Agricultural Water Management 232 (2020) 106044

Contents lists available at ScienceDirect

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

Numerical simulations of the eﬀects furrow surface conditions and fertilizer
locations have on plant nitrogen and water use in furrow irrigated systems

T

Keith L. Bristowa,*, Jirka Šimůnekb, Sarah A. Helaliab, Altaf A. Siyalc
a

CSIRO Agriculture and Food, PMB Aitkenvale, Townsville, QLD 4814, Australia
Department of Environmental Sciences, University of California Riverside, Riverside, CA 92521, USA
cU.S.-Pakistan Center of Advanced Studies in Water, Mehran University of Engineering and Technology, Jamshoro, Pakistanb

A R T I C LE I N FO

A B S T R A C T

Keywords:
Furrow irrigation
Triggered irrigation
Transpiration
Deep drainage
Solute transport
Nitrogen leaching
Soil evaporation
HYDRUSThe HYDRUS model can be used to evaluate the eﬀects of diﬀerent soil surface treatments at the bottom of the
furrow, diﬀerent initial nitrogen fertilizer locations, and diﬀerent furrow irrigation rates on deep drainage andsolute leaching in furrow irrigated systems. This paper extends our 2012 study, in which we considered only one
irrigation cycle and ignored the eﬀects of plants. As a result of considering only one irrigation cycle, a large
amount of water was used to change the water storage in the transport domain and only limited deep drainage ofwater and leaching of fertilizer at the bottom of the domain occurred in most scenarios investigated. To obtain amore realistic and complete picture, we have in this study considered multiple irrigation cycles to reﬂect actualﬁeld practices better and accounted for root water and nitrogen uptake and plant transpiration. As in our previous study, soil surface treatments at the bottom of the furrow include untreated, compacted and an impermeable membrane, and fertilizer is initially placed at one of ﬁve diﬀerent locations in the furrow or the ridge.
We have also evaluated (1) the eﬀectiveness of triggering irrigation based on a pre-set soil water pressure head ata speciﬁc location in the ridge compared with prescribed irrigation at a regular time interval to supply water andnitrogen, and (2) the eﬀects of plant water and nitrogen uptake on the furrow water balance, inﬁltration, soil
evaporation, deep drainage, transpiration and nitrogen leaching. Our simulations show that deep drainage andnitrogen leaching can be substantially reduced by using an impermeable membrane on the bottom of the furrow
and that a substantial additional reduction in leaching can be achieved by triggering irrigation rather than using
a ﬁxed time schedule. We also show that the initial location of fertilizer has a substantial eﬀect on nitrogen
uptake and leaching.

1. Introduction

are therefore urgently needed for furrow irrigated crops (Bar-Yosef,
1999).
Simulation models such as HYDRUS (2D/3D) and its predecessors
SWMS-2D, CHAIN-2D and HYDRUS-2D (Šimůnek et al., 2008, 2016b)
have been widely used to improve the design, management, and performance of various irrigation systems, including surface and subsurface drip irrigation and furrow irrigation. Šimůnek et al. (2016b)
identiﬁed more than 25 papers that used the above models to evaluate
the eﬀect of various factors on furrow irrigation systems and here we
include a subset of the 25 references most relevant to this paper(Benjamin et al., 1994; Abbasi et al., 2003a,Abbasi et al., 2003b,Abbasi
et al., 2003c, 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; Siyal et al., 2012; Soroush et al., 2012; Ebrahimian et al., 2012,

About 90 % of irrigated crops across the world are irrigated using
surface irrigation, including basin, border, or furrow irrigation methods(Tiercelin and Vidal, 2006). Furrow irrigation is the most commonlyused method due to its simplicity of design and low capital costs(Walker and Skogerboe, 1987). However, unlike micro-irrigation
methods, such as surface and subsurface drip irrigation, furrow irrigation is much less eﬀective in delivering the required amounts of waterand nitrogen directly to the plant roots. This results in large quantities
of water and nitrogen being 'lost' below the crop root zone. Consequently, areas with furrow irrigation are often a major source of nitrate,
resulting in pollution of groundwater systems (e.g., Artiola, 1991; Prattand Jury, 1984). Improved management strategies that increase irrigation eﬃciency and reduce nitrogen losses by leaching to groundwater⁎

Corresponding author.
E-mail addresses: Keith.Bristow@csiro.au (K.L. Bristow), Jiri.Simunek@ucr.edu (J. Šimůnek), shela001@ucr.edu (S.A. Helalia),
aasiyal.uspcasw@faculty.muet.edu.pk (A.A. Siyal).
https://doi.org/10.1016/j.agwat.2020.106044
Received 6 November 2019; Received in revised form 16 January 2020; Accepted 23 January 20200378-3774/ © 2020 Published by Elsevier B.V.

Agricultural Water Management 232 (2020) 106044

K.L. Bristow, et al.

used to carry out computer simulations. HYDRUS uses numerical solutions of the Richards' and convection-dispersion equations for variably-saturated water ﬂow and solute transport in soils, respectively:

2013a,b; Zerihun et al., 2014). These models, which simulate waterﬂow and/or solute transport in soils, proved to be ﬂexible and costeﬀective tools for analyzing and evaluating various management/irrigation scenarios.
One of these studies was the study of Siyal et al. (2012), who
evaluated the eﬀects of diﬀerent soil surface treatments at the bottom of
the furrow, diﬀerent initial nitrogen fertilizer locations, and diﬀerent
furrow irrigation rates on deep drainage and solute leaching in a furrow
irrigated system. Siyal et al. (2012) assumed that the soil at the bottomof the furrow was either a) untreated; it retained its normal surface
features and soil hydraulic properties, b) compacted; the soil hydraulicconductivity of the surface soil was reduced by 80 %, or c) covered with
an impermeable membrane so that the bottom of the furrow was impermeable to water ﬂow. Siyal et al. (2012) also assumed that the nitrogen fertilizer was initially located at one of 5 diﬀerent locations,
ranging from the bottom of the furrow to the top of the ridge.
The strength of the Siyal et al. (2012) study was that it enabled
evaluation of the worst-case scenario in terms of deep drainage andnitrogen leaching in the absence of plants. The main limitation of the
Siyal et al. (2012) study was that it used only one irrigation cycle andthe eﬀects of plants were neglected. Their results showed that deep
drainage and nitrogen leaching were signiﬁcantly aﬀected by the initialsoil moisture conditions since a large amount of water was used tochange the soil water storage in the root zone (transport domain) andonly limited leaching occurred in most scenarios. To obtain a more
realistic and complete picture, one must consider multiple irrigation
cycles to reﬂect actual ﬁeld practices better and account for plant waterand nitrogen uptake, which aﬀect deep drainage and nitrogen leaching.
The reason for applying irrigation and fertilizer is to supply plants withwater and nitrogen and a full analysis should consider how much of theapplied water and fertilizer can be taken up by the plants.
The furrow irrigation model of Siyal et al. (2012) was further extended by Šimůnek et al. (2016a) to consider a) processes of precipitation and evaporation as a source/loss of water from the furrow
and b) diﬀerent timings of fertigation with irrigation water. Šimůnek
et al. (2016a) then used this extended furrow irrigation model toevaluate the eﬀects of diﬀerent soil surface treatments at the bottom of
the furrow and diﬀerent timings of fertigation on root water and solute
uptake, deep drainage and solute leaching in a loamy soil.
To overcome the limitations of the study of Siyal et al. (2012), in
this manuscript, we expand their analysis by considering a) multiple
irrigation cycles during one month and b) the eﬀects plants have on
deep drainage and leaching by accounting for root water and solute
uptake. This allows us to analyze how much of the applied water andnitrogen can be taken up by the plant roots, rather than be leached fromthe crop root zone. We also consider an irrigation strategy where irrigation is triggered when a critical soil water pressure head is reached ata speciﬁed location in the root zone (Dabach et al., 2013), rather thanbeing provided at regular time intervals.
The objectives of this study are i) to evaluate the eﬀectiveness of
diﬀerent furrow management strategies to improve supply of water toplants and to reduce water losses due to evaporation and deep drainage,ii) to evaluate the eﬀects of diﬀerent initial fertilizer locations on the
supply of nitrogen to plants and leaching from the crop root zone, iii) toevaluate the eﬀectiveness of triggered irrigations compared with prescribed irrigations to supply water and nitrogen to plants and limit
leaching from the soil proﬁle, and iv) to assess the combined eﬀects ofplant water and nitrogen uptake with diﬀerent furrow management
strategies and diﬀerent irrigation strategies to minimize deep drainage
and nitrogen leaching.

