Journal of Natural Disaster Science, Volume 25, Number 1, 2003 pp17-22

Estimation of Sediment Discharge Taking into Account
Tributaries to the Ishikari River
Kazutake ASAHI
Division of Environmental and Resource Engineering, Hokkaido University, Sapporo, Japan
Kazuo KATOSUIKO Research Company, Sapporo, Japan
Yasuyuki SHIMIZU
Division of Environmental and Resource Engineering, Hokkaido University, Sapporo, Japan(Received for 3. Oct., 2002 and in revised form 14 Jul., 2003)

ABSTRACTIn managing the Ishikari River, it is necessary to evaluate sediment discharge along its entire length.
Sediment discharge from tributaries into the main stream therefore was in vestigated. Two numericalmodels that take into account tributaries are proposed which were tested for the 1981 Ishikari Riverflood. The sediment discharges calculated with these models were compared with recoded values. Results
show that it is necessary to consider tributary effects directly and that sediment discharged from tributaries contributes to the output sediment discharged from the river’s mouth.

1. INTRODUCTION
The Ishikari River flows from Mt. Ishikari (elev. 1967m)
in the Taisetsu Mountains and is the second-longest river inJapan (Fig.1). Its basin (14,330km2) spreads over the westcentral area of Hokkaido, northern Japan. As many as 70
tributaries flow into the Ishikari River, among them the
Chitose, Yubari, and Uryuu rivers. The extensive plains along
the Ishikari River are at the center of Hokkaido. Evaluationof the sediment transport rate therefore is important in managing the is river and its environment.
Flood control on the Ishikari dates from 1910, when thefirst development plan for Hokkaido was initiated, thereafterFig. 1

cutoffs were established and dredging done to prevent flooding. Dramatic flooding of the basins in the lower reaches has
occurred occasionally after heavy rainfall because water does
not readily infiltrate the peaty marshland and lowlands thatmake up the basin. Moreover a 1981 flood caused severe
damage in the basins of the Ishikari River, including in
Sapporo, Hokkaido's center of economy and government.
A number of studies of the Ishikari River therefore havebeen made. Itakura, Yamaguchi et al. (1986) reported theeffects of placing alternating bars in the lower reaches of theriver. Shimizu (1995) used computer technology to show thatgrain size distribution and bed deformation could be calculated for the transport of bed and suspended loads. The relationship between sedimentation, sediment discharge and tributaries has however is unknown.
The 1-Dimensional bed variation model is a powerfultool with which to evaluate sedimentation over a long periodof time in a large area. A 1-Dimensional numerical model ishere used to investigate sediment discharge and sedimentation
along the Ishikari River and representative tributaries.
Two models were tested with data for the 1981 flood.
The first that of Shimizu (1995), models water dischargeusing a curve approximated from data on the main stream.
The second models discharge by directly assessing the effectsof tributaries. i.e., by analyzing the water discharges from themain stream and its tributaries. Based on the calculated
results, a method for determining the effects of tributaries on
the main stream, in terms of sediment discharge and sedimentation, is proposed.

Map of the Ishikari River.

KEY WORDS: tributaries, sediment discharge, sedimentation, the Ishikari River, numerical calculation

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K. ASAHI, K. KATO AND Y. SHIMIZU

