Case Study

Numerical Evaluation of Nitrate Distributions in the Onion
Root Zone under Conventional Furrow Fertigation

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Sanjit K. Deb 1; Parmodh Sharma 2; Manoj K. Shukla 3; Jamshid Ashigh 4; and Jiří Šimůnek 5
Abstract: HYDRUS (2D/3D) model was used to simulate spatial and temporal distributions of nitrate-nitrogen (NO3 -N) within and below theonion root zone under conventional furrow fertigation with the urea-ammonium-nitrate (UAN) liquid fertilizer. The simulated water contents inthe furrow irrigated onion field agreed well with the measurements. Simulations produced similar patterns of the measured NO3 -N concentration
profiles throughout the growing season. NO3 -N concentrations remained higher and accumulation of NO3 -N was observed within the root zone.
Higher NO3 -N within the root zone was dependent on the rate of the UAN fertilizer application, quantity of NO3 -N removed by root uptake, andNO3 -N drainage fluxes below the root zone. Simulations also suggested that NO3 -N below the root zone during different growth stages remainedmuch higher than a recommended (for drinking water) standard concentration level (10 mg L−1 ). This resulted in higher NO3 -N drainage fluxes,
particularly during the fertigation events between the establishment and vegetative growth stages. This indicates the need to apply mostfertigation events at an early stage of bulb formation to provide the maximum NO3 -N demands by onions and to reduce potential NO3 -N
leaching. DOI: 10.1061/(ASCE)HE.1943-5584.0001304. © 2015 American Society of Civil Engineers.
Author keywords: Furrow irrigation; Fertigation; Nitrate leaching; HYDRUS (2D/3D) model; Onion; Simulation.

Introduction
Of all the essential nutrients, nitrogen (N) is required by crops in thelargest quantity and is most frequently the limiting factor in crop
productivity. From various sources of N losses in irrigated agriculture that decrease the availability of N to crops, leaching is considered a major source of nitrate (NO−3 ) loss (Sharma et al. 2012a, b).
Apart from the economic considerations of nutrient losses, fertilization practices in irrigated agriculture directly and indirectly affectthe composition of groundwater recharge and aquifer biogeochemistry (Böhlke 2002). The highly soluble complex ion NO−
3 , whichis only weakly adsorbed by particles in most soils, is a common
contaminant of groundwater (Spalding and Exner 1993; González–Delgado and Shukla 2014). Groundwater contamination by NO−
3leaching continues to be of great agroenvironmental concern inclimatic regions where irrigated agriculture is dominating and excessive N fertilizers are applied to arable soils every year.
In addition to soil properties, N fertilizers, and water appliedby irrigation or received through precipitation, a type of irrigation
1

Assistant Professor, Dept. of Plant and Soil Science, Texas Tech Univ.,
P.O. Box 42122, Lubbock, TX 79409; formerly, Postdoctoral Fellow, Dept.
of Plant and Environmental Sciences, New Mexico State Univ., MSC 3Q,
P.O. Box 30003, Las Cruces, NM 88003 (corresponding author). E-mail:sanjit@nmsu.edu; sanjit.deb@ttu.edu
2
Statistical Programmer, PVR Technologies, King of Prussia, PA
19406; formerly, Graduate Research Assistant, Dept. of Plant and Environmental Sciences, New Mexico State Univ., Las Cruces, NM 88003.
3
Professor, Dept. of Plant and Environmental Sciences, New Mexico
State Univ., Las Cruces, NM 88003.
4
Field Scientist, DOW AgroSciences Canada Inc., London, ON
N6H4Z8; formerly, Associate Professor, Dept. of Extension Plant Sciences,
New Mexico State Univ., Las Cruces, NM 88003.
5
Professor, Dept. of Environmental Sciences, Univ. of California,
Riverside, CA 92521.
Note. This manuscript was submitted on November 2, 2014; approvedon August 14, 2015; published online on October 14, 2015. Discussion
period open until March 14, 2016; separate discussions must be submitted
for individual papers. This paper is part of the Journal of Hydrologic Engineering, © ASCE, ISSN 1084-0699.
© ASCEsystem also plays an important role in NO−
3 leaching to groundwater (Al-Jamal et al. 1997; Sharma et al. 2012a, b). The problem
of NO−
3 leaching can be exacerbated in agricultural areas, such as in
the arid and semiarid southern New Mexico, where surface or flood
irrigation systems are widely practiced on highly permeable coarse
textured soils. Irrigation systems such as sprinkler or drip to alleviate NO−
3 leaching require large initial capital expenditures whenconverting from low energy furrow irrigation. Furrow irrigation
remains the commonly used method in arid and semiarid regionsof the world to irrigate vegetables and row crops, and in particular, the specialty crop onion (Allium cepa) in southern New
Mexico. New Mexico produces onions primarily for the freshmarket, and on average, onions are New Mexico’s most profitable
crop. During the 2011 to 2013 seasons, New Mexico supplied
28–31% of summer, nonstorage onions consumed in the UnitedStates (USDA 2014). Approximately 2,400 ha of onions wereplanted, and 2,350 hectares were harvested annually (2011–2013), producing approximately 138,840 t at a value of $47 million(USDA 2014).
NO−
3 leaching is a common problem in frequently fertilized
agricultural crops in southern New Mexico. Accumulation or distribution of NO−
3 in the crop root zone and its leaching vary considerably with crops (Weed and Kanwar 1996; Al-Jamal et al.
1997; Sharma et al. 2012b) because crops differ in rooting depths,
rooting densities, N and water requirements, and crop uptake efficiencies (Peterson and Power 1991). Al-Jamal et al. (1997) reported
that NO−
3 loadings to groundwater were greater for onion than forchile pepper (Capsicum annuum) in the furrow irrigation systems insouthern New Mexico. In another study, NO−
3 loadings below theroot zone under furrow irrigation systems were found to be thehighest for onion, followed by chile pepper and cotton (Gossypium
spp.) (Sharma et al. 2012b).
Direct measurements of simultaneous water flow and NO−
3accumulation within or losses below the crop root zone are not only
laborious, time-consuming, and expensive, but also highly
challenging, primarily because of uncertainties associated withestimating drainage fluxes and solute concentrations in theleachate, even under well-controlled experimental conditions

