A feedback Based Linked Simulation-Optimization ...

A feedback Based Linked Simulation-Optimization Approach to identify the Unknown Groundwater Pollution Sources. Sreenivasulu Chadalavada a, b, Bithin Datta c,* and Ravi Naidu a, b

Key Words: Pollution Source, Simulation-Optimization, Groundwater, Genetic Algorithm

*Corresponding Author Dr. Bithin Datta Department of Civil Engineering James Cook University, Townsville Queensland Phone: +61 7 47814983 Fax:

+61 7 47816788

Email: [email protected]

a

Center for Environmental Risk Assessment and Remediation University of South Australia, Australia 5095 b c

CRC for Contamination Assessment and Remediation of the Environment Deaprtment of Civil Engineering, James Cook University QLD 4811 Australia

Abstract The characterization of source zones helps us to gain an understanding of the complexity of the contaminated site before engaging in expensive remediation technologies. A methodology is developed in this study which essentially deals with the application of combination of simulation and optimization based models for site characterization and optimal pollution management to a real life contaminated aquifer site. The methodology consists of models within an iterative feedback system, with the capacity of feeding back real-time measurements of pollutant concentrations for the sequential optimal designs and characterization of the contaminated aquifer study area. The resulting linked-simulation optimization model considers the delineation of the contaminant plume, optimally characterizing the site in terms of pollutant sources and the optimal monitoring network leading to the remediation and/or management of the contaminated aquifer. As part of the methodology s simulation-optimization code was developed by linking a groundwater flow and transport model with an optimization code for the purpose of identifying the unknown pollution sources. The proposed methodology addresses the source identification process with limited information available regarding the observed contamination data for the identification of unknown pollution sources. Performance of the developed methodology is evaluated by choosing an illustrative hypothetical study area. The performance evaluation suggests that the source identification process is improved by finding the unknown contaminant source fluxes with an error of 11.4 % after a couple of iterations in the feedback based methodology developed. The results obtained also been compared to the results obtained from embedded approach and it reveals that the feedback based methodology developed in the thesis proves better performance.

1.0.

Introduction

The widespread land and water contamination has the potential to cause economic, trade, ecosystem and human health impacts. Over the past couple of decades the problem has been growing and there is also a growing realization of the extent of the problem. For instance, it is now accepted practice to confirm the contamination status of land and groundwater before use or transfer of title. Globally, the total cost of environmental management of land and groundwater contamination and waste management is estimated to be in excess of $1 trillion ( Industry Environment Policy, 2002), and around $5-8 billion is estimated for Australia (Powell, 1992). The installation of monitoring wells is pivotal for understanding the groundwater hydraulics and subsurface contamination at the same time the process is expensive. The systematic study of the subsurface system with the available scanty data regarding the groundwater flow and the subsurface contamination can help us to arrive at the optimum number of monitoring wells for the effective site characterization. The efficiency of any remediation strategy depends on how effectively we characterized the contamination source. Generally the contamination source zone is characterized in terms of its location, magnitude and duration. But most of the real world contaminated sites lack the proper information which can be used to source zone characterization. One of the problems is identifying the unknown pollution sources. This aspect helps us to solve the social and legal problems by identifying the parties responsible for contamination. Therefore having understood the difficulties involved in the contaminated site characterization process, a novel feedback based methodology has been developed.

The methodology consists of models within an iterative feedback system, with the capacity of feeding back real-time measurements of pollutant concentrations for the sequential optimal designs and characterization of the contaminated aquifer study area. The resulting linked-simulation optimization model considers the delineation of the contaminant plume, optimally characterizing the site in terms of pollutant sources and the optimal monitoring network leading to the remediation and/or management of the contaminated aquifer. The developed methodology can be applicable for characterization of contaminated aquifer sites with limited data availability, and for developing optimal strategies for remediation or control of contamination. Characterization of contaminated site is a continuous, dynamic process of building and revising a site conceptual model that gathers the relevant aspects of contaminated site, including the source zone. Understanding the fate and transport of pollutants in the subsurface system holds the key in managing the groundwater systems. While many models have been developed on the fate and transport of contaminants in ground water (Konikow et. al. (1989), Clement (1997) and, Zheng and Wang (1999)), there is limited technology that encompasses source characterization, fate and transport modeling. Given the primary objective of this work being the development of a cost-effective tool for source characterization and ground water contaminant plume delineation using minimum number of samples, the following literature focuses on the identification process of subsurface unknown pollution sources. Designing of an optimal monitoring network constitutes the principle component of the feedback based methodology. This component of the

