Journal of Hydrology 605 (2022) 127313

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Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol

Research papers

Reservoir operation under accidental MTBE pollution: A graph-based
conflict resolution framework considering
spatial-temporal-quantitative uncertainties
Sadegh Vanda a, Mohammad Reza Nikoo b, *, Parnian Hashempour Bakhtiari a, Malik Al-Wardy c,
Jan Franklin Adamowski d, Jiří Šimůnek e, Amir H. Gandomi faDepartment of Civil and Environmental Engineering, Shiraz University, Shiraz, IranCollege of Engineering, Department of Civil and Architectural Engineering, Sultan Qaboos University, Muscat, Omanc
Department of Soils, Water and Agricultural Engineering, Sultan Qaboos University, Muscat, Omand
Department of Bioresource Engineering, McGill University, 21111 Lakeshore Road, Saint-Anne-de-Bellevue, QC, CanadaeDepartment of Environmental Sciences, University of California, Riverside, USAf
Faculty of Engineering & IT, University of Technology Sydney, Sydney, Australiab

A R T I C L E I N F O

A B S T R A C T

This manuscript was handled by Corrado Cor­
radini, Editor-in-Chief

Given the hazardous effects of sudden dam reservoir contamination — as might occur upon the intrusion of thefuel additive methyl tert-butyl ether (MTBE) — the contaminant’s effect on the quality of allocated waters requires
careful study. Employed to determine optimal reservoir operational rules in the case of sudden MTBE pollution, arisk-based simulation–optimization model was developed to simultaneously minimize unsatisfied water demand,
the risk of violations of water quality standards, and the reservoir recovery time. Risks were assessed byconsidering various often-neglected pollution scenarios as a combination of location, quantity, and the season ofpollution intrusion. The appropriateness of operational rules proved to depend upon thermal conditions and
MTBE intrusion properties, confirming the necessity of considering location-quantity-season uncertainties. Socialand regional conditions also occupied a dominant role in determining the level of satisfaction achieved under
different water allocation strategies. Accordingly, by considering environmental conditions and local rules, agraph model for conflict resolution was established and used to reach a set of compromise operational rules. The
developed framework could serve as a guide for water utilities to determine efficient reservoir operational rules
after a sudden contaminant intrusion.

Keywords:
CE-QUAL-W2 simulation model
Conditional value at risk
GMCR+ decision support system
Surrogate models

1. Introduction
Dam construction is a common solution to cope with year-roundagricultural and domestic water demands, especially in areas subject
to a hot and dry climate. Generally, dam reservoir water withdrawals arescheduled according to specific operational rules that depend on envi­
ronmental conditions, quantity and quality of available water, and dam
characteristics (e.g., Kerachian and Karamouz, 2006; Ashofteh et al.,2015; Pourshahabi et al., 2020). Among these influencing factors, thedanger of large dam reservoirs being intentionally or accidentally sub­jected to pollutant intrusion is of the utmost importance. Pollutant
intrusion accidents most commonly occur as a result of human error, e.
g., failure in the transportation of hazardous chemicals (Li et al., 2014).

A sudden toxic chemical discharge into the Rhine River from a chemical
warehouse fire via fire-fighting water runoff in 1986 (Giger 2009), theaccidental contamination of Kyrgyzstan’s Lake Issyk-Kul and Barksoon
River with sodium cyanide, spilled near the Kumtor gold mine in May
1998 (Pannier, 1998), pollution of Cayuga Inlet Creek (West Danby, NY)with diesel oil following a train derailment (Lytle and Peckarsky 2001),
and a spill of arsenic-rich tailings from a pyrite mine in southern Spain(Kraus and Wiegand 2006), are only a few examples of sudden chemical
contamination causing serious damage to aquatic life and contributing
to ecosystem degradation. This issue is rather more critical in developing
countries. For example, on March 4, 2003, a truck accident released
30,400 L of methyl tert-butyl ether (MTBE) into the Khalife-Tarkhan River(near Sanandaj, Upper Gheshlagh River basin, Kordestan, Iran). The spill* Corresponding author.
E-mail addresses: m.reza@squ.edu.om (M.R. Nikoo), mwardy@squ.edu.om (M. Al-Wardy), jan.adamowski@mcgill.ca (J. Franklin Adamowski), jiri.simunek@ucr.
edu (J. Šimůnek), Gandomi@uts.edu.au (A.H. Gandomi).
https://doi.org/10.1016/j.jhydrol.2021.127313
Received 28 April 2021; Received in revised form 29 November 2021; Accepted 2 December 2021
Available online 20 December 2021
0022-1694/© 2021 Elsevier B.V. All rights reserved.

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Fig. 1. Flowchart of the proposed model for risk-based optimal reservoir operational rules under sudden MTBE pollution.

reached the Gheshlagh Reservoir within 24 hr, thereby limiting access tosafe water and restricting water allocations (Afshar et al., 2017). Since
pollutant intrusion accidents can lead to highly hazardous and acutely
critical situations with highly undesirable consequences, even slightprobabilities of contamination should be considered. In addition toemploying physical barriers such as protective guard rails for accident
prevention, appropriate operational responses must also be provided
when these accidents do occur.
Several studies have employed modified optimization algorithms(Haddad et al., 2008; Afshar et al., 2011) to provide operational
response strategies that balance concerns regarding freshwater quality
and the quantity of water available to meet demands (Chaves et al.,
2003; Kerachian and Karamouz, 2007; Castelletti et al., 2014; Azadi
et al., 2019). Accordingly, it is critical that the operational rules devel­
oped and implemented in response to a reservoir’s sudden pollution anddecline in water quality should be valid and effective. A range of sim­
ulation–optimization models has been applied to determine standard
reservoir operational rules and allocate stored water according to water
quality-quantity limitations (Liu et al., 2020; Nourani et al., 2020).
While operational rules to manage sudden water contamination in­cidents in reservoirs are essential to avoid adverse effects on the healthof water consumers, they have not been broadly studied (Saadatpour

