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Water allocation using game theory under climate change
impact (case study: Zarinehrood)
Hasti Hemati and Ahmad Abrishamchi
ABSTRACT
The combined effects of climate change and growing water demand due to population growth,
industrial and agricultural developments cause an increase of water scarcity and the subsequent
environmental crisis in river basins, which results in conflicts over the property rights and allocation
agreements. Thus, an integrated, sustainable and efficient water allocation considering changes in
water resources due to climate change and change of users’demands is necessary. In this study, the
drainage basin of Zarinehrood was chosen to evaluate the function of selective methods. Assessing
climate change impact scenarios of the Fifth IPCC reports, e.g., RCP2.6, RCP4.5, RCP6.0 and RCP8.5,
have been used. For downscaling outputs of GCMs an artificial neural network (ANN) and for bias
correction a quantile mapping (QM) method have been used. Using a bargaining game and the Nash
bargaining solution (NBS) with two methods, one symmetric and two AHP methods, the water
available for users was allocated. Results indicate an overall increase in temperature and
precipitation in the basin. In bargaining game solutions, AHP provided better utilities for players than
symmetric method. These results show that with water management programs and use of a
cooperative bargaining game, water allocation can be done in an efficient way.
Key words |AHP, ANN, climate change, game theory, nash bargaining solution, QM
HIGHLIGHTS
•Using ANN for downscaling.
•Using QM for bias correction.
•Using game theory for allocation.
•Using AHP method on calculating negotiation power.
•Evaluating all of the methods.
Hasti Hemati (corresponding author)
Ahmad Abrishamchi
Department of Civil Engineering,
Sharif University of Technology,
Tehran,
Iran
E-mail: hasti_hemati@yahoo.com
INTRODUCTION
Water allocation is central to the management of water
resources. Due to geographically and temporally unevenly
distributed precipitation (Al Radif 1999), rapidly increasing
water demands driven by the world population, effects of
climate change on river flow and other stresses, and degra-
dation of the water environment (UN-CSD 1994), there
are increasing scarcities of water resources in countries.
Conflicts often arise when different water users (including
the environment) compete for limited water supply. The
need to establish appropriate water allocation method-
ologies and associated management institutions and
policies is recognized by researchers, water planners, and
governments. Many studies have been carried out in this
domain, but there are still many obstacles to reaching equi-
table, efficient, and sustainable water allocations (Dinar
et al. ; Syme et al. 1999; UN-ESCAP 2000). Alongside
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these conflicts, there are also indications that recent climate
changes have already affected many physical and biological
systems. The impact of these effects includes extreme occur-
rence of flooding and droughts.
Various methods and models have been used in
water resources allocation, including simulation methods,
optimization methods, water rights, game theory, and
complex adaptive systems (Di Nardo et al. ). Water
resources allocation problem usually involves various
rational decision-maker interactions, and water resources
allocation needs to consider multiple objectives (such as
economic, social, environmental, etc.), which yields multi-
objective decision-making problems. This kind of allocation
model solves water resources allocation problems via optim-
ization approaches, which reflect the indirect interaction
between decision-makers, but ignore the direct interaction
between decision-makers, making them impractical in real-
world applications (Madani ). Game theory is a theory
of decision-making and equilibrium during the process
of direct interaction between decision-makers (Loáiciga
). Therefore, water resources allocation based on
game theory is a promising method for reducing this
deficiency. Moreover, compared with traditional water
resources allocation, which only focuses on the interests of
the whole society, using the game theory to study the con-
flict of water resources allocation allows full consideration
of the influences of all decision-makers. It is recognized
that there are different interests in decision-makers in the
process of water resources allocation, and game theory
can be used to maximize the benefits of all water users
while achieving the rational allocation of water resources.
Therefore, using the game theory to study the conflict of
water resources allocation is more practical. In recent
years, water resources allocation based on game theory
has been studied and extended. Carraro et al. ()system-
atically expounded the application of non-cooperative
negotiation theory in water resources conflict. Parrachino
()applied cooperative game theory to water resource
issues, and their results showed that cooperation over
scarce water resources was possible under various physical
conditions and institutional arrangements. Madani et al.
