Irrig Sci (2015) 33:289–302
DOI 10.1007/s00271-015-0466-4

ORIGINAL PAPER

Modeling soil water dynamics in a drip‑irrigated intercropping
field under plastic mulch
Xianyue Li1 · Haibin Shi1 · Jiří Šimůnek2 · Xuewen Gong1 · Zunyuan Peng1

Received: 4 May 2014 / Accepted: 31 March 2015 / Published online: 10 April 2015
© Springer-Verlag Berlin Heidelberg 2015

Abstract Intercropping, drip irrigation, and the use ofplastic mulch are important management practices, whichcan, when utilized simultaneously, increase crop production and save irrigation water. Investigating soil water
dynamics in the root zone of the intercropping field undersuch conditions is essential in order to understand the combined effects of these practices and to promote their wider
use. However, not much work has been done to investigate
soil water dynamics in the root zone of drip-irrigated, strip
intercropping fields under plastic mulch. Three field experiments with different irrigation treatments (high T1, moderate T2, and low T3) were conducted to evaluate soil watercontents (SWC) at different locations, for different irrigation treatments, and with respect to dripper lines and plants(corn and tomatoes). Experimental data were then used
to calibrate the HYDRUS (2D/3D) model. Comparison
between experimental data and model simulations showedthat HYDRUS (2D/3D) described different irrigation
events and SWC in the root zone well, with average relative
errors of 10.8, 9.5, and 11.6 % for irrigation treatments T1,
T2, and T3, respectively, and with corresponding root mean

Communicated by N. Lazarovitch.
* Xianyue Li
Lixianyue80@126.com* Haibin Shi
Shb@imau.edu.cn* Jiří Šimůnek
Jiri.Simunek@ucr.edu
1

College of Water Conservancy and Civil Engineering, Inner
Mongolia Agricultural University, Huhhot 010018, China

2

Department of Environmental Sciences, Universityof California Riverside, Riverside, CA 92521, USA

square errors of 0.043, 0.035, and 0.040 cm3 cm−3, respectively. The results showed that the SWC in the shallow rootzone (0–40 cm) was lower under non-mulched locations
than under mulched locations, irrespective of the irrigation treatment, while no significant differences in the SWC
were observed in the deeper root zone (40–100 cm). The
SWC in the shallow root zone was significantly higher forthe high irrigation treatment (T1) than for the low irrigation
treatment, while, again, no differences were observed in the
deeper root zone. Simulations of two-dimensional SWC
distributions revealed that the low irrigation treatment (T3)
produced serious severe water stress (with SWCs near thewilting point) in the 30–40 cm part of the root zone, andthat using separate drip emitter lines for each crop is well
suited for producing the optimal soil water distribution pattern in the root zone of the intercropping field. The resultsof this study can be very useful in designing an optimal
irrigation plan for intercropped fields.

Introduction
Intercropping is the agricultural practice of growing two or
more crops side by side in one field. For example, a deeprooted crop can be planted with a shallow-rooted crop or atall crop with a shorter crop. One-third of all cultivated land
in China is used with an intercropping technique (Zhang
and Li 2003) because when compared to monoculture, thismanagement practice largely improves water-use efficiency(WUE) (Tanwar et al. 2014), nitrogen-use efficiency (Roweet al. 2005), light- and radiation-use efficiency (Awal et al.
2006), and land-use efficiency (Dhima et al. 2007; Tanwar
et al. 2014). Intercropping has played an important rolein increasing the crop production and farmers’ income inmany countries, including China (Zhang et al. 2007), India

13

290

(Singh et al. 2013), Egypt (Schader et al. 2005), Malawi(Makumba et al. 2006), and the United States (Parajuleeet al. 1997). However, the spatial root distribution, root
water uptake, and crop water requirements of two crops in
an intercropping field are different compared to monoculture, displaying a non-uniform soil water pattern and cropcompetition for water and nutrients. Additionally, different
crops have different water requirements and need different
irrigation amounts at different times in order to increase
WUE.
In the Hetao Irrigation District, in the Yellow River basinof Northwest China, water scarcity is the most critical factor restricting agricultural development (Xu et al. 2010).
Additionally, the traditional flood irrigation technique produces very low WUE and can hardly resolve the problem
of inconsistent water requirements of two crops in an intercropping field. On the other hand, drip irrigation can precisely control the irrigation amount, increase crop yields,
reduce water loss (Yaghi et al. 2013), and reduce the riskof soil degradation and salinity (e.g., Keller and Bliesner
1990; Burt and Isbell 2005). Additionally, drip irrigation
can easily be operated to account for the different irrigation
requirements of the two crops.
Although soil water dynamics was investigated by several scientists for either intercropping fields (e.g., Sampathkumar et al. 2012) or mulched drip irrigation (e.g., Wanget al. 2014), it has not been studied in a system that couples
both intercropping and mulched drip irrigation. Soil water
dynamics in the root zone under such conditions is very
complex, and its understanding is critical for optimizing
irrigation management. It is thus important to investigate
soil water dynamics under such conditions before promoting the complex management of intercropping, mulching,and drip irrigation agro-techniques.
Although many scientists have studied soil water
dynamics in drip-irrigated fields (e.g., Hussein et al. 2011;
Ityel et al. 2011; Badr and Abuarab 2013), it is still difficult
to design strategies optimizing irrigation amounts, irrigation frequencies, and emitter depths to obtain the highest
WUE (Kandelous et al. 2012). The use of computer simulations with validated mathematical models to optimize management practices is a fast and inexpensive approach thathas received a lot of attention during the last few decades.
In general, there are two types of approaches for simulating
the soil water distribution in the drip-irrigated field. One
approach is based on the analytical solutions of the governing flow equation, such as the solution of Philip (1984)
used in the WetUp model (Cook et al. 2003). Another, more
widely used approach is based on the numerical solution of
the Richards equation, such as in the HYDRUS (2D/3D)(Šimůnek et al. 2008), Drip-Irriwater (Arbat et al. 2013), or
APRI (Zhou et al. 2007) models.