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(van der Laan et al. 2010). Simulation models have become valuable research tools for predicting complex and interactive processesof water flow and solute transport in and below the root zone.
Models are useful for identifying potential environmental risks
associated with leaching of surface-applied fertilizers, such as withfurrow fertigation, the process of applying soluble fertilizers[e.g., liquid N fertilizer consisting of a mixture of urea, ammonium−(NHþ4 ), and nitrate (NO3 )] along with irrigation. Yet, few computer
simulation models, with the exception of HYDRUS (2D/3D)(Šimůnek et al. 2012), have the capability to analyze water flow
and nutrient transport in multiple spatial dimensions. The HYDRUS
model has been extensively used for simulating water flow andsolute transport in a variety of soil geometries, irrigation systems,
and fertigation strategies for different crops [e.g., Cote et al. (2003),
Gärdenäs et al. (2005), Hanson et al. (2006), Crevoisier et al.
(2008), and Siyal et al. (2012)]. Notably, HYDRUS (2D/3D) has
also proven to be an effective tool in improving our understandingof the soil-plant-atmosphere water relations in irrigated orchards ofsouthern New Mexico (Deb et al. 2013).
A previous field study by Sharma et al. (2012a) has generated
considerable information on nitrate-nitrogen (NO3 -N) leaching−1[i.e., 0.2259 × NO−
3 (mg L )] from an onion field under conventional furrow fertigation in southern New Mexico. Numericalsimulations of two-dimensional water flow and urea-ammoniumnitrate reactions and transport in the onion root zone, while accounting for root water and nutrient uptake by onion, can further
improve our understanding of the dynamic nature of these processes under furrow fertigation. The scarcity of quantitative information on simultaneous water flow and NO3 -N movement anddistribution within and below the crop root zone under furrow fertigation is equally true for the frequently fertilized onion. Therefore, the main objective of this study was to use the HYDRUS(2D/3D) model to simulate spatial and temporal distributions of
NO3 -N within and below the onion root zone under furrow fertigation. HYDRUS (2D/3D) could provide an additional tool for
examining NO3 -N distributions in the furrow irrigated onion production system.

Materials and Methods
Field Description
The study was carried out on a conventional furrow irrigated onion(Allium cepa) field at New Mexico State University’s Leyendecker
Plant Science Research Center (PSRC) in Las Cruces, New Mexico(32° 11.46′ N, 106° 44.40′ W and 1,128 m above mean sea level).
Soil at the study site is classified as Glendale (fine-silty, mixed,
calcareous, thermic typic Torrifluvents) and Harkey (coarse-silty,
mixed, calcareous, thermic typic Torrifluvents). The study regionis arid, with an average air temperature of 17.7°C and annual precipitation of 29.7 cm (Gile et al. 1981). The field was under onion–sudan (Sorghum sudanense) grass rotation for several years. Onion
was transplanted on November 1, 2006 and harvested on July 14,
2007 [corresponds to 255 DAT (days after transplanting)]. Approximately 3–4 weeks before transplanting, the field was preparedfollowing the conventional tillage practices, including disking followed by chiseling. Triple superphosphate was broadcasted at a rateof 200 kg P2 O5 ha−1 on the field before plowing. The entire field
was plowed to the depth of 20 cm to incorporate sudan grass stubble into the top soil layer, and then leveled using laser leveling technique. A lister was used to make furrows. Following the commonlyused practice in southern New Mexico, onions were transplanted in
two rows on each ridge.
© ASCE

Table 1. Dates of Fertigation Events in the Furrow Irrigated Onion Field
during the Growing Season
Number ofapplication
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
a

Irrigation/
fertigation dateDays after
transplanting(DAT)

N application
ratea(kg N ha−1 )November 5, 2006
November 17, 2006
November 29, 2006
December 15, 2006
January 8, 2007
February 9, 2007
February 23, 2007
March 6, 2007
March 16, 2007
March 27, 2007
April 5, 2007
April 13, 2007
April 20, 2007
April 27, 2007
May 12, 2007
May 25, 2007
June 1, 2007
June 7, 2007
June 15, 2007
June 21, 2007
June 29, 2007

4
16
28
44
68
100
114
125
135
146
155
163
170
177
192
205
212
218
226
232
240

12.3
—
12.3
—
—
49.2
—
49.2
—
49.2
—
49.2
—
49.2
24.6
—
—
12.3
—
12.3
—

Fertilized with the urea-ammonium-nitrate (UAN) liquid fertilizer.

Onions were irrigated 21 times (Table 1) during the growing
season. The water table was located at a depth greater than 2 mfrom the soil surface (Deb et al. 2011), and the field was irrigatedwith groundwater. The amount of water applied during each irrigation event was measured with a flow meter (McCrometer, Hemet,
California). Staff gauges were installed in the furrow to continuously measure the depth of irrigation water during an irrigation
event. On average, water application rate of 7500 L h−1 furrow−1
for a 210 m long row was used, and water supply was stopped when
the furrow was filled to about half the ridge height. Onions werefertilized with the urea-ammonium-nitrate (UAN) liquid fertilizer(32–0–0) (Table 1). Furrow fertigation was applied at a rate of
12.3 kg N ha−1 per irrigation during the establishment stage ofonion growth (1 to 90 DAT), 49.2 kg N ha−1 per irrigation during
the development (vegetative) and early stage of bulb formation(91 to 166 DAT), and 24.6 to 49.2 kg N ha−1 per irrigation during
the bulb formation or bulb growth stage (167 to 207 DAT),and 12.3 kg N ha−1 per irrigation during the bulb enlargement or
maturity stage (208 to 255 DAT).
Numerical Modeling
HYDRUS (2D/3D) Software
The two–dimensional water flow and NO−
3 dynamics were simulated using the finite element model HYDRUS (2D/3D), version
2.03.450 (hereinafter referred to as HYDRUS) (Šimůnek et al.
2012). Detailed descriptions of the governing equations for waterflow and solute transport and of the interactive graphical, Windowsbased user interface can be found in the HYDRUS (2D/3D) technical(Šimůnek et al. 2012) and user manuals (Šejna et al. 2013),
respectively. HYDRUS numerically solves the Richards’ equation,
which describes the isothermal Darcian water flow in a variablysaturated, rigid, isotropic porous medium and can be expressed
as follows:

