300

Floods: From Risk to Opportunity (IAHS Publ. 357, 2013).

Evaluation of flood discharge hydrographs and bed variations
in a channel network on the Ota River delta, Japan
T. GOTOH1, S. FUKUOKA1 & R. TANAKA2

1 Research and Development Initiative, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan
goto510@tamacc.chuo-u.ac.jp
2 Chugoku Regional Development Bureau, MLIT, 3-20 Hattyoubori, Naka-ku, Hiroshima-City, 730-0013, Japan

Abstract A channel network consisting of the Ota River floodway and five branched rivers is formed on the
Ota River delta. To estimate bed variation and flood discharge distributions in the channel network of the
Ota River delta is important for proper river management. The objective of this study is to develop thecalculation method of flood flows and bed variations by using time series of water surface profiles measured
in the channel network of the Ota River delta. We developed a quasi-3D numerical model for the flood flow
and bed variation analyses using time series of observed water surface profiles. The unsteady quasi-3D
analysis of flood flows and 2D analysis of bed variations using time series of observed water surface profiles
are found to provide good explanations for the flood discharge distributions and bed variations of thechannel network on the Ota River delta.
Key words channel network; Ota River delta, Japan; time series of observed water surface profiles;
flood discharge distributions; bed variation

INTRODUCTION
A channel network is formed on the Ota River delta, located in Hiroshima prefecture, Japan. The
channel network consists of the Ota River Floodway and five branched rivers. Each river flows
into Hiroshima Bay and the maximum difference in tidal changes is about 4 m. Therefore,
evaluating flood flows, bed variations and flood discharge hydrographs is required for proper rivermanagement of the Ota River delta.
Many researchers have studied flood flows and bed variations in a channel network. They
mainly developed the flood routing methods of an unsteady 1D flow analysis method in a channels
network (e.g. Yen & Osman, 1976; Kanemoto et al., 1992; Choi & Molinas, 1993). Ayub et al.
(2007) studied the sediment dynamics from Ganges River system to Bengal Bay. They developed the2D flood flow and bed variation analysis method and simulated bed variations and sedimenttransport with wide seasonal variation and tidal changes. However, in these analyses, hydraulicparameters such as channel resistances have not been properly evaluated, because channel
resistances contain various influences such as effects of channel shapes, bed profiles, vegetation, etc.
Effects of river bed profiles, bed variations, vegetation, bifurcation structures, confluences, etc.
appear in the time series of observed water surface profiles (Fukuoka, 2005). Fukuoka et al. (2004)
proposed the unsteady 2D flow analysis method using time series of observed water surface
profiles in order to estimate flood discharge hydrographs in any river sections. And, the calculation
method using time series of observed water surface profiles has been applied to estimate the flood
discharge hydrographs for various river conditions. Fukuoka et al. (2006) evaluated the flood
discharge hydrographs in the reach with the branched section of the Tone River and the Edo Riverby a 2D calculation method for flood flow using time series of observed water surface profiles.
Abe et al. (2009) applied this calculation method to levee breach experiments in the Joganji Riverand evaluated the inundation discharge hydrographs. Uchida et al. (2011) have developed thecalculation method of tributary flood discharge hydrographs using the time series of observed
water surface profiles along the main channel. This idea can be applied to estimate flood flows andbed variations during a flood in a channel network.
The objective of this study is to develop the quasi-3D calculation method for flood flows andbed variations by using time series of observed water surface profiles in the channel network of the
Ota River delta.

Copyright  2013 IAHS Press

Evaluation in a channel network on the Ota River delta

301

Fig. 1 Ota River delta.

