Agricultural Water Management 127 (2013) 74–84

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

Evaluation of water movement and nitrate dynamics in a lysimeter
planted with an orange tree
V. Phogat a,∗ , M.A. Skewes a , J.W. Cox a,b , J. Alam c , G. Grigson a , J. Šimůnek daSouth Australian Research and Development Institute, GPO Box 397, Adelaide, SA 5001, Australia
The University of Adelaide, PMB1, Glen Osmond, SA 5064, Australiac
Rural Solutions SA, GPO Box 1671, Adelaide, SA 5001, AustraliadDepartment of Environmental Sciences, University of California, Riverside, CA 92521, United Statesba r t i c l e

i n f oArticle history:
Received 10 October 2012
Accepted 26 May 2013
Keywords:
Modelling
Lysimeter
Drip irrigation
Fertigation
OrangeDeep drainage
Nitrate leachinga b s t r a c t
Adoption of high input irrigation management systems for South Australian horticultural crops seeks toprovide greater control over timing of irrigation and fertilizer applications. The HYDRUS 2D/3D model wasused to simulate water movement in the soil under an orange tree planted in a ﬁeld lysimeter suppliedwith 68.6 mm of irrigation water over 29 days. Simulated volumetric water contents statistically matchedthose measured using a capacitance soil water probe. Statistical measures (MAE, RMSE, tcal ) indicating thecorrespondence between measured and simulated moisture content were within the acceptable range.
The modelling efﬁciency (E) and the relative efﬁciency (RE) were in the satisfactory range, except RE at
day 19. Simulated daily and cumulative drainage ﬂuxes also matched measured values well. Cumulativedrainage ﬂux was 48.9% of applied water, indicating large water losses even under controlled water
applications. High drainage losses were due to light texture of the soil and high rainfall (70 mm) during
the experimental period. Simulated root water uptake was 40% of applied water.
The calibrated HYDRUS model was also used to evaluate several scenarios involving nitrate fertigation.
The numerical analysis of NO3 -N dynamics showed that 25.5% of applied fertilizer was taken up by theorange tree within 15 days of fertigation commencement. The rest of the applied NO3 -N (74.5%) remainedin the soil, available for uptake, but was also vulnerable to leaching later in the growing season. The
seasonal simulation revealed that NO3 -N leaching accounted for 50.2% of nitrogen applied as fertilizer,
and plant N recovery amounted to 42.1%. The scenario analysis further revealed that timing of a nitrogen
application in an irrigation event had little impact on its uptake by citrus in the lysimeter. However,slightly higher NO3 -N uptake efﬁciency occurred when fertigation was applied late in the daily irrigation
schedule, or was spread out across all irrigation pulses, rather than being applied early or in the middle.
Modelling also revealed that pulsing of irrigation had little impact on nitrate leaching and plant uptake.
Applying less irrigation (50% or 75% of ETC ) resulted in higher nitrate uptake efﬁciency. This study showedthat timing of water and fertilizer applications to an orange crop can be better regulated to enhance the
efﬁciency of applied inputs under lysimeter conditions.
© 2013 Elsevier B.V. All rights reserved.

1. Introduction
High frequency irrigation systems involve fastidious planningand complex designs, so that timely and accurate additions of waterand fertilizer can result in sustainable irrigation. At the same timethese production systems are becoming more intensive, in an effort
to optimise the return on expensive and scarce resources such as
water and nutrients. Advanced fertigation systems combine drip
irrigation and fertilizer application to deliver water and nutrients
directly to the roots of crops, with the aim of synchronising the∗ Corresponding author. Tel.: +61 8 83039567; fax: +61 8 8303 9473.
E-mail address: vinod.phogat@sa.gov.au (V. Phogat).
0378-3774/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.agwat.2013.05.017

applications with crop demands (Assouline, 2002), and maintaining the desired concentration and distribution of ions and waterin the soil (Bar-Yosef, 1999). Hence a clear understanding of water
dynamics in the soil is important for the design, operation, andmanagement of irrigation and fertigation under drip irrigation (Liet al., 2004). However, there is a need to evaluate the performance of these systems, because considerable localised leaching
can occur near the driplines, even under deﬁcit irrigation conditions(Hanson et al., 2008). The loss of nutrients, particularly nitrogen,from irrigation systems can be expensive and pose a serious threat
to receiving water bodies (Van der Laan et al., 2010).
Citrus is one of the important horticultural crops being grownunder advanced fertigation systems in Australia. Fertigation delivers nutrients in a soluble form with irrigation water directly into

V. Phogat et al. / Agricultural Water Management 127 (2013) 74–84

the root-zone, thus providing ideal conditions for rapid uptake ofwater and nutrients. Scholberg et al. (2002) demonstrated that
more frequent applications of a dilute N solution to citrus seedlings
doubled nitrogen uptake efﬁciency compared with less frequent
applications of a more concentrated nutrient solution. Delivery of
N through fertigation reduces N losses in the soil-plant system
by ammonia volatilisation and nitrate leaching (Alva et al., 2008).
However, poor irrigation management, i.e., an application of waterin excess of crop requirements, plus the storage capacity of thesoil within the rooting depth, can contribute to leaching of waterand nutrients below the rootzone. Therefore, optimal irrigation
scheduling is important to maximise the uptake efﬁciencies ofwater and nutrients (Alva et al., 2005).
Most of the citrus production along the Murray River corridor
is on sandy soils, which are highly vulnerable to rapid leachingof water and nutrients. Nitrogen is the key limiting nutrient andis therefore a main component of fertigation. An increasing useof nitrogenous fertilizers and their subsequent leaching as nitratefrom the rootzone of cropping systems is recognised as a potential source of groundwater contamination, because the harvested
crop seldom takes up more than 25–70% of the total applied fertilizer (Allison, 1996). Several researchers have reported substantial
leaching (6–45%) of applied N under citrus cultivation in ﬁeld conditions (Wang and Alva, 1996; Paramasivam et al., 2002; Sluggett,2010). Similarly, in lysimeter experiments, Boaretto et al. (2010)
showed 36% recovery of applied nitrogen by orange trees, while
Jiang and Xia (2008) reported N leaching of 70% of the initial N
value, and found denitriﬁcation and leaching to be the main processes for the loss of N. These studies suggest that knowledge ofthe nitrogen balance in cropping systems is essential for designingand managing drip irrigation systems and achieving high efﬁciency
of N fertilizer use, thereby limiting the export of this nutrient as apollutant to downstream water systems.
Quantifying water and nitrogen (N) losses below the root zone
is highly challenging due to uncertainties associated with estimating drainage ﬂuxes and solute concentrations in the leachate,even under well-controlled experimental conditions (Van der Laanet al., 2010). Moreover, direct ﬁeld measurements of simultaneous
migration of water and nitrogen under drip irrigation is laborious, time-consuming and expensive (Bar-Yosef and Sheikholslami,
1976; Kachanoski et al., 1994). Hence simulation models havebecome valuable research tools for studying the complex and interactive processes of water and solute transport through the soil
proﬁle, as well as the effects of management practices on crop yields
and on the environment (Pang and Letey, 1998; Li et al., 2003). In
fact, models have proved to be particularly useful for describing
and predicting transport processes, simulating conditions which
are economically or technically impossible to carry out in ﬁeld
experiments (Li and Liu, 2011).
Several models have been developed to simulate ﬂow and transport processes, nutrient uptake and biological transformations of
nutrients in the soil (Subbaiah, 2011). HYDRUS 2D/3D (Šimůnek
et al., 2008, 2011) has been used extensively for evaluating theeffects of soil hydraulic properties, soil layering, dripper discharge
rates, irrigation frequency and quality, timing of nutrient applications on wetting patterns and solute distribution (e.g., Cote et al.,
2003; Gärdenäs et al., 2005; Assouline et al., 2006; Hanson et al.,2006; Ajdary et al., 2007; Patel and Rajput, 2008; Šimůnek andHopmans, 2009; Phogat et al., 2009, 2010, 2012, 2013; Li and Liu,
2011; Ramos et al., 2012) because it has the capability to analysewater ﬂow and nutrient transport in multiple spatial dimensions(Cote et al., 2003).
In the absence of experimental data we can use multidimensional models solving water ﬂow and nutrient transport equations
to evaluate the multi-dimensional aspect of nitrate movement
under fertigation (Cote et al., 2003; Gärdenäs et al., 2005; Hanson

