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Simulating hedging rules for effective reservoiroperation by using system dynamics: a case study ofDez Reservoir, IranFarshid Felfelani a , Amir Jalali Movahed a & Mahdi Zarghami ba Department of Civil Engineering , Sharif University of Technology , 11365-11155 , Tehran ,Iranb Faculty of Civil Engineering, University of Tabriz, 51666-14965 , Tabriz , IranPublished online: 06 Jun 2013.

To cite this article: Farshid Felfelani , Amir Jalali Movahed & Mahdi Zarghami (2013): Simulating hedging rules for effectivereservoir operation by using system dynamics: a case study of Dez Reservoir, Iran, Lake and Reservoir Management, 29:2,126-140

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Lake and Reservoir Management, 29:126–140, 2013C© Copyright by the North American Lake Management Society 2013ISSN: 1040-2381 print / 2151-5530 onlineDOI: 10.1080/10402381.2013.801542

Simulating hedging rules for effective reservoiroperation by using system dynamics: a case study

of Dez Reservoir, Iran

Farshid Felfelani,1 Amir Jalali Movahed,1 and Mahdi Zarghami2,∗1Department of Civil Engineering, Sharif University of Technology, 11365-11155, Tehran, Iran

2Faculty of Civil Engineering, University of Tabriz, 51666-14965, Tabriz, Iran

Abstract

Felfelani F, Movahed AJ, Zarghami M. 2013. Simulating hedging rules for effective reservoir operation by usingsystem dynamics: a case study of Dez Reservoir, Iran. Lake Reserv Manage. 29:126–140.

Some of the most important challenges facing water managers are to increase water supply and reduce its demand. Asingle systematic method is needed to address both issues, such as the System Dynamics (SD) modeling approach.In this approach all the factors, parameters, and their influences on the problem are considered by causal loops andstock-flow diagrams. The multipurpose Dez Reservoir in southwestern Iran is a good case study for this approach,and we simulated 10 years under differing operation strategies to develop the most appropriate operation policy. Ahydrologic time series analysis was conducted to generate simulated inflow to the reservoir, and differing policies,including hedging rules and a “goal-seeking hedge,” were applied. By using performance criteria and a new measureentitled “corrected reliability,”, the most appropriate scenarios were identified. We found that using the goal-seekinghedge in combination with water demand management offers the best chance for effectively meeting demands andminimizing supply shortages.

Key words: performance criteria, reservoir operation, time series analysis

High population growth combined with limited water re-sources has led to water shortages that present a seriouschallenge for many countries. As a result, many are devel-oping management policies to address the problem. Louckset al. (2005) and Mays and Tung (2002) provided an ap-propriate basis for traditional approaches to water resourcesplanning. Wurbs et al. (1985) presented a review paper list-ing more than 700 references as a bibliography on tech-niques of reservoir operation. Yeh (1985) also conducted anappropriate review on different reservoir simulation and op-timization approaches and noted that, despite improvementspresented in the literature, a practical method for reservoiranalysis has not yet been achieved, in part because operatorsare excluded from the policy-making process and partly be-cause simplified computer programs and operation policiesare not suitable for complicated, actual cases. Nonetheless,since 1985 there has been much work done in reservoiranalysis using different practical methodologies.

∗Corresponding author: mzarghami@tabrizu.ac.ir; zarghaami@gmail.com

One efficient tool in reservoir operation modeling that is at-tracting attention from water resources researchers is SystemDynamics (SD), a simulation technique based on feedbackof system elements. Keyes and Palmer (1993) developed anSD model for drought studies, and following that, Matthiasand Frederick (1994) used SD modeling to study sealevel variation in coastal regions. Along with these studies,Simonovic et al. (1997) and Simonovic and Fahmy (1999)used SD approach for long-term planning of water resourcesand policy analysis of the Nile River basin.

In recent years, use of SD as an effective simulationapproach in various studies on water resources managementhas accelerated. Zhang et al. (2008) developed a complexSD model to integrate Tianjin, China, water resourcesmanagement and then presented reasonable predictiveresults for policy-making on water resource allocation andmanagement. Fagan et al. (2010) developed a dynamicsystem-modeling framework to provide a comprehensive setof dynamic performance metrics, integrating all subsystemsof the water cycle. In Iran, Bagheri et al. (2010) adopted anSD modeling approach to examine the impacts of various

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Figure 1.-Release function according to standard operating policy for reservoirs (color figure available online).

reconstruction projects as well as water managementpolicies on the ability of the Bam urban water system tomeet increased demand trends. In a recent study, Zarghamiand Akbariyeh (2012) modeled Tabriz’s urban water systemusing an SD approach to simulate conditions in the nearfuture until 2020.

