agricultural water management 86 (2006) 102–113

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Evaluation of urea–ammonium–nitrate fertigation withdrip irrigation using numerical modeling
Blaine R. Hanson a, Jirka Šimůnek b, Jan W. Hopmans a,*ab

LAWR, University of California, 123 Veihmeyer Hall, Davis, CA 95616, United States
Environmental Sciences, University of California, Riverside, CA, United Statesarticle info

abstract

Article history:

Microirrigation with fertigation provides an effective and cost-efficient way to supply water

Accepted 12 June 2006

and nutrients to crops. However, less-than-optimum management of microirrigation sys-

Published on line 30 August 2006

tems may cause inefficient water and nutrient use, thereby diminishing expected yield
benefits and contributing to ground water pollution if water and nitrogen applications are

Keywords:

excessive. The quality of soils, ground, and surface waters is specifically vulnerable in

Irrigation

climatic regions where agricultural production occurs mostly by irrigation such as in

Nitrogen management

California. Robust guidelines for managing microirrigation systems are needed so that

Microirrigation

the principles of sustainable agriculture are satisfied. The main objective of this research

Nitrate leaching

was to use an adapted version of the HYDRUS-2D computer model to develop irrigation andfertigation management tools that maximize production, yet minimize adverse environmental effects. This software package can simulate the transient two-dimensional or axisymmetrical three-dimensional movement of water and nutrients in soils. In addition, themodel allows for specification of root water and nitrate uptake, affecting the spatial
distribution of water and nitrate availability between irrigation cycles. Recently, we analyzed four different microirrigation systems in combination with five different fertigation
strategies for various soil types using a nitrate-only fertilizer, clearly demonstrating theeffect of fertigation strategy on the nitrate distribution in the soil profile and on nitrateleaching. In the present study, the HYDRUS-2D model was used to model the distribution ofsoil nitrogen and nitrate leaching using a urea–ammonium–nitrate fertilizer, commonlyused for fertigation under drip irrigation. In addition, the distribution of phosphorus andpotassium was modeled. Model simulations are presented for surface drip and subsurface
drip tape, each associated with a typical crop in California.
# 2006 Elsevier B.V. All rights reserved.

1.

Introduction

Microirrigation with fertigation provides an effective and costefficient way to supply water and nutrients to crops (BarYosef, 1999). However, less-than-optimum management of
microirrigation systems resulting in excessive water andnitrogen applications may result in inefficient water andnutrient use, thereby diminishing expected yield benefits andcontributing to ground water pollution. The quality of soils,
ground, and surface waters is specifically vulnerable inclimatic regions where agricultural production occurs mostly
by irrigation, such as in California. Liquid nitrogen (N)fertigation, using mixtures of urea, ammonium, and nitratecompounds, is widely used with microirrigation. Robust
guidelines for managing microirrigation systems are needed
so that the principles of sustainable agriculture are satisfied.

* Corresponding author. Tel.: +1 530 752 3060; fax: +1 530 752 5262.
E-mail addresses: brhanson@ucdavis.edu (B.R. Hanson), Jiri.Simunek@ucr.edu (J. Šimůnek), jwhopmans@ucdavis.edu (J.W. Hopmans).
0378-3774/$ – see front matter # 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.agwat.2006.06.013

