12th International Conference on Hydroscience & Engineering
Hydro-Science & Engineering for Environmental Resilience
November 6-10, 2016, Tainan, Taiwan.

Analysis of Discharge Capacity and Flood Storage Rate during 2015 Large Flood in the Kinu River
Kosuke Tabata1, Shoji Fukuoka1, Keisuke Deguchi2
1. Research and Development Initiative, Chuo University
Tokyo, Japan
2. Kanto Regional Development Bureau, Ministry of Land, Infrastructure, Transport and Tourism
Saitama, Japan

ABSTRACT
It is necessary to enhance a safety level of flood control in the Kinu
River which suffered from huge inundation damage in 2015 flood.
However, it is not clear how marked longitudinal change in river crosssections affected discharge capacity and flood storage volume. We
developed a numerical model applying BVC method and 2D bed
variation using observed water surface profiles during the 2015 flood in
the Kinu River taking account of the inundation due to levee
overtopping and breach. The model provided valuable explanations forthe discharge capacity and flood flow storage volume.

KEY WORDS: Kinu River; 2015 flood; flood flow and bed variation
analysis; water surface profiles; levee over topping and breach;discharge capacity; flood storage rate
INTRODUCTION
The Kinu River is one of major tributaries of the Tone River which is
the largest river in Japan. It is necessary to enhance a safety level offlood control in the Kinu River which suffered from huge inundation
damage due to levee overtopping and breach in the 2015 large flood. In
the Kinu River, especially lower reach from 4 km to 46 km, thelongitudinal changes of cross-section are quite large, which affectdischarge capacity and storage rate of floods. Therefore, it is important
to examine quantitatively the hydraulics of the 2015 flood for the future
river improvement works.
Some researches on bed variations or riverbed stabilities at the upper
reach in the Kinu River have been carried out, but there are almost no
researches of discharge capacity, flood storage volume and bed
variations focusing on river characteristics of the lower reach. Fukuoka
has proposed the numerical method for flood flows and bed variations
using time series of observed flood water surface profiles on the basisof the idea that effects such as plan forms, cross-sections and bed
variations appear in time series of observed water surface profiles. Thismethod has been applied for understanding of flood flows and bed
variations mechanism in many Japanese rivers (Fukuoka and Watanabe
2002, Tabata and Fukuoka 2014).
The objective of this paper is to develop the numerical model of flood
flow and 2D bed variation of the 2015 flood in the Kinu River where
extensive inundation due to overtopping and levee breach occurred.
Also we calculate the inundation volume, discharge capacity and flood
storage rate during the 2015 flood in the Kinu River.

OUTLINES OF THE OBJECTIVE AREA AND THE 2015
FLOOD
Fig.1 and Fig.2 show the plan form and longitudinal distribution of riverwidth and riverine bamboos in the reach from 0.0 km to 46 km of theKinu River. Solid lines in Fig.2 show the distances from the center ofriver channel to the levees and banks. In the stretch from 3.0 km to 4.0
km, the river width is narrow, approximately 100 m. From 4.0 km to 37.0
km the river width varies from 200 m to 400 m and the main channel
meanders. In the upper reach of 37.5 km, it increases and reaches to
1,300 m wide at 40.25 km. There are densely growing bamboos in theflood plain (pink areas in Fig.2) whose heights are roughly 3-10 m.
Fig.3 shows the water level hydrograph at Mitsukaido (11.0 km). The
2015 flood continued for two days and the water level exceeded over
H.W.L. for about 6 hours at Mitsukaido. The Kinu River flood brought
inundations due to overtopping at 6 embankment points (white x marks in
Fig. 1) and levee breach on the left bank at 21.0 km (red x mark in Fig. 1).
Water levels were measured at drainage pump stations and flood
regulating gates in addition to water level gauging stations as shown in
Fig.1. By these water level gauges, temporal water surface profiles
during the flood were measured in detail.

NUMERICAL METHOD AND CONDITIONS
Numerical Method
We develop a numerical model of flood flow and 2D bed-variation
analysis using observed flood water surface profiles in the Kinu River.
In this study, the BVC (Bottom Velocity Computation) method
developed by Uchida and Fukuoka (2011) is applied to the flood flow
analysis. The BVC method is quasi-3D flow analysis model which iscapable of evaluating vertical distribution of horizontal velocities andbottom velocities by introducing depth-averaged horizontal vorticity
equations and horizontal momentum equations on water surface toshallow water equations.
The bed variation is computed by the continuity equation for sedimentand grain sizes (Hirano 1971) using bed load formula (Ashida andMichiue 1972) and suspended load formulas (Itakura and Kishi 1980;
Lane and Kalinske 1941). The transport of the suspended sediment iscomputed by 2D advection and diffusion equations.