75

Fig. 1. Drainage pipes and a ﬁlter sock placed at the bottom of the lysimeter.

et al., 2006). However, earlier simulation studies have reported contradictory results on nitrate distribution in soils. For example, Coteet al. (2003) reported that nitrate application at the beginning of anirrigation cycle reduced the risk of leaching compared to fertigation
at the end of the irrigation cycle. On the other hand, Hanson et al.
(2006) reported that fertigation at the end of an irrigation cycle
resulted in a higher nitrogen use efﬁciency compared to fertigation
at the beginning or middle of an irrigation cycle. These studies very
well outlined the importance of numerical modelling in the design
and management of irrigation and fertigation systems, especiallywhen there is a lack of experimental data on nutrient transport insoils. However, there is still a need to verify the fate of nitrate insoils with horticultural crops and modern irrigation systems.
Therefore, a lysimeter was established to observe water movement and drainage under drip irrigated navel orange, and to
calibrate the HYDRUS 2D/3D model against collected experimental
data. The model was then used, in the absence of experimental dataon nitrate, to develop various modelling scenarios to assess the fateof nitrate for different irrigation and fertigation schemes.

2. Materials and methods
2.1. Lysimeter setup
The study was conducted on a weighing lysimeter assembled
and installed at the Loxton Research Centre of the South Australian
Research and Development Institute. The lysimeter consisted of a
PVC tank (1 m diameter × 1.2 m height) located on 1.2 m × 1.2 m
pallet scales ﬁtted with 4 × 1 tonne load-cells, and connected to
a computerised logging system which logged readings hourly. A
specially designed drainage system placed at the bottom of thelysimeter consisted of radially running drainage pipes, which wereconnected to a pair of parallel pipes, which facilitated a rapid exitof drainage water from the lysimeter (Fig. 1). These pipes were covered in a drainage sock and buried in a 25-cm layer of coarse washedriver sand at the base of the lysimeter, which ensured easy ﬂushingof water through the drainage pipe. A layer of geo-textile material
was placed over the top of the sand layer to prevent roots growing
down into it, as this layer was intended to be only a drainage layer.
A healthy young citrus tree (about 3 years old) was excavatedfrom an orchard at the Loxton Research Centre and transplanted
into the lysimeter. A soil proﬁle approximately 85 cm deep wastransferred to the tank with the tree and saturated to remove air
pockets and to facilitate settling. The ﬁnal soil surface was around
10 cm below the rim of the tank. Soil samples were collected from

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V. Phogat et al. / Agricultural Water Management 127 (2013) 74–84

between irrigation cycles. The solute transport equation considers advective–dispersive transport in the liquid phase, as well as
diffusion in the gaseous phase. The theoretical part of the model
is described in detail in the user (Šejna et al., 2011) and technical(Šimůnek et al., 2011) manuals.
2.4. Estimation of soil hydraulic parameters
The van Genuchten–Mualem model of soil hydraulic properties(Mualem, 1976; van Genuchten, 1980) was selected for numericalsimulations:(h) = r +(h) = ss − rn m[1 + (˛h) ]

h<0

h≥0

(2)
1/m m

K(h) = Ks Sel [1 − (1 − Se
Fig. 2. Layout of drippers and location of EnviroSCAN soil moisture sensors in thelysimeter.

0 to 20, 20 to 40, 40 to 60, 60 to 85, and 85 to 110 cm depths tomeasure bulk density and to carry out particle size analysis.
Two months after transplanting, the lysimeter was installed
amongst existing trees in the orchard. Measurements were initiated after about six months, in order to enable the plant to adjust to
the lysimeter conditions. The lysimeter was equipped with Sentek®
EnviroSCAN® logging capacitance soil water sensors installed adjacent to the drip line (approximately 15 cm away from the dripper)
at depths of 10, 20, 40, 60, and 80 cm to measure changes in the volumetric soil water content. Drainage water was directed throughﬂexible piping into a large bin installed below ground level. The
experimental site was approximately 240 m from an establishedweather station, which measured air temperature, relative humidity, wind speed (at 2-m height), rainfall, and net radiation.
2.2. Irrigation
Irrigation was applied using 3 pressure compensated emitterswith a discharge rate of 4 L h−1 . Emitters were located on a circle
25 cm away from the tree trunk at an equal distance from eachother (Fig. 2). The irrigation schedule was based on the averagereference evapotranspiration (ET0 ) during the last 10 years at thesite, multiplied by the crop coefﬁcient (0.7) taken from Sluggett(2010). The cumulative crop evapotranspiration (ETC ) during the
29 day experimental period was equal to 65.3 mm, and daily ETC
varied from 1.68 to 3.39 mm. Irrigation was initiated on 16 August2010 and terminated on 13 September, 2010. Irrigation and rainfall
were recorded daily and drainage volume was measured 3 times
per week throughout the trial period. Daily irrigation was appliedin 5 short pulses (1–3 min long) using an automated irrigation controller, with 2 h breaks between irrigation pulses. The amount ofirrigation water applied (68.6 mm) was slightly higher than ETC for
the period. A total of 70 mm of rainfall fell during the experimental
period, including a single event of 52 mm on 3 September 2010.

Se =

(1)

) ]

 − rs − r

2

(3)
(4)

where Se is the effective ﬂuid saturation (dimensionless),  r and  s
are the residual and saturated water contents [L3 L−3 ], respectively,
K(h) is the unsaturated hydraulic conductivity function [L T−1 ],Ks is the saturated hydraulic conductivity [L T−1 ], ˛ [L−1 ], n, andm (both dimensionless) are empirical shape parameters wherem = 1 − (1/n), and l is the pore connectivity parameter (dimensionless). The l parameter was estimated by Mualem (1976) to be about
0.5 as an average for many soils and this value was adopted in thisstudy. Hysteresis was not considered in this study even thoughalternating drying and wetting cycles occurred during the experimental period. By calibrating the ˛ parameter, we obtained anaverage single retention curve somewhere between the main drying and wetting curves.
Since direct measurement of soil hydraulic parameters (i.e.,  r , s , Ks , ˛, n and l) in the ﬁeld or laboratory is time consuming andcostly, they were estimated using the ROSETTA model (Schaap et al.,2001), using particle size and bulk density data determined on soil
samples taken from lysimeter depths of 0–20, 20–40, 40–60, 60–85,
and 85–110 cm. Values of selected hydraulic parameters (˛ and Ks )for different soil layers were further ﬁne-tuned using an inverse
modelling technique. The calibration of the saturated hydraulicconductivity Ks and the ˛ parameter was done using selected values (17) of experimental water contents and leaching data. Finalvalues of soil hydraulic parameters utilised in the model are shownin Table 1.
2.5. Crop evapotranspiration
HYDRUS requires separate values of potential evaporation (Ep )and potential transpiration (Tp ) as inputs. These inputs were calculated on a daily basis from values of reference evapotranspiration(ET0 ), collected at the Loxton Meteorological Station, following thedual crop coefﬁcient method (Allen et al., 1998). In this approach,evapotranspiration of the crop (ETC ) is estimated using the following equation:

2.3. HYDRUS software

ETC = (Kcb + Ke ) × ET0

Soil water content and nitrate dynamics were simulatedusing version 2.01 of the computer simulation model HYDRUS
2D/3D (Šimůnek et al., 2011). This programme numericallysolves Richards’ equation for variably-saturated water ﬂow, andadvection–dispersion equations for both heat and solute transport. The model additionally allows speciﬁcation of root water
uptake, which affects the spatial distribution of water and nitrate

where Kcb is the basal crop coefﬁcient and Ke is the evaporation
coefﬁcient. Unpacking this equation into its component parts gives
two further equations:(5)

Tp = Kcb × ET0(6)

Ep = Ke × ET0(7)

