Optimum management of cyclic storage systems: A simulation ...

E671

Jahanpour et al | http://dx.doi.org/10.5942/jawwa.2013.105.0142 Journal - American Water Works Association Peer-Reviewed

Optimum management of cyclic storage systems: A simulation–optimization approach Mohammad Amin Jahanpour,1 Abbas Afshar,1 and Saeed Alimohammadi2 1Iran

University of Science and Technology, Tehran, Iran and Water University of Technology, Tehran, Iran

2Power

A semidistributed system dynamics simulation model was coupled with a genetic algorithm to develop a novel simulation– optimization approach for conjunctive water use management. The proposed simulation–optimization method uses the concept of cyclic storage systems as a framework to solve conjunctive use problems. As a highly sophisticated conjunctive use template, a cyclic storage system includes two major sub systems: surface water and groundwater. In this research, the

dynamic behavior of a cyclic storage system was simulated using system dynamics methodology. The real-world case study chosen was Kineh Vars Reservoir and its irrigating area, located downstream of the Abhar Rud watershed in west-central Iran. Operating rules for the system were optimized to satisfy water demands over a planning period of 40 seasons, minimizing the total costs of system construction, operation, maintenance, and elements replacement.

Keywords: conjunctive use, cyclic storage system, genetic algorithm, system dynamics

Conjunctive use of surface and groundwater resources has received considerable attention as a way to reduce the major negative effects associated with construction of large-scale surface impoundment systems. A passive form of conjunctive use may simply rely on surface water in wet years and on groundwater in dry years. In an active form of conjunctive use, the regulated and/ or unregulated surface water is intentionally diverted to percolate or be injected into aquifers for later use. A cyclic storage system (CSS), as defined by Alimohammadi et al (2009), refers to cyclic recharge and recovery of an aquifer as a natural storage facility during the planning horizon. A CSS consists of physically integrated and operationally interconnected surface water and groundwater subsystems with full, direct interactions between the subsystems (Figure 1). On the basis of the new definition given by Alimohammadi and co-workers (2009), CSSs might be treated as competing and potentially interconnected parallel storage facilities that are intended to reduce most of the problems associated with largescale surface impoundments. An efficient operation policy of such an interconnected, jointly operated CSS calls for conjunctive operation rules that determine the optimum combination of releases and the amount of water transfer between the system components. In a CSS, both regulated and unregulated water flows from the surface reservoir can be used for cyclic recharge of the aquifer. The key element of a CSS—the feature that distinguishes it from the commonly practiced conjunctive use of groundwater and surface water—is the determination of physical means for operational interconnections between the two subsys-

tems, allowing large-scale cyclic recovery and recharge of the aquifer with regulated water from the surface reservoir (Figure 1). Because it incorporates a flexible attitude to system management, a CSS has the potential to increase the yield, efficiency, supply reliability, and cost-effectiveness of the system.

LITERATURE REVIEW Model descriptions. Simulation models account for the physical behavior of surface water and groundwater systems, whereas optimization models account for the conjunctive management aspects of the systems (Basagaoglu & Mariño, 1999). During the past years, a variety of coupled simulation–optimization (SO) models have been developed and widely applied to arrive at proper operating strategies for conjunctive management problems. Previous SO models differed in both the simulation model used to represent system behavior and the optimization techniques used to solve the management problems. The classical optimization techniques previously employed in conjunctive use studies include linear programming (Raul et al, 2012; Ramesh & Mahesha, 2009), nonlinear programming (Alimohammadi et al, 2009; Afshar et al, 2008; Pulido-Velázquez et al, 2006), and dynamic programming (Safavi & Alijanian, 2010). Conjunctive management models are often known to be nonconvex and highly nonlinear. In the case of highly nonlinear optimization problems in which the convexity of the objective function and the feasible region cannot be ensured, solutions computed by gradient-based nonlinear programming solvers may be quite far from the global optimum. Furthermore, the gradient-based solvers

2013 © American Water Works Association

E672


FIGURE 1

Interactions between components of a cyclic storage system

Reservoir

River

Operation policy

Demand area

Aquifer

Adapted from Alimohammadi et al, 2009

must evaluate the derivatives, which is often a time-consuming procedure. In recent years, researchers have used heuristic optimization techniques that do not require computing derivatives and have proven more efficient in converging to the global optimum. Some of these techniques are simulated annealing algorithm (Rao et al, 2004), genetic algorithm (GA; Fayad et al, 2012; Afshar et al, 2010; Safavi et al, 2010), particle swarm optimization (Ostadrahimi et al, 2012; Gaur et al, 2011; Sedki & Ouazar, 2011), and harmony search (Ayvaz, 2009). Most SO models in conjunctive use studies not only differ in the optimization methodology but also vary in the simulation approach. The literature review found that normal numerical methods (finite difference, finite element, and analytic element methods) and surrogates such as artificial neural networks have commonly been used as simulation models in the previous SO studies. Event-oriented thinking versus system thinking. Regardless of the methodologies, previous SO models of conjunctive use studies have always been developed within an event-oriented thinking framework. Generally speaking, the overall idea of the development of the previous models was grounded on the intuitive assumption that the outputs or events result from the collective effect of a series of inputs or causes acting sequentially (unidirectional thinking procedure). However, because of the dynamic instinct of interactions in water resources systems, such procedural, unidirectional, and mechanistic simulation models may be doomed to provide unrealistic, or at least questionable, results (Hjorth & Bagheri, 2006). In fact, an event-oriented view or linear causal thinking cannot address the complex dynamic behavior of water resource systems adequately (Sterman, 2000). System thinking, on the other hand, provides methods and techniques to apply nonlinear causal thinking to the problems with complex dynamic behavior. System dynamics (SD) facilitates recognition of dynamic interactions among the disparate but intercon-

