Journal of Hydrology 527 (2015) 1045–1053
Contents lists available at ScienceDirect
Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol
Optimal design of seasonal flood limited water levels and its application
for the Three Gorges Reservoir
Pan Liu a,b,⇑, Liping Li a,b, Shenglian Guo a,b, Lihua Xiong a,b, Wang Zhang a,b, Jingwen Zhang a,b,
Chong-Yu Xu a,c
a
b
c
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
Hubei Provincial Collaborative Innovation Center for Water Resources Security, Wuhan 430072, China
Department of Geosciences Hydrology, Section of Physical Geography and Hydrology, University of Oslo, Norway
a r t i c l e
i n f o
Article history:
Received 2 March 2015
Received in revised form 28 May 2015
Accepted 30 May 2015
Available online 6 June 2015
This manuscript was handled by Geoff
Syme, Editor-in-Chief
Keywords:
Reservoir operation
Seasonal flood limited water level
Three Gorges Reservoir
Seasonal flood
Risk
s u m m a r y
Reservoirs perform both flood control and integrated water resources development, in which the flood
limited water level (FLWL) is the most significant parameter of tradeoff between flood control and conservation. This study was aimed at developing the varied seasonal FLWL to obtain more economic benefits without decreasing the original flood prevention standards. The Copula function was used to build
the joint distribution of seasonal floods, which clarified the relationship between the frequencies of the
seasonal flood quantiles and those of the annual maximum. A constraint was then established to meet the
requirement that the total flood risk of the seasonal FLWL should be less than that of the original FLWL.
The seasonal FLWL can optimally be determined because numerous schemes of seasonal design floods are
able to satisfy a given flood prevention standard. As a result, a simulation-based optimization model was
proposed to maximize multiple benefits, such as flood control, hydropower generation and navigation.
Using the case study of the China’s Three Gorges Reservoir (TGR), the proposed method was demonstrated to provide an effective design for the seasonal FLWL, which decreases a slight FLWL for the main
flood season to largely increase the FLWL of the pre-flood and post-flood seasons. The optimal designed
seasonal FLWL scheme involves tradeoffs among flood control, hydropower generation and navigation,
and enhancement of the economic benefits without increasing the flood risk.
Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction
Reservoirs are one of the most efficient key infrastructure components in integrated water resources development and management (Guo et al., 2004; Loucks and van Beek, 2005). According to
the World Commission on Dams (WCD, 2000), most large reservoir
projects worldwide are failing to produce the level of benefits that
provided the economic justification for their development.
Currently, with the rapid development of social economy and
water requirements, the water resources shortage problem has
deteriorated, and the function of reservoirs, in terms of flood water
utilization, has become increasingly important in China (Li et al.,
2010; Zhou and Guo, 2014; Ouyang et al., 2015).
The reservoir flood limited water level (FLWL), which should
not be kept high during the flood season to offer adequate storage
⇑ Corresponding author at: State Key Laboratory of Water Resources and
Hydropower Engineering Science, Wuhan University, Wuhan 430072, China. Tel.:
+86 27 68775788; fax: +86 27 68773568.
E-mail address: liupan@whu.edu.cn (P. Liu).
http://dx.doi.org/10.1016/j.jhydrol.2015.05.055
0022-1694/Ó 2015 Elsevier B.V. All rights reserved.
for flood prevention according to the Chinese Flood Control Act, is
the most significant parameter of tradeoff between the activities of
flood control and conservation (Liu et al., 2008; Yun and Singh,
2008; Li et al., 2010). The conventional FLWL is determined by
the reservoir routing of the annual design flood hydrographs.
However, the designed flood, based on the annual maximum sample, neglects flood seasonality, and hence, the conventional FLWL is
often a fixed value during the entire flood season. Due to the flood
seasonality, varied seasonal FLWL are able to obtain more economic benefits without decreasing the original flood prevention
standard. For example, in China (MWR, 2006; Zhou and Guo,
2014), the United States (USACE, 1998) and Vietnam (Ngo et al.,
2007), such measurements have been implemented for the
improvement of floodwater utilization.