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Irrig Sci (2015) 33:289–302

Because of the flexibility of HYDRUS (2D/3D) toaccommodate different types of boundary conditions
and the root uptake of water and nutrients, and becauseof its ease of use due to a graphical, user-friendly interface, the model has been widely and successfully used
to simulate water movement under drip irrigation in
many studies (e.g., Cote et al. 2003; Skaggs et al. 2004;
Lazarovitch et al. 2009; Kandelous et al. 2012; Abou Lilaet al. 2013; Dabach et al. 2013). For example, Skaggs
et al. (2004) compared experimental soil water distributions for drip irrigation with different irrigation amounts
and different irrigation durations (20, 40, and 60 L m−1
of applied water) with the results of numerical simulations with HYDRUS (2D/3D), in which the soil hydraulic properties were obtained using pedotransfer functions(Schaap et al. 2001). Their results supported the use of
HYDRUS (2D/3D) as an important tool for investigating and designing drip irrigation management practices.
Although higher irrigation frequencies were suggested
in the literature to be a better drip irrigation practice(Assouline et al. 2006), the numerical simulations by
Abou Lila et al. (2013) showed that the lower irrigation
frequency actually produced a bigger wetted soil volume
without an increase in water percolation below the plantroots. Skaggs et al. (2010) evaluated the effects of theapplication rate, pulsed water applications, and the antecedent water content on the spreading of water from drip
emitters using both field experimental data and numerical
HYDRUS (2D/3D) simulations. Their results showed that
it was mainly the soil texture and the antecedent watercontent that determined the spreading and distribution ofsoil water, while irrigation frequency and flow rate had
only very little impact (Skaggs et al. 2010). Dabach et al.
(2013, 2015) used HYDRUS (2D/3D) to optimize theirrigation threshold, i.e., the pressure head at a selected
location, which triggers irrigation when reached; theplacement of the triggering location; and the amount ofirrigation water applied during one irrigation episode, inorder to increase WUE.
Few studies have been carried out for drip irrigation
under mulched conditions (e.g., Liu et al. 2013; Wang et al.
2014). For example, Liu et al. (2013) introduced a conceptof a partitioning coefficient to describe the effect of plastic
mulch on prevention of evaporation. They used the numerical HYDRUS (2D/3D) model to simulate temporal variations in soil water contents (SWC) in a drip-irrigated cotton
field under plastic mulch. However, they only calibrated themodel (e.g., Liu et al. 2013; Wang et al. 2014) and did notevaluate the effect of the presence or absence of mulchingon the SWC distribution.
In intercropping fields, it may be necessary to use different irrigation practices than in monoculture in order toIrrig Sci (2015) 33:289–302

291

satisfy different water requirements of two crops. Consequently, the numerical model must accommodate more
complicated boundary conditions and root distribution patterns existing in intercropping fields. Sampathkumar et al.
(2012) used experimental data to evaluate soil water movement in a drip-irrigated intercropping field under plastic
mulch, without comparing the experimental data with theresults of a numerical model. On the other hand, De Silva
et al. (2008) used HYDRUS (2D/3D) to numerically evaluate root water uptake and soil water movement in a region
with a mixture of natural vegetative cover (i.e., trees andgrasses), and concluded that different irrigation amounts
and frequencies should be used for different plant species
in irrigated strip intercropping fields. However, it is difficult
to collect information about complex boundary conditions
and other operational parameters required by a numericalmodel for intercropping fields. On the other hand, when
the numerical model is calibrated, it can provide a fast andinexpensive approach for investigating soil water dynamics
in a drip-irrigated intercropping field under plastic mulch.
The main objectives of this study were (i) to calibrate
and validate the HYDRUS (2D/3D) model using the experimental data, (ii) to evaluate the soil water distribution
under a mulched drip irrigation system in an intercropping
field, and (iii) to compare soil water distributions under different irrigation practices.
Table 1  Design of different irrigation treatments
Treatment

Irrigation amount(mm per irrigation event)
Tomato

Corn

T1

22.5

30

T2

16.5

22.5

T3

10.5

15

Materials and methods
Field experiment
The field experiment was carried out from April 1 to September 26, 2012 at the Dunkou Agroecosystem Experimental Station (40°20′15′′N, 107°1′45′′E, altitude 2004 m),
located in the western Hetao Irrigation District, in the Yellow River basin of Northwest China. Average annual precipitation is 198 mm, and average annual evaporation froma free water surface is 2460 mm. The main soil texture in
the region is sandy clay loam. The groundwater table during our study was between 73 and 232 cm deep, with theaverage depth of 134 cm during the crop growth period.
Drip lines were laid out in a “one drip line, one mulch,
two crop rows” pattern (i.e., two rows of crops were irrigated with one drip line and mulched with a 70-cm-wideplastic mulch). The drip tape diameter was 16 mm, the wall
thickness 0.4 mm, and the discharge rate of the pressurecompensated emitter was 2.4 L h−1 at a line pressure of
50 kPa. The strip intercropping consisted of four rows oftomato and two rows of corn. Three irrigation treatmentswith different (low T3, moderate T2, and high T1) irrigation amounts were used (Table 1), and each was replicatedthree times in a completely randomized block design ofnine plots. While the T1 treatment was meant to represent
a control, full irrigation treatment, the T2 and T3 treatments
represented moderate and severe deficit irrigations. A compound fertilizer (18 % N, 46 % P2O5, and 1.5 % SO42−)
of 350 kg ha−2 was uniformly applied to the plots before
sowing. Drip tapes with an emitter spacing of 30 cm and alength of 22 m were placed between two rows of tomatoes
and corn, providing water and fertilizer for two adjacentrows of plants. The cropping pattern is shown in Fig. 1.
Each treatment had two water meters (with a precision of
0.001 m3) to control irrigation amounts.

