Agricultural Water Management 98 (2011) 1431–1440

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

Evaluation of fertigation scheduling for sugarcane using a vadose zone
ﬂow and transport model
V. Ravikumar a,∗ , G. Vijayakumar a , J. Šimůnek d , S. Chellamuthu a , R. Santhi b , K. Appavu caWater Technology Centre, TNAU, Coimbatore 641003, India
Department of Soil Science & Agricultural Chemistry, TNAU, Coimbatore 641003, IndiacCentre for Natural Resources Management, TNAU, Coimbatore 641003, IndiadDep. of Environmental Sciences, University of California Riverside, Riverside, CA 92521, United Statesba r t i c l e

i n f oArticle history:
Received 27 January 2011
Accepted 27 April 2011
Available online 20 May 2011
Keywords:
Drip irrigation
Fertigation
Modelling
Sugarcane
HYDRUSa b s t r a c t
Micro-irrigation has become an optimal means for providing water and nutrients to crops. There is anample space for improving fertilizer use efﬁciency with micro-irrigation, if the movement and reactions offertilizers in the soil are well understood. However, the rhizosphere dynamics of nutrients is very complex,
depending on many factors such as soil temperature, pH, water content, and soil and plant characteristics. Many factors cannot be easily accurately quantiﬁed. However, using state-of-the-art modelling
techniques, useful and reliable information can be derived.
An attempt was made to evaluate the reactive transport of urea in the root zone of a sugarcane cropunder drip irrigation, and to quantify the ﬂuxes of urea, ammonium, and nitrate into the crop roots,
volatilization ﬂuxes, and deep drainage using a numerical model. This quantiﬁcation helped in designing
an optimal fertigation schedule. Various parameters used in the model were taken from either the literature or the ﬁeld study. A typical scenario, based on the recommended total quantity of urea for sugar
cane crop under drip irrigation in India, was tested using HYDRUS-2D. The total amount of urea wasdivided into fortnightly doses, depending on the stage of crop growth. For this scenario, the modelledcrop uptake was found to be 30% higher than the crop demand. Consequently, an optimal fertigation
schedule was developed that reduced the use of urea by 30% while at the same time providing enough
N for its assimilation at all stages of crop growth. This type of modelling study should be used before
planning ﬁeld experiments for designing optimal fertigation schedules.
© 2011 Elsevier B.V. All rights reserved.

1. Introduction
Micro-irrigation has become an optimal means for providing
water and nutrients to crops. In countries where the cost of water isvery low, such as India, the adoption of micro-irrigation has initiallybeen very slow. Recently however, drip irrigation combined withfertigation has been found to beneﬁt farmers because of the very
high efﬁciency of fertilizer use for such irrigation schemes. There isan ample scope for improving the efﬁciency of fertilizer use throughfertigation, if the movement and reactions of fertilizers in the soil
are well understood.
Simple conventional fertilizers containing nitrogen, phosphorous, and/or potassium can be applied using drip irrigation if they
are soluble in water. Due to the lower solubility of phosphate fertilizers, the practice of using fertigation for phosphorous is lesscommon. Potash fertilizers are better soluble than phosphorous,∗ Corresponding author. +91 9865113161.
E-mail address: veeravikumar@hotmail.com (V. Ravikumar).
0378-3774/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.agwat.2011.04.012

and therefore farmers use fertigation for potash fertilizers to someextent. The chief source of nitrogenous fertilizers is urea. Urea isquite soluble in water, and thus fertigation with urea is very popular among farmers. Urea is a highly reactive fertilizer and begins
reacting immediately after its dissolution in water. First, urea isnitriﬁed into ammonium, and subsequently, into nitrate (Fig. 1).
While urea is electrically neutral, ammonium ions are positively
charged and hence adsorb to the negatively charged clay particles
well. Consequently, the leaching of ammonium ions from the soil
is signiﬁcantly reduced. In the soil, ammonium is converted into
nitrate, which is a negatively charged ion. Therefore, nitrate does
not adsorb to clay particles and hence the possibility of nitrateleaching to groundwater is very high. Plant roots absorb nitrogenin all three nitrogen forms: urea, ammonium, and nitrate. Somequantity of ammonium also gets volatilized into ammonia gas.
Ammonia volatilization is highly dependent on soil pH and soil wetness. Under anaerobic conditions, nitrate can also be denitriﬁed into
nitrous oxide. However, in the case of drip irrigation, the processof denitriﬁcation can be neglected, because most of the time soil is
not under saturation.

