open seminar.pptx

Open Seminar
Presented By:
Prachi Singh
Research Scholar,
Reg. no.:2015RCE07
Supervised By:
Prof. R. M. Singh
CED, MNNIT Allahabad
IDENTIFICATION OF GROUNDWATER POLLUTION
SOURCES AND CHARACTERIZATION OF RELEASE
HISTORY UNCERTAINTY
DEPARTMENT OF CIVIL ENGINEERING
MOTILAL NEHRU NATIONAL INSTITUTE OF TECHNOLOGYALLAHABAD
ALLAHABAD - 211004 (INDIA)
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OUTLINE
 Introduction
 Literature Review
• Literature Gaps
• Objectives
 Methodology
 Performance Evaluation of Developed Methodology
 Conclusions
 Future scope of work
2

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INTRODUCTION
• Groundwater is a highly useful and abundant natural resource.
• Groundwater is vulnerable to pollution and depletion, and needs to be
managed carefully.
• Once groundwater is contaminated, it may be difficult or impossible to clean
up.
• The detection of groundwater contamination is complex phenomenon in
comparison to that of surface water.
3

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• Identification of groundwater pollution sources is essential for simulation of
contaminant transport model.
• Contamination of groundwater may be associated with specific point sources
or non-point source.
• Groundwater contamination is affected by geological controls such as the
degree of confinement of an aquifer, the hydraulic properties of the aquifer
and overlying soil.
4

Literature Review
Peck et al. (1988) classified groundwater models in three categories:
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A. Prediction models
B. Management Models
C. Identification / Evaluation Models

A. PREDICTION MODEL
•These models are based on solution of governing flow
and/or transport equations either analytically or
numerically.
•These models simulate the behavior of the system to
predict the response of the system to various stresses.
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LITERATURE REVIEW
S.
No.
Author and
Year
Review
1 Konikow and
Bredehoeft
(1978)
A computer code was developed for simulating 2D solute transports in
groundwater. It uses an alternating-direction implicit procedure to solve the
finite-difference approximation to the groundwater flow equation, and the
method of characteristics to solve the solute transport equation.
2 Atmadza and
Bagtzoglu
(2001)
A comprehensive review was performed of methods for identifying the
source location and release history, including the optimization approach,
probabilistic and geostastical simulation approach, analytical solution and
regression approach, and direct approach
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S.
No.
Author and Year Review
3 Khalil et al (2005) The SVM was applied surrogates for a relatively complex and
time‐consuming mathematical model to simulate nitrate
concentration in groundwater at specified receptors in Sumas
aquifer, USA. Prediction results showed the ability of learning
machines to build accurate models with strong predictive
capabilities.
4 Leichombam and
Bhattacharjya (2015)
The computational time of model was reduced using approximate
simulation models (ANN). Total 30 wells located in a hypothetical
study area were replaced with 10 wells and simulations were
performed under three different scenarios of management. The
results of study raveled that ANN technique can be utilized for
reducing the computational time, effectively.
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S.
No.
Author and
Year
Review
5 Gurarslan and
Karahan (2015)
Numerical simulations of flow and pollutant transport in
groundwater were carried out using MODFLOW and
MT3DMS software.
6 Leichombam and
Bhattacharjya
(2016)
The linked simulation-optimization approach for efficient
identification of pollutant sources in an aquifer was adopted.
For reducing the computational time of the groundwater flow
and transport processes, ANN model has been used as an
approximate simulator.
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S.
No.
Author and
Year
Review
7 Chen et al
(2016)
Groundwater Modeling System software, which is the
most sophisticated groundwater modeling tool available,
was used to numerically model groundwater flow and
contaminant transport for the Wang-Tien landfill site,
Taiwan.
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B. Groundwater management models
• Utilize the mathematical programming technique while
incorporating management objectives and/or policy constraints.
• The governing equations for groundwater flow and transport can be
used as binding constraints in the management model.
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LITERATURE REVIEW
S.
No.
Author and
Year
Review
1 Aguado and
Remson (1974)
The results suggested that physical behavior of a groundwater system may
be included as an integral part of the optimization model in the embedding
technique.
2 Rosenwald and
Green (1974)
They used response matrix approach for systems involving high non-
linearity, the performance of the response matrix approach was reported to
be unsatisfactory.
3 Gorelick and
Remson (1982)
The response matrix approach was utilized in the pollutant source
management models. They used steady state case for groundwater
management.
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S.
No.
Author and
Year
Review
4 Gorelick (2005) The groundwater management models were classified into
two categories: (i) groundwater hydraulic management
models, and (ii) groundwater policy evaluation and allocation
models.
The results suggested that the numerical difficulties are likely
to arise for large scale problems.
5 Willis and Yeh
(2007)
A comprehensive discussion on groundwater management
models was performed. The limitations and advancement of
models were also discussed.
6 Galeati and
Gambolati (2010)
The response matrix was utilized to develop a management
model. The developed model was applied to assist the design
of the dewatering system for the electronuclear plant to be
built in Trino Vercellese, Italy.
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S. No. Author and Year Review
7 Elango and Rouve
(2017)
Limitations of embedding technique in terms of
handling large number of constraints are
presented.
8 Tung and
Kolterman (2018)
The researchers mentioned about numerical
difficulties of embedding approach for large-
scale groundwater problems with considerable
heterogeneity.
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9 Rogers et al. (2016) The simulated annealing was applied as a search objective
such as cost is mapped onto the energy of the system and
the feasible solutions onto the state of the system
10 Kirkpatric et al. (2017) The results suggested that SA algorithms are generally
useful for solving problems formulated in discrete or
combinatorial form
11 Marryott et al. (2018) The combined SA with a two dimensional flow and
transport simulation model was applied to analyze
alternate design strategies for groundwater remediation at
contaminated field sites. They found that the
computational expense of SA was large yet comparable to
other nonlinear optimization techniques
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S. No. Author and
Year
Review
12 Wagner (1995b) Genetic algorithms can be computationally superior to
classical methods for problems which either can solve
13 Mayer et al.,
2002
The derivative based classical optimization methods
have been criticized with regard to their inability to
handle the non-smooth objective function, local
minima and non-convexity
14 Singh and Datta
(2006)
The research concluded that search algorithm of GA is
in many ways similar to directed random search
procedure. This similarity is very useful in formulating
and solving a linked optimization-simulation model
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16 Ranjithan et al.
(1993)
A neural network based screening tool for identifying
critical realizations was presented from a large set of
hydraulic conductivity realizations. The methodology
used linear programming optimization technique and is
dependent upon sequential calls to the flow and
transport code
17 Rogers and Dowla
(1994)
A simulation model was applied to train an ANN. The
trained network begins a search through pumping
pattern realizations chosen by the genetic algorithm
predicting the outputs
18 Morshed and
Kaluarachchi (1998)
Potential application of ANN and GA for was discussed
for groundwater management.
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19 Rogers et al.
(1995)
The ANN, combined with optimization models was applied for
hypothetical scenarios of one or several contaminant plumes
moving through a ground water region with a number of pumping
wells. The goal of remediation was to find a few optimal pumping
strategies from a vast number of possible pumping strategies, and
to keep contamination concentration in some specified monitoring
wells lower than the regulatory limit.
20 ASCE task
committee
(2000)
The ability of the ANNs to identify a relationship from given
patterns make it possible for the ANNs to solve large scale
complex problems such as pattern recognition, nonlinear modeling,
classification, association, and control.
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C. Identification model
•Useful for identification of parameters, boundary conditions and
input stresses for aquifers.
•Identify unknown sources of groundwater pollution, or estimate
aquifer parameters.
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Groundwater
identification model
Source identification
model
Simultaneous
identification of
source and flow and/or
transport parameters
Uncertainty
characterization in
identification models
Figure: Types of Groundwater identification model