V. Phogat et al. / Agricultural Water Management 127 (2013) 74–84

77

Table 1
Soil hydraulic parameters (van Genuchten parameters) used in the model.
Soil depth (cm)Soil Texture r (cm3 cm−3 ) s (cm3 cm−3 )˛a (cm−1 )nb

Ks a (cm h−1 )

lc

0–20
20–40
40–60
60–85
85–110

Loamy sandLoamy sandLoamy sand
Sandy loam
Coarse sand

0.06
0.06
0.05
0.05
0.03

0.37
0.36
0.34
0.33
0.40

0.02940.02680.03080.03000.0950

1.92
1.91
1.99
1.85
2.68

4.87
4.46
4.72
3.30
29.70

0.5
0.5
0.5
0.5
0.5

a
b
c

Optimised during calibration.
Obtained from ROSETTA data base.
Assumed a ﬁxed value.

where Tp is potential transpiration; and Ep is potential soil evaporation.
The Kcb values for different months were taken from Allenet al. (1998), assuming 70% canopy cover and no ground cover,since the lysimeter was placed in a well-grown citrus orchard,
and the lysimeter soil surface was kept free of weeds during theexperimental period. Estimated Tp and Ep values during the experimental period varied from 1.5 to 3.2 mm day−1 and from 0.5 to
1.1 mm day−1 , respectively. The total Tp and Ep during the experimental period were 59.3 and 21.1 mm, respectively. Note that thepotential ETC (80.4 mm) was larger than the 10-year average, which
was used for irrigation (68.6 mm). However, since additional rainfall occurred during the experiment, no shortage of water was
expected.
HYDRUS reduces the potential transpiration (Tp ) to the actual
transpiration (Ta ) by integrating actual water uptake over the entire
root zone, while considering water and salinity stresses. HYDRUS
implements a scheme whereby the actual evaporation (Ea ) remains
equal to the potential evaporation (Ea ) as long as the pressure headat the boundary is higher than a critical pressure head hCritA, considered to be −10,000 cm in our study. When the pressure head on
the soil surface boundary falls below hCritA, the potential evaporation is reduced.
The total rainfall was considered to be equal to the effective
rainfall for the purpose of modelling, and canopy interception was
not considered because throughfall and stemﬂow account for about
90–95% of precipitation in citrus (Li et al., 1997). Runoff was also
not considered as the lysimeter was a closed system, which does
not allow for surface runoff.
2.6. Root distribution and water uptake functions
A citrus tree has a relatively shallow, well branched frameworkof woody laterals and ﬁne ﬁbrous roots. Root density decreases substantially below a depth of 60 cm, with very few roots at 120 cm(Castle, 1980; Paramasivam et al., 2001). Mikhail and El-Zeftawi(1979) reported that the citrus root depth in the Murray Darling
Basin in Australia ranges from 60 to 90 cm, depending on the soil
type (being deeper in deep sandy soils). However, in a closed system like a lysimeter, where lateral growth is constrained, roots
are expected to grow further in the vertical direction compared
to lateral growth. Hence, the root distribution for an orange tree
in a lysimeter was described using the Vrugt et al. (2001) model,
with most roots extending 50 cm radially and 85 cm vertically. The
two-dimensional root water uptake model adapted in HYDRUS isexpressed as:ˇ(r) = 1 −

z
zm



1−



r
∗
∗
e−(pz /zm |z −z|+pr /rm |r −r|)rm(8)where the parameters used in the model for citrus were as follows:
the maximum rooting depth (zm ) was taken equal to the maximum depth of the lysimeter (85 cm) and rm was ﬁxed equal to
the radius of the lysimeter, i.e., 50 cm. The visual observation ofroots while transferring the plant to the lysimeter also suggested

similar values for these parameters. Based on the visual observation, z* was considered to be 30 cm and r* was taken as 25 cm.
These values depict the zone of the maximum water availability(just below the drippers). Empirical coefﬁcients pz and pr wereassumed to be 1.5 and 2, respectively, to correspond to the optimum uptake in the lysimeter conditions, considering the above
listed parameters. Similar root distributions were used in all simulations, although in reality the spatial root distribution may differ
depending on water availability and inherent soil variability.
In the HYDRUS software, a sink term is used to account for water
uptake by plant roots using the water stress response function
˛(h) (Feddes et al., 1978). This function includes ﬁve variables that
describe the dependence of the extraction of water from the soilon pressure head. The values used for these parameters (h1 = −10,h2 = −25, h3max = −200, h3min = −1000, and h4 = −8000 cm) weretaken from Taylor and Ashcroft (1972) for orange.
Even though the root distribution was the same in all scenarios,
the spatial distribution of root water uptake may vary in different
scenarios, because the variable distribution of moisture (pressurehead) in the soil proﬁle affects root water uptake.
2.7. Flow domain and its discretization
The simulation domain was represented by a 110-cm deep
and 100-cm wide cylindrical cross section. Drip irrigation wasmodelled as a circular line source 25 cm from the centre of thelysimeter with a uniform water ﬂux (q0 ) along the drip line.
This simpliﬁcation was made to enable HYDRUS to model thisproblem in a 2D axi-symmetrical mode (Fig. 3), rather than ina full 3D mode, which would be computationally much moredemanding. Additionally, since the surface wetted area and input
ﬂux densities under drippers were dynamic, an option that wewould not be able to model with HYDRUS in a 3D mode, we
assumed that the simpliﬁcation of the problem to axi-symmetrical
2D was adequate. Moreover, the drainage system laid out in thelysimeter (Fig. 1) also supported the use of an axi-symmetrical
domain as the drainage pipes run in a circular fashion to collect andﬂush drainage water out of the lysimeter. The transport domain was
discretized into 3294 ﬁnite elements, with a very ﬁne grid (1 cm)
around the dripper and near the outﬂow (seepage face), with gradually increasing element spacing farther from these two locations(up to 4 cm). Simulations were carried out over a period of 29 days.
2.8. Initial and boundary conditions
The variable water ﬂux (q0 ) representing drip irrigation was represented by the water application rate over the modelled drip line
surface area:q0 =3 × 4000(r22 − r12 )= 7.636 cm h−1(9)where r1 and r2 are the inner and outer radii of the circular driplinedischarge boundary, assumed to be 20 and 30 cm, respectively,

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V. Phogat et al. / Agricultural Water Management 127 (2013) 74–84

2.9. Nitrate modelling
Since most soils on which citrus is grown in South Australia arecoarse textured soils with good drainage, high oxygen levels, loworganic matter, and low microbial populations, denitriﬁcation andmineralisation was assumed to be negligible in this study. Similarly,
the soil adsorption of nitrate was also considered to be negligible
since both nitrate and solid surfaces are negatively charged. Plant
uptake of non-adsorbing nutrients like nitrate is controlled mainly
by mass ﬂow of water uptake (Barber, 1995). Therefore, it was
assumed that nitrate was either passively taken up by the tree withroot water uptake (Šimůnek and Hopmans, 2009) or moved downward with soil water. Spatial distribution of nitrate in the transportdomain was thus simulated using the convection–dispersion equation for a nonreactive tracer. Molecular diffusion was neglected as
it was considered negligible relative to dispersion. The longitudinal
dispersivity was considered to be 5 cm, with the transverse dispersivity being one-tenth of this (i.e. 0.5 cm). Similar values of theseparameters have been used in other studies (Gärdenäs et al., 2005;
Hanson et al., 2006).

Fig. 3. Schematic of a lysimeter with boundary conditions used in numerical simulations.

4000 is the dripper recharge rate (cm3 h−1 ), and 3 is the numberof drippers.
The remainder of the soil surface was subjected to the atmospheric boundary condition, deﬁned by potential evaporation (Ep ),potential transpiration (Tp ), and rainfall. Vertical sides were no
ﬂow boundaries except for a seepage face (5 cm) at the right bottom boundary, which represents a water outlet allowing drainage
from the lysimeter. Cauchy and Neumann solute transport boundary conditions were imposed at the soil surface and the seepage
face, respectively. The initial soil water content distribution (Fig. 4)
was based on EnviroSCAN measured values and varied from 0.07 to
0.4 cm3 cm−3 from the top to the bottom of the lysimeter, having
a positive downward gradient. The soil proﬁle was assumed to be
initially solute free.

