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

Study on the width of rivers in valley bottom plains
T. Sakaguchi

Graduate School of Science and Engineering, Chuo University, Tokyo, Japan

S. Fukuoka

Research and Development Initiative, Chuo University, Tokyo, Japan

ABSTRACT: Flood disasters caused by torrential rainfalls have recently been increasing in Japan. Oneof the representative disasters is Yosasa River flood disaster in 1998. Far exceeding capacity of flow
made river widths and channel shape change by severe bank erosions. But, there are few observation
data such as discharge and the water level hydrographs of flood disasters in the middle and small-scalerivers. ­Quantitative investigations on appropriate river width and water depth have not been conductedsufficiently.
In this study, we applied two-dimensional flood flow analysis for the 1998 flood occurred in the Yosasa
River and proposed a decision method of river width required for large floods in rivers flowing valley
bottom plains.
1INTRODUCTION

Flood disasters caused by torrential rainfalls havebeen increasing in Japan. Especially, flood flows in
the middle and small-scale rivers flowing throughthe valley bottom plains appear to cause greatdamages in floodplain. One of the representative
disasters is Yosasa River flood disaster in 1998.
The Yosasa River lying on the northeast of Tochigi
Prefecture (see Fig. 1) is one of the tributaries of
the Naka River and has a drainage area of about
343.5 km2. Far exceeding capacity of flow causes
severe bank erosions, and it made markedly riverwidths and channel shape change. After the flood,Figure 1. Map of the Yosasa River basin.

the Yosasa River was improved up to the level of
one in fifty. But, because there are few observation
data such as discharge and water level, the appropriate river width and water depth in the rivers
through valley bottom plain has not been investigated so far.
There are several researches on the Yosasa Riverdisaster in 1998. For example, Suga et al. (2001)
investigated causes of the lateral erosion damages.
Nakagawa et al. (2000) estimated the dischargehydrograph of the 1998 flood by using the tankmodel for the upstream area of the Yosasa River.
They also estimated the maximum river width after
the flood by using one dimensional bed variation
analysis and the regime theory. And, they examined the channel variation process of the Yosasa
River from comparison between the above calculations and aerial photographs taken after the flood.
In this paper, we assume that the largest floodin the past had formed the present valley width
and the landform, and the valley bottom haschanged by many large floods but the valley width
has remained nearly unchanged. We believe thatthe 1998 Yosasa River flood is a sufficiently large
flood, but it would be small enough compared withthe past largest flood which had formed the valley width. On the standpoint that the above concept is acceptable for the study of the river width
in the valley bottom plain, we discuss the riverwidth required for the 1998 Yosasa River flood.
We regard the 1998 flood discharge as the channelforming discharge, which formed the landform of
the valley bottom after the 1998 flood.

2013

In the valley bottom plains, there are some areas
where the flow velocity and depth on the inundation area have extremely small compared with themain stream. Actual flow width where flood water
was flowing must be estimated.
At first, we applied two-dimensional flood
flow analysis for the 1998 Yosasa River flood andexamined an evaluation method of the flow width
which required for the flood by considering theflow velocity and depth in the inundation area.
Then, we present a decision method of appropriate river width for large floods flowing valley bottom plains.
2

Figure 3. State of flood flow around 6.0 km.

Description of the Yosasa Riverdisaster in 1998

Figure 2 shows aerial photographs in the reachfrom 3.8 km to 7.0 km upstream of the junctionof the Naka River and the Yosasa River. Upper
photograph and lower photograph were taken
before (Aug. 1993) and after (Oct. 1998) the flood,respectively. Yellow lines shown in the photographs
indicate the main channel width at the time before
the flood and flow width evaluated from the aerial
photographs taken after the flood. The upper photograph also shows that the river channel width
was approximately 20 m to 30 m at the time before
the flood. The lower photograph shows that theflood flows overflowed the banks and made the
new channels, and water width of the main channel expanded several times. Figure 3 shows thestate of the right bank around 6.0 km and white

Figure 4. Comparison between aerial photographs
before (upper) and after (lower) 1988 flood.