The simplest policy for reservoir operation is called “stan-dard operating policy” (SOP), which strives to meet a tar-get demand “T.” In practice, operators avoid continuouslychanging release openings, so slopes would be implementedas steps in most situations (Fig. 1).

According to SOP, if the water availability (storage + inflow)is less than water demand, all the water will be released inthe time period, and if it exceeds T plus the maximum reser-voir capacity (K), a spill will occur (Loucks et al. 2005).

In practice, most operators do not comply with SOP, andmore appropriate policies are used. Hedging, a reductionin water supply with the aim of saving some water in thereservoir to mitigate future water deficits in case of an ex-tended period of drought, is an important real-time reservoiroperation policy (Zhao et al. 2011). Bower et al. (1962)first provided a systematic economic description of hedgingrules for water resources systems; since then, hedging ruleshave become popular, and differing formulations have beenpresented by researchers. Draper and Lund (2003) listed themost common hedging rules (Fig. 2 and 3) as follows:� One-point hedging, where a line (slope <1) connects the

origin of the SOP diagram to a point on the target levelof release. The less the slope of the line, the more therelease is reduced in times of drought (Shih and ReVelle1994).

Figure 2.-One-point, 2-point, and 3-point hedging rules (color figure available online).

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Figure 3.-Continuous and zone-based hedging rules.

� Two-point hedging, where a line (slope <1) connects afirst point somewhere up from the origin on the shortagepart of the SOP rule to a second point on the deliverytarget line (Bayazit and Unal 1990, Srinivasan and Phili-pose 1996). By this strategy, releases are reduced abruptlybelow the demand to maintain some storage over the du-ration of an extended, anticipated drought.

� Three-point hedging, where an intermediate point is spec-ified in the 2-point hedging rule, introducing 2 linear por-tions. Unlike 1-point hedging, this approach allows a lessabrupt decrease in releases at the start of a drought, butthen more dramatic reductions if the drought intensifiesor lengthens.

� Continuous hedging, where the slope of the hedging por-tion of the rule is not constant and can vary continuously(Hashimoto et al. 1982). Thus the reductions below thedemand are minimized at the start of a drought condition.

� Zone-based hedging, where hedging values are definedas discrete proportions of release targets for differentzonal levels of water availability (Hirsch 1978). To someextent this rule is much easier for the dam operators toimplement.

In recent studies, You and Cai (2008) applied theoreti-cal hedging policies to Lake Okeechobee in south-centralFlorida to explore the potential advantages of hedging poli-cies for reservoir operation. Rittima (2009) developed areservoir operation model of Mun Bon and Lam Chae reser-voirs in Thailand to simulate a variety of common hedgingrules including 1-point hedging, 2-point hedging, and zone-based hedging. Following this study, Shiau (2009) evaluatedthe effects of hedging by using 2 conflicting objectives: (1)a total shortage ratio and (2) a maximum 1-month shortageratio, which represent the long- and short-term water short-

age characteristics for water supply, respectively. They alsoemployed a multiobjective genetic algorithm to solve thisoptimization problem. Eum et al. (2010) calculated opti-mal water release for droughts by combining a future valuefunction derived with a sampling stochastic dynamic pro-gramming model with a hedging rule. Guo et al. (2012)proposed a bi-level model and a set of water-transfer rulesto solve the multireservoir operation problem in interbasinwater transfer–supply projects. In this model, they consid-ered water transfer and water supply together, so that themultireservoir system manager, at the upper level of thehierarchy, optimizes water–transfer curves to spatially allo-cate transboundary water resources. The individual reservoirmanager can then optimize hedging rule curves to pursuethe best water supply accompanying the action of watertransfer.

These studies used several SD models to simulate reser-voir processes; however, none evaluated different hedgingrules in VENSIM (2010) or used a stochastic simulation ofreservoir inflows, and few of the studies were conducted onmultipurpose reservoirs. Therefore, in this study a compre-hensive introduction of the real case of Dez Reservoir inIran was introduced; then an SD modeling to evaluate thecommon hedging rule by comparison with a new type wasdeveloped; and finally the model was validated. We thencompared the results by performance measures to find themost appropriate approach in real applications.

