Floods, from Defence to Management – Van Alphen, van Beek & Taal (eds)© 2006 Taylor & Francis Group, London, ISBN 0 415 39119 9Flood risk analysis toward floodplain risk management
H. Kawaguchi, T. Suetsugi & T. KusakabeRiver Division, National Institute for Land and Infrastructure Management, Ministry of Land,
Infrastructure and Transport, Japan

ABSTRACT: Active seasonal rain fronts and a lot of typhoons in 2004 brought heavy rain and flood in Japan.
This paper discusses the background of increasing damage based on those examples. Severe flood damage dueto the dyke break occurred in Niigata Prefecture. Especially many houses were broken and many people failed
to evacuate from inundated area in Nakanoshima area along Kariyata River. Numerical analysis for flood flow
is useful to manage floodplain risk. General flood simulation is presently being used to predict flooding water
depth and to make hazard map for evacuation of people in river basin etc. Objects of the general numericalanalysis are not to predict damage due to abrupt flooding flow near dyke break point. We developed a newnumerical analysis model by FDS (Flux Difference Splitting) method for abrupt flooding flow and swept-awayof houses. We made clear the relationship between the flood flow from the Kariyata River and swept-away ofhouses due to dyke break using the numerical model.

1INTRODUCTION

Generally, it is said that structural and non-structural
measures are needed to mitigate flood damage.
Structural measures are performed by dyke, dam andflood-diversion channel etc. Non-structural measures
are taken through planning for evacuation and flood
protection as well as publication of a hazard map.
Flood simulation became important for floodplain
risk management.
In this paper we discusses the flood damage thatoccurred in Japan during the year 2004 and we tried
to make some improvements on new simulation technique by FDS method to estimate flood risk withdyke break of Kariyata River.

2FLOOD RISK IN JAPAN AND FLOODDAMAGE IN 2004

2.1

Weather condition and excess flood

During the year 2004, seasonal rain fronts were so
active and many typhoons hit Japan. We had about
470 times of heavy rain with more than 50 mm/hourin that year only. This can be said tremendous since
we had only 271 times of heavy rain like that from1996 to 2003 in annual average.
Excess flood beyond improved dyke arose in various places in 2004. Except for the cases of some large

rivers with high graded dyke, there are only few
examples in which the measure are taken for theexcess flood, and that has been causing serious damages in the area people and property accumulated
along river.
2.2

Flood damage

Many houses were destroyed completely or partiallyby heavy rain along with seasonal rain front in
Niigata and Fukushima pref. in July 2004 andtyphoon No.18. More than 50,000 houses were damaged by typhoon No.16, 18 and 23. Dyke breaks
occurred at 6 point by the excess flood of Kariyata
River in Niigata. The flood probability is estimated tobe 1/150. The amount of the damage from storm andflood reached 1.2 trillion yen only by immediate damage related to public infrastructures of the road andfarm products, etc. The number of missing and deadfrom the storm and flood damage reached 227, whichis the largest numbers since 1984. Among 194 peopleof age available, 119 were senior citizen of 65 years
old or more. There was seen a feature that death riskof senior citizen was high.
2.3

Background of damage increase

As already stated, the scale of heavy rain and windbrought by the active seasonal rain front and a lot oftyphoons was big and has never experience before.

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Except for weather condition, the possible causes ofincreasing flood damages are as follows.

4

1. Insufficient improvements of small and middle
rivers
2. Accumulation of population and property along
small and middle rivers
3. Increases of handicapped persons who need to help
in flood time
4. Communication gap of information for evacuation
5. Shortage of assistance by local community
6. Untapped experience in the past flood disaster7. Frequent occurrence of excess flood.

4.1

Big damage, which 3 persons were dead and 16
houses swept away etc., be brought about by largepart of above-mentioned background in the flood of
Nakanoshima area along Kariyata River. A lot of person did not evacuate due to rapid water rise by flooding with dyke break. Numerical analysis to predictflood flow can be helped to evacuation and moreover
it is useful to manage floodplain risk.