agricultural water management 86 (2006) 102–113

The mathematical formulation with corresponding analyticalsolutions of transient transport in soils to include transformation of ammonia and nitrate for steady state water flow waspresented by Misra et al. (1974). Wagenet et al. (1977) extended
the theory to include urea transport, determining the controlof soil oxygen concentration, and initial urea concentration on
urea hydrolysis. The various N transformation processes insoils occur mostly by microbial processes that are predicted byfirst-order reaction kinetics, but are complex because of theircoupled nature and their control by soil environmental
conditions such as soil water and temperature. Nitrogentransport and transformations with transient water flow toinclude plant uptake, nitrification, denitrification, immobilization, mineralization, and ionic exchange was modeled forthe first time by Selim and Iskandar (1981) by simultaneously
solving the transport equations for the different N species withthe purpose to evaluate nitrogen fate for a wide range of
nitrification rate, ammonium retardation and N-uptake
values. Other one-dimensional models, that were specificallydeveloped for N-transport in soils, include the simulation
model by Tanji et al. (1981), DAISY (Hansen et al., 1990),
LEACHN (Hutson and Wagenet, 1991), COUP (Jansson andKarlberg, 2001), and the lumped parameter model LPM (Lingand El-Kadi, 1998).
While high field-scale uniformity is possible under microirrigation, the distribution of both water and nitrate about thedrip line is very nonuniform. Both soil water content andchemical concentration will be the highest near the drip line
after application, but water and chemicals will redistribute
thereafter as controlled by soil physical properties. Because of
the typical nonuniform wetting patterns, it is essential to use
multi-dimensional modeling to develop optimal fertigation
practices for optimum nutrient use efficiency. In the absenceof experimental data, we can use mathematical solutions of
the governing multi-dimensional water and nutrient transport
equations to evaluate the multi-dimensional aspects of nitratefertigation. Yet, few computer simulation models have thecapability to analyze water flow and nutrient transport in
multiple spatial dimensions, with the exception of HYDRUS2D (Somma et al., 1998; Šimůnek et al., 1999; Cote et al., 2003)
and FUSSIM2 (Heinen, 2001). The HYDRUS model allows for
specification of root water and nitrate uptake, affecting the
spatial distribution of water and nitrate availability between
irrigation cycles. As documented by Weinbaum et al. (1992)
and later by Hopmans and Bristow (2002), few studies
evaluated the interrelationships between rates and spatial
distribution of N application, root distribution and growth, andtotal plant uptake. Most recently, a first step in this general
direction was achieved by Gärdenäs et al. (2005), where four
different microirrigation systems were analyzed in combination with five different fertigation strategies for various soil
types, clearly demonstrating the effects of root distribution
and fertigation strategy on the uniformity of water andnutrients around drip lines and their effects on water drainage
and associated nitrate leaching.
In concept, the rhizosphere dynamics of water and nutrient
uptake is very complex, and may have to consider differentiation between passive and active nutrient uptake, while
including N mineralization (Bar-Yosef, 1999), denitrification
and rhizosphere acidity (Pierre and Banwart, 1973). In order to103

not be overcome by these many complications of which therelative magnitude and relevance is yet to be determined, thisstudy makes the typical assumption that root uptake ofammonium and nitrate is strictly passive and assumes thatthe other listed mechanisms are not occurring.
The main objective of this study was to use a state-of-theart modeling tool to evaluate irrigation and fertigation
practices. For that purpose we applied the HYDRUS-2D model(Šimůnek et al., 1999) to evaluate the control of fertigation
strategy with microirrigation on both the movement and fateof a liquid urea–ammonium–nitrate fertilizer, mixed withphosphorus and potassium in the irrigation water for two
commonly used microirrigation systems.

2.

Materials and methods

The modeling of water flow and fertigation scenarios was
conducted using an adapted version of the computer simulation model HYDRUS-2D (Šimůnek et al., 1999). This software
package can simulate the transient two-dimensional or axisymmetrical three-dimensional movement of water andnutrients in soils. In addition, the model allows for specification of root water and nitrate uptake, affecting the spatial
distribution of water and nitrate availability between irrigation cycles. The database of the model contains the values ofthe parameters specifying the hydraulic properties for thevarious soil types that are required for the simulation model.
For each soil type and emitter type, the spatial patterns ofwater content and nitrate concentration were determined forvarious fertigation strategies. These strategies included
different nutrient injection durations, different injection
times relative to the irrigation set time, and different
concentrations. Model simulations will be presented for two
different pressurized irrigation systems, each associated witha typical crop and representing two commonly used microirrigation systems in California: surface drip (DRIP; grape) andsubsurface drip tape (SUBTAPE; processing tomatoes).

2.1.

Modeling domain and nitrogen reactions

The irrigation layouts for the two selected microirrigation
systems with characteristic dimensions, including emitterand irrigation line spacing, are presented in Fig. 1, whereas
relevant irrigation application and model parameters arepresented in Table 1. DRIP (Fig. 1A) is considered a point source
so that axisymmetric-radial geometry is assumed, whereas
the SUBTAPE (Fig. 1B) layout was simulated using the linesource model with a rectangular geometry, because of themultiple outlets along the tape. The model domain for thesemicroirrigation system layouts represents the area exploredby roots, based on field measurements and experience (Bassoi
et al., 2003; May and Hanson, 2005). More detailed information
about the simulation model and model parameters can befound in Gärdenäs et al. (2005).
Irrigation water concentrations of phosphorus and potassium were 1.0 M L3, while applied irrigation water concentrations for urea, ammonium, and nitrate were 0.5, 0.25, and0.25 M L3, respectively, with nitrogen concentrations corresponding to the proportion of nitrogen in the fertilizer solution

104

agricultural water management 86 (2006) 102–113

Fig. 1 – Simulation domains for: DRIP (A) and SUBTAPE (B).

consisting of 16.5% urea nitrogen, 7.4% ammonium nitrogen,and 7.4% nitrate nitrogen. These input concentrations
expressed in M L3 allows for general use of the model.
Specifically, input concentrations can be multiplied with fieldapplied amounts at equal proportions, so that simulated andexperimental results can be compared. Using these proportional concentrations, it should be clear that the total nitrateconcentration in the soil solution can never be higher than
1.0 M L3, irrespective of transformations between N species.
HYDRUS-2D allows simultaneous simulation of multiple
solutes that can be either independent of each other (P and/or
K) or subject to the first-order degradation reactions (nitrogenspecies). The first-order decay chain of urea is described asfollows (Tillotson et al., 1980):