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∂θ
¼ ∇ðK∇HÞ − Sr∂t

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where θ = volumetric water content (cm3 cm−3 ); K = unsaturated
hydraulic conductivity (cm d−1 ); H = hydraulic head (cm); Sr =a sink term that represents the volume of water removed from a unit
volume of soil per unit time attributable to plant water uptake(cm3 cm−3 d−1 ); ∇ = spatial gradient operator; and t = time (d).
Soil hydraulic properties (i.e., unsaturated retention and hydraulicconductivity functions) in Eq. (1) were described using the van
Genuchten–Mualem functional relationships (van Genuchten 1980;
Mualem 1976) as follows:θðψÞ ¼

8
<θ þ
r

:

θs − θr½1 þ ðjαv ψjn Þm
θs

ψ<0

ð2Þ

ψ≥0

m 2
KðψÞ ¼ K s Sle ½1 − ð1 − S1=m
e Þ 

ð3Þ

where θs = saturated volumetric water contents ðcm3 cm−3 Þ; θr =residual volumetric water contents ðcm3 cm−3 Þ; ψ = soil water pressure head; αv = reciprocal of the air–entry ψðcm−1 Þ; m ¼
1 − 1=nðn > 1Þ; n = pore-size distribution index (unitless); Se =effective saturation (unitless) given as Se ¼ ½θðψÞ − θr =ðθs − θr Þ;
l = pore-connectivity parameter (unitless); and K s = saturated
hydraulic conductivity (cm d−1 ). The sink term ðSr Þ without theosmotic stress was described according to the root water uptake
model of Feddes et al. (1978), as implemented in the HYDRUS.
HYDRUS allows simultaneous simulation of multiple solutes
that can be either independent of each other or subject to thefirst-order degradation reactions (e.g., N species). The solute transport equation considers advective-dispersive transport in the liquid−
phase, and diffusion in the gaseous phase. Urea, NHþ
4 , and NO3
were considered for the N species simulations. The governing
solute transport equations, which describe the transport of each−
N species, namely, urea, NHþ
4 , and NO3 , can be written as follows:∂θc1¼ ∇ðθD∇c1 Þ − ∇ðqc1 Þ − μa θc1 − Sr c1
∂t
∂θc2
∂s
þ ρ 2 ¼ ∇ðθD∇c2 Þ − ∇ðqc2 Þ − μv θc2 − μn θc2∂t∂t
þ μa θc1 − Sr c2∂θc3¼ ∇ðθD∇c3 Þ − ∇ðqc3 Þ þ μn θc2 − Sr c3
∂t

ð4Þ

ð5Þ
ð6Þ

where c1 , c2 , and c3 = liquid phase concentrations (mg cm−3 ) of−urea, NHþ4 , and NO3 , respectively; D = dispersion coefficient2−1
tensor ðcm d Þ; q = volumetric flux density ðcm d−1 Þ; ρ = bulk
density of the soil (g cm−3 ); s2 = adsorbed concentration of
−1
−1
NHþ
4 (g g ); μa = first-order rate constant ðd Þ representing
þnitrification of urea to NH4 ; μv = first-order rate constant ðd−1 Þrepresenting volatilization of NHþ
4 to ammonia ðNH3 Þ; and μn =first-order reaction rate constant ðd−1 Þ representing nitrification ofþ−NHþ
4 to NO3 . Note that volatilization of NH4 and subsequentþ
NH4 transport by gaseous diffusion was neglected in this study.
Urea and NO−
3 were assumed to be present only in the dissolved
phase [i.e., the distribution coefficient ðK d Þ¼ 0 cm3 g−1 ]. The reþlationship between NHþ
4 in the solution (c2 ) and NH4 absorbedðs2 Þ is described by means of a linear adsorption isotherm as
follows:© ASCEs2 ¼ K d c2