12th International Conference on Hydroscience & Engineering
Hydro-Science & Engineering for Environmental Resilience
November 6-10, 2016, Tainan, Taiwan.

Tone river
40k
45k

Hirakata

Kinu River

35k
River width :400~1,300m

30k
25k

0k

Kamaniwa

20k
5k

10k

Kawashima

15k

Mitsukaido

Kokai River
Water level gauging station
Drainage pump station or flood regulating gate

Levee breach
Overtopping

Pressure type water level gauges

800
600
400

9/8 12:00
25

Levee (right bank)
The Tone River confluence
Main channel

Sasayama flood gate

0
-200
-400
-600
-800

Hillside
HillsideRiverine bamboos

Mitsukaido

Levee breachRiverine bamboos

9/9 12:00

9/10 12:00 9/11 12:00 9/12 12:00 9/13 12:00 9/14 1
observed water level hydrograph at Mitsukaido

20

200

elevation (Y.P.m)

Distance from center of channel (m)Fig. 1 Plan form of the Kinu River.

Kamaniwa

Hirakata
Kawashima

Levee (left bank)0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
Longitudinal distance from the Tone River confluence (km)H.W.L.

15
10
5cross-section at Mitsukaido

0
-100

0

100

200
300
transverse distance (m)400Fig. 3 Observed water level hydrograph and crosssection at Mitsukaido.

Fig. 2 Longitudinal distribution of the river width and riverine bamboos.

RESULTS AND CONSIDERATIONSThe numerical model was applied for the reach from 4.25 km to 46.0
km. The upstream and downstream boundary conditions were given byobserved water level hydrographs at the Kawashima gauging stationand Shintei drainage pump station. Since over topping flows over leveecrests occurred in the 2015 flood, the numerical grid was made taking
account of topography of levees and inland areas at several places
where heights of levee crest were low. Discharge hydrographs
outflowing from the levee breached point was estimated so that thecalculated water surface profiles agreed with the observed ones aroundthe levee breached point (Fukuoka et al. 2008), especially Sasayama
flood regulating gate which is located at the opposite bank of levee
breach point considering observed breach time and temporary changeof breach width. Fig.4 shows grain size distributions used for the
analysis. The bed materials are mainly composed of gravels at upstream
from 37.2 km where the river width is narrower compared to its
upstream reach, and are mainly composed of sand at downstream of
37.2 km. Manning roughness coefficients of the main channel andflood plain were set based on the longitudinal distributions of theaveraged particle diameters and the ground cover conditions,
respectively. The vegetation permeability coefficients of the densely
bamboos were adjusted finely so that the calculated water surface
profiles agreed with the observed ones during the 2015 flood on thewhole. Manning roughness coefficients and vegetation permeability
coefficients used in the analysis are shown in Table 1.

Flood Flows and Bed Variations
Volume percentage finer than (%)

Conditions for Numerical Computations

100

90
80
70

4.25～5.1k

60

5.1k～27k50
40

27k～35k30

35k～37.2k

20

37.2k～46k

10
0
0.01

0.1

1

100

10

Diameter (mm)Fig. 4 Grain size distributions used for the analysis.
Table 1 Manning roughness coefficient and vegetation permeability
coefficient.
-1/3

SectionManning roughness coefficient (m ・s)
main channel
flood plain

vegetation permeability
coefficient (m/s)

4.25～5.1km

0.028

0.025～0.040

10～70

5.1～27km

0.025

0.025～0.075

10～70

27～35km0.025

0.025～0.055

10～70

35～37.2km

0.030

0.030～0.055

10～40

37.2～46km

0.035

0.025～0.055

10～70

500

12th International Conference on Hydroscience & Engineering
Hydro-Science & Engineering for Environmental Resilience
November 6-10, 2016, Tainan, Taiwan.

Fig. 5 shows the comparison between the computed and observed water
surface profiles and longitudinal distributions of the averaged bed
elevations in the Kinu River. In this figure, we can see that thecomputed water surface profiles could coincide with the observed oneson the whole. Also the water surface profiles at the peak time almost
matched observed flood marks. Computed averaged bed elevations
after the flood almost agreed with observed ones.

40
Hirakata
38k

35

Elevation (Y.P.m)

25

9/10 12:00
9/10 6:00
9/10 3:00

Pump st.

9/10 0:00

Pump st.

Pump st.

Pump st.
Shintei(Pump st.)43k

Kamaniwa

Mitsukaido
30

Kawashima
41k

Flood Gate

9/9 21:00

Pump st.

water surface profile(obs.)
water surface profile(cal.)

Pump st.

6k

Pump st.