Fig. 1  Schematic showing the cropping pattern (with two double rows of tomatoes and one double row of corn), the arrangement of drip tapes,
and the locations of TDR probes and surface mulch

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6

300

5

250

Crop Height (cm)Fig. 2  Leaf area index (LAI)
and the crop height of tomato
and corn during the growing
seasonIrrig Sci (2015) 33:289–302

Leaf Area Index (LAI)

292

4
3
2

Tomato

1

Corn

0
131

151

171

191

211

231

251

271

DOY

Corn was planted on day of year (DOY) 111, and tomatoes were transplanted on DOY 131. After transplanting,all three fields with different irrigation treatments received
a large flood irrigation (about 55 mm) on DOY 132. Different irrigation amounts (high T1, moderate T2, and lowT3) were then adopted for tomatoes and corn in the same
irrigation treatment (Table 1). Drip irrigation was applied
on DOY 167, 175, 190, 196, 199, and 214 to both crops.
Since tomatoes were harvested on DOY 221, there was no
irrigation applied to the tomato strip after this date. Cornreceived two additional irrigations on DOY 222 and 228,
since it was harvested on DOY 270.
Meteorological data, including solar radiation (S-LIBM003), photosynthetically active radiation (S-LIA-M003),
air temperature and relative humidity (S-THB-M002), airpressure (S-BPA-CM10), wind speed (S-WCA-M003), andprecipitation (S-BPA-CM10), were collected at the meteorological station (HOBO, USA) located approximately
500 m from the experimental field. Data were recorded at
1-h intervals, stored in a datalogger (H21-001 DT-80), andregularly downloaded. Reference crop evapotranspiration(ET0) was calculated using the Penman–Monteith equation(Allen et al. 1998). The SWC was measured using TDR
probes (TRIME-PICO-IPH, IMKO GmbH, Germany),
which were installed between two rows of tomatoes (P1),in the bare section between rows of tomatoes and corn
(P2), and between two rows of corn (P3) in each treatment
plot (Fig. 1). TDR measurements were taken once every
5 days at soil depths of 0–10, 10–20, 20–40, 40–60, 60–80,
and 80–100 cm. Additional gravimetric measurements wereused to verify TDR measurements (Skaggs et al. 2004).
The leaf area and the plant height were regularly measured
using the leaf area meter (Li-3000, LI-COR, USA) and atape (the accuracy is about 0.1 cm) (Gao et al. 2010). The
leaf area index (LAI), displayed in Fig. 2, was then calculated using the FAO method (Allen et al. 1998).
Data about the horizontal and vertical distributions ofcrop roots were obtained by digging a soil transect on theexperimental site (Gao et al. 2010) on June 6, June 22, July21, and August 20. The working surface of the soil profile was smoothed, the face of the pit was trimmed to be

13

200

Tomato

150

Corn

100
50
0
131 151

171 191 211 231

251 271

DOY

vertical, and then the vertical plane was divided into square,
5 × 5 cm cells between the tomato strip (P1) and the corn
strip (P3). The entire sampling area was 100 × 100 cm.
The sample volumes were 125 cm3. Root samples werecollected and washed off using a root washing machine(Delta-T, CSIRO, Australia). The root length was measured using the root system scanner (Perfection4870photo,
Epson, Japan) and then analyzed using the WinRHIZO
software. The root length density was calculated (Gao et al.
2010), and the average of the last three measurements wasused as an input in HYDRUS (2D/3D) during the second
simulation period (explained below).
Numerical model
Drip irrigation is a fully three-dimensional (3D) flow problem (Kandelous et al. 2011). However, under certain conditions, the effects of individual emitters along the drip
line can be neglected, and the problem of drip irrigation
can be considered as a line source, with infiltration andredistribution being two-dimensional processes (Skaggs
et al. 2004; Kandelous et al. 2011; Liu et al. 2013).
Although, in general, wetting patterns mainly depend on
the emitter’s spacing, irrigation duration, initial SWC, andsoil hydraulic properties (Skaggs et al. 2004, 2010), theprincipal concerns of this study are the effects of mulchingand different crops on SWC distributions. The HYDRUS(2D/3D) code (Šimůnek et al. 2008) was used to evaluate
collected experimental data. HYDRUS (2D/3D) uses theGalerkin finite element method to numerically solve thegoverning equation (Richards 1931) for variably saturated
water flow:




∂
∂h
∂
∂h
∂θ(h)
=
+ K(h) − S(h)
K(h)
+
K(h)
∂t
∂x
∂x
∂z
∂z
(1)
where θ is the volumetric soil water content (cm3 cm−3); his the pressure head (cm); K(h) is the unsaturated hydraulic conductivity (cm day−1); t is time (day); x and z are thehorizontal and vertical coordinates (cm), respectively; andS is the sink term (day−1). The root water extraction S was

Irrig Sci (2015) 33:289–302

293

Fig. 3  Average measured
spatial root distribution during
two simulation periods: a DOY
111–138 and b DOY 139–270

computed according to the Feddes model (Feddes et al.
1978):(2)

