Proceedings of ninth International Conference on Hydro-Science andof ICHE2010,
Engineering (ICHE 2010), IITProceedings
Madras, Chennai,
India. IIT Madras, Aug 2-5,2010
EVALUATING FLOOD DISCHARGEAND
BED
VARIATIONINTHE OTA RIVER FLOODWAY
2 - 5 August 2010

EVALUATING FLOOD DISCHARGE AND BED VARIATION
IN THE OTA RIVER FLOODWAY
Takahisa GOTOH1, Shoji FUKUOKA2 and Toru ABE3

Abstract: The evaluation of bed variations during a flood is important for understanding ofphysical and ecological environment in river estuaries. The Ota River estuary has thebranched section of the Kyu Ota River and the Ota River Floodway. The Ota River Floodway
has the tidal flats with habitats for many creatures in the brackish river. To evaluate the bed
variations in the Ota River Floodway, we have to understand the discharge ratio in the riverbifurcation. The bed variation in the river bifurcation is induced by three dimensional flow
due to the river bend, floodgates and divergent flows. So, we apply the unsteady quasi-three
dimensional flow and bed variation analysis using time series of the observed water surface
profiles in Sep.2005’s flood. The bed variation during the flood is investigated in relation totidal changes by this method. Therefore, the calculation method is found to provide fairly
good results for bed variation during the flood. And, the discharge ratio in the riverbifurcation is evaluated by this method.
Keywords: the Ota River Floodway; river estuary; river bifurcation; bed variation;
unsteady quasi three dimensional flood flow and bed variation analysis;time series of observed water surface profiles
INTRODUCTION
River estuaries with tidal flats are habitats for many creatures. So, it is important to evaluate
the bed variation during a flood in river estuaries. Generally, to evaluate bed variations
during a flood, we have assumed that longitudinal profile of flood marks indicates the water
surface profile in the flood peak discharge. But, those longitudinal profiles are different inriver estuaries owing to the tidal changes. So, it is required to develop the unsteadycalculation method for estimating flood flows and bed variations during the flood in theestuary.
Fukuoka, Watanabe et al. (2004) indicated the unsteady 2D flow analysis method using timeseries of observed water surface profiles. The calculation method is able to estimate thetemporal changes of hydraulic conditions during the flood (e.g. water levels and dischargehydrograph). Until now, the calculation method has been applied to the several problems in
1 Doctor Course Student of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo,112-8551, Japan, Email: goto_510@civil.chuo-u.ac.jp
2 Professor, Research and Development Initiative, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo, 1128551, Japan, Email: sfuku@tamacc.chuo-u.ac.jp
3 Director of River Office, Otagawa River Office, Chugoku Regional Development Bureau, MLIT, 3-20
Hattyoubori, Naka-ku, Hiroshima-City, 730-0013, Japan1

Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
EVALUATING FLOOD DISCHARGE AND BED VARIATION IN THE OTA RIVER FLOODWAY

Gionn Ohashi
Gion suimon
Nagawaku
Gion Floodgate
Kusatsu

6.0km

1.0km
-3.0km7.0km

Ota River Floodway

Oshiba Floodgate-1.0kmWater level Observation point
Discharge Observation section

