沙漠研究 19-1, 61- 64 (2009 )Journal of Arid Land Studies“Desert Technology IX ”
Refereed Paper

Runoff Model Development and Validation for Afforestationin Arid Land of Western Australia
Suguru KOYANAGI1, Hironori TABUCHI1, Hiroyuki HAMANO2, Hideki SUGANUMA1,
Katsuhiko KUROSAWA1, Toshinori KOJIMA1
Abstract: As a countermeasure against global warming, large scale afforestation of arid landhas been done by fixing atmospheric CO2 into plants. In arid land, however most of therainwater is lost by runoff and evaporation. Effective use of rainwater is required forafforestation. Thus, we made an original runoff model to evaluate water distribution in aresearch area. In this study, we report determination of parameters in the original runoff
model with Digital Elevation Model (DEM) to estimate water movement for the selection ofafforestation place. From the comparison of actual and numerical results, the two sensitive
parameters were decided and the characteristics of runoff water movement were elucidatedhydrologically. Moreover, validation on expansion of mesh size for application of this modelin large scale area was done. However, numerical results with large size mesh hadn’t been
approximated to small size mesh, because of roughness information of large size mesh. It was
our assignment of future investigation.
Keywords: Afforestation, DEM, Mesh size, Runoff, Simulation

1. Introduction
For the mitigation of global warming issue, a large scale afforestation of arid land has been promoted
to fix atmospheric carbon on land which is not effectively used. Arid land area is huge in the world but
the most important problem is lack of water for afforestation because of the small amount of rainfall andoccurrence of runoff on soil surface. Most of runoff water is evaporated without using for plants,
therefore, it is necessary to use runoff water effectively for arid land afforestation. The authors havedemonstrated the improve the land condition for afforestation by introducing artificial technologies(Yamada et al., 2003).
The purpose of this study is to estimate the distribution of runoff water by using the original runoff
model for selection of the best afforestation places. In this report, two sensitive parameters in the original
runoff model were decided to estimate water movement for the selection of afforestation place. Moreover,expansion of mesh size by using our model was validated to calculate in large scale area.
2. Materials and Methods
2.1. Research area
We have set a research place (4×5km) near Sturt
meadows station, Leonora, Western Australia (Fig. 1). In thisarea, most rainwater flows into a catchment called Jim’s pool.
Average annual rainfall is about 200 mm. And, hardpan 4km
layer with extremely low permeability locates from several
tens of centimeters and a few meters in depth. Therefore,water is hard to penetrate into the ground, and then plants’
growth is inhibited.

5km
Rainfall gauge
MiddleTopDamBottom

2.2. Observed data
Rainfall data was obtained from rainfall gauges at Top,
Middle, Bottom, and water level was obtained from water level
instrument in a catchment area called Jim’s pool.
1

Jim’s pool
Waterlevellevel gauge)
gauge)（(WaterFig.1. Research area and set instruments.

Faculty of Science and Technology, Seikei University, Musashino, Tokyo, Japan; Fax no. 0522-37-3871, Tel. no.
0422-37-3750, E-mail: kojima@st.seikei.ac.jp
2Asian Environment Research Group, National Institute for Environmental Studies, Ibaraki, Japan62

The model validation was performed by comparison
between obtained data and numerical results of water levelin the main catchment area.

Table 1. Input data used in runoff model.

Altitude

DEM [Digital Elevation Model]
10, 20, 50, 100m mesh2.3. Concept of original runoff modelTime stpe
0.25, 0.5, 1, 2, 5 s
Input data in original runoff model was showed Table
Soil depth
Uniformity 0.15m
1. Soil depth and Soil water content range were estimatedfrom actual data. A suitable value of time step wasSoil water
0.05 – 0.4
validated with each mesh. And, effect of mesh size content range
expansion was validated with some size meshes.
This model consists of three main steps after rainfall (penetration, evaporation and runoff).
2.3.1. Penetration
Penetration rate equation was estimated by analyzing cylinder intake rate method with Horton’s
equation (Horton, 1939), and also used penetration adjustment (PR) which was one of fitting parameters inthis model for difference between experiment and actual penetration rate.