S(h) = τ (h) · β(x, z) · Tp Lt−1

where Tp is the potential transpiration rate (cm day ), Lt
is the surface length associated with transpiration (cm),β(x,z) is the root water uptake distribution function (cm−2),and τ(h) is the root water uptake stress reduction function(0 < τ < 1), which includes the following parameters: (a)P0 and POpt are the pressure heads, below which roots start
extracting water from the soil and roots start extracting
water at the maximum possible rate, respectively; (b) P2H
and P2L are the limiting pressure heads, below which roots
can no longer extract water at the maximum rate (assuming potential transpiration rates r2H and r2L, respectively);and (c) P3 is the pressure head, below which root water
uptake ceases (the wilting point). The following parametervalues for corn were adopted from the HYDRUS (2D/3D)
database (Šimůnek et al. 2006; Wesseling and Brandyk
1985): P0 = 15 cm, P3 = −8000 cm, POpt = −30 cm,
P2H = −325 cm, P2L = −600 cm, r2H = 0.5 cm day−1, andr2L = 0.1 cm day−1.
The standard version of HYDRUS (2D/3D) permits theuse of the root water uptake stress reduction function for
only one crop, while in the intercropping system there are
two types of crops with different capacities of root water
uptake and with different sensitivities to environmental
stresses (e.g., saturation or salinity). We have resolved thisproblem by considering root water uptake in the model tobe directly proportional to the crop root distribution, andthus by adjusting the spatial root distribution in the soil
profile, we can affect root water uptake from different partsof the soil profile as well (similarly as done by De Silva
et al. 2008). We introduced the ratio of root water uptake
per unit root length between corn and tomato (k), assumingthat k was identical to the ratio of potential transpirations
between corn and tomato monoculture. The ratio k wasfound to be about 0.96 based on the ratio of crop coefficients during the growing season of corn and tomato (Allenet al. 1998). The region was equally divided into two parts,and the root distribution of a tomato strip was multipliedby k. Since HYDRUS (2D/3D) cannot model root growth,
the entire simulation was divided into two parts (Fig. 3).
During earlier times, between DOY 111–138, the root zoneof both crops was small and did not intersect each other.
During later times, between DOY 139–270, in which roots
quickly developed and heavily overlapped, there werehigher crop transpiration rates and a larger effect of root
distributions on the soil water dynamics. The average root
distribution during this time period was adopted in calculations in order to reduce the error of not considering a
dynamic root growth (Fig. 3).
The HYDRUS (2D/3D) software was easily parameterized as the root distribution is internally normalized (Liuet al. 2013). We assumed that the root length was a relative value equal to 1.0 in the 10 × 10 cm square directly
beneath the corn stem. The relative root length in otherareas, Root(x, z), was calculated as:

Root(x, z) =σ (x, z)σ0(3)where Root(x, z) is a characteristic value of a normalized,
dimensionless spatial distribution of the root length, σ0 is
the root length in the 10 × 10 cm square directly beneath

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Irrig Sci (2015) 33:289–302

Fig. 4  Schematic of the flow
domain and boundary conditions used in the HYDRUS(2D/3D) simulations

the corn stem (cm), and σ(x, z) is the root length in othersquares (cm). In the HYDRUS (2D/3D) software, the spatial root distribution function assigned to each node, β(x, z),
is a normalized relative root length (Šimůnek et al. 2006):

Root(x, z)
Root(x,z)dΩΩ

β(x, z) = (4)where Ω is the root zone domain. Additionally, the soil
water content distribution at the end of the first simulation
period was used as the initial soil water content distribution
for the second simulation period.
Initial and boundary conditions

The initial spatial SWC distribution was estimated basedon samples taken from the intercropping field on DOY
110. We assumed that the initial SWC was uniform in
the horizontal direction and linearly varied with depth,
from about θ = 0.18 cm3 cm−3 at the soil surface to about
θ = 0.39 cm3 cm−3 at the bottom of the simulated region(110 cm depth).
Fifteen observation points were defined in HYDRUS(2D/3D) that were located at depths of 5, 15, 30, 50, and80 cm at three horizontal locations in the middle of thetomato strip (P1), bare strip (P2), and corn strip (P3),as shown in Fig. 4. The simulation was carried out for
160 days. The horizontal width of the flow domain was set
to 100 cm, which was the spacing between two lateral drip
emitters in the tomato and corn strips. The vertical size ofthe flow domain was fixed at 110 cm.
The “No Flow” boundary condition was used at verticalsides of the flow domain. The upper boundary was divided
into the no-mulch section in the middle 30 cm, where the“Atmospheric” boundary condition was used (Neuman13

et al. 1974), and the mulch section, where the “TimeVariable Flux” boundary condition (35 cm on each side)
was imposed. The “Time-Variable Pressure Head” boundary condition was imposed at the bottom of the transportdomain where the pressure head that was measured at regular intervals was imposed. It should be noted that to fully
account for complex conditions at the soil surface, the surface energy balance should be solved for each section of
the soil surface (e.g., plastic mulch), taking into accountdifferent properties of different sections of the soil surface(such as albedo). However, since such option is currently
not available in HYDRUS (2D/3D), the approach described
below was adapted instead.
Reference crop evapotranspiration (ET0) was calculated using the Penman–Monteith equation (Allen et al.
1998) during the experimental period by using collected
meteorological data. Daily potential evapotranspiration (ETp) (Fig. 5), required by the model, was obtainedby multiplying ET0 with the crop coefficient (Kc) (Allenet al. 1998):

