14th International Symposium on River Sedimentation, September 16-19, 2019, Chengdu, China

Estimating Sediment Discharge Hydrographs in Downstream Rivers with aLarge Amount of Sediment Yielded by a Heavy Rainfall
Shoji Fukuoka1*, Takahisa Gotoh1, Kotaro Okayasu2
1 Research and Development Initiative, Chuo University, Japan
2 Tosa Road Office, Shikoku Regional Development Bureau, MLIT, Japan*Corresponding author, e-mail: sfuku@tamacc.chuo-u.ac.jp
Abstract
It is important to estimate the sediment discharge hydrograph during a flood with large amounts ofsediment transports because the sediment discharge hydrograph gives an upstream boundary
condition for the flood flow and bed variation analysis. In 1995, the record breaking largest flood of
the Hime River occurred and brought a large-scale sediment depositions and channel migrations dueto the flood. Those large-scale bed variations caused a levee breach and damages of river structures.
The study presented the concept of the bed variation analysis in rivers where main channel
migrations and large-scale sediment depositions occurred due to a large amount of inflow sediment
discharge from mountainous areas. The inflow sediment discharge hydrograph was estimated by theintroduction of the new concept for the flood flow and bed variation analysis. The presented method
was applied to 1995 flood of the Hime River and could reproduce the large-scale sedimentdepositions and the channel migrations due to the flood.
.
Keywords: Upstream sediment boundary condition, Sediment discharge hydrograph, Bedaggradation, Channel migration, Sediment yield
1 Introduction
The record breaking heavy rainfalls have caused large amounts of sediment yields in the upstream
devastated mountainous basins and have brought sediments-related disasters in the lower reach ofrivers. It is important to establish the estimation method for the sediment discharge hydrograph inrivers with a large amount of sediment yield during floods.
The Hime River basin contains the Itoigawa-Shizuoka Tectonic Line, in which has brought a large
amount of sediment yields due to heavy rainfalls. The record breaking largest flood of the HimeRiver occurred in 1995. The flood caused large-scale sediment depositions and channel migrations in(a) Right after the 1995 flood around 4.0km

Figure.1 Aerial photo during
1995 flood in the Hime River(b) In 2015 around 4.0km
Figure.2 The situations that the bed materials
became finer due to the large flood

14th International Symposium on River Sedimentation, September 16-19, 2019, Chengdu, China

(c)

(a)

Aerial photo in 1947(b)

Aerial photo in 1993

Aerial photo right after 1995 flood

Figure.3 Plan views of the river channels in 1947, 1993 and right after 1995 flood

Figure.4 Longitudinal distribution of channel width in 1947 and after 1995 flood
the lower reach of the Hime River. And, the flood brought a levee breach and damages of riverstructures. Fig.1 shows the aerial photo during the 1995 flood. And Fig.2 shows river beds right after
the 1995 flood in comparison with 2015 river beds. The bed materials right after the flood became
finer due to the large amounts of fine sediments yielded from devastated mountainous areas. Fig.3(a)indicates regions of sandbar formations, remained vegetations and location of lowest bed elevation
after the 1995 flood superposed on aerial photographs of 1947. And Fig.3(b) and Fig.3(c) indicate
plan views of the river channel before and right after the flood. The straight main channel wasformed in the middle of the river in 1993. However, the main channel after the 1995 flood
meandered due to sandbar formations by the large-scale sediment depositions. Thus, a large amountof sediment deposition increases the risk of levee breaches. Fig.4 shows longitudinal distribution ofchannel width in 1947 and after the flood of 1995. The channel width and the meandering pattern ofthe main channel after the 1995 flood almost agree with those of the river channel in 1947. These14th International Symposium on River Sedimentation, September 16-19, 2019, Chengdu, China

Figure.5 Change in the measured cross sectional
shapes before and after the flood (6.0km)

Figure.6 Longitudinal volume of themeasured sediment deposition

Figure.7 Change in the measured particle size
distribution of sediment material before andafter the flood