3.0km

Yaguchi-daiichi

4.0km

Misasa-bashi
Kouhei-bashi

8.0k
7.0km
9.0km
Kyu Ota River

11.0km10.0kmFigure1. Study area of the Ota Riverrivers (e.g. Fukuoka, 2005). Kawaguchi, Fukuoka et al. (2009) proposed the unsteady 2D
flow and bed variation analysis method using the time series of the measured water surface
profiles for evaluating development and decay of the alternate bars in the experimental
channels. Suzuki, Fukuoka et al. (2009) evaluated the bed variation and sand transport during
the flood in the Chikugo River estuary by the unsteady 2D flow and bed variation analysis
method using the time series of the observed water surface profiles. Okamura, Fukuoka et al.
(2010) estimated flood flows and bed variations in the Tone River-mouth with sand waves byapplying quasi-three dimensional flow and bed variation analysis method using time series ofthe observed water surface profiles.
In the Ota river estuary, tidal changes are relatively large. The difference in tidal levels
between flood tide and ebb tide is about 4m at the river mouth in the spring tide. The tidalchanges affect the conditions in the river bifurcation between the Ota River Floodway and the
Kyu Ota River. The Ota River Floodway has extensive tidal flats with habitats for many
creatures in the brackish river. So, it is required to evaluate the flood flows and bed variations
during the flood for comprehension of the physical environment in the Ota River Floodway.
This requires us to understand the ratio of flood discharge in the river bifurcation.
Generally, three dimensional flow develops and affects bed variations in river bifurcations(e.g. Murota,A., 1960). The river bifurcation in the Ota River is located just downstream of
the river bend. There are floodgates at the each river. Therefore, the three dimensional flowof flood flows is developed due to the river bend and the floodgates in addition to effects ofdivergent flows. So, we need a practical model, which evaluates the effects of the three
dimensional flow, to make clear the ratio of flood discharge in the river bifurcation.
Uchida and Fukuoka (2009) developed unsteady quasi-three dimensional flow analysis
which can evaluate velocity distributions near river bed by using the depth averaged
horizontal vorticity equations in addition to the shallow water equations.
The objective of this study is to make clear the ratio of the flood discharge in the Ota Riverbifurcation and to clarify the bed variations during the flood in the Ota River estuary byunsteady quasi-three dimensional flow and bed variation analysis method using time series ofthe observed water surface profiles.

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Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
EVALUATING FLOOD DISCHARGE AND BED VARIATION IN THE OTA RIVER FLOODWAY

Sediment deposition during 1988 to 1993
4

Elevation (m)

6.6km
6.2km

5.8km

Movable weir
Fixed weir

Gion
Floodgate

2005.92005.3
2003
1998
1993
1988

2
1
0
-1

Sandbar Sediment deposition-2

Oshiba Floodgate

0

12
10
8
6
4
2
0
-2
-4 Bed scouring-50
50

2005.92005.32003
1998

Bed scouring
150

50

100

150

200

250

300

350

Lateral distance (m)The Kyu Ota River

Figure2. Aerial photograph in the riverbifurcation
Elevation (m)3250Lateral distance (m)Figure4. Cross section in main channel
at 6.2km point

350

Volume percentage
finer than (%)
通過質量百分率(％)

The Ota River
Floodway

Height offloodplain

Figure3. Cross section in main channel at
6.0km point
100
90
80
70
60

7.0km
10.4km
13.0km0.0km
5.0km-2.0kmRiver bifurcation

50
40
30
20
10
0
0.01

0.1

1

10

100

1000

Grain粒径(mm)size (mm)Figure5. Grain size distribution in the Ota River

CHANNEL CONDITIONS AND OBSERVATION SITUATIONS IN THE STUDY
AREA
Figure 1 shows the channel conditions and water level and discharge observation points in
the Ota River. The Ota River bifurcation was designed so that the ratio of flood discharge is 2
to 1 based on the river improvement planning in 1948 (The Ota River Floodway : 4000(m3/s),
the Kyu Ota River : 2000(m3/s)).To design the shape of the river bifurcation and theconstruction of the floodgates, the model experiments were conducted in PWRI from 1958 to1959 (Kikkawa,H. and Takami,M., 1959). However, the discharge ratio in the riverbifurcation is changed by the current river improvement planning. In the current river
improvement planning, the design flood discharge in the Ota River Floodway is 4500(m3/s)
and the Kyu Ota River is 3500(m3/s). So, it is required to evaluate the ratio of flood
discharge under the actual conditions for river managements.
The Oshiba-Floodgate located in the Kyu-Ota River consists of the fixed weir and movable
weir with the three gates. And, the Gion-Floodgate located in the Ota River Floodway
consists of movable weir with three gates. The floodgate is constructed in order to control theordinary flow discharge. So, the Gion floodgate is full opened if the flood discharge is over430(m3/s).
The Ota River Floodway is composed of compound channel from 5.8km to 0.0km andsimple channel from 0.0km to -3.4km.

3Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
EVALUATING FLOOD DISCHARGE AND BED VARIATION IN THE OTA RIVER FLOODWAY

In the Ota River, the medium scale floods occurred in July 1993 and in June and
September 1999 (Maximum discharge is about 4000(m3/s) at Yaguchi-daiichi observation
point). And, the large scale flood occurred in September 2005, which is largest flood in thepast years (Maximum discharge is about 7200(m3/s) at Yaguchi-daiichi observation point).
The water levels is measured by automatic water level gauges at Yaguchi-daiichi,
Nagawaku, Gionsuimon, Gion-ohashi and Kusatsu observation point. And, the water level
gauges were installed at 200m intervals of longitudinal distance from 8.0km to 13.4km inorder to investigate the behavior of vegetations during the flood (Gotoh and Fukuoka, 2008).
As above, the time series of the water surface profiles were observed in detail with thebranched section in the Ota River estuary. The flood discharge hydrograph was observed byfloats at Yaguchi-daiichi observation section.
THE TEMPORAL CHANGES IN BED PROFILES
The temporal changes in bed profiles in the Ota River bifurcation
Figure 2 shows the aerial photograph which has been taken in 2003 at the river bifurcation.
Figure 3 and Figure 4 show the temporal changes in the observed bed profiles at the sectionof 6.0km and 6.2km, respectively. In the river bifurcation, the sandbar has been formed
upstream of the floodgates due to sediments deposition during the flood. The vegetation on
the sandbar began to grow from about 1988. The great amount of sediment deposition on the
sandbar was yield by the middle scale flood during the period 1988 to 1993. However, thesandbar was maintained after 1993, because the height of sandbar has become almost sameheight of the floodplain and the fixed weir of the Oshiba Floodgate. The bed scouring
occurred in front of the sandbar and outer bank bed due to the secondary flow by the river
bend as shown in Figure 4. Therefore, the calculation method which can evaluate the effect of
the three dimensional flow is needed.
Figure 5 shows the grain size distribution in the section studied. The bed materials around11.0km, where the bed slope is about 1/600, consist of many cobbles and gravel (see the bed
slop in Figure 9). And, the bed materials in the Ota River Floodway, where the bed slope isabout 1/3300, mainly consist of sands. At the sandbar in the river bifurcation, the bed
materials consist almost entirely of sands which are similar to that in the Ota River Floodway.
Temporal changes in bed profiles in the Ota River Floodway
Figure 6 shows the contours of the observed bed profiles in 1994, 2001 and 2005. The
contours of the bed profiles indicate the difference from the mean bed elevation of eachsection in 2001. Figure 7 shows the observed bed profiles of cross section at -0.8km before
and after the flood in 2005 and the water level hydrograph at Nagawaku and Kusatsu
observation points in 1999’s flood and 2005’s flood.
In the Ota River Floodway, the main channel was dredged to build the floodway. But, there
are extensive tidal flat near the river side, which is about 1m higher than bed elevation of themain channel (see Figure 7). In the main channel of the floodway, the alternate bars with
about 1km wavelength are formed as shown in Figure 6. Figure 8 shows the hydraulicconditions during the floods in September 2005 and June 1999 on the bed profiles
classification diagram by Kuroki and Kishi (1984). The hydraulic conditions used in the
figure are the calculation results by the model of the following the chapter. From this figure,the alternate bars occur during the floods in the Ota River Floodway.

