International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur

Comparison of three flood runoff models in the Shonai River basin, JapanTOSHIHARU KOJIMADivision of Fluvial and Marine Disasters, Disaster Prevention Research Institute, Kyoto University,
Gokasho, Uji, 611-0011, Kyoto, Japan.
e-mail: kojima@rdp.dpri.kyoto-u.ac.jp
KAORU TAKARA
Division of Fluvial and Marine Disasters, Disaster Prevention Research Institute, Kyoto University,
Gokasho, Uji, 611-0011, Kyoto, Japan.
YASUTO TACHIKAWA
Division of Fluvial and Marine Disasters, Disaster Prevention Research Institute, Kyoto University,
Gokasho, Uji, 611-0011, Kyoto, Japan.

Abstract Distributed parameter runoff models are recently developed and expected to be used inpractice. They can take into account spatial distribution of rainfall, land surface conditions and theirchanges, which affect the runoff from river basins. This paper introduces a grid-cell based distributed
rainfall-runoff model that was developed by the authors in 1997. The model uses hydraulics-based
overland flow theory and geographic information such as digital elevation models (DEM), land
cover/use based on either the National Land Information developed by Geological Survey Institute(GSI) or remote sensing imageries.
The objective of this paper is to compare this distributed runoff model with two models conventionallyused in Japan: the storage function model and the slope-channel system kinematic wave model. The
models are assessed in terms of runoff prediction accuracy in the Shonai River (Shonai-gawa) basin at
Shidami (532 km2).
This paper discusses some problems to improve the precision of the distributed runoff model and to put
it to practical use, by comparing the three models on the basis of the indices for the model parameter
sensitivity, such as the difference in peak time, peak discharge and hydrograph shape between observed
and simulated hydrographs. The slope-channel system kinematic wave model can reproduce theobserved hydrographs well with the optimum model parameters, which are almost the same as theconventionally recommended values. Although the grid-cell based distributed model also can reproduce
the observed hydrographs well, it has a tendency to give earlier peak than the observed671International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur

one. Further investigation is necessary to improve this tendency by adjusting the roughness coefficientof channel much affecting the peak time. In the storage function model, the optimum parameters dependon flood events. Variation in optimum parameters is greater than the other runoff models.
Key wordgrid-cell based distributed model; storage function model; kinematic wave model; GIS;DEM

INTRODUCTION
Distributed parameter runoff models are recently developed and expected to be used in practice. They
can take into account spatial distribution of rainfall, land surface conditions and their changes, which
affect the runoff from river basins. The authors developed a grid-cell based distributed rainfall-runoff
model in 1997. The model which is physically-based uses geographic information such as digital
elevation models (DEM), land cover/use based on either the National Land Information developed byGeological Survey Institute (GSI) or remote sensing imageries. However, the accuracy and practicalityof the distributed runoff model has not been sufficiently confirmed.
This paper compares the conventional lamped model with the distributed runoff model, and discusses
some problems to improve the precision of the distributed runoff model and to put it to practical use. The
following three runoff models are compared in this paper.
z

storage function modelzslope-channel system kinematic wave modelz

grid-cell based distributed runoff model

TEST SITE AND DATAThe Shonai River basin is about 1,010 km2. Its lower basin is almost urbanized area, while 70% of its
upper basin is forest area, 15% is urbanized area and 15% is other land use area. It is expected to expand
the urbanized area in the both of upper and lower basin. Figure 1 shows the location of the precipitation
stations (raingauges) and the discharge sites (gauging stations) in the Shonai River basin. Discharge isobserved at Shidami, Tajimi, Toki and Mizunami. The test basin in this study is about 532 km2 at
Shidami upper site in the Shonai River basin. There are ten precipitation stations in the test basin. The
runoff models are applied to seven flood events (see Table 1). These flood events have relative large
ones from 1990 to 1995. Most of the events are the annual maximum peak discharge.
Effective rainfall is estimated with the rainfall-retention curves (Figure 2), which were obtained for672