nected subsystems that drive the dynamic behavior of the entire system (Mirchi et al, 2011). By identifying and capturing the causal loops among the components, SD methodology, unlike the unsystematic thinking-based approaches, simulates the dynamic behavior of complex systems realistically. This characteristic of SD methodology makes it a suitable simulation approach for dealing with water resources systems (Afshar et al, 2012; Hjorth & Bagheri 2006). The qualitative modeling tools of SD, such as causal loop and stock–flow diagrams, can be used to provide a graphical representation of a conjunctive water resources system, facilitating a holistic understanding of the problem. SD methodology in use. The literature review found that SD methodology has been successfully used for facilitating the public understanding of water resources management options and alternatives (Gastélum et al, 2009; Stave, 2003), reservoir operation simulation (Simonovic et al, 1997), flood control and flood damage reduction (Ahmad & Simonovic, 2004), conjunctive use simulation (Chang et al, 2011), facilitating reservoir nutrient simulation process and assessment of alternative management strategies (Afshar et al, 2012), and computer-aided negotiation models for consensus-based decision-making (Islam et al, 2011). Further discussion about the application of SD methodology to deal with dynamically complex problems in water resources management studies is available elsewhere (Mirchi et al, 2012; Winz et al, 2009). Previous efforts have routinely developed SD models by using different software packages such as Vensim1 (Chang et al, 2011; Wang et al, 2011; Stave, 2003), Stella 2 (Ahmad & Simonovic, 2004; Simonovic et al, 1997), Powersim3 (Gastélum et al, 2009), and Goldsim4 (Islam et al, 2011). These software packages provide a set of graphical objects and mathematical functions for graphical representation and development of SD models. Although these software packages are highly efficient for development of SD models, the resulting simulation models will be limited to use within the specific software packages. This limitation makes the integration of any developed SD model with any optimization algorithm highly difficult and casedependent, if not impossible. In the current study, this drawback was eliminated by developing the SD methodology and hydrology model in a separate programming platform, enabling the authors to directly couple it with a heuristic search algorithm. In the current research, an SD simulation model was combined with a GA optimizer to develop an optimum operation policy for the conjunctive use of groundwater and surface water subsystems in a CSS template. Although use of SD methodology to analyze different types of water resources management problems has a fairly long history (as shown by the literature review), the simulation technique described in this article has never been reported to be coupled with a heuristic optimization algorithm for development of the optimum operation policy of a conjunctive use system.

METHODOLOGY Coupling of an SD simulation module with a GA optimization module was used to find the most efficient operation policy to address water demands while minimizing system construction and operation costs. In this SO model, the SD module is used to


E673


simulate the surface and groundwater as well as related interactions, verify model constraints, assign penalties in the case of violation of constraints, calculate water deficits, evaluate system construction and operation costs, and evaluate the objective function of any trial solution. The proposed SO model performs an iterative procedure in which the GA optimization module frequently invokes the simulation module to simulate and assess any trial solution identified by GA. The search process continues until one of the predetermined termination criteria is reached. SD module of a CSS. SD is a method for operationalizing system thinking that provides a holistic understanding of water resources systems and promotes strategic decision-making. Closed-loop or nonlinear causal thinking facilitates consideration of key causal loops and interconnections characterizing the system’s structure, which collectively shapes the behavior of complex systems. At the core of SD models are positive and negative causal relationships. As an example of a positive causal relationship, an increase in hydraulic conductivity will increase surface discharge to the groundwater. In contrast, increased evaporation will cause the stored water in the reservoir to decrease, an example of a negative causal relationship. Table 1 shows the graphical notation and mathematical definition of causal relationships. In systems with closed-loop interactions, combinations of positive and negative causal relationships form causal loops, which can be graphically presented by a causal loop diagram. Developing a system’s causal loop diagram, as the conceptual modeling step, helps developers to graphically capture the causal relationships between the interactive subsystems. For example, in a CSS, both natural river inflow and water transfer from the downstream aquifer raise the reservoir’s stored water and thus form positive causal relationships. Increase in reservoir storage will then create the potential for a bigger lake (positive causal relationships). However, a bigger lake will cause higher evaporation losses, which in turn will result in a decrease in the reservoir storage (negative causal relationship). Releases from the reservoir to the river, the artificial recharge, and the demand area are also considered negative causal relationships. Figure 2 shows a causal loop diagram illustrating the dynamic behavior of the storage of

TABLE 1

System dynamics notations

Diagram Causal loop diagram

Item

Notation

Positive causal relationship

  ∂B + A → B ,  > 0   ∂A

Negative causal relationship

Stock and flow diagram

Stock

 ∂B  − A → B ,  < 0   ∂A 

a hypothetical reservoir. Based on the system causal loop diagram, a stock–flow diagram may be developed to provide a better presentation of the accumulation and/or depletion of stock(s) and also the flow of quantities in the system. The graphical notation of stocks, flows, auxiliaries, and connectors is shown in Table 1. Stocks are used to represent the variables that accumulate or deplete over time. Flows denote the activities or variables that cause a stock variable to change. For example, the water stored in a reservoir can be modeled as a stock variable that is controlled by flow variables such as inflows, releases, and other associated losses. Auxiliary variables, such as water level in a river and construction costs, are functions of stock variables or constants that are used to formulate the model. Stocks, flows, and auxiliary variables are connected by the connectors, which simply carry information between the variables of an SD model. SD model characteristics. Mathematically speaking, an SD model is a system of high-order and nonlinear ordinary differential equations that describe causal loops and dynamic interactions among model objects. The initial condition of the model is assumed to be predefined so equations may be considered as initial value problems, which may be solved by numerical methods for subsequent time steps. By following this process, dynamic behavior of the system will be simulated during the intended period. Detailed description of SD theory is available elsewhere (Sterman, 2000). In the current study an SD simulation model was developed following the methodology explained previously. The integrity of the numerical method used to solve differential equations of the model was verified by modeling the Bass diffusion model (Bass, 1969). This famous model, widely influential in forecasting, marketing, and management sciences, has been used by other SD provider software packages for both illustration and verification purposes. The Bass model and other examples were used to adjust the time steps so that the required accuracy during an acceptable length of time was achieved. The unit response matrix method was used to analyze groundwater level variations in wells. MODFLOW, the US Geological Survey modular finite-difference flow model (McDonald & Harbaugh, 1996), was calibrated based on the field data, and then unit response coefficients for point (pumping and recharging wells) and surface (seepage in demand area and rainfall on aquifer) excitations were developed in the CSS. These unit responses were embedded in the SD simulation module as a subsystem.