and Afshar, 2013; Shokri et al., 2014; Haddad et al., 2014; 2015;
Amirkani et al., 2016). A pollution intrusion response management
model was developed by Saadatpour and Afshar (2013) to simulta­
neously minimize reservoir recovery time and reduce water quality
standard violations for different injection masses and locations, but it
neglected the effects of intrusion timing. However, it is acknowledgedthat seasonal changes in water temperature, wind speed, reservoir sur­face area, and hydraulic conditions can theoretically affect both reser­voir dynamics and the fate of pollutants within surface water bodies(Stocking and Kavanaugh, 2000). Assuming the possibility of injections
in each of four seasons, Shokri et al. (2014) and Amirkani et al. (2016)
demonstrated an apparent seasonality effect on the operational rules
developed for a volatile pollutant spill. For example, the numericalexperiment designed by Shokri et al. (2014) showed that, in terms ofpollutant duration and maximum concentration, the intrusion of a vol­atile pollutant in spring offered fewer risks than at other times. Whilestudies investigating the effect of different climatic conditions occurringwith seasonal changes (Tahir et al., 2008; Ashofteh et al., 2015), or
various pollutant characteristics (e.g., mass and intrusion location;
Saadatpour and Afshar, 2013) have successfully generated optimal
operational rules appropriate to a particular single factor, uncertainties
arising from the simultaneous and potentially synergistic effects of2

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Journal of Hydrology 605 (2022) 127313

multiple factors have not been investigated. To reduce the risk ofapplying inefficient operational rules in the case of unavoidable in­cidents, these uncertainties should clearly be addressed in the process ofdetermining optimization model objectives.
A further key issue in the case of sudden reservoir pollution is thetype of pollutant involved. Since the transport of petrol (gasoline) is
common in various parts of the world, it is important that the intrusionof various petrol additives, such as methyl tert-butyl ether (MTBE; IUPAC:
2-Methoxy-2-methylpropane), into bodies of water receive particularattention. However, among pollutants threatening the quality of surface
water bodies such as dam reservoirs, MTBE intrusion has garnered
limited attention (Amirkani et al., 2016; Shokri et al., 2014). Shokri
et al. (2014) added the capacity to simulate the fate and transport of
MTBE to the existing two-dimensional, laterally-integrated hydrody­
namics and transport reservoir simulation model, CE-QUAL-W2. This
capacity was included in the modified version of the CE-QUAL-W2
model and was shown to be reliable in a subsequent study (Afshar
et al., 2017). Nonetheless, the performance of operational rules after
MTBE intrusion has not been extensively investigated.
Reliable operational rules should be compatible with social andregional conditions, including stakeholders’ demands and goals(Daneshmand et al., 2014). In most previous studies (e.g., Kerachian andKaramouz, 2006 and 2007; Shirangi et al., 2008; Haddad et al., 2014;
Yang et al., 2014), operational rules were obtained from simu­
lation/simulation–optimization models with conflicting goals. In suchcases, attempts were made to resolve existing conflicts over selecting
operational rules using conflict-resolution methods such as Young or
Nash bargaining theories. Among conflict resolution methods, the graphmodel for conflict resolution (GMCR) has demonstrated an inherent
superiority in the analysis of the strategic aspects of water disputes(Dowlatabadi et al., 2020; Mooselu et al., 2021; Wu et al., 2019; Madaniand Hipel, 2007). By modifying classical game theory, GMCR has ach­
ieved an uncomplicated flexible structure that requires only minimal
information to model and analyze the strategic conflicts/disputes be­
tween decision-makers with multiple conflicting objectives. Despite thenecessity to consider local rules and the priorities of influential
decision-makers, the implementation of GMCR has yet to be consideredin selecting optimal compromise reservoir operational rules.
In the present study, a multi-objective simulation–optimization
model was developed to determine optimal dam water withdrawals (a.k.
a. “operational rules”) from reservoir outlets under sudden MTBE
pollution. This was carried out by simultaneously minimizing unsatis­
fied water demand, the risk of frequency-magnitude violations of water
quality standards, and the risk of modified reservoir recovery time
(RRT). The developed model sought to address the shortcomings ofprevious studies and drive progress in establishing operational rules bytaking advantage of the following approaches:

Fig. 2. Thirty-six (4 × 3 × 3) pollution scenarios: Four values (18◦ , 29◦ , 10◦ ,and 2.7 ◦ C) were taken as seasonal average temperatures in the spring, summer,
fall, and winter, respectively; segments located close to the dam outlets (#15),
in the middle of the reservoir (#9), and at the distal end of the reservoir (#2)
were chosen to represent the effect of distance of the pollutant intrusion fromthe reservoir outlets; MTBE contamination levels of 100, 200, and 300 m3
represent low, medium, and high levels of pollutant intrusion over one day,respectively.

upon thousands of input–output sets to train and validate thesurrogate model,
ii. Replacement of the simulation model by a surrogate model
thanks to a combined principal component analysis-multilayer
perceptron (PCA-MLP) artificial neural network, serving to
reduce the model’s runtime and computational burden,iii. Coupling optimization and surrogate models in the MATLAB®
environment to determine the optimal reservoir operational rules
under sudden MTBE pollution.
2. Methodology
A detailed explanation of the proposed model’s main methodologicalsteps in determining optimal reservoir operational rules is illustrated
schematically in Fig. 1. The proposed multi-objective framework (Fig. 1)
includes five steps: (i) developing pollution scenarios, (ii) running areservoir simulation, (iii) replacing the calibrated CE-QUAL-W2 simu­
lation model with an appropriate reservoir surrogate model, (iv)
determining optimal reservoir operational rules, and (v) determining
the compromise operational rule. These steps are thoroughly discussed
in the following sections.

i. Including uncertainties related to climatic conditions andpollutant characteristics by considering various pollutant intru­
sion scenarios,
ii. Assessing uncertainties arising from the potential synergistic ef­
fects of different climatic conditions and various pollutant
characteristics,
iii. Addressing uncertainties by determining optimization model
objectives for the worst-case scenarios, using the conditional
value at risk (CVaR),
iv. Determining the compromise operational rule among the Paretofront solutions with the help of conflict-resolution models, using
the GMCR + decision support system.