ð1Þ

ð7Þ

NHþ
4 was assumed to adsorb to the solid phase and a K d value of
3.5 cm3 g−1 was used based on similar values reported in several
studies [e.g., Ling and El-Kadi (1998) and Hanson et al. (2006)].
Eqs. (4)–(6) are linear as the reaction rate constants μa , μv , and μn ,and the distribution coefficient for NHþ
4 ðK d Þ are concentration
independent. The μa acts as a sink in Eq. (4) and as a source in
Eq. (5). Similarly, the μn acts as a sink in Eq. (5) and as a source
in Eq. (6). Molecular diffusion was neglected because it was considered negligible relative to hydrodynamic dispersion. The longitudinal dispersivity was considered equal to one-tenth of the profile
depth (i.e., 11 cm) and the transverse dispersivity equal to one–tenth of the longitudinal dispersivity (i.e., 1.1 cm) (Beven et al.
1993; Cote et al. 2003; Hanson et al. 2006). Because of the lackof experimental data, the parameters μa and μn were also takenfrom the literature. The value was found to be between 0.02 and0.72 for μa and between 0.36 and 0.56 for μn in the literature(e.g., Hanson et al. 2006). As suggested by Hanson et al. (2006)
in their simulations with HYDRUS–2D, the μa and μn especially for
fertigation with the UAN fertilizer were taken as 0.38 and 0.2 d−1 ,respectively.
The last term in Eqs. (4)–(6) represents the passive root nutrient
uptake, i.e., the movement of nutrients into roots by convective
mass flow of water, which is directly coupled with root water uptake (Šimůnek and Hopmans 2009), and therefore, the products ofroot water uptake (Sr ) and concentrations of respective species(i.e., c1 , c2 , and c3 , respectively). Because unlimited passive nutrient uptake for N species was considered, the maximum concentration of the root solute uptake was set to a concentration value
larger than the dissolved simulated concentrations (c1 , c2 , and c3 ),which allowed all dissolved nutrients to be taken up by plant roots
with root water uptake.
Numerical Flow Domain and Its Spatial Discretization
The flow domain, 102 cm wide and 110 cm deep from the ridge,
considered for simulating water flow and transport of N species−(i.e., urea, NHþ
4 , and NO3 ) in the root zone of a furrow irrigation
system is shown in Fig. 1. The width of the flow domain(102 cm) represents two halves of a 46 cm furrow [including
both the bottoms (lengths AB and EF) and sloping sides (lengths
BC and DE)] and a complete 56 cm ridge (length CD) at theupper boundary (Fig. 1). The finite element mesh was generatedusing the MESHGEN module of HYDRUS. The finite element
mesh was refined such that the size of the elements was smaller
near the soil surface along the ridge and two halves of the furrow
where infiltration and evaporation, i.e., changes in the soil watercontent and corresponding pressure heads, were most rapid. The
size of the elements was larger along the left and right boundaries (lengths AH and FG, respectively; Fig. 1), and the bottom
boundary (length GH; Fig. 1) of the flow domain. The numbersof finite element nodes, boundary 1D-elements, and 2D-elements(triangles) in the flow domain were 8,282, 344, and 16,218, respectively. Observation nodes were located below the bottom of
the furrow at soil depths of 20 and 50 cm from the ridge, whichcorresponded to the measurement locations of soil water contents
during the onion growing season.
Initial and Boundary Conditions
The ridge surface (length CD; Fig. 1) was specified as an atmospheric boundary, defined by potential evaporation, potential transpiration, and rainfall. Both the bottom surfaces (AB and EF;
Fig. 1) and sloping sides (BC and DE) of the furrow were assigned
time-variable head boundary conditions, which were adjusted
dynamically depending upon the water level (i.e., saturation

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Fig. 1. Schematic of the flow domain with boundary conditions used in
HYDRUS (2D/3D) simulations

conditions) in the furrow and conditions in the flow domain (i.e., theroot zone). These boundaries switched from time-variable headboundary conditions to atmospheric boundary conditions when
the pressure head (ψ) across these boundaries became negative(i.e., unsaturated conditions). In HYDRUS, the actual evaporation
remains equal to the potential evaporation (Ep ) as long as ψ at theatmospheric boundary is higher than a critical pressure head ψcrit(considered to be −15,000 cm in this study). Once the ψcrit value isreached, i.e., the soil surface dries out to the ψcrit value, the actual
evaporation rate is decreased from the Ep value. In the study areas,
the water table was deep (>2 m from the soil surface), and did notaffect flow in the transport domain of interest. Therefore, the bottom of the flow domain (GH; Fig. 1) was assigned a free drainage(i.e., a unit hydraulic gradient) boundary condition for gravitational
flow to occur from the bottom of the 110 cm well-drained soil profile. Because of symmetry, the nodes representing the left and rightboundaries (AH and FG, respectively; Fig. 1) of the flow domain
were set as no-flux boundaries because no flow or solute transport
occurred across these boundaries.
The initial distribution of the volumetric water contents (θ) at the
day of transplanting (November 1, 2006) was based on gravimetrically measured values in the furrows at six soil depths (0–10,
10–30, 30–40, 40–60, 60–85, and 85–110 cm from the ridge). The
initial θ distribution varied from 0.17 at the ridge to 0.22 cm3 cm−3
at the bottom of the 110-cm soil profile. Because sudan grass was
not fertilized, the flow domain was considered N free at the beginning of the simulation, and the initial concentrations of urea, NHþ4,þ−and NO−
3 were thus assumed to be zero. The urea, NH4 , and NO3
fluxes out of the flow domain could occur only from the bottom
free drainage boundary. The cumulative leaching of mass of each−
N species (urea, NHþ
4 , and NO3 ) out of the bottom boundary wascontrolled by the concentration of each N species at that depth
and the corresponding water flux density as computed from
Eq. (1). A third-type (Cauchy) boundary condition was specified
at the time-variable head, atmospheric, and free drainage water flowboundary conditions. The Cauchy boundary condition defined the−concentration flux of each N species (urea, NHþ
4 , and NO3 ) acrossthe boundary.
© ASCE