In this reaction pathway urea is hydrolyzed by heterotrophic bacteria to form ammonium, which is sequentiallynitrified by autotrophic bacteria to nitrite and nitrate, that is
subsequently denitrified to form di-nitrogen (N2 and N2O).
Ammonium is a volatile species that can also be present in thegas phase (gas). Since the nitrification from nitrite to nitrate isa much faster reaction than nitrification of ammonium, both
nitrification reactions are often lumped, thereby neglecting
the nitrite species.

2.2.

Coupled water flow and solute transport equations

The spatial distributions of transient water content andvolumetric flux were obtained using a numerical solution of
the Richards equation:
@uðhÞ
@
¼
@t
@xi

"
Ki j ðhÞ!#@hþ Kiz ðhÞ SðhÞ
@x j(1)where u is the volumetric water content [L3 L3], h the pressure
head [L], S the sink term [L3 L3 T1], representing root water
uptake as a function of spatial position and time, xi (i = 1, 2) the
spatial coordinates [L], t the time [T], and Kij are components of

105

agricultural water management 86 (2006) 102–113

Table 1 – Irrigation system characteristics
DRIP (grape)

SUBTAPE (tomatoes)

Irrigation
Discharge rate, Q0 (L day1)
Irrigation intensity, qo (cm day1)
Irrigation duration, P (days)
Irrigation interval, DP (days)
Emitter (d) and line ðwÞ spacing (cm)Depth of emitter (cm)

90.72
1.63
1.5
3.5
183  304
011.975
2.66
1.15
3.5
30  150
20

Water demand:ET0 (cm day1)
Crop coefficient, Kc

0.7
0.85

0.7
1.06

Simulated domain
Width, W (cm)Radius, R (cm)Depth, Z (cm)

n.a.
90
200

75
n.a.
100

Root water uptake
The critical water pressure heads in Feddes model h1, h2, h3max, h3min, h4 (cm)1, 2, 1000, 1000, 8000

1, 2, 800, 1500, 8000

Root zone
Root distribution model
Maximum rooting depth, zm (cm)Depth with max root density, z* (cm)
Maximum lateral root extension, rm (cm)Distance r with max root density, r* (cm)Non-symmetry coefficients, pz and pr

Vrugt model
90
0
90
0
1.0,1.0

Vrugt model
100
20
75
0
1.0,1.0

n.a., not applicable.

the hydraulic conductivity tensor K [L T1] defined as the
product of the relative hydraulic conductivity, Kr(h), and thesaturated hydraulic conductivity tensor, Ks [L T1]. Since in our
simulations we assume that the porous medium is isotropic,
the saturated hydraulic conductivity tensor has the off-diagonal entries equal to 0 and the diagonal terms equal to thesaturated hydraulic conductivity, Ks [L T1]. The Richards
equation was solved using HYDRUS-2D that provides numerical solutions for both two-dimensional (SUBTAPE) and axisymmetrical three-dimensional (DRIP) problems (Gärdenäs
et al., 2005).
The partial differential equations governing two-dimensional nonequilibrium chemical transport of solutes involvedin a sequential first-order decay chain during transient waterflow in a variably saturated rigid porous medium are:
@uc1
@s1
@
þr
¼
@xi
@t
@t

uDi j;1

@c1
@x j

!


@qi c1@xi

 mw;1 uc1  ms;1 rs1  Scr;1
@uck
@s
@
þr k ¼@xi@t@tuDi j;k

@ck
@x j

!


(2)

@qi ck mw;1 uck  ms;k rsk@xiþ mw;k1 uck1 þ ms;k1 rsk1  Scr;k ;k e ð2; ns Þ

(3)where c and s are solute concentrations in the liquid [M L3]and solid [M M1] phases, respectively; qi the ith component of
the volumetric flux density [L T1], mw and ms first-order rate
constants for solutes in the liquid and solid phases [T1],
respectively, providing connections between individual chain
species, r the soil bulk density [M L3], S the sink term
[L3 L3 T1] in the water flow equation (Eq. (1)), cr the concentration of the sink term [M L3], Dij the dispersion coefficienttensor [L2 T1] for the liquid phase, subscript k the kth chain
number, and ns is the number of solutes involved in the chain
reaction. The last term in both equations represents passive
nutrient uptake through the product of root water uptake, S,
and species concentration.
The adsorption isotherm relating sk and ck is described by alinear equation of the formsk ¼ Kd;k ck(4)where Kd,k [L3 M1] is the distribution coefficient of species k.
Eq. (2) represents either the first species in the chain
reaction (urea) or an independent species (P and K), while
Eq. (3) represents second and other solutes in the sequential
first-order decay chain (ammonium and nitrate). Note that thefirst-order decay coefficient m acts as sink in Eq. (2) and as asource in Eq. (3). Relative concentrations can be used since alltransport and reaction parameters (Kd, m) are concentration
independent and thus both transport equations are linear.