2.1. Development of pollution scenarios
To include the uncertainties related to the pollutant’s fate andtransport through the reservoir, operational rules were developed thatconsidered different pollution scenarios. Based on a priori knowledge ofthe processes affecting the fate of MTBE in reservoirs and sensitivity
analyses, pollutant intrusion time, pollutant quantity, and intrusion
location were identified as parameters of influence. Accordingly, threepollutant concentrations (low, medium, and high), three intrusion sites
within the reservoir (adjacent to the reservoir outlets, in the middle of
the reservoir, and farthest from the outlets), and four intrusion times(first day of summer, spring, fall, and winter) were factorially combined
to establish 36 (3 × 3 × 4) different pollution scenarios (Fig. 2). Within
this framework, the possibility of pollutant intrusion within any season
served to address the seasonality effects on thermal conditions (i.e., airand water temperature), reservoir surface area (interchangeably used

To facilitate the modeling process and provide a comprehensive
framework, the following procedures were implemented:
i. Repeated executions of the calibrated CE-QUAL-W2 water quality
and hydrodynamic model in a MATLAB® environment, drawing
3

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Journal of Hydrology 605 (2022) 127313

layers of the reservoir. Using the data regarding topography, inflow,
weather, stream temperatures, and release values, the CE-QUAL-W2
model was calibrated in two stages: (i) reservoir geometry calibration,and (ii) reservoir hydrodynamic calibration.
To define and calibrate the finite difference model for the reservoir,
information regarding reservoir geometry was gathered from a topo­
graphic map of the region and a viable volume-area-elevation diagram
for the dam’s reservoir. These served, respectively, to determine thebathymetric cross-sections and evaluate the volume-area-elevation
curve generated by the reservoir model. As the calibration of reservoir
hydrodynamic features was sensitive to depth-temperature profiles andreservoir water surface elevation, monthly vertical temperature profiles
and daily Water Surface Elevation (WSE) information was employed in
the calibration of the developed reservoir hydrodynamic model.
With respect to the fate and transport of MTBE, a modified source/
sink equation, which considered MTBE surface exchanges and biodeg­
radation processes, including volatilization and absorption from the top
layer (water surface) and possible zero- or first-order decay processes(Eq. (1)), was solved by the model in the form (Wells, 2019):

Fig. 3. Schematic representation of the fate and transport processes modeledby CE-QUAL-W2 for MTBE in reservoirs.

with reservoir level), wind speed, water demands, and reservoir inflows.
The three pollutant intrusion locations were selected to acknowledge thevariability of reservoir response to the intrusion location and provide areliable general optimization model. The selection of intrusion locations
well-distributed across the reservoir’s expanse, rather than at high-risk
intrusion locations alone, was considered in developing the numericalexperiment in this study.
These scenarios shed light on how changes in water temperature,
wind speed, and reservoir surface area might affect the fate of MTBE.
Drawing upon the observations of Stocking and Kavanaugh (2000), who
evaluated the impact of several environmental variables on the fate of
MTBE in standing waters, one can postulate that water temperature andwind speed increases might accelerate the elimination of MTBE byincreasing the rate of MTBE volatilization and decreasing its half-life. On
the other hand, an increase in reservoir surface area would decelerate
the elimination of MTBE by decreasing the rate of MTBE volatilization.

20)
20)
SgVol = − k0 θ(T−− k1 θ(T−
φg −
g
g

1
KLO2 CGKLFφg
hKT

(1)

where,
SgVol is the source/sink term for the volatile generic constituent
concentration,
k0 is the zero-order decay coefficient (g m− 3 s− 1 at 20 ◦ C),
θg is the temperature correction factor (with a typical range of
1.02–1.05 (Heald et al., 2005),
T is water temperature (oC),k1 is the first-order decay coefficient (s− 1 at 20 ◦ C),
φg is the volatile generic constituent concentration,
KLO2 is the reaeration coefficient for oxygen,
CGKLF is the unitless user-defined gas transfer factor (0.776 forMTBE), andhKT is depth of the surface layer computational cell (m).
As the focus was to develop a surrogate-based optimization model
rather than one drawing upon a calibrated CE-QUAL-W2 model, zeroorder decay was neglected, while first-order decay was determinedusing a k1 coefficient value of :2.2. Reservoir simulation
Several processes, including volatilization, advection, biodegrada­tion, photooxidation, adsorption, and abiotic degradation, are involved
in deciding the fate of MTBE in standing water (Stocking and Kava­
naugh, 2000). However, given the physicochemical properties of MTBE
(i.e., a high tendency to dissolve in aqueous media, a relatively low
Henry’s constant, and low adsorption to sediments) and its attendant
behaviour in a body of water, many of these processes were insignificant
or slow, leaving volatilization, advection, and decay processes as thepreeminent pathways of MTBE elimination (Afshar et al., 2017).
Accordingly, MTBE can be classified as a generic constituent that does
not interact significantly with any of the water quality state variables
and hydrodynamics (Wells, 2019).
A well-known two-dimensional, laterally-averaged, hydrodynamics
and water quality simulation model, CE-QUAL-W2, has been widelyused to model both vertical and horizontal pollutant propagation inreservoirs and lakes (Kim and Kim, 2006; Yu et al., 2010; Soleimani
et al., 2016; Heidarzadeh and Nejad, 2017; Azadi et al. 2019; Burigato
et al., 2019; Wells, 2019). Considering MTBE as a volatile generic con­stituent, the CE-QUAL-W2 model takes into account changes in MTBE
concentrations caused by spilling of MTBE into the lake, vertical mixingof the water body, discharge of MTBE through reservoir outflows, sur­face exchange of MTBE from the reservoir surface, and decay processes(Fig. 3).
Here, the CE-QUAL-W2 simulation model was calibrated andemployed to determine the MTBE concentration at reservoir outlets overa 70-day simulation period for different magnitudes, locations, andtimings of MTBE intrusion. The simulation period of 70 days was
adjusted to equal the maximum RRT of the various pollution scenarios.
Recognizing the ability of the CE-QUAL-W2 model to simulate thermal
stratification in reservoirs (Gelda et al., 1998; Rangel-Peraza et al.,2012), this model was also used to estimate the temperature of different

k1 =

ln2
t0.5

(2)

