STUDY ON DETERMINATION METHOD OF AMOUNT OF DAM
DISCHARGE ACCORDING TO THE RUNOFF
CHARACTERISTICS
MAMORU MIYAMOTO
Public Works Research Institute, 1-6, Minamihara, Tsukuba-shi, Ibaraki-ken, 305-8516
Japan
MASAAKI AKIBA
Kyusyu Regional Development Bureau, Ministry of Land Infrastructure and Transport, 112-1Nishihara, Kumamoto-shi, Kumamoto-ken, 862-0929 Japan
HIDEO TOYA
Foundation of River and Watershed Environment Management, 1-9-12 Irifune, Chuo-ku,
Tokyo, 104-0042 Japan
TADASHI YAMADA
Dept. of Civil Engineering, Faculty of Science and Engineering, Chuo University, 1-1327 Kasuga, Bunkyo-ku, Tokyo, 112-8551 Japan
The effects of flood control and water use by a dam operation is looked at from the point
of view of total management of a large-scale river basin. We propose a method of
discharge control by dam operation intended to increase the efficiency of flood control
and water availability. In this method, the future rainfalls are estimated in advanced and
the reservoir is discharged accordingly in order to make it possible to accommodate the
resulting future flows. With this method, it is possible to achieve higher flood control
efficiency as well as a superior degree of conservation of water for usage because the
total amount of advanced discharge is based on the area under the recession part of the
flood hydrograph. Therefore, it is possible to have higher storage in reservoirs even
during the flooding season, providing more opportunities of using reservoirs for other
purposes in addition to flood control. Furthermore, it is possible to safely create artificial
floods time to time in order to maintain the health of the river system.
INTRODUCTION
In the large-scale river basin, we should perform total river management considering
whole basin. Especially, the necessity of total flood control by the dams and the lowering
of retention and retarding function in the upstream region, the damage from the
inundation by river water, the outgoing correspondence of flood damage information
have been required. However, the land condition is severe for Japan that is located in
Asia, Monsoon region. In rainy season and typhoon stage, it falls heavy rainfall in short
time. And, stream gradient of many rivers is steep. Water resources of per capita are
never abounding in the viewpoint of the water use. The flow control by the dams is
1
2
mentioned as method that is effective for both of flood control and water use under the
severe conditions like this.
The study on the optimum discharge in large-scale basin by dams is carried out in
great numbers. Those are the one that applied Dynamic Programming by Little (1955) in
the flow control process by those many. They can be divided roughly into two of study
on the optimum operation and study on the optimum design. On the former, the DCL
method is proposed on optimum operation of dams by Takeuchi (1974). On the latter, it
was analyzed with Dynamic Programming that added the operating condition on the
optimum design of the dams by Takasao and Ikebuchi (1975). However, it has not come
to the real operation because of difficulty of the fusion of flood control and water use and
complexity of the water resources planning system. For such present state, authors
considered dam operation of simple substance as a first step of this study. The total flow
control shall be considered in the back. These papers propose the discharge method that
is very simple and rational for both of flood control and water use.
PRESENT STATE OF DAM MANAGEMENT
In this study, Kusaki dam that is located on Watarase River has be made to be an object.
The distributed capacity of Kusaki dam is shown in figure1. The catchment area of
Kusaki dam basin is 254km2. They can discharge 640m3 in the maximum from normal
orifices. In the Kusaki dam, the inflow over 500m3/s has been defined as a flood, and the
fundamental operations rules in the flood are as Eq. (1).
QOUT  ( QIN  500 )  0.1  500 [m3/s]
(1)
The largest record discharge from Kusaki dam is 904m3/s recorded on September
10th, 2001. The time series of inflow and discharge, reservoir level that was observed in
this time on Kusaki dam is shown in the figure2. In this flood, total amount of rainfall
was 504mm; maximum hourly rainfall was 26.4mm; the peak inflow to the dam was
1119m/s. It is proven from the figure2, the dam became almost for filling with water in
September 10th 4 a.m., 2001, and amount of almost equal to the inflow was discharged.
420
0
1500
： Inflow
3
Discharge（ m /s）
Lowest level
(EL.403.7m)
50
： Storage level
： Rate of control volume
1000
20
： Discharge 40
500
0
0
24
48
72
96
hourly rainfall (mm/h)
100
440
Storage level
(m)
Flood season
control level
(EL.440.6m)
Rate of regulatory volume
（％）
2001/9/8 14:00～9/18/2:00
Surcharge level
(EL.454m)
120
Hour
Figure 1. Capacity distribution
figure of Kusaki dam
Figure 2. Time series of inflow and
discharge, reservoir level
3
CALCULATION OF PRELIMINARY DISCHARGE
It is very effective to lower the reservoir level before floods inflow by the preliminary
discharge in the case of the flood control by the dam. However, the multiple purpose
dam also has the role as water use with flood control. Then, authors calculated the
amount of inflow that flowed in recession division of the inflow hydrograph to the dam.
And authors propose the method that discharge a mount of the minimally inflow. It is
possible to efficiently control floods by this discharge method. Additionally, reservoir
level is recovered even in the minimum after the flood finished to flood season control
level. Authors calculated the analytical solution using runoff parameters that get at
observed data in order to work out total inflow in the recession division of floods. On the
calculation of the analytical solution, equation (2) was used.