The existing method to determine the seasonal FLWL is flood
routing the seasonal design flood hydrographs using the predetermined reservoir operating rules (MWR, 2006). After the entire
flood season is divided into two or three sub-seasons (Liu et al.,
2010), the seasonal FLWL is determined as follows: (1) estimate
the seasonal design flood and hydrograph based on the seasonal
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P. Liu et al. / Journal of Hydrology 527 (2015) 1045–1053
maximum flood samples, and (2) determine the seasonal FLWL
based on the seasonal design flood hydrograph, i.e., routing the
flood by setting it as the initial water level under the condition that
the flood prevention risks are not increased. This approach can be
conducted through a trial and error method. However, the conventional method often sets all seasonal flood frequencies to 1/T when
the original flood prevention standard is a return period of T
because of the unclear relationship between the seasonal and
annual floods. Indeed, it is a challenge to evaluate the flood risk
of the designed seasonal FLWL (Singh et al., 2005).
The conventional seasonal flood frequency analysis methods,
which address the seasonal floods as univariate distributions and
neglect their corrections, fail to provide a complete description of
hydrologic events (Baratti et al., 2012). Thus, the seasonal design
of floods should consider both the marginal distribution and their
corrections, which can be depicted via a multivariate joint distribution. The Copula function, a promising mathematical tool for investigating multivariate problems, has been applied in hydrologic
analysis (e.g., Xiong et al., 2014). The advantages of the Copula
function for the model joint distributions are numerous: (1) flexibility in choosing an arbitrary marginal distribution and the structure of dependence, (2) extension to more than two variables, and
(3) separate analysis of the marginal distribution and the structure
of dependence (Durrans et al., 2003; Chen et al., 2010; Li et al.,
2013). Based on this logic, the relationship between the frequencies of seasonal flood quantiles and the annual flood prevention
standard can be clarified; as a result, the seasonal FLWL can be
derived without increasing the flood risk.
Simulation and optimization are the most commonly used
methods to derive the reservoir operating rules (Yeh, 1985;
Labadie, 2004; Rani and Moreira, 2010; Liu et al., 2014; Zhu
et al., 2014). Simulation-based optimization can be resolved by
using the genetic algorithm (GA) because of its ability to perform
global searching and its independence of the particular problem
(Oliveira and Loucks, 1997; Cai et al., 2001; Koutsoyiannis and
Economou, 2003; Chang et al., 2005; Liu et al., 2006, 2011;
Herman et al., 2014; Li et al., 2014).
Compared with the previous researches (Yun and Singh, 2008;
Liu et al., 2008; Li et al., 2010; Zhou and Guo, 2014), this study provide a novel method to optimal design the seasonal FLWL by considering the correlation among seasonal floods, with a
simulation-based optimization model. The objectives of this study
are: (1) to clarify the relationship between seasonal and annual
floods, and (2) to design the seasonal FLWL via an optimization
method. The remainder of this paper is organized as follows. In
Section 2, we present the seasonal floods design model via a
Copula method, which forms one of constraints for the
simulation-based optimization model that is used to design the
seasonal FLWL. Section 3 addresses a case study of China’s
Three Gorges Reservoir (TGR). Finally, conclusions are given in
Section 4.
2. Methodology
The following steps are used to optimize the reservoir seasonal
FLWL (Fig. 1).
(1) Based on the Copula function, a design flood module is
established to produce the seasonal design floods and hydrographs, which are used to evaluate the flood risks by using
reservoir routing (Section 2.1).
(2) Without increasing the above risks, a multi-objective criterion is used to evaluate the seasonal FLWL, and then, the
Pareto solutions are found by using a simulation-based
optimization (Section 2.2).
Fig. 1. Flowchart of the method for the optimal design of seasonal flood limited
water levels for reservoirs.
2.1. Copula-based seasonal design floods
It is often assumed that various seasonal maximum floods are
independent. However, different seasonal maximum floods have
a slight correlation, rather than being significantly independent.
The Copula function is an efficient way to construct a joint distribution of multiple variables, regardless of the marginal distribution
functions (Durrans et al., 2003; Chen et al., 2010; Li et al., 2013).
Consequently, the Copula function provides an effective method
to express not only the independent variables but also their correlation for seasonal floods.
