STOCHASTIC SEDIMENT DEPOSITION PROCESSES OF LARGERESERVOIRS IN JAPAN1

2

Tetsuya SUMI and Sameh A. KANTOUSH
1. Water Resources Research Center, Disaster Prevention Research Institute, Kyoto University,
Uji-shi, Japan, (sumi.tetsuya.2s@kyoto-u.ac.jp)
2. Water Resources Research Center, Disaster Prevention Research Institute, Kyoto University,
Uji-shi, Japan, (kantoush@ky3.ecs.kyoto-u.ac.jp)

ABSTRACT
Sediment deposition and its accumulation as a function of time in years in a large reservoir depend on
the flow and sediment hydrographs. In this paper, a stochastic sediment deposition in Japanese
reservoirs is discussed. In Japan, sediment deposition in large reservoirs has been measured annually
since the 1930. Such long-term annual sedimentation records are unique and represent some of themost useful global data to assess temporal trends in total sediment yields from larger catchments.
There are two objectives to use that small probability of the huge extreme event of sediment in:predicting and design the operation and to propose new countermeasure. Among several probability
distribution models, GEV (Generalized Extreme Value) model is the best goodness of fit to actual
annual sedimentation records and each extreme sedimentation records has been evaluated by return
period of 1/50-1/200 yrs.

1.

INTRODUCTION

Sediment delivery to rivers is probably the most problematic off-site consequence of soil erosion incatchments. The input of sediment by erosion processes into rivers, reservoirs and ponds results inhigh sediment deposition rates and frequent dredging operations (Verstraeten and Poesen, 2001).
Predicts of temporal variation of sediment yield are needed for design of flood bypass system, andstudies of reservoir sedimentations and river morphology. The evaluation of sediment yield in rivers,
where total load consists predominantly of suspended load, plays an important role in the design ofsoil and water conservation and sediment control practices as well as in the design and managementof dams, and other hydraulic structures. To this end, stochastic modelling techniques have been
applied successfully to obtain reliable estimates of sediment yield. These techniques are superior to
traditional methods which make use of discharge-concentration rating curves. Stochastic modelling
accounts for the time series nature of rainfall, runoff and sediment yield processes (Anselmo et al.,
1981; Sharma et al., 1979). It was used for short sampling intervals by Anselmo et al. (1981). An
accurate estimate of sediment yield and reservoir sediment deposition rates should be made during
the planning of new reservoirs. At present, sediment yield predictions are achieved mainly throughsimple empirical models that relate the annual sediment delivery by a river to catchment properties,
including drainage area, topography, climate and vegetation characteristics (e.g. Verstraeten andPoesen, 2001). The amount of sediment trapped in a reservoir during a certain period of time is thedifference between the sediment carried into the reservoir by the inflow and the sediment released
with the outflow. Several deterministic methods have been developed to predict the amount of
sediment carried into a reservoir as a function of watershed characteristics (Ackermann and Corinth,
1962; Gupta, 1974).
Reservoir sediments typically represent an important record of a catchment's erosion history.
Reservoir based studies have been successfully applied as a means of reconstructing long-term
sediment yields (e.g. Labadz et al., 1991). However, most have limited temporal resolution and are
unable to generate information on seasonal or event-scale processes. The complexity of catchment
sediment delivery and reservoir sedimentation mechanisms means that most physically-based or
mechanistic models are highly parameterized and require extensive field calibration.

