Irrig Sci (2016) 34:53–69
DOI 10.1007/s00271-015-0487-z

ORIGINAL PAPER

The effect of different fertigation strategies and furrow surface
treatments on plant water and nitrogen use
Jirka Šimůnek1 · Keith L. Bristow2 · Sarah A. Helalia1 · Altaf A. Siyal3

Received: 12 April 2015 / Accepted: 30 November 2015 / Published online: 21 December 2015
© Springer-Verlag Berlin Heidelberg 2015

Abstract Furrow irrigation and fertigation systems
should be designed and managed to optimize the availability of water and fertilizer to plants and minimize theirlosses through evaporation, deep drainage and leaching.
We developed a furrow irrigation submodule for HYDRUS(2D/3D) and used it to evaluate the effects of different furrow soil surface treatments and different timings of fertigation on root water and solute uptake, deep drainage and solute leaching in a loamy soil. Numerical simulations showedthat more water was available for transpiration in the treatments with plastic placed at the furrow bottom compared tothe control treatments. However, more water was lost due
to evaporation and less water was drained from the soil profile for these treatments. The highest and lowest root solute
uptake was achieved when fertigation was applied in the
middle and at the beginning of the irrigation cycle, respectively. The least amount of solute was leached from the soil
profile for treatments with the plastic bottom and when fertigation was applied at the end of the irrigation cycle. The
Communicated by J. Hornbuckle.
* Jirka Šimůnek
Jiri.Simunek@ucr.edu
Keith L. Bristow
Keith.Bristow@csiro.au
Altaf A. Siyal
aasiyal.uspcasw@muet.edu.pk
1

Department of Environmental Sciences, Universityof California Riverside, Riverside, CA 92521, USA

2

CSIRO Agriculture Flagship, PMB Aitkenvale, Townsville,
QLD 4814, Australia

3

U.S.‑Pakistan Centers of Advanced Studies in Water, Mehran
University of Engineering and Technology, Jamshoro,
Pakistanscenarios with plastic and irrigation in alternate furrows
showed a reduction in transpiration and yield, more water
loss due to deep drainage, and less water lost due to evaporation. However, similar crop yields were obtained for thisalternate furrow strategy as for the control furrow surface
treatments. When only half the water was used for irrigation in this scenario, the reduction in yield was less than
20 % compared to the control treatments, producing higher
water-use efficiency.

Introduction
Fertigation can be defined as the injection of various watersoluble chemicals, such as fertilizers or soil amendments,
into agricultural irrigation systems, including drip, sprinkler and surface irrigated systems (Sabillón and Merkley2004). Fertigation is most commonly used with drip andsprinkler systems (e.g., Cote et al. 2003; Hanson et al.
2006), while its use with surface irrigation methods ismuch less common (Sabillón and Merkley 2004; Soroush
et al. 2012; Ebrahimian et al. 2014). Since furrow irrigation is the most frequently used irrigation method internationally, furrow fertigation has great potential to become acost-effective method of applying fertilizers to agricultural
fields (Soroush et al. 2012). To be successful, the furrow
irrigation and fertigation systems should be designed andmanaged so that the application and distribution of waterand fertilizer are efficient and uniform, with minimal surface runoff at the lower end of the field, and minimal deep
drainage and leaching below the crop root zone (Sabillón
and Merkley 2004).
Timing of fertigation during an irrigation cycle, andresulting availability of applied fertilizers to plants, hasreceived considerable attention in the past (e.g., Hou et al.

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2007), especially for drip irrigated systems (e.g., Coteet al. 2003; Gärdenäs et al. 2005; Hanson et al. 2006). For
example, Cote et al. (2003) used the HYDRUS-2D model(Šimůnek et al. 2008) to evaluate the spatial distributionof a fertilizer, which was applied either at the beginning orat the end of subsurface drip irrigation. They concluded,
contrary to general expectations, that for highly permeable
coarse-textured soils, nutrients applied at the beginning ofan irrigation cycle will reside in larger amounts near to andabove the emitter than when applied at the end of an irrigation cycle, thereby making them less susceptible to leaching losses. Gärdenäs et al. (2005) evaluated five different
fertigation strategies for three different microirrigation
systems. They assumed that fertilizers can be applied in ashort pulse either at the beginning, in the middle, or at theend of an irrigation cycle, in the middle half of the irrigation cycle, or continuously. They considered a micro-sprinkler system, subsurface and surface irrigation tapes, andsubsurface drip irrigation systems. Gärdenäs et al. (2005)
concluded that fertigation applied at the beginning of anirrigation cycle tends to increase seasonal nitrate leaching
and that fertigation applied at the end of an irrigation cycle
tends to reduce nitrate leaching. While Cote et al. (2003)
evaluated only one irrigation cycle, Gärdenäs et al. (2005)
simulated a 1-month time period with multiple irrigation
cycles, which may explain the different results obtained inthese two studies.
There are many studies that evaluated fertigation timing in furrow irrigation (e.g., Bouwer et al. 1990; Playán
and Faci 1997; Sabillón and Merkley 2004; Adamsen et al.
2005; Burguete et al. 2009; Ebrahimian et al. 2013b). For
example, Bouwer et al. (1990) and Soroush et al. (2012)
recommended that in order to avoid leaching of fertilizers
to groundwater, fertigation should be applied toward theend of an irrigation event. Playán and Faci (1997), however, concluded that applying fertilizer at a constant rateduring the entire irrigation event is usually the best solution, since an instantaneous release of fertilizer into theirrigation stream often produces low fertilizer uniformities
in the field. Sabillón and Merkley (2004) reported that timing of fertigation is significantly affected by soil infiltration
characteristics, furrow length and slope.
Adamsen et al. (2005) carried out field experiments tocompare different strategies for timing injection of bromide, as a surrogate for nitrate, into the irrigation water
during border irrigation. The bromide was injected either
during the first half, the middle half, or the last half of theirrigation, or during the entire irrigation. Adamsen et al.
(2005) concluded, similarly to Playán and Faci (1997) and
Abbasi et al. (2003c), that the best distribution uniformity
is obtained when bromide was injected during the entire
irrigation event. Burguete et al. (2009) developed a simulation model, which considered overland water flow, solute