International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur

urban, paddy and bare land at Uji, Kyoto, Japan, and for forest at the Takatoki River, Shiga, Japan(Chikamori et al., 1998). The base flow - direct flow separation is based on the following concept. Thebase flow increases from the time which the hydrograph begins to increase, and it decreases after the
peak time (Figure 3). The land use area rates of each sub basin, each slope and each cell are determinedusing the Digital National Land Information (KS-202-1; 100-m grid land use data). These land use rates
are used to determine the amount of the effective rainfalls and the model parameters. For example, if theforest area and the urbanized area are 70% and 30% respectively, and the equivalent roughness
coefficient of forest class and urban class are 0.5 and 0.25 respectively, the equivalent roughness
coefficient at the cell is 0.5 x 70% + 0.25 x 30% = 0.425.

Figure 1. Test basin.

Table 1. Flood event list.

No

Date

Biwajima

TajimiFlood 017/9/1990

annual maximum

annual maximum

Flood 1

18/9/1991

annual maximum

annual maximum

Flood 2

9/9/1993

annual maximum

Flood 3

14/9/1993

Flood 4

16/9/1994

Flood 529/9/1994

annual maximum

annual maximum

Flood 6

2/7/1995

annual maximum

annual maximum

annual maximum673

International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur

Figure 2. Rainfall-retention curves of each land use class.

Direct flow

Base flow

Figure 3. Illustration of base flow and direct flow separation.

EVALUATION OF EACH MODEL
Three runoff models are applied to the seven past flood events and simulate the hydrographs which arecompared with the observed hydrographs. The model parameters are optimized by evaluating theconformity of the observed and simulated hydrographs. The following five indices are used to evaluate
the models in terms of the accuracy of simulated hydrograph.
z

COR: Correlation coefficient between observed and simulated hydrographs during the runoff
event

z

MIRE: Mean relative error between observed and simulated hydrographs during the runoff event674

International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpurz

R.RMSE: Relative root mean square error between observed and simulated hydrographs during
the runoff eventz

TE: Peak time errorz

RPE: Relative peak discharge error

Storage function model. In the storage function runoff model, the storage-discharge relation is given as
follows.
S = Kq P∂S= re (t − T ) − q∂twhere S is volume of storage, q is direct discharge, K and P are model parameters, re is effective rainfall,t is time and T is the so-called delay time.
The practical rainfall-runoff model for flood prediction in the Shonai River basin has been constructedby the Shonai River Work Office, Ministry of Land, Infrastructure and Transport (MLIT), Japan. The
model divides the whole basin into twenty sub-basins and six stream sections. The storage function
model estimates the discharge volume in each sub-basin and each stream section. The model parameters
K and P have been calibrated by the Office using historical hydrological data. The authors simulated thehy drographs using the storag e function mo d e l w i t h t h e f i x e d v a l u e o f P a n d t h e
0.1 to 1.0 times of K in the study area. Figure 4 is the variations of the evaluation indices for Flood 1.
Figure 4 shows that if we use 0.2 x K as the value of K, we may minimize the error between observed
and simulated hydrographs (see COR, MRE, R.RMSE in Figure 4).

675

International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur

Figure 4. Variations of the evaluation indices of the storage function model for Flood 1. The horizontal
axis shows a magnification of K value.

676International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur(a) Flood 2(b) Flood 3(c) Flood 4(d) Flood 5

Figure 5. Variations of the three evaluation indices of the storage function model.

The authors also simulated the hydrographs with the storage function model, using the 0.05, 0.1, 0.2, 0.4,
0.6, 0.8, 1.0, 1.5 and 2.0 times of K in the study area. Figure 5 shows the variations of COR, MRE and
R.RMSE at Shidami. Figure 5 shows that the optimum magnification factors of K are about 0.2 for
Flood 2, about 0.2 to 0.4 for Flood 3, about 0.4 to 0.6 for Flood 4 and about 0.4 to 0.6 for Flood 5
respectively. The optimum parameters of the storage function model change much depending on theflood events.