∂θ∂ ⎡ ⎛ A ∂h⎤=
K ⎜K ij+ K izA ⎞⎟ ⎥ − S∂t∂x i ⎢ ⎝
∂x j
⎠
⎦
⎣

(1)

∂qi c
∂θc
∂ ⎛ ij ∂c ⎞
=
− Scr
⎜θD
⎟ −
∂t
∂x i ⎝∂x j ⎠∂x i(2)

In Eq. 1, θ is the volumetric water content [L3L−3], h is the pressure
head [L], S is a sink term accounting for plant water uptake [T-1], xi (i= 1,2) are the spatial coordinates [L], t is time [T], KijA are components
of a dimensionless anisotropy tensor KA, and K is the unsaturated hydraulic conductivity function [LT-1] given by the product of the relative
hydraulic conductivity Kr and the saturated hydraulic conductivity Ks[LT-1]. In Eq. 2, c is the solute concentration [ML−3], qi is the i-thcomponent of the volumetric ﬂux density [LT-1], Dij is the dispersion
coeﬃcient tensor [L2T-1], and cr is the concentration of the sink term
[ML−3]. Note that although HYDRUS (2D/3D) solves a more generalsolute transport equation than Eq. 2, only terms considered in this study
are given here.
Numerical solution of the Richards’ equation (Eq. 1) requires as
input the soil hydraulic parameters describing the soil water retention
curve and the hydraulic conductivity function. In this study, we use theanalytical model of van Genuchten (1980) to describe these two functions. The soil hydraulic parameters for a loamy soil were taken fromthe soil catalog provided by the HYDRUS software and are the same as
those used by Siyal et al. (2012) and Šimůnek et al. (2016a). The valuesof these parameters are: the residual water content = 0.078, the saturated water content = 0.43, the shape parameters α and n are 0.036
cm−1 and 1.56, respectively, and the saturated hydraulic conductivity=24.96 cm/day.
2.2. Flow domain, initial and boundary conditions
The same ﬂow domain and initial and boundary conditions, as inSiyal et al. (2012), were used in this study (Fig. 1). The transport domain was 100 cm wide and 100 cm high. The ridge was 40 cm wide.
The furrow was 15 cm deep and 30 cm wide, and the side of the furrow
had a slope of 45°. The initial pressure head varied linearly between 200 cm at the bottom of the domain and - 300 cm at the top of the ridge.

2. Material and methods
Fig. 1. Initial soil water pressure head (cm) in the ﬂow domain and boundary
conditions imposed on the ﬂow domain during simulations (Siyal et al., 2012;
with permission).

2.1. Governing equations for water ﬂow and solute transport
The HYDRUS (2D/3D) software package (Šimůnek et al., 2008) was
2

Agricultural Water Management 232 (2020) 106044

K.L. Bristow, et al.

Boundary conditions imposed on the ﬂow domain included an atmospheric boundary condition at the top of the ridge, a free drainage
boundary condition at the bottom of the soil proﬁle, a no-ﬂow
boundary condition at both vertical sides, and special boundary conditions were applied at the base of the furrow (see Section 2.4 below) to
reﬂect the diﬀerent surface conditions being investigated.

2.5. Irrigation strategies
Water application rates of 1200, 1400, 1600, 1800 and 2000 L h−1
furrow-1 for a 100 m long furrow, corresponding to area-based application rates of 12, 14, 16 18, and 20 mm h-1, or to rates of 60, 70, 80, 90
and 100 cm2 h-1 in our two-dimensional domain, respectively, werecompared in this study. The switch-oﬀ depth, which determines when
the supply of irrigation water is stopped was set at 10 cm (Siyal et al.,2012). Irrigation was applied every ﬁve days for 30 days. A second
irrigation strategy where irrigation was triggered (Dabach et al., 2013,2015) when the soil water pressure head in the middle of the ridge and15 cm below the top of the ridge reached a pre-set value of -500 cm wasalso included for comparative purposes. An optimal location of thetriggering point and an optimal triggering pressure head for diﬀerent
plants and soil types is a topic of ongoing research (Dabach et al., 2013,2015). Note that this triggering point is located in the middle of the rootzone with the highest root density (see Fig. 3 below). According to thestress response function described in the next Section, irrigation istriggered when root water uptake is reduced by about 4 %.

2.3. The furrow irrigation submodule
The furrow irrigation submodule, as developed in Appendix A of
Siyal et al. (2012) and extended by Šimůnek et al. (2016a), was used tosimulate furrow irrigation and dynamic position of the water level inthe furrow during irrigation. Šimůnek et al. (2016a) extended themodel of Siyal et al. (2012) by adding the atmospheric boundary condition at the water surface in the furrow and thus allowing evaporationfrom and precipitation to the water surface. In this submodule, thewater level in the furrow is calculated from the water balance, accounting for the applied irrigation, inﬁltration and the change in water
volume in the furrow. When water is present in the furrow, the timevariable pressure head boundary condition is applied to the furrow
boundary that is below the surface water level, reﬂecting the dynamic
nature of the water level in the furrow. An atmospheric boundary
condition is applied in the furrow when it is empty of water, and above
the water level in a furrow when it is not. An atmospheric boundary
condition considers precipitation (P = 0) and potential evapotranspiration (ETp=Ep+Tp = 1.0 cm/d) ﬂuxes. Potential evapotranspiration (ETp) equal to 1 cm/day corresponds to conditions inJanuary in north Queensland, Australia. Note that we assume that plantleaves cover only the ridge and that the leaf area index is about 3.5,
which corresponds to a surface cover fraction of about 80 %. At the topof the ridge, we assume that a fraction (80 %) of incoming energy(ETp= Ep+Tp = 1.0 cm/d) is intercepted by plants (potential transpiration Tp = 0.8 cm/d) and the remaining fraction (20 %) by the soil
surface (potential evaporation Ep = 0.2 cm/d). All incoming energy inthe furrow reaches either the water level in the furrow (during irrigation) or the bottom of the furrow (between irrigations) (Ep=ETp = 1.0cm/d).