Figure.8 Estimation procedure for the inflow
sediment discharge hydrographresults demonstrate that when a flood accompanied by a large amount of sediments occurs, thechannel width and the meandering patterns of the Hime River return to the state of the channel asshown in 1947.
In order to clarify the mechanism of flow and bed variation under such an extremely large flood, it
is necessary to estimate the sediment discharge hydrographs which give the upstream boundary
conditions of the flood flow and bed variation analysis. In general, the equilibrium sediment
discharge or sediment concentrations by the empirical formulas have been given to the upstream
boundary conditions for the flood flow and bed variation analysis. However, this method is notsuitable for rivers with large amounts of sediment transports.
In this study, we presented the concept of bed variation analysis in rivers where channel
migrations and large-scale sediment depositions occurred due to a large amount of inflow sediment
discharge. And the sediment discharge hydrographs at an upstream boundary condition of the bed
variation analysis was estimated based on the presented concept of the analysis. The presented
method was applied to reproduce the large-scale bed aggradations and channel migrations of the1995 flood in the Hime River with.
2 River bed aggradation and channel migration by July 1995 flood in the Hime RiverFig.5 shows the cross sectional shape of the river bed at 6.0km before and after 1995 flood. The
main channel before the flood was located in the center of the channel. The main channel at the flood
was shifted to the bank side. The river bed along the levee was scoured and the vegetation on thesandbars was washed away.
Fig.6 indicates a longitudinal volume of the sediment deposition measured after the flood. About
0.5 million m3 of sediments were deposited in the river reach from 0.0km to 7.2km by the flood.
Fig.7 shows the particle size distributions before and after the flood. At 7.0km, sediment diameter ofD60 was about 200 mm before the flood and varied to about 100mm after the flood. The large

14th International Symposium on River Sedimentation, September 16-19, 2019, Chengdu, China

Figure.9 Calculation method of upstream
boundary condition for the suspended sediment

Figure.11 Discharge hydrograph and inflow
sediment discharge hydrograph (the same
shape as discharge hydrograph)

Figure.10 Concept of setting inflow
suspended sediment discharge hydrograph

Figure.12 Longitudinal distributions ofchange in the measured and calculated mean
bed elevation after the flood (Case1 to Case4)amounts of fine sediments were deposited longitudinally in the main channel and shifted the thalweg
from the middle of the channel to the levee side.
3 Concept of flood flow and bed variation analysis in rivers with a large amount of sedimenttransport
From Chapter 2, it was assumed that most of inflow sediments were fine and transported insuspension during the flood. The estimation of the suspended sediment discharge hydrograph at theupstream boundary is important to calculate the channel migrations and sediment depositions. It
could be possible to estimate the inflow sediment discharge hydrograph by conducting flood flow
and bed variation analysis in stages so as to agree with the observed and the calculated sedimentdeposition and channel migration after the flood. Fig.8 shows the estimation procedure of the inflow
sediment discharge hydrograph. It is necessary to determine both the total inflow sediment volume
and the shape of the hydrograph in order to estimate the inflow sediment discharge hydrograph. Thus,
the estimation of inflow sediment hydrograph was conducted in two steps.
The first step was determination of the total inflow sediment discharge volume. The flood flow andbed variation analysis was conducted by setting different inflow sediment discharge volumes. And
the inflow sediment volume was determined by reproducing the bed aggradation shown in Fig.6. The
shape of the inflow sediment discharge hydrograph was the same as the shape of the dischargehydrograph.
The second step was determination of the shape of inflow sediment discharge hydrograph. The
total inflow sediment volume was the value estimated in the first step, and the calculation wasperformed by setting different shapes of inflow sediment discharge hydrographs. The shape of the14th International Symposium on River Sedimentation, September 16-19, 2019, Chengdu, China

Figure.13 Observed and calculated water
surface profiles and river bed profiles of Case3

