Agricultural Water Management 111 (2012) 87–104

Contents lists available at SciVerse ScienceDirect

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

Two-dimensional modeling of water and nitrogen fate from sweet sorghum
irrigated with fresh and blended saline waters
T.B. Ramos a,∗ , J. Šimůnek b , M.C. Gonçalves a,c , J.C. Martins c , A. Prazeres c , L.S. Pereira aaCEER-Biosystems Engineering, Institute of Agronomy, Technical University of Lisbon, Tapada da Ajuda, 1349-017, Lisbon, Portugal
Department of Environmental Sciences, University of California, Riverside, CA, 92521, USAc
Estação Agronómica Nacional, INIA, Instituto Nacional de Recursos Biológicos, Quinta do Marquês, Av. República, 2784-505, Oeiras, Portugalb

a r t i c l e

i n f oArticle history:
Received 21 October 2011
Received in revised form 18 May 2012
Accepted 21 May 2012
Available online 8 June 2012
Keywords:
HYDRUS-2D
Saline irrigation water
Nitrates leaching
Sorghum yields

a b s t r a c t
The need for reducing irrigation water demand and non-point source pollution all across Europe has madesweet sorghum [Sorghum bicolor (L.) Moench], due to its lower water and nutrient requirements, an interesting alternative to other traditional summer crops in European Mediterranean regions. HYDRUS-2D wasused to model the fate of nitrogen in a plot planted with sweet sorghum grown under Mediterranean
conditions between 2007 and 2010, while considering drip irrigation scenarios with different levels of
nitrogen and salty waters. HYDRUS-2D simulated water contents, ECsw , and N NH4 + and N NO3 − concentrations continuously for the entire duration of the ﬁeld experiment, while producing RMSE between
simulated and measured data of 0.030 cm3 cm−3 , 1.764 dS m−1 , 0.042 mmolc L−1 , and 3.078 mmolc L−1 ,respectively. Estimates for sweet sorghum water requirements varied between 360 and 457 mm depending upon the crop season and the irrigation treatment. Sweet sorghum proved to be tolerant to saline
waters if applied only during one crop season. However, the continuous use of saline waters for morethan one crop season led to soil salinization, and to root water uptake reductions due to the increasing
salinity stress. The relation found between N NO3 − uptake and dry biomass yield (R2 = 0.71) showedthat nitrogen needs were smaller than the uptakes estimated for the scenario with the highest levels of
nitrogen application. The movement of N out of the root zone was dependent on the amount of waterﬂowing through the root zone, the amount of N applied, the form of N in the fertilizer, and the timing and number of fertigation events. The simulations with HYDRUS-2D were useful to understand thebest strategies toward increasing nutrient uptake and reducing nutrient leaching. In this sense, N NO3 −uptakes were higher when fertigation events were more numerous and the amounts applied per event
smaller.
© 2012 Elsevier B.V. All rights reserved.

1. Introduction
Non-point source pollution is among the most important andwidespread environmental problems in European Mediterranean
agricultural regions. Farmers usually apply high rates of water andnitrogen fertilizer to insure that crop needs are fulﬁlled, while producing inefﬁcient water and nitrogen use, and increasing leachingpotential of nutrients into the groundwater.
The European Commission implemented the Council Directive
91/676/EEC in 1991, also referred to as the Nitrates Directive,
which imposed upon EU-Member States the establishment of various action programs for reducing water contamination caused
or induced by agricultural sources. However, 20 years later
many European regions with higher agriculture intensity continue∗ Corresponding author. Tel.: +351 214403500; fax: +351 214416011.
E-mail address: tiago ramos@netcabo.pt (T.B. Ramos).
0378-3774/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.agwat.2012.05.007

registering high nitrate concentrations in a signiﬁcant number ofgroundwater monitoring stations. In particular, many monitoring
stations in the European Mediterranean Member States showed
relatively high values throughout 2004–2007. Nitrate vulnerable
zones covered 3.7% of Portugal, 6.8% of Cyprus, 12.6% of Spain and
Italy, 24.2% of Greece, and 100% of Malta’s territories (European
Commission, 2010a,b).
In these water-scarce European Mediterranean regions, the useof crops with lower water and nutrient needs has recently been
considered to be an adequate alternative to traditional crops suchas corn, in order to reduce nutrient loads into the groundwater (Barbanti et al., 2006). Sweet sorghum (Sorghum bicolor (L.)
Moench) was regarded among the most interesting annual crops
to be grown in these environmentally stressed areas (Almodaresand Hadi, 2009; Vasilakoglou et al., 2011). Sweet sorghum is adrought resistant crop with relatively low water requirements andhigh water-use efﬁciency (Mastrorilli et al., 1995, 1999; Steduto
et al., 1997; Katerji et al., 2008), and is moderately tolerant to88

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

salinity (Maas, 1990; Hoffman and Shalhevet, 2007). Sweetsorghum is furthermore an important alternative source for renewable energy because of its ability to store large quantities of
non-structural carbohydrates (sucrose, glucose, and fructose) in its
stems that can be converted into fuel ethanol (Prasad et al., 2007;
Zhao et al., 2009; Almodares and Hadi, 2009).
A large number of analytical and numerical modeling tools areavailable to evaluate the effects of different agricultural practices
on nitrogen leaching, nutrient uptake, and crop yield (e.g., Johnsson
et al., 1987; Hutson and Wagenet, 1991; Ma et al., 2001; Šimůnek
et al., 2008; Doltra and Muñoz, 2010). Simulation models canrapidly perform a long-term analysis of the effects of introducing
new crops and/or new agricultural practices in nitrate vulnerable zones, and help develop action programs to minimize nutrient
loads into groundwater as required by the Nitrates Directive.
Some of those physical-based models have been calibrated
and/or validated to simulate water movement (Fernando, 1993;
Cameira et al., 2005), nutrient transport (Cameira et al., 2003,
2007), soil salinity distribution (Gonçalves et al., 2006; Ramos et al.,2011), and runoff and soil erosion (Fontes et al., 1992) in different regions of Portugal. Semi-empirical water balance models havealso been developed to improve irrigation scheduling and reducewater losses (Pereira et al., 1995; Rosa et al., 2012). However, theseapproaches have been only one-dimensional and neglected waterand solute ﬂuxes, and pressure head and concentration gradientsin the horizontal direction. Additionally, one-dimensional models
fail to adequately simulate micro-irrigation systems (such as drip
emitters, drip tape, and micro-sprinklers), which can efﬁciently
apply water and nutrients in the right amounts and precise locations throughout a ﬁeld (Gärdenäs et al., 2005). Since drip irrigation
is often used in Portugal it seems only adequate to ﬁnd modelingapproaches that are more suitable to represent complex physicaland chemical processes that take place in the soil proﬁle under thisirrigation system.
The HYDRUS (2D/3D) software package (Šimůnek et al., 2006,2008) is the state-of-the-art model for simulating water, heat, andsolute movement in two- and three-dimensional variably saturated porous media that can become a valuable tool for establishingsound agricultural practices in European Mediterranean agricultural regions. The model has been extensively used for simulating
the fate of nutrients in soils by evaluating and comparing microirrigation and fertigation strategies for different crops (Cote et al.,
2003; Gärdenäs et al., 2005; Hanson et al., 2006; Ajdary et al., 2007;
Crevoisier et al., 2008). It has also been used for a wide range ofapplications of interest for water scarce regions, such as improving irrigation management with poor quality waters (Gonçalves
et al., 2006; Hanson et al., 2008; Roberts et al., 2008, 2009; Ramos
et al., 2011). Furthermore, HYDRUS-2D (a two-dimensional module of HYDRUS (2D/3D)) results are often used as a reference fordeveloping or validating new simulation models (Mmolawa andOr, 2003; Doltra and Muñoz, 2010; Mailhol et al., 2011).
The main objective of this study was to use the HYDRUS-2D software package to model nitrogen fate in a plot with sweet sorghum
grown under Mediterranean conditions while considering different drip fertigation and water quality scenarios. From 2007 to 2010
(i.e., during three crop seasons), sweet sorghum was subjected tothe application of different amounts of nitrogen, different fertigation events, and to irrigation with waters of different quality. Field
data were used to calibrate and validate HYDRUS-2D for predicting(i) soil water contents and ﬂuxes, (ii) the electrical conductivity ofthe soil solution (ECsw ), (iii) water uptake reductions due to the useof saline waters, and (iv) N NH4 + and N NO3 − concentrations inthe soil and leaching. Water and nutrient balances were calculated
based on HYDRUS-2D predictions for three crop seasons and for theentire simulation period. The modeling approach helped us understand the best irrigation and fertigation management practices toTable 1Main physical and chemical soil characteristics.
Depth (cm)Alvalade
0–30

30–75

75–100Coarse sand, 2000–200 ␮m (%)
Fine sand, 200–20 ␮m (%)
Silt, 20–2 ␮m (%)
Clay, <2 ␮m (%)
TextureBulk density (g cm−3 )pH (H2 O)
Organic matter (%)

8.3
52.4
26.3
13.0
Loam
1.49
7.27
2.30

6.5
46.2
29.3
18.0
Silty loam
1.51
7.23
2.26

5.8
42.0
27.6
24.6
Loam
1.61
7.21
1.66

Soil initial conditions:
Water content (cm3 cm−3 )ECsw (dS m−1 )N NH4 + (mmolc L−1 )N NO3 − (mmolc L−1 )

0.18
2.17
0.01
0.31

0.18
2.99
0.01
0.47

0.18
4.68
0.01
1.43

van Genuchten–Mualem parameters:
0.050
 r (cm3 cm−3 )0.380
 s (cm3 cm−3 )0.027
˛ (cm−1 )
1.21
 (–)
−4.41
 (–)
Ks (cm d−1 )
16.6

0.108
0.380
0.115
1.19
−5.37
84.4

0.000
0.375
0.045
1.17
−6.48
21.0

Solute transport parameters:
εL (cm)

25.8

12.2

25.8

ECsw , electrical conductivity of the soil solution;  r , residual water content;  s ,saturated water content; ˛ and , are empirical shape parameters; , pore connectivity/tortuosity parameter; Ks , saturated hydraulic conductivity; εL , longitudinal
dispersivity.

be adopted in future practical applications for increasing nutrient
uptake and reducing nutrient leaching.
2. Materials and methods
2.1. Experimental setup and measurements
The ﬁeld experiment was conducted at the Alvalade Experimental Station (37◦ 56 48 N and 8◦ 23 40 W), southern Portugal, fromMay 2007 to April 2010. The climate in the region is dry, sub-humid,with hot dry summers and mild winters with irregular rainfall.
Rainfall was 371, 299, and 676 mm in 2007/2008, 2008/2009, and2009/2010, respectively, with 91, 63, and 35 mm of rain during thecorresponding crop growth seasons. The soil was classiﬁed as a
Eutric Fluvisol (FAO, 2006). The soil’s main physical and chemical
properties are presented in Table 1. Field and laboratory methodologies used for characterizing the soil proﬁle were extensively
described by Ramos et al. (2011).
The ﬁeld experiment involved irrigation of sweet sorghum (S.
bicolor (L.) Moench var. saccharatum (L.) Mohlenbr) with synthetic
saline waters blended with fresh irrigation waters and waters withnitrogen (NH4 NO3 ) during three crop seasons. The crop hybrid
selected for this experiment was the sweet sorghum “Madhura”,
developed in India. Sweet sorghum was sown on May 18, 2007,
May 15, 2008, and May 15, 2009. The row spacing used was 0.75 m
and the distance between plants was 0.15 m. Irrigation started onJune 1, 2007 (15 days after sowing, or DAS), June 13, 2008 (30 DAS),
and June 3, 2009 (20 DAS). The total amount of water applied was425, 522, and 546 mm in 2007, 2008, and 2009, respectively.
The drip irrigation system was used to mix and deliver synthetic saline irrigation waters, fresh irrigation waters, and fertilizer(NH4 NO3 ) to the experimental plots following the irrigation
scheme documented in Ramos et al. (2009, 2011). This system consisted of three drip lines connected together in order to form a
triple joint lateral placed along each sweet sorghum line (Fig. 1).
The ﬁrst of the laterals was connected to the salt stock solution

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

89

Fig. 1. Layout of the triple emitter source design (adapted from Ramos et al., 2009). The salt gradient decreases from sub-group A to C and the fertilizer gradient decreases
from group I to IV.

