Proc. of the 2nd Asia Pacific Association of Hydrology and Water Resources (APHW) Conference,July 5-8, 2004, Suntec Singapore International Convention Exhibition Centre, Singapore,vol. 2, pp. 268-275, 2004

A NEW HYDROLOGIC RES PONSE FUNCTION PHYSICALLYDERIVED FROM DEM AND REMOTE SENSING IMAGE
Shen CHIANG
Graduate School of Civil Engineering, Kyoto University
Yoshida Hon-machi, Sakyo-ku, Kyoto, 606-8501, Japan
Yasuto TACHIKAWA, Toshiharu KOJIMA and Kaoru TAKARA
Disaster Prevention Research Institute, Kyoto University
Gokasho, Uji, Kyoto 611-0011, Japan

This study proposes a physically-based distributed instantaneous unit hydrograph byadopting the concept of IUH, which is derived based on physical runoff mechanism by
combining DEMs, remote sensing and kinematic wave approximation. The heterogeneityof the watershed can be well represented by DEMs, remotely sensed data and kinematicwave approximation in the proposed physically-based distributed instantaneous unithydrograph. As for ungauged area or the area with poor hydrologic record, thegeomorphologic IUH proposed in the study is expected to be a reference for water
resources designing and evaluation.
INTRODUCTION
Physically-based spatially distributed models provide a thorough description ofwatershed hydrologic scheme through rainfall to runoff simulation. However, massive
computation task and CPU time diminish the advantage of this kind of models. An IUH
based on a time -area method concept derived by viewing a watershed as a distributed
nonlinear system is proposed in this study, which well describes a watershed hydrologic
behavior within lighter computational burden.
The central idea of the time -area method is a time contour or an isochrone. If one
uses orthogonal grid-based data to describe watershed relief, an isochrone is a contour
joining those grid cells in the watershed which are separated from the outlet by the same
travel time. Hence, the time -area diagram indicates the distribution of travel time ofdifferent parts of the watershed drains to the outlet [1]. Through describing the water
movement mechanism by kinematic wave approximation, the travel time to the outlet iscalculated; and e xploring the relationship between the travel time and the number of gridcells, a histogram (i.e. time-area diagram) is extracted.
The hydrologic response function is viewed as a time -varient characteirestic functionin the study and is developed to include the effect of water movement mechanism in theoutput watershed hydrograph. Since the IUH is derived by using kinematic wave
approximation, the time base of the IUH is related to the given rainfall intensity.
Superpostioning of different IUHs is adopted when a hydrograph is composed bydifferent rainfall duration.
In this study, a distributed instantaneous unit hydrograph is established and applied
2to the Yasu River basin(377km ), which is located in Shiga Prefecture, midwest side of12Honshu, Japan. The distributed instantaneous unit hydrograph proposed herein reflects
topographic feature(e.g.: land cover, slope, etc.) of the basin in the hydrologic response
function, including the water movement scheme in rainfall-runoff processes.
DERIVATION OF DISTRIBUTED INSTANTANEOUS UNIT HYDROGRAPH
A concept of the instantaneous unit hydrograph has been revealed by Clark [2] in 1945.
His time-area curve is the earliest geomorphologic rainfall-runoff model in the world.
This kind of model needs no hydrologic record. Only geomorphologic data to establish
the relationship between rainfall and runoff is requested. In this study, kinematic
approximation is used to calculate the time of water movement between DEM grid cells .
Then by dividing the basin into several isochrones, the time -area histogram which
denotes the relationship between travel time and area is derived.
Process of DEM
The DEMs data used in the study is 50m grid digital map, published by Geographical
Survey Institute, Japan, in 1997. The DEM process algorithm used in this study is basedon the algorithm proposed by Jenson and Domingue [3] and Jenson and Trautwein [4].
Comparing the elevation of the central grid to its eight adjacent cells, the flow directionof the central grid is determined. According to the flow direction, the flow path from thespecific grid to the outlet of the basin and the drainage area of the grid is retrieved; andthe distance of each grid inside the basin to the outlet is calculated according to the lengthof the flow path as shown in Figure 1.