Figure.14 Observed loci of the main channel
and calculated ones of Case3

inflow sediment discharge hydrograph was estimated by reproducing the observed bed aggradationand channel migrations after the flood.
4 Analysis of flood flow and bed variation considering a large amount of inflow sediment
discharge
4.1 Calculation method and condition
The computation was performed in the reach from -0.6km to 7.3km. Fig.9 explains the calculation
method of upstream boundary condition for suspended sediment transport analysis. At the upstream
end, the reach for generating a large amount of suspended sediment transported from the upstreambasin was set from 8.8km to 9.3km. The width and slope of this reach were given by the averageriver width and bed slope of the study area of the Hime River. The transition reach (7.3km to 8.8km)
was installed between the suspended sediment generation reach and the bed variation calculation
reach. The bed topography of the transition reach was given by the topography of the actual
measured river channel. The suspended sediment discharge hydrograph was formed in the transition
reach and supplied to the upstream boundary condition for the bed variation calculation in thedownstream. Such a suspended sediment discharge hydrograph was assumed to be a unit suspended
sediment discharge hydrograph. The inflow suspended sediment discharge hydrograph wasdetermined by multiplying the proportional coefficient to the unit suspended sediment dischargehydrograph so as to agree with the measured downstream sediment deposition and channel migration
after the flood. Fig.10 shows a schematic diagram of the inflow suspended sediment dischargehydrograph given at the upstream boundary.
The BVC method (Uchida and Fukuoka, 2014) was applied to calculate the three dimensionalflows under complicated river conditions. The discharge hydrograph in Fig.11 obtained from therunoff analysis was given to the upstream boundary condition of the flood flow analysis. And theobserved tidal levels at Toyama Bay was given to the downstream boundary condition. The twodimensional bed variation analysis was conducted and suspended sediment transports werecalculated by the depth integrated two-dimensional advection diffusion equation of suspended
sediment concentrations.
4.2 Estimation of inflow sediment discharge hydrograph
The first step shown in Fig.8 was performed for determination of the total inflow sediment
discharge volume. Here, Hashinoki et al. (2007) reported that the sediment yielding volume in theupper mountainous basin in July 1995 flood was about 8.6 million m3. In our study, this value wasreferred to the inflow sediment volumes of Case1 to Case4. The shape of inflow sediment dischargehydrograph was the same as that of the discharge hydrograph. Four different inflow sedimentvolumes were given in Fig.11.
Fig.12 shows the measured and calculated results of changes in the mean bed elevations by thefloods in Case1 to Case4. The calculation results of Case1 and Case2 were not able to reproduce themeasured bed aggradation because of small inflow sediment volume The results of Case4 showed14th International Symposium on River Sedimentation, September 16-19, 2019, Chengdu, China

Figure.15 Inflowhydrographs

sediment

discharge

Figure.17 Observed loci of the main channel
and calculated ones Case5

Figure.16 Longitudinal distributions ofchange in the measured and calculated mean
bed elevation after the flood (Case3，Case5,
Case6 and Case7)

Figure.18 Observed loci of the main channel
and calculated ones of Case6that the calculated sediment depositions were larger than the measured one because the inflow
sediment volume was too large. On the other hand, the results of Case3 in which the inflow sedimentvolume was about 7 million m3 reproduced relatively the measured longitudinal sediment deposition.
Fig.13 shows the comparison of the longitudinal observed flood marks and the calculated water
surface profiles at the peak discharge in Case3. And the comparison between the observed andcalculated longitudinal distributions of the bed elevation is also shown in Fig.13. The calculated
water surface profiles and bed profiles almost explained the longitudinal distribution of the observed
ones. From the above, it was demonstrated that the total inflow sediment volume that could
reproduce longitudinal sediment deposition was about 7 million m3. Fig.14 shows the observed
thalweg in the main channel after the flood and the temporal changes in the calculated thalweg of
Case3. The main channel calculated in the Case3 still remained at the middle of the channel and themain channel did not shift to the levee as shown in the observed one.
The second step was performed for determination of the inflow sediment discharge hydrograph.
Since landslides in the upper river basin occurred intensively at the time around the peak discharge(Hashinoki et.al., 2007), the inflow sediment discharge hydrograph of Case5 was assumed as shownin Fig.15. Furthermore, since the peak of suspended sediment discharge hydrograph generally occurs
earlier than the flood peak discharge (Kinoshita, 1984), the peak of the inflow sediment dischargehydrograph which was two hours earlier than Case5 was assumed (Case6 in Fig.15). The total inflow
sediment volume of Case5 and Case6 were about 7 million m3 determined in the first step. And thetotal inflow sediment volume of Case7 was about 9 million m3 with the same shape of hydrograph as
Case6. Case7 was set to verify the total inflow sediment discharge volume obtained in the first step.
Fig.16 shows the longitudinal distribution of the measured and calculated changes in mean bed
elevations in Case5 to Case7 due to the flood. As in Case3, the results of Case5 and Case6 which theinflow sediment volume was about 7 million m3 reproduced approximately the measured bed
aggradation. However, in Case7 with an inflow sediment volume of about 9 million m3, thecalculated longitudinal sediment depositions were larger than the measured one from 5.0km to 7.0km
where the river width was wide. Therefore, it is found that the inflow sediment volume of14th International Symposium on River Sedimentation, September 16-19, 2019, Chengdu, China
Yamamoto point

