunwanted vegetation growth.
The values of fw and fI,Es fractions (Table 2) were estimatednumerically for ﬁeld conditions described in Section 2.3. However, values of these (fw and fI,Es ) and other empirical fractionsand variables commonly used in FAO-56 may differ under cropped
conditions. These values (fw and fI,Es ) and other parameters shownin Table 2 were used to estimate Es , Tp and ETC for wine grapes
under ﬁeld conditions for two seasons using the original and modiﬁed procedures. In the original FAO-56 procedure the parameters
shown in Table 2 were used except the fI,Es fraction.
A similar comparison between the original and modiﬁed procedures for wine grape ET components (Es , Tp and ETC ) was also
made for theoretical uniform soils (loamy sand, loam, clay loam;
Table 1) in order to understand the impact of soil texture on simulated results due to incorporation of the fraction of irrigation depth
moving to the evaporation zone (fI,Es ) into the FAO-56 procedure.
The values of various soil parameters and various fractions used inthis estimation in different soils are shown in Table 3. Crop related
and climate related data (marked in parenthesis of Table 2) weretaken from the ﬁeld condition dataset for 2011–12 season (Table 2).
Total available water (TAW) in the top 1 m of the soil proﬁle in loamy
sand, loam and clay loam soils was estimated to be 40, 120 and
190 mm, respectively (Table 3). The REW and TEW values for these
theoretical soils were taken from Allen et al. (1998). The values ofthe fw and fI,Es fractions estimated in the previous section for uniform textures (loamy sand, loam and clay loam) given in Table 3
were used in the modiﬁed procedure. However, for the estimationof ET components by the original procedure, all parameters were
the same except for the fI,Es fraction (Table 3), which is not requiredin the original FAO 56 procedure.

Table 3
Values of different parameters used to estimate daily transpiration (Tp ) and daily
evaporation (Es ) for wine grape in hypothetical uniform soils (loamy sand, loam andclay loam) following the original and modiﬁed FAO-56 DCC approaches.
Parameters

 fc c wp cfw , SDId
fw , Rainb
fI,Es a,d
TAW (mm)c
RAW (mm)c
TEW (mm)c
REW (mm)c

ValuesLoamy sand

Loam

Clay loam

0.1
0.06
0.03
1
0.05
40
25.5
12
6

0.20
0.08
0.07
1
0.16
120
73.4
19
9

0.28
0.09
0.09
1
0.17
190
116.2
24
10

a

Used only in the modiﬁed FAO-56 approach.
Measured at ﬁeld site.
Taken from literature.
dSimulated using Hydrus-2D.
bc

3. Results and discussion
3.1. Estimation of the fI,Es and fw fractions for the ﬁeld site
Results of HYDRUS-2D simulations of water movement underthe ﬁeld conditions and selected theoretical scenarios are presented in Table 4 and Fig. 4. In the ﬁeld soil (s-ls-ls-ls), simulation
results indicated that more than one-third of applied irrigationentered the evaporation zone (fI,Es = 0.42), leading to a 0.22 wetted
fraction (fw ) at the soil surface when the initial moisture content
varied from air dry at the soil surface to ﬁeld capacity at the bottomof the domain (top of Table 4, top right of Fig. 4). However, the fI,Es
and fw fractions varied greatly depending upon the initial moisture
content in the soil (Table 4). The fraction of irrigation water entering
the evaporation zone (fI,Es ) was reduced by a third under uniformly
dry initial soil conditions (0.05–0.05), and increased slightly when
initial soil conditions were wetter (0.08–0.20). Skaggs et al. (2010)
also observed increased spatial spreading with higher antecedentwater content after 24 h of simulation due to reduction in poresavailable to hold the applied water. Similarly, Provenzano (2007)
also reported higher spatial distribution of applied water under SDI
after a ﬁxed time in response to greater initial moisture content.
The initial water content had a similar impact on the fraction of thewetted surface (fw ).

196

V. Phogat et al. / Agricultural Water Management 178 (2016) 189–200

Fig. 4. Water content distribution and the wetted soil surface fraction (fw ) in different soils as simulated by HYDRUS-2D. The letters in parenthesis represent the texturalclass (s = sand, ls = loamy sand, sl = sandy loam, l = loam, cl = clay loam, c = clay) in the soil proﬁle.