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Irrig Sci (2016) 34:53–69

transport and infiltration, and used it to evaluate the effectsof irrigation discharge, fertilizer application timing and furrow geometry on fertilizer uniformity. Ebrahimian et al.
(2013b) used genetic algorithms and the one-dimensionalsurface and two-dimensional subsurface models to optimize timing of fertigation in alternate furrow irrigation.
They concluded that by optimizing the start time and theduration of fertilizer injection, they could reduce nitratelosses due to deep percolation and surface runoff by up to
50 %.
In standard irrigation furrows, water infiltration into thesoil profile is driven by gravitational forces in the downward vertical direction and by capillary forces horizontallyand upward into the ridge. In furrows, in which verticallydownward infiltration from the bottom of the furrow iseither reduced or eliminated altogether (Siyal et al. 2012),
water infiltration is driven mainly by capillary forces horizontally and upward into the ridge. The recommendations
for fertigation timing, some of which appear contradictoryeven for standard furrows (e.g., Soroush et al. 2012; Playán
and Faci 1997), may thus be different for these non-conventional furrows (with reduced downward infiltration) andmay resemble drip irrigation systems, in which capillary
forces play an important role.
The HYDRUS (2D/3D) model and its predecessors,
such as SWMS-2D and HYDRUS-2D, have been widelyused in the past to simulate water flow and/or solute transport for furrow irrigation systems (e.g., Benjamin et al.
1994; Abbasi et al. 2003a, b, 2004; Rocha et al. 2006;
Wöhling et al. 2004a, b, 2006; Mailhol et al. 2007; Warrick
et al. 2007; Wöhling and Schmitz 2007; Wöhling and Mailhol 2007; Crevoisier et al. 2008; Lazarovitch et al. 2009;
Ebrahimian et al. 2012, 2013a, b; Zerihun et al. 2014). For
example, Benjamin et al. (1994) simulated fertilizer distribution in the soil under broadcast fertilization for conventional and alternate furrow irrigation. They concluded that
fertilizer applied on the non-irrigated furrows may not betaken up by plants because of the low water content in theupper layer of this furrow. Rocha et al. (2006) carried out
an extensive sensitivity analysis to investigate the effects ofvarious soil hydraulic properties on subsurface water flow
below furrows. Abbasi et al. (2003a, b, 2004) obtained satisfactory agreement between measured and predicted soil
water contents and solute concentrations along the blockedend furrow cross-section using the HYDRUS-2D model.
Similarly, Mailhol et al. (2007) and Crevoisier et al. (2008)
found that the HYDRUS-2D model performed well in
simulating soil matric potential, nitrate concentrations andnitrogen leaching in conventional and alternate furrow irrigated systems in season-long studies, which included bothroot water and nutrient uptake.
Wöhling and Schmitz (2007) developed a numerical model that coupled 1D surface flow (zero-inertia),

Irrig Sci (2016) 34:53–69

HYDRUS-2D, and a crop growth model. This model wasthen used to adequately predict advance and recession
times, soil moisture and crop yield (Wöhling and Mailhol
2007). Ebrahimian et al. (2012) compared the performanceof the HYDRUS-1D and HYDRUS-2D simulation models
to simulate water flow and nitrate transport for conventional furrow irrigation, fixed alternate furrow irrigation,and variable alternate furrow irrigation using different fertigation strategies. Ebrahimian et al. (2013a, b) used theone-dimensional surface and two-dimensional subsurface
models to minimize nitrate losses in two types of alternate
furrow fertigation systems.
While some of these studies involved only simulations(e.g., Rocha et al. 2006; Warrick et al. 2007; Lazarovitch
et al. 2009), in many studies the HYDRUS (2D/3D) model
was calibrated and tested using experimental data (e.g.,
Abbasi et al. 2003a, b, 2004; Wöhling and Mailhol 2007;
Crevoisier et al. 2008; Zerihun et al. 2014), providing its
future users with confidence that the model can adequately
describe these complex systems. However, very few ofthese studies, with the exception of Gärdenäs et al. (2005)
and Wöhling and Schmitz (2007), considered multiple irrigation/fertigation cycles and the effects of plants on subsurface flow and transport processes. Most studies evaluatedonly a single irrigation cycle and neglected the effects ofplant roots on subsurface processes.
While many of the studies discussed above focused onflow and transport along a furrow, Abbasi et al. (2003a, b)
and Siyal et al. (2012) evaluated subsurface flow and transport in the soil profile perpendicular to the furrow. Siyal
et al. (2012) developed a furrow irrigation submodel for
HYDRUS (2D/3D) and then used this model to analyze theeffects of different furrow irrigation rates, different treatments of the soil surface at the bottom of the furrow, anddifferent initial locations of the fertilizer on water and solute leaching in a furrow irrigated system. Siyal et al. (2012)
did not, however, apply fertilizers with the irrigation water
nor did they consider root water uptake. On the contrary,
they assumed that the fertilizer (nitrogen) was initiallylocated at five different locations, ranging from the bottomof the furrow to the top of the ridge, and allowed the solute
to move with the water without being intercepted by plantroots. The different soil treatments at the bottom of the furrow included (a) untreated (So), i.e., it remained as a control
with normal soil hydraulic properties, (b) compacted (Sc),with its hydraulic conductivity reduced by 80 % of So, and(c) covered with an impermeable polymer membrane (Sp)with zero conductivity.
The objectives of this study are (a) to extend the furrow irrigation submodel of Siyal et al. (2012) to include processes ofprecipitation, evaporation and fertigation in the furrow, (b) toevaluate this model with respect to different water and solute
fluxes and volumes, and corresponding solute concentrations,55in the furrow, as well as in the soil profile, (c) to evaluate theeffectiveness of different treatments of the furrow bottom andfertigation timing strategies to supply water and nutrients toplants, and (d) to evaluate the combined effects of plant waterand nutrient uptake with different furrow treatments and fertigation strategies to limit water and nutrient leaching and toprovide optimal conditions for plants. Rather than evaluating
only a single irrigation/fertigation cycle, which may not fully
address the long-term processes such as root water and nutrient
uptake and leaching, the objective of this study is to evaluate
cumulative effects of a series of irrigation/fertigation cycles.

Materials and methods
Numerical simulations of the furrow irrigation system werecarried out with the HYDRUS (2D/3D) software package(Šimůnek et al. 2008), which was updated with the modified furrow mass balance submodule (Siyal et al. 2012).
Below, we first describe the additional modifications incorporated into the furrow mass balance submodule of Siyal
et al. (2012) and follow with a brief description of the
HYDRUS (2D/3D) software.
The furrow mass balance module
Siyal et al. (2012) developed a furrow irrigation module,
which calculated the water level in the furrow based on themass balance in the furrow for a specified irrigation flux,
Qp, and calculated infiltration flux, Qin. The infiltration
flux was calculated using the HYDRUS (2D/3D) software,
which adjusts boundary conditions at the bottom and sidesof the furrow in response to changes in the water level inthe furrow (Fig. 1).
In addition to the irrigation and infiltration processes
considered by Siyal et al. (2012), in this study we also
account for precipitation, evaporation and fertigation. The
mass balance equation for water in the furrow is expressedas:dS= Qp (t) − Qin (t) + (P − E)bdt(1)where S is the volume of water in the half-furrow [L2], Qp
and Qin are irrigation and infiltration fluxes to/from thehalf-furrow [L2T−1], respectively, P and E are precipitationand evaporation rates [LT−1], respectively, and b is the halfwidth of the water surface in the furrow [L]. The height of
the water level in the furrow, hw [L], is calculated in thesame ways as in Siyal et al. (2012) except that we now also
include the last term of (1) to account for precipitation andevaporation.
The module requires as input the description of thegeometry of the furrow (α and a), the supply rate (Qp),

