Advances in River Sediment Research – Fukuoka et al. (eds)© 2013 Taylor & Francis Group, London, ISBN 978-1-138-00062-9

On the flow resistance and bed variations during Hii River flood
Y. Okada

Science and Engineering, Chuo University, Tokyo, Japan

S. Fukuoka

Research and Development Initiative, Chuo University, Tokyo, Japan

K. TachiIzumo River Office, Ministry of Land, Infrastructure and Tourism, Izumo-shi, Shimane, Japan

ABSTRACT: Main channel of the Hii river divides into braided channels, and large sand waves areformed on the bars. It is considered that the flow resistance changes with bed elevation of the main
channel during a flood. Therefore, evaluating the temporal variation in the flow resistance is importantto understand the flood flows and bed variations in the Hii river. In this study, first, the temporal variation in the resistance during the 2011 May flood of the Hii river is evaluated by the Manning’s roughness
coefficient in quasi-steady flow analysis. Next, the unsteady flow analysis is conducted using the temporal variation in the roughness coefficient determined by the quasi-steady flow analysis to investigate
the mechanism of bed variation in the Hii river. From these investigations, we conclude that the analysis
method presented in this study is useful for the flood flow analysis in the Hii river.
1INTRODUCTION

There are a large amount of sediment yields in theHii river basin, Shimane Prefecture, Japan, where
the Hii river runs through. As shown in Figure 1,
the Lake Shinji located at the Hii river mouth has

Figure 1. Plan-form and observation points in theobjective area of the Hii river.

reduced the discharge capacity by raising the waterlevel of the lower Hii river. Ground levels of urban
areas along the river are lower than the river bedlevels. Therefore, people lived there has sufferedfrom flood damages for a long time. Moreover, thedischarge capacity of the current channel is not
sufficient for the design flood discharge. For thesereasons, the diversion channel is being constructed
to decrease the flood discharge to the lower Hii
river (see Fig. 1). However, because of a lack ofunderstanding of the flood flows and bed variations in the current channel, effects of the diversion channel on the bed variation in the upstream
and downstream of the diversion section have notbeen understood sufficiently. At first, it is important to understand the mechanism of bed variationin the current channel.
The main channel in the Hii river divides into
braided channels, and large sand waves are formedon the bars as shown in Figure 2. Ueno et al. (1996)
observed spatial distribution of bed forms by theecho-sounder during floods. They showed that theheight of the sand waves changed corresponding
to the increasing and decreasing water levels during the floods. Fukuoka (2011) showed that themechanism of bed variations during floods could
explain with reasonable accuracy by conducting the quasi-three-dimensional flood flow andtwo-dimensional bed variation analysis so as tocoincide with temporal changes in observed water379

Figure 2. Bed forms of the Hii River (May 2011).

surface profiles. This analysis method is based on
the idea that the various phenomena including
flow resistance due to the sand waves and bed variations in rivers are reflected in temporal changes
in observed water surface profiles. In the Hii river,
the water depth is relatively shallow even during
floods. It means that bed variation and sand waves
control characteristics of the flood flows and sediment transports in the Hii river.
Detailed water level observations were conducted
in 2011 May flood. Both quasi-steady and unsteadyflow analyses are conducted in this study. The temporal variation in the flow resistance is evaluated by
the Manning’s roughness coefficient. First, the temporal variation in the roughness coefficient during
the flood is estimated by quasi-three-­dimensional
flow and two-dimensional bed variation analysis
under the assumption of the quasi-steady flow.
Next, the unsteady ­quasi-three-dimensional flow
and two-dimensional bed variation analysis considering the temporal variation in the roughness
coefficient estimated by the quasi-steady flow analysis was conducted to investigate the mechanismof bed variation in the Hii river.