ETp = Kc · ET0(5)where Kc is the synthetic crop coefficient for an intercropping field as recommended by the FAO 56 paper (Allenet al. 1998), which can be calculated as follows:Kc =f1 h1 Kc1 + f2 h2 Kc2
f1 h 1 + f 2 h 2(6)where f1 and f2 are fractions of the soil surface planted bytomatoes and corn in an intercropping field, i.e., 0.67 and
0.33, respectively; h1 and h2 are the heights of tomato andcorn, respectively (Fig. 2); and Kc1 and Kc2 are crop coefficients for tomato and corn under monoculture conditions,
i.e., 1.15 and 1.20, during the middle growth stage, and295

ETp (mm)Fig. 5  Potential evapotranspiration (ETp), precipitation (P),and irrigation (I) for treatment
T1 during the entire growing
season. Note that irrigation
amounts for tomato and corn
are different, and that there are
two additional corn irrigations
on DOY 222 and DOY 228

6

0

5

10

4

20

3

30

2

40

1
0

P (mm)I (mm)

Irrig Sci (2015) 33:289–302

110

130

150

P

ETp

I (Corn)

I (Tomato)

170

190

210

50

230

250

60
270

DOY

Table 2  Parameters of thevan Genuchten model of soil
hydraulic properties used in the
study (value—optimized value,
S. E.—standard error)

Soil layers (cm)θr (cm3 cm−3)

α (1/cm)

Value

Value

S. E.

θs (cm3 cm−3)

n (−)
S. E.

Value

Ks (cm day−1)

l

S. E.

0–20

0.083

0.01

0.054

0.016

1.20

0.03

0.472

170

0.5

20–110

0.092

0.02

0.101

0.025

1.16

0.02

0.484

306

0.5

ϕ=

Q
L × 2πR

0.7–0.9 and 0.35–0.6 at the later growth stage, respectively.
The FAO 56 paper recommends reducing these values by
10–30 % under plastic mulch conditions. A reduction of
15 % was adopted in our study, and the crop coefficientswere considered for tomato and corn (Kc-ini) with values of
0.2 and 0.3 at the initial stage, 0.98 and 1.02 at the middle stage (Kc-mid), and 0.6 and 0.3 at the later stage (Kc-end),
respectively. Daily potential evapotranspiration (Fig. 5) was
then divided into potential transpiration (Tp) and potential
evaporation (Ep), as required by HYDRUS (2D/3D), as follows (Campbell and Norman 1989):(10)

where ϕ is the input irrigation flux (cm day−1), Q is the discharge rate (2.4 L h−1), R is the radius of the drip emitter (0.8 cm), and L is the spacing between drip emitters(30 cm). The following values of ϕ were used for the twocrops and three irrigation treatments: 31.35 cm day−1 fortomato and 41.79 cm day−1 for corn for treatment T1,
22.99 and 31.35 cm day−1 for treatment T2, and 14.63 and20.90 cm day−1 for treatment T3, respectively.

Tp = (1 − e−k·LAI )ETp

(7)

Soil hydraulic parameters

Ep = ETp − Tp

(8)

Soil hydraulic properties characterizing soil water retention
and hydraulic conductivity were described using the analytical functions of van Genuchten (1980) as follows:

where k is the radiation extinction coefficient, which is 0.45
for tomato (Cavero et al. 1998) and 0.49 for corn (Lindquist
et al. 2005), and LAI is the leaf area index (Fig. 2).
Evaporation should theoretically be completely prevented when plastic mulch is used. However, due to theaging of plastic, there will always be some evaporation.
The potential evaporative flux trough plastic mulch can becalculated according to Liu et at. (2013) as:

Emulch = Cp · Ep

(9)where Emulch is the evaporative flux through the mulching boundary and Cp is a partitioning coefficient of plastic
mulch. According to Liu et al. (2013), its lowest value is
0.07.
The two drip emitters were represented as quarter circles
with a 0.8-cm radius located in upper corners of the flow
domain (Fig. 4). During irrigation, fluxes of drip emitterswere described in HYDRUS (2D/3D) as:

Se (h) =1θ (h) − θr=θs − θr(1 + |αh|n )m

K(θ) = Ks Sel [1 − (1 − Se1/m )m ]2(m = 1 − 1/n) (11)(12)

where Se is the relative saturation; Ks is the saturated
hydraulic conductivity (cm day−1); θs and θr are the saturated and residual water contents, respectively (cm3 cm−3);
and n, α, l (0.5) are empirical shape factors (Table 2).
The saturated hydraulic conductivity was determinedusing the constant head method (Booltink et al. 1991), andthe saturated soil water content was measured gravimetrically. The inverse approach was used to optimize parameters (θr, n, α) and to calibrate the HYDRUS (2D/3D) model(Hopmans et al. 2002; Lazarovitch et al. 2007). The SWC
measured at P1 and P2 locations of treatment 2 between

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DOY 60 and DOY 124 was used to calibrate the van
Genuchten–Mualem parameters using the Levenberg–Marquardt nonlinear minimization method.
Model performance
The model performance was evaluated using the root meansquare error (RMSE) (e.g., Skaggs et al. 2004; Kandelous
et al. 2011), the mean absolute error (MAE) (e.g., Doltra
and Muñoz 2010), and the mean relative error (MRE) (e.g.,
Cook et al. 2003; Zhou et al. 2007):n

1
RMSE =(Pi − Oi )2
n
i=1

1/2

(13)

n

1
|Pi − Oi |
MAE =
n

(14)

i=1

MRE =

n
1 
|Pi − Oi |
n
i=1

Oi

× 100 %

(15)

where Pi is the predicted value, Oi is the observed value,
and n is the number of compared values.