20

levee crest (left bank)levee crest (right bank)

15

HWL

10
groundsill

5

groundsill

groundsill​

groundsill

0
4

5

6

7

groundsill

8

groundsill*6k，38k，41k，43k: Observations by pressure type water level gausing

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
Longitudinal distance from the Tone River confluence (km)averaged bed elevation(before flood)
averaged bed elevation(after flood) cal.
averaged bed elevation(after flood) obs.
observed flood markFig. 5 Comparison between the computed and observed water surface profiles and longitudinal distributions of the averaged bed elevations in the
Kinu River.

Fig. 7 shows the computed hydrographs of the total inundation
discharge in the left bank side due to overtopping and levee breach. The
inundation discharges due to overtopping increased until 12:50 10 Sep.
when the levee breach occurred, and then decreased. The inundation
due to levee breach continued for about 10 hours. The computation
model revealed that the inundation volume due to overtopping was
26,420,000 m3 and one due to levee breach was 12,770,000 m3. The
measured total inundation volume was about 40,000,000 m3, which
agreed well with the computed result.

Discharge Capacity and Flood Storage Rate
The water level almost reached or was over the levee crest except forthe stretch around Kamaniwa. This fact indicates that the Kinu Riverwas lacking in discharge capacity on the whole. Especially thedischarge capacity was not enough in the reach around Hirakata. In
general, temporal water surface profiles in large rivers are almost
parallel to the longitudinal riverbed surface during the flood. However,as shown in Fig.5, the water surface profiles in the reach from 37.0 km
to 43.0 km around Hirakata became almost horizontal as the water level
5,500
5,000

Hirakata

Kawashima

4,500

Discharge (m3/s)

Solid line: Computed discharge
Plot: Observed discharge

Kamaniwa

4,000
3,500

Mitsukaido

3,000
2,500
2,000
1,500
1,000
500
0
9/9 18:00

9/10 12:50 levee breach (on left bank at 21.0km)
9/10 0:00

9/10 6:00

9/10 12:00

9/10 18:00

9/11 0:00

9/11 6:00

Fig. 6 Comparison between the computed and observed dischargehydrographs.
width of breach point : 20m 80m 200m
2,000
Inundation
discharge(m3/s)

Fig. 6 shows the comparison between the computed and observed
discharge hydrographs at the observation stations in the Kinu River.
The solid lines and plots indicate the computed and observed values
which are considered the inundation volume due to overtopping andlevee breach. The discharge observations carried out at the threeobservation stations Hirakata (37.0 km), Kamaniwa (27.4 km) and
Mitsuaido (11.0 km) during the 2015 flood. Although there are no
confluences along the reach from Hirakata to Kamaniwa, the observed
discharges between the time of flood starting (10 Sep. at 8:00) andflood peak (10 Sep. at 11:00) at Hirakata are smaller than ones at
Kamaniwa which is located at downstream of Hirakata. The computed
discharges at Kamaniwa and Mitsukaido could elucidate the observed
ones, while the peak discharges estimated slightly larger than observed
ones. The difference between computed and observed discharge at
Hirakata is a subject for the future investigation.

1,500
1,000
500
0
9/9 18:00

45.9km(overtopping)44.1km(overtopping)
32.8km(overtopping)
24.75-25.35km(overtopping)21.0km(overtopping and levee breach)
total

9/10 0:00

9/10 6:00

9/10 12:00

9/10 18:00

9/11 0:00

9/11 6:00

Fig. 7 Computed inundation discharge hydrographs due to overtopping
and levee breach.

12th International Conference on Hydroscience & Engineering
Hydro-Science & Engineering for Environmental Resilience
November 6-10, 2016, Tainan, Taiwan.

increased, while they were parallel to the longitudinal riverbed surface
until 10 Sep. at 0:00. This is considered as follows. Fig.8 and Fig.9
show the temporal changes in depth averaged velocity contours andstream lines at the reach from 37.0 km to 42.0 km and velocity
contours in the cross-section at 40.25 km where river width is very

wide in 1,300 m. The velocities were quite large in the main channel at
2:00. Since the water level rose over the elevation of flood plain as theflood discharge increased at 5:00, flows in the main channel with large
velocities and flows on the flood plain with small velocities were
exchanged by complex meandering patterns. Then velocities became

A v era g ed
v elo city
（ m /s）

V elo city
（ m /s）

Relative depth = 0.00
(Single meanderingchannel flow)
9/10 2:00
Relative depth = 0.27
(Single meanderingchannel flow)
9/10 5:00
Relative depth = 0.37
(Compound meanderingchannel flow)

9/10 2:00

9/10 11:00

9/10 5:00

9/10 11:00

Fig. 8 Temporary changed in depth averaged velocity contours andstream lines in the reach from 36.0 km to 42.0 km.
5,500
5,000