24n
0
q t dt 

q10  1  24na0 q0
a0   1

(  1 ) / 

1
(2)
+7
[10 ]
  QIN  QOUT dt  V QIN ( t )
Total rainfall[mm]
Total inflow in 4days
from recession beginning
3
[m /4days]
Where q**:runoff rate[mm/h] in recession
： Analytical solution
： Observed
curve. Also, a0 ,  are runoff parameters.
(LINE2)
5
： Analytical solution
N is number of days.
LINE2
(LINE1)
： Analytical solution
With the analytical solution in the
4
(LINE3)
recession division, relation between
： Total rainfall
inflow after 2 hours since the after rainfall
3
LINE1
finished and all afterwards inflow for 4
days were shown in figure3. The amount
2
of preliminary discharge was calculated
600
LINE3
using 3 cases shown in figure3 (In this
400
1
paper, these will be defined as Line1,
200
Line2 and Line3). It can be called the
0
0
0
200
400
600
advantageous discharge for the flood
3
Peak inflow[m /s]
control in using Line2. It can be called the
Figure3. Relationship of peak
advantageous discharge for the water use
inflow and total volume of
in using Line3.
The discharge that
recession division
satisfied Eq.(3) may be carried out in
order to discharge amount of inflow in the recession division.
The left side is a total amount discharged as a preliminary discharge, and right sides are
all of the inflow that flows into the recession division of an inflow hydrograph.
t
0
(3)
It is differentiated in the time (t).
QOUT  QIN 
dV dQIN