Figure 2. Comparison between aerial photographs
before (upper) and after (lower) 1988 flood.

broken line shows the center line of the main channel before the flood occurred. The flood flow madea cutoff channel over the floodplain and washedaway the houses there. At 5.3 km (Point P shownin Fig. 2), there were houses and vegetations, butthese were carried away by the flood flow.
Figure 4 shows the comparison of aerial photographs before and after 1998 flood in the reachfrom 8.0 km to 12.0 km. The inundation flow
washed out vegetations and caused bed scouring at the meandering reach around 10.3 km
and 11.5 km. Vegetations were dense along thechannel in the reach from 9.0 km to 12.0 km,
but these were drifted by the flood. Some vegetations remain in the outer bank of meanderingreach around 9.5 km, and a house located behindthese vegetations remained there (Point R shownin Fig. 4). On the other hand, houses along theriver channel were carried away (Point Q shown inFig. 4). So, 1998 Yosasa River flood overflowed
the banks and expanded throughout the valley
bottom plains, and it changed the planar shape2014

of the main channel by severe bank erosions andformed new channels.
3 two-dimensional flood flow
analysis
3.1

Analysis conditions and bed elevation data

In the flooding on valley bottom plains, there aremany areas where the flow velocity and depth on
the inundation area are extremely small comparedwith the main stream. It is difficult to estimate thevelocity and depth distributions on the inundation
area from cross-sections and flood marks dataobtained after the flood. Therefore, we conducted
the steady two-dimensional flood flow analysis
using the peak discharge of the 1998 flood andcalculated velocity and depth distributions on theinundation area. Then, we investigated the flow
width (river width) which should be consideredas the channel-forming discharge. Here, the bed
elevation data measured after the flood was used
for the analysis on the following assumption. Thelandform in the valley bottom plains observed
after the flood would be formed in the peak of theflood. The study area is from 4.5 km to 13.0 km
where the flood flows overflowed the banks andexpanded on the floodplain (shown in Fig. 5).
The upstream boundary condition was given by
the peak discharge 1,740 m3/s and downstream

boundary condition was given by the height offlood marks. The peak discharge was estimatedby the Tochigi Prefectural Government from thestorage function model on the precipitation dataobtained at rainfall gauging stations in the Yosasa
River basin and its neighborhood. It was muchlarger discharge than the average capacity of flow(400 m3/s) in the study area. After the flood, Tochigi
Prefectural Government surveyed the cross-sections and the flood marks every 100 m. But, thecross-sectional survey was conducted only themain channels and its neighboring part indicatedby the black line in Figure 6. These survey data are
not sufficient for the analysis which includes theinundation area. Then, we utilized topographic
maps of 1:1000 scale (shown in Fig. 7) preparedin March 1969. Bed elevations in the map were
described by points and contour lines every 0.1 m
and 1 m, ­respectively. Because the land use of thefloodplain in the study area has been paddy fields
since around 1955 (Sato, 2001), the landform of
the floodplain remains unchanged since 1969. For
this reason, the landform in the floodplain shownby the brown line in Figure 6 was created on thebasis of bed elevation data in the topographic
map. The Manning’s roughness coefficients were
set to 0.049 for main channel and 0.054 for thefloodplain so that longitudinal distribution of theflood marks and observed edge of the inundationwater could be reproduced.

Figure 5. Study area in the Yosasa River.

Figure 6. River cross section in the Yosasa River.

Figure 7. Topographic map of 1:1000 scale.

2015

3.2

Analysis results

Figure 8 shows the comparison between floodmarks and calculated water surface profile in thereach from 4.5 km to 13.0 km. Although the calculated water surface profile seems to coincidewith the flood marks on the whole, the difference
between them is noticeable around 6.5 km andreaches about 4 m in the maximum. Figure 9a,b shows the cross-sectional forms at 5.9 km and10.5 km sections. The Yellow points shown inFigure 9a, b are the height of the edge of inundation water. In the reach where the calculated water
surface profile coincides with the flood marks, theflood mark almost coincides with the height of theedge of inundation water as shown by Figure 9b.
On the other hand, the flood mark greatly differs from the height of the edge of inundationwater as shown by Figure 9a in the reach wherethe difference is relatively large. If the water level
had reached to the height of the flood mark, theinundation area should have further expanded on
the floodplain. For this reason, it is judged that
there was the error in flood mark observationsin the reach from 5.0 km to 6.5 km. Figure 10
shows the comparison between observed and calculated edge of the inundation water. The relation

Figure 8. Comparison between observed and calculated water surface profiles.

Figure 9. Correspondence relationship between the height of water edge and flood mark.

Figure 10. Comparison between observed and calculated edge of inundation water.