methodology provides the feedback information in terms of observed contaminant concentrations to the source identification model in the identification process. The concept of optimal groundwater monitoring network design has attracted many researchers for the past two decades. Loaiciga et al. (1992) gives a comprehensive review of the methodologies, existing models and important concepts used to design monitoring network design for detection of groundwater pollution. An integer program optimization model was developed by Meyer and Brill (1988) to design an optimal groundwater quality monitoring network which maximizes the probability of detection of pollutant plumes that exceed a specified concentration. An optimal monitoring network design by McKinney (1992) considered the minimization of the uncertainty in groundwater simulation model predictions by choice of new locations at which aquifer properties are to be measured. An optimal monitoring network designed by Hudak et al (1993) considered the flow and transport process in multi-layered contaminated aquifer. Meyer et. al (1994) considered the minimization of number of monitoring wells and maximization of probability of detecting a contaminant leak, and minimization of expected area of contamination at the time of detection to design the optimal monitoring network design. Simulated Annealing has been used for solving the optimization technique. Wu (2004) also developed an optimal monitoring network for a real world problem in Daqing, China. He selected the sites for monitoring groundwater levels by applying the finite-element method coupled with Kalman filtering to the area in which the groundwater resources have been extensively exploited. The reduction of redundant wells in the design of optimal monitoring network design ( Nunes et al ,2004)

will be useful when the network is to be designed for dynamic

properties. Reed and Minsker (2004) designed an optimal monitoring network for multiple objectives which are conflicting in nature using NSGA-II (Deb et al 2002). Kollat and Reed (2005) compared the performances of four state-of art evolutionary multi-objective algorithms on a four objective long-term groundwater monitoring design test case. This work gives an understanding of the application of different multi objective evolutionary algorithms in designing the optimal monitoring network design. Using similar approach, Wu et al (2006) evaluated and compared two methodologies such as Monto Carlo Simple Genetic Algorithm (MCSGA) and noisy Genetic Algorithm, for cost effective sampling network design. Recently Dhar and Datta(2008) considered the multi-objective optimization model for designing the cost effective procedure where one of the conflicting objectives is to minimize the cost involved. Chadalavada and Datta (2008) designed the optimal monitoring for a transient groundwater flow and transport systems in a dynamic frame work. Two monitoring network design models are formulated and performance evaluations of these models have been done using an illustrative hypothetical study area. In most of the real world problems identification of unknown source zones plays vital role in source characterization which in turn is the key for adopting the efficient remediation strategy for the contaminated sites. But this has been addressed only in limited number of studies. Gorelick et al.(1983) demonstrated two hypothetical study areas for identification of unknown pollutant sources using least squares regression and linear programming together with response matrix. They considered both steady state and transient flow conditions for transport phenomena. A review of distributed parameter modeling for groundwater management has been done by Gorelick (1983). Use of combined simulation-

nonlinear programming for aquifer remediation has been considered by Gorelick et al (1984).A nonlinear multiple –regression is used by Wagnor and Gorelick (1986) to estimate aquifer parameters and linear source term for a one dimensional hypothetical column system. Datta et al (1989) used statistical pattern recognition techniques in developing an expert system to identify groundwater contamination sources. The flow and transport process has been simulated using the response matrix approach. The effects of parameter uncertainty and measurement errors on source identification have also been studied. The simultaneous estimation of parameters (Wagnor, 1992) and optimal identification of contaminant sources plays important role in contaminated site characterization. The random walk method for identifying the pollution sources is used by Bagtzoglou et al(1992). Skaggs and Kabala (1994) developed a methodology to recover the release history of contaminant plume from current spatial measurements of concentration by using Tikhov regularization. The performance evaluation of their methodology has been carried out by investigating the effects of measurement errors, parameter estimation errors, and numerical instability. The recent advances in simulation-optimization based methodologies for groundwater management has been reviewed by Wagnor (1995). Mahar and Datta (1997) developed dynamic optimal monitoring network for improved identification of pollutant sources in groundwater. The performance evaluations for the simple spatial and temporal combination of potential sources were demonstrated by the methodologies adopted by Wagner (1992).

Mahar and Datta (2000) considered the

transient groundwater system in identifying the pollution sources. Mahar and Datta (2001)

proposed a methodology which utilizes an optimization model with flow and transport equations embedded as constraints. They extended the source identification methodology to the simultaneous estimation of aquifer parameters as well as identification of unknown pollutant sources. Atmadja and Bagtzoglou(2001a,2001b) and Bogtzaglou and Atmadja (2003) discussed some of the recent methodologies in this area. Singh and Datta (2006) used Genetic Algorithm (GA) - based simulation optimization approach for optimal identification of unknown pollutant sources. The combination of source characteristics, data availability conditions and concentration measurement error levels are identified for performance evaluation of the developed methodology. Singh and Datta(2006) solved the source identification problem employing the Artificial Neural Network(ANN) technique. The characterization of source zones helps us to gain an understanding of the complexity of the contaminated site before engaging in expensive remediation technologies. As the literature review suggests that the very limited work has been done as regarding optimal characterization of source zones of contaminated aquifers. Keeping this view in mind a methodology has been proposed which essentially deals with the application of combination of simulation and optimization based models for site characterization and optimal pollution management to a real life contaminated aquifer site.