Table 2
Discharge rates of the laterals applying salt (Na+ ), nitrogen (N) and fresh water (W) in each experimental plot. There is an overall constant cumulative discharge at eachdripping point of 18 L h−1 m−1 (Ramos et al., 2009).
Treatment

A
B
C

Application rates (L h−1 m−1 )Group IGroup II++Group III

Group IV

Na

N

W

Na

N

W

Na

N

W

Na+

N

W

12
6
0

6
6
6

0
6
12

12
6
0

4
4
4

2
8
14

12
6
0

2
2
2

4
10
16

12
6
0

0
0
0

6
12
18

(NaCl), while the second one was connected to the nitrogen reservoir. The third lateral delivered fresh water and was used to obtaina constant water application rate for each dripping point along
the triple joint lateral (the drip discharge of 18 L h−1 m−1 ; which+

represents 24 mm h−1 considering an area for each dripping pointof 100 cm × 75 cm). Gradients of applied salt (Na+ ) and nitrogen(N) concentrations were then produced by placing different emitters in each dripping point along the corresponding laterals andTable 3
Waters blended in each experimental plot during the three crop seasons.
Sub-group

Irrigation water

Water applied (mm)Group IGroup IIGroup III

Group IV

2007

(N3)
2008

2009

2007

(N2)
2008

2009

2007

(N1)
2008

2009

2007

(N0)
2008

2009

A (S2)

Saline water
Water + NH4 NO3
Fresh water

228.0
19.3
177.7

184.0
30.0
308.0

316.0
20.0
210.0

228.0
12.9
184.1

184.0
20.0
318.0

316.0
13.3
216.7

228.0
6.4
190.6

184.0
10.0
328.0

316.0
6.7
223.3

228.0
0.0
197.0

184.0
0.0
338.0

316.0
0.0
230.0

B (S1)

Saline water
Water + NH4 NO3
Fresh water

114.0
19.3
291.7

92.0
30.0
400.0

158.0
20.0
368.0

114.0
12.9
298.1

92.0
20.0
410.0

158.0
13.3
374.7

114.0
6.4
304.6

92.0
10.0
420.0

158.0
6.7
381.3

114.0
0.0
311.0

92.0
0.0
430.0

158.0
0.0
388.0

C (S0)

Saline water
Water + NH4 NO3
Fresh water

0.0
19.3
405.7

0.0
30.0
492.0

0.0
20.0
526.0

0.0
12.9
412.1

0.0
20.0
502.0

0.0
13.3
532.7

0.0
6.4
418.6

0.0
10.0
512.0

0.0
6.7
539.3

0.0
0.0
425.0

0.0
0.0
522.0

0.0
0.0
546.0

N3, N2, N1, N0, nitrogen gradient; S2, S1, S0, salinity gradient.

90

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

Table 4Characteristics of the irrigation waters blended in each experimental plot.
Irrigation waters

Year

ECiw (dS m−1 )N NH4 + (mmolc L−1 )N NO3 − (mmolc L−1 )Fresh waters

2007–2009

0.81

0.03

0.15

Saline waters

2007
2008
2009

7.60
9.60
10.60

0.03
0.03
0.03

0.15
0.15
0.15

Waters with nitrogen

2007
2008
2009

9.50
6.77
7.34

95.0
67.7
73.4

95.0
67.7
73.4

ECiw , electrical conductivity of the irrigation water.

varying their discharge rates to obtain various mixtures between
the three lines. Table 2 lists the different discharge rates of theemitters applying salts, nitrogen, and fresh water to each experimental plot. Table 3 presents the amount of saline waters, fresh
waters, and waters with nitrogen applied in each experimental
plot. The blended amounts thus varied between experimental plots,
while the total amount of water applied per irrigation event andper crop season, as well as the quality of the irrigation waters
before blending (Table 4), remained identical in all experimental
plots.
The experimental ﬁeld (Fig. 1) was thus divided into four groups(I–IV), each with three triple joint laterals, establishing a N gradientdecreasing from group I to group IV. Each group was then divided
into three sub-groups, A, B and C, each with a surface area of 6.75 m2(2.25 m wide × 3 m long), and with the Na+ gradient decreasingfrom A to C. The emitters were spaced 1 m apart, with a total ofnine dripping points in each of the 12 experimental plots. Twolaterals of fresh water bordered the different groups (Fig. 1). Eachsub-group area was bordered with earthen ridges, which prevented
surface runoff from crossing over during rainfall and irrigation. The
crop was irrigated three times per week from June to September
with irrigation lasting 30–60 min per event. Fig. 2 presents daily
irrigation rates that were applied during three irrigation seasons.
Application amounts averaged 15, 16, and 17 mm per irrigation
event in 2007, 2008, and 2009, respectively. Nitrogen fertilization
was applied in four (2007), six (2008), and three (2009) irrigation
events during the vegetative stage (July).
In the plots with the highest application of the synthetic saline
waters (sub-group A), and those irrigated only with the locallyavailable fresh water (sub-group C), TDR probes with waveguides
from the Trase System (Soil Moisture Equipment Corp., Goleta, CA)
and ceramic cups were installed at depths of 20, 40, and 60 cm tomeasure soil water contents and collect soil solutions, respectively.
Only one TDR probe and one ceramic cup were installed in each
depth. The soil solution was monitored for ECsw and the concentrations of N NH4 + and N NO3 − . Soil water content measurements
and soil solutions were taken twice a week during irrigation seasons, generally 24 h after an irrigation event, and twice a month
during the rest of the year.
The crop was harvested manually on September 27, 2007 (132
DAS), on September 30, 2008 (138 DAS), and on September 29, 2009(137 DAS). The dry biomass of sweet sorghum was determined byharvesting all sorghum plants in each experimental plot and ovendrying at 70 ◦ C to a constant weight. Further details can be foundin Ramos et al. (2012).

2.2. Modeling approach
Modeling of water ﬂow and solute transport was carried out
for all experimental plots included in sub-group A, irrigatedwith the highest application of synthetic saline waters, and in

sub-group C, irrigated only with the water available in the region.
The HYDRUS-2D software package (Šimůnek et al., 2006) was used
to simulate the transient axisymmetrical (or radially symmetrical)
three-dimensional movement of water and nutrients in the soil.
In this approach, an individual emitter is represented as a point
source located on the axis of rotation (Figs. 3 and 4). The axisymmetrical domain geometry representing the experimental conditions
is shown in Fig. 4. The transport domain was set as a rectangle
with a width of 37.5 cm (half the lateral spacing, i.e., the halfdistance between triple joint laterals placed along the sorghumrows) and a depth of 100 cm. The transport domain was discretized
into 2774 nodes, which corresponded to 5342 triangular elements(Fig. 4b). Observation nodes, corresponding to the locations where
TDR probes and ceramic cups were installed, were placed at depthsof 20, 40, and 60 cm, and at a radial distance of 20 cm away fromthe emitter source (Fig. 4a) and along the crop row (Fig. 3). A timevariable ﬂux boundary condition was applied at the left part of thesoil surface, approximately the ﬁrst 20 cm to the right of the point
emitter source, located at the top left corner of the soil domain(Fig. 4b). The ﬂux boundary condition with the ﬂux q was deﬁned
as:q=

volume of water applied
surface wetted area × duration(1)

where the volume of water applied (L3 ) varied for different irrigation events, the surface wetted area (L2 ) was approximately
1256 cm2 (i.e., 3.14 × 202 ), and the irrigation duration was adjusted
to permit water to inﬁltrate into the soil without producing positive surface pressure heads. The application time was divided into
multiple intervals to allow for the application of irrigation watersof different qualities within a particular irrigation event. While thedripper discharge was constant and the irrigation duration variable in the experiment, for numerical convenience (and to avoid
positive surface pressures, which sometimes existed in reality), we
adjusted irrigation ﬂux to produce the applied irrigation volume
for a particular irrigation event, i.e., discharge rates of the emitters given in Table 2 were adjusted to apply the same volume ofwater but during longer time periods. Possible positive pressure
heads at the ﬂux boundary, which would make the numerical code
unstable, were avoided by distributing the surface ﬂux over a relatively large surface area and by spreading irrigation over a sufﬁcient
time period to allow water to inﬁltrate (from 0.2 to the entire day,
depending on the volume applied). The atmospheric boundary condition was assumed for the remainder of the soil surface during
periods with irrigation and for the entire soil surface during periods without irrigation. A no ﬂow boundary condition was set at theleft and right sections of the soil proﬁle, so that no water and solute
movement from neighboring emitters could be considered. A freedrainage boundary condition was assumed at the bottom of the soil
proﬁle.

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

91

10
8

30

6
20
4
10

ETO (mm)

Downward flux (mm)

40

2

0
18-05-07

14-11-07

12-05-08

08-11-08
Time (d)07-05-09

Rain

03-11-09

0
02-05-10

Irrigation

ETO

Fig. 2. Daily values of precipitation, irrigation, and reference evapotranspiration rates in Alvalade between 18th May 2007 and 2nd May 2010.

2.2.1. Water ﬂow
The spatial distributions of transient soil water contents andvolumetric ﬂuxes were obtained using a numerical solution of the
Richards equation for radially symmetric Darcian ﬂow:
1 ∂
∂(h)
=
r ∂r
∂t



r K(h)

∂
∂r



+

∂
∂z





K(h)

∂h
+ K(h)∂z− S(r, z, t)(2)

where  is the volumetric soil water content (L3 L−3 ), h is the soil
water pressure head (L), t is time (T), r is the radial space coordinate(L), z is the vertical space coordinate (L), K is the hydraulic conductivity (L T−1 ), and S is the sink term accounting for water uptake
by plant roots (L3 L−3 T−1 ). The unsaturated soil hydraulic properties were described using the van Genuchten–Mualem functional
relationships (van Genuchten, 1980) as follows:
Se (h) =(h) − r1=ms − r(1 + |˛ h| )1/m m

K(h) = Ks Se [1 − (1 − Se

) ]

(3)

uniform value throughout the soil proﬁle (Table 1). Since HYDRUS2D simulations were started 2 weeks before the ﬁrst irrigation
event, the effects of the initial condition on long term simulations(2007–2010) of solute transport could be neglected.
2.2.2. Solute transport
Solute transport in a homogeneous porous medium and in athree-dimensional axisymmetrical domain was computed using
the convection-dispersion equations (CDE) for each chemical
species (ECsw , N NH4 + , and N NO3 − ) considered in our study, as
follows:
∂ ck
∂ c̄
∂
+ k =
∂t
∂t
∂r
+

1
r



2

(4)

in which Se is the effective saturation,  r and  s denote theresidual and saturated water contents (L3 L−3 ), respectively, Ks
is the saturated hydraulic conductivity (L T−1 ), ˛ (L−1 ) and  (–)
are empirical shape parameters, m = 1 −1/, and  is a pore connectivity/tortuosity parameter (–). The van Genuchten–Mualem
parameters are presented in Table 1. They were obtained by ﬁtting Eqs. (2) and (3) to laboratory data measured on undisturbed
soil samples taken from a representative soil proﬁle, as described in
Ramos et al. (2011). The initial water content in the soil was set to a

−



Drr



Drr

∂ck
∂c
+ Drz k
∂r
∂z

∂ck
∂c
+ Drz k∂r∂z∂qr ckqr ck∂qz ck
+
+
r
∂r
∂z

+



∂
∂z





Dzz

∂ck
∂c
+ Drz k∂z∂z+ k − S croot,k(5)where  is the volumetric water content (L3 L−3 ), c, c, and croot
are solute concentrations in the liquid phase (M L−3 ), solid phase(M M−1 ), and sink term (M L−3 ), respectively,  is the soil bulk density (M L−3 ), qr and qz are the components of the volumetric ﬂux
density (L T−1 ), Drr , Dzz , and Drz are the components of the dispersion tensor (L2 T−1 ),  represents chemical reactions of solutes
involved in a sequential ﬁrst-order decay chain (M L−3 T−1 ), S isagain the sink term accounting for water uptake by plant roots

Fig. 3. Location of a point source emitter and monitoring sites in the experimental plot.

