沙漠研究 22-1, 307 -310 (2012 )"ICAL 1 / DT X"

Journal of Arid Land Studies－Refereed Paper－Effect of Difference in Rainfall Patterns and Intensities
on Runoff Simulation Results in Arid Land
Osamu YOKOHAGI1), Hironori TABUCHI1), Hideki SUGANUMA1),
Katsuhiko KUROSAWA1) and Toshinori KOJIMA*1)2)
Abstract: Currently, a sustainable carbon fixation system with large scale afforestation in arid land has been established for themitigation of global warming. We have set a research site near Leonora (rainfall 200 mm: evapotranspiration 2,400-2,600 mm) inWestern Australia. In arid land, the most important problem is water shortage for afforestation, because of the small amount ofrainfall. In addition, large amount of runoff water flows out without being used by plants in this area. In this study, we developed an
original runoff model for understanding water behavior to select appropriate afforestation sites. This model consists of threesimulation processes which are penetration, evaporation and runoff as water behavior. This model has two fitting parameters. One
is corrective coefficient of penetration (PR) and the other is equivalent roughness coefficient (N). To estimate these two parameters, aclosed hydrographic basin (6 × 5 km2) including a water collecting pond and its DEM (Digital Elevation Model) data with spatial
resolution of 10 meters were used. Rainfall gauges with rainfall amount resolution and time resolution as 0.2 mm and 0.5 s,respectively, were set near the main creek flowing into the pond, and water level indicator was set in the pond. This model simulation
was conducted using one hour cumulative data or one minute cumulative data calculated from these rainfall measurement dataobtained on 24th March 2003. We also evaluated effects of various patterns of rainfall intensities on calculated results of runoff water
behavior using other rain data.
Key Words: Afforestation, Arid land, Carbon fixation, Hydrologic simulation, Runoff model

2. Materials and Methods
1. Introduction
For the mitigation of global warming, we have to establish
a sustainable carbon fixation system, thus large scaleafforestation of arid land which was not used for crop
cultivation, has been proposed and tested in Western Australia.
The biggest problem for establishment of afforestation is thelack of available water because of the rainfall shortage and thelarge amount of runoff water loss by evaporation. To avoid
such disadvantages, our afforestation system has adopted thewater-harvesting system. Also the afforestation area should
be selected to use runoff water efficiently (Yamada et al., 2003).
In the present series of studies, we aimed to develop an
original runoff model for arid land afforestation, and selectlarge scale afforestation by numerical calculation about water
behavior. This study focused on the effect of difference inrainfall patterns and intensities of input rainfall data on original
runoff model. We compare different patterns of rainfall data
input (1 minute cumulative input and 1 hour cumulative input).
Also we used not only ideal rainfall data with almost samerainfall at the three rainfall gauges but also other rainfall datacomparing results of numerical calculation.
* Corresponding Author: kojima@st.seikei.ac.jp
3-3-1, Kichijoji-kitamachi, Musashino, Tokyo, 180-8633, Japan
1) Department of Materials and Life Science, Faculty of Science and Technologies, Seikei University, Japan
2) Centre for Ecosystem Management, School of Natural Sciences, Edith Cowan University, Australia

2.1. Research area
We have set a research place (6 × 5 km2) which includes anenclosed basin (inside dot-line) near Sturt Meadows station(STM), Leonora, Western Australia as shown in Figure 1. In
this area, most runoff flows into a catchment pond called Jim’spool. Average annual rainfall of STM is about 200 mm andevapotranspiration is about 2,400-2,600 mmA), which isclassified into arid land (Kojima et al., 2006). Furthermore,
hardpan layer with extremely low permeability locates betweenabout several tens centimeters deep and a few tens meters deep.
2.2. Observed data
Rainfall gauges (resolution: 0.2 mm, measurement unit: 0.5s) were installed at three points along the main creek tocatchment pond (shown by the squares in Fig. 1). Water level
gauge installed at catchment pond (shown by the circle in Fig. 1)
and water level data were obtained for every hour (Hamano etal., 2010). In this study, we adopted a rainfall data recorded on
24th March 2003. Those data recorded with the three rainfall
gauges were very similar, and it was considered as a uniform
rainfall event throughout the target area. We used the data as

of the fitting parameters in this model was employed forcorrecting difference between experiment and actual
penetration rate as shown in Eq. (4) (Kojima et al., 2010).