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V. Ravikumar et al. / Agricultural Water Management 98 (2011) 1431–1440

Ammonia
volatilization

Urea
Input

Ammonium

Urea

Root
UptakeLeaching

Root
UptakeLeaching

NitrateRoot
UptakeLeaching

Fig. 1. Urea transformations and fate in soils.

Cumulative N assimilation

Fertigation scheduling is the amount of fertilizer to be applied
at any point in time so that before the next fertigation the plant
has been able to assimilate a sufﬁcient quantity of the fertilizer.
Fig. 2 shows a typical cumulative N assimilation by plants withrespect to days after planting. For instance, let us assume that during the time period between t1 and t2 , sugarcane plants in an area
assimilates 20 kg/ha of nitrogen. Let us also assume that during
this time period, one can expect 4 kg/ha of volatilization loss and1 kg/ha of deep drainage loss. If, in this situation, 25 kg/ha of nitrogen is applied at time t1 , 20 kg/ha of nitrogen will be available forthe plant in the root zone. This method of applying fertilizers iscalled a “growth curve nutrition approach”. Butler et al. (2002) haveadopted a growth curve nutrition approach for fertigation scheduling for sugarcane. One disadvantage of this approach is that it does
not take into account the carry-over of a nutrient from previous
periods. Additionally, for the situation discussed above, the spatial
and temporal distribution of urea, ammonium, and nitrate may besuch that less than 25 kg/ha of nitrogen can be taken up by the roots.
Therefore, a certain quantity of excess nitrogen must be applied inorder to provide sufﬁcient amount of nitrogen to meet assimilation
requirements.
Numerical simulations of water ﬂow and urea-ammoniumnitrate reactions and transport in the vadose zone, while accounting
for root water and nutrient uptake, can help in understanding of
the dynamic processes in the vadose zone. Speciﬁcally, it would bepossible to account for the carry-over of nutrients from previous
periods to the current fertigation period. Such a modelling study
could lead to an optimal scheduling of nutrient applications for any
time period. This is the motivation for the present work.

∆N

Extensive ﬁeld experiments were conducted to understand themechanisms involved in the movement and transformations of various nitrogen forms and to improve the fertigation strategies by,for example, Thorburn et al. (2003), Li et al. (2004), and Rajput
and Patel (2006). On the other hand, Heinen (2001) demonstrated
numerically using the FUSSIM2 model that the number of fertigation treatments could be signiﬁcantly reduced when planningthe fertigation experiments. Similarly, HYDRUS-2D (Šimůnek et al.,2006) has been used extensively for evaluating short term nitrogen
fertigation strategies and the effects of soil hydraulic properties, soil
layering, dripper discharge rates, irrigation frequency, and timingof nutrient applications on wetting patterns and solute distribution(e.g., Cote et al., 2003; Gärdenäs et al., 2005; Ajdary et al., 2007;
Patel and Rajput, 2008). Hanson et al. (2006) also used HYDRUS-2D
for developing short term fertigation strategies while accounting
for transformations of urea in soil. Additionally, Mmolawa and Or(2003) developed a semi-analytical model for predicting the movement of nitrates under plant uptake conditions. They compared theresults of their semi-analytical model with the HYDRUS-2D modeland with the ﬁeld data and concluded that both models performed
well. Finally, Šimůnek et al. (2008) provided a long list of references,in which HYDRUS had been validated for drip irrigation and otherapplications.
Nutrient dynamics in the rhizosphere is very complex anddepends on many factors, such as soil temperature, pH, water content, and soil and plant characteristics. In addition, the temporaland spatial variations of these factors are highly dynamic. Many factors cannot be accurately quantiﬁed easily. At the same time, whenreviewing the literature, it becomes clear that with state-of-theart modelling techniques, useful and reliable information can bederived about rhizosphere processes. Many of the references cited
above dealt only with short term fertigation management strategies. We could not come across any literature using HYDRUS forlong term fertigation scheduling. The main objective of this study isthus to develop an optimal urea fertigation schedule for a sugarcane
crop grown under drip irrigation in sandy clay loam soil for a site
speciﬁc climatic conditions (Coimbatore, India) using HYDRUS-2D(Šimůnek et al., 2006).

2. Materials and methods
2.1. The HYDRUS-2D softwaret1

t2

Days after Planting
Fig. 2. A typical N assimilation curve.