677

International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur

Although we used effective rainfall produced with the rainfall-retention curve, effective rainfall often
used in practical work by the MLIT is based on a combination of the runoff ratio and the saturated
rainfall, in the Shonai River basin. Figure 6 represents how the determination of the effective rainfall

Figure 6. Application of the storage function model to Flood 1 and Flood 4. The upper panels are rainfall
rate, the middle panels are hydrographs obtained by using the effective rainfall conventionally used, andthe lower panels are using the modified effective rainfall (produced with the rainfall-retention curve).

affects the simulated hydrographs. The upper panels are rainfall rate, the middle panels are the simulatedhydrograph with the effective rainfall using the runoff ratio and the saturated rainfall, and the lower
panels with the rainfall-retention curve. The traditional model underestimates the peak volume for the
short-term rainfall concentration events (such as Floods 0, 1, 2, 3, and 5), and overestimates the peakvolume for the long-term rainfall continued events (such as Floods 4 and 6). Figure 6 shows that thestorage function model needs to optimize the model parameters by the flood events because the peakvolume depends on the events.
Slope-channel system kinematic wave model. The slope-channel system model considers a sub-basin as
the river channel section and the rectangular slopes at its both sides, in which the kinematic wave model
is applied to simulate overland flow. This runoff model requires the topographical properties of the land
surface, such as slope angle, slope length and river length. These topographical properties are678

International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur

automatically calculated by tracing the drainage path based on DEM. The drainage path is produced
from a 50-m DEM. This paper investigates the sensitivity of the equivalent roughness, which represents
land use class of each slope. The land use is classified into six categories in this study area. The authors
only checked about the model parameters of urban, river and forest, which affect the simulatedhydrograph most. The fixed values of each land use class are 1.0, 0.05, 0.3, 1.5 and 0.025

Figure 7. Variations of the evaluation indices of the slope channel system kinematic wave model for
Flood 1. The horizontal axis shows different equivalent roughness coefficients for forest class, whileother parameters are fixed.

679

International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur

Figure 8. Variations of the evaluation indices of the slope channel system kinematic wave model for
Flood 1. The horizontal axis shows different equivalent roughness coefficients for river class, while otherparameters are fixed.

Figure 9. Variations of the evaluation indices of the slope channel system kinematic wave model for
Flood 1. The horizontal axis shows different equivalent roughness coefficients for urban class, whileother parameters are fixed.

680

International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur

for 'forest', 'urban', 'grass', 'paddy field' and 'river' respectively. These values are conventionally used inJapan (River Bureau, Ministry of Construction, 1998).
Figure 7 shows the variations of the evaluation indices when the equivalent roughness coefficient offorest class varies 0.25 to 2.0 for Flood 1. The variations of the evaluation indices in Figure 7 such as
COR, MRE, R.RMSE and RPE show that the accuracy of the simulated hydrograph at Shidami gets
worse when the equivalent roughness coefficient of forest class is smaller than 1.0. Figure 8 shows thevariations of the evaluation indices if the equivalent roughness coefficient of river class is 0.001 to 0.1
for the Flood 1. Figure 9 shows the variations of the evaluation indices if the equivalent roughness
coefficient of urban class is 0.025 to 1.0 for the Flood 1. The variations of the roughness coefficient ofriver and urban classes almost never affect the values of the evaluation indices.
Grid-cell based distributed runoff model. The grid-cell based distributed runoff model which wasdeveloped by the authors in 1997. This model has the following features (Kojima et al., 1998).
1) A d-m square area on a node point of a d-m DEM is considered as a sub-basin, which is called a cell.
The whole of river basin consists of many square cells.
2) A DEM produces drainage paths. A drainage path connects upper cell with lower cell. A discharge
from upper cell to lower cell flows to only one direction of eight neighborhood cells.
3) In each cell, the total amount of outflows from upper cells is the inflow to the cell, and the outflow
from the cell is calculated using the kinematic wave model with the inflow and the rainfall over thecell.

Figure 10. Illustration of a grid-cell based distribution runoff model.

