Agricultural Water Management 211 (2019) 111–122

Contents lists available at ScienceDirect

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

Experimental and numerical evaluation of a ring-shaped emitter for
subsurface irrigation

T⁎

Reskiana Saefuddina, Hirotaka Saitoa, , Jiří Šimůnekb
abTokyo University of Agriculture and Technology, Fuchu, Tokyo, 183-8509 Japan
University of California, Riverside, CA 92521 USA

A R T I C LE I N FO

A B S T R A C T

Keywords:
Subsurface irrigation
Ring-shaped emitter
Macroscopic
Capillary length
Water use eﬃciency (WUE)
Numerical simulation

A low-cost subsurface irrigation system can generate beneﬁts for small-scale farmers who have scarce water
resources. A ring-shaped emitter made from a standard rubber hose has been developed and introduced forsubsurface irrigation in Indonesia. It is a low-cost irrigation technology based on indigenous materials and skills.
To build a ring-shaped emitter of the original design, a rubber hose is bent into a ring shape with a diameter ofabout 20 cm, and then ﬁve 5-mm holes are drilled into it at even intervals. Next, the entire ring-shaped hose iscovered with a permeable textile so that water can inﬁltrate in all directions around the buried emitter. Water isapplied from a water tank connected to the emitter by adjusting the pressure head imposed at the inlet of theemitter. Although it has been successfully used in practice, the performance of the ring-shaped emitter has notbeen evaluated in detail. Additionally, because the ring-shaped hose is fully covered with the textile, it may be
diﬃcult to detect any malfunctions or repair it. To promote the ring-shaped emitter for subsurface irrigation
among small-scale farmers in arid or semi-arid regions, it is important to design an emitter that is easy tomaintain. This study proposes a reduction in the number of holes and a change of covering method. Because thenumber of experiments that can be carried out to evaluate the performance of alternative ring-shaped emitters is
usually limited, numerical simulations can be performed in addition to experiments. The main objectives of thisstudy thus were 1) to experimentally investigate the water movement around a buried ring-shaped emitter and2) to numerically evaluate the eﬀect of modifying the design of the ring-shaped emitter on soil water dynamics
around the emitter. Numerical simulations were carried out using HYDRUS, one of the most complete packages
for simulating variably-saturated water ﬂow in two- or three-dimensional domains. HYDRUS simulations in a
fully three-dimensional domain were performed using the soil hydraulic parameters that were optimized against
experimental data collected during experiments with the original ring-shaped emitter. Simulation results conﬁrmed that reducing the number of holes does not signiﬁcantly aﬀect the water availability in silt for model
plants, such as tomato and strawberry, and that covering the entire emitter is not necessary. Partially covering
the emitter allows one to maintain the emitter much more easily compared to the original fully-covered emitter.

1. Introduction
Some of the modern irrigation technologies designed for large-scale
farming with complex and expensive devices tend to fail when introduced in rural areas of developing countries where farming is generally practiced on a much smaller scale. In these areas, maintaining
complex irrigation systems can become a roadblock to promoting
modern technologies because there may not be enough well-trainedengineers and it may be diﬃcult to ﬁnd parts to repair these systems.
Therefore, the use of indigenous skills and materials is crucial to introducing irrigation technologies in such communities.
Subsurface irrigation with a ring-shaped emitter (Saefuddin et al.,⁎2014) is one of the irrigation techniques recently developed and introduced in rural areas of Indonesia for cultivating annual and perennial crops (e.g., Sumarsono et al., 2018). An emitter made from arubber hose is economically aﬀordable, especially for small-scale
farmers. After a rubber hose is bent into a ring shape with a diameter ofabout 20 cm, ﬁve 5-mm holes are drilled into it at even intervals. An
entire ring-shaped hose is then covered with a permeable textile so that
irrigation water can be distributed through the permeable textile in all
directions around an emitter. When used in the ﬁeld conditions, anumber of ring-shaped emitters can be connected to a pipeline which
delivers water from a water source, such as a reservoir, a water tank, ora faucet. A constant pressure head can be maintained at the inlet when

Corresponding author.
E-mail address: hiros@cc.tuat.ac.jp (H. Saito).

https://doi.org/10.1016/j.agwat.2018.09.039
Received 10 April 2018; Received in revised form 9 August 2018; Accepted 21 September 20180378-3774/ © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license(http://creativecommons.org/licenses/BY/4.0/).

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Fig. 1. Top view (a) and cross-section (b) of the soil container used in the laboratory experiments with a ring-shaped emitter.

holes that were fully covered by a permeable textile. While the emitter
was developed to aid plant cultivation, the laboratory experiments werecarried out without any plants in this study to avoid any diﬃculties
associated with plant root water uptake. The collected experimental soil
moisture data were used to calibrate HYDRUS. The calibrated model
was then validated by comparing its prediction against additional experimental data.
The third objective was achieved by simulating changes in the soil
water content around buried emitters of diﬀerent designs. As an indirect quantitative proxy for evaluating the three-dimensional wetted
volume around the buried emitter, corresponding root water uptake
rates were computed. When water around the emitter is not uniformly
distributed, the roots around the buried emitter may not be able touptake water at an optimum rate because some parts of the root system
are under stress. The root water uptake rate, therefore, can be used as
an indirect indicator of how buried ring-shaped emitters of diﬀerent
designs performed compared to the original ring-shaped emitter.