dQIN dt
(4)
4
The amount of discharge was decided from them, and the reservoir level of the same
time was calculated by Eq.(5), and the safety of the water use capacity was verified.
A( h )
dh
 QOUT  Q IN
dt
(5)
Surcharge water level
(EL.454.0m)
440
Flood season
control level
(EL.440.6m)
： Storage level (Line1)
： Storage level (Actual discharge)
420
Lowest water level
(EL.403.7m)
： Actual inflow
： Inflow(peak500)
： Actual discharge
from dam
： Discharge
from dam
(Line1)
1000
3
500
0
460
Surcharge level
(EL.454.0m)
440
： Storage level (Line2)
： Storage level (Line3)
： Storage Level (Actual discharge)
420
400
： Actual inflow
： Inflow(PEAK500)
1000
Flood season
control level
(EL.440.6m)
Lowest water level
(EL.403.7m)
： Actual discharge
from dam
： Discharge
from dam
(Line2)
： Discharge
from dam
(Line3)
3
400
Discharge(m /s)
Storage level(m)
460
Discharge(m /s)
Storage level(m)
Next, whether the reservoir level recovers, in the case of rain stopped in the early
stage, was verified. On the assumption of the case in which it decreases in point of time
which becomes 500m3/s of the inflow, the amount of discharge was calculated. The time
series of inflow, discharge from dam, reservoir level in calculating the amount of
discharge using Line1 is shown in the figure4. And case of using Line2,3 is shown in the
figure5. It is proven to recover on the reservoir level to flood season control level, when
Line1 and Line3 were used. The negative discharge had been calculated, when Line2
was used, and it was replaced with the normal value. As the result, the reservoir level was
not recovered to flood season control level.
500
0
0
24
48
72
96
120
144
168
Hour
Figure 4. Time series of inflow and
discharge, reservoir level
0
24
48
72
96
120
144
168
Hour
Figure 5. Time series of inflow and
discharge, reservoir level
In actual dam operation, it is desirable that the amount of preliminary discharge is
decided by the method for show until now. Consequently, the amount of preliminary
discharge quantity is decided using Line1 and The 10% discharge was carried out as well
as the current dam operation after the inflow exceeds 500m/s. The dam operation is
shown in the figure6. It is proven from figure6 that the flow control has been started in
the condition that reservoir level was lowered to about 10m by the preliminary discharge.
Consequently, it did not need to carry out the proviso operation. (The proviso operation
means that the almost equal quantity with the inflow is discharged in spite of the case in
which the inflow is very abounding) It is very advantageous to avoid this proviso
operation in the flood control. Similarly, the case in which Line2 was used is shown in
the figure7. Not only the flood is efficiently controlled, but also the security of the water
use capacity has also been done even in this case. Then, it is beforehand higher than the
restriction water-level assuming the prophase discharge, and the set is possible in respect
of the reservoir water level. Then, assuming the preliminary discharge, it is possible to
heighten the reservoir level than flood season control level. And, it may be able to be new
5
Surcharge level
(EL.454m)
Storage lavel
(Current flow control)
440
Flood season
control level
(EL.440.6m)
Storage level[m]
(by Line1)
420
3
1000
3
Discharge[m /s]
（ by Line1）
Surcharge level
(E.L.454m)
440