f t = f c + ( f 0 − f c ) × exp(− K f t ) =(2.00 × 10 −5 + 3.06 × 10 −5 × exp − 3.42 × 10 −3 × t)

(1)f θ = −1.530 × 10 −3 × θ 3 + 1.487 × 10 −3× θ 2 − 4.782 × 10 − 4 × θ + 7.115 × 10 −5

Fig. 1. Research area and locations of instruments.

an ideal rainfall event for the present model development andvalidation.
2.3. Concept of original runoff model
The present runoff model has been developed to predictwater behavior in arid area by inputting only Digital Elevation
Model (DEM) data and rainfall data. However, this modelneeds some measured parameters such as soil depth and initial
volumetric water content of soil θ [-] as local environmental
conditions. In this study, we adopted 0.15 m for soil depth as
the measured averaged data and 0.05 for the initial volumetricwater content of soil, the lowest value of the range of possible
value between 0.05 and 0.4 (Kojima et al., 2010), because of
the actual dry condition.
Time difference method with an interval (time step) for
approximating real-time progress was employed to the model.
As the water movement expression, penetration, evaporation
and runoff after rainfall were calculated in all meshes. DEM
with 10m grid spacing (10 m mesh) was purchased from
Kevron Aerial Survey Pty. Ltd. and employed as the elevation
data in this model. Previous studies revealed that calculation
results were affected by time step. The optimal time step
depends on the mesh size (Kojima et al., 2010). In this study,
optimal time step was set as 0.5 s for 10 m mesh.
2.4. Penetration
Penetration rate was estimated by analyzing the results ofcylinder intake rate method with Horton’s equation (Eq. (1))(Horton, 1939). In our model, we modify Eq. (1) giving time
variation of penetration rate to give Eq. (2) by giving
penetration rate as a function of volumetric water content ofsoil θ, which is calculated by Eq. (3)Also penetration rate adjustment factor (PR) which was one

θ=W/0.15(3)Fθ = fθ PR

( 4)

(2)

ft : Permeation rate at time, t [m/s], f0 : Initial permeation rate[m/s], fc : Saturated hydraulic conductivity [m/s], Kf : Constantvalue [s-1], t : Time [s], fθ : Permeation rate at volumetric watercontent of soil, θ [m/s], θ : Volumetric water content of soil [-],
W : penetrated water depth [m], Fθ : Corrected permeation rate[m/s], PR : Correction factor for fθ [-]2.5. Evaporation
Evaporation rate was evaluated as the sum of that fromsurface water and that from soil. Water surface evaporation
rate was given as annually average pan evaporation rate as
shown in Eq. (5). Evaporation rate from soil was divided into
two drying steps from the result of evaporation experimentfrom soil. Constant evaporation rate ES1 was considered to bealmost same as evaporation rate from surface water. Thus,
ES1 was supposed to be equal to EL as shown in Eq. (6). Andalso, decreasing evaporation rate ES2, which is slower
evaporation rate with decreasing water content of soil, wasestimated from evaporation experiment from soil as shown in
Eq. (7) (Kojima et al., 2010).