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Source Identification Model

S.
No.
Author
and Year
Review
1 Gorelick et
al. (1983)
The linear programming and multiple regressions were utilized to
estimate the source information. Also, the linear programming method
and multiple regression method were respectively used to minimize the
sum of the absolute errors. The results showed that both methods could
properly identify the source location, although the estimated release
concentration was incorrect in the transient case.
2 Hwang and
Koerner
(1983)
A modified finite element model was applied using limited monitoring
well data to identify the pollution source by minimizing the sum of the
squared errors between the sampling and simulated concentrations.
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S.
No.
Author and
Year
Review
3 Bagtzoglou et al.
(1992)
An approach using particle method was proposed to provide
probabilistic estimates of source location and time history in
heterogeneous site. Their study indicated that the simulation
with a conditional conductivity field performs as well as the
simulation with a perfectly known conductivity field
4 Gorelick et al.
(1993)
Both gradient type and non gradient type method were
employed to estimate the best fit parameters of the release
function.
5 Aral and Guan
(1996)
The genetic algorithm (GA) was proposed to determine the
contaminant source location, leak rate, and release period. The
results obtained from GA agreed with those obtained from
linear and nonlinear programming approaches.
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S. No. Author and
Year
Review
6 Mahar and
Datta (2000)
In this study, the finite difference method was employed to
approximate a two-dimensional groundwater flow and the transport
equation. They formulated the source estimation problem as the
constrained optimization form and solved the objective function by
non-linear programming. This study successfully identified the
source information for the flow in both steady and transient states
7 Aral et al.
(2001)
A new approach called Progressive Genetic Algorithm (PGA) was
proposed. The GA was combined with the groundwater simulation
model for the source identification problem. Their results indicated
that the initial guess does not influence the identified solution.
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8 Singh et al. (2002) The identification of unknown pollution sources using artificial
neural network was performed. A simplified problem by
incorporating observation from a single well location. However,
the results were promising even with large measurement errors.
9 Datta and
Chakrabarty (2003)
The linked optimization-simulation approach was proposed when
the simulation model was assumed to be externally linked to the
optimization model. This approach was found to be capable of
solving very large-scale identification problems
10 Singh et al. (2003) Application of ANN methodology was applied to some more
complex scenarios under varying data availability and
concentration measurements errors

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S. No. Author and
Year
Review
11 Singh et al.
(2004)
Unknown pollution source were identified using an artificial neural
network. They considered simple as well as complex scenarios.
12 Mahinthakumar
and Sayeed
(2005)
A hybrid genetic algorithm-local search (GA-LS) method was
employed to solve the groundwater source identification problem.
GA was first applied to obtain the results which then as the initial
guesses for the local search to obtain the global optimum. The
results indicated that the GA-LS methods are very effective for the
groundwater source identification problem

S.
No.
Author and
Year
Review
13 Sun (2007) A geostatistical approach was proposed for contaminant source
identification in a two-dimensional aquifer where the model
uncertainty is caused by variability in hydraulic conductivity.
14 Zhang et al
(2008)
A methodology was developed for incorporating probabilistic and
fuzzy variables in one framework so as to solve a groundwater flow
PDE (Probability density Equation) with uncertain parameter. This
work provided state of the art knowledge to apply the technique of
hybrid uncertainty propagation through a groundwater model.
15 Bhattacharjya
and Datta
(2009)
ANN-GA based simulation-optimization model for solving coastal
aquifer management model was developed. They have replaced the
numerical groundwater simulation model by an approximate ANN
model. Most of the time, the model obtains the near optimal solution
of the problem.
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S. No. Author and
Year
Review
16 Barnali
(2009)
The support vector machines (SVM) was integrated in a geographic
information system (GIS) for identifying contaminated wells. Results
showed superior performance with the NN as compared to SVM
especially on training data while testing results were comparable.
17 Bashi et al
(2010)
Methodology was proposed for estimating location and amount of
leakage from an unknown pollution source using groundwater quality
monitoring data. The main characteristics of an unknown
groundwater pollution source were estimated using SVM, ANN,
MODFLOW, and MT3D.
17 Sreekanth and
Datta (2011)
The potential applicability of genetic programming (GP) in
groundwater problems as surrogate models was evaluated.
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S. No. Author and
Year
Review
18 Amirabdollahi
an and Datta
(2013)
A comprehensive review on the contaminant source identification
models was presented. An integration of source identification and
monitoring network design is also discussed.
19 Borah and
Bhattacharjya
(2014)
A hybrid optimization approach was presented that initially solves the
problem using ANN-based simulation-optimization model. The
solution obtained by the ANN-based model then used as the initial
solution for the GMS-based model. This approach was
computationally more efficient than the GMS-based approach and
also more accurate than the ANN-based model.
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S. No. Author and
Year
Review
20 Chaubey and
Kashyap (2015)
The simulation model was based upon linked simulation-
optimization approach and invokes a finite difference based
simulator and a Sequential Unconstrained Minimization
Technique (SUMT) based optimizer.
20 Leichombam and
Bhattacharjya
(2016)
Linked simulation-optimization approach was adopted for
efficient identification of pollutant sources in an aquifer. For
reducing the computational time of the groundwater flow and
transport processes, ANN model has been used as an
approximate simulator.
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Simultaneous identification of source and flow
and/or transport parameters

