Proceedings of ninth International Conference on Hydro-Science andof ICHE2010,
Engineering (ICHE 2010), IITProceedings
Madras, Chennai,
India. IIT Madras, Aug 2-5,2010
Bed2 Formand
Bed
Variation
duringFloods of the Tone River Mouth- 5 August 2010

BED FORM AND BED VARIATION DURING FLOODSOF THE TONE RIVER MOUTH
Seiji Okamura1, Shoji Fukuoka2 and Takayuki Takemoto3
Abstract: In this paper, the characteristics of the flood flow and bed variation of the Tone
River mouth during the 2007 flood is elucidated by the surveyed bed form, the observed dataof the flood, and numerical analysis. It is examined that the water surface gradient became
steep at the reach downstream of 5km from the river mouth and became mild at the reach
upstream from 5km at the 2007 flood peak occurred at low tide. This paper clarifies thereasons for the steep water surface gradient as follows. At first, the existence of the sandwaves considered as dunes are verified by the longitudinal survey of the bed form in the Tone
River mouth. Next, the gravel bed material around the narrow river mouth maintains the bed
elevation during the flood. At last, the unsteady analysis of flood flow and bed variation
using observed temporal changes in water surface profiles demonstrates that the gravel bed
material and the bed resistance due to sand waves causes the steep water surface profile just
upstream of the river mouth.
Keywords: water surface profile; flood; bed variation; sand wave; 2D unsteady flow
analysis
INTRODUCTION
We are faced with the problem that the discharge capacity of the Tone River mouth isdecreased by the steep water level rising in the mouth. To solve this problem, it is important
to clarify the characteristics of flood flows and bed variations of the Tone River mouth during
floods.
The longitudinal water surface profile and its temporal variation upstream of the rivermouth are interrelated with bed variation and tidal level change during floods. So, it isnecessary to develop the unsteady analysis based on the observed temporal changes in water
surface profiles to clarify the characteristics of flood flows and bed variations in the rivermouth (Fukuoka, 2005, Kawaguchi, Fukuoka et al., 2009, Suzuki, Fukuoka et al., 2009).
The sand waves sometimes appear during floods at the river mouth where the bed slope ismild. In that case, the water surface profile varies with the bed resistance due to the sandwaves. At the Ishikari River mouth, the observation of the temporal changes in water surface
1 Doctor Course Student of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo,
Japan, Email: okamura@civil.chuo-u.ac.jp
2 Professor, Research and Development Initiative, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo, Japan,
Email: sfuku@tamacc.chuo-u.ac.jp
3 Engineer, Kanto Regional Development Bureau, Ministry of Land, Infrastructure, Transport and Tourism,
I4149 Sawara, Katori-city, Chiba, Japan, Email: takemoto-t2hq@ktr.mlit.go.jp

1Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
Bed Form and Bed Variation during Floods of the Tone River Mouth

profiles and the survey of the bed form were conducted during the 1981 flood. Kuroki &Kishi (1983) and Shimizu et al. (1986) investigated the change in the bed resistance due tothe bed form during the flood and conducted numerical analysis of the flood flow and bed
variation, containing the bed resistance due to the sand waves.
In this paper, the characteristics of the flood flow and bed variation during the 2007 floodin the Tone River mouth is elucidated by the numerical analysis based on the observation of
the bed form and temporal changes in longitudinal water surface profiles.

Flow

Training Dikes
Channel Center Line

Figure1. Planform of the Tone River mouth
Elevation（Y.P.m）

2
0
-2
-4
-6
-8
-10

(b) Enlarged view of this section

10k

9k

8k

7k
6k
5k
4k
3k
Longitudinal distance from river mouth (km)

2k

1k

0k

-1k

(a) From -1km to 10km section
Elevation（Y.P.m）

2
0
-2
-4
-6
-8
-10

2k

1k
Longitudinal distance from river mouth (km)0k(b) Enlarged view of section from 0km to 2km
Figure2. Longitudinal bed form of the Tone River mouth
THE LONGITUDINAL BED FORM IN THE TONE RIVER MOUTH
Figure 1 shows the plan form of the Tone River mouth. The discharge capacity of the rivermouth is not enough because of the training dikes which decreases the channel width.