2.6. Root water and nitrogen uptake
The approach of Feddes et al. (1978) was used to describe plantwater uptake:S (h) = α (h) b (x , z ) Lt Tp(3)

where S is deﬁned as the volume of water removed per unit time from aunit volume of soil due to root water uptake [T−1], α(h) is a prescribed
dimensionless water stress response function of the soil water pressure
head (0≤α≤1), b(x, z) is the normalized water uptake distributionfunction [L-2], Lt is the width [L] of the soil surface associated with thetranspiration process (Lt = 40 cm; surface of the furrow ridge, see thedeﬁnition of the transport domain below), and Tp is the potential
transpiration rate [LT−1] (Tp = 0.8 cm/d). Water uptake is assumed to
be zero close to saturation (above h1) and when the soil is dry (forh < h4, the wilting point pressure head). Water uptake is considered
optimal between pressure heads h2 and h3, whereas for pressure heads
between h3 and h4 (or h1 and h2), water uptake decreases (or increases)
linearly with h (Feddes et al., 1978). The following parameters of thestress response function (typical for many crops) were used in ourstudy: h1 = -10 cm, h 2= −25 cm, h3 = -200 cm, and h4 = -8000 cm.
The spatial distribution of roots of a hypothetical plant is describedusing the two-dimensional root distribution function b(x,z) of Vrugt
et al. (2001, 2002):

2.4. Soil surface management and fertilizer placement strategies
The same soil surface management and fertilizer placement strategies, as in Siyal et al. (2012), were considered in this study (see Fig. 2).
It was assumed that the soil at the bottom of the furrow was either a)untreated; it retained its usual surface features and soil hydraulicproperties (S0), b) compacted; its hydraulic conductivity was reduced
by 80 % while the retention parameters were considered to remain thesame (Sc), or c) covered with an impermeable membrane so that thebottom of the furrow was impermeable (Sim). Nitrogen fertilizer was
mixed into the top 1−3 cm of the soil a) at the bottom and center of the
furrow (P1), b) on the sides of the furrow (P2), c) on the bottom andsides of the furrow (P3), d) on the furrow sides near the ridge top (P4),and e) on the top and center of the ridge (P5) (Fig. 2).
While the HYDRUS model allows one to consider the fate andtransport of multiple solutes of various properties subject to ﬁrst-orderdegradation chain reactions, such as the nitriﬁcation chain from urea toammonium and nitrite and nitrate (e.g., Hanson et al., 2006; Ramos
et al., 2012; Li et al., 2015), only one nonreactive solute species anddimensionless concentrations were used in our simulations. The initialconcentration of this nonreactive solute, which could be considered as asurrogate for nitrate readily available for transport and plant uptake, in
the initial placement area was adjusted so that the initial solute mass inthe soil proﬁle was equal to 1 (100 %). This enabled us quick evaluationof the fractions of nitrogen fertilizer that were used by plants, leachedfrom the soil root zone, and remained in the soil proﬁle.

pz ⎞⎛x ⎞ −⎛ Z z | z *− z| + Xpx | x * − x | ⎞m⎠b (x , z ) = ⎛1 −1−e ⎝ m
Zm ⎠ ⎝
Xm ⎠
⎝
⎜

⎟⎜

⎟

(4)

where Xm and Zm are the maximum rooting lengths in the x- and zdirections [L], respectively; x and z are distances from the origin of theplant in the x- and z-directions [L], respectively; and px [-], pz [-], x*[L], and z* [L] are empirical parameters. The plant was assumed to becentered in the middle of the ridge; the extent of roots in the vertical(Zm) and horizontal (Xm) direction was 60 and 35 cm, respectively;
parameters x* and z* (sometimes referred to as Depth and Radius ofMaximum Intensity) were 30 and 20 cm, respectively; and parameters px
and pz were set at one (1). These parameters produced the root distribution function presented in Fig. 3.
Only passive root nitrogen uptake was considered (Šimůnek andHopmans, 2009), i.e., cr in Eq. (2) was assumed to be equal to the nitrogen concentration at any particular location. No compensation mechanisms that would increase root uptake in one part (unstressed) of theroot zone in response to reduced uptake in another part (stressed) of theroot zone were considered in our study.
In the simulations carried out in this study, it is assumed that theparameters required to simulate root water and nitrogen uptake, i.e.,3Agricultural Water Management 232 (2020) 106044

K.L. Bristow, et al.

Fig. 2. Schematic showing (a) the diﬀerent soil surface management treatments (Si) and (b) fertilizer placements (Pn) analyzed in this study (S0 - original soil; Sc compacted soil; Sim – impermeable membrane, and P1 - fertilizer at the bottom of furrow; P2 - fertilizer on the sides of furrow; P3 - fertilizer on the bottom and sides ofthe furrow; P4 - fertilizer on the furrow sides near the ridge top; P5 - fertilizer on the top at the center of the ridge).

3.1. Furrow water balance

the spatial root distribution, the water stress response function, andpotential transpiration are constant in time. Potential root water uptake
and its spatial distribution are thus static. The actual root water andnitrogen uptake and their spatial distributions are however dynamic asa result of temporal and spatial variable distributions of water content
and nitrogen concentration in response to individual irrigation events.
Actual transpiration and nitrogen uptake will, therefore, diﬀer between
diﬀerent scenarios.

The total amount of irrigation water applied during one irrigation
cycle depends on several factors, including soil surface management,
which aﬀects the inﬁltration rate, and the applied irrigation rate. Fig. 4
shows water levels in the furrow for the three diﬀerent soil surface
conditions, i.e., S0, Sc, and Sim for 5 diﬀerent irrigation rates. Fig. 5
shows cumulative irrigation and inﬁltration ﬂuxes for the ﬁrst scenario(S0) and diﬀerent ﬂuxes. Similar graphs could be produced for the othertwo soil surface conditions. Fig. 4 shows that the switch-oﬀ depth isreached fastest for the Sim treatment with an impermeable bottom andslowest for the S0 treatment with the standard untreated bottom. It also
shows that the switch-oﬀ depth is reached faster for larger irrigation
rates.
Figs. 4 and 5 indicate that most water is applied, in each treatment,
when the lowest irrigation rate is used. This is because when water isapplied at a lower rate it is applied during a longer time period. Since
inﬁltration rates are relatively similar (Fig. 5, right), the lowest irrigation rate produces the slowest increase in the water level in the
furrow, reaching the switch-oﬀ depth much slower than the higher irrigation rates. Consequently, irrigation water for smaller irrigation rates
is applied longer, resulting in more water being applied (Fig. 5, left).
Fig. 6 shows water levels in the furrow for the three soil surface
treatments, i.e., S0, Sc, and Sim, for ﬁve diﬀerent irrigation rates whenirrigations are triggered by the soil water status in the root zone. Thisﬁgure shows that irrigations are triggered less often for lower irrigation
rates, which, as explained above, provide larger amounts of applied
water. Since larger amounts of water are applied when lower irrigation