1 Murty and Scott
(1977)
The values of longitudinal and transverse dispersivities were
analyzed. The researchers used interpolation technique to
develop concentration polynomials which were further used
to minimize the observed and calculated concentrations.
2 Umari et al. (1979) The longitudinal and transverse dispersivities were estimated
using an optimization approach. The quasi-linearization
technique was utilized.
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S. No. Author and
Year
Review
3 Kitanidis and
Vomvoris (1983)
Geostatistical approach was applied for estimating
hydrogeologic parameters from input output
measurements.
4 Hoeksema and
Kitanidis (1984)
geostatistical techniques were utilized to solve a two
dimensional steady state flow problem
5 Kuiper (1986) Two geostatistical approaches were discussed for
estimation of hydraulic conductivity in a two
dimensional steady groundwater flow system.
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8 Afrin et al. (1987) The data requirements for groundwater contaminant transport
modeling were discussed and evaluated.
9 Mike et al. (1987) The parameter estimation techniques and their utility for
estimating hydraulic and transport parameters in the
unsaturated zone was evaluated.
10 Peck et al. (1988) Estimation of groundwater flow parameters into three
approaches- direct, indirect, and geostatistical.
In the direct approach, the model parameters are treated as
dependent variables. The unknown aquifer parameters are
estimated by solution of the partial differential equation. Thus,
the direct solution of the inverse problem may be obtained.
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11 Poeter and Hill
(1997)
Requirements and benefits of nonlinear least squares
regression method of inverse modeling for a simple
groundwater flow problem. The literature dealing with
parameter identification in solute transport is sparse. Solute
transport in natural ground-water system is a coupled process,
one that consists of the flow of ground water as well as the
transport of mass.
12 Zimmerman et al.
(1998)
Seven geostatistical based approaches in solving the inverse
problems for estimation of aquifer transmissivity were
analyzed.
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13 Mahar and Datta
(2001)
An optimization model in which the flow and transport
equations are embedded as constraints for simultaneous
estimation of aquifer parameters as well as identification of
unknown pollutant sources was developed. The proposed
methodology performs satisfactorily in identifying the
locations, determining the magnitudes, and specifying duration
of the unknown ground-water pollution sources, even when the
aquifer parameters are unknown.
14 Zheng and Bennett,
2002)
The outcomes suggested that in forward problem, input
parameters are specified and used to calculate model dependent
variables. In inverse problem, field observed values of model
dependent variables are used to derive optimal input
parameters.
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S. No. Author and
Year
Review
15 Jha and Datta
(2013)
An adaptive simulated annealing (ASA)-based solution algorithm
was shown to be computationally efficient for optimal
identification of the source characteristics in terms of execution
time and accuracy. The results suggested that ASA was Faster and
More efficient than GA based solution.
16 Srivastava
and Singh
(2014, 2015)
A methodology for identification of unknown pollution sources
in complex real groundwater problem was presented. In this
study, uniform random generation and Latin hypercube sampling
(LHS) method of random generation are used to generate
source fluxes. These source fluxes are used in groundwater flow
and transport simulation model to generate necessary data for ANN
model building processes. They reported that among two processes,
LHS technique was found more promising.
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S. No. Author and
Year
Review
17 Gurarslan and
Karahan
(2015)
Numerical simulations of flow and pollutant transport in
groundwater were carried out using MODFLOW and MT3DMS
software. The optimization processes were carried out using a
differential evolution algorithm. The performance of the developed
model was tested on two hypothetical aquifer models using real and
noisy observation data
18 Jha and Datta
(2015)
Transport of contaminant in the groundwater was simulated using a
3D transient advective dispersive contaminant transport model.
Adsorption or chemical reaction of the contaminant was not
considered in the contaminant transport model. Adaptive simulated
annealing (ASA) was employed for solving the optimization
problem.
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19 Azghadi et al.
(2016)
MODFLOW and MT3D, groundwater quantity and quality
simulation models, are used to simulate the spatial and
temporal variations of a water quality indicator in groundwater.
Monte Carlo analysis, a regression based optimization approach
was applied. This work presented a new regret-based
optimization model which minimizes the number of monitoring
wells and average regret in estimating undetected polluted area.
20 Ayvaz (2016) Groundwater flow and pollution transport processes were
simulated by modeling the given aquifer system on
MODFLOW and MT3DMS models. The developed simulation
model is then integrated to a newly proposed hybrid
optimization model where a binary genetic algorithm and a
generalized reduced gradient method are mutually used.
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Uncertainty Characterization In
Identification Models

S. No. Author and
Year
Review
1 Sauty (1980) Solute transport modeling showed huge uncertainty due to the
lack of reliable field data. On the other hand, specific field
situations cannot be extrapolated over larger distances, even in
the same site, as suggested by results of this study.
2 Yen et al.
(1986)
The modeling uncertainty were partitioned into 5 parts: (1) the
natural uncertainty caused by the inherent randomness of
natural process; (2) the model uncertainty stemmed from
defective model which is not able to represent the real physical
processes; (3) the uncertainty of model parameter; (4) the
uncertainty derived from observation error; and (5) the
operating uncertainty caused by human factors.
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41
Continued....

3 Gorelick (1987) Monte-carlo approach was utilized for assessing the impact of
spatial variability in hydraulic conductivity upon optimal
groundwater containment capture curve design.
4 Gorelick (1988) Three basic approaches were discussed to treat uncertainties in
groundwater modeling: (i) sensitivity analysis, (ii) monte carlo
analysis, and (iii) stochastic programming.
5 Chan (1994) A partial infeasibility method was proposed for chance
constrained aquifer management to create hydraulic capture
zone to immobilize a plume of contaminants in a confined
aquifer with uncertain hydraulic transmissivity
6 Ganoulis (1996) The probability theory was applied for the characterization of
aleatory uncertainty.
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42
Continued....

S.
No.
Author and
year
Review
7 Moller and beer
(2003)
The parameter uncertainty was classified into three categories –
stochastic, informal and lexical uncertainties. Stochastic uncertainty is
best described by classical probability theory. Informal uncertainty
results from an information deficit, such as when only a small number
of observations are available
8 O’ hagon and
oakley (2004)
The facility with which probality theory effectively captures epistemic
uncertainty was examined.
9 Prasad and
mathur (2007)
A methodology was developed wherein ANN-GA technique is used to
find the uncertainties in output parameters due to imprecision in input
parameters of a groundwater flow and transport simulation model.
Their results show that there is considerable reduction in
computational effort when compared to vertex method.
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Continued....

10 Datta et al. (2009) The results show that the source release history reconstruction
problems are particularly sensitive to hydraulic conductivity
and porosity
11 Jha and datta
(2013)
Three sets of numerical experiments were carried out to study
the effects of uncertainty in the estimation of hydrogeological
parameters. Contaminant concentration observation data were
generated using a distribution of (1) hydraulic conductivity,(2)
porosity, and (3) both.
12 Srivastava and
Singh (2015)
Uncertainty analysis in source identification due to flow
parameter, transport parameter and constant head boundary
estimation was performed using fuzzy vertex alpha cut
techniques.
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Continued....

S.
No.
Author and
Year
Review
13
Azghadi1 et. al.
(2016)
Monte Carlo analysis was used for analysis of uncertainties in both pollution source
characteristics and parameters of groundwater quality simulation model
14 Lin et al (2017)
An approach was presented for obtaining limited sets of realizations of hydraulic
conductivity (K) of multiple aquifers using simulated annealing (SA) simulation and
spatial correlations among aquifers to simulate realizations of hydraulic heads and
quantify their uncertainty in the Pingtung Plain, Taiwan. The high heterogeneity in
vertical hydraulic conductivities suggested imperativeness of uncertainty analysis in
groundwater system simulations.
15
Turnadge et al
(2018)
Sensitivity and uncertainty analysis of a regional-scale groundwater flow model was
performed for Gunnedah basin, Australia. The model parameters to which prediction
sensitivity was tested were the horizontal (KH) and vertical (KV) hydraulic
conductivity and specific storage (SS). The uncertainties in the initial parameters and
model components were reduced progressively through data collection, sensitivity and
uncertainty analysis.
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Research Gaps
• Various approaches based on statistical methods, simulation optimization
techniques, data driven or soft computing techniques etc. have been
utilized by a number of researchers to address the source identification
problem. Each of these methodologies has its advantages and limitations.
• Optimization based methodology using response matrix approach, in
general considers the linearity of the groundwater systems. Gorelick
(1983) concluded that numerical difficulties are likely to arise for large
scale problems using embedding technique. Methods based on embedding
techniques are more computationally intensive and not suitable for very
large problems.
Continued....

7/3/2023 47
Research gaps
• Singh and Datta (2006), Datta et. al (2009) used linked simulation-optimization
methodology to incorporate the simulation model with the optimization
model. The method can be applied to large scale groundwater aquifer system
but their performances are computationally expensive as there requires a large
number of iterations to reach an optimal solution.
• Wagner (1992), Yeh et. al. (2007) etc. applied statistical based approaches to
solve source identification problem. However, the problems considered for
statistical approach are generally of simplified source locations or boundary
conditions. Large dimensions problem with multiple source locations and
observations are difficult to solve using these methods.
Continued....

