Numerical Simulations of Soil Water Dynamics under
Surface Drip Irrigation Using HYDRUS-2D
M Yu
1
, Z Hu
2
, B Liu
1
and K Zhang
3,*
1
College of Civil Engineering and Architecture, Zhejiang University, Hangzhou
310058, China
2
Design and Research Institute of Environmental Protection Sciences of Zhejiang
Province, Hangzhou 310007, China
3
Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China
Corresponding author and e-mail: K Zhang, kfzhang@nit.zju.edu.cn
Abstract. Irrigated agriculture plays a crucially important role in food production worldwide.
Micro-irrigation has proved an effective approach to optimise and potentially save water use
in agriculture. In this study, numerical simulations using HYDRUS-2D were performed to
investigate soil water dynamics after surface drip irrigation on a clay loam soil. Two emitter
radii of 5 cm and 10 cm for drip irrigation were assumed. The initial soil water content was
set at the point that trigged irrigation, and the soil at the water discharge surface remained
saturated during irrigation. Results showed that the irrigated amount of water for the emitter
radius of 10 cm was 1.07, 1.97 and 2.86 L for the irrigation durations of 1, 2 and 3 h,
respectively, about 1.55, 1.66 and 1.48 times higher than those for the emitter radius of 5 cm.
Correspondingly, the soil wetting depth for the emitter radius of 10 cm was 13.5, 18.4 and
21.0 cm, respectively, about 20.1%, 35.8% and 22.5% higher than those for the emitter radius
of 5 cm.
1. Introduction
Irrigated agriculture plays an important role in food production worldwide. A huge amount of water
is wasted due to over application of irrigation or inefficient irrigation methods. As a result, water
resources are increasingly becoming scarce.
It is well accepted that micro irrigation is an effective method to use water in agriculture
efficiently. Nowadays, drip irrigation has widely been applied and shown its great potential in saving
agricultural water [1-3]. Numerous studies have also been carried out to use numerical models to
optimize irrigation scheduling and amount. Amongst all the simulation tools, HYDRUS software
package [4, 5] has been widely and successfully used, and achieved a large body of practically useful
results [6-9].
In this study, HYDRUS-2D was employed to investigate soil water movement during and after
surface drip irrigation on a clay loam soil with the emitter radii of 5 cm and 10 cm. The simulated
results, including water infiltration amount and soil wetting depth, could potentially be useful for
managing agricultural water use.
260
Yu, M., Hu, Z., Liu, B. and Zhang, K.
Numerical Simulations of Soil Water Dynamics under Surface Drip Irrigation Using HYDRUS-2D.
In Proceedings of the International Workshop on Environmental Management, Science and Engineer ing (IWEMSE 2018), pages 260-265
ISBN: 978-989-758-344-5
Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
2. The theory
2.1. Governing equations for soil water movement
The Richards’ equation, describing soil water movement under axis-symmetric conditions for drip
irrigation, can be expressed as:
1 h h
t r z
K
rK K
r r z z