92

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

Fig. 4. Location of observation points within the soil proﬁle (a) and an axisymmetrical domain geometry with the ﬁnite element discretization used in HYDRUS-2D simulations(b).

(L3 L−3 T−1 ), and subscript k represents chemical species present
in our study (ECsw , N NH4 + , and N NO3 − ).
The components of the dispersion tensor are given by (Bear,
1972):

 Drr = εLq2rq2
+ εT z +  D0
|q|
|q|

q2z
q2
+ εT r +  D0
|q|
|q|
qr qz
 Drz = (εL − εT )|q|
 Dzz = εL

(6)

where |q| is the absolute value of the volumetric ﬂux density (L T−1 ),εL and εT are the longitudinal and transversal dispersivities (L), D0
is the molecular diffusion coefﬁcient of the solute in free water(L2 T−1 ), and is the tortuosity factor. Table 1 gives the εL values used in our study. They were obtained by ﬁtting analyticalsolutions of the CDE to observed breakthrough data measured on
undisturbed soil samples taken from a representative soil proﬁleof Alvalade as described in Gonçalves et al. (2001). The value of εT
was simply set as one tenth of εL (e.g., Mallants et al., 2011).

The distribution of solutes between the soil liquid and solid
phases was related in Eq. (5) with the following linear adsorption
isotherm:
ck = Kd,k ck(7)where Kd,k (L3 M−1 ) is the distribution coefﬁcient for the consideredchemical species. Nitrate (N NO3 − ) and ECsw were assumed to bepresent only in the dissolved phase (Kd = 0 cm3 g−1 ), which simpliﬁed Eq. (5) for these two chemical species. Ammonium (N NH4 + )was assumed to adsorb to the solid phase according to Eq. (7) withthe distribution coefﬁcient Kd of 3.5 cm3 g−1 (Hanson et al., 2006).
Since the fertilizer used in our study was NH4 NO3 , nitriﬁcationof the N NH4 + species to N NO3 − was assumed to be the main
N process occurring in the soil. HYDRUS-2D incorporates this process in Eq. (5) by means of a sequential ﬁrst-order decay chain as
follows:
N−NH+ = −N−NO− = −43w,N−NH+  cN−NH+ −4

4s,N−NH+  c̄N−NH+
4

4

(8)
where w and s are the ﬁrst-order rate constants for solutes in theliquid and solid phases (T−1 ), respectively. The ﬁrst-order reaction

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

93

terms, representing nitriﬁcation of N NH4 + to N NO3 − , thus act asa sink for N NH4 + and as a source for N NO3 − . The values for w
and s were set to be 0.2 d−1 . The parameters Kd , w , and s weretaken from a review of published data presented by Hanson et al.
(2006), and represent the center of the range of reported values.
The last term of Eq. (5) represents a passive root nutrient uptake,i.e., the movement of nutrients into roots by convective mass ﬂow
of water, directly coupled with root water uptake (Šimůnek andHopmans, 2009). This term was deﬁned as:

shallow under surface drip irrigation starting few days after sowing(Klepper, 1991; Allen et al., 1998; Zegada-Lizarazu et al., 2012). In
addition, ﬁeld observations carried out in November 2010 found no
signiﬁcant amounts of roots below this depth.
In this study we considered that during the growing seasons Tp rates were obtained by combining the daily values ofreference evapotranspiration (ET0 ), determined with the FAO
Penman–Monteith method and the dual crop coefﬁcient approach(Allen et al., 1998, 2005), as follows:

croot (r, z, t) = min[c(r, z, t), cmax ]ETc = (Kcb + Ke )ET0(9)where cmax is the a priori deﬁned maximum concentration of theroot solute uptake. Since we considered unlimited passive nutrient
uptake for nitrogen species, cmax was set to a concentration value
larger than the dissolved simulated concentrations, c, allowing all
dissolved nutrients to be taken up by plant roots with root water
uptake. Since for ECsw a zero uptake was considered, cmax was set
to zero.
2.2.3. Potential and actual evapotranspiration rates
The sink term (S) in Eqs. (2) and (5) was calculated using themacroscopic approach introduced by Feddes et al. (1978). In thisapproach, the actual local uncompensated root water uptake wasobtained as follows (Feddes et al., 1978; van Genuchten, 1987;
Skaggs et al., 2006a; Šimůnek and Hopmans, 2009):
S(h, h , r, z, t) = ˛(h, h , r, z, t)Sp (r, z, t)= ˛(h, h , r, z, t)ˇ(r, z, t)Tp (t)At(10)

where Sp (r,z,t) and S(h,h ,r,z,t) are the potential and actual volumesof water removed from a unit volume of soil per a unit of time
(L3 L−3 T−1 ), respectively, ˛(h,h ,r,z,t) is a prescribed dimensionless stress response function of the soil water (h) and osmotic (h )pressure heads (0 ≤ ˛ ≤ 1), ˇ(r,z,t) (L−3 ) is a normalized root density
distribution function, Tp is the potential transpiration rate (L T−1 ),and At is the area of the soil surface associated with transpiration[L2 ]. The actual transpiration rate, Ta (L T−1 ), was then obtained byintegrating Eq. (10) over the root domain, ˝ (L3 ), as follows:Ta (t) = Tp (t)˝r ˛(h, h , r, z, t)ˇ(r, z, t)d˝

(11)

The root distribution is deﬁned in HYDRUS-2D according to Vrugt
et al. (2001):
˝(r, z) =



1−

r
rm



1−

z
zm



∗

∗

e−((pr /rm )|r −r|+(pz /zm )|z −z|)(12)where rm and zm are the maximum radius and depth of the rootzone (L), respectively, z* and r* are the locations of the maximum root water uptake in vertical and horizontal directions (L),respectively, and the pr and pz values are taken to be equal to
one except for r > r* and z > z* when they become zero. The following parameters of the Vrugt et al. (2001) model were used in thesimulations: rm = 37.5 cm, zm = 65 cm, r* = 10 cm, z* = 10 cm. We considered a simple root distribution model in which the roots of sweetsorghum expanded horizontally into all available space between
sorghum lines (rm = 37.5 cm), were concentrated mainly around thedrip emitter (r* = 10 cm, z* = 10 cm) where water and nutrients wereapplied, and extended to a depth of 65 cm (zm = 65 cm). We assumed
that plants had no need of expanding their roots below this depth
since water and nutrients were being applied at the soil surface
and their life cycle lasted only ﬁve months. The parameters fordeﬁning the maximum root water uptake in vertical and horizontal
directions (z and r* ) were also based on the scenarios developed byGärdenäs et al. (2005) and Hanson et al. (2006, 2008). The selectionof the maximum rooting depth was also based on the work carriedout by Ramos et al. (2011) and the fact that root depths are relatively(13)

where ETc is the evapotranspiration (L T−1 ), Kcb is the basal crop
coefﬁcient, which represents the plant transpiration component(–), and Ke is the soil evaporation coefﬁcient (–).
Standard sweet sorghum Kcb values (Allen et al., 1998) were
adjusted for the Alvalade climate, taking into consideration thecrop height, wind speed, and minimum relative humidity averages for the period under consideration. The Kcb coefﬁcient was
further adjusted to account for the salinity and nitrogen stress,
affecting sweet sorghum growth in each experimental plot, using
the procedure for non-pristine agricultural vegetation (Allen et al.,1998):
Kcb mid = Kc min + (Kcb full − Kc min )(1 − e(−0.7 LAI) )(14)

where Kcb mid is the estimated basal Kcb during mid-season when
the leaf area index (LAI) (L2 L−2 ) is smaller than for full coverconditions, Kcb full is the estimated basal Kcb during mid-season(at the peak plant size or height) for vegetation having LAI > 3,
and Kc min is the minimum Kc for bare soil (0.15–0.20). For theseestimations, LAI was monitored in each experimental plot during different stages of the sorghum cycle, using a non-destructive
method to avoid removing plants from the experimental area.
Length (L) and width (W) of crop leafs were measured on random
plants grown in each experimental plot. These dimensions werethen related to previously calibrated LAI values with the following
equation:n

LAI = 0.7586(L × W )

(15)

i=1

where LAI are the values measured using a LI-COR area
meter (Model LI-3100C, LI-COR Environmental and Biotechnology
Research Systems, Lincoln, NE) and n is the number of green leafs
on each measured sorghum plant. Cubic splines were then ﬁtted
to LAI data to obtain a continuous function throughout the crop
seasons.
The evaporation coefﬁcient Ke was calculated as (Allen et al.,1998, 2005):
Ke = Kr (Kc max − Kcb ) ≤ few Kc max(16)

where Kr is a dimensionless evaporation reduction coefﬁcientdependent on the cumulative depth of water depleted (evaporated)from the topsoil, Kc max is the maximum value of Kc (i.e., Kcb + Ke )after rain or irrigation, and few is the fraction of the soil surface
from which most evaporation occurs. Table 5 presents the crop
coefﬁcients and other crop related parameters estimated in eachgrowing season.
During non-growing seasons, the procedure to estimate ETc wasgreatly simpliﬁed by using the single crop coefﬁcient approachand a Kc of 0.15 to account for a bare soil with a small percentage of weeds. Transpiration and evaporation were also separated
as a function of leaf area index (Ritchie, 1972) using a ﬁctitious LAI
value of 1.0.
In all experimental plots, it was assumed that the potential root
water uptake was reduced due to water stress as a result of the
adopted irrigation schedule, which could lead to insufﬁcient or94

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

Table 5
Crop and soil parameters used for estimating plant transpiration and soil evaporation in each sorghum growing season.
Parameter

2007

2008

2009

Planting date
Harvest date
Av. wind speed (m s−1 )Av. RH min (%)

May 18September 27
2.2
26

May 15September 27
2.4
32

May 15September 27
2.3
24

Length stages (d):
Lini
Ldev
Lmid
Llate
fw (irrigation)
REW (mm)
TEW (mm)
Ze (cm)

63
25
24
21
0.3
9
35.2
15

64
26
25
24
0.3
9
35.2
15

64
26
25
23
0.3
9
35.2
15

LAImax (m2 m−2 ):Highest value
Plot
Lowest value
Plot

5.1
I-C
3.3
IV-B

4.7
III-A
2.8
IV-A

5.4
II-B
2.6
IV-A

Kcb ini
Kcb mid
Kcb endKcb full
Kc max

0.15
1.23
1.07
0.15–1.23
1.16–1.35

0.15
1.21
1.06
0.15–1.21
1.14–1.38

0.15
1.24
1.09
0.15–1.24
1.01–1.29

RH, relative humidity; Lini , Ldev , Lmid , and Llate , length of crop initial, development, mid-season, and end season stages, respectively; fw , fraction of soil surface wetted byirrigation (0.3–0.4: an interval used in calibration; an optimal value is given in the table); REW, readily evaporable water; TEW, total evaporable water, Ze , depth of thesurface soil layer that is subject to drying by way of evaporation (10–15 cm); LAImax , maximum leaf area index measured in the experimental plots; Kcb ini , Kcb mid , and Kcb
end , basal crop coefﬁcient during crop initial, mid-season, and end season stages, respectively; Kc full , estimated basal Kcb during mid-season (at peak plant size or height) for
vegetation having LAI > 3; Kc max , maximum value of Kc following rain or irrigation.