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where cp is the solute concentration of irrigation water(fertigation) [ML−3; or dimensionless], and c is the average solute concentration of the furrow water and hence theconcentration of the infiltrating water [ML−3]. Note that weassume that precipitation and evaporation fluxes are devoidof solutes and that there is an instantaneous and complete
mixing of solute in the furrow. Precipitation will therefore
lead to dilution of solute in the furrow water, while evaporation will lead to increasing concentrations. The module
requires as input the solute concentration in the irrigationwater (cp) and the timing of fertigation (i.e., the beginningand the end time of fertigation). The module then calculates
the solute concentration in the furrow water, c, which issubsequently used in a Cauchy (concentration flux) boundary condition together with the local infiltration flux calculated by HYDRUS.
Fig. 1  Schematic showing a half-furrow and the implementation ofa special boundary condition accounting for variable water depth in
the furrow (Qp is the irrigation water supply rate, cp is the solute concentration in the incoming irrigation water, Qin is the water infiltration rate from the furrow into the soil profile across the furrow walls,c is the solute concentration in the furrow water and in the infiltration water, S is the volume of water in the half-furrow, hw is the waterlevel in the furrow, α is the angle defining the slope of the ridge side,
a is the half-width of the bottom of the furrow, b is the half-widthof the water surface, and P and E are precipitation and evaporation
fluxes, respectively)

precipitation and evaporation fluxes (P and E), and theneither the duration of irrigation or the maximum water level(hw,max) that can be reached before water supply is stopped.
The module calculates the position of the water level in the
furrow by considering the irrigation flux, which is the resultof the numerical solution of the Richards equation for specified dynamic boundary conditions. The relevant parts ofthe boundary below and above the water level in the furrow
are in HYDRUS assigned the time-variable pressure head
(Dirichlet) and seepage face boundary conditions, respectively. HYDRUS calculates which part of the seepage faceboundary is active (with a prescribed zero pressure head)
and which is inactive (with a prescribed zero flux or atmospheric boundary conditions). Once the furrow is empty ofwater, the atmospheric BC is applied at the furrow bottom
in addition to the sides of the ridge (Siyal et al. 2012).
The mass balance equation for solute in the furrow isexpressed as:
d(Sc)
dc
dS
=S +c
= Qp (t)cp − Qin (t)c
dt
dt
dt


dc
S
= Qp (t)cp − Qin (t)c − c Qp (t) − Qin (t) + (P − E)b
dt


dc
= Qp (t) cp − c − c[(P − E)b]
S
(2)
dt

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Governing water flow and solute transport equations
Variably-saturated water flow in soil is described in
HYDRUS by the modified Richards equation:
 

∂
∂θ
A ∂h
A
=
K Kij
+ Kiz
−S
(3)
∂t
∂xi
∂xj
where θ is the volumetric water content [L3L−3], h is thepressure head [L], S is a sink term accounting for root water
uptake [T−1], xi (i = 1,2) are spatial coordinates [L], t is
time [T], KAij are components of a dimensionless anisotropy
tensor KA, and K is the unsaturated hydraulic conductivity
function [LT−1] given as the product of the relative hydraulic conductivity Kr and the saturated hydraulic conductivity
Ks [LT−1].
The soil hydraulic parameters for loam [the same soil
as used by Siyal et al. (2012)] were taken from the soil
catalog provided by the HYDRUS software. The valuesof these parameters are: residual water content = 0.078;
saturated water content = 0.43; shape parameters α and n
are 0.036 cm−1 and 1.56, respectively; saturated hydraulic conductivity = 24.96 cm/day. For this soil, the field
capacity is 0.165 (pressure head −330 cm) and the watercontent at the wilting point (pressure head −15,000 cm) is
0.088 cm3 cm−3. The critical pressure head and water content values when evaporation falls below its potential valueare −10,000 cm and 0.091, respectively.
Solute transport is described in HYDRUS by the convection–dispersion equation:


∂
∂qi c
∂c
∂θc
=
θ Dij
−
− Scr
(4)
∂t
∂xi
∂xj
∂xi
where c is the solute concentration [ML−3], qi is the i thcomponent of the volumetric flux density [LT−1], Dij isthe dispersion coefficient tensor [L2T−1], and cr is the concentration of the sink term [ML−3]. The longitudinal andIrrig Sci (2016) 34:53–69

57

Fig. 2  Schematic representation of the transport domain showing the main hydrological fluxes (left) and initial and boundary conditions (right;
see also Siyal et al. 2012)transverse dispersivities were set at 10 and 1 cm that is at
one-tenth and one-hundreds of the depth of the soil profile(Beven et al. 1993), respectively. Note that no reactions
are considered in (4) so it can only be used to describe
the transport of nonreactive solutes such as chloride andnitrate.
Root water and nutrient uptake
Root water uptake is described in HYDRUS using theapproach of Feddes et al. (1978):(5)

S(h) = α(h)b(x, z)Lt Tp−1

where S is the root water uptake rate [T ], α(h) is a water
stress response function, b(x, z) is a normalized function
describing the spatial distribution of water uptake [L−2],
Lt is the width [L] of the soil surface associated with thetranspiration process (Lt = 40 cm; surface of the furrow ridge, see the definition of the transport domain in
Fig. 2), and Tp is the potential transpiration rate [LT−1](Tp = 0.8 cm/day). The following parameters of the stressresponse function (typical for many crops) were used in ourstudy: h1 = −10 cm, h2 = −25 cm, h3 = −200 cm, andh4 = −8000 cm (Feddes et al. 1978).
The two-dimensional root distribution function b(x,z) of
Vrugt et al. (2001, 2002) was used to describe the spatial
distribution of roots:


 p

x x ∗ −xxz
− z |z∗ −z|+ Xpm
|
|
1−
e Zm
b(x, z) = 1 −
(6)
Zm
Xm

where Xm and Zm are the maximum rooting lengths in thex and z directions [L], respectively; x and z are distancesfrom the origin of the plant in the x and z directions [L],respectively; and px [-], pz [-], x ∗ [L], and z∗ [L] are empirical parameters. The plant was centered in the middle of theridge. The maximum extent of roots in the vertical (Zm)and horizontal (Xm) directions was set at 60 and 35 cm,
respectively, parameters x ∗ and z∗ (sometimes referred toas Depth and Radius of Maximum Intensity) were set at
30 and 20 cm, respectively, and parameters px and pz wereset at one for x < x ∗ and z < z∗, and zero elsewhere. Notethat the spatial distribution of roots was considered to beconstant in time, i.e., no root growth was included in thesimulations.
Only non-compensated root water uptake and passiveroot nutrient uptake (Šimůnek and Hopmans 2009) wereconsidered in this study, i.e., cr in (4) was assumed to beequal to the solute concentration at any particular location.
Using this approach allows us to better evaluate the availability of water and solutes to plant roots.
Flow domain, initial and boundary conditions
Figure 2 (left) shows a schematic representation of thetransport domain with the main hydrological fluxes. It was
assumed that the total incoming energy (ETp) was equal
to 1 cm/day, which corresponds to conditions in January
in north Queensland, Australia. This incoming energy was
divided at the top of the furrow into potential evaporation(Ep) of 0.2 cm/day and potential transpiration (equivalent toroot water uptake) (Tp) of 0.8 cm/day. All incoming energy

