沙漠研究 22-1, 215 -218 (2012 )"ICAL 1 / DT X"

Journal of Arid Land Studies－Refereed Paper－

Numerical Calculation of Soil Water Movement in a Water Harvesting Systemwith Sand Ditches Using HYDRUS-2D
Tadaomi SAITO*1), Hiroshi YASUDA2), Haruyuki FUJIMAKI2), Koji INOSAKO1) and Yukuo ABE3)
Abstract: A water harvesting system with ditches filled with highly permeable materials that has potential to reduce soil water
evaporation has been proposed. Laboratory experiments were carried out using a soil tank with dielectric sensors and various fillersfor the ditch to evaluate the water storage ability of this system. The soil water movement in the system was simulated using
HYDRUS-2D, and the results were compared with the measured results. The simulated water content distributions and cumulative
water influxes were relatively in good agreement with the measured results in the infiltration process. The estimated evaporation
rates did not agree well with the measured rates especially at the late stage in the evaporation process when the atmospheric boundary
conditions were applied to the model. This may be due to excluding the calculation scheme of vapor flux in the model.
Key Words: Arid region, Ditch, Simulation, Soil water content, Water harvesting

1. Introduction
Rain water harvesting systems are traditional agriculturalways to collect and recharge runoff water into soils by suchmeans as ditches and dams. They are essential for sustainableagriculture and afforestation without depending on irrigation
systems in arid and semi-arid regions. In general, the mostimportant point in evaluating the effect of water harvesting isdetermined how much water is collected and recharged into thesoil. However, a large amount of water is lost from the soil
and collected water surface due to high evaporation conditions
in arid environments. As a measure for this problem, a new
method of water harvesting that has potential to reduce soil
water evaporation has been proposed by means of ditches filledwith highly permeable materials (Saito et al., 2000; Abu-Zreiget al., 2000). In this method, a ditch is dug and then filledwith highly permeable materials (e.g. sand) as a device tocollect runoff water. It can be expected that runoff water
infiltrates promptly into the ditch, and the infiltrated water thenseeps to the adjacent soil through the side and bottom of theditch due to the high matric potential gradient between thematerial in the ditch and adjacent soil. In addition, thismethod can reduce the amount of evaporation from the soil
surface since the infiltrated water is stored deeper in the soil
profile. Considering its distribution shape of the soil water,
this method would be suitable for applying to trees. Thisfilled ditch, called “sand ditch”, is simple and cost-effective,
therefore it can be applied to large fields along contour lines.
The effectiveness of sand ditches has been confirmed

through laboratory and field experiments. Abu-Zreig et al.
(2000) reported that sand ditches increased water storage andinfiltration depth in an olive field in Jordan. Saito et al.
(2006) carried out laboratory experiments using various fillers
for the ditches to evaluate their water storage ability and to
examine suitable fillers. In addition to such experimental
approaches, numerical modeling of the system is important togeneralize the results. Simulation of the system may provide
optimal designing of the ditch and filler based on the regional
environmental conditions through numerical experiments.
The objective of this study, therefore, was to model the water
harvesting system with sand ditches. The soil water
movement in the system was simulated using HYDRUS-2D(Šimůnek, et al., 2005), and the results were compared with themeasured results from laboratory experiments.

2. Materials and Methods
2.1. Experimental soil and filler in the ditch
A homogeneous and dry experimental soil was made bymixing silica sand with 10% by weight of Kibushi clay. Fivetypes of large porous and highly permeable materials wereemployed as the filler in the ditch namely: sand mixed with 5%
clay, sand, gravel, chopped plastic pipes and rice chaff. The
ditches filled with the above fillers are rafter to as clay-ditch(CD), sand-ditch (SD), gravel-ditch (GD), pipe-ditch (PD) andrice chaff- ditch (RD), respectively. Some physical propertiesof the experimental soil and fillers are listed in Table 1. In
addition to five types of the ditch treatments, non-ditch (ND)
treatment was also performed as a control.