excessive supply of water to the crop. It was also assumed thatthe potential root water uptake was further reduced by osmotic
stress, resulting from the use of blended saline water. The effectsof water and salinity stresses were considered to be multiplicative
as described by van Genuchten (1987) (i.e., ˛(h,h ) = ˛1 (h)˛2 (h )in Eq. (10)), so that different stress response functions could be
used for the water and salinity stresses. Root water uptake reductions due to water stress, ˛1 (h), were described using the piecewise
linear model proposed by Feddes et al. (1978). The water uptake
is at the potential rate when the pressure head is between h2
and h3 , drops off linearly when h > h2 or h < h3 , and becomes zero
when h < h4 or h > h1 . The following parameters of the Feddes et al.
(1978) model were used: h1 = −15, h2 = −30, h3 = −325 to −600,
h4 = −8000 cm.
Root water uptake reductions due to salinity stress, ˛2 (h ), were
described by adopting the Maas (1990) salinity threshold and slope
function. The salinity threshold (ECT ) for sweet sorghum corresponds to a value for the electrical conductivity of the saturation
extract (ECe ) of 6.8 dS m−1 , and a slope (s) of 16% per dS m−1 . As
required by HYDRUS-2D, these values were converted into ECsw
assuming that the ECsw /ECe ratio (kEC ) was 2, which is a common
approximation used for soil water contents near ﬁeld capacity inmedium-textured soils (U.S. Salinity Laboratory Staff, 1954; Skaggs
et al., 2006b).
2.3. Statistical analysis
Model validation was carried out by comparing ﬁeld measured
values with HYDRUS-2D simulations using various quantitative
measures of the uncertainty, such as, the mean error (ME), mean
absolute error (MAE) and the root mean square error (RMSE), givenby:1(Oi − Pi )
N
N

ME =

i=1

(17)

1
|Oi − Pi |
N
N

MAE =

(18)

i=1


RMSE =

N(Oi − Pi )2
i=1

N−1

(19)

where Oi and Pi are observation values and model predictionsin the units of a particular variable, and N is the number ofobservations.
The dual crop coefﬁcient approach used here to estimate atmospheric demands requires various crop and soil parameters thatneed to be adjusted to particular experimental conditions. Therefore, these parameters, i.e., lengths of various growth stages, thebasal crop coefﬁcients during initial (Kcb ini ), mid-season (Kcb mid )and end season (Kcb end ) growth stages, the total evaporable water(TEW), the readily evaporable water (REW), the thickness of evaporation soil layer (Ze ), and the fraction of soil surface wettedby irrigation (fw ) were ﬁrst calibrated by trial and error using
HYDRUS-2D and the experimental data from the ﬁrst crop season (2007), and then used to deﬁne the atmospheric demands
for the second (2008) and third crop seasons (2009). The optimized parameters were considered to be calibrated when the
RMSEs found for the soil water content, ECsw , and N species
were lower than those reported in Ramos et al. (2011), i.e.,
RMSE␪ < 0.04 cm3 cm−3 ; RMSEECsw < 2.04 dS m−1 ; RMSEN−NH4 + <0.07 mmolc L−1 ; and RMSEN−NO − < 2.60 mmolc L−1 . Ramos et al.
3(2011) used the one-dimensional version of HYDRUS (i.e., HYDRUS1D, Šimůnek et al., 2008) and the single crop coefﬁcient approach
to simulate the same solutes for similar experimental conditions,albeit with a different crop. Therefore, when RMSEs obtained
here with a more complex approach, i.e., using a dual crop
coefﬁcient procedure and a more appropriate geometrical description, were lower than those obtained previously with a simpler
methodology, optimized parameters were considered to be calibrated. All other necessary HYDRUS-2D input material parameters,

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

3.1. Soil water balance
The HYDRUS-2D simulations began on May 18, 2007 and werecarried out for the ﬁrst crop and subsequent rainfall seasons (i.e.,
for 362 days) in order to calibrate the crop and soil parameters thatwere needed for estimating atmospheric demands using the dual
crop coefﬁcient approach. Table 6 presents the statistical indicators
used to evaluate the level of agreement between water contents
measured using TDRs and those simulated using the calibrated
HYDRUS-2D model for three depths of plots I-A and I-C. The subsequent simulations with calibrated HYDRUS-2D began again on May
18, 2007 and were carried out continuously for the following 1078
days.
Fig. 5 shows the water contents measured at depths of 20, 40,
and 60 cm in plots I-A and I-C, and compares these values with
HYDRUS-2D simulations. Water contents increased to full saturation near the emitter after an irrigation or rain event, and thendecreased gradually during the following hours and days, until thenext irrigation or rain event took place. Deeper depths showedsmaller water content variations since root water uptake and soil
evaporation were more pronounced at shallower depths. Similar
results were also obtained for the remaining plots (not shown).
A ME of −0.007 cm3 cm−3 and a RMSE of 0.030 cm3 cm−3 were
found between measured and simulated water contents during theentire simulation period. Deviations between measured and simulated water contents can be attributed to different causes, including
errors related to ﬁeld measurements and to model input and model
structure errors. They will be discussed below in detail.
Table 7 presents the output components of the soil waterbalance (i.e., potential transpiration, actual transpiration, soil evaporation, and percolation) in all experimental plots located in
sub-groups A and C. The input components, i.e., irrigation and rainfall amounts, were already given in Section 2 and in Table 3. Since
HYDRUS-2D does not have a crop growth module, the potential root
water uptake (PRWU), i.e., potential transpiration (Tp ) obtained ineach experimental plot, was given as input for deﬁning the atmospheric boundary conditions. Tp varied between 360 (plot IV-A,
2008) and 457 mm (plots I-C and II-A, 2009). Plots located in groupIV, where no nitrogen was applied, generally had lower Tp values. In groups I–III, Tp averaged 394, 397, and 450 mm in 2007,2008, and 2009, respectively. In group IV, Tp was lower, averaging
382, 379, and 413 mm during the same time periods. Consideringthat nitrogen requirements of sweet sorghum are relatively low(Barbanti et al., 2006), the amount of nitrogen applied in plot III(N1 = 130–190 kg/ha y−1 of N) was apparently sufﬁcient to maximize Tp . Plots located in groups I and II may thus have experienced
some ‘luxury’ uptake, i.e., a continued uptake of nitrogen beyond
what was required for immediate growth.

Water content (cm3 cm-3)

20 cm

0.4
0.3
0.2
0.1
0.0
18-05-07 04-12-07 21-06-08 07-01-09 26-07-09 11-02-10 30-08-10

0.5
Water content (cm3 cm-3)

3. Results and discussion

0.5

40 cm

0.4
0.3
0.2
0.1
0.0
18-05-07 04-12-07 21-06-08 07-01-09 26-07-09 11-02-10 30-08-10

Water content (cm3 cm-3)

such as soil hydraulic and solute transport parameters, were
determined in the laboratory. Note that since our modelingapproach is process-based, rather than conceptual, our input
parameters can be obtained/measured independently. In general,
we ﬁnd that it is superior to measure input material parameters independently rather than ﬁtting them. The correspondence
between measurements and model predictions would have obviously been better, had the input parameters been ﬁtted using
numerical modeling. However, the model that can be successfully run with independently measured input material parameters
is more robust for practical applications than calibrated models. Moreover, with this approach we not only validate the usedmodeling approach but also applied laboratory methodologies andvarious involved experimental procedures.

95

0.5

60 cm

0.4
0.3
0.2
0.1 Season
1

Season2

Season3

0.0
18-05-07 04-12-07 21-06-08 07-01-09 26-07-09 11-02-10 30-08-10
Time
Measured data (Plot I-A)

HYDRUS-2D simulation (Plot I-A)

Measured data (Plot I-C)

HYDRUS-2D simulation (Plot I-C)

Fig. 5. Measured and simulated water contents at depths of 20 (top), 40 (middle),
and 60 cm (bottom) in plots I-A and I-C.

Tp values obtained in plots irrigated with saline waters (subgroup A) were generally lower that those obtained in plots irrigatedwith fresh waters (sub-group C). However, the differences were
found to be very small since sweet sorghum is moderately tohighly tolerant to salinity, depending on the variety (Maas, 1990;
Vasilakoglou et al., 2011). The largest Tp differences were found in
2009, in plots IV-A and IV-C (58 mm). Thus, in plot IV-A, the plantdevelopment was particularly affected by the continuous application of synthetic saline waters.
Apart from minor Tp variations found in the experimental plots,
which resulted mainly from the differences in the spline functions
ﬁtted to the LAI measurements taken in each plot and in each crop
season, Tp values estimated for sweet sorghum can be consideredlow. Ramos et al. (2011) estimated Tp for maize to vary between
600 and 800 mm. Water requirements estimated in this study forsweet sorghum are much lower than those for traditionally grown,
irrigated crops in Portugal. Sweet sorghum thus seems to be a reasonable alternative crop to be grown in water scarce European
Mediterranean regions.
Actual root water uptake, i.e., actual transpiration (Ta ), as simulated by HYDRUS-2D, varied between 264 (plot IV-A, 2009) and
334 mm (plot I-C, 2009). Tp reductions due to water stress werea function of the adopted irrigation schedule. Within the same
crop season, transpiration reductions were very similar since the96

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

Table 6
Results of the statistical analysis between measured and simulated soil water contents, electrical conductivities of the soil solution (ECsw ), and N NH4 + , and N NO3 −concentrations.
ECsw (dS m−1 )N NH4 + (mmolc L−1 )N NO3 − (mmolc L−1 )Data from 2007/2008 (calibration data):
N82
ME−0.007
MAE
0.024
RMSE
0.033

36
−0.216
0.602
0.854

93
0.029
0.029
0.042

75
−0.2180.617
1.253

Data from 2008/2010:
N
ME
MAE
RMSE

276
−0.007
0.023
0.028

211
−0.668
1.255
1.877

241
0.019
0.026
0.043

263
−1.6682.244
3.427

Data from 2007/2010 (all data):
358
N−0.007
ME
MAE
0.023
RMSE
0.030

247
−0.602
1.160
1.764

334
0.022
0.027
0.042

338
−1.346
1.883
3.078

Water content (cm3 cm−3 )StatisticN, number of observations; ME, mean error; MAE, mean absolute error; RMSE, root mean square error.