Case studyThe Dez River, located in the southwestern part of Iran(Fig. 4), is formed by the joining of the Caesar and Bakhtiaryrivers. Based on water volume, the Dez River is the second

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Figure 4.-Location of the Dez River and Dez Dam in Iran (color figure available online).

largest river in Iran, and the Dez Dam, with a height of 203 m,is one of the tallest arch dams in Iran. It was constructed onthe Dez River in Khuzestan province to supply hydroelec-tric power, supply water for agriculture and urban demands,and to control flooding. Based on the observed flood hy-drographs, January, February, March, May, November, andDecember are the flooding months in the study area (Malek-mohammadi et al. 2011). The 3.3 billion cubic meter capac-ity and the 520 megawatt hydropower production are notablefeatures of this reservoir, which irrigates about 125,000 haof the downstream agriculture zones. These properties placethis dam in a prominent water management role in south-western Iran.

MethodsIn this study, the SD approach was used to simulate reservoiroperation. In the proposed methodology, the main steps areto define the dynamic hypothesis and develop causal loopand stock-flow diagrams (Sterman 2000). In SD, variablesare either stocks, flows, or auxiliary. Stocks are accumula-tions, such as the amount of water in a reservoir. Generally,stock variables characterize the state of the system and cre-ate the information used to make decisions and determineactions. Flow variables define rates that can change stockvariables. For example, the amount of water in a reservoir(a stock variable) is changed by inflows and outflows (flowvariables; Simonovic 2009, Hassanzadeh et al. 2012). Thestock value at any time (t) when the reservoir has one inlet

and one outlet is calculated by:

Stock(t) =∫ t

t0

[Inflow (t)

−Outflow (t)]dt + Stock (t0 ), (1)

where, Stock(t) = Stock in time t; Inflow(t) = Inflow in timet; Outflow(t) Outflow(t) = Outflow in time t; and Stock(t0) =Stock in time t0. The auxiliary variables are neither stocksnor flows. They are functions of stocks or flows.

Dynamic hypothesis, causal loop,and stock-flow diagrams

In the context of SD, behavior of the main variables mustbe studied before drawing the causal loop and stock-flowdiagrams. This process, called “presenting a dynamic hy-pothesis,” is essential to accurately define and address dif-fering aspects of the problem. If the dynamic hypothesis isproperly established, then drawing causal loop, stock-flowdiagrams, and formulating variables is easier.

The river inflow is expected to be oscillating and stochas-tic due to its dependency on precipitation, which is also astochastic variable. The reservoir storage is directly relatedto river inflow so that in rainy months the reservoir storageincreases and in dry months it decreases. The total waterdemand, including urban, agricultural, and environmentaldemands, exerts a major influence. These demands are con-trolled by population and agricultural zone growth rates.

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Figure 5.-Causal loop diagram for water management in Dez Reservoir (color figure available online).

According to the dynamic hypothesis and the relationsamong dependent and independent variables, causal loopand stock-flow diagrams were developed. The causal loopwas developed to build stock-flow diagram and to formu-late variables (Fig. 5). We then developed the stock-flowdiagram of the SD model (not illustrated here due to spaceconsiderations).

Algebraic signs at the heads indicate the polarity of therelationship. A positive polarity indicates that an increase inthe independent variable causes an increase in the dependentvariable and vice versa. A negative polarity indicates that anincrease in the independent variable causes a decrease in thedependent variable and vice versa. Positive loops reinforceand negative loops balance the main independent variable,which is the reservoir storage.

Parameter definitions

After the causal loops and the stock-flow diagram were de-termined, we identified critical points in the SD model anddescribed the variables. The main assumptions in modelingare:

1. The monthly simulation time interval for the hydrologictime series analysis in this survey was from 1961 to2011. By means of time series analysis (details presentedlater), data forecasting was conducted for 120 months(10 years), which was used as reservoir inflow in the SDmodel.

2. Satisfying urban water demand and hydropower energyproduction were assumed the higher priorities, and agri-cultural and environmental demands were lower priori-ties.