Water ﬂow and fertilizer movement was simulated using
the HYDRUS-2D software. This software can simulate the transient two-dimensional movement of water and the transport andreactions of adsorbing nutrients in soils. The model allows forV. Ravikumar et al. / Agricultural Water Management 98 (2011) 1431–1440

speciﬁcation of root water uptake and evaporation from the soil
surface. The model is capable of simulating spatial and temporalvariations of water content and nutrient concentrations in the rootzone. The model is further capable of accounting for transformations of urea to ammonium, ammonium to nitrate, and ammonia
volatilization in soils. The present version of HYDRUS has several
limitations for evaluating fertigation scheduling: the spatial distribution of roots is constant in time and their dynamic growth cannot
be considered, only passive uptake of nutrients can be consideredwhen more than one solute is simulated, and temporal variabilityof surface ponded radius is not accounted for (see Gärdenäs et al.,2005; Hanson et al., 2006). Active nutrient uptake can be considered only in the recent version of HYDRUS and only for one solute(Šimůnek and Hopmans, 2009), while in this study we consider
three solutes simultaneously (i.e., urea, ammonium and nitrate).
However, these limitations are not prohibitive for using HYDRUS
to evaluate different fertigation schedules.
Sugarcane is an annual crop. The crop harvested after the ﬁrst
planting is called plant sugarcane. During the ﬁrst harvest of theplant, the root portion of the cane is left in the soil and only theshoot portion is harvested. The new shoots then develop from theremaining root portion. These new shoots are called ratoon sugarcane and are normally harvested for two to ﬁve years. Hence, theassumption of not considering the dynamic root growth during thecrop season of ratoon sugarcane may not affect the results much.
Root interception, mass ﬂow, and diffusion are the three mainprocesses by which nutrients are taken up by plants (e.g., Šimůnek
and Hopmans, 2009). However, Nitrogen uptake by sugarcane cropis up to 99% through mass ﬂow (Netaﬁm, 2011). Since most of
the nitrogen uptake by sugarcane is by mass ﬂow, the assumption of passive uptake in HYDRUS also does not represent a major
constraint.
Finally, to overcome the last limitation, the average ponded
surface area for a speciﬁc soil and dripper discharge rate wereexperimentally found and used in simulations.

Location ofDripper &
Plant

20
cm

55
cm

Variable flux
Boundary

Atmospheric
Boundary75

No Flow
Boundary

Free Drainage

Fig. 3. Modelled transport domain and boundary conditions.

van Genuchten-Mualem model (van Genuchten, 1980), which isdeﬁned as follows:(h) = r +s − r

n m

for h < 0

(1 + ˛h )(h) = s

The transport domain, 75 cm wide and 75 cm deep, consideredin numerical simulations is shown in Fig. 3. The soil textural classin the study area is sandy clay loam. A time-variable ﬂux boundary condition was applied at the left section of the soil surface torepresent drip irrigation. This boundary condition was switched tothe atmospheric boundary condition during periods without irrigation. The atmospheric boundary condition was also consideredon the remainder of the soil surface. Other boundary conditions areshown in Fig. 3. The free drainage boundary was assumed to havea unit hydraulic gradient.

1/m m

K(h) = Ks Sel (1 − (1 − Se

2.3. Coupled water ﬂow and solute transport equations
The spatial distribution of transient water contents and pressure heads was obtained using a numerical solution of the Richards’
equation:(1)

where  is the volumetric water content (cm3 /cm3 ), K is the unsaturated hydraulic conductivity (cm/d), H is the hydraulic head (cm),and Sw is a sink term, accounting for plant water uptake (1/d),  isthe spatial gradient operator, and t is time (d).
The analytical model describing the unsaturated retention andhydraulic conductivity functions adopted in this work is the

m=1−

1
;
n

(2)

for h ≥ 02

) )

 − rSe =s − r2.2. Modelled transport domain and boundary conditions∂= ∇ · (K · ∇ H) − Sw
∂t

1433

(3)
(4)

n>1

(5)

where (h) and K(h) are volumetric water contents (cm3 /cm3 ) andunsaturated hydraulic conductivities (cm/d) at the soil water pressure heads of h (cm), respectively;  r and  s denote residual andsaturated water contents (cm3 /cm3 ), respectively; Se is the effective saturation, Ks is the saturated hydraulic conductivity (cm/d),
˛ is the inverse of air-entry value or (bubbling pressure (1/cm), n
is the pore size distribution index, and l is the pore connectivity
parameter.
The solute transport equation solved for each chemical species
is as follows:
For urea:∂c1= ∇ · (D∇ c1 ) − ∇ · (qc1 ) − a c1 − Sw c1∂t(6)