Aka river around 20.0 km (see Fig. 1). Because
main channel width is narrow due to the separation levee in this area, bed scouring near the riverbank has been concerned. On the other hand, main
channel width in the downstream of the confluence
point becomes wide and the main channel divides
into braided channels. In the diversion section, low
sand embankment is constructed in a main channel for irrigation purpose as shown in Figure 3. The
embankment has been washed away every flood
events. Transported sands have been deposited tothe downstream and affected the main channel
widths around the diversion section year by year.
As shown in Figure 2, a large sand bar develops inmain channel, and vegetation grows densely on thebar around 13.0 km point.
It was 2011 May flood that the maximum waterlevel was recorded after the pressure type water level
gauges were installed. The peak discharge of thisflood was 1200 m3/s at the Kamishima (18.6 km)
observation station. From observed data of crosssectional bed shapes, the height of the sand waves
is estimated from 0.5 to 1.0 meters in the objective area. Figure 4 shows the cross-sectional bed

Figure 3.

Sand embankment in the main channel.

2 objective area and flood
Figure 1 shows plan-form and observation points
in the objective area. In this area, the time series
data of the discharge and water level have been
observed at the Kamishima (18.6 km), Ohtsu(12.4 km) and Nadabun (4.0 km) observation stations and simple pressure type water level gauges
with data logger were installed at the points designated by triangles. The diversion channel is being
constructed at 14.4 km point. The water level
gauges were densely installed to investigate water
surface profiles in the upstream and downstreamof the diversion section.
The Hii river has a separation levee in theupstream area of the confluence point with the380

Figure 4. The cross-sectional bed shape and the flood
marks at 14.8 km point.

shape and the flood marks at 14.8 km point. The
difference between the flood marks and bed elevation is about 3.0 meters on the average. This meansthat Hii river floods are shallow water flows. It isconsidered that bed variation and sand wave deformation during the flood have a large influence on
temporal changes in water surface profiles.
3 analysis method
In this study, we estimate the temporal variation in
the flow resistance and investigate the mechanismof bed variations from 14.0 km to 15.6 km during
the flood.
3.1

Governing equations

Since the diversion section is located in a curved
reach, the three-dimensionality of the flow plays
important roles on the flood flows and sedimenttransports. For the above reason, quasi-threedimensional flow analysis (Uchida & Fukuoka,2011) is adopted in this study. The bed variation
analysis takes both bed load and suspended load
into account. A rate of the bed load transport
is calculated by Ashida and Michiue formula­(Ashida & Michiue, 1972). The concentration ofthe suspended load is calculated by a three-dimensional advection-diffusion equation (Okamura &­Fukuoka, 2012) to evaluate the high sediment concentration transport near the bed and effects of thevertical distribution of the velocity properly. The
equation is written as:∂ck 1  ∂∆η ⋅ uξ ck ∂∆ξ ⋅ uη ck ++∂η∂ξ
∂t J 
+(∂ck uσ − σ t − w0 k∂σ)∂  ∂ck  ∂  ∂ck = εs
+ εs∂ξ  ∂ξ  ∂η  ∂η ε s  ∂ck ∂θ ξ ∂ck ∂θ η  ∂  ∂ck ++  εs∂η ∂ξ  ∂z  ∂z J  ∂ξ ∂η+ qsuk (z = z )b3.2 Quasi-steady flow analysis
The flow resistance is evaluated by the roughness coefficient of the Manning’s equation. Sincevarious resistances during a flood occur in a river,determination of the roughness coefficient by theunsteady flow analysis is not easy. We estimate theroughness coefficient by quasi-steady quasi-threedimensional flow and two-dimensional bed variation analysis for this reason. The upstream anddownstream boundary conditions are given byobserved water level hydrographs at the Kamishima(18.6 km) and Shinji Lake (−1.0 km) observation
stations shown in Figure 1.
The upstream and downstream boundary conditions are given by the water level hydrographs shownby solid lines in Figure 5. The water level hydrographs
are divided by 8 time zones (A–H). The divided timezones correspond to the time when the discharge
was measured. The observed water surface profiles
reflect the temporal variation in the resistance dueto the bed elevation variation. The roughness coefficients are determined so that the calculation results
agree with the observed water surface profiles anddischarges at the ­Kamishima (18.6 km) observation station in each time zone (A–H). Here, because
the discharge measurement was not conducted in
the period of low water level, the discharge at theKamishima observation station is estimated byusing the rating curve in A, G and H time zones.
3.3 Unsteady flow analysis

 ∂  ∂c  ∂  ∂ck  + cos θ ηξ    ε s k  + εs    ∂ξ  ∂η  ∂η  ∂ξ  +Here, σ ­direction is divided by six grids between
water and bed surfaces. The vertical velocities uσwere given by continuity equation. The pick up rateof suspended load from bed surface is calculatedby Kishi-Itakura formula (Itakura & Kishi, 1980).
The critical tractive forces for dk and mean particle
size dm are calculated by the modified ­Egiazaroff
formula (Asida & Michiue, 1972) and Iwagaki­formula (Iwagaki, 1956), respectively.