Fig. 4. Initial distribution of volumetric soil water content (cm3 cm−3 ) in thelysimeter.

2.10. Fertigation scenarios
Citrus trees in this region are fertilised from early September
till March, and in drip systems fertilizers are mostly applied withthe second irrigation pulse for the day. All fertigation scenarios reported here are hypothetical. Fertigation was assumed tobe supplied with the same quantity of water as in irrigations
without fertigation and to conform to the 2D axi-symmetrical
domain. For the initial scenario, 5 fertigation pulses were applied
from 30 August 2010 at the rate of one fertigation pulse eachday. These were followed by 2 days without fertigation and thenanother 5 daily fertigation pulses. The resultant dose of N (144 g
KNO3 or 20 g N per tree) for the period from 16 August till 13
September (1 month) was calculated based on recommended fertilizer application practices for 5–6 year old orange tree. The seasonal
recommended dose of nitrogen for an orange tree of this age is 139 g
N applied from September to March (Treeby et al., 2012). Hencefor the seasonal simulation, nitrogen was assumed to be appliedin equal monthly doses (20 g N for 7 months), in similar pulses as
described for the experimental period. The simulation was run for
300 days in order to evaluate the fate of seasonally applied nitrogen(140 g N) fertilizer in citrus.
Further scenarios examining the impact of timing of nitrogen
application on the efﬁciency of nitrogen uptake simulated a fertilizer application either at the beginning (PF1), middle (PF2), orend (PF3) of the daily irrigation scheme. Since the daily irrigationconsisted of 5 pulses, fertigation was applied during the 2, 3 and 4
irrigation pulse in the PF1, PF2 and PF3 scenarios, respectively. It
is a common practice that the initial and ﬁnal irrigation pulses are
fertilizer free to ensure a uniform fertilizer application and ﬂushingof the drip lines.
In addition to these simulations, two continuous fertigation
scenarios were also performed to compare pulsed and continuous fertigation. The ﬁrst scenario consisted of applying the sameamount of fertilizer (as applied in single pulse fertigation) spread
across all irrigation pulses (PF), except for the last irrigation pulse
to enable ﬂushing. The second scenario consisted of continuous
irrigation of the same duration and irrigation amount as underpulsed treatments, with fertigation at all times (CF), except for thesame period of ﬂushing at the end of irrigation. The fertigation
scheme in PF1, PF2, PF3 and continuous scenarios was assumed
to start from 17 August 2010. All fertigation simulations were run
as for the irrigation experiment, that is for 29 days (from 16 August,2010 to 13 September, 2010).

V. Phogat et al. / Agricultural Water Management 127 (2013) 74–84

79

Fig. 5. Comparison of measured (M) and simulated (S) water contents in the soil at selected times (T).

To evaluate the impact of the quantity of irrigation water on
nitrate leaching, additional simulations were run for all scenarioswith 50% (I50 ), 75% (I75 ), and 125% (I125 ) of irrigation water appliedin the ﬁeld experiment (I100 ).
2.11. Statistical analysis
The performance of the model was evaluated by comparing
measured (M) and HYDRUS-2D simulated (S) values of moisture
distribution in the soil at different times using various quantitative measures of the uncertainty, such as, the mean absolute error(MAE), the root mean square error (RMSE), and the paired t-test(tcal ) given by:
1  
Mi − Si 
N
N

MAE =

(10)

The range of r2 lies between 0 and 1, which describes how muchof the observed dispersion is explained by the prediction. A valueof zero means no correlation at all, whereas a value of 1 means thatthe dispersion of the predictions is equal to that of the observations(Krause et al., 2005). The model efﬁciency (E) proposed by Nash andSutcliffe (1970) is calculated as:
E =1−

N

RE = 1 −tcal =

d
Sm

(11)

i=1

1/n1 + 1/n2

d = x1 − x2 and Sm =;n1 s12 + n2 s22
n1 + n2 − 2.

(12)Here, n and s are the number of comparable paired points andstandard deviation, respectively; subscripts 1 and 2 are indicativeof their respective measured and predicted values, d is the difference between measured (x1 ) and simulated (x2 ) mean values, Sm
is the standard deviation of the mean, and tcal are the calculated
t-test values. For a perfect match between measured and simulated values MAE = RMSE = 0. Differences between mean measured
and simulated values are signiﬁcant if the tcal > ttab at (n1 + n2 − 2)
degrees of freedom.
In addition to the error indices listed above, other efﬁciency
measures evaluating the model performance investigated in thisstudy were the coefﬁcient of determination (r2 ), the model efﬁciency (E), and the relative model efﬁciency (RE). The coefﬁcient ofdetermination r2 is deﬁned as the squared value of the coefﬁcientof correlation according to Bravais-Pearson. It is calculated as:⎛
r2 = ⎝ 

N
i=1
N
i=1





Mi − M̄Mi − M̄

Si − S̄
N
i=1

⎞2





Si − S̄



⎠

(13)





(14)

The criteria described above (r2 , E) quantify the difference
between observations and predictions with respect to the absolute values. As a result, an over- or under-prediction of higher
values has, in general, a greater inﬂuence than those of lower values(Krause et al., 2005). To counteract this, efﬁciency measures basedon a relative deviation can be derived from E as:

i=1


 N
1
2
RMSE = (Mi − Si )N
− Si )2i=1 (Mi2N
Mi − M
i=1

N
i=1
N
i=1



Mi − Si /Mi

Mi − M̄/M̄

2

2

(15)

where RE represents the relative efﬁciency. The purpose of considering a range of statistical parameters was to evaluate the relative
importance of various tests for assessing the model performance.
The value of E and RE in Eqs. (14) and (15) may range from minus
inﬁnity to one, with one representing a perfect ﬁt of the data. E ≤ 0means that the mean value of the observations (measurements)
would have been a better predictor than the model, and efﬁciency
values between 0 and 1 are generally viewed as acceptable levelsof performance (Moriasi et al., 2007).
3. Results and discussion
3.1. Soil water distribution and water balance
The water content distribution in the soil reﬂects water availability to plants, and plays a crucial role in water movement throughand out of the root zone. Volumetric water contents simulated by
HYDRUS 2D/3D are compared in Fig. 5 with the measured values
obtained using EnviroSCAN probes 15 cm away from the dripper.
Simulated values matched measured values well, both spatially andtemporally. However, deviations between simulated and measured
values were observed at day 19 of simulation, particularly in theupper 50 cm of the soil proﬁle; at later times this difference was
not observed.
Simulated and observed daily and cumulative drainage are compared in Figs. 6 and 7, respectively. Both variables showed a close
match between simulated and measured values. It can be seen thatsimulated daily drainage remained slightly below observed values(Fig. 6), except for the initial higher leaching on day 1. However, the80

V. Phogat et al. / Agricultural Water Management 127 (2013) 74–84

Table 2
Statistical estimates between measured and simulated values of moisture content at different time of simulation.
Statistical parameters

MAE
RMSE
tcal (P = 0.05)
r2
E
RE

Days of simulation
2

5

9

12

16

19

22

26

29

0.006
0.011
−0.209
0.93
0.91
0.88

0.006
0.009
−0.152
0.94
0.93
0.90

0.007
0.011
−0.205
0.93
0.91
0.88

0.007
0.009
−0.095
0.94
0.94
0.91

0.011
0.014
0.164
0.88
0.86
0.82

0.022
0.028
−1.158
0.68
0.17
−0.05

0.005
0.007
0.020
0.96
0.96
0.95

0.014
0.018
0.313
0.84
0.78
0.75

0.014
0.017
0.392
0.86
0.78
0.76

MAE: Mean absolute error; RMSE: Root mean square error; tcal : Calculated value of paired t-test; r2 : Coefﬁcient of determination; E: Nash and Sutcliffe efﬁciency; RE: Relative
efﬁciency.