THE OTA RIVER DELTA
A channel network on the Ota River delta consists of the Ota River floodway which wasconstructed in order to reduce flood inundation in Hiroshima City and five branched rivers (Kyu
Ota River, Kyobashi River, Temma River, Motoyasu River and Enko River, see Fig. 1). Eachchannel flows into Hiroshima Bay where maximum tide difference is about 4 m. At the bifurcation
section of the Ota River floodway and the Kyu Ota River, the Gion-Floodgate is located at the sideof Ota river floodway and consists of a movable weir with three gates. Oshiba-floodgate is locatedat the side of the Kyu-Ota River and consists of a fixed weir and movable weir with the three gates.
The characteristics of cross-sectional shape in each channel are as follows. The Ota River floodway is composed of compound cross-sectional channel from 5.8 km to 0.0 km and simple cross-sectional channel from 0.0 km to –3.4 km. The channel widths of the Ota River floodway are about
400 m to 500 m. The branched river is composed of simple cross-sectional channel. The channel
widths of the branched rivers (Kyu Ota River, Kyobashi River, Temma River and Motoyasu River)are about 70–150 m from each bifurcation section to 0.0 km. In the downstream of 0.0 km, thechannel widths of the branched rivers gradually increase to about 300 m around the river mouth (seeFig. 1).
Figure 1 shows water level observation stations and discharge observation sections of Ota
River delta. For understanding the dynamics of flood flow and bed variation in the Ota River delta
we installed many water level gauges along the each channel. Flood discharge hydrographs were
measured by floats technique at Yaguchi-daiichi (Ota River 11.6 km), Gion-Oohashi (Ota Riverfloodway 5.2 km), Misasabashi (Kyu Ota River 4.2 km) and Kouheibashi (Kyobashi River 5.0 km)
observation station. So, we can validate the calculated inflow discharge hydrograph to the Ota
River Floodway, Kyu Ota River and Kyobashi River. The cross-sectional bed shape around thebifurcation sections were surveyed at about 50 m intervals of longitudinal distance.
Figure 2 shows the water level hydrographs in the July 2010 flood. In this flood, the high tideoccurred about an hour earlier than the flood peak. Figure 3 shows the grain size distributions inthe section studied. The bed materials around 13.0 km consist of many cobbles and gravel. On theother hand, the bed materials in the Ota River floodway and the branched rivers (Kyu Ota River,
Temma River, Motoyasu River) mainly consist of sands containing little silt and clay.

302

T. Gotoh et al.
12

Yaguchi- daiichi 11.6km
Nagawaku 6.0km
Gion- oohashi 5.2km
Kusatu - 3.4km

Water level (m)

10
8
6
4
2
0
-2
-4
7/ 14 0:00

7/ 14 12:00

7/ 15 0:00

7/ 15 12:00

Time (hour)

7/ 16 0:00

Fig. 2 Water level hydrographs in the flood of 2010.

Volume percentage finer than (%)

100
90
80
70
60
50

7.0kmOta R.
10.4kmOta R.
13.0km Ota R.
0.0km Ota River F.
5.0km Ota River F.
- 2.0kmOta River F.
1.9kmKyu Ota R.
3.0.kmKyu Ota R.
5.0.kmKyu Ota R.
1.0kmTemma R.
2.2km Temma R.
1.0kmMotosasu R.

40
30
20
10
0
0.01

0.1

1

10

Grain size (mm)100

Fig. 3 Grain size distributions in the channels of the Ota River delta.

FLOOD DISCHARGE HYDROGRAPHS AND BED VARIATIONS OF A CHANNELSNETWORK ON THE OTA RIVER DELTA
Flood calculation method using time series of observed water surface profiles of a channel
networkIn the channel network it is difficult to determine channel resistances and discharge distribution
ratio at bifurcation sections, since flood flows in each channel have an influence on each other.
The effects of channel resistance, discharge distributions, etc. appear in the time series of observed
water surface profiles. So, we determine channel resistances to agree with time series of observe
water surface profiles. Therefore, this analysis method using the observed water surface profiles isable to evaluate flood flows, bed variations and discharge distributions in actual river conditions of
the Ota River delta.
Figure 4 shows the flow chart of determination of channel resistances and flood discharge
distributions in the channel network. In this study, the channel resistance and flood discharge
distribution ratio at bifurcation sections were determined from upstream sections toward
downstream sections by a calculation method using time series of observed water surface profiles,
since the inflow discharge upstream of the channel network is the discharge hydrograph measured
at Yaguchi-daiichi observation station. The detailed determination procedure is as follows.
First, we conduct the unsteady quasi-3D flood flow and 2D bed variation analysis in whichchannel flow resistances are given by conditions of channel shape, bed profile and vegetation.
When the calculation results do not reproduce the temporal observed water surface profiles, mean
bed profiles after the flood in section (0) and discharge hydrograph at Yaguchi-daiichi observation