For ammonium:∂c2∂s2=∇ · (D∇ c2 )−∇ · (qc2 )−v c2 −n c2 +a c1 −Sw c2 (7)+∂t∂t
For nitrate:∂c3= ∇ · (D∇ c3 ) − ∇ · (qc3 ) + n c2 − Sw c3∂t(8)

where ci is the liquid phase concentration of the chemical
species i (subscripts 1, 2, and 3 represent urea, ammonium, andnitrate, respectively) (g/cm3 ), D is the dispersion coefﬁcient tensor (cm2 /day), q is the volumetric ﬂux density (cm/day),  is thebulk density of the soil (g/cm3 ), s2 is the adsorbed concentrationof ammonium (g/g), a is the ﬁrst-order reaction rate constant(1/d) representing nitriﬁcation of urea to ammonium, v is theﬁrst-order reaction rate constant (1/d) representing volatilizationof ammonium to ammonia and n is the ﬁrst-order reaction rate
constant (1/d) representing nitriﬁcation of ammonium to nitrate.
The relationship between ammonium in solution (c2 ) andadsorbed (s2 ) is described as follows:
S2 = Kd c2(9)where Kd is the distribution coefﬁcient for ammonium (cm3 /g).
The dispersion tensor has the following components:
Dxx = εLq2q2x+ εT z + D0
|q|
|q|

q2z
q2
+ εT x + D0
|q|
|q|
qx qz
Dxz = (εL − εT )|q|Dzz = εL(10)

where |q| is the absolute value of the volumetric ﬂux density (cm/d),qx and qz are the volumetric ﬂux densities in x and z directions(cm/d), εL and εT are the longitudinal and transverse dispersivities(cm), respectively, D0 is the coefﬁcient of the molecular diffusion forsolute in free water (cm2 /d), and  is the tortuosity factor. The longitudinal dispersivity along the direction of ﬂow is taken as 5 cm andthe transverse dispersivity is taken as 0.5 cm. Molecular diffusion
is neglected.
Eqs. (1), (6), (7), and (8) are coupled equations that are solved
sequentially. Solution of Eq. (1) provides the spatial and temporal distributions of water content (). The root uptake term (Sw ) is
also obtained when solving Eq. (1). The reaction rate constants (a ,v , and n ) and the distribution coefﬁcient for ammonium (Kd ) areconcentration independent and hence Eq. (6) through (8) are linear equations. When solving Eqs. (6) through (8), the distributionof  and Sw is known and the unknowns are the solute concentrations, namely concentrations of urea (c1 ), ammonium (c2 ), andnitrate (c3 ), respectively. The ﬁrst-order reaction term representing nitriﬁcation of urea to ammonium (a ) acts as sink in Eq. (6)and as source in Eq. (7). Similarly, the ﬁrst-order reaction term representing nitriﬁcation of ammonium to nitrate (n ) acts as sink in
Eq. (7) and as source in Eq. (8). The last terms in Eqs. (6) through (8)are the products of root water uptake (Sw ) and concentrations ofrespective species, and hence represent the passive uptake of urea,
ammonium, and nitrate, respectively.
2.4. Estimation of evaporation and transpiration
Calculations are carried out for Coimbatore, in the western partof the southernmost state of India Tamil Nadu. The geographic location of Coimbatore is 11◦ 01 N and 76◦ 58 E and has an altitude ofabout 398 m. Coimbatore has a tropical wet and dry climate. It
gets most rainfall during two monsoons. The South West monsoon
comes from June to August. After a warm, humid September, theNorth East monsoon comes from October till early December. The
average annual rainfall is around 700 mm, with the South Westand North East monsoons contributing 28 and 47%, respectively,
to the total rainfall. Fig. 4 provides monthly climatic variations at
Coimbatore.
HYDRUS needs as input potential evaporation from the soil surface and potential transpiration through plants. Both evaporationfrom the soil surface and transpiration by plants were calculated ona daily basis using the dual crop coefﬁcient approach of Allen et al.
(1998). In the dual crop coefﬁcient approach, the evapotranspiration of the crop (ETc ) is estimated using the following equation:
ETc = (Kcb + Ke ) × ETo(11)

Mean Max. Temperature

Mean Min. Temperature

Rainfall

160
140
120
100
80
60
40
20
0

180
160
140
120
100
80
60
40
20
0

Rainfall (mm)V. Ravikumar et al. / Agricultural Water Management 98 (2011) 1431–1440

Temperature (Centigrade)1434

Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun
MonthsFig. 4. Monthly climate data at Coimbatore, India.

