National Workshop on Water Resources System ...

National Workshop on Water Resources System Modeling 9th and 10th March 2017

Coordinators Dr. R. Saravanan Dr. R. Balamurugan Mr. M. S. Karthikeyan Dr. V. Lenin Kalyanasundaram Supported by UGC – Centre of Advanced Study - I CWR Department of Civil Engineering, Anna University Organized by Centre for Water Resources Anna University, Chennai – 600 025

National Workshop on “WATER RESOURCES SYSTEM MODELING” 09th & 10th March 2017 Centre for Water Resources, Department of Civil Engineering, College of Engineering Guindy, Anna University

CONTENTS 1

Role of models in water management: A review Dr .R.Sakthivadivel

1

2

Introduction to modeling of water resources systems Dr. S. Mohan

11

3

Geomatics in real time flood forecasting Dr. D. Thirumalaivasan

43

4

Contaminant Transport modeling in aquatic environment Dr. Shasidar

70

5

Soft systems methodology for Flood Modeling Dr. B.V. Mudgal

91

6

Data Mining application to water resources system modeling Dr. S. Mohan

118

7

Evolutionary Algorithms for Multi Objective Optimization for Reservoir Operation Dr. D. Nagesh Kumar

139

8

A brief note on chaos and its applications in hydrological time series Dr. V. Jothiprakash, R. Vignesh, T.A. Fathima

153

9

Computational intelligence for Groundwater simulation and optimization modeling Dr. R. Saravanan / Dr. R. Balamurugan

171

10

Field investigation to assess the performance of different recharge structures in Tamil Nadu Raicy Mani Christy, Parimala Renganayaki, J. Jagadeshan, Elango Lakshmanan,

181

11

Smart Sensor Network for Drinking Water Quality Monitoring in Water Distribution Mains S. Kavi Priya, G. Shenbagalakshmi, T.Revathi

196

12

Water Quality Modelling of Ariyankuppam River/ Estuary R. Sathya Priya

225


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 CONTAMINANT TRANSPORT MODELING IN AQUATIC ENVIRONMENT Dr. Shashidhar, Faculty, Department of Civil Engineering, IIT Hyderabad, 502285 E-mail: [email protected]

INTRODUCTION Water is an important natural resource moves from one region to another as a part of hydrologic cycle and human intervention. Use of thousands of inorganic and organic chemicals increased since the advent of industrial revolution. Uncontrolled release of domestic and industrial effluents has contaminated the surrounding environment, including the groundwater resources all over the world.

Contaminants which enter

aquatic system travel long distances along with the water and make the water unusable. During the movement, contaminants whether as a toxic liquid or as a solution of a toxic chemical species dissolved in water by natural as well as anthropogenic activities eventually can affect water quality. Contamination generally refers to the presence of a substance where it should not be or at concentrations above background. Pollution is contamination that results in or can result in adverse biological effects to resident communities. All pollutants are contaminants, but not all contaminants are pollutants. Contaminants can enter a water body in many ways: (i) by direct injection, (ii) by design, (iii) by accident, and (iv) by neglect. For example, sources of groundwater contamination include: (i) hazardous waste landfills, (ii) industrial waste ponds, (iii) accidental releases (leaks and spills) of large amounts of chemical substances during the transport and from storage facilities, (iv) agricultural operations utilizing chemicals, and (v) direct or indirect artificial recharge of groundwater with contaminated water. Similarly, our surface water sources are contaminated by the disposal of municipal and industrial wastes directly into rivers and lakes, and by the return flows from the agricultural lands. The contamination of surface and groundwater resources has been and still is a major issue all over the world. Environmental aspects of groundwater resources have become a prime concern in the last few decades, and many aquifers have been designated as super fund sites for remediation. Further more stringent regulations are being implemented by the regulating agencies for the storage and disposal of industrial wastes, fuels and chemicals in order to safe guard, the groundwater. It is obvious that contaminant source activities cannot be Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 completely eliminated, and perhaps our water bodies will continue to serve as receptors of vast quantities of waste. In such a scenario, the goal of water quality protection efforts must necessarily be the control and management of these sources to ensure that released pollutants will be sufficiently attenuated within the region of interest, and the quality of water at points of withdrawal is not impaired. This goal can be achieved only if control and management are based on definitive knowledge of the transport and fate of pollutants in the aqueous environment. MODELING A model may be defined as a selected simplified version of a real system and phenomena that take place within it, which approximately simulates the system’s excitation-response relationships that are of interest. In the context of contaminant transport, modeling means quantification of the physical, chemical, and biological processes that govern the transport and transformation of pollutants in surface and subsurface environments through mathematical equations.

These mathematical

equations could be algebraic or partial differential equations, and could be many equations coupled to each other. These equations are derived by the application of basic laws of mechanics such as conservation of mass, momentum, and energy principles. Furthermore, several of these equations in a mathematical model could be empirical, i.e., they are based on the description of experimental observations through a best fit or regression equation. A complete mathematical model also incorporates a methodology for solving these equations.

The solution methodology may give either an exact

(analytical) solution, or it could give approximate solutions based on the application of numerical techniques. Basically, mathematical models integrate process descriptions (governing equations) with pollutant properties and environmental (site) characteristics, including the boundary conditions, to yield quantitative estimates of subsurface transport and fate. MODELING PROCESS The step wise modeling processes discussed below is showed in Figure 1.


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Figure 1: The modeling process.

Step 1: Identification of the information required for making management decisions. In order to select the most desirable plan, the decision maker needs to assign values to a set of measures, which are used to evaluate the success of a selected plan in achieving the desired objectives. The actual values of the various measures depend on the managed system and on its response to the implementation of a proposed plan. Accordingly, we need information on such parameters as future water levels and concentrations of relevant chemical species, spring discharge, quality of pumped water, etc. These, in turn, are used to evaluate the criteria, or objective function, employed for selecting the preferred management alternative. Information of this kind may also be required in order to ensure that a proposed alternative does not violate constraints imposed on the managed system. Examples of constraints are regulatory limits on contaminant concentrations, and on the leakage to an underlying aquifer. Step 2: Development of a conceptual model. The real system and its behavior may be very complicated, depending on the amount of details we wish, or need to include in describing them. The art of modeling is to simplify the description of the system and its behavior to a degree that will be useful for the purpose of planning and making management decisions in specific cases. The simplifications are introduced in the form of a set of assumptions that expresses our


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 understanding of the system and its behavior. Assumptions should be related to such characteristics as domain’s hydrogeology, stratigraphy, dimensionality of the model, behavior of the system, properties of the fluid, transport process, boundary conditions, regulations etc. Step 3: Development of a mathematical model.

Transport of a Conservative Contaminant in a River / Stream: Any contaminant transport model is based on numerical solution of the governing equations, which describe the physical, chemical, and biological processes involved in the transport and transformation of the contaminant. Sophistication level of the model depends upon the intended use of the model, availability of data for calibration, and whether appropriate assumptions can be made to simplify the governing equations. In this section, the process of deriving the governing equations is illustrated through the simple example of a model for the contaminant transport of conservative contaminants in rivers and streams. A conservative pollutant is one, which does not undergo any chemical or physical transformation as it moves in the water body. Similar procedures can be used for building other contaminant transport models. Consider a river reach as shown in the Fig. 2 in which the flow direction is from A to B. The concentration of a pollutant as a function of time is known at the point A. It is required to find the concentration of contaminant at any other location in the river, given the river cross sectional shape, flow rate variation in the river at point A, time variation of the control depth at some downstream location, channel slope, and channel roughness. The governing equation can be derived by applying the principle of conservation of mass to a differential control volume as shown in figure 2. Following assumptions are first made: (i) the flow is one-dimensional and the flow velocity can be represented by its cross sectional average value, (ii) the concentration at any cross section can be represented by its cross sectional average value. The concentration of contaminant within the control volume will vary with time depending on the rate at which the contaminant enters the control volume and the


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 rate at which it leaves the control volume. This is expressed in mathematical form using the Reynolds Transport equation. Control Volume Water Surface

A

B

Longitudinal View

Bed

Cross Section

Fig. 2 Schematic Diagram for Transport in a River

 Cdv  Mass Flow Rate Out  Mass Flow Rate In  0 t cv

(1)

in which,  = density of water, C = concentration of contaminant (in ppm), and t = time. Mass flux out and mass flux in depend on the mechanism for the transport of a material.

In this particular case, three mechanisms, namely (i) advection, (ii)

molecular diffusion, and (iii) dispersion come into picture. Advection refers to bulk movement of contaminant along with the flow. The advective flux of the contaminant is equal to flow rate multiplied by the concentration of the contaminant. Advective flux is equal to zero when there is no flow.

Advective Flow Rate  .Q.C

(2)

in which, Q = volume flow rate of water. Contaminant can also move from one location to another location even if there is no flow.

Consider pulse injection of a dye at one single point in a jar of water.

Eventually the dye would have occupied the whole jar. This movement of dye occurs due to random motion of molecules, and is known as “diffusive transport.

The

diffusive transport can be described by the Fick’s law of diffusion, which states that Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 diffusive flux is proportional to the concentration gradient. Therefore, the diffusive flow rate across any plane is given as follows:

Diffusive Flow Rate   D m .A.

C x

(3)

in which, Dm = molecular diffusion coefficient. There is a third process, which affects the movement of contaminant from one cross section to another.

This is known as dispersion mechanism.

In fact, the term

hydrodynamic dispersion is generally used to include (i) molecular diffusion (already discussed), (ii) turbulent diffusion, and (iii) dispersion due to averaging procedure. Flow in rivers is almost always turbulent, and the flow velocity, which is used in modeling (as given in Eqs. 1 –3) is the temporal mean value, averaged over turbulent time scales. The instantaneous concentration is equal to its temporal mean value plus the fluctuating component.

This applies to instantaneous velocities as well.

Thus

C*  C  C'

and

V*  V  V' (4)

in which, V = velocity, superscript * indicates the instantaneous value, and the superscript ‘ indicates the fluctuating component.

Equation 2 for the advective

transport uses the temporal mean value, and not the instantaneous value. Thus the effect of turbulence on contaminant mixing is not considered in this equation. It is obvious from our observations on laminar and turbulent flows that the mixing in turbulent flows is more pronounced than in laminar flows. This turbulent mixing of contaminant is usually modeled by a term similar to molecular diffusion i.e.,

Flow Rate due to turbulent Diffusion   D t .A. in which, Dt = turbulent diffusion coefficient.

C x

(5)

It should be understood that the

molecular diffusion occurs due to fluctuations at molecular level, and therefore, Dm is a contaminant property.

On the other hand, turbulent diffusion occurs due to


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 fluctuations at macro level i.e, it occurs due to flow characteristics. Therefore, Dt should be a function of flow properties. In a one-dimensional model, the advective transport as given by Eq. 2 considers only the cross sectional average values of velocity and concentration. However, it is well known that the longitudinal velocity is zero next to a solid boundary (due to no slip condition), and it varies within a cross section. It is maximum at a point farthest from the solid boundaries, and slightly below the free surface. Similarly, the concentration could also vary from point to point within a cross section. Equation 2 for advective transport does not take this variation into account. It may be noted here that average of multiplied values of two fluctuating variables is not equal to multiplication of their averaged values. Like in the case of turbulence effects, this effect of spatial variation of concentration and velocity within a cross section, on the bulk movement of contaminant, can be modeled through a diffusion like equation.

Dispersion Flow Rate due to spatial Averaging   Da . A.

C x

(6)

in which, Da is a dispersion coefficient for averaging effects. Like Dt, Da is a function of flow properties only. Substitution of Eqs. (2), (4), (5), and (6) in Eq. (1), evaluating it for the control volume shown in Fig. 1, and subsequent simplification leads to the following governing equation.

CA    C  ADl  QC   t x x  x 

(7)

In which, A = cross sectional area, and Dl = Dm+Dt+Da is called hydrodynamic dispersion coefficient.

For flow conditions typically encountered in the field

situations, the molecular effects are much smaller compared to the turbulence effects and spatial averaging effects. Therefore, Dl typically tends to be a function of flow property only.

Dependence of Dl on flow properties could be described through

“turbulence” models.

However, such a procedure would require consideration of

three-dimensional nature of the flow, which we are trying to avoid in the first place, by making the one-dimensional flow assumption. Therefore, Dl is typically described Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 using an empirical equation in the contaminant transport models for water quality modeling in rivers.

It should be noted that since these are empirical equations,

caution should be applied while choosing a particular equation for a given situation. Two of these equations are given below for the sake of completeness. D l  5.93 R U*

(8)

in which, R = hydraulic radius, and U* = shear velocity. Fisher has given the following equation for the same purpose.

D l  0.011

W 2U2 RU*

in which, W = mean channel width.

(9)

Strictly speaking, for any particular field

application, the dispersion coefficient should be obtained using parameter estimation procedures or by calibration of the contaminant transport model. Flow Equations: It may be noted here that Eq. (7) contains A and Q as other dependent variables besides C. Therefore, we require two more equations to completely describe the contaminant transport process.

For an unsteady open channel flow situation,

principles of conservation of mass and momentum can be used to derive these equations. They are known as Saint Venant Equations. For a steady flow situation, Q = constant with respect to x and t, and is equal to known flow rate in the river. However, the cross sectional area may change due to non-uniform conditions. In such situations, A is not a function of time, and its variation with distance can be obtained by solving the gradually varied flow equation. Standard step method can be used for this purpose. In the case of steady as well as uniform flow conditions, the flow depth is independent of distance as well, and it is calculated using the Manning equation. Many times such an assumption is made to simplify the equations when there are no control structures in the region where transport calculations are to be made. Simplified equation for transport of a conservative contaminant for the above condition is given below.


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C C  2C V  Dl 2 t x x

(10)

It may be noted here that Eq. (7) should be applied only where the assumption of one-dimensional flow is valid.

It should not be applied when the flow is two-

dimensional, as in the case of estuary flows.

Very close to the point where

contaminant is released in the river, complete mixing of contaminant across the cross section would not have occurred. Application of Eq. (7) to such regions will give erroneous results. Also, Eq. (7) does not take into account (i) the effect of water withdrawal from the river through pumping or diversion, (ii) addition of water to the river through tributaries, and (iii) addition of contaminant to the river in the form of non-point source pollution. Although these effects are not included here for want of space, it should be noted that it is not very difficult to include these effects. It is once again pointed out that Eqs. (7) and (10) pertain to transport of a conservative contaminant. Also, it is assumed that adsorption of contaminant on to the soils on the channel bed and sides is not significant.

Transport of BOD and DO in Streams / Rivers: River water quality, in general, can be represented by the concentration of dissolved oxygen (DO) in the water. A higher value of DO indicates a better quality of water, and indicates that the amount of biodegradable organic waste in the water is less. Typically pollution standards are set in terms of maintaining a minimum level of DO at the points of abstraction, at all times. The concentration of DO in water depends on the amount of oxygen consumed by the microbes to degrade the organic waste, and the re-aeration of water by which atmospheric oxygen enters into water. Thus, the transport of dissolved oxygen depends on the transport of biodegradable organic waste. The amount of oxygen consumed by the microbes depends upon the amount of biodegradable organic waste present in water. In fact, the amount of organic waste in water is usually expressed in terms of bio-chemical oxygen demand or BOD. The re-aeration of water depends upon the difference between the saturated concentration of dissolved oxygen, DOsat and the actual DO. Transport of BOD and DO in rivers and streams, thus depend upon the bio-chemical reactions the organic waste undergoes, in addition to the advection and dispersion processes described


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 earlier. These reactions take place even when there are no advection and dispersion (zero flow and zero spatial gradients in concentration).

The complete transport

equation for a reactive contaminant, with reference to Fig. 1, can be written as

CA    C  dCA  QC  ADl   t x dt x  x  in which, the last term represents the rate of change of mass of contaminant within the control volume due to bio-chemical reactions. This, in general, can be quantified by studying the reaction kinetics. The reaction kinetics is best understood through experimentation, and mathematical representation of the experimental observations using an appropriate empirical equation. For example, in the case of transport of (11)

BOD, a first order reaction equation is usually used. In this, the rate of decrease in BOD is taken as proportional to the BOD present. Equation (11) can be written for BOD as given below.

BA    B   QB  ADl  A ( K1  K 3 ) B  t x x  x 

(12)

in which, B = BOD concentration, K1 = reaction rate coefficient for depletion of BOD due to microbial action (de-oxygenation rate coefficient), and K3 = reaction rate coefficient for depletion of BOD due to settling. K1 and K3 are empirical coefficients, which should be determined by conducting appropriate experiments. In a similar way, the transport equation for DO can be written as

Do A    D o   QD o   ADl  A(K1 )B  A.K 2 (DOsat  Do )  t x x  x 

(13)

in which, Do = concentration of dissolved oxygen, and K2 = atmospheric re-aeration coefficient. Given the flow conditions i.e., the values of Q and A, Eq. (12) needs to be solved first to obtain the BOD value at any location, and at any time. These values of BOD can then be substituted in Eq. (13), and Eq. (13) can then be solved to obtain the variation of DO.


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 It may be noted here that transport equation for any reactive or non-conservative pollutant can be written in a similar way, by first understanding the reaction pathways, and reaction kinetics. In fact, transport equations given here for BOD and DO are the most simplified equations, as far as representation of reaction term is concerned. The most popular water quality model, QUAL2E considers the effects of (i) nitrogen cycle, (ii) the phosphorous cycle, and (iii) the algal respiration, in addition to the BOD, while writing the reaction term in DO transport equation. This, of course, makes it mandatory to write a transport equation for each component in the entire cycle (Eg: organic nitrogen, algae, nitrite nitrogen etc.), and all these equations need to be solved together in order to find the temporal and spatial variation of DO in rivers.

Solute Transport in Groundwater:

Mass transport is the process responsible for the movement of contaminants in the groundwater systems. Miscible contaminant transport in porous media is controlled by physical, chemical, and biological processes. In the presentation here, only the physical processes, and the adsorption process are considered. The primary physical processes are advection, molecular diffusion, and mechanical dispersion. Mechanical dispersion, unique to porous media flows, arises due to tortuous nature of flow through the pores whose arrangement and size is randomly distributed (Fig. 3). Darcy law for groundwater flows gives an average value across any surface bounding the Representative Elementary Volume. This is not the actual velocity at any point. Pore velocity is simply taken as the Darcy velocity by the porosity. This gives an idea about the order of magnitude of the velocity within a pore. However, velocity (both magnitude and direction) varies within a pore as shown in Fig. 3.

Thus the Darcy velocity we use in quantifying the advective transport represents only an average effect. This does not reflect the effect of pore size distribution on the point velocities at any particular point in the sub-surface, and consequently the effect of point velocity distribution on the movement of contaminant. To account for the effect of pore


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 size distribution on the transport, an additional term, similar to the molecular diffusion term, is added to the contaminant transport equation. This term is called the mechanical dispersion term.

Hydrodynamic dispersion is given by the addition of mechanical

dispersion and the molecular diffusion.

Existence of dispersion mechanism in groundwater flows becomes clear when we consider spreading of a solute, which is being continuously injected at a point. Although the bulk flow occurs along the X-direction, the solute spreads sideways also, as shown in Fig. 4. Variation of concentration with distance at any time would be as shown in Fig.5. The dotted line indicates the variation if only the advection were to be present. The continuous line indicates how the actual variation would be.