3. Results and discussion
The Results section is organized as follows. The ﬁrst Section (3.1)
deals with water balance in the furrow. The diﬀerence between constant incoming irrigation (during irrigation events) and time-variable
inﬁltration produces time-variable water levels in the furrow, which are
discussed in this section. Water ﬂuxes associated with the subsurface
are described next. In Section 3.2, we discuss inﬁltration, which is an
input into the soil proﬁle. Water losses in terms of evaporation and deep
drainage are discussed in Sections 3.3 and 3.4, respectively. Next, inSection 3.5, we discuss the productive use of water, i.e., transpiration,root water uptake, and irrigation water use eﬃciency (deﬁned here as aratio of transpiration/irrigation). The change in water storage in thesubsurface, a component that closes the subsurface water balance, isdiscussed in section 3.6. Finally, components of the nitrogen balance,
including nitrogen leaching, plant nitrogen uptake and nitrogen storage
in the crop root zone, are discussed in the last Section (3.7).

4Agricultural Water Management 232 (2020) 106044

K.L. Bristow, et al.

Fig. 3. Spatial root distribution function b(x,z) (top). The bottom left is b(x,z) along the soil surface and the bottom right is b(x,z) along the vertical cross-section
through the middle of the domain.

Fig. 4. Water levels in the furrow for the diﬀerent soil surface conditions S0 (top left), Sc (top right), and Sim (bottom) for irrigation rates (IR) of 60 (IR 60), 70 (IR 70),80 (IR 80), 90 (IR 90), and 100 (IR 100) cm2 h−1.

5Agricultural Water Management 232 (2020) 106044

K.L. Bristow, et al.

Fig. 5. Cumulative irrigation (left) and inﬁltration (right) for treatments S0 and for irrigation rates (IR) of 60 (IR 60), 70 (IR 70), 80 (IR 80), 90 (IR 90), and 100 (IR100) cm2 h−1.

rates are used, it takes longer for this water to be ‘used’ by plants, soil
evaporation, and deep drainage. This ﬁgure also shows that irrigations
are triggered later for treatment S0 than for treatments Sc and Sim. Thisis again because more water is applied to treatment S0 in each irrigation
cycle.
It should also be emphasized that four irrigation events were triggered for IR 80, IR 90, and IR 100 for all surface treatments. On theother hand, for IR 70, four irrigation events were triggered only fortreatments Sc and Sim, while only 3 irrigation events were triggered fortreatment S0. Finally, for IR 60, only three irrigation events were triggered for treatments S0 and Sc, while four irrigation events were triggered for treatment Sim. However, this irrigation event was not completed during the 30-d simulation. This factor, i.e., a diﬀerent numberof irrigation events for triggered irrigation scenarios, can explain someof the nonlinearities and unexpected results discussed below.

3.2. Inﬁltration
Fig. 7 shows cumulative inﬁltration during one month (30 days)
expressed in absolute values (Fig. 7, top) and as a percentage of potential evapotranspiration (Fig. 7, bottom). Cumulative potential evapotranspiration ETp is equal to 3000 cm2 (i.e., 1 cm/d * 30 d *100 cm =3000 cm2). Cumulative inﬁltration is displayed for diﬀerent surface
treatments, diﬀerent irrigation rates, and irrigations applied at regularintervals or triggered by soil water status in the ridge.
Total inﬁltration decreases with an increasing irrigation rate. Whenthe irrigation rate is low, it takes much longer before the switch-oﬀ
depth is reached, during which time the water inﬁltrates into the soil
proﬁle (see Fig. 4). When the bottom of the furrow is compacted orimpervious, the switch-oﬀ depth is reached much faster, and less water
is applied. This is true for irrigation applied at a regular interval of 5days or triggered by soil water conditions in the ridge. The diﬀerences
between diﬀerent furrow surface treatments are much smaller when"triggered" irrigations are applied since, in this case, the soil proﬁleFig. 6. Water levels in the furrow for soil surface treatments S0 (top left), Sc (top right), and Sim (bottom) for irrigation rates (IR) of 60 (IR 60), 70 (IR 70), 80 (IR 80),90 (IR 90), and 100 (IR 100) cm2 h−1 for triggered irrigations.
6Agricultural Water Management 232 (2020) 106044

K.L. Bristow, et al.

Fig. 8. Evaporation from the top of the ridge (top) and the furrow (bottom) as afunction of surface treatment (S0 - original, Sc - compacted, and Sim - impermeable membrane), for irrigation rates (IR) of 60 (IR 60), 70 (IR 70), 80 (IR80), 90 (IR 90), and 100 (IR 100) cm2 h−1, and irrigations applied at regularintervals and triggered (tr).

Fig. 7. Cumulative inﬁltration (top - expressed in absolute values, bottom expressed as a percentage of potential evapotranspiration) as a function of thesurface treatment (S0 - original, Sc - compacted, and Sim - impermeable membrane), for irrigation rates (IR) of 60 (IR 60), 70 (IR 70), 80 (IR 80), 90 (IR 90),
and 100 (IR 100) cm2 h−1, and irrigations applied at regular intervals or triggered (tr).

are substantially reduced (less than 50 % of potential Ep) compared toirrigations at predetermined intervals. In general, evaporation losses fortriggered irrigation are less than half of those for irrigations at predetermined intervals. Also, note that evaporation losses are more or lessindependent of the soil surface treatment.
Cumulative evaporation from the furrow bottom and sides (Fig. 8;
bottom) can be compared with potential evaporation, which is approximately equal to 1800 cm2 (Ep = 1.0 cm/d; cum(Ep) = 1.0 cm/d *60 cm * 30 d = 1800 cm2; note that this formula should exclude time(about 1 d) when the furrow bottom is ﬂooded with water and evaporation does not occur directly from the furrow bottom). Cumulative
potential evaporation for the Sim treatment is 900 cm2 (Ep = 1.0 cm/d *30 cm * 30 d = 900 cm2). For the furrow, we assume that all incomingenergy is converted to potential evaporation (Ep = 1.0 cm/d). Noteagain that evaporation losses from the furrow are substantially reduced
when we used triggered irrigation compared to irrigation at prescribedintervals. Evaporation losses from the furrow are lowest for the treatment with the impermeable membrane since, in this case, water canevaporate only from the sides of the furrow.

