沙漠研究 24-1, 93-96 (2014)
Ἃ₍◊✲ 24-1, 93 - 96 (2014)
Journal of Arid Land Studies
Journal of Arid Land Studies－ DT11 Refereed Paper －㸫DT11 Refereed Paper㸫Effect of Difference in Vegetation Type on Runoff Simulation Resultsin Arid Land
Osamu YOKOHAGI1), Toshinori KOJIMA*1), 2), Hideki SUGANUMA1) and Tadaomi SAITO3)
Abstract: We have established a research site for afforestation near Leonora (annual rainfall 200 mm evapotranspiration 2,400-2,600mm y-1) in Western Australia. In arid land, the most serious problem is water shortage for afforestation, because of the rainfall
deficiency and fluctuation. In addition, because of high rainfall intensity, large amount of runoff water flows out without being usedby plants. To understand water behavior for selecting appropriate afforestation sites, we developed an original numerical runoff
model to simulate water behavior. This model consists of three simulation processes which are penetration, evaporation and runoff aswater behavior. This model has two fitting parameters. One is penetration rate adjustment factor (PR) and the other is equivalentroughness coefficient (N). This model simulation was conducted using one minute cumulative data calculated from rainfall
measurement data obtained on 24th March 2003. In this study we also carried out cylinder intake rate tests at bare ground (vegetation
cover: less than 1%) and grass fields (vegetation cover: 1-10%) to estimate the effect of vegetation type. We made experimental
equations according to three types of infiltration formula (Kostiakov, Philip and Horton), and then incorporated them into thepenetration process model, which notably affected runoff simulation results.
Key Words: Afforestation, Arid land, Carbon fixation, Hydrologic simulation, Runoff model

1. Introduction
For the mitigation of global warming, we have to establish
a sustainable carbon fixation system. Hence large scaleafforestation of arid land, which was not used for crop
cultivation, has been proposed and demonstrated in Western
Australia (Yamada et al., 2003; Kojima et al., 2006). The
biggest problem for establishment of afforestation is the lack ofavailable water because of the rainfall shortage and the large
amount of runoff water loss by evaporation.
To avoid such disadvantages, our afforestation system hasadopted a water-harvesting system. Also the afforestation
area should be selected to use runoff water efficiently (Kojimaet al., 2010). In the present series of studies, we aim todevelop an original runoff model for arid land afforestation,and select areas suitable for large scale afforestation by
numerical calculation about water behavior. This study
focused on the effect of differences in three types of infiltration
formula (Kostiakov, Philip and Horton) made from different
types of cylinder intake rate tests at bare ground (vegetation
cover: less than 1%) and grass fields (vegetation cover:1-10%).

2. Materials and Methods
2.1. Research area
We have established a research site (6 × 4.8 km2) which
includes an enclosed basin (inside of the dot-line) near Sturt
Meadows Station (STM), Leonora, Western Australia asshown in Figure 1 (UTM coordinate system zone 51: Upper
left 301990, 6823670; Lower right 307980, 6818880). In thisarea, 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 mm y-1 A), which isclassified into arid land (Kojima et al., 2006).
Furthermore, a hardpan layer with extremely low
permeability is located between about several tens ofcentimeters deep and a few tens of 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). A waterlevel gauge was installed at the catchment pond (shown by thecircle in Fig. 1) and water level data were obtained for everyhour (Hamano et al., 2010). In this study, we used rainfall
data recorded on 24th March 2003. Rainfall data recorded* Corresponding Author: kojima@st.seikei.ac.jp
3-3-1, Kichijoji-Kitamachi, Musashino, Tokyo, 180-8633, Japan1) Department of Materials and Life Science, Seikei University, Japan
2) Centre for Ecosystem Management, School of Natural Sciences, Edith Cowan University, Australia3) Department of Biological and Environmental Sciences, Tottori University, Japan

㸦Received, September 14th, 2013; Accepted, February 10th, 2014㸧

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Table 1. Infiltration formula.
Kostiakov

I=ktmPhilipHorton

0.5

f t =f c+(f 0䠉f c)eI =St +At-Kt

㻝

I= 3.03t0.82

I =2.82t +0.92t

0.5

f t =1.20+(1.363)e-0.0541t

2I= 1.37t

0.72

I =1.28t +0.27t

0.5

f t =1.13+(0.722)e-0.0657t

㻟I= 4.92t

0.78

I =4.80t +1.38t

0.5

f t =1.88+(2.480)e-0.0579t

I : Permeability [mm], k : Coefficients [mm/minm], t : Time [min], m :Coefficients [-], S : Water absorbency [mm/min0.5], A : Final infiltration
rate [mm/min], ft : Permeation rate at time t [mm/min], f0 : Initial
permeation rate [mm/min], fc : Saturated permeation coefficient [mm/min],
K : Coefficients [min-1], t : Time [min] 1: faster penetration bare ground 2:
slower penetration bare ground 3: grass field.