the emitter is connected to a water tank. Sumarsono et al. (2018) applied 25-cm pressure head to the buried ring-shaped emitter to cultivate
annual and perennial crops.
Although ring-shaped emitters have been successfully used for cultivating, for example, melon on an island of Indonesia where precipitation is limited (Saefuddin et al., 2014), its current design andoperation are purely empirical. Understanding soil water movement
and the spatial extent of the wetted volume around an emitter is crucial
to achieving optimum operation of subsurface irrigation with a ringshaped emitter and to modifying its design to improve usability andwater-use eﬃciency. In addition, the current design of the ring-shaped
emitter does not allow one to easily detect malfunctions because theemitter is fully covered with a permeable textile. As a result, it is noteasy to repair it quickly.
For faster promotion of the technology, it is important to have adesign that is easy to maintain. It has not yet been evaluated whether
the number of holes can be reduced and/or whether it is possible tocover emitters only partially with a permeable textile. Because thenumber of experiments that can be carried out is usually limited, numerical simulations can be used instead to evaluate the performance of
ring-shaped emitters of various designs and under diﬀerent soils andenvironmental conditions. Using numerical simulations, a design that ismore robust may be developed.
In this study, the HYDRUS (2D/3D) model (Šimůnek et al., 2016)
was used to simulate soil water movement during subsurface irrigation
with a ring-shaped emitter. The model is referred to simply as HYDRUS
in the reminder of the manuscript. A number of past studies conﬁrmed
the suitability of HYDRUS for simulating water movement duringsubsurface irrigation. For example, Skaggs et al. (2004) compared
HYDRUS-simulated water contents for a subsurface line-source drip
irrigation with observed ﬁeld data for three diﬀerent emitter discharge
rates. Kandelous and Šimůnek (2010b) used HYDRUS to evaluate laboratory and ﬁeld data involving water movement in clay loam frompoint water sources buried at diﬀerent depths and with diﬀerent discharge rates. Kandelous et al. (2011) validated HYDRUS to simulate
water movement from a subsurface drip irrigation system by comparing
simulated results with measured soil water contents in several ﬁeld
experiments.
The main objectives of this study were 1) to experimentally investigate the water movement around a buried ring-shaped emitter
during irrigation, 2) to validate the capacity of HYDRUS to simulate
such water movement, and 3) to numerically evaluate the eﬀects of
modiﬁed designs of the ring-shaped emitter on soil water dynamics
during irrigation. Laboratory experiments were ﬁrst carried out tomonitor changes in the soil water content at diﬀerent positions during
irrigation using the buried original ring-shaped emitter with ﬁve drilled

2. Materials and methods
2.1. Laboratory experiments with the ring-shaped emitter
The laboratory experiments were carried out using a container(50 cm in diameter at the top, 40 cm in diameter at the bottom, and55 cm in height) ﬁlled with air-dried soil (Fig. 1). Two soil types, silt
and sand, were used in the experiments. Soils were packed in 5-cm
increments at the predetermined bulk density of 1.41 g cm−3 and 1.52 g
cm−3 for silt and sand, respectively. A 10-cm thick gravel layer was
installed at the bottom of the container. For each experiment, the original ring-shaped emitter was installed at a depth of 15 cm. The emitter
was connected to a Mariotte tank (10 cm in diameter and 44 cm inheight) to control the water pressure head applied at the inlet (referred
to as the inlet pressure). In this study, a constant pressure head of either
1 cm or 5 cm was maintained at the inlet of the buried emitter for 10 h
to apply water through the emitter. Although a much higher pressure
head was imposed at the inlet in ﬁeld cultivation practices (e.g.,
Sumarsono et al., 2018), either 1 cm or 5 cm was used in this experiment to avoid a positive back pressure at the outlets (Shani et al., 1996;
Lazarovitch et al., 2005). During the experiments, the volume of waterin the Mariotte tank was recorded every 30 min to obtain the water
application rate (i.e., the emitter discharge rate).
The ring-shaped emitter used in this study was made from a rubber
water hose. The hose, which had a 1 cm inner diameter, was bent into aring shape with a diameter of about 20 cm. There were 5 small holes
with 0.5 cm in diameter drilled at even intervals on one side of the ring.
The entire ring was covered with a permeable textile so that applied
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Fig. 2. Schematic of the original ring-shaped emitter used in the laboratory experiment.

where Xm, Ym, and Zm are the maximum rooting lengths in the x, y, andz directions [L], respectively, and Px [-], Py [-], Pz [-], x* [L], y* [L], andz*[L] are empirical parameters. These empirical parameters are included to account for asymmetrical root water uptake in any direction
and to allow for a maximum root water uptake at any location (X0, Y0,
Z0) where (0 < X0 < Xm, 0 < Y0 < Ym, 0 < Z0 < Zm). Following Vrugt
et al. (2001), Px, Py, and Pz were all set to unity for x > x*, y > y*, andz > z*. More details about HYDRUS can be found in Šimůnek et al.
(2011, 2016) and Radcliﬀe and Šimůnek (2010).

water could inﬁltrate in all directions into the soil. The original ringshaped emitter is referred to as the 5 F emitter in the remainder of themanuscript. The schematic of the ring-shaped emitter is depicted inFig. 2. When the ring-shaped emitter was installed in the soil, its 5 holes
were all facing down to block any soil particles from entering the holes.
There were 8 capacitance soil moisture sensors, EC5, a product of
METER Environment, installed around the buried emitter to monitorchanges in the soil water content. Fig. 1 shows the position of thesensors in the container. Four sensors were installed at depths of 10, 20,
30, and 40 cm directly above and below the emitter and four additional
sensors were installed at the same depths in the center of the emitter.
Since the ring-shaped emitter was installed at a depth of 15 cm, the four
sensor installation depths were 5 cm above, and 5, 15, and 25 cm below
the emitter, respectively. The soil moisture sensors were individuallycalibrated for the soils used in the experiments. Soil water retention
data for the sand and silt soil were determined using a suction plate anda pressure plate apparatus. The van Genuchten-Mualem model was
ﬁtted to the data using the RETC software package (van Genuchten
et al., 1991).