The Frank Copula function is used to describe the relationship
among sub-season floods. Let the entire flood season be divided
into three sub-seasons, namely, the pre-flood, main flood and
post-flood seasons (Liu et al., 2010), the Copula function is built
as follows:
n
1
h1 1
Cðu1 ; u2 ; u3 Þ ¼ h1
Þ ð1 ½1 ð1 eh2 Þ
1 log 1 ð1 e
o
ð1 eh2 u1 Þ ð1 eh2 u2 Þh1 =h2 Þð1 eh1 u3 Þ
ð1Þ
where h1 and h2 are the dependence parameters of the Frank Copula
function and h2 P h1 ; h1 ; h2 2 ½0; þ1Þ and u1, u2, u3 represent the
marginal distribution function. Note that the joint distribution
could be established similarly when the entire flood season is
divided into two sub-seasons.
The Copula joint seasonal distribution can be validated by using
the annual maximum quantiles, x0, as a special case, i.e.,
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P. Liu et al. / Journal of Hydrology 527 (2015) 1045–1053
PðY > x0 Þ ¼ PðY 1 > x0 [ Y 2 > x0 [ Y 3 > x0 Þ ¼ 1 Cðu1 ; u2 ; u3 Þ
ð2Þ
(1) Maximization of flood control storage, V f ðZ x Þ, during reservoir routing. Flood control storage can be described by the
average flood control storage volume below the reservoir
normal pool level:
Based on the Frank Copula function, the relationship between
the annual flood prevention standard (described with a return period of T) and the frequency quantiles of the three sub-seasons can
be expressed as follows:
h1
1=T P 1 þ h1
Þ
1 logf1 ð1 e
Max V f ðZ x Þ ¼ 1k
1
h1 =h2
1
ð1 e
1
ð4Þ
i¼1
ð1 ½1 ð1 eh2 Þ ð1 eh2 ð1PX2 Þ Þð1 eh2 ð1PX 3 Þ Þ
h1 ð1P X Þ
k
X
V f ;i
where k is the number of flood events, and Vf,i is the reservoir
volume below the normal pool level for flood control, which
is the function of the seasonal FLWL, Zx, and can be used to
represent the reservoir storage capacity for flood control:
Þ
Þg
where x1, x2 and x3 are the floods in the pre-flood season, the main
flood season and the post-flood season, respectively, and P X1 , P X2
and P X3 are the seasonal frequencies for the three sub-seasons.
Based on the seasonal frequency quantiles, the seasonal design
flood hydrographs can be designed for the three sub-seasons (Zhou
and Guo, 2014). Next, the FLWL can be determined by first setting
its value as the initial reservoir water level and then using reservoir
flood routing to satisfy the unchanging flood prevention standard
through a trial and error method.
Finally, the seasonal design floods and FLWL are derived as
follows:
V f ¼ V z maxðV 1 ; V 2 ; . . . ; V l Þ
ð5Þ
where l is the operation horizon; Vj (j = 1, 2, . . ., l) are the
reservoir volumes during flood routing; and Vz is the reservoir storage associated with the normal pool level.
(2) Minimization of the flood risk R(Zx) of the reservoir downstream (Apel et al., 2006).
1
Min RðZ x Þ ¼ mn
n X
m
X
Ri;j
ð6Þ
i¼1 j¼1
where Ri,j is the occurrence on the jth day of the ith year
when the release Oi,j is greater than the safety streamflow
of downstream reach; n is the number of years; and m is
the number of days during the flood seasons.
(3) Maximization of the hydropower benefits, which can be
described by the annual hydropower generation and the
hydropower reliability during the flood seasons as follows:
(1) Set the seasonal frequencies (PX 1 , P X 2 and P X 3 ) for the three
sub-seasons, which should be satisfied with Eq. (3) when
the original flood prevention standard is a T-year return
period.
(2) Calculate the seasonal frequency quantiles, and then design
their seasonal flood hydrographs.
(3) Determine the seasonal FLWL by using reservoir flood routing when the seasonal flood hydrographs are inputted as the
inflow.
Max Ea ðZ x Þ ¼ 1n
n X
m
X
Ni;j
ð7Þ
i¼1 j¼1
2.2. Simulation-based optimization of FLWL
Max H r ðZ x Þ ¼
For a given design flood prevention standard, different combinations of P X 1 , PX 2 and P X 3 can satisfy Eq. (3). As a result, numerous
seasonal FLWL schemes can satisfy the flood prevention requirements. Fig. 2 shows that three FLWL schemes have the same flood
prevention standard. However, different schemes offer different
economic benefits when they are used for operations. Therefore,
the seasonal FLWL must be optimally designed to improve the
reservoir benefits.