Table 4
Effect of soil texture, soil stratiﬁcation, and initial water content on the evaporation
fraction (fI,Es ) and the wetted surface fraction (fw ), as simulated using Hydrus 2D.
TextureInitial water content

fI,Es efw es-ls-ls-ls
s-ls-ls-ls
s-ls-ls-ls

0.05–0.17a
0.05–0.05b
0.08–0.20c

0.42
0.28
0.44

0.22
0.18
0.30

b) Uniform soil texturels
Loamy sand
Loam
l
cl
Clay loam

0.06–0.10d
0.08–0.20d
0.10–0.29d

0.05
0.16
0.17

0.03
0.07
0.09

c) Soil heterogeneity
DuplexDuplexTriplexTriplex0.10–0.29d
0.10–0.34d
0.06–0.29d
0.06–0.34d

0.16
0.19
0.02
0.01

0.12
0.16
0.00
0.00

a) Field soils
Sand-loamy sandSand-loamy sandSand-loamy sand

sl-cl
sl-c
ls-sl-clls-sl-ca

Initial water content based on measured values.
Initial water content was low throughout the proﬁle.
cInitial water content varied from slightly wetter than air dry at the surface tohigher than ﬁeld capacity at the bottom of the proﬁle.
dInitial water content varied from air dry at the surface to ﬁeld capacity at thebottom of the proﬁle.
eSimulated using Hydrus-2D.
b

3.2. Impact of soil texture and hydraulic properties on the fI,Es
and fw fractions
HYDRUS-2D simulations indicate that the fI,Es fraction in homogeneous and isotropic light textured (loamy sand) soil was minimal(0.04) for the same irrigation system parameters as used at the ﬁeld
site (Table 4). However, in medium- and heavy-textured soils fI,Es
increased 4 times compared to light-textured soils. This implies
that light textured soils are less prone to evaporation losses under
SDI as compared to medium and heavy textured uniform soils. It
is well known that capillary rise in medium- and heavy-textured
soils is always higher than in light-textured soils due to their higher
micro porosity. The fraction of the wetted surface (fw ) was higher
in clay loam (0.09) than in loam soils (0.07) (Table 4 and Fig. 4).
HYDRUS simulations also indicated that soil heterogeneity had
a pronounced impact on the fraction of irrigation water lost toevaporation. Amongst the duplex soils generally encountered inAustralia, the sandy loam-clay combination had a higher surface
wetness and evaporation fraction than other soil proﬁles (Table 4).
When installed at a depth of 25 cm (as at the ﬁeld site), the SDI was
located in the light-textured soil just above the interface between
the light and heavy-textured soils. In this proﬁle, the heavy textured

soil acted as a physical barrier to downward water movement as
the hydraulic gradient wasn’t sufﬁcient to overcome the boundary effect. Consequently the tendency of water movement towards
the soil surface and laterally was increased, which led to a higher
fraction of applied water reaching the evaporation zone. Similar observations were recorded by Finger (2012) for duplex soils
with low permeability subsoils; the subsoil restricted downward
movement, allowing water to spread laterally and upwards undersubsurface irrigation.
Another modelled scenario (Triplex) involved a relatively coarse
soil at the surface (0–15 cm) underlain by a ﬁner soil (15–30 cm)(where the SDI was located), and a heavy soil below 30 cm. This
scenario effectively reduced the evaporation fraction and restrictedwater movement to the soil surface because the soil interface at a
depth of 15 cm acted as a barrier to water movement towards thesurface. Hence, the presence of contrasting soil layers with different hydraulic parameters in the proﬁle may act as a physical barrier
and restrict water movement, and the location of the interfaces
relative to the drip line depth can dramatically inﬂuence evaporation ﬂuxes. These results suggest that a detailed soil analysis
is important before designing subsurface drip systems, especiallyto determine the optimum installation depth (see below), so that
undesirable water losses (Es ) can be minimized.
3.3. Impact of irrigation depth and drip design parameters on thefI,Es and fw fractions
The impact of applying different irrigation depths (5, 7.5, 10,12.5, and 15 cm) in different soil textures on the fI,Es and fw fractions
is shown in Fig. 5. While the fI,Es fraction gradually decreased withan increase in the irrigation depth in loamy sand, in loam it initially
increased up to an irrigation depth of 10 cm and then decreased.
In clay loam the fI,Es fraction increased with an increase in the irrigation depths, although the magnitude of the increase gradually
decreased with larger irrigation depths. A larger extent of gravity
compared to capillary forces in the coarse textured soils reduced
the fraction of upward movement of applied irrigation water. On
the other hand, the fw fraction showed an increasing trend with anincrease in irrigation depths in all soils. Average values of the fw
fraction were about 2.5 times higher in loam and clay loam thanin loamy sand (Fig. 5), indicating a signiﬁcant role of soil texture inevaporation losses from the soil.
The depth of the drip line placement in the soil had a pronounced
impact on simulated evaporation ﬂuxes and wetted surface fraction in different soils (Fig. 6). A drip line placed 10 cm deep in a