where Kcb is the basal coefﬁcient, Ke the evaporation coefﬁcient,and ETo is the reference crop evapotranspiration computed using
the Penman–Monteith combination equation using the relevantmeteorological data and the ETo calculator (Raes, 2009). The Kcb
is deﬁned as the ratio of ETc to the ETo when the soil evaporationis zero and the soil surface is dry and the transpiration component
is fully met by sufﬁcient water available in the root zone below thesoil surface (Allen et al., 1998). The Kcb component also includes the
diffusive evaporative water movement from the root zone below
the surface. The soil evaporation coefﬁcient (Ke ) describes the evaporation component from the soil surface. If the soil is wet following
a rain or irrigation, the value of Ke may be large. The sum of Ke andKcb can never exceed a maximum value (Kcmax ) determined by theenergy available for evapotranspiration. More details about how toevaluate these coefﬁcients can be found in Allen et al. (1998).
Values of the basal crop coefﬁcient (Kcb ) used for different stagesof crop are as follows: for the initial 30 days, Kcb is equal to 0.15,
for the next 50 days during the development stage, the Kcb linearlyvaries from 0.15 to 1.2, for the next 180 days of mid stage, the Kcb
is constant with a value of 1.2, and for the ﬁnal 60 days, the Kcb
linearly varies from 1.2 to 0.7 (Allen et al., 1998).
It was assumed that irrigation was applied when the cumulative
sum of evaporation and transpiration in the wetted fraction of soil
exceeded 10 mm during the ﬁrst 30 days and 20 mm thereafter.
A constant irrigation depth of 7.5 mm was maintained throughout
the entire season. The irrigation interval varied from 2 to 3 days on
non-rainy days and longer during rainy days. 58 irrigation events
took place during the growth season (Fig. 5).
It was also assumed that the crop was planted on July 1st, 2008.
Daily values of transpiration and evaporation were calculated for
230 days using the procedure outlined above (Fig. 5). The total crop
evapotranspiration during 230 days was 861 mm and the total irrigation was 435 mm. The balance of 426 mm was met by the rainfall.

Fig. 5. Evaporation, transpiration, irrigation and rainfall during 230 days of simulation (note: different scales on two vertical axes).

V. Ravikumar et al. / Agricultural Water Management 98 (2011) 1431–1440

1435

Table 1
Fertigation days and urea doses for different fertigation scenarios.
Fortnightly periods

Fertigation day

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

1a
15
28
42
57
74
88
102
116
135
146
161
181
197
212

Total

Scenario 1

Scenario 2 (simple balancing)

Scenario 3 (with carry-over from previous time periods)

30
35
40
45
45
45
45
45
30
30
30
30
30
30
30

1.8
12.7
14.5
21.7
21.7
25.4
47.1
54.3
54.3
47.1
43.5
29.0
25.4
25.4
10.9

2
15
15
22
22
25
70
70
70
70
19
–
–
–
–

540

435

400

The ﬁrst day corresponds to 1 July.

2.5. Root water uptake
The sink term, Sw , in Eq. (1), and (6)–(8), represents the volume
of water removed per unit time from a unit volume of soil due
to plant water uptake. The water stress is accounted for using themodel suggested by Feddes et al. (1978), which is implemented in
HYDRUS:Sw (h) = ˛(h)Sp(12)

where h is the soil water pressure head (cm), ˛(h) is the water
stress response function, which varies between 0 and 1, and Sp is thepotential root water uptake rate (1/d). Fig. 6 gives a schematic plotof the stress response function as used by Feddes et al. (1978). The
values of limiting pressure heads used in this work are as follows:
h1 = −10 cm; h2 = −25 cm; h3 = −1000 cm; h4 = −8000 cm.
The potential root water uptake rate is non-uniformly distributed within the root zone:
Sp = b(x, z)St Tp(13)

Stress Response FunctionaFertigation amount of urea (kg/ha)

1

0
h4

h3

h2

h1

0

Soil water suction headFig. 6. Stress response function according to Feddes et al. (1978).

where b(x,z) is the normalized root water uptake distribution in
the vertical x–z plane (1/cm2 ), St is the length of the soil surface
associated with the transpiration (cm), and Tp is the potential transpiration rate (cm/d). HYDRUS distributes the root water uptake

Table 2
Nitrogen concentrations in irrigation water.
15 day periods

Urea applied (Scenario1) (kg/ha)

(1)

(2)

Urea applied(mmol/ha)Col(2)/0.06a × 1000
(3)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

30
35
40
45
45
45
45
45
30
30
30
30
30
30
30

500,000
583,333
666,666
750,000
750,000
750,000
750,000
750,000
500,000
500,000
500,000
500,000
500,000
500,000
500,000a

Nitrogen (N)(mmol/ha)Col(3) × 2b(4)1,000,000
1,166,667
1,333,333
1,500,000
1,500,000
1,500,000
1,500,000
1,500,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000

N per cm of lateral (one side)
mmol per cm length of lateralCol(4)/1333333c(5)

N concentration(mmol/cm3 )Col(5)/16.667d
(6)