controls how many irrigations are applied and at what time (see Fig. 6).
Fig. 7, which shows cumulative inﬁltration as a fraction of cumulative potential evapotranspiration (ETp), indicates that triggered irrigation keeps the amount of applied water close to 100 % ETp (or evenbelow for the impermeable or compacted bottom of the furrow). Interestingly, there were only small diﬀerences between applied irrigation volumes when irrigation was triggered by conditions in the soil andﬂow through the bottom of the furrow was restricted, contrary to
standard irrigation when irrigation volumes substantially increased
with the decrease of the irrigation rate. For normal conditions, one
would need to use either a lower switch-oﬀ depth or a longer time interval between irrigations to get closer to 100 % ETp and to avoid signiﬁcant leaching losses.
3.3. Evaporation
Fig. 8 shows cumulative evaporation ﬂuxes from the top of the ridge
and the furrow during one month (30 days) for diﬀerent surface
treatments, diﬀerent irrigation rates, and irrigations applied at regularintervals or triggered by soil water status in the Ridge. Cumulative
actual evaporation from the top of the ridge (Fig. 8, top) can be compared with cumulative potential evaporation, which is equal to 240 cm2(Ep = 0.2 cm/d; cum(Ep) = 0.2 cm/d * 40 cm * 30 d = 240 cm2). Notethat we set potential evaporation at 0.2 cm/d at the top of the ridge
because the remaining incoming energy is intercepted by the plant (Tp= 0.8 cm/d). Also note that for triggered irrigations, evaporation losses

3.4. Deep drainage
Fig. 9 shows drainage at the bottom of the soil proﬁle during one
month (30 days) for diﬀerent furrow surface treatments and diﬀerent
irrigation rates, and irrigations applied at prescribed regular intervals
or triggered by the soil water status in the ridge. The drainage loss
reﬂects the amount of irrigation water applied in the diﬀerent
7Agricultural Water Management 232 (2020) 106044

K.L. Bristow, et al.

Fig. 9. Drainage losses from the soil proﬁle as a function of the furrow surface
treatment (S0 - original, Sc - compacted, and Sim - impermeable membrane), forirrigation rates (IR) of 60 (IR 60), 70 (IR 70), 80 (IR 80), 90 (IR 90), and 100 (IR100) cm2 h−1, and irrigations applied at regular intervals and triggered (tr).

Fig. 11. Irrigation water use eﬃciency as a function of surface treatment scenario (S0 - original, Sc - compacted, and Sim - impermeable membrane), forirrigation rates (IR) of 60 (IR 60), 70 (IR 70), 80 (IR 80), 90 (IR 90), and 100 (IR100) cm2 h−1, and irrigations applied at regular intervals and triggered (tr).

treatments. The largest drainage loss occurred in the treatment withstandard soil surface features and soil hydraulic properties, with lower
applied rates of irrigation, and for irrigations applied at a regular timeinterval. Drainage losses are dramatically reduced when the bottom of
the furrow is covered with an impermeable membrane, and even more
so when irrigations are triggered according to the preset soil water
status in the ridge. It must be emphasized that triggered irrigations,especially in the treatment with the impermeable membrane on thebase of the furrow, can practically eliminate drainage losses.

transpirations (e.g., Klocke et al., 2004; Payero et al., 2006; Oster et al.,2012; Ragab et al., 2015), the scenarios with triggered irrigation willthus likely lead to a slight loss of crop yield (on average by about 6 %).
Scenarios with the impermeable membrane almost always show similar
plant transpiration as the other soil surface treatments. However, this isachieved with much less water.
Fig. 11 shows the irrigation water use eﬃciency (WUE) for thediﬀerent surface treatments, diﬀerent irrigation rates, and irrigations
applied at regular intervals or triggered by soil water status in the ridge.
We deﬁne irrigation water use eﬃciency as the ratio of actual transpiration to the amount of applied irrigation water. WUE is always
substantially higher for treatments with a reduced conductivity at thebottom of the furrow. It is also markedly higher for the treatment with
an impermeable membrane compared with the compacted soil treatment. In general, scenarios with triggered irrigations have higher WUE
than scenarios with irrigation at a regular time interval. However, thisincrease in WUE for scenarios with triggered irrigation is accompanied
by a slight decrease in actual transpiration (Fig. 10), and correspondingly in crop yield.
Relatively low WUEs, even for triggered irrigation, which have beenshown to almost eliminate downward leaching, are due to relatively
large evaporation losses from the furrow and an increase in water
storage in the soil proﬁle. While furrow irrigation eﬃciencies, which
can range from about 30 % (Fahong et al., 2004) up to about 65 %(Arabiyat et al., 1999), are in general much lower than well managed
subsurface drip irrigation systems (Ayars et al., 1999), furrow irrigation
remains considerably cheaper than drip systems and thus widely usedaround the world. Note that in our simulations potential transpiration(0.8 cm/d (Tp) * 40 cm (ridge width) = 32 cm2/d) is only about 30% of
the incoming energy (1.0 cm/d (ETp) *100 cm (surface with) = 100
cm2/d), and WUE of 40% is a relatively good outcome for these conditions.

3.5. Transpiration
The ultimate goal of irrigation is to supply crops with the rightamount of water, at the right place and at the right time to maximize
plant transpiration, and hence crop yield. Fig. 10 shows the cumulative
actual transpiration as an absolute value. Cumulative potential transpiration is 960 cm2 (Tp = 0.8 cm/d, and cum(Tp) = 0.8 cm/d * 40 cm* 30 d = 960 cm2) during one month (30 days) irrespective of diﬀerent
surface treatments, diﬀerent irrigation rates, and irrigations applied at aregular interval or triggered by a pre-set condition (soil water pressurehead) in the ridge. Cumulative transpiration is large for all scenarios(more than 90 % of potential transpiration). However, cumulativetranspiration values are smaller (by about 6 %) for scenarios withtriggered irrigation, likely because of less irrigation water applied inthese scenarios (Fig. 7). Since the loss in crop yield is often assumed tobe directly correlated with the ratio of cumulative actual and potential

3.6. Change in water storage
The change in water storage in the soil proﬁle (Fig. 12) was similar
for all scenarios with prescribed irrigation (i.e., triggered). While theinitial soil water storage was about 1690 cm2, which reﬂected theaverage soil water content of about 0.18 cm3 cm-3, the pseudo-steadystate (i.e., the same saturation conditions were obtained at the end ofeach irrigation cycle) was reached after 2 irrigation cycles, with theaverage water storage of about 2660 cm2, which reﬂected the averagesoil water content of about 0.28 cm3 cm-3. There were only small differences between diﬀerent furrow surface treatments and diﬀerent irrigation rates. Similar results were also obtained for a system with

Fig. 10. Total transpiration as a function of the furrow surface treatment (S0 original, Sc - compacted, Sim - impermeable membrane), for irrigation rates (IR)of 60 (IR 60), 70 (IR 70), 80 (IR 80), 90 (IR 90), and 100 (IR 100) cm2 h−1, andirrigations applied at regular intervals and triggered (tr).
8Agricultural Water Management 232 (2020) 106044

K.L. Bristow, et al.