2.3. Soil hydraulic parameter estimation
HYDRUS also has the ability to inversely estimate soil hydraulicparameters from transient variably-saturated water ﬂow data, such as
from water ﬂow data collected during subsurface water application
experiments with the original-design ring-shaped emitter. The inverse
method implemented in HYDRUS is based on the minimization of an
objective function, which expresses the discrepancy between observed
and predicted water ﬂow variables. HYDRUS uses the MarquardtLevenberg optimization algorithm (Marquardt et al., 1963) to minimize
the objective function. In this study, a soil hydraulic parameter set thatminimizes the objective function given below was estimated. The objective function O was deﬁned as the sum of two components:

2.2. Root water uptake mode in HYDRUS
In this study, HYDRUS was used to simulate water movement in soil
during subsurface irrigation with a ring-shaped emitter. In HYDRUS,
root water uptake is modeled as a sink term in the Richards equation
using the stress response function proposed by Feddes et al. (1978). A
compensated root water uptake model is also implemented by introducing a threshold value, referred to as the root adaptability factor,of a dimensionless water stress index, which is deﬁned as the ratio of
actual and potential transpiration (Šimůnek and Hopmans, 2009). If thewater stress index is above the root adaptability factor, reduced root
water uptake in one part of the root zone is fully compensated for byroot water uptake from other parts of the root zone where the water
stress is smaller, so that the actual transpiration rate is equal to thepotential transpiration rate. If the water stress index is below the root
adaptability factor, reduced water uptake is only partially compensated. The ratio of actual to potential transpiration is then equal to theratio of the water stress index to the root adaptability factor, which isless than unity. In this study, the compensated root water uptake modelwith the root adaptability factor of 0.25 was used when comparing
diﬀerent conﬁgurations of the ring-shaped emitter.
The following three-dimensional root distribution function b(x, y, z)of Vrugt et al. (2001) is implemented in HYDRUS :

mθ

i=1
j=1
nq

+ ∑ wk [qc* (tk ) − qc (tk , β)]2
k=1

(2)

where θj is the soil water content (SWC) at the sensor position x and qc
is the cumulative emitter discharge at the inlet of the buried ringshaped emitter [L3T−1]. The superscript * represents speciﬁc measurements at time ti for SWCs and tk for the cumulative discharge. Whilemθ is the number of sensor locations, nθj is the number of measurements
at each sensor position. In this objective function, θj (x, t j, β) andqc (tk , β) are the corresponding model predictions for the vector of optimized soil hydraulic parameters, β, and vj, wi,j, and wk are weights
associated with a particular measurement. During parameter estimation, the selected parameters of the van Genuchten-Mualem model (vanGenuchten, 1980) were optimized.
Since the original ring-shaped emitter used in the experiment was
fully covered by a permeable textile, we assumed that water inﬁltrated
through the textile in all directions. Therefore, the system could bemodeled as an axisymmetrical three-dimensional domain. The domain
geometry used in the axisymmetrical three-dimensional model is shownin Fig. 3. Similar axisymmetric modeling approaches have been used inmany other studies with a subsurface point water source (Cote et al.,pb (x , y, z ) = [1 −nθjO (β, θ, q) = ∑ vj ∑ wi, j [θj* (x, ti ) − θj (x, ti, β)]2yxz −( px |x* − x| + y |y* − y| + pz |z *− z|)
Ym
Zm
][1 −
][1 −
] e Xm
Xm
Ym
Zm
(1)
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Fig. 4. Schematics (top views) of ring-shaped emitters of diﬀerent designs.
Black sections depict locations of holes covered with permeable textile andwhite sections depict rubber hoses without cover (i.e., impermeable parts).

the vertical coordinates.