FIGURE 2

Reservoir supply’s causal loop diagram

Reservoir inflows

Flow

+

Lake area

+

Reservoir water supply

+

Auxiliary Connectors

Reservoir outflows


–

–

Evaporation losses

E674


GA module. The GA is a general-purpose search algorithm for optimization of nonconvex and nonlinear problems. Using natural rules of survival in pursuit of the ideas of adaptation, the GA searches for optimal solutions of complex problems in both discrete and continuous domains. The mutation operator makes the GA less likely to become trapped in local optima than gradientbased methods. It searches a wide area of the decision space and is able to address numerous variables without requiring objective function derivative computations. An elitist real-coded single-objective GA was developed as the optimization module of the model. The simulated binary crossover (SBX) method, developed by Deb and Agrawal (1995), was used as the crossover operator. The probability distribution of children solutions around their parents is adjustable in the SBX method. As an improvement, an automated changing pattern was defined to modify this probability distribution each time that the GA seems to be trapped in a local optimum. This modification results in the production of children with different distances from their parents, which in turn increases the chance of producing better solutions. If the best solution remains unchanged for a predefined number of generations, the changing pattern triggers, and a new SBX’s probability distribution is selected. Unless the termination criteria are met, it is assumed that the solution is converged to a premature condition if no improvement in the best solution is observed after a predefined number of generations. At this point, the changing pattern triggers, and the SBX’s probability distribution changes. (In the current research, it was observed that the proposed strategy forced the GA to resume several times during the optimization process.) The GA optimization process terminates when either the predefined maximum number of generations is reached or no significant improvement is observed during a determined number of successive generations (stall generations). SO model. After development and validation of SD simulation and GA optimization modules, both modules were coupled to form the SO model. During a model run, the optimization module frequently invokes the simulation module to evaluate the chromosomes. Each chromosome represents a trial solution, which consists of genes that are decision variables. In the current study, system operation policy coefficients were decision variables, which were to be optimized. Thus the genes of chromosomes were the coefficients of system operation rules. System operation policy determines the rules for the interactive operation of the whole cyclic system. It forms the core of the system, managing all time-dependent water transfer systems: • reservoir release to the river, • reservoir release to the demand area, • reservoir release to the artificial recharge area, • aquifer pumpage to the reservoir, • river diversion to the artificial recharge area, • river diversion to the demand area, and • aquifer pumpage to the demand area. All of these mentioned water allocations in a CSS are directly managed by system operation rules. Every operation rule (Eq 1) is assumed to be a linear function of the selected and easily monitored key variables of the system:

Rs(t) = ax × Qs(t) = bx × Ss(t – 1) + cx × (t) × ANDM + dx × s–w(t)(1)

in which Rx(t) is any water allocation in the time step t; ax, bx, cx, and dx are the operation rules’ coefficients; Qs(t) is the natural inflow to reservoir, time step t; Ss(t) is the reservoir storage volume at the end of time step t; ANDM is the annual demand volume; η(t) is the seasonal fractions of ANDM, and sw(t) is the drawdown in water level at time step t. By optimizing the operation policy coefficients (as the decision variables), the GA minimizes the total costs of system construction and operation (as the objective function) while satisfying a predefined demand during the planning time. Moreover, with the operation policy coefficients optimized, it will be possible to determine the optimum value of other system variables, such as the reservoir capacity and the design capacity of water allocation systems. Problem formulation. The objective function of the optimization problem is the present value of costs (PVC) of the system. Therefore the GA model is formulated as follows: Minimize PVC = PVCconst + PVCop

(2)

PVCconst = Cconst(S) + Cconst(Rsar) + Cconst(Rsd) + Cconst(Divar) + Cconst(Divd) + Cconst(Rgs)(3) PVCop = Cop(W) + Cop(AR) + Cop(S) + Cop(Rsd) + Cop(Rsop)+ Cop(Divd) + Cop(Divop) + Cop(Rgs)(4)

in which PVCconst and PVCop are the sum of the present value of construction costs and operation costs, respectively; Cconst(S) and Cop(S) are the reservoir construction and operation costs, respectively; Cconst(Rsar) and Cop(Rsar) are the construction and operation costs, respectively, of the conveyance system from reservoir to artificial recharge area; Cconst(Rsd) and Cop(Rsd) are the construction and operation costs, respectively, of the conveyance system from reservoir to demand area; C const (Div ar ) and Cop(Divar) are the construction and operation costs, respectively, of the diversion system from river to artificial recharge area; Cconst(Divd) and Cop(Divd) are the construction and operation costs, respectively, of the diversion system from river to demand area; Cconst(Rgs) and Cop(Rgs) are the construction and operation costs, respectively, of the conveyance system from aquifer to reservoir; Cop(W) is the operation cost of groundwater pumping; and Cop(AR) is the operation cost of groundwater recharge. Cop(W) is calculated as in Eq 5: NT NK



Cop (W) =



t = 1 k = 1

uar (l,t) × qar (l,t)  [lw (k) 1 sw (k,t)] × qw (k,t) (1  rs)t

 (5)

in which NT and NK are the number of time steps and pumping wells, respectively; ucw(k,t) is the unit cost for pumpage from well k in time step t; lw(k) is the initial drawdown in pumping well k; rs is the annual interest rate; sw(k,t) is the drawdown in water level of pumping well k at the beginning of time step t; and qw(k,t) is the pumping rate in pumping well k, time step t.


E675


ucw(k,t) = [uelif × ucen × hour(t) × 3,600/efp(k)]/kqv(6)

in which uelif is the energy required to pump a unit volume of water to a unit height, ucen is the unit cost of energy, hour(t) is pumpage hours in time step t, efp(k) is the pumping efficiency of well k, and kqv is the conversion factor (discharge to volume). NT

NL

Cop (AR)  



t  1 l  1

uar (l,t) × qar (l,t)  (7) (1  rs)t

in which NL is the number of charging wells; uar(l,t) is the unit recharging cost in recharge well l, time step t; and qar(l,t) is the recharging rate in well l, time step t. Cop(S) = ucd × Cconst(S)(8) NT

s

Cop (Rd )  

t  1 NT

s

Cop (R ar)  

t  1

s

uccd(t) × Rd (t) (9)  (1  rs)t s

uccar(t) × R ar (t) (10)  (1  rs)t

NT

ucdivd(t) × Divd (t) Cop (Divd)    (11) (1  rs)t t  1 NT

Cop (Divar)  

t  1

ucdivar(t) × Divar (t)  (12) (1  rs)t s

NT ucp(t) × Rg (t) g Cop (Rs )    (13) (1  rs)t t  1

in which ucd is the unit operation cost coefficient of the reservoir; uccd(t), uccar(t), ucdivd(t), ucdivar(t), and ucp(t) are the unit operation cost coefficients of reservoir to demand area system, reservoir to artificial recharge area, river diversion to demand area system, river diversion to artificial recharge area, and aquifer to reservoir system, respectively, at time step t. Subject to: out,min out out,max qriv (t) # qriv (14) # qriv

qw (k,t) # qwmax

(k = 1,2 . . , NK)(15)

min sw # sw (k,t) # swmax NT

NK

 

t  1 k  1

(k = 1, 2 . . , NK)(16)

NT

NT

NT

t  1

t  1

t  1

qw (k,t) #  Rsar (t) + Divar (t) +  qrets (t) NT

NT

t  1

t 

CASE STUDY (17)

