Journal of Hydrology 531 (2015) 977–991
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Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol
Integrated optimal allocation model for complex adaptive system
of water resources management (II): Case study
Yanlai Zhou a,b,⇑, Shenglian Guo b, Chong-Yu Xu b,c, Dedi Liu b, Lu Chen d, Dong Wang a
a
Changjiang River Scientific Research Institute, Wuhan 430010, China
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
c
Department of Geosciences, University of Oslo, Norway
d
College of Hydropower & Information Engineering, Huazhong University of Science & Technology, Wuhan 430074, China
b
a r t i c l e
i n f o
Article history:
Available online 23 October 2015
This manuscript was handled by Geoff
Syme, Editor-in-Chief
Keywords:
Water resources management
Complex adaptive system
Optimal allocation
Multi-objective
Agent-based
Dongjiang River
s u m m a r y
Climate change, rapid economic development and increase of the human population are considered as
the major triggers of increasing challenges for water resources management. This proposed integrated
optimal allocation model (IOAM) for complex adaptive system of water resources management is applied
in Dongjiang River basin located in the Guangdong Province of China. The IOAM is calibrated and validated under baseline period 2010 year and future period 2011–2030 year, respectively. The simulation
results indicate that the proposed model can make a trade-off between demand and supply for sustainable development of society, economy, ecology and environment and achieve adaptive management of
water resources allocation. The optimal scheme derived by multi-objective evaluation is recommended
for decision-makers in order to maximize the comprehensive benefits of water resources management.
Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction
This is part 2 of the paper on integrated optimal allocation
model (IOAM) for complex adaptive system of water resources
management. It presents case study, results and discussion in
accordance to the application of IOAM described in Part 1. The
Dongjiang River basin located in the Guangdong Province of China
is selected as a case study. The main objective of this application is
to determine the capability of the proposed methods to adaptively
manage water resources allocation.
2. Case study description
The Dongjiang River basin is one of the main sources for available surface water in the Guangdong Province of China found in
numerous reservoirs and rivers. The river tributaries contain
Lijiang river, Xinfengjiang river, Qiuxiangjiang river, Gongzhuangshui river, Xizhijiang river and Zengjiang river from upstream to
downstream in Dongjiang River basin. The administrative cities
include Meizhou city Heyuan city, Shaoguan city, Huizhou city,
Dongguan city, Shenzhen city, and Zengcheng city in Dongjiang
River basin. Three kinds of nodes including reservoir node, water
⇑ Corresponding author at: Changjiang River Scientific Research Institute, Wuhan
430010, China. Tel./fax: +86 27 68773568.
E-mail address: zyl23bulls@whu.edu.cn (Y. Zhou).
http://dx.doi.org/10.1016/j.jhydrol.2015.10.043
0022-1694/Ó 2015 Elsevier B.V. All rights reserved.
user node and hydrological station node are used to generalize
the elements of Dongjiang river basin. Three reservoirs with strong
regulation capacity, i.e., Xinfengjiang reservoir, Fengshuba reservoir and Baipenzhu reservoir are selected as reservoir nodes. Four
hydrological stations, i.e., Heyuan, Xizhijiang, Boluo and Guanhaikou are selected as hydrological station nodes. The behaviors
of water user nodes include water intake from river and water
return to river. The Dongjiang River basin in the Guangdong province is divided into six water use regions with water-intakes
No. 1–6 according to the locations of reservoir node, water user
node and hydrological station node. Sketch of the Dongjiang River
basin is shown in Fig. 1. Characteristics of Dongjiang River basin
and reservoirs are shown in Tables 1 and 2.
3. Results and discussion
3.1. Calibration of integrated optimal allocation model
3.1.1. Model inputs, boundary conditions and algorithm parameters
The meteorology, hydrology, reservoir and hydropower station
parameter, production and domestic water use and demand, ecological water demand, sewage treatment, population, economic
growth rate as well as optimal algorithm parameter data, etc.,
are required for input of integrated optimal allocation model. The
data includes: (1) meteorological and hydrological data extracting
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Y. Zhou et al. / Journal of Hydrology 531 (2015) 977–991
Water-intake No.1
Water-intake No.3
Water-intake No.2
Water-intake No.4
Water-intake No.5
Water-intake No.6
Fig. 1. Sketches of Dongjiang River basin in the Guangdong Province of China.
from Portal of Chinese Science and Technology Resource (http://
www.escience.gov.cn), rainfall of 2010 year selected as typical year
is close to annual average rainfall in Dongjiang river basin; (2) the
characteristic parameters of Xinfengjiang reservoir, Fengshuba
reservoir and Baipenzhu reservoir in Dongjiang river basin, as
shown in Table 2, extracting from Dongjiang River Basin Administration (http://www.djriver.cn); (3) production and domestic
water use and demand, as well as sewage treatment parameters,
extracting from Water Resources Department of Guangdong Province (http://www.gdwater.gov.cn); (4) Tennant described an
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Y. Zhou et al. / Journal of Hydrology 531 (2015) 977–991
Table 1
The characteristics of Dongjiang River basin.