2. GOVERNING EQUATIONSThe numerical model used follows that of Shimizu(1995) which was verified by the use of data from the 1981
flood. However. His model however did not consider theeffects of tributaries sufficiently. Our study uses numericalmodels to assess the effects of water and sediment discharged
from tributaries into the main stream.
Change in the speed of a stream is faster than bed andgrain size transformation. Generally, the kind of models used
are quasi-steady state ones. Furthermore the stream is considered to be in sub-critical flow. A non-uniform flow model, in
which the water level at the river mouth and discharge fromthe tributaries are given respective for the boundary andhydraulic conditions. Channel width, bed elevation and grain
size distribution as the initial conditions are given as an
approximated curve obtained from measured data. And bed
valiation is conducted with bed and suspended loads.
Two models are used to from a numerical model which
considers tributaries effects on flow and sediment discharges.
2.1. Outline of two models are explained as follows(1) Model I : Input data from the approximated curve
Fig.2 shows the input discharge image for Model I. In
that model, a curve approximated from existing data, that isin only for the main stream, is used for the input discharge.
That is, the confluence point of the tributary is not considered directly and discharge roughly follows the curve approximated from actual measurements. Only the suspended load isconsidered as sediment inflow. This method is effective whenobservatories are located only in the main channel.
(2)Model II : Input data from measurements
Fig.3 shows the input discharge image for Model II. In
that model the measured discharges, for both the main channel and the tributaries, are used directly. Increases in the discharges of the main stream are observed only at the sites ofconfluence.
Sediment discharge by and the sedimentation of tributaries also are calculated in this model. Only the suspended
loads entering main stream from the tributaries are dealt withbecause bed load was not considered in Model I, and almost
all sediment enters the main stream from it tributaries as suspended loads.

2.2. 1-dimensional continuity and momentum equations
The continuity and momentum equations of 1-dimensional
steady flow are
Q=uhB
(1)

where x is the distance from the river mouth, Q the discharge, u the cross-sectional averaged velocity, h the water
depth, B the channel width, h the water surface elevation(H＝h＋η), η the bed elevation, g the acceleration due togravity, A the cross-sectional area of flow, qx the inflow fromthe side, and ie the energy gradient. qx comprises the inflow
from tributaries, ground water, and surface runoff.
Kishi and Kuroki's formula is used to estimate bed friction;

where u* is shear the velocity(=√ghie ) and dm the averagegrain size of the bed material.
ie is obtained from Eqs.(1) and (3);2.3. Sediment transport
The bed load transport rate per unit width is calculated
by Ashida and Michiue's formula;where subscript i is the grain size, s the specific gravity ofthe sediment particles, di the diameter of the bed material,pi the volumetric fraction of the sediment particles, τ*i thenon-dimensional bed shear stress［=u*ci /(sgdi)］, τ*i the nondimensional critical shear stress［u*ci /(sgdi)］, and u*ci the critical shear velocity calculated by Egiazaroff and Asada's formula;where u*cm is the critical shear velocity for dm calculated by
Iwagaki's formula. In this study, the effective bed shear stressequals the total bed shear stress.

Fig. 3Fig. 2

Approximated curve used for input discharge: Model (I).

Actual recorded measurements used for input discharge:
Model (II).

ESTIMATION OF SEDIMENT DISCHARGE TAKING INTO ACCOUNT TRIBUTARIES TO THE ISHIKARI RIVER

The pick-up rate of the suspended load per unit area iscalculated by the formula of Itakura and Kishi;

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where Σi is the summation of the bed material transportload.
3. CALCULATION CONDITIONS

where qsui the pick-up rate, and ωf i the fall velocity calculated by Rubey's formula. ρ and ρs are the respective specificdensities of the water and sediment particles. Furthermore,a'=B* /τ*−1/η0 , η0=0,5, K=0.08, and a*=0.14. Generally,
B*i =0.143, but here the shielding effect is determined using
the formula of Oki and Kuroki;

where B*0 =0.143, and［τ*cio=u*2ci /(sgdi)］. u*cio the critical shear
velocity for di in the uniformity bed as calculated by
Iwagaki's formula.
The continuity equation of the depth-averaged suspended sediment concentration is<cxi> in Model I<c'i>=<cxi> in Model II
where <ci> the depth-averaged suspended sediment concentration and <cxi> the depth-averaged suspended concentration of
the tributaries at the confluences. cbi is the reference concentration of lateral flow. Here it is be obtained fromci =cbi exp(−βξ)(12)