(2010) demonstrated that the application of game theory
in the field of water resources can be divided into five
parts, i.e., water or benefit allocation among water users,
groundwater management, transboundary water allocation,
water quality management, and other types of water
resources management. Dinar et al. ()divided the
application of game theory in the conflict of water resources
allocation into three aspects: (1) the application of non-
cooperative negotiation theory in water resources allocation
conflict; (2) the application of graph model in water
resources allocation conflict; (3) application of Nash
bargaining theory and Nash–Harsanyi bargaining theory
to water resources allocation problems. In the above
water resources allocation conflict research, Rogers ()
originally applied game theory to the conflict of water
resources allocation problems in transboundary river
basins. In recent studies, Eleftheriadou & Mylopoulos
()implemented game theoretical concepts in a case
study of Greek–Bulgarian negotiations on the Nestos/
Mesta transboundary river. Hipel et al. ()applied the
graph model of non-cooperative game to the conflict of
water resources allocation, and their proposed method has
been widely used. Madani & Lund ()traced changes in
delta conflict by game theory. Kucukmehmetoglu ()
introduced a composite method that integrates both Pareto
frontier and game theory in the Euphrates and Tigris
rivers. Zarghami et al. ()introduced a mathematical
model which integrates both the leader–follower concept
and the bargaining theory in the case of the Zarrinehrud
River basin. Li et al. ()developed a generalized unco-
operative planar game theory model for water distribution
in a transboundary river basin. Degefu et al. ()proposed
a cooperative bargaining approach for solving the water
sharing problem in the Nile River basin.
The impacts that climate change may have on water
availability are largely affected by water allocations and
the countermeasures undertaken (IPCC 2014). Climate
change is believed to cause changes both in water quantity
and water quality. The prospect of these changes will help
decision-makers formulate mitigation and adaptation
strategies to effectively deal with the impacts posed by
climate change. A variety of general circulation models
(GCMs) has been developed to project climate over long-
term horizons under pre-determined greenhouse gas emis-
sion scenarios. Their projections often provide the source
of data used for assessing impacts of climate change in var-
ious fields, such as agriculture, water resources, and the
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environment. The GCM outputs are coarse in resolution (a
horizontal resolution of GCM is generally about 300 km)
and have the statistical characteristics of an average area
rather than of a point quantity (Osborn & Hulme ).
However, hydrological models often require regional and
finer-scale projections, and this coarse resolution constrains
the usefulness of GCMs in climate change impact studies. In
several previous studies (Mimikou et al. ;Stone et al.
;Booty et al. ), future climate scenarios were gener-
ated by adding predicted changes by GCMs into baseline
scenarios. Dibike & Coulibaly ()argued that the
simple shifts in climate variables were very crude. In order
to utilize GCM outputs in regional studies, two approaches,
namely, dynamic downscaling, such as using regional circu-
lation models (RCMs), and statistical downscaling, have
been developed. Murphy ()indicated that there is no
clear difference in the performance level between these
two techniques in terms of downscaling monthly climate
data. Arnbjerg-Nielsen & Fleischer ()studied the
impact of climate change and identified suitable adaptation
strategies due to flooding posed by climate change from
an economic perspective. Two types of models, namely,
deterministic (i.e., conceptual and physically based)
models and data-driven or statistical models (e.g., artificial
neural networks (ANNs)) have been implemented to
evaluate the impacts of climate change in water resources.
As an alternative approach to deterministic models, the
ANN approach has been employed in various fields includ-
ing hydrology and water resources (Govindaraju ).
Some of the advantages of using a data-driven modeling
approach include needing less data and less extensive
user expertise and knowledge into physical processes. In
predicting event-based stormwater runoff quantity, the
reliability of the ANN approach has been proven in several
studies. For example, Minns & Hall ()and Chua et al.