Evaluation in a channel network on the Ota River delta

303

station, the channel flow resistances in section (0) and downstream of section (0) are adjusted so as
to agree with temporal observed water surface profiles in section (0) and discharge hydrograph at
Yaguchi-daiichi observation station. The channel flow resistances downstream of section (0) arealso adjusted by the observed water level hydrograph at the Nishihara observation station. The
channel flow resistances in section (0) are adjusted so as to agree with temporal observed water
surface profiles in section (0) (see Fig.4).
Next, channel flow resistances downstream of section (1) are adjusted with the observed waterlevels at Ushita observation station which is the downstream end of section (1). We adjust
Manning’s roughness coefficients in section (1) with temporal observed water surface profiles in
section (1). If the calculation results reproduce the temporal observed water surface profiles andmean bed elevations in section (1) and section (0), the discharge hydrograph of each river in section(1) are evaluated by this method. A similar process is conducted from section (1) to section (5).
Determination of Manning’s roughness coefficients from river bed material
Determination of vegetation permeability coefficients from vegetation conditions
i →0

Adjust Manning’s roughness
coefficients and vegetation
permeability coefficients so as toagree with observed water
surface profiles in (i) section anddownstream of (i) section

Unsteady quasi 3D flows and bed variation analysis
Comparison between observed and calculated water surface profiles
and discharge hydrograph at Yaguchi-daiichi

Do calculation results explain
observed water surface profiles,
discharge hydrograph and mean
bed elevation in (i) section ?

No i →0
Adjust Manning’s roughness
coefficients and vegetation
permeability coefficients so as toagree with observed water
surface profiles in (i) section anddownstream of (i) section

Yes i→ 1
Unsteady quasi 3D flows and bed variation analysis
Comparison between observed and calculated water surface profiles

No

Do calculation results explain observed
water surface profiles and mean bed
elevation in (i) section ?

Yes → i+1
i=imax?

No

End

Fig. 4 Flow chart of determination of flood discharge distribution ratio in the Ota River delta.

In the calculation method, the calculated discharge hydrographs in section (1) and (2) are
validated by using observed discharge hydrographs in section (1) and (2). We check the channels
resistances by comparing with bed materials and bed profiles when those are determined so as toagree with time series of observed water surface profiles.
Therefore, the present calculation method gives the discharge hydrographs in each river reachby determining the channels resistances’ so as to agree with temporal observed water surface
profiles.
The unsteady quasi 3D flow and 2D bed variation analyses using time series of observed
water surface profiles
It is necessary to consider 3D effects of flood flows which control bed variation at the bifurcation
sections. We applied the unsteady quasi 3D flow analysis (Uchida et al., 2009) and 2D bed
variation analysis using the time series of the observed water surface profiles. The vertical velocity
distributions assumed by a cubic curve are determined by using depth averaged velocity and thedifference between water surface and bottom velocities. The shear stresses on the river bed andvegetations resistance are calculated by equation (1):

304

T. Gotoh et al.

~ ~(τ swξ ,τ swη ) = ( gn 2 / h1 3 + gh / K 2 ) u 2 + v 2 (U ,V )(1)