* Corresponding Author: tadaomi@muses.tottori-u.ac.jp
Faculty of Agriculture, Tottori University, 4-101 Koyama-Minami, Tottori, 680-8553, Japan
1) Faculty of Agriculture, Tottori University
2) Arid Land Research Center, Tottori University3) Alliance of Research on North Africa, University of Tsukuba

2.2. Experimental setup and procedure
Figure 1 shows the schematic diagram of the experimental
apparatus. The experimental soil was carefully placed in an
acrylic test soil tank (inside dimension: 89 × 48 × 15 cm).
The inside walls of the soil tank were previously treated byexperimental soil with bonding adhesive to prevent fingeringand preferential flow of water along the wall. A ditch wasdug out (41 × 9 × 15 cm) at the side of the tank as shown in
Fig.1, and filled with highly permeable materials. Dielectricsoil moisture sensors (ThetaProbe ML2x, Delta-T Devices Ltd,Cambridge, UK: ADR method) were set up at 26 points along
the side of the soil tank. All of the equipments were placedon weighing machines to measure evaporation rate.
After the equipments were set up, assumed runoff water
was uniformly showered over the soil surface using anirrigation device. Depth of the poured water was 40 mm perunit area. The poured water was ponded on the soil surface
until infiltration was completed. The ponding time of eachditch treatment was measured as an index to evaluate thepromotion of infiltration by the ditch. This ponding term isreferred to as “infiltration process” in this paper. Following
the completion of the infiltration, the soil tank was uncovered
to allow evaporation. The soil water was evaporated underconstant meteorological conditions during 7 days (168 h); thisterm is referred to as “evaporation process”. Soil surface
temperature was automatically regulated at 25ºC bytemperature control devices, which were connected
thermocouples and incandescent lamps. Room temperature
was also kept at 25ºC. Wind velocity was kept constant by
five blower devices.

2.3. Simulation of soil water movement
The HYDRUS-2D software package (Šimůnek et al.,2005) was used to simulate the soil water movement in both
infiltration and evaporation processes. The modified vanGenuchten model (Vogel and Cislerova, 1988) was employed
as the soil hydraulic model to adjust the air-entry value of theexperimental soil since the soil was clayey. The soil
hydraulic parameters given to the model were basicallydetermined by referring the values in Table 1 and retention
curves for each soil and filler. However, in order to stabilize
the calculations, some parameter values such as the hydraulicconductivities of the fillers were adjusted within the range that
had little influence on the water movement.
The simulations were separately performed for theinfiltration and evaporation processes. In the calculation of
the infiltration process, we applied the time variable pressure
condition corresponding to the measured ponding depth as theupper boundary condition for each treatment. The final timeof the calculation was also set at the measured ponding time.
The simulation of the evaporation process was started after
finishing the calculation of the infiltration process. The
simulated water content distributions at the end of theinfiltration process were imported as the initial water content
conditions of the evaporation process. Two types of upperboundary conditions were applied for the evaporation process:(i) time variable flux condition corresponding to the measured
evaporation rate and (ii) atmospheric boundary condition. In
this paper, we show the simulated results for ND, CD, SD and
GD in the infiltration process, and for ND and SD in theevaporation process.

3. Results and Discussion
3.1. Experimental results
The experimental results were described and discussed indetail by Saito et al. (2006). All of the with-ditch treatments
promoted the infiltration of the poured water and reduced thecumulative evaporation compared to ND (non-ditch) treatment(Figs. 2 and 3). The tendency can be seen that the large porefillers have high water storage ability.

Fig. 1. Schematic diagram of the experimental apparatus.

3.2. Simulated results
Figures 4 and 5 show the distributions of volumetric watercontent at the ends of the infiltration and evaporation processes,respectively. The simulated distributions were in relatively
good agreement with the measured distributions in theinfiltration process. The simulated water content was a little
higher than the measured water content in each ditch in theinfiltration process; this was probably because the actual
saturated water content in the test soil tank was lower than theTable 1. Physical properties of the experimental soil and fillers.
Bulk density
Saturated hydraulic
Saturated volumetricconductivity
water content
Mg m-3cm s-1m3 m-3

Soil and filler in the ditch

Experimental soil
Sand mixed with 5% clay (CD)Sand (SD)Gravel (GD)
Chopped plastic pipes (PD)
Rice chaff (RD)16
Ponding time
Cumulative evaporation (168 h)

2121.581
40.5
00.288
0.326
0.396
0.495
0.734
0.840

Measured

Cumulative evaporation (mm)2.5

Ponding time (h)9.78×10-5
1.30×10-3
1.05×10-1
6.35
12.9
1.29

1.81
1.69
1.67
1.30
0.28
0.12

0ND

CDSD

GD

PDRD

Fig. 2. Comparison of the ponding time in the infiltration process andcumulative evaporation at the end of evaporation process.
Estimated

Cumulative evaporation (mm)15.0

Fig. 4. Distributions of volumetric water content at the end of theinfiltration process: ND = non-ditch, CD = clay-ditch, SD =sand-ditch and GD = gravel-ditch.