()demonstrated the ability of ANNs to model event-
based rainfall-runoff by using synthetically generated data
and experimentally collected data, respectively. In addition,
Jain & Prasad Indurthy ()compared deterministic
models and statistical models including ANNs for predicting
event-based rainfall-runoff. They found that ANNs
consistently outperformed the other models. Also, Bai
et al. ()used a multiscale deep feature learning method
to predict inflows to the Three Gorges reservoir along the
Yangtze River between Chongqing and Hubei Province,
China.
The objective of this paper is to analyze water allocation
in Zarinehrood river basins, Iran, considering impact of
climate change on its hydrologic parameters. Assessing
climate change impact, an ANN for downscaling outputs
of GCMs and for bias correction a quantile mapping (QM)
method have been used. Then, considering some assump-
tions for predicting future demands, a water resources
management program has been used to assess the water
available for allocating to users. Using a bargaining game
and the Nash bargaining solution (NBS) with two methods,
one symmetric and the other AHP method, the water
available for users has been allocated.
METHODOLOGY
Artificial neural network
An ANN is a computational tool based on the biological
processes of the human brain (Sudheer et al. ). Its
capability to predict output variables by using a series of
interconnected nodes that recognize relations between
input and output variables makes ANN models powerful
tools for hydrologic analyses (Mutlu et al. ). Model
inputs are weighted and passed to internal nodes in
hidden layers, which develop functions for output (Figure 1).
There can be one or more of these hidden layers between
the input and output. Compared with conventional rain-
fall-runoff models, ANN models require fewer parameters
but still provide reliable results in hydrological forecasting
(Riad et al. ). The complexity of physical processes
involved in the conventional hydrologic models has trig-
gered the increasing use of ANN models (Rezaeianzadeh
et al. ) for hydrologic predictions. Several studies
have been conducted that show the advantages of using
ANN models for rainfall-runoff modeling in terms of the
required data to establish rainfall-runoff relations, and
research continues in developing the best data and
methods for these applications (Shamseldin ;De Vos
& Rientjes ). Developing ANN models begins with the
evaluation and determination of suitable input variables.
Data selection for suitable model performance mostly
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requires a trial-and-error process to evaluate the appropriate
combinations of input variables and data allocation for
training, testing, and validation of the model. Calibration
of the model, also known as training, is conducted by apply-
ing adjustments within the ANN model weights/links in
order to reduce the error in the network outputs. Through
this training process, a learning system is developed that is
capable of determining the relation between rainfall, temp-
erature, and flow data. Thus, validation of ANN models is
focused on evaluating the trained model, which can then
be used to determine flow to the reservoir under specific,
hypothesized climate/weather conditions.
One of the most widely used methods in time series fore-
casting is the classical multi-layer perceptron network
(MLP) with the back-propagation (BP) learning algorithm
(Bishop ). Often, the MLP model is also combined
with statistical models in hybrid systems (Tseng et al.
). The MLP model is one of the basic models but
often produces very good results. The algorithm is based
on minimizing the error of neural network output compared
to targets. To maintain mathematical rigor, the weights will
be adjusted only after all the test vectors are applied to the
network. Therefore, the gradients of the weights must be
memorized and adjusted after each model in the training
set, and the end of an epoch of training, and the weights
will be changed only once, because the idea is to find the
minimum error function in relation to the connection’s
weights. In a local minimum, the gradients of the error
become zero and the learning no longer continues. A sol-
ution is multiple independent trials, with weights
initialized differently at the beginning, which raises the prob-
ability of finding the global minimum. For large problems,
this thing can be hard to achieve and then local minimums
may be accepted, with the condition that the errors are small
enough. Also, different configurations of the network might
be tried, with a larger number of neurons in the hidden layer
or with more hidden layers, which, in general, lead to smal-
ler local minimums. Still, although local minimums are
indeed a problem, practically they are not unsolvable. An
important issue is the choice of the best configuration for
the network in terms of the number of neurons in hidden
layers. In most situations, a single hidden layer is sufficient.