Gradual variation of

concentration is a manifestation of dispersion.

V = Darcy velocity A = Cross sectional area n = porosity Flow rate = V x A

Schematic of Pore

Velocity Distribution within the pore Tortuous paths taken by water Fig. 3: Movement of Water within Pores


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Spread of the solute Injection

At T3

point

At T1

Flo

At T2

Fig. 4: Evidence for Dispersion in Groundwater Flows

Concentration Only Advection

Advection & Dispersion

Distance Fig.5: Illustration of Advection and Dispersion

The governing equation for two-dimensional transport of a solute in a subsurface flow can be derived by applying the principle of conservation of mass to a representative elementary volume. This equation for the transport of a non-reactive solute under steady, saturated one-dimensional flow conditions in an isotropic porous medium can be written as:

C uC  2C  2C   Dxx 2  Dyy 2 t x x y

(14)

in which, u = pore water velocity in x-direction = Darcy velocity divided by the porosity (n), Dxx = dispersion coefficient in x-direction, Dyy = dispersion coefficient in y-direction, C =

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Centre for Water Resources, Anna University, Chennai (15)

National Workshop on Water Resources System Modeling 9th and 10th March 2017 concentration of the solute, and t = time. Dispersion coefficients in Eq. (14) may be computed using the following equations: Dxx   l u  D *

D yy   t u  D *

in which, l and t are the longitudinal and transverse dispersivities, respectively, and D* = effective molecular diffusion coefficient. These coefficients are generally determined either experimentally, or through parameter estimation studies using field data. It should also be noted that they are a strong functions of the scale. This means that direct use of laboratory determined dispersivities for large scale field conditions will give erroneous results. Equation (14) does not include the source terms, and therefore, cannot be used if pumping or injection is being carried out within the domain. It may be noted that similar equation can be written for multi-dimensional transport under multi-dimensional flow conditions. In such a case, advection will be considered in all three directions, and the multi-dimensional dispersion will be described through a Dispersion coefficient tensor.

Equation (14) describes the transport of a non-reactive solute through groundwater. However, many solutes dissolved in groundwater are also subjected to a number of different processes through which they can be removed from groundwater system. This affects the movement of the solute front. These processes can be grouped into biological and chemical processes. These processes include: (i)

sorption: solute clings to the solid surface of the aquifer

(ii)

ion exchange: one solute gets replaced by by another solute at the solid surface

(iii)

chemical precipitation: dissolution reactions

(iv)

aqueous complexation: mobility of a chemical is altered due to formation 4of complexes with other chemicals in the solution

(v)

biological transformations: living organisms in the subsurface degrade or transform the solutes by aerobic or anaerobic processes.


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 All these processes should be considered while developing the transport model by appropriately representing the process in terms of a reaction term.

A thorough

knowledge of chemical and bio-chemical reaction kinetics is essential for this purpose. Here, we consider only the sorption process to illustrate how the model equation changes due to reaction process.

Sorption: This is a process by which the solute clings on to solid surface present in the aquifer. This involves the exchange of molecules and ions between the solid phase and liquid phase. Sorption process includes: (i)

hydrophobic partitioning of organic chemicals (absorption) in the organic coatings or organic matter contained in the subsurface;

(ii)

adsorption of organics and metals to the surface of particles by electrostatic and /or surface coordination chemistry; and

(iii)

ion exchange of metal ions at exchange sites and in the interlayers of clays. Under equilibrium conditions, the relation between the solute concentration in the adsorbed phase and in the aqueous phase is commonly described by adsorption isotherm.

Here, we will assume that this type of modeling is valid for all sorption

reactions. Many models for adsorption isotherms (Linear, Freundlich, Langmuir etc.) have been suggested in the literature for modeling single component adsorption process. The popular Freundlich equilibrium adsorption is described as below: S  kd C a

(16)

in which, S = concentration of the chemical in the solid medium, C = concentration of the chemical in the solution, kd and “a” are experimental constants. It should be noted that Eq. (16) is valid under equilibrium conditions, which means that sorption is attained instantaneously and remains constant. This assumption is valid when the rate of sorption is much greater than the rate of change of solute concentrations due to any other cause and / or the rate of sorption is much greater than the rate of groundwater flow. If this assumption is not valid, then non-equilibrium sorption involving reaction kinetics may be needed. Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 Equation (14) can be expanded to include the effect of sorption on mass balance as given below:

C uC  2C  2C  S   Dxx 2  Dyy 2  b t x x y n t

(17)

in which, n = porosity, ρb = bulk density of the soil, and S = concentration of chemical in the solid medium. Substitution of Eq. (16) in Eq. (14) results in a single equation for C as a function of time and space. It may be noted here that transport equation for a reactive contaminant undergoing any type of reaction can be derived in a similar manner. Step 4: Development of mathematical solution Governing equations for contaminant transport processes as described in the previous section are partial differential equations. These partial differential equations are difficult to solve because they have a hyperbolic nature coming from the advective part, and a parabolic nature coming from the dispersive part. Inclusion of reaction term adds further difficulties. Development of solutions for these equations has engaged researchers for the last four decades, and a lot of research is still going on. Analytical solutions for the transport equation are available for very idealized conditions. For example consider the one-dimensional advection-dispersion equation along with the initial and boundary conditions as given below:

C C  2C V  Dl 2 t x x

C ( x, 0 ) = 0 for all x C (0, t ) = C0 for all t

Concentration gradient = 0 for all t at far field.

Analytical solution for this problem can be written as follows:

C ( x, t ) 

C0 2

  x  Vt erfc  2 Dt  l 

      exp Vx erfc  x  Vt D   2 Dt  l l  

   


(18)

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 in which, erfc (…) = complementary error function of the argument. Similarly, analytical solutions do exist for quite a few cases, but they all are based on many simplifying assumptions. In general, for practical field problems, governing equations for transport problems are solved using numerical methods. Both finite-difference and finite element methods have been developed for this purpose. Both these methods are applied to a discretized solution space. Governing partial differential equations are approximated by algebraic equations, applicable to discrete points in the solution space. Finite-difference methods are easy to understand and it is easy to develop computer programs based on this method. However, they are good for only one-dimensional problems. These methods require idealization of spatial domain in case of two and three-dimensional problems. Finite-element methods are most suitable in such cases. However, they are more difficult to code. In recent years, finite-volume methods have been developed for solving two and three-dimensional transport problems. They combine the best of both finite-difference and finite-element methods. Step 5: Model validation. Once a model has been selected for a particular problem at a particular site, the model must be validated. Model validation is the process of making sure that the model correctly describes all the relevant processes that affect the excitationresponse relations of interest to an acceptable degree of accuracy. The only way to validate a model is an experiment. Although it is desirable to perform the model validation for the actual site of interest, we often validate the model in principle, i.e., ensuring that it represents the phenomena, by conducting controlled field or laboratory experiments.

Step 6: Model calibration. Model calibration is the activity that combines model validation and parameter estimation at a specific site of interest. These activities are actually executed simultaneously. Thus, in the procedure of calibration, the values of model coefficients for a site are determined by solving an inverse problem, using field data from that site.


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 Step 7: Uncertainty analysis. Briefly, we want to know how sensitive the predicted values are to changes in the values of model coefficients. If these effects are not significant we can accept the predicted values and make decisions. If, however, the predicted values are sensitive to changes in parameter values, we must reduce the range of uncertainty in the values of these parameters. In most cases, this means that we must invest more resources in order to acquire more and more accurate data. Sensitivity analysis can also be used to assess the reliability of parameters determined in the calibration procedure.

Step 8: Stochastic analysis. A stochastic analysis not only takes into account the simple statistical measures of mean and standard deviation of the input data, such as the hydraulic conductivity and the natural replenishment, but it also examines the temporal and spatial correlations of these data.

APPLICATION OF CONTAMINANT TRANSPORT MODELS Since the advent of computers in the second half of the last century, mathematical models have become common tools for the assessment and prediction of movement of contaminants in groundwater systems. A few of these applications are described in this section in order to get the reader interested in this subject. Waste Load Allocation Problem: Many industrial units and municipalities use rivers for dumping their wastes.

Many

communities take water from these rivers for drinking, agricultural, and industrial purposes. If the dumping occurs on the upstream side while the abstraction on the downstream side, naturally communities taking water from the river would be concerned about the affect of upstream dumping on the quality of water, and they would like the government to control this pollution by passing laws. On the other hand, polluters may not be willing to find alternative solutions because of economic reasons. In this context, it may be noted that polluted waters from the upstream may get purified, naturally by the river itself, by the time they reach the abstraction point, if the abstraction is taking place


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 far downstream of the location where dumping is occurring. This also strongly depends upon the quantity of dumping and quality of the waste. Waste load allocation problem pertains to stipulating, by the monitoring agency, the quantity and quality of the waste that can be discharged into the river by a particular polluting unit, such that the quality of water at downstream abstraction points does not fall below the safe limits. This management decision problem requires the use of a contaminant transport model in conjunction with an optimization model, which optimally allocates the loads. The optimal allocation could be based on cost minimization, equity in sharing the cost of treatment etc. Environmental Impact Assessment of Large Water Resources Projects: Inter linking of rivers is one of the major project government of India is interested to implement. However, there are many reasons why some people, in the donor basins, are apprehensive about this project. One of the reasons is possible deterioration in quality of water in the donor basin, on the downstream side of the diversion point. If large amounts of water are diverted from a river, the quantity released to the downstream side may not be sufficient, and thus velocities may not be high enough. This reduces the selfcleansing ability of the river, and therefore the industries and municipalities located on the downstream side should spend more money to treat their wastes before releasing them into the river. Also, the quality of water gets altered, and this definitely will have some effect on the fragile ecology of mangroves and estuaries. Building of a large dam and creation of reservoir results in the decrease of velocity on the upstream side, which in turn reduces the self-cleansing ability of the river. To counter this, wastewater that is being released into the river should get treated to higher levels of standards. For example, it is estimated that the Chinese government needs to spend some 25 billion dollars to treat the wastewater that is being discharged into Yangtze river because of creation of the Three Gorges dam, which is the world’s largest dam. This environmental impact assessment problem requires the use of a contaminant transport model. Source Identification Problem: Contaminants such as Hydrocarbons and various organic solvents, used in industry enters in to the unsaturated zone as a result of spills, leaks from faulty storage tanks or pipes, leakage from corroded drums, and burst of pipelines. Many times, it is required to


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 identify where the contamination in a water body is coming from, who is responsible for this contamination so that proper legal action can be taken, and who should pay for the cleanup operation. This is called a source identification problem. identification of sources of pollution, especially in the case of groundwater sources is not that easy and may be possible to determine, using appropriate contaminant transport models, magnitude, location, and time of occurrence of leakage. Such several source identification problems have been solved earlier in the developed countries. Design of Cleanup Methods for Field Conditions: Many new technologies are being developed to cleanup the groundwater resources insitu. One such example is the in-situ bio-remediation technique. This technique is based on creating conditions conducive for appropriate microbes to grow in-situ.

These

microbes can then transform the highly toxic chemicals to less toxic chemicals through bio-chemical processes. Development of these techniques always starts with carefully conducted laboratory studies to understand the bio-chemical reactions. These laboratory studies can be used to develop appropriate transport models.

Before actually

implementing these techniques to a particular field condition, applicability of the developed technology can be assessed using the transport model. Such assessment should be made before large investments are made. Many commercial software packages like Modflow, SUTRA and BIOF&T, Bioslurp etc., for groundwater quality modeling are available for application to field problems. A basic knowledge of transport phenomenon, and numerical methods is absolutely essential if these models are to be applied appropriately by any individual. Otherwise the numbers that are spewed out by the mathematical model may be misunderstood, and the user may develop a false sense of security.

SUGGESTED TEXT BOOK: 1. Schnoor, J.L., “Environmental Modeling”, Johm Wiley, 1996. 2. Jacob Bear and Alexander H.-D. Cheng, Modeling Groundwater Flow and Contaminant Transport, Springer Dordrecht Heidelberg London New York, 2010.


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ACKNOWLEDGEMENTS Parts of this notes are based on the material given in the 1. Jacob Bear and Alexander H.-D. Cheng, Modeling Groundwater Flow and Contaminant Transport Theory and Applications of Transport in Porous Media, Springer Dordrecht Heidelberg London New York, 2010. 2. Lecture note on Contaminant Transport modeling , QIP Short Term Course on Hazardous Waste Management, July 07-18, 2003, IIT Madras. 3. M.S. thesis “Analysis of solute transport in porous media for nonreactive and sorboing solutes using hybrid FCT model” by C. Srinivasan, I.I.Sc., Bangalore.


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Evolutionary Algorithms for Mulitobjective Optimal Reservoir Operation D. Nagesh Kumar Professor, Department of Civil Engineering, Indian Institute of Science, Bangalore - 560 012, India. (Email: [email protected]) Abstract

Optimal operation of water resources systems especially multipurpose multi reservoir systems is a challenging task in many real world applications. When compared to traditional optimization techniques, evolutionary algorithms offer several advantages in performing multi objective optimization and generating very efficient Perato optimal front. In the recent past evolutionary computation techniques have been receiving increasing attention regarding their potential as global optimization techniques for complex problems. This popularity is mainly due to the robustness, ease of use and wide applicability of evolutionary algorithms. In this work, several soft computing techniques such as Genetic Algorithms (GA), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO) and fuzzy logic will be discussed and their role in multi objective optimization for deriving optimal reservoir operation will be presented. Some case studies based on these techniques will be presented. Relative merits of these techniques and their scope in efficient utilization of water resources systems will be discussed.


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HYDROLOGICAL PROCESSES Hydrol. Process. 21, 2897– 2909 (2007) Published online 10 January 2007 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/hyp.6507

Multi-objective particle swarm optimization for generating optimal trade-offs in reservoir operation M. Janga Reddy and D. Nagesh Kumar* Department of Civil Engineering, Indian Institute of Science, Bangalore - 560 012, India

Abstract: A multi-objective particle swarm optimization (MOPSO) approach is presented for generating Pareto-optimal solutions for reservoir operation problems. This method is developed by integrating Pareto dominance principles into particle swarm optimization (PSO) algorithm. In addition, a variable size external repository and an efficient elitist-mutation (EM) operator are introduced. The proposed EM-MOPSO approach is first tested for few test problems taken from the literature and evaluated with standard performance measures. It is found that the EM-MOPSO yields efficient solutions in terms of giving a wide spread of solutions with good convergence to true Pareto optimal solutions. On achieving good results for test cases, the approach was applied to a case study of multi-objective reservoir operation problem, namely the Bhadra reservoir system in India. The solutions of EM-MOPSOs yield a trade-off curve/surface, identifying a set of alternatives that define optimal solutions to the problem. Finally, to facilitate easy implementation for the reservoir operator, a simple but effective decision-making approach was presented. The results obtained show that the proposed approach is a viable alternative to solve multi-objective water resources and hydrology problems. Copyright  2007 John Wiley & Sons, Ltd. KEY WORDS

multi-objective optimization; particle swarm optimization; elitist-mutation; reservoir operation; hydropower; irrigation; water quality; Pareto optimal solutions

Received 2 December 2005; Accepted 26 June 2006

INTRODUCTION Most of the water resources and hydrology problems are characterized by multiple objectives and/or goals, which often conflict and compete with one another. Optimization of multi-purpose reservoir systems involves solving multi-objective problems. For example, for a reservoir system having hydropower and flood control as key purposes, the two major objectives can be maximization of the hydropower generation from the reservoir and minimization of flood risk or flood damage. Obviously, these two objectives are in conflict and compete with each other. The higher the level of the reservoir, the more the hydropower generation possible because of the high water head, yet less water storage will be available for flood control purposes and vice-versa. Clearly, one can identify, within the active storage capacity of that reservoir, a Pareto optimum region where the enhancement of the first objective can be achieved only at the expense or degradation of the second, namely flood control (Haimes et al., 1990). Also the units of these two objectives are non-commensurable. The first objective, which maximizes the hydroelectric power, is generally measured in units of energy and not necessarily in monetary units, whereas the second objective can be measured in terms of acres of land, livestock, or human lives saved. If the objectives are non-commensurate, the classic methods of optimization cannot be applied easily. Of the several * Correspondence to: D. Nagesh Kumar, Department of Civil Engineering, Indian Institute of Science, Bangalore - 560 012, India. E-mail: [email protected] Copyright  2007 John Wiley & Sons, Ltd.

approaches developed to deal with multiple objectives, tradeoff methodologies have shown promise as effective means for considering non-commensurate objectives that are to be subjectively compared in operation determination (Cohon and Marks, 1975). Therefore efficient generation of a set of alternatives for multiple objectives is very important with minimum computational requirements. Scope for multi-objective optimization using meta-heuristic techniques Reservoir operation modeling has an exhaustive literature presenting various optimization techniques in order to solve various kinds of problems (Yeh, 1985). However, in order to focus on the goal of this paper, a brief overview is given here. Most of the researchers on reservoir operation problems have tried conventional techniques to generate tradeoffs among multiple objectives. For example, Tauxe et al. (1979) have applied a multi-objective dynamic programming (DP) model for analyzing a reservoir operation problem involving three conflicting objectives. Thampapillai and Sinden (1979) and Mohan and Raipure (1992) analyzed the tradeoffs for multiple objective planning through linear programming (LP). To handle multiple objectives, many studies have used either the weighing approach or the constraint method. The constraint method was used for generation of noninferior set and trade-off curves for reservoir operation problems (e.g. Croley and Rao, 1979; Yeh and Becker, 1982; Liang et al., 1996 and Wang et al., 2005).

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M. J. REDDY AND D. NAGESH KUMAR

The conventional optimization methods such as DP, LP, and non-linear programming (NLP) are not suitable to solve multi-objective optimization problems (MOOP), because these methods use a point-by-point approach, and the outcome of these classical optimization methods is a single optimal solution. For example, the weighted sum method will convert the MOOP into a single objective optimization. By using a single pair of fixed weights, only one point on the Pareto front can be obtained. Therefore, if one would like to obtain the global Pareto optimum, all possible Pareto fronts must first be derived. This requires the algorithms to be executed iteratively, so as to ensure that every weight combination has been used. Obviously, it is impractical to reiterate the algorithms continually to exhaust all the weight combinations. Hence the algorithms should have an ability to ‘learn’ from previous performance to direct the proper selection of weights in further evolutions. Also conventional methods may face problems, if the optimal solution lies on nonconvex or disconnected regions of function space (Deb, 2001). Recently, meta-heuristic techniques such as evolutionary algorithms (EAs) and swarm intelligence techniques are becoming increasingly popular for solving optimization problems. In the recent past, evolutionary techniques have been successfully applied for single objective optimization (Oliveira and Loucks, 1997; Wardlaw and Sharif, 1999; Raju and Nagesh Kumar, 2004) and MOOPs (Yapo et al., 1998; Vrugt et al., 2003; Khu and Madsen, 2005), due to their efficiency and ease in handling non-linear and non-convex relationships of realworld problems. These techniques have some advantages over the classical optimization techniques (Deb, 2001). They use a population of solutions in each iteration and offer a set of alternatives in a single run. They use randomized initialization and stochastic search in their operation. Therefore, they can locate the search at any place over the entire search space and are able to overcome the problems of local optima. Thus population based stochastic search techniques are more appropriate to solve MOOPs. Achieving a well-spread and diverse Pareto solution front is the primary goal of MOOP. Among the elitist multi-objective EAs (MOEAs), strength Pareto EA (SPEA) (Zitzler and Thiele, 1999), Pareto-archived evolutionary strategy (PAES) (Knowles and Corne, 2000) and non-dominated sorting genetic algorithm (NSGA-II) (Deb et al., 2002) have been successfully demonstrated for solving MOOP. Among the meta-heuristic techniques, until recently particle swarm optimization (PSO) was applied only to single objective optimization tasks. However, the high speed of convergence of the PSO algorithm attracted researchers to develop multi-objective optimization algorithms using PSO (Kennedy and Eberhart, 2001). Also, the PSO seems to have some advantages in terms of the better exploration and exploitation provided by local and global search capabilities of the algorithm. In the present study, a novel approach for multiple-objective Copyright  2007 John Wiley & Sons, Ltd.