+  qraq (t) +  qseep (t) NT



t  1

) (t) × ANDM – (R

s d

NK

)

(t) + Divd (t) +  qw (k,t)) = 0 k  1

out,min in which qout is riv (t) is the river outflow during time step t; qriv the minimum allowed river outflow during any time step; qout,max riv is the maximum allowed river outflow during any time step; qwmax is the maximum allowed pumpage of a well during any time step; swmin is the minimum and swmax is the maximum allowed drawdown, respectively, in wells during any time step; qrets(t) is fraction of water delivered to demand area that percolates into the aquifer, time step t; qraq(t) is seepage from river to aquifer, time step t; qseep(t) is the fraction of precipitation that percolates into the aquifer, time step t; K is the hydraulic conductivity of the river semipervious streambed; L is the river length; W is the river width; M is the thickness of river semipervious streambed; and bot hriv and hriv are the elevations of the river water surface and semipervious streambed, respectively. PVCconst consists of the construction cost of the reservoir [Cconst(S)], conveyance system from the reservoir to the artificial recharge site [Cconst(Rsar)] and the demand area [Cconst(Rsd)], diversion system from the river to the artificial recharge area [Cconst(Divar)] and the demand area [Cconst(Divd)], and conveyance system from the aquifer to the reservoir [Cconst(Rgs)]. The construction cost of any system component is considered to be a function of the design capacity of that component [Cconst(xi) = f (Capacity[xi])]. Pumping and recharging wells are assumed to be already constructed in the study area; therefore, only their operational costs are considered. System operational cost (PVCop) consists of the present value of groundwater pumping [Cop(W)] and recharging [Cop(AR)] costs as well as the operation, maintenance, and replacement costs of other system elements. As shown in Eq 5, the groundwater pumping cost is a function of the consumed energy (Eq 6) and may be calculated by multiplying the pumping head by the pumping volume (Basagaoglu et al, 1999). Eqs 7 to 13 describe the operational costs of the system components. Eqs 14 to 19 describe significant model constraints. River outflow is limited but also must satisfy the environmental flow requirements (Eq 14). Discharge of wells (Eq 15) and their water level fluctuations (Eq 16) are also confined. At the end of the planning time, total pumpage from the wells must not exceed the total recharges to the aquifer (Eq 17). The deficit constraint (Eq 18) ensures that in every time step the total water transferred to the demand area satisfies and does not exceed the existing demand. Seepage from the river to the aquifer is defined as in Eq 19 (McDonald & Harbaugh, 1988). Other simple model constraints control lower and/or upper bounds of the decision variables and also limit water allocations and reservoir storage to nonnegative values during the simulation time.

(18)

K×L×W bot qraq (t) =  × (hriv (t) – hriv )(19) M

Description of study area. The study area, based on the previous study of Alimohammadi et al (2009), includes the Kineh Vars Reservoir and its irrigating area, which is located downstream of the Abhar Rud watershed in Zanjan province in Iran (latitude 36˚791899 N and longitude 49˚491399 E). The study area is situated in a semiarid region with an annual precipitation of 365 mm, a mean annual river discharge of 31.57 × 106 m3, and an annual total water demand of 26 × 106 m3. Seasonally varying data and


E676


the model parameters are shown in Table 2. Aquifer characteristics, construction cost functions, operation cost coefficients, and all other relevant data shown in the table were taken from a technical report (Abhar Consulting Engineers, 2005). Figure 3, part A, provides a layout plan view of the system showing the location of the reservoir, irrigation, and urban areas relative to the river and within the study area. Figure 3, part B, an enlarged image of the aquifer shows the spatial distribution of its hydraulic characteristics. In the view shown in part B, the aquifer is assumed to have a rectangular shape (8 × 10 km). Except at the stream inlet and outlet, the aquifer has an impermeable boundary. The groundwater level is assumed to have a uniform distribution in the entire aquifer at the start of the simulation. Data selection and planning horizon. From the 31 years of available data on the seasonal natural flow of the river, a 10-year period was selected such that the period included both dry and wet years and the mean value of flows was close to the mean value of flows for the entire 31-year period. Table 2 shows natural inflow to the reservoir for the selected 10 years. The planning horizon of the model was 10 years (from fall 1990 to summer 2000) and consisted of 40 seasonal time steps. Water demands, including agricultural and urban demands, are also shown in the table. The demand area may receive water from the aquifer, the river, or directly from the reservoir. In addition, Table 2 includes the environmental flows, i.e., the quantity of water flows required to sustain freshwater and downstream ecosystems. It was assumed that 10% of the total water delivered to the demand area percolates into the aquifer and another 10% returns to the river downstream as the irrigation return flow. A surface reservoir, a hydraulically connected stream–aquifer system, a demand

FIGURE 3

TABLE 2

Model parameters and data Seasonal Values of Main Variables Fall

Winter

Spring

1990–1991

2.34

6.54

7.37

0.58

16.83

1991–1992

2.85

5.96

33.59

1.16

43.57

1992–1993

3.59

8.63

9.48

0.87

22.58

1993–1994

5.15

15.70

15.32

0.94

37.12

1994–1995

15.84

13.60

19.58

1.76

50.78

1995–1996

4.96

11.75

49.20

1.45

67.35

1996–1997

4.95

7.89

6.17

0.91

19.92

1997–1998

3.69

10.41

17.85

0.93

33.15

1998–1999

2.77

5.51

2.57

0.52

11.36

1999–2000

1.84

5.17

5.80

0.24

13.06

ep(t)—mm

185.5

77.1

348.5

717.1

1328.2

Qs(t)—x 106 m3

Summer Annual

prc(t)—mm

96.91

136.52

123.00

8.58

365.00

out,min (t)—x 106 m3 qriv

0.262

0.262

0.542

0.542

1.608

(t)

0.111

0.056

0.424

0.409

1

Model Parameters 6 3 qmax w = 3 x 10 m per season

rs= 0.08

smin w = –10 m max sw = 10 m

NT = 40

ANDM = 26 x 106 m3

NL = 3

NK = 3

ANDM—annual demand volume, ep(t)—evaporation rate, time step t, (t)—demand distribution, time step t, NK—number of pumping wells, NL—number of recharging wells, NT—number of time max steps, prc(t)—precipitation on aquifer surface, time step t, qw —maximum allowed pumpage of a out,min (t)—environmental flow requirement in river, time step t, Q (t)— well during any time step, qriv s natural inflow to reservoir, time step t, rs—annual interest rate smax w —maximum allowed drawdown min—minimum allowed drawdown in wells during any time step in wells during any time step, sw