E L = 7.67 ×10 −8
ES 1 = E L

(5)

(6)

ES 2 = E L × 54.0 × (θ − 0.05)

2.677

(7 )

EL : Water surface evaporation rate [m/s], ES1 : Constantevaporation rate [m/s], ES2 : Decreasing evaporation rate [m/s]
2.6. Runoff
Runoff from the target mesh to the adjacent meshes (fourdirections) was calculated by using Manning’s equation (Ven TeChow, 1959). Manning’s equation includes roughness coefficient,n representing stream resistance, while in the present model,
equivalent roughness coefficient N was introduced as one of thefitting parameters (Eq. (8)). Manning’s equation is the equation
for a river with uniform flow, and it couldn’t express water
movement at a catchment pond. Thus, in this model, error trap

was introduced in the runoff calculation. In order to avoid
phenomenon of water level oscillation, the flow of water is stopped
when levels become horizontally flat. Thus, water level
difference before one time step of runoff calculation can’t bereversed after one time step of runoff calculation (Kojima et al.,2010).
1 2 1v = R 3 I 2 (8)Nv : Velocity [m/s], N : Equivalent roughness coefficient [sm-1/3]
I : Water surface inclination [m/m], R : Hydraulic radius [m]2.7. Fitting parameters
This model includes two fitting parameters. The fitting
parameters are correction factor for ft (PR) to correct thedifference between experimental penetration rate and actual
penetration rate and equivalent roughness coefficient (N) that
represents stream resistance of soil surface. Both of theparameters also include the averaging effect inside a wide mesh.
In the previous study, sensitivity study of N and PR wasconducted (Kojima et al., 2010).

which gives the best fit for one hour cumulative input. The
numerical results for one minute cumulative input give
seriously higher value of water level than the observed one andnumerical results from one hour cumulative input. The
present results indicate strong effects of instantaneous rainfall
intensity on the runoff phenomena. Consequently we decided
Table 1. One hour cumulative rainfall data.
Time[h]
0-1
1-2
2-3
3-4
4-5
5-6
6-7
7-8
8-9
9-10Rainfall[mm]2003/3/24
2004/6/1
00
1.6
1.8
9.2
8.4
2.8
0.8
000
0.4
00000000

Table 2. Maximum rainfall intensities for two rainfall input patterns.
Max Rainfallintensity [mm/s]

2.9. Other rainfall data
In the previous study the runoff model was applied only tothe rainfall data on 24th March 2003. In the present study, wealso conducted the calculation for the rainfall data on 1st June
2004 and decided fitting parameters. One hour cumulative
rainfall data of the latter were shown in Table 1.

3. Results and Discussion
3.1. Effect of difference in rainfall patterns
Difference in overall cumulative rainfall data between one
hour cumulative and one minute cumulative rainfall input datais shown in Figure 2. Difference in rainfall intensity is also
shown in Table 2. From Table 2, one minute cumulative
rainfall input gives more instantaneously strong rainfall
intensity than one hour cumulative rainfall input. The
numerical results of time variation of the water level of thecatchment pond for the different rainfall patterns are shown in
Figure 3, with the parameters of N = 0.011 s m-1/3, PR = 24.5

1 hour cumulative
1 min cumulative

0.00256
0.00667

Cumulative rainfall [mm]2018

1 h cumulative rainfall data

16

1 min cumulative rainfall data

14
121086
4
20060

120

Time [min]180240300

Fig. 2. Overall cumulative rainfall data using one hour cumulativeand one minute cumulative rainfall data.
Water level at catchment pond[mm]2.8. Rainfall input
The previous study used 1 hour cumulated rainfall data
converted from observed rainfall data (Kojima et al., 2010).
However, instantaneous intensity of rainfall is often muchlarger than the time averaged one. Thus in the present study,
one minute cumulated rainfall input was used and thecalculation results of water behavior was compared with that of
1 hour cumulated rainfall input to evaluate the effect the time
resolution for rainfall.

1000
950

Observation

900

Calculated with
1 h cumulativedata
Calculated with
1 min cumulative
data

850
800
750
700
650600060120 180 240 300 360 420 480 540 600

Time [min]Fig. 3. Observed time variation of water level of catchment pond on
24th March 2003 and numerical results with two different
rainfall input patterns (N = 0.011 s m-1/3, PR = 24.5).