25

Drainage (l)20Measured
Simulated

15
10
5
0
1

3

5

8 10 12 15 16 17 18 19 22 23 24 25 26 29
Time (Days)

Fig. 6. Temporal changes in observed and simulated daily drainage volumes.

total drainage observed in the lysimeter was matched closely by themodel. The high peak on day 21 represents the effect of high rainfall on that day, which also was very well predicted by the model.
However, the cumulative drainage (Fig. 7) remained slightly overpredicted during the initial 15 days, after which the simulated andobserved values matched well.
Model evaluation was performed using a number of model
performance parameters calculated using measured and modelgenerated soil water contents (Table 2). The mean absolute error(MAE) varied from 0.006 to 0.22 cm3 cm−3 and the root meansquare error (RMSE) ranged between 0.007 and 0.028 cm3 cm−3 ,which indicated small deviations between measured and simulated values. However, the maximum values of MAE and RMSE wereobserved at day 19, conﬁrming the deviations shown in Fig. 5 at thistime. However, the values of paired t-test (tcal ) between measured
and simulated water contents showed insigniﬁcant differences at
5% level of signiﬁcance at all times. Values of the coefﬁcient of determination (r2 ) varied between 0.68 and 0.96, indicating a reliablegeneration of water contents by the model at all days of simulations. Similarly, the Nash and Sutcliffe efﬁciency coefﬁcient (E)values ranged from 0.17 to 0.96, indicating a good performanceof the model for the prediction of water contents in this study.

Cumulative drainage (l)70Measured60

However, the relative efﬁciency (RE) value at day 19 (−0.05) reveals
unsatisfactory performance of the model at that point according
to the criteria suggested by Moriasi et al. (2007). The values of
MAE, RMSE, r2 , E, and RE for the drainage ﬂux were 2.87, 4.14, 0.97,
0.94, and 0.78 (not shown here), respectively, which also showeda robust performance of the model for drainage ﬂuxes from thelysimeter.
The close match of both water contents (except at day 19)
and drainage ﬂuxes indicates that the HYDRUS 2D/3D software
can be successfully used to predict water movement and drainage
ﬂuxes in a lysimeter planted with a citrus tree. Other studies havealso reported good performance of this software for various soil,
water, and crop conditions under pressurised irrigation systems(e.g., Assouline et al., 2006; Ajdary et al., 2007; Patel and Rajput,
2008; Phogat et al., 2012, 2013; Ramos et al., 2012).
Simulated water balance components over the 29 day experimental period are shown in Table 3. It can be seen that simulated
drainage, which is similar to the amount measured in the lysimeter,
represents 48.9% of the total water balance. A much higher seasonal drainage (58.4–67.8% of the total water applied) has beenreported for a lysimeter planted with an orange tree in a ﬁne sandy
soil (Boman and Battikhi, 2007). High drainage is bound to occur inhighly permeable, coarse textured soils, such as the sand/loamy soil
used in this study, where water drains easily and quickly from theroot zone because gravity dominates over capillarity (Cote et al.,2003). However, Sluggett (2010) estimated deep drainage in therange of 6.1–37.2% under citrus trees growing in light textured
soils in the Sunraysia region of Australia. A major contributor to thehigh drainage measured in this experiment was the high amountof water applied, mostly as a result of large rainfall events.
Simulated plant water uptake was estimated to be 40% of thewater application, indicating low irrigation efﬁciency of the drip
system. The daily plant uptake varied from 1.2 to 3.14 mm (notshown here). However, plant uptake is a very complex process,and depends on a number of parameters describing the root andcanopy development. Since the HYDRUS model does not support a
dynamic behaviour of the root system and considers only the static
root parameters, root uptake was optimised on the basis of a changing transpiration rate over time. Additionally, since in the present
study we dealt with a tree, for which the root distribution development over time is not as fast as observed for seasonal crops like

Simulated

50

Table 3
Simulated components of the water balance after 29 days.

40
30
20

Components

(mm)

(%)

Sources

Irrigation
RainfallSoil depletion

68.6
70.2
9.1

46.4
47.5
6.1

Sinks

Root uptake
Drainage
Evaporation

59.2
72.3
16.4

40.0
48.9
11.1

10
0
0

5

10

15
Time (Days)

20

25

Fig. 7. Evolution of observed and simulated cumulative drainage.

30

V. Phogat et al. / Agricultural Water Management 127 (2013) 74–84

81

Fig. 8. Spatial distribution of soil solution nitrate (mg cm−3 ) around an orange tree at selected times after commencement of fertigation, up to the end of applications (15days).

Table 4
Simulated components of nitrogen balance, at 15 and 285 days of fertigationcommencement.
Time

Root uptake
Leaching
Soil storage

15 days

285 days

(g)

(%)

(g)

(%)

5.13
0
14.88

25.5
0.0
74.5

58.84
70.05
10.75

42.1
50.2
7.7

cereals, the root development was considered relatively constantfor the modelling purpose. Hence, a static root distribution andvariable atmospheric conditions produced a good approximationof plant uptake, as has been revealed in a number of earlier studies
that used HYDRUS for modelling purposes (Sansoulet et al., 2008;
Phogat et al., 2012, 2013; Ramos et al., 2011, 2012; Tournebize et al.,2012)
3.2. Nitrate distribution and uptake
Simulated distribution of nitrate (NO3 -N) at selected times after
commencement of fertigation is shown in Fig. 8. Concentrationof NO3 -N was maximum at the centre of the plume below thedripper, with a gradual decrease in N concentration towards theouter boundaries of the plume. Subsequent irrigation and fertigation pulses resulted in enlargement of the plume, with a rapid
lateral and vertical movement of NO3 -N. It is worth noticing thatafter 15 days of fertigation (29 days of simulation) all nitrate
still remained in the lysimeter, reaching a depth of 70 cm. The
maximum nitrate concentration at this time was at 20 cm. The simulated NO3 -N uptake accounted only for 25.5% of applied nitrogen(Table 4). The remaining nitrogen was still available in the soil forplant uptake, provided it was not transformed by soil biologicalprocesses. No nitrate leaching was predicted by the model within
this initial 15 day period. The total seasonal recovery of applied
N (applied through 70 daily fertigation pulses) amounts to 42.1%
by the orange tree, while 7.7% of added NO3 -N was retained in thesoil at the end of the season. These results agree with the ﬁndings ofParamasivam et al. (2002) who reported 40–53% nitrogen uptake ina ﬁeld experiment on citrus. Similarly, Boaretto et al. (2010) showed
36% recovery of applied nitrogen by an orange tree in a lysimeter.
The seasonal distribution of nitrate in the soil at 30-day intervals
after the fertigation commencement is shown in Fig. 9. It can be seenthat nitrate rapidly moved downwards and dispersed in the lysimeter, reaching a depth of 95 cm after 30 days. However, the zoneof the maximum concentration remained close to the soil surface.
Subsequent fertigation pulses further pushed N near to the leachingoutlet at 60 days and N dispersed throughout the lysimeter, beyond
which regular N leaching was observed with subsequent fertigations. However, the concentration of N remained much higher inthe upper soil depth (30 cm) till 180 days of fertigation, enablingits continued uptake by the orange tree. The nitrogen concentration thereafter reduced drastically in the upper zone (0–30 cm) as aresult of the withdrawal of fertigation after 195 days of simulation(180 days of fertigation). At 210 days after commencement of fertigation (30 days after fertigation ceased), the NO3 -N concentrationin the domain ranged between 0 and 0.4 mg cm−3 , and continued to
decline until it completely moved out of the upper 40 cm soil depth
at 270 days. At the end of the simulation (285 days after fertigation began and 105 days after fertigation ceased), only a very small
amount of nitrate (7.7%) remained in the lysimeter, with higher
concentration occurring at the bottom of the lysimeter (Table 4),
indicating higher vulnerability of this N to leaching. Major leachingof NO3 -N took place after 90 days of simulation, amounting to 61%

Fig. 9. Distribution of NO3 -N (mg cm−3 ) in the lysimeter at indicated days of fertigation commencement.