Water-intake
Region
Administrative city
Administrative county
Area of Dongjiang River
sub-basin (km2)
No. 1
Upstream in Fengshuba reservoir node
Meizhou
Heyyuan
Xingning
Heping
Longchuan
272
300
1055
No. 2
Upstream in Xinfengjiang reservoir node
Heyyuan
Heping
Lianping
Dongyuan
Xinfeng
490
1962
1805
1232
Shaoguan
No. 3
Area between Xinfengjiang reservoir
node and Heyuan hydrological station node
Heyyuan
Longchuan
Heping
Dongyuan
1225
1496
2200
No. 4
Xizhijiang river basin
Huizhou
Huidong
Huiyang district
2775
992
No. 5
Area between Heyuan hydrological station
node and Boluo hydrological station node
excluding Xizhijiang river basin
Heyuan
Heyuan district
Zijin
Huizhou district
Boluo
362
2751
1439
1655
Area between Boluo hydrological station
node and Guanhaikou hydrological station node
Huizhou
Boluo
Longmen
Zengchen district
Dongguan district
Shenzhen district
1200
2267
1744
2472
1864
No. 6
Huizhou
Zengchen
Dongguan
Shenzhen
Table 3
Monthly inner-river ecological water demand in four hydrological control stations
based on Tenant method.
Table 2
The characteristics of three reservoirs in Dongjiang river basin.
Item
Unit
Xinfengjiang
Fengshuba
Baipenzhu
Located river
/
Catchment area
Crest elevation
Total reservoir
volume
Normal pool level
Volume under
normal pool level
Inactive water level
Inactive volume
Installation capacity
Guaranteed output
Annual average
power generation
Regulation ability
Initial water level
Initial volume
km2
m
Billion m3
Xinfengjiang
river
5734
124.0
13.896
Dongjiang
river
5150
173.3
1.94
Xizhijiang
river
856
88.2
1.19
m
Billion m3
116.0
10.80
166.0
1.54
75.0
0.57
m
Billion m3
MW
MW
Billion
kW h
–
m
Billion m3
93.0
4.30
302.5
90.0
0.90
125.0
0.24
160.0
38.0
0.55
62.0
0.19
24.0
7.9
0.08
Multi-year
108.30
8.18
Annual
156.63
1.10
Multi-year
69.88
0.38
effective methodology for determining ecological water demand to
protect aquatic resources in river, based on average flow (Tennant,
1976). The Tennant method has been used to calculate year or
month ecological water demand of aquatic resources in regions
with missing ecological data. However, the disadvantage of this
method is that it cannot consider the seasonal or daily ecological
water demand of aquatic resources especially in flood season. Since
the Tennant method has a powerful ability of practical problems in
China (Zhou and Guo, 2013), it is selected as estimating month ecological water demand in this study. Therefore, the ecological water
demand is estimated using Tennant method with observed month
inflows from 1986 to 2005 year in four hydrological control stations, Heyuan, Xizhijiangkou, Boluo and Guanhaikou, as shown in
Table 3; (5) population, economic growth rate extracting from
Statistic Bureau of Guangdong Province (http://www.gdstats.gov.
cn, Guangdong Statistical Yearbook, 2010 year); (6) parameters of
non-dominated sorting genetic algorithm II (NSGA-II), i.e., population size = 1000, maximum iteration = 10,000, probability of crossover = 0.60 and probability of mutation = 0.10 (Reed et al., 2003;
Hydrological
station
Monthly inner-river
ecological water demand
from April to September
(m3/s)
Monthly inner-river
ecological water demand
from October and December,
and from January to March in
the next year (m3/s)
Heyuan
Xizhijiangkou
Boluo
Guanhaikou
285
65
480
280
270
40
352
220
Kapelan et al., 2005); (7) the weighting factors of annual average
Gini coefficient between population and water consumption
(AGini-P), annual average Gini coefficient between gross domestic
product and water consumption (AGini-GDP) and annual average
Gini coefficient between available water resources and water consumption (AGini-AWR) are 1/3, 1/3 and 1/3, respectively, in order
to balance the importance among population, gross domestic product, available water resources and water consumption; (8)
parameters of accelerating genetic algorithm (AGA), i.e., population
size = 400, maximum iteration = 100, probability of crossover = 0.80 and probability of mutation = 0.20 (Chen and Yang,
2007; Fang et al., 2009).
3.1.2. Simulation results under baseline period
Because simulation results of four objectives are Pareto optimal
set, not unique solution, boxplots of evaluating indexes for different objectives are compared with observed values in typical year
2010.
(1) Social objective analysis
The simulation results of water consumption for best and worst
of social objectives are compared with observed values of water
consumption in different water-intakes and Dongjiang river basin,
as shown in Fig. 2(a). The simulation values of water consumption
in the best of social objective are 273.29, 621.21, 525.50, 1607.03,
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Y. Zhou et al. / Journal of Hydrology 531 (2015) 977–991
Fig. 2. Pareto fronts and observed values of (a) water consumption, (b) economic value-added by agriculture, (c) economic value-added by industry, (d) water supply for
agriculture, (e) water supply for industry, (f) total sewage discharge, (g) discharge of COD, (h) discharge of ammonia–nitrogen and (i) outer-river ecological water shortage in
different water-intakes under baseline period.
706.41, 6878.85 and 10612.29 million m3, respectively for waterintakes No. 1–6 and Dongjiang river basin. The simulation values
of water consumption in the worst of social objective are 259.42,
542.06, 517.24, 1572.96, 641.66, 6696.62 and 10229.96 million m3,
respectively for water-intakes No. 1–6 and Dongjiang river basin.
The observed values of water consumption are 263.84, 575.10,
521.12, 1590.43, 678.03, 6801.07 and 10429.59 million m3,
respectively for water-intakes No. 1–6 and Dongjiang river basin.
Y. Zhou et al. / Journal of Hydrology 531 (2015) 977–991
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Fig. 2 (continued)
Moreover, the boxplot Fig. 2(a) shows that the observed value of
water consumption is located in the interval of water consumption
between the best and worst of social objectives.
(2) Economic objective analysis
The economic data includes agricultural production and industrial production. The agricultural production is composed of rice
paddy, irrigated land, vegetable field, aquafarm, orchard and cattle.