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Research Gaps
• Some of the researchers also used data driven or soft computing techniques such
as ANN, GA to simulate groundwater flow and transport process in identification
model. Singh and Dutta (2006), Leichombam and Bhattacharjya (2016), used
approximate simulation models to reduce the computational time. However,
incorporation of approximate simulation model needs to be calibrated and
validated on simulated data for a particular scenario. Also, it has been reported
that approximate models show reduced predictive efficiency compared to actual
simulation model.
Continued....

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Research Gaps
•Dimensionality [input] reduction in large groundwater source identification
problems is one of the crucial issues which have not been adequately
addressed in literature. Srivastava and Singh (2014) emphasized their work on
selection of methods used for characterization of inputs for development of
source identification model. However their characterization is limited to
statistical properties of the breakthrough curve. It is imperative to use suitable
breakthrough curve transformation and data mining techniques for
breakthrough curve characterization. Continued....

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Research Gaps
• Several researchers performed both flow and transport modelling without considering
uncertainty characterization in identification of unknown pollution sources (Freeze et
al.1990; Guan and Aral 2004, 2005; Dou et al. 2005; Prasad and Mathur 2007 and
Zhang et al 2008) . In previous literatures, mostly uncertainty in aquifer flow
parameters is discussed. Very few researchers discussed uncertainty in both flow and
transport parameters.
• To address the research gaps, the objectives of the thesis have been prepared.

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Objectives
Prime Objective:
Identification of unknown pollution sources in groundwater system and uncertainty analysis.
Specific Objectives:
1. Development of groundwater simulation model for the contaminated aquifer.
2. Characterization of breakthrough curve using statistical parameters.
3. Characterization of breakthrough curve using multilevel data mining.
4. Development of source identification models for spatially and temporally varying unknown
pollution sources in groundwater using ANN and SVM.
Continued....

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5. Development of multistage identification models for improved identification using ANN
and SVM.
6. Development of models for simultaneous identification of unknown pollution sources
and estimation of flow and transport parameters in groundwater.
7. Uncertainty characterization in developed source identification models due to
uncertainty in flow parameters.
8. Uncertainty characterization in developed source identification models due to
uncertainty in flow and transport parameters.
9. Development of source identification model for multilayer (heterogeneous)
contaminated aquifer using ANN and SVM.
52

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COMPLEXITY OF SOURCE IDENTIFICATION PROBLEM
• Contaminant is observed in arbitrarily located observation wells that are
sparsely distributed limiting the amount of data available for prediction.
• Presence of multiple potential sources with spatial and temporal variation may
create a very complex scenario, and it becomes difficult to identify actual
sources out of large number of potential sources.
• It may not be possible to simulate the groundwater system accurately due to
modeling and measurement errors, uncertainties associated with estimation of
flow and transport parameters, boundary conditions and initial conditions.
• This is an inverse problem, which is generally ill posed and non-unique.
53

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Pollution source
Observation wells
Figure: Modelling components of source
identification problem
54
Legends:

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Methodology
for source
identification
using ANN
model
55

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Methodology
for source
identification
using SVM
model
56

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Methodology
for source
identification
using Hybrid
Model
57

Breakthrough Curve Characterization
Where n = no. of observation wells
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Values
from all
well
locations
ANN/
SVM
CD1(t)
CD2(t)
.
.
Cdi(t)
Ca(t)
C 1(t)
C 1(t)
.
.
C n(t)
Q (i,j,k)
Data
mining
/statistical
characteri
zation
Data
mining
58

7/3/2023 59
Data Mining
Need for data mining
◦ A database/data warehouse may store terabytes of data
◦ Complex data analysis may take a very long time to run on the complete
data set
Data mining
◦ A reduced representation of the data set that is much smaller in volume but
yet produce the same (or almost the same) analytical results.
Data reduction strategies
◦ Data cube aggregation
◦ Attribute Subset Selection
◦ Numerosity reduction — e.g., fit data into models
◦ Dimensionality reduction - Data Compression
◦ Discretization and concept hierarchy generation

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Data Mining: Principal Component Analysis (PCA)
Given N data, find Principal components that can be best used to represent data
Steps
◦ Compute principal components
◦ Each input data is a linear combination of the principal component vectors
◦ The principal components are sorted in order of decreasing “significance” or
strength
◦ Since the components are sorted, the size of the data can be reduced by
eliminating the weak components, i.e., those with low variance. (i.e., using the
strongest principal components, it is possible to reconstruct a good
approximation of the original data)
• Works for numeric data only
• Used for handling sparse data

GROUNDWATER FLOW EQUATION
The groundwater system model MODFLOW solves numerically the 3-D groundwater flow
equation by finite-difference method (Pinder and Bredehoeft, 1968).
𝜕
𝜕x
Kxx
𝜕h
𝜕x
+
𝜕
𝜕y
Kyy
𝜕h
𝜕y
+
𝜕
𝜕x
Kzz
𝜕h
𝜕z
− W = Ss
𝜕h
𝜕t
Where,
x, y, z are Cartesian coordinate axes,
h = Potentiometric head,
Kxx, Kyy, Kzz = Hydraulic conductivities along x, y and z axes,
W = Volumetric flux per unit volume and represents sources and/or sinks of water,
SS = Specific storage of the porous material, and t = Time.
7/3/2023 61

GROUNDWATER TRANSPORT EQUATION
The groundwater contaminant transport model MT3DMS solves numerically the 3-D
groundwater transport equation by finite-difference method (Pinder and Bredehoeft, 1968).
Where,
C = concentration of pollutants dissolved in groundwater, t = time
xi = distance along the respective Cartesian coordinate axis
Dij = hydrodynamic dispersion coefficient tensor
vi = seepage or linear pore water velocity
Cs= concentration of the sources or sinks
= chemical reaction term for each of the N species considered.
  




















 N
k
k
s
s
i
i
j
ij
i
R
C
q
C
v
x
x
C
D
x
t
C
1

7/3/2023


N
k
k
R
1
62

Artificial Neural Networks
7/3/2023
Inputs
Output
An artificial neural network is composed of many artificial neurons that are linked
together according to a specific network architecture. The objective of the neural
network is to transform the inputs into meaningful outputs.
63

7/3/2023 64
Support Vector Machine (SVM)
• Support Vector Machine (SVM) is a supervised machine learning
algorithm which can be used for both classification or regression
challenges.
• Support Vector Machines grew out of the ideas of machine learning
where the final hypothesis is obtained by minimizing the error on the
training data (empirical error) as well minimizing the structural risk, i.e.
the probability of erroneous
Sec. 15.1

7/3/2023 65
Figure: Illustrative representation of SVM
A support vector machine constructs
a hyperplane or set of hyperplanes
in a high- or infinite-dimensional
space, which can be used
for classification, regression, or
other tasks like outliers detection.