where, t0.5 is the MTBE half-life (Heald et al., 2005). In the present
context, the value of t0.5 was assumed to be 28 days. The correction
formulation presented by Elmore and West (1961) served to adjust thereaeration and first-order decay coefficients for other temperatures. In
this regard, the temperature correction factor (θg ) was adjusted to 1.024,
according to Wells (2019). Moreover, as suggested by O’Connor (1983),
the reaeration coefficient, as a function of wind speed, was considered todetermine the wind effects on MTBE evaporation from the top layer.
2.3. Reservoir surrogate model
Generally speaking, the implementation of CE-QUAL-W2 has beenaccompanied by considerable computational burdens. This limitation
worsened when recurrent simulations were required, such as within
simulation–optimization frameworks for fitness evaluations (Saa­datpour et al., 2020). To address the simulation–optimization model
runtime concerns, the calibrated CE-QUAL-W2 simulation model was
replaced by a modified version of the PCA-MLP surrogate model intro­
duced by Vanda et al. (2021). Based on their proposed framework,
principal component analysis (PCA) was coupled with a multilayer
perceptron architecture (MLP) artificial neural network (ANN) model toassess the operational responses to pollution intrusion scenarios.
Traditionally, a large dataset of inputs and outputs, procured by4

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Journal of Hydrology 605 (2022) 127313

repeated execution of the developed simulation model, is required totrain and validate the ANN-based surrogate models. However, theredundant information in datasets prepared in this manner would not
only potentially prevent the ANN model from accurately detecting therelationship between the input and output datasets, but might also resultin an imprecise and time-consuming surrogate model. Within thisframework, the PCA tool, therefore, served to: (i) reduce the dimensionsof input and output data, (ii) reduce the model complexity brought
about by high dimensionality, and (iii) minimize the overfitting risk of
the MLP surrogate model.

population size, operator probabilities, etc.) to determine a trade-off
curve among conflicting objectives (Shrestha and Rode, 2008). To
obtain optimal reservoir operational rules, three objective functions
were prepared:i. To satisfy agricultural water demand, the unsatisfied water demand(Z1 ) was minimized:
Z1 = Minimize(UnD)(3)

where, UnD was the seasonal maximum unsatisfied water demand,
calculated using Eqs. (S7) to (S10), Section S.3, Supplementary Material.

2.3.1. Development of the PCA-MLP model
In accordance with Vanda et al. (2021), the two matrices of daily
release strategies and their associated daily pollution concentrationlevels at reservoir outlets, whose dimensions had been reduced using the
PCA tool, were respectively introduced to the MLP model as input andoutput matrices. However, given that reservoir response can varysignificantly according to the time, location, and magnitude of thepollution intrusion, the use of such input–output data to train the MLP
model was not applicable here. To address this, a representative training
dataset was established, in which potential combinations of the four
factors of time, location, and magnitude of the pollution intrusion, as
well as daily release strategies were included. To do so, 500 different
operational rules (release strategies) for discharging water from tworeservoir outlets, applied over a 70-day period (a 140 × 500 matrix),
were generated individually for each of the four seasons. This allowed
the inclusion of seasonal effects on initial reservoir storage and daily
reservoir inflow, making it possible to evaluate the feasibility of oper­
ational rules regarding reservoir capacity and the law of continuity on adaily basis (Karamouz et al., 2003). The 3 magnitudes and 3 locations ofpollution intrusion were then combined with each release strategy
generated, resulting in 18,000 [(500 + 500 + 500 + 500) × 3 × 3]
possible scenarios.
Each possible pollutant intrusion scenario was introduced to the MLP
model through a vector including 140 daily releases and four charac­
teristics of the intrusion scenario (i.e., the values of air temperature,
location, quantity, and time of pollutant intrusion). This led to a 144 ×18000 matrix representing the MLP input dataset. To estimate seasonalpollution concentrations at reservoir outlets under all scenarios (i.e.,
500 × 3 × 3), the CE-QUAL-W2 model was forced with 500 associatedrelease scenarios, 3 quantities, and 3 locations of pollution intrusion.
This process was repeated for four seasons (i.e., the four different timesof pollutant intrusion), resulting in a 140 × 18000 matrix of MTBE
concentration levels, considering the 70-day simulation period and thetwo reservoir outlets. This generated two matrices, one of 144 × 18000
and another of 140 × 18000, representing the input and output datasets,
respectively.
As an MLP neural network model may be subject to overfitting if
trained with such a large input–output dataset (Vanda et al., 2021), thesize of the input–output dataset must be reduced while maintaining
critical information. This necessity was met due to: (i) the developmentof two distinct MLP models, one for each outlet, and (ii) the use of the
PCA tool (for more detail, see Supplementary Material, Section S.2). The
MLP model for each outlet (hereafter referred to as PCA-MLP) was thentrained and validated against the prepared input-target dataset (seeSupplementary Material, Section S.2), included within the optimization
model. This served to determine MTBE concentrations at reservoir
outlets under all pollution scenarios.

ii. To maintain the quality of water released for downstream con­sumption, the risk of frequency-magnitude violations of water
quality standards (Z2 ) was also minimized:
Z2 = Minimize(CVaRαSV )(4)where, CVaRαSV is the conditional value at risk (CVaR) of the standard
quality violation at a confidence level of α (g m− 3), determined based on
the pollution scenarios’ calculated frequency-magnitude violations ofwater quality standards [Eqs. (S12) and (S13), Section S.3, Supple­
mentary Material]. The frequency-magnitude violations were obtainedby combining the relative frequency (i.e., the number of standard vio­
lations to the total simulation period) and magnitude (i.e., the magni­
tude of standard violations to the total MTBE intrusion mass) violations
with different weights [Eqs (S14) to (S18), Section S.3, Supplementary
Material].
iii. To ensure that hydropower generation can proceed at maximum
capacity as soon as possible, the risk of modified RRT (Z3 ) was
minimized:
Z3 = Minimize(CVaRαRRT )(5)

where, CVaRαRRT is the CVaR of modified RRT at a confidence level of α ,calculated as a function of the losses of modified RRT across the pollu­
tion scenarios. The losses of modified RRT were determined by assessing
the maximum RRT of each outlet, and the difference in total MTBE
intrusion and discharged mass, for all the pollution scenarios [Eqs (S20)
to (S25), Section S.3, Supplementary Material].
Considering MTBE’s high capacity to volatilize from the water sur­face, it can be instructive to explain the importance of including an
objective function based on quality restrictions (i.e., Z2 ) within theframework of this study. Although by nature MTBE will volatilize fromthe water surface, its low Henry’s Law constant and high aqueous sol­ubility would lead it to more readily dissolve in water than volatilize.
When released in rivers and streams, this property increases its persis­
tence and mobility in the environment, such that its half-life in rivers
and streams can exceed one day (Squillace et al., 1996). For instance,
following the introduction of MTBE into Massachusetts’ Merrimack
River (January 28, 2000), elevated levels of MTBE were detected in theriver water for several days (US EPA, 2008). Hence, for a river-reservoir
system where a pollutant has been spilled into an upstream reservoir,
introducing an objective function based on quality restrictions isessential to ensure the attainment and maintenance of downstream
water quality standards.
2.5. Compromise operational rule2.4. Optimal reservoir operational rules