Fig. 1. Flow Area and Locations of Instruments.

by three rainfall gauges were very similar on that day, so thesedata were considered to indicate a uniform rainfall event
throughout the target area.
2.3. Concept of original runoff model
The present runoff model has been developed to predictwater behavior in arid areas by inputting only Digital Elevation
Model (DEM) data and rainfall data. DEM with 10 m grid
spacing (10 m mesh) was purchased from Kevron Aerial
Survey Pty. Ltd. and used as the elevation data in this model.
However, this model needs some measured parameters such as
soil depth and initial volumetric water content of soil ș [-] aslocal environmental conditions. In this study, we adopted
0.15 m for the soil depth as the measured averaged data and0.05 for the initial volumetric water content of soil, the lowest
value of the range of possible values between 0.05 and 0.4(Kojima et al., 2010) considering the actual dry condition.
Time difference method with an interval (time step) for
approximating real-time progress was used in the model. As
water movement expression, the penetration, evaporation andrunoff after rainfall were calculated in all meshes. Previous
studies revealed that calculation results were affected by timestep, and 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. PenetrationPenetration rate was estimated by analyzing soil infiltration
experimental results by the cylinder intake rate method of two
points in bare ground (1. faster 2. slower) and one point in thegrass field (3.). We also used three types of infiltration

formula for simulation (Table 1) for their analysis. In ourmodel, we modify infiltration formula in Table 1 giving time
variation of permeation I or penetration rate ft into fș,
penetration rate as a function of volumetric water content ofsoil ș. Also penetration rate adjustment factor (PR), whichwas one of the fitting parameters in this model, was employed
for correcting differences between experiment and actual
penetration rate as shown in Eq. (1) (Kojima et al., 2010).

FTf T PR ࠉࠉ(1)where Fș is corrected permeation rate [mm/min]; fș ispermeation rate at water content of soil ș [mm/min]; PR ispenetration rate adjustment factor [-].
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 annual average pan evaporation rate as
shown in Eq. (2). Evaporation rate from soil was divided into
two drying steps from the result of the 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. (3). And
also, decreasing evaporation rate ES2, which is slower
evaporation rate with decreasing water content of soil, wasestimated from the evaporation experiment from soil as shownin Eq. (4) (Kojima et al., 2010).
EL=7.6710-8(2)(3)
ES2=EL
ES2=EL54.0(ș-0.05)2.677(4)where EL is water surface evaporation rate [m/s]; ES1 isconstant evaporation rate [m/s]; ES2 is 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 (VenTe Chow, 1959). Manning’s equation includes roughness

95

coefficient, n, representing stream resistance, while in thepresent model, equivalent roughness coefficient, N, wasintroduced as one of the fitting parameters (Eq. (5)).
Manning’s equation is the equation for a river with uniform
flow, and it could not express water movement at a catchment
pond. Thus, in this model, error trap was introduced in therunoff calculation. In order to avoid the phenomenon ofwater level oscillation, the flow of water is stopped when levels
become horizontally flat. Thus, water level difference before
one time step of runoff calculation cannot be reversed after one
time step of runoff calculation (Kojima et al., 2010).
1 2 3 12v
R I ࠉࠉ(5)Nwhere v is velocity [m/s]; N is equivalent roughness coefficient[sm-1/3]; I is water surface inclination [m/m]; R is hydraulicradius [m].

Fig. 2. Comparison of calculation results and observation data(Kostiakov equation of point 1 and N=0.015 sm-1/3).
2018162.7. Fitting parameters
This model includes two fitting parameters. The fitting
parameters are penetration rate adjustment factor (PR) andequivalent roughness coefficient (N). Both of parameters also
include the averaging effect inside a wide mesh.

RMSE

141210864202.8. Evaluation methods
In this study, we calculated simulation model changing
fitting parameter N with increment of 0.001, and fitting
parameter PR with increment of 0.1. The differences
between calculation results and the observed data wereevaluated by RMSE (Root Mean Square Error) values, and we
decided that optimized combination of N and PR had thesmallest RMSE value.