Industrial production is made up of textile, papermaking, petrochemical, metallurgy, food processing, building material, electron,
machinery, thermal power industry, commercial and catering
industry. The simulation results of economic value-added and
water supply in best and worst of economic objectives are compared with observed values in different water-intakes and
Dongjiang river basin, as shown in Fig. 2(b)–(e). Take economic
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Y. Zhou et al. / Journal of Hydrology 531 (2015) 977–991
Fig. 2 (continued)
value-added by agriculture for example, the simulation values of
economic value-added by agriculture in the best of economic
objective are 0.833, 1.574, 1.663, 3.873, 1.795, 5.554 and
15.292 billion yuan, respectively for water-intakes No. 1–6 and
Dongjiang river basin. The simulation values of economic valueadded by agriculture in the worst of economic objective are
0.755, 1.469, 1.492, 3.318, 1.555, 4.937 and 13.526 billion yuan,
respectively for water-intakes No. 1–6 and Dongjiang river basin.
The observed values of economic value-added by agriculture are
0.758, 1.482, 1.547, 3.447, 1.616, 5.165 and 13.98 billion yuan,
respectively for water-intakes No. 1–6 and Dongjiang river basin.
Besides, the boxplot Fig. 2(b)–(e) shows that the observed values
are located in the interval of simulated values between the best
and worst of economic objectives, respectively.
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Y. Zhou et al. / Journal of Hydrology 531 (2015) 977–991
1
1
Social objective
Environmental objective
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
Economic objective
Fig. 3. The contour plot for Pareto set of economic, environmental and social
objectives under baseline period.
basin, as shown in Fig. 2(i). It is worth mentioning that all of innerriver ecological water shortages are zero in water-intakes No. 1–6
and Dongjiang river basin. Moreover, the maximum, observed and
minimum ecological outer-river ecological water shortages in
Dongjiang river basin are only 0.3621, 0.3493 and 0.3282 milliom m3, respectively. Therefore, both of outer-river and innerriver ecological water demands are basically satisfied in waterintakes No. 1–6 and Dongjiang river basin. The simulation values
of outer-river ecological water shortages in the best of ecological
objective are 0.0060, 0.0044, 0.0123, 0.0187, 0.0201 and
0.2668 million m3, respectively for water-intakes No. 1–6. The simulation values of outer-river ecological water shortages in the
worst of environmental objective are 0.0066, 0.0048, 0.0135,
0.0206, 0.0222 and 0.2943 million m3, respectively for waterintakes No. 1–6. The observed values of ecological outer-river ecological water shortages are 0.0064, 0.0047, 0.0130, 0.0197, 0.0214
and 0.2841 million m3, respectively for water-intakes No. 1–6.
Besides, the boxplot Fig. 2(i) shows that the observed values are
located in the interval of simulated values between the best and
worst of environmental objectives, respectively.
(5) Analysis of competitive relationship between optimal
objectives
(3) Pollutant index analysis
Because of availability of pollutants in Dongjiang River basin,
total sewage discharge, COD and ammonia–nitrogen are selected
as pollutant indexes. The simulation results of total sewage discharge, discharge of COD and discharge of ammonia–nitrogen in
best and worst of environmental objectives are compared with
observed values in different water-intakes and Dongjiang river
basin, as shown in Fig. 2(f)–(h). Take total sewage discharge for
example, the simulation values of total sewage discharge in the
best of environmental objective are 47.57, 115.19, 102.18,
524.00, 218.43, 2463.65 and 3471.02 million ton, respectively for
water-intakes No. 1–6 and Dongjiang river basin. The simulation
values of total sewage discharge in the worst of environmental
objective are 49.20, 119.38, 105.77, 542.91, 225.79, 2522.28 and
3565.33 million ton, respectively for water-intakes No. 1–6 and
Dongjiang river basin. The observed values of total sewage discharge are 48.47, 117.46, 104.12, 535.11, 222.37, 2497.18 and
3524.72 million ton, respectively for water-intakes No. 1–6 and
Dongjiang river basin. Moreover, the boxplot Fig. 2(f)–(h) shows
that the observed values are located in the interval of simulated
values between the best and worst of environmental objectives,
respectively.
(4) Ecological objective analysis
The simulation results of outer-river and inner-river ecological
water shortages in best and worst of ecological objectives are compared with observed values of outer-river and inner-river ecological water shortages in different water-intakes and Dongjiang river
Because outer-river and inner-river ecological water demands
are basically satisfied in Dongjiang river basin, the competitive
relationship between ecological objective and other optimal objectives is unremarkable. The contour plot for Pareto set of economic,
environmental and social objectives is shown in Fig. 3. The values
of economic, environmental and social objectives are standardized
before they are used in Fig. 3. Fig. 3 shows that the competitive
relationship between economic objective and environmental
objective is remarkable. Besides, the superior economic objective
matches with the inferior environmental objective as well as the
value of social objective decrease with the increasing values of economic and environmental objectives. However, the relationship
between economic and environmental objectives is not singlevalued, but multi-valued mapping with the value of social objective. The reasons are that (1) water resources are allocated equally
according to population, GDP and available water resources in different administrative regions in order to maximize the social benefit, however, water resources are allocated preferentially for
administrative region with high economic benefit per unit water
consumption so as to maximize economic benefit; (2) underdeveloped region are usually rich in water resources, but has low population and low water use efficiency with high discharge of sewage
and pollutant, water resources are allocated preferentially for
underdeveloped region in order to maximize the social benefit.