2.3.

Parameter values and boundary conditions

2.3.1.

Parameter values

Urea (Eq. (2)), ammonium and nitrate (Eq. (3)) were considered
for the nitrogen species simulations. While urea and nitrate
were assumed to be present only in the dissolved phase (i.e.,
Kd = 0 cm3 g1), ammonium was assumed to adsorb to the solid
phase using a distribution coefficient Kd of 3.5 cm3 g1. Similarvalues were reported in the literature: Kd = 3–4 cm3 g1 by Lotseet al. (1992), Kd = 1.5 cm3 g1 by Selim and Iskandar (1992), and
Kd = 3.5 cm3 g1 by Ling and El-Kadi (1998). The first-order decaycoefficient mw for urea, representing hydrolysis, was set to be106

agricultural water management 86 (2006) 102–113

0.38 day1. Again, similar values were used in the literature, forexample by Ling and El-Kadi (1998) who considered hydrolysis
to be in the range of 0.36, 0.38, and 0.56 day1. Nitrification fromammonium to nitrate was modeled using the rate coefficient of
0.2 day1, which represents the center of the range of values
reported in the literature, e.g., 0.2 day1 by Jansson and Karlberg(2001), 0.02–0.5 day1 by Lotse et al. (1992), 0.226–0.432 day1 bySelim and Iskandar (1992), 0.15–0.25 day1 by Ling and El-Kadi(1998), and 0.24–0.72 day1 by Misra et al. (1974). Volatilization ofammonium and subsequent ammonium transport by gaseous
diffusion was neglected.
Although HYDRUS-2D allows for denitrification, the presented simulations did not account for any denitrification to
occur. Although we included denitrification initially, results
were unsatisfactory because of the large sensitivity of
denitirification rates on the model results; yet little information on denitrification rate as a function of the soil moistureregime under drip irrigation is available. Therefore, denitrification was not considered at this time.
There is also relatively large uncertainty concerning thevalues of the distribution coefficients for phosphorus andpotassium. In our simulations we used values derived fromSilberbush and Barber (1983), i.e., Kd = 59.3 cm3 g1 for phosphorus and 28.7 cm3 g1 for potassium. For phosphorus, this isin the range of 19 cm3 g1 reported by Kadlec and Knight (1996)
and of 185 cm3 g1 reported by Grosse et al. (1999). We
assumed that the bulk density was equal to 1.5 g cm3, thelongitudinal dispersivity was equal to 5 cm, with the transverse dispersivity being one-tenth of the longitudinal dispersivity, and neglected molecular diffusion as it wasconsidered negligible relative to dispersion.

2.3.2.

Initial and boundary conditions

Each of the fertigation scenarios was preceded by 56 days offlow-only simulations, to approach a ‘pseudo-equilibrium’
condition before irrigation with fertigation started. This wasdone to ensure that the initial soil water regime was not a
factor in the transport and leaching predictions (Gärdenäs
et al., 2005). The initial condition for this initialization period
was set to a uniform soil water pressure head of 400 cm. The
soil hydraulic parameters of the van Genuchten (1980) modelfor the loam were taken from Carsel and Parrish (1988). The
transport domain was considered to be solute free at the
beginning of the fertigation simulation.
All boundaries were assumed to be no flow boundaries withthe exception of the bottom of the soil profile and the boundary
representing the irrigation device. A unit gradient boundary
condition for water flow and the Neumann boundary condition
for solute transport were used at the bottom of the soil profile.
System dependent boundary conditions representing irrigation
devices were described in detail by Gärdenäs et al. (2005) and arelisted in Table 1. The selected parameters for the Feddes et al.
(1978) water stress response function were taken from van Dam
et al. (1997), and are presented in Table 1 as well. Root
distribution in the soil profile was assumed to be describedusing Vrugt’s model (Vrugt et al., 2001). The values of the root
distribution parameters in Table 1 reflect typical root systems
for the two irrigated cropping systems and were introduced byGärdenäs et al. (2005) to represent maximum rooting depths ofabout 100 cm.

2.3.3.