3. Results and Discussion
3.1. Numerical results using penetration equation for baregroundCalculation results using Kostiakov’s equation and point 1
data are shown in Figure 2. From the graph, water level
raised around 120 minutes after rain started, which was causedby rainwater that fell near the catchment pond. Although,after 240 minutes, surface runoff water far from upstream
reached the catchment pond and water level raised again. In
the prediction of surface runoff near the catchment pond, there
were few effects of differences in the fitting parameters.
However, in the prediction of surface runoff water from fararea, changed fitting parameters affect calculation results. We
applied the same evaluation for the various combinations of PRand N (N: 0.010-0.020, PR: 15-25).
Figure 3 shows comparison of RMSE values and variousfitting parameter pairs (N, PR) of Kostiakov equation (point 1).

17.5

1818.5

PR[-]

1919.52020.5

Fig. 3. Comparison of RMSE values and various fitting parameterpairs (N, PR) of Kostiakov equation (point 1).
Table 2. Best fit parameter pairs of numerical results 1: faster
penetration bare ground 2: slower penetration bare ground3: grass field.
NKostiakov
PR RMSEN

Philip
PR RMSE

NHortonPR RMSE1㻝 0.015 19.6

5.04

0.014 18.2

4.96

0.015 20.6

4.78

2 0.0144.95.05

0.014

4.5

6.22

0.014

7.3

4.68

3 0.014 30.5

4.85

0.014 31.5

5.07

0.015 35.4

4.89

Best fit parameter pairs were found to be N=0.015 and
PR=19.6, which is given in Table 2.
The best fit results for using Philip and Horton equations
are also shown in Table 2.
Furthermore the evaluations using the penetration data at
point 2 are also conducted as for point one and their results areshown in Table 2.
3.2. Numerical results using penetration equation forgrass fields
As well as bare ground, we conducted the numericalcalculation using infiltration formula by grass fields.
Calculation results of Kostiakov’s equation of point 3 are96

the area surrounding Jim’s Pool is almost bare ground, thoughseveral times differences were observed among the obtained
values of best fit. PR between points 1 and 2 areunconvincing. Also, simulation results of using infiltration
formula made from point 3 (grass fields) gave fitting parameter
PR in the range of 30-35. In order to apply our model to awide area, it is necessary to change the penetration equation
with appropriate soil properties.

Fig. 4. Comparison of calculation results and observation data(Kostiakov equation of point 3 and N=0.014 sm-1/3).

shown in Figure 4, including the best fit one.
3.3. Discussion of best fit parameter pairs
Comparing the calculation results of bare ground, fitting
parameter of N is almost the same of 0.014~0.015 for all ninecases. But, these results are different from Manning’s
roughness coefficient, n of 0.025~0.06 for smoothest androughest natural streams. (Ven Te Chow, 1959). We consider
that differences between fitting parameter N and Manning’s
roughness coefficient n are caused by used mesh size in thismodel, because inside the each rectangular mesh is flat andwater flow is expanded to the entire mesh. However, actual
terrain is rough and water flow is not wide compared to meshsize. Further, there is a large difference in the best fit valuesof the fitting parameter of PR. When using the penetration
equation for faster penetration rate point, PR is about 20, while
for slower penetration rate point, PR is a one digit value.
Using the grass field data, PR is over 30. We found that thepenetration rate is different due to differences of soil properties.

4. Conclusion
In this study, we used three types of infiltration formula
made from 3 points of cylinder intake rate tests at bare groundand grass fields. Calculation results for best fit using
infiltration formula and bare ground intake rate test data gave
almost constant fitting parameters N. On the other hand, inthe case of fitting parameters PR gave far different values ofPR among infiltration formula made from point 1 (penetration
rate is relatively fast) and point 2 (penetration rate is relativelyslow). Regardless of the type of formula, simulation resultsof using the infiltration formula and data point 2 (penetration
rate is relatively slow), the values of fitting parameter PR are in
the range of 4-8. This result is close to the report that
infiltration rates measured by cylinder intake rate test were fiveto six times higher than that observed under natural rainfall(Rao et al., 1998). The present results are convincing because

Acknowledgement
This work was conducted under the support of the Mitsui& Co., Ltd. Environment Fund, JSPS KAKENHI Grant
Numbers (22254002, 25304004) and the Global Environment
Research Fund of The Ministry of Environment of Japan(GHG-SSCP project).
NoteA) Bureau of Meteorology, Australia (http://www.bom.gov.au/
jsp/ncc/climate_averages/evapotranspiration/index.jsp?
maptype=6&period=an#maps)

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