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Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
EVALUATING FLOOD DISCHARGE AND BED VARIATION IN THE OTA RIVER FLOODWAY

Difference from the mean bed elevation in 2001

Tidal flat

River mouth-1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20(m)

-3.0km-3.0kmTidal flat（a） In 1994

-2.0km0.0k（b） In 2001

Tidal flat

Flow

0.0km

Flow

（c） In 2005

Figure6. Contour of the observed bed profiles in the Ota River Floodway
Time (minutes)

0

500

1000

1500

2000

2500

3000

8

Elevation (m)

6

2001
2500

②

4

①

2
0
-2
-4
-50

3000

2005
8.00
Tidal levels(2005.9)
Nagawaku(2005.9)
6.00
Tidal levels(1999.6)
Nagawaku（1999.6)

4.00

Tidal flat

50

Tidal flat

150
250
Lateral distance (m)350

Figure7. The observed bed profiles of cross section at -0.8km before and after the flood and thewater level hydrograph of flood in June 1999 and September 2005
In the Figure 8, the relations between and (BI00.2/h) behave on the different loop in thesefloods due to tidal changes. The flood in June 1999 coincided with the time of the flood peakand ebb tide (see Figure 7). The flood peak of the 2005’s flood occurred about two hours
earlier than flood tide. In 2005’s flood, the plots on the Figure 8 move to the area where thealternate bars occur due to the falling tide in the flood receding period.
Generally, the flood receding period is much longer than flood rising period in case of not
only large scale flood but also small and medium scale flood. Ebb tides occur more than once
during the flood receding period. Because the water surface profiles become steep by fallingtide, the dimensionless shear stress increases and keeps high value in the flood receding5Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
EVALUATING FLOOD DISCHARGE AND BED VARIATION IN THE OTA RIVER FLOODWAY
102005.91999.6

Falling tide (in 2005’s flood)

Alternate 

1

No bars①②

0.1

Multiple sandbars
0.01
1

10

BI00.2/h100

Figure8. Bed profiles classification diagram (Kuroki and Kishi, 1984)
period (period ①,②). Therefore, this fact indicates that displacement, development anddeformation of the alternate bars during the flood are affected by falling tide.
THE BED VARIATION DURING THE FLOOD AND THE RATIO OF FLOODDISCHARGE IN THE OTA RIVER ESTUARY
The unsteady quasi 3D flow and bed variation analysis method using time series ofobserved water surface profiles
The effects of vegetations, river conditions and bed variations during the flood appear in theobserved temporal changes in the water surface profiles. So, the calculation method using thetime series of the observed water surface profiles is useful to understand flood flows and bed
variations during a flood. Okamura, Fukuoka et al. (2010) have dynamically explained the
bed variation in the Tone River mouth during the flood. They conducted the unsteady quasi
3-D flow and bed variation analysis method using the time series of the observed water
surface profiles. In the Ota River estuary, the three-dimensional flow by the river bifurcationand the alternate bars is important for the bed variations. Therefore, we conducted theunsteady quasi three-dimensional flow and bed variation analysis method using the timeseries of the observed water surface profiles. Equations of motion (1), (2), equation ofcontinuity (4) and vorticity equations (5) are as follows. The bed surface velocity is
calculated by equation (6). The vertical velocity distributions assumed as quadric curve are
obtained by using depth averaged velocity and bed surface velocity, if vertical velocity
gradients on the water surface are zero. The bed variation analysis is used conventional
method which consists of bed load formula (Ashida and Michiue, 1972) and continuity
equations for sediment and grain sizes (Hirano, 1971). The critical tractive force for sedimentmixtures is calculated by the modified Egiazaroff formula (Egiazaroff, 1965; Ashida andMichiue, 1972).

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Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
EVALUATING FLOOD DISCHARGE AND BED VARIATION IN THE OTA RIVER FLOODWAY

20

22:00Cal.(9/6)
2:00Cal.(9/7)
5:00Cal.(9/7)
18:00Cal.(9/7)
0:00Obs.(9/7)
3:00Obs.(9/7)
12:00Obs.(9/7)
Flood marks

Water level (m)15100:00Cal.(9/7)
3:00Cal.(9/7)
12:00Cal.(9/7)
22:00Obs.(9/6)
2:00Obs.(9/7)
5:00Obs.(9/7)
18:00Obs.(9/7)

River bifurcation

5
0
-5
-10
-5.3

Mean bed levels
-3.3

-1.3

0.7
2.7
4.7
6.7
8.7
Longitudinal distance from river mouth (km）

10.7

12.7

14.7

Figure9. Comparison between observed and calculated water surface profilesh~~~ ~   ~   
U ~ U ~ U ~ ~ ~Uh ~ Vh ~  J V U cos Uh ~ Vh ~ 
t