3. The Dez River basin has 125,000 ha of arable land thatshould be irrigated by Dez Dam outflow.

4. Computation of future demands was based on populationgrowth.

5. During the forecasting interval, sediment volume of thereservoir was assumed constant and equal to the presentsediment volume, which is about 700 million cubic me-ters (Mm3). For a complete model the sedimentation ratiocould be formulated with more detailed and also nonlin-ear relations; however these data were not available forthis research.

Storage:

Reservoir storage in each time interval. The initial value(about 2 × 109m3) is set as the storage value at the beginningof the simulation interval. According to Loucks et al. (2005),the storage at the beginning of the second time interval ofthe year y can be computed by:

S2y = S1y + Q1y − R1y − E1y, (2)

where, S1y is the previous reservoir storage, Q1y indicatesthe total inflow in the previous month, R1y is equal to reser-voir spill and release of the previous month, and E1y ex-presses the total evaporation of the month before.

Total inflow:

The Dez River flow, which is forecasted for 120 months(discussed in hydrologic time series modeling).

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Evaporation:

Large numbers of empirical equations are available to com-pute the evaporation value, such as the formula of UnitedStates Geological Survey or United States Bureau of Recla-mation:

E = 4.57T + 43.3, (3)

where, E is the evaporation in cm/y and T indicates themean annual temperature in C that can be computed fromthe height above sea level by some empirical relations.

f(Area-Storage) and f(Level-Storage):

To compute evaporation and spill, the water level-storageand water level-area diagrams (Fig. 6) of the Dez Reservoirwere used and defined as a lookup graph in VENSIM.

Release:

Defined according to SOP (Fig. 1 and equation 4) as:

R1y =⎧⎨⎩

S1y + Q1y − K if S1y + Q1y − Rmin > K

Rmin if K ≥ S1y + Q1y − Rmin ≥ 0S1y + Q1y Otherwise

,

(4)

where, K is the reservoir capacity, Rmin is minimum releaseto be made if possible, S1y is used to consider the previousreservoir storage, and Q1y is the total inflow in the previousmonth.

Minimum release (Rmin):

Equal to minimum demand, including minimum urban, agri-cultural, and environmental demands. Hydropower demandis considered in the next section.

Hydroelectric power production:

The primary function of the Dez Dam. The total megawatt-hours of energy produced in period t can be calculated by(Loucks et al. 2005):

MWHt = 2.725QTt Hte, (5)

where, Ht is the storage head (vertical distance betweenthe water surface elevation and the maximum of either theturbine elevation or the downstream discharge elevation),QT

t expresses the total flow through the turbines in periodt, and e is the plant efficiency. Note that the Dez Dam isequipped with a 520 megawatt hydropower plant designed toproduce about 2000 gigawatt-hours of hydroelectric energy

13.2223.2233.2243.2253.2263.22

120

130

140

150

160

170

180

190

200

0 0.5 1 1.5 2 2.5 3

Area (106 m2)

Wat

er h

eigh

t (m

)

Volume (109 m3)

Volume Area

Figure 6.-Water height–volume–area graphs of Dez reservoir (color figure available online).

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every year. In this study, supplying hydroelectric energy andsatisfying urban water demand were the first priorities.

Flood control:

Throughout the flood-prone months, the reservoir shouldhave sufficient available storage to accommodate probableflood volumes; according to Malekmohammadi et al. (2011),a 845.28 Mm3 volume should be reserved for a 1000-yearflood, and in our SD model, this recommendation was im-plemented for the flood-prone months.

Urban demand:

Computed from the population in each time interval as:

Urban demand = Population

×Water Per Capita. (6)

According to the Iran Ministry of Power and Energy lo-cal policies, 50% of the whole water demand in Khuzestanprovince, including 21 cities and 1200 villages, should besatisfied by Dez Dam. The total population of this area wasestimated to be about 2,957,600 in 2011. The average ur-ban water demand per capita in Iran is about 250 L/d, butbecause of the warm climate of Khuzestan province, thisreaches 400 L/d, or an average monthly value of 12 m3 perperson. However, for more accurate modeling, instead ofthis average value, the actual monthly urban water demandper capita of the Khuzestan province was used (Fig. 7).

Population:

Statistics show a net growth rate in this area; therefore, thepopulation at the end of the next month is calculated bymultiplying the population in the present month by the netannual growth rate (i). After n months, the new populationP is calculated from the initial population P0 as:

Figure 7.-Monthly pattern of urban water demand per capita in Dezreservoir area.