3FLOOD SIMULATION DUE TO DYKE
BREAK BY FDS METHOD
Basic equation

Basic equation for flood flow simulation is2-dimensional shallow water equation of conservative form. The basic equation is discritized by FDS(Flux Difference Splitting) method as follows.
Because importance of the simulation is to represent
advective current on river channel and floodplain
around broken dyke, it is thought that diffusion term
is smaller than the other terms. Then, the basic equation is the following with the use of conservative vector U, flux vector E on x axis, flux vector F on y axis
and source term from gravity and friction on earth S.
(1)

EXISTING STUDY ON FLOODSIMULATION

Iwasa and Inoue et al. developed 2-dimensional
unsteady flood flow simulation model to analysis for
Yodo River etc. Kuriki and Suetsugi et al. developed
general flood simulation model introduced force byhouses as roughness coefficient. However the generalflood simulation model is used to predict flooding
water depth and to make hazard map for evacuationof people in river basin etc. In the simulation model,
formula of overflow discharge from river was used.
Objects of the general numerical analysis are not topredict damage due to abrupt flooding flow near dyke
break point.
Fukuoka and Kawashima et al. developed
2-dimensional shallow water model on general coordinate system for urban residential area. It made clearthat hydrodynamic force acting on non-submergedhouses is represented by difference of pressure on
upstream and downstream side of house assuming ashydrostatic pressure and that flood flow and hydrodynamic force is represented with good accuracy bymodeling road and houses adequately.
Akiyama and Shigeeda et al. developed
2-dimensional shallow water model by FDS method.
Temporal profile of experimental flood flow and hydrodynamic force by unsteady flow was represented withgood accuracy.
We developed new 2-dimensional flood simulation
model by FDS method to represent flood flow in river
channel, abrupt flooding flow in floodplain and sweptaway of houses for floodplain risk management.

where h is water depth, u and v is velocity, g is gravity, zb is elevation of the earth, n is Manning’s roughness coefficient.
The basic equation is transformed to hyperbolicpartial differential equation with use of characteristic
velocity vector to make fluctuation frame clear,because the flood simulation aims at advective flood
flow near dyke break point. Equation (1) can be transformed to hyperbolic equation with Jacobian of Flux
E and F.
(2)where Jx  *E/*U, Jy  *F/*U and c( gh is wave
speed.
Using right eigen vector ex and ey, the equation (2)is the following equation with characteristic velocity
vector $x, $y.

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(3)

numerical flux difference is distributed to only downstream calculation point.

(5)
The equation (3) means that partial differentiation* x(e x1*U) and * y(e x1*U) are replaced to original space after the partial differentiation is transported by the characteristic velocity. Equation (4)discritized from equation (3) by finite difference
method in next section is equal to discritized equationfrom integration of equation (3) by finite volume
method. Transportation by multi-dimensional characteristic wave is not calculated in this basic equation
for the flood flow simulation strictly. But it is thoughtthat accuracy of this simulation is enough to predictrisk of swept-away of houses by hydrodynamic force,
because of comparison of experimental and numerical results in existing study.
4.2

Discretization

Fx and Fy, which are numerical flux across cell interface, are estimated due to discritization of basic equation by finite volume method in Cartesian coordinate
system.

~ | is represented by folCharacteristic velocity |x~lowing function +(x) to remove non-physical expansion shock wave, because numerical flux of equation(5) do not satisfy entropy condition.

In the same way, numerical flux on y-axis is discritized. Gravity term is discritized by direction ofcharacteristic wave as well as pressure term.
5NUMERICAL EXPRESSION OF THE FLOODDAMAGE AND MODELING OF HOUSETO BE SWEPT AWAY

Photo 1 shows location of houses and warehouses tobe swept away on aerial photograph before flood(4)
Flood flow around broken dyke is mixed subcritical andsupercritical flow. So freezing Jacocian Jx and Jy locallyis needed to assure physical conservation in area where
physical discontinuous jump exists between calculatepoints. That is *E  Jx*U and *F  Jx*U. Roe’s velocity and wave speed is used to calculate characteristic
velocity, right and left eigen vector on cell interface.