：
：
420
Storage level
(Current flow control)
Storage level
(by Line2)
Flood season
control level
(E.L.440.6m)
Lowest water level
(E.L.403.7m)
： Observed
1000
： Discharge
(Current flow control)
3
Discharge(m /s)
3
Discharge[m /s]
(current flow comtrol)
Observed[m /s]
3
Discharge(m /s)
Hourly rainfall[mm/h]
0
10
20
30
40
460
400
Lowest water level
(EL.403.7m)
400
1500
Hourly rainfall(mm/h)
Storage level(m)
460
Storage level(m)
developed water resources. Furthermore, the possibility of preventing the smoothing of
the river discharge of downstream from Kusaki dam by this artificial flood was also
shown, because the largest 800m3/s was discharged in the preliminary discharge using
Line2.
Authors examined the effectiveness of this discharge method in the different flood.
The flood as an object is the one on August first, 1982 which recorded the largest record
inflow. The case in which the preliminary discharge was decided using Line1 is shown in
the figure8. The case in which the preliminary discharge was decided using Line2 is
shown in the figure9. The flood is also efficiently controlled in both. Above all, the
possibility of new development water resources was greatly shown in the case of using
Line2.
： Discharge
(by Line2)
500
500
0
0
24
48
72
96
0
0
120
24
48
Hour
： Storage level
(Current flow control)
： Storage level
(by Line1)
400
3
Discharge(m /s)
：
：
：
Flood season
control level
(E.L.440.6m)
Lowest level
(E.L.403.7m)
Observed discharge
Discharge
(Current flow control)
Discharge
(by Line1)
1000
120
460
Surcharge level
(E.L.454m)
440
： Storage level
(Current flow control)
： Storage level
(by Line2)
420
Flood season
control level
(E.L.440.6m)
Lowest level
(E.L.403.7m)
400
1500
： Obseved inflow
： Discharge
(Current flow control)
： Discharge
(by Line2)
1000
500
0
0
Storage leve(m)
Surcharge level
(E.L.454m)
440
3
460
1500
96
Figure 7. Time series of inflow and
discharge, reservoir level
Discharge(m /s)
Storage level(m)
Figure 6. Time series of inflow and
discharge, reservoir level
420
72
Hour
500
24
48
72
96
120
Hour
Figure 8. Time series of inflow and
discharge, reservoir
0
0
24
48
72
96
120
Hour
Figure 9. Time series of inflow and
discharge, reservoir
6
EFFECT ON DOWNDTREAM OF THE PRELIMINARY DISCHARGE
The following were noticed: How the flow control by the preliminary discharge responds
in Watarase River that effect of decreasing the flood water level. Then, authors calculated
the whole Tone river channel as the unsteady flow. Figure10 shows Kusaki dam and the
flood water level comparison site in the Tone river channel network for the calculation.
Takatsudo of the 22km downstream site from Kusaki dam and Ashikaga of the 42km
downstream site from Kusaki dam were accounted for the pending issue site. (In this
paper, these will be called Takatsudo, Ashikaga since then.) Water level and discharge of
the flow control by the preliminary discharge in this 2 pending issue site were compared
with the case in which there is no control by the dam and case in which the current flow
control was carried out.
(1) Fundamental equation and calculation condition.
In flow condition reproduction in the river, it
is calculated using continuous equation and
basic formula of unsteady flow (SaintVenant equation). Continuous equation and
momentum equation are respectively shown
in equation (6) and equation (7).
A Q
(6)