where τ swξ and τ swη = channel flow resistances by river bed roughness and vegetation in direction~of ξ and η ; n = Manning’s roughness coefficients; K = vegetation permeability coefficients ; U~
and V = velocities in direction of ξ and η ; u and v = velocities in directions x and y, respectively.
In the branched rivers (Kyu Ota River, Kyobashi River, Temma River, Motoyasu River), there
are a number of bridges with piers. The effects of drag forces on bridge piers are estimated byequation (2):~ ~( Fξ , Fη ) = 0.5 × C D A / J u 2 + v 2 (U ,V )(2)where Fξ and Fη = drag forces by pier in direction, respectively; Cd = 1.0; Cd = drag force
coefficients ; A = project area of pier; J = Jacobian.
The conventional bed variation analysis is conducted by using bed load formula (Ashida &Michiue, 1972) and continuity equations for sediment and grain sizes (Hirano, 1971). The criticaltractive force for sediment mixtures is calculated by the modified Egiazaroff formula (Egiazaroff,
1965; Ashida & Michiue, 1972). The suspended sediment transport is calculated by depth
averaged continuity of concentrating of suspended load.
The boundary conditions are time series of observed water level hydrographs at Yaguchidaiichi (11.6 km) and Hiroshima Port observation stations.
Calculation results
Table 1 shows Manning’s roughness coefficients and vegetation permeability coefficients which
are determined so as to satisfy temporal observed water surface profiles. It is found that Manning’s
roughness coefficient values contain effects of topography such as sand waves because thecoefficients are large compared with those caused by bed materials. (e.g. Manning’s roughness
coefficient in the Temma River is about 0.012 (m-1/3 ⋅ s) by using Strickler’s empirical formula.)
Table 1 Manning’s Roughness coefficients and vegetation permeability coefficients.
Manning’s roughness coefficients (m–1/3 s)
Ota River, Ota River floodway
12.4–5.8 km
Main channel
0.03
Flood channel
0.035
5.8–2.0 km
Main channel
0.028
Flood channel
0.035
2.0–(–3.4 km)
Main channel
0.022
Flood channel
0.035
Vegetation permeability coefficients (m/s)
Ota River8.0–9.6 km
Right bank40
10.4–10.8 km
Right bank50
10.8–11.4 km
Right bank40
8.0–8.8 km
Left bank50
9.6–10.6 km
Left bank50

Kyu Ota River
6.2–2.2 km
2.2–(–1.6 km)
Kyobashi River
5.2–2.4 km
2.4–(–0.8 km)
Kyu Ota River
6.2–5.0 km

0.025
0.022
0.033
0.02

Temma River
3.6–(–2.4 km)
Motoyasu River
2.6–(–2.4 km)
Enko River
2.6km–(–3.1 km)

0.03
0.022
0.035

40

Figure 5 shows the comparison between observed and calculated water surface profiles andmean bed elevations. The calculated water surface profiles show good agreement with observed
water surface profiles while they are a little higher than observed water surface profiles in theflood rising period. After 14:00 h, the water surface profile slope became steeper downstream ofabout 1.0 km due to the ebb tide. Water surface profiles in the Temma River, Kyu Ota River and305

Evaluation in a channel network on the Ota River delta

Water level (m)

12.00
10.00
8.00
6.00
4.00
2.00
0.00
- 2.00- 4.00

-4

-2

0

2

4

6

6

Water level (m)Water level (m)

12

5

4
3
2
1
0
-1
-2
-3

4
3
2
1
0
-1
-2
-3
-4

-2

-1

0

1

2

3

4

5

6

7

-1

6

5

5

4

4

Water level (m)

6

3
2
1
0
-1
-2
-3
-4

-2

-1

0

1

2

3

Longitudinal distance from river mouth (km)

0

1

2

3

4

5

Longitudinal distance from river mouth (km)Longitudinal distance from river mouth (km)Water level (m)

10

6

5

-4

8

Longitudinal distance from river mouth (km)

3
2
1
0
-1
-2
-3
-4

4

-4

-3

-2

-1

0

1

2

Longitudinal distance from river mouth (km)3

Fig. 5 Comparison between observed and calculated water surface profiles.
0.6

Bed variation (m)Bed variation (m)

0.5
0.3
0.1

- 0.1
- 0.3
- 0.5

Cal
10:00

-4

Obs
13:00

-2

8:00
15:00

0

0.4
0.2
0
- 0.2
- 0.4
- 0.6

2

Longitudinal distance (km)

4

-2

Obs

8:00

10:00

14:00

16:00

Cal

-1

0

12:00

1

2

3

4

Longitudinal distance (km)Fig. 6 Change in the mean bed elevations.