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(ETp = 1 cm/day) was assumed to reach the water in the
furrow, or the bottom and sides of the furrow. The total
potential flux at the soil surface of the transport domain
during one irrigation cycle was thus equal to 700 cm2/week(= 1 cm/day × 100 cm × 7 day/week).
Figure 2 (right) shows the dimensions of the transportdomain with two half-furrows and the applied initial andboundary conditions, which were the same as in Siyal et al.
(2012). The soil profile was assumed to be initially solute
free. Simulations were carried out for soil hydraulic properties representing a loamy soil (according to a HYDRUS
catalog).
Description of the simulated scenarios
Simulations were carried out for 28 days (4 weeks) to show
the combined/cumulative effects of multiple irrigation/
fertigation cycles. Irrigations were applied every 7 days
(once per week; unless indicated otherwise) with the irrigation flux set at 1200 Lh−1 furrow−1 for a 100 m long
furrow, corresponding to an area based application rate of
12 mm h−1, or to a flux of 60 cm2h−1 in our two-dimensional domain. Contrary to Siyal et al. (2012) who used
the so-called ‘switch-off depth’ to end the irrigation event,in this study we applied a pre-set amount of irrigation at a
fixed 7 day cycle. We compared the effects of two different amounts of irrigation by setting the duration at either
4 or 6 h. This gives irrigation volumes that correspond to
69 % (4 h × 60 cm2 h−1 × 2 = 480 cm2/week) and 103 %(6 h × 60 cm2 h−1 × 2 = 720 cm2/week) of total ETp,
respectively.
The same soil surface treatments as in Siyal et al.
(2012) were considered in this study (see Fig. 2 in Siyal
et al. (2012)). The soil at the furrow bottom was either (a)untreated, i.e., it remained in standard conditions with normal soil hydraulic properties (So), which served as the control, (b) compacted with its hydraulic conductivity of the
top 2 cm of soil reduced by 80 % (Sc) compared with thecontrol, or (c) was covered with an impermeable membraneso that the hydraulic conductivity was zero at the bottom of
the furrow (Sp).
Since it may be difficult to maintain surface plastic on
the base of the furrow while allowing access to the fieldby agricultural machinery, the Sp treatments were rerunfor situations where both the plastic and irrigation are present only in alternate furrows, while the in-between furrow
retains its natural condition (So). For the alternate furrow
irrigation, we considered three scenarios. In scenario one(Sa1), the same duration of irrigation was used as for the
Sp treatments, which resulted in half of the irrigation water
being applied to the field. In scenario two (Sa2), the duration of irrigation was doubled, which resulted in the sameamount of irrigation water being applied to the field as for

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the Sp treatments. In scenario three (Sa3), the same durationof irrigation was used as for the Sp treatments, but the frequency of irrigation was doubled (i.e., irrigation occurred
every 3.5 days), which resulted in the same amount ofirrigation water being applied to the field as for the Sp
treatments.
Four fertigation strategies were considered. The first
three involved 1 h fertigation events, applied at the beginning (B), in the middle (M) and at the end (E) of the irrigation cycle. The fertigation at the end was started 1.5 h
before the end of the irrigation cycle to allow half an hour
without fertigation before ending the irrigation cycle. The
fourth fertigation strategy involved application of fertigation throughout the irrigation cycle. Simulations were carried out using a dimensionless solute concentration, and thesolute concentration of the irrigation water was selected
so that 100 units of mass were applied during the 1-month
simulations (i.e., during the four irrigation cycles). This
allows us to present calculated solute fluxes, such as leaching and root uptake, as a percent of the total applied. For
the 1-h long fertigations, the solute concentration in irrigation water was calculated as:
Sc = nf nir Qp Cp tp
and
Cp =

Sc
nf nir Qp tp=

1002(half - furrows) × 4(irrigation cycles) × 60(m2 /h) × 1(h)= 0.20833(7)

where nf is the number of half-furrows in the transportdomain, nir is the number of irrigation cycles, and tp is theduration of fertigation [T]. Concentrations were lowered
appropriately for the continuous fertigation. We would liketo emphasize that our current model considers only processes in the plane perpendicular to a furrow and neglects
processes along the furrow, such as the advancement and/or
recession of the irrigation water front.

Results and discussion
Dynamics of the water and solute mass balance in the
furrowFirst, we will evaluate the functioning of the newly developed “Furrow” module and its coupling with the HYDRUS(2D/3D) model during one irrigation/fertigation cycle. We
will describe both water and solute mass balances, as well
as all main fluxes into/out of the furrow.
Figures 3, 4, 5, 6 and 7 show the dynamics of waterand solute in the furrow during one irrigation cycle forIrrig Sci (2016) 34:53–69

Fig. 3  Volume of water in the (half) furrow, and cumulative irrigation, infiltration, and evaporation fluxes for treatments So (left) andSp (right). The end of irrigation (0.25 day) is indicated by a vertical59

dashed line. The end of infiltration (when all water infiltrated into thesoil profile) is at about 0.41 day (left) and 0.70 day (right)

or 1.5 h before the end of irrigation. This concentration
will provide 100 units of fertigation during four irrigation cycles (0.20833 × 4 irrigation cycles × 2 half-furrows × 60 cm2/h × 1 h = 100 cm2 = 100 %). Potential
evapotranspiration is equal to 1 cm/day.
Water balance and fluxes

Fig. 4  Water level in the furrow during one irrigation cycle for treatments So (normal) and Sp (plastic). The end of irrigation (0.25 day) is
indicated by a vertical dashed line

treatments with either the standard untreated bottom of the
furrow (So; referred to as the “control”) (left) or with theimpermeable membrane placed on the bottom of the furrow(Sp; referred to as “plastic”) (right). Irrigation is applied at
a rate of 60 cm2/h for 6 h and fertigation is applied at adimensionless concentration of 0.20833 during 1 h either
at the beginning of irrigation, in the middle of irrigation,

Figure 3 shows cumulative irrigation, infiltration, andevaporation fluxes to/from the (half) furrow, as well as thewater volume in the furrow during one irrigation cycle.
Figure 4 shows the water level and Fig. 5 shows the irrigation and infiltration fluxes during the same time. Irrigation is applied for 6 h (0.25 day) and water infiltrates fromthe furrow to the soil profile for about 10 h (0.41 day) intreatments So and about 18.5 h (0.70 day) in treatments Sp.
Since the irrigation flux is larger than the infiltration flux
(Fig. 5), the water volume and the water level in the furrow
increases during the first 6 h (Figs. 3, 4). Once irrigation
stops, the water level starts to decrease, until all water infiltrates (Figs. 4, 5). The dynamics in the water level (Fig. 4)
is closely linked with the volume of water in the furrow(Fig. 3). It increases faster in the furrow with the plastic at

Fig. 5  Irrigation (red) and infiltration (blue) fluxes [cm2/day] during one irrigation cycle for treatments So (left) and Sp (right). The end of irrigation (0.25 day) is indicated by a vertical dashed line

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Fig. 6  Concentrations in furrow water during one irrigation cycle when fertigation is applied either at the Beginning, in the Middle, or at theEnd of irrigation for treatments So (left) and Sp (right). The end of irrigation (0.25 day) is indicated by a vertical dashed line