Figure 8.-Agricultural water demand per unit of area per month forDez reservoir area.

P = P0

(1 + i

12

)n

. (7)

Agriculture demand:

About 125,000 ha of the agricultural lands in Khuzestanprovince is irrigated by the Dez Dam. Average requiredwater per unit of irrigated area is about 967 (m3/hec/month),but for more accurate modeling, instead of using the averagevalue, the actual monthly required water per unit area basedon the monthly agricultural consumption pattern was used(Fig. 8). It was further assumed that this monthly agriculturedemand pattern remained constant during the simulationtime interval.

Environmental demand:

To maintain acceptable environmental conditions down-stream, the river should be maintained at a minimum flow.Although no method has been established to determine thisenvironmental demand for the Dez Dam, a value based onliterature values was computed as follows:

Environmental demand = 0.2

× mean annual minimum flow

= 0.2 × (16.394 × 3600 × 24 × 30), (8)

in which 16.394 is the mean minimum flow in m3 /sec andconverted to m3 /month.

After descibing these parameters, their formulas were incor-porated into VENSIM (Table 1).

Hydrologic time series modeling for DezRiver flow

The stochastic and seasonal characteristic of the reservoirinflows (river flow) suggested a seasonal hydrologic timeseries mode for this case study. The flow data (Fig. 9) werea nonstationary time series. This is confirmed by the Auto

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Tab

le1.

-Som

eva

riabl

efo

rmul

atio

nsto

beus

edin

SD

mod

el.

Var

iab

len

ame

Fo

rmu

lati

on

inV

EN

SIM

Stor

age

(m3 )

Stor

age

=∫ (T

otal

Inflo

w−

Eva

pora

tion

−R

elea

se−

Spill

way

)dt

Hyd

ropo

wer

Flo

w(m

3 /mon

th)

IFT

HE

NE

LSE

(Sto

rage

+To

talI

nflow

-Eva

pora

tion>

=R

eser

voir

Cap

acity

-Flo

odC

ontr

ollin

gV

olum

e(H

elp5

),M

AX

(IF

TH

EN

EL

SE(S

tora

ge+T

otal

Inflo

w-E

vapo

ratio

n>=

Min

imum

stor

age

acco

rdin

gto

Pow

erH

ouse

Inta

kele

vel,

MIN

(0.6

∗ (St

orag

e+

Tota

lInfl

ow-E

vapo

ratio

n-Se

dim

entV

olum

e),M

inim

umN

eede

dFl

ow),

0),F

lood

Con

trol

ling

Vol

ume(

Hel

p5)-

Res

ervo

irC

apac

ity+

Stor

age

+To

talI

nflow

-Eva

pora

tion)

,IF

TH

EN

EL

SE(S

tora

ge+

Tota

lInfl

ow-E

vapo

ratio

n>=

Min

imum

stor

age

acco

rdin

gto

Pow

erH

ouse

Inta

kele

vel,

MIN

(0.6

∗ (St

orag

e+

Tota

lIn

flow

-Eva

pora

tion-

Sedi

men

tVol

ume)

,Min

imum

Nee

ded

Flow

),0)

)P

rodu

ced

Ene

rgy

(MW

H)

2.72

5e-0

06∗ H

ydro

pow

erflo

w∗ W

ater

Lev

el∗ E

ffici

ency

Eva

pora

tion

(m3 /m

onth

)E

vapo

ratio

n=

Are

a×

(4.5

7×

Tem

p+

43.3

)/10

0Sp

illw

ay(m

3 /mon

th)

IFT

HE

NE

LSE

((St

orag

e+

Tota

lInfl

ow-R

elea

se-E

vapo

ratio

n-H

ydro

pow

erflo

w>

Res

ervo

irC

apac

ity),

(Sto

rage

+To

talI

nflow

-Eva

pora

tion-

Rel

ease

-Hyd

ropo

wer

flow

-Res

ervo

irC

apac

ity),

0)R

elea

se(m

3 /mon

th)

IFT

HE

NE

LSE

(Rm

in<

=H

ydro

pow

erflo

w,0

,MIN

(Sto

rage

+To

talI

nflow

-Eva

pora

tion-

Hyd

ropo

wer

flow

,Rm

in-H

ydro

Pow

erflo

w))

Rm

in(m

3 /mon

th)