Performance Evaluation of
Developed Methodology
7/3/2023 66

7/3/2023 67
Model Performance Assessment and
Evaluation Criteria
S. no. Parameter Equation Source
1 Average percent error
(APE)
𝐴𝑃𝐸 =
𝑖=1
𝑛
(𝑦𝑖
𝑜𝑏𝑠
− 𝑦𝑖
𝑠𝑖𝑚
)
𝑛
∗ 100
Kim et al, 2016
2 Nash-Sutcliffe
efficiency (MENash) MENash
= 1 −
𝑖=1
𝑛
(𝑦𝑖
𝑜𝑏𝑠
− 𝑦𝑖
𝑠𝑖𝑚
)2
𝑖=1
𝑛
(𝑦𝑖
𝑜𝑏𝑠
− 𝑦𝑖
𝑚𝑒𝑎𝑛
)2
Nash and Sutcliffe,
1970
3 Percent Bias
𝑃𝐵𝐼𝐴𝑆 =
𝑖=1
𝑛
(𝑦𝑖
𝑜𝑏𝑠
− 𝑦𝑖
𝑠𝑖𝑚
)∗ 100
𝑖=1
𝑛
𝑦𝑖
𝑜𝑏𝑠
Gupta et al., 1999
4 Root mean square error
𝑅𝑀𝑆𝐸 = 𝑖=1
𝑛
(𝑦𝑖
𝑜𝑏𝑠
− 𝑦𝑖
𝑠𝑖𝑚
)2
𝑛
McKeen et al., 2005
5 Normalized error
𝑁𝐸 =
𝑖=1
𝑛
(𝑦𝑖
𝑜𝑏𝑠
− 𝑦𝑖
𝑠𝑖𝑚
)
𝑖=1
𝑛
𝑦𝑖
𝑜𝑏𝑠
Gupta and Kling,
2011
Where , YI
obs=actual value , Yi
sim = model predicted value.

7/3/2023
Impermeable Boundary
99.58 m 87.72 m
O8
S2 O5 O6 O7
PW
S3 O4 800 m
S1 O2 O3
O1
100 m 88 m
Impermeable Boundary
1300 m
Figure 2. Study Area
Constant
head
(linearly
varying)
Constant
head
(linearly
varying)
Study Area - 1
Figure: Study Area – 1
(Source: Mahar and Datta, 2000)
68
• Confined aquifer
• Area = 1.04 km2 (1.3 km*0.8 km).
• The aquifer is simulated for single layer in the
computational grid.
• Grid size: 8 Rows x 13 columns
• Boundary condition:
North and South as no flow
East and West as constant head

7/3/2023
Table: Source flux at different locations for illustrative study area
Time
Step
Source flux (g/s)
S1 S2 S3
1 47.0 30.0 0.0
2 15.0 58.8 0.0
3 47.0 0.0 0.0
4 0.0 35.0 0.0
• In the aquifer , there are three contaminant sources: S1, S2, and S3.
• The pollution source in terms of magnitude, location, and time period as considered
by the Mahar and Datta (2000) are as follows:
Note: Out of three pollutant sources only two are considered as active, while the other one is taken as inactive.
Source: Mahar and Datta, 2000
69

7/3/2023
A pumping well is located at the centre of the study area and is considered as transient. The
pumping rate assigned for different stress periods are as follows:
Time
step
Discharging rate
(m3/day)
1 273.024
2 163.296
3 327.456
4 163.296
5 273.024
6 327.456
7 163.296
Time
step
Discharging
rate (m3/day)
8 273.024
9 381.024
10 217.728
11 163.296
12 327.456
13 273.024
14 163.296
Time
step
Discharging
rate (m3/day)
15 381.024
16 217.728
17 273.024
18 163.296
19 327.456
20 217.728
- -
Table: Pumping rate of water in pumping location
70

7/3/2023
There are eight observation wells in the aquifer. The flow and transport simulation
are made for five years using 20 stress periods.
Parameter Values
Hydraulic Conductivity Kxx =Kyy 0.0002 m/s
Initial Head 100 m
Effective Porosity (ɳ) 0.25
Longitudinal Dispersivity 40.0 m
Transverse Dispersivity 9.6 m
Specific Storage (S) 0.002
Initial Contaminant Concentration 100 ppm
Table: Different hydrogeological parameter
71

7/3/2023 74
90 Days 180 Days 270 Days 360 Days 450 Days
Contaminant transport at different time steps

7/3/2023 75
Contaminant transport at different time steps

7/3/2023
A total of 250 input-output patterns were generated, of which 175 were used for
training, and 75 were used for testing.
Eleven type of models were generated using ANN for identification.
Three different modelling approaches were opted i.e ANN, SVM and Hybrid (ANN-
SVM) .
Six different standard performance statistics were employed for these model
development. These are root mean square error (RMSE), Nash-Sutcliffe efficiency
(MENash), coefficient of correlation (R), average percentage error (APE), percent bias
(PBIAS), and normalized error (NE)
77
Model Description

7/3/2023 78
Model Description
• Type 1 with twenty temporal simulated concentration as input, twelve source flux
as target values per pattern.
• Type 2, with one characterised input values by using data mining of twenty
temporal concentration values and twelve source flux as target values per pattern.
• Type 3, with five statistical characterised input values viz. average, skewness,
kurtosis, standard deviation, maximum and twelve source flux as target values per
pattern.
• Type 4, with one characterised input values by using data mining of five statistical
characterized values and twelve source flux as target values per pattern.
• Type 5, with eight characterised input values one from each of 8 wells by using
data mining of twenty temporal concentration values and twelve source flux as
target values per pattern.

7/3/2023 79
Model Description
Type 6, with one characterised input values by using data mining of 8 inputs of Type 5 and
twelve source flux as target values per pattern.
Type 7, with eight characterised input values by one from each of 8 wells using data mining
of five statistically characterized values and twelve source flux as target values per pattern.
Type 8, with one characterised input values by using data mining of 8 inputs of Type 7 and
Type 9, with ninety six input values from the predicted source flux from 8 wells from Type 1
and twelve source flux as target values per pattern.
Type 10, with tweleve average value of source flux predicted from Type 1 model as input and
Type 11, with twelve predicted source flux from Type 9 as input and twelve source flux as
target values per pattern.

Table: Model type and Input-output Characterization
7/3/2023
Models No of
models
Input characterization (BTC characterization) Output characterization
Type 1 8 Twenty temporal simulated concentration (no
characterization of BTC)
Magnitude of source fluxes
at S1, S2 and S3 (12
outputs)
Type 2 8 Data mining using factor analysis (FA) of twenty
temporal values (1 inputs in each observation well)
outputs)
Type 3 8 Statistical characterization parameters (5 inputs in
each observation well)
I. Average
II. Skewness
III.Kurtosis
IV.Standard deviation
V. Maximum
outputs)
80

7/3/2023
Models No of
models
Input characterization (BTC characterization) Output
characterization
Type 4 8 Data mining using factor analysis (FA) of five
statistically characterized values (1 inputs in each
observation well)
Magnitude of source
fluxes at S1, S2 and
S3 (12 outputs)
Type 5 1 Eight characterised inputs, one from each of 8 wells
using factor Analysis (FA)
Magnitude of source
S3 (12 outputs)
Type 6 1 Data mining using factor analysis (FA) of eight values
in Type 5 models (1 inputs)
Magnitude of source
fluxes at S1, S2 and S3
(12 outputs)
Type 7 1 Eight characterised input values., one from each of 8
wells using data mining of five statistically
characterized values
Magnitude of source
S3 (12 outputs)
81

7/3/2023 82
Models No of
models
Input characterization (BTC
characterization)
Output
characterization
Type 8 1 Data mining using factor analysis (FA) of
eight values in Type 7 models (1 inputs)
Magnitude of source
S3 (12 outputs)
Type 9 1 Ninety six input values from the predicted
source flux from 8 wells (12 predicted output
from each metamodels) from Type 1 models
Magnitude of source
S3 (12 outputs)
Type 10 1 Twelve average values from ninety six input
values of Type 9 models.
Magnitude of source
S3 (12 outputs)
Type 11 1 Twelve predicted output from type 9 models Magnitude of source
S3 (12 outputs)