Irrigation system parameters

The irrigation requirement, Qreq (L day1), was computed fromthe crop-specific potential evapotranspiration (ETc) (cm day1)
and the irrigated soil area, A ¼ dw, where d (cm) and w (cm)represent emitter distance and irrigation line distance,
respectively. Selected ETc values are typical values for
California irrigated crops. The model also included anevaporation component for the DRIP simulations (Gärdenäs
et al., 2005). The applied irrigation volume per irrigation cycle, I[cm3], was estimated for each crop from Qreq, the irrigationinterval, DP [days], and the irrigation efficiency, fi. For all
irrigation systems, we assumed an irrigation efficiency of 85%(Hanson, 1995). Thus, plant water uptake was less than theapplied water for all scenarios. Finally, the irrigation cycle
duration, P (day1), was determined from the total irrigation
volume, I, and the emitter discharge rate, Qo. Specific values
for each of the two studied microirrigation systems arepresented in Table 1.

2.4.

Fertigation scenarios

Similar to the study of Gärdenäs et al. (2005), we considered
three fertigation strategies to evaluate water and nutrient
use efficiency and nitrate leaching. These are based onrecommendations of the microirrigation industry andgrower’s practices. These are (B) fertigation for a total
duration of 2 h, starting 1 h after the beginning of theirrigation cycle; (E) fertigation for a duration of 2 h, starting3 h before the end of the irrigation cycle; and (M50), starting
the first and last 25% of each irrigation with fresh water, andfertigation during the remaining 50% in the middle of theirrigation cycle. The fresh water irrigations prior and after
each fertigation are common practices that ensure uniformity of fertilizer application and flushing of the drip lines.
Each irrigation cycle was simulated for 28 days and included
eight irrigation cycles with fertigation. The irrigation cycle
length (P) and other crop-specific irrigation characteristics
are presented in Table 1.

3.

Results and discussion

The effects of different fertigation strategies on the soil
distribution of urea, ammonium, and nitrate around a drip line
between the first and second irrigation and at the end of thesimulation period are illustrated in Figs. 2–6. The effect of the B
strategy is discussed in detail for the DRIP system for the total
simulation period of 28 days, while only presenting the main
results of the other strategies. Time t = 0 is the start of thefertigation simulation after the 56 days of flow-only simulations. All fertilizer concentrations are expressed as nominal
concentrations, relative to the concentration of the fertilizer in
the irrigation water. The same mass of fertilizer was applied
for each fertigation strategy.

3.1.

Distributions around drip line

3.1.1.

Soil water content

Soil water content at the start of DRIP irrigation was relatively
low near the soil surface (Fig. 2). The water content wasagricultural water management 86 (2006) 102–113

107

Before irrigation with the SUBTAPE system, water content
values were smallest near the surface, decreasing withhorizontal distance from the drip line (Fig. 2). The soil was
slightly wetter at depths below about 35 cm. After irrigation,
most wetting occurred above the 70 cm soil depth andextending to near the soil surface. Horizontal water movement was limited to about 35 cm from the drip line. Soil watercontents beyond 35 cm at the end of the irrigation were thesame as those at the start of irrigation.

3.1.2.

Fig. 2 – Volumetric soil water content distributions at thestart and conclusion of irrigation for DRIP and SUBTAPE
microirrigation systems.

maximum between the 60 and 140 cm soil depth, and wascontrolled by root water uptake. After each irrigation, thewetted region exhibited a vertically elongated pattern andextended to nearly 60 cm horizontally and 100 cm verticallydirectly beneath the emitter. A zone of relatively wet soil
occurred near the surface between 40 and 60 cm from the drip
line. This distinct wetting front position is the combined resultof wetting front advance during irrigation and a decreased root
distribution density away from the drip line.

Fig. 3 – Spatial distributions of potassium and phosphorus
concentration (M LS3) in soil solution at the end of thesimulation period (28 days) for the B strategy of DRIP.