PSO (MOPSO) is developed. To demonstrate the efficiency of the proposed approach, results obtained are compared with NSGA-II, and evaluated with standard performance measures that are frequently used for performance evaluation of MOEAs. The proposed approach for solving a multi-objective decision problem in reservoir operation has a great potential for application, due to its attractive feature of generation of large number of well spread Pareto optimal solutions in a single run. The other approaches suggested in this paper for decision making, provide an opportunity for the reservoir operator to choose the desired alternative from a set of Pareto-optimal solutions.

PARTICLE SWARM OPTIMIZATION Swarm intelligence is a new area of research, from which the PSO technique has been evolved through a simple simulation model of the movement of social groups such as birds and fish (Kennedy and Eberhart, 2001). The basis of this algorithm is that local interactions motivate the group behaviour, and individual members of the group can profit from the discoveries and experiences of other members. Social behaviour is modeled in PSO to guide a population of particles (socalled swarm), moving towards the most promising area of the search space. The changes of the position of the particles within the search space are based on the social psychological tendency of individuals to emulate the success of other individuals. In PSO, each particle represents a candidate solution. If the search space is D-dimensional, the ith individual (particle) of the population (swarm) can be represented by a D-dimensional vector, Xi D xi1 , xi2 , . . . , xiD T . The velocity (position change) of this particle, can be represented by another D-dimensional vector, Vi D vi1 , vi2 , . . . , viD T . The best previously visited position of the ith particle is denoted as Pi D pi1 , pi2 , . . . , piD T . Defining g as the index of the global guide of the particle in the swarm, and superscripts denoting the iteration number, the swarm is manipulated according to the following two equations: n n n n vnC1 id D [w vid C c1 r1 pid xid /t n C c2 r2n pngd xid /t] nC1 nC1 n D xid C t vid xid

1 2

where d D 1, 2, . . . , D; i D 1, 2, . . . , N; N is the size of the swarm population; is a constriction factor which controls and constricts the velocity’s magnitude; w is the inertial weight, which is often used as a parameter to control exploration and exploitation in the search space; c1 and c2 are positive constant parameters called acceleration coefficients; r1 and r2 are random numbers, uniformly distributed in [0,1]; t is the time step usually set as 1 and n is iteration number. The successful application of PSO in many single objective optimization problems reflects its effectiveness, and it seems to be particularly suitable for multiobjective Hydrol. Process. 21, 2897– 2909 (2007) DOI: 10.1002/hyp

MOPSO FOR GENERATING OPTIMAL TRADE-OFFS IN RESERVOIR OPERATION

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optimization due to its efficiency in yielding better quality solutions while requiring less computational time (Kennedy and Eberhart, 2001). The main difficulty in extending PSO to multi-objective problems is to find the best way of selecting the guides for each particle in the swarm. The difficulty is noticeable, as there are no clear concepts of local and global bests that can be clearly identified, when dealing with many objectives rather than a single objective. Recently a few proposals on extensions of PSO technique to multi-objective optimization have been reported (for example, Parsopoulos and Vrahatis, 2002; Hu et al., 2003; Li, 2003; Coello et al., 2004). In this paper, an efficient method is presented for PSO to solve MOOPs. The approach uses Pareto dominance criteria for selecting non-dominated solutions; an external repository (ERP) for storing best solutions found (elitism); crowding distance operator for creating effective selection pressure among the swarm to reach true Pareto optimal fronts; and incorporates an effective elitist-mutation (EM) strategy for effective exploration of the search space. The proposed elitist-mutated multiobjective particle swarm optimization (EM-MOPSO) algorithm is discussed in detail in the following sections.

Elitist-mutated multi-objective particle swarm optimization The main algorithm consists of initialization of population, evaluation, and reiterating the search on swarm by combining PSO operators with Pareto-dominance criteria. In this process, the particles are first evaluated and checked for dominance relation among the swarm. The non-dominated solutions found are stored in an ERP, and are used to guide the search particles. It uses variable size ERP, in order to improve the performance of the algorithm to save computational time during optimization. If the size of ERP exceeds the restricted limit, then it is reduced by using the crowded comparison operator, which gives the density measure of the existing particles in the function space. Also, an efficient EM strategy is employed for maintaining diversity in the population and for exploring the search space. The combination of these operators helps the algorithm to effectively propagate the search towards true Pareto optimal fronts in further generations.

MULTI-OBJECTIVE PARTICLE SWARM OPTIMIZATION

Step 1. Initialize population. Set iteration counter t D 0. 1. The current position of the i-th particle Xi is initialized with random real numbers within the specified decision variable range; each particle velocity vector Vi is initialized with uniformly distributed random number in [0,1]. 2. Evaluate each particle in the population. The personal best position Pi , is set to Xi . Step 2. Identify particles that give non-dominated solutions in the current population and store them in an ERP. Step 3. t D t C 1. Step 4. Repeat the loop (step through PSO operators): 1. Select randomly a global best Pg for the i-th particle from the ERP. 2. Calculate the new velocity Vi , based on Equation (1), and the new Xi by Equation (2). 3. Repeat the loop for all the particles. Step 5. Evaluate each particle in the population. Step 6. Perform the Pareto dominance check for all the particles: if the current local best Pi is dominated by the new solution, then Pi is replaced by the new solution. Step 7. Set ERP to a temporary repository, TempERP and empty ERP. Step 8. Identify particles that give non-dominated solutions in current iteration and add them to TempERP. Step 9. Find the non-dominated solutions in TempERP and store them in ERP. The size of ERP is restricted to the desired set of non-dominated solutions; if it exceeds, use the crowding distance operator to select the desired ones. Empty the TempERP.

Brief concepts of multi-objective optimization are presented first and then the proposed algorithm is explained. Multi-objective optimization and Pareto optimality A general MOOP can be defined as: minimize a function fx, subject to p inequality and q equality constraints. min . fx D ff1 xf2 x . . . fm xgT x2D where x 2 Rn , fi : Rn ! R and x 2 Rn : li x ui , 8i D 1, . . . ., n gj x ½ 0, 8j D 1, . . . ., p DD hk x D 0, 8k D 1, . . . ., q

3

4

where m is number of objectives; D is feasible search space; x D fx1 x2 . . . xn gT is the set of n-dimensional decision variables (continuous, discrete or integer); R is the set of real numbers; Rn is n-dimensional hyper-plane or space; and li and ui are lower and upper limits of i-th decision variable. The MOOP should simultaneously optimize the vector function and produce Pareto optimal solutions. Pareto front is a set of Pareto optimal (non-dominated) solutions, being considered optimal, if no objective can be improved without sacrificing at least one other objective. On the other hand, a solution x Ł is referred to as dominated by another solution x, if and only if, x is equally good or better than x Ł with respect to all objectives (Haimes et al., 1990). Copyright  2007 John Wiley & Sons, Ltd.

EM-MOPSO algorithm The developed EM-MOPSO algorithm can be summarized in the following steps.

Hydrol. Process. 21, 2897– 2909 (2007) DOI: 10.1002/hyp

2900


Step 10. Perform EM operation on specified number of particles. Step 11. Check for termination criteria; if the termination criterion is not satisfied, then go to step 3; otherwise output the non-dominated solution set from ERP. The main operators used in this algorithm are explained below. Variable size external repository The selection of the global best guide of the particle swarm is a crucial step in a multi-objective PSO algorithm. It affects both the convergence capability of the algorithm as well as maintaining a good spread of non-dominated solutions. As ERP stores non-dominated solutions found in the previous iteration, any one of the solutions can be used as global guide. But we want to ensure that the particles in the population move towards the sparse regions of the non-dominated solutions and speed up the convergence towards the true Pareto optimal region. To perform these tasks, the global best guide of the particles is selected from a restricted variable size ERP. This restriction on ERP is done using the crowding distance operator. This operator ensures that those nondominated solutions with the highest crowding distance values are always preferred to be in the ERP. The other advantage of this variable size ERP is that it saves considerable computational time during optimization. As the ERP size increases, the computing requirement becomes greater for sorting and crowding value calculations. Thus for effective exploration of the function space, the size is initially set to 10% of maximum ERP, and then the value is increased in a stepwise manner, so that at the start of 90% of maximum iterations, it reaches the maximum size of ERP. Selecting different guides for each particle from a restricted repository allows the particles better exploration of the true Pareto optimal region. This kind of selection is novel and it effectively improves the performance of the algorithm. Crowding distance assignment operator This operator is adopted from Deb et al. (2002). The crowding distance value of a solution provides an estimate of the density of solutions surrounding that solution. Crowding distance is calculated by first sorting the set of solutions in ascending objective function values. The crowding distance value of a particular solution is the average distance of its two neighboring solutions. The boundary solutions that have the lowest and highest objective function values are given infinite crowding distance values, so that they are always selected. This process is done for each objective function. The final crowding distance value of a solution is computed by adding all the individual crowding distance values in each objective function. For sorting, an efficient quick sorting procedure is used. The pseudo-code of crowding distance computation is given below. Copyright  2007 John Wiley & Sons, Ltd.

1. Get the number of non-dominated solutions in the ERP l D jERPj 2. Initialize distance. For i D 1 to l ERP[i].dist D 0 3. Compute the crowding distance of each solution. For each objective m, Sort using objective value. ERP D sort ERP, m Set the boundary points to a large value so that they are always selected. ERP[1].dist D ERP[l].dist D 1 For i D 2 to (l-1) ERP[i].dist D ERP[i].dist C ERP[i C 1].m min ERP[i 1].m/fmax m fm

Elitist-mutation operator To maintain diversity in the population and to explore the search space, a novel strategic mechanism called EM is incorporated into the algorithm. This acts on a predefined number of particles. In the initial phase of this mechanism, it tries to replace the infeasible solutions with the mutated least crowded particles of ERP and at the later phase, it tries to exploit the search space around the sparsely populated particles in ERP along the Pareto fronts. This is a special strategic mechanism, which enhances the performance of MOPSO while extending from traditional PSO algorithm. Thus the EM operator helps to uniformly distribute the non-dominated solutions along the true Pareto optimal front. The pseudo-code of the elitist mutation mechanism is given below. 1. Randomly select one of the objectives from m objectives. Sort the fitness function of particles in descending order and get the index number descending order sorted particles (DSP) for the respective particles. 2. Use crowding distance assignment operator and calculate the density of solutions in the ERP and sort them in descending order of crowding value. Randomly select one of the least crowded solutions from the top 10% of ERP as guide (g). 3. Perform EM on a predefined number of particles (NMmax ). Let Rp —be the size of repository; pem - probability of elitist mutation; Sm - mutation scale used to preserve diversity; rand - uniformly distributed random number U(0,1); intRnd (a, b) - uniformly distributed integer random number in the interval [a, b]; randn - Gaussian Hydrol. Process. 21, 2897– 2909 (2007) DOI: 10.1002/hyp


random number N(0,1); and VR[i]- range of decision variable i.

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EM-MOPSO APPLICATION AND PERFORMANCE EVALUATION

g D intRnd1, 0Ð1 ð Rp

In order to demonstrate the efficiency of the proposed EM-MOPSO, it is first tested for a few standard test problems taken from the MOEAs literature and its performance is evaluated with results of NSGA-II.

For d D 1 to dim

Test problems

For i D 1 to NMmax l D DSP[i]

if rand < pem Ł

Ł

X[l] [d] D ERP[g][d] C Sm VR[d] randn else X[l] [d] D ERP[g][d] End For End For If the mutated value exceeds the bounds, then it is limited to the upper or lower bound. The velocity vector of the particle remains unchanged during this EM step. Constraint handling In order to handle the constrained optimization problems, this study adopts the constraint handling mechanism proposed by Deb et al. (2002). This is a simple, but very effective procedure reported in the literature. In this approach, a solution i is said to be a constraineddominate solution j if any of the following conditions hold good: 1. Solution i is feasible and solution j is not. 2. Both solutions i and j are infeasible, but solution i has a smaller overall constraint violation. 3. Both solutions i and j are feasible and solution i dominates solution j. By using all the above steps, the EM-MOPSO approach is coded in user friendly mathematical software package MATLAB 6Ð5 and is run on PC/WindowsXP/ 256MB RAM/2GZ computer. The applicability and efficiency of the proposed approach is demonstrated in the following sections.

The four test functions considered to test the performance of the proposed algorithm are given in Table I (Deb, 2001). The first test problem (BNH) is a MOOP, with two objectives subject to two constraints. The second test problem (KITA) is a MOOP, with maximization of two objectives subject to three constraints. This problem has non-convexity in its Pareto optimal region. The third test problem (CONSTR) is a MOOP, with two objectives subject to two constraints. This problem has the difficulty that a part of the unconstrained Pareto optimal region is not feasible. Thus the resulting constrained Pareto optimal region is a concatenation of the first constraint boundary and some part of unconstrained Pareto optimal region. The fourth test problem (SRN) is a MOOP, with two objectives subject to two constraints. Here the constrained Pareto optimal set is a subset of the unconstrained Pareto-optimal set, which gives difficulty in finding the true Pareto optimal region for the algorithm. Sensitivity of EM-MOPSO parameters The sensitivity analysis of the PSO model is performed with different combinations of each parameter. In this analysis, it is observed that by considering the proper value for the constriction coefficient, the inertial weight does not have much influence on the final result of the model (Nagesh Kumar and Janga Reddy, 2006). So in this study the inertial weight (w) is fixed as 1. Also, it is found that the value of constriction coefficient equal to 0Ð9 yields better results for the given model. After a number of trials, it was found that constant parameters c1 D 1Ð0 and social parameter c2 D 0Ð5 resulted in better quality solutions. The same values are used for all the test problems.

Table I. Test problems used in the study Problem

Variable bounds

Objective functions

Constraints

BNH

x1 2 [0, 5] x2 2 [0, 3]

g1 x D x1 52 C x22 25 g2 x D x1 82 C x2 C 32 ½ 7Ð7

KITA

xi 2 [0, 7] i D 1, . . . , 3

CONSTR

x1 2 [0Ð1, 1Ð0] x2 2 [0, 5]

SRN

xi 2 [20, 20] i D 1, 2

Minimize f1 (x) D 4x12 C 4x22 f2 (x) D x1 52 C x2 52 Maximize f1 x D x12 C x2 f2 x D 0Ð5x1 C x2 C 1 Minimize f1 (x) D x1 f2 (x) D 1 C x2 /x1 Minimize f1 (x) D x1 22 C x2 12 C 2 f2 (x) D 9x1 x2 12

Copyright  2007 John Wiley & Sons, Ltd.

g1 x D x1 /6 C x2 6Ð5 0 g2 x D 0Ð5x1 C x2 7Ð5 0 g3 x D 5x1 C x2 30 0 g1 x D x2 C 9x1 ½ 6 g2 x D x2 C 9x1 ½ 1 g1 x D x12 C x22 225 g2 x D x1 3x2 10


2902


Size of elitist-mutated particles (NMmax ). The number of particles to be elitist mutated is selected after ensuring that the population does not lose control on search at the cost of exploring for better non-dominated solutions. To experiment with the size of elitist mutated particles, the number of particles is varied as 5, 10, 15, 20, 25 and 30 for the problems having a maximum population of 100. The best results are found for NMmax D 20 and is kept constant for all the test problems considered in this study. Probability of elitist mutation (pem ). pem is varied from 0 to 0Ð5 for sensitivity analysis. It is found that best performance occurs at pem D 0Ð2, and is kept constant for all the test problems considered in the study. Elitist-mutation operator mutation scale (Sm ). The other parameter used in EM operation is mutation scale (Sm ). After various experiments, it is found that a value of Sm in the range of 0Ð2 to 0Ð01 gives good performance. This is selected after ensuring that at the initial stage it did not deteriorate the search while exploring the search space or stagnate the search at the end of iterations. Simulation results To run the EM-MOPSO algorithm, the following parameters are used: size of population D 100; constant parameters c1 D 1Ð0 and c2 D 0Ð5; inertial weight w D 1; constriction coefficient D 0Ð9; size of ERP D 100; the size of elitist-mutated particles is set to 20, the value of pem was set to 0Ð2; and the value of Sm decreases from 0Ð2 to 0Ð01 over the iterations. To run the NSGA-II model, the initial population was set to 100, crossover probability to 0Ð9, and mutation probability to 1/n (n is the number of real variables). The distribution index values for real-coded crossover and mutation operators are set to 20 and 100 respectively (Deb et al., 2002). Maximum number of iterations in a run is set to 250 for both the algorithms. The same parameter settings were used for all the problems. To evaluate the performance of the proposed EM-MOPSO algorithm, this study uses two performance measures, set coverage metric (SC) and spacing metric (SP) (Deb, 2001). The details of these performance metrics are presented in APPENDIX- A. Table II shows the best, worst, mean, variance and standard deviation (SD) values of the two performance metrics (SC and SP) obtained from 10 independent runs using EM-MOPSO and NSGA-II. The set coverage metrics SC (A, B) and SC (B, A) give a measure of how many solutions of A are covered by B and vice versa. Here, the value SC A, B D 1 means that all solutions in B are weakly dominated by A, while SC A, B D 0 represents the situation when none of the solutions in B are weakly dominated by A. It can be seen that with respect to the SC metric, the average performance of EM-MOPSO is the best for test functions BNH, KITA and SRN, whereas NSGA-II performs best for the CONSTR problem. This metric shows the efficiency of EM-MOPSO in achieving better convergence to true Copyright  2007 John Wiley & Sons, Ltd.