Field Measurements and Model Input Requirements
The characterization of the soil profile (0–110 cm soil depths) at
this onion field were reported in Deb et al. (2011) and Sharma et al.
(2012a). Briefly, the soil texture is sandy loam down to 80 cm soil
depth and sand below 80 cm. Therefore, the 110 cm flow domain
was assumed to be a homogeneous, with a bulk density varying
from 1.3 to 1.5 mg m−3 (average ¼ 1.4 mg m−3 ). The value of K s
ranged from 49 to 107 cm d−1 within the 110 cm soil profile, withan average value of 50 cm d−1 . The average soil pH and electricalconductivity (EC) for the 0–60 cm depths were 7.4 and 2.0 dS m−1
and were 8.0 and 0.8 dS m−1 for depths greater than 60 cm, respectively. On average, within the 0–60 cm depths, soil organic matter,
phosphorus (P), and potassium (K) were 0.43%, 11.6 mg L−1 , and57.3 mg L−1 , and at soil depths > 60 cm, were 0.02%, 2.2 mg L−1 ,and 29 mg L−1 , respectively.
The soil water retention curve was determined using the pressure chamber method at ψ of 0 (at saturation), −300, −500,−1,000, −3,000, −5,000, −10,000, and −15,000 cm H2 O. The
values of θs (¼ 0.43 cm3 cm−3 ), θr ð¼ 0.07 cm3 cm−3 Þ, αv
ð¼ 0.003 cm−1 ), and n (= 2.03) were estimated by fitting thevan Genuchten (1980) soil water retention model to the measured
drainage curve data using the RETC code (van Genuchten et al.
1991). The value of the parameter l was assumed to be 0.55
(Deb et al. 2011). Temporal variations in volumetric water contents(θ) in the soil profile at a location below the bottom of a furrow atsoil depths of 20 and 50 cm from the ridge were measured using a
set of two time domain reflectrometry (TDR) sensors (CS640)(Campbell Scientific, Logan, Utah). A total of eight TDR sensors
were installed at four field locations below the bottom of the furrows to record the volumetric soil water content every 10 min during the onion growing season.
Irrigation water samples were collected during each month andanalyzed for EC, pH, NO3 -N, and chloride. Bulk soil samples
were collected monthly from the furrows at six soil depths down
to 110 cm from the ridge. The gravimetric water content was determined for each bulk soil sample. Bulk soil samples were air
dried for 48 h, grounded, and passed through a 2-mm diameter
sieve. A Technicon Autoanalyzer II (Technicon Instruments,
Tarrytown, New York) with the cadmium reduction column technique was used to analyze soil-KCl extracts for NO3 -N (Maynard
and Kalra 1993).
HYDRUS requires as time-variable inputs separate values ofpotential evaporation ðEp Þ from the soil surface and potential transpiration ðT p Þ through the plants. Meteorological variables wereobtained from the PSRC weather station, which included precipitation, solar radiation, air and soil surface temperatures, windspeed, and relative humidity measured on an hourly basis at 2 mabove the soil surface. The daily reference evapotranspiration
for grass ðET 0 Þ was estimated based on the FAO–56 Penman–
Monteith equation (Allen et al. 1998) using the daily weather data.
The estimated ET 0 was then multiplied by a crop coefficient ðK c Þto estimate onion evapotranspiration ðET c Þ. K c values for onion
were estimated using the following equation developed by AlJamal et al. (1999):
K c ¼ 0.522 − 6.48 × 10−4 × GDDi þ 1.98 × 10−6 × GDD2i− 8.75 × 10−10 × GDD3i
GDDi ¼ T avg − T b

ð8Þ
ð9Þ

where GDDi = growing degree days for day i (T avg > T b , else
GDD ¼ 0) (°C day); T avg = average of daily maximum and minimum air temperatures (°C); and T b = crop-specific base air

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temperature of 4°C for onion (Al-Jamal et al. 1999). When the soil
surface was wet following irrigation or rainfall and during early
periods after irrigation, Ep was estimated according to Snyder et al.
(2000), and T p was then obtained by subtracting Ep from ET c . Deb
et al. (2011) found that during dry soil conditions, the contributionof the total upward water vapor flux to the total water flux near thesoil surface at this onion field was approximately 10%. Therefore,
ET c was partitioned into Ep (¼ 0.10ET c ) and T p (¼ 0.90ET c )under dry soil conditions. ET c , Ep , and T p during the growing

Fig. 2. Potential evapotranspiration (ET c ), soil evaporation (Ep ), andtranspiration (T p ) during the onion growing season, which were used asboundary conditions at the soil surface (Fig. 1) in HYDRUS (2D/3D)
simulations

period, used as boundary conditions at the soil surface in the
HYDRUS model, are shown in Fig. 2.
In HYDRUS, the spatial distribution of roots is constant in time
and their dynamics cannot be considered. As root distributiondiffers within the growing season, the onion growing season was
split into four growth stages: (1) the establishment stage of onion
growth (1–90 DAT); (2) development (vegetative) and early stageof bulb formation (91–166 DAT); (3) bulb formation or bulb growthstage (167–207 DAT); and (4) bulb enlargement or maturity stage−(208–255 DAT). Water flow and transport of urea, NHþ
4 , and NO3
was simulated during each of the four growth stages separately.
−
Final volumetric water content, urea, NHþ
4 , and NO3 distributionsin the flow domain (Fig. 1) from the earlier growth stage were used
as initial conditions for the subsequent stage.
Onions were transplanted in two rows on each ridge. Onion has
a shallow rooting depth (<50 cm) (Al-Jamal et al. 1997; Sharma
et al. 2012a, b). Therefore, during each of the four growth stagesof onion, rooting depths and root distributions were observed by
excavating a soil pit to a soil depth of 80 cm. Soil cores below the
furrow (i.e., both the bottom and side of the furrow) and the ridge
were collected at 10-cm depth increments down to a depth of
80 cm. Collected soils were washed to extract roots, which werethen scanned. An analysis of scanned root images for the root size
distribution and the root length density was performed. The majority of the roots were found below the ridge and sloping side of the
furrow, and in particular, within the 0–10 cm soil depths during
the establishment stage, and within the 0–30 cm soil depths during
the development (vegetative) and early stage of bulb formation,
bulb formation or bulb growth, and bulb enlargement or maturity
stages. Except for the establishment stage when the maximum rooting depth was 30 cm, the maximum rooting depth of 50 cm during
the other three growth stages was observed.
In HYDRUS, root water uptake reductions attributable to
the water stress were described using the piece-wise linear modelFig. 3. Comparisons between the measured and simulated daily mean volumetric water contents below the bottom of the furrow at soil depths of:(a) 20 cm; (b) 50 cm during the onion growing season; error bars of the measured values are standard errors of the means; RMSE, ME, and d are theroot mean square error, mean bias error, and index of agreement [Eqs. (10)–(12)], respectively, between the measured and simulated volumetric watercontents© ASCE