7/3/2023
Model Evaluation: ANN models
Errors / Type of model APE (%) Correlation
coefficient
(R)
Normalized
error (NE)
PBIAS (%) MENASH RMSE (%)
Train Test Train Test Train Test Train Test Train Test Train Test
ANN type 1 284.92 454.96 0.879 0.87 0.3 0.3 0.02 0.26 0.61 0.59 1.06 1.07
ANN type 2 450.02 705.31 0.42 0.43 0.47 0.46 0.31 -0.2 0.12 0.12 1.63 1.6
ANN type 3 377.83 644.06 0.75 0.73 0.39 0.39 0.34 -0.3 0.37 0.34 1.37 1.38
ANN type 4 446.12 717.69 0.43 0.437 0.47 0.46 0.112 -0.39 0.12 0.117 1.631 1.6
83

7/3/2023
Errors / Type of
model
APE (%) Correlation
coefficient
(R)
Normalized
error (NE)
ANN type 5 428.15 594.35 0.21 0.23 0.48 0.46 0.19 1.98 0.07 0.08 1.67 1.62
ANN type 6 430.47 618.36 0.27 0.27 0.48 0.47 -0.9 -0.62 0.07 0.08 1.67 1.63
ANN type 7 283.74 434.8 0.67 0.65 0.36 0.35 0.33 0.08 0.46 0.42 1.26 1.28
ANN type 8 413.48 623.72 0.26 0.27 0.47 0.46 0.47 1.24 0.08 0.08 1.66 1.63
84

7/3/2023
Errors / Type of
model
APE (%) Correlation
coefficient
(R)
Normalized
error (NE)
ANN type 9 21.9 84.22 0.99 0.98 0.05 0.08 -0.02 -0.16 0.98 0.97 0.25 0.31
ANN type 10 33.9 118.4 0.98 0.99 0.06 0.06 0.03 -0.18 0.97 0.98 0.29 0.25
ANN type 11 25 89.32 0.99 0.98 0.05 0.08 0.007 -0.02 0.98 0.96 0.26 0.33
85

Model Comparison: ANN vs. SVM
7/3/2023
Errors /
Type of
model
APE (%) Correlation
coefficient
(R)
Normalized
error (NE)
ANN type 1 284.92 454.96 0.879 0.87 0.3 0.3 0.02 0.26 0.61 0.59 1.06 1.07
SVM type 1 185.55 382.07 0.96 0.93 0.16 0.24 -0.03 0.35 0.83 0.72 0.66 0.87
86

Errors /
Type of
model
APE (%) Correlation
coefficient
(R)
Normalised
error (NE)
ANN type 9 21.9 84.22 0.99 0.98 0.05 0.08 -0.02 -0.16 0.98 0.97 0.25 0.31
SVM type 9 4.47 282.31 0.99 0.89 0.01 0.25 7E-11 -0.54 0.99 0.49 0.13 0.88
1 Stage
Hybrid
type 9
18.12 53.19 0.99 0.99 0.03 0.04 -1E-09 -0.02 0.98 0.99 0.21 0.16
Model Comparison: ANN, SVM and Hybrid
7/3/2023 87

Errors / Type of
model
APE (%) Correlation
coefficient
(R)
Normalised
error (NE)
ANN type 10 33.9 118.4 0.98 0.99 0.06 0.06 0.03 -0.18 0.97 0.98 0.29 0.25
SVM type 10 4.71 283.13 0.99 0.89 0.012 0.25 0.0006 -0.55 0.99 0.50 0.13 0.88
1 Stage Hybrid
type 10
23.69 86.99 0.98 0.98 0.05 0.07 1E-06 -0.13 0.98 0.96 0.25 0.30
2 Stage Hybrid
type 10
27.44 85.16 0.98 0.98 0.06 0.07 -0.05 -0.02 0.97 0.97 0.26 0.26
7/3/2023 88

Errors /
Type of
model
APE (%) Correlation
coefficient
(R)
Normalised
error (NE)
ANN type
11
25 89.32 0.99 0.98 0.05 0.08 0.007 -0.02 0.98 0.96 0.26 0.33
SVM type
11
47.54 148.9 0.98 0.96 0.05 0.14 2E-10 0.23 0.97 0.88 0.26 0.51
1 Stage
Hybrid
type 11
31.27 74.47 0.98 0.99 0.05 0.05 5E-10 -0.04 0.97 0.98 0.29 0.20
7/3/2023 89

Models Evaluation
• Model 9 (intermediate model) gave best results for all the three
modelling approach.
• But, the hybrid model utilizing ANN and SVM found to be best
with NE 3% for training sets and 4% for testing set.
7/3/2023 90

7/3/2023 91
0
0
1 4 7 1013161922252831343740434649525558616467707376
Flux
(gm/sec)
No. of datasets
Source-1 observed [90 days] Simulated [90 days]
0
0
1 4 7 1013161922252831343740434649525558616467707376
Flux
(gm/sec)
No. of datasets
Source-1 observed [180] Simulated [180]
0
0
1 4 7 1013161922252831343740434649525558616467707376
Flux
(gm/sec)
No. of datasets
0
0
1 4 7 1013161922252831343740434649525558616467707376
Flux
(gm/sec)
No. of datasets
0
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76
Flux
(gm/sec)
No. of datasets
0
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76
Flux
(gm/sec)
No. of datasets
0
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76
Flux
(gm/sec)
No. of datasets
0
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76
Flux
(gm/sec)
No. of datasets
0
0
1 4 7 10131619222528313437404346495255586164677073767982
Flux
(gm/sec)
No. of datasets
0
0
1 4 7 10131619222528313437404346495255586164677073767982
Flux
(gm/sec)
No. of datasets
0
0
1 4 7 10131619222528313437404346495255586164677073767982
Flux
(gm/sec)
No. of datasets
0
100
0
100
1 4 7 10131619222528313437404346495255586164677073767982
Flux
(gm/sec)
No. of datasets
Graph between observed and simulated datasets

IDENTIFICATION
RESULTS
7/3/2023 92

Comparison of actual and predicted flux
Comparison of actual and predicted source flux for each source at each time
intervals are compared by ANN type 9, SVM type 9 and hybrid (ANN+SVM)
type 9
It is revealed from NE values (21% from ANN model, 36.6% from SVM
Model and 14.1% from hybrid model ) that hybrid type 9 Model (i.e., first
stage generation of source fluxes using ANN and second stage prediction using
SVM) give better results than ANN and SVM models.
7/3/2023 93

7/3/2023
Comparison of actual and
predicted source fluxes for
ANN Model 9
S1(g/s) S2(g/s) S3(g/s) NE
Actual Predi
cted
Actual Predict
ed
Actual Predict
ed
21%
47.00 42.24 30.00 30.16 0 0.701
15.00 17.29 58.80 57.73 0 12.03
37.00 30.73 0 3.556 0 2.725
0 5.584 35.00 35.96 0 6.802
94
Comparison of actual and
predicted source fluxes for
SVM Model 9
Actual Predict
ed
Actual Predic
ted
Actual Predic
ted
36.6%
47.00 43.52 30.00 34.62 0 4.30
15.00 27.04 58.80 38.91 0 0
37.00 32.09 0 4.49 0 2.59
0 3.62 35.00 19.96 0 6.74