2.4. Numerical analysis of alternative emitter conﬁgurations
One of the main objectives of this study was to numerically investigate the eﬀect of changing ring-shaped emitter conﬁgurations,especially the number and locations of holes and the textile cover, on
the spatial extent of the wetted volume around the buried emitter. In
addition to the original ring-shaped emitter with ﬁve drilled holes fully
covered by a permeable textile, ring-shaped emitters with a reduced
number of holes and only partially covered by the textile were considered. Modiﬁed emitters with 2, 3, 4, and 5 holes, referred to as 2 P,
3 P, 4 P, and 5 P emitters, respectively, were considered in this study.
The original ring-shaped emitter is referred to as 5 F. Fig. 4 shows a top
view of the ﬁve diﬀerent ring-shaped emitters considered in this study.
The black sections of the ring represent the locations covered with thetextile (i.e., permeable sections), while the white sections represent thering without the textile (i.e., impermeable sections). The partiallycovered emitters were designed to increase the ease of inspection andmaintenance.
The numerical simulations were carried out in a fully three-dimensional domain so that the asymmetry in the hole conﬁgurations
could be modeled without any simpliﬁcations. The three-dimensional
simulation domain was discretized into 41,016 three-dimensional triangular prismatic elements with ﬁner elements around the emitter(with sizes of 1 cm) and gradually increasing element sizes farther fromthe emitter (up to 2.5 cm). The initial and boundary conditions of thesesimulations were similar to those used in the axisymmetrical three-dimensional case. The time-variable ﬂux/head boundary condition was
speciﬁed in the nodes representing the ring with the textile (dark blueparts in Fig. 4). The inlet pressure head was kept constant at 1 cm
during the water application in all simulations following the experimental setup. If a much higher inlet pressure head is applied at the
inlet, a positive back pressure may build up at the outlets of the emitter,
which can lead to a substantial decrease in the emitter discharge rate
(Shani et al., 1996). In this numerical analysis, the water application
was stopped when the predeﬁned amount of water (e.g., 720 cm3 perday), which meets the plant water requirement, was injected. The eﬀectof the emitter design was ﬁrst assessed by simulating changes in the soil
water content over 24 h after 720 cm3 of water was applied to initiallydry soils.
In practice, it is important to know the eﬀect of preceding irrigations on the soil water dynamics during subsurface irrigation with thering-shaped emitter. The simulations were thus also carried out for
504 h (i.e., 21 days), during which water was applied 7 times (i.e., 7

Fig. 3. An axisymmetric three-dimensional simulation domain used in the numerical analysis of water ﬂow from a buried ring-shaped emitter. Eight red dotsin the domain depict positions of moisture sensors. (For interpretation of thereferences to colour in this ﬁgure legend, the reader is referred to the web
version of this article).

2003; Gärdenäs et al., 2005; Provenzano, 2007; Kandelous andŠimůnek, 2010a; Kandelous et al., 2011; Naglič et al., 2014). A circle
with a 1-cm diameter located at a 15-cm depth in the domain represents
the cross-section of the buried ring-shaped emitter (Fig. 3). The entire
ﬂow domain was discretized into 661 nodes and 1246 triangular ﬁnite
elements, with their sizes gradually increasing away from the emitter.
The ﬁnite element mesh was generated using an automatic triangulation algorithm that is implemented in HYDRUS. Changes in the soil
water content through time were simulated at 8 observation nodes that
corresponded with the positions of the soil moisture sensors installed asshown by red dots in Fig. 3. The observed average initial water content(θin) was assigned to the entire ﬂow domain as the initial water content.
The average initial water contents were 0.044 cm3 cm−3 and0.046 cm3 cm−3 for silt and sand, respectively. The van GenuchtenMualem model parameters ﬁtted to experimental retention curves wereused as initial estimates of optimized parameters. As for Ks, the values
provided in the ROSETTA Soil Catalog (Ks = 29.7 cm h-1 for sand and0.35 cm h-1 for silt) were used as initial estimates.
While an atmospheric boundary condition was used at the soil
surface, no ﬂux boundary conditions were used at the bottom and bothsides of the domain during the simulation. As for the nodal points along
the perimeter of the emitter, a boundary condition that changes from a
constant pressure head condition to a no ﬂux condition at a speciﬁedtime was used. This boundary condition is referred to in HYDRUS as thetime-variable ﬂux/head boundary condition. While a constant pressure
head equal to the pressure head imposed during the laboratory experiment was used in nodes along the emitter during the water application time (the ﬁrst 10 h), a no-ﬂux boundary condition was used after
the water application was stopped (after 10 h). This boundary condition
applies a speciﬁed pressure head to the lowest nodal point of theemitter and adjusts pressure heads in the other nodal points based on114

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irrigation cycles). In this numerical analysis, water was applied every
three days (i.e., at 0, 72, 144, 216, 288, 350, 412, and 484 h from thestart of simulation). The amount of water applied during each irrigation
cycle matched the cumulative potential transpiration of the model
plants over 3 days. The inlet pressure head was again kept constant at
1 cm during the water application.
The comparison of wetted volumes around the buried ring-shaped
emitters of diﬀerent designs is not straightforward in the case of threedimensional simulations. Calculated water contents at particular locations cannot provide suﬃcient information on the spatial extent of thewetted volumes. In this study, the eﬀect of diﬀerent emitter designs on
the spatial extent of the wetted volume was assessed using the soil
water stress a plant would have been exposed to. Assuming that theplant roots are distributed symmetrically around the buried ring-shaped
emitter, a non-uniformity in the spatial extent of the wetted volume
may cause stress to the plant roots. For example, when some parts of thesoil are too dry, the plant roots in these regions cannot uptake water at
an optimum rate. The uncompensated root water uptake model was
ﬁrst used to indirectly assess the non-uniformity of the spatial extent of
the wetted volume around the buried emitter. The compensated root
water uptake model was then used to assess whether such non-uniformity would aﬀect actual plant root water uptake.
Two model plants, tomato and strawberry, were considered in thisstudy because of their contrasting spatial root distributions. It has to bementioned that both crops are known for their high proﬁtability as it isespecially important to investigate the eﬀectiveness of subsurface irrigation with the ring-shaped emitter for highly proﬁtable crops. Fig. 5
shows the spatial root distribution deﬁned using the Vrugt’s model forboth tomato and strawberry. The spatial root distribution was considered constant with time during simulations (i.e., the root growth wasneglected). While Table 1 summarizes the spatial root distribution
parameters for tomato and strawberry, Table 2 lists the corresponding