Dry biomass (kg/ha)

30000
25000
20000
15000
y = 198.83x - 41438.86

10000

2

R = 0.51

5000
250

270

290

310

330

350

Ta (mm)data from sub-group A

data from sub-group C

Fig. 6. Relationship between actual transpiration (Ta ), as simulated by HYDRUS-2D,
and dry biomass yield (Y).

irrigation schedule was the same in all experimental plots. In theplots located in sub-group C, irrigated only with fresh waters, Tp
was reduced due to water stress by 25.3–27.4%, 21.9–22.8%, and26.3–26.9% in 2007, 2008, and 2009, respectively. Water stress wasthus a function of the adopted irrigation schedule during each season and did not vary among experimental plots.
In plots located in sub-group A (irrigated with saline waters),
Tp was further reduced due to salinity stress. During 2007, Ta
estimated for the different plots included in sub-group A was generically the same as in sub-group C (irrigated with fresh waters),
i.e., sweet sorghum showed to be tolerant to the levels of salinity
reached in the soil solution of all experimental plots irrigated withfresh or synthetic saline waters. However, in 2008 and 2009, Tp suffered reductions (in sub-group A) of 24.2–26.9%, and 31.3–33.3%,
respectively, due to the combined effects of water and salinity
stresses, i.e., 2.3–4.7% (in 2008) and 4.6–7.0% (in 2009) higher
than Tp reductions found in the plots irrigated only with fresh
waters (sub-group C). In the following years, the salinity stressthus became increasingly higher (in sub-group A). Hence, soil salinization and the increase of the salinity stress was related to thecontinuous and increasing amount of synthetic saline waters being
applied in each experimental plot.
Fig. 6 relates actual transpiration Ta calculated using HYDRUS2D with the experimentally determined sorghum yield (Y), given
in terms of dry biomass, by means of the empirical relationship,
Y = f (Ta ). This relationship, generally thought to be approximately
linear, is valid for a particular plant (canopy) at a particular site
subject to standard tillage and nutrition conditions (Novák and van

Genuchten, 2008). The relation found in our study was somewhat
poor, with the agreement between Ta and dry biomass reaching R2of only 0.51. Since HYDRUS-2D does not account for a crop growthmodule, this result was not particularly surprising. Nevertheless,had water been the only limiting factor in our experiment, the relation would likely have been better. However, this could not be easily
observed in our study since the amount of water applied per year
was the same, while the total water depths applied during each crop
season were apparently not different enough to establish a closer
relation. The relation in Fig. 6 essentially resulted from the effects
that water quality had on Ta and crop yield. While plots irrigatedwith fresh water (sub-group C) had higher sorghum yields and Ta
values, plots irrigated with saline waters (sub-group A) had lower
sorghum yields and Ta values (Fig. 6). Nitrogen also did not inﬂuence the Y(Ta ) relation since N stress at a given period can mainly
affect sorghum yield, while LAI, and consequently Ta , remain high.
Finally, the soil water balance (Table 7) in each experimental plot shows relatively high percolation. Percolation reached162–174, 292–299, and 292–309 mm in 2007, 2008, and 2009,
respectively. These values correspond to 31–34%, 50–51%, and
51–54% of the water applied during crop seasons, i.e., from sowing to harvest. While percolation was expected to be large, sinceapplication rates during irrigation seasons were high, the values
estimated for crop seasons of 2008 and 2009 may be somewhat
deceiving. They result from running HYDRUS-2D continuously forthe entire simulation period. Since cumulative percolation obtained
during the entire simulation period (2007–2010) only reached
36–37% of the applied water, and considering that root water
uptake was much higher during crop seasons, percolation in 2008
and 2009 also accounted for the water stored below the root zone.
Therefore, we ended up not being able to actually quantify percolation due to the adopted irrigation schedule, since the waterbalance evaluated for each crop season also accounted for thewater that was no longer accessible to plants. Nevertheless, theeffects of nitrogen applications and water quality on drainage were
small. Plots with higher root water uptake showed generally lower
percolation.

3.2. Salinity build-up and distribution
Fig. 7 shows ECsw measured at the 20, 40, and 60 cm depth inplots I-A and I-C, and compares these values with HYDRUS-2D simulations. Similar results were also found for the remaining plots of
sub-groups A and C. Within the same sub-group (Fig. 1), ECsw varied due to the effect of nitrogen fertigation on root water uptake.

ECsw (dS m-1)

1119
1105
–
–

302
309
206
181

296
299
207
192

168
174
174
177

25

97

20 cm

20
15
10

930
1036

0
18-05-07 04-12-07 21-06-08 07-01-09 26-07-09 11-02-10 30-08-10

ECsw (dS m-1)

1270
1363

25

1111
1102

264
324
384
442
299
309

273
311
360
398
294
298

168
173

384
380

290
284

5

40 cm

20
15
10

–
–

183
176

190
192

5
168
169

Tp (mm)E (mm)P (mm)

Group IVTa (mm)E (mm)P (mm)

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

ECsw (dS m-1)

983
1051
1373
1390

25

60 cm

20

Season1

Season2

Season
3

15
10
5

1107
1097

291
328
434
449
294
302

296
312
402
404
295
299

296
295
394
395
167
172

Tp (mm)P (mm)

Group IIITa (mm)018-05-07 04-12-07 21-06-08 07-01-09 26-07-09 11-02-10 30-08-10

Time

–
–

Measureddata (PlotI-A)

HYDRUS-2D simulation(PlotI-A)

Measureddata (PlotI-C)

HYDRUS-2D simulation(PlotI-C)

Fig. 7. Measured and simulated electrical conductivities of the soil solution at 20(top), 40 (middle), and 60 cm (bottom) depth in plots I-A (irrigated with the highest
application of synthetic saline waters) and I-C (irrigated with fresh waters only).
Tp , potential transpiration; Ta , actual transpiration; E, evaporation; P, percolation.

981
1045
–
–
Cumulative ﬂuxes (2007–2010)
A
1382
982
C
1401
1065

1101
1083

1374
1377

170
177
305
331
172
174
307
334
Season 3 (2009)
A
456
457
C

292
298

457
449

200
197
283
301
191
192
291
316
Season 2 (2008)
A
398
C
406

292
293

383
390

170
164
294
297
391
396
173
163
280
298

E (mm)Ta (mm)162
170

Ta (mm)Tp (mm)Tp (mm)Season 1 (2007)
386
A
C
399

P (mm)

Group IIGroup I
Sub-plot

Table 7
Output components of the soil water balance in each experimental plot.

E (mm)

0
18-05-07 04-12-07 21-06-08 07-01-09 26-07-09 11-02-10 30-08-10

Between sub-groups (but within the same group), ECsw varied dueto the effect of water quality on root water uptake.
The statistical indicators (Table 6) obtained while comparing
measured and simulated ECsw for three depths of all plots in subgroups A and C resulted in a ME of −0.602 dS m−1 and a RMSE of
1.764 dS m−1 .
Figs. 8 and 9 show the simulated distributions of ECsw in plots
I-A and I-C, respectively, at the beginning and at the end of eachcrop season. Based on model simulations, the continuous use ofsynthetic saline irrigation waters led to soil salinization in plot I-A
over the years (Fig. 8). At harvest, simulations showed that ECsw
increased considerably to values above 24 dS m−1 in the region
around the drip emitter. At the beginning of each crop season thatessentially correspond to the end of the rainfall leaching periods,
simulated ECsw values were also increasingly higher throughout
the years, especially at deeper depths.
Considering that the Maas (1990) salinity threshold parameter for sweet sorghum corresponds to ECsw of 13.2 dS m−1(ECe = 6.8 dS m−1 ; kEC = 2), the part of the soil domain with ECsw
above this threshold was already considerable during harvest in
2007. However, ECsw only increased above the threshold ECsw near
the end of the crop season when irrigation ceased and the soil dried

98

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

Fig. 8. Simulated distributions of the electrical conductivity of the soil solution inplot I-A (irrigated with synthetic saline waters) during sowing (top) and harvest(bottom) of each crop season. The drip emitter was located in the top left corner of
each contour plot.

out (Fig. 7). Therefore, transpiration was not signiﬁcantly reduced
due to the salinity stress during that year (Table 7). In 2008 and2009, the threshold value was reached earlier, with the region
around the drip emitter with ECsw values above 13.2 dS m−1 being
much larger than in 2007. Hence, transpiration was increasingly
reduced due to the salinity stress as a result of the accumulation ofsalts in the soil domain.
On the other hand, irrigation with fresh waters, having a relatively low salinity (ECiw > 0.8; Table 4), also led to larger ECsw at theend of each crop season, but the levels reached were always lower
than 9 dS m−1 and decreased signiﬁcantly due to rainfall leaching (Fig. 9). Therefore, in sub-group C, root water uptake was notaffected by the salinity stress.
3.3. Nitrogen balance
Fig. 10 shows N NH4 + and N NO3 − concentrations measured
at a depth of 20, 40, and 60 cm in plots I-C and IV-C, and compares these values with HYDRUS-2D simulations. Figs. 11 and 12
show the simulated distributions of N NH4 + and N NO3 − concentrations in plot I-A during the second crop season. In groups
I through IV, N NH4 + and N NO3 − concentrations varied according to the amounts of nitrogen applied in each experimental plot. In
sub-group A-C (but within the same group), N NH4 + and N NO3 −concentrations varied due to the effects of water quality on root
water uptake.

Fig. 9. Simulated distributions of the electrical conductivity of the soil solution inplot I-C (irrigated with fresh waters only) during sowing (top) and harvest (bottom)
of each crop season. The drip emitter was located in the top left corner of eachcontour plot.

The statistical indicators (Table 6) obtained while comparing measured and simulated N NH4 + concentrations for threedepths, and for all experimental plots located in sub-groups
A and C, showed a ME of 0.022 mmolc L−1 and a RMSE of
0.042 mmolc L−1 . Corresponding statistical indicators for N NO3 −concentrations resulted in a ME of −1.346 mmolc L−1 and a RMSE
of 3.078 mmolc L−1 .
Table 8 shows the nitrogen balances evaluated for each experimental plot during the three crop seasons included in thesimulation period. While most components of the nitrogen balance
were restricted to the duration of a crop season, leaching was calculated to also include the solute mass lost during the subsequent
rainfall period. Nitrogen leaching was directly related to water ﬂow
through the bottom boundary of the soil domain. Therefore, since
the percolation component of the water balance was high, so was
the nitrogen leaching component here. The movement of N out of
the root zone also depended on the amount of applied N, the formof N in the fertilizer, and the time and number of fertigation events.
Based on model simulations, most of the applied N NH4 + was
rapidly nitriﬁed into N NO3 − , not reaching depths deeper than
20 cm and not being signiﬁcantly taken up by plant roots. On the one
hand, N NH4 + adsorbs to the solid phase and thus its movement issigniﬁcantly retarded compared to N NO3 − , and on the other hand,due to rapid nitriﬁcation, it does not stay long enough in the rootzone to be taken up by plant roots. Fig. 11 exempliﬁes how, basedon model simulations, N NH4 + concentrations never increased at
depths below 20 cm during the crop season of 2008. Also, at theT.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

20 cm

0.5

N-NH4+ (mmolc L-1)

N-NO3- (mmolc L-1)

40

99

30
20
10

0.4
0.3
0.2
0.1

0
0.0
18-05-07 04-12-07 21-06-08 07-01-09 26-07-09 11-02-10 30-08-10 18-05-07 04-12-07 21-06-08 07-01-09 26-07-09 11-02-10 30-08-10

0.5

40 cm

N-NH4+ (mmolc L-1)

N-NO3- (mmolc L-1)

40
30
20
10

0.4
0.3
0.2
0.1

0
0.0
18-05-07 04-12-07 21-06-08 07-01-09 26-07-09 11-02-10 30-08-10 18-05-07 04-12-07 21-06-08 07-01-09 26-07-09 11-02-10 30-08-10

0.5

60 cm
30
20 Season
1

Season2

Season3

10

N-NH4+ (mmolc L-1)

N-NO3- (mmolc L-1)

40

0.4
0.3
0.2

Season1

Season2

Season
3

0.1

0
0.0
18-05-07 04-12-07 21-06-08 07-01-09 26-07-09 11-02-10 30-08-10 18-05-07 04-12-07 21-06-08 07-01-09 26-07-09 11-02-10 30-08-10

Time
Measureddata (PlotI-C)

HYDRUS-2D simulation (PlotI-C)

Measureddata (PlotIV-C)HYDRUS-2D simulation (PlotIV-C)

Fig. 10. Measured and simulated N NO3 − (left) and N NH4 + (right) concentrations at 20 (top), 40 (middle), and 60 cm (bottom) depth in plots I-C (the highest applicationof N) and I-C (no fertigation events).