Study area layout (A) and spatial distribution of the hydraulic characteristics of the aquifer (B)

A

B

* * * + + + + Watershed layout boundary Watershed boundary Impervious boundary of the aquifer River

Agriculture area Urban area Wells and recharge basin Kineh Vars Reservoir

* * * + + + + -

* * * + + + + -

* **** **** **** ++++ ++++ ++++ ++++ ++++ - - - - - - - - - -

Hydraulic conductivity—m/s 1 × 10–5 5 × 10–5 9 × 10–5 Impervious boundary of the aquifer


* * * * + + + + -

* * * * + + + + -

* * * * + + + + -

Storage coefficient * 0.10 + 0.14 – 0.12

E677


FIGURE 4

Stock–flow diagram of the case study

As

ep Es

Reservoir

R sd

Demand area

Rsriv Divd

Qs

q rets

River q retr hriv

R gs

Divar

R sar out

q riv

R gd prc

Aquifer

As—reservoir surface area, Divar—diversion from river to artificial recharge area, Divd—diversion from river to demand area, ep—evaporation rate, Es—water lost through evaporation, hriv—elevation of river water surface, prc—precipitation on aquifer surface, qrivout —river outflow, qraq—seepage from river to aquifer, qretr—fraction of water delivered to demand area that joins the river outflow, qrets— fraction of water delivered to demand area that percolates into the aquifer, Qs—natural inflow to reservoir, Rgd—water transferred from aquifer to demand area, Rgs—water transferred from aquifer to reservoir, Rsar —water transferred from reservoir to artificial recharge area, Rsd—water transferred from reservoir to demand area, Rsriv—reservoir release to the river Rectangles represent stock, “bow ties” represent flow, circles represent auxiliary, and solid and dotted arrows represent connectors.

area, and a recharge basin containing three observation and supply wells were the basic components of this CSS (Figure 3, part A). Site studies showed the vicinity of the pumping wells to be the most suitable place for the recharge purpose; therefore, pumping wells are also considered as recharging wells. The maximum allowed pumping and recharging rate of the wells is 3 × 106 m3 per season. The cross section of the river is approximated by a rectangle 20 m wide and 10 m deep. Longitudinal slope and Manning’s coefficient of the river are 0.0001 and 0.02, respectively. The semipervious streambed layer of the river is 1 m thick; its hydraulic conductivity is 6 ×10–6 m/s.

MODEL APPLICATION AND RESULTS Model parameters and calibration. Figure 4 shows the stock–flow diagram developed for the case study. As discussed in the methodology section, in SD theory stock variables represent the quantities that accumulate or deplete over time, whereas flow variables denote the activities that cause a stock variable to change. In the developed stock–flow diagram shown in Figure 4, reservoir, aquifer, river, and demand area are modeled as stock variables, whereas the water carrying systems (that transfer water between the stocks) are modeled as flow variables. Other model parameters and system variables are modeled as auxiliaries.

Curved, dashed connectors identify causal loops inside the stock–flow diagram. Straight, bold connectors are used to show the flow elements that affect stock elements directly. The differential equation system that governs the dynamic behavior of the system causal loops was developed based on this diagram. The equations were initial value ordinary differential equations and were solved using the Runge–Kutta method. To monitor groundwater level variations in the wells, unit response matrixes were embedded in the simulation module. In order to generate unit response coefficients for the point (pumping and recharging wells) and surface excitations (deep percolation from the demand area and rainfall infiltration to the aquifer), MODFLOW was used. Initially, MODFLOW was calibrated based on the field data. Then multiple runs were performed, each time with only a unit excitation in the system, and the required responses were saved. Eventually, to generate the response matrix of an element, its responses with respect to all excitations were aggregated. The study area consisted of six point excitations (three pumping and recharging wells) and two surface excitations (deep percolation from the demand area and the rainfall infiltration to the aquifer). Three pumping and recharging cells were excited units. Response matrixes for this CSS model were previously developed and verified by Alimohammadi and colleagues (2009).


E678


TABLE 3

Mass balance verification in subsystems Reservoir—x 106 m3

Aquifer—x 106 m3

River—x 106 m3

Demand Area—x 106 m3

Initial storage

2.100

Total aquifer pumpage

116.143

Reservoir inflow

312.969

Reservoir release to demand area

Final storage

0.000

Aquifer pumpage to demand area

116.143

Diversion to demand area

143.857

River diversion to demand area

143.857

Natural inflow

315.700

Aquifer pumpage to reservoir

0.000

Diversion to artificial recharge area

66.892

Aquifer pumpage to demand area

116.143

Inflow from aquifer

0.000

Seepage from river to aquifer

8.746

Returned from demand area

26.000

Deficit

Direct release to demand area

0.000

Total artificial recharge

66.892

Seepage from river to aquifer

Direct release to artificial recharge area

0.000

Percolation from precipitation

14.600

Outflow

119.473

312.969

Percolation from demand area

26.000

Release to river Evaporation

0.000

0.000

8.746

4.831

Total reservoir inputs + initial storage

317.800

Total aquifer recharge

116.238

Total river inputs

338.969

Total water demand

260.000

Total reservoir outputs + final storage

317.800

Total aquifer discharge

116.143

Total river outputs

338.969

Total water supply

260.000

Values in the table are cumulative values for the 10-year planning period.

applied to the model, no system development (zero cost) was obtained. This evident outcome, considered another verification measure of model performance, is defined as the initiating point of the graph in Figure 5 (i.e., point [0,0]). In earlier research (Alimohammadi et al, 2009), a semidistributed optimization model for the design of the current case study

FIGURE 5

Increasing behavior of total system costs versus the increasing values of annual demand

450 400 Total System Costs—billion rial

Formation of the SO model. The SD simulation module was coupled with the GA to form the SO model. On the basis of multiple preparatory runs, the tournament selection method, SBX, and polynomial mutation operator proved to be a promising set of genetic operators to prevent the GA from premature convergence to local optima. Two elite chromosomes were considered. The SBX crossover fraction was 40%. The penalty factor was set to 100, and a uniform mutation pattern was chosen with a rate of 10% and a mutation range of 5%. The problem was solved for 28 continuous decision variables. As termination criteria, the maximum number of generations was set at 40,000, and the maximum number of stall generation was set at 500. The hardware configuration on which the model was run was a central processing unit5 with a core speed of 3.2 GHz and a 4-gigabyte double data rate memory card. With this hardware configuration, the GA could process with the average speed of almost four generations per second. With a population size of 100 chromosomes, the GA stopped after nearly 17,000 generations by experiencing 500 stall generations. The SO model was solved for a planning horizon of 40 seasonal time steps. The solution resulted in a PVC of 84.69 billion Iranian rials ($6.89 million; currency exchange rate as of Sept. 10, 2013), zero nonfeasibility, and zero water deficits. To verify the solution, the law of conservation of mass was demonstrated in all subsystems (i.e., reservoir, aquifer, river, and demand area). Table 3 shows the cumulative values of significant system variables within these subsystems. Evaluation of mass balance of the transferred water within the subsystems found no apparent violation of the mass conservation law. Comparison of models. For the same planning period, the model was solved for different values of annual demand. Figure 5 shows the increasing behavior of the system’s PVC versus the increasing values of annual demand. As would be expected, when zero annual water demands and zero environmental requirements were