Fig. 7  Solute mass applied (Fertigation; black line), solute mass infurrow water (Solute in Furrow; blue line), and solute mass infiltrated(Solute Infiltration; red line) during one irrigation cycle when ferti-

gation is applied either at the beginning (solid lines), in the middle(dashed lines), or at the end (dotted lines) of irrigation for treatments
So (left) and Sp (right)

the bottom (Sp) because of reduced infiltration comparedto the So treatments (Fig. 4). On the other hand, the subsequent decrease in the water level (volume) is significantly
slower in the Sp treatments compared to the So treatments,
again due to reduced vertically downward infiltration(Fig. 4). Evaporation is considerably smaller than the otherfluxes (Fig. 3). The volume of water in the furrow is thus
approximately equal to the difference between cumulative
irrigation and cumulative infiltration (Fig. 3).
Figure 5 shows that the infiltration process is complex infurrow irrigation. In the So treatments, initially all applied
irrigation water infiltrates into the soil profile and thus
infiltration and irrigation fluxes are the same. Once water
starts ponding in the furrow, the infiltration curve follows
a typical hyperbolic curve, similar to that for one-dimensional infiltration from ponding (e.g., Kostiakov, Philip andHorton, etc.). However, as the water level in the furrow
increases, a larger surface area becomes active in the infiltration process (not only the bottom of the furrow, but also
increasingly on the sides of the furrow), and the infiltration
rate starts increasing. Once irrigation stops, the water levelin the furrow starts decreasing, and so does the infiltration
rate, until it becomes zero once all water has infiltrated.
In the Sp treatments, the initial infiltration rate is muchsmaller than for the So treatments because the bottom of the
furrow is impermeable and only a small fraction of the furrow sides are exposed to ponding water. As for the So treatments, as the water level in the furrow increases a larger
surface area becomes active in the infiltration process, andthe infiltration rate starts increasing. Once irrigation stops,
the water level in the furrow starts decreasing, and so does
the infiltration rate, albeit at a much slower rate than for
the So treatments due to the impermeable bottom, until it
becomes zero when all water has infiltrated.

13

Solute balance and concentrations
Fertigation is applied at a dimensionless concentration of
0.20833 during 1 h either at the beginning of irrigation, inthe middle of irrigation, or 1.5 h before the end of irrigation. During one irrigation cycle, the applied solute mass to
one half-furrow is 12.5 % (0.20833 × 60 cm2/h × 1 h = 1

Irrig Sci (2016) 34:53–69

2.5 cm2). Figures 6 and 7 show results for all three fertigation strategies. It is assumed that there is a complete mixingof water in the furrow (applied irrigation water is instantaneously mixed with water already in the furrow) so theconcentration can be represented by a single value.
Figure 6 shows the average solute concentrations in
the furrow for the three fertigation strategies. When soluteis applied at the beginning of the irrigation cycle (Fig. 6;
Beginning), the concentration in the furrow water is equal
to the concentration in the irrigation water. Once fertigation stops and infiltration continues, water in the furrow isquickly diluted by continued inflow of irrigation water andthe concentration decreases rapidly. When solute is appliedlater in the irrigation cycle (Fig. 6; Middle and/or End),
incoming irrigation water mixes with the volume of water
already in the furrow so the highest concentrations that arereached have lower values than when fertigation is appliedat the beginning of the irrigation cycle. Once infiltration
stops (at 0.25 day), furrow concentrations stop decreasing
and remain more or less the same. There is only a small
increase in concentration during this period (after irrigation stops and the remaining furrow water keeps infiltrating
into the soil profile) as a result of evaporation, which concentrates solutes in the furrow water. This effect, which isrelatively minor, is much more pronounced for the Sp treatments because of the slower infiltration rates and longer
duration of the infiltration process.
Figure 7 shows the solute mass in the furrow and cumulative fertigation and infiltration fluxes. When solute isapplied at the beginning of the irrigation cycle, it immediately infiltrates into the soil profile, so less solute mass isstored in the furrow. When solute is applied later in the irrigation cycle and mixes with water in the furrow, the initial
furrow concentrations are lower than when solute is appliedat the beginning (Fig. 6). Consequently, solute infiltrates
slower into the soil profile and more solute is stored in the
furrow over longer periods of time (Fig. 7). At the end of
the irrigation cycle, all water infiltrates into the soil profileand thus the final solute mass is equal to zero and solute
mass applied (fertigation) and infiltrated are the same.
Dynamics of the water and solute mass balance in the
soil
Water fluxes
Table 1 shows the cumulative values of the differenthydrological fluxes and the change in water storage in thetransport domain, the duration of irrigation and infiltration, water-use efficiency (WUE), and the plant yield forthe 6- and 4-h irrigations for the So, Sc, Sp treatments and
Sa scenarios (during the first irrigation cycle). Note thatin Table 1, the plant yield is defined as the ratio of the61

actual to potential transpiration, expressed as a percentage(=100 × Ta/Tp), and that drainage is reported at a depth of−100 cm, i.e., at the bottom of the soil profile.
Values in Table 1 can be compared with the total amountof applied irrigation water (60 cm2/h × 0.25(0.1666) day × 24 h × 2 half-furrows × 4 irrigation cycles = 2880
(1920) cm2 for 6 (4) hour irrigations), cumulative potential transpiration (0.8 cm/day × 40 cm × 28 day = 896 cm2), cumulative potential evaporation from the surface ofthe ridge (0.2 cm/day × 40 cm × 28 day = 224 cm2) andcumulative potential evaporation from the furrow (1.0 cm/
day × 60 cm × 28 day = 1680 cm2).
Table 1 shows that although irrigation volume is thesame in all three standard treatments (So, Sc, and Sp) and
two alternate furrow scenarios (Sa1 and Sa3), infiltration
is different, because water is lost from the furrow due toevaporation (ETp) from the water surface. Since water
stays the longest in the furrow with the plastic bottom (seeInfiltration duration), most water is lost via evaporation inthis scenario, and least water infiltrates into the soil profile(about 3 % less), compared to the control. Similar effects
can also be seen for the alternate furrow Sa scenarios, withlonger residence time of water in the furrow, but with asmaller surface exposed to evaporation.
Infiltration durations increase with increased restrictions
on direct downward infiltration from the base of the furrow
in the So treatment to the Sc and Sp treatments. Infiltration
durations are practically the same for the Sp treatment andthe Sa1 and Sa3 treatments, which all have the plastic bottom
and the same irrigation volume. This is because reported
irrigation durations are for the first irrigation cycle, wheninfiltration fronts from the two neighboring furrows of the
So treatment do not overlap and are thus similar to thosefrom alternative furrows (the Sa1 and Sa3 treatments).
Since root water uptake is optimal only for pressure
heads between the two stress response function pressure heads h2 (= −25 cm) and h3 (= −200 cm) and isreduced for pressure heads outside of this interval, actualroot water uptake is always reduced from its optimal value(Tp = 0.8 cm/day) (Fig. 8). Root water uptake is reduced
not only immediately after irrigation, since the pressure head around the furrow is higher than h2, but also
after irrigation stops because then a part of the root zone
becomes drier than h3. Figure 8 shows that plants are lessstressed in the Sp treatment (right) than in the So treatment(left), reflecting better root zone distribution of water andits availability in this treatment (Fig. 9). Figure 9 showsthat while in the So treatment water infiltrates predominantly downward and thus out of reach of plant roots, in
the Sp treatment, in which vertically downward infiltration is prevented, water moves predominantly sideways
into the root zone and upward into the ridge, increasing
root water uptake. Note that there is very little stress in the13

62
Table 1  Cumulative fluxes(cm2) over 28 days (4 irrigation
cycles) for 6 (top) and 4(bottom) hour irrigations for the
So (control), Sc (compacted), Sp(plastic) treatments and the Sa(alternate furrow) scenarios

Irrig Sci (2016) 34:53–69
Fluxes6-h irrigations
Infiltration
Transpiration
Evaporation from ridge
Evaporation from furrow
Drainage
Change in storage
Yield (%)
WUE (%)
Irrigation duration (day)Infiltration duration (day)4-h irrigations
Infiltration
Transpiration
Evaporation from ridge
Evaporation from furrow
Drainage
Change in storage
Yield (%)
WUE (%)
Irrigation duration (day)Infiltration duration (day)Furrow treatments