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proposed by Feddes et al. (1978), which includes five variables that
describe the dependence of the extraction of water from the soil on
ψ. All critical ψ values for the functional form of Feddes et al.
(1978) [i.e., ψ1 (oxygen deficiency point) = −10; ψ2 ¼ −25;
ψ3;high ¼ −450; ψ3;low ¼ −550, and ψ4 ¼ −8,000 cm for the establishment stage, and ψ1 ¼ −10; ψ2 ¼ −25, ψ3;high ¼ −550,
ψ3;low ¼ −650, and ψ4 ¼ −8,000 cm for the remaining growthstages] were taken from the HYDRUS database (Taylor andAshcroft 1972). Water uptake above ψ1 and below ψ4 is assumed
to be zero. Water uptake is maximal between ψ2 and ψ3 (reduction
point). Between ψ1 and ψ2 and between ψ3 and ψ4 , a linear variation is assumed. The value of ψ3 depends on the water demand of
the atmosphere, and the true ψ3 is interpolated from low (ψ3;low )and high (ψ3;high ) values of ψ3 and T p .
HYDRUS evaluation was carried out by comparing field measured volumetric water contents (θ) with model simulations using
the quantitative measures of model uncertainty reported in Deb
et al. (2013), such as the root mean square error (RMSE), themean bias error (ME), and an index of agreement (d), which aredefined asﬃ
rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
PN2
i¼1 ðSi − M i Þ
RMSE ¼NME ¼

d ¼ 1.0 − PN

ð10Þ

PN

i¼1 ðSi − M i Þ

ð11Þ

N
PN

i¼1 ðSi − M i Þ2i¼1 ðjSi − M avg j þ jM i − M avg jÞ

2

ð12Þ

where N = number of paired measured and simulated values; Si =ith simulated value; M i = ith measured value; and M avg = averageof measured values. The value of RMSE reflects a magnitude of
the mean difference between measured and simulated results. The
value of ME indicates a systematic error or bias in the model prediction, i.e., positive and negative values of ME indicate a tendency for an over-prediction or under-prediction, respectively.
The index of agreement (d) is not sensitive to systematic model
over- or under-prediction (Krause et al. 2005). The d value ranges

Fig. 4. Simulated spatial distributions of volumetric water contents (cm3 cm−3 ) (displayed using color maps) and nitrate-nitrogen (NO3 -N) concentrations (mg L−1 ) (displayed using contour lines with labels) at selected times before and after a furrow fertigation event during the development(vegetative) and early stage of bulb formation: (a) on 145 DAT (days after transplanting), 1 day before the fertigation event; (b) during the fertigation
event on 146 DAT; (c) early periods after (i.e., 6 h) the fertigation; (d) on 151 DAT, 5 days after the fertigation; (e) on 154 DAT, 8 days after thefertigation; (f) on 157 DAT, 2 days after the successive irrigation (without fertilizer) event on 155 DAT© ASCE

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between 0 (i.e., no agreement) and 1 (i.e., a perfect fit between
simulated and measured values).

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Results and Discussion
HYDRUS-simulated and measured volumetric water contents (θ)
below the bottom of the furrow at soil depths of 20 and 50 cm
are presented in Fig. 3. HYDRUS predicted both sharp increases
in the volumetric water content following irrigations and thengradual decreases after irrigations. However, the ME value indicated that the model slightly overpredicted θ values at a depthof 20 cm [Fig. 3(a)]. The model predicted slightly higher peak values of θ following irrigations. The model underpredicted θ at 50 cm
depth, and the predicted drainage curves were always slightly below the measured curves [Fig. 3(b)]. A comparison between themeasured and simulated θ values yielded relatively lower RMSE
of 0.022 cm3 cm−3 and higher d of 0.96 at soil depths of 20
and 50 cm, respectively (Fig. 3). Small differences between themeasured and simulated θ values may be partially attributed tomeasurement errors, which are inevitable under field conditions(Deb et al. 2011, 2013).
Overall, statistics of RMSE, ME, and the index of agreement (d)for simulated and measured θ values [Eqs. (10)–(12)], presented inFig. 3, suggest that although HYDRUS was not calibrated to optimize water flow parameters there was generally a close agreement

between the measured and simulated θ values throughout the growing season. This close agreement was primarily attributable to thefact that the measured θr , θs , αv , n, l, and K s parameters used forthe parameterization of the van Genuchten–Mualem constitutive
relationships [Eqs. (2)–(3)] were within the range of the a-priori
parameter distribution and their optimized values previously reported in a HYDRUS–1D model (Šimůnek et al. 2013) validation
study in this onion field (Deb et al. 2011). Moreover, similar discrepancies (i.e., RMSE, ME, and d) between the measured andsimulated θ values were reported in Deb et al. (2013).
Simulated spatial distributions of volumetric water contents andNO3 -N concentrations, and changes in volumetric water contents
and NO3 -N profiles at selected times before and after the fertigation
event (at a rate of 49.2 kg N ha−1 per irrigation; Table 1) on 146
DAT are displayed in Fig. 4. On 145 DAT [1 day before the fertigation event; Fig. 4(a)], NO3 -N concentrations remained muchhigher within the upper 0 to 15 cm soil depths below the ridgeand side of the furrow.
The relatively high NO3 -N concentration near the ridge reflected the distribution of NO3 -N accumulated with time fromthe previous fertigation on 125 DAT (Table 1), suggesting that supply of NO3 -N by the UAN fertilizer and nitrification of NHþ
4 exceeded the NO3 -N removal by root uptake (discussed later). As
shown in Figs. 4(b and c), NO3 -N increased below the bottom of
the furrow and moved laterally and vertically as a result of the fertigation. 5 to 8 days after the fertigation event [Figs. 4(d and e)],Fig. 5. Simulated spatial distributions of nitrate-nitrogen (NO3 -N) concentrations within the flow domain at different times during the onion growing
season: (a and b) on 46 DAT (days after transplanting) and 100 DAT of the establishment stage of onion growth; (c and d) on 118 DAT and 150 DAT ofthe development (vegetative) and early stage of bulb formation; (e) on 174 DAT of the bulb formation and bulb growth stage; (f and g) on 210 DAT and
238 DAT of the bulb enlargement or maturity stage; (h) on 254 DAT prior to the harvest on 255 DAT© ASCE