There are no precise rules for choosing the number of neur-
ons. In general, the network can be seen as a system in
which the number of test vectors multiplied by the number
of outputs is the number of equations and the number of
weights represents the number of unknowns. The equations
are generally non-linear and very complex and so it is
very difficult to solve them exactly through conventional
means. Choosing the activation function for the output
layer of the network depends on the nature of the problem
to be solved. For the hidden layers of neurons, sigmoid func-
tions are preferred, because they have the advantages of
being both non-linear and differential. The biggest influence
of a sigmoid on the performances of the algorithm seems to
be the symmetry of origin.
The Levenberg–Marquardt method is one of the
fastest learning algorithm methods for MLP networks
(Hagan & Menhaj ; Lourakis 2005; Sotirov ). The
Levenberg–Marquardt (LM) algorithm is an iterative tech-
nique that locates the minimum of a multivariate function
that is expressed as the sum of squares of non-linear real-
valued functions (Sotirov ). It has become a standard
technique for non-linear least-squares problems (Lourakis
Figure 1 |ANN model layers.
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2005), widely adopted in a broad spectrum of disciplines.
LM can be thought of as a combination of steepest descent
and the Gauss–Newton method.
As noted above, the LM algorithm is a variant of the
Gauss–Newton method and was designed to approach
second-order training speed without having to compute
the Hessian matrix (Hagan & Menhaj ). Typically, for
the learning of feed-forward neural networks, a sum of
squares is used as the performance function.
Simulated precipitation outputs from global climate
models (GCMs) can exhibit large systematic biases relative
to observational datasets (Mearns et al. ;Sillmann
et al. ). As GCM precipitation series are used as inputs
to process models (e.g., Hagemann et al. ;Muerth
et al. ) and gridded statistical downscaling models
(e.g., Wood et al. ;Maurer & Hidalgo ;Maurer
et al. ), algorithms have been developed to correct and
minimize these biases as sources of error in subsequent
modeling chains. Systematic errors in climate model outputs
can be ascribed to different sources. For example, Eden et al.
()classify errors in GCM precipitation fields as being
due to: (1) unrealistic large-scale variability or response to
climate forcing, (2) unpredictable internal variability that
differs from observations (e.g., as might happen if the
sampled historical period happens to coincide with the posi-
tive phase of the Pacific decadal oscillation in observations
and the negative phase in the climate model), and (3)
errors in convective parameterizations and unresolved sub-
grid-scale orography. Quantile mapping is often applied for
two very different reasons: (1) as a bias correction applied
to climate model and observed fields at similar scales and
(2) for downscaling from coarse climate model scales to
finer observed scales. In this study, quantile is applied as
the bias correction step of a larger downscaling framework.
The QM for precipitation preserves model-projected relative
changes in quantiles, while at the same time, correcting sys-
tematic biases in quantiles of a modeled series with respect
to observed values.
Quantile mapping
Quantile mapping equates cumulative distribution functions
(CDFs) F
o,h
and F
m,h
of, respectively, observed data x
o,h
,
denoted by the subscript o, and modeled data x
m,h
, denoted
by the subscript m, in a historical period, denoted by the sub-
script h. This leads to the following transfer function:
^
xm:p(t)¼F1
o:h{Fm:h[xm:p(t)]} (1)
for bias correction of x
m,p
(t), a modeled value at time t
within some projected period, denoted by the subscript p.
If CDFs and inverse CDFs (i.e., quantile functions) are esti-
mated empirically from the data, the algorithm can be
illustrated with the aid of a quantile–quantile plot, which
is the scatterplot between empirical quantiles of observed
and modeled data (i.e., the sorted values in each sample
when the number of observed and modeled samples are
the same). In this case, QM amounts to a lookup table
whose entries are found by interpolating between points in
the quantile–quantile plot of the historical data. The transfer
function is constructed using information from the historical
period exclusively; information provided by the future
model projections is ignored. QM, like all statistical postpro-
cessing algorithms, relies strongly on an assumption that the
climate model biases to be corrected are stationary (i.e., that
characteristics in the historical period will persist into the
future). As it is beyond the scope of this paper to address
this assumption, we instead point to studies by Maraun
et al. ()and Maraun ()for more insight. For empiri-
cal CDFs, Equation (1) is only defined over the historical
range of the modeled dataset. If a projected value falls out-
side the historical range, then some form of extrapolation
is required, for example using parametric distributions fol-
lowing Wood et al. ()or the constant correction
approach of Boé et al. (). Regardless, one way in
which frequent extrapolation can be avoided is to explicitly
account for changes in the projected values, for example, by
first removing the modeled trend in the long-term mean
prior to QM, which will shift the future distribution so that
it tends to lie within the support of the historical distri-
bution, and then reimpose it afterwards. For a ratio
variable like precipitation, trends are removed and then
reimpose by scaling and rescaling:
^
xm:p(t)¼F1
o:hFm:h
xm:hxm:p(t)
xm:p(t)
xm:p(t)
xm:h
(2)
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where x
m,h
and x
m,p
(t) are, respectively, estimates of the
long-term modeled mean over the historical period and at
time tin the projected period p.