(1)

where, ck = concentration of suspended loadof the each particle size dk, σ t = grid movement velocity of σ direction, w0k = falling velocity of dk, εs = ­diffusion coefficient, qsuk = Pick up
rate of suspended load of dk from bed surface.

We investigate the mechanism of bed variationin 14.0 km–15.6 km by using the quasi-three­dimensional unsteady flow and two-dimensional
bed variation analysis and the roughness coefficient estimated by the quasi-steady flow analysis.
The upstream and downstream boundary conditions are given by the water level hydrographs
shown by plots in Figure 5.
3.4 Analysis conditions
In this analysis, the initial bed forms are createdbased on the data of cross-sectional bed shapes
measured on December 2010. The measurements
were conducted at intervals of 200 meters from381

Figure 5. Boundary conditions of quasi-steady and unsteady flow analysis.

Table 1. Manning’s roughness coefficient of the main
channel in each time zone.

AB
C
DEFG
H
Figure 6.
analysis.

10 km∼15 km(m-1/3 ⋅ s)

15 km∼19 km(m-1/3 ⋅ s)

0.030
0.030
0.038
0.032
0.045
0.048
0.043
0.031

0.035
0.035
0.039
0.031
0.043
0.039
0.035
0.023

0.026
0.026
0.030
0.026
0.032
0.030
0.027
0.022

Particle size distributions used to the14.0 km to 15.6 km and at intervals of 500 metersin the other areas. Figure 6 shows particle size
distributions used for the analysis. They are determined from the data of bed materials survey in theobjective area in 2002.
4 analysis results
and considerations
4.10 km∼10 km(m-1/3 ⋅ s)

Temporal variation in the flow resistanceduring 2011 May flood

Table 1 shows the Manning’s roughness coefficients of the main channel estimated by the quasisteady flow analysis in the time zones (A–H). Theflow resistance varies with the variation in waterlevel in each area, and the Manning’s roughness
coefficients almost correspond to changes in waterlevels. The height of the sand waves seems to be amaximum at the peak water level.

Attention has been paid on the rise of the waterlevel in the river mouth. Funabashi et al. (2006)
showed that the main causes of the water rise were
the growth of the sand waves and the sedimentdeposition as seen in Figure 7. Table 1 shows thatthe roughness coefficient in the 0.0 km–10.0 km
varies over a wide range and has a maximum value
0.048. This proves that the sand waves develop
actively compared with the other areas and has asignificant influence on the water level rising in thelower Hii river.
4.2 Flood flow and bed variation analysis
considering the flow resistance variation
during a flood
Figure 8 shows comparison between observed andcalculated water surface profiles and average bed
elevations by the unsteady flow analysis. The calculated water surface profiles were determined so
as to coincide with observed ones. The variation ofthe average bed elevations seem to be small fromthe comparison between brown plots and black382

Figure 7. The growth of the sand waves before andafter 2006 flood at 2.0 km point.

Figure 8.

broken line in Figure 8. Figure 9 shows that thecalculated discharge hydrographs can also explain
the observed discharge hydrographs at three observation stations. From these considerations, we canestimate the temporal variation in the flow resistance by using the quasi-steady flow analysis. It isconcluded that the analysis presented in this study
gives a useful method for the flood flow and bedvariation analysis in the Hii river.
Figure 10 shows contours maps of the bed variation from 14.0 km to 15.6 km during the 2011
May flood. Figure 10a and Figure 10b show that
calculation results of the bed variations are about
0.1 meters on the average in the peak water level
and about 0.3 meters on the average in the falling
period. The comparison between Figures 10b, c,shows that the bed variations extend downstream
in the falling period. Figure 11 shows a relationship between the calculated sediment dischargehydrographs and flood discharge hydrograph at
14.8 km point. We can see that amount of thesuspended load is much larger than that of thebed load. The bed load is increasing in the falling period, although the variation pattern of thesuspended load almost corresponds to that of theflood discharge. This reason may be explained asfollows. In the falling period, irregularity of the bedheight increases as in Figure 10, and flood flows

Comparison between observed and calculated water surface profiles and average bed elevations.