Table II. Resulting statistics by EM-MOPSO and NSGA-II for test problems, considered in the study. In SC(A, B), A is EM-MOPSO and B is NSGA-II. Bold numbers indicate the best performing algorithm Test problem

Statistic

Best Worst BNH Mean Variance SD Best Worst KITA Mean Variance SD Best Worst CONSTR Mean Variance SD Best Worst SRN Mean Variance SD

Performance metric Set coverage metric (SC)

Spacing metric (SP)

SC(A, B) SC(B,A)

EMNSGA-II MOPSO

0Ð1400 0Ð0900 0.1111 0Ð0003 0Ð0176 0Ð2900 0Ð1200 0.2400 0Ð0015 0Ð0394 0Ð1600 0Ð0700 0Ð1181 0Ð0008 0Ð0281 0Ð1400 0Ð0400 0.0978 0Ð0014 0Ð0370

0Ð1200 0Ð0500 0Ð0877 0Ð0005 0Ð0233 0Ð2400 0Ð1300 0Ð1811 0Ð0013 0Ð0355 0Ð1700 0Ð1000 0.1344 0Ð0004 0Ð0201 0Ð1400 0Ð0400 0Ð0944 0Ð0009 0Ð0305

0Ð6357 0Ð7559 0.6941 0Ð0015 0Ð0385 0Ð0374 0Ð4254 0.1359 0Ð0196 0Ð1401 0Ð0374 0Ð0431 0.0406 0Ð0000 0Ð0017 1Ð0768 1Ð3929 1.2439 0Ð0114 0Ð1055

0Ð6408 0Ð8928 0Ð7756 0Ð0053 0Ð0727 0Ð0496 0Ð5117 0Ð1464 0Ð0227 0Ð1507 0Ð0372 0Ð0487 0Ð0437 0Ð0000 0Ð0041 1Ð3402 1Ð7073 1Ð5860 0Ð0179 0Ð1337

Pareto optimal fronts than NSGA-II. With regard to the spacing metric (SP), as compared to NSGA-II, EMMOPSO gives smaller SP values for all the test problems considered in the study. The smaller SP indicates that the algorithm gives better distribution of solutions. Thus EM-MOPSO maintains the best distribution of solutions for all the test problems. For illustration purposes, a sample result for each of the test problems considered is shown in the plots in Figure 1. Thus the results obtained clearly show that the proposed method does not have any difficulty in achieving a good spread of Pareto optimal solutions for constrained multi-objective optimization.

CASE STUDY To demonstrate the efficacy of the proposed approach, the Bhadra reservoir system in India is taken up as a case study for developing optimal reservoir operation policy. Figure 2 shows the location map of the Bhadra reservoir system. The Bhadra dam is located at latitude 13° 420 N and longitude 75° 380 2000 E. The Bhadra reservoir is a multi-purpose project providing facilities for irrigation, hydropower generation and meeting water quality requirements downstream. The schematic diagram of the reservoir system is given in Figure 3. Most of the inflows into the reservoir are received during the monsoon season of 4 months. But the demands are distributed throughout the year. The reservoir provides water for irrigation of 6367 ha and 87 512 ha under Hydrol. Process. 21, 2897– 2909 (2007) DOI: 10.1002/hyp

2903


(a) BNH 50

(b) KITA 8.6

EM-MOPSO 40

EM-MOPSO

8.4

NSGA-II

NSGA-II

8.2 f2

f2

30 20

8.0 7.8

10

7.6

0 0

30

60

90

120

7.4 −4.0 −2.0

150

0.0

f1

2.0 f1

4.0

6.0

8.0

(d) SRN

(c) CONSTR 10

EM-MOPSO

8

EM-MOPSO

0

NSGA-II

NSGA-II

−50

f2

f2

6

−100

4

−150

2

−200 −250

0 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0

50

100

f1

150

200

250

f1

Figure 1. Non-dominated solutions obtained using EM-MOPSO and NSGA-II for the test problems (a) BNH, (b) KITA, (c) CONSTR and (d) SRN

left and right bank irrigation canals respectively. The irrigated area spread over the districts of Chitradurga, Shimoga, Chikmagalur, and Bellary in Karnataka state, comprises predominantly of red loamy soil, except in some portions of the right bank canal area, which consists of black cotton soil. Major crops grown in the command area are paddy, sugarcane, permanent garden, and semidry crops. Also under this project there are three sets of turbines, one set each on the left bank canal and the right bank canal and the other set at the river bed level of the dam, generating hydropower. The operating head above river bed, ranges from 38Ð56 m to 54Ð41 m for the right bank turbine (PH2), and from 36Ð88 m to 56Ð69 m for left bank turbine (PH1) and bed turbines (PH3). The mean tail water levels of right bank, left bank, and bed turbines are at 32Ð736 m, 12Ð802 m and 6Ð706 m above the bed level respectively. It can be noted that the water released to left bank and right bank canals goes through turbines only when the water is within the limits of turbine operating range, otherwise it will be released directly for irrigation. Water quality is also a major concern to the reservoir authorities due to continuous development of industries in the downstream region. So the water quality objective requires certain minimum water levels to be maintained in the river downstream. Salient features of the reservoir are given in Table III. Data pertaining to monthly inflows and other details were collected from water resources development organization (WRDO), Bangalore covering a period of 69 years (from 1930–1931 to 1998–1999). The monthly crop water requirements were calculated using Food and Agricultural Organization (FAO) Penman-Monteith method (Allen et al., 1998). Copyright  2007 John Wiley & Sons, Ltd.

Model formulation The objectives of the reservoir operation model are: minimizing the irrigation deficits, maximizing the hydropower generation and maximizing the satisfaction level of water quality. These are conflicting and/or competitive objectives. For example, conflict may arise during dry periods: for minimization of irrigation deficits, more water is to be released to satisfy irrigation demands; while for maximization of hydropower production, higher level of storage in the reservoir is required to produce more hydropower energy; and for maximizing the satisfaction level of water quality, steady release of water is required to meet river water quality requirements downstream. Thus, solving the allocation problems of this reservoir system is interesting from the multi-objective perspective. In order to simplify the water quality objective, in this study it is assumed that if we discharge a prespecified amount of water into the downstream river, the river water quality can be maintained. The water quality demands are chosen after carefully studying the historical data and previous studies on river water quality maintenance. To maintain even distribution of irrigation deficits if any, the irrigation objective is taken as squared deviation of demand to release. The competing objectives of the system are expressed as follows: Minimize sum of squared deviations for irrigation annually: SQDV D

12 tD1

D1,t IR1,t 2 C

12

D2,t IR2,t 2

5

tD1

where SQDV is the sum of squared deviations of irrigation demands from releases. D1,t and D2,t are the Hydrol. Process. 21, 2897– 2909 (2007) DOI: 10.1002/hyp

2904


Figure 2. Location map of the Bhadra project command area

Table III. Salient features of Bhadra reservoir system

Bhadra river Right turbine capacity = 13,200 kW PH2

Reservoir

Right bank canal capacity= 71 m3/s Irrigated area = 87, 512 ha Annual demand = 1, 911 Mm3

Left turbine capacity = 2,000 kW PH1

PH3

Left bank canal Bed turbine capacity = 10 m3/s capacity=24,000 kW Irrigated area = 6, 367 ha Annual demand = 227 Mm3

Figure 3. Schematic diagram of the Bhadra reservoir project

Description

Quantity

Gross storage capacity Live storage capacity Dead storage capacity Average Annual inflow Left bank canal capacity Right bank canal capacity Left bank turbine capacity (PH1) Right bank turbine capacity (PH2) Riverbed turbine capacity (PH3)

2025 Mm3 1784 Mm3 241 Mm3 2845 Mm3 10 m3 /s 71 m3 /s 2000 Kw 13 200 Kw 24 000 kW

Maximize annual hydropower production: irrigation demands for the left bank canal and right bank canal command areas respectively in period t in Mm3 ; IR1,t and IR2,t are the irrigation releases into the left and right bank canals respectively in period t in Mm3 . Copyright  2007 John Wiley & Sons, Ltd.

PD

12

pR1,t H1,t C R2,t H2,t C R3,t H3,t

6

tD1


2905


where P is the total energy produced in M kWh; p is power production coefficient; R1,t , R2,t and R3,t are the releases to left bank, right bank and river bed turbines respectively in period t in Mm3 . H1,t , H2,t , H3,t are the net heads available to the left bank, right bank and bed turbines respectively in meters during period t (here, head is a nonlinear function of initial and final reservoir storage). Maximize satisfaction level of river water quality: WQ D

min

t

8tD1,2,...,12

7

where, t is satisfaction level of water quality in period t and is given by,  if R3,t QDmin,t  0 R3,t QDmin,t t D if QDmin,t R3,t QDmax,t   QDmax,t QDmin,t 1 if R3,t ½ QDmax,t 8 where, QDmin,t and QDmax,t are the minimum and maximum water demands to maintain water-quality in period t in Mm3 for the river downstream of the dam. The optimization is subject to the following constraints: Storage continuity: StC1 D St C It R1,t C R2,t C R3,t C Et C Ot 8t D 1, 2, . . . , 12

9

where St D Active reservoir storage at the beginning of period t in Mm3 ; It D inflow into the reservoir during period t in Mm3 ; Et D the evaporation losses during period t in Mm3 (here, Et is a nonlinear function of initial and final storages of period t); Ot D overflow from the reservoir in period t in Mm3 ; Storage limits: Smin St Smax

8t D 1, 2, . . . , 12

10

where Smin and Smax are the minimum and maximum active storages of the reservoir in Mm3 . Maximum power production limits: pR1,t H1,t E1,max

8t D 1, 2, . . . , 12

11

pR2,t H2,t E2,max

8t D 1, 2, . . . , 12

12

pR3,t H3,t E3,max

8t D 1, 2, . . . , 12

13

where, E1,max , E2,max , and E3,max are the maximum amounts of power in M kWh, that can be produced (turbine capacity) by the left, right and bed level turbines respectively. Canal capacity limits: IR1,t C1,max

8t D 1, 2, . . . , 12

14

IR2,t C2,max

8t D 1, 2, . . . , 12

15

where, C1,max and C2,max are the maximum canal carrying capacities of the left and right bank canals respectively. Copyright  2007 John Wiley & Sons, Ltd.

Irrigation demands: D1 min,t IR1,t D1 max,t

8t D 1, 2, . . . , 12 16

D2 min,t IR2,t D2 max,t

8t D 1, 2, . . . , 12 17

where, D1 min,t and D1 max,t are minimum and maximum irrigation demands for left bank canal respectively; D2 min,t and D2 max,t are minimum and maximum irrigation demands for right bank canal respectively in time period t. Water Quality Requirements: R3,t ½ MDTt

8t D 1, 2, . . . , 12

18

where, MDTt D minimum release to meet downstream water quality requirement in Mm3 . It can be noted that, in this study, under favorable range of reservoir storage for power production, the releases made through power turbines also serve to meet irrigation demands of the left bank and right bank canals during irrigation requirement periods. However, if the reservoir storage is not within the limits of the turbine power production range, then the water is released only to meet irrigation demands through sub-ways to irrigation canals. Since the water released for irrigation is restricted to its demands, any excess water is not a penalizing problem in the first objective function as given in Equation (5). RESERVOIR OPERATION MODEL APPLICATION AND RESULTS To apply the EM-MOPSO for reservoir operation model, the following parameters are selected. The initial population of the EM-MOPSO is set to 200; c1 and c2 are set to 1Ð0 and 0Ð5 respectively; w is set to 1Ð0; and is set to 0Ð9; the number of non-dominated solutions to be found is set to 200. For the EM step, the size of elitist-mutated particles is set to 30, the value of pem was set to 0Ð2; and the value of Sm decreases from 0Ð2 to 0Ð01 over the iterations. Then EM-MOPSO is run for 500 iteration steps. To run the NSGA-II model, the initial population was set to 200, crossover probability to 0Ð9, and mutation probability to 1/n (n is the number of real variables). The distribution index values for real-coded crossover and mutation operators are set to 20 and 100 respectively. NSGA-II is also run for 500 generations. The average monthly inflow into the reservoir computed for each calendar month over a period of 69 years (from 1930–1931 to 1998–1999) is used as inflow data to implement the above model. Two-objective model To show the effectiveness of the proposed MOPSO, for solving the reservoir operation problem, first it is applied to irrigation and hydropower as two objectives of the model. The reservoir operation model consists of minimizing irrigation deficits (Equation (5)) and maximizing the hydropower (Equation (6)) subject to satisfying the constraints from Equations (9) to (18). Hydrol. Process. 21, 2897– 2909 (2007) DOI: 10.1002/hyp

2906


The reservoir operation model for three objectives consists of minimizing the irrigation deficits (Equation (5)), maximizing the hydropower (Equation (6)) and maximizing the satisfaction level of water quality (Equations (7) and (8)) subject to satisfying the constraints from Equations (9) to (18). Figure 5 shows the results of 200 non-dominated solutions obtained using EM-MOPSO after 500 iterations. There are a number of alternatives that can be chosen at various satisfaction levels of the multiple objectives. Depending on the circumstances prevailing under the reservoir system and by analyzing the tradeoff between the multiple objectives, the reservoir operator can make an appropriate decision. The details of decision making for application are presented in the following section. Table IV. Resulting statistics by EM-MOPSO and NSGA-II for the two-objective reservoir operation model. In SC(A,B), A is EM-MOPSO and B is NSGA-II. Bold numbers indicate the best performing algorithm Performance metric Set coverage metric (SC)

Best Worst Mean Variance SD

225 215 205 f2

195 185 175 165

EM-MOPSO

155

NSGA-II

145 0

25000

50000

75000

100000

125000

f1 Figure 4. Non-dominated solutions obtained using EM-MOPSO and NSGA-II for two-objective reservoir operation model. The two objectives are f1 - squared deviation of irrigation Mm3 2 , f2 -hydropower production, M kWh

1 0.8 0.6 0.4 0.2

Three-objective model

Statistic

235

f3

To check the performance, 10 independent runs were carried out for the two-objective reservoir operation model using both the algorithms. Table IV shows the resulting statistics for both the EM-MOPSO and NSGAII models. It can be observed that with respect to set coverage metric, the average value of SC(A, B) is higher than the SC(B, A) value (here A is EM-MOPSO and B is NSGA-II). The metric SC(A, B) refers to the percentage of solutions in B that are weakly dominated by solutions of A. Thus in this case, EM-MOPSO is performing better than the NSGA-II. Similarly, for the spacing metric, from Table IV it can be observed that the mean value of SP metric for EM-MOPSO is lower than that for NSGA-II. This indicates that best distribution of Pareto solutions is obtained in EM-MOPSO. For demonstration purposes a sample result corresponding to median value of SC(A,B) is shown in Figure 4. It can be seen that EM-MOPSO is able to generate a set of well-distributed Paretooptimal solutions. In this case NSGA-II fails to yield the extreme solutions, whereas our proposed method is able to provide extreme solutions comfortably (the minimum squared deviation of irrigation as 0 Mm3 2 and maximum hydropower production as 227Ð845 MkWh). Thus again these results demonstrate that the proposed method is very useful for real life systems application.

Spacing metric (SP)

SC(A, B)

SC(B,A)

EM-MOPSO

NSGA-II

0Ð2000 0Ð8788 0.5582 0Ð0435 0Ð2085

0Ð0400 0Ð6350 0Ð2878 0Ð0317 0Ð1780

206Ð1277 294Ð1276 258.2752 1419Ð9885 37Ð6827

246Ð2255 787Ð7765 504Ð3212 32 583Ð4308 180Ð5088


0 250 2

200

1.5 1

150 f2

100

0.5 0

x 105

f1

Figure 5. Non-dominated solutions obtained for three-objective reservoir operation model using EM-MOPSO. f1 -sum of squared deficits of irrigation releases Mm3 2 ; f2 -hydropower production, M kWh; f3 -satisfaction level of water quality

Decision making In any application, for final decision making, the decision maker might be interested in minimum possible number of well representative solutions for further analysis. So it is important that after obtaining many solutions which are true Pareto Optimal with uniform spread and wide coverage, we need to reduce the large set of solutions to a few representative solutions. In order to do that, various clustering algorithms are available. A simple clustering algorithm, which reduces the large number of final Pareto solutions (N) to a few representative solutions (N), is described here. Clustering technique First each solution in ERP is considered to reside in a separate cluster. Thus initially there are N clusters. Thereafter the cluster distances between all pairs of clusters are calculated. Then the two clusters with the minimum cluster distance are combined together to form one big cluster. The procedure is repeated by calculating the cluster distances for all the pairs of clusters obtained Hydrol. Process. 21, 2897– 2909 (2007) DOI: 10.1002/hyp


by merging the two closest clusters. This process of merging clusters is continued until the number of clusters in the ERP is reduced to N. Thereafter, in each cluster, the solution with the minimum average distance from other solutions in the cluster is taken as a representative solution for that cluster. The step-by-step procedure of the algorithm is given below (Deb, 2001). 1. Initialize cluster set C; each individual i in ERP constitutes a distinct cluster. i.e. Ci D fig, so that C D fC1 , C2 , . . . ., CN g 2. If, jCj N go to Step 5, otherwise go to Step 3. 3. For each pair of clusters, calculate the cluster-distance by using Equation (19). d12

1 D jC1 j.jC2 j

di, j

19

simple procedure called Pseudo-weight vector approach is employed in this study and the details of the procedure are given below. Pseudo-weight vector approach In this approach, a pseudo-weight vector is calculated for each obtained solution. For minimization problems, the approach is described here. From the obtained set of and maximum fmax values solutions, the minimum fmin i i of each objective function i are noted. Thereafter the Equation (20) is used to compute the weight wi for the i-th objective function (Deb, 2001): wi D

fmax fi x/fmax fmin i i i M fmax fm x/fmax fmin i i m

20

mD1

i2C1 ,j2C2

where the function d12 reflects the distance between two individuals i1 and i2 (here the distance in objective space is used). 4. Find the pair (i1 , i2 ) which corresponds to the minimum cluster-distance. Merge the two clusters Ci1 and Ci2 together. This reduces the size of C by one. Go to Step 2. 5. Choose only one solution from each cluster and remove all others from the cluster. The solution having the minimum average distance from other solutions in the cluster is chosen as the representative solution of the cluster (centroid method). To reduce the large number of alternatives, the number of clusters is chosen as 20. According to the cluster algorithm described above, this reduces the large set of non-dominated solutions to a few representative solutions. Figure 6 shows the 20 representative clustered Pareto-optimal solutions for the three-objective reservoir operation model. To facilitate final decision making, (i.e. to understand how each of the objectives can influence the decision) a

1 0.8 0.6 f3

2907

0.4 0.2

This equation calculates the relative distance of the solution from the worst (maximum) value in each objective function. Thus, for the best solution for the i-th objective, the weight wi is to be a maximum. The numerator in the right side of the above equation ensures that the sum of all weight components for a solution is equal to one. Once the weight vectors are calculated, a simple strategy is to choose the solution closer to a user-preferred weight vector. For example, if an 80% weightage for f1 and a 20% weightage for f2 are desired, the corresponding weight vector closer to that non-dominated solution can be selected for final decision making. Based on pseudo-weight vector approach, the weights that can be given for each objective are shown in Table V, which gives the objective values for each of the representative Pareto optimal solutions and its respective weight (shown in parenthesis) for each alternative. This provides ease in decision making for policy implementation. After analyzing the available alternatives, based on individual preferences, the final decision can be made. Suppose the reservoir operator decides to implement a policy with weights 0Ð5, 0Ð1 and 0Ð4 for irrigation deficit, hydropower production and water quality satisfaction levels respectively, then a solution closer to that set of weights i.e. 9th solution from the Table V can be selected. The model readily gives the corresponding policy for implementation. Figure 7 shows the corresponding releases to be made into the left bank canal, right bank canal and bed turbine. Figure 8 shows the corresponding initial storages required for ensuring such releases. Thus this kind of analysis can be implemented effectively with the proposed EM-MOPSO technique for derivation of reservoir operation policies.