end of the irrigation season (September 6, 2008), N NH4 + concentrations in the soil proﬁle were already very low. Leachingof nitrogen occurred mainly in the N NO3 − form. Fig. 12 shows
relatively high N NO3 − concentrations below the root zone(>65 cm) during the entire crop season of 2008. N NO3 − leaching reached 41–70% of the total amount of N NO3 − available inthe soil system, whether it came from direct application or fromN NH4 + nitriﬁcation. The higher the number of fertigation events,
the lower the amount of N applied per event, and thus the lower theamount of leached N NO3 − . In 2007, when nitrogen was applied inonly four fertigation events, N NO3 − leaching varied between 51%
and 53% of the total amount of N NO3 − available in the soil system. In 2008, when nitrogen was applied in six fertigation events,
only 41% of the total amount of available N NO3 − leached. Finally,in 2009, when only three fertigation events took place, 68–70% of
the total amount of available N NO3 − was leached. Since N NH4 +was rapidly nitriﬁed and N NO3 − easily leached, model simulations produced relatively low concentrations of both solutes in thesoil proﬁle at harvest and at the beginning of the following year’s
crop season. Simulations were thus in agreement with N NH4 +and N NO3 − concentrations measured in the saturation extractof samples collected at 20, 40, and 60 cm depth of every experimental plot. Experimental N NH4 + concentrations were always

lower than 0.17 mmolc L−1 , while N NO3 − concentrations reacheda maximum value of 10.28 mmolc L−1 in deeper soil layers.
Nutrient uptake by plant roots occurred mainly in the N NO3 −form as well. The number of fertigation events also signiﬁcantly
inﬂuenced the amount of N NO3 − taken up by plant roots. Nutrient uptake varied between 23% and 42% of the total amount of
N NO3 − available in the soil system. In 2007, N NO3 − uptake
reached 37% of the applied N NO3 − . In 2008, with two additional fertigation events, nutrient uptake increased to 39–42% of
the applied N NO3 − . Finally, in 2009, with only three fertigation
events, N NO3 − uptake decreased to values between 23% and 25%of the total amount of available N NO3 − . The higher number of fertigation events also led to higher yields. The average dry biomassyield measured in all plots with the N supply (groups I-III) was 19.3,
20.4, and 18.3 ton/ha in 2007, 2008, and 2009, respectively. However, in this last analysis we have to also take into consideration
the increase in the salinity stress from one crop season to the next
in plots irrigated with saline waters, which negatively inﬂuenced
the crop yield.
The effects of the salinity stress on nutrient uptake (andinversely on nutrient leaching) was relatively small since sweetsorghum has a medium to high tolerance to salinity, and consequently there were only small reductions in transpiration due to the100

Table 8
Nitrogen balance in each experimental plot during the three crop growth seasons.
Plot

N NH4 +
soilInitial(kg/ha)N NH4 +
applied(kg/ha)aMass balance error =N NH4 +
adsorbed(kg/ha)N NH4 +
sorghum
uptake(kg/ha)N NH4 +
weeds
uptake(kg/ha)N NH4 +
decay
(kg/ha)N NH4 +
soilend(kg/ha)N NO3 −
soilInitial(kg/ha)N NO3 −
applied(kg/ha)N NO3 −
leached(kg/ha)N NO3 −
sorghum
uptake(kg/ha)N NO3 −
weeds
uptake(kg/ha)

0
0

1
1

3
3

0
0

259
259

0
0

10
10

266
266

271
272

198
200

6
6

104
101

4.03
3.77

0
0

1
1

5
5

0
0

280
280

0
0

38
37

295
295

249
248

245
250

13
17

152
144

4.05
2.74

0
0

1
0

2
2

0
0

205
206

0
0

81
81

217
217

350
350

118
123

3
6

76
69

4.20
2.84

0
0

4
2

10
10

0
0

744
746

0
0

10
10

777
777

870
870

583
600

11
11

4.36
3.37

0
0

1
1

2
2

0
0

175
175

0
0

10
10

180
181

185
186

135
135

4
4

71
69

4.10
3.73

0
0

1
1

3
3

0
0

187
188

0
0

26
26

200
200

171
169

161
166

9
12

106
100

3.86
2.61

0
0

1
1

1
1

0
0

136
137

0
0

56
56

148
148

231
231

80
82

2
4

51
47

6.01
4.71

0
0

3
2

7
7

0
0

499
500

0
0

10
10

528
529

586
586

392
403

7
7

4.99
3.99

0
0

0
0

1
1

0
0

90
90

0
0

10
10

94
94

100
102

73
72

2
2

38
38

2.44
1.84

0
0

0
0

2
2

0
0

95
95

0
0

14
14

106
106

87
88

88
90

5
6

54
52

2.34
1.07

0
0

0
0

1
1

0
0

70
70

0
0

29
29

80
80

125
124

42
45

1
2

29
26

3.59
2.18

0
0

1
1

3
3

0
0

255
255

0
0

10
10

279
279

312
314

211
217

4
4

2.87
1.62

0
0

0
0

0
0

0
0

6
6

0
0

10
10

9
9

16
16

7
7

0
0

5
5

1.94
1.70

0
0

0
0

0
0

0
0

2
2

0
0

2
2

11
11

8
7

4
5

0
0

4
3

3.19
2.00

0
0

0
0

0
0

0
0

2
2

0
0

2
2

12
12

10
9

4
5

0
0

4
3

3.27
1.52

0
0

0
0

0
0

11
11

0
0

10
10

32
32

33
32

1
1

3.33
2.24

0
0

Ninput −Noutput

Ninput ×100


.

16
18

N NO3 −
soilend(kg/ha)Massbalanceerrora(kg/ha)T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

Group I
Season 1 (2007)
A
5
259
C
5
259
Season 2 (2008)
A
0
286
C
0
286
Season 3 (2009)
A
0
208
0
208
C
Cumulative masses (2007–2010)
A
5
753
C
5
753
Group II
Season 1 (2007)
A
5
174
C
5
174
Season 2 (2008)
A
0
192
C
0
192
Season 3 (2009)
A
0
139
C
0
139
Cumulative masses (2007–2010)
A
5
504
5
504
C
Group III
Season 1 (2007)
A
5
87
C
5
87
Season 2 (2008)
A
0
97
C
0
97
Season 3 (2009)
A
0
71
0
71
C
Cumulative masses (2007–2010)
A
5
254
C
5
254
Group IV
Season 1 (2007)
A
5
2
2
C
5
Season 2 (2008)
A
0
2
0
2
C
Season 3 (2009)
2
A
0
0
2
C
Cumulative masses (2007–2010)
A
5
6
C
5
6

N NH4 +
leached(kg/ha)T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

101

Fig. 11. Simulated distributions of N NH4 + concentration in plot I-A during crop season 2, after sowing (May 15, 2008), after the ﬁrst fertigation event (July 17, 2008), after
the forth fertigation event (August 2, 2008), after the sixth and last fertigation event (August 14, 2008), at the end of the irrigation period (September 9, 2008), and at harvest(September 30, 2008). The drip emitter was located in the top left corner of each contour plot.

increase of the osmotic stress. Although nutrient uptake was somewhat lower in the plots irrigated with saline waters, only in groupI, which had the highest applications of nitrogen, were the differences in N uptake between plots larger. However, even here, thedifference in the cumulative N uptake between plots I-A and I-C wasonly 17.9 kg/ha. This was not signiﬁcant enough to conclude that
one could save on nitrogen applications by considering the quality of the irrigation water when deﬁning an optimum fertigation
schedule.
Fig. 13 shows the relationship between the N NO3 − plant
uptake calculated using HYDRUS-2D and the experimentally determined dry biomass yield expressed using a logarithmic function
with a R2 of 0.71. This logarithmic function ﬁtted to experimental

data shows that an additional incremental increase of N NO3 −uptake produces diminishing returns in the total dry biomass
response. Each additional unit of N NO3 − taken up by plant roots
added less to the total biomass output than the previous unit did.
After a certain level of N NO3 − uptake was reached (estimated here
to be between those registered for groups II-III, i.e., 130–180 kg/ha),further increases in nutrient uptake did not contribute directly tothe increase of the dry biomass yield. Group I thus involved some
‘luxury’ uptake, since the amount of N NO3 − taken up by plantroots did not contribute signiﬁcantly to the dry biomass yield. Moredetailed results of the effect of brackish waters on nitrogen needs
and dry biomass yield of sweet sorghum can be found in Ramos
et al. (2012).

Fig. 12. Simulated distributions of N NO3 − concentration in plot I-A during crop season 2, after sowing (May 15, 2008), after the ﬁrst fertigation event (July 17, 2008), after
the forth fertigation event (August 2, 2008), after the sixth and last fertigation event (August 14, 2008), at the end of the irrigation period (September 9, 2008), and at harvest(September 30, 2008). The drip emitter was located in the top left corner of each contour plot.

102

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

Dry biomass (kg/ha)

30000
25000
20000
15000

y = 2818.59Ln(x) + 6223.58

10000

2

R = 0.71
5000
0

50

100

150

200

250

300

N-NO 3- uptake (kg/ha)
data from sub-group A

data from sub-group C

Fig. 13. Relationship between N NO3 − uptake, as simulated by HYDRUS-2D, anddry biomass yield (Y).

3.4. About model validation
Deviations between measured data and simulated variables(Table 6) can be attributed to different causes, including errors
related to ﬁeld measurements, and to model input and model structure errors.
Field measurements: The most relevant source of errors related
to ﬁeld measurements refers to the representativeness of TDR measurements and ceramic cup samplings at different depths. TDR
probes measure spatially averaged water contents over a certain
soil volume, the size of which depends on the size and orientation of TDR probes (Ferré et al., 2002). However, the distributionof water under drip irrigation is highly spatially non-uniform(Gärdenäs et al., 2005; Hanson et al., 2006). Water contents werehighest near the drip emitter after an irrigation event and thenredistributed throughout the soil proﬁle. Therefore, TDR probes
averaged water contents over soil regions with different moisturestatus, while HYDRUS-2D reports water contents for a precise soil
location (Fig. 4). Note that due to the dimensionality (axisymmetrical) of our calculations, by averaging water content over a certain
area around the observation node, we would obtain an averagevalue for a circular pipe, rather than for a straight cylinder overwhich TDR averages its measurements. Likewise, measurements
taken with suction cups were averaged over a sampling area of acertain volume, the size of which depends on soil hydraulic properties, the soil water content, and the applied suction in the ceramiccup (Weihermüller et al., 2005, 2011). Measured values thus did
not represent point values as the simulations did. Spatial soil variability can also affect concentrations measured by suction cups, anissue extensively studied by Weihermüller et al. (2011).
Model input errors: The accuracy of the soil hydraulic properties, which were measured on undisturbed soil samples taken
not in each experimental plot, but from a representative soil
proﬁle, and their representativeness in describing water inﬁltration and redistribution in different experimental plots seem to beimportant sources of error to consider. Soil hydraulic properties
were determined in the laboratory on soil samples of a certain
size (from 100 to 630 cm3 ) and may not be representative of themuch larger simulated ﬂow domain under ﬁeld conditions. For
example, soil samples are normally saturated in the laboratory
by capillarity, with water entering the sample through the bottom, decreasing the possibility of the air being trapped inside. For
this reason, saturation values are usually much higher in the laboratory than under ﬁeld conditions (Šimůnek et al., 1998), where
this obviously cannot be accomplished. This may explain someof the deviations found in simulated water contents at a depthof 20 cm (Fig. 5) where HYDRUS-2D tended to simulate higher
values during irrigation seasons than what ﬁeld data showed.