Bargaining game
There is a high risk of water conflicts in the allocation of
water resources in international basins. Cooperative nego-
tiations among countries are often required to solve the
water resources sharing problems in these basins (Kampra-
gou et al. ), which can produce greater economic,
ecological, and political utility and make sure the allocation
is fair and stable (Sadoff & Grey ). One of the theoreti-
cal games which simulates these negotiations and
cooperation is asymmetric bargaining game (Houba et al.
). This bargaining solution is based on Nash bargaining
equilibrium solution (Nash ). Bargaining problem can
be represented as B:(S, D, u
1
,u
2
,…,u
n
)where Sis the
feasibility space, {ui(S), i¼1, 2, ...,n} is the utility func-
tion of the claimant, D¼d
1
,d
2
,d
3
,…,d
n
is disagreement
point, and ui:S!Ris the feasible solution. For any strategy
selection sϵSthe allocations should satisfy ui(di)ui(S).
The utility configuration set of the bargaining problem can
be expressed as {ui(S), i¼1, 2 ...,n}. Assuming the bar-
gaining weight of each subject: W¼(w
1
,w
2
,…,w
n
),
P
n
i¼1
wi¼1.The only solution that satisfies the following max-
imization condition is the Nash bargaining solution:
uN(s)¼{sϵSjmax[(u1(s)u1(d1))w1(u2(s)u2(d2))w2
... (un(s)un(dn))wn]} (3)
Bargaining power calculation
Each player’s weight will be obtained by AHP method,
which was first proposed by Saaty in 1971. It is one of the
methods used for solving multi-criteria decision-making
(MCDM) problems in political, economic, social, and man-
agement sciences (Saaty ). Through AHP, opinions
and evaluations of decision-makers can be integrated, and
a complex problem can be devised into a simple hierarchy
system with higher levels to lower ones (Lee et al. ).
Then, the qualitative and quantitative factors can be
evaluated in a systematic manner. The application of AHP
to a complex problem involves six essential steps (Murtaza
;Lee et al. ):
•Defining the unstructured problem and stating the objec-
tives and outcomes clearly.
•Decomposing the complex problem into a hierarchical
structure with decision elements (criteria and alternatives).
•Employing pairwise comparisons among decision
elements and forming comparison matrices.
•Using the eigenvalue method to estimate the relative
weights of decision elements.
•Checking the consistency property of matrices to ensure
that the judgments of decision-makers are consistent.
•Aggregating the relative weights of decision elements to
obtain an overall rating for the alternatives.
The weights gained by AHP will be implemented as sub-
jective weights in the entropy method. This measure of
uncertainty is given by Shannon & Weaver ()as:
E¼P
P1
P2
.
.
.
Pm
0
B
B
B
@
1
C
C
C
A
,X
m
i¼1
Pi¼1 (4)
The entropy of the set of project outcomes of attribute
jis
Ej¼KX
m
i¼1
[Piln Pi] (5)
in which, E
j
is the entropy of attribute j,mis the number of
alternatives, P
i
is the probability of the i-th alternative that is
preferred by the decision-maker.
where kis a constant defined as
K¼1
ln m(6)
it guarantees that 0E
j
1.