350 300 250 200 150 100 50 0

0

10

20

30

40

50

ANDM—106 m3 ANDM—annual demand volume, PVC—present value of costs Dashed arrows address solution for ANDM = 26 x 106 m3 (case study) and PVC = 84.69 billion rials ($6.89 million). (Conversion reflects the exchange rate on Sept. 10, 2013.)


E679


area, and transfer from the aquifer to the demand area are shown in Figures 6, 7, 8, and 9, respectively. The design capacity of the reservoir was determined by identifying the maximum reported storage of the reservoir through the entire planning time. On multiple time steps (including springs), the reservoir storage is almost at its full capacity of 9.293 × 106 m3; this underscores the fact that the reservoir capacity has been adjusted such that the utilization of this small capacity is maximized and any unnecessary development has been avoided. Figure 6 shows variations in reservoir storage and reservoir release during the planning time. A small reservoir with a capacity of 9.293 × 106 m3 in the CSS has efficiently regulated the highly variable natural runoff to satisfy 260 × 106 m3 of the downstream water demands and 16.08 × 106 m3 of the river environmental requirements during the 40 seasons of planning time. Evaporation from the surface reservoir was found to average 0.483 × 106 m3 per year, which represents 1.53% of the total inflow to the reservoir. After the construction and operation cost parameters of this case study were applied to the cost equations (Eqs 5 and 11), it was observed that in this particular case, for a given volume of water to be transferred to the demand area, the aquifer pumping cost was significantly lower than the operation cost of the river diversion system to the demand area. Furthermore, a river diversion system would incur construction costs whereas wells and pipelines may be

was developed by embedding the unit response matrixes into a nonlinear problem solver. Table 4 shows the resulting design capacities and a comparison of the construction and operation costs in the current study and the previous study (Alimohammadi et al, 2009). Compared with the results of the 2009 study, the new solution slightly decreases total costs (0.56%) while eliminating any water deficit. Because of differences in simulation technique and model formulation, however, no judgment can be made about the relative performance of the optimization models. The most obvious differences between the 2009 solution and the current one can be attributed to the significant decrease in the reservoir volume and increase in the river diversion system capacity offered by the new solution compared with the 2009 results. Because water transfer from the reservoir to the artificial recharge and demand areas would be prohibitively expensive given the distances involved, these transferring systems were excluded by the optimization algorithm. Instead such transfers are made possible through the river. The natural runoff, after being regulated in the surface reservoir, is released to the river for diversion to both the demand and artificial recharge areas. A water transfer system from the aquifer to the reservoir was also found to be unnecessary and was excluded by the optimization algorithm. Model policies and constraints. The operation policies for reservoir release to the river, diversion from the river to the demand area, diversion from the river to the artificial recharge

TABLE 4

Comparison between previous and current solutions Parameter

Alimohammadi et al, 2009

Current Work

Methodology

Embedding simulation formula in Lingo*

Linked simulation optimization model

Optimization method

Nonlinear problem solver

GA

Model paradigm

Procedural

Object-oriented

Considering causal loops in system

No

Yes

Deficit—x 106 m3

1.09

0.00

Nonfeasibility

0.00

0.00

PVC—billion rials ($)

85.17 ($6.93 million)

84.69 ($6.89 million)

PVCconst billion rials ($)

PVCop billion rials ($)

Capacity x 106 m3

PVCconst billion rials ($)

PVCop billion rials ($)

Capacity x 106 m3

55.964 ($4.56 million)

3.358 ($273,000)

17.321

44.170 ($3.95 million)

2.650 ($216,000)

9.293

Reservoir Transfer system from reservoir to demand area

0.000

0.000

0.000

0.000

0.000

0.000

Transfer system from reservoir to artificial recharge area

0.000

0.000

0.000

0.000

0.000

0.000

Transfer system from aquifer to reservoir

0.000

0.000

0.000

0.000

0.000

0.000

5.172 ($421,000)

9.357†

0.838 ($68,000)

6.046†

Diversion system from river to demand area

5.089 ($414,400)

2.054 ($167,200)

2.009†

20.484 ($1.67 million)

Diversion system from river to artificial recharge area

6.744 ($549,000)

1.627 ($132,400)

5.714†

7.656 ($623,200)

Pumping wells

NA‡

5.811 ($473,000)

NA‡

NA‡

1.629 ($132,600)

NA‡

Recharge wells

NA‡

4.067 ($331,000)

NA‡

NA‡

2.095 ($170,500)

NA‡

GA—genetic algorithm, NA—not applicable, PVC—present value of costs, PVCconst—present value of construction costs, PVCop—present value of operation costs *LINDO Systems, Chicago, Ill. per season and recharging wells are assumed to be already constructed in the study area.

†Capacity

‡Pumping

Conversions of rials to dollars reflect the exchange rate on Sept. 10, 2013.