V. Phogat et al. / Agricultural Water Management 178 (2016) 189–200

0.25

197

0.20
ls

0.20

l

0.15

0.15

fI,Es

ls

0.10

fw

l

0.10

cl

cl
0.05

0.05
0.00

0.00
5

7.5
10
12.5
Irrigation depth (cm)

15

5

7.5

10
12.5
Irrigation depth (cm)15

Fig. 5. Impact of irrigation depths on the fraction of irrigation contributing to evaporation (f1,Es ) and the fraction of the soil surface wetted by irrigation (fw ) in different soils(ls = loamy sand, l = loam, cl = clay loam) as simulated by HYDRUS-2D. The initial water content varied from dry at the surface to ﬁeld capacity at the bottom in all simulations.

0.80

0.20
ls

0.60

l

cl

0.12

0.40

cl

fw

fI,Es

ls

0.16

l

0.08
0.20
0.04
0.00
0

10

20
30
Emitter depth (cm)

0.00

40

0

10

20
30
Emitter depth (cm)

40

0.20

0.10

0.16

0.08

0.12

ls

0.08

l

0.04

cl

0.00
1.6

2
2.5
3
Discharge rate (L/h)

4

0.06

fw

fI,Es

Fig. 6. Impact of the emitter depth on the fraction of irrigation contributing to evaporation (f1,Es ) and the fraction of the soil surface wetted by irrigation (fw ) in different soils(ls = loamy sand, l = loam, cl = clay loam) as simulated by HYDRUS-2D. The initial water content varied from dry at the surface to ﬁeld capacity at the bottom in all simulations.

0.04
0.02
0.00
1.6

2
2.5
3
Discharge rate (L/h)

4Fig. 7. Impact of the emitter discharge rate on the fraction of irrigation contributing to evaporation (f1,Es ) and the fraction of the soil surface wetted by irrigation (fw ) in
different soils, as simulated by HYDRUS-2D (initial water content varied from dry at the surface to ﬁeld capacity at the bottom in all simulations).

uniform soil had 25 to 64% of applied water available for evaporation depending on the soil texture, which was slightly lower thana dripline laid out at the soil surface (27–78%). Placing a drip line
deeper than 10 cm gradually reduced the evaporation ﬂux. The fI,Es
fraction decreased by about two thirds for drip placed at a depthof 20 cm compared to drip on the soil surface in loamy sand, while
this reduction was just over half in clay loam. Placing the drip 40 cm
deep reduced the evaporation fraction to almost zero in uniform
and isotropic soils. However, soil properties and soil heterogeneity
play a key role in the spatial distribution of irrigation water. It is
expected that drip placed at a depth of 40 cm is likely to increasewater losses via deep percolation. Similar observations have been
made in other studies as well (Evett et al., 1995; Diamantopolous
and Elmaloglou, 2012). Hence, a trade-off exists between reducing
evaporation losses and increasing deep percolation losses undersub-surface drip irrigation. A similar effect of the drip placementon the wetted fraction (fw ) was observed (Fig. 6). However, theextent of the reduction in the evaporation fraction (fI,Es ) was higher
than the corresponding reduction in the wetted fraction (fw ) as thedepth of the drip line placement increased (Fig. 6). On the other
hand, applying the same quantity of water with different drip discharge rates showed little impact on fI,Es and fw within a given soil
type (Fig. 7), for example for loam soils (green bars) fI,Es = 0.18-0.19,
fw = 0.07.
The drip line spacing strongly inﬂuenced the wetted fraction (fw )of the soil surface (Fig. 8). When the drip line spacing was reducedby two thirds, the wetted fraction increased proportionally, as thetotal surface area for one drip line (a denominator in fraction calculations) was reduced. Hence, the surface drip with 100 cm spacing
wetted about 60% of the soil surface, whereas fw decreased to 20%
when the drip spacing increased to 300 cm. This proportional relationship was roughly maintained as the dripline depth increased,
until fw approached zero for the 35 cm depth.