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NO3 -N concentrations below the ridge and the furrow (both thebottom and side of the furrow) remained much higher within
the root zone (0 to 50 cm soil depths), and in particular, within theupper 0–30 cm depths, where the majority of roots were observed.
On 157 DAT [i.e., 2 days after the successive irrigation event
without a fertilizer application; Fig. 4(f)], NO3 -N concentrations
decreased within the 0–50 cm depths of the flow domain. As shownin Fig. 4(f), spatial distributions of higher NO3 -N concentrations
immediately below and within the ridge and of lower concentrations directly below the bottom of the furrow suggest the dominant
effect of the downward movement of irrigation water below the
furrow, which is the driving force moving NO3 -N out of the soil
below the furrow. Therefore, the zone of the maximum NO3 -N concentrations remained at a depth of 0–30 cm below the ridge and sideof the furrow, enabling its continued uptake by onions. However,NO3 -N concentrations gradually increased in deeper depths (below
30 cm) with time after a fertigation event [Figs. 4(a–e)]. NO3 -N,
which is only weakly adsorbed to the soil particles (unlike NHþ
4)(González-Delgado and Shukla 2014) and has high mobility, wastransported with irrigation water. Because the majority of roots
were within the upper 0–30 cm depths during this development(vegetative) and early stage of bulb formation, NO3 -N below the
50 cm soil depth (i.e., the maximum rooting depth observed at thisgrowth stage) was not available for uptake by onions, leading toeventual leaching losses.
In general, NO3 -N concentrations increased with time during
the soil drying period after the fertigation event [Figs. 4(d and e)],particularly within the upper 30 cm soil depth below the ridge
and the furrow. The increase in NO3 -N concentrations with increasing soil drying can be explained by NHþ
4 nitrification in the soil as
nitrification only occurs under aerobic conditions (Rodríguez et al.
2005). This also suggests that nitrification under the furrow fertigation with the urea-ammonium-nitrate (UAN) liquid fertilizer isparticularly important near the soil surface at the ridge and the furrow. In a HYDRUS–2D simulation, although reported for the drip
fertigation, Hanson et al. (2006) also found that NO−
3 concentrations throughout the soil profile increased with time, particularly
near the soil surface, because of the hydrolysis and nitrification of
the applied urea-ammonium-nitrate fertilizer, in contrast to thestudy that used nitrate-only fertilizer (Gärdenäs et al. 2005).
Spatial distributions of simulated NO3 -N concentrations in theflow domain at different times are shown in Fig. 5. Note thatmonthly field observations of NO3 -N concentrations within the
0 to 110 cm soil depths during the growing season were also madeat the same times. Higher NO3 -N concentrations were found in theroot zone (above the 50 cm soil depth) than below the root zone

Fig. 6. Simulated nitrate-nitrogen (NO3 -N) concentration profiles at the bottom and sloping side of the furrow (at a distance of 12 and 22 cm fromthe point A, respectively; Fig. 1), at the ridge (at 36 cm from A; Fig. 1), and measured NO3 -N concentration profiles at the furrow at different times
during the onion growing season: (a and b) on 46 DAT (days after transplanting) and 100 DAT of the establishment stage of onion growth; (c and d) on
118 DAT and 150 DAT of the development (vegetative) and early stage of bulb formation; (e) on 174 DAT of the bulb formation or bulb growth stage;(f and g) on 210 DAT and 238 DAT of the bulb enlargement or maturity stage; (h) on 254 DAT prior to the harvest on 255 DAT; error bars of themeasured values are standard errors of the means© ASCE

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during all four growth stages of onion. NO3 -N concentrations
within the root zone also remained much higher even after an irrigation (without fertilizer) event. For example, after the fertigation
event on 28 DAT (Table 1), higher NO3 -N concentration was observed below the furrow on 46 DAT [Fig. 5(a)], even after the irrigation (without fertilizer) event on 44 DAT (Table 1). However, as
shown in Figs. 5(c–h), NO3 -N concentrations below the root zone
(below 50 cm) were much higher than the U.S. Environmental Protection Agency’s drinking water standard of 10 mg L−1 (U.S. EPA
2012). The observation of higher NO3 -N concentrations below theroot zone was in agreement with other studies that were carried out
on a furrow-irrigated onion field in semiarid southern New Mexico[e.g., Sharma et al. (2012b)].
Fig. 6 compares simulated depth distributions of NO3 -N concentrations at locations in the furrow (both at the bottom and sideof the furrow) and at the ridge with the measured NO3 -N concentration profiles observed in the furrow during the growing season.
Changes in the measured mean NO3 -N concentration profiles atselected times were compared with the simulated ones at locationsin the furrow and at the ridge (Fig. 6) to understand the NO3 -N
distribution and redistribution processes following irrigation andfertigation. HYDRUS simulations produced similar patterns of
NO3 -N concentration profiles as those measured, with the NO3 -N
concentrations remaining higher in the root zone throughout thegrowing season [Figs. 6(a–h)].
Overall, measured depth distributions of NO3 -N concentrations
at different times during different growth stages of onion were comparable with the simulated NO3 -N concentration profiles at the
furrow and at the ridge [Figs. 6(a–h)]. Agreement between themeasured and simulated depth distributions of NO3 -N concentrations was less satisfactory only for measurements on 238 DAT and
254 DAT, as shown in Figs. 6(g and h), respectively. Differenceswere likely caused by the solute transport parameters such as K d ,μa , and μn in the model parameterization, which were taken fromthe literature and were not optimized for these particular conditions.
Differences might also relate in part to measurement errors, particularly on 238 DAT and 254 DAT. It is worth noting that, as reported
in other studies, even a calibrated model could produce poor agreement between the measured and simulated depth distributions ofsolute concentrations below the furrows because of the substantial
spatial and temporal variations in solute transport parameters[e.g., Abbasi et al. (2004)].
Simulated cumulative total actual evaporation and transpiration,and cumulative amount of NO3 -N removed from the flow domain
by root water uptake during the four growth stages of onion are
shown in Figs. 7(a–d). Root nutrient uptake was simulated assuming that all uptakes [i.e., last term in Eqs. (4)–(6)] were passive,
through the root water uptake pathway only. Therefore, the increasein actual transpiration (i.e., root water uptake) generally resulted
in an increase in root NO3 -N uptake [Figs. 7(a–d)]. Simulated
cumulative bottom boundary water and NO3 -N fluxes during thefour growth stages are presented in Figs. 8(a–d). Higher NO3 -N
concentrations, simulated by the HYDRUS within the root zone
[Figs. 5(a–h) and 6(a–h)], were dependent on fertigation rates(Table 1), NO3 -N uptake by onions [Figs. 7(a–d)], and NO3 -N
leaching below the root zone [Figs. 8(a–d)].
During the development (vegetative) and early stage of bulb
formation (91–166 DAT), and during the bulb formation or bulb