(Agr

icul

ture

Dem

and

+U

rban

Dem

and

+E

nvir

onm

enta

lDem

and)

∗ Hed

ging

Rul

eTo

talD

isch

arge

(m3 /m

onth

)(R

elea

se+

Spill

way

+H

ydro

pow

erflo

w)

Agr

icul

ture

dem

and

(m3 /m

onth

)A

gric

ultu

rete

rrai

n∗ Req

uire

dW

ater

per

Are

aU

nit(

Hel

p2)∗ A

gric

ultu

reD

eman

dA

men

dmen

t

Urb

anflo

w(m

3 /mon

th)

IFT

HE

NE

LSE

(Tot

alD

isch

arge

>U

rban

Dem

and,

Urb

anD

eman

d,To

talD

isch

arge

)A

gric

ultu

reflo

w(m

3 /mon

th)

IFT

HE

NE

LSE

((To

talD

isch

arge

-Urb

anFl

ow)>

Agr

icul

ture

Dem

and,

Agr

icul

ture

Dem

and,

(Tot

alD

isch

arge

-Urb

anFl

ow))

Dow

nSt

ream

flow

(m3 /m

onth

)To

talD

isch

arge

-Urb

anFl

owH

ydro

pow

erL

oss

(m3 /m

onth

)IF

TH

EN

EL

SE(H

ydro

pow

erflo

w>

=M

inim

umN

eede

dFl

ow,0

,Min

imum

Nee

ded

Flow

-Hyd

ropo

wer

flow

)To

talS

hort

fall

(m3 /m

onth

)A

gric

ultu

reSh

ortf

all+

Urb

anSh

ortf

all+

Env

iron

men

talS

hort

fall

+H

ydro

pow

erSh

ortf

all

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Felfelani et al.

Figure 9.-Fifty-year time series of inflow to Dez River.

Correlation Function (ACF) and Partial Auto CorrelationFunction (PACF) histograms.

Differencing is one way to transform a nonstationary series,such as a seasonal series, to a stationary one (Salas et al.1980). We fit an Autoregressive Integrated Moving Average(ARIMA) model with the first-order differencing to the timeseries data (Box et al. 1994) as follows:

Z(t) + 0.78 Zt−1 + 0.62 Zt−2 + 0.32 Zt−3

+ 0.86 Zt−6 + 0.67 Zt−7 + 0.54 Zt−8

+ 0.27 Zt−9 = −645086.7 + εt

+ 0.68 εt−6 − 0.26 εt−8. (9)

The normality test of residuals indicates that the estimatedmodel was appropriate. We also compared synthetic data tothe actual time series and confirmed the goodness of fit forthe selected seasonal ARIMA model (Fig. 10). We used thismodel to generate time series of flow data and implementedit as a look-up variable in VENSIM.

Validating the SD model

Structure assessment tests

Structure assessment tests are used to assess whether a modelis consistent with knowledge of a real-world system (Ster-man 2000). Using the most recent 5 years of available stor-age volume data, the model results show acceptable corre-lation with the observations (Fig. 11).

Extreme condition tests

Some conventional tests are also used to assess the SD modelin extreme conditions and to verify its logic (Sterman 2000).In the first case, we assumed that initial storage and totalinflow were zero; hence, we expected parameters such asevaporation, release, storage, and spillway to become zeroafter simulation. In the second case we assumed the initialstorage of the reservoir to be equal to its capacity, whichmeans the reservoir is full and all output flows are equalto zero except total inflow and spillway; therefore, we ex-pected to find equal values for the spillway and the totalinflow. Both extreme validation tests yielded the expectedresults.

0

0.5

1

1.5

2

2.5

3

3.5

Riv

er F

low

(10

9m

3p

er m

onth

)

Month-Year

Actual Time Series Synthetic Time Series Forecast

Figure 10.-Synthetic time series vs. actual data accompanied by forecasted time series (color figure available online).

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0

1.5

3

4.5

0 10 20 30 40 50 60

Stor

age

(109

m3 )

Time (Month)

Observed Value Model Value

Figure 11.-Validating the Dez Reservoir SD model through storage parameter for 5 years (color figure available online).

Comparison among scenarios withperformance criteria evaluationPreliminary plan

For the preliminary policy, supplying required hydroelectricenergy and urban demand be considered our first priority.