DRIP—BThe contour plots in Figs. 3–6 show the simulated concentrations of nutrients in the soil water. Both potassium andphosphorus were present only immediately adjacent to thedrip line at all times (Fig. 3), independent of irrigation type or
fertigation scenario. This was the case at all times, as both
fertilizers are highly adsorbed by the soil, preventing their
movement further down the soil profile. It should be pointed
out at this time that the model simulations only consideredmatrix flow, thus excluding the possibility of rapid transportof nutrients by preferential flow. The B fertigation strategy
generally resulted in a band of urea along the periphery of
the wetted soil volume (Fig. 4) with little or no urea near the
drip line, except immediately after fertigation (t = 3.63).
There was relatively little change during subsequent irrigation cycles, indicating that little urea accumulation occurredin the soil profile. However, urea concentrations decreased
with time between irrigations as a result of hydrolysis. As
expected, at 3.63 days, the urea was concentrated near the
drip line, immediately after fertigation. Some slight preferential lateral movement occurred, likely because ofoccasional soil surface ponding and larger horizontal water
potential gradients.
As for K and P, ammonium remained concentrated in theimmediate vicinity of the drip line at all times for all fertigation
strategies (Fig. 4). There was only slight movement, because ofsoil adsorption and subsequent fast nitrification and/or root
uptake.
In contrast to ammonium, nitrate moved continuously
downwards during the 28-day simulation period, as nitrate is
not adsorbed, whereas denitrification was assumed negligible.
As expected, high nitrate concentrations occurred near the
drip line immediately after fertigation (t = 3.63) due to nitrate
injection and nitrification, but little nitrate remained near the
drip line at the end of the irrigation (t = 5.00, Fig. 4), because ofroot uptake and dispersion during downward transport. At
this time, most of the nitrate was distributed near the
periphery of the wetted region due to leaching following thefertigation. However, by the start of the next irrigation(t = 7.00), nitrate levels near the drip line increased, the resultof nitrification of ammonium. The relatively high concentration of nitrate near the drip line at t = 7.00 reflected the
distribution of ammonium. Between irrigations, nitrate concentrations near the drip line decreased with time due toredistribution and root water uptake. In general, except for
times immediately after fertigation, nitrate concentrations
were relatively low, with the highest values along the wetting
front. Bands of nitrate reflect the wetting patterns after eachirrigation cycle. At the end of the last irrigation event of thesimulation period, nitrate was distributed throughout the

108agricultural water management 86 (2006) 102–113

Fig. 4 – Spatial distributions of soil solution urea, ammonium, and nitrate (M LS3) for the B strategy of DRIP for various days
during the simulation period. The times (days) correspond to end of first irrigation (1.50), beginning of the second irrigation(3.5), beginning of second fertigation (3.54), end of second fertigation (3.63), end of second irrigation (5.00), beginning ofthird irrigation (7.00), end of last irrigation (26.00), and end of simulation period (28.00).

wetted soil profile to a soil depth of about 150 cm, indicating
potential leaching after 28 days.

3.1.3.

the profile were smaller than those of the B strategy except near
the drip line, where higher concentrations occurred for the E
strategy compared to the B strategy.

DRIP—EIn the case of fertigation at the end of the irrigation cycle (Fig. 5),
urea concentrations were maximum near the drip line withconcentrations decreasing with time between irrigation cycles
as a result of hydrolysis and water redistribution. A noticeablesecond front occurred at a larger depth because of water
movement by irrigation prior to the start of fertigation (t = 4.88).
As before, ammonia concentrations remained high near the
drip line. Nitrate was concentrated near the edge of the wetted
region due to irrigation before fertigation (Fig. 5). After
fertigation (t = 4.96), nitrate was maximum near the drip line,
but then decreased slightly by the end of the irrigation (t = 5.00).
As with the B strategy, nitrate concentrations increased near
the drip line due to ammonium nitrification by the start of thenext irrigation (t = 7.00). At the end of the last irrigation event of
the simulation period, nitrate was distributed throughout thewetted soil profile to a soil depth of about 150 cm, similar to thatof the B strategy. However, nitrate concentrations throughout

3.1.4.

DRIP—M50

Fertigation during the middle 50% of the irrigation event
caused a more uniform and more extended urea distribution
throughout the wetted region compared to the other fertigation strategies (Fig. 5), because of larger fertigation times.
Henceforth, maximum urea concentrations near the drip line
were lower than for the B and E scenarios. Because of its
adsorption, ammonium distributions around the drip line
were similar to those of the other scenarios. As with urea,
nitrate was distributed more uniformly throughout the wetted
region as compared to the other scenarios (Fig. 5). After
fertigation (4.63 days), nitrate concentrations throughout the
profile increased with time, particularly near the drip line asshown for the distribution at 7.00 days. Because of hydrolysis
and nitrification, nitrate accumulated in the soil profile withtime, extending vertically to about 150 cm below the drip line
and 80 cm horizontally by the end of the simulation period.

agricultural water management 86 (2006) 102–113

109

Fig. 5 – Spatial distributions of soil solution urea and nitrate (M LS3) for selected times of the E and M50 strategies of DRIP. For
the E strategy, the times (days) correspond to the beginning of second fertigation (4.88), end of second fertigation (4.96), endof second irrigation (5.00), beginning of next irrigation (7.00), and end of simulation period (28.00). For the M50 strategy, thetimes (days) correspond to the same sequence of events as described for the E strategy.

3.1.5.