#ðNi;j P Pf Þ
mn
ð8Þ
where Ni,j is the hydropower generation on the jth day of the
ith year and #ðN i;j Pf Þ counts the number of days that
hydropower generation is satisfied with the firm output Pf .
(4) Maximization of the navigation benefits, which can be
described by the reliability of navigation Nv(Zx):
1
Max Nv ðZ x Þ ¼ mn
n X
m
X
Si;j
ð9Þ
i¼1 j¼1
Flood limited water level (m)
2.2.1. Optimization model
2.2.1.1. Objectives. A multi-objective criterion is proposed to evaluate and optimize the seasonal FLWL as follows:
where Si,j is the navigation conditions on the jth day of the
ith year, which is determined by the reservoir water level
and the release.
Scheme 1
Convenonal fixed scheme
Scheme 2
Date
Fig. 2. Sketch of three FLWL schemes with the same flood prevention standard.
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P. Liu et al. / Journal of Hydrology 527 (2015) 1045–1053
(5) Maximization of the reservoir carryover storage, which can
be described by the average end water level as follows:
Max Z e ðZ x Þ ¼ 1n
n
X
Z i;m
ð10Þ
i¼1
where Zi,m is the reservoir water level on the end date of the
flood season of the ith year.
In summary, Eqs. (4) and (6) describe the reservoir ability for
flood control, and Eqs. (7) and (8) describe hydropower generation.
The navigation benefits are described by Eq. (9), and the reservoir
refill index is considered in Eq. (10).
2.2.1.2. Constraints.
(1) Reservoir water balance equation:
widely applied in reservoir operation (e.g., Liu et al., 2006, 2011).
The multi-objective GA known as non-dominated sorting genetic
algorithm-II (NSGA-II) (Deb et al., 2002) is implemented to identify
a large set of Pareto solutions to this simulation-based optimization model because it is powerful both in theoretical (Deb et al.,
2002) and practical problems (Kim et al., 2006; Liu et al., 2011).
Note that the five objectives compete with each other. The traditional algorithms often transform the multi-objective into a single
objective problem using weighting factors to achieve the optimal
solution (Zhou and Guo, 2014). The Pareto solutions are derived
based on fast-non-dominated-sort and crowded-comparison operation in NSGA-II (Deb et al., 2002).
3. Case study
V i;jþ1 ¼ V i;j þ ðIi;j Oi;j Þt i ¼ 1; 2; . . . ; n j ¼ 1; 2; . . . ; m 1
ð11Þ
where Ii,j and Oi,j are the reservoir inflow and release on jth
day of the ith year, respectively, and t is the time interval.
(2) Compared with the designed single FLWL, the flood control
ability should not be reduced, i.e., Eq. (3) applies, along with
the following:
V f ðZ x Þ P V f ðZ 0 Þ
ð12Þ
RðZ x Þ 6 RðZ 0 Þ
ð13Þ
where V f ðZ 0 Þ and RðZ 0 Þ are the flood control performances
using the designed single FLWL Z0. The above constraints
indicate that a feasible scheme should be satisfied with the
risk not only for observed streamflow but also for the
designed seasonal flood.
2.2.2. Solving method
Because the seasonal FLWL is nonlinearly related to the reservoir benefits, the above model is difficult to be optimized by using
classical optimization methods, such as linear programming and
dynamic programming (Ahmad et al., 2014). Consequently, a
simulation-based optimization model is used to derive the seasonal FLWL.
GA is an optimization method that is based on the simulation of
natural genetics and the natural selection mechanism and has been
3.1. Three Gorges Reservoir
The Three Gorges Reservoir (TGR), located in the Yichang City of
China’s Hubei Province (Fig. 3), is used for a case study. The TGR is
vitally important and is the backbone project for the water
resources management of China’s largest river, the Yangtze River.
The upstream of the Yangtze River is intercepted by the TGR, with
a main course length of approximately 4.5 103 km and a contributing drainage area of 1.0 106 km2. The mean annual runoff
at the dam site is 451 billion m3.
Fig. 4 shows the index water levels and storage zones of the TGR
(MWR, 2009). With a normal pool level of 175 m, the total storage
capacity is 39.3 billion m3. The conventional FLWL is a fixed value,
145 m.