1

Japanese watersheds are frequently affected by very heavy storms with daily precipitation of morethan 300 mm, which causes significant sediment erosion. In Japan, sediment deposition behindcertain large dams has been measured annually since the 1930’s (Miyazaki and Onishi, 1996;
Hiramatsu et al., 2002). Such long-term annual sedimentation records are unique and represent someof the most useful global data to assess temporal trends in total sediment yields from larger
catchments. Miyazaki and Onishi (1996) examined the timing of sediment supply and transport bycomparing annual rainfall data with changes in the volume of dam deposits. Imaizumi and Sidle (2005)
investigated the relationship between sediment supply and transport processes in Miyagawa dam
catchment. In Miyagawa Dam 11 catchment, percentages of landslides reaching channels varied from
56% in 1997–2000, 12 to 75% in 1976-1981, and were correlated with the maximum hourly rainfall.
In civil engineering practice many parameter estimation methods for probability distribution functions
are in circulation. The choice of statistical estimation methods for probability distribution functions is
one of the most challenging problems within civil engineering, and one that is filled with many
controversies. Many attempts (for instance, Burcharth and Liu, (1994), and Van Gelder and Vrijling,(1997)), have been made to find out which estimation method is preferable for the parameter
estimation of a particular probability distribution in order to obtain a reliable estimate of the p-quantiles.
In Fill and Stedinger (1995), it was shown that for realistic generalized extreme value (GEV)
distributions and short records, a simple index-flood quantile estimator performs better than twoparameter (2P) GEV quantile estimators with probability weighted moment (PWM) estimation using a
regional shape parameter and at-site mean and L-coefficient of variation (L-CV), and full threeparameter at site GEV/PWM quantile estimators. However, as regional heterogeneity or record lengths
increase, the 2P-estimator quickly dominates. Fill and Stedinger (1995) generalizes the index floodprocedure by employing regression with physiographic information to refine a normalized T-year flood
estimator. In Naghavi and Yu (1996), it is shown that the quantile prediction accuracy of the logPearson type III (LP3) distribution depends largely on the accuracy of the parameter-estimation
method used. In Takara and Stedinger (1994) the use of two-parameter distributions is recommended
from the viewpoint of quantile estimation accuracy for datasets having sample skewness greater than
0.38 and less than 1.8. They found that the quantile lower bound estimators are likely to provide moreaccurate quantile estimators than other procedures.
Extreme-regime sedimentation is commonly of interest in lake sediment research because of its
associations with hydrologic and geomorphologic catchment hazards (e.g., Gomez et al. 2002). The
emphasis of such studies is usually on temporal variability in the sedimentary record. Comparatively
little research has been carried out on the within-reservoir areal variability of sedimentation (e.g.,
Gilbert, 2003).
In this paper, a stochastic sediment deposition in Japanese reservoirs is discussed. There are two
objectives to use that small probability of the huge event of sediment in: predicting and design theoperation and to propose new countermeasure. Based on annual sedimentation records in Japanese
reservoirs, several probability distribution models are compared by the goodness of fit from theviewpoint of quantile estimation accuracy and each extreme sedimentation records has been
evaluated by the selected model.

2.

RESERVOIR SEDIMENTASTION IN JAPANIn Japan, approximately 2,730 dams over 15 meters in height have been constructed for water
resource development or flood control purposes, but the total reservoir storage capacity is only up to
23 billion m3. The sediment yields of the Japanese rivers are relatively high due to the topographical,
geological and hydrological conditions and this has consequently caused sedimentation problems tothose reservoirs.
Based on the annual research conducted for 877 reservoir which have gross storage capacities ofover one million m3, specific sediment yields in these catchment areas are ranging from several
hundred to several thousand m3/km2/year, and the specific sedimentation volume becomes higher incentral high mountainous regions along the Median Tectonic Line and the Itoigawa-Shizuoka Tectonic
Line as shown in Figure 1.

2

単位は㎥/㎢/年
3/km2/yrm

Figure 1

Specific reservoir sedimentation volume in Japan

Annual storage capacity losses in those reservoirs are ranging approximately from 1.0 to 0.1 %. In
other words, it is noted that the reservoir lives are approximately 100 to 1000 years. Reservoir
sedimentation problems are represented by such as the siltation of intake facilities, aggradations of
upstream river bed, reservoir storage capacity loss and, sometimes, lack of sufficient sediment supply
to downstream which may cause river bed degradation or coastal erosion.

3.
3.1

STOCHASTIC SEDIMENT DEPOSITION IN RESERVOIRSAnnual Sedimentation records in Reservoirs

Figure 2 shows Tenryu river system which is one of thehighest sediment yield rates in Japan. In the middle
reach, Sakuma dam was constructed in 1957 by JPower. Figure 3 shows annual sedimentation record in
Sakuma dam. After completion, high rates up to 4.3
million m3/yr had been recorded for 1957-1969. After
that, it has been gradually decreased such as to 1.65
and 1.55 million m3/yr for 1970-1982 and 1983-2001,
respectively. This is because that slope protection
works in the upstream catchments have been
progressed and, also, extreme flood events caused bylarge typhoons have not been fitted in these years.
Figure 4 shows annual sedimentation record in Miwa
and Koshibu dams which are located upstream of theTenryu river as shown in Figure 3. These wereconstructed by the Ministry of Land, Infrastructure,
Transport and Tourism (MLIT) for multipurpose dams.
In the Tenryu river, there was a large flood in 1982
caused by severe rainy front which produced extreme
sedimentation in these reservoirs at the same time. In
Miwa and Koshibu reservoirs, they were more than 15
times and 6 times of the average annual ones andoccupying more than 20 and 13 % of the total
sedimentation volumes, respectively.