0.750
0.875
1.000
1.125
1.125
1.125
1.125
1.125
0.750
0.750
0.750
0.750
0.750
0.750
0.750

0.04500.05250.06000.06750.06750.06750.06750.06750.04500.04500.04500.04500.04500.04500.0450One mmol of urea = 0.06 g.
2 atoms of nitrogen exist for every molecule of urea.
cSpacing between crop rows is taken as 1.5 m. Therefore, 666,666 cm length of laterals exist in one hectare; for one side of a lateral, it is again divided by 2.
dFertigation is performed during 1 h.
Discharge for 1 h for one side of a lateral per cm length = 16.667 cm3 /cm.
b

1436

V. Ravikumar et al. / Agricultural Water Management 98 (2011) 1431–1440

Table 3
Nitrogen balance for 230 days of simulation obtained using HYDRUS.
No.

Process

Cumulative nitrogen (kg/ha)

1
2
3
4
5
6
7
8

Urea applied
Root uptake of urea
Root uptake of ammonium
Root uptake of nitrate
Volatilization of ammonium
Leaching of nitrate
Leaching of ammonium and urea
Nitrogen left in the soil after 230 days

according to Vrugt et al. (2001):b(x, z) =



1−

x
xm



1−

z
zm


e

p

− X x |X ∗ −X |+ Z z |Z ∗ −Z |mm
P

Scenario 1

Scenario 2

Scenario 3

257.1426.74
29.41
101.42
32.11
11.852
Insigniﬁcant
55.61

184.80
24.66
24.63
74.46
24.17
3.72
Insigniﬁcant
33.14

170.43
22.40
25.01
79.52
24.83
4.11
Insigniﬁcant
14.55


(14)

In this equation, the origin is taken at the location of the plant,
zm and xm are the maximum width and depth of the root zone (cm),respectively, z* and x* are the locations of the maximum root water
uptake in vertical and horizontal directions (cm), respectively, andthe px and pz values are taken to be equal to one except for x > x*
and z > z* when they become zero.
2.6. Irrigation and fertigation
For HYDRUS, the data must be given in terms of depth of water
applied on the time-variable ﬂux boundary. The duration of irrigation is considered 3 h and 15 min for each irrigation event. The
fertigation strategy involved applying fresh water for the ﬁrst 2 h,
fertilizer with irrigation water for the next 1 h, and fresh water
again for the last 15 min to ﬂush the lines. The ﬁrst fertigation
event took place on the ﬁrst day of planting (July, 1st). The subsequent fertigation events were adjusted to the irrigation eventswith a fertigation interval of approximately 15 days (Table 1). The
N assimilation data for the ratoon sugarcane plant for the CB4176 variety (Netaﬁm, 2011) is as follows: 40 kg/ha during the ﬁrst 4
months, 95 kg/ha during the following 2 months, and 120 kg/ha forthe last 2 months.

Fig. 8. Comparison of root uptake of nitrogen simulated using HYDRUS with thenitrogen requirement by sugarcane.

A recommendation of 540 kg/ha of urea, provided by the Jain
Irrigation System, Ltd. (http://jains.com/), is examined ﬁrst. This isa typical recommendation followed by many farmers in India. The
application of 540 kg/ha of urea was divided into fortnightly intervals according to the growth stage (Table 2). Different columns ofTable 2 illustrate the procedure adopted to calculate concentrations

140

140
Total N Uptake

Nitrogen( kg/ha)

120

Total N Uptake
120

Plant need

100

100

80

80

60

60

40

40

20

20

0

0
0

100

200

Days after planting

a. Simple Balancing
Fig. 7. Distribution of root water uptake function.

Plant need

300

0

100

200

300

Days after planting

b. Carry over from Previous Periods

Fig. 9. Root nitrogen uptake for scenarios matching plant uptake with fertigation
doses.

V. Ravikumar et al. / Agricultural Water Management 98 (2011) 1431–1440

of N in irrigation water for a single dripper step by step. Thisapproach is referred to below as Scenario 1.
Based on the simulated results obtained in Scenario 1, two typesof modiﬁcations of this policy were done. The results of Scenario
1 provide the overall nitrogen uptake efﬁciency. Fortnightly (twoweeks) urea requirements can be evaluated by using the N assimilation data for different stages of the crop and the Scenario 1 nitrogen
uptake efﬁciency. These biweekly urea requirements are referred
to as Scenario 2 and called “simple balancing policy”, since they arecalculated only based on the plant need for a given fortnight and anassumption that the soil available N for plant uptake before fertigation is zero. In reality, the actual amount of N taken up by the plants
may be either more or less than the plant need and some N may
remain in the soil. Therefore, simple balancing policy of Scenario 2
is also suboptimal and its level of sub-optimality may be evaluatedusing HYDRUS. Scenario 2 was then modiﬁed by trial and error by
adjusting fertigation doses until the simulated N uptake and theplant need match closely. The ﬁnal optimal run is referred to as
Scenario 3.