The TGR is the greatest hydro-development system ever built in
the world, providing multiple benefits, including flood control,
hydropower generation and navigation improvement. In particular, flood control is the most important role of the TGR because
the TGR downstream is the plain region of the middle and lower
reaches of the Yangtze River, which is a populous and developed
area that suffered frequent and disastrous flood threats in the past.
With a flood control storage (storage between the FLWL and normal pool level) of 22.15 billion m3, the downstream flood prevention standard can be improved from the 20-year return period to
the 100-year return period. Equipped with 32 sets of 700 MW
hydraulic turbo generators and 2 sets of 50 MW hydraulic turbo
generators, the TGR is the largest hydropower station in the world,
with the total capacity of 22,500 MW.
Fig. 3. Location of the TGR and TGR basin in China.
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P. Liu et al. / Journal of Hydrology 527 (2015) 1045–1053
3.2. Conventional FLWL
175m
155m
The conventional operating rules of the TGR during flood seasons are as follows: the reservoir water level is gradually
decreased from the dry control water level (155 m) to the
FLWL (145 m) from June 1st to 10th, and then, the reservoir
water level is kept at this fixed FLWL during the entire flood season. When the inflow exceeds the downstream safety discharge,
the flood peak is reduced by retaining redundant floodwater. In
this case, the floodwater is released through the spillways when
the hydropower generation reaches its maximum capacity. Once
the flood has subsided, the reservoir water level should return to
145 m to offer adequate storage for another potential flood. The
reservoir is refilled to the normal pool level of 175 m from
October.
The current conventional operating rules during the flood season are easy to implement, but the floodwater utilization rate is
lower due to the surplus water released from the reservoir in the
pre-flood season and the post-flood season. In addition, the reservoir is difficult to refill to the normal pool level during a dry year
(Liu et al., 2006). Therefore, it is necessary to re-design the FLWL
of the TGR to make full use of the floodwater without reducing
the flood prevention standard.
Normal pool level
Flood control
storage
Dry control water level
145m
Flood limited water level
Conservaon storage
Dead water level
Dead storage
Fig. 4. Sketch of index water levels and storage zones of the TGR.
Table 1
Comparison of the seasonal and annual designed floods for the TGR, where Qm denotes maximum discharge, and W3d, W7d, and W15d denote maximum water volumes of 3-days,
7-days and 15-days, respectively.
Scheme
Flood duration
Annual maximum flood
Pre-flood season
Main flood season
Post-flood season
Return period (year)
Cv
Cs/Cv
10,000
1000
100
20
Qm (m3/s)
W3d (billion m3)
W7d (billion m3)
W15d (billion m3)
51,400
128.4
272.0
513.7
0.21
0.21
0.19
0.19
4.0
4.0
3.5
3.0
111,800
279.1
540.5
999.7
97,800
244.3
481.3
895.5
82,900
207
416.7
780.6
71,400
178.2
365.6
688.4
Qm (m3/s)
W3d (billion m3)
W7d (billion m3)
W15d (billion m3)
Qm (m3/s)
W3d (billion m3)
W7d (billion m3)
W15d (billion m3)
Qm (m3/s)
W3d (billion m3)
W7d (billion m3)
W15d (billion m3)
31,600
77
160
288
50,800
127
268
500
33,600
83
179
345
0.25
0.234
0.225
0.213
0.21
0.21
0.19
0.19
0.281
0.284
0.283
0.279
4.0
4.0
4.0
3.0
4.2
4.1
3.8
3.55
2.0
2.0
2.0
2.0
76,200
178.6
355.5
593.2
111,500
277.3
538.9
996.4
77,400
192.8
409.4
783.2
65,800
155.2
311.4
527.8
97,400
242.4
478.3
886.7
68,500
170.4
363.1
695.1
54,800
130.2
263.7
455.6
82,200
205.1
412.4
767.2
58,400
145.3
310.7
595.4
46,200
110.8
226.4
397.7
70,600
176.3
360.7
672.8
50,200
124.6
267.3
513.0
120000
Empirical posion of annual maximum
P3 distribuon of annual maximum
Joint distribuon of seasonal maximum
100000
80000
60000
40000
20000
Fig. 5. Comparison of the seasonal and annual designed flood curves for the TGR.