3.1.3. Multi-objective evaluation of simulation result under baseline
period
Multi-objective evaluation module is used to evaluate the efficiency of optimal module and select out the optimal scheme of
Table 4
The result of multi-objective evaluation under baseline period.
Scheme
Number
IGini
AGDP (108 yuan)
VPIST (104 ton)
Projection value
Rank in population size 1000
Social objective
1
2
0.30255
0.31484
16,237
16,134
352,555
350,203
1.0694
0.1379
16
995
Economic objective
3
4
0.30444
0.30912
16,496
15,845
356,566
347,134
0.9990
0.5006
120
645
Environmental objective
5
6
0.30912
0.30444
15,845
16,496
347,134
356,566
0.5006
0.9990
645
120
The best scheme
The worst scheme
7
8
0.30266
0.31460
16,452
16,134
354,061
352,555
1.0747
0.1033
1
1000
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Y. Zhou et al. / Journal of Hydrology 531 (2015) 977–991
Fig. 4. The trend graphs for annual rainfall and runoff series in different water-intakes under future period.
water resources allocation. Because outer-river and inner-river
ecological water demands are basically satisfied in water-intakes
No. 1–6 and Dongjiang river basin, the competitive relationship
between ecological objective and other optimal objectives is
unremarkable. Therefore, only three multi-objective functions are
selected as multi-objective evaluation indices, i.e., (1) minimizing
the integrated Gini coefficient (IGini), (2) maximizing the annual
average GDP (AGDP), (3) minimizing the volume of pollutant index
of sewage treatment (VPIST), excluding minimizing the ecological
water shortage (EWS). Because population size is equal to 1000
in NSGA-II algorithm, 1000 Pareto set of economic, environmental
and social objectives are applied to multi-objective evaluation of
simulation result under baseline period. The result of
multi-objective evaluation is shown in Table 4, just showing
scheme No. 1 with the best of social objective, scheme No. 2 with
the worst of social objective, scheme No. 3 with the best of economic objective, scheme No. 4 with the worst of economic objective, scheme No. 5 with the best of environmental objective,
scheme No. 6 with the worst of environmental objective, scheme
No. 7 with the best scheme in Pareto set and scheme No. 8 with
the worst scheme in Pareto set. It is shown that the projection values of schemes No. 1–8 are 1.0694, 0.1379, 0.9990, 0.5006, 0.5006,
0.9990, 1.0747 and 0.1033, respectively, and the ranks of schemes
No. 1–8 are 16, 995, 120, 645, 645, 120, 1 and 1000, respectively. It
is worth mentioning that the superior economic objective matches
with the inferior environmental objective, and vice versa. Besides,
the variables of unit projection vector are equal to 0.9651, 0.2199
and 0.1422 for social objective IGini, economic objective AGDP
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Y. Zhou et al. / Journal of Hydrology 531 (2015) 977–991
Population (104)
3,000
2,900
Value-added by secondary industry (10 yuan)
3,100
Feasible zone of population between
middle and low growth rate
2,800
2,700
2,600
2020
2030
26,000
19,000
12,000
5,000
2010
2020
Year
(a)
(b)
65,000
55,000
Feasible zone of value-added by secondary industry
33,000
Year
2030
225,000
Feasible zone of value-added by tertiary industry
Domestic water demand (104m3)
Value-added by tertiary industry (108yuan)
2,500
2010
40,000
8
Feasible zone of population between
high and middle growth rate
45,000
35,000
25,000
15,000
5,000
2010
2020
2030
Feasible zone of domestic water demand
210,000
195,000
180,000
165,000
150,000
2010
2020
Year
Year
(c)
(d)
2030
Fig. 5. The feasible zones of (a) population, (b) economic value-added by secondary industry, (c) economic value-added by tertiary industry and (d) domestic water demand
in Dongjiang river basin under future period.
and environmental objective VPIST, respectively. It indicates that
the social objective is the most important evaluation index. Moreover, the importance of environmental objective is superior to that
of environmental objective in order to maximizing the comprehensive benefits of water resources management.
Therefore, the recommendation of Pareto optimization schemes
as follows: (1) the scheme No. 1 is recommended for decisionmakers in order to maximize the social benefit, (2) the scheme
No. 3 or 6 is recommended for decision-makers in order to maximize the economic benefit, (3) the scheme No. 4 or 5 is recommended for decision-makers in order to maximize the
environmental benefit, (4) the scheme No. 7 is recommended for
decision-makers in order to maximize the comprehensive benefits
of water resources management under baseline period.
3.2. Scenario analysis under future period
Scenario analysis for water resources management is defined as
the process of estimating the expected value of a portfolio after a
given period of time, assuming specific changes in the values of
the portfolio’s key factors that would affect comprehensive benefits of water resources management, such as changes in meteorol-
ogy, hydrology, population development and economic
development (Swart et al., 2004). Moreover, the scenario analysis
enables decision-makers to face the future calmly and it is selected
as the uncertainty analysis method for water resources management (Pallottino et al., 2005; Lautenbach et al., 2009; Ehlen and
Vargas, 2013; Thiam et al., 2015).
3.2.1. Meteorological and hydrologic scenario analysis
Meteorological and hydrological data extracts from Portal of
Chinese Science and Technology Resource (http://www.escience.gov.cn). Because of availability of meteorological and hydrological
data in Dongjiang river basin, rainfall and runoff series from
1986 year to 2005 year are selected as meteorological and hydrologic scenario under future period 2011–2030 year. The trend
graph for annual rainfall and runoff series of future period in different water-intakes is shown in Fig. 4. It is shown that (1) variation
tendency between rainfall and runoff is synchronous in Dongjiang
river basin, (2) the years from 2011 to 2015 year are dry years, the
years from 2016 to 2020 year are wet years and alternation
between dry year and wet year happens from 2020 to 2030 year
in Dongjiang river basin.