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Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
Bed Form and Bed Variation during Floods of the Tone River Mouth

Figure 2 shows the longitudinal bed forms along the channel center line shown in Figure 1.
Bed elevations are surveyed at 50m intervals in 2003 and 20m intervals in 2009
longitudinally. While the undulation of bed form is mild from 5km to 10km section, the bed
form downstream of 5km section is rugged. In the reach, the large scale waves (wave lengthis about 500m, wave height is about 4m) and the small scale waves (wave length is about
50m, wave height is about 1m) are generated, as shown in Figure 2(b). The small scale waves
are considered as dunes for the following reason. The water depth of the section is from 5m
to 10m during floods. Generally, the wave length and wave height of the dune estimatedabout ten times longer than the water depth and from one-fifth to one-tenth of the water depth,
respectively.
As above, existence of the sand waves considered as dunes are verified by the longitudinalsurvey of the bed form in the Tone River mouth.
TEMPORAL CHANGES IN LONGITUDINAL WATER SURFACE PROFILES AND
BED VARIATION DURING 2007 FLOOD
A large flood occurred in the Tone River in September 2007. During the flood, temporal
data of water levels were measured at many observation points in the reach 30km upstream
from the river mouth.

The Pacific Ocean

The Tone River

Observation stations of water level
Observation cross-sections of discharge

Figure3. Planform of the Tone River and observation stations of 2007 flood
Figure 3 shows observation stations of water levels and discharge in the reach 30km
upstream from the river mouth. The discharge was measured at 27km and 5km. Crosssectional bed forms were measured at 5km by the Acoustic Doppler Current Profiler (ADCP)
during the flood.
Figure 4 shows observed water level hydrographs and discharge hydrographs of the 2007
flood. Figure 5 shows temporal changes in observed longitudinal water surface profiles. The
peak discharge was about 6,000m3/s and the water level near the river mouth was close tohigh water level. The flood peak occurred in the stage of low tide as shown in Figure 4. The

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Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
Bed Form and Bed Variation during Floods of the Tone River Mouth

water surface gradient became steep just upstream of the river mouth and became mild at thereach upstream from 5km as shown in Figure 5.
28km
18.4km5km
0.7km
Tidal level

4.0
Water lovel(Y.P.m)

3.5
3.0
2.5
2.0
1.5
1.0
0.5

Discharge(㎥/s)

0.0

9/6

8000
7000
6000
5000
4000
3000
2000
1000
0

9/7

9/8

9/9

9/8

9/9

Observed discharge at 27km
Observed discharge at 5km
9/6

9/7

Figure4. Observed water level hydrographs and Observed discharge hydrographs

Water lovel（Y.P.m）

4.0
3.0
2.0

9/7 12:00
9/7 18:00
9/8 0:00
9/8 6:00

1.0
0.0
-2k

0k

2k

4k

6k

8k

10k

12k

14k

16k

18k

20k

22k

24k

26k

28k

30k

20k

22k

24k

26k

28k

30k

(a) Flood rising period
Water level（Y.P.m）

4.0
3.0

9/8 12:00
9/9 0:00
9/9 9:00
9/10 0:00

2.0
1.0
0.0
-2k

0k

2k

4k

6k

8k

10k

12k

14k

16k

18k

(b) Flood falling period
Figure5. Observed temporal changes in water surface profiles

4Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
Bed Form and Bed Variation during Floods of the Tone River Mouth