0 250 2

200

1.5 150 f2

100

1

0.5 0

CONCLUSIONS x 105

f1

Figure 6. Representative non-dominated solutions obtained from clustering of EM-MOPSO generated solutions. f1 -sum of squared deficits of irrigation releases Mm3 2 ; f2 -hydropower production, M kWh; f3 -satisfaction level of water quality Copyright  2007 John Wiley & Sons, Ltd.

In this study, a novel approach for multi-objective optimization based on swarm intelligence principles is proposed and applied to develop efficient operating alternatives for multi-objective reservoir operation. The proposed MOPSO approach combines PSO technique Hydrol. Process. 21, 2897– 2909 (2007) DOI: 10.1002/hyp

2908


Table V. Filtered or representative Pareto optimal solutions for the three-objective reservoir operation model. The values in brackets show the pseudo weights obtained for the respective objective Sl. No. Sum of squared deficits of irrigation releases Mm3 2

Hydropower (M kWh)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

146Ð94 199Ð25 232Ð14 223Ð42 209Ð53 202Ð89 192Ð85 144Ð72 161·66 161Ð25 210Ð89 177Ð37 227Ð08 178Ð42 179Ð74 205Ð14 170Ð16 189Ð37 217Ð66 160Ð49

868Ð18 (0Ð60) 32 580Ð11 (0Ð56) 1 56 619Ð52 (0Ð00) 99 357Ð97 (0Ð16) 64 860Ð54 (0Ð28) 40 728Ð10 (0Ð31) 24 705Ð84 (0Ð37) 252Ð88 (0Ð93) 2796·60 (0·51) 1903Ð16 (0Ð68) 69 078Ð16 (0Ð25) 8392Ð71 (0Ð56) 1 30 367Ð73 (0Ð08) 9315Ð25 (0Ð47) 9851Ð96 (0Ð50) 44 503Ð89 (0Ð38) 3686Ð70 (0Ð74) 19 680Ð38 (0Ð58) 81 005Ð89 (0Ð21) 1542Ð24 (0Ð74)

R1

Release (Mm3)

200

Water quality satisfaction level

(0Ð02) (0Ð44) (0Ð50) (0Ð40) (0Ð36) (0Ð28) (0Ð24) (0Ð00) (0·10) (0Ð13) (0Ð34) (0Ð22) (0Ð45) (0Ð19) (0Ð21) (0Ð37) (0Ð22) (0Ð34) (0Ð36) (0Ð13)

R2

0Ð66 0Ð03 1Ð00 1Ð00 0Ð77 1Ð00 0Ð91 0Ð11 0·77 0Ð31 0Ð89 0Ð40 1Ð00 0Ð67 0Ð55 0Ð47 0Ð07 0Ð16 1Ð00 0Ð20

(0Ð39) (0Ð00) (0Ð50) (0Ð44) (0Ð36) (0Ð42) (0Ð39) (0Ð07) (0·39) (0Ð20) (0Ð40) (0Ð23) (0Ð47) (0Ð33) (0Ð29) (0Ð24) (0Ð03) (0Ð09) (0Ð43) (0Ð13)

R3

150

100

50

0 1

2

3

4

5

6 7 Month

8

9

10

11

12

Figure 7. Release policy obtained for selected optimal point, showing releases for left bank canal (R1), right bank canal (R2) and river bed (R3)

comparison operator to promote solution diversity. In addition, a special EM operator is incorporated into the algorithm. This strategic mechanism keeps diversity in the population and consequently helps for effective exploration of Pareto optimal front. The proposed EMMOPSO was first tested for a few standard test problems from the literature and it was found that the approach is quite robust and very competitive to NSGA-II in terms of yielding a diverse set of solutions along the true Pareto optimal fronts. On achieving satisfactory performance for test problems, EM-MOPSO is applied to a reservoir operation problem, namely the Bhadra reservoir project. The multiple objectives involve minimization of irrigation deficit, maximization of hydropower and maximization of satisfaction level of downstream water quality requirements. First a two-objective model is solved and EMMOPSO efficiency is demonstrated by comparing it with the results of NSGA-II. The results obtained clearly show the superiority of the proposed approach. Then the EM-MOPSO approach is extended to a three-objective model and many Pareto optimal solutions are generated. A clustering algorithm is employed to reduce the large set of Pareto optimal solutions to a small number of convenient representative alternatives. To facilitate ease in decision making, a pseudo-weight vector approach is employed. This provides an idea about the relative weight of each alternative and its preference over others. By analyzing the weight combinations, depending on the preference of the reservoir operator, a suitable policy can be implemented. The main advantages of the proposed EM-MOPSO approach are that it is easy to implement and easy to use, and yet robust in yielding efficient Pareto frontiers. Hence it can be concluded that, for multi-objective water resources and hydrology problems, the proposed technique is a viable tool for multi-objective analysis and decision making, and can be used in any practical situation.

APPENDIX A

Storage (Mm3)

2000

Set coverage metric This metric gives the relative spread of solutions between two sets of solution vectors A and B. The set coverage metric calculates the proportion of solutions in B, which are weakly dominated by solutions of A (Deb, 2001).

1600 1200 800

CA, B D

400 0

1

2

3

4

5 6 7 Month

8

9 10 11 12 13

Figure 8. Monthly initial storages to be maintained in the reservoir corresponding to the selected optimal point

with Pareto dominance criteria to evolve non-dominated solutions. It uses a variable size ERP and a crowded Copyright  2007 John Wiley & Sons, Ltd.

jfb 2 Bj9a 2 A : a bgj jBj

21

the value C(A, B) D 1 means that all solutions in B are weakly dominated by A, while C(A, B) D 0 represents the situation when none of the solutions in B are weakly dominated by A. Since the domination operator is not symmetric, i.e. C(A, B) is not necessarily equal to 1-C(B, A), it is necessary to calculate both C(A, B) and C(B, A) Hydrol. Process. 21, 2897– 2909 (2007) DOI: 10.1002/hyp


to understand how many solutions of A are covered by B and vice versa. Spacing metric The spacing metric aims at assessing the spread (distribution) of vectors throughout the set of nondominated solutions. It is calculated with a relative distance measure between consecutive solutions in the obtained non-dominated set (Deb, 2001): jQj 1 di d2 22 SD jQj iD1

i k where di D mink2Q^k6Di M the mD1 jfm fm j and d is

jQj mean value of the distance measure d D iD1 di jQj. fkm and fim are the values of m objective function for k and ith member in the population. The desired value for this metric is zero, which means that the elements of the set of non-dominated solutions are equidistantly spaced.

REFERENCES Allen RE, Pereira LS, Raes D, Smith M. 1998. Crop Evapotranspiration, Guidelines for Computing Crop Water Requirements, FAO Irrigation and Drainage Paper 56 . Food and Agricultural Organization of the United Nations: Rome. Coello CAC, Pulido GT, Lechuga MS. 2004. Handling multiple objectives with particle swarm optimization. IEEE Transactions on Evolutionary Computation 8: 256– 279. Cohon JL, Marks DH. 1975. A review and evaluation of multiobjective programming techniques. Water Resources Research 11(2): 208– 220. Croley TE II, Rao KNR. 1979. Multi-objective risks in reservoir operation. Water Resources Research 15(4): 1807– 1814. Deb K. 2001. Multi-objective Optimization Using Evolutionary Algorithms. John Wiley and Sons: Chichester. Deb K, Pratap A, Agarwal S, Meyarivan T. 2002. A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transaction on Evolutionary Computation 6: 182– 197. Haimes YY, Tarvainen K, Shima T, Thadathil J. 1990. Hierarchical Multiobjective Analysis of Large-scale Systems. Hemisphere publishing co.: New York. Hu X, Eberhart RC, Shi Y. 2003. Particle swarm with extended memory for multiobjective optimization. 2003 IEEE Swarm Intelligence Symposium Proceedings. IEEE Service Center: Indianapolis, IN; 193– 197. Kennedy J, Eberhart RC. 2001. Swarm Intelligence. Morgan Kaufmann: San Mateo, CA.


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Khu ST, Madsen H. 2005. Multiobjective calibration with Pareto preference ordering: an application to rainfall-runoff model calibration. Water Resources Research 41(3): W03004, Doi:10Ð1029/2004WR003041. Knowles JD, Corne DW. 2000. Approximating the nondominated front using the Pareto archived evolution strategy. Evolutionary Computation 8: 149– 172. Li X. 2003. A nondominated sorting particle swarm optimizer for multiobjective optimization. In Proceedings Genetic and Evolutionary Computation—GECCO 2003—Part I , Vol. 2723, Cant´u-Paz E, Foster JA, Deb K, Davi L, Roy R, O’Reilly UM, Beyer HG, Standish RK, Kendall G, Wilson SW, Harman M, Wegener J, Dasgupta D, Potter MA, Schultz AC, Dowsland KA, Jonoska N, .Miller JF (eds.). LNCS: Berlin, Germany; 37–48. Liang Q, Johnson LE, Yu YS. 1996. A comparison of two methods for multiobjective optimization for reservoir operation. Water Resources Bulletin 32(2): 333– 340. Mohan S, Raipure DM. 1992. Multiobjective analysis of multireservoir system. Journal of Water Resource Planning and Management ASCE 118: 356–370. Nagesh Kumar D, Janga Reddy M. 2006. Multipurpose reservoir operation using particle swarm optimization. Journal of Water Resource Planning and Management ASCE (in press). Oliveira R, Loucks DP. 1997. Operating rules for multireservoir systems. Water Resources Research 33(4): 839– 852. Parsopoulos K, Vrahatis M. 2002. Particle swarm optimization method in multiobjective problems. Proceedings of the 2002 ACM Symposium on Applied Computing (SAC’2002). ACM Press: Madrid; 603–607. Raju KS, Nagesh Kumar D. 2004. Irrigation planning using genetic algorithms. Water Resources Management 18(2): 163– 176. Tauxe GH, Inman RR, Mades DM. 1979. Multi-objective dynamic programming with application to reservoir. Water Resources Research 15(6): 1403– 1408. Thampapillai DJ, Sinden JA. 1979. Tradeoffs for multiple objectives planning through linear programming. Water Resources Research 15: 1028– 1034. Vrugt JA, Gupta HV, Bastidas LA, Bouten W, Sorooshian S. 2003. Effective and efficient algorithm for multiobjective optimization of hydrologic models. Water Resources Research 39(8): 1214, Doi:10Ð1029/2002WR001746. Wang YC, Yoshitani J, Fukami K. 2005. Stochastic multiobjective optimization of reservoirs in parallel. Hydrological Processes 19: 3551– 3567. Wardlaw R, Sharif M. 1999. Evaluation of genetic algorithms for optimal reservoir system operation. Journal of Water Resources Planning and Management ASCE 125(1): 25–33. Yapo PO, Gupta V, Soorishian S. 1998. Multi-objective global optimization for hydrological models. Journal of Hydrology 204: 83–97. Yeh WW-G. 1985. Reservoir management and operations models: a stateof-the-art review. Water Resources Research 21(12): 1797– 1818. Yeh WW-G, Becker L. 1982. Multiobjective analysis of multreservoir operations. Water Resources Research 18(5): 1326– 1336. Zitzler E, Thiele L. 1999. Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Transaction on Evolutionary Computation 3: 257–271.



A brief note on chaos and its applications in hydrological time series V. Jothiprakash1, R. Vignesh2, T.A. Fathima2 1

Professor, 2Research Scholar, Dept. of Civil Engg. Indian Institute of Technology

Bombay, Powai, Mumbai, India. [email protected], [email protected], [email protected] 1. Introduction The most influential concept in hydrology is the water cycle that links the movement of water on Earth, subsurface and atmosphere. Hydrological sciences are in built with strong fundamental equations such as water balance equation, energy balance, empirical flux laws (Darcy’s law, Fick’s law) etc (Blöschl 2005). Hydrological processes possess extreme variability at all scales in both space and time driven by variations in physiographic factors such as climate, soils, vegetation, topography, geology, as well as by human activity (Sivapalan et al 2001). As mentioned earlier, even though it is concreted with a number of equations and techniques, there has not been a unified approach in understanding the variability in the hydrological processes. Examining patterns in the hydrological processes will assist in making better predictions in future. The evidence of variability is clearly documented in rainfall, air temperature, soil moisture, snow cover, groundwater level, and streamflow, or any other hydrological quantity. A detailed review on the variability scale issues is discussed (Blöschl and Sivapalan., 1995). Hydrological data plays a major role in studying the variations as well as provides guidance and information for hydrological modeling and effective water resources planning and management. Thanks to the advanced technologies such as powerful computers, measurement devices, remote sensors, geographic information systems (GIS), digital elevation models (DEM), and networking facilities, there has been revelation in the data measurement and collection (Sivakumar and Singh, 2012). For the past three decades, the subject of time series analysis has been evolving at an astonishing rate (Farmer and Sidorowich, 1987; Casdagli, 1989; Hipel and McLeod, 1994). The main aim of time series analysis is to understand the underlying internal structure in the observed data. Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 2.Hydrologic time series and modelling Time series represents collection of magnitude of a physical quantity ‘xw,t’ recorded at a space ‘w’ during time ‘t’ which can be either discrete or continuous. Mostly these observations are made at equally spaced, discrete time intervals (Brockwell and Davis, 2002). The observations made upon a single variable of a process forms a univariate time series. A basic assumption in any time series prediction depends on the past values of the variable under study and is independent of the other variables. It also helps to determine the behaviour of the time series, which further helps in predicting future values of the time series (Brockwell and Davis, 2002). The time series forecast models can be broadly classified into four types such as empirical models, conceptual models, physically based models and sophisticated soft computing models like artificial neural network (ANN), adaptive neuro fuzzy inference system (ANFIS), genetic programming (GP), model tree (MT) and recently chaotic models (Jothiprakash and Magar, 2009). It is assumed that all other dependent characteristics are inherently captured in the observed series itself, if longer length of data is available (Magar and Jothiprakash, 2011). Fairly, a large number of mathematical models have been developed and applied to predict hydrological time series. There is no unified mathematical approach for modelling and predicting future value using time series models. As already mentioned, the difficulty came up from the fact that hydrological processes exhibit considerable spatial and temporal variability. Grebogi et al. (1983) indicated that even simple deterministic systems influenced by a few non-linear interdependent variables might give rise to very complicated structures. In spite of its highly erratic spatial and temporal variability of rainfall, forecasting is possible in a stochastic way even though the time series is complex and non-linear (Casdagli, 1989; Casdagli, 1992; Baohui et al., 2004a; Baohui et al., 2004b). Even though fairly large numbers of deterministic, stochastic and soft computing models are available, researchers are seeking better models for more accurate prediction of hydrological processes especially the peak values. 2.1 Time series modelling In hydrology time series has been generally modelled either by deterministic or by stochastic approach (Klemes, 1978; Koutsoyiannis and Pachakis, 1996; Jevtoc and Schweitzer, 2009). In both the cases non-linear behaviour of time series is not taken into account (Kantz and Schreiber, 2003). Thus, a new behaviour has been evolved which is Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 a bridge between deterministic and stochastic behaviour, called chaotic behaviour; which states that random input is not the only source of irregularity but non-linear chaotic system can also produce very irregular data (Kantz and Schreiber, 2003). The idea of deterministic dynamical systems and chaos played a key role in the unification of ideas concerning non-linear modelling by placing them in the framework of dynamical systems (Sannasiraj et al., 2004). A brief description of all the approaches is as follows: 2.1.1 Deterministic approach Deterministic model assumes that the output is certain, if the input is fixed (Rutherford, 1978). Simple deterministic models can be developed by statistical methods like linear regression and non-linear curve fitting techniques (Magar and Jothiprakash, 2011). Complex models can be developed from diffential equations considering all the parameters which are dependant and can be solved by various numerical methods like finite difference method, finite element method, path simulation etc (Gershenfeld, 1999). Physically based as well as conceptual models results in better predictions, but require extensive data, large computational demands, over-parameterisation effects, and parameter redundancy effects makes them difficult to develop and apply for real life data scarce situation (de Vos and Rientjes, 2005). 2.1.2 Stochastic approach A natural process may depend upon many external and internal factors and it is difficult to identify those dependent factors and apply all of them for future prediction. In such cases, where the influence of several unknown factors is sizable, the exact prediction may not be possible. However, it may be possible to predict within a known confidence interval, or to predict them with a probability that a particular value will be observed at a particular time. This is called as stochastic time series modelling (Box and Jenkins, 1976). In case of stochastic models, there will be a random component and it will have different outputs for a unique input for various model runs. Usually differencing and autoregressive models are used for predicting such series, leading to linear stochastic models (Box and Jenkins, 1976; Nelson, 1995). 2.1.3 Chaotic approach An approach that can couple deterministic and stochastic approach and serve as a middle ground would often be the most appropriate (Strogatz, 1994; Williams, 1997). ‘Chaos theory‘ can offer such a coupled deterministic stochastic approach, since its underlying concepts of non-linear interdependence, hidden determinism and order, Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 sensitivity to initial conditions are highly relevant in hydrology (Sivakumar et al., 2007). All models which are used to predict the hydrological processes require identification of variable (dimension) which governs the future values (Shivamoggi, 1997). The number of dimensions that governs a particular process can be identified through non-linear chaotic analysis. Analyzing data for chaotic behaviour can reveal whether an erratic looking time series is actually deterministic, lead to more accurate short-term predictions. The chaos theory has made revised concepts about determinism Vs randomness, many new and improved techniques in non-linear analysis has been developed (Williams, 1997). 3. Methodology: Nonlinear dynamic methods and chaos Relatively there is no accepted definition for chaos, chaos is sustained and disorderly-looking long-term evolution that satisfies certain mathematical criteria and that occurs in a deterministic nonlinear system (Gleick, 1987). Poincare was also the first person to glimpse the possibility of chaos, in which a deterministic system exhibits aperiodic behavior that depends sensitively on the initial conditions, thereby rendering long-term prediction impossible. The implication was that the system was inherently unpredictable – tiny errors in measuring the current state of atmosphere (or any other chaotic system) would be amplified rapidly, eventually leading to embarrassing forecasts. But Lorenz also showed that there was structure in the chaos when plotted in 3 dimensional plots, the solutions to his equation fell on to a butterfly-shaped set of points, called as “butterfly effect”. The science of chaos is a burgeoning field and the available methods to investigate the existence of chaos in a time series are still in the state of infancy. There are different methods available: correlation dimension method (Grassberger and Procaccia, 1983a), the Lyapunov exponent method (Wolf et al., 1985), the False Nearest Neighbor method (Kennel et al 1992), the nonlinear prediction method (Farmer and Sidorowich, 1987; Casdagli, 1989), and the surrogate data method (Theiler et al., 1992a, b; Schreiber and Schmitz, 1996). 3.1 Phase space reconstruction The fundamental starting point of most approaches in nonlinear and chaotic analysis is the construction of a phase space portrait of the considered system. The state of a system can be described by its state variables. The state of a system typically changes in time, and, hence, the vector in the phase space describes a trajectory representing the time evolution, the dynamics, of the system. The shape of Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 the trajectory gives hints about the system. Phase space reconstruction is essentially a graph or a co-ordinate diagram, whose coordinates represent the variables necessary to describe the state of the system at any moment (Packard et al. 1980). The trajectories of the phase space diagram describe the evolution of the system from some initial state (assumed to be known) and, hence, represent the history of the system. Given a single-variable (or multi-variable) series, Xi, where i = 1, 2,. . ., N, a multi-dimensional phase space can be reconstructed according to the Takens’ delay embedding theorem (Takens, 1981), as follows: (1) where j = 1, 2, . . ., N - 1(m - 1)τ/∆t; m is the dimension of the vector Yj, called embedding dimension; and τ is an appropriate delay time taken to be a suitable integer multiple of the sampling time ∆t. A correct phase space reconstruction in a dimension m generally allows interpretation of the system dynamics (if the variable chosen to represent the system is appropriate) in the form of an m – dimensional map fT, given by: (2) where Yj and Yj+T are vectors of dimension m, describing the state of the system at times j (current state) and j + T (future state), respectively. 3.2 Correlation dimension method Grassberger-Procaccia algorithm is used to determine the chaotic behaviour of the time series (Grassberger and Procaccia, 1983a). The observed basic time series (xt) is lagged based on the chosen delay time (τ) and these lagged series (xt-τ xt-2τ, xt-3τ….) are used along with the observed series for constructing a phase space. The correlation dimension method involves systematically locating the events of a time series at each datum point, in turn. The summation and normalisation has been carried out using Heaviside step function (H(u)) and the output is the correlation integral Cr: 2 n   N(N-1)

C(r)  lim



H(r-|Yi-Yj|)

(3)

i,j(1 Na+ > Mg2+ > Ca2+ > SO4

2-

> HCO3- and Cl- > Na+ >

Mg2+ > SO4 2- > Ca2+ > HCO3- respectively as shown in the Schoeller diagram (Figure 8).