2.0.

Methodology

The source characterization methodology proposed in this work consists of a number of components interrelated with each other, and utilizing feedback information. The distinct components are:1) A model for simulating the groundwater flow and contaminant transport processes in the aquifer, 2) An optimization algorithm for arriving at an optimal monitoring network design based on available site information at various time steps, 3) An optimization model for optimal identification of the unknown pollutant sources in terms of magnitude, location and time. A feedback based methodology is developed utilizing the different component mentioned herein. The important aspect of this methodology is the utilization of feedback information obtained from sequentially designed monitoring networks. The aim is to gradually improve the unknown groundwater contamination source identification process, utilizing the information obtained from transient monitoring networks. The developed methodology is schematically represented in flowchart shown in Fig.1. The various components of the methodology involving the computational tools and the interlinking of these tools are briefly described as follows. A groundwater flow and contaminant transport simulation model is essential for describing the flow and transport processes occurring in any contaminated site. Also, the simulation of the pollutant transport process can be used to predict future contamination scenario. Due to the complex nature of most study areas it will not be possible to use analytical simulation models. Therefore, a suitable set of numerical simulation models for flow and transport

processes have been selected. In most of the real time contaminated site problems the basic concern of the decision makers is the lack of the sufficient observation data. Often very limited information is available regarding the site hydrogeology as well as the contamination process. The methodology proposed in this study utilizes the simulation model for simulating the spatial and temporal distribution of contaminant concentration data in designing an optimal monitoring network, which supports the source identification process by giving the sequential feedback information in terms of contaminant concentrations. 2.1. Optimal Monitoring Network Design Development of an optimal monitoring network plays vital role in contaminated site characterization process in terms of delineating the plume as well as serving as contaminated data base. The methodology proposed here utilizes the optimal monitoring network design as a tool for gathering the contamination related information to be used in the source identification model in a feedback-response system. The process of site characterization process starts with a limited historic data and scanty contaminant concentration data at few observation locations over the site. The design of optimal monitoring network should be able to identify the set of monitoring wells required for sampling by considering the available contamination information in an efficient way. The number of monitoring wells to be drilled in a drilling campaign subject to the budgetary allocations. Therefore the design should aim at the identifying the optimal monitoring locations within the budgetary locations as well as detecting the contaminant plume. Having considered the necessity of an optimal monitoring network, a network design model has been formulated for this purpose. The formulation and the procedure of network design are explained as follows.

Network Design Model: The objective function for the network design model is defined as: Minimize weighted squired sum of the mass estimation errors at all the potential monitoring locations over all realizations where a monitoring well is not to be installed as per the design criteria subject to implicit budgetary limitations. The formulation of objective function is given below.

M

2

N

Minimize:

M s ,ij i 1

M k ,ij PijWi X i

………………………… (1)

j 1

Subjected to: 0 , For (Cij – C*) < 0

Pij

………………………… (2)

Pij = 1, For (Cij – C*) >=0

…………………………(3)

1 - Ti = Xi for all i

………………………… (4)

M

Ti

T

i 1

Xi = (0,1) Ti = (0,1)

M

………………………… (5)

Where: i

= Index number for potential monitoring location M = Total number of potential monitoring locations. j

= Index number for representing a particular realization

M s ,ij = Simulated contaminant mass at ith potential location for jth realization

M k ,ij = Kriged contaminant mass at ith potential location for jth realization

Wi = Weight assigned to potential location, i Wi = (Cij – C*) Cij = Simulated concentration at ith potential location for jth realization

C* = Threshold value of contaminant concentration Ti = A binary decision variable, 1 indicates a monitoring well is to be installed at potential location i, and 0 indicating otherwise T

= Maximum number of wells permitted to be installed for the given period

Xi = Compliment of Ti = Belongs to As discussed above in the formulation, the objective of the network design model is not to install a monitoring well where the weighted squired sum of the errors between the