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V. Phogat et al. / Agricultural Water Management 178 (2016) 189–200

estimated by the DCC approach (up to 4%). This impact would ultimately transmit to the estimation of basal crop coefﬁcients, net
irrigation and irrigation scheduling, and could affect the growthand yield of the crop.
Based on the results reported above it is recommended that the
impact of sub-surface irrigation on the movement of water into theevaporation zone be incorporated into the existing FAO-56 procedure to improve estimates of ET components for crops under
SDI. We have described and demonstrated a potential method forincorporating this component, using the fraction of irrigation water
contributing towards evaporation losses (fI,Es ). However, the valuesof these fractions can vary in more complex and highly dynamic
cropped conditions.

0.70
0.60

100 cmfw

0.50

200 cm0.40

300 cm

0.30
0.20
0.10
0.00
0

5

10

15
20
25
dripline depth (cm)

30

35

40

4. Conclusions

Fig. 8. Effect of the drip line spacing on the wetted surface fraction (fw ) for different
emitter depths in a loam soil, as simulated by HYDRUS-2D (water content varied
from dry at the surface to ﬁeld capacity at the bottom in all simulations).

Optimization of irrigation is necessary for managing scarcewater resources and for enhancing the water productivity and efﬁciency of irrigated systems. This requires a reduction in undesirable
losses of water due to evaporation, especially under controlled
irrigation with subsurface drip. Evaporation under SDI can be effectively estimated if an accurate evaluation of the fraction of irrigationwater entering the evaporation zone can be made. This study estimated potential values of this fraction for different soils, irrigation
depths and drip design parameters and integrated this into the
FAO-56 DCC approach for the estimation of evaporation and ET partitioning for SDI of wine grapes. This method can further improve
our understanding of evaporation losses under highly water efﬁcient irrigation systems, particularly in sparsely vegetated crops.
As an improvement to the existing FAO-56 procedure, whichassumes that all irrigation water contributes to evaporation losses,
we have proposed to incorporate into the existing DCC procedurea variable which deﬁnes the fraction of irrigation water contributing towards evaporation losses (fI,Es ). We have demonstrated how
an understanding of the impact of soil texture, soil heterogeneity,
irrigation depth, and design parameters of an irrigation system on
fI,Es can help in developing an appropriate irrigation system design
according to soil parameters at the site, consequently reducing
evaporation under ﬁeld conditions. Annual estimation of evaporation and transpiration ﬂuxes under SDI of wine grapes showed
considerable variation in these ﬂuxes. The overestimation of annual
evaporation using the existing FAO-56 DCC approach ranged from
5 to 6% under conditions at the ﬁeld site over two seasons. However, this over-estimation was shown to increase further (up to18%) for different soil textures, and may vary under other crop andclimatic conditions. Understanding these variations can be helpfulwhen devising efﬁcient irrigation scheduling for crops under SDI,and can assist in reducing undesirable water losses through evapo-