The GMCR theory is typically modeled with GMCR-II and GMCR +decision support systems. Hipel et al. (1997) first explored a strategic
groundwater contamination conflict using GMCR-II. Since then, manystudies have employed these decision support systems and highlighted
their capacity to aid in the investigation of the often challenging dis­putes over water resource allocation (e.g., Kassab et al., 2006; Kilgour
and Hipel, 2005; Kinsara et al., 2015; Liu et al., 2017). The GMCR +Using a Non-Dominant Sorting Genetic Algorithm (NSGA-II) (Debet al., 2002), coupled with fixed PCA-MLP surrogate models, a threeobjective optimization model was developed to determine optimalreservoir operational rules. A fast and elitist multi-objective genetic al­
gorithm, NSGA-II employs standard genetic algorithm parameters (e.g.,5S. Vanda et al.

Journal of Hydrology 605 (2022) 127313

Fig. 4. Location of the Narmab dam reservoir within Golestan Province, Iran.

Fig. 5. The (a) longitudinal profile and (b) plan view of the 16 segments of the Narmab dam reservoir representing the MTBE concentration on the 278th Julian-day(fall season), two days after the intrusion of 300 m3 pollutant from segment #9. The double arrow represents the pollutant intrusion location.

6

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Journal of Hydrology 605 (2022) 127313

Fig. 6. The Pareto-front solutions of the developed risk-based optimization model.

decision support system was employed in the present study to determine
a compromise operational rule among optimal rules. Local/govern­
mental stakeholders were considered decision-makers, and their op­
tions, based on their priorities and goals, were identified as a conflictmodel. The feasibility, reversibility, and prioritization of options werethen specified to analyze the model. Finally, the stability of the desired
resolution was examined based on general metarationality (GMR), Nashstability (Nash), symmetric metarationality (SMR), and sequential sta­bility (SEQ) solution concepts (Nash, 1951; Howard, 1971; Takahashi
et al., 1984; Kinsara, 2018).

demands met all year long under any circumstance. In contrast, theDepartment of the Environment insisted on minimizing environmental
pollution, preferring the time-consuming process of within-reservoir
pollution control rather than the release of polluted water. Beyond
these water quality-magnitude conflicts, the Ministry of Energy, which
operates the hydroelectric power plant, preferred the shortest possible
reservoir recovery to generate electricity, with the dam at full capacity
as often as possible. This conflict was further explored using the devel­
oped GMCR.
4. Results and discussion

3. Case study

The proposed simulation–optimization model determined optimal
operational rules by assessing different values of daily releases fromreservoir outlets for 36 different pollution scenarios (as illustrated inFig. 2).
Including uncertainties, the model minimized the risk of modified
RRT and frequency-magnitude violations of water quality standards
after the sudden intrusion of MTBE by coupling the optimization modelwith the validated PCA-MLP surrogate model. Fig. 6 shows the 12
Pareto-front solutions produced by NSGA-II for a population size of
1,520 after reaching the specified maximum number (2 0 0) ofgenerations.
Values of RRT ranged between 0.6 and 0.9 (Fig. 6), where 0 ≤ RRT ≤
1.0 , and RRT = 0 and RRT = 1.0, respectively, represent a lack of MTBE
contamination in water discharged from reservoir outlets and noreservoir recovery after 70 days of imposed reservoir recovery opera­
tional rules. The same ranges were followed for the risk of frequencymagnitude violations of water quality standards.
Setting out compromise reservoir operational rules based solely on
the Pareto-front solutions was a challenging issue given the conflict
between the Ministries of Agriculture, Energy, and Environment
regarding two aspects of RRT and the quantity of water discharged fromreservoir outlets (Fig. 6). The decision variables corresponding to thePareto-front solutions served to determine three affecting parameters

The efficiency of the developed model was tested against data fromthe Narmab dam in Golestan province, Iran. Constructed to meet thegrowing agricultural and domestic water demands of the cities of Minoo
Dasht, Azad Shahr, and Gonbad Kavoos, the Narmab dam supplies water
to a cultivated area of 190 km2, as well as generating hydroelectric
power. At an average level, the Narmab dam reservoir holds 115.43 ×
106 m3 of water (Sedghamiz et al., 2018) (Fig. 4).
The CE-QUAL-W2 simulation model of the Narmab dam reservoir
considered 23 layers and 16 segments in simulating the fate and trans­
port of MTBE within the dam reservoir (Fig. 5). The simulation model
was calibrated using the data mentioned in Section 2.2, collected over afull year (2012) by the Golestan Province Regional Water Agency. Sea­
sonal thermal conditions and other climatic parameters were taken fromestablished values for different climate periods in the study area.
Addressing a multi-dimensional issue with several objectives, thepresent study developed compromise operational rules for the Narmab
dam, minimizing unsatisfied water demand, violations of water quality
standards, and modified RRT for its reservoir under sudden pollution
intrusion, thereby meeting the respective and sometimes-competing
priorities of the Ministries of Agriculture, Environment, and Energy
regarding the quantity and quality of water released. In one such sce­nario, the Ministry of Agriculture wished to see agricultural water
7

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Journal of Hydrology 605 (2022) 127313

Fig. 7. Cumulative water releases corresponding to the Pareto-front solutions (MCM = 106 m3).