Alternate furrow scenarios

Control, So

Compacted, Sc

Plastic, Sp

Sa1

Sa2

Sa3

2880
−828
−27
−637
−687
700
92.4
28.3
0.25
0.4128

2824
−836
−67
−605
−582
731
92.7
29
0.25
0.5428

2775
−870
−99
−422
−579
806
97
31.1
0.25
0.699

1387
−664
−41
−213
−152
320
74.1
46.1
0.25
0.699

2787
−802
−90
−239
−1027
633
89.5
27.8
0.5
1.068

2770
−770
−104
−335
−788
772
85.9
26.7
0.25
0.699

1920
−727
−6
−551
−128
529
81.1
37.9
0.16666

1889
−733
−25
−527
−78
530
81.8
38.2
0.16666

1864
−819
−34
−357
−59
576
91.4
42.7
0.16666

943
−567
−19
−189
−27
122
63.3
59.1
0.16666

1853
−731
−59
−227
−385
455
81.5
38.1
0.3333

1841
−684
−57
−312
−253
535
76.3
35.6
0.16666

0.28850.4082

0.537

0.537

0.833

0.537

Scenarios Sa2 have 12- and 8-h irrigations. Additional information includes the duration (day) of irrigationand infiltration, change in water storage in the transport domain (cm2), the plant yield (%), and the wateruse efficiency (WUE) (%)

Fig. 8  Actual transpiration rate (= root water uptake) for the 6-h irrigation for treatments So (left) and Sp (right)

Sp treatment (Ta ≈ Tp, Fig. 8), in which water contents inthe entire soil profile, except for the shallow surface layerof the ridge, are above field capacity. This is also obvious
from the cumulative transpiration values shown in Table 1,
which display an increase in transpiration with the reduction in the downward flow through the bottom of the furrow(from treatments So, to Sc, and Sp). There is a further reduction in transpiration for the Sa scenario (alternate furrows

13with plastic and irrigation), since part of the root zone, furthermost from the furrow with plastic and irrigation, is not
fully supplied with water, resulting in water contents below
field capacity and reduced root water uptake (see Fig. 9).
While there is a reduction in transpiration in the alternate
furrow Sa scenarios, in which the same amount of water isapplied as in the original scenarios (i.e., in Sa2 and Sa3), thisIrrig Sci (2016) 34:53–69

63

Fig. 9  Soil water content profiles (t = 6 h in the last irrigation cycle) for the control treatment So (left), the treatment with plastic Sp (middle),
and the scenario with alternate furrow irrigations Sa (right)

reduction is only in the order of 10 % compared to the Sp
treatment and 3–7 % compared to the So treatment.
The same trend is also displayed by the corresponding
yield values. Yield is considerably higher for the Sp treatment compared to the So treatment, by 4 and 10 % for the
6- and 4-h irrigations, respectively. Yield for the 4-h irrigation of the Sp treatment is almost the same as yields for the
6-h irrigation for the So and Sc treatments. Yield for the Sa2
scenarios (alternate furrows; double irrigation duration) is
similar to the So treatment, since the positive effect of plastic in all furrows is reduced when it is present only in alternate furrows and irrigation durations have to be extended
to provide the same amount of water. As with transpiration,yields for the alternate furrow scenarios, in which the sameamount of water is applied as in the original treatments(i.e., in the Sa2 and Sa3 scenarios), are reduced by roughly
10 % compared to the Sp treatment and of 3–7 % comparedto the So treatment (Table 1). It should be noted that when
only half the water is applied in the Sa1 scenarios comparedto the original treatments, the reduction in yield is less than
20 % compared to the So treatment, producing considerably
higher water-use efficiency, which may be important in situations where water resources are limited. It should also be
noted that our simulations probably underestimate yield forthe alternate furrow scenarios, since plant roots are likely toadjust to receiving irrigation from only alternate furrows,
which is a process that our simulations do not include.
Water-use efficiency (WUE) is typically defined as theratio of crop biomass produced to the total water transpiredby the plant (Bacon 2004). Since we do not have a plant
growth model that calculates biomass produced, we cannot report water-use efficiency using this definition. Rather,
we report WUE in Table 1 as the percentage of water transpired by the plants relative to the total irrigation water.

Note that this definition underestimates WUE since itconsiders a change of storage over considered time period
as water lost. Similarly, to the discussion above on yield,
WUE increases with a reduction in the amount of irrigation water that infiltrates directly below the furrow and isconsiderably higher for the Sp treatment compared to the
So treatment, for both 6 and 4-h irrigations. WUE is higher
by about 9–10.5 % for 4-h irrigations compared to 6-h irrigations, although this increase is at the expense of yield.
Less water (percentagewise) is lost to evaporation anddrainage and more is used for transpiration for 4-h irrigations compared to 6-h irrigation. The highest WUE, i.e.,
the largest fraction of irrigation water is used for transpiration, was achieved in the Sa1 scenario when alternate furrows are used for irrigation and when only half of the total
water is applied compared with that applied in scenarios
where every furrow is irrigated. WUE for the Sa2 scenarios(alternate furrows; double irrigation duration) is similar to
the So treatment. This is because the positive effect of plastic is reduced when it is present only in alternate furrows
and irrigation durations have been increased to provide thesame amount of water. WUE for the alternate furrow scenarios, in which the same amount of water is applied as in
the original treatments (i.e., in the Sa2 and Sa3 scenarios), is
reduced by about 20 and 5 % compared to the Sa1 scenario
and Sp treatment, respectively (Table 1).
Figure 10 shows evaporation from the surface of theridge for the 6-h irrigation for treatments So and Sp, while
Table 1 gives cumulative evaporation values for all treatments. Since more water flows from the furrow horizontally into the ridge, it is wetter in the Sp treatments compared to the So treatments. As a result, considerably morewater is lost to evaporation from the surface of the ridge.
Evaporation from the ridge surface increases from So to Sc

13

64

Irrig Sci (2016) 34:53–69

Fig. 10  Actual evaporation flux (cm/day) from the surface of the ridge for the 6-h irrigation for treatments So (left) and Sp (right)

Fig. 11  Actual evaporation flux from the bottom and sides of the furrow for the 6-h irrigation for treatments So (left) and Sp (right)

to Sp (Table 1). It would be beneficial to minimize evaporation from the ridge in the Sp treatment by also covering theridge surface with a plastic membrane.
Figure 10 also shows the dynamics of the actual evaporation fluxes during the four irrigation cycles. Between
irrigations, the soil surface becomes dry and evaporationis reduced to almost zero. After irrigation, the soil surface
becomes moist and evaporation increases (compare to
Ep = 0.2 cm/day). The first irrigation cycle shows higher
evaporation due to the relatively high initial soil water content than during the following three irrigation cycles, during which the evaporation patterns are similar. Note thatduring the first irrigation cycle, contrary to the other irrigation cycles, the actual evaporation is initially equal to thepotential evaporation, since the initial pressure head at thesoil surface was assumed to be −300 cm, which does not
limit evaporation, while at the beginning of the other irrigation cycles the soil surface was very dry, and thus limiting evaporation. Also note that there is a slight increasein evaporation rates between the second and forth irrigation
cycles. This is a result of the gradual increase in water storage after each irrigation, which contributes to the increasing soil evaporation with time.