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Figure 8. Schoellar diagram of ion concentrations in pond and observation well 4.3

Check dam

4.3.1 Groundwater level Groundwater level in the check dam and the nearby wells were compared to assess the impact of recharge from the check dam. The groundwater levels in wells show same fluctuation as that of the check dam, representing strong correlation with the monsoonal recharge. This indicates that the main recharge source in the area is recharge from the check dam. The wells near the check dam show a water level rise of 1 - 2.5 m due to the impact from the check dam (Parimalarenganayaki and Elango, 2014). Figure 9 shows water level in the check dam and two observation wells.

Figure 9. Water levels in the check dam and monitoring wells


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 4.3.2 Recharge estimation The recharge from the check dam was calculated by considering the storage volume and water level using water balance method. The check dam is actually capable of storing 0.8 Mm3 of water. It is estimated that approximately 1.14 Mm3 of water has been recharged by the check dam during 2011-2012 and the remaining has been lost through evaporation Parimalarenganayaki and Elango, 2013). The volume of water recharged from the check dam is shown in figure 10.

Figure 10. Volume of water recharged from the check dam 4.3.3 Groundwater quality The groundwater quality of the nearby wells of the check dam was assessed to understand the impact from the check dam. The maximum EC of water in the check dam was 1180 μS/cm and that of nearby wells is 1600 μS/cm, indicating the impact of check dam. The order of dominance of major cations and anions in groundwater and water from check dam are as Na, Ca, Mg and K for cations and HCO3, Cl, SO4 for anions and CO3. The major types of water in the area are Ca–Na–HCO3, Na–Cl, Ca–Mg–Cl and Ca–HCO3. Schoeller plot of water stored in the check dam and groundwater of the study area is shown in figure 11. The numbers in legend indicates well numbers; 1, 2 and 27 are wells closer to cke dam and remaining are wells away from the checkdam. Figure 11 shows that groundwater in wells closer to the check dam have less concentrations of ions as compared to groundwater in wells away


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 from the check dam. This confirms the impact of check dam on groundwater quality improvement in the nearby wells.

Figure 11. Schoeller diagram of water stored in the check dam and groundwater from the wells located closer to the check dam, away from check dam. The numbers in legend indicates well numbers (Parimala, Ph.D Thesis, 2014) 4.4.

Dugwell rechareg structure

4.4.1 Groundwater level The groundwater level in the nearby well of the induced recharge structure was tremendously improved due to the induced recharge. A groundwater level rise of 14.5 m bgl from 9.1 was seen in the dug well after the implementation of recharge structure as shown in figure 12. This is considerable high when compared with the water level in the nearby observation well which was from 11.5 m from 14.8 m (bgl) after the implementation of recharge structure. 4.4.2 Groundwater quality The electrical conductivity of groundwater in the dug well decreased from 1342 to 945 µS/cm (Figure 12). This is due to the dilution of major and minor ions in groundwater due to the enhanced recharge after implementation of recharge structure. The fluoride concentration also decreased from 3.1 mg/l to 1.41 mg/l in the dug well due to dilution by the filtered rainwater passing through induced recharge


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 structure into dug well. However, the decrease in fluoride concentration in the nearby observation well was comparably less, but proportional to the rise in water level. This indicates that groundwater level is directly proportional to the fluoride concentration in the dug well. However, this relationship is not verified in some wells, where the concentration of F- in groundwater has inverse relationship with the depth of the well.

Figure 12. The groundwater level, EC and fluoride concentration in the dug well before and after construction of recharge structure 5.

FEASIBILITY

The assessment of feasibility of the method is very important. The percolation pond was effective in augmenting groundwater resources in this site. But, physical clogging was a major problem faced during this study due to the accumulation of suspended particles in water causing the progressive clogging at the pond bottom (Raicy et al., 2014).

However, this could be solved by the implementation of

recharge shaft. This design considerably improved the recharge. The groundwater quality in the observation well was also improved through recharge of water from the percolation pond. The implementation of several such recharge structures in this area is expected to improve the groundwater potential of the area on a regional


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 scale. In case of check dam, the impact was found be more within 3 km2 away from the check dam along the flow direction. The groundwater level in the wells located within 500 m from the dam has increased by 2.5 m. Even though the recharge by the check dam was 51% more than the normal rain fall recharge, check dams are not economically feasible. In case of dug well recharge structure, the implementation of induced recharge structure in wells having positive correlation of groundwater level with F- concentration will be beneficial. However, in wells having negative correlation with the depth of wells, this method is not suitable. The groundwater level rise in all the recharge structures has been compared to assess the feasibility of the structures. Dugwell recharge could augment the groundwater level more than the other structures as shown in figure 14. When comparing the change in water level due to the impact of recharge structure, percolation pond and pond with shaft have very less change in water level because the very shallow groundwater level in the area. Therefore, though the recharge by shaft was two twice more than that by pond, the maximum rise in water level was almost same. As the groundwater level in the Dharmapuri district is very deep, the recharge structure could augment the water level very well. When comparing the volume of water recharged per year, percolation ponds are found to have very less recharge and check dam have high recharge. Even though the maximum water level change was found to be in the dug well, the recharge was comparably less due to the very less rain fall and small size of recharge structure 6.

CONCLUSION

All the four recharge structures show improvement in both groundwater quality and groundwater level in the nearby areas. Even though the percolation pond could improve the groundwater level in surrounding area, the quality of groundwater was improved more only by the addition shaft inside the pond. The wells in the surrounding area of the check dam showed same fluctuation of groundwater level, indicating the effect of check dam. The groundwater level is raised up to 9.1 m (bgl) from 14.5 m after construction of induced dug well recharge structure. Fluoride concentration also decreased from 3.1 mg/l to 1.44 mg/l due to dilution from the filtered rainwater passing through from recharge structure to dug well. The advantage of this artificial recharge structure is low cost and all rural community of an area can


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 implement this method to moderate the alarming level of fluoride concentration in groundwater. Acknolledgement: The authors acknowledge co funding of the study on percolation pond and recharge shaft under the "Saph Pani" project of the European Commission within the Seventh Framework Program (Grant agreement no. 282911) and Basic Science Research of University Grant Commission are acknowledged. Also the Women’s Scientist program of Department of Science and Technology and University Grant Commission are also acknowledged for the funding of studies on check dam and dug well recharge respectively. REFERENCES Jagadeshan, G. Elango L. (2015). “Geogenic sources for fluoride rich groundwater and induced recharge through dug well for mitigation”, at 26th International Union of Geodesy and Geophysics (IUGG) General assembly, Prague, Czech Republic. June 22 - July 2, 2015. Jagadeshan, G. Elango, L. (2015) Suitability of Fluoride-Contaminated Groundwater for Various Purposes in a Part of Vaniyar River Basin, Dharmapuri District, Tamil Nadu. Water Quality Exposure and Health, 07/2015; 7(23):1-10. Parimala Renganayaki, S. and Elango, L. (2014) Assessment of effect of recharge from a check dam as a method of managed aquifer recharge by hydrogeological investigations. Environmental Earth Sciences, DOI 10.1007/s12665-014-3790-8. Parimala Renganayaki, S. and Elango, L. (2013) Impact of recharge from a check dam on groundwater quality and assessment of suitability for drinking and irrigation purposes, Arabian Journal of Geosciences, DOI 10.1007/s12517-013-0989-z. UNICEF (2008) UNICEF handbook on water quality. United Nations Children’s Fund, New York Vijaya sankar M; S Abideen; M Babu selvam; T Gunansekaran; M I Hussain syed Bava; International Journal of Science, environment and technology, 2014, 3,1,348356.


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 Smart Sensor Network for Drinking Water Quality Monitoring in Water Distribution Mains S. Kavi Priyaa, G. Shenbagalakshmib, T.Revathic a

Assistant Professor (Senior Grade), Department of Information Technology, Mepco

Schlenk Engineering College (Autonomous), Sivakasi. b

Junior Research Fellow, Department of Information Technology, Mepco Schlenk

Engineering College (Autonomous), Sivakasi. c

Professor, Department of Information Technology, Mepco Schlenk Engineering

College (Autonomous), Sivakasi. E-Mail c

ID:

a

[email protected],

b

[email protected],

[email protected]

Abstract About twenty percent of the communicable diseases in India are spread by drinking unhealthy water.

Waterborne diseases are caused by the pathogenic

microorganisms which are directly transmitted when the contaminated water is consumed by the public. Hence, a novel technique to monitor the quality parameters of drinking water supplied through distribution pipes by the municipality at consumer sites using energy efficient wireless sensor network is proposed. The key ingredients are to construct an energy efficient network to achieve data correlation and fast data transmission to report the water quality to the users quickly. A contamination detection algorithm is proposed to assess the water contamination risks based on which the drinking water quality is predicted as desirable/acceptable/rejected with better accuracy using fuzzy logic. It detects the region of contaminated water flow within the water distribution network and alerts the consumers in the water contaminated regions. In addition, the valve fitted in the pipes prevents the further flow of water in the contaminated region. The simulation results show that the algorithm detects water contamination faster with better accuracy within an optimal sensor network lifetime with reduced energy consumption.

Keywords:

Water quality monitoring, water distribution system, wireless sensor

network, fuzzy logic, energy efficiency, network lifetime.


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1. Introduction Hygienic drinking water is an important resource that is significant for the well-being of all human beings. Drinking water services are facing new disputes in their realtime functioning because of the limited availability of water resources, population growth and increased consideration towards protecting the water supplies from deliberate or inadvertent contamination. There is a need for improved real time water monitoring methods since the accessible laboratory-based methods are too slow to develop immediate response and does not afford a level of public healthiness in reality. Invasion of hazardous contaminant agent across the water distribution pipe walls through breaks and cross connection leads to adverse effects in the human beings. Conventional methods on the water quality process engross the manual collection of the water samples at various localities and at different period. It is then analyzed for water quality in the laboratory using analytical methods. Such processes are no longer considered to be more efficient as discussed in (John Hall et al., 2007; Srinivas Panguluri, 2009; and Theofanis P.Lambrou, 2013). Even though the current methods include the analysis of both the chemical and biological components, it has several disadvantages: a) as they are laboratory-based, there is a long time gap between the sampling period and contamination detection b) lack of data aggregation from all the sensors for thorough analysis of water quality information. In (Andre Cloete et al., 2016) smart sensors are designed for real time water quality monitoring where individual sensor readings are noted to determine the unsafe level without aggregating history of readings from all the sensor nodes. Therefore, there is an explicit need for in-pipe real time water quality monitoring algorithm with efficient data correlation among sensor nodes and contamination detection algorithm to determine water contamination risks. For monitoring the water distribution networks and to reduce the water contamination risks in pipes, Wireless Sensor Networks (WSN) has been deployed in many major cities (Janice Skadsen et al., 2008).

As the pipelines are placed

underground there are major issues such as: a) inconvenience to replace the batteries of the sensor nodes after depletion, b) energy efficiency of the node and network lifetime and c) efficient measurement of water quality data for enduring Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 workability. From the findings of (John Hall et al., 2007), it is clear that to infer the quality of water, it is sufficient to monitor the parameters such as turbidity, temperature, pH, electrical conductivity, oxidation-reduction potential, and dissolved oxygen. Given the nonexistence of reliable in-pipe real time water quality monitoring algorithms for measuring physical, chemical and biological contaminants, in the proposed work all these crucial parameters are monitored. The proposed work predicts the quality of drinking water that flows in the pipes, analyze and stops the contaminated water flow with a closing valve in the contaminated region inside the pipe (i.e. no further flow of water is allowed in the pipe). The households could also be informed with the real time water quality flow levels compared to desirable level. A water distribution network using wireless sensor networks is designed as in the Fig. 1. At each instance, when the water supply is scheduled in the distribution network the sensor nodes will be in active mode to broadcast data to the sink node. This paper proposes energy efficient algorithms to satisfy the following goals: First, the sensor node energy consumption is balanced. Second, sensing performance is not compromised (i.e. accurate monitoring of water contamination risk with contamination detection algorithms). Third, the sensor nodes will always be connected, to ensure water quality report reaches the sink node without delay.

Fig.1 - Model of water distribution network system The main contributions of the paper are as follows: 

Minimizing the energy consumption and balancing the energy among the sensor nodes to increase the network lifetime.



Contamination detection algorithm is designed to predict the water quality rendered by the fuzzy rule descriptor for accurate and early detection of water quality in pipes.


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 

Real time data quality monitoring problems are addressed by EEMRP (Energy Efficient Multipath Routing Protocol) to maximize the data correlation among the sensor nodes and to forward the water quality information to the sink node (users/officials) using shortest path routing to reduce data delivery time. The performance of the proposed work is evaluated by conducting extensive experiments through simulation and compared with the contemporary algorithms proposed in the literature. The experimental outcomes signify that the proposed algorithm is promising and the solution to the energy efficiency, data correlation and contamination detection algorithm that detects water contamination risks outperforms with the existing algorithms. The rest of this paper is structured as follows: Section 2 reviews the related work on algorithms developed for the real time water quality monitoring using wireless sensor networks. Section 3 deals with the proposed model for the water quality monitoring process. Section 4 addresses the network design for water distribution mains and energy efficiency. A novel contamination detection algorithm for assessing water contamination risks and analysis based on fuzzy rules is detailed. The energy efficient routing algorithm for quality data transfer to sink is then narrated. The simulation results of the proposed work and the performance of the designed methods are explained in Section 5. Finally, Section 6 concludes the proposed work and explains the scope for future enhancement.

2. Related Research Works Water quality monitoring methods are expected to provide a good balancing between data correlation and effective detection of contamination risk in water irrespective of issues. As wireless sensor nodes are energy-constrained devices that have limited lifetime the resources, energy and memory should be used efficiently. These limitations cause a number of challenges in designing the routing protocol, network design, data aggregation mechanism and data quality (Ioannis Ch Paschalidis et al., 2012; Ting Lu et al., 2017). (Jae-Hwan Chang et al., 2004) modeled the energy consumption as a function of the traffic flow routing decisions. In this work, the problem of maximizing network lifetime is cast as a linear optimization problem and the authors proposed the flow augmentation algorithm to solve it efficiently. The results show that energy balancing is a good approximation to network lifetime


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 maximization. (Aubin Jarry and Olivier Powell, 2006) considers a different scenario in which each sensor node may either transmit data to its one hop neighbors with unit energy consumption, or directly to the sink node through long range communication but at a higher energy cost. In this paper, the author describes the problem of maximizing network lifetime equivalent to the problems of flow maximization and energy-balancing. The algorithm OTTC proposed by (Mehdi Kadivar et al., 2009) works well with fully distributed and low quality information. It deals with the weight of the links and compute the transmission radius based on the one- and two-hop neighbor’s information. Hence, an energy efficient algorithm is designed in the proposed work to prolong the network lifetime and preserve network connectivity. In this algorithm, both energy balancing and energy efficiency of every sensor node is considered to continuously detect the contamination events in the distribution networks. Since the pipelines are buried in the water distribution network, the battery replacement or battery recharging is a critical task. Even though the replacement or recharging of battery is possible, it is a costly and slow process that degrades the overall network performance. (Chenn-Jung Huang et al., 2011; SalouaChettibi and SalimChikhi, 2016) used duty cycle-based process for energy scavenging. These approaches suffer from two main drawbacks. 1) The tradeoff between low duty cycling and data latency, and 2) Fail to respond in an emergency situation due to depletion of the node. Hence, to overcome these problems long-lasting energy harvesters are used in combination with the rechargeable batteries in the later period. (Ren-Shiou Liu et al., 2010) claims that the random nature of the harvested energy requires an optimal data rate, transmission power control, and data routing are carried out accordingly. The affordable best data rate allocation and flow routing under the constrained network lifetime in the sensor network are extensively studied in (Xin Wang and Koushik Kar, 2006; Yi Shi et al., 2008). A fuzzy controller for environmental powered wireless sensor designed as in (Prauzek P.Kromer et al., 2016) is implemented in the hardware and it deals with the imprecise or missing data. The proposed work focuses on the data quality by incorporating spatial data correlations among the sensor nodes. Once the sensor data are correlated, a contamination detection algorithm is designed to identify the water contamination at a particular sensor node in the water Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 distribution system. An efficient event handling system as in (Charalampous Konstantopoulos et al., 2016) is important for fast notification about events in an effective manner. A fuzzy quality descriptor is used to predict the contamination risks in the real time water supply unit. (Farzad Aminravan et al., 2015) designed a fuzzy based multi-level information fusion using rule based systems which helps to detect the anomalies with the help of signal patterns. A limited number of event detection software is commercially available. CANARY software as in (David B.Hart et al., 2010) is a freely available tool that indicates possible contamination events by using a series of arithmetic and numerical techniques to identify the commencement of anomalous water quality incidents from online raw sensor data. Contamination detection and data validation methodologies are also developed based on multisensor data fusion methods. Given the size of the water distribution networks, pipe length and number of households served the proposed work emphasis on the spatiotemporal sampling. The sampling should be significantly increased in order to collect the water quality samples at significantly more locations (if possible at all consumer sites). The spatio-temporal data provided by the water distribution network supports complicated decisions in relation to the drinking water quality, including the detection of the location, source of the hazardous agents and pathogens. It also provides the water quality information to the consumers and municipal authorities. (Andrea M.Dietrich et al., 2014) accepts the consumer complaints and is able to detect massive changes in water quality based on the taste, odors and appearance parameters. (Lina Perelman et al., 2013) deployed online water quality monitoring sensors in the water distribution mains and acts as an early warning system to enhance system security. For contamination detection as in (Mashor Housh et al., 2015) the authors designed a model in water distribution networks to minimize false positive. In (Kavi Priya et al., 2015), the author describes a fuzzy based optimization for solving the multi constraint routing problem and (Abbas Mardani et al., 2015) discussed various fuzzy multiple criteria decision making techniques

and

applications. (Wen-Tsai Sung et al., 2012) designed a temperature system monitoring based on the adaptive fuzzy logic in wireless sensor networks and it provides better accuracy when compared with the standard fuzzy logic methods for computing the temperature. The regulation of anesthesia using a self-organizing Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 fuzzy logic controller during surgical procedures is designed in (Chih-Hao Syue et al., 2016). (Rawia Ahmed Hassan EL-Rashidy et al., 2015) proposed a fuzzy logic model to assess the network mobility of road transport system. These ideas motivated to develop a fuzzy logic for water quality monitoring in the water distribution mains. Various techniques are discussed in the literature for describing the quality criterion for drinking water and decision making process. But most of the data on the water quality relate to the deterministic approach in decision-making, it compares the values of parameters of water quality with prescribed limits provided by different regulatory bodies is used without considering the uncertainty involved in various steps throughout the entire procedure in (Andre Lermontov et al., 2011) . But, during the last few decades, one of the most popular and commonly used methods was Water Quality Index (WQI). The author (Curtis G. Cude, 2001) takes decisions based on the comparison of water quality prescribed limits with different water quality indices. This approach has a problem with the parameters in the index equation that influences the final score of WQI dramatically lacking valid scientific justification. Due to these restrictions of deterministic and WQI approach, advanced methodologies are required to account imprecise, and vague information in decision making. The uncertainties involved in the water quality using Mamdani Fuzzy Interference System with values ranging from 0 to 1 to form an applicable fuzzy set instead of the conventional scale of 0 to 100 are discussed in (Saberi Nasr et al., 2012). To handle the uncertainty in the imprecise environment of decision making, the methodologies related to fuzzy set theory are tested with real time environmental problems (Curtis G. Cude, 2001; Zhi Pei, 2015). In the proposed work, an attempt is made to classify the drinking water in the water distribution mains by considering the importance of uncertainty handling and adaptability using the fuzzy set theory for decision-making in the imprecise environment. The literature study of the discussed papers helps to identify the various methodologies used in the sensor deployment in water distribution mains and to predict the quality of the water. The key objective of this proposed work is to enhance the network lifetime and at the same time assisting the distribution of good quality water to the public.