The aim of this study was to establish a numericalmodel takes into account the effect of tributaries on sediment
discharge and sedimentation. The conditions in the two models were set to be the same.
A curve approximated from existing data was used forthe initial bed elevation (=η), channel width (=B), and bed
material grain size (=d i) in the main stream and its tributaries(Figs.4 and 5). The approximate expressions for the mainstream used for calculation were
η= 2.49 exp (0.0245 Kp)−7(16)
B = 457.91 exp (−0.0089 Kp)(17)where η is the bed elevation, B the channel width andKp the distance from the river’s mouth(km). Grain size profiles (d10, d50, and d90) and of the bed materials in mainstream were
d10=0.1682 exp (0.0145 Kp)(18)
d50=0.3883 exp (0.0273 Kp)(19)
d90=1.4530 exp (0.0258 Kp)(20)d10, d50, d90 respectively being the 10%, 50%, 90% grain
sizes(mm) in the bed. The initial grain size distribution in the
bed material is defined by those formulas as the normal distribution. Fig.6 shows the classification of bed material forthe normal distribution. Bed elevation, channel width, andgrain size profiles for the initial condition in the tributaries
were obtained in the same way.
The two models were tested by reproducing the 1981
Ishikari River flood. Fig.7 shows a hydrograph of that flood.
Ishikari Bridge, Naie Bridge, Inou Bridge, and Kamikawa aredischarge observation stations in the main channel of thewhere z is the distance from the bed, ε=ku*h/6, k is the
Karman constant(=0.4) , β=ωf i h/ε, and ξ=z/h. The volumetric fraction of the bed material grain size, is obtained from

Fig. 4

Longitudinal profile of bed elevation and channel width.

pi ; pi ; ∂η/ ∂t>0
pi * ; pi ; ∂η/ ∂t<0 , ηb <η
pi * ; pi o ; ∂η/ ∂t>0 , ηb <η
where δ is the exchange layer thickness, t the time, and λis the void ratio. cBxi is the reference concentration of lateralflow from tributaries. pi ' and pi o are the volumetric fractionsof the sediment particles in the bed and the suspended loads,
and for the initial bed.
The time-dependent change in bed elevation is obtained
from the continuity of bed material transport;*'

Fig. 5Longitudinal profile of d10, d50, d90.

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K. ASAHI, K. KATO AND Y. SHIMIZU

Ishikari River. Fig.8 shows the location of each station, andits distance from river’s mouth. In advance, the discharge andwater depth at the river’s mouth respectively were given as
the hydraulic and boundary conditions. First, the water surface elevation of the main stream was obtained from Eqs.(1)and (2). The water surface elevations of the tributaries thenwere calculated based on the main stream water depth ateach confluence. Bed shear stress was obtained with Eq.(6),and the bed load, suspended load, and suspended concentration respectively were calculated with Eqs.(5), (7), and (11).
On the basis of these values the sediment discharge, volumetric bed material fraction and bed elevation were obtained.
The calculations were continued from the start to end of thehydrograph.
Flowchart
The calculation procedure is given below. Repeatingthese procedures were conducted in the calculation.
1) Calculation of the water surface elevation in the main
channel. Eqs.(1) and (2).
2) Calculation of the water surface elevation in the tributaries; Eqs.(1), and the water surface elevation at confluencein the main channel; Eqs.(2).
3) Calculation of the bed shear stress; Eq.(6).

Fig. 6

4) Calculation of the amount of sediment; Eqs.(5) and (7).
5) Calculation of the suspended sediment concentration;
Eq.(11).
6) Updating of the bed elevation; Eq.(15).
7) Updating of the volumetric fraction of the bed material;
Eq.(14).
8) Updating the of the time.
4. NUMERICAL VERIFICATION AND RESULTS
Figs.9 and 10 show the longitudinal sediment discharge
profile along the Ishikari River, averaged by the hour, as calculated respectively by Model I and II . The findings foreach model show that sediment discharge increases in thedownstream direction.
In the lower reaches the suspended load predominates,
whereas in the upper reaches the suspended and bed loads
are roughly equal. The effect of confluence on sediment discharge to the main stream in not found in the calculated
results for Model I. Results of Model II clearly show that
sediment discharge enters the main stream from its tributaries.
The sediment discharge obtained for Model II is greater thanthat for Model I because the former model includes the
inflow from the tributaries. The results show that the effectsof the Chubetsu, Uryuu, and Sorachi rivers, which flow into
the upper reaches of the Ishikari River have particularlymarked effects, on the sediment discharge of the main

Grain size classification.