The degree of diversification of information provided by
the outcomes of attribute jcan be defined as:
dj¼1Ej,j¼1, 2, ...,n(7)
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then the weights of attributes can be obtained by
Wj¼dj
Pm
i¼1dj
,j¼1, 2 ...,n(8)
Then the mean value of weights that is the outcome
from each matrix is considered as the weights of each
attribute.
For a better understanding of this research’s steps and
progress, a flowchart is presented in the Appendix, Figure A1.
CASE STUDY
In this study, the drainage basin of Zarinehrood was chosen
to evaluate the function of selective methods. The drainage
basin of Zarinehrood, with an area of 1,100 square kilo-
meters, is the largest sub-basin of Urmia which is located
in the north-west of Iran, and a valuable water resource
that supplies water needs such as drinking, industrial,
agricultural, and environmental, and makes 40% inflow to
Urmia Lake.
Five synoptic stations were chosen to cover the whole
basin which had observation data of more than 30 years,
also the observation data of these stations were driven by
the Water Resources Department from 1985 to 2017. In
this study, for assessing climate change impact on hydrologi-
cal parameters of the basin, scenarios of the Fifth IPCC
reports, e.g., RCP2.6, RCP4.5, RCP6.0, and RCP8.5, were
used. Historical and RCP data for precipitation, maximum
and minimum temperature were downloaded from https://
pcmdi.llnl.gov/mips/cmip5 in NetCDF format. The infor-
mation related to the study area was extracted, comparing
and using evaluation indexes in the differences of three
CMIP5 models’historical data with observation data of
the area, and GFDL-CM3 was chosen to be used. For down-
scaling outputs of GCMs, a perceptron neural network
(PNN) with three layers was developed, in which for train-
ing, a Levenberg–Marquardt algorithm and a sigmoid
activation function were used. For training the algorithm,
historical and observation data from 1985 to 2017 in all
three parameters were used, for choosing the appropriate
PNN layers and dots, three evaluation methods were used,
and future data from 2018 to 2050 predicted in the following
steps. Because raw data reduces the speed and accuracy of
PNN, at first, inputs were standardized by the following
formula:
Xn¼XiXmin
Xmax Xmin
(9)
where Xnis standardized parameter, i,min and max,
respectively, are row, minimum, and maximum of the par-
ameter in the series.
After downscaling, a QM method for bias correction
was used. In this step, difference in quantiles of observation
and simulated historical data in a form of polynomial func-
tion was applied on downscaled RCP data to minimize the
overall errors. In order to distribute the individual station’s
parameters to the whole basin, Thiesson polygon method
was used; in this method every station is in the middle of
a polygon that overall covered the basin, and parameters
were calculated by the following formula
P¼A1P1þA2P2þ...þAnPn
A1þA2þ...þAn
(10)
where A
1
,A
2
,…,A
n
are polygon area and P
1
,P
2
,…,P
n
are
parameters related to the central station.
Then, a rainfall-runoff model based on SCS method and
using precipitation of climate change scenarios was devel-
oped. Next, using time series and historical data an
ARMA(p,q) model for forecasting evaporation was created.
Then, considering some assumptions for predicting future
demands and using SOP (standard operating policy)
method for reservoirs in the area, a water resources manage-
ment program was developed to assess the water available
for allocating to users. The water allocation among users is
based on meeting the drinking, environmental, and indus-
trial demand and the remainder for agriculture demand.
For allocation of available water among users, game
theory concepts regarding consideration of their inter-
actions is used. The set of players for the game consisted
of West Azarbaijan, East Azarbaijan, Kordestan and
because of the sensitive situation of Urmia Lake it has
been considered as the fourth player of the game. A bargain-
ing game with the NBS in two ways, one symmetric and two
using AHP method, was created. In this game, optimization
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game terms are as follow:
[f(QWA)f(dWA )]wWA [f(QEA)f(dEA )]wEA
[f(QKRD)f(dKRD )]wKRD [f(QURL)f(dURL )]wURL (11)
s.t:
QWE þQEA þQKRD þQURL Rt(12)
(Dmin)WA QWA DWA (13)
(Dmin)EA QEA DEA (14)
(Dmin)KRD QKRD DKRD (15)
(Dmin)URL QURL DURL (16)
wWA þwEA þwKRD þwURL ¼1 (17)
Dmin ¼Ddr (18)
where WA,EA,KRD, and URL indices are, respectively,
West Azarbaijan, East Azarbaijan, Kordestan as players, f
is utility function, wis weight of each player, R
t
is available
water in each period of time, Dis demand of each player,
D
min
and D
dr
are minimum and drinking demand.