7/3/2023
Comparison of actual and predicted source
fluxes for 1 stage Hybrid Model 9
Actual Predicted Actual Predicted Actual Predicted
14.1%
47.00 43.18 30.00 29.33 0 2.116
15.00 17.46 58.80 56.37 0 4.507
37.00 35.65 0 1.365 0 3.957
0 1.693 35.00 31.04 0 3.263
95

Comparison of Actual and Predicted
Concentration
Using type 9 models, the temporal concentration values are
simulated for all 8 observation wells.
 The Actual and predicted concentration are compared for each
observation wells and are graphically represented in fig.
The graphical evaluation of concentration curve reveals that
predicted values are very close to observed values.
7/3/2023 96

0
200
400
600
90 270 450 630 810 990 1170 1350 1530 1710
Concentration
(mg/l)
time (days)
Well 1 ANN actual
SVM HYBRID
0
1000
2000
3000
90
180
270
360
450
540
630
720
810
900
990
1080
1170
1260
1350
1440
1530
1620
1710
1800
Concentration
(mg/l)
time (days)
Well 2
ANN actual
SVM HYBRID
0
500
1000
90 270 450 630 810 990 1170 1350 1530 1710
Concentration
(mg/l)
time (days)
Well 3
ANN actual
SVM HYBRID
0
500
1000
90
180
270
360
450
540
630
720
810
900
990
1080
1170
1260
1350
1440
1530
1620
1710
1800
Concentration
(mg/l) time (days)
Well 4
ANN actual
SVM HYBRID
7/3/2023 97
Concentration curve from different model

0
200
400
600
90 270 450 630 810 990 1170 1350 1530 1710
Concentration
(mg/l)
time (days)
Well 8 ANN actual SVM HYBRID
0
500
1000
90 270 450 630 810 990 1170 1350 1530 1710
Concentration
(mg/l)
time (days)
Well 7
ANN actual
SVM HYBRID
0
500
1000
1500
90
180
270
360
450
540
630
720
810
900
990
1080
1170
1260
1350
1440
1530
1620
1710
1800
Concentration
(mg/l)
time (days)
Well 6 ANN actual
SVM HYBRID
0
1000
2000
3000
90 270 450 630 810 990 1170 1350 1530 1710
Concentration
(mg/l)
time (days)
Well 5 ANN actual
SVM HYBRID
7/3/2023 98

Simultaneous Identification Model
7/3/2023 99
• Simultaneous identification models for identifying unknown sources of
groundwater contamination and for simultaneous estimation of flow
and transport parameters.
• Observed concentration data are used to simultaneously identify
unknown source fluxes causing the contamination and estimate the
parameter values.

Simultaneous Identification
of source flux and flow
parameter
7/3/2023 100
• For simultaneous identification
of source flux and flow
parameters.
• Flow parameter : Hydraulic
conductivity .
Simultaneous Identification of
source flux, flow and transport
parameters
For simultaneous identification of
source flux, flow and transport
parameters.
Flow parameter : Hydraulic
conductivity
Transport Parameters :
 Porosity
 Longitudinal dispersivity
 Transverse dispersivity

Simulation Model with Specified Parameters
Generation of Input Output Patterns with
Simulated Concentration as input , and
corresponding surface flux, flow and / or
Transport Parameter
Development of ANN , SVM, Hybrid Models
Use of Developed Model for Simultaneous Identification
Methodology for Simultaneous Identification

7/3/2023
Simultaneous Identification (Flow) Comparison
Errors / Type
of model
APE (%) Correlation
coefficient (R)
Normalised error
(NE)
ANN type 1 357.56 592.03 0.74 0.68 0.37 0.38 -0.08 -0.95 0.37 0.31 1.39 1.41
SVM type 1 113.99 505.61 0.98 0.54 0.14 0.37 1.1E-08 -2.77 0.9 0.27 0.53 1.45
ANN type 9 92.06 129.49 0.91 0.82 0.15 0.22 0.21 -0.53 0.84 0.69 0.69 0.91
SVM type 9 7.44 136.5 0.99 0.48 0.07 0.32 7.44 1.68 0.97 0.56 0.34 1.46
Hybrid type 9 39.12 117.30 0.97 0.87 0.08 0.16 1.1E-10 -0.099 0.94 0.77 0.35 0.67
ANN type 10 111.98 201.61 0.88 0.83 0.2 0.22 -0.09 -0.7 0.79 0.7 0.77 0.91
SVM type 10 20.67 137.91 0.99 0.62 0.12 0.35 9.93 10.52 0.87 0.51 0.55 1.34
Hybrid type 10 64.57 131.72 0.95 0.85 0.12 0.19 9.4E-11 -0.31 0.9 0.73 0.49 0.77
ANN type 11 77.11 145.61 0.92 0.82 0.15 0.22 -0.12 -0.78 0.85 0.69 0.66 0.93
SVM type 11 7.51 202.66 0.99 0.49 0.07 0.34 7.48 3.73 0.97 0.37 0.34 1.46
Hybrid type 11 77.69 144.37 0.93 0.82 0.13 0.21 1.1E-10 -0.52 0.88 0.69 0.59 0.9
2 Stage Hybrid
type 11
52.09 142.6 0.96 0.87 0.099 0.17 -0.13 -0.15 0.92 0.75 0.43 0.73
102

Models Evaluation
modelling approach.
7/3/2023 103

7/3/2023 104
Parameter or
source
duration and
location
Actual
value
Estimated
value
NE(%)
Kx(=Ky)(m/d) 17.28 18.57
17.04%
S1, T1 47.00 53.17
S1, T2 15.00 14.24
S1, T3 37.00 27.29
S1, T4 0 0
S2, T1 30.00 35.12
S2, T2 58.80 51.74
S2,T3 0 5.38
S2,T4 35.00 30.60
S3,T1 0 0.53
S3,T2 0 1.73
S3,T3 0 10.52
S3,T4 0 2.70
ANN model 9
Parameter or
source
duration and
location
Actual
value
Estimated
value
NE(%)
Kx(=Ky)(m/d) 17.28 17.06
24.09%
S1, T1 47.00 57.73
S1, T2 15.00 34.93
S1, T3 37.00 35.33
S1, T4 0 0
S2, T1 30.00 33.12
S2, T2 58.80 35.12
S2,T3 0 6.73
S2,T4 35.00 30.99
S3,T1 0 11.25
S3,T2 0 0
S3,T3 0 0
S3,T4 0 18.16
SVM model 9
Comparison of actual and predicted parameters from Type 9
Simultaneous identification model

7/3/2023 105
Parameter or
source
duration and
location
Actual
value
Estimated
value
NE(%)
Kx(=Ky)(m/d) 17.28 17.27
11.33%
S1, T1 47.00 44.13
S1, T2 15.00 12.05
S1, T3 37.00 36.26
S1, T4 0 0
S2, T1 30.00 32.76
S2, T2 58.80 57.77
S2,T3 0 0
S2,T4 35.00 31.77
S3,T1 0 12.10
S3,T2 0 12.17
S3,T3 0 10.05
S3,T4 0 0
ANN- SVM
model 9
Comparison of actual
and predicted
parameters from
Hybrid type 9
simultaneous