Yamamoto point(a) Case3
Yamamoto point(a) Case3
Yamamoto point(b) Case5
6.0

5.0

山本
Yamamoto point(b) Case5

Yamamoto point

6.0

河道中央への土砂堆積
Sediment deposition
5.0

河床変動量(m)Bed variation (m)0.0-2.0 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0

FlowScouring
洗掘

Figure.19 Calculated bed variations of Case3,Case5 and Case6

0.8

1.2

1.6

2.0

水深(m)
Water
depth (m)Deposition
堆積(c) Case6

0.4(c) Case6
Figure.20 Calculated loci of the main channelof Case3, Case5 and Case6

approximately 7 million m3 could reproduce the longitudinal distribution of the observed bedvariations.
Fig.17 shows the observed thalweg in the main channel after the flood and the temporal changes in
the calculated thalweg of Case5. In Case5, the migration of the main channel did not occur at thetime of peak discharge (7/11 20:00), but at the time of second peak (7/12 9:00), the main channel
shifted from the middle of the channel toward the left and right banks. And the main channel
meandered as shown in Fig.17.
Fig.18 shows the observed thalweg in the main channel and the calculated thalweg of Case6. In
Case6 where the peak of inflow sediment discharge hydrograph was 2 hours before the peakdischarge, the main channel shifted from the middle of the river toward the left and right bank at thepeak discharge (7/11 20:00). The results of Case 6 could reproduce that the main channel shifted
toward the left and right banks in comparison with the results of Case 5. Fig.19 shows the contour ofthe calculated bed variations of Case3, Case5 and Case6, respectively. And Fig.20 shows thecalculated main channel loci of Case3, Case5 and Case6. The main channel loci in Fig.20 wererevealed by flowing low discharge (Q = 200 m3/s) to the each calculated bed topography after theflood. The calculation results of Case6 indicated that the sediment deposition volume in the middleof the channel from 5.0km to 6.0km was larger than in the results of Case3 and Case5, and themigration of the main channel was clearly shifted to the levees. It can be seen that the large scale
sediment deposition in the middle of the channel caused the bed scouring along the left and rightbanks and the migrations of the main channel. As a result, when the amount of inflow sediment was
7 million (m3) and the inflow sediment discharge hydrograph which peaked 2 hours before the peakdischarge was given at the upstream boundary, the calculation results could reproduce the observed
large-scale bed aggradation and channel migration in the lower reach of the river.
5 Conclusions
We found the method of the bed variation analysis in rivers where main channel migrations andlarge-scale sediment depositions occurred due to a large amount of inflow sediment discharge frommountainous areas. And the inflow sediment discharge hydrograph at the upper boundary wasestimated by the introduction of the new concept for the flood flow and bed variation analysis. The
developed method was applied to the 1995 record breaking flood of the Hime River and could
provide a good explanation for the flood and large scale bed variations.

14th International Symposium on River Sedimentation, September 16-19, 2019, Chengdu, China

References[1] Kinoshita, R. (1984). “Present status and future prospects of river flow analysis by the aerialphotograph”. Proceedings of JSCE, No.345, 1-19.
[2] Hashinoki, T., Mizuyama, T., Satoh, K., and Murakami, M. (2007). “Research on sedimentyield and sediment discharge which considers timing of sediment yield”. Journal of the Japan
Society of Erosion Control Engineering, Volume 59, Issue 5, 15-22.
[3] Uchida, T. and Fukuoka, S. (2014). “Numerical calculation for bed variation in compound
meandering channel using depth integrated model without assumption of shallow water flow”.
Advances in Water Resources, Volume 72, 45-56.