 

 





(1)

 z

z 

 ~
1  ~  gh ~s  cos ~s   sw   Jd  h~ 
Jd  h~   Jh ~ cos ~ ~  ~ cos ~ ~ 
 

J 
 


 

~
~
~


 ~  ~  
V ~ V ~ V ~ ~ ~h Uh ~ Vh ~  J U V cos Uh ~ Vh ~ 
t

 


 
 z

z 

 ~

 
1  ~
 gh ~s  cos ~s   sw   Jd  h~ 
Jd  h~   Jh ~ ~ cos ~  ~ ~ cos ~ 

 
J 
 


 






















( sw , sw )  (

















gn 2 gh~ ~
) u 2  v 2 (U ,V )h1 3 K 2



(2)



(3)

n ：Manning’s roughness coefficients， K ：Vegetation permeability coefficients
J

~ ~
~ ~
h J dUh J dV h


0
t



(4)

~ ~
~ ~
i h J dUi h J dVi hJ J ERi  Pi   Di
t



(5)

ERi : expansion, contraction and rotation term of vorticity vector, Pi: production term ofvorticity vector, Di: horizontal turbulence mixing and dispersion term.
2(6)ui   j h ， ui  U i  ubi ， ubi ：Bed surface velocity
3

Calculation results
Figure 9 shows the comparison between the observed and calculated water surface profiles.
Figure 10 and Figure 11 show the comparison between the observed and calculated contoursof the change in the bed profiles before and after the flood in the river bifurcation. The streamline of depth averaged velocity and bed surface velocity in the peak discharge is indicated on
Figure 11. The calculated water surface profiles with time variation are good agreement withthe observed water surface profiles (Figure 9).

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Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
EVALUATING FLOOD DISCHARGE AND BED VARIATION IN THE OTA RIVER FLOODWAY

Scouring

Deposition
1.0(m)-1.0(m)Scouring

Deposition-1.0(m)1.0(m)

Stream line of depth
averaged velocity
Stream line of bed surface
velocity

Gion Floodgate (full open)

Gion Floodgate (full open)
6.0km

6.0km

6.6km

6.6km
6.4km

6.4km

6.2km
Fixed weir

6.2km

Movable weir
(full open)

Fixed weir

Movable weir
(full open)

Figure11. Contour of calculated change in the
bed profiles before and after theflood

Figure10. Contour of observed change in the
bed profiles before and after theflood

The bed variation in the Ota River bifurcation is characterized by the bed scouring in frontof the sandbar and outer bank bed and the sediment deposition just upstream of the Gion
Floodgate (see Figure 10). The sediment deposition by the calculation is a little smaller thanobserved sediment deposition. However, the calculation results explain the observed
characteristics of bed scouring in front of the sandbar and at the outer bank bed by evaluating
the three dimensional flow.
Figure 12 shows the contour of the observed bed profiles before the flood in the floodway.
Figure 13 and Figure 14 show the comparison between observed and calculated change in the
bed profiles before and after the flood in the floodway. In the Ota River Floodway, the bed
scouring occurred upstream of the sandbars, and the sediment deposition occurreddownstream of the sandbars, as shown in Figure 12 and Figure 13. The calculation results in
the Ota River Floodway explain the above characteristics of the observed bed variation, as
shown in Figure 13 and Figure 14. Therefore, the calculation method using the time series ofthe observed water surface profiles provide to fairy good estimate the flood flow and bed
variation during the flood.
Figure 15 shows the contour of the change in the calculated bed profiles in the peakdischarge. Under the peak discharge, the bed variation don’t occur so much in the Ota River
Floodway. In the flood receding period, the bed variation in the Floodway occurred much
more than flood rising period owing to falling tide. So, it is indicated that bed variation in theriver estuary varies with tidal changes.
Figure 16 shows the calculated and observed discharge hydrograph and the discharge ratio
in the river bifurcation. The discharge ratio is defined as ratio of discharge of the Kyu Ota
River to the total discharge. It is indicated that 38% amount of the total discharge is diverged
to the Kyu Ota River. This ratio is a little smaller than its resultant of the model experiments(Kikkawa and Takami, 1959) due to the sediment deposition and the vegetation on the
sandbar.