Fig. 8. RRT for three operational rule categories for 36 pollution scenarios. Note: The horizontal axis shows the pollution scenarios; for instance, scenarios 1 to 9
belong to the Spring season, and scenario 1 is an MTBE pollution scenario with 100 m3 intrusion flow from segment #2. See Fig. 2 for more details on the speci­
fications of scenarios.

from each decision-maker’s point of view, taking advantage of the postprocessing capability provided in the optimization model. One of theaffecting parameters was labeled “modified RRT,” which imposed theMinistry of Energy functions’ direct effect. The “released MTBE” and“satisfied water demand,” of major concern for the Ministries of Envi­ronment and Agriculture, respectively, were also introduced as affecting
parameters.
The cumulative values of the decision variables (daily operationalrules) over 70 days of the simulation are shown in Fig. 7. The RRT risk
values for the Pareto-front solutions revealed that the determined
operational rules were all capable of completely removing the MTBE
pollution in less than 70 days. Consequently, the wide range of cumu­
lative water release values under the operational rules indicated thatwater releases were not the only factor in MTBE pollution elimination,
but that, considering the volatility of MTBE, thermal conditions mightalso exert potential effects. Thermal conditions, wind speed, andreservoir surface vary seasonally; accordingly, any operational rules
determined through this process would only be reliable when seasonal
performances are assessed. Furthermore, the time to reach the peakpollutant concentration at reservoir outlets, the maximum pollutant
concentration, and the RRT values of each operational rule might beaffected by the reservoir configuration’s role in the elimination ofpollution, which would be significantly different given different
pollutant intrusion locations (Vanda et al., 2021).
Optimal reservoir operational rules were divided into three cate­gories: “Evaporation-based Rule,” “Evapo-release-based Rule,” and“Release-based Rule” for low, medium, and high releases, respectively(Fig. 7). The release-based rule attempted to control MTBE pollution bymassive flow releases; this might pose serious hazards to the environ­ment. In contrast, the evaporation-based rule required closing thereservoir outlets and employing the reservoir’s capacity to control the
MTBE pollution through MTBE volatilization. The RRT values of each8

S. Vanda et al.

Journal of Hydrology 605 (2022) 127313

Fig. 9. (a) The total quantity of MTBE released over the 70-day simulation period and (b) the satisfied water demand for three operational rule categories for 36
pollution scenarios. Note: The horizontal axis shows the pollution scenarios.

category, as average values of all solutions in the category1, are shown in
Fig. 8.
The fate of MTBE after spilling into surface water strongly depends
on specific site characteristics that control chemical processes as well as
physical and biological ones. In terms of the duration of pollutant
presence and its maximum concentration, intrusion during the warmer
season was expected to be less hazardous than in other seasons,regardless of the reservoir operational rules (Shokri et al., 2014;
Stocking and Kavanaugh, 2000). Indeed, in the present case, the RRT
was significantly shorter during the warmer seasons (spring and sum­mer) than in the fall or winter (Fig. 8). Moreover, in spring and summer,
the RRTs of evaporation-based and evapo-release-based rules were
substantially shorter (usually zero) than those of the release-based rule.
In contrast, the relative duration of RRTs was distinctly longer in thecolder seasons. At first glance, these results may seem surprising as
release-based rules would apparently benefit from both volatilizationand contaminated water release; however, the high longitudinal transfer
rate and vertical mixing of the water body under release-based rules
transferred MTBE to the underlying reservoir layers, which significantly
reduced the possibility of MTBE removal by volatilization and resulted
in a rational increase of RRT in warm seasons.
Seasonal variations in RRT (Fig. 8) show quantity and intrusion
location of MTBE in warm seasons to have a negligible effect on RRTvalues in the case of evaporation-based and evapo-release-based rules,
whereas their effect was quite apparent for release-based rules. The
relation between the RRT values and MTBE intrusion location andquantity became more highly significant in the colder seasons for all

specified operation rules. Analogously, analysis of the released MTBE
(Fig. 9a) shows that in fall and winter, considering both the lower air
temperatures and the characteristics of release-based rules, the possi­
bility of removing pollution by volatilization was reduced, and a ma­
jority of the injected MTBE reached the reservoir outlets. Moreover, as
the MTBE intrusion location approached the reservoir outlets, the res­ervoir’s role in removing MTBE was diminished, thereby increasing theamount of discharged pollution. Hence, the level of impact of MTBE
quantity and intrusion location on the effectiveness of operation rules ishighly dependent on pollution season (thermal conditions) and theoperation rule selected.
Considering RRT values, evaporation-based rules were satisfactory inTable 1
Options for the conflicts between the Ministries of the Environment, Agriculture,and Energy over reservoir pollution control.
Ministry

Options

EnergyReach a minimum RRT with no reduction in power generation (RRT
up to 1 week) (Non-stop)
Reduce the power generation for a limited time (RRT of 1 week to 40days) (Stand-by)
Stop power generation (RRT of 40 to 70 days) (Shutdown)
Insist on pollution control inside the reservoir with no release (Norelease)
Limit the amount of released MTBE to a maximum of 3 × 106 g(Restricted release)
Limit the amount of released MTBE to a maximum of 1.5 × 107 g(Controlled release)
Warn the water consumers about the water pollution (the released
MTBE exceeds 1.5 × 107 g) (Warn-only)
Meet all water demand (more than 80%) (Fully-satisfied)
Meet more than 45% of the water demand (Partially-satisfied)
Meet the water demand up to 45% (Poorly-satisfied)
Meet less than 25% of the agricultural water demand (Not-satisfied)

Environment

Agriculture

1

As an example, the RRT of the evaporation-based rule was equal to theaverage of RRT values related to the Pareto-front solutions number 7 and 9 to12.
9

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Journal of Hydrology 605 (2022) 127313

Table 2
The feasible states of the conflicts between the Ministries of Agriculture, Energy, and Environment over reservoir pollution control.
Ministry

Options

State number
1
2

3

4

5

6

7

EnergyNon-stop
Stand-by
Shutdown
No-release
Restricted release
Controlled releaseWarn-only
Fully-satisfied
Partially-satisfied
Poorly-satisfied
Not-satisfied