The bargaining weights of players were determined by
AHP method and Shannon entropy. First, considering
each demand of every player, an effective factor was calcu-
lated for each one of the demands. Then, according to the
effective factors, an overall importance weight for each
player was determined and used to apply to NBS
optimization.
RESULTS AND DISCUSSION
In this paper, a water allocation considering the impacts of
climate change was studied.
Based on the Fifth IPCC report, an ANN model for
downscaling and a QM model for bias correction impacts
of climate change on Zarinehrood basin for precipitation,
minimum and maximum temperature in a period of 33
years, were predicted. An output example of the process of
QM correction presented in Figure 2, shows that the accu-
racy percentage trend of simulated data gets closer to
observation data.
Figure 2 |Quantile mapping correction.
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As for downscaling, three evaluation methods, agree-
ment index (AI), root mean square error (RMSE), and
Pearson correlation coefficient (r) were used, with results
for five synoptic stations presented in Table 1. Correlation
between observation and simulated data is between 0.6
and 0.8, which shows that in this interval the algorithm
simulated data in a linear way and the reset of simulation
is non-linear. The AI index is approximately near 1 which
shows an acceptable connection between sets of data
(Meyers et al. 2005).
After correction of each station, distribution to the
whole basin was projected and the final results of each par-
ameter calculated for each scenario. Overall results show a
decrease in both minimum and maximum temperatures, in
which, from RCP2.6, to RCP4.5, to RCP6.0, and to RCP8.5
rises are greater, with RCP8.5 having a peak of almost
þ3.6 C. As for precipitation, there are rises at peak daily
rainfall, but the overall monthly precipitation has a nega-
tive trend, in which from RCP2.6, to RCP4.5, to RCP6.0,
and to RCP8.5 decreases in rainfall are greater. For
example, better comparison results for one of the stations,
i.e., Mahabad, are presented in Figure 3. For this station an
average yearly observation precipitation was 395 mm, and
the values for RCPs from RCP2.6, to RCP4.5, to RCP6.0,
and to RCP8.5 are around 390, 365, 345, and 335 mm.
Two scenarios, RCP2.6 and RCP8.5, are chosen for the
next step in allocation.
Using an ARMA(10,1) model for evaporation esti-
mation, SOP method for reservoir’sreleaseandSCS
method for rainfall-runoff, water available for allocation
was determined. The results show a positive trend at the
end of the prediction interval for RCP2.6 and a negative
one for RCP8.5.
Calculating bargaining weights using Shannon entropy,
Eindex for each player dividing by demands, and E
j
,d
j
,
and W
j
for each demand, are presented in Tables 2 and 3.
Based on the results of each demand’s weights from
Shannon entropy, the bargaining power of players’set:
{WA, EA, KRD, URL} are, respectively, {0.425, 0.234, 0.06,
0.281}. These powers show that sensitivity and importance
among players (from the first to the last) are player WA,
URL,EA, and KRD.
Using symmetric NBS and asymmetric NBS based on
AHP method, the results of players’utility function are
represented in Table 4.
Table 4 shows that with a symmetric assumption for
bargaining, utilities are not the same and the player with
the largest demand has the highest utility and the same
goes for the lowest demand and utility; but, asymmetric
powers which are determined by AHP provide the almost
same utility for all players which means a higher satisfaction
and lower chance of leaving the agreement in the players’
set. For a fair and stable game set, bargaining power based
on the demands of each player and each demand’s priority
should be considered.
CONCLUSION
In this study, water allocation under the effects of climate
change based on game theory was implemented for the
Zarinehrood River basin located in the north-west part of
Iran. The main objective is to work and evaluate selected
methods on achieving this goal.