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2.7. Input data for HYDRUS
While many of the input parameters required by HYDRUS weretaken from the literature, some parameters were estimated fromthe ﬁeld work.
2.8. Data from the literature
The soil hydraulic parameters for sandy clay loam were takenfrom the Rosetta Lite program (Schaap et al., 2001), which is incorporated in HYDRUS. They are as follows: the residual water content( r ) is 0.063, the saturated water content ( s ) is 0.384, the saturated
hydraulic conductivity (Ks ) is 13.2 cm/day, the pore connectivity
parameter (l) is 0.5, and the values of ˛ and n are 0.021 cm−1 and
1.33, respectively.
The ﬁrst-order rate constant for nitriﬁcation of urea to ammonium (a ) is assumed to be 0.38 per day, for nitriﬁcation ofammonium to nitrate (n ) 0.2 per day (Hanson et al., 2006), andfor volatilization of ammonium to ammonia (v ) 0.0552 per day

Fig. 10. Spatial distribution of urea concentrations (mmol/cm3 ) for Scenario 3.

1438

V. Ravikumar et al. / Agricultural Water Management 98 (2011) 1431–1440(Bolado Rodriguez et al., 2005). The distribution coefﬁcient forammonium (Kd ) is assumed to be 3.5 cm3 /g (Hanson et al., 2006).
2.9. Data from the ﬁeld work
The measured bulk density was 1.53 g/cm3 . We assumed a line
source with drippers spaced at 60 cm and with each dripper having
a discharge rate of 2 litres per hour (L/h). The radius of the ponded
area for the 2-L/h dripper in a sandy clay loam soil was experimentally found to be 20 cm. Therefore, a 20-cm boundary length
was used to represent irrigation from surface drippers. Two litres
per hour per dripper at a spacing of 60 cm on a 20 cm recharge
boundary leads to a ﬂux of 20 cm2 /day per cm length of the lateral.
The root growth of the sugarcane crop was studied in the ﬁeld
by observing the maximum root depth and maximum root radius atregular time intervals in excavated transects. The maximum root
depth (zm ) and the maximum root radius (xm ) were found to beequal to 75 and 37.5 cm, respectively. The spatial pattern of water
uptake was evaluated from tensiometer measurements. Ten tensiometers were installed for this purpose at ﬁve different depths(15, 20, 25, 35, and 40 cm) below the lateral and at a distance of
15 cm from the lateral. From soil moisture depletion during one
irrigation cycle, we estimated the depth (z*) and radius (x*) withmaximum root uptake to be 20 cm and 0 cm, respectively. Fig. 7
shows the distribution of root water uptake obtained using Eq. (14)and the above-determined root parameters.
2.10. Numerical simulations
HYDRUS-2D was used to solve the ﬂow and transport equations for speciﬁed initial and boundary conditions. Numericalsimulations produced the spatial and temporal distribution of volumetric water contents, and the solution concentrations of urea,
ammonium, and nitrate. The initial water content in the soil wasFig. 11. Spatial distribution of ammonium concentrations (mmol/cm3 ) for Scenario 3.

V. Ravikumar et al. / Agricultural Water Management 98 (2011) 1431–1440

0.25 cm3 /cm3 , and the soil was assumed not to contain initiallyany residual N. The initial concentrations of urea, ammonium, andnitrate were thus assumed to be zero. Simulations were carried out
for 230 days from the date of planting (July 1st).

3. Results and discussion
Table 3 shows the nitrogen balance for the 230-day simulations
obtained using HYDRUS for all three scenarios. During the 230-day
period for Scenario 1, 12% of N was volatilized, 5% was leached, and
61% was taken up by plant roots (the nitrogen use efﬁciency). Fig. 8
shows the root N uptake in all three N forms for Scenario 1. It canbe seen that the total nitrogen uptake throughout the crop season
is above the crop need. At the end of the 230-day time period, thecrop N uptake is 30% higher than the plant N need (Netaﬁm, 2011).
Table 3 shows that about 60% of the applied urea was taken
up by plants in Scenario 1. From Table 3, it can also be observed