q
t x
Q

t
 Q2
 A
 
x


2
  gA h  n g Q Q  0
4
x
AR 3
(7)
where, A(m): Water conduction cross
section, Q(m/s): Flow rate, q(m/s): Side flow
Figure 10. River channel network
input, α: Energy correction coefficient,
for calculation
h(m): Water depth, g: Gravitational
acceleration, n: Manning roughness Coefficient and R(m): hydraulic radius
Coefficient of roughness of river channel calculated value is given on Watarase river
from trace investigation of the flood in 2001 and 2002 at the every segment, and it is
divided into river channel except for Watarase river in 3 types of tail reach, middle reach,
upper reach, and 0.02 has been given to tail reach, 0.025 to middle reach and 0.03 to
upper reach. Boundary condition on upstream end of Kusaki dam upstream is given the
observed inflow data in Kusaki dam, and upper reach boundary condition of Watarase
river basin is given the observed inflow data only from the left basin. Boundary condition
on upstream end except for Watarase River, the hydrograph of the flow is given as runoff
depth of observation inflow in Kusaki dam multiplied with each catchment area.
Boundary condition on downstream end is given as the time series of tidal level observed
in Shibaura to Edo river mouth and measured in Kashima to Tone river mouth.
(2) Evaluate the effect of decreasing flood water level
Flood control effect of the flow control by the preliminary discharge was examined. The
case, in which the amount of preliminary discharge was decided by using Line1 for the
flood in September, 2001 was made to be an object. Its dam operation as be shown in the
figure6. The hydrograph of the water level in this time Takatsudo and Ashikaga is shown
7
in the figure11 and 12. At Takatsudo, it is proven that the peak water level is lowered
58cm in comparison with the current flow control by the preliminary discharge. And,
peak water level of flood without flow control is lowered 78cm by the preliminary
discharge. In Ashikaga, it is proven that the peak water level is lowered 26cm in
comparison with the current flow control by preliminary discharge. And, peak water level
of flood without flow control is lowered 43cm by the preliminary discharge. In the case
of the current flow control, the flow discharged as the proviso operation formed the peak.
Because the proviso operation was able to be avoided in the dam operation by
preliminary discharge, it was possible to demonstrate the flood control effect more.
40
： Without flow control
： Without flow control
： Current flow control
： Current flow control
： Flow control by Line1
38
Water level (m)
Water level(m)
152
150
： Flow control by Line1
36
34
148
0
24
48
72
96
32
0
120
24
48
72
96
Hour
Hour
Figure 11. Hydrograph of water
level in Takatsudo site
Figure 12. Hydrograph of water
level in Ashikaga site
120
3
3
Discharge (m /s)
Discharge from Kusaki dam (m /s)
(3) The evaluation of the timing of discharge from Kusaki dam in Tone River
Authors examined the effect of the timing of preliminary discharge and later stage
discharge, proviso operation from Kusaki dam on the Tone River which is a main river.
Therefore, the discharge from Kusaki dam was evaluated time-related in the Kurihashi
site (upstream 130km from the river
8hours
mouth). The discharge at Kurihashi
shouldn’t be quantitatively evaluated,
Flood
： 2001/9/8–14
600
and authors noticed waveform of the
30000
Flow control
： By Line1
hydrograph and timing of the peak
generation. The figure13 is show the
： Total discharge
hydrograph of total discharge at
： Discharge from 400
20000
Kusaki dam
Kurihashi site and discharge from
Kusaki dam. The scale of the
discharge from Kusaki dam was
200
10000
shown in the shaft of the right
considering the difference in the
whole quantity. On the Kurihashi site,
it is proven that the peak of the
0
0
0
48
96
144
192
discharge from Kusaki dam is arising
Hour
8 hours before from the peak of the
Figure 13. Hydrograph of discharge
total discharge. Therefore, the timing
in Kurihasi site
8
of preliminary discharge or late stage discharge by Kusaki dam does not affect the
generation of the peak in the Kurihashi site. Reversely, the timing of the peak generation
accords, if the flood control is not carried out in Kusaki dam, and the scale of the flood in
Tone River will increase.
CONCLUSION
In this paper, the decision procedure of dam discharge which is possible in proportion to
runoff characteristic of the dam basin was proposed, and the effectiveness was verified
from both of flood control and water use. The knowledge got by the above is enumerated.
1) It was understood that to estimate all inflows after the peak from the peak inflow was
possible by the relationship between peak inflow and all inflows in the recession
division. Most of the inflow is over 3000×10, and the flow equal to or over the
water use capacity of Kusaki dam will flow in the recession division.
2) Discharge method for carrying out preliminary discharge the flow which flows in the
recession division of the hydrograph was proposed. In addition, it was shown that the
reservoir level was recovered, if Line1, the mean value, is used, even if the rain
stopped in the early stage and it did not become a flood after discharging.
3) It is possible that it is set the dam reservoir level beforehand higher than flood season
control level, if the preliminary discharge is carried out much enough like the case
Line2 which is safe for the flood control. Then, it was shown that it could be new
development water resources.
4) Because 800 at the maximum is discharged in preliminary discharge using Line2,
The possibility of preventing the smoothing of river flow by the artificial flood in
downstream of a dam, which fulfils the role for the environment was shown.
5) In the case of current flow control for the flood 2001 in Takatsudo and Ashikaga in
downstream of Kusaki dam, the flow discharged by proviso operation is the peak. In
the flow control of the preliminary discharge, flood water level effect of decreasing
was more demonstrated in the downstream, since it did not need to carry out proviso
operation.
6) It is proven that the peak generation is not affected on the timing of preliminary
discharge and later stage discharge by the Kusaki dam since it does not agree with
peak generation time on the point of main river. Reversely, the timing of the peak
generation accords, if the flood control is not carried out in Kusaki dam, and the
scale of the flood in Tone River will increase.
REFERENCES
[1] Takasao T., Ikebuchi S. and Kojiri T., “Dynamic programming for multi-reservoir
system design based on the water quantity control”, In Japanese, Journal of Japan
society Civil Engineering, JSCE, Division2, Vol.241, (1975), pp 39-50.
[2] Takeuchi K., “Optimal control of water resource-systems using marginal loss
functions of remaining reservoir storages”, In Japanese, Journal of Japan society of
Civil Engineering, JSCE, Division2, (1974), pp 93-103.
[3] Kure S., Koshizuka Y. and Yamada, T., “Extraction of runoff characteristics from
flow recession characteristics of hydrograph”, In Japanese, Annual Journal of
Hydraulic Engineering, JSCE, Vol.48, (2004), pp 13-18.