Y1
N2
N
N
Y
N
N
Y
N
N
N

Y
N
N
N
N
Y
N
Y
N
N
N

N
N
Y
N
N
Y
N
Y
N
N
N

Y
N
N
N
N
N
Y
Y
N
N
N

N
N
Y
N
N
N
Y
Y
N
N
N

Y
N
N
Y
N
N
N
N
Y
N
N

Environment

Agriculture

1

N
N
Y
N
Y
N
N
Y
N
N
N

…

14

15

16

N
N
Y
N
N
N
Y
N
Y
N
N

Y
N
N
Y
N
N
N
N
N
Y
N

N
Y
N
Y
N
N
N
N
N
Y
N

24

25

26

N
N
Y
N
N
N
Y
N
N
Y
N

Y
N
N
Y
N
N
N
N
N
N
Y

N
Y
N
Y
N
N
N
N
N
N
Y

24

25

26

N
N
N
N

✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Y
Y
Y
Y

✓
✓
✓
✓
✓
✓
✓
✓
N
N
N
N

…

…

Y: Yes, 2N: No

Table 3
Stability analysis and equilibrium results (a complete table is provided in the Supplementary Material, Section S.4).
Ministry

Stability

Energy

GMR1
Nash2
SEQ3
SMR4
GMR
Nash
SEQ
SMR
GMR
Nash
SEQ
SMR
GMR
Nash
SEQ
SMR

Environment

Agriculture

Equilibrium

1

State number
1
2

3

✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Y
Y
Y
Y

✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Y
Y
Y
Y

✓
✓
✓
✓
✓
✓
✓
✓
N
N
N
N

4

5

✓
✓
✓
✓
✓
✓
✓
✓
N
N
N
N

✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Y
Y
Y
Y

6

7

✓
✓
✓
✓
✓
✓
✓
✓
N
N
N
N

✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Y
Y
Y
Y

…

14

15

N
N
N
N

✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Y
Y
Y
Y

16

✓
✓
✓
✓
✓
✓
✓
✓
N
N
N
N

…

…

GMR: general meta-rationality, 2Nash: Nash stability, 3SEQ: sequential stability, 4SMR: symmetric meta-rationality.

spring and summer, while release-based rules were a better choice in fall
and winter. However, when other factors (Fig. 9) were included,
arriving at a decision was more complicated. The total quantity of
released MTBE was greater under released-based rules, and this differ­ence was greater in the colder seasons (Fig. 9a), the period when theserules should technically have been better alternatives (e.g., Fig. 8). In asimilar manner (Fig. 9b), evaporation-based rules performed poorly inmeeting water demands, especially in hot seasons, which may raise
objections against their selection for such an application.
The most appropriate compromise solution was selected by exam­
ining the strategic conflicts between the ministries using the GMCR +decision support system. First, the decision-makers’ options and pref­
erences were modeled. Table 1 shows the viable options for the multiministry conflict over reservoir pollution control.
Considering the possibility of selecting/deselecting any of these op­
tions, 211 = 2,048 states were possible in this conflict, some of whichwere not feasible. Each ministry’s set of options (Table 1) was mutually
exclusive and should be selected individually. For the Ministries of En­
ergy, Environment, and Agriculture, respectively, there existed 1024,
532, and 352 states in which two of a single ministry’s options wereselected as unfeasible (as explained in Table S2, Supplementary Mate­rial). Furthermore, a state in which a decision-maker chose no option
was also deemed non-feasible, and, consequently, 76 more states were
removed. The remaining states not deemed feasible arose from thegoverning environmental/physical conditions. Simultaneous selectionsof “Stand-by” and “Controlled release,” “Stand-by” and “Warn-only,”“Stand-by” and “Fully-satisfied,” “Controlled release” and “Partiallysatisfied” were impossible, making a further 30 states not feasible. With
2,014 non-feasible states, 34 feasible states remained (Table 2) (thecomplete table is provided in the Supplementary Material, Section S.4).
Next, the feasible states were ranked considering each decisionmaker’s relative preferences (Table S4, Supplementary Material, Section
S.4). The stability of feasible states was then assessed by four stability
criteria (Nash, SEQ, GMR, and SMR) to determine possible equilibrium(Table 3). Since each option corresponds to a certain range of theaffecting parameters, the affecting parameters were sorted and catego­
rized to determine the compromise solutions among the Pareto-fronts(Fig. 10; the exact values of affecting parameters are provided in Sup­
plementary Material, Section S.5).
The relative overlap in the goals of the Energy and Agriculture
ministries is an arguable point with regard to the release of polluted
water from reservoir outlets. Despite such overlaps, the inherent con­flicts of existing goals and desires needed to be investigated, especiallywhen the purpose was to obtain a compatible solution through gametheory-based GMCR modelling. The combination of these two goals asa single objective may accordingly disturb the developed model’srobustness and eliminate the bargaining possibility between the au­thorities selected. This is clearly illustrated in Fig. 10, where consideringsolution #3 during the warmer seasons (spring and summer), would
fully satisfy the Ministry of Energy’s desires, while the Ministry ofAgriculture would find the conditions less desirable, but acceptable.
Based on seasonal compromise solutions for the spring (Fig. 11), theMinistry of Energy could choose between the “Non-stop” and “Stand-by”
options; the Ministry of Environment could select between “No-release”
and “Restricted release,” while the Ministry of Agriculture could choose
from “Partially-satisfied,” “Poorly-satisfied,” or “Not-satisfied” options.
To facilitate conflict resolution, solution 3, corresponding to stable state
7, was adopted (Table 2 and Fig. 10). The same pattern was followed in10

S. Vanda et al.

Journal of Hydrology 605 (2022) 127313

Fig. 10. Sorting and categorizing the values of affecting parameters by the available options. Note: the outcomes are sorted top-to-bottom for each season according
to the available options; the seasonal ideal scenario is provided in Fig. 11.

other seasons, with solution 3 adopted in summer and solution 12 in fall
and winter. It is noteworthy that in fall and winter, the Ministry of En­
ergy had no choice but to shut down the power generators in agreementwith states 2, 4, and 6. Hence, in these seasons, state 1 was the stablestate considering the GMCR unilateral moves (Fig. S3, Supplementary
Material, Section S.5).
The RRT, released MTBE, and satisfied water demand of solution 3(release-based rule) and solution 12 (evaporation-based rule) under
different pollution scenarios (Fig. 12) showed that solution 12 could
control the MTBE pollution in a shorter time (Fig. 12a) with less envi­
ronmentally destructive effects (Fig. 12b) than solution 3. However, thesatisfied water demand of 22.5% vs. 46.0% (spring) and 23.2% vs.
46.8% (summer) (Fig. 12c), for solutions 12 and 3, respectively, finally
led to an agreement on solution 3.
11

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Journal of Hydrology 605 (2022) 127313

Fig. 11. Seasonal compromise solutions produced by the GMCR model.