3

Miwa dam

Koshibu dam

Sakuma dam

Figure 2

Tenryu River System

Sedimentation（1,000ｍ3 ）Annual sedimentation(1,000ｍ3)
13,00012,00011,00010,000
9,000
8,000
7,000
6,000
5,000
4,000
3,000
2,000
1,000
0
-1,000Planned sedimentation capacity
Annual sedimentation
Actual sedimentation
Planned sedimentation

Average annual sedimentation

1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006

130,000
120,000
110,000
100,000
90,00080,00070,00060,00050,00040,00030,00020,00010,0000-10,000

Sakuma Dam

Yaers

Figure 3
Sedimentation（1,000ｍ3 ）14,000

Annual sedimentation records in Sakuma dam
Annual sedimentation(1,000ｍ3)

Miwa Dam

7,000

Actual sedimentation

12,000

6,000

10,000Planned sedimentation capacity

8,000

5,000
4,000

6,000

Planned sedimentation

Annual sedimentation

4,000

3,000
2,000

2,000

1,000
Average annual sedimentation

00-1,000
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006

-2,000

Yaers

Sedimentation（1,000ｍ3 ）Koshibu Dam

Annual sedimentation(1,000ｍ3)

24,0003,000
Planned sedimentation capacity

20,0002,500

Annual sedimentation
Actual sedimentation

16,00012,000

2,000
1,500

8,000

Planned sedimentation
Average annual sedimentation

4,000
0

1,000
500
0
-500

1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006

-4,000

Yaers

Figure 4

Annual sedimentation records in Miwa and Koshibu reservoirs

4

Sedimentation（1,000ｍ3 ）16,000

Yahagi Dam

Annual sedimentation(1,000ｍ3)
6,000

Planned sedimentation capacity

14,0005,250

12,0004,500

10,000

Actual sedimentation

3,750

8,000

3,000

6,000

2,250
Annual sedimentation

4,000
2,000

1,500
Planned sedimentation
750

Average annual sedimentation

0

0
-750
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006

-2,000

Yaers

Figure 5

Annual sedimentation records in Yahagi reservoirs

Miwa dam
Sediment trap weir
(H=15.0m)
Diversion weir
(H=20.5m)

1959, H=69m
V=29.95
V=29.95 MCM
A=311km
A=311km2

Purpose: Multipurpose
Flood control, Irrigation
Water power
Rainfall (mm/hr)

Sediment bypass
tunnel 2005,
A=50m2 L=4300m

Inflowdischarge

TunneloutletBypass discharge

Bypass operation in 2006

Figure 6

Sediment bypass scheme at Miwa dam, Tenryu River

These extreme events have been also occurred in other dams such as at Yahagi dam as shown in
Figure 5. In 2000, a severe flood disaster caused by rainy front had also yielded huge amount of
sediment from the catchments and extreme sedimentation was produced after that.
In case of Miwa dam completed in 1959, extreme runoff events occurred in 1959, 1961, 1982 and1983 causing serious disasters and sediment yield in the river basin. Since 1966, gravel have been
constantly removed according to a maintenance plan and then approximately 5.32 million m3
sediment have been dredged in 33 years up to 1998. If those gravel is not removed, the total
sedimentation is approximately 19.47 million m3, and estimated the mean annual sedimentation is0.47 million m 3. From the view point of the eternal reservoir sedimentation management, a sediment
bypass system (comprised of a 20.5m high diversion weir and a 4,300m long bypass tunnel with amaximum discharging capacity of 300m 3/s) is constructed in March 2004 to reduce sedimentation of
the reservoir. Figure 6 shows the schematic diagram of the bypass system. During large flood event in2006, almost half of flood flow containing high sediment concentration was diverted through bypass
tunnel (Red line).
In Koshibu dam and Yahagi dam, almost the same sediment bypass systems are under construction.
In case of designing these structures, we should consider the stochastic characteristics of flood events
to optimize design of bypass capacity which define possible sediment transport rate during large flood
events.