SUBTAPE—B, E, and M50

The various species distributions for urea and nitrate for thethree fertigation scenarios are presented in Fig. 6. Overall,results are comparable with the DRIP irrigation system, exceptthat spatial distribution patterns are controlled by the buried
irrigation drip line, thereby carrying ammonia and nitrate tolarger depths. As expected, phosphorus and potassium
remained close to the drip line (results not shown). For the
B strategy, urea and nitrate were moved away from the drip
line during irrigation, whereas both species remained near the

drip line for the E strategy. After irrigation at t = 4.65 days,
nitrate concentrations near the drip line increased due tonitrification. Whereas urea concentrations decreased between
irrigation cycles as a result of hydrolysis, nitrate concentrations accumulated with time throughout the soil profile during
the 28-day irrigation period. Between irrigation events thenitrate concentrations decreased because of root uptake.
The nitrate concentrations below the drip line for the B
scenario were lower than those above the drip line due tocapillary upward movement during irrigation, which was the

110agricultural water management 86 (2006) 102–113

Fig. 6 – Spatial distribution of urea and nitrate (M LS3) for selected times for the B, E, and M50 strategies for SUBTAPE. The
respective times correspond to the beginning of the second fertigation, end of the second fertigation, end of the second
irrigation, beginning of the next irrigation, and end of the simulation period for each fertigation strategy.

agricultural water management 86 (2006) 102–113

opposite for the E strategy. For the M50 strategy, nitrate wasdistributed more uniformly throughout the wetted region ascompared to the B and E strategies (Fig. 6).

3.2.

Mass balance

Since we used dimensional concentrations in our simulations,the dimension of mass in the mass balance calculations areeither [M] for the axi-symmetric geometry of DRIP or [M cm1]for the two-dimensional geometry of SUBTAPE, and includes
the sorbed mass.

3.2.1.

DRIP

The mass balance was conducted for two zones, the upper
100 cm or root zone (zone 1) and the lower 100 cm (zone 2). It
was assumed that the accumulated nitrate in zone 2
eventually will leach out of the simulated soil domain,
because of the absence of roots in zone 2. As expected, theurea mass was maximal at the end of the each fertigation
event, but decreased with time thereafter until the next
fertigation event (Fig. 7), because of subsequent hydrolysis.
The mass values of the first fertigation event reflect mass
ratios of the applied fertilizer mixture. No accumulation of111

urea occurred in the profile and no urea moved to zone 2 as all
urea either converted to ammonium by hydrolysis. The urea
mass was similar for all fertigation strategies. Ammonium
accumulation was limited to zone 1, and no ammonia waspresent in zone 2 because of the relatively quick nitrificationand slow transport due to sorption.
We computed a slight increase in ammonium between
irrigation events, indicating that its supply from fertilizer andurea hydrolysis exceeded removal by plant uptake andnitrification. Typically, the mass of ammonium increased
between the end of the fertigation and the end of the irrigation
during which that fertigation event occurred, due to hydrolysis. In contrast, nitrate accumulated with time for all
fertigation strategies indicating that supply of nitrate by thefertilizer and nitrification of ammonium exceeded removal byplant uptake and leaching. Because of the transport of nitrateby the infiltrating irrigation water, nitrate also accumulated inzone 2 during the second half of the simulation period.
The N mass balance at 28 days is shown in Table 2. More N
root uptake occurred for the E strategy compared to the B and
M50 strategies. The accumulated N pertains to zone 1 only, as
it was assumed that all nitrate in zone 2 (below rooting zone)
will potentially leach. Leached N (below zone 1) was theFig. 7 – Total mass (M) of urea, ammonium, and nitrate with time during the simulation period for the B strategy of DRIP and
for the E strategy of SUBTAPE.

112

agricultural water management 86 (2006) 102–113

Table 2 – Nitrogen mass balance for DRIP and SUBTAPE
microirrigation systems and B (fertigation near beginning of irrigation), E (fertigation near the end of irrigation), and M50 (fertigation during the middle 50% of theirrigation event) fertigation strategies

DRIP
Input (M)Root uptake (M)Accumulated (M)Leached (M)Leached (%)
FUE (%)SUBTAPE
Input (M cm1)
Root uptake (M cm1)
Accumulated (M cm1)
Leached (M cm1)
Leached (%)
FUE (%)

B

E

M50

60400
30600
25272
4120
6.8
50.7

60400
39185
20090
1560
2.6
64.9

60400
33052
24690
3139
5.2
54.7

133
59.7
68.4
5.1
3.9
46.6

133
58.6
70.4
5.1
4.0
45.8

133
57.3
70.4
5.7
4.4
44.8

FUE is the fertilizer use efficiency. M denotes mass of nitrogen.

smallest for the E strategy. The mass balance showed leaching
percentages of 6.8, 2.6, and 5.2% for the B, E, and M50
fertigation strategies, respectively. These leaching percentages were slightly lower than those found using a nitrate-only
fertilizer (Gärdenäs et al., 2005). As expected, no leaching ofammonium or urea took place.
The fertilizer use efficiency (FUE), calculated as the ratio of
the mass of N uptake to the mass applied, ranged from 50.7 to
64.9% (Table 2). The E scenario showed the highest efficiency
and the B strategy was the lowest.