Motoyasu River downstream of 1.0 km are much steeper than those of the Ota River floodway
owing to channel width reduction.
Figure 6 shows time change in calculated and observed mean bed elevations in the Temma
River and the Ota River floodway, respectively. It is found that the mean bed elevations change
about 20 cm during the 2010 flood in the Ota River delta. The calculated bed variations are able toexplain the observed bed variations upstream and downstream of 0.0 km.
The maximum change in the bed elevations downstream of 0.0 km occurred between 15:00 hand 16:00 h when the water surface profiles are steepest in the flood (see Fig. 7). In contrast, themaximum bed variations upstream of 0.0 km occurred in the flood peak. This shows that the306

T. Gotoh et al.

calculation method using time series of observed water surface profiles is especially important tounderstand the flood flow and bed variation in the estuary.
The sediment transport in the Ota River Floodway and Temma River are shown in Fig. 8. Since
suspended load is more than bed load downstream of 0.0 km, it is found that effects of suspended
load on bed variations downstream of 0.0 km are large compared with upstream of 0.0 km.

0.1

9h- 10h11h- 12h13h- 14h

15h- 16h

0.2

Bed variation (m)Bed variation (m)

0.2
0.15
0.05
0

0.1
0.05
0

- 0.05- 0.05
- 0.1

- 0.1

- 0.15- 0.15
- 0.2

0.15

- 0.2
-4

-3

-1

-2

0

1

2

3

4

5

9h- 10h13h- 14h

-2

-1

0.006
0.005
0.004
0.003
0.002
0.001
0

-4

-3

-2

-1

0

1

2

Longitudinal distance (km)

3

4

5

Sediment discharge (m3/s)

Sediment discharge (m3/s)

Bed load 11:00
Suspended load 11:00
Bed load 16:00
Suspended load 16:00

0.007

1

2

3

Longitudinal distance (km)Fig. 7 Change in the mean bed elevations in each hour.

0.008

0

11h- 12h15h- 16h

0.008
0.007
0.006

Bed load 11:00

Suspended load 11:00

Bed load 16:00

Suspended load 16:00

0.005
0.004
0.003
0.002
0.001
0

-2

-1

0

1

2

Longitudinal distance (km)

3

4

5000

1

4500

0.9

4000

0.8

3500

0.7

3000

0.6

2500

0.5

2000

0.4

1500

0.3

1000
500
0
7/ 14 6:00

7/ 14 8:00

7/ 14 10:00

Yaguchi- daiichi
Kyu Ota River
Yaguchi- daiichi Obs.
Discharge ratio

Flood way
Flood way Obs.
Kyu Ota River Obs.
Discharge ratio Obs.

7/ 14 12:00

7/ 14 16:00

7/ 14 14:00

Discharge(m3/s)

Discharge(m3/s)

Fig. 8 Sediment transport of suspended load and bed load.
2500

2000

1200
1000

0.5

0.3

7/ 14 10:00

7/ 14 12:00

7/ 14 14:00

7/ 14 16:00

1200

1
0.9
0.8
0.7

0.2
0.1

0
0
7/ 14 4:00 7/ 14 6:00 7/ 14 8:00 7/ 14 10:00 7/ 14 12:00 7/ 14 14:00 7/ 14 16:00 7/ 14 18:00(c) Kyu Ota River and Temma River

7/ 14 8:00

0
7/ 14 18:00(b) Kyu-Ota River and Kyobasi River

0.3

200

0.2
0.1

0
7/ 14 6:00

0
7/ 14 18:00

0.4

400

0.4

0.1

0.5

600

0.8

0.6

500

0.2

0.6

800

1
0.9

0.7

1000

1000

Discharge(m3/s)

Discharge(m3/s)

1400

Misasabashi
Kyu Ota R. 3.0k
Temma R.
Ratio of discharge

Misasabashi
Kyobashi Obs.
Ushita Obs.
Ratio of discharge Obs.

1500(a) Ota River Floodway and Kyu Ota River
1600

UshitaKyoubashi
Misasabashi Obs.
Ratio of discharge

800

1
Kyu Ota R. 3.0k
Kyu Ota R. 2.0k
Motoyasu R.
Ratio of discharge

0.9
0.8
0.7
0.6

600

0.5
0.4

400

0.3
0.2

200

0.1
0
0
7/ 14 4:00 7/ 14 6:00 7/ 14 8:00 7/ 14 10:00 7/ 14 12:00 7/ 14 14:00 7/ 14 16:00 7/ 14 18:00(d) Kyu Ota River and Motoyasu River

Fig. 9 Observed and calculated hydrographs and discharge distribution ratio at river bifurcation sections.