13

Figure 11 shows the evaporative flux from the bottom
and sides of the furrow. The horizontal projection of thisboundary (exposed to evaporation) is 60 cm and thus thepotential flux is 60 cm2/day. In the Sp treatments, the bottom of the furrow is covered with plastic so only 30 cm of
the boundary is exposed to evaporation. During irrigation,
part of the furrow is filled with water and evaporation islimited only to the sides above the water level. Once thefurrow is empty, evaporation takes place from the entire
furrow (bottom and sides; 60 cm) in the So treatments andonly through the sides (30 cm) of the furrow in the Sp treatments. Once irrigation stops, evaporation is high, since thebottom and sides of the furrow are wet. Evaporation gradually decreases between irrigations as the bottom and sidesof the furrow become dry after the critical evaporationpressure head is reached (Fig. 11). Cumulative soil evaporation from the furrow is highest for the So treatments andsmallest for the Sp treatments (Table 1). Cumulative evaporation from the furrows is considerably lower for the Sa
scenarios (Table 1), since evaporation from the dry furrow
is insignificant and evaporation occurs predominantly fromthe side of the irrigated furrow with the plastic bottom.

Irrig Sci (2016) 34:53–69

65

Fig. 12  Deep drainage flux at the bottom of the soil profile for the 6-h irrigation for treatments So (left) and Sp (right)

Figure 12 and Table 1 shows that drainage is considerably higher for the So treatments than for the other twotreatments (Sc and Sp). In the So treatments, most water
infiltrates vertically downward through the bottom of the
furrow and moves unhindered toward the bottom of the
profile, bypassing the bulk of the crop root zone. In the twoother treatments, vertically downward infiltration is either
reduced (Sc) or completely eliminated (Sp). Consequently,
greater fractions of applied water move horizontally into
the broader root zone and upward into the ridge. On theother hand, drainage is considerably higher in the Sa scenarios, in which the same amount of irrigation water is applied[either by doubling the irrigation time (Sa2) or irrigation frequency (Sa3)] as in the original treatments. This is because
the application of water is less well distributed by being
applied only to alternate furrows. Obviously, there is muchless drainage in the Sa1 scenario (Table 1), in which only
half the amount of irrigation water was applied. Figure 12
also shows that drainage is relatively small during thefirst irrigation cycle and then increases with each irrigation cycle as more of the applied irrigation water reaches
the bottom of the soil profile. This figure also shows thatthe analysis of only one irrigation cycle (which is the casefor many of the studies discussed in the Introduction) cannot provide a full picture of the processes and cumulative
effects occurring in the root zone and soil profile.
Solute fluxes
Table 2 shows various components of the solute mass balance, such as cumulative root solute uptake, cumulative
solute leaching (at a depth of 100 cm), and the change insolute mass in the transport domain for the 4- and 6-h irrigations for the three surface treatments (So, Sc, and Sp), as
well as for the alternate furrow irrigation scenarios (Sa1,
Sa2, and Sa3), and the four fertigation strategies.
Table 2 shows that for the So treatment and 6-h irrigation, solute leaching is highest (8.8 %) and lowest (5.6 %)when fertigation is applied at the beginning and the endof the irrigation cycle, respectively. Similar leaching is
obtained when fertigation is applied either in the middle (6.3 %) or continuously (6.7 %) throughout the entire
irrigation cycle. These observations are similar to thoseof Gärdenäs et al. (2005), who also concluded for different micro-irrigation schemes that fertigation applied at the
beginning of an irrigation cycle tends to increase nitrateleaching and that fertigation applied at the end of an irrigation cycle tends to reduce nitrate leaching. Note that similarly to Gärdenäs et al. (2005), and contrary to Cote et al.
(2003) who studied only one irrigation cycle, we have analyzed multiple irrigation cycles. Similarly, Bouwer et al.
(1990) and Soroush et al. (2012) concluded that leaching of
fertilizers to groundwater can be minimized when fertigation is applied toward the end of an irrigation event.
The highest (23 %) and lowest (18 %) root solute
uptake is obtained when fertigation is applied in the middle and at the beginning of the irrigation cycle. Similarlyhigh solute uptakes as when the fertigation is applied in
the middle of the irrigation cycle are obtained when thefertilizer is applied continuously. This conclusion is consistent with Playán and Faci (1997), who concluded that
applying fertilizer at a constant rate during the entire irrigation event is usually the best solution. Similar relative
results are obtained for the Sp treatments, except that root
solute uptake is about 4–6 % higher (Fig. 13), and soluteleaching is about 2–4 % lower (Fig. 14). There are muchsmaller differences between different fertigation timings in the Sa2 and Sa3 scenarios (with alternate furrows).
Root solute uptake is between 20–22 and 26–28 % of theapplied volume for the 6- and 4-h irrigations. However,there is much higher leaching for these two alternate furrow scenarios. Solute leaching is considerably higher for
the Sa2 scenarios with 6-h irrigations, ranging between 17
and 23 % when fertigation is applied at the end and at the
beginning of the irrigation cycle, respectively. There ishigher root solute uptake (by about 8 and 4 % for 6- and13

66
Table 2  Components of thesolute mass balance including
fertigation (%), root uptake(%), leaching (%), and change
in storage (%) over 28 days
(4 irrigation cycles) for 6and 4-h irrigations for the
So (control), Sc (density), Sp(plastic) treatments, and the
Sa (alternate furrow plastic)
scenarios, with fertigation
applied at the beginning (B), in
the middle (M), at the end (E),or continuously (F) throughout
the irrigation cycle

Irrig Sci (2016) 34:53–69
Treatments
Control, So
Fertigation timing
6-h irrigations
Fertigation (%)
Root uptake (%)
Leaching (%)
Change in storage (%)
4-h irrigations
Fertigation (%)
Root uptake (%)
Leaching (%)
Change in storage (%)

Compacted, Sc

Plastic, Sp

B

M

E

F

B

M

E

F

B

M

E

F

100
18
8.8
69

100
23
6.3
71

100
21
5.6
75

100
22
6.7
72

100
21
6.0
71

100
24
4.4
72

100
23
4.0
75

100
23
4.6
73

100
26
4.4
69

100
27
3.8
70

100
26
3.5
72

100
27
3.8
71

100
21
0.5
78

100
25
0.3
75

100
24
0.3
76

100
24
0.4
76

100
24
0.1
75

100
27
0.1
75

100
26
0.1
76

100
26
0.1
75

100
30
0.0
66

100
32
0.0
69

100
31
0.0
70

100
31
0.0
69

Alternate furrow scenarios
Sa1

Sa2

Sa3

Fertigation timing

B

M

E

F

B

M

E

F

B

M

E

F

6-h irrigations
Fertigation (%)
Root uptake (%)
Leaching (%)

100
29
1.7

100
30
1.4

100
30
1.2

100
30
1.4

100
20
23

100
23
19

100
21
17

100
22
19

100
21
15

100
22
13

100
21
13

100
22
14

69

69

71

70

56

59

63

59

64

65

67

65

100
28
0.0

100
31
0.0

100
29
0.0

100
29
0.0

100
26
7.3

100
28
5.9

100
26
5.3

100
27
6.0

100
26
3.2

100
26
2.9

100
26
2.8

100
26
3.0

Change in storage (%) 72

71

71

70

66

67

70

68

71

72

73

72

Change in storage (%)
4-h irrigations
Fertigation (%)
Root uptake (%)
Leaching (%)