Figure 1. Distance to the outlet of the basin. (unit: m)
Use of kinematic wave approximation
The distance-area curve obtained above is simply space related, and no temporal
relationship is included.
To obtain the temporal relationship kinematic wave
approximation is used for transferring the spatial relationship into a temporal one. For
this purpose, land use data for determining roughness coefficients and rainfall data for
outflow calculation is necessary.

3

Figure 2. Using kinematic wave approximation to calculate the travel time between grids.
Consider a profile of a single grid cell as shown in Figure 2. For a given rainfall
excess intensity ie, the equilibrium flow discharge for a given drainage area (contributionarea) A is equal to ieA. By calculating the discharge of each grid inside the basin, thedistributed instantaneous unit hydrograph of the basin is retrieved through describing themechanism of the water movement.
To consider the direct runoff velocity change due to rainfall excess intensity,
kinematic wave approximation is included into the extraction of the IUH. With thevelocity of water movement between grids, the travel time of water movement isobtained.
The momentum equation of kinematic wave can be expressed in the form as Eq.(1):q = α ( y ⋅ cos θ ) m(1)where q denotes discharge per unit width, a and m are constants, y denotes water depth
vertical to the datum and θ denotes the angle between flow direction and the horizon.
This reveals the relationship between the velocity and water depth.
By comparing the equation with Manning’s equation, a is expressed in the form asEq.(2):α=sin θn(2)where n denotes Manning roughness coefficient. Substituting Eq.(2) into Eq.(1), andtransferring the unit width discharge q into water discharge by multiplying rainfall
intensity and drainage area A, water depth y is represented as Eq.(3) as below:
11

 nm
 n Ie ⋅ A  m
y = sec θ ⋅ q  = sec θ ⋅ 
 sin θ  sin θ B (3)

4where B denotes the width of the cell orthogonal to the flow direction. By retrieving thewater depth of the grid, travel time t of the grid is solved by dividing distance by watermovement velocity as shown in Eq. (4)t=D ⋅ sec θV(4)where V denotes water movement velocity.
Roughness coefficient determination
The roughness coefficient was determined from ASTER remo te sensing image
classification (Figure 3). ASTER is a high efficiency optical sensor equipped on satellite
TERRA which covers a wide spectral region from the visible to the thermal infrared by
14 spectral bands. A 2nd level processed image is used. Data acquisition date is 8th , Dec.
2003. The ERDAS IMAGINE is used as a tool to proceed the atmosphere correction,geometric correction and land cover classification.

Figure 3. ASTER image, the white line delineate watershed boundary.

5Figure 4. Land cover classification by using the ASTER image.
Table 1. The category of the land cover and its percentage inside the basin.
Categories

Artificial

Percentage

12.65%

Paddy
field
12.40%

Otherusage
0.02%

WaterForest

Wasteland

Grass

0.04%

52.62%

6.60%

2.72%

The land cover is divided into 8 categories: paddy field, forest, artificial object,wasteland, cloud, other usage, water and grass land. Figure 4 shows the result ofclassification. After the procedure of classification, the area classified as cloud is
replaced by using an existing land use data. The land use data is acquired through theweb page of Ministry of Land, infrastructure and transport, Japan. Time of land use dataacquisition is 1997. Table 1 shows the percentage of each category inside the watershed.
The value of the Manning roughness coefficient was calibrated by several rainfall eventswith the land use classification.
Rainfall data
The rainfall data was collected from four rainfall gauging stations inside the Yasu Riverbasin; Yasu, Minakuchi, Kouka and Oogawara. The average precipitation was calculated
according to the weight of each rainfall station obtained by using Thiessen polygon
method.
Utilization of IUH
Rainfall event with different rainfall intensity will cause different outflow hydrograph.
That is because the overland flow velocity increases with rainfall intensity. The IUH
proposed in this sutdy can well reflect such hydraulic phenomenon. As shown in Figure
5, the peak magnitude of the proposed IUH is rising while rainfall excess intensity isincreasing. Also the time of the peak of the proposed IUH declines with rainfall excess
intensity is raised. This implys that the proposed model can well reflect the nonlinearlity
caused by different rainfall excess intensity.