5

3.2

Stochastic Analysis of Annual Sedimentation Records

3.2.1

Frequency Analysis of Hydrological Extreme Events

Based on the annual sedimentation records, we can evaluate probability of these extreme events.
Takara, K. (2009) shows frequency analysis of hydrological extreme events as follows.
We have been regarding hydrological events as random variables. Frequency of hydrological extreme
events is therefore a concern of decision makers in practical works for water resources planning andhydraulic design of flood control facilities. To describe the probability distribution of a random variable
X, we use a cumulative distribution function. The value of this function Fx ( x ) is simply the probability Pof the event that the random variable takes on value equal to or less than the argument:
Fx ( x )=P [X  x ](1)This is the probability that during the year the random variable in question, X, will not exceed some x ;Fx ( x ) is, therefore, regarded as non-exceedance probability. Hereafter, we use a simpler expression
F ( x ) for Fx ( x ). The probability density function f (x) of X is related to F ( x ) as:
F(x) =x f (t )dt

(2)



For a particular value or threshold x p with a non-exceedance probability p, there is a relationship:T=1n(1  p)(3)

in which T is the return period or recurrence interval (year) that corresponds to the hydrologicalvariable X = x p and n is the annual average number of occurrence of X during the period in whichF( x ) is estimated. x p is often called as quantile or T -year event. Note that if we deal with annual
maximum data series, n = 1:
T=

1
1 p

(4)

The 50-year event (T = 50) has a non-exceedance probability p = 0.98. Likewise, T = 100 then p = 0.99
and T = 200 then p = 0.995. Since p = F ( x p ), if we set T or p, we can obtain the quantile (T -year
event) x p by using the inverse function of F :x p = F -1(p)(5)

which gives the value of x p corresponding to any particular value of p or T. Now the frequency ofhydrological extreme value (annual maximum value) is related to frequency, return period or nonexceedance probability.

3.2.2

Probability Distribution Models

There are many reasonable probability distributions (frequency analysis models) for modeling extreme
events. Important families include the normal, extreme-value type I and type II, and Pearson type III(or Gamma) distributions.

6

The probability density function (pdf) of the lognormal distribution with three parameters (LN3) is: 1  ln( x  c)   2 
1Yf ( x) 
exp   Y( x  c) 2
 2  (6)in which x is a hydrological variable; a is lower bound parameter; Y = the mean of y = ln (x - a);  Y =the standard deviation of y. Its cumulative distribution function (CDF) is in a from of the well-known
standard normal distribution function  as:s
 y  Y 1
 1 
F ( x)   
exp   t 2 dt  s   2
 2 
 Y 

in which s y  YY(7)

is the reduced (or standardized) variable of the original variable y. The Gumbel

distribution's CDF is: x  c F ( x)  exp  exp  

a 



(8)

The generalized extreme-value (GEV) distribution has a CDF with a parameter k  0:1k
 xc 
F ( x)  exp  1  k a  
 (9)If k = 0, the GEV distribution is equivalent to the Gumbel distribution shown as Eq. (8). Another family
Pearson type III (Gamma) distribution's CDF for c< x <  is: xc
F ( x)  G  , / ( a )
 


(10)

where (a) is the gamma function and G (a, x) is the "incomplete gamma function" defined as:


x

0

0

( )   e u u 1du, G( , x)   e u u 1du

(11)

For a set of hydrologic extreme-value time series data (annual maxima data), hydrologists often try
several distributions and select one to calculate the estimate of quantile (T-year event) x p for aconcerned non-exceedance probability p, which corresponds to the return period T by using Eq. (5).
Note that we can obtain analytical solutions for the extreme-value theory such as the Gumbel and
GEV distributions, respectively:x p  a ln ln p  c

(12)

and

xp  a( ln p) k  1  c
k

7

(13)

However, since the families of the normal and Pearson type III distributions cannot have suchanalytical solutions, they require computational solutions. Many statistical textbooks include thestandard normal distribution table, which shows the computational solutions for this purpose.
If we had sufficient knowledge of a hydrologic phenomenon, one could derive its population probability
distribution without depending on observed data. If we had sufficiently long record of the phenomenon,
we could determine its frequency distribution precisely, as long as the distribution did not change overtime. But we should select a model that approximates the population distribution based on the limited
knowledge and data generally available. When fitting distributions to a set of hydrologic extreme-value
time series data, we often find that several distributions achieve almost the same goodness of fit, but
can generate different estimates of extreme quantiles.
Takara and Takasao (1990) propose an attractive model selection procedure. Conventional model
selection procedures have generally used goodness-of-fit criteria and/or tests. When two or more
distributions achieve almost the same good results in fitting, the proposed procedure will select the
final distribution in terms of both the goodness of fit and the stability of quantile estimators, which ispreferable from a practical viewpoint. While it is not difficult to estimate quantile variability, quantile
accuracy (which is really of greater concern) is more difficult to determine because the true distributionof the events and its associated parameters are unknown. Takara and Stedinger (1994) summarizedMonte Carlo studies comparing and evaluating various fitting methods for the lognormal (LN), Pearson
type III (PHI), log-Pearson type III (LPIII), Gumbel (EV1) and generalized extreme-value (GEV)
distributions. To screen candidate distributions, Takara and Takasao (1990) used Standard Least
Squares Criterion (SLSC) to evaluate goodness of fit of each distribution to a hydrological extremevalue dataset quantitatively.