Table 1
Parameters describing the spatial root distribution of two model plants (tomato
and strawberry) using the Vrugt model (Vrugt et al., 2001).
Parameters

TomatoStrawberry

Maximum rooting depth, Zm (cm)Depth with maximum root density, z* (cm)
Maximum rooting radius, Xm (cm)Radius of Maximum intensity, x* (cm)
Maximum rooting radius, Ym (cm)Radius of maximum intensity, y* (cm)Non-symmetry coeﬃcient, Pz, Px, and Py
Surface area associated with transpiration (cm²)

40
25
20
0
20
0
1, 1, 1
1200

30.5
5
20
0
20
0
1, 1, 1
1200

Table 2The modiﬁed parameters for the stress response function of Feddes et al. (1978) for tomato and strawberry.
Threshold parameters
Tomatoh1 (cm)h2 (cm)h3 (cm)h4 (cm)Strawberryh1 (cm)h2 (cm)h3 (cm)h4 (cm)

Value

−10
−20
−100
−150
−10
−20
−150
−200

parameters of the stress response functions. These values were modiﬁed
from those available in HYDRUS to improve the computational stability. The simulations were carried out for two soil textures: silt andsand. A typical potential evapotranspiration (Tp) rate of 6 mm d−1

Fig. 5. Spatial root distributions based on the Vrugt’s model (Vrugt et al., 2001) for a) tomato and b) strawberry in a three-dimensional simulation domain. Diﬀerent
colors depict diﬀerent root densities.
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Fig. 6. Soil water contents (SWCs) measured by 8 moisture sensors positioned in 4 depths (10, 20, 30, and 40 cm from the soil surface) during the subsurface water
application experiments in silt (a and b) and sand (c and d). Open circles depict SWCs observed at the positions directly above (i.e., 5 cm above) and below (i.e., 5, 15,
and 25 cm below) the emitter (installed at a 15-cm depth), whereas open triangles show SWCs observed at the corresponding depths in the center of the soil
container. Two diﬀerent inlet pressure heads (i.e., 1 cm (a and c) and 5 cm (b and d)) were applied during the experiments. Lines depict corresponding SWCs
simulated using HYDRUS. While HYDRUS was calibrated using the data collected with the 1-cm inlet pressure head (a and c), it was validated using the data observedwith the 5-cm inlet pressure head (b and d).

(Shani et al., 2007), which corresponds to 720 cm3 of water per day,was used in the analysis. Simulations were carried out using the soil
hydraulic parameters inversely estimated as described in Section 2.3.
The ring-shaped emitter was placed in a depth of 15 cm, similarly as
during the experiment.

directly below the emitter increased faster than SWCs observed at 5 cm
directly above the emitter regardless of the inlet pressure applied because the gravitation enhanced the ﬂow in the downward direction.
During the redistribution process, SWCs gradually decreased at both
locations. On the other hand, SWCs in the same depths (5 cm above andbelow the buried emitter) at the center of the buried emitter started
increasing much later due to the lateral distance from the emitter (i.e.,
the water source). As expected, SWCs 5 cm below the emitter increasedmuch faster than those 5 cm above the emitter. When the inlet pressure
head was 1 cm, SWCs at the center kept increasing but never reached
the same peaks as above and below the emitter at both depths. SWCs atother depths (i.e., 30 and 40 cm below the surface) never increased
during the experiment.
The main diﬀerence between silt and sand was that observed SWCs
did not increase 5 cm above the buried emitter (dark blue symbols in
Figs. 6 cd for the depth of 10 cm) in sand. Additionally, when the applied inlet pressure head was 5 cm, increases in SWCs 5 cm and 15 cm
below the buried emitter (i.e., in depths of 20 and 30 cm) were especially large. These results indicate that downward water movement was
dominant in the sand proﬁle while water moved more radially, including lateral and upward directions, from the emitter in the silt
proﬁle. This diﬀerence can be attributed to diﬀerent macroscopic capillary lengths, λc, given below, of these two soils (Radcliﬀe andŠimůnek, 2010).

3. Results and discussions
3.1. Laboratory experiments
Subsurface water application experiments were carried out using
the original ring-shaped emitter (5 F) on two diﬀerent soils: silt andsand. Fig. 6 depicts soil water contents (SWCs) observed at 8 locations.
Fig. 7 observed cumulative discharge rates as a function of time for two
applied inlet pressure heads (1 and 5 cm) and two soils. Open triangles
in Fig. 6 show SWCs at the center of the buried ring-shaped emitter infour depths (i.e., 10 cm, 20 cm, 30 cm, and 40 cm), whereas open circles
show SWCs directly below and above the buried ring-shaped emitter inthe same four depths.
For silt, SWCs 5 cm directly below and above the buried ring-shaped
emitter (i.e., 10 and 20 cm depths) increased a few hours after the
beginning of the water application for both inlet pressure heads. This
indicates that water inﬁltrated radially in all directions around theburied emitter regardless of the inlet pressure head applied. SWCs increased earlier and faster when the inlet pressure head of 5 cm wasapplied compared to those with the 1 cm inlet pressure head. An initially steep increase in SWCs became more gradual after a few hours,
before ﬁnally reaching their maximum values after about 10 h at thetime when the application of water stopped. An increase in SWCs 5 cm

h

λc =

∫hi 0 K (h) dh
K (h 0) − K (hi )The macroscopic capillary length λc can be interpreted as the measureof the eﬀects of capillarity as opposed to gravity. The macroscopic
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Fig. 7. Observed (dots) and simulated (line) cumulative irrigations for silt (a and b) and sand (c and d) for the applied inlet pressure heads of 1 cm (a and c) and 5 cm
(b and d). The data collected using the 1-cm inlet pressure head were used for model calibration, the data collected using the 5-cm inlet pressure head were used formodel validation.