Bed elevation（Y.P.m）-1

Average elevation of river bed

-3
-5
-7

Deepest elevation of river bed

-9

-11
-2k

Before 2007 flood
After 2007 flood
0k

2k

4k

6k

8k

10k

12k

14k

16k

18k

20k

22k

24k

26k

28k

30k

Figure6. Bed elevation change before and after 2007 flood
1

Before 2007 flood
During 2007 flood（9/8 12:00）
After 2007 flood

Elevation（Y.P.m）

0
-1
-2
-3
-4
-5
-6
-100

100

300
500
Lateral distance（m）

700

900

Figure7. Cross-section of 5.0km
Figure 6 shows the comparison of average elevation and lowest elevation of river bed
before and after the flood. Although the river bed elevation decreases about 0.5m around0.0km point, the bed elevation was maintained for the most part of the 0.0-30.0km section.
Figure 7 shows the cross-section at 12 o’clock on September 8th just after the flood peakwhich was surveyed by ADCP at the 5.0km point. The bed elevation just after the flood peakcoincides with the bed elevation after the flood.
As above, although the flood peak occurred at low tide and water surface gradient became
steep just upstream of the river mouth, the bed elevation was maintained during the 2007
flood.
BED MATERIAL GRAIN SIZE AND BED VARIATION AT THE RIVER MOUTH
Figure 8, 9 shows the planer distribution of grain size of bed material in the surface layer
and these grain size distributions, respectively. Whereas the bed material is composed of silt
or sand in most areas around the river mouth, the gravel component dominates the bed
material from -1.0km to 0.5km section, where the channel width is decreased by the training
dikes. Figure 10 shows the vertical profiles of average grain size surveyed at left and rightside of -0.5km and 0.0km cross-section. The comparison of cross-sectional bed form before
and after 2007 flood is also shown in Figure 10. At the left side, although the sand exists insurface layer, the gravel exists in lower layer. At the right side, the gravel exists from river5

Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
Bed Form and Bed Variation during Floods of the Tone River Mouth

bed to the depth of about 5m from river bed. The river bed elevation at the right side of 0.5km and 0.0km cross-section is maintained due to the gravel bed materials even though
there are located at the outer side of the narrow curved channel. Non-dimensional shear
stresses (τ*) for material grain size from 3mm to 10mm is estimated by using the observed
water surface gradient at flood peak. These values are from 0.04 to 0.12, slightly over the
Non-dimensional critical shear stress (τ*c=0.05). Therefore, the bed elevation at the narrow
river mouth was maintained. This is one of the reasons for the water surface gradient became
steep just upstream of the river mouth.

Volume percentage finer than(%)

100

Gravel
Sand
Silt

70
60

Silt

Sand

0.01

0.1
1
10
Grain size(mm)Gravel

50
40
30
20
10
100

Figure9. Grain size distributions

6

6

Before 2007 flood
After 2007 flood

2
0
-2

0.22
0.21
3.22
2.07
2.68
2.54

-4
-6

3.12
4.09
3.30
3.27
6.48
3.72

400

500
600
700
Lateral distance（m）

800

2
0
-2

0.19
0.70
2.17
2.34
2.53
2.51

-4
-6
-8

Numbers present average grain size (mm)

-10
300

Before 2007 flood
After 2007 flood

4
Elevation（Y.P.m）

4
Elevation（Y.P.m）

80

0
0.001

Figure8. Planer distribution of bed material-890

Numbers present average grain size (mm)

-10
200

900

(a) -0.5km cross-section

3.29
3.59
1.19

300

400
500
600
Lateral distance（m）

700(b) 0.0km cross-section

Figure10. Vertical profiles of average grain size of -0.5k and 0.0k cross-section

6

800
GravelSand
Silt

Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
Bed Form and Bed Variation during Floods of the Tone River Mouth

UNSTEADY NUMERICAL ANALYSIS OF FLOOD FLOW AND BED VARIATIONUSING OBSERVED WATER SURFACE PROFILES
To clarify the characteristics of the flood flows and bed variations during floods of theTone River mouth, we develop the unsteady numerical analysis of flood flow and bed
variation using observed temporal changes in water surface profiles to 2007 flood. The
analysis is conducted based on the method of Kawaguchi, Fukuoka et al. (2009), Suzuki,
Fukuoka et al. (2009). This analysis consists of quasi-three-dimensional unsteady flow
analysis (Uchida and Fukuoka, 2009) and two-dimensional bed variation analysis (Fukuoka,
Watanabe et al., 1998), employing the general coordinate system. The boundary conditions of
upstream and downstream ends are defined as observed water levels at 28km point andastronomical tide levels of the Choshi tidal observatory at sea 4km from the river mouth,
respectively. The planer shape of training dikes and the drag force acting on piers of the
Choshi Ohashi Bridge are considered in the analysis as shown in Figure 11.
Bed elevation(Y.P.m)Choshi Ohashi Brigde
Training dikes