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Y. Zhou et al. / Journal of Hydrology 531 (2015) 977–991
3.2.2. Population development scenario analysis
Population data extracts from Statistic Bureau of Guangdong
Province (http://www.gdstats.gov.cn, Guangdong Statistical Yearbook, from 2001 and 2010 year). Three kinds of population growth
rates in different water-intakes are set up for population development scenario of future period, i.e., high, middle and low growth
rate of population. The Malthusian growth model is essentially
exponential growth based on a constant rate (Holdren, 1971).
The model is named after Malthusian model, the form as follows:
PðtÞ ¼ P0 ert
ð1Þ
where P0 is the initial population size in baseline period 2010 year;
r is the population growth rate, sometimes called Malthusian
parameter; t is the time; P(t) is the population in time t.
The feasible zone of population in Dongjiang river basin under
future period is calculated by the Malthusian growth model, as
shown in Fig. 5(a). It is shown that (1) uncertainty of population
growth in Dongjiang river basin increases as time goes on, (2) population quantity lies between 26.63 million and 27.10 million by
the end of 2015 year, population quantity lies between 27.53 million and 28.47 million by the end of 2020 year as well as population quantity lies between 28.91 million and 30.69 million by the
end of 2030 year.
3.2.3. Economic development scenario analysis
Economic development scenario analysis in Dongjiang river
basin involves economic value-added by secondary industry and
tertiary industry as well as water price development scenario.
(1) Economic value-added by secondary industry and tertiary
industry
Economic data including economic growth rate as well as proportion of agriculture, secondary industry and tertiary industry
extracts from Statistic Bureau of Guangdong Province
(http://www.gdstats.gov.cn, Guangdong Statistical Yearbook, from
2001 to 2010 year). Two kinds of economic growth rates in different water-intakes are set up for economic development scenario of
future period, i.e., high and low growth rate of economy. The feasible zones of economic value-added by secondary industry and tertiary industry in Dongjiang river basin under future period are
shown in Fig. 5(b) and (c), respectively. It is shown that (1) uncertainty of economic value-added by secondary industry and tertiary
industry in Dongjiang river basin also increases as time goes on,
(2) economic value-added by secondary industry lies between
1274.6 billion and 1692.7 billion yuan by the end of 2015 year,
economic value-added by secondary industry lies between
1591.2 billion and 2180.2 billion yuan by the end of 2020 year as
well as economic value-added by secondary industry lies between
2411.2 billion and 3705.5 billion yuan by the end of 2030 year,
(3) economic value-added by tertiary industry lies between
1489.2 billion and 1902.1 billion yuan by the end of 2015 year,
economic value-added by tertiary industry lies between
2123.9 billion and 3210.2 billion yuan by the end of 2020 year as
well as economic value-added by tertiary industry lies between
3625.2 billion and 6108.8 billion yuan by the end of 2030 year.
water demand, water price and net income per capita in Dongjiang
river basin from 2001 to 2010 year, the form as follows:
NICU
145:06
WP
NICR
DWDR ¼ 30:006 ln
37:305
WP
DWDU ¼ 34:384 ln
ð2Þ
ð3Þ
where DWDU is domestic water demand in urban area, DWDR is
domestic water demand in rural area, NICU is net income per capita
in urban area, NICR net income per capita in rural area and WP is
water price.
Two kinds of growth rates of water price in different waterintakes are set up for economic development scenario of future
period, i.e., high and low growth rate of water price. Based on
above development scenario of population as well as economic
value-added by secondary industry and tertiary industry, the feasible zone of domestic water demand is calculated by Eqs. (2) and (3)
in Dongjiang river basin under future period, as shown in Fig. 5(d).
It is shown that domestic water demand increases with the
increasing population and net income per capita, decreases with
the increasing water price.
3.2.4. Setup development scenario for future period
Above all, the feasible zone of economic value-added by secondary industry and tertiary industry only provides economic constraint for optimal module in the paper Part 1 (Zhou et al., 2015).
Growth rates of secondary industry and tertiary industry will be
adjusted adaptively according to industrial production water
agent. Besides, rainfall and runoff series from 1986 year to
2005 year are selected as meteorological and hydrologic scenario
in Dongjiang river basin under future period 2011–2030 year.
Therefore, administrative policies including population development and water price become one of portfolio’s key factors that
would affect comprehensive benefits of water resources management. Six kinds of development scenarios No. 1–6 about administrative policies are set up for population development and water
price in future period, i.e., scenario No. 1 with high growth rate
of population and high water price, scenario No. 2 with high
growth rate of population and low water price, scenario No. 3 with
middle growth rate of population and high water price, scenario
No. 4 with middle growth rate of population and low water price,
scenario No. 5 with low growth rate of population and high water
price and scenario No. 6 with low growth rate of population and
low water price. The scenarios No. 2 and No. 5 have the highest
and lowest water demand, respectively.
3.3. Simulation results under future period
At the same time, the input data of integrated optimal allocation model under future period includes: (1) meteorological and
hydrological data; (2) the characteristic parameters of reservoirs;
(3) production and domestic water use and demand, as well as
sewage treatment parameters; (4) ecological water demand;
(5) population, economic growth rate; (6) parameters of NSGA-II
are the same as baseline period; (7) the weighting factors of
AGini-P, AGini-GDP and AGini-AWR are the same as baseline period; (8) parameters of AGA are the same as baseline period.