ft = fc + ( f0 − fc ) × ef T = f t PR−kft

ft: Adjusted penetration rate at t [m/s], f0 : Initial penetration rate [m/s], fc: Penetration rate approaching
minimum value [m/s], kf : Constant value [1/s], t : Time [s], fT: Penetration rate at t [m/s], PR : Penetration
adjustment [-]Moreover, estimated equation of the relation between fT and soil water content at t (Өt) was madefrom the relation between fT and Cumulative penetration volume at t (Vt) on the experiment. Өt [-] =Cumulative penetration volume per unit area (Vt ) [m3]/ Soil volume per unit area (Vs)[m3]
2.3.2. Evaporation
Evaporation was divided into evaporation from liquid and from soil.
From liquid : Annually average pan evaporation rate (EL =7.67×10-8 m/s)
From soil : Evaporation from soil was divided by two drying steps from a result of evaporation
experiment from soil.
a. Constant ratio drying step: Constant ratio drying rate (ES1 [m/s]) equation was considered almost
evaporation from soil surface. Thus, ES was supposed EL.
b. Decreasing drying step: Decreasing drying rate (ES2 [m/s]) equation was estimated with EL fromthe relation between ES2 and soil water content (Ө) [-] on evaporation experiment from soil.
a. E = E b. E = E × 53.0 × (θ − 0.05 )2.67
S1

L

S2L

2.3.3. Runoff
Runoff calculation from objective mesh toward 4 direction meshes was used Manning’s equation(Chow, 1959) including one of fitting parameters, i.e. roughness coefficient (n).
-1/3
1 2 / 3 1 / 2 v: Ave. velocity [m/s], n : Roughness coefficient [m s]RI
I: Slope of water surface [-], R : Effective water depth [m]nManning’s equation is the equation for river of uniform flow, and it couldn’t be expressed water
movement at like pond. Thus, this model was used error trap in runoff calculation.
Generally, the flow of water is occurred to become the horizontal. Thus, water level difference
before 1time step of runoff calculation can’t be reversed after 1time step of runoff calculation.
So, to become the horizontal, the limit value of runoff toward dawn flow meshes calculated from
Manning’s equation was set by the average water level of objective and down flow meshes before every
time step of runoff calculation.

v =3. Results and Discussion
3.1. Time step
It was considered that runoff calculation results were influenced by change of time step. Therefore,
determination of the suitable time step was required for validation of fitting parameters and mesh size. The
first, its validation was performed between 5 patterns (time step = 0.25, 0.5, 1, 2, 5 s) by using 20 m mesh

63

10Precipitation
Observation
Time=0.25
Time=0.5
Time=1
Time=2Time=5750
700

20300246810Time [h]12141620600

300246810Time [h]12141618Fig. 4. Determination of a suitable couple of n andPR with 20m mesh.

W ater level at catchment [mm]

650

20

PR=13.25

650

PR=13.530246810Time [h]121416180900

Precipitation [m m ]10700

PR=13Fig. 3. Determination of PR to n = 0.012 with 20m mesh

850

Precipitation
Observation
n=0.010, PR=12.75
n=0.012, PR=13.25
n=0.015, PR=14Observation

70000800

Precipitation

7501890010800600Fig. 2. Validation of Time step with 20m mesh

750

850

850
10800
750
700

20Precipitation
10m mesh
50m mesh

650

Precipitation [mm]

800

650

W ater level at catchm ent [m m ]W ater level at catchm ent [m m ]