681

International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur

Figure 10 shows the concept of a grid-cell based distribution runoff model. The equivalent roughness ofeach cell is determined based on the land use class of the cell. The cell with river is considered as the'river' class. Figure 11 shows the variations of the evaluation indices if the equivalent roughness
coefficient of 'forest' is 0.25 to 2.0 for Flood 1. Figure 12 shows the variations of the evaluation indiceswhen the equivalent roughness coefficient of 'river' class is 0.001 to 0.1 for Flood 1. Figure 13 shows thevariations of the evaluation indices when the equivalent roughness coefficient of 'urban' class is 0.025 to
1.0 for Flood 1.
When the roughness coefficients of 'river' and 'urban' class get small, the peak discharge errors almost
never change, but MRE and R.RMSE get worse a little at the Shidami site. COR, MRE and R.RMSE get
worse at the Shidami site when the roughness coefficient of 'forest' class is smaller than 1.5. The
variations of the model parameters of the grid-cell based distributed runoff model hardly ever affect theaccuracy of the simulated hydrographs as does the slope-channel kinematic wave model.
COMPARISON WITH THE EACH RUNOFF MODELSFor Flood 1, any runoff models can simulate good hydrographs at the lowest site Shidami. The storage
function model (Smodel in the figures) overestimates the discharge volume at the upper site such as
Mizunami and Toki, such as Figure 14.

Figure 11. Variations of the evaluation indices of the grid-cell based distributed runoff model for Flood
1. The horizontal axis shows different equivalent roughness coefficients for forest class, and otherparameters are fixed.

682

International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur

Figure 12. Variations of the evaluation indices of the grid-cell based distributed runoff model for Flood
1. The horizontal axis shows different equivalent roughness coefficients for river class, and otherparameters are fixed.

Figure 13. Variations of the evaluation indices of the grid-cell based distributed runoff model for Flood
1. The horizontal axis shows different equivalent roughness coefficients for urban class, and otherparameters are fixed.

683

International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur(a) Shidami(b) Mizunami

Figure 14 Comparison of the simulated and the observed hydrographs for Flood 1.

Figure 15 shows the hydrographs for Flood 5. The grid-cell based runoff model (Cmodel) simulates thehydrographs with early peak time, and it underestimates the peak discharge volume. Although thestorage function model reproduces the observed hydrographs well at Shidami, it overestimates thepeak discharge volume at the other observation sites. The slope-channel kinematic wave model(Kmodel) can reproduce the observed hydrographs well.

Mizunami(a) Shidami(b) Mizunami

Figure 15 Comparison of the simulated and the observed hydrographs for Flood 5.

684

International Conference on Urban Hydrology for the 21st Century
14-16 October, Kuala Lumpur

CONCLUSIONS
The authors compared three runoff models, and investigated the model parameter sensitivities. The
following findings were acquired:1)

In the storage function model, further investigation is necessary for the model parameters and thedetermination of the effective rainfall to improves the accuracy of the simulation. The optimum
model parameters depend on the flood events.

2)

The slope-channel system kinematic wave model can reproduce the original hydrographs well. The
optimum model parameters which do not depend on the flood events are almost the same as theconventionally recommended values.

3)

Although the grid-cell based distributed runoff model also can reproduce the original hydrographs
well, it has a tendency to give earlier peak than the observed one. Further investigation isnecessary to improve this tendency by adjusting the roughness coefficient of river class muchaffecting the peak time.

4)

The slope-channel kinematic wave model is better runoff model than the other two models because
it can reproduce the shape of the original hydrographs well.

REFERENCES
Chikamori, H., T. Oka, K. Takara and G. Okubo (1998). "Study on application of geographic
information system to construction of rainfall-runoff model", Theory and Applications of GIS, 6(1),19-28.
Kojima, T., K. Takara, T. Oka. and T. Chitose (1998). "Effect of resolution of raster spatial data on flood
runoff simulation." Annual Journal of Hydraulic Engineering, JSCE, 42, 157-162.
Kojima, T., K. Takara and Y. Tachikawa (2002). "Study on improvement of flood runoff analysis basedon distributed models.", Advances in River Engineering, 8, 437-442.
River Bureau, Ministry of Construction (1998), "River/Sabo Technical Standard (Proposal)
Investigation Section", Sankai-do.

685