Water level at catchment pond[mm]1000

4. Conclusion

950
Observation

900

N=0.014 s m-1/3 PR=21.0

850
800
750
700
650
600
060 120 180 240 300 360 420 480 540 600

Time [min]Fig. 4. Observed time variation of water level of catchment pond on

Our original model was modified to use one minutecumulative rainfall input, and as a result it can express moredetail response to instantaneously strong rainfall intensity than
one hour cumulative rainfall input. We decided fittingparameters as N=0.014 s m-1/3, PR=21.0 for the data on 24th
March 2003, whose values did not differ so much. Though
the calculated results for other rainfall data on 1st June 2004 did
not fit observation data, it is expected that small modification of
the fitting parameters will give better fit of numerical results tothe observation.

24th March 2003 and numerical results with one minuteWater level at catchment pond[mm]rainfall input data (N = 0.014 s m-1/3 and PR = 21.0).

Acknowledgement
This work was conducted under the support of the Mitsui& Co., Ltd. Environment Fund, Grant-in-Aid for Scientific
Research (22254002) of Japan Society for the Promotion ofScience and the Global Environment Research Fund of The
Ministry of Environment of Japan (GHG-SSCP project).

800
Observation

750

N=0.014 s m-1/3 PR=21.0

700
650
600

NoteA) Bureau of Meteorology, Australia (http://www.bom.gov.au/
jsp/ncc/climate_averages/evapotranspiration/index.jsp?map
type=6&period=an#maps)

550
500
450
400060120180240300360420480540600

Time [min]References

Fig. 5. Water level at Catchment Pond on 1st June 2004.

to use one minute cumulative rainfall input, i.e., closer to theactual rainfall pattern, for further numerical analysis.
3.2. Fitting parameters for one minute cumulative input
We conducted the numerical calculation using original
runoff model with one minute cumulative rainfall data.
Calculation results are shown in Figure 4. The observed
water level was well reproduced with one minute cumulative
rainfall and with fitting parameters of N = 0.014 s m-1/3 and PR= 21.0. It was demonstrated that the observed data were well
reproduced with a little bit different fitting parameters.
3.3. Calculation of other rainfall data
We conducted the numerical calculation using the original
runoff model with one minute cumulative rainfall data on 1stJune 2004 using the same fitting parameters of Figure 4.
Calculation results are shown in Figure 5. Calculation results
did not well fit the observation data. As shown in theprevious section, small difference among the rainfall gages datamay affect the calculation result of water level of catchment
pond, however small modification may improve the matching
between numerical and observed results.

Hamano H., Takahashi N., Yamada K., Kojima T., Law J.
(2010): Measurement of Runoff Ratio in a Medium-scale
Watershed for Afforestation of Arid Land. Kagaku Kogaku
Ronbunshuu, 36(4): 351-354.
Horton R.E. (1939): Analysis of runoff-plat experiments withvarying infiltration-capacity. Trans. American GeophysicalUnion, 20(4): 693–711.
Kojima T., Hamano H., Abe Y., Saito M., Tanouchi H.,
Egashira Y.,Takahashi N., Law J., Yamada K. (2006): Basic
Data of Research Project on Large Scale Afforestation ofArid Land for Carbon Fixation near Leonora in WesternAustralia. J. Arid Land Studies, 16(3): 167-174.
Kojima T., Koyanagi S., Tabuchi H., Suganuma H., KurosawaK., Takahasi N., Hamano H. (2010): Development of a
Runoff Model for Arid Land Afforestation in Western
Australia. Kagaku Kogaku Ronbunshu, 36(5): 532-538.
Ven Te Chow (1959): Open-Channel Hydraulics. McGraw-Hill
Publishing Company, Inc., New York, pp. 98-123.
Yamada K., Kojima T., Abe Y., Saito M., Egashira Y.,
Takahashi N., Tahara K., John L. (2003): Restructuring
Afforestation of hardpan Area to Sequester Carbon. Journalof Chemical engineering of Japan, 36(3): 328-332.