99.9
98
99
99.5
95
90
80
30
40
50
60
70
20
10
5
0.5
1
2
0.05
0.1
0.005
0.01
Probability (%)
0
0.001
Flood peak (m3/s)
Seasonal maximum flood
Statistical parameter
Mean
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P. Liu et al. / Journal of Hydrology 527 (2015) 1045–1053
3.3. Optimization of seasonal FLWL
maximum is close to that of the annual maximum by using the
validation Eq. (2). For example, Fig. 5 shows how the constructed
Copula joint distribution fits the designed original annual maximum curves, where the Frank Copula parameters of the flood peak
are h1 ¼ 0:4347 and h2 ¼ 0:8100.
Fig. 6 shows the surface for the seasonal design floods with a
100-year return period, based on the Frank Copula function. It is
shown that numerous schemes of seasonal design floods can
3.3.1. Seasonal design floods
The Pearson Type Three (PE3) probability curve is used for the
marginal distribution of seasonal floods. Table 1 presents a seasonal design flood for the TGR, which indicates that the seasonal
flood quantiles are decreased compared with those of the annual
maximum flood. However, the joint distribution of the seasonal
x 104
Main flood season (m3/s)
10
9.5
9
8.5
8
5
6
6
7
x 104
7
8
Pre-flood season
(m3/s)
8
9
10
9
10
Post-flood season (m3/s)
x 104
Fig. 6. Surface formed by the design discharges of the pre-flood, main flood and post-flood seasons, which have a joint 100-year return period.
46.7
100
99.6
151.5
97.4
Navigaon
reliability (%)
140.2
End water
level (m)
Direcon of increasing
preference
22.5
Convenonal FLWL
21.0
Flood storage
volume (Billion m3)
44.0
Hydropower generaon
(Billion kWh)
80
Hydropower
reliability (%)
Fig. 7. Parallel line plot for the operational profits of selected Pareto solutions and the conventional FLWL.
Table 2
Selected Pareto solutions of the seasonal FLWL schemes.
Scheme
Conventional
Preference end water level
Preference hydropower generation
Preference flood control
Recommended
Flood control
storage (billion m3)
Hydropower
generation
(billion kW h)
Hydropower
reliability (%)
Navigation
reliability (%)
Average water
level on 30th
September (m)
Flood limited water level (m)
Pre-flood
Main flood
Post-flood
21.03
22.23
21.35
22.47
21.47
46.00
45.03
46.69
45.03
46.59
99.45
97.39
99.55
99.51
99.49
100.00
100.00
100.00
83.64
100.00
145.00
151.50
144.88
141.59
145.58
145.00
147.36
152.62
150.44
152.67
145.00
142.29
144.29
142.03
144.02
145.00
151.50
144.88
141.59
145.58
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P. Liu et al. / Journal of Hydrology 527 (2015) 1045–1053
satisfy a given flood prevention standard. The proposed method is
able to produce a set of seasonal floods that meet the requirements
of the annual flood prevention standard.
3.3.2. Simulation-based optimization
The daily streamflow record during June 1st to September 30th
from 1882 to 2010 at the Yichang hydrologic station was used as
Water level (m)
155
Convenonal FLWL
Preference flood control
Preference hydropower generaon
Preference end water level
Opmal (recommended)
150
145
140
Jun
Jul
Aug
Sep
Oct
Fig. 8. Selected four seasonal FLWL schemes.
156
80000
Inflow
Opmal release
Convenonal release
Opmal water level
Convenonal water level
60000
152
50000
148
40000
30000
Water level (m)
Discharge (m3/s)
70000
144
20000
10000
0
Jun
Jul
Aug
Sep
Oct
140
(a) Wet year (1981).
156
Inflow
Opmal release
Convenonal release
Opmal water level
Convenonal water level
Discharge (m3/s)
40000
152
30000
148
20000
Water level (m)
50000
144
10000
0
Jun
Jul
Aug
Sep
Oct
140
(b) Normal year (1904).
156
Inflow
Opmal release
Convenonal release
Opmal water level
Convenonal water level
Discharge (m3/s)
40000
152
30000
148
20000
Water level (m)
50000
144
10000
0
Jun
Jul
Aug
Sep
Oct
140
(c) Dry year (2008).
Fig. 9. Reservoir operation of the conventional FLWL and the optimal FLWL for three representative years.