Figure11. Planform of calculation grid and counter diagram of bed elevation

Elevation（Y.P.m）

4
3

Observed
9/7 12:00
9/7 18:00
9/8 6:00

Calculated
9/7 12:00
9/7 18:00
9/8 6:00(a) Calculation case1 (Flood rising period)

2
1

Maning’s roughness coefficient n=0.015
0
-2k

0k

2k

4k

6k

8k

10k

12k

14k

16k

18k

20k

22k

24k

26k

28k

30k

26k

28k

30k

Longitudinal distance from river mouth (km)Elevation（Y.P.m）

4
3

Observed
9/7 12:00
9/7 18:00
9/8 6:00

Calculated
9/7 12:00
9/7 18:00
9/8 6:00(b) Calculation case2 (Flood rising period)

2
1

Maning’s roughness coefficient n=0.014

n=0.028
0
-2k

0k

2k

4k

6k

8k

10k

12k

14k

16k

18k

20k

22k

24k

Longitudinal distance from river mouth (km)Figure12. Temporal changes in observed and calculated water surface profiles

7Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
Bed Form and Bed Variation during Floods of the Tone River Mouth

Elevation（Y.P.m）

-1
-3
-5
-7
-9
-11
-2k

0k

2k

4k

Average elevation of bed
before flood Obs.
after flood Obs.
after flood Cal.

Lowest elevation of bed
before flood Obs.
after flood Obs.
after flood Cal.

6k

14k

8k

10k

12k

16k

18k

20k

22k

24k

26k

28k

30k

Longitudinal distance from river mouth (km)Figure13. Comparison between observed and calculated bed elevation before and after
the 2007 flood (calculation case2)
At first (as calculation case1), we use the uniform value of the Manning’s roughness
coefficient n=0.015, assuming that the bed form is flat in all areas of the section in question.
Figure 12 (a) shows temporal changes in the observed and the calculated water surface
profiles for calculation case1. The calculated water surface profile at 12 o’clock on
September 7th (low stage of 2007 flood) coincides with the observed water surface profile.
At 6 o’clock on September 8th (the flood peak), the calculated water level increases from 1.0km to 1.0km section due to decrease of the channel width and the calculated water surface
profile downstream of 1.0km coincides with observed water level. However, the gradients ofthe calculated water surfaces are milder than that of observed water surfaces from 1.0km to
5.0km section.
This steep water surface gradient downstream of 5.0km section is considered as the bed
resistance due to sand waves, as shown in Figure 2. So next (as calculation case2), theManning’s roughness coefficient is determined so as to minimize the difference between theobserved and the calculated water surface profiles. As a result, the observed temporalchanges in water surface profiles is accurately re-created by deciding the Manning’s
roughness coefficient n=0.028 from 0.0km to 5.0km section where the sand waves exist and
n=0.014 upstream from 5.0km section, respectively.
Figure 13 shows the comparison between observed and calculated bed elevation before andafter the 2007 flood for calculation case2. The calculated bed variation is similar to observed
bed variation in that the bed elevation is maintained in most parts of the section in question
and the bed elevation decreases about 0.5m at 0.0km point. The calculated dischargehydrograph corresponds with the observed discharge hydrograph as shown in Figure 14.
10000

Discharge(㎥/s)

8000
6000
4000
27.0km Obs
5.0km Obs
27.0km Cal
5.0km Cal

2000
0

-2000

9/6

9/7

9/8

9/9

Figure14. Comparison between observed and calculated discharge

8Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
Bed Form and Bed Variation during Floods of the Tone River Mouth

Water level(Y.P.m)

3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

Discharge(m3/s)

We also apply the model using same resistance distribution to the 2008 flood whose peakdischarge was 3,000m3/s about half that of 2007 flood as shown in Figure 15. As a result, theobserved temporal changes in water surface profiles are accurately re-created as shown in
Figure 16.
As above, the large bed resistance due to sand waves in 0.0-5.0km section is estimated at
the Manning’s roughness coefficient n=0.028. According to the relation between the bed
forms and the bed resistances researched by Kishi and Kuroki (1972), for the hydraulicconditions of the 2007 flood, the value of the Manning’s roughness coefficient of dunes is
estimated as about n=0.040. Non-uniformity of bed form of the Tone River mouth and thedifference of scale between the Tone River and the experiment channels are regarded as thereasons for the discrepancy.