capillary length was 7.56 cm and 5.27 cm for silt and sand, respectively,
when integrating from hi = 0 cm to h0 = −200 cm. Since sand typicallyhas a much lower macroscopic capillary length than other soils, waterﬂowing from a source will move much less laterally or upward than
downward.
The cumulative discharge increased almost linearly for both soils
when the applied inlet pressure head was 1 cm. There was no obvious
diﬀerence in the cumulative discharge between silt and sand. When theinlet pressure increased to 5 cm, while the cumulative discharges forboth soils increased almost linearly with time, the cumulative discharge
after 10 h of water application in sand was much larger than in silt.

Table 3The van-Genuchten-Mualem model (van Genuchten, 1980) parameters optimized for silt and sand. Both saturated and residual water contents are marked
with * as they were not optimized during the inverse modeling.
Parameters

θr*

θs*

α

n

Ks (cm/h)lSilt (Initial)
Silt (Optimized)
Sand (Initial)
Sand (Optimized)

0.034
0.034
0.045
0.045

0.400
0.400
0..430
0.430

0.249
0.041
0.012
0.137

2.992
1.734
2.421
2.421

0.35
0.215
29.7
0.38

0.50
0.50
0.50
4.09

Table 4
Summary statistics between simulated and observed soil water contents (SWC)
at 8 locations where the soil moisture sensors were installed. RMSE, ME, MAE,
respectively, are root mean square error, mean error, and mean absolute error
computed between simulated and observed SWC.

3.2. Model calibration
To calibrate the HYDRUS model for the analysis of water movement
during the subsurface water application from the buried ring-shaped
emitter, the experimental data observed with the 1-cm inlet pressure
head were used. The data collected during the experiments performed
with the 5-cm inlet pressure head were then used to validate HYDRUS
with calibrated parameters. The soil hydraulic parameters were optimized for both soils by minimizing the objective function given by Eq.
(2). Table 3 lists the optimized van Genuchten-Mualem parameters forthe sand and silt, while Table 4 summarizes statistics of discrepancies
between observations and simulations. For both soils, ﬁtted values of
SWCs and cumulative discharges agreed reasonably well with observed
values. Both SWRCs and unsaturated hydraulic conductivity functions
shown in Fig. 8 agree well with the common shape of the typical curves
for both silt and sand (e.g., Jury and Horton, 2004).
The optimized soil hydraulic parameters were then used in HYDRUS
to compare simulated and observed SWCs at 8 sensor positions and the

Soil

Inlet pressure head (cm H2O)

RMSE
(cm3 cm−3)

ME(cm3 cm−3)

MAE(cm3 cm−3)

Silt

1
5
1
5

0.019
0.026
0.015
0.061

−0.0570.038−0.002−0.016

0.011
0.015
0.009
0.032

Sand

cumulative discharges during the experiments performed with the inlet
pressure head of 5 cm for both soils. Table 4 summarizes also errors
between observations and predictions for simulations with the optimized parameters for experiments with the inlet pressure head of 5 cm.
Figures 6bd show both observed and predicted SWCs at 8 sensor positions, whereas Figures 7bd show both observed and predicted117Agricultural Water Management 211 (2019) 111–122

R. Saefuddin et al.

Fig. 8. Soil water retention curves (left) and unsaturated hydraulic conductivity functions (right) for silt and sand described using the van Genuchten-Mualem modelwith optimized parameters.

conﬁgurations were compared (5 F, 5 P, 4 P, 3 P, and 2 P).
Fig. 10 shows simulated cumulative discharges as a function of theelapsed time for diﬀerent emitter designs computed over 24 h for initially dry silt and sand when 720 cm3 of water was applied. For bothsoils, as expected, the duration needed to reach the same inﬁltration
amount depended strongly on the number of holes. As the number ofholes decreased, the duration increased. Although these simulation
results show almost constant discharge rates regardless of the emitter
design, it has to be mentioned that the emitter discharge rate duringsubsurface irrigation cannot be kept constant in practice unless acompensated emitter is used.
Fig. 11 shows simulated uncompensated (top) and compensated(bottom) cumulative root water uptake (RWU) of tomato over 24 h in
the silt (left) and sand (right) proﬁles for diﬀerent ring-shaped emitters.
Fig. 12 summarizes the results shown in Fig. 11 for tomato, as well as
for strawberry (which were not shown in Fig. 11), using the water use
eﬃciency (WUE), which can be computed as the ratio of cumulative
RWU to cumulative irrigation at 24 h. Uncompensated RWU was used
as an indirect, quantitative proxy measure of the non-uniformity in thewetted volume around the buried emitter. Compensated RWU was thencomputed to investigate whether such non-uniformity has any eﬀect on
actual plant RWU.
Although uncompensated cumulative RWU in silt increased more
slowly when the number of holes was reduced, cumulative uncompensated RWU was almost the same at the end of the simulation for
all emitter designs (Fig. 11a). Even though the wetted volume expanded
more slowly with the smaller discharge rate in silt when the number ofholes was smaller, uncompensated RWU eventually caught up withthose for more holes as the wetted volume evolved radially in all directions (as can also be seen in Fig. 9). As for sand, the initial trend isbasically the same as for silt; the higher the number of holes, the higher
uncompensated RWU. However, uncompensated RWU computed forthe 3 P or 2 P emitters in sand, unlike in silt, could not catch up withthose for 5 F, 5 P, or 4 P after the water application was stopped. It wasalso observed that the 5 F emitter had slightly smaller cumulative RWU
after 24 h compared to emitters that were partially covered (i.e., 5 P and
4 P). When a ring-shaped emitter with only a small number of holes isused in the sand proﬁle, applied water tends to move downward rather
than radially around the emitter, as predicted numerically in the axisymmetrical three-dimensional domain for sand (Fig. 9b,d). These results are also summarized in Fig. 12. For both soils, the WUE decreased
as the number of holes decreased.
Cumulative RWU increased signiﬁcantly in both soils when thecompensated RWU model was used (Fig. 11cd). For silt, while compensated RWU with a smaller number of holes was much smaller thanthat for the emitter with more holes at earlier time, they were almost
the same at the end of simulation. This can be also seen in the computed
WUE for compensated RWU for silt for both model plants (Fig. 12). As