82

V. Phogat et al. / Agricultural Water Management 127 (2013) 74–84

18
16

NO3-N (g)

14
12
10
8
6
4
2
0

30

60

90

120 150 180 210 240 270 300
Days of simulation

Fig. 10. Seasonal leaching of applied nitrogen (NO3-N) at 30-days interval of simulation.

of total N leaching between 90 and 180 days (Fig. 10), which corresponds to heavy precipitation of 95 mm on day 115 and 68 mm
on day 152 of simulation. Paramasivam et al. (2001) and Nakamura
et al. (2008) also reported that unexpectedly prolonged irrigationor high rainfall following fertilizer applications led to higher NO3 -N
leaching losses.
Total nitrate leaching amounted to 50.2% of the N applied as
fertilizer (Table 4). Nitrate losses of similar magnitude (35–53%)
have also been reported by Syvertsen and Sax (1999) and Boman
and Battikhi (2007) in a lysimeter grown orange tree. On the other
hand, low NO3 -N leaching losses ranging from 2 to 16% of theapplied nitrogen have been reported in some studies on citrus(Paramasivam et al., 2001; Syvertsen et al., 1993). The migrationof nitrate to deeper layers is highly dependent on the amount ofirrigation and rainfall, as this is the driving force moving nitrate
out of the root zone. Lower nitrate leaching estimated in this study
may have been a consequence of improved irrigation and fertilizer management through the drip system. Hence improved water
efﬁciency under drip irrigation, by reducing percolation and evaporation losses, can contribute considerably towards environmentallysafer fertilizer applications (Mmolawa and Or, 2003).
In addition to the factors discussed above, a choice of appropriate source, amount, frequency, and timing of fertilizer applications
and the rate of N transformation into NO3 are other important factors that determine the amount of NO3 -N leaching out of the vadosezone (Alva et al., 2006).
3.3. Scenario analysis
Temporal distribution of nitrate for different fertigation scenarios is presented in Fig. 11. Although nitrate movement appears to be
similar in all scenarios, small differences can be observed in nitrate
distribution in the soil for some scenarios. In scenarios PF and PF3,
in which fertilizer was applied with all pulses in low concentrations
or towards the end of irrigation, the N concentration after 2, 7, and14 days was slightly higher in the centre of the plume where root
activity was at a maximum. However, the nutrient uptake varied
within a narrow range (46.8–47.4%) under normal irrigation (I100 ),indicating an insigniﬁcant impact of fertigation timing under conditions experienced in our lysimeter study. Contrary to this, Hanson
et al. (2006) reported 14% higher nitrate uptake when fertilizer wasapplied at the end of the irrigation event in a HYDRUS simulationthat was based on historical irrigation and fertigation data. A similar observation was also made by Paramasivam et al. (2002) andAlva et al. (2006) in ﬁeld experiments. Gärdenäs et al. (2005) also
concluded that fertigation applied towards the end of the irrigation
cycle generally reduces the potential for nitrate leaching under
micro-irrigation systems, with the exception of clayey soils.

Fig. 11. Spatial distribution of nitrate (mg cm−3 ) at selected times for different
pulsed fertigation scenarios [fertigation at the beginning of irrigation (PF1), fertigation in the middle of irrigation (PF2), fertigation towards the end of irrigation(PF3), fertigation in all pulses (PF)] and for continuous irrigation with fertigation(CF).

A short fertigation pulse (1–3 min) used in our study, as compared to the other studies, may have reduced differences among
various scenarios. However, these results imply that fertigation ina short pulse towards the end of the irrigation event or low concentration fertigation with all pulses could increase the efﬁciencyof nitrogen fertigation as compared to other options.
Nitrate distribution in the domain after 21 and 28 days weresimilar in all scenarios (Fig. 11), and all differences disappeared by
21 days of simulation. It can be shown that while nitrate distribution varied during one application phase, they were similar for all
scenarios at the end of each irrigation cycle. Also, nitrate moved
to a similar soil depth (60 cm) after 28 days in all scenarios. These
scenarios did not produce any NO3 -N leaching because of the shortsimulation period.
A comparison of nitrate uptake between pulsed (PF) and continuous (CF) irrigations revealed that scenarios with pulsed irrigation(PF) had almost alike nitrate uptake (47.4%) as fertigation with
continuous irrigation (CF) (47.2%) (Table 5). Similar results wereobtained in scenarios with different irrigation quantities (50%, 75%,
and 125% of normal irrigation). A negligible impact of pulsing on
moisture distribution pattern and drainage has been reported inearlier studies for different dripper discharge rates and spacings(Skaggs et al., 2010; Phogat et al., 2012). This observation further
conﬁrms that pulsing has little impact on solute distribution in thesoil under optimal irrigation applications as compared to continuous irrigation.

V. Phogat et al. / Agricultural Water Management 127 (2013) 74–84
Table 5
Nitrogen (NO3 -N) balance under variable irrigation application [50% of ETC (I50 );75% of ETC (I75 ); 100% of ETC (I100 ); and 125% of ETC (I125 )] for different fertigation
scenarios.
Components of NO3 -N balance

Fertigation scenariosa
PF1

PF2

PF3

PF

CF

I50 Treatment
Applied (g)Root uptake (g)Leaching (g)Uptake efﬁciency (%)

20.01
11.08
0
55.38

19.99
11.05
0
55.25

19.99
11.13
0
55.67

19.99
11.07
0
55.37

19.96
11.22
0
56.21

I75 Treatment
Applied (g)Root uptake (g)Leaching (g)Uptake efﬁciency (%)

19.99
10.11
0.01
50.55

19.99
10.11
0.01
50.55

19.99
10.20
0.01
51.01

19.99
10.17
0.01
50.88

19.97
10.27
0.01
51.44

I100 Treatment
Applied (g)Root uptake (g)Leaching (g)Uptake efﬁciency (%)

19.99
9.36
0.10
46.83

19.99
9.38
0.09
46.92

19.99
9.45
0.08
47.28

19.98
9.53
0.08
47.72

19.96
9.42
0.11
47.21

I125 Treatment
Applied (g)Root uptake (g)Leaching (g)Uptake efﬁciency (%)

19.99
8.64
0.86
43.22

19.99
8.70
0.79
43.52

19.99
8.74
0.71
43.69

19.99
8.74
0.80
43.72

19.99
8.71
0.88
43.57

a
P: Pulsed irrigation, C: Continuous irrigation, F: Fertigation at all times, F1: Fertigation pulse at the beginning of irrigation, F2: Fertigation pulse in the middle ofirrigation, F3: Fertigation pulse towards the end of irrigation.

Modelling simulations were also performed to evaluate theimpact of variable irrigation applications on nitrate movement for
scenarios discussed above (Table 5). It can be seen that plant NO3 N uptake gradually reduced as the amount of irrigation increased.
The nitrogen uptake efﬁciency for the 50% irrigation (I50 ) treatment
varied from 55.3 to 56.2% for all scenarios of fertilizer applications,which was about 8.5% higher than uptake recorded for the normal
irrigation (I100 ). On the other hand, a higher amount of irrigation(125%) than normal reduced nitrate uptake of an orange tree by
further 3.4–3.6%. At the same time, the zone of maximum nitrateconcentration moved to a depth of 40–60 cm (not shown here),
where root uptake decreased exponentially due to the reduction
in root density. Nitrate at this depth is neither available for trees,
since the majority of active ﬁbrous roots of orange trees are in the
top 15–30 cm depth (Alva and Syvertsen, 1991; Zhang et al., 1996),
nor can it be easily transformed because of the limited microbial
population and available carbon at this depth (Paramasivam et al.,
1999; Alva et al., 2006). This can potentially lead to eventual leaching losses to receiving water bodies. Hence over-irrigation not only
led to a profound water loss, but also brought about a reduction inplant nitrogen uptake and an increase in potential danger of appreciable NO3 -N leaching losses in all fertigation scenarios. Therefore,
the combination of inadequate management of irrigation and nitrogen fertilizers in commercial agriculture may lead to considerable
nitrate losses out of the root zone, and may increase the risk ofnitrate contamination of ground water aquifers.
4. Conclusions
In the past, models have proved to be particularly useful for
describing and evaluating transport processes, simulating conditions which are too difﬁcult economically or impossible technicallyto be tested in controlled ﬁeld experiments. In this study, modelling
was combined with a lysimeter study to calibrate the HYDRUS
model against water content and drainage measurements under
an orange tree. Additional simulations were run to evaluate nitrate83