1439

that in Scenario 1, 55.6 kg/ha of nitrogen remained in the soil after
230 days. Though some fraction of this nitrogen may be usefulfor root extraction after 230 days, all this nitrogen is assumed
to exist in the soil below the root zone. Scenario 2 was obtained
based on the growth curve nutrition approach. The plant need foreach fortnight was obtained by dividing the plant need by 0.6, as
60% of applied urea is taken up by plants. Urea doses calculated
for Scenario 2 are shown in Table 1. The total amount of urea
applied in Scenario 2 is 435 kg/ha. Fig. 9a shows comparison ofplant demand and simulated N plant uptake for this scenario. It
can also be observed that during the periods of peak N requirement, plant uptake is less than what plants need. This is because,for higher application rates, fertilizer uptake does not occur at
60% efﬁciency. However, it should be noted that the total nitrogen uptake at the end of the simulation period is higher than
the requirement. Nevertheless, this kind of fertigation is suboptimal, as the time of N uptake does not always match the time ofrequirement.

Fig. 12. Spatial distribution of nitrate concentrations (mmol/cm3 ) for Scenario 3.

1440

V. Ravikumar et al. / Agricultural Water Management 98 (2011) 1431–1440

Scenario 3 was devised by trial and error so that the simulated
plant uptake and plant needs are closely matched. The doses of urea
obtained for Scenario 3 are also shown in Table 1. The total amountof urea applied for Scenario 3 is 400 kg/ha, which is 35 kg less thanfor Scenario 2. From Fig. 9b, it can be seen that plant uptake andcrop needs closely match. There is a slightly higher uptake during
the time period after 200 days. Though fertigation is stopped on
the 165th day, the higher crop uptake still occurs because of theresidual nitrogen remaining in the soil. This nitrogen exists in thesoil because during earlier periods, more urea was applied to meetthe requirements in the periods 7 through 10.
Table 1 reports the days on which fertigation occurred andthe quantity of urea applied during each fertigation event. Notethat fertigation events did not occur at exactly biweekly intervals,
since each fertigation is associated with irregular irrigations. Fig. 10shows the spatial distribution of urea immediately after the 3rd
through 11th fertigation event for Scenario 3. Spatial distributionsof urea after different fertigation events are quite similar except forthe one on 119.6th day because of the rainfall that caused signiﬁcantleaching.
Fig. 11 shows the spatial distribution of ammonium for Scenario
3 at the same times as in Fig. 10, with three additional times on
day 174, 200, and 230. While ammonium initially builds up in theroot zone until about day 147, its concentrations are subsequently
reduced due to plant uptake and nitriﬁcation, without any replenishment by further fertigations. Due to its adsorption to the soil,ammonium is concentrated near the dripper.
Fig. 12 shows the spatial distribution of nitrate on the same days.
Initially, till about day 90, nitrate concentrations in the root zone
are relatively low since almost all nitrate is taken up by the plants.
There is some build up of nitrate at the soil surface at distances
beyond the root zone, because of evaporation and a lack of local
root water/nutrient uptake. This process can be better understoodby observing the distribution of root water uptake shown in Fig. 7.
There is signiﬁcant leaching of nitrate due to rain after 106 days.
4. Summary and conclusions
The rhizosphere dynamics of nutrients is very complex anddepends on many factors, such as soil temperature, pH, water content, and soil and plant characteristics. Also, the temporal andspatial variations of these factors are highly dynamic. Many factors cannot easily be accurately quantiﬁed. The objective of thiswork thus was to evaluate the nutrient dynamics and root uptakeof nutrients by the sugarcane crop grown under drip irrigation withthe state-of-the-art modelling tools and to examine whether fertigation scheduling could be optimized. An attempt has been madeto better understand the reactive transport of urea in the root zoneof the sugarcane crop and to quantify the ﬂux of urea, ammonium,
and nitrate into crop roots, ammonia volatilization ﬂux, and deep
drainage. This quantiﬁcation helped in designing a satisfactory fertigation schedule that produced a reduction in the use of urea by
30%, while at the same time providing enough N for its assimilation
at all stages of crop growth. Various parameters used in the model
were taken from the literature and a few of them were taken fromthe accompanying ﬁeld study.
Our results indicate that HYDRUS can be very helpful in improving the fertigation schedules using the growth curve nutrition
approach. However, a ﬁeld-scale validation will be required before
this approach can be recommended to farmers. We are planning tocarry out such ﬁeld-scale study and will report our results in thisjournal once the study is concluded.

Acknowledgements
The work was carried out under the project namely, Modelling
Urea transport for nitrogen scheduling in drip irrigation funded by
the Department of Science and Technology, Government of India.
The authors are very much grateful for this ﬁnancial support. The
authors are also grateful to the two reviewers for their suggestions
and comments that helped in signiﬁcantly improving the quality ofthe manuscript.
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