cumulative discharges. For silt, both SWCs and cumulative discharges
were predicted well using the optimized parameters. For sand, however, predicted SWCs did not agree well with observed ones, especially
15 cm directly below (i.e., in the depth of 30 cm) where SWCs were
overestimated and 5 cm directly above (i.e., in the depth of 10 cm)
where SWCs were underestimated. This indicates that more downward
water ﬂow occurred during the experiment than predicted by the HYDRUS simulation. When the applied inlet pressure head was 5 cm, thepreferential-type ﬂow may have occurred underneath the drilled holesof the emitter that enhanced downward water movement. This type of
ﬂow clearly creates a non-uniform asymmetrical wetted volume aroundthe buried emitter, which may not be an ideal situation for plant roots
to uptake water. Sand is known to be susceptible to preferential ﬂow or
ﬁnger-type ﬂow when it is initially dry. In places where preferential
ﬂow paths are formed, the soil becomes strongly wettable, increasing its
ability to conduct water downward through these pathways (Dekker
and Ritsema, 1994). It may, therefore, not be a good idea to apply ahigh inlet pressure when a ring-shaped emitter is installed in an initiallydry sandy soil proﬁle.
Fig. 9 shows the spatial extent of the simulated wetted areas aroundthe buried emitter in the axisymmetrical three-dimensional domain
after 1, 5, 10, 15, 20, and 24 h using the optimized soil hydraulicparameters listed in Table 3. For each soil, the wetted area (i.e., thewetted volume) was larger when the inlet pressure head was higher.
The higher water content around the emitter may cause positive pressure heads building up around the outlets of the emitter that caneventually lead to a decrease in the emitter discharge rate. As expected,
while in silt the wetted area expanded radially with time during thewater application (i.e., during the ﬁrst 10 h), downward water movement clearly outpaced lateral or upward movement in the sand proﬁle.
These results can again be explained by the diﬀerences in the soil hydraulic characteristics, especially the macroscopic capillary length, λc,of the two soils used. This study clariﬁed that HYDRUS is indeed auseful tool for analyzing soil water dynamics during the water application with the buried ring-shaped emitter (i.e., subsurface irrigation),as also indicated by a number of other subsurface drip irrigation studies(Bufon et al.,2012; Lazarovitch et al.,2007; Kandelous et al., 2012; ElNesr et al., 2014; Ghazouani et al., 2015).
3.3. The eﬀect of alternative emitter designs on soil water dynamics
The eﬀects of changing the ring covering method and reducing thenumber of holes on the spatial extent of the wetted volume around theburied ring-shaped emitter were numerically investigated using
HYDRUS. The optimized soil hydraulic parameters listed in Table 3
were used in this analysis. Root water uptake (RWU) was computed as
an indirect, quantitative proxy measure to evaluate the spatial extent of
the wetted volume. As described in Section 2.4, ﬁve diﬀerent emitter
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Fig. 9. Water contents in the axisymmetric three-dimensional ﬂow domain simulated using HYDRUS with the calibrated van Genuchten-Mualem parameters. (a) siltwith the 1-cm inlet pressure head, (b) sand with the 1-cm inlet pressure head, (c) silt with the 5-cm inlet pressure head, and (d) sand with the 5-cm inlet pressure
head.

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Fig. 10. Cumulative inﬁltration computed for diﬀerent ring-shaped emitters using HYDRUS with the optimized soil hydraulic parameters for silt (a) and sand (b)under tomato cultivation.

water application rate was smaller and consequently that there wasmuch less water lost to deep percolations even for sand. In summary.
these simulation results conﬁrm that the number of holes can be reduced to 2 or 3 regardless of the soil types considered in this study.