Fig. 14. Plant nitrogen uptake as a function of the initial placement of fertilizer(P1 - base, P2 - sides, P3 - base and sides, P4 - sides near ridge, P5 - top of ridge),the surface treatment scenario (S0 - original, Sc - compacted, and Sim - impermeable membrane), and for irrigation applied at regular intervals andtriggered (tr). The irrigation rate is 90 cm2 h−1.

Fig. 12. The change in storage in the soil proﬁle as a function of the surface
treatment scenario (S0 - original, Sc - compacted, and Sim - impermeable
membrane), for irrigation rates (IR) of 60 (IR 60), 70 (IR 70), 80 (IR 80), 90 (IR90), and 100 (IR 100) cm2 h−1, and irrigations applied at regular intervals andtriggered (tr).

experimental studies of Kemper et al. (1975), Hamlett et al. (1990),
Clay et al. (1992), Mailhol et al. (2001), and Waddell and Weil (2006)
who all reported that placing fertilizer near the top of the ridge has abeneﬁcial impact on both yield (its increase) and nitrogen leaching (itsdecrease). Leaching also substantially decreased when irrigations were
triggered by the soil water status in the ridge, rather than prescribed ata regular time interval.
Fig. 14 shows plant nitrogen uptake as a function of the initialplacement of fertilizer, surface treatment, and irrigation applied atregular intervals and triggered by the soil water status in the ridge. The
irrigation rate is 90 cm2 h−1. The initial location of the fertilizer exerts
a major control on plant nitrogen uptake. There is substantial nitrogen
uptake when the fertilizer is placed at the top of the ridge (either in thecenter (about 90 % of fertilizer is taken up by roots) or on the sides(about 80 %) of the ridge). There is less uptake of nitrogen (about 60 %)when the fertilizer is placed at the sides of the furrow. Much lower
uptake (10–30 %) occurs when the fertilizer is placed at the bottom of
the furrow, as most of it is leached (Fig. 13). When the fertilizer is
initially placed at the bottom of the furrow, it is mostly out of reach ofplants and is mainly leached. There are only relatively small diﬀerencesin plant nitrogen uptake as a function of the soil surface treatment at
the bottom of the furrow and when irrigations are triggered or applied
at a regular time interval.
Fig. 15 shows the ﬁnal solute storage in the soil proﬁle as a functionof the initial placement of fertilizer, surface treatment, and fortriggered irrigations and an impermeable membrane at the bottom of
the furrow. Larger diﬀerences were only observed for systems withtriggered irrigation and with original or compacted soil at the bottom of
the furrow.
3.7. Nitrogen leaching, plant nitrogen uptake and nitrogen storage
While simulations evaluating water balance components were carried out for six diﬀerent irrigation rates (i.e., 60, 70, 80, 90, and 100
cm2 h-−1 applied either at a constant time interval of 5 days or triggered by conditions in the soil), simulations evaluating solute balancecomponents were carried out for ﬁve diﬀerent initial solute placements
but only one irrigation rate (again at either a prescribed regular timeinterval of 5 days or triggered by the soil water status in the ridge) of 90
cm2/d (scenarios IR90 and IR90-tr, discussed above). The same irrigation rate was used as the base case in the study of Siyal et al. (2012).
Solute leaching decreased substantially with the decrease in permeability of the bottom of the furrow, from untreated, to compacted, toimpermeable (Fig. 13). As expected, leaching was largest when thenitrogen fertilizer was applied at the base, base and sides, and sides ofthe furrow. Leaching was minimal when fertilizer was applied at the topof the ridge. These numerical results are in agreement with

Fig. 13. Solute leaching as a function of the initial placement of fertilizer (P1 base, P2- sides, P3 - base and sides, P4 - sides near ridge, P5 - top of ridge);
surface treatment (S0 - original, Sc - compacted, and Sim - impermeable membrane); and for irrigations applied at regular intervals and triggered (tr). The
irrigation rate is 90 cm2 h−1.

Fig. 15. Final solute storage as a function of the initial placement of fertilizer(P1 - base, P2 - sides, P3 - base and sides, P4 - sides near ridge, P5 - top of ridge),
surface treatment (S0 - original, Sc - compacted, and Sim - impermeable membrane), and for irrigations applied at regular intervals and triggered (tr). The
irrigation rate is 90 cm2 h−1.
9Agricultural Water Management 232 (2020) 106044

K.L. Bristow, et al.

irrigations applied at regular intervals and triggered with the irrigation
rate of 90 cm2 h−1. The ﬁnal fertilizer storage in the soil proﬁle is (moreor less) inversely proportional to the fertilizer leaching. Although theplant nitrogen uptake (Fig. 14) was more or less independent of thesurface treatment of the soil at the bottom of the furrow or whether
irrigations were triggered or applied at a regular time interval, more
fertilizer remained in the soil proﬁle with the decrease in permeabilityof the bottom of the furrow, and would potentially be available for
future uptake rather than leached, especially when the fertilizer was
initially placed at (or close to) the bottom of the furrow. Smaller differences in solute storage were recorded between diﬀerent surface
treatments when the fertilizer was initially placed at the top of theridge.

scenario. Since several governing equations describing this system (e.g.,the Richards equation or plant stress response functions) are nonlinear,obtained results cannot be directly transferred to other systems with
diﬀerent soils, plants, fertilizers, and weather scenarios. The simulation
results discussed in this manuscript only present expected trends thatwould have to be conﬁrmed by similar numerical simulations for these
diﬀerent conditions.

4. Conclusions

Acknowledgments

In this study, we extended the original analysis of Siyal et al. (2012)by including multiple irrigation cycles, improved irrigation schedulingbased on the soil water status and root water and nutrient uptake toobtain a more realistic and complete picture of the overall water andnitrogen balance in furrow irrigated systems.
Our simulations have shown that drainage from the root zone can besubstantially reduced by modifying the soil surface properties of thebottom of the furrow. When the bottom of the furrow was compacted,
drainage was reduced by almost half. A further large reduction indrainage could be achieved by using an impermeable membrane on thebase of the furrow. An additional and substantial decrease in drainage
can be achieved using triggered irrigation based on a pre-set soil water
status in the ridge. Using triggered irrigation can additionally also
substantially reduce water losses through soil evaporation from boththe top of the ridge and the sides and bottom of the furrow by about 50% or more. This reduction in water loss by drainage and soil evaporation is accompanied by a relatively small decrease in transpiration(from about 98 % to about 92 %) compared with irrigation applied at aprescribed time interval. The reduction in transpiration and water loss
associated with triggered irrigation is accompanied by a substantial
increase in irrigation water use eﬃciency. Overall, our simulations indicate that signiﬁcant savings of irrigation water and reduction in deep
percolation and leaching can be achieved by modifying the soil surface
properties of the bottom of the furrow.
Solute leaching is driven by deep drainage from the crop root zone.
Substantial amounts of nitrogen are leached when the fertilizer is initially placed at the bottom of the furrow but can be greatly reduced bymodifying the soil surface properties of the bottom of the furrow. Whenfertilizer is applied to the sides of the furrow or at the top of the ridge,
nitrogen leaching is essentially eliminated, with about 60%–80% of thenitrogen being taken up by the plant. There are negligible diﬀerences innitrogen uptake between the diﬀerent soil surface treatments.
Diﬀerences in root nitrogen uptake are mainly determined by the initialplacement of the fertilizer.
The HYDRUS (2D/3D) model coupled with the "furrow module”
proved to be a powerful tool for analyzing water ﬂow and solutetransport processes in the crop root zone in furrow irrigation and inevaluating various factors aﬀecting this system; including irrigation
rates, soil hydraulic properties at the base of the furrow and root waterand nitrogen uptake. It must, however, be emphasized that this model
considers processes only in two dimensions perpendicular to the actual
furrow. It cannot account for ﬂow in the third dimension, such as theadvance or recession of irrigation water in the furrow. Nor can it account for the actual mixing of nitrogen with water in the furrow. The
development of a pseudo-three-dimensional model that accounts forwater ﬂow down the furrow and all subsurface soil processes discussed
above is currently under development (Brunetti et al., 2018; Liu et al.,2019).
It should further be emphasized that the presented simulations werecarried out for a single hypothetical soil, plant, fertilizer, and weather