simulated and kriged contaminant masses at the designated potential monitoring well location. The objective function is solved using the Genetic Algorithm (GA)(Goldberg 1989) based optimization model to come up with optimal monitoring locations. This solution technique will be explained ahead. Designing of an optimal monitoring network mentioned using the above mentioned network design model requires number of steps. The description of the monitoring network design is given as follows. The procedure to design the optimal monitoring network starts with utilizing the contaminant concentrations available with the arbitrary existing monitoring wells. Using this information, the contaminant concentrations at the potential monitoring wells are estimated using the popular geostatistical technique called kriging. The principles of this technique are explained earlier. The problem of uncertainty in the data is addressed by considering the finite number of realizations. Here a realization refers to the scenario of contaminant concentration distribution for a set of random input parameters. Considering the M number of potential monitoring well locations and the N number of realizations , Kriged contaminant concentrations are estimated at ith potential monitoring location and for jth realization. From this value kriged contaminant mass M k ,ij by multiplying the kriged concentration estimate by the effective pore volume of the cell representing the ith potential monitoring location. Effective pore volume is defined as the volume of the cell multiplied by the effective porosity of the subsurface porous medium. The flow and transport simulation model coupling the MODFLOW (Harbaugh et al. 2000) and MT3DMS (Zheng and Wang, 1999) are solved to simulate the contaminant concentrations at the potential monitoring locations. The randomized sets of input data are

utilized to obtain the contaminant plume realizations over the study area. The simulated contaminant mass estimate M s ,ij is calculated in a similar way of calculating the kriged contaminant mass estimate mentioned earlier. The squired terms of the error between these two mass estimates are assigned a weight, which is defined as the deviation of simulated contaminant concentrations from the threshold value. The objective function for the network design model considers the potential monitoring locations where contaminant concentrations exceed the threshold value. Potential locations where the contaminant concentrations are below the threshold concentrations are not of importance and can be neglected from the cluster of potential monitoring locations. The term Pij acts as flag term, such that this term equal to zero when the concentration deviation is equal to or negative and one when the deviation is positive. The network design model addresses the budgetary considerations in terms of maximum number of monitoring wells permitted at a management period. Therefore the objective function of the network design model is solved using GA to identify the optimal monitoring locations from the potential monitoring locations. While solving the objective function, the network design model takes care that the optimal locations are not chosen from the existing monitoring locations. The optimal locations obtained through the solving of network design model are utilized in giving feed back to the source identification model in the process of identifying the unknown pollution sources. The objective function and the principles of source identification model developed as part of this methodology are explained in detail in the following content.

2.2. Source Identification Model Contamination sources are characterized in terms of magnitude, location and duration of the activity. A source identification model is proposed in this methodology to identify the unknown pollution sources. A mathematical model representing the source identification process proposed in the methodology can be given as follows: T

2

O

Minimize:

Csimi , j

Cobsi. j

……………………… (6)

i 1 j 1

Subjected to: Csim i , j = F(S)

……………………… (7)

Where: T = total number of contaminant concentration observation time periods O= Total number of observation locations. Csim i , j = Simulated contaminant concentration at the ith time period, and jth location. Cobsi . j =Observed contaminant concentration at ith time period, and jth location.

F(S) = Representation of simulation model as function of source terms. Simulated contaminant concentrations at any spatial location, for a set of candidate source solutions, S. These values are obtained from the simulation models linked to optimization algorithm. F(S) represents the numerical simulation model. Simulated contaminant

concentrations are function of source terms, which are the decision variables of the source identification model. The above mentioned equality constraint represent the set of binding constraints for the objective function. Therefore the source identification model searches for the simulated concentrations so that the objective function (squared difference between the simulated and observed contaminant concentrations) is minimized at the specified observation locations. The source identification model presented above is solved through the process of linked simulation-optimization approach. The optimization algorithm which solves the above mentioned source identification model needs the simulated contaminant concentrations which will be obtained from a flow and transport simulation model. Therefore the optimization algorithm has to be linked with flow and transport simulation model to evaluate the objective function in searching for the optimal source terms. The concept of linked simulation-optimization model is presented below. 2.3. Linked Simulation-Optimization Model A linked simulation-optimization model is developed for the optimal identification of unknown pollution sources. The process of linking the physical simulation model with an optimization algorithm is computationally rigorous and the most efficient way to deal the groundwater systems. As part of methodology a computer code has been written which links the simulation model and optimization algorithm. Finite difference groundwater flow MODFLOW 2000 (Harbaugh et al. 2000) and contaminant transport model MT3DMS (Zheng and Wang, 1999) have been used as simulation model to simulate the groundwater flow and pollutant transport processes respectively. These numerical models are able to effectively simulate the complex physical and chemical processes in the subsurface system.