3. Proposed Framework Architecture


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 The architecture of the proposed work is designed as four tier architecture. The framework as depicted in Fig. 2. consists of water distribution system in layer one that includes pipelines, reservoirs, energy harvesting sensor network, i.e. solar panel and network design for the sensor node deployment followed by the data correlation among the sensor nodes and web services at the customer end. The purpose of the water distribution system is to design the water distribution mains that carry water from the storage reservoir to the building or houses that is being served. The main requirements are the ability to deliver good quality and quantity of water required and to resist all the external and internal forces acting on the pipe that contaminates water. As the sensor nodes capacities are limited, the network is designed in such a way to determine the node participation so as to improve the network goals. The second layer involves the deployment of data acquisition devices and the sensors which can detect/sense EColi, Temperature, pH, Turbidity, OxidationReduction Potential and Dissolved Oxygen sensor. These sensors augment each other and collect the necessary data used in decision process and effectively detect the contamination in the water.


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 Fig. 2 - Framework architecture Major functionality of the third tier is to process the sensed data with event detection algorithms. This includes data transmission to the network layer, database management on the server side. The proposed Energy Aware Multipath Routing Protocol handles all these events and prevents the contaminated water flow in the pipeline and sends the needed information to the sink node. Application tier (client side) forms the top most tiers in the water quality monitoring framework. People interact with the web server to get details about the drinking water quality they consume with the help of mobile app and web query.

4. Design The proposed work comprises of three modules: (i) Energy efficient algorithm to enhance the network’s lifetime; (ii) Maximize the quality of the sensed data and incorporate data correlation among the sensor nodes; (iii) Fuzzy based water quality analysis for contamination detection to act as early warning system. All these algorithms are repeated at every sensor node in the water distribution network to improve the overall performance of the network.

4.1. Energy efficient Algorithm For every sensor node in the water distribution network, balanced energy consumption has to be taken into account to prolong the lifetime of the network (Francesco Carrabs et al., 2015). Unbalanced energy consumption leads to the depletion of the nodes sooner and stops data communication. In order to balance the energy consumption, the residual energy of the neighboring nodes is considered to adjust the transmission power levels are used in the existing network designs (Roger Wattenhofer et al., 2004; Mehdi Kadivar et al., 2009; KaviPriya et al., 2015). In such algorithms, the energy consumption of the nodes can be minimized by selecting the nearest neighboring nodes with high residual energy. In such selection process, nodes use high transmission power levels and in turn deplete its own limited energy. In the proposed work, a better network is designed to achieve energy efficiency in the Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 water distribution network to improve the network’s lifetime. Each sensor node in the water distribution network should be capable of detecting contamination in water, guaranteeing all the sensor nodes are functioning for a long time. Table 1- Energy efficiency algorithm

The proposed energy preserved water distribution network consists of N sensor nodes where the sensor network is represented as a directed graph N is the set of nodes and E is the set of link (i, j) with (i, j)

N. The

nodes in the water distribution network are modeled and defined by the set N=1, 2…, n

n N. All the nodes are connected through a maximum transmission power level

TPLmax. Each link in (i, j) exists if and only if each sensor nodes (i, j) with transmission power level

≤

(where k is a node) communicates

with the other sensor nodes in the network. If not, there is no pair link between (i, j) nodes. Initially, each sensor node i in the water distribution network send a “HELLO MESSAGE” and its maximum transmission range

and node ID. After

successful reception, “ACK” is received from every neighborhood say j. Node i collects ID and TPLij as well as energy Energy(j) into its order set of neighborhood Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 node j. Later, the receiving power level TPLr is also calculated when node i receives node j’s message. In the proposed algorithm, the node i’s list is determined by the neighborhood list. In order to collect other node’s lists in the network, each node is required to broadcast “HELLO MSG” to its 1-hop and 2-hop neighborhoods, which incorporates its ID and remaining energy of the node. Finally, node i have to decide its own transmission level by communicating along with all the nodes in the water distribution network. This algorithm constructs a set of list and Table 1 shows the algorithm to consider one-hop and two-hop neighborhood list to determine the transmitting power range of the nodes. As there is a list, it is enough for each node to search for the optimal power level rather than the transmission threshold entries.

Based on the node’s list, the power level of a node as in Eq. 1 i ∈ N is listed as

follows: ={

=

Here, each node i, where i

,

,

=

}

(1)

N selects its own transmission range one less than its

current range if the selected power level gives a high gain than its current power level. Else, the node i changes to the earlier act it was performing. At time‘t’ each node calculates its residual energy and when it is lower than the allocated energy, each node sends an “Energy Request Message”. The request message is sent to the one-hop and two-hop neighboring nodes to trace the remaining battery level available. An energy equality based on Eq. 2 is calculated to prove how well the energy is balanced among the group of sensor nodes in the water distribution network. The residual energy of the set of sensor nodes is given as input data to the Eq. 2 at time t.

(2)


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Here, EQ (t) represents energy equality and n signifies a set of nodes and N is the group of nodes.

represents the remaining energy of ith node at interval t with

inequality metric

. Hence, energy efficiency (EE) as in Eq. 3 mixes average and

equality by weighting the average by energy equality as illustrated

=

(3)

As the energy efficiency is high, all the nodes in the water distribution network enhance the network lifetime and the next objective is to maximize the quality of the sensor data by means of data aggregation and energy efficient routing.

4.2. Maximizing Monitoring Quality in Sensor Networks The aim is to maximize the quality of collected data (monitoring water quality parameters), by integrating the spatiotemporal data correlation among the sensor nodes into data rate allocation and routing, where the quality of collected data at time slot‘t’ is defined as in Eq. 4: Consider a node n

and the nodes contribution to

the network wide data quality can be represented by a non-negative function =

(4)

where the value of the rate

is determined by the function x, where the parameters are

of n and the rate

of its correlated master neighbors j

slot allocated for sensing the necessary data are between

and

The time in the specified

interval. When the assigned data rate to the node n approaches its maximum, the requested data rate is minimized. As there are multiple sources of water supply a weight between 0 and 1 is assigned for each and every source node. For each source node rate weight is set to 1 and acts as a master node. Due to high correlation between their sampling readings, another node will become the slave of the master and its rate weight is strictly less than 1. Algorithm for the monitoring quality maximization problem is described in Table 2. The proposed algorithm in Table 3 constructs the shortest path trees iteratively. With every iteration of i and

a shortest path tree


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 Table 2 - Algorithm for maximizing water quality monitoring

spanning all source nodes is constructed, the remaining demands from all source nodes will be routed to the sink such that at least one tree edge is saturated. Finally, update the length of each edge in the tree, where the length of an edge will be determined by the amount of data flow through the edge. Hence, the problem of real time data monitoring is successfully addressed by the algorithms in Table 2 and Table 3 and transfer good quality data to the sink node by the shortest path routing algorithms. The data collected will be further analyzed to predict the contamination of water in the water distribution network. 4.3.

A Fuzzy Water Quality Analysis for Contamination Detection

A simple fuzzy logic is used to check the quality of the water and distribute the water status to the household is shown in the Fig. 3. The fuzzy set is defined in terms of a membership function that maps a domain of interest to the interval [0, 1]. The membership function of the set A in Eq. 5 defined over a domain X takes the form (5)


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 Table 3 - Shortest path tree

The set A is defined in terms of its membership functions as in Eq. 6 and Eq. 7 (6) Or

(7) The membership function

has to be normalized to ensure that

the value one somewhere on X by dividing by the maximum value of

takes

. The use of

fuzzy numbers and aggregation of fuzzy sets are proposed as a suitable mechanism to handle the uncertainties in decision-making on water quality monitoring. Fuzzy membership functions that are constructed for all the 6 parameters are trapezoidal on the basis of expert perception and prescribed limits as in Table 4 for the classification of water quality. Based on the quality range prescribed by Bureau of Indian Standards (BIS) and Indian Council of Medical Research (ICMR), the parameter pH is described as in the Eq. 8, Eq. 9 and Eq. 10.


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Fig. 3- Fuzzy logic system – water quality monitoring

(8)

Desirable Accepted

(9)

Rejected: (10) An input membership function defines fuzzy sets by mapping crisp inputs from its domain (all possible concentrations of water quality parameters) to degrees of membership (from 0 to 1). Therefore water quality is categorized as “desirable”, “acceptable”, “rejected” as in Fig.4. In this approach, water classes are defined as fuzzy sets as degrees of membership with flexible boundaries rather than binary/crisp Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 sets. In the case of fuzzy evaluation approach, the six parameters are divided into three categories on the basis of drinking water quality criteria. As per classification pH, temperature and dissolved oxygen were kept in first group, oxidation-reduction potential and electrical conductivity were categorized in second group while turbidity is individually considered as separate group due to their importance in drinking water quality criteria.

Fig. 4 - Hierarchical classification of water quality monitoring system Based on the drinking water quality, a total of 40 rules as in Fig. 5 were fired using mamdani (Saberi Nasr et al., 2012) implications of max.min operators to assess the drinking water quality. The fuzzy interference system shown above checks with the rules and defuzzification is done to calculate the exact valve and decision making of water quality is carried out. An alarm is generated to notify the administrator of the municipal office when the water parameters exhibit sudden and significant changes, given the quality ranges are as suggested by drinking water quality standards in Table 4. The consumers are given a message by means of web query or mobile application when contamination is detected. Hence, the proposed contamination detection method enables the system to act as an “early warning system” for feasible potable water quality deterioration at the point of installation (e.g. homes, pipes in water distribution network) by considering the decision made by the fuzzy descriptor.


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Fig. 5 - Fuzzy interference system for describing water quality

Table 4 - Limits prescribed by BIS and ICMR for the parameters.

5. Simulation and Results The simulation is focused to show the performance of the early warning system in terms of energy efficiency, improved network lifetime with good detection accuracy and quality data. The sensor network is simulated in Ns-2 (Network Simulator 2) with 50 nodes, 100 nodes, 150 nodes and 200 nodes. In the simulated sensor network, the sensor nodes are deployed based on the energy efficient algorithm. In this section, performance of the energy efficient algorithm is validated and compared with OTTC (Mehdi Kadvir et al., 2009) in terms of energy efficiency. The standard parameters and values applied in experiments are done based on the related algorithms in (Theofanis P. Lambrou et al., 2013). In the simulation, nodes are randomly deployed in a field of size of (500m

500m) and all the sensor nodes

have fixed positions and are stationary. The other settings are listed in Table 5. Table 5 - Simulation parameters


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With the experimental setup shown above, 50 nodes are randomly deployed and the residual energy of each node is calculated according to a Poisson distribution. The rate value λ of the distribution is 20. Fig.6. illustrates the network constructed by the OTTC (One-hop and Two hop Topology Control) algorithm appears as node in a circle, which uses high transmission power level. However, it is not energy efficient and nodes drain its limited energy due to the high transmission power level. Consequently, the network’s lifetime will end prematurely. Furthermore, in contrast with OTTC, the constructed network of proposed algorithm as illustrated in Fig.7 has less transmission power levels. OTTC requires large information exchange, as it updates transmission power adjustment, which to know the network is connected or not all other nodes in the networks. Thus, the EA improves the network’s lifetime.

Fig. 6 - OTTC network design


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Fig. 7 – Energy efficient network design In another scenario, the algorithms are run for 200 seconds. As shown in Fig.8 the average residual energy of the proposed energy efficient algorithm in each variety of nodes is more than the average residual of OTTC algorithm, and the average-residual energy decreases as the number of nodes increases. In other words, as shown in Fig. 9 the proposed algorithm achieves energy efficiency and energy equality simultaneously and minimizes the probability of energy draining. In addition, it enhances the network’s lifetime more than that by OTTC algorithm.

Fig. 8 - Average residual energy of EE and OTTC


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Fig. 9 - Minimum residual energy of EE and OTTC By considering the designed network, the performance of maximizing water quality and shortest path algorithms as in Table 2 and Table 3 respectively are analyzed. The value for all the parameters turbidity, oxidation reduction potential, electrical conductivity, pH and temperature are obtained in real time by using WQMS Water Quality Monitoring System, Global Water (a xylem brand). The real time values are stored in a file and the file is given as input to the NS-2 Simulator for further water quality prediction and analysis. Fig. 10 represents the performance curves, by changing the confidence threshold

from 0.2 to 0.8 and the uniform weight w from 0

to 0.8. For unweighted case, each source node has an identical weight of 1. Fig. 11 clearly shows that the weighted data rate allocation gradually improves the data quality of the network significantly when compared with the unweighted rate allocation.

Fig. 10- Impact of

= 0.4 on the data quality when


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Fig. 11 - Impact of


Fig. 12 - Impact of


The proposed algorithm shows a better performance when the uniform weight is set to 0 for the slave nodes or assigned with a variable weight. Both bandwidth and energy are reallocated to the master and stand-alone nodes that are with low rate nodes. When

= 0.4, the data quality ratio will be 18%, 15%, 11%, 8%, and 6% by

varying the uniform rate weight w from 0 to 0.8 with step 0.2. Similarly, when

= 0.6,

the data quality ratio of the proposed algorithm is at least 16%, 10%, 8%, 6%, and 5% by varying w from 0 to 0.8. When

= 0.8, the data quality ratio is at least 13%,

7%, 6%, 5%, and 3% varying w from 0 to 0.8. When the variable rate is used the data quality ratio is around 13%. In summary, with the increase in confidence threshold, the data quality ratio becomes worsen, no issue whether it is a uniform weight or a variable weight assignment. Fig. 12 also represents that when the uniform weight w is fixed and the larger the confidence threshold improvement. When

, the data quality has less

is quite large only few nodes in the network becomes the

slave nodes. The experimental result of quality maximizing is therefore promising.


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Fig. 13 - Energy consumption per packet

Fig.14 - Average end-to-end delay for the network

Fig. 15 - Packet delivery ratio The designed protocol EEMRP (Energy Efficient Multipath Routing Protocol) to support the water quality monitoring system is compared with the other routing protocols such as AODV and DSR. The proposed routing scheme improves the network lifetime by forwarding the data packets through the optimal shortest path. The optimal path is obtained by considering the maximum residual energy of the next hop sensor node, high link quality, minimum hop counts, etc.


217


Fig. 16 – System throughput The total energy consumption per packet is represented in Fig. 13. The results show that the proposed EEMRP consumes less energy when compared with the other protocols. As the proposed protocol employs energy efficiency, energy equality and transmission power control the overall network energy consumption has been reduced. The Fig. 15 shows the improved packet delivery ratio and that of network total throughput is given in Fig. 16. The results show that EEMRP performs better than other protocols since it has a quality data flow from all source nodes to the sink by calling the shortest path routing mechanism. The shortest path tree has a set of descendent nodes that helps to maximize the data flow from source to the sink. So, the average end-to-end delay is minimized as shown in Fig.14. Hence, the proposed water quality monitoring algorithms has improved energy efficiency, detects the water contamination with better accuracy as of fuzzy rules are applied, maximizes water quality monitoring level and overall the network lifetime is maximized.

6.

Conclusion and Future work

In this paper, a complete design and implementation of wireless sensor network for real time drinking water quality monitoring in the water distribution network is presented. Since water is an important resource, real time monitoring of the water quality plays a major role. The proposed monitoring algorithm monitors the water quality efficiently by considering the parameters such as pH, temperature, turbidity, oxidation-reduction potential, electrical conductivity and dissolved oxygen. As, energy harvesters such as solar panels are used, it helps to minimize the energy consumption and balances the network connectivity. The proposed system improves Centre for Water Resources, Anna University, Chennai

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 energy efficiency; maximize the monitoring data quality; fuzzy rules to qualify the real time water quality in the pipeline. The proposed algorithm outperforms in assessing the water contamination risk with minimum time constraint and prevents the water flow in the contaminated region. The analytical and numerical results indicate that the designed water quality monitoring algorithms outperforms in terms of energy efficiency, accurate and fast detection, and improved network lifetime. The derived solution can also be applied to different IoT (Internet of Things) scenarios such as smart cities, city transport system etc. Future work involves deploying the sensors and data logger in the real pipeline and provides better improved solutions for the real time hardware monitoring of the water quality in pipes.

Acknowledgements This work is jointly supported by Department of Science and Technology, Government of India under Water Technology Initiative (WTI) scheme with sanction order no: DST/TM/WTI/2K14/216. The authors express their sincere gratitude to Dr.Neelima Alam, Scientist-D, Technology Mission Cell, Department of Science and Technology, Govt. of India, New Delhi for encouragement and guidance. We also acknowledge our principal Dr.S.Arivazhagan and Management of Mepco Schlenk Engineering College, Sivakasi for their support in our research work.