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Figure 9. Discharge hydrographs at the observation stations.

Figure 10. Contours maps of bed variation from 14.0 km to 15.6 km during 2011 May flood.

tend to concentrate in the deeper parts of braided
channels. It would be increasing the transport rateof the bed road.
From the comparison between Figure 10c,d, the analysis reproduces bed scoring around15.0 km where the main channel width is relatively
narrow but doesn’t reproduce the ­longitudinalbed ­variation including the deposition around14.4 km where the main channel width is gradually expanding. In addition, although the bed variation occurred about 0.5 meters on the average, thecalculated bed variation remains about 0.3 meterson the average. This difference may be explained asfollows. Applicability of the present bed variation

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Figure 11. Relationship between calculated sediment discharge hydrographs and flood discharge hydrograph at
14.8 km point.

model for the braided channel is questioned. The
bed variation in braided channel is closely related toplan form, cross-sectional form and sediment particles. The Hii river has almost uniform sand particles which move even in the normal flow condition.
Their effects on the formation of braided channel
are examined in detail. Flood flows concentrate in
the deeper parts of the braided channels, and cause
the non-equilibrium sediment transport due to thespatial difference of the flow velocity in the low
water level. As a result, the bed variation would belarge. Since the initial bed forms in this study are
created from the data of cross-sectional bed shapes
measured at intervals of 200 meters, the initial bed
forms couldn’t reproduce properly the deeper partsof the channel. In addition, the sediment is transported rather actively even in the ordinary flow
conditions, and bed forms changes in shape continuously. Since initial cross-sectional bed shapes
used were measured on December 2010, the initial
bed forms may be different from those of the 2011
May flood. It is required to measure initial crosssectional bed shapes properly for further improvement of the flood flow and bed variation analysis
in the Hii river.
5 conclusions
1. The temporal change in the flow resistance due
to bed variation during May 2011 flood in theHii river was evaluated by the Manning’s roughness coefficient using in the quasi-steady flowanalysis.
2. The unsteady flow analysis could reproduce
the temporal changes in observed water ­surface

profiles and discharge hydrographs at the observation stations by using the temporal variationin the roughness coefficient estimated by thequasi-steady flow analysis. We concluded that
two-step analysis method presented in this study
was useful for the flood flow and bed variation
analysis in the Hii river.
3. We pointed out the importance of the initial
bed forms in braided channel for the further
improvement of the flood flow and bed variation analysis in the Hii river.
references
Fukuoka, S. 2011. What is the fundamentals of river
design-utilization of visible techniques of sedimentladen-flood flows. Advances in River Engineering 17:
83–88. JSCE.
Funabashi, S., Watanabe, S. & Fukuoka, S. 2007. The
cause and mechanism of water level rise near themouth of the Hii River. Annual Journal of HydraulicEngineering 51: 1003–1008. JSCE.
Okamura, S. & Fukuoka, S. 2012. Numerical analysisof unsteady flow and bed variation using temporalchanges in water surface profiles during 1981 floodof the Ishikari River Mouth. 3rd International Symposium on Shallow Flows (ISSF), Iowa city, USA,CD-ROM.
Uchida, T. & Fukuoka, S. 2011. A bottom velocity
computation method for estimating bed variation ina channel with submerged groins. Journal of JSCE
B1-67(1): 16–29.
Ueno, T., Utami, T., Kinoshita, R., Ikeuchi, K.,
Hukuda, K., Ikeda, T. & Tsuneyasu, M. 1996. On theobservation of flood flows in the Hii River—The time
variation of bed configurations in flood flow-. Annualsof Disas. Perv. Res. Inst., Kyoto Univ. B-2 39: 527–541.

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