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Figure 5. Relationship between rainfall excess intensity to peak magtude of IUH andtime of IUH peak.

Figure 6. Use of rainfall excess intensity and its related IUH to retrieve outflowhydrograph.
Minshall [5] found that one UH could not adequately define the shape of a hydrographderived from a storm of unit duration. Consequently, different UHs are required torepresent the watershed runoff reponse if the rainfall intensity varied. As shown inFigure 6, different IUHs and its related rainfall excess intenstiy is used to compose theoutflow hydrograph. By applying the tools and data mentioned above, a physically based
watershed instantaneous hydrograph is extracted.
SIMULATION RESULTS
Two storm events at Yasu River basin were simulated as shown in Figure 7 and 8 as
below. As in Figure 7, the error of peak discharge is 1.27%, and the error of time to peakis 2 hour. As in Figure 8, the error of peak discharge is 6%, and the error of time to peakis 1 hour.

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Figure 7. simulation result of 1997/07/26

Figure 8. Simulation results of 1998/09/21

Table 2. Simulation results.
Rainfall
Event
EQ p
ET p
R2IOA

1997/07/26.03-1997/07/30.03

1998/09/21.00-1998/09/30.00

1.27%
2hr
0.93490.9791

6%
1 hr
0.77
0.90

EQP (%) = ( QP )simulated − ( QP )recorded( QP )recorded
ET P (hr) = (T P)simulated ? (T P)recorded

Qp : peak discharge
Tp : time to peakR2 =1-(∑(Qrecorded-Qsimulated)2 /∑(Qrecorded- Qrecorded ) 2 )Q: discharge
2IoA = 1.0 −∑ [(Qrecorded)i − (Qsimulated) i ]∑ ( (Q) − Qrecorded + (Qsimulated)i − Qsimuilated) 2

recorded i

The results show that the instantaneous unit hydrograph simulated the rainfall-runoff
relationship of the basin well. The detail of the rainfall events and simulation results isshown in Table 2.
CONCLUSIONS
Manipulating UH to estimate the stream flow hydrograph of the specific point needs lotsof hydrologic record (e.g. rainfall data, discharge data). For ungauged areas and those8basins where the hydrologic environment is changed by human activity or urbanization, it
is inadequate to adopt the method.
To solve the problem, a geomorphologic instantaneous unit hydrograph is proposed.
The heterogeneity of the watershed, orographical feature and land cover can be well
represented by using DEMs, remote sensing images and kinematic wave approximation.
The time base of the proposed IUH is determined by rainfall excess intensity. Timeof peak and peak magnitude of the IUH also change with different rainfall excess
intensity. This means the proposed IUH can reflect the impact of varied rainfall intensity.
Use of remote sensing images to determine roughness coefficient makes the model enable
to reflect the impact of land cover changing. This implies the method is capable to adapt
to a watershed with poor hydrologic records. The method can be recognized as a goodreference for water resources planning and design for ungauged areas and those basins
where the hydrologic environment has been changed by human activity or urbanization.

REFERENCES[1] Singh, V. P., “Hydrologic systems, rainfall-runoff modeling”, Vol. 1, Prentice Hall,(1988).
[2] Clark, C. O., “Storage and the unit hydrograph ”, Tran. ASCE, Vol.110,
No.2261, (1945), p p .1419-1446.
[3] Jenson, S. K. and Domingue, J. O., “Extracting Topographic structure from digital
elevation data for geographic information system analysis”, PhotogrametricEngineering and Remote Sensing, Vol. 54(11), (1988), pp.1593-1600.
[4] Jenson, S. K. and Trautwein, C. M., “Methods and applications in surface
depression analysis”, Proceedings of Auto-Carto 8, Baltimore, Maryland, (1987),
pp.137-144.
[5] Minshall, N. E., “Predicting storm runoff on small experimental watersheds”, J. of
the Hydraulics Division, Proceedings of the American Society of Civil Engineers,
86(HY8), (1960), pp 17-38.