leaching under long term conditions, and the impact of timing of
fertigation on the fate of applied nitrogen.
Moisture content distributions and leaching volumes predictedby HYDRUS 2D/3D matched well with the measured values in thelysimeter, with a very low mean absolute error (MAE), root meansquare error (RMSE) and paired t-test values. The performance ofHYDRUS was robust, as revealed by high values of r2 , Nash andSutcliffe efﬁciency (E) and relative efﬁciency (RE) analysis. Numerical simulations and the lysimeter study showed huge drainage
losses (48.9%) in a lysimeter with a sandy soil irrigated with surface
drippers. Model simulations were further used to evaluate nitrate
uptake by an orange tree for various fertigation scenarios. Simulations showed that the timing of fertigation in scenarios withpulsed irrigation and continuous irrigation (CF) had little impact
on nitrate uptake by an orange tree. Predicted seasonal nitratelosses accounted for 50.2% of the fertilizer applied in the lysimeter.
Nitrate uptake by an orange tree in a lysimeter was regulated by theamount of irrigation applied. Higher uptake efﬁciency (55.6%) was
obtained with the application of less water (50% of normal) thannormal (47.1%). On the other hand, the uptake efﬁciency decreasedby 3.5% with the application of 25% higher amount of irrigation thannormal.
Results of this study suggest that in sandy soils, leaching losses
and nitrate uptake by an orange tree in lysimeter were driven byamount of water application, either through irrigation or unexpected rainfall. However, there is a need to extend the modellingstudy over a full season or multiple years to assess total nitrateleaching and plant uptake under ﬁeld conditions.
Acknowledgements
Financial support of the National Programme for Sustainable
Irrigation, Agriculture NSW and SARDI is gratefully acknowledged.
References
Ajdary, K., Singh, D.K., Singh, A.K., Khanna, M., 2007. Modelling of nitrogen leaching from experimental onion ﬁeld under drip fertigation. Agricultural Water
Management 89, 15–28.
Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration guidelines
for computing crop water requirements. In: FAO Irrigation and Drainage Paper
No. 56. FAO, Rome, Italy.
Allison, F.E., 1996. The fate of nitrogen applied to soils. Advances in Agronomy 18,
219–258.
Alva, A.K., Paramasivam, S., Fares, A., Delgado, J.D., Mattos Jr., D., Sajwan, K.S., 2005.
Nitrogen and irrigation management practices to improve nitrogen uptake efﬁciency and minimize leaching losses. Journal of Crop Improvement 15, 369–420.
Alva, A.K., Paramasivam, S., Obreza, T.A., Schumann, A.W., 2006. Nitrogen best management practice for citrus trees I. Fruit yield, quality, and leaf nutritional status.
Scientia Horticulturae 107, 233–244.
Alva, A.K., Paramasivam, S., Mattos Jr., D., Quaggio, J.A., 2008. Advances in nitrogen
fertigation of citrus. Journal of Crop Improvement 22, 121–146.
Alva, A.K., Syvertsen, J.P., 1991. Irrigation water salinity affects soil nutrient distribution, root density, and leaf nutrient levels of citrus under drip fertigation. Journalof Plant Nutrition 14, 715–727.
Assouline, S., 2002. The effects of microdrip and conventional drip irrigation onwater distribution and uptake. Soil Science Society of America Journal 66,
1630–1636.
Assouline, S., Moller, M., Cohen, S., Ben-Hur, M., Grava, A., Narkis, K., Silber, A., 2006.
Soil–plant system response to pulsed drip irrigation and salinity: Bell pepperCase study. Soil Science Society of America Journal 70, 1556–1568.
Barber, S.A., 1995. Soil Nutrient Bioavailability: A Mechanistic Approach. John Wiley& Sons, New York.
Bar-Yosef, B., 1999. Advances in fertigation. Advances in Agronomy 65, 1–77.
Bar-Yosef, B., Sheikholslami, M.R., 1976. Distribution of water and ions in soils irrigated and fertilized from a trickle source. Soil Science Society of America Journal
40, 575–582.
Boaretto, R.M., Junior, D.M., Quaggio, J.A., Cantarella, H., Trivelin, P.C.O., 2010.
Nitrogen-15 uptake and distribution in two citrus species. In: 19th World
Congress of Soil Science, Soil Solutions for a Changing World, August 1–6, 2010,
Brisbane, Australia, pp. 156–159.
Boman, B.J., Battikhi, A.M., 2007. Growth, evapotranspiration, and nitrogen leachingfrom young lysimeter grown orange trees. Journal of Irrigation and Drainage
Engineering 133 (4), 350–358.

84

V. Phogat et al. / Agricultural Water Management 127 (2013) 74–84

Castle, W.S., 1980. Citrus root systems: their structure, function, growth, and relationship to tree performance. In: Proceedings of 4th International Citriculture
Conference, Sydney, Australia, August 15–23, 1980. International Society of Citriculture, Sydney, Australia, pp. 62–69.
Cote, C.M., Bristow, K.L., Charlesworth, P.B., Cook, F.J., Thorburn, P.J., 2003. Analysis
of soil wetting and solute transport in subsurface trickle irrigation. Irrigation
Science 22, 143–156.
Feddes, R.A.P., Kowalik, J., Zaradny, H., 1978. Simulation of ﬁeld water use and crop
yield. Simulation Monographs Pudoc, Wageningen, The Netherlands.
Gärdenäs, A.I., Hopmans, J.W., Hanson, B.R., Šimůnek, J., 2005. Two-dimensionalmodeling of nitrate leaching for various fertigation scenarios under microirrigation. Agricultural Water Management 74, 219–242.
Hanson, B.R., Hopmans, J.W., Šimůnek, J., 2008. Leaching with subsurface drip
irrigation under saline shallow groundwater conditions. Vadose Zone Journal
7, 810–818.
Hanson,B.R.,
Šimůnek,
J.,
Hopmans,
J.W.,
2006.
Evaluationofurea–ammonium–nitrate fertigation with drip irrigation using numericalmodelling. Agricultural Water Management 86, 102–113.
Jiang, C., Xia, Z., 2008. Lysimeter studies on nitrogen transport and transformation
as affected by contaminated water irrigation. Journal of Hydrologic Engineering
13 (5), 341–346.
Kachanoski, R.G., Thony, J.L., Vauclin, M., Vachaud, G., Laty, R., 1994. Measurementof solute transport during constant inﬁltration from a point source. Soil Science
Society of America Journal 58, 304–309.
Krause, P., Boyle, D.P., Base, F., 2005. Comparison of different efﬁciency criteria forhydrological model Assessment. Advances in Geosciences 5, 89–97.
Li, Y.C., Alva, A.K., Calvert, D.V., Zhang, M., 1997. Stemﬂow, throughfall andcanopy interception of rainfall by citrus tree canopies. Horticulture Science 32,
1059–1060.
Li, J., Liu, Y., 2011. Water and nitrate distributions as affected by layered-textural soil
and buried dripline depth under subsurface drip fertigation. Irrigation Science,
http://dx.doi.org/10.1007/s00271-010-0255-z.
Li, R., Ma, J., Zhang, R., 2003. Estimating nitrate leaching with a transfer function
model incorporating net mineralization and uptake of nitrogen. Journal of Environmental Quality 32, 1455–1463.
Li, J., Yoder, R.E., Odhiambo, L.O., Zhang, J., 2004. Simulation of nitrate distribution under drip irrigation using artiﬁcial neural networks. Irrigation Science 23,
29–37.
Mikhail, E.H., El-Zeftawi, B.M., 1979. Effect of soil type and rootstocks on root distribution, chemical composition of leaves and yield of Valencia oranges. Australian
Journal of Soil Research 17, 335–342.
Mmolawa, K., Or, D., 2003. Experimental and numerical evaluation of analytical volume balance model for soil water dynamics under drip irrigation. Soil Science
Society of America Journal 67, 1657–1671.
Moriasi, D.N., Arnold, J.G., Van Liew, M.W., Bingner, R.L., Harmel, R.D., Veith, T.L.,
2007. Model evaluation guidelines for systematic quantiﬁcation of accuracy inwatershed simulations. Transactions of the ASABE 50, 885–900.
Mualem, Y., 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research 12, 513–522.
Nakamura, K., Watanabe, S., Hirono, Y., 2008. Applications and problems of numerical modeling of Nitrogen transport in agricultural soils using HYDRUS. In: Saito,
H., Sakai, M., Toride, N., Šimůnek, J. (Eds.), Proceedings of Third HYDRUS Workshop. Tokyo, Japan, June 28.
Nash, J.E., Sutcliffe, J.V., 1970. River ﬂow forecasting through conceptual models part
I—A discussion of principles. Journal of Hydrology 10, 282–290.
Pang, X.P., Letey, J., 1998. Development and evaluation of ENVIRO-GRO, an integrated
water, salinity, and nitrogen model. Soil Science Society of America Journal 62,
1418–1427.
Paramasivam, S., Alva, A.K., Fares, A., Sajwan, K.S., 2001. Estimation of nitrate leaching in an Entisol under optimum citrus production. Soil Science Society ofAmerica Journal 65, 914–921.
Paramasivam, S., Alva, A.K., Fares, A., Sajwan, K.S., 2002. Fate of nitrate and bromide in an unsaturated zone of a sandy soil under citrus production. Journal ofEnvironmental Quality 31, 671–681.
Paramasivam, S., Alva, A.K., Prakash, O., Cui, S.L., 1999. Denitriﬁcation in the vadosezone and in surﬁcial groundwater of a sandy entisol with citrus production. Plant
and Soil 208, 307–319.
Patel, N., Rajput, T.B.S., 2008. Dynamics and modeling of soil water under subsurface
drip irrigated onion. Agricultural Water Management 95 (12), 1335–1349.
Phogat, V., Malik, R.S., Kumar, S., 2009. Modeling the effect of canal bed elevation
on seepage and water table rise in a sand box ﬁlled with loamy soil. Irrigation
Science 27, 191–200.
Phogat, V., Yadav, A.K., Malik, R.S., Kumar, S., Cox, J., 2010. Simulation of salt andwater movement and estimation of water productivity of rice crop irrigatedwith saline water. Paddy Water and Environment 8, 333–346.