(1)
m
r
n
sr
1
1h
Θ







(2)
0.5 1 m m 2
( ) [1 (1 ) ]
s
K h K

(3)
Where
is the volumetric soil water content, h is the soil pressure head, z is the vertical
coordinate, r is the radial coordinate, t is the time, K is the soil hydraulic conductivity,
s
and
r
are
the saturated and residual soil water content, respectively,
and n are the shape parameters,
respectively,
m 1 1 n
, K
s
is the saturated soil hydraulic conductivity,
is the relative
saturation.
2.2. Model parameter values and initial conditions
The simulated soil was a clay loam type with the hydraulic properties shown in Table 1 [10]. The
initial soil water content was set to be at the mid-point between the field capacity and the permanent
wilting point, below which crop transpiration was limited for most crops and thus irrigation was
required [11].
Table 1. The soil hydraulic parameters used in the simulations [10]
θ
s
(cm
3
/cm
3
)
α
(1/cm)
n
(-)
K
s
(cm/d)
0.410
0.019
1.31
6.24
The computed domain was 30 cm in the vertical direction and 25 cm in the radial direction. Two
emitter radii of 5 cm and 10 cm were used. The soil was assumed to be saturated within the emitter
radius during irrigation, and the irrigated amount was simulated.
3. Results and discussion
3.1. Water infiltration
The simulated cumulative water infiltration under irrigation radius of 5 cm and 10 cm is shown in
Figure 1. Basically the relationship between the cumulative infiltration and time was in a linear
manner. In terms of the infiltrated depth of water, it is about 61.2% greater under the radius of 5 cm
than that under the radius of 10 cm. This may be attributed to the fact that under the radius of 5 cm
the irrigated water has a larger volume of soil to permeate, resulting in a faster infiltration rate.
However, in terms of the total irrigated amount, the opposite was found to be the case. The total
irrigated amount of water for the irrigation radius of 10 cm was 1.07, 1.97 and 2.86 L after 1, 2 and 3
Numerical Simulations of Soil Water Dynamics under Surface Drip Irrigation Using HYDRUS-2D
261
h irrigation, respectively, about 1.55, 1.66 and 1.48 times higher than those for the irrigation radius of
5 cm.
Figure 1. The simulated cumulative infiltration under different emitter radii.
3.2. Vertical soil water content distribution
Figure 2 shows the vertical soil water distribution at different time intervals for the irrigation duration
of 2 h. Generally speaking, the patterns of soil water content distribution were similar with each other
in both cases. In the upper region, soil water content was close to be saturated during irrigation, and
then decreased with time due to re-distribution. Compared with those of the emitter radius of 5 cm,
the wetting depth and the wetted soil volume were both greater for the emitter radius of 10 cm. For
example, the wetted soil volume was about 10.0 and 52.4 L at the time intervals of 1 h and 8 h for the
irrigation radius of 5 cm, while the corresponding values were about 5.0 and 22.8 L for the irrigation
radius of 10 cm.
(a) Emitter radius: 5 cm. (b) Emitter radius: 10 cm.
Figure 2. The variation of soil water content distribution in the vertical direction with
time (irrigation duration: 2 h).
0
20
40
60
80
0 1 2 3 4
Emitter radius: 5 cm
Emitter radius: 10 cm
Infiltration (cm)
Time (h)
-30
-25
-20
-15
-10
-5
0
0 0.1 0.2 0.3 0.4 0.5
1 h
2 h
4 h
8 h
16 h
24 h
Soil depth (cm)
Soil water content (cm
3
/cm
3
)
-30
-25
-20
-15
-10
-5
0
0 0.1 0.2 0.3 0.4 0.5
1 h
2 h
4 h
8 h
16 h
24 h
Soil depth (cm)
Soil water content (cm
3
/cm
3
)
IWEMSE 2018 - International Workshop on Environmental Management, Science and Engineering
262
3.3. Soil water content contour
The simulated soil water content contour at time intervals for the emitter radius of 5 cm and irrigation
duration of 2 h is shown in Figure 3. It can be seen that the wetted distance in the vertical and radial
directions was approximately identical. The irrigated water was stored in the volume of about 10.2 L
after 2 h irrigation, and the volume increased to about 29.8 L after 24 h. The final water content in
the wetted region was relatively uniform, ranging from 0.1 to 0.15 cm
3
/cm
3
. This indicates that water
flow in the soil was relatively easy due to the good capacity of water drainage.
3.4. Wetting depth
The effects of irrigation radius and time on soil wetting depth are given in Figure 4. Clearly,
the wetting depth increased more rapidly with time during irrigation and shortly after irrigation. The
increase rate of the wetting depth was much smaller after 5 h for all the simulated cases. The emitter
radius was positively related to the soil wetting depth. For example, the final wetting depth was 29.1
cm for the emitter radius of 10 cm and irrigation duration of 3 h, while the value was reduced to 21.7
cm for the emitter radius of 5 cm. For the same emitter radius, a longer irrigation duration resulted in
a bigger soil wetting depth, but they were not proportionately correlated.
1 h 2 h 4 h
8 h 16 h 24 h
Figure 3. Soil water content contour at different time intervals after the beginning of
irrigation (emitter radius: 5 cm, irrigation duration: 2 h).
Numerical Simulations of Soil Water Dynamics under Surface Drip Irrigation Using HYDRUS-2D
263
(a) Emitter radius: 5 cm. (b) Emitter radius: 10 cm.
Figure 4. Effects of the emitter radius and irrigation duration on the soil wetting depth.
4. Conclusions
Based on the results presented the above, the following conclusions could be drawn: (1) The
cumulative infiltration amount was approximately linearly correlated with time in the studied cases.
(2) The soil wetting distance in both the vertical and radial directions was close to each other. (3) The
soil wetting depth was positively correlated with irrigation radius and irrigation time, but they were
not proportionately related.
Acknowledgement
The authors are grateful to the following funding bodies to carry out this study: National Natural
Science Foundation of China (51379187), National Natural Science Foundation of Zhejiang Province
(LY17E090001), and Ningbo Science and Technology Bureau, China (2016C10057).
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