For the first phrase of the study, which is assessing
climate change impacts, models were developed on the
Table 1 |ANN evaluation index
Station
Maximum temperature Minimum temperature Precipitation
RMSE r AI RMSE r AI RMSE r AI
Takab 0.001 0.788 0.9063 0.001 0.745 0.9130 0.003 0.755 0.9425
Mahabad 0.005 0.679 0.9112 0.004 0.684 0.9215 0.004 0.678 0.9544
Zarineh 0.004 0.682 0.9532 0.005 0.649 0.9461 0.001 0.622 0.9167
Maragheh 0.004 0.780 0.9074 0.003 0.753 0.9713 0.003 0.798 0.9538
Saghez 0.002 0.752 0.9637 0.006 0.632 0.9889 0.002 0.695 0.9442
9H. Hemati & A. Abrishamchi |Water allocation using game theory under climate change impact Journal of Water and Climate Change |in press |2020
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future runoff from three factors, minimum and maximum
temperature and rainfall, using the Fifth IPCC report. The
results with three evaluation indices showed that ANN
models for downscaling together with QM model for bias
correction can be used as a predictive algorithm that pro-
vides a good predictive accuracy. Testing of the trained
ANN produced a similarly good fit. In general, the use of
these two methods together can give a good confidence
quantity limit.
Considering the complexity and systemics of water
resources allocation to establish a bargaining power
Table 2 |E index
Players Environmental Agricultural Industrial Drinking
WA 0.322904 0.309192 0.366285 0.32762
EA 0.283974 0.365298 0.360781 0.36733
KRD 0.233706 0.202665 0.288856 0.366341
URL 0.355355 –––
Figure 3 |Precipitation, maximum and minimum temperatures.
Table 3 |Ej, dj, and Wj for each demand
Index Environmental Agricultural Industrial Drinking
E
j
0.862688 0.632734 0.732833 0.765561
d
j
0.137312 0.367266 0.267167 0.234439
W
j
0.1365 0.3650 0.2655 0.2329
Table 4 |Players’utility
Player
2.6 8.5
AHP Symmetric AHP Symmetric
WA 60.39 56.06 50.25 43.84
EA 63.98 60.14 52.95 57.35
KRD 65.6 88.08 59.94 83.49
URL 63.25 64.55 57.22 56.45
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evaluation index system of countries in the negotiations and
use in the bargaining game of water resources distribution
make the bargaining game model more reasonable and rea-
listic (Svejnar ). Hence, this work has made efforts to
find water allocation methods that are fair, efficient, and sus-
tainable. When the minimum survival water demand is
considered, the disagreement points are more reasonable
than when the minimum survival water demand is not con-
sidered. This method could avoid the unreasonable
phenomenon in which there are disagreement points
below the minimum water supply, or zero. The proposed dis-
agreement points can guarantee basic water demands are
met. In the process of water resources allocation, calcu-
lation of the bargaining weights using the AHP method
can result in an efficient, equitable, and sustainable benefit
among stakeholders, which could be more in line with
actual water resources allocation. The results can be utilized
as a basis for supporting decision-makers of a river basin to
resolve social conflicts.
Regarding Zarinehrood basin, results show an increase
in peak daily rainfall but reduction in overall precipitation
which follows water deficiency. Also, an increase in temp-
erature results in evaporation growth and this too follows
with a reduction in available water. Allocation using bar-
gaining power driven by the AHP method showed an
equity in participants’utility which follows satisfaction of
parties and a more stable union with a minimum chance
of leaving the agreement.
In general, considering climate change’s three par-
ameters, demands of each player, each demand’s priority,
and the lowest point of demand, and also taking
into account Urmia Lake as a player due to its critical
situation, made this water allocation prediction good and
fair.
For improvement of this study, using a different rainfall-
runoff model, multi-model climate change methods, and
another assumption on demands are recommended.
SUPPLEMENTARY MATERIAL
The Supplementary Material for this paper is available
online at https://dx.doi.org/10.2166/wcc.2020.153.
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