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National Workshop on Water Resources System Modeling 9th and 10th March 2017 Ioannis Ch. Paschalidis, Ruomin Wu, 2012, Robust Maximum Lifetime Routing and Energy Allocation in Wireless Sensor Networks, Center for Information and Systems Engineering, 1-32. Jae Hwan Chang, Leandros Tassiulas, 2004, Maximum Lifetime Routing in Wireless Sensor Networks, IEEE/ACM Transactions on Networking, Vol. 12(4), 609 – 619. Janice Skadsen, R. Janke, W. Grayman, W. Samuels, M. Tenbroek, B. Steglitz, S. Bahl, 2008, Distribution System On-line Monitoring for Detecting Contamination and Water Quality Changes, Journal AWWA. John Hall, Alan D. Zaffiro, Randall B. Marx, Paul C. Kefauver, E. Radha Krishnan, Roy C. Haught, and Jonathan G. Herrmann, 2007, On-line Water Quality Parameters as Indicators of Distribution System Contamination, Journal AWWA, 66-77. KaviPriya.S, T.Revathi, K.Muneeswaran, K.Vijayalakshmi, 2015, Heuristic routing with bandwidth and energy constraints in sensor networks, Journal of Applied Soft Computing, 12 - 25. Lina Perelman, Avi Ostfeld, 2013, Operation of remote mobile sensors for security of drinking water distribution systems, Water Research, Vol.47 (13), 4217–4226. Mehdi Kadivar, M.E. Shiri, Mehdi Dehghan, 2009, Distributed topology control algorithm based on one- and two-hop neighbors’ information for ad hoc networks, Computer Communications, 368–375. Prauzek, P.Krömer, J.Rodway, P.Musilek, 2016, Differential evolution of fuzzy controller for environmentally-powered wireless sensors, Journal of Applied Soft Computing, 193 - 206. Rawia Ahmed Hassan EL-Rashidy, Susan M.Grant-Muller, 2015, An Operational Indicator for Network Mobility using Fuzzy Logic, Expert Systems with Applications, Vol.42, 4582 – 4594. Ren-Shiou Liu, Prasun Sinha, Can Emre Koksal, 2010, Joint Energy Management and Resource Allocation in Rechargeable Sensor Networks, IEEE Communications Society, IEEE INFOCOM. Saberi Nasr, M. Rezaei, M. Dashti Barmaki, 2012, Analysis of Groundwater Quality using Mamdani Fuzzy Inference System (MFIS) in Yazd Province, Iran, International Journal of Computer Applications, Vol.59(7), 45-53.


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Author’s Biography

S. Kavi Priya


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 S.Kavi Priya has received her BE – CSE (2002), ME - CSE (2005) and is currently pursuing PhD at Anna University, Chennai, India. She is currently working as Assistant Professor (senior grade) in Mepco Schlenk Engineering College, Sivakasi, Tamilnadu. She has 13 years of academic experience and she has published 9 papers in International journal. Her research interests are Wireless Sensor Networks, Image Processing and Neural Networks. She is the lifetime member of CSI and ISTE.

E-mail: [email protected]

G.Shenbagalakshmi

G.Shenbagalakshmi has received her BTech – IT (2008), ME - CSE (2013) and is currently pursuing PhD at Anna University, Chennai, India. She is currently working as Junior Research Fellow in Mepco Schlenk Engineering College, Sivakasi, Tamilnadu. Her interests are Network Security, Wireless Sensor Networks and Artificial Intelligence.


T.Revathi


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National Workshop on Water Resources System Modeling 9th and 10th March 2017 T.Revathi received her B.E. – EEE (1986), M.E. - CSE (1995) and Ph.D. degree at M.S. University, Tirunelveli, India. She is currently working as HOD and Senior Professor in Mepco Schlenk Engineering College, Sivakasi, Tamilnadu. She has 30 years of teaching experience. She has published 23 papers in International journal and 22 papers at national level. Her interests are Networks, Big Data Analytics, and Sensor Networks. She is the lifetime member of CSI and ISTE.



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SATHYA PRIYA R M.Tech Environmental Engineering Thiagarajar College of Engineering Madurai. WATER QUALITY MODELLING OF ARIYANKUPPAM RIVER/ ESTUARY ABSTRACT Rivers are the major source of freshwater. Estuaries being a transition zone between the river and sea help in stabilizing shorelines, protecting coastal areas and providing economic, cultural and ecological benefits to the communities. Rivers and estuaries deliver invaluable ecosystem services. Human interventions in such ecosystems lead to pollution of water bodies and adjoining areas. In recent days, water quality of rivers and estuaries are found to be highly altered leading to the depletion of quantity and quality of water further resulting in diminishing species existing in such ecological systems. Studies and researches highlighted the need for protection and restoration of such polluted rivers and estuaries. Ariyankuppam river located in the Puducherry district is a standing example of uncontrolled pollution, due to discharge of untreated waste water. This project takes an initiative to study the hydrodynamic characteristics of the river and estuary with the help of a modeling software called MIKE 21. The results of this study helped in understanding the flow and current patterns of the river, which paved way in proceeding with the development of water quality models of the river in order to suggest remedial measures to restore the water quality of the river and estuary. 1. INTRODUCTION Rivers are the greatest source of freshwater on earth. The earth’s distribution of fresh water accounts to 3% of which 0.3% falls under the category of surface water within which 2 % of water is contributed by rivers. Rivers play a significant role by ensuring indispensible supply of water, providing excellent habitat and food for different kinds of organisms on earth. Estuaries being the transition zone between the river and the maritime environment are extremely productive and generate more organic material. Unique communities of plants and animals are supported by sheltered waters of the estuary. There are nearly 98 coastal rivers and 8 estuaries in India out of which 14 rivers are considered to be the major rivers in the country. However due to the human interventions like discharge of untreated sewage, industrial effluents and agricultural waste dumping either directly or indirectly into the water bodies pollute them and change

the characteristics of the river and estuarine ecosystem. A large number of Indian rivers are found to be severely polluted as a result of discharge of untreated domestic sewage. Therefore, understanding the present characteristics of the water body ecosystem and the impact of human interventions will help in preventing adverse impacts due to further activities. About 60% of the development of towns and cities occur along the bank of the rivers because of its multi-sectoral benefits. According to a statistical data on water quality, every day 2 million tons of sewage, industrial and agricultural waste is discharged into the world’s water which is equivalent to the weight of the entire human population of 6.8 billion people. The UN estimates the amount of waste water produced annually is about 1500 km3, six times more water than exists in all rivers of the world. According to the WHO studies major cities in India produce nearly 38,354 MLD of sewage, but the urban sewage treatment capacity being 11,786 MLD only. The Central Pollution Control Board, a Ministry Of Environment and Forest government of India entity, has established a national water quality monitoring network comprising 1429 monitoring stations in 28 states and in 6 union territories on various rivers and water bodies across the country. Water samples are routinely analysed for 28 parameters. The scientific analysis of water samples from 1995 to 2008 indicates that the water bodies are severely polluted mainly due to discharge of domestic waste water in untreated form mostly from the urban centres of India. 2. SCOPE OF THE WORK The nation’s economic development is found in two fundamental assets viz, its people and its natural resources. The natural resources must be protected, enhanced and utilized to uplift the economic growth of the country. Puducherry is a centre of tourist interest with 10,12,849 tourists visiting Paradise beach, Manakulla Vinayakar temple, The Basilica Chruch, Auroville and so on. A total fish yield of 73,505 fishes (marine & inland) in the year 2014-2015 has proved to be the back bone of Puducherry’s economy. In view of this status of Puducherry, it is highly significant to study the water quality of Puducherry coastal waters and the sources based on which appropriate decision can be taken for its improvement and hence harmony of the society. The fact about the present status of rivers in India clearly highlight the degradation of water quality due to disposal of untreated waste and other human interventions in the adjoining areas of the rivers. Polluted rivers face a serious health hazard, fish mortality and change in the water quality affecting the habitat of various organisms sustaining in the ecosystem. This increasing concern with the source water quality has simulated interest in the study of numerical models as a tool for understanding the relevant

processes in the source water body with the purpose to predict the effects of changing conditions and to simulate the future scenario in order to suggest for better remedial measures and manage the ecosystem. Generation of a hydrodynamic model for the Ariyankuppam river and estuary will help in studying the dynamic flow characteristics of the river. This understanding will help in further understanding of the water quality of the river with the help of models. The results of the water quality models help in formulating new restoration ideas and plans to be implemented in order to restore the water quality of the river and estuarine ecosystem. This will solve problems like serious health hazard to marine biota and human, experienced due to these pollutants, fish mortality witnessed in the river can be controlled and the reported decrease of fish growth in the coastal waters of Puducherry region can also be enhanced. 3. STUDY AREA The union territory of Puducherry is located on the eastern cost of Peninsular India. The income of this region was initially based on agriculture and fishing. Economic growth then shifted the trend towards industrialization and urbanization putting pressure on natural resources causing the environment to degrade. Sankaraparani river also known as Gingee or Varahanadhi drains into Bay of Bengal on the southern side of Puducherry region. It has its source at the hills of Malayanur in the South Arcot district of Tamil Nadu. The river splits into two branches namely, Chunnambar in south and Ariyankuppam river in the north. The total length of Sankaraparani river is 78.5kms of which 34 kms length of the river is present in Puducherry. The river is not a perennial river and flows only during rainy season and flood. Ariyankuppam river and its estuary which are the area under study is situated in Puducherry between latitude 11°55’N to 12°30’N and longitude 70°05’E to 80°05’E. The location of this river is shown in the figure 1. This is a medium river basin with drainage of about 100 km2. Puducherry in its aerial extent is about 293 km2. The total population of Puducherry being 7.35 lakhs generates, 60 MLD of waste water, treatment facilities are available only for 13 MLD and the remaining 47MLD of waste water being discharged into the sea through backwaters and creeks in untreated form. Major industries like paper manufacturing, alcoholic beverages, chemicals, pharmaceuticals discharge a total treated water of about 7000 KLD into this river. The waste generated from the nearby areas of Ariyankuppam river is also let out directly into it leading to the deterioration of the water quality in the river. Ariyankuppam river has now become a river of uncontrolled pollution. It is mainly polluted due to the untreated discharge of industrial effluents, domestic waste water and agricultural drainage. Studies say that some of the salt water

fishes coming into the tidal inlet for breeding have been affected by these pollutants. Large cases of fish mortality are also witnessed in this region. Fish growth is found to be decreasing and the consumption of these fishes thriving in the polluted waters also affects the health of human.

Figure 1: Study area- Ariyankuppam river, estuary and the adjacent coast 4. DATA COLLECTION The driving forces affecting the health and morphology of water bodies are the hydrodynamics of the river, bathymetry of the river, currect and flow pattern in the river, waves in the coastal and estuarine portion of the study area, the local terrain morphology and the meteorology of the area. Therefore, in order to study the health of the Ariyankuppam river a hydrodynamic and a water quality model is prepared. In the process of development of these models, the first step is to collect the required data pertaining to the study area. This includes base-map of the Ariyankuppam river is required. The satellite image of Ariyankuppam river is then rectified and georeferenced using Arc-GIS software. The boundary of the study area is demarcated and detached. Figure 2 shows the points selected for rectifying the satellite image of the study area.

Figure 2: Points selected for the process of rectification of the study area Hydrodynamic model was set up over fine resolution flexible mesh bathymetry at the study area. Figure 3 shows the available bathymetry data measured with a help of an eco-sounder by the survey conducted by NIOT along the Ariyankuppam river, estuary and the nearby coast.

Figure 3: Available bathymetry data along the study area Tide data is obtained from the observations using direction wave recorders by the survey conducted by NIOT. Tidal predictions obtained from the global model are also used for the modeling purpose. Wind is the basic input parameter for simulation. Successful wave forecast depend on accurate wind fields deduced from meteorological models and analysis. In the present study, wind data was obtained from the database of ECMWF's interim reanalysis (ERA-

Interim). Wind data for Puducherry region covering the study area (11°53’N to 11°53’N and 79°48’N to 79°51’N) was collected from ECMWF database. The wind data was obtained with a spatial resolution of 13890 x 13890 m and temporal resolution of 6 hours for a period from January 2010 to December 2012. The data for wind was obtained as U & V components of wind velocity (m/s) at 10 m height, calculated from decomposing the wind magnitude and direction along the two horizontal axes: x and y. Typical wind pattern is shown in figure 4.

Figure 4: Grid showing U component of wind pattern from ECMWF data Water quality data of Ariyankuppam river are obtained from a secondary source at three locations along the river viz, upstream source, tidal inlet and in the kakkayanthoppu region. 5. METHODOLOGY AND VALIDATION OF HYDRODYNAMIC MODELLING The software tool used for developing a hydrodynamic model is MIKE 21. The hydrodynamic model in the MIKE 21 is a general numerical modeling system for the simulation of water levels and flows in estuaries, bays and coastal areas. The model is based on the solution of the two-dimensional incompressible Reynolds average NavierStokes equations, subjected to the assumptions of Boussinesq and of hydrostatic pressure. Finite Element technique adopted which is based on an unstructured mesh and uses a cell-centred finite volume solution technique. Meshes in MIKE 21 intelligently adapt that paves way to meet high resolution requirements in certain areas. A hydrodynamic model can be used in studying the present characteristics of the river and also to predict the future period of time for which we need the required parameters. It is used to predict the variations in surface elevation, currents, temperature and salinity. A comparison of all these parameters for different points will explain the current and flow pattern of the river.

Model meshing is done to the demarcated study area, in order to describe the water depths in the model area, to obtain model results with a desired accuracy, for obtaining a model simulation times acceptable to the user. In order to obtain a smooth mesh the angle of the triangles in the mesh is given as 30°. The bathymetry data are superimposed on the mesh file. With the available bathymetry data for a portion of the study area, the software interpolates the bathymetry completely over the study area. The accuracy of the interpolated data will depend on the proper meshing of the study area.

Figure 5: Meshed study area and the interpolated bathymetry for the study area

As a part of data collection, tidal data have been obtained and after meshing the bathymetry data is being projected for the whole study area. Using these data the tidal level predictions are done for the year 2012. By the end of the calibration process, the tidal level predictions in the north and the southern boundary are obtained for the year 2012. Model validation is done by comparing the measured and the modeled tidal level data for the overall study area simulated for a period of 15 days with 1000 time steps. If the graph matches to a considerable extent then the next step of model development is done, if not the process from model meshing is repeated till the validation graph is found to be considerable. 0.8000 0.6000 0.4000 0.2000 0.0000 10/10 12/10 14/10 16/10 18/10 20/10 22/10 24/10 -0.2000

measured modeled

-0.4000 -0.6000 -0.8000

Figure 6: Validation done by comparing the modeled and measured data 6. METHODOLOGY AND RESULTS OF WATER QUALITY MODELLING Water quality is an important component for clean environment, good health and to protect ourselves from the exposure to contaminated waters. To understand and quantify the changes in water quality and their impacts forcasting the fate of the system is essential. Water quality modeling is used to predict the fate of pollution causing agents in a water body by using mathematical and numerical simulations using analytical and statistical methods. Water quality models are essential decision making tools for cost effective management of our water resources by applying various strategies to the model and choosing the best by analyzing the results of the model. Eco-Lab system solves the system of differential equations describing the physical, chemical and biological interactions involved in the survival of bacteria, degradation of organic matter, resulting oxygen conditions and excess levels of nutrients in coastal areas. The combination of MIKE21 hydrodynamic flow model and Eco-Lab model is called coupling. The coupled models are a powerful tool applied in the water

quality studies for modeling coastal areas, estuaries and rivers. The coupled model will help in establishing the relationship between the variables and also to analyze the effects on the water body due to any change in the system. Oxygen- dissolved oxygen is needed by organisms like fishes, but when sewage enters an aquatic ecosystem, the micro-organisms bloom, leaving less oxygen for the fishes and lead to their extinction. A BOD-DO model will describe the oxygen depletion due to the release of BOD, excess concentration of nutrients and the degradation of organic substances in the water bodies. In the process BOD–DO model preparation four state variables are considered viz, biochemical oxygen demand, dissolved oxygen, temperature and salinity. The current speed and water depth of the river are obtained from the results of hydrodynamic model and are fed as input to the ECO-Lab model to prepare BOD-DO model. The wind speed data obtained from the ECMWF, are also fed as input to account for wind forcings. The initial and boundary conditions defining the water quality parameters for the model are also extracted and fed to the model.

The results of the model are shown in the figure. The values of biochemical oxygen demand and dissolved oxygen are found to be high in the upstream side of the river. Since the quality of waste water discharged in the upstream river is worse, the model results denote the upstream source to be a major polluting source of the river.

Figure 7: Results of the model depicting BOD and DO respectively 7. CONCLUSION Water quality of the river assessed with the help of hydrodynamic and water quality model depicts the worse pollution caused in the river. The value of different water quality parameters shows that the upstream source of waste water discharge needs efficient treatment before its disposal. The result of the model also proves the rapid decline rate of fish breeds in the river due to the reduction of dissolved oxygen in the river. Therefore, in order to protect the quality of the river and to improve the economic status of the Ariyankuppam area through more fish growth will be possible only if the discharged waste water were treated before disposal. An advection-Dispersion model can also be under-taken as a continuation of these models in order to further study about the transport of the pollutants. Thus these water quality models serve as a successful tool to predict different water quality parameters for the upcoming years, which further will pave way to take judicial decisions on undertaking suitable remedial measures to protect the river. 8. REFERENCES • Arvind Kumar Rai, (2012). “A study on the sewage disposal on water quality of Harmu river in Ranchi city Jharkhand, India”.International Journal of Plant, Animal and Environmental Sciences.

• Balachandran K.K, (2007).”Report on Ecosystem modeling of Cochin backwaters by National Institute of Oceanography, Regional Centre”, Kochi. • Beiras R, Bellas J, Fernandez Z, Lorenzo J.I, Cobelo- Garcia A, (2003) “Assessment of coastal marine pollution in Galicia; metal concentrations in seawater, sediments and mussels versus embryo-larval bioassays”. Mar Environ Res 56:531-553. • Capuzzo J.M, Burt B.V, Duedall I.W, Park P.K, Kester D.R. (1985) “Nearshore waste disposal”, John Wiley and Sons Inc. Publications, New York, USA. • Impact of Industrial Effluents and Sewage on the Water quality of River Godavari at Bhadrachalam Temple Town in South India, (2006), 12 (3):543 -552. • Rama Devi V, Miranda W.J, Abdul Azis P.K,(1996).“ Deterioration of water quality An overview on the pollution problems of the Ashtamudi estuary”. Pollut Res 15:367-370. • Report on Hydrodynamic modeling by Gladstone Ports Corporation, Australia. • Singh, S. K and Rai, J.P.N, (2003).”Pollution Studies on River Ganga in Allahabad, Pollution Research”, 22: pp 469-472. • Sreenivas, B.S, Ramana, V.V, Ramesh, K, Charya, M. A, (2006). “Impact of Industrial Effluents and Sewage on the Water quality of River Godavari at Bhadrachalam Temple Town in South India”, 12 (3):543 -552. • Subramanian B.R. (2005), “Report on Ecosystem modeling for Muthupet lagoon along Vedaranyam coast (Tamil Nadu) by Dept of Ocean development”, ICMAM, Chennai. • Tran K.C, Euan J, Isla M.L, (2002). “Public perception of development issues: impact of water pollution on a small coastal community”, Ocean Coastal Manage 45:405-420. • Vijayakumari G, M.A. Sivasankaran and V. Murugaiyan, (2012). ”Studies on the pollution levels in Ariyankuppam backwater, Puducherry region published in International Journal of Science, Environment and Technology”, Vol.1,No5,363 – 376.