Phogat, V., Mahadevan, M., Skewes, M., Cox, J.W., 2012. Modelling soil water andsalt dynamics under pulsed and continuous surface drip irrigation of almondand implications of system design. Irrigation Science 30 (4), 315–333.
Phogat, V., Skewes, M.A., Mahadevan, M., Cox, J.W., 2013. Evaluation of soil plantsystem response to pulsed drip irrigation of an almond tree under sustained
stress conditions. Agricultural Water Management 118, 1–11.
Ramos, T.B., Šimůnek, J., Goncalves, M.C., Martins, J.C., Prazeres, A., Castanheira,N.L., Pereira, L.S., 2011. Field evaluation of a multicomponent solute transport model in soils irrigated with saline waters. Journal of Hydrology 407,
129–144.
Ramos, T.B., Šimůnek, J., Goncalves, M.C., Martins, J.C., Prazeres, A., Pereira, L.S., 2012.
Two-dimentional modelling of water and nitrogen fate from sweet sorghum
irrigated with fresh and blended saline waters. Agricultural Water Management
111, 87–104.
Sansoulet, J., Cabidoche, Y.M., Cattan, P., Ruy, S., Šimůnek, J., 2008. Spatiallydistributed water ﬂuxes in an andisol under banana plants: experiments and three-dimensional modelling. Vadose Zone Journal 7, 819–
829.
Schaap, M.G., Leij, F.J., van Genuchten, M.Th., 2001. ROSETTA: a computer programfor estimating soil hydraulic parameters with hierarchical pedotransfer functions. Journal of Hydrology 251, 163–176.
Scholberg, J.M.S., Parsons, L.R., Wheaton, T.A., McNeal, B.L., Morgan, K.T., 2002. Soil
temperature, nitrogen concentration, and residence time affect nitrogen uptake
efﬁciency in citrus. Journal of Environmental Quality 31, 759–768.
Šejna, M., Šimůnek, J., van Genuchten, M.Th., 2011. The HYDRUS software package forsimulating two- and three-dimensional movement of water, heat, and multiple
solutes in variably-saturated media. User Manual, Version 2. PC Progress, Prague,
Czech Republic, pp. 280.
Šimůnek, J., van Genuchten, M., Šejna, Th.M., 2008. Development and applications of
the HYDRUS and STANMOD software packages and related codes. Vadose Zone
Journal 7, 587–600.
Šimůnek, J., Hopmans, J.W., 2009. Modeling compensated root water and nutrient
uptake. Ecological Modelling 220, 505–521.
Šimůnek, J., van Genuchten, M.Th., Sejna, M., 2011. The HYDRUS software package forsimulating two- and three-dimensional movement of water, heat, and multiple
solutes in variably-saturated media. Technical Manual, Version 2 PC Progress,
Prague, Czech Republic, pp 258.
Skaggs, T.H., Trout, T.J., Rothfuss, Y., 2010. Drip irrigation water distribution pattern:
Effects of emitter rate, pulsing and antecedent water. Soil Science Society ofAmerica Journal 74, 1886–1896.
Sluggett, A.F., 2010. Solute dynamics in advanced fertigated horticulture. In: Thesis.
School of Chemistry, Physics and Earth Science, Flinders University, SA, Australia.
Subbaiah, R., 2011. A review of models for predicting soil water dynamics during trickle irrigation. Irrigation Science, http://dx.doi.org/10.1007/
s00271-011-0309-x (published online).
Syvertsen, J.P., Sax, S.M., 1999. Fertigation frequency, wetting patterns, and nitrateleaching from lysimeter grown citrus trees. Proceedings of Florida State Hortcultural Society 112, 9–14.
Syvertsen, J.P., Smith, M.L., Boman, B.J., 1993. Tree growth, mineral nutrition andnutrient leaching losses from soil of salinized citrus trees. Journal of Agriculture,
Ecosystem and Environment 45, 319–334.
Taylor, S.A., Ashcroft, G.M., 1972. Physical Edaphology. Freeman and Co, San
Francisco, CA, USA, pp. 434–435.
Tournebize, J., Gregoire, C., Coupe, R.H., Ackerer, P., 2012. Modelling nitrate transport
under row intercropping system: Vines and grass cover. Journal of Hydrology
440–441, 14–25.
Treeby, M., Falivene, S., Phogat, V., Skewes, M., 2012. Knowledge and tools to manage
fertigation technologies in highly productive citrus orchards for minimal environmental footprint. Final Report to National Program for Sustainable Irrigation.
NSW DPI, Dareton, Australia, pp. 41.
Van der Laan, M., Stirzaker, R.J., Annandale, J.G., Bristow, K.L., du Preez, C.C.,
2010. Monitoring and modelling draining and resident soil water nitrate concentrations to estimate leaching losses. Agricultural Water Management 97,
1779–1786.
van Genuchten, M.Th., 1980. A closed form equation for predicting the hydraulicconductivity of unsaturated soils. Soil Science Society of America Journal 44,
892–898.
Vrugt, J.A., Hopmans, J.W., Šimůnek, J., 2001. Calibration of a two dimensional root
water uptake model. Soil Science Society of America Journal 65, 1027–1037.
Wang, F.L., Alva, A.K., 1996. Leaching of nitrogen from slow release urea
sources in sandy soils. Soil Science Society of America Journal 60,
1454–1458.
Zhang, M., Alva, A.K., Li, Y.C., Calvert, D.V., 1996. Root distribution of grapefruit trees
under dry granular dry broadcast vs. fertigation method. Plant and Soil 183,
79–84.