Results and discussion
Calibration and validation
The T2 treatment data were used to calibrate the soil
hydraulic parameters (Table 1), and the T1 and T3 treatment data were used to validate the model and its optimized parameters. Since relatively similar trends in SWCs
were obtained for the three treatments, the results only for
the T1 treatment (validation) are presented in Fig. 6. Figure 6 documents that a relatively good agreement between
experimental and simulated data was obtained. Overall,
temporal changes in SWCs in the upper soil layers (0–10,
10–20, and 20–40 cm) were larger than in the deeper layers (40–60 and 60–100 cm), since these layers were more
directly affected by irrigation, precipitation, evaporation,and transpiration. After all irrigation and rainfall events,
SWCs increased quickly in the upper soil layers (0–40 cm),
especially in the very top layers (0–20 cm), and mainly
under the tomato and corn strips. On the other hand, SWC
fluctuations in the bare strip were less dramatic, since thisarea was not directly affected by irrigation.
During the entire crop growth season, the mean relative errors (MRE) for all three treatments and all locations
were smaller than 20 % (Table 3), with the average MRE
for treatments T1, T2, and T3 being 10.7, 9.5, and 11.6 %,13

respectively. The root mean square errors (RMSE) for thethree treatments were 0.043, 0.035, and 0.040 cm3 cm−3,
respectively. The average errors in upper layers wereslightly larger than in deeper layers, reflecting higher
SWC variations due to irrigation, precipitation, and root
water uptake (Table 3). The lowest errors were obtained
for the deepest soil layer of 60–100 cm. From these values, it could be concluded that SWCs simulated using
HYDRUS (2D/3D) agreed well with those measured, andthat HYDRUS (2D/3D) is well suited for simulating watercontents in a drip-irrigated strip intercropping field underplastic mulch.
SWC differences between different locations
In Table 4 (for all three treatments) and Fig. 7 (only fortreatment T1), we compare SWCs for a time period ofdrip irrigation between DOY 167 and DOY 220. Table 4
and Fig. 7 indicate that there were significant differences(p < 0.05) between SWCs at the P1, P2, and P3 locationsin the top soil layers (0–10 and 10–20 cm), and that thesedifferences gradually decreased with depth, especially forthe bottom soil layer (60–100 cm) where no visible differences were observed. Although the overall trend in SWC
variations was very similar for all three treatments during
the growth period, it was obvious that there were differences in SWCs among different treatments due to different
irrigation amounts in the upper soil layers. However, there
were insignificant differences in SWCs in the deeper layersof 40–60 and 60–100 cm (Table 4; Fig. 7).
The SWCs in the main root region (0–40 cm) were highest at P1 and lowest at P2, and there were significant differences in SWCs at these three locations (p < 0.01). The
SWCs at these three locations (P1, P2, and P3) were statistically different because of different flow processes atthese locations, such as root water uptake, evaporation,and irrigation. The maximum difference in the SWC wasobserved between the P1 and P2 locations (Table 4), withthe average SWC in the upper soil layer (0–40 cm) at theP1 location being about 30 % higher than at the P2 location. This was caused mainly by the absence of irrigationand mulch at the P2 (bare strip) location, especially during
DOY 167–208 (Fig. 7). There was a competition for waterand fertilizer uptake between the two crops.
Since there were very few roots in the deep root zone
(40–100 cm) and the effect of irrigation there was negligible, this zone was largely affected by the shallow groundwater. Table 4 shows that the average SWCs were very similar at the three locations at depths of 60–100 cm, and that
there were no statistically significant differences between
T1 (p = 0.720), T2 (p = 0.956), and T3 (p = 0.979),
because SWCs at these depths were almost unaffected byirrigation (see also Fig. 7).

Soil water content (cm 3cm-3)

Soil water content (cm 3cm-3)

Soil water content (cm 3cm -3)

Irrig Sci (2015) 33:289–302
T omato0.5

Soil water content (cm 3cm -3)

Bare

0.5
0.4

0.4

0.3

0.3

0.3

0.2

0.2

Simulated

0.1

0-10cm0
110

150

Observed
190

230

270

0.2
Simulated

0.1

0-10cm0
110

0.1

Observed

150

190

230

270

0.5

0.5

0.4

0.4

0.4

0.3

0.3

0.3

0.2

Simulated

0.1

10-20cm

0
110

150

Observed
190

230

270

0.1

10-20cm

0
110

150

0.1

Observed
190

230

270

0.5

0.4

0.4

0.4

0.3

0.3

0.3

0.1
0

150

Observed
190

230

270

0.4
0.3

230

270

Simulated

150

Observed
190

230

270

0.2

0.2

20-40cm190

10-20cm

0
110

0.5

Simulated

150

0.2

Simulated

0.5

0.2

Simulated
Observed

0-10cm

0
110

0.5

0.2

Corn

0.5

0.4

110

Soil water content (cm 3 cm -3)

297

Simulated

0.1

20-40cm

0
110

150

0.1

Observed
190

230

270

0
110

0.5

0.5

0.4

0.4

0.3

0.3

Simulated

20-40cm
150

Observed
190

230

270

0.2

0.2

0.2
0.1

Simulated

40-60cm

0
110

150

Observed
190

230

270

Simulated

0.1

40-60cm

0
110

150

190

230

Simulated

0.1

Observed
270

40-60cm

0
110

0.5

0.5

0.5

0.4

0.4

0.4

0.3

0.3

0.2
0.1

Simulated60-100cm

0
110

150

Observed

190
DOY

230

270

0

110

190

230

270

0.3
0.2

0.2
0.1

150

Observed

Simulated60-100cm

150

Observed

190
DOY

230

270

0.1
0

110

Simulated60-100cm

150

Observed

190
DOY

230

270

Fig. 6  Simulated and observed SWCs at P1 (under tomatoes, left), P2 (in the bare section, middle), and P3 (under corn, right) locations fortreatment T1 at different depths