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Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
EVALUATING FLOOD DISCHARGE AND BED VARIATION IN THE OTA RIVER FLOODWAY

Difference from the mean bed elevation in 2001
-2.00 -1.60 -1.20 -0.80 -0.40 -0.00 0.40 0.80 1.20

0.0km

-1.0km-2.0km(m)

Figure12. Contour of the observed bed profiles in the Ota River Floodway in 2001
Deposition

Scouring

-1.7

-2.9
-2.3

-3.4

-1.1

-0.6

0.0km
0.0

-1.7

-2.3

-2.9

-2.9

-3.4
-1.1

-1.7

-0.6
-1.1

-3.4

-1.7

-0.6

-2.3

0.0

-0.6

-2.3
-2.9
-2.9

-1.7

.4

0.0
-1
.7
-4.0

0.5(m)-0.5(m)-1.0km-3-2.0km-2.9-2.3-1.-01.6

Figure13. Contour of the observed change in the bed profiles before and after the flood-2.0km-1.
0-1.5-1.0km

-0.5

0.0
-1.0

-3.0

-2.0

-3.5

-4.0

Scouring

Deposition-0.5(m)0.5(m)

-0.5

-1.5

-2.5

-2
-2.0

-3.0

-1.0

.5

-1.5 -0.5

-2.0

-1.0
0.0

-3

.0

-3.5

-1.5
0.0 -0.5

-3.5

-3.0

-3.0

-2.0

0.0
-1.0

-2.5 -2.0-2.
5

Figure14. Contour of the calculated change in the bed profiles before and after the flood
Deposition

Scouring-2.0km
-1.5-2 -2.5

-3
-4
-3.5

.5
--31

-2-1

-4-3.5

-3.5
-3

-1.50

-1
-2
-3.5

-1.0km-0.5 -2-0.5
0

0

-1
-1.5

-1.5
-2.5

-1

-2-2.5
-0.5
-0.5

-1

-2

-2

-0.5

-2.5
-3

-3

-2.5

-0.5(m)-3.5-3
0

0
-0.5
-1.5
-2.5

-3
-1.5

0

-2.5
-1

0

-3

-2.5

-3.5
-1.5-2 -1

0.5(m)

0.0km
-1
-1.5
-2.5

-2

-1.5-2-2-2.5-0.5-0.5
0Figure15. Contour of the calculated change in the bed profiles in the peak discharge

Discharge(m3/s)

9000

Yaguchi-daiichi
Ota River Floodway
Ratio of discharge

Yaguchi-daiichi (obs.)
Kyu Ota River

1
0.9

8000

0.8

7000

0.7

6000

0.6

5000

0.5

4000

0.4

3000

0.3

2000

0.2

1000

0.1

Ratio of discharge

10000

0
0
2005/9/6 2005/9/6 2005/9/7 2005/9/7 2005/9/7 2005/9/7 2005/9/7
20:00
22:00
0:00
2:00
4:00
6:00
8:00

Time

Figure16. Observed and calculated hydrograph and discharge ratio in the river bifurcation9

Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010
EVALUATING FLOOD DISCHARGE AND BED VARIATION IN THE OTA RIVER FLOODWAY

CONCLUSIONS
The following conclusions were derived from the observation and calculation results.
1) Unsteady quasi three dimensional analysis of flood flows and bed variations using timeseries of observed water surface profiles is found to provide fairly good results for bed
variation with branched section in the Ota River estuary. Moreover, the ratio of flood
discharge in river bifurcation is evaluated by the calculation method.
2) It is found that alternate bars are formed in the Ota River Floodway by the observed bed
profiles. From the bed profiles classification diagram and the contour of the calculatedchange in bed profiles, the alternate bars are developed in flood receding period due totidal changes.
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