E680


FIGURE 6

Reservoir simulation results

Reservoir storage Natural inflow to the reservoir Reservoir release to the river

50 40

Volume— × 106 m3

35 30 25 20 15 10 5 0

0

8

4

12

16

20

24

28

32

36

40

Time—season

assumed to have already been constructed. Thus it would seem to be more efficient to supply most of the water demands from the aquifer; however, this scenario cannot lead to feasible solutions because of the model constraints, which explicitly limit groundwater use (Eqs 6 and 11) and fluctuation of water level in the wells (Eqs 9 and 10) to predefined values. Based on the most balanced condition found by the optimization algorithm, approximately 55% of the total demand is satisfied through the river diversion, and the remaining 45% is met by the pumping wells. The obtained optimum operation policy satisfied all of the predefined demands while avoiding unnecessary water

FIGURE 7

transfer to the demand area (Figure 7). In addition, as required by Eq 14 (a model constraint), ecological water needs of the river downstream were met during the entire planning periods. As an important model constraint, Eq 17 states that at the end of the planning horizon, the total pumpage of the aquifer should not exceed its total input. This ensures that no operation policy will decrease the aquifer storage after the simulation period. The aquifer section of Table 3 lists all aquifer inputs and outputs. The bottom two rows of the section indicate that the total input to the aquifer is greater than its total output. Figure 10 shows seasonal variation of the water level in the wells, i.e., drawndown in water level of pumping wells 1, 2, and 3 at the beginning of time step t. As shown, water levels fluctuate within the predefined range of –10 m to 10 m, as required by Eq 16. The constraints that limit the groundwater pumpage and recharge to a predefined maximum value (3 × 106 m3 per season in the current study) have also been met (Figures 8 and 9). Natural recharge from the river to the aquifer is found to average nearly 0.875 × 106 m3 annually, or about 8% of the aquifer’s total inputs. Such a significant value underscores the importance of considering river–aquifer interactions in the studies of conjunctive water resources management. As shown in Figure 4, this interaction directly affects the dynamic behavior of the river system and thus plays an important role in river diversion policy.

CONCLUSION This research proposed a novel combination of SD simulation methodology and GA optimization approach to determine the optimal operation policy for conjunctive use of groundwater and surface water in a CSS template. The GA was tailored to couple with the SD simulation model through the development of both the GA and SD modules in a single programming platform. When applied to a real-world project in west-central Iran, the proposed

FIGURE 8

Water supply to the demand area

River diversions to the artificial recharge area

Diversion form the river to the demand area Total transfer from the aquifer to the demand area Demand

12

Well 1 Well 2 Well 3 Total diversion from the river to the recharge area

6

8

Volume—× 106 m3

Volume—× 106 m3

10

6 4

4

2

2 0

1

5

9

13

17

21

25

29

33

37

0

1

5

Time—season

9

13

17

21

25

Time—season


29

33

37

E681


FIGURE 9

Pumpage from wells

FIGURE 10

Well 1 Well 2 Well 3 Total supply from the aquifer to the demand area

10

Water level fluctuation in wells

Well 1 Well 2 Well 3

12

Drawdown—(+) or Rise (–)—m

9

Volume—× 106 m3

8

6

4

2

0

6 3 0 –3 –6 –9 –12

1

5

9

13

17

21

25

29

33

37

0

4

8

12

16

20

24

28

32

36

40

Time—season

Time—season

methodology was shown to efficiently allocate available surface water and groundwater sources to satisfy projected demand. The real-coded GA optimization module identified the optimal operation policy of the CSS to minimize the total system costs while satisfying all of the predefined water demands and still meeting all of the system constraints. Groundwater level variations at different time steps were calculated by the unit response matrixes embedded in the simulation module. The current research showed that in a CSS, optimum operation of the aquifer as a parallel storage to the surface impoundment may significantly reduce the design capacity of the surface reservoir and its associated negative effects. However, uncontrolled exploitation of an aquifer most likely will lead to persistent deleterious results such as continuous water level drawdown, progressive water quality deterioration, and gradual reduction of the aquifer storage capability. Such irreversible damages jeopardize the ability of future generations to meet their own needs and so are in opposition to the concept of sustainable development, which is based on intergenerational equity. To ensure sustainability, overexploitation of the aquifer was prohibited by the model constraints, which limited aquifer abstraction and fluctuation of groundwater level in the observation wells. Model constraints also controlled the river flow to provide enough environmental flows, i.e., the quantity of water flows required to sustain freshwater and downstream ecosystems. A noticeable amount of natural recharge from the river to the aquifer was observed, which highlights the importance of considering this interaction in conjunctive use models. In fact, as a natural phenomenon, seepage from the river to the aquifer may be considered a free aquifer-recharging plan, thus decreasing the need for other, expensive artificial methods. This is particularly highlighted in rivers with significant hydraulic

conductivity, where the higher levels of seepage lead to higher levels of natural recharge. The main feature of the current study was the novel combination of the SD methodology (as the simulation module) with GA (as the optimization module) to form an SO scheme that optimizes CSS operation. As demonstrated here, SD methodology enables developers to practically model causal loops in a complex system and avoid the simplifying assumptions that lead to inaccuracy in calculations. Furthermore, the object-oriented structure and the graphical representation of SD methodology enhance transparency of the model structure and interactions, which in turn simplifies further development of the model. As discussed in the literature review, researchers who used SD to simulate various water systems were limited to running a few simulation scenarios to find a setting of model parameters to achieve a better management plan for the system. However, the model proposed in the current work removes this limitation by coupling an SD simulation module with a heuristic optimization algorithm, making it possible to achieve the global optimum set of model parameters to obtain the best operation policy of the system. By using this new methodology, researchers not only benefit from the transparency, flexibility, and extensibility of SD methodology in the simulation modules, but also are able to use metaheuristic search algorithms to solve the optimization problem in an SO scheme. Taking advantage of the transparency of the model structure in the proposed methodology, the authors are working to design an object-oriented development environment to optimally design CSSs. An integrated development environment can help researchers create and design CSSs, avoiding the time wasted by regenerating simulation codes for CSS common elements such as surface reservoirs and wells. In addition, such a development environ-


E682


ment would make it easier to share, view, and develop CSS models constructed by other researchers.

Basagaoglu, H. & Mariño, M.A., 1999. Joint Management of Surface and Ground Water Supplies. Groundwater, 37:2:214.

About the Authors

Basagaoglu, H.; Mariño, M.A.; & Shumway, R.H., 1999. -Form Approximating Problem for a Conjunctive Water Resource Management Model. Advances in Water Resources, 23:1:69.

Mohammad Amin Jahanpour (to whom correspondence should be addressed) is a researcher in the School of Environmental and Civil Engineering at the Iran University of Science and Technology (IUST), Narmak, POB 1684613114, Tehran, Iran; amin@ aminjahanpour.com. He has a BS degree from Bu-Ali-Sina University in Hamedan, Iran, and an MS degree from IUST. For the past two years, he has worked on conjunctive water use management at the university’s Center of Excellence for Enviro-Hydroinformatics Research. In addition, he has four years of experience developing offline and online computer applications in the fields of optimum design and operation of conjunctive water resources systems, simulation and optimization of reservoirs and aquifers operation, metaheuristic optimization algorithms, system dynamics, and artificial neural networks. Abbas Afshar is a professor in the School of Civil and Environmental Engineering at IUST. Saeed Alimohammadi is an assistant professor at the Power and Water University of Technology in Tehran.