A strong correlation (R2 = 0.92) was observed between fI,Es and
fw as a function of soil properties (data from Table 1) whereas thecorrelation was moderately good (R2 = 0.66) for drip design parameters (data from Figs. 6 and 7), as shown in Fig. 9. These results
reinforce the conclusion made above that a comprehensive analysis of soil and drip design parameters is important before drip
systems are installed, in order to minimise irrigation losses due toevaporation.
3.4. Comparison of the modiﬁed approach with FAO-56 forestimating seasonal evaporation
The modiﬁed FAO-56 procedure incorporating the fI,Es fractions according to Eq. (8) was compared with the existing FAO-56
approach for estimating annual ET components for a grapevine
irrigated with SDI. Annual evaporation (Es ) estimated using thestandard FAO-56 procedure was 208.7 mm and 184.2 mm during
the 2010–11 and 2011–12 seasons, respectively (Table 5). However,annual Es values estimated with the modiﬁed procedure amounted
to 197.9 mm and 173.3 mm during the 2010–11 and 2011–12 seasons, respectively. Average annual evaporation was thus slightly
overestimated (5–6%) using the standard FAO-56 procedure compared to using the modiﬁed procedure. However, this deviation inseasonal evaporation can increase further depending on the soil
texture. Predicted scenarios in uniform soils showed that the difference in seasonal Es between the original and modiﬁed FAO-56
procedures varied between 7 and 18% when soil texture increased
from loamy sand to clay loam (Table 5). Overestimation of theevaporation ﬂux had a depressing impact on the transpiration ﬂux

0.40

0.25

a) soil propertiesb) drip parameters

0.20

0.30

fw

fw

0.15
0.20

0.10
y = 0.63x - 0.004
R² = 0.92

0.10
0.00
0.00

0.20

fI,Es

0.40

y = 0.25x + 0.028
R² = 0.66

0.05

0.60

0.00
0.00

0.20

0.40
0.60
fI,Es

0.80

1.00

Fig. 9. Relationship between the fraction of the surface wetted (fw ) and the fraction of the irrrigation contribution to evaporation (f1,Es ) as inﬂuenced by a) soil characteristics
and b) drip design parameters, simulated by HYDRUS-2D.

V. Phogat et al. / Agricultural Water Management 178 (2016) 189–200

199

Table 5
Impact of the wetted (fw ) and evaporation (fI,Es ) fractions on the seasonal ET components for SDI-irrigated wine grape, estimated by the original FAO-56 procedure and themodiﬁed approach for two seasons in ﬁeld soil, and predicted scenarios for uniform soils using 2011–12 ﬁeld data.
Soil type

Wetted fraction (fw )a

Evaporation
fraction (fI,Es )a

Es (mm)ETC (mm)

Tp (mm)Field soil (2010–11)
Original FAO 56
Modiﬁed FAO-56
Over-estimation (%)

0.22
0.22

–
0.42

208.7
197.9
5.5

587.1
584.3
0.5

378.4
386.4
−2.1

Field soil (2011–12)
Original FAO-56
Modiﬁed FAO-56
Over-estimation (%)

0.22
0.22

–
0.42

184.2
173.3
6.3

532.8
530.4
0.5

348.6
357.0
−2.4

Uniform loamy sand soil (2011–12)
0.03
Original FAO-56
Modiﬁed FAO-56
0.03
Over-estimation (%)

–
0.05

99.6
93.0
7.2

472.8
471.8
0.2

373.2
378.8
−1.5

Uniform loam soil (2011–12)
Original FAO-56
Modiﬁed FAO-56
Over-estimation (%)

0.07
0.07

–
0.16

138.3
125.9
9.8

582.0
578.7
0.6

443.6
452.8
−2.0

Uniform clay loam soil (2011–12)
Original FAO-56
Modiﬁed FAO-56
Over-estimation (%)

0.09
0.09

–
0.17

159.5
135.0
18.2

647.1
641.4
0.9

487.6
506.4
−3.7

a

Simulated using Hydrus-2D.

ration. We believe that a procedural change in the estimation of Es
for the FAO-56 approach would help in improving the estimationof evaporation and transpiration under sparsely vegetated and SDIirrigated soil conditions, and that this information can be utilized
when developing better irrigation management practices for crops
under SDI. However, there is still a need to evaluate the impact ofthe proposed modiﬁcation on the evaporation losses under different crops, soils, and climatic conditions.

Acknowledgements
The work was conducted by the South Australian Research andDevelopment Institute, a member of the Wine Innovation Cluster
at the Waite Precinct in Adelaide, and is supported by Australiangrape growers and winemakers through their investment body,the Grape and Wine Research and Development Corporation, withmatching funds from the Australian Government. We would also
like to acknowledge the support of Treasury Wine Estates and theirstaff at the Markaranka vineyard for facilitating site access and support, and for installing the SDI trial used for this project. We thankthe editors and anonymous reviewers for their constructive inputs
during the review phase of the paper.

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