Fortunately, higher temperatures in warmer seasons accelerated theprocess of pollution control inside the reservoir, and the amount of
released polluted water in both solutions remained within an acceptable
range (Fig. 12b). In fall and winter, the results given by solutions 3 and
12 were similar. Solution 12 remained more environmentally friendly inthese seasons, but required a longer RRT and provided less water de­mand satisfaction than solution 3, which made a choice difficult. With
the developed GMCR model (Fig. 11), the decision-makers chose solu­
tion 12, considering the slight differences in RRT and acceptable valuesof unsatisfied water demand for both solutions. It was apparent that thecompromise operational rules developed in this study were in directcontradiction with those chosen by strictly comparing RRT values. This
contrast indicated the importance of including regional conditions indetermining reliable reservoir operational rules after sudden reservoir
pollution.
The MTBE concentrations at the reservoir outlets for solutions 3 and
12 for different pollution scenarios (Fig. 13 and Fig. S4, respectively)
show that the maximum daily MTBE release from the reservoir outlets inthe cold seasons (fall and winter) was considerably greater than in thespring and summer (Fig. 13). Moreover, the time required for the daily
released MTBE to reach its maximum was much shorter in the coldseasons, confirming the direct effect and importance of reservoir

thermal conditions in controlling the amount of MTBE released
downstream.
5. 1. Analysis of solution reliability
As inadequate calibration of the developed CE-QUAL-W2 model andimplementation of the surrogate model can lead to errors in the opti­
mization process, one must evaluate the reliability of the operationalrules obtained. A post-audit concept was employed in this study toinvestigate the robustness of the CE-QUAL-W2 and PCA-MLP models
employed to estimate the reservoir responses under different pollutant
intrusion scenarios. The post-audit concept requires the introduction of
meaningful changes to the model to see whether expected shifts occur inthe results considering the model’s expected behavior. As a reasonablestraightforward test, post-audit evaluates the simulation model’s ca­
pacities by assessing the occurrence of anticipated changes (Wells,2019). Variations in RRT, released MTBE, and satisfied water demandvalues for three operational rule categories and for 36 pollution sce­narios were investigated (Figs. 8 and 9). The different operational pol­icies, i.e., “Evaporation-based Rule,” “Evapo-release-based Rule,” and“Release-based Rule” led to responses from the reservoir that were
acceptable based on the existing understanding of the processes
12S. Vanda et al.

Journal of Hydrology 605 (2022) 127313

Fig. 12. (a) The RRT, (b) total released MTBE over 70-day simulation period, and (c) satisfied water demand of solutions 3 and 12 for different scenarios. Note: The
horizontal axis shows the pollution scenarios.

modeled, as well as knowledge of the system being simulated. Accord­
ingly, based on the post-audit, errors due to the calibration and imple­
mentation of a surrogate were deemed negligible.

uncertainties related to the location and quantity of MTBE input should
also be taken into account to reduce the risk of operational rules’ in­adequacy in the worst possible pollution cases. Due to the optimization
model’s conflicting objectives, a compromise solution was chosen
through a GMCR model. The compromise solutions were actually indirect contrast with the preliminary judgments, with a release-based
rule selected for warmer seasons. At the same time, the decisionmakers agreed on an evaporation-based rule for fall and winter. The
significant impact of environmental conditions, priorities of thedecision-makers, and local rules on selecting appropriate operationalrules indicate the importance of implementing conflict-resolution
models in managing water allocation from reservoirs. In ongoing
work, the proposed framework is being combined with a pollutant
detection framework, such as that introduced by Pourshahabi et al.
(2018), to examine the possibility of real-time reservoir operation under
accidental pollution.

6. Summary and conclusions
As large dam reservoirs are often exposed to intentional or accidental
pollution, an appropriate operational response when sudden reservoir
pollution occurs is key to avoiding harmful health effects. The model
developed in this study imposed optimal operational rules by simulta­
neously minimizing the unsatisfied water demand, the risk of frequencymagnitude violations of water quality standards, and the risk of modi­
fied reservoir recovery time (RRT). It considered 36 different pollution
scenarios (a combination of location, quantity, and time of pollution
intrusion). The gasoline additive MTBE was considered as the injected
pollutant. A direct effect of thermal conditions on the relative perfor­
mance of different operational rules used to control MTBE pollution wasnoted. The evaporation-based rules performed satisfactorily in springand summer due to the higher temperatures, whereas release-based
rules provided a superior alternative in the colder seasons. Accord­
ingly, reliable operational rules can only be determined when thepollution intrusion time uncertainties are included.
Similarly, the significant difference between the objective values
related to the pollution scenarios in each season indicated that theCRediT authorship contribution statement
Sadegh Vanda: Investigation, Methodology, Software, Formal
analysis, Visualization, Validation, Writing – review & editing.
Mohammad Reza Nikoo: Supervision, Conceptualization, Resources,
Methodology, Software, Validation, Writing – review & editing. Par­nian Hashempour Bakhtiari: Writing – original draft, Writing – review
13

S. Vanda et al.

Journal of Hydrology 605 (2022) 127313

Fig. 13. MTBE concentrations at the reservoir outlets for solution 3 for different pollution scenarios.

14

S. Vanda et al.

Journal of Hydrology 605 (2022) 127313& editing, Visualization. Malik Al-Wardy: Conceptualization, Writing –review & editing. Jan Franklin Adamowski: Conceptualization,
Writing – review & editing. Jiří Šimůnek: Conceptualization, Writing –review & editing. Amir H. Gandomi: Conceptualization, Writing – re­view & editing.

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The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.
org/10.1016/j.jhydrol.2021.127313.
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