13

298
Table 3  Error analysis fordifferent treatments (T1, T2, and
T3) at different locations (P1,
P2, and P3) and different depths

Irrig Sci (2015) 33:289–302
Depth (cm)/error

T1

0–10

10–20

20–40

40–60

60–100

Table 4  Simulated average
SWCs (cm3 cm−3) at different
depths and locations (P1, P2,
and P3), and for different
treatments (T1, T2, and T3)
between DOY 167 and DOY
220

Treatment/location

T2

T3

T3

P1

P2

P3

P1

P2

P3

P1

P2

P3

MAE (cm3 cm−3)
MRE (%)RMSE (cm3 cm−3)
MAE (cm3 cm−3)
MRE (%)RMSE (cm3 cm−3)
MAE (cm3 cm−3)
MRE (%)RMSE (cm3 cm−3)
MAE (cm3 cm−3)
MRE (%)RMSE (cm3 cm−3)
MAE (cm3 cm−3)
MRE (%)

0.04
11.86
0.05
0.03
10.74
0.05
0.03
10.8
0.04
0.04
10.75
0.04
0.03
8.22

0.04
18.32
0.05
0.03
11.85
0.04
0.02
9.17
0.03
0.02
7.83
0.03
0.02
4.56

0.05
15.99
0.07
0.05
15.60
0.07
0.04
13.05
0.05
0.02
6.70
0.03
0.02
5.77

0.02
8.36
0.03
0.02
7.27
0.03
0.02
6.80
0.02
0.02
7.56
0.03
0.04
10.69

0.04
17.51
0.04
0.02
10.35
0.03
0.02
7.15
0.02
0.02
8.43
0.03
0.02
7.05

0.03
11.74
0.05
0.03
10.98
0.04
0.04
16.36
0.05
0.02
7.24
0.03
0.02
5.23

0.04
18.25
0.05
0.04
16.53
0.05
0.02
10.10
0.03
0.02
7.19
0.03
0.02
5.11

0.04
17.66
0.05
0.03
10.03
0.03
0.02
5.86
0.02
0.03
9.47
0.04
0.03
7.47

0.04
17.23
0.06
0.05
18.32
0.06
0.03
14.28
0.04
0.03
9.02
0.03
0.03
7.55

RMSE (cm3 cm−3)

0.04

0.02

0.02

0.05

0.03

0.02

0.02

0.04

0.03

Treatments/locations
T1

T2

Depths0–10 cm

10–20 cm

20–40 cm

40–60 cm

60–100 cm

P1

0.3657A

0.3358A

0.3084A

0.2980A

0.3740A

P2

0.2490B

0.2585B

0.2451B

0.2960A

0.3740AP3

0.3627A

0.3292AB

0.3030A

0.2939A

0.3738A

P1

0.3510A

0.3188A

0.2841A

0.2900A

0.3734A

P2

0.2379B

0.2430B

0.2336B

0.2949B

0.3735A

P3

0.3476AB

0.3114A

0.2778A

0.2840A

0.3732A

P1

0.3312A

0.2965A

0.2533A

0.2885A

0.3736A

P2

0.2322B

0.2345B

0.2289B

0.2944B

0.3736A

P3

0.3278AB

0.2890AB

0.2477AB

0.2822A

0.3733A

Values followed by the same letter within a column are not significantly different at p ≤ 0.05 according to
Duncan’s multiple range test

Two‑dimensional soil water distributions
Two-dimensional soil water distributions (Fig. 8) for different irrigation treatments were analyzed to evaluate themovement of soil water in the root zone during the time
period between DOY 214 and DOY 216 (i.e., after the sixth
irrigation cycle). The SWCs increased 1 day after irrigationin all three treatments, especially in the top 0- to 30-cmsoil layer around the emitters. Because of a low amountof irrigation water, the infiltration front moved only about
30 cm in both vertical and horizontal directions from drip
emitters.
When the soil water content is below the wilting point, itcannot be used any longer by crops (Allen et al. 1998). The
soil water content at a wilting point is about 0.21 cm3 cm−3

13

for a given soil texture according to the UNSODA database (Leij et al. 1996) and about 0.17–0.24 cm3 cm−3
according to Allen et al. (1998). As a result, a severe“water stress zone” (with water contents near the wilting point) developed between the two drippers at a depthof about 30–40 cm. When the amount of irrigation water
was reduced in treatments T2 and T3, the “water stresszone” increased in size. The size of the “water stress zone”
was about 48 cm2 in treatment T1 (evaluated using AutoCAD 2007 (Autodest Inc., USA) and simulated results),
which resulted in a negligible stress on root water uptake(Fig. 8a). The “water stress zone” was about 530 cm2 intreatment T2, which caused a slight restriction of the crop
growth (Fig. 8c). On the other hand, this area was about1134 cm2 in treatment T3, which clearly affected the crop

299

0.4
0.3
0.2

0-10cm

0
110

150

190

230

270

0.4
0.3
0.2
0.1

10-20cm

0
110

150

190

230

0.5
0.4
0.3
0.2
0.1

270

0.5
0.4
0.3
0.2
0.1
0
110

T omatoCorn
Bare

40-60cm
150

190

230

270

Bare
Corn
Bare

20-40cm

0
110

150

190

230

270

DOY

DOY

DOY

Soil water content (cm 3 cm -3 )T omatoCorn
Bare

Soil water content (cm 3 cm -3 )0.1

T omato
Corn
Bare

0.5

Soil water content (cm 3 cm -3 )0.5

Soil water content (cm 3 cm -3 )Soil water content (cm 3 cm -3 )Irrig Sci (2015) 33:289–302