Fig. 7. Simulated cumulative total water fluxes (total actual evaporation and transpiration rates) (cm2 ) and cumulative amount of nitrate-nitrogen(NO3 -N) (mg cm−1 ) removed from the flow region by root uptake during: (a) the establishment stage of onion growth; (b) the development(vegetative) and early stage of bulb formation; (c) the bulb formation or bulb growth stage; (d) the bulb enlargement or maturity stage© ASCE

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Fig. 8. Simulated cumulative bottom boundary water (×1,000 cm2 ) and nitrate-nitrogen (NO3 -N) (mg cm−1 ) fluxes during: (a) the establishment
stage of onion growth; (b) the development (vegetative) and early stage of bulb formation; (c) the bulb formation or bulb growth stage; (d) the bulb
enlargement or maturity stage

growth stage (167–207 DAT), the accumulation of higher NO3 -N
concentrations simulated by the HYDRUS below the furrow bottom and the ridge on 150 DAT [Figs. 5(d) and 6(d)] and 174
DAT [Figs. 5(e) and 6(e)] suggested that the supply of NO3 -N by
the UAN fertilizer exceeded the NO3 -N removal by root uptake[Figs. 7(b and c)], respectively). It is worth noting that whereas
the root NO3 -N uptake likely involves both passive and active
mechanisms [e.g., Šimůnek and Hopmans (2009)], considering
only passive NO3 -N uptake might underestimate the simulated total
NO3 -N uptake [Figs. 7(b and c)] and overestimate downward
NO3 -N leaching on 150 DAT and 174 DAT [Figs. 8(b and c)].
The accumulation of higher NO3 -N concentrations within the rootzone [Figs. 5(f) and 6(f)], but markedly lower NO3 -N removal byroot uptake [Fig. 7(d)] and lower NO3 -N leaching [Fig. 8(d)] wereobserved on 210 DAT.
Similar to measurements, simulated NO3 -N concentrations
gradually decreased during different growth stages of onion(155–255 DAT), particularly from the early stage of bulb
formation through the bulb enlargement or maturity stage[e.g., Figs. 5(f–h) and 6(f–h)], primarily because of higher NO3 -N
uptake [Figs. 7(b–d)]. Several studies reported that onion crops
need a maximum amount of N during the bulb formation and bulb
growth stage [e.g., Halvorson et al. (2002) and Sharma et al.
(2012b)]. Simulations of NO3 -N distributions indicated that mostfertigation events could be applied at an early stage of bulb formation to supply the maximum NO3 -N demands of onions. This
would also reduce the NO3 -N leaching that occurred during otherperiod, particularly between the establishment stage and an earlystage of development (or vegetative growth) [Figs. 8(a and b)].
© ASCE

However, there is a need to extend this numerical modeling study
over multiple growing seasons to assess total NO3 -N uptake byonion and NO3 -N leaching under conventional furrow fertigation
with the UAN fertilizer.
HYDRUS simulations also quantified the distributions of urea
−1
and ammonium-nitrogen (NH4 -N) [i.e., 0.78 × NHþ
4 (mg L )]within and below the crop zone. However, because urea andNH4 -N concentrations were not measured in the field, focus here
is only on spatial and temporal distributions of NO3 -N within andbelow the onion root zone. Further investigation into HYDRUS’s
ability, particularly a field validation, to adequately quantify distributions of all N species (urea, NH4 -N, and NO3 -N) within andbelow the onion root zone under a conventional furrow fertigation
with the UAN fertilizer is suggested.

Summary and Conclusions
The HYDRUS model was used as a tool to simulate water flow andNO3 -N transport in the onion root zone for furrow fertigation with
the UAN fertilizer. HYDRUS-simulated volumetric water contents
agreed well with the measurements. Simulations produced similar
patterns of monthly measured NO3 -N concentration profiles. Overall, measured depth distributions of NO3 -N concentrations within
and below the root zone during different growth stages of onion
were comparable with the simulated NO3 -N concentration profiles.
During the growing season, NO3 -N concentrations were generally
higher within the root zone (50 cm soil depth from the ridge). Accumulation of NO3 -N was also observed within this soil depth.

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Higher NO3 -N concentrations were dependent on the rate of the
UAN fertilizer application, quantity of NO3 -N removed fromthe root zone region by root uptake, and NO3 -N leaching below
the root zone. Simulations also suggested that NO3 -N below theroot zone (below 50 cm soil depth) during different growth stages
remained much higher than a recommended standard for theNO3 -N concentration level of 10 mg L−1 (for drinking water). This
resulted in higher NO3 -N drainage fluxes, particularly during theperiod between the establishment and vegetative growth stages andthus, warrants the need to apply most fertigation events at an earlystage of bulb formation to increase NO3 -N uptake and reduceNO3 -N leaching. Further field validation of the HYDRUS aimed
at examining distributions of all N species (urea, NH4 -N andNO3 -N) within and below the onion root zone under a conventional
furrow fertigation with the UAN fertilizer is suggested.

Acknowledgments
The authors thank New Mexico State University Agricultural
Experiment Station for funding this research.

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