In addition, if there is enough water storage, this policy willtry to satisfy the whole demand (maximum of Rmin and hy-dropower demand) every month. The results presented inFigs. 12–14 (representing simulated reservoir storage, thedeficits in satisfying demands and the treatment of reservoirreleases for different scenarios), respectively, show the ef-ficiency of every policy. By applying the preliminary plan

0.0

0.5

1.0

1.5

2.0

2.5

Res

ervo

ir S

tora

ge

Month-Year

Consumption Amendment Without Hedging

Hedge (0.95) Hedge (0.90)

Hedge (0.85) Goal Seeking Hedge

Figure 12.-Dez Reservoir storage (109 cubic meters) for differing hedging scenarios (color figure available online).

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8W

ater

Sho

rtfa

ll (1

08m

3 )

Month-Year

Without Hedging Hedge (0.95)

Hedge (0.90) Hedge (0.85)

Goal Seeking Hedge

Figure 13.-Water shortfall diagram for different hedging scenarios (color figure available online).

(without hedging), the reservoir storage reached the valueof 201 Mm3; however, we had severe failures to meet alldemands, such as shortfall of 160 Mm3 by the end of thesimulation period. The results of this policy are clearly un-satisfactory.

Using the hedging rule

In some cases, severe deficits in satisfying demands wouldhave irreparable consequences on downstream agronomyor industries. Water resources engineers endeavor to reduce

0

1

2

3

4

5

6

7

8

9

10

Rel

ease

(108

m3 )

Month-Year

Without Hedging Hedge (0.95)Hedge (0.90) Hedge (0.85)

Goal Seeking Hedge Consumption Amendment

Figure 14.-Dez Reservoir releases for different hedging scenarios (color figure available online).

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the severity of deficits by using methods like hedging rule.Under a hedging rule, demands are not satisfied completelyin each simulation time period, even with adequate waterstorage. The goal of hedging is to hold a volume as insur-ance against the most severe deficits that might occur duringdrought. The simplest case, a 1-point hedge, is implementedby applying reducing coefficients like 0.85, 0.90, and 0.95to the demands, which means that only 85, 90, or 95% of thetarget demands, respectively, would be satisfied in each timeinterval. The single-point hedge introduces obvious disad-vantages by using a constant reducing coefficient across allmonths. We propose a different approach, the “goal seekinghedge.” Our central assumption in this approach is that whenextreme conditions are actually encountered, hedging can berelaxed so that the “insurance” built up by hedging duringless-severe conditions is then used to combat the most se-vere effects. In this rule, instead of using a constant reducingcoefficient, a variant coefficient is implemented that reflectsthe volume of deficits in the previous periods, so that in themore severe deficits, less hedging (more delivery) is appliedas follows:

Hedging Coefficienti

= max

⎛⎝α,

⎛⎝1 − 1

i

i∑j=1

D(j ) − v(j )

D(j )

⎞⎠

⎞⎠ , (10)

where, α is the lower limit of coefficient, v(j ) is the deficitvolume, D(j ) is the total demand volume in each period,and i is the total number of time steps.

Our results indicate that by applying hedging rule, the reser-voir condition improves, and by implementing the goal-seeking hedge, we can reach the most stable conditionfor the reservoir during the simulation process (Figs. 12and 13). Thus, by applying the goal-seeking hedge, severedeficits in satisfying demands disappear. Further positive ef-fects of this hedging rule are shown by using performancecriteria.

Reducing demands by using special policies

In the Dez River basin, about 90% of water is consumedby agricultural demands; therefore, reduction in agriculturalconsumption through modernization of irrigation methodsand equipment would greatly reduce water demand. In addi-tion, the average water consumption per capita in Khuzestanis about 400 L/d, which is 3 times the average consumptionper capita in Iran; therefore, the government could apply spe-cial policies to reduce water consumption, such as increasingwater and energy costs for users, a tactic recently applied inother countries and elsewhere within Iran (Moshiri 2013).

To simulate a 20% reduction in agricultural and urban waterconsumption as well as hydroelectric energy consumption,a parameter called “demand amendment” is included in theSD model. This 20% reduction in water consumption willimprove the reservoir storage condition without applyingthe hedging rule (Fig. 12), and no deficits will occur duringthe simulation process (Fig. 13).