Fig. 13  Cumulative root solute uptake for the 6-h irrigation for treatments So (left) and Sp (right) when fertigation is applied at the beginning of
the irrigation cycle

4-h irrigations, respectively) for the Sa1 scenarios, compared to all other scenarios. Since only half of the irrigation water is applied in these scenarios, there is only limited leaching below the root zone and fertilizers remain
accessible to the plant roots. Note that the numbers in columns of Table 2 do not always add up to 100 %, due to

13rounding errors and small mass balance errors (up to 2 %)in numerical calculations.
Figure 15 shows the concentration profiles at the endof the simulations for the So and Sp treatments and Sa2 scenarios. While in the Sp treatment, the concentrations are thehighest along the surface of the ridge due to the effects ofIrrig Sci (2016) 34:53–69

67

Fig. 14  Cumulative solute leaching for the 6-h irrigation treatments So (left) and Sp (right) when fertigation is applied at the beginning of theirrigation cycle

Fig. 15  Concentration profiles (t = 28 days) for treatments So (left) and Sp (middle), and scenario Sa2 (right)

evaporation and relatively low at the bottom of the furrow
where evaporation is prevented by the plastic cover, in the
So treatment, the concentrations are the highest along thesurface of the furrow (both bottom and sides) since evaporation occurs on all these surfaces. However, some solute,
below the bottom of the furrow, is outside of the rootzone
and thus out of reach of plant roots in the So treatment.
In the So treatment, the concentrations are the lowest in
the middle of the ridge, since very little infiltration waterreaches this part of the soil profile, which is relatively dry
throughout the simulation. Both these factors reduce root
solute uptake for the So treatment. Figure 15 also showsthat fertilizer does not reach the entire root zone when irrigation is applied in only one furrow (in the Sa2 scenario),
resulting also in lower root solute uptake (Table 2). Significantly more pronounced vertical movement of fertilizer in
the So treatment compared to the Sp treatment is also apparent in Fig. 15. Even more pronounced vertical movement isapparent for the Sa2 scenario, in which double the amountof water and solute is applied in one (left) plastic covered
furrow.
Table 2 also shows that the results are qualitatively similar for the 4-h irrigation scenarios, except that root solute
uptake is about 2–4 % higher and solute leaching is virtually eliminated (below 1 % for all treatments except for thealternate furrow scenarios).
Figure 14 shows that solute leaching starts earlier for the
So treatment (after about 8 days) than for the Sp treatment(after about 15 days) and also that solute leaching fluxes
are higher for the So treatment than for the Sp treatment(see also Table 2). Figure 14 also shows that the dynamics
of solute fluxes is similar to water fluxes (Fig. 12). Soluteleaching fluxes clearly reflect the irrigation cycles.
Figure 16 shows that root solute uptake gradually
increases as solute spreads through the root zone, which
was initially solute free, and thus becomes more available
to plant roots. This function is simply a derivative of thefunction displayed in Fig. 13. Note the short dips in root

13

68

Fig. 16  Root solute uptake for the 6-h irrigation treatment So when
fertigation is applied at the beginning of the irrigation cycle

solute uptake immediately after the beginning of irrigations. These are caused by a reduction in root water uptake
due to water stress that results from oversaturation of a partof the root zone. Figure 16 suggests that cumulative fertilizer uptake given in Table 2 would be higher if the rootzone had been supplied with fertilizer from the very beginning, rather than assuming it was solute free.

Conclusions
We have developed a furrow irrigation submodule for
HYDRUS (2D/3D), which considers processes including
irrigation, infiltration, evaporation and fertigation. Using
these fluxes and the mass balance calculations, this submodule calculates the water level and solute concentrationin the furrow and dynamically adjusts boundary conditions
for the soil transport domain. The resulting coupled model
was used to assess the effects different soil surface management strategies and different timings of fertigation had onroot water and solute uptake along with deep drainage andsolute leaching over a 1-month time period.
Our simulations showed that more water was available for transpiration for treatment Sp with zero infiltration through the bottom of the furrow compared with thenormal furrow bottom control treatment (So). As a result,a higher yield (with an increase from 92 to 97 % of potential transpiration) was also obtained for the Sp treatments.
In contrast, a larger fraction of applied water was lost due
to evaporation from water taking longer to infiltrate fromthe furrow but less water drained from the root zone for the
Sp treatments compared with the control (So) or compacted
furrow bottom (Sc).
Simulations for the Sa2 and Sa3 scenarios with plastic
and irrigation in alternate furrows and the same amountof applied water as in the standard Sp treatments showeda reduction in transpiration and yield, more water lost due

13

Irrig Sci (2016) 34:53–69

to deep drainage, but much less water lost due to evaporation from the furrow. This could be of interest in someareas if the concern is less about leaching and groundwaterpollution and more about reducing evaporative losses andpreserving accessible water resources. Similar crop yields
were obtained for the alternate furrow scenarios (Sa2 andSa3) as for the control (So) and compacted (Sc) furrow treatments. However, the yield for the Sa scenarios were much
lower than for the standard Sp treatments. When only half
the water is used for irrigation in the Sa1 scenarios compared to the original treatments (So, Sc, and Sp), the reduction in yield is still less than 20 % compared to the So
scenario. These scenarios produced considerably higher
water-use efficiency, which may be advantage in regions
where water resources are limited.
The highest root solute uptake (27 and 32 % for the 6and 4-h irrigation cycles, respectively) was achieved for theSp (plastic) treatments when fertigation was applied in the
middle of the irrigation cycle. In general, higher root solute
uptake was achieved with plastic (Sp), followed by the compacted furrow bottom (Sc) and the normal control furrow
bottom (So). In general, most solute was taken up by plantroots when fertigation was applied in the middle of the irrigation cycle, followed by fertigation at the end of, or continuously throughout the irrigation cycle. The least amountof solute was taken up when fertigation was applied at the
beginning of the irrigation cycle, but the differences were
not particularly large (<4 %).
The least amount of solute was leached from the soil
profile for the treatment with the plastic bottom (Sp) when
fertigation was applied at the end of the irrigation cycle.
Considerably more leaching was simulated in the alternate furrow scenarios when the same amount of water wasapplied as in the original treatments. Higher solute uptake
was achieved in the alternate furrow strategy (Sa) than for
the normal (So) and compacted (Sc) furrow bottom treatments, but it was much lower than for the standard plastic
treatment (Sp). The significant benefits that can accrue by
using plastic sheeting to eliminate the vertical downward
infiltration from the base of the furrow warrants further
study, with the aim to deliver practical strategies to further
improve water and nutrient management and use in furrow
irrigated systems.
The new “furrow” module coupled with HYDRUS(2D/3D) proved to be a powerful tool for analyzing waterflow and solute transport processes in the furrow and thesoil profile. However, this combined tool still considers processes only in a two-dimensional soil profile perpendicular
to the actual furrow. It cannot thus fully account for flow inthe third dimension, such as the advance and recession ofwater in the furrow, and the actual mixing of fertilizer withwater in the furrow. Development of a full three-dimensional model that accounts for surface fluxes in the furrowIrrig Sci (2016) 34:53–69

and all subsurface soil processes discussed above will be
required to fully describe complex three-dimensional furrow
irrigated systems. Such three-dimensional models could be
used to evaluate additional factors such as different slopes.

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