(2) Water price
Water price, net income per capita and domestic water demand
in city and country extracts from Statistic Bureau of Guangdong
Province (http://www.gdstats.gov.cn, Guangdong Statistical Yearbook, from 2001 to 2010 year). Domestic water demand is the
function of water price and net income per capita (Zhao et al.,
2004; Yuan et al., 2014) based on the fitting curve of domestic
3.3.1. Pareto optimal set of different schemes
The best economic objective matches with the highest water
supply for industry, resulting in the lowest ecological water supply.
Because the water demand of scenarios No. 2 with high growth
rate of population and low water price is highest in six development scenarios, the simulation result of scenario No. 2 is selected
as analysis of ecological objective. The simulation values of
Y. Zhou et al. / Journal of Hydrology 531 (2015) 977–991
987
Fig. 6. The trend graph of (a) GDP and discharge of ammonia–nitrogen, (b) AGini-P and AGini-GDP, (c) AGini-AWR and IGC, (d) water supply for secondary industry and
tertiary industry, (e) water supply for agriculture and total water supply for industry in Dongjiang river basin, (f) water supply for secondary and tertiary industry in waterintakes No. 1–5, (g) water supply for secondary and tertiary industry in water-intake No. 6 and (h) water supply for agriculture in water-intakes No. 1–5 and water supply for
agriculture in water-intake No. 6 under future period.
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Y. Zhou et al. / Journal of Hydrology 531 (2015) 977–991
outer-river and inner-river ecological water shortages in the best
of economic objective are only 1.72 and 0.75 million m3, respectively for Dongjiang river basin under scenario No. 2. Besides, the
reliabilities of inner-river ecological water supply are 100.0%,
98.3%, 100.0% and 100.0%, respectively for hydrological stations
Heyuan, Xizhijiangkou, Boluo and Guanhaikou. Therefore, outerriver and inner-river ecological water demands are basically satisfied in Dongjiang river basin, the competitive relationship between
ecological objective and other optimal objectives is also unremarkable under six development scenarios in future period 2011–
2030 year. The reason is that the Xinfengjiang reservoir, Fengshuba
reservoir and Baipenzhu reservoir play a major role in regulating
runoff in Dongjiang river basin, in order to meet the ecological
water demand.
3.3.2. Correlation analysis between different optimal objectives
Twenty Pareto set of social, economic, ecological and environmental objectives with minimum, 25%, 50%, 75% and maximum
are selected for correlation analysis between different optimal
objectives. The schemes No. 1–20 are sorted by the ascending
sequence of economic objective in the following figures. Besides,
all of evaluation indexes are annual average values in the following
results. The simulation result of development scenario No. 1 is
taken for example, so as to analyze correlation between different
optimal objectives.
(1) Correlation analysis between economic objective and environmental objective
The trend graph of GDP and discharge of ammonia–nitrogen in
Dongjiang river basin under future period is shown in Fig. 6(a). It is
shown that (1) the GDP increases from scheme No. 1 to No. 20, (2)
the discharge of ammonia–nitrogen also increases with the
increasing GDP from scheme No. 1 to No. 20 and (3) the correlation
between GDP and discharge of ammonia–nitrogen is positive.
(2) Correlation analysis between economic objective and social
objective
The trend graphs of AGini-P, AGini-GDP, AGini-AWR and IGC in
Dongjiang river basin under future period are shown in Fig. 6
(b) and (c), respectively. Fig. 6(b) and (c) are shown that (1) the values of AGini-P, AGini-GDP and IGC decrease with the increasing
GDP from scheme No. 1 to No. 20 and the correlation between
those of Gini coefficients and GDP is negative as well as (2) the
value of AGini-AWR increases with the increasing GDP from
scheme No. 1 to No. 20 and the correlation between AGini-AWR
and GDP is positive. The reasons are that (1) water resources are
allocated preferentially for the sections of agriculture and out river
ecological water use in regions with low water consumption per
10,000 yuan of GDP in order to decrease the value of AGini-GDP,
(2) water resources are allocated preferentially for the developed
regions with low water consumption per capita in order to
decrease the value of AGini-P, (3) water resources are allocated
preferentially for underdeveloped region with high water consumption per capita and abundant water resources in order to
decrease the value of AGini-AWR and (4) the value of IGC is controlled mainly by the same trend changes of AGini-GDP and
AGini-P when AGini-GDP, AGini-P and AGini-AWR have the same
weighting factors.
3.3.3. Analysis of adaptive economic factors
Because the competitive relationship between ecological objective and other optimal objectives is unremarkable as well as
domestic water supply only provides constraint for optimal module in the paper Part 1 (Zhou et al., 2015), adaptive economic
factors including agriculture, secondary industry and tertiary
industry are analyzed for complex adaptive system of water
resources management.
Firstly, the trend graphs of water supply for secondary industry,
tertiary industry and agriculture as well as total water supply for
industry in Dongjiang river basin under future period are shown
in Fig. 6(d) and (e), respectively. Fig. 6(d) and (e) are shown that
(1) the values of water supply for secondary industry, tertiary
industry and total water supply for industry increase with the
increasing economic benefit from scheme No. 1 to No. 20, (2) the
trend change of water supply for agriculture is unremarkable with
the increasing economic benefit from scheme No. 1 to No. 20 and
(3) secondary industry and tertiary industry are the dominant economic factors resulting in the increasing economic benefit. In other
words, water resources are allocated preferentially for secondary
industry and tertiary industry in order to increase the value of economic objective.