To distribute flux difference according to characteristic velocity, for example, numerical flux Fx isas follow. In the case of subcritical flow, numericalflux difference is distributed to up and downstream
calculation point. In the case of supercritical flow,

Photo 1. Nakanoshima floodplain in Kariyata River andlocation of houses to be swept away.

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disaster. Photo 2 shows contour lines of height ofsediment deposition on aerial photograph after flood
disaster. Houses to be washed out gathered along
east-west road and around broken dyke. It is understood that local scour by flooding flow expands in thewest floodplain from dike break point of Kariyata
River and sediment deposition is larger in direction
across left dike and along east-west road. Figure 1
shows floodplain elevation after flood disaster, which
is taken by laser profiler, sediment deposition showedin Photo 2, and houses location from electronic map.
It is understood from these data and aerial photographthat sixteen houses and warehouses including a temple near dyke break point were swept away. Houses
and dyke in Figure 1 is introduced as impermeableboundary condition. Elevation within the enclosure ofleft dyke and north-south road in the figure is higher
than that of the area where houses was swept away
and great sediment was deposited. Flooding flow bydyke break is thought to be mainly two flows. One isvertical direction flow against the left dyke which
gradient of water surface is largest immediately after
the dyke is broken. Another is flow along east-westroad which resistance against flood flow is smaller.
Figure 2 is organized eyewitness report about dyke
break width in July and August 2004. In the numerical analysis, dyke break width is increased at intervalof 2 m as given condition from these reports. One ofthe eyewitness who bank up sandbags on the dyke
give testimony that earth on back slope of the dyke
was scoured at first, revetment concrete blocks
remained baldly, flood ran off toward housing estate
at a blast as soon as the revetment blocks was broken
and a temple which flood hit directly was broken

down in front of his eyes. And the dyke break wasseeing to be widening downstream. Swept-away ofhouse is mainly caused by water pressure with risingwater level on upstream face of house. In numericalanalysis, house is swept away when moment acting on
downstream bases of house is over threshold value.
The threshold value is decided from information ofhouses to be swept away in TV news taken after about
8 minutes after left dyke break. In numerical analysis,
after the house is swept away, grids of house arechanged into grids that flood flows. Hydrodynamic
force F and moment M calculated by the following
equation.
(6)
where n is unit vector which inside direction of houseboundary is positive and ds is differentiation aroundhouse boundary.

Figure 1. Floodplain topography in Nakanoshima.

Dyke break width (m)

6040

20
Given condition
Eyewitness
012:00

Photo 2. Floodplain damaged and contours of sedimentdeposition height (unit: cm).

14:00
16:00
Time (2004.7.13)

18:00

Figure 2. Dyke break width of eyewitness report and given
condition in the calculation.

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6

CALCULATED CONDITION AND
REPRESENTABILITY FOR FLOOD
FLOW

It is thought that momentum flux in Kariyata Riveraffected flow in floodplain strongly because of information about flood flow and dyke break of previous
section. Therefore, flood flow is represented in theriver from 9 to 9.88 km from confluence for ShinanoRiver and in the floodplain of 680 m  634 m which
included houses to be swept away (Figure 6). It is calculated from 12:00 to 18:00 in July 13, 2004 (Figure 3).
22Elevation (T.P.m)

20
18Calculation

16
Ooseki St.

14

Imamachi St.

12Upstream end
10Downstream end

8
8:00

12:00

16:00

20:00

24:00

Time

Figure 3. Boundary condition in upstream and downstream end.
22

Elevation (T.P.m)

Right dyke

17

It is given as calculation condition that dx  dy  2 m,dt  0.05 sec, Manning’s roughness coefficientn  0.035 in the river channel and n  0.02 in thefloodplain. Upstream and downstream condition of
Kariyata River in the calculated area is given by waterlevel data interpolated from Ooseki observation station at about 10.5 km, Imamachi observation station
at about 8.8 km and trace data on right and left dyke
in Figure 5. Figure 4 shows bed profile data in observation and calculation. Vertical wall and approximate
value of observed bed profile data is given in consideration of stability of numerical model. A part of highwater channel revetment remained and high water
channel did not scoured in the place where dyke wasbroken in Photo 3. In the calculation, floodplain elevation nearby dyke break point is given in grid to flow
newly after dyke is lost.
Figure 5 shows maximum water level among floodin calculation and observation. It is represented in
calculation that longitudinal profile of traced waterlevel in observation and difference of water level
between left and right dyke by centrifugal force inbending section at 9.6 km.
Figure 6 shows calculated maximum water depth
and traced water depth in floodplain measured in thefield. Figure 6 shows projection into each axis.
Calculated maximum depth is recorded at 3 hours
14 minutes after left dyke break. Water depth is also
shown at grids of houses to be swept away. Developednumerical model could represent water depth withgood accuracy around the broken dyke, in the direction across the left dyke and along east-west road.