Additionally, the soil was considered homogeneous in HYDRUS2D simulations, and more complex physical phenomena, suchas spatial and temporal variability of the soil hydraulic properties and the probable existence of preferential ﬂow paths in the
different experimental plots, were neglected. Considering these
additional phenomena in HYDRUS simulations would likely havehelped improve the agreement between measured and simulated
data.
It is also important for water ﬂow simulations to accurately
estimate plant transpiration and soil evaporation. The dual crop
coefﬁcient approach used is generally considered accurate (Tolkand Howell, 2001; Howell et al., 2004; Liu and Luo, 2010), but iscomplex and requires various crop and soil parameters that need
to be adjusted to experimental conditions. Finally, the crop parameters, such as those used in the Feddes et al. (1978) model, weretaken from the literature and do not take differences among cropvarieties into account. The Maas (1990) threshold and slope parameters, which were mainly intended to serve as a guideline to relative
tolerances among crops, may vary with cultivars, climate, soil conditions, and cultural practices. Thus, estimates of uptake reductions
must be regarded with some uncertainty (Skaggs et al., 2006b). The
same can be said about the empirical relationship between ECe andECsw .
Model structure (or modeling approach) errors: Limitations
involved in considering an axisymmetrical domain to represent
the three-dimensional movement of water and nutrients have to
be considered. This approach has been widely used for analyzing
surface and buried drip irrigation experiments (Cote et al., 2003;
Skaggs et al., 2004; Gärdenäs et al., 2005; Lazarovitch et al., 2005;
Hanson et al., 2006; Ajdary et al., 2007; Kandelous and Šimůnek,
2010a,b; Ravikumar et al., 2011). Nevertheless, Kandelous et al.
(2011) pointed out some of the limitations of this approach to
be considered. Namely, the fact that ﬂow from each emitter only
remains axisymmetrical until the wetting patterns from neighboring emitters begin overlapping each other. Kandelous et al.
(2011) state that the axisymmetrical representation is only anapproximation of the fully three-dimensional problem and that thenumerical results should increasingly depart from reality as timeand irrigation volumes increase. Using a fully three-dimensionalmodel, which is also available in HYDRUS (2D/3D), could improvewater content simulations. In Ramos et al. (2011), a 1D versionof HYDRUS, used for simulating a similar experiment, produced a
RMSE (0.04 cm3 cm−3 ) larger than the 2D approach (0.03 cm3 cm−3 )adapted in this study. Thus, adopting the 2D version of HYDRUS
proved to be beneﬁcial in lowering the simulation errors. However,numerical modeling is not that straightforward, and the notionthat using a fully three-dimensional model would immediately
bring better correspondence between measured and simulated
data is unrealistic. The agreement between measured and simulated N NO3 − obtained here can serve as an example, sincethese results were worse than those obtained by Ramos et al.
(2011). Considering a cylindrically shaped (0.375 m wide) simulation domain (Fig. 3) could be another possible model structure
error, since the drip emitters’ grid was in fact rectangular (0.75 m
wide × 1 m long). This means that, in reality, water and solutes
could redistribute in a larger soil domain than that considered insimulations.
Modeling of the N species: There are some additional considerations that need to be taken into account with regards to modelingthe nitrogen fate and transport. The approach to model the transport of the nitrogen species using the sequential ﬁrst-order decay
chain reactions is relatively simple and has produced satisfactory
results in many different studies (Ajdary et al., 2007; Mailhol et al.,2007; Crevoisier et al., 2008). However, this approach can only consider nitrogen processes that are involved in a sequential-ﬁrst orderdecay chain, such as nitriﬁcation (N NH4 + transformation into

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

N NO2 − , and then further into N NO3 − ), denitriﬁcation (N NO3 −transformation into N2 and N N2 O), and volatilization (N NH4 +transformation into N NH3 ). Other nitrogen reactions, with probable relevance for long-term applications such as ours, simply
cannot be accounted for using this approach. Examples of such reactions are nitrogen ﬁxation from the atmosphere, mineralization ofcrop residues and other organic wastes, mineralization of the soil
humus fraction, and so on. The relevance of these processes on N
dynamics can be documented in Fig. 10, which shows that N NH4 +and N NO3 − concentrations in the soil increased after fertigation
events during crop seasons, and then decreased due to plant uptake
and leaching. During fertigation events, simulations matched themeasured data well since nitriﬁcation was the main process occurring in the soil. However, the deviation between measured andsimulated N data was visually more pronounced during non-crop
seasons, due to the limitations discussed above. For example, sweetsorghum was harvested at the end of the growing season so thatits biomass production could be estimated. This involved cutting
the entire plant above the ground while leaving roots in the soil.
Residual N NH4 + and N NO3 − concentrations measured during
non-crop seasons could, to some extent, be attributed to the mineralization of the root system, and thus were not considered in model
simulations.
Additionally, only the passive nutrient uptake mechanism wasconsidered in our approach. Since root nitrogen uptake likely
involves both passive and active mechanisms (e.g., Šimůnek andHopmans, 2009), considering only passive uptake likely underestimated the total N uptake and overestimated downward N leaching,providing thus the most conservative assessment of N leaching.
However, the extent of this underestimation is currently unknown.
Finally, deviations between measured and simulated N data could
also be attributed to other model limitations and relevant physicalphenomena that were not considered in our modeling approach,such as root growth.
4. Conclusions
The irrigation scheme used in this study allowed investigation of the response of sweet sorghum to irrigation scenarioswith different levels of nitrogen and different water qualities
between 2007 and 2010. The water contents, ECsw , N NH4 + andN NO3 − concentrations simulated continuously during the entire
ﬁeld experiment, compared well with collected experimental data,
having a RMSE of 0.030 cm3 cm−3 , 1.764 dS m−1 , 0.042 mmolc L−1 ,and 3.078 mmolc L−1 , respectively. Possible causes of deviations
between measured data and simulations were likely related to ﬁeld
measurements, model input data, and model structure errors, andwere extensively discussed, showing HYDRUS-2D advantages andlimitations for this application. However, model simulations helped
to understand the best irrigation and fertigation management practices to be adopted in order to increase nutrient uptake and reduce
nutrient leaching.
Sweet sorghum transpiration was estimated to vary between
360 and 457 mm depending on the crop season and the irrigation scenario considered. The lower water needs of sweet sorghum,
compared to other traditional crops grown in water-scarce European Mediterranean regions, make it a good alternative to othercrops for these environmentally stressed regions.
Sweet sorghum appears to be tolerant to the use of saline waters.
Only during the second crop season, but mainly during the 3rd year,
started the sweet sorghum transpiration be reduced due to theincrease in the salinity stress and salt accumulation over time. Thus,in water-scarce regions where even saline waters can be viewed as
an important source of irrigation water during drought seasons,the use of marginal waters showed viability for irrigating sweetsorghum during a limited time period.

103

HYDRUS-2D successfully estimated the fate of nitrogen inﬁeld plots grown with sweet sorghum under European Mediterranean conditions. The logarithmic function describing the relation
between estimates of N NO3 − uptake and the dry biomass yield(R2 = 0.71) showed that sweet sorghum N requirements were lower
than estimated N uptakes for the scenario with the highest levels of
applied nitrogen, revealing some luxury uptake in these plots. The
leaching of N out of the root zone depended closely on drainage, theamount of N applied, the form of N in the fertilizer, and the time andnumber of fertigation events. Based on model simulations, leachingof nitrogen occurred mainly in the N NO3 − form, reaching 41–70%of the total amount of N NO3 − available in the soil system. According to HYDRUS-2D, higher N NO3 − uptakes were obtained when
the number of fertigation events was larger.
Acknowledgments
This work was funded by the Project PTDC/AGRAAM/66004/2006 of the Fundação para a Ciência e a
Tecnologia (FCT). T. B. Ramos was funded by the FCT grant
SFRH/BD/60363/2009.
References
Ajdary, K., Singh, D.K., Singh, A.K., Khanna, M., 2007. Modelling of nitrogen leachingfrom experimental onion ﬁeld under drip irrigation. Agricultural Water Management 89, 15–28.
Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration – guidelines for computing crop water requirements. Irrig. Drain. Pap. 56. FAO, Rome,
Italy.
Allen, R.G., Pereira, L.S., Smith, M., Raes, D., Wright, J.L., 2005. FAO-56 dual crop coefﬁcient method for estimating evaporation from soil and application extensions.
Journal of Irrigation and Drainage Engineering 131, 2–13.
Almodares, A., Hadi, M.R., 2009. Production of bioethanol from sweet sorghum: areview. African Journal of Agricultural Research 4, 772–780.
Barbanti, L., Grandi, S., Vecchi, A., Venturi, G., 2006. Sweet and ﬁbre sorghum(Sorghum bicolor (L.) Moench), energy crops in the frame of environmental
protection from excessive nitrogen loads. European Journal of Agronomy 25,
30–39.
Bear, J., 1972. Dynamics of Fluids in Porous Media. Elsevier, New York.
Cameira, M.R., Fernando, R.M., Pereira, L.S., 2003. Monitoring water and NO3 N
in irrigated maize ﬁelds in the Sorraia Watershed, Portugal. Agricultural Water
Management 60, 199–216.
Cameira, M.R., Fernando, R.M., Ahuja, L.R., Pereira, L.S., 2005. Simulating the fate ofwater in ﬁeld soil–crop environment. Journal of Hydrology 315, 1–24.
Cameira, M.R., Fernando, R.M., Ahuja, L.R., Ma, L., 2007. Using RZWQM to simulate
the fate of nitrogen in ﬁeld soil–crop environment in the Mediterranean region.
Agricultural Water Management 90, 121–136.
Cote, C.M., Bristow, K.L., Charlesworth, P.B., Cook, F.J., Thorburn, P.J., 2003. Analysis
of soil wetting and solute transport in subsurface trickle irrigation. Irrigation
Science 22, 143–156.
Crevoisier, D., Popova, Z., Mailhol, J.C., Ruelle, P., 2008. Assessment and simulation of water and nitrogen transfer under furrow irrigation. Agricultural Water
Management 95, 354–366.
Doltra, J., Muñoz, P., 2010. Simulation of nitrogen leaching from a fertigated crop
rotation in a Mediterranean climate using the EU-Rotate N and Hydrus-2D models. Agricultural Water Management 97, 277–285.
European Commission, 2010a. On implementation of Council Directive 91/676/EEC
concerning the protection of waters against pollution caused by nitrates fromagricultural sources based on Member State reports for the period 2004–2007.
Report from the Commission to the Council and the European Parliament 47,
Brussels.
European Commission, 2010b. On implementation of Council Directive 91/676/EEC
concerning the protection of waters against pollution caused by nitrates fromagricultural sources based on Member State reports for the period 2004–2007.
Accompanying document to the report from the Commission to the Council andthe European Parliament. Commission Staff Working Document 118, Brussels.
FAO, 2006. World reference base for soil resources. A framework for internationalclassiﬁcation, correlation and communication. World soil resources reports 103.
Food and Agriculture Organization of the United Nations, Rome.
Feddes, R.A., Kowalik, P.J., Zaradny, H., 1978. Simulation of ﬁeld water use and crop
yield. Simulation Monographs Pudoc. Wageningen, The Netherlands.
Fernando, R.M., 1993. Quantiﬁcação do balanço hídrico de um solo regado na
presença de uma toalha freática. Simulação com o modelo SWATRER. PhD thesis.
Institute of Agronomy, Technical University of Lisbon, Lisbon, Portugal.
Ferré, T.P.A., Nissen, H.H., Šimůnek, J., 2002. The effect of the spatial sensitivity of
TDR on inferring soil hydraulic properties from water content measurements
made during the advance of a wetting front. Vadose Zone Journal 1, 281–288.