Secondly, the trend graphs of water supply for secondary and
tertiary industry in water-intakes No. 1–5 as well as water supply
for secondary and tertiary industry in water-intake No. 6 under
future period are shown in Fig. 6(f) and (g), respectively. Fig. 6(f)
and (g) are shown that (1) the values of water supply for secondary
and tertiary industry in water-intakes No. 1–6 increase with the
increasing economic benefit from scheme No. 1 to No. 20, (2) water
supply for secondary and tertiary industry in water-intakes
No. 1–5 lies between 1562.27 million m3 and 1602.82 million m3
with change amplitude 2.60% as well as between 185.75 million m3 and 189.68 million m3 with change amplitude 2.11%,
(3) water supply for secondary and tertiary industry in waterintake No. 6 lies between 1937.01 million m3 and 2149.89 million m3 with change amplitude 10.99% as well as between
700.86 million m3 and 784.31 million m3 with change amplitude
11.91% and (4) the magnitude and change amplitude of water supply for secondary and tertiary industry in water-intake No. 6 is
much higher than those of water supply for secondary and tertiary
industry in water-intakes No. 1–5. The reasons are that (1) economic benefit per unit water consumption in water-intake No. 6
is much higher than that in water-intake No. 1–5, (2) water supply
for secondary and tertiary industry in water-intake No. 6 is the
dominant factors resulting in the increasing economic benefit. In
other words, water resources are allocated preferentially for secondary and tertiary industry in water-intake No. 6 in order to
increase the value of economic objective in Dongjiang river basin.
Thirdly, the trend graph of water supply for agriculture in
water-intakes No. 1–5 and water-intake No. 6 under future period
is shown in Fig. 6(h). It is shown that (1) water supply for agriculture in water-intakes No. 1–5 decreases with the increasing economic benefit from scheme No. 1 to No. 20, (2) water supply for
agriculture in water-intakes No. 6 increases with the increasing
economic benefit from scheme No. 1 to No. 20. In comparison with
Fig. 6(e), that is the reason why the trend change of water supply
for agriculture in Dongjiang river basin is unremarkable with the
increasing economic benefit from scheme No. 1 to No. 20. Besides,
in comparison with Fig. 6(b) and (c), it is shown that (1) the values
of AGini-P and AGini-GDP decrease with the increasing water supply for agriculture in water-intake No. 6, (2) the value of AGiniAWR increases with the increasing water supply for agriculture
in water-intake No. 6, (3) the values of AGini-P and AGini-GDP
increase with the increasing water supply for agriculture in
water-intake No. 1–5 and (4) the value of AGini-AWR decreases
with the increasing water supply for agriculture in water-intakes
No. 1–5. The season is that (1) the increasing water supply for agriculture will result in decreasing GDP per unit water consumption,
increasing water consumption per capita and decreasing the values
of AGini-P and AGini-GDP in water-intake No. 6, (2) the increasing
water supply for agriculture will bring about increasing GDP per
Y. Zhou et al. / Journal of Hydrology 531 (2015) 977–991
unit water consumption, decreasing water consumption per capita
and increasing the values of AGini-P and AGini-GDP in waterintakes No. 1–5, (3) the decreasing water supply for agriculture
in water-intake No. 6 and increasing water supply for agriculture
in water-intakes No. 1–5 will lead to decreasing the value of
AGini-AWR because the ratio between water consumption and
local water resources in water-intake No. 6 is much higher than
that in water-intakes No. 1–5. Therefore, the recommendation of
decision-making for maximizing the social objective as follows:
(1) the decision of increasing water supply for water-intake No. 6
and reverse decision in water-intakes No. 1–5 is made so as to
decrease the value of AGini-P, (2) the decision of increasing water
supply for secondary and tertiary industry as well as decreasing
water supply for agriculture in water-intakes No. 1–5 and reverse
decision in water-intake No. 6 is made in order to decrease the
value of AGini-GDP, (3) the decision of decreasing water supply
for water-intake No. 6 and reverse decision in water-intakes No.
1–5 is made so as to decrease the value of AGini-AWR.
3.3.4. Analysis of administrative policies
Six kinds of development scenarios No. 1–6 about administrative policies are set up for population development and water price
in future period. The simulation results of domestic water supply
and discharge of ammonia–nitrogen are average value of 1000 Pareto set.
The simulation result of domestic water supply in water-intakes
No. 1–5 and 6 under different development scenarios is shown in
Fig. 7(a) and (b). It is shown that (1) domestic water supply in scenarios No. 2 and 4 with low water price is much higher than that in
scenarios No. 1 and 3 with high water price, (2) domestic water
(a) Water-intakes No.1-5
989
supply in scenarios No. 1 and 2 with high growth rate of population
is much higher than that in scenarios No. 5 and 6 with low growth
rate of population and (3) the scenarios No. 2 with high growth
rate of population and low water price and No. 5 with low growth
rate of population and high water price have the highest and lowest domestic water supply, respectively. The simulation result of
discharge of ammonia–nitrogen under different development scenarios in Dongjiang river basin is shown in Fig. 7(c). It is shown
that discharge of ammonia–nitrogen in scenarios No. 2 and 4 with
low water price is much higher than that in scenarios No. 1 and 3
with high water price, (2) discharge of ammonia–nitrogen in scenarios No. 1 and 2 with high growth rate of population is much
higher than that in scenarios No. 5 and 6 with low growth rate of
population and (3) the scenarios No. 2 with high growth rate of
population and low water price and No. 5 with low growth rate
of population and high water price have the highest and lowest
discharge of ammonia–nitrogen, respectively. In other words, the
discharge of ammonia–nitrogen increases with the increasing
domestic water supply.