For the purpose of optimization process Genetic Algorithm has been used. Genetic Algorithms are probabilistic based optimization algorithms work on the basic principles of survival of the fittest and follow the principle of natural evolutionary process. This algorithm is efficient, robust and chances of getting the global optimal solution are high when compared to the traditional optimization algorithms like gradient based search methods. The optimization process using the Genetic Algorithm starts with initial set of random solutions generally called population. The existing population undergoes three important processes namely selection, crossover, and mutation to generate the child population. This process continues for number of iterative steps namely generations, until the optimal value is reached, or a stopping criterion is satisfied. The fitness function involves the decision variables namely the parameters of interest. In this string decision variables are the pollution source terms. The pollution sources are identified in terms of location, magnitude and duration of the activity. The source identification model is an optimization model which is designed in such a way that the fitness function involving the source terms will be estimated at each generation for all members of the population (solution sets) . Therefore linking of the optimization algorithm based model and the groundwater flow and transport simulation model would ensure that the optimization model can be solved by utilizing the simulation results iteratively. The simulation model in effect represents a set of constraints of the optimization model. Simulating the behavior of the aquifer systems through external linking makes the optimization process computationally feasible. It also allows any sophisticated mathematical simulation model to be linked to the optimization

algorithm based model. So the source identification model is solved utilizing the linked simulation-optimization approach. The process of linking a simulation model with an optimization algorithm is shown Fig-2. 2.4. Feed-Back based Identification process The principle objective of the work is the development of a feedback based methodology to identify the unknown pollution sources. This section will describe how a feedback based source identification methodology can be developed based on the models, simulation tools, solution techniques described earlier. The first step in this methodology is to identify the preliminary source terms based on the available existing arbitrary observed contaminant concentration measurements. Source identification model described in the equation (6) is used to identify the preliminary estimates of source terms. The basic concentration information available with the site will be utilized for the preliminary identification process. Ideally the source terms estimated utilizing this arbitrary information will be poor in quality and the aim of this methodology is that how these preliminary source estimates are improved in a sequential iterative process. The source identification model will be solved using the linked simulation-optimization approach for the preliminary estimates. The simulation model used in this methodology to simulate the spatial and temporal distribution of contaminant concentrations need not be a calibrated and validated because the methodology developed will drive the process in

sequential steps to obtain the simulation model which represents the subsurface system in a more reliable and efficient manner. In the second step the simulation model utilizes the preliminary source estimates to simulate the contamination process. Uncertainty involves with any process can be minimized when there is availability more reliable data. The amount of data and the uncertainty in the system are generally inversely proportional to each other. At the same time acquiring more data in the context of methodology by drilling the number of more wells also an expensive process and budgetary considerations will try to limit that. Therefore there should be process of getting the additional data in an optimal manner considering the budgetary limitations. The source identification process requires the additional observation wells to improve the source estimates from the preliminary ones obtained. So the concept of optimal monitoring network design has been made an integral part of source identification process. The monitoring network design model developed in this methodology will try to come up with optimal observation wells utilizing the initial arbitrary observation data. The network design model also considers the budgetary limitations in the form of maximum number of monitoring wells allowed in a management period. The component of optimal monitoring network will work as the feedback giving system. That means the network design model solves for the additional optimal monitoring wells based on the simulation scenarios derived from the pollution source estimates obtained. When the pollution source terms are to be estimated for a future period of duration T1 years from the time the preliminary source estimates are estimated, the contaminant concentrations are simulated ending T1 years using the contaminant transport

model utilizing the preliminary pollution source terms obtained at time t. The network design model will be solved for the design of optimal monitoring network design for the period starting t and ending T1 years. The additional observation locations obtained for this period will be utilized to estimate the pollution source terms for the same period. It is understood that the monitoring is giving the feedback to the source identification model based on which estimates, the optimal monitoring network is designed. The source identification model solved at this stage shall give the improved pollution source terms from the preliminary estimates because of the more number of observation locations obtained from the monitoring network designed. The same procedure is continued for further time periods and the optimal source estimates shall show the improvement with the progress of time period. The methodology developed will be a useful tool in source zone characterization, which plays vital role in remediation of any contaminated site. The performance evaluation and the application of methodology to a real time contaminated site will be discussed in the further chapters.

3.0. Performance Evaluation Performance Evaluation of the developed methodology has been conducted for a simple hypothetical study area comprising of a portion of an aquifer with homogeneous and isotropic conditions. The size of the study area is 732 x549m2 and is discretized into 91.5m x 91.5 m grids. A constant head boundary condition is specified for East and West sides and no flow boundary condition is specified for the North and South sides. A pond situated inside the study area recharges water in to the aquifer at the rate of 2.15 l/s. The

contaminant of interest in this study area is conservative in nature and the initial concentration of contaminant is zero. There are two potential contaminant sources S1, S2 with possibility of releasing time varying fluxes into the groundwater. One of the two sources is considered as dummy for the identification process, i.e. only one of the two sources is active. The schematic diagram of the hypothetical study area is shown in Fig.3. 3.1. Simulation of Observation Concentrations In order to evaluate the performance of the developed methodology, contaminant concentrations at the observation locations have been simulated using the groundwater flow and transport models. The evaluation of objective function of the source identification model, the observed contaminant concentrations are necessary. Generally contaminant concentrations at observation locations are obtained through field measurements, but in this case for the performance evaluation for the hypothetical study area, observed concentrations are simulated using a numerical model. In this study, finite difference groundwater flow model, MODFLOW (Harbaugh et al. 2000) and the transport model MT3DMS (Zheng and Wang, 1999) are used for simulation of groundwater flow and contaminant transport respectively. It is assumed that the parameters regarding the pollution source and the subsurface hydrogeology are known for the groundwater system shown in the study area. The flow and transport parameters used for the simulation of observation concentrations are tabulated in Table1. In order to simulate the observed contaminant concentrations these known parameter values are given as input to the flow and transport model.