3.2.2.

SUBTAPE

For the SUBTAPE irrigation system, the soil profile was split
into three zones: zone 1 above the drip line, zone 2 below the
drip line to the 75 cm soil depth, and zone 3 the bottom 25 cmof the soil profile. It was assumed that the accumulated nitrate
in zone 3 would eventually leach out of the simulated soil
domain because of the lack of roots in zone 3. The urea massdecreased with time following fertigation, however, more urea
was found in zone 2 compared to zone 1 (Fig. 7), because of thelocation of the subsurface tape. No urea was present in zone 3.
Both ammonium and nitrate mass accumulated during thesimulation period, with more mass in zone 2 than in zone 1.
This behavior occurred for all fertigation strategies. No
ammonium was present in zone 3. Nitrate leached into zone
3 near the end of the simulation period. Urea, ammonium, andnitrate masses were higher in zone 1 and lower in zone 2 for
the B strategy as compared to the E and M50 strategies. This
result reflects the increased opportunity for upward flow ofwater and dissolved N species by capillarity near the beginningof irrigation of the B scenarios.
The results of the mass balance at 28 days (Table 2)
indicated similar N uptake for all fertigation strategies.
Accumulated and leached masses were also similar for all
strategies. Leaching percentages were 3.9, 3.9, and 4.4% for the
B, E, and M50 fertigation strategies, respectively. FUE’s were
nearly equal between strategies (44.8–46.6%), with slightdifferences caused by upward movement above the drip line.

4.

Conclusions

We conclude that the HYDRUS-2D computer simulation modelis an effective modeling tool for assessing fertigation
strategies using a urea–ammonium–nitrate fertilizer commonly used for fertigation with microirrigation. The model
described the movement of urea, ammonium, and nitrateduring irrigation and accounted for the reactions of hydrolysis,
nitrification, and ammonium adsorption.
In contrast to the previous study (Gärdenäs et al., 2005)
which used a nitrate-only fertilizer, the model showed that aurea–ammonium–nitrate fertilizer increased the nitrate concentration near the drip line, an area where root density isgreatest and most of the plant root uptake of nitrate takes
place. This was also the case for the B strategy with a long
irrigation after fertigation. Nitrification of ammonium maintained nitrate concentrations near the drip line compared to
the nitrate-only fertilizer, in part caused by the sorption ofammonium prior to nitrification, thereby delaying downward
transport of soil nitrate.
The results also showed that urea moves readily with theinfiltrating irrigation water, potentially moving this nitratesource away from the soil zone with maximum root density.
For all strategies, urea did not accumulate in the soil profile,
but quickly decreased with time after fertigation by hydrolysis
and associated conversion to ammonium. Because of its
adsorption to the soil, most of the ammonium remained near
the drip line, with low concentrations near the edge of thewetting zone.
Nitrate mass accumulated in the soil profile, moving down
to depths deeper than 150 cm for the DRIP system and deeper
than 100 cm for SUBTAPE. Higher nitrate mass occurred above
the drip line for the B strategy compared to the other strategies
for SUBTAPE. The leached nitrate mass was smallest for the E
fertigation strategy and largest for the B strategy for the DRIP
system. No trends were clearly determined for any fertigation
strategy for the SUBTAPE irrigation system, mainly due toupward flow and associated movement of N species above thedrip line.
Slightly smaller leaching percentages were computed forthe urea–ammonium–nitrate fertilizer compared to thenitrate-only fertilizer. Fertilizer use efficiency ranged from
50.7% (B strategy) to 64.9% (E strategy) for DRIP and was about
44–47% for SUBTAPE. Based on these results we conclude that
fertigations consisting of short injection times near the
beginning of long irrigation events should be avoided forsurface drip systems. The fertigation strategy is less of a factor
for subsurface drip systems.
For the presented irrigation scenarios the position of thedrip lines coincided with the plant rows. Thus, the input root
distributions reflect typical wetting patterns as determinedfrom field data, with maximum soil water content and root
density near the drip lines and decreasing with distance anddepth from the drip line. For other scenarios where drip lines
are placed away from the plant rows, we expect different
spatial distributions of roots and soil water content, as roots
will adapt to changing soil water regimes. An additional
limitation of our model results comes about from theabsence of denitrification. The disregard of denitrification

agricultural water management 86 (2006) 102–113

was intentional as there is no information available on
denitrification rates for soil moisture regimes under microirrigation. Nevertheless, our simulation results provide
guidance on the appropriate fertigation strategy for many
typical microirrigation scenarios.

Acknowledgement
We acknowledge funding by the California FREP, Fertilizer
Research and Education Program.

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