Evaluation in a channel network on the Ota River delta

307

Figure 9 shows the calculated and observed discharge hydrographs and the discharge ratio at
each bifurcation section. The discharge distribution ratio is defined as the ratio of discharge ofbranched river to total discharge. It is demonstrated that the calculation method using time seriesof observed water surface profiles can estimate well the discharge distributions in the channel
network. The discharge distribution ratio at each river bifurcation is found nearly constant withtime, regardless of tidal changes.
CONCLUSIONS
The following conclusions were derived from in this study:(1) Unsteady quasi-3D flood flow analysis and 2D bed variation analysis using time series ofobserved water surface profiles in a channel network is developed to estimate dynamics offlood flow and bed variation. It is found that the calculation method provides fairly goodresults for flood flow and bed variation in the channel network of the Ota River delta.
(2) The bed variation in the channel network of the Ota River delta is closely related to timeseries of water surface profiles affected by tidal changes. Therefore, the calculation method
using time series of observed water surface profiles of flood flow is important for evaluating
flood flows and bed variations in the estuary.
(3) The calculation method including sediment transport of suspended sediments is important for
estimating bed variations around the river mouth of the Ota River delta because the river bed
materials consist of fine sands and channel widths gradually increase to about 300 m from70 m around the river mouth.
REFERENCES
Abe, T., Fukuoka, S. & Tsukamoto, Y. (2009) Calculation method of inundation discharge hydrograph from the temporalchanges in water surface profiles due to river levee breach. J. Hydraul. Coastal & Environ. Engng 65(3), 167–178.
Ashida, K. & Michiue, M. (1972) Study on hydraulic resistance and bed-load transport rate in alluvial streams. Proc. JSCE 206,
59–69.
Ayub, Ali, Mynett, A. E. & Azam, Mir Hammadul (2007) Sediment dynamics in the Meghna Estuary, Bangladesh, a model
study. J. Waterway, Port, Coastal & Ocean Engng 133, 255–263.
Choi, G. W. & Molinas, A. (1993) Simultaneous solution algorithm for channel network modeling. Water Resour. Res. 29(2),321–328.
Egiazaroff, I. V. (1965) Calculation of nonuniform sediment concentration. J. Hydraul. Div. 91(HY4), 225–247.
Fukuoka, S. (2005) Flood Hydraulics and Channel Design. Morikita Publishing Company.
Fukuoka, S., Watanabe, A., Tabata, K., Kazama, S. & Gocho, H. (2006) Evaluation of hydrograph of flood discharge androughness coefficient at the branched section in the Tone River and the Edo River. Ann. J. Hydraul. Engng 50,
1165–1171.
Fukuoka, S., Watanabe, A., Hara, T. & Akiyama, M. (2004) Highly accurate estimation of hydrograph of flood discharge andwater storage in river by using an unsteady two-dimensional flow analysis based on temporal change in observed water
surface profiles. J. Hydraul. Coastal & Environ. Engng 761(II), 45–56.
Hirano, M. (1971) River-bed degradation with armouring. Proc. JSCE 195, 55–65.
Kanemoto, M., Tsunematsu, Y. & Kanemaru, A. (1992) Comparison of numerical analysis for flood flows in open channel
networks. Proc. Hydraul. Engng 323–330.
Uchida, T., Fukuoka, S. & Hamabe, R. (2011) Numerical simulations using water levels observed at a mainstream for flood
flow in river system with several lateral inflows. Ann. J. Hydraul. Engng 55, 1081–1086.
Uchida, T. & Fukuoka, S. (2009) A depth integrated model for 3D turbulence flows using shallow water equations andhorizontal vorticity equations. In: 33rd IAHR Congress: Water Engineering for a Sustainable Environment, 1428–1435.
Yen, B. C. & Osman, A. A. (1976) Flood routing through River Junctions. Rivers 76(1), 212–231.