According the methodology the solution results for the source parameters should conform the same source parameters given as input to simulate the observed contaminant concentrations. Among the two potential source locations one is active and the other one is dummy location. Choosing of dummy location makes sure the reliability of the solution results of the source terms. Therefore in this study among S1 and S2, S1 is active and S2 is dummy. The activity of the pollution source S1 is confined to for only five years from the starting. The total simulation period is considered as 10 years and it is divided in to three management periods T1 (between first and sixth year), T2 (between sixth and eighth year) and T3 (between eighth and tenth years). 3.2. Preliminary Identification of Pollution Sources The first step in the feedback based methodology developed in this study is to identify the pollution source terms using the available existing arbitrary observation data. The source identification model is solved using the linked simulation-optimization approach utilizing the initial arbitrary observed contaminant concentration measurements. The source estimates that we obtain at this stage may not represents the actual one because the identification process is based on the limited data which is arbitrary in nature. Therefore in this study the source identification model is solved for the first management period consisting of initial 6 years, using the initial arbitrary locations, I1, I2, and I3. Inorder to assess the performance of model estimated source terms with the actual source terms for a management period, an index called Normalised Error Estimate (Mahar and Datta 2001) is used. Another index called Percent Average Estimation Error (PAEE). The NEE is defined as the ratio of the sum of the differences between the model estimated and actual source

estimates to the sum of actual source terms over all potential source releasing periods at all potential source locations. The PAEE is defined as the ration of the deviation between the actual and estimated fluxes to the actual source fluxes. The NEE estimated for the preliminary source identification is 54.72 percent, which tells that the estimated source terms are far from the actual ones and needs to be improved. The source fluxes for the two sources in the first management period are given in the Table 3.According to the methodology improvement in the source identification process can be achieved by additional observation data comes from sequential designing of optimal monitoring networks. 3.3. Design of Optimal Monitoring Network The basic purpose of designing the optimal monitoring network is to improve the identification of the unknown sources of groundwater pollution in a planned and efficient way. When we come across a situation where limited information about the contamination i.e. limited number of observation locations are available, the optimal monitoring network approach helps us to improve the source identification process, and identify the unknown contaminant sources more reliably. In order to design the monitoring network for the proposed study area it is assumed that there are only three existing arbitrary observation locations available to monitor the groundwater contamination. The source identification model is first solved using data from this initial monitoring network. The solution of the source identification model gives us the source flux terms for the first management time period. The source terms obtained for this

management period are only preliminary.

Therefore, we need to refine the source

identification process by choosing more number of observation locations through development of a newer optimal monitoring network. The solution of the source identification model is again utilized as a feedback to the simulation model to simulate the transport process. The simulation results are then used to design a new optimal monitoring network. For the second management period the source fluxes from sources S1and S2 obtained for the first management period are used to simulate the contaminant concentrations at the end of eight year. The maximum number of monitoring wells permitted in the second management period is specified as three. An optimal monitoring network is designed for the period between sixth and eigth years, using the optimal network design model, which has been discussed earlier. Therefore, total number of observation locations used to identify the optimal source fluxes for the second management period is six. The new optimal contaminant source fluxes are obtained by solving the source identification model utilizing the total six observation locations at the end of 8 years. The optimal source fluxes at the second management period are designated as S12 and S22 for each time step in the 5 years. The resulted source fluxes for this management period are tabulated in Table 4. For the third management period, the optimal source fluxes obtained at the end of 8 years are utilized to simulate the contaminant concentrations at the end of tenth years. In the second management period, the maximum number of monitoring wells is specified also as three.

The new optimal monitoring network for the third management period is designed using the network design model utilizing the already existing six observation locations. The source identification model is then solved to identify the optimal source fluxes at the end of 10 years, utilizing the now existing total nine observation locations. These source fluxes are designated as S13 and S23 for each time step in the 5 years. The estimated source fluxes are compared for two sources S1 and S2 in the figures 5 (a) and 5(b). Mahar and Datta (2001) proposed an embedded approach to solve the pollution source identification problem. In this approach the governing equations of groundwater flow and contaminant transport process are embedded in to optimization model as equality binding constraints. Because of these equality constraints the flow and transport process is simulated by solving the optimization model. The results obtained by the present methodology and the embedded approach are tabulated in Table 5.