3.3.5. Multi-objective evaluation of simulation results under future
period
Only the three multi-objective functions are selected as multiobjective evaluation indices, i.e., (1) minimizing IGini, (2) maximizing AGDP, (3) minimizing VPIST, excluding minimizing EWS,
similarly in baseline period. Take development scenario No. 2 with
the highest water demand for example, the result of multiobjective evaluation is shown in Table 5, just showing scheme
No. 1 with the best of social objective, scheme No. 2 with the worst
of social objective, scheme No. 3 with the best of economic
(b) Water-intake No.6
(c) Discharge of ammonia-nitrogen in Dongjiang river basin
Fig. 7. The simulation results of domestic water supply in water-intakes No. 1–5 and 6 and discharge of ammonia–nitrogen in Dongjiang river basin under different
development scenarios.
990
Y. Zhou et al. / Journal of Hydrology 531 (2015) 977–991
Table 5
The result of multi-objective evaluation under development scenario No. 2 in future period 2011–2030 year.
Scenario
Scheme
Number
IGini
AGDP (108 yuan)
VPIST (104 ton)
Projection value
Rank in population
size 1000
No. 2
Social objective
1
2
3
4
5
6
7
8
0.33057
0.33737
0.33240
0.33304
0.33304
0.33240
0.33058
0.33734
43,428
42,284
45,015
41,123
41,123
45,015
43,794
42,026
353,022
343,190
358,941
342,575
342,575
358,941
353,600
346,938
1.1641
0.1518
1.1271
0.5620
0.5620
1.1271
1.2093
0.1225
25
995
59
760
760
59
1
1000
Economic objective
Environmental objective
The best scheme
The worst scheme
objective, scheme No. 4 with the worst of economic objective,
scheme No. 5 with the best of environmental objective, scheme
No. 6 with the worst of environmental objective, scheme No. 7
with the best scheme in Pareto set and scheme No. 8 with the
worst scheme in Pareto set.
It is shown that the projection values of schemes No. 1–8 are
1.1641, 0.1518, 1.1271, 0.5620, 0.5620, 1.1271, 1.2093 and
0.1225, respectively, and the ranks of schemes No. 1–8 are 25,
995, 59, 760, 760, 59, 1 and 1000, respectively. It is worth mentioning that the superior economic objective matches with the inferior
environmental objective, and vice versa. Besides, the variables of
unit projection vector are equal to 0.8718, 0.3794 and 0.3097 for
social objective IGini, economic objective AGDP and environmental
objective VPIST, respectively. It indicates that the social objective is
the most important evaluation index. Moreover, the importance of
environmental objective is superior to that of environmental
objective in order to maximizing the comprehensive benefits of
water resources management.
Therefore, the recommendation of Pareto optimization schemes
as follows: (1) the scheme No. 1 is recommended for decisionmakers in order to maximize the social benefit, (2) the scheme
No. 3 or 6 is recommended for decision-makers in order to maximize the economic benefit, (3) the scheme No. 4 or 5 is recommended for decision-makers in order to maximize the
environmental benefit, (4) the scheme No. 7 is recommended for
decision-makers in order to maximize the comprehensive benefits
of water resources management under future period.
4. Conclusion and recommendations
An integrated optimal allocation model was developed for complex adaptive system of water resources management. The Dongjiang River basin located in the Guangdong Province of China
was selected as a case study. The following conclusions were
drawn:
(2) Water resources are allocated preferentially for the sections
of secondary and tertiary industry in order to maximize the
value of economic objective.
(3) Water resources are allocated preferentially for the sections
of agriculture and out river ecological water use in order to
minimize the value of environmental objective, because of
high discharge of sewage and pollutant in the sections of
secondary and tertiary industry. Because the competitive
relationship between economic objective and environmental
objective is remarkable, the water supply for secondary and
tertiary industry plays an important role in driving evolution
of complex adaptive system of water resources
management.
(4) Since the outer-river and inner-river ecological water
demands are basically satisfied in Dongjiang River basin,
the competitive relationship between ecological objective
and economic objective is unremarkable.
(5) The recommendation of Pareto optimization schemes as follows: r the scheme No. 1 is recommended for decisionmakers in order to maximize the social benefit, s the
scheme No. 3 or 6 is recommended for decision-makers in
order to maximize the economic benefit, t the scheme
No. 4 or 5 is recommended for decision-makers in order to
maximize the environmental benefit, u the scheme No. 7
is recommended for decision-makers in order to maximize
the comprehensive benefits of water resources management
under baseline period and future period.
This paper summarizes the results from a first attempt of integrated optimal allocation model for complex adaptive system of
water resources management combining with adaptive allocation,
dynamic allocation and multi-objective optimization. However,
the uncertainties of data input and model structure need be studied furtherly.
Acknowledgements
(1) The social objectives including AGini-GDP, AGini-P and
AGini-AWR are used to evaluate the equity of water
consumption. The features of AGini-GDP, AGini-P and
AGini-AWR are as follows: r water resources are allocated
preferentially for the sections of agriculture and out river
ecological water use in regions with high water consumption per 10,000 yuan of GDP in order to minimize the value
of AGini-GDP, s water resources are allocated preferentially
for the developed regions with low water consumption per
capita in order to minimize the value of AGini-P, t water
resources are allocated preferentially for underdeveloped
region with high water consumption per capita and abundant water resources in order to minimize the value of
AGini-AWR. The integrated Gini coefficient of AGini-GDP,
AGini-P and AGini-AWR plays an important role in driving
evolution of complex adaptive system of water resources
management.
This study is financially supported by the International
Cooperation in Science and Technology Special Project of China
(2014DFA71910), National Natural Science Foundation of China
(51509008 and 51509012), Natural Science Foundation of Hubei
Province (2015CFB217 and 2015CFA157) and Open Foundation of
State Key Laboratory of Water Resources and Hydropower
Engineering Science in Wuhan University (2014SWG02).
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