3.2.3

Return Period of Annual Sedimentations in Reservoirs

Based on the procedure proposed by Takara and Takasao (1990), we selected suitable probability
distribution models for annual sedimentation records in Miwa, Koshibu and Yahagi dams which are
shown in Figures 4 and 5. Table 1 shows selected models and calculated annual sedimentation
volumes for several return periods. Generalized extreme-value (GEV) distribution is the best fitting inthree dams. Based on the model, we can estimate return periods of actual maximum annual
sedimentation such as from 1/58 yrs to 1/170 yrs. We should consider the small probability of thesehuge events in both operating and assessing long term sustainability of reservoirs. It is also importantto optimize designing of countermeasures such as capacity of sediment bypass tunnels.
Table 1Return Period of Annual Sedimentation in Miwa, Koshibu Yahagi dams
Miwa Dam
Data number
50
Function
Gev
SLSC
0.063
1/2 years
125
1/3 years245
1/5 years437
1/10 years
807
1/20 years
1,372
1/30 years
1,832
1/50 years
2,604
1/80 years
3,563
1/100 years
4,126
1/150 years
5,368
1/200 years
6,458
1/400 years
10,024

Koshibu Dam
Data number
38
Function
Gev
SLSC
0.042
1/2 years248
1/3 years393
1/5 years
600
1/10 years
948
1/20 years
1,404
1/30 years
1,737
1/50 years
2,244
1/80 years
2,815
1/100 years
3,127
1/150 years
3,774
1/200 years
4,304
1/400 years
5,869

Unit: 1,000m3
Yahagi Dam
Data number
31
Function
Gev
SLSC
0.057
1/2 years
184
1/3 years317
1/5 years506
1/10 years
815
1/20 years
1,193
1/30 years
1,449
1/50 years
1,810
1/80 years
2,178
1/100 years
2,365
1/150 years
2,722
1/200 years
2,988
1/400 years
3,654

Actual maximum
annual sedimentation(1,000ｍ3)
VolumeReturn period
4,241
1/105 years

Actual maximum
annual sedimentation(1,000ｍ3)
VolumeReturn period
2,404
1/58 years

Actual maximum
annual sedimentation(1,000ｍ3)
VolumeReturn period
2,830
1/170 years

Gev: Generalized Extreme-Value Distribution Model
SLSC: Standard Least Squares Criterion (Takara and Takasao, 1990)

8

4.

CONCLUSIONS

Sediment deposition and its accumulation as a function of time in years in a large reservoir depend on
the flow and sediment hydrographs. In this paper, a stochastic sediment deposition in Japanese
reservoirs is discussed as follows.
1) In Japan, sediment deposition in large reservoirs has been measured annually since the 1930.
Such long-term annual sedimentation records are unique and represent some of the most usefulglobal data to assess temporal trends in total sediment yields from larger catchments.
2) During more than 30 yrs operation, we can find several extreme annual sedimentations mostly
caused by severe rainfall events. In order to evaluate these extreme sedimentation volumes,
probability distribution models can be used as the same as other hydrological extreme events.
3) Based on annual sedimentation records in Japan, several distribution models have been
compared by the goodness of fit from the viewpoint of quantile estimation accuracy which
procedure is proposed by Takara and Takasao (1990).
4) Generalized extreme-value (GEV) distribution is the best fitting probability distribution model in
Miwa, Koshibu and Yahagi dams. Based on the model, we can estimate return periods of actual
maximum annual sedimentation in these dams such as from 1/58 yrs to 1/170 yrs.
5) We should consider the small probability of these huge events from the view point of return period
and sedimentation volume in one event, both in operating reservoir for long term sustainability andin optimized designing of countermeasures such as capacity of sediment bypass tunnels.

5.

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