4.0. Discussion of the performance evaluation results The iterative feedback response for identification of the unknown contaminant sources is initiated by estimating the preliminary source fluxes using the initial arbitrary observation locations. The preliminary source fluxes are compared with the actual source fluxes at the potential source locations, S1 and S2. The comparison of actual and model estimated source fluxes is carried out by calculating the Normalised Error (Mahar and Datta, 2001) estimates. These errors of estimation can serve as the measure of the methodology performance. The normalized error estimate obtained for this preliminary source flux estimates is 54.97 percent, therefore, there is substantial error is estimating the source

fluxes using the available concentration measurement data from the arbitrary network. This is evident when we compare the estimated source fluxes with the actual ones. The source estimates obtained at the end of first management period, T1 are used as input to the simulation model to simulate the contaminant concentrations over the study area. The direction of the contaminant plume is observed to be moving towards east from west following the head gradient. In order to achieve the improved source estimates achieved at the management period, T1 the additional observation locations are necessary.

The

additional observation locations are chosen by solving an optimal monitoring network design model which utilizes the source estimates obtained in the previous step. The network design attempts to select the optimal observation locations from the available potential observation locations as per the defined objective. For this purpose several potential monitoring locations have been identified over the study area and are shown in Fig.8. Therefore optimal monitoring network has been designed for the period starting from 6th year and ending in 8th year. The source fluxes are estimated at the end of 8th year time period using a total of six observation locations, which includes the first three initial arbitrary locations. The normalised error calculated for the second management period is 19.9 percent. It is considerably less compared to the error estimate obtained for the first time period.

As per the methodology the source estimates should improve with the

increased number of observation locations. This shows that additional observation wells at designed optimal locations can certainly improve the source estimates substantially. The location of the observation locations certainly has a role in source identification process. The design of the optimal monitoring network approach addresses this issue. The

observation wells located in the down gradient of contaminant plume have higher chances of detecting the contaminant plume thereby improving the source estimates. The objective function for the designing of the monitoring network is to minimize the mass estimation error using the designed monitoring network. Therefore, the designed network would try to locate the monitoring wells where the predicted concentrations are generally large, thereby placing wells down gradient of the contaminant plume.

This monitoring locations

observation data should improve the source identification errors. The source estimates obtained for this management period is used in the simulation model as input to simulate the contaminant concentrations at the six observation locations identified at the end of second management period. Applying the same procedure additional three observations locations are located by designing the optimal monitoring network for the period starting from 8th year to 10th year. The source identification model is solved for the optimal source estimates at the end of 10 years. The normalised error calculated at this time period is 11.4 percent. The normalised error estimation has gradually decreased from first management period to the third management period.

It is observed that the sequential process of

designing a monitoring network and using the measurement data in a iterative feedback mode can improve the source identification. The error has decreased from 54.72 % to 11.4 % in three sequential management periods and establishes the principles of the developed methodology.

5.0. Conclusions Performance evaluation of the feedback based methodology developed in this study illustrates the potential applicability of the methodology for identifying the unknown pollution sources in the groundwater aquifers. The developed methodology utilizes the available concentration data from arbitrary monitoring wells located on the site. The network design model presented in the methodology to design the optimal monitoring network incorporates the preliminary source estimates computed by the source identification model. This approach of monitoring network helps the source identification process in giving the feedback information in terms of concentration observation data to the identification model. The designed optimal network improves the initial arbitrary monitoring network in sequential management periods. The performance evaluation clearly showed that the source identification process can be improved by the design and implementation of monitoring network in sequential time steps. The results obtained by using the methodology were compared to the embedded approach proposed by Mahar and Datta(2001) and shows that feedback based methodology performance is efficient. Though the extensive evaluation process of the methodology is not carried out, the methodology can establish the applicability to the real world contaminated site problems. The evaluation has been carried out for a simple and well defined hypothetical steady area which is homogenous and isotropic in nature. But this methodology can be applied to heterogeneous and anisotropic study area as the simulation model utilised in this study for the simulation of groundwater flow and pollutant transport can consider the complex subsurface conditions. Therefore the feedback based linked simulation- optimization source

identification model can be used to identify the unknown pollution sources for any contaminated having the robustness of the simulation model and optimization algorithm implemented in the methodology.