FOOTNOTES 1Ventana

Systems, Mass. Systems, Lebanon, N.H. Constructor and Powersim Studio, Bergen, Norway. 4GoldSim Technology Group, Issaquah, Wash. 5Phenom II X2 555, AMD, Sunnyvale, Calif. 2isee

3Powersim

Bass, F.M., 1969. A New Product Growth for Model Consumer Durables. Management Science, 15:5:215. Chang, L.C.; Ho, C.C.; Yeh, M.S.; & Yang, C.C., 2011. An Integrating Approach for Conjunctive-use Planning of Surface and Subsurface Water System. Water Resources Management, 25:1:59. Deb, K. & Agrawal, R.B., 1995. Simulated Binary Crossover for Continuous Search Space. Complex Systems, 9:2:17. Fayad, H.; Peralta, R.C.; & Forghani, A., 2012. Optimizing Reservoir– Stream–Aquifer Interactions for Conjunctive Use and Hydropower Production. Advances in Civil Engineering, 2012:910203. http://dx.doi.org/10.1155/2012/910203. Gastélum, J.R.; Valdés, J.B.; & Stewart, S., 2009. A Decision Support System to Improve Water Resources Management in the Conchos Basin. Water Resources Management, 23:8:1519. Gaur, S.; Chahar, B.R.; & Graillot, D., 2011. Analytic Elements Method and Particle Swarm Optimization Based Simulation–Optimization Model for Groundwater Management. Journal of Hydrology, 402:3:217. Hjorth, P. & Bagheri, A., 2006. Navigating Towards Sustainable Development: A System Dynamics Approach. Futures, 38:1:74. Islam, N.; Arora, S.; Chung, F.; Reyes, E.; Field, R.; Munévar, A.; Sumer, D.; Parker, N.; & Chen, Z.Q.R., 2011. CalLite: California Central Valley Water Management Screening Model. Journal of Water Resources Planning and Management, 137:1:123. McDonald, M.G. & Harbough, A.W., 1988. A Modular Three-dimensional Finite Difference Groundwater Flow Model. Techniques of Water Resources Investigation, Book 6, US Geological Survey, Reston, Va. Mirchi, A.; Madani, K.; Watkins, D.; & Ahmad, S., 2012. Synthesis of System Dynamics Tools for Holistic Conceptualization of Water Resources Problems. Water Resources Management, 26:9:2421.

Peer Date of submission: 12/23/2012 Date of acceptance: 07/24/2013

Ostadrahimi, L.; Mariño, M.A.; & Afshar, A., 2012. Multi-reservoir Operation Rules: Multi-swarm PSO-based Optimization Approach. Water Resources Management, 26:2:407:427.

REFERENCES Abkhan Consulting Engineers, 2005. Abhar River Basin Conjunctive Use Project. Abkhan Consulting Engineers, Tehran, Iran. Afshar, A.; Saadatpour, M.; & Mariño, M.A., 2012. Development of a Complex System Dynamic Eutrophication Model: Application to Karkheh Reservoir. Environmental Science Journal, 29:6:373. http://dx.doi.org/10.1089/ ees.2010.0203. Afshar, A.; Zahraei, A.; & Mariño, M.A., 2010. Large-scale Nonlinear Conjunctive Use Optimization Problem: Decomposition Algorithm. Journal of Water Resources Planning and Management, 136:1:59. Afshar, A.; Ostadrahimi, L.; Ardeshir, A.; & Alimohammadi, S., 2008. Lumped Approach to a Multi-period–Multi-reservoir Cyclic Storage System Optimization. Water Resources Management, 22:12:1741. Ahmad, S. & Simonovic, S.P., 2004. Spatial System Dynamics: New Approach for Simulation of Water Resources Systems. Journal of Computing in Civil Engineering, 18:4:331. Alimohammadi, S.; Afshar, A.; & Mariño, M.A., 2009. Cyclic Storage Systems Optimization: Semidistributed Parameter Approach. Journal AWWA, 101:2:90. Ayvaz, M.T., 2009. Application of Harmony Search Algorithm to the Solution of Groundwater Management Models. Advances in Water Resources, 32:6:916.

Pulido-Velázquez, M.; Andreu, J.; & Sahuquillo, A., 2006. Economic Optimization of Conjunctive Use of Surface Water and Groundwater at the Basin Scale. Journal of Water Resources Planning and Management, 132:6:457. Ramesh H. & Mahesha, A., 2009. Conjunctive Use in India’s Varada River Basin. Journal AWWA, 101:11:74. Rao, S.V.N.; Bhallamudi, S.M.; Thandaveswara, B.S.; & Mishra, G.C., 2004. Conjunctive Use of Surface and Groundwater for Coastal and Deltaic Systems. Journal of Water Resources Planning and Management, 130:3:255. Raul, S.; Panda, S.; & Inamdar, P., 2012. Sectoral Conjunctive Use Planning for Optimal Cropping Under Hydrological Uncertainty. Journal of Irrigation and Drainage Engineering, 138:2:145. Safavi, H.R. & Alijanian, M.A., 2010. Optimal Crop Planning and Conjunctive Use of Surface and Groundwater Resources by Fuzzy Dynamic Programming. Journal of Irrigation and Drainage Engineering, 137:6:383. Safavi, H.R.; Darzi, F.; & Mariño, M.A., 2010. Simulation–Optimization Modeling of Conjunctive Use of Surface Water and Groundwater. Water Resources Management, 24:10:1965. Sedki, A. & Ouazar, D., 2011. Simulation–Optimization Modeling for Sustainable Groundwater Development: A Moroccan Coastal Aquifer Case Study. Water Resources Management, 25:11:2855.


E683


Simonovic, S.P.; Fahmy, H.; & El-Shorbagy, A., 1997. Use of Object-oriented Modeling for Water Resources Planning in Egypt. Water Resources Management, 11:4:243. Stave, K.A., 2003. A System Dynamics Model to Facilitate Public Understanding of Water Management Options in Las Vegas, Nevada. Journal of Environmental Management, 67:4:303. Sterman, J.D., 2000. Business Dynamics, Systems Thinking and Modeling for a Complex World. McGraw-Hill, Boston.

Wang, X.J.; Zhang, J.Y.; Liu, J.F.; Wang, G.Q.; He, R.M.; Elmahdi, A.; & Elsawah, S., 2011. Water Resources Planning and Management Based on System Dynamics: A Case Study of Yulin City. Environment, Development and Sustainability, 13:2:331. Winz, I.; Brierley, G.; & Trowsdale, S., 2009. Use of System Dynamics Simulation in Water Resources Management. Water Resources Management, 23:7:1301.