2016

between them shows good agreement on the whole,although there is the reach which cannot be reproduced the observed edge of the inundation watersuch as around 6.9 km and 12.2 km points.
The red broken line and velocity vectors in­Figure 10 show the center line of river channel
before the flood damage and calculated depthaverage velocity vectors at the peak discharge,respectively. The maximum velocity vectors do
not coincide with the red broken line in the curved
reach around 5.0 km, 6.0 km, 8.5 km, and 11.5 km.
It is understood that the flood flows took a cutoff route over the channel and flowed through thewhole width of valley bottom plain. The calculated
velocities range from 3 m/s to 5 m/s in the mainstream. On the other hand, the water width was
expanded and inundated around 5.3 km, 7.5 km
and 12.0 km and the water depth is about 0.3 m
and the velocity is 0.5 m/s near the water edge ofthese places. It is assumed that the flow did notcause the bank erosion and bed scouring at thewater edge of these places even in the flood peak.
We believe that the water edge of these places does
not correspond to the flow width (river width) forthe channel-forming discharge.
4 flow width of the Yosasa
river in 1998 flood
The flow width corresponding to the channel­forming discharge is investigated based on theanalysis results of the 1998 flood. Whether theflow causes bank erosions and bed scouring at
the water edge would depend on the magnitudeof water depth and velocity. However, it is not
appropriate to use the water depth and velocitychanging at respective locations as the condition
for determining the flow width. Therefore, the flow
width is evaluated by following method. First, thecalculated unit discharge is integrated transversely
from the inner bank to the main stream at eachcross-section in meandering reach such as 7.5 km
section in Figure 11a and from the both left andright banks to main stream in the straight reachsuch as the 6.9 km section in Figure 11b. When theintegrated discharge becomes a certain percentage of the total discharge at integrated transverse
distance, the length which subtracts the integrated
transverse distance from the total water surface
width is a flow width to be determined.
Figure 12 shows the calculated lines of wateredge in which the 99% and 97% of the peak discharge are assumed to flow in the river. Figure 13
shows thus determined longitudinal distributionsof the water width. Observed edge of inundationwater spreads about 400 m in the meanderingreach (around 6.0 km, 9.3 km, and 12.0 km) as
shown by the blue line of Figure 12. The purple
line shows the distribution of the flow width B99 inwhich the 99% of the peak discharge flows. There
are plateaus at the both sides of river in the reacharound 10.0 km which consists mainly of simple
cross-sectional channel. The difference between theFigure 11. Evaluation method of the flow width in straight and meandering channels.

Figure 12. Comparison between the lines of water edge which the 99% and 97% of the peak discharge flows.

2017Figure 13. Longitudinal water width profiles.

Figure 14. Water depths at water edge.

Figure 15. Flow velocities at water edge.

actual water width and flow width B99 is relatively
small. On the other hand, the flow width B99 is
considerably narrower than the actual water widthin the reach from 5.0 km to 9.0 km and around12.0 km. But, the flood hardly flows in floodplainin these reaches. In addition, the flow width B99 isrelatively uniform compared with the actual waterwidth. The red line in Figure 13 shows the flow
width B97 in which the 97% of the peak discharge
flows. There is almost no difference between theflow width B99 and B97. Figures 14 and 15 show
the longitudinal distributions of the water depth
and velocity at the water edge in which the 99% of
the peak discharge is assumed to flow in the river.
Here, the water edge of the outer bank of meandering reach is removed from the figures. Since
the velocity is about 1.0 m/s and the water depth isabout 1 m at the water edge, the flow would cause
the bank erosion and bed scouring. Therefore, we
assume that the flow width B99 of the 1998 floodis regarded as the river width determined by thechannel-forming discharge. We examine the relationships of the dimensionless width and depth
versus the dimensionless channel-forming discharge by Fukuoka (2010, 2012, 2012) in the following Section 5.
5 the relationships among
dimensionless river widthand water depth versus
dimensionless channel-forming
discharge
Fukuoka (2010, 2012, 2012) has derived the relationships of dimensionless river width and depth
versus dimensionless channel-forming discharge inalluvial rivers, considering floods and river basincharacteristics and it can be represented with­Equations 1, 2. Furthermore, Fukuoka has indicated2018that the ­desirable range of cross-sectional form of
alluvial rivers is represented by the ­Equation 1, 2.
 Q 2.80  gId 5 r0.40