Evaluation of strategies by useof performance criteria

A performance evaluation was used to make a more accuratecomparison among scenarios. According to Hashimoto et al.(1982), 3 kinds of criteria can be used to evaluate waterresources systems:

(1) Reliability, which describes the likelihood of a systemfailure:

Rel = 1 −∑M

j=1 d(j )

T, (11)

where, d(j ) is the duration of the jth excursion into a failureperiod, M is the number of failure events, and T is the totalnumber of time steps. This definition of reliability calculatesthe possibility of satisfying demands, but it does not considerthe severity of deficits in each period; therefore, this criterionwould not distinguish between a 1 Mm3 deficit and a 100Mm3 deficit. This study uses a new type of reliability, thecorrected reliability, to overcome this limitation:

Corrected Reliability

= 1

T

T∑j=1

D(j ) − v(j )

D(j ), (12)

where, v(j ) is the deficit volume that corresponds to d(j )and D(j ) is the total demand volume that corresponds tod(j ).

(2) Resilience, which indicates how quickly a system recov-ers from a failure:

Res =[∑M

j=1 d(j )

M

]−1

. (13)

In this study, some of the scenarios reach conditions withno deficits, where M = 0, and these could not be evaluatedusing resilience criteria.

(3) Vulnerability, which indicates the severity of the conse-quences of a failure and is based on Kundzewicz and Kindler(1995) relation:

Vul = max(v(j )). (14)

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Tab

le2.

-Per

form

ance

crite

riaan

dsu

stai

nabi

lity

crite

rion

eval

uatio

nre

sults

for

diffe

rent

scen

ario

s

Sce

nar

ios

Co

rrec

ted

Rel

iab

ility

Res

ilien

ceV

uln

erab

ility

(Mm

3 )S

ust

ain

abili

ty

1.W

ithou

tH

edgi

ng0.

8709

013

6.94

0

2.H

edge

(0.9

5)0.

8971

0.04

262

.92

0.03

13.

Hed

ge(0

.9)

0.91

920.

0642

46.5

30.

051

4.H

edge

(0.8

5)0.

9152

0.09

4347

.35

0.07

55.

Goa

l-Se

ekin

gH

edge

0.90

020.

1313

60.2

70.

098

6.C

onsu

mpt

ion

Am

endm

ent

0.99

170

0—

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Simulating hedging rules for reservoir operation

Another formula for computing the vulnerability criterionwas presented by Kjeldsen and Rosbjerg (2001):

Vul = 1

M

∑M

j=1v(j ), (15)

where, M is the number of failure events and v(j ) is thedeficit volume corresponding to d(j ).

Numerous sustainability criteria in the analysis of waterresources systems have been proposed (e.g., Loucks 1997,Matheson et al. 1997). According to Kjeldsen and Rosbjerg(2001), a sustainability index of S can be calculated for eachscenario of i:

S(i) = Rel(i) Res(i)[1 − V ul(i)

sum of Vul(i) from all scenarios

]. (16)

From equations 11–16, the performance criteria and the sus-tainability criterion for different scenarios were calculated(Table 2). For the first and the sixth scenarios, the resiliencecriterion becomes zero for differing reasons (Table 2). In thefirst scenario (without hedging), the model cannot recoverwhen it reaches the first failure, so the resiliency criterionbecomes zero. In the last scenario the value for resiliencyis zero because no deficits occurred during the simulationprocess; therefore, the sustainability criterion is irrationalfor the consumption amendment scenario and was not cal-culated.

Except for the last scenario (consumption amendment), thenew type of hedging rule (goal-seeking hedge) clearly yieldssuperior results and provides the most sustainable water usepolicy (Table 2).

ConclusionsIn this study, 3 types of scenarios were considered and eval-uated for effective reservoir management. In the preliminaryplan, we attempted to satisfy all demand; however, the sim-ulation showed that severe deficits may occur, and reservoirstorage can reach a critical condition at the end of the simula-tion period. By applying the hedging rule as the second sce-nario, the average deficit in satisfying the demand is signif-icantly reduced. In this process, a new type of hedging rule,termed the goal-seeking hedge, was also evaluated. This ap-proach gave the highest value of the sustainability criterionand was more suitable than the common 1-point hedging.Nonetheless, according to performance criteria evaluations,the best and the most sustainable conditions can be achievedby applying a 20% consumption reduction. We concludefrom this study that applying the goal-seeking hedge policy

in addition to controlling water consumption through specialpolicies will result in the best outcome.

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