water was slowly discharged from the emitter with less holes, RWU
slowly increased. This implies that reducing the number of holes does
not aﬀect the amount of water available for plant root uptake over 24 hin silt. When the compensated RWU model was used for sand, thegeneral trend was the same as for the uncompensated RWU model,
except that cumulative compensated RWU was much larger.
The eﬀect of preceding irrigations was then assessed for diﬀerent
emitter designs by computing compensated cumulative RWU over 21days (i.e., 504 h), during which seven irrigation cycles were considered(Fig. 13). Cumulative compensated RWUs after 21 days for diﬀerent
emitter designs were almost the same for silt. On the other hand, forsand, cumulative compensated RWU is strongly aﬀected by the emitter
design. For 5 F, unlike the 24-hour simulation case shown in Fig. 11,
cumulative RWU starts being reduced after 8 days, while cumulative
RWUs computed for the emitters with fewer holes continuously increase. At the end of the simulation, simulated cumulative RWU for 3 P
reaches the highest value, and thus the highest WUE, among diﬀerent
evaluated designs. For 5 F, the water application rate was too high forplant roots to uptake. As a result, there was a signiﬁcant amount ofwater lost to deep percolation. For the emitters with fewer holes, the4. Summary and conclusions
The experimental results showed that water moved radially aroundthe emitter in silt, while downward water movement was dominant insand when water was applied using the buried ring-shaped emitter. The
diﬀerence in the ﬂow pattern can be attributed to the diﬀerence in themacroscopic capillary length of the soil, which can be interpreted as ameasure of the contribution of capillarity as opposed to gravity’s eﬀect
on unsaturated water movement. HYDRUS, a model simulating variably-saturated water ﬂow in porous media, was then calibrated using
the experimental data collected from the experiments with the 1-cm
inlet pressure head. The calibrated soil hydraulic parameters were used
to simulate changes in soil water contents (SWCs) for the experimentswith the 5-cm inlet pressure head. While SWCs were predicted well for
silt, SWCs above the buried emitter were overestimated and thoseFig. 11. Uncompensated (a and b) and compensated (c and d) cumulative root water uptake computed for the buried ring-shaped emitters of diﬀerent designs using
HYDRUS with the optimized soil hydraulic parameters for both silt (a and c) and sand (b and d) under tomato cultivation.
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Fig. 12. Water use eﬃciency (WUE) computed for emitters of diﬀerent designs after 24 h for the 10-h water application and tomato (a) and strawberry (b) cultivation
using compensated and uncompensated root water uptake models in HYDRUS.

proxy measure to assess the non-uniformity in the spatial extent of thewetted volume around the emitter. Two model plants, tomato andstrawberry, were considered because of their contrasting root distributions. Both uncompensated and compensated RWU were thencomputed. While the former was used to assess the non-uniformity inthe spatial extent of the wetted volume, the latter was used to investigate whether such non-uniformity had any eﬀect on plant root
water uptake.
In addition to the original 5-hole emitter that was fully covered by apermeable textile, four separate emitter designs with a diﬀerent numberof holes were analyzed. The new emitter proposed in this study was

directly below the emitter were underestimated for sand. Although the
ﬁtted saturated hydraulic conductivity for sand was too small, this result indicates that downward water movement was predominant, suggesting the occurrence of preferential ﬂow.
With the optimized soil hydraulic parameters, HYDRUS was used toinvestigate the eﬀects of alternative emitter designs on the spatial extent of the wetted volume around the buried emitter during the subsurface water application. Had the spatial distribution of the SWC been
non-uniform, some parts of the plant root system would have beenstressed, resulting in the reduction in root water uptake. In this analysis,
plant root water uptake was therefore used as an indirect, quantitative

Fig. 13. Cumulative inﬁltration computed for diﬀerent ring-shaped emitters using HYDRUS with the optimized soil hydraulic parameters for silt (a) and sand (b)under tomato cultivation with seven irrigation cycles over 21 days. Compensated (c and d) cumulative root water uptake computed during the same duration of 21days for both silt (c) and sand (d).
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only partially covered by the textile around the holes to simplify the
maintenance of the emitter. Numerical simulations with these alternative emitter designs showed that the lower number of holes did not
signiﬁcantly aﬀect uncompensated RWU in silt. However, in sand, cumulative uncompensated RWU decreased when the emitters with reduced number of holes were used in the initially dry soil, suggesting
non-uniformity in the wetted volume. The non-uniformity in the wetted
volume in silt for the emitter with fewer holes was not signiﬁcantly
diﬀerent because water moved radially from the emitter, diminishing
the eﬀect of the spatial hole conﬁguration. For sand, on the other hand,the non-uniformity in the wetted volume was larger, as indicated byuncompensated RWU.
Such non-uniformity in the wetted volume does not aﬀect the longterm performance of the ring-shaped emitter with fewer holes even forsand because of the slow discharge rate. Simulated compensated RWU
for both model plants revealed that reducing the number of holes insand gradually increased RWU as slowly inﬁltrating water allowed
plant roots to uptake water continuously. This may not be beneﬁcial
when considering the diurnal water uptake pattern of plants, whenhigher RWU occurs in daylight time.
These results show that, regardless of the soil type, reducing thenumber of holes and changing the covering method may result in amuch better water use eﬃciency and easier maintenance. Overall, thisstudy demonstrates that HYDRUS is a useful tool for analyzing soil
water dynamics around the buried ring-shaped emitter during the
subsurface water application.

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Acknowledgments
This study was partially supported by JSPS Grant-in-aid ScientiﬁcResearch program (17H03885). We would like to thank Dr. Satyanto
K.Saptomo and Prof. Budi Indra Setiawan of Bogor Agricultural
Univesity for letting us to use their ring-shaped emitter. The authors
greatly acknowledge constructive and critical comments of two anonymous reviewers and the editor that helped to improve the manuscript.
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