104

T.B. Ramos et al. / Agricultural Water Management 111 (2012) 87–104

Fontes, J.C., Pereira, L.S., Smith, R.E., 1992. Runoff and erosion in volcanic soils of
Azores: simulation with OPUS. Catena 56, 199–212.
Gärdenäs, A., Hopmans, J.W., Hanson, B.R., Šimůnek, J., 2005. Two-dimensional modeling of nitrate leaching for various fertigation scenarios under micro-irrigation.
Agricultural Water Management 74, 219–242.
Gonçalves, M.C., Leij, F.J., Schaap, M.G., 2001. Pedotransfer functions for solutetransport parameters of Portuguese soils. European Journal of Soil Science 52,
563–574.
Gonçalves, M.C., Šimůnek, J., Ramos, T.B., Martins, J.C., Neves, M.J., Pires,
F.P., 2006. Multicomponent solute transport in soil lysimeters withwaters of different quality. Water Resources Research 42, W08401,
http://dx.doi.org/10.1029/2005WR004802.
Hanson, B.R., Šimůnek, J., Hopmans, J.W., 2006. Evaluation of urea-ammoniumnitrate fertigation with drip irrigation using numerical modeling. Agricultural
Water Management 86, 102–113.
Hanson, B.R., Šimůnek, J., Hopmans, J.W., 2008. Leaching with subsurface drip irrigation under saline, shallow ground water conditions. Vadose Zone Journal 7,
810–818.
Hoffman, G.J., Shalhevet, J., 2007. Controlling salinity. In: Hoffman, G.J. (Ed.),
Design and operation of farm irrigation systems. , 2nd ed. American Society of Agricultural and Biological Engineers, St. Joseph, Michigan, USA,pp. 160–207.
Howell, T.A., Evett, R., Tolk, J.A., Schneider, A.D., 2004. Evapotranspiration of full-,deﬁcit-irrigated, and dryland cotton on the Northern Texas High Plains. Journalof Irrigation and Drainage Engineering 130, 277–285.
Hutson, J.L., Wagenet, R.J., 1991. Simulating nitrogen dynamics in soils using a deterministic model. Soil Use and Management 7, 74–78.
Johnsson, H., Bergström, L., Jansson, P.-E., Paustian, K., 1987. Simulated nitrogendynamics and losses in a layered agricultural soil. Agriculture Ecosystems andEnvironment 18, 333–356.
Kandelous, M.M., Šimůnek, J., 2010a. Comparison of numerical, analytical andempirical models to estimate wetting pattern for surface and subsurface drip
irrigation. Irrigation Science 28, 435–444.
Kandelous, M.M., Šimůnek, J., 2010b. Numerical simulations of water movement ina subsurface drip irrigation system under ﬁeld and laboratory conditions using
HYDRUS-2D. Agricultural Water Management 97, 1070–1076.
Kandelous, M.M., Šimůnek, J., van Genuchten, M.Th., Malek, K., 2011. Soil water content distributions between two emitters of a subsurface drip irrigation system.
Soil Science Society of America Journal 75, 488–497.
Katerji, N., Mastrorilli, M., Rana, G., 2008. Water use efﬁciency of crops cultivated in
the Mediterranean region: review and analysis. European Journal of Agronomy
28, 493–507.
Klepper, B., 1991. Crop root system response to irrigation. Irrigation Science 12,
105–108.
Lazarovitch, N., Šimůnek, J., Shani, U., 2005. System-dependent boundary condition
for water ﬂow from subsurface source. Soil Science Society of America Journal
69, 46–50.
Liu, Y.J., Luo, Y., 2010. A consolidated evaluation of the FAO-56 dual crop coefﬁcientapproach using the lysimeter data in the North China Plain. Agricultural Water
Management 97, 31–40.
Ma, L., Ahuja, L.R., Ascough II, J.C., Shaffer, M.J., Rojas, K.W., Malone, R.W., Cameira,M.R., 2001. Integrating system modeling with ﬁeld research in agriculture: applications of the root zone water quality model (RZWQM). Advances in Agronomy
71, 233–292.
Mailhol, J.C., Crevoisier, D., Triki, K., 2007. Impact of water application conditions
on nitrogen leaching under furrow irrigation: experimental and modelling
approaches. Agricultural Water Management 87, 275–284.
Mailhol, J.C., Ruelle, P., Walser, S., Schütze, N., Dejean, C., 2011. Analysis of AET
and yield predictions under surface and buried drip irrigation systems using
the Crop Model PILOTE and Hydrus-2D. Agricultural Water Management 98,
1033–1044.
Mallants, D., van Genuchten, M.Th., Šimůnek, J., Jacques, D., Seetharam, S., 2011.
Leaching of contaminants to groundwater. In: Swartjes, F.A. (Ed.), Dealing
with Contaminated Sites. From Theory to Practical Applications. Springer, The
Netherlands, pp. 787–850.
Maas, E.V., 1990. Crop salt tolerance. In: Tanji, K.K. (Ed.), Agricultural Salinity Assessment and Management. Manual on Engineering Practice, vol. 71. American
Society of Civil Engineers, Reston, VA, pp. 262–304.
Mastrorilli, M., Katerji, N., Rana, G., Steduto, P., 1995. Sweet sorghum in Mediterranean climate: radiation use and biomass water use efﬁciencies. Industrial Cropand Products 3, 253–260.
Mastrorilli, M., Katerji, N., Rana, G., 1999. Productivity and water use efﬁciency ofsweet sorghum as affected by soil water deﬁcit occurring at different vegetative
growth stages. European Journal of Agronomy 11, 207–215.
Mmolawa, K., Or, D., 2003. Experimental and numerical evaluation of analytical volume balance model for soil water dynamics under drip irrigation. Soil Science
Society of America Journal 67, 1657–1671.
Novák, V., van Genuchten, M.Th., 2008. Using the transpiration regime to estimate
biomass production. Soil Science 173, 401–407.
Pereira, L.S., van den Broek, B., Kabat, P., Allen, R.G., 1995. Crop–Water Simulation
Models in Practice. Wageningen Pers, Wageningen, The Netherlands.

Prasad, S., Singh, A., Jain, N., Joshi, H.C., 2007. Ethanol production from sweetsorghum syrup for utilization as automotive fuel in India. Energy and Fuel 21,2415–2420.
Ramos, T.B., Gonçalves, M.C., Castanheira, N.L., Martins, J.C., Santos, F.L., Prazeres, A.,
Fernandes, M.L., 2009. Effect of sodium and nitrogen on yield function of irrigated maize in southern Portugal. Agricultural Water Management 96, 585–594.
Ramos, T.B., Šimůnek, J., Gonçalves, M.C., Martins, J.C., Prazeres, A., Castanheira,N.L., Pereira, L.S., 2011. Field evaluation of a multicomponent solute transportmodel in soils irrigated with saline waters. Journal of Hydrology 407, 129–144,
http://dx.doi.org/10.1016/j.jhydrol.2011.07.016.
Ramos, T.B., Castanheira, N.L., Gonçalves, M.C., Fernandes, M.L., Januário, M.I.,
Lourenço, M.E., Pires, F.P., Martins, J.C., 2012. Effect of combined use of brackish water and nitrogen fertilizer on biomass and sugar yield of sweet sorghum.
Pedosphere, in press.
Ravikumar, V., Vijayakumar, G., Šimůnek, J., Chellamuthu, S., Santhi, R., Appavu, K.,
2011. Evaluation of fertigation scheduling for sugarcane using a vadose zone
ﬂow and transport model. Agricultural Water Management 98, 1431–1440.
Ritchie, J.T., 1972. Model for predicting evaporation from a row crop with incomplete
cover. Water Resources Research 8, 1204–1213.
Roberts, T., Lazarovitch, N., Warrick, A.W., Thompson, T.L., 2009. Modeling salt accumulation with subsurface drip irrigation using HYDRUS-2D. Soil Science Societyof America Journal 73, 233–240.
Roberts, T., White, S.A., Warrick, A.W., Thompson, T.L., 2008. Tape depth and germination method inﬂuence patterns of salt accumulation with subsurface drip
irrigation. Agricultural Water Management 95, 669–677.
Rosa, R.D., Paredes, P., Rodrigues, G.C., Alves, I., Fernando, R.M., Pereira, L.S., Allen,
R.G., 2012. Implementing the dual crop coefﬁcient approach in interactive
software: 1. Background and computational strategy. Agricultural Water Management 103, 62–77.
Šimůnek, J., Wang, D., Shouse, P.J., van Genuchten, Th.M., 1998. Analysis of a ﬁeld
tension disc inﬁltrometer experiment by parameter estimation. International
Agrophysics 12, 167–180.
Šimůnek, J., van Genuchten, Th.M., Šejna, M., 2006. The HYDRUS software package
for simulating two- and three-dimensional movement of water, heat, and multiple solutes in variably-saturated media. In: Technical Manual. Version 1.0. PC
Progress, Prague, Czech Republic, 241 p.
Šimůnek, J., van Genuchten, M.Th., Šejna, M., 2008. Development and applications of
the HYDRUS and STANMOD software packages, and related codes. Vadose Zone
Journal 7, 587–600.
Šimůnek, J., Hopmans, J.W., 2009. Modeling compensated root water and nutrient
uptake. Ecological Modelling 220, 505–521.
Skaggs, T.H., Trout, T.J., Šimůnek, J., Shouse, P.J., 2004. Comparison of HYDRUS-2D
simulations of drip irrigation with experimental observations. Journal of Irrigation and Drainage Engineering 130, 304–310.
Skaggs, T.H., van Genuchten M.Th. Shouse, P.J., Poss, J.A., 2006a. Macroscopic
approaches to root water uptake as a function of water and salinity stress.
Agricultural Water Management 86, 140–149.
Skaggs, T.H., Shouse, P.J., Poss, J.A., 2006b. Irrigating forage crops with saline waters:
2. Modeling root uptake and drainage. Vadose Zone Journal 5, 824–837.
Steduto, P., Katerji, N., Puertos-Molina, H., Unlü, M., Mastrorilli, M., Rana, G., 1997.
Water-use efﬁciency of sweet sorghum under water stress conditions. Gasexchange investigations at leaf and canopy scales. Field Crops Research 54,
221–234.
Tolk, J.A., Howell, T.A., 2001. Measured and simulated evapotranspiration of grainsorghum grown with full and limited irrigation in three High Plains soils. Transactions of ASABE 44, 1553–1558.
U.S. Salinity Laboratory Staff, 1954. Diagnosis and Improvement of Saline and Alcaly
Soils. USDA Handbook 60. Washington, USA.
van Genuchten, M.Th., 1980. A closed form equation for predicting the hydraulicconductivity of unsaturated soils. Soil Science Society of America Journal 44,
892–898.
van Genuchten, M.Th., 1987. A numerical model for water and solute movement
in and below the root zone. Res. Rep. 121, U.S. Salinity Laboratory, USDA, ARS,
Riverside, California.
Vasilakoglou, I., Dhima, K., Karagiannidis, N., Gatsis, T., 2011. Sweet sorghum productivity for biofuels under increased soil salinity and reduced irrigation. Field
Crops Research 120, 38–46.
Vrugt, J.A., Hopmans, J.W., Šimůnek, J., 2001. Calibration of a two dimensional root
water uptake model. Soil Science Society of America Journal 65, 1027–1037.
Weihermüller, L., Kasteel, R., Vanderborght, J., Pütz, T., Vereecken, H., 2005. Soilwater extraction with a suction cup: results of numerical simulations. Vadose
Zone Journal 4, 899–907.
Weihermüller, L., Kasteel, R., Vanderborght, J., Šimůnek, J., Vereecken, H., 2011.
Uncertainty in pesticide monitoring using suction cups: evidence from numerical simulations. Vadose Zone Journal 10, 1287–1298.
Zegada-Lizarazu, W., Zatta, A., Monti, A., 2012. Water uptake efﬁciency and aboveand belowground biomass development of sweet sorghum and maize under
different water regimes. Plant Soil 351, 47–60.
Zhao, Y.L., Dolat, A., Steinberger, Y., Wang, X., Osman, A., Xie, G.H., 2009. Biomassyield and changes in chemical composition of sweet sorghum cultivars grown
for biofuel. Field Crops Research 111, 55–64.