7.5

Non- ditch
Clay- ditch
Sand- ditch
0.002448

72

96

Gravel- ditch
Pipe- ditch
Rice chaff- ditch
120

144

168

time (h)Fig. 3. Cumulative evaporation during the evaporation process.

saturated water content used in the calculation which wasobtained from column saturation (Table 1). The calculated
cumulative water influxes were also in relatively good
agreement with the amount of the poured water.
In the evaporation process, the distribution trends ofsimulated water content were in moderate agreement with themeasured distributions (Fig. 5). The soil water content at
near-surface (0 - 10 cm) was overestimated in all of thesimulated results. At the end of the evaporation process (168h), the cumulative evaporation values calculated under theboundary conditions (i) were approximately equal to themeasured values in both ND and SD, in contrast, the calculatedvalues under the boundary conditions (ii) were 77 and 231%

Fig. 5. Distributions of volumetric water content at the end of theevaporation process (168 h): ND = non-ditch and SD =sand-ditch. The boundary condition (i) is the time variable flux
condition corresponding to the measured evaporation rate. Theboundary condition (ii) is the atmospheric boundary condition.

of the measured values in ND and SD, respectively.
The variations of the estimated evaporation rates with time
under the boundary conditions (ii) are presented in Figure 6.
The estimated rates were in relatively good agreement with theEvaporation rate (mm/h)

0.6
ND: Measured
ND: Estimated (Boundary condition ii)

0.5
0.4

SD: Measured
SD: Estimated (Boundary condition ii)

0.3
0.2
0.1
0.0

024489672
Time (h)120144

168

simulated using HYDRUS-2D. The simulated water content
distributions and cumulative water influxes were relatively ingood agreement with the measured results in the infiltration
process. The estimated evaporation rates did not agree wellwith the measured rates especially at the late stage in theevaporation process when the atmospheric boundary
conditions were applied to the model. Introducing thecalculation scheme of vapor flux to the model and obtaining
optimal hydraulic parameter values especially at low watercontent range will contribute to the accurate estimation of theevaporation rate.

Fig. 6. Variations of the measured and estimated evaporation rates
with time. The plots are the measured evaporation rate that
corresponds to the time variable flux used for the boundary
condition (i). The lines are the evaporation rate estimated by themodel under boundary condition (ii).

Acknowledgements
This research was supported by Grants-in-Aid for
Scientific Research (21780224) by Japan Society for thePromotion of Science.

measured rates at the initial steady state stage of evaporation inboth ND (h < 12) and SD (h < 4). However, the evaporation
rate of ND was underestimated at the second (12 < h < 36) andthird stages (h > 36), and the rate of SD was underestimated at
the second stage and was overestimated at the third stage.
These estimation errors at the late stages may be caused by
excluding the calculation scheme of vapor flux in the model.
Further improvement of the model, introducing the calculation
scheme of vapor flux, will contribute to the accurate estimationof water content distribution and evaporation rate. Obtaining
optimal hydraulic parameter values especially at low watercontent range also seems to be effective for more accurate
calculation at late stages of evaporation processes.
In addition, the parameter value of hCritA in HYDRUS-2D
is important to estimate evaporation rate at low water contentrange. The hCritA means absolute value of the minimum
allowed pressure head at the soil surface defined fromequilibrium conditions between soil water and atmosphericvapor (Šimůnek et al., 2008); this parameter decides the lowest
water content in the calculation. Theoretically, this parameteris decided by metrological conditions; however, the values
were actually affected by the soil types. Seeking the optimalvalue of the hCritA for each soil type may be needed as apractical technique for better calculation.

References

4. Conclusion
The soil water movements in a water harvesting systemwith ditches filled with highly permeable materials was

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