Flood storage rate (m3/s)

4,500
4,000

Fig. 9 Temporary change in velocity contours in the cross-section at 40.25
km.

dS/dt(=Qin-Qout)
Discharge at Kawashima
Discharge at Kamaniwa

3,500
3,000

9/10 2:00~ Overtopping

2,500

9/10 9:20 Flood peak at Kawashima

2,000

9/10 11:20
Flood peak at Kamaniwa

1,500

9/10 12:50 Levee breach

1,000
500
0

9/9 18:00

values were almost 32 % and 17 % of the peak discharges at
Kawashima and Kamaniwa, respectively. Also the flood storage
volume in the reach from 4.25 km to 46.0 km which were estimated bytime integrating storage rate from 9 Sep. at 18:00 to 10 Sep. at 13:00
was 78,000,000 m3. It was the value which eliminated the inundation
volume and almost comparable to water volume during the flood infour dams located in the upstream area of the Kinu River. This meansthat the flood storage volume in the Kinu River was quite large,
because of the plan shape of the river.

CONCLUSIONS
9/9 21:00

9/10 0:00

9/10 3:00

9/10 6:00

9/10 9:00

9/10 12:00 9/10 15:00 9/10 18:00

Fig. 10 Flood storage rate in the reach from 4.25 km to 46.0 km in the
Kinu River.
small at the flood peak as shown in velocity contour at 11:00 in Fig.8
and Fig.9. It was investigated that flow characteristics in compound
meandering channels depend on the relative depth which is defined by
the ratio of the depth on the flood plain to the depth in the main channel(Okada and Fukuoka 2002). When the relative depth is from around 0.3
to 0.5, flows in the main channel and on the flood plain mix intensively,
then shear stresses increase and average velocities in cross-section
decrease. At the flood peak level the relative depth was 0.37. Then, theaverage velocities decreased due to mixing, and the water level rose.
Next we estimated the flood storage rate by the following equation.

dS dt = Qin − Qout

(1)

Where, S: flood storage volume, t: time, Qin: computed dischargehydrograph at 46.0 km, Qout: computed discharge hydrograph at 4.25
km.
Fig.10 shows the flood storage rate in the reach from 4.25 km to 46.0
km in the Kinu River. The computed flood storage rate were 1,670 m3/s
and 790 m3/s at the flood peak at Kawashima and Kamaniwa. These

We applied the numerical model for analysis of flood flow and 2D bed
variation to the 2015 large flood in the Kinu River, using observed
water surface profiles taking account of inundations due to both ofovertopping and levee breach. The following conclusions were derived
in this study.
(1) It was estimated that the total inundation volume due toovertopping was 26,420,000 m3 and the inundation volume due tolevee breach on the left bank at 21.0 km was 12,770,000 m3.
(2) The developed model clarified that the discharge capacity was notenough in the meandering reach around Hirakata. Because therelative depth in meandering river flow was 0.37, velocities
decreased and the water level rose highly.
(3) The flood storage rate was 1,670 m3/s at the time of peak discharge
at Kawashima and almost equivalent to 32 % of the peak discharge.
Furthermore, the flood storage volume in the reach from 4.25 km to
46.0 km was 78,000,000 m3 and it was indicated that the flood
storage volume in the Kinu River was quite large.

REFERENCES
Fukuoka, S., Abe, T. and Tsukamoto, Y. (2008). Calculation Method of
Inundation Discharge Hydrograph from the Temporal Changes in
Water Surface Profile Due to Levee Breach, Advances in Hydro-

12th International Conference on Hydroscience & Engineering
Hydro-Science & Engineering for Environmental Resilience
November 6-10, 2016, Tainan, Taiwan.

Science and Engineering, Vol.8.
Fukuoka, S. and Watanabe, A. (2002). Estimating Channel Storage andDischarge Hydrographs of Flooding, Proceedings of 5th International
Conference on Hydro-Science & Engineering.
Okada, S. and Fukuoka, S. (2002). Land-form Features in Compound
Meandering Channels and Classification Diagram of Flood Flows
Based on Sinuosity and Relative Depth, Proceedings of theInternational Conference on Fluvial Hydraulics, River Flow, 205-212.

Tabata, K. and Fukuoka, S. (2014). New Computation Method for Flood
Flows and Bed Variations in a Low-lying River with Complex River
Systems, Proceedings of International Conference on Fluvial
Hydraulics, River Flow, 1791-1798.
Uchida, T. and Fukuoka, S. (2011). Numerical Simulation of Bed
Variation in a Channel with a Series of Submerged Groins,
Proceedings of the 34th IAHR World Congress, 4292-4299.