5000
4000
3000
2000
1000
0

28km
5km
Tidal level

8/30 0:00

8/31 0:00

9/1 0:00

Observed discharge
Calculated discharge
8/30 0:00

8/31 0:00

9/1 0:00

Figure15. Observed water level and discharge hydrographs of the 2008 flood

Water level（Y.P.m）

3.0
2.5
2.0
1.5

Observed
8/31 4:00
8/31 7:00
8/31 10:00

1.0
0.5
0.0
-2k

0k

2k

4k

6k

8k

10k

12k

14k

16k

18k

20k

22k

24k

Calculated
8/31 4:00
8/31 7:00
8/31 10:00

26k

28k

30k

Figure16. Temporal changes in observed and calculated water surface profiles of the 2008
flood
CONCLUSIONSIn this paper, the characteristics of the flood flow and bed variation during the 2007 floodin the Tone River mouth is elucidated by the numerical analysis based on the observation of
the bed form and temporal changes in longitudinal water surface profiles.
Main conclusions are drawn as follows.

9Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
Bed Form and Bed Variation during Floods of the Tone River Mouth

1. Existence of the sand waves considered as dunes are verified by the longitudinal survey ofthe bed form in the Tone River mouth.
2. The water surface gradient became steep just upstream of the river mouth and became mild
at the reach upstream from 5km at the 2007 flood peak occurred at low tide.
3. The gravel bed material around the narrow river mouth maintains the bed elevation during
the flood. This is one of the reasons for the steep water surface gradient just upstream of
the river mouth.
4. The unsteady analysis of flood flow and bed variation using observed temporal changes inwater surface profiles estimates the bed resistance due to sand waves in 0.0-5.0km section.
REFERENCES
Fukuoka, S. 2005. Flood hydraulics and river channel design, Morikita publishing company.
Kawaguchi, H., Todo M. and Fukuoka, S. 2009. Analysis of channel bed variation anddischarge hydrograph based on time-series data of water surface profiles, Annual Journalof Hydraulic Engineering, Vol.53, pp.751-756, JSCE.
Suzuki, K., Fukuoka, S. and Matsuo, K. 2009. Bed material structure and sand transport byflood flows in the estuary of the Chikugo River, Proceedings of the third International
Conference on Estuaries and Coasts, Vol.1 pp.101-108.
Kuroki, M. and Kishi, T. 1983. Study on the changes of flow resistance and sand waves in
Ishikari River, Annual Journal of Hydraulic Engineering, Vol.27, pp.747-752, JSCE.
Shimizu, Y., Itakura, T., Kishi, T. and Kuroki, M. 1986. Bed variations during the 1981August flood in the lower Ishikari River, Annual Journal of Hydraulic Engineering,
Vol.30, pp.487-492, JSCE.
Uchida, T. and Fukuoka, S. 2009. A Depth Integrated Model for 3D Turbulence Flows Using
Shallow Water Equations and Horizontal Vorticity Equations, 33rd IAHR Congress:
Water Engineering for a Sustainable Environment, pp.1428-1435.
Fukuoka, S., Watanabe, A. and Okada, S. 1998. Bed topography analysis in a compound
meandering channel by using 3D numerical model with approximation of hydrostatics
pressure, Annual Journal of Hydraulic Engineering, Vol.42, pp.1015-1020, JSCE.
Kishi, T. and Kuroki, M. 1972. Bedforms and resistance to flow in erodible-bed channels (I),
Bulletin of the Faculty of Engineering Hokkaido University, Vol.67.

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