High water channel

12

Low water channel

7
0

0.25

0.5

0.75

1

Dimensionless distance

Elevation (T.P.m)

Figure 4. Cross-sectional profile in the Kariyata River.

22

Photo 3. Situation of dyke break.

OosekiSt.

ImamachiSt.

20- Õ(Left)i ¶ŠÝ
TraceTrace- Õ(Right)
i‰ŠEÝŒvZ i ¶ŠÝCal.(Left)ŒvZi ‰ECal.(Right)

188.8

99.5

10

Distance from confluence of Shinano River (km)Figure 5. Trace water level on left and right dyke and maximum calculated water level.

1003

10.5

Figure 6. Trace water depth in floodplain and calculated maximum water depth (at 3 hours and 14 minutes after dykebreak).

Figure 7. Calculation results of velocity vector, inundated district and total number of houses to be swept away immediately
after dyke break (from 2 minutes to 40 minutes after dyke break).

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Figure 8. Calculation results of water level in the river channel, water depth in floodplain and total number of houses to be
swept away immediately after dyke break (from 2 minutes to 40 minutes after dyke break)

7

SWEPT-AWAY OF HOUSES BY FLOOD
FLOW

Figure 7 shows calculation results of velocity vector
averaged in water depth and inundated district from 2to 40 minutes after dyke break. The velocity vector ischanged length and color according to magnitude. It
is understood that the velocity of flooding flow neardyke break point is more than 7 m/s and the velocity
inside bending section of river channel is about 3 m/s.
The inundated district is decided by threshold value
0.003 m. The inundated district is the area where water
depth is more than 0.003 m.
Figure 8 shows contours of water level in river
channel at intervals of 0.1 m and water depth distribution in floodplain from 2 to 40 minutes after dyke
break. Grids that houses were not swept away are notcalculated because houses were not submerged infield data.
Flood flows along north side of temple at 2 minutes after dyke break. And the direction of the velocity vector near dyke break point is toward southeast at
the same time. The temple is swept away and thevelocity vector changes toward southwest at 4 minutes
after dyke break. Comparing with two water surfaces
at 2 and 4 minutes after dyke break, longitudinal
gradient of water surface along left dyke is larger inthe upstream of dyke break point and smaller in thedownstream. The velocity vector toward southwest
gets bigger when dyke break width is larger. The
above-mentioned tendency about water surface in theriver strengthens.
The reason that direction of velocity vector
changes southeast into southwest is as follows.
(1) Gradient of water surface nearby dyke breakpoint is largest in direction across the left dyke
immediately after dyke break.
(2) Beginning to widen dyke break, gradient of water
surface is larger at upstream of dyke break pointwith degradation of water surface.
Flood flow running off from the river after thedyke break is affected by the river flow. Total 1, 2, 4, 8
and 14 houses were swept away at 4, 11, 19, 28 and 40
minutes respectively after the dyke break.
8CONCLUSION

We developed new numerical analysis model by FDS
method for abrupt flooding flow and swept-away ofhouses. We made clear the relationship between theflood flow from the Kariyata River and swept-away ofhouses due to dyke break using the numerical model.
Useful flood simulation model for floodplain risk
management is proposed.

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area and the study of damage reduction, Journal of
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Iwasa, Y., Inoue, K., et al. 1980., Hydraulic analysis of overland flood flows by means of numerical method, DisasterPrevention Research Institute annuals: 23, B-2.

Kuriki, M., Suetsugi, T., et al. 1996., Technical memorandum of PWRI: 3400.
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