We thank the Commonwealth Scientiﬁc and Industrial Research
Organisation (CSIRO), Canberra, Australia, for supporting Professor
Jirka Šimůnek’s visit to Townsville, Australia, to initiate this study.

Declaration of Competing Interest
The authors declare that they have no known competing ﬁnancial
interests or personal relationships that could have appeared to inﬂuence the work reported in this paper.

Appendix A. Supplementary data
Supplementary material related to this article can be found, in the
online version, at doi:https://doi.org/10.1016/j.agwat.2020.106044.
References
Abbasi, F., Jacques, D., Šimůnek, J., Feyen, J., van Genuchten, M.T., 2003b. Inverse estimation of the soil hydraulic and solute transport parameters from transient ﬁeld
experiments: heterogeneous soil. Trans. ASAE 46 (4), 1097–1111.
Abbasi, F., Feyen, J., van Genuchten, M.T., 2004. Two-dimensional simulation of waterﬂow and solute transport below furrows: model calibration and validation. J. Hydrol.
290 (1–2), 63–79.
Abbasi, F., Šimůnek, J., Feyen, J., van Genuchten, M.T., Shouse, P.J., 2003a.
Simultaneous inverse estimation of soil hydraulic and solute transport parametersfrom transient ﬁeld experiments: homogeneous soil. Trans. ASAE 46 (4), 1085–1095.
Abbasi, F., Šimůnek, J., van Genuchten, M.T., Feyen, J., Adamsen, F.J., Hunsaker, D.J.,
Strelkoﬀ, T.S., Shouse, P.J., 2003c. Overland water ﬂow and solute transport: model
development and ﬁeld-data analysis. J. Irrig. Drainage Eng. 129 (2), 71–81.
Artiola, J.F., 1991. Non-uniform leaching of nitrate and other solutes in a furrow-irrigated, sludge amended ﬁeld. Commun. Soil Sci. Plant Anal. 22, 1013–1030.
Bar-Yosef, B., 1999. Advances in fertigation. Adv. Agron. 65, 1–75.
Benjamin, J.G., Havis, H.R., Ahuja, L.R., Alonso, C.V., 1994. Leaching and water ﬂow
patterns in every-furrow and alternate-furrow irrigation. Soil Sci. Soc. Am. J. 58 (5),1511–1517.
Brunetti, G., Šimůnek, J., Bautista, E., 2018. A hybrid ﬁnite volume-ﬁnite element modelfor the numerical analysis of furrow irrigation and fertigation. Comput. Electron.
Agric. 150, 312–327. https://doi.org/10.1016/j.compag.2018.05.013.
Clay, S.A., Clay, D.E., Koskinen, W.C., Malzer, G.L., 1992. Agrichemical placement impacts on alachlor and nitrate movement through soil in a ridge tillage system. J.
Environ. Sci. Health B 27, 125–138.
Crevoisier, D., Popova, Z., Mailhol, J.C., Ruelle, P., 2008. Assessment and simulation ofwater and nitrogen transfer under furrow irrigation. Agric. Water Manag. 95 (4),354–366.
Dabach, S., Lazarovitch, N., Šimůnek, J., Shani, U., 2013. Numerical investigation of irrigation scheduling based on soil water status. Irrig. Sci. 31 (1), 27–36. https://doi.
org/10.1007/s00271-011-0289-x.
Dabach, C., Shani, U., Lazarovitch, N., 2015. Optimal tensiometer placement for highfrequency subsurface drip irrigation management in heterogeneous soils. Agric.
Water Manag. 152, 91–98 2015.
Ebrahimian, H., Liaghat, A., Parsinejad, M., Abbasi, F., Navabian, M., 2012. Comparisonof one- and two- dimensional models to simulate alternate and conventional furrow
fertigation. J. Irrig. Drainage Eng. 138 (10), 929–938. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000482.
Ebrahimian, H., Liaghat, A., Parsinejad, M., Playan, E., Abbasi, F., Navabian, M., 2013a.
Simulation of 1D surface and 2D subsurface water ﬂow and nitrate transport in alternate and conventional furrow fertigation. Irrig. Sci. 31, 301–316. https://doi.org/
10.1007/s00271-011-0303-3.
Ebrahimian, H., Liaghat, A., Parsinejad, M., Playan, E., Abbasi, F., Navabian, M., Lattore,
B., 2013b. Optimum design of alternate and conventional furrow fertigation tominimize nitrate loss. J. Irrig. Drainage Eng. 139 (11), 911–921. https://doi.org/10.
1061/(ASCE)IR.1943-4774.0000635.
Feddes, R.A., Kowalik, P.J., Zaradny, H., 1978. Simulation of Field Water Use and Crop
Yield. John Wiley & Sons, New York, NY.
Hamlett, J.M., Baker, J.L., Horton, R., 1990. Water and anion movement under ridge
tillage: a ﬁeld study. Trans. ASAE 33, 1859–1866.
Hanson, B.R., Šimůnek, J., Hopmans, J.W., 2006. Numerical modeling of urea-

10Agricultural Water Management 232 (2020) 106044

K.L. Bristow, et al.