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List of Figures Figure 1. Flow chart for the developed methodology Figure 2. Schematic diagram of the feedback based methodology Figure 3. Illustrative study area chosen for performance evaluation. Figure 4 (a) Massfluxes obtained for the third management period for Source 1 Figure 4 (b) Massfluxes obtained for the third management period for Source 2 Figure 5. Study area showing the observation locations at different management periods Figure 6. Comparison of embedded and the feedback based approach Figure 7. Efficiency comparison of feedback based and embedded approaches

Figure-1. Flow chart for the developed methodology Start

GA parameter initialization

Generate initial population of contaminant source terms

Decoding

Evaluation of objective function

Flow and Transport Simulation Model

Get the simulated contaminant concentrations, Csim i , j

No Is the population is last one

Is the termination condition is satisfied

Estimated optimal source terms

No Selection

Satisfied with Results?

Crossover

Mutation

Stop

Figure 2. Schematic diagram of the feedback based methodology

Start

Read the contaminant concentration values at the available observation locations Ni for the management period Ti Estimate the optimal source terms using the linked simulationoptimization source identification model for Ti

Simulate the contaminant transport process for the management period Ti+1 (Ti+dt) utilizing the source estimates obtained for the T1 period

Design and implement the optimal monitoring network consisting of Ni+1 (Ni+dn) observation locations for the management period T2 using the network design model

Read the observation concentration values at the Ni+1locations and utilize this information as the feedback to the source identification model

Solve the source identification model for the revised source estimates using the Ni+1 observation locations for the period Ti+1

Further refinement of source estimates required?

Stop

Figure 3. Illustrative study area chosen for performance evaluation.

C o n s t a n t H e a d

C o n s t a n t

No Flow Boundary S2 

S1

Pond

pond





H e a d

No Flow Boundary  = Initial Observation well Location  = Pollution Source

Figure 4 (a) Massfluxes obtained for the third management period for Source 1

Figure 4 (b) Massfluxes obtained for the third management period for Source 2

Figure 5. Study area showing the observation locations at different management periods No Flow Boundary

C o n s t a n t H e a d

S2

3

S1

3 1

2 2

Pond

pond

1

3

2

1

C o n s t a n t

H e a st 1 = Monitoring locations for 1 management periodd No Flow Boundary  = Pollution Source

2 = Monitoring locations for 2nd management period 3 = Monitoring locations for 3rd management period

Figure 6. Comparison of embedded and the feedback based approach

Figure 7. Efficiency comparison of feedback based and embedded approaches

List of Tables Table 1(a): Hydrogeological model parameters for the simulation model Table 1(b): Pollution source parameters for the simulation model Table 2. Pollution Source estimates for the first management period Table 3. Pollution Source estimates for the second management period Table 4. Comparison of source estimates obtained during last iteration Table 5. Comparison of feedback based methodology and embedded approach

Table 1(a): Hydrogeological model parameters for the simulation model Sl. No

Model Parameter

Value

1

Horizontal Hydraulic Conductivity(Kxx)

0.0001

2.

Vertical Hydraulic Conductivity(Kyy)

0.0001

3

Porosity of the media

0.2

4

Longitudinal Dispersion

30.5

5

Lateral Dispresion

12.2

6

Length of model grid cell in X Direction (dx)

91.5

7

Length of model grid cell in Y Direction (dx)

91.5

8

Time Step

3

9

Flow Rate from Pond(q)

2.15

Table 1(b): Pollution source parameters for the simulation model Sl. No

Releasing Period

Mass Flux(g/s)

1

Year1

48.8

2

Year2

0

3

Year3

10.0

4

Year4

42.0

5

Year5

36.0

Table 2. Pollution Source estimates for the first management period. Releasing Year Year-1 Year-2 Year-3 Year-4 Year-5

Source Location S1 S2 S1 S2 S1 S2 S1 S2 S1 S2

Model value(g/s) 48.12 15.29 2.34 3.71 7.59 4.18 34.18 12.66 29.73 19.62

Actual Value(g/s) 48.8 0 0 0 10 0 42 0 36 0

Table 3. Pollution Source estimates for the second management period. Releasing Year Year-1 Year-2 Year-3 Year-4 Year-5

Source Location S1 S2 S1 S2 S1 S2 S1 S2 S1 S2

Model value(g/s) 47.70 0.46 2.00 1.80 6.09 3.85 41.35 6.44 34.65 4.64

Actual Value(g/s) 48.8 0 0 0 10 0 42 0 36 0

Table 4. Comparison of source estimates obtained during last iteration.

Releasing Year Year-1 Year-2 Year-3 Year-4 Year-5

Model value(g/s) 48.71 4.61 8.67 40.82 34.09

Actual Value(g/s) 48.8 0 10 42 36

PAEE(%) 0.18 0.00 13.33 2.80 5.31

Table 5. Comparison of feedback based methodology and embedded approach.

Releasing Year Year-1 Year-2 Year-3 Year-4 Year-5

Feedback Based(g/s) 48.71 4.61 8.67 40.82 34.09

Embedded (%) 46.44 0.19 9.16 37.33 38.53

Actual(g/s) 48.8 0 10 42 36