900
850

0

900

Precipitation [m m ]0Precipitation [mm]Water level at catchment [mm]950

Observation
20m mesh
100m mesh

600

300246810
Time [h]12141618Fig. 5. Validation of mesh size expansion fromchange of runoff water flowing intocatchment.

and same parameters (n = 0.015, PR = 14, Total rainfall 13.6 mm) (Fig. 2).
As a result, increase of time step influenced rainwater flowing into catchment i.e. water movement inthis model. However, there were little differences between the results of less than 2 s. So, a suitable
time step with 20 m mesh was decided to 2 s or less. And, the results with 10 m mesh by same method
were showed their differences were little with time step to 0.5 s or less.
So, the calculation with 10 m mesh was performed with 0.5 s and with 20 m or more size mesh wasperformed with 1 s.
3.2. Fitting parameters determination
Two sensitive fitting parameters (n, PR) in this model were related to runoff water flowing into thecatchment. Both n and PR influence to quickness of rising water level and water level after runoff water
flowed. However, main effect of “n” was the former, and main effect of “PR” was the latter.
Parameter fitting was performed from comparison between numerical results and actual data on waterlevel at catchment. The first, each “PR” was decided on final water level to each “n” selected (ex. Fig. 3).
The next, a suitable couple of parameter was decided on quickness of rising water level from some couples
of “n” and “PR” (ex. Fig. 4).
In arid land, there are little rainfall events, and most of them have regional rainfall patterns.
Therefore, a suitable couple of parameter in this model was estimated by nearly uniform rainfall in theresearch place (Used rainfall pattern: total rainfall 13.6 mm (± 0.2 mm between rainfall gauges in researcharea)).
As a result, a suitable fitting parameters couple of 10 m mesh (the most advanced mesh) was decided

64(n = 0.012, PR = 13)

0.31.0Penetration
R atio of w ater volum e[-]3.3. Validation of mesh size expansion
Evaporation
This study was aimed to selection of theafforestation in large scale area (more than 1000.2
Boundary outflow
km square). Time step had been decided byanalysis of the simulation results, and mesh size
Surface water fromshould be investigated.
rainfall
The basis of comparison data was the most
0.1
Initial surface water
advanced data calculated with 10 m mesh withit’s suitable parameters (Time step = 0.5 s, n =Difference of initial
0.012, PR = 13). The runoff calculation ofsurface water
large size mesh (20, 50, 100 m) was performed
0Total water = 2.89×105 m3
with same parameters without time step = 1 s.
10m
20m
50m
100m
The calculated water level at Jim’s poolestimated by various mesh size is shown inFig. 6. Water volume ratio in flow area of otherFigure 5 and water balance after 18 hours aftersize mesh (18 hours after rainfall).
rainfall in flow area is shown in Figure 6.
They were indicated mesh size expansion influence both of water movement and water balance.
Especially, in the results of large size meshes, surface water and boundary outflow water from flow area
decreased, and most of other rainwater became penetration water.
As a result, it was considered the calculation with large size mesh couldn’t express rainwater gathered
and flowed because of roughness information. Therefore, in the simulation results with larger mesh,surface water tends to spread horizontally and penetrate into the soil on large area by comparison withthose simulated with small mesh (or actual condition).
4. Conclusions
An original runoff model was developed and validated by using the observed data. The best
combination of the parameters with 10 m mesh was decided (Time step = 0.5 s, n = 0.012, PR = 13) in ourmodel. And, as the result of mesh size expansion validation in our model, it was considered thecalculation with large size mesh couldn’t express rainwater gathered and flowed because of roughness
information. Therefore, application of our model to large size mesh calculation was required thecountermeasures for its assignment.
Acknowledgements
This work was supported by grants from Mitsui & Co., Ltd. Environment Fund and from the Global
Environment Research Fund of The Ministry of the Environment (GHG-SSCP Project).
References
Chow V.T. (1959): Open-Channel Hydraulics, McGrow-Hill Book Company Inc., 98-99.
Horton R.E. (1939): Analysis of runoff-plat experiments with varying infiltration-capacity, Trans. American Geophysical Union,20(4): 693-711.
Yamada K., Kojima T., Abe Y., Saito M., Egashira Y., Takahashi N., Tahara K., John L. (2003): Restructuring and Afforestation of
hardpan Area to Sequester Carbon. Journal of Chemical engineering of Japan, 36(3): 328-332.