Fig. 7

The hydrograph of observation station (1981. 8).

Fig. 8Distance of Observation from the river s mouth.

Fig. 9Calculated Bed and Suspended Loads in the Ishikari River:
Model I.

ESTIMATION OF SEDIMENT DISCHARGE TAKING INTO ACCOUNT TRIBUTARIES TO THE ISHIKARI RIVER

21

Fig. 12 Comparison of Suspended Sediment Discharges at Ishikari Brige.

Fig. 10Calculated Bed and Suspended Loads in the Ishikari River:
Model II.

The approximated curve is written
Qs=4×10−9Q2.3526(21)
where Qs(m3/sec) the suspended sediment discharge andQs(m3/sec) the discharge.
Fig.12 compares recorded values of the suspended sediment at Ishikari Bridge with values found with Models I andII.
The results obtained with Model II clearly agree moreclosely with the measured values. Because in Model II thesuspended load which flows into the main stream from thetributaries is greater than that in Model I the estimation of
the sediment discharge from the tributaries in Model I is litter estimation than actual phenomenon.
Model II therefore is valid. The findings of this study
show the importance of tributaries in contributing to the sediment discharge of the main stream.
5. CONCLUSION
Two models that consider the effects of tributaries were
examined based on records for the 1981 Ishikari River flood.
It was confirmed that Model II, which directly takes into
account the effects of tributaries, can be used to estimate thesediment discharge of the Ishikari River of the main channel.
Because sediment eutering from the tributaries was found tocontribute to the runoff sediment discharge from the river’s
mouth, tributary effects on flow discharge and sediment discharge mast be considered directly.
REFERENCES

Fig. 11

Relationship between Discharge and suspended Load at
Ishikari Brige.

stream.
Fig.11 shows the relationship between the discharge andsuspension of sediment in the Ishikari River. An approximated curve, which agrees with the measured values, wasobtained from that data. This approximate is considered torepresent the actual values for the Ishikari River.

Rubey, W. W., 1933. Settling velocity of gravel, sand and silt partices. Amer. Jour. Sci., 25;325-338.
Itakura, T. and Kishi, T., 1980. Open-channel flow with suspended
sediments. Proc. of ASCE, HY8, 1325-1343.
Shimizu, Y., 1995. Formation of river bed and grain-size profile inalluvial rivers. Journal of JSCE, No.521/I-32, 69-78.

APPENDIX-NOTATIONThe symbols used in this paper are
Q = water discharge;u = cross-sectional averaged velocity;h = water depth;

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K. ASAHI, K. KATO AND Y. SHIMIZU

B = channel width;
H = water surface elevation;
η = bed elevation;g = acceleration of gravity;
A = cross-sectional area of flow;qx = water discharge of inflow from unit side length;i e = energy gradient;d m = averaged grain size of bed material;
d i = grain diameter of bed material;
q bi = bed load transport rate per unit width;q sui = pick-up rate from unit area;
p i = volumetric fraction of sediment particle;u * = shear velocity;u *ci = critical shear velocity;u *cm = critical shear velocity for ;τ*i = non-dimensional bed shear stress;
τ*ci = non-dimensional critical shear stress;
ωfi = fall velocity;s= submerged specific gravity of sediment;ρ = specific density of water;ρs = specific density of sand;c i = suspended sediment concentration;c bi = reference concentration of lateral flow;k = von Karman constant;δ = exchange layer thickness;
p i = volumetric fraction of sediment particles andλ = void ratio