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P. Liu et al. / Journal of Hydrology 527 (2015) 1045–1053
the inflow for TGR to optimize the seasonal FLWL in the simulation–optimization model. The water level at June 1st was set to
155 m based on the TGR operating rules (MWR, 2009). The
multi-objective genetic algorithm NSGA-II (Deb et al., 2002) is used
for optimization. With a generation of 50,000, the population number is set to 400 because it takes one day to complete the computation. Because three sub-seasons are pre-defined, their seasonal
frequencies that are satisfied with the original flood prevention
standard can be treated as three real decision variables to be
optimized.
3.3.3. Operational profits
Fig. 7 shows multiple Pareto solutions for various seasonal
FLWL schemes using a parallel line (Kasprzyk et al., 2012;
Herman et al., 2014). The figure indicates that flood control competes with hydropower generation. Table 2 lists five seasonal
FLWL schemes: the conventional, preference end water level, preference hydropower generation, preference flood control and recommended FLWL. As shown in Fig. 7 and Table 2, most derived
Pareto solutions have an overall better performance than the conventional FLWL in the flood storage volume, hydropower generation, the reliabilities of navigation and hydropower as well as the
end water level. The analytic hierarchy process (AHP) (Saaty,
1990) is used to determine numerical priorities of Pareto solutions
by trading off the multiple objectives, where the flood control is
more important than hydropower generation and navigation.
Thus the recommended FLWL is selected and used as the optimal
FLWL for the further analysis.
Fig. 8 shows these five selected schemes, demonstrating that
the optimized schemes decrease the FLWL and enhance the flood
control ability during the main flood season. These schemes
increase the FLWL of pre-flood and post-flood seasons, thereby
improving hydropower generation and navigation for the entire
flood season. Note that the FLWL can be increased to above the
conventional fixed FLWL by using the dynamic control method
(Li et al., 2010; Chou and Wu, 2013) when hydrologic forecasting
is used (Pianosi and Soncini-Sessa, 2009; Zhao et al., 2011).
Table 2 indicates that the produced seasonal FLWL schemes can
increase flood control storage compared with the conventional
FLWL scheme. The flood risks are estimated by reservoir routing
the designed seasonal floods and the observed streamflow from
1882 to 2010. The risks are found to be less than or equal to that
of the conventional FLWL. In particular, the preferred flood control
scheme is able to enhance the flood prevention ability without significantly decreasing the sources of profits, such as hydropower
generation and navigation.
As presented in Table 2, the recommended FLWL scheme produces 46.59 billion kW h hydropower, with a flood-control storage
level of 21.7 billion m3, which is acceptable because it is greater
than that of the conventional FLWL. In addition, the end water level
is higher than the conventional one, which means that more
hydropower can be produced.
Table 2 indicates that the reliability for navigation reaches
100%, that is, the recommended seasonal FLWL does not affect
navigation.
3.3.4. Operation of typical years
Three typical years, 1981, 1904 and 2008, are selected to
describe the wet, normal and dry years, respectively, because their
empirical probabilities of the water volume are nearly 25%, 50%
and 75%, respectively. Fig. 9 shows the reservoir simulation results
of the recommended and conventional FLWL for three typical
years. The recommended seasonal FLWL has a lower water level
compared with that of the conventional one during the wet year,
indicating an improved flood control ability.
4. Conclusions
This study focused on the optimization of the seasonal FLWL.
The Copula function was used to build the joint distribution of
seasonal floods and then form a constraint of the simulation-based
optimization model. Based on the results of a case study of
China’s TGR, the following conclusions could be drawn:
(1) Because numerous schemes of seasonal design floods can be
satisfied with a given flood prevention standard, the seasonal FLWL can be derived by using the optimization
method.
(2) The TGR results indicate that the optimal design of the seasonal FLWL can effectively tradeoff among the various benefits, including flood control, hydropower generation and
navigation. The optimal design of the seasonal FLWL can
enhance the utilization rate of water resources during the
flood season without reducing the original flood prevention
standards.
Although a framework for the optimal design of the seasonal
FLWL has been established, a number of issues, such as determining the acceptable risk and dynamic control of FLWL based on
hydrologic forecasting, require further research.
Acknowledgments
This study was supported by the National Natural Science
Foundation of China (51422907) and the Program for the New
Century Excellent Talents in University (NCET-11-0401). The
authors thank the editor and the anonymous reviewers for their
comments, which helped improve the quality of the paper.
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