 Q B≤≤ 6.33  gId 5 drr Q h≤ 0.14 
 gId 5 drr

0.40

(1)

0.38

(2)

where Q = discharge; B = river width; h = waterdepth; I = energy slope; dr = representative particle diameter; and g = gravitational acceleration.
­Figure 16 shows the relationships of the dimensionless river width and depth versus dimensionless discharge corresponding to the flow width B99.
Data plotted are 86 sections of every 100 m in thereach from 4.5 km to 13.0 km. Particle diameter d60(0.2 m) is used as the representative diameter. The
slope I was given by the energy slope Ie. The blue
colored plots show the relationships of dimensionless values where the plateaus are approaching theboth sides of river (around 13.0 km, 10.0 km, and4.5 km). Because the flow width is unable to expand
due to the geographical and geological effects, thedimensionless river widths are plotted in the lower
region. The yellow colored plots show the relationships of dimensionless values where the difference
between the actual water width and flow width
B99 shown by Figure 13 is relatively small (around9.0 km and 11 km). The dimensionless river widthis larger than that indicated by the blue plots inthese sections. Since the 1998 Yosasa River floodis the smaller than the past large flood which wasconsidered to form the present valley width, thedimensionless river width is distributed around theupper limit indicated by the blue line in Figure 16.
The green colored plots show the relationship ofdimensionless values where the flow width B99 is
considerably narrow compared with the actual
water width (around 6.0 km and 8.0 km). Because
the area having an extremely small velocity andwater depth were excluded from the investigationof the flow width, the dimensionless river width
becomes almost the same as yellow plots. The plots
are distributed over a wide range because of thegeographical and geological effects such as the valley width and the river terrace, but the plots range
around the upper limit on the whole.
From the above discussions, the relationshipamong the dimensionless river width and depth
and the dimensionless channel-forming discharge
in the valley bottom plain which was formed in thenarrow and long valley are the similar to those of
alluvial channels. It means that Equations 1, 2 areuseful for determination of width of rivers throughvalley bottom plains.
The flow width expands to the dimensionless
river width shown in Figure 16 when a large flood
would occur. It would be possible to decrease theflood damage in the important areas by taking
measures so as to suppress the spreading of inundation water along the purple line of Figure 12
even when the flood discharge increases.

Figure 16. Relationships between dimensionless river width and depth versus dimensionless discharge.

2019

6 conclusions
Principal conclusions are drawn as follows.
I. In the middle and small-scale rivers with a few
basic data, topographic maps of 1:1000 scale
are useful for re-creating landforms in inundation areas required for the flow analysis.
II. We investigated the relationships between thedimensionless flow width and dimensionlesschannel-forming discharge to the 1998 Yosasa
River flood and clarified that these relationships in the rivers through valley bottom plain
were similar to alluvial channel relationshipderived by Fukuoka.
referencesFukuoka, S. 2012. Dimensionless width and depth andsediment transport rate in stable rivers, 3rd International Symposium on Shallow Flows, Iowa city, USA,CD-ROM.
Ito, K., Suga, K., and Ikeda, H. 2001. Practical Consideration on bank erosion and channel shift by a big floodof low frequency in the Yosasa River, Annual Journalof Hydraulic Engineering, JSCE. Vol. 45: pp. 781–786(in Japanese).
Nakagawa, H., Takahashi, T., and Satofuka, Y. 2000.
Channel Variation of the Yosasa River Tributary ofthe Naka River due to 1998 flood, Annual Journal ofHydraulic Engineering, JSCE. Vol. 44: pp. 395–400 (inJapanese).
Sato, T. 2001. Flood damage and land conditions in theNakagawa River basin, Japan caused by heavy rainfall
at the end of August 1998, Natural disaster research
report, the National Research Institute for Earth Science and Disaster Prevention. Vol. 37: pp. 137–216 (inJapanese).

Fukuoka, S. 2010. River engineering adaptations against
the global warming—towards generalization of closeto-nature rivers, Journal of JSCE, JSCE, F. Vol. 66,No. 4: pp. 471–489 (in Japanese).
Fukuoka, S., Sakaguchi, T. 2012. Desirable range ofdimensionless width and depth versus dimensionless discharge and application to rivers at design andimprovement stages, Annual Journal of ­HydraulicEngineering, JSCE. Vol. 56: pp. I_1423–I_1428 (inJapanese).

2020