0.5
0.4
0.3
0.2
0.1
0
110

T omatoCorn
Bare

60-100cm
150

190

230

270

DOY

DOY

Fig. 7  A comparison of simulated SWCs at P1 (tomato), P2 (bare), and P3 (corn) locations at different depths for the T1 treatment

growth (Fig. 8e). However, since the SWC in soil layers
below a depth of 60 cm was mainly influenced by the shallow groundwater, especially in the 80- to 100-cm-soil layer,
there was almost no water stress on plant water uptake inthis domain (Fig. 8a–f).
Numerical simulations indicate that the non-mulchedregion between two crop strips (i.e., the bare strip, P2) was
little influenced by irrigation, and thus, the SWC was significantly lower in this region than in the two other strips.
The “water stress zone” can be found in the bare strip (P2)
for all three treatments. There was no water stress in otherstrips (P1 and P3) for treatment T1. However, the water
stress was found for both tomatoes (P1) and corn (P3)strips in treatments T2 and T3. The water stress in the P3
strip was higher than in the P1 strip because of higher transpiration and root water uptake in the corn strip. During
soil water redistribution, 2 days after irrigation, the SWCs
gradually increased at the P2 position and did not affectthe crop growth any longer in this region for treatment T1(Fig. 8b). However, a small “water stress zone” could befound in the non-mulched region for treatment T2 (Fig. 8d).
In treatment T3, the water stress was significant (Fig. 8f),
indicating that the irrigation was not sufficient either. Figure 8 also shows that the effect of irrigation on the SWC isin all three treatments very low at depths below 40 cm andalmost none below the depth of 60 cm where only about
3.4 % of the total root mass can be found. Consequently,

almost identical SWC was found at these depths in all threetreatments.

Conclusion
The HYDRUS (2D/3D) model was parameterized and calibrated to simulate the soil water movement in a drip-irrigated, strip intercropping field under plastic mulch. Simulated SWCs at observation points at different locations
and for different irrigation treatments were found to be ingood agreement with experimental data. The average errors
were all lower than 20 %, while the average MREs were
10.7, 9.5, and 11.6 %, and the average RMSEs were 0.043,
0.035, and 0.040 cm3 cm−3 for irrigation treatments T1, T2,
and T3, respectively.
SWCs were significantly affected by irrigation amounts,
and significant differences in SWCs were observed
between different locations. There were also significant
differences in SWCs in the shallow root region (0–40 cm)
between P1 (highest water contents), P2 (lowest watercontents), and P3 locations. SWC differences at different
locations gradually decreased with depth, and there wereno visible differences in the deep root region (40–100 cm).
Additionally, the SWCs in the non-mulched region (location P2) were similar for all treatments. The average
SWC in the shallow root region was largely influenced

13

300

Irrig Sci (2015) 33:289–302

Fig. 8  Two-dimensional soil
water distributions after thesixth irrigation cycle for the T1(top; a, b), T2 (middle; c, d),and T3 (bottom; e, f) treatments;
1 day after irrigation (left; a,c, e) and 2 days after irrigation(right; b, d, and f)

by irrigation. The higher the irrigation amounts used, thehigher the SWCs observed.
The analysis of two-dimensional soil water content distributions revealed that the soil water distributions wereaffected by irrigation and root distributions. A severe “water
stress zone” (with water contents near the wilting point)
appeared in the 30- to 40-cm-soil layer, located mainly inthe non-mulched region (the bare strip) in a drip-irrigatedintercropping field under plastic mulch. The size of the“water stress zone” increased with decreasing irrigation,and it reached 1134 cm2 for the lowest irrigation amount(T3 treatment). Water redistribution following irrigation

13

increased the SWCs in the crop strips and reduced thewater stress in this area compared to the bare strip. The
optimal soil water distribution pattern in the root zone of
the intercropping field can be easily maintained using separate drip emitter lines for each crop. However, low irrigation amounts would still cause water stress in crop strips.
Although redistribution of water following irrigation gradually reduced this stress for treatment T2 after about 2 days,
for treatment T3, the water stress remained present evenafter water redistribution.
The numerical model HYDRUS (2D/3D) proved to be a
powerful tool for investigating dynamics of soil water in a

Irrig Sci (2015) 33:289–302

drip-irrigated intercropping field under plastic mulch. Fully
calibrated model could be used to quickly evaluate different irrigation management strategies without the need for alaborious field work. However, much work needs to be done
to design optimal irrigation strategies, such as irrigation frequencies, emitter depths, and emitter rates (e.g., Kandelous
et al. 2012) for these complex conditions. Additional modifications of HYDRUS (2D/3D), such as considerations ofroot growth for multiple crops; the surface energy balance;and coupled movement of water, vapor, and energy, would
also be greatly beneficial for such analysis.
Acknowledgments This research was jointly supported by the
Innovation Team Program of Educational Ministry (IRT13069), theNational Natural Science Foundation of China (51109105, 51349003,
and 51469022), the State Science and Technology Support Program(2011BAD29B03), the Post-Doctor Foundation of China (2011M500547,
2012T50250), Natural Sciences Foundation of Inner Mongolia, and theProgram for Young Talents of Science and Technology in Universities of
Inner Mongolia Autonomous Region (NJYT-12-B10).

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