Šimůnek, J., Bristow, K.L., Helalia, S.A., Siyal, A.A., 2016a. The eﬀect of diﬀerent fertigation strategies and furrow surface treatments on plant water and nitrogen use. Irrig.
Sci. 34 (1), 53–69. https://doi.org/10.1007/s00271-015-0487-z.
Šimůnek, J., van Genuchten, M.T., Šejna, M., 2016b. Recent developments and applications of the HYDRUS computer software packages. Vadose Zone J. 15 (7), 25. https://doi.org/10.2136/vzj2016.04.0033.
Siyal, A.A., Bristow, K.L., Šimůnek, J., 2012. Minimizing nitrogen leaching from furrow
irrigation through novel fertilizer placement and soil management strategies. Agric.
Water Manag. 115, 242–251.
Soroush, F., Mostafazadeh-Fard, B., Mousavi, S.F., Abbasi, F., 2012. Solute distribution
uniformity and fertilizer losses under meandering and standard furrow irrigation
methods. Aust. J. Crop Sci. 6 (5), 884–890.
Tiercelin, J.R., Vidal, A., 2006. Traite´ d’Irrigation, 2nd ed. Lavoisier, Technique andDocumentation, Paris, France.
van Genuchten, M.Th., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892–898.
Vrugt, J.A., Hopmans, J.W., Šimůnek, J., 2001. Calibration of a two-dimensional root
water uptake model. Soil Sci. Soc. Am. J. 65 (4), 1027–1037.
Vrugt, J.A., van Wijk, M.T., Hopmans, J.W., Šimůnek, J., 2002. One-, two-, and threedimensional root water uptake functions for transient modeling. Water Resour. Res.
37 (10), 2457–2470.
Waddell, J.T., Weil, R.R., 2006. Eﬀect of fertilizer placement on solute leaching underridge tillage and no till. Soil Tillage Res. 90, 194–204.
Walker, W.R., Skogerboe, G.V., 1987. Surface Irrigation: Theory and Practice. PrenticeHall Inc., Englewood Cliﬀs, New Jersey 386 p.
Warrick, A.W., Lazarovitch, N., Furman, A., Zerihun, D., 2007. Explicit inﬁltration
function for furrows. J. Irrig. Drain. Eng. 133 (4), 307–313.
Wöhling, T., Mailhol, J.C., 2007. A physically based coupled model for simulating 1D
surface - 2D subsurface ﬂow and plant water uptake in irrigation furrows. II: model
test and evaluation. J. Irrig. Drain. Eng. 133 (6), 548–558.
Wöhling, T., Schmitz, G.H., 2007. A physically based coupled model for simulating 1D
surface - 2D subsurface ﬂow and plant water uptake in irrigation furrows. I: model
development. J. Irrig. Drain. Eng. 133 (6), 538–547.
Wöhling, T., Schmitz, G.H., Mailhol, J.C., 2004a. Modeling two-dimensional inﬁltrationfrom irrigation furrows. J. Irrig. Drain. Eng. 130 (4), 296–303.
Wöhling, T., Singh, R., Schmitz, G.H., 2004b. Physically based modeling of interacting
surface–subsurface ﬂow during furrow irrigation advance. J. Irrig. Drain. Eng. 130(5), 349–356.
Wöhling, T., Fröhner, A., Schmitz, G.H., Liedl, R., 2006. Eﬃcient solution of the coupled
one-dimensional surface - two-dimensional subsurface ﬂow during furrow irrigation
advance. J. Irrig. Drain. Eng. 132 (4), 380–388.
Zerihun, D., Sanchez, C.A., Lazarovitch, N., Warrick, A.W., Clemmens, A.J., Bautista, E.,
2014. Modeling ﬂow and solute transport in irrigation furrows. Irrig. Drain. Syst. Eng.
3 (2), 16. https://doi.org/10.4172/2168-9768.1000124. 124.

ammonium-nitrate fertigation with drip irrigation using numerical modeling. Agric.
Water Manag. 86, 102–113.
Kemper, W.D., Olsen, J., Hodgdon, A., 1975. Fertilizer or salt leaching as aﬀected bysubsurface shaping and placement of fertilizer and water. Proceed. Soil Sci. Soc. Am.
39, 115–119.
Klocke, N.L., Schneekloth, J.P., Melvin, S., Clark, R.T., Payero, J.O., 2004. Field scale
limited irrigation scenarios for water policy strategies. Appl. Eng. Agric. 20, 623–631.
Lazarovitch, N., Warrick, A.W., Furman, A., Zerihun, D., 2009. Subsurface water distribution from furrows described by moment analyses. J. Irrig. Drain. Eng. 135 (1),
7–12.
Li, Y., Šimůnek, J., Zhang, Z., Jing, L., Ni, L., 2015. Evaluation of nitrogen balance in a
direct-seeded-rice ﬁeld experiment using Hydrus-1D. Agric. Water Manag. 148,
213–222. https://doi.org/10.1016/j.agwat.2014.10.010.
Liu, K., Huang, G., Xu, X., Xiong, Y., Huang, Q., Šimůnek, J., 2019. A coupled model for
simulating water ﬂow and solute transport in furrow irrigation. Agric. Water Manag.
213, 792–802.
Mailhol, J.C., Ruelle, P., Nemeth, I., 2001. Impact of fertilisation practices on nitrogenleaching under irrigation. Irrig. Sci. 20, 139–147.
Mailhol, J.C., Crevoisier, D., Triki, K., 2007. Impact of water application conditions on
nitrogen leaching under furrow irrigation: experimental and modeling approaches.
Agric. Water Manag. 87 (3), 275–284.
Oster, J.D., Letey, J., Vaughan, P., Wu, L., Qadir, M., 2012. Comparison of transient statemodels that include salinity and matric stress eﬀects on plant yield. Agric. Water
Manag. 103, 167–175.
Payero, J.O., Melvin, S.R., Irmak, S., Tarkalson, D., 2006. Yield response of corn to deﬁcit
irrigation in a semiarid climate. Agric.Water Manage 84, 101–112.
Pratt, P.F., Jury, W.A., 1984. Pollution of the unsaturated zone with nitrate. In: In: Yaron,
B., Dagan, G., Goldshmid, J. (Eds.), Pollutants in Porous Media. Ecological Studies(Analysis and Synthesis) 47 Springer, Berlin, Heidelberg.
Ragab, R., Battilani, A., Matovic, G., Stikic, R., Psarras, G., Chartzoulakis, K., 2015.
SALTMED model as an integrated management tool for water, crop, soil and N-fertilizer water management strategies and productivity: ﬁeld and simulation study.
Irrig. Drain. 64, 13–28.
Ramos, T.B., Šimůnek, J., Gonçalves, M.C., Martins, J.C., Prazeres, A., Pereira, L.S., 2012.
Two-dimensional modeling of water and nitrogen fate from sweet sorghum irrigatedwith fresh and blended saline waters. Agric. Water Manag. 111, 87–104. https://doi.
org/10.1016/j.agwat.2012.05.007.
Rocha, D., Abbasi, F., Feyen, J., 2006. Sensitivity analysis of soil hydraulic properties on
subsurface water ﬂow in furrows. J. Irrig. Drain. Eng. 132 (4), 418–424.
Šimůnek, J., Hopmans, J.W., 2009. Modeling compensated root water and nutrient uptake. Ecol. Model. 220 (4), 505–521. https://doi.org/10.1016/j.ecolmodel.2008.11.
004.
Šimůnek, J., van Genuchten, M.T., Šejna, M., 2008. Development and applications of the
HYDRUS and STANMOD software packages and related codes. Vadose Zone J. 7 (2),587–600. https://doi.org/10.2136/VZJ2007.0077.

11