7/3/2023
Errors / Type
of model
APE (%) Correlation
coefficient (R)
Normalised error
(NE)
ANN type 1 316.91 544.61 0.55 0.46 0.31 0.33 -0.32 -1.57 0.43 0.38 1.38 1.37
SVM type 1 235.70 266.01 0.88 0.52 0.27 0.38 4.15 3.03 0.51 -0.84 1.52 2.58
ANN type 9 57.201 109.18 0.96 0.9 0.11 0.17 0.027 -1.08 0.92 0.8 0.54 0.89
SVM type 9 17.42 18.27 0.97 0.98 0.17 0.18 17.40 17.95 0.78 0.77 1.31 1.28
Hy type 9 44.23 63.17 0.98 0.93 0.06 0.12 1E-09 -0.25 0.97 0.87 0.31 0.57
ANN type 10 103.82 165.45 0.93 0.89 0.14 0.16 -0.05 -0.29 0.87 0.8 0.7 0.81
SVM type 10 46.588 306.702 0.94 0.61 0.11 0.28 1.1E-09 -0.64 0.89 0.137 0.517 1.34
Hy type 10 62.04 93.65 0.96 0.9 0.09 0.15 1E-09 -0.25 0.93 0.82 0.49 0.71
ANN type 11 66.719 125.02 0.95 0.9 0.11 0.17 -0.005 -1.29 0.91 0.8 0.56 0.89
SVM type 11 33.78 38.36 0.97 0.96 0.33 0.38 33.83 38.41 0.03 -0.23 2.86 3.10
Hybrid type 11 56.85 106.3 0.96 0.89 0.11 0.17 1E-09 -1.16 0.92 0.8 0.52 0.89
2 Stage Hybrid
type 11
45.23 105.99 0.98 0.93 0.07 0.12 -0.08 -0.31 0.96 0.87 0.37 0.58
106
Simultaneous identification Model (Flow and Transport) Comparison

Models Evaluation
modelling approach.
7/3/2023 107

7/3/2023 108
Parameter or
source
duration and
location
Actual value Estimated
value
NE(%)
Kx(=Ky)(m/d) 17.28 15.45
23.31%
ε 0.25 0.18
αL 40 35.21
αT 9.6 8.26
S1, T1 47.00 22.18
S1, T2 15.00 28.40
S1, T3 37.00 38.52
S1, T4 0 0
S2, T1 30.00 18.41
S2, T2 58.80 65.81
S2,T3 0 7.16
S2,T4 35.00 46.92
S3,T1 0 13.42
S3,T2 0 10.95
S3,T3 0 19.31
S3,T4 0 18.97
Parameter or
source
duration and
location
value
NE(%)
Kx(=Ky)(m/d) 17.28 17.12
28.14%
ε 0.25 0.2
αL 40 39.63
αT 9.6 9.51
S1, T1 47.00 34.68
S1, T2 15.00 35.21
S1, T3 37.00 35.25
S1, T4 0 35.53
S2, T1 30.00 33.19
S2, T2 58.80 35.04
S2,T3 0 37.31
S2,T4 35.00 33.98
S3,T1 0 33.91
S3,T2 0 32.43
S3,T3 0 36.01
S3,T4 0 36.19
Comparison of actual and predicted parameters from Type 9
Simultaneous identification model

7/3/2023 109
Parameter or
source
duration and
location
value
NE(%)
Kx(=Ky)(m/d) 17.28 17.99
14.53%
ε 0.25 0.23
αL 40 41.28
αT 9.6 10.10
S1, T1 47.00 36.85
S1, T2 15.00 21.80
S1, T3 37.00 28.23
S1, T4 0 0
S2, T1 30.00 24.85
S2, T2 58.80 71.38
S2,T3 0 4.39
S2,T4 35.00 47.50
S3,T1 0 13.32
S3,T2 0 15.10
S3,T3 0 27.1
S3,T4 0 0
ANN model 9
and predicted
parameters from
Hybrid type 9
simultaneous

Uncertainty Analysis
Uncertainty in model parameters is one of the main causes of uncertainty in model
outputs.
In present study, fuzzy alpha-cut (FAC) technique is utilized to handle the uncertainty
of flow and transport parameters in source identification and simultaneous models.
Uncertain parameters are considered to be fuzzy numbers with some membership
functions.

• Figure shows a parameter P
represented as a triangular fuzzy
number with support of A0.
• The wider the support of the
membership function, the higher the
uncertainty.
• The fuzzy set that contains all
elements with a membership of a e
[0,1] and above is called the a-cut of
the membership function.
Figure: Fuzzy number, its support and a-cut
[Source: Schulz & Huwe (1997)]

• For each α -level of the parameter, the minimum and maximum values of the output
are determined.
• This data is then directly used to construct the corresponding fuzziness of the output
which is used as a measure of uncertainty.
• The measure of uncertainty used for the FAC technique is the ratio 0.1-level support
to the value for which the membership function is equal to 1 (Abebe et al., 2000).

113
In the present work, Hybrid type 9 models developed for source identification and
simultaneous identification of sources and parameters are further utilized for
uncertainty characterization.
Two different Scenarios are considered for both source identification and
simultaneous identification model uncertainty i.e. uncertainty in flow parameters
and uncertainty in flow and transport parameters. In every scenario ±50%
uncertainty is considered
Uncertainty in flow parameters: The hydraulic conductivity was considered as
uncertain parameter for uncertainty analysis. The central value of the triangular
fuzzy representation is 17.28 m/day. The specified ranges (8.64-25.92) are upper and
lower values in triangular representation.

114
Uncertainty in flow and transport parameters: The hydraulic conductivity,
porosity, longitudinal and transverse dispersivity was considered as uncertain
parameter. The central value for porosity, longitudinal and transverse dispersivity are
0.25, 40m and 9.6m. The specified ranges for porosity (0.125-0.375), longitudinal
dispersivity (20-60) and transverse dispersivity (4.8-14.4) are upper and lower
values in triangular representation.

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Flux Uncertainty
F1 0.53
F2 0.36
F3 0.97
F4 1.64
F5 0.99
F6 1.81
F7 4.86
F8 55.94
F9 1.54
F10 3.99
F11 0.49
F12 68.90
Avg. Uncertainty
11.84
Flux Uncertainty
F1 1.75
F2 0.29
F3 69.30
F4 1.20
F5 11.96
F6 42.88
F7 3.33
F8 12.83
F9 0.40
F10 1.06
F11 0.74
F12 23.14
Avg. Uncertainty
14.07
Uncertainty Characterization
Table: Uncertainty in model predicted source flux due to
uncertain flow parameters.
Table: Uncertainty in model predicted source flux due to
uncertain flow and transport Parameter

Source Identification
Models for multilayer
contaminated aquifer
7/3/2023 116

Location: longitude 23°2′29′′ N and 23°2′36′′ N and
latitudes 120°16′1′′ E and 120°16′22′′ E
Study Area: Wang-Tien landfill, Tainan City, Taiwan
Area: 750 m north-south and 1000 m east-west
Grid : 75 X 100
Elevation : 8.75 and 25 m AMSL
Vertical Profile:
Depth 37m below ground surface divided into 4
different layers.
Boundary Condition:
East and west as Constant Head
North and south as no flow
7/3/2023 117
(Source: Chen et al., 2016)
Figure: Study Area 2
[Source : USGS]
Figure: Layer details
Study Area 2

7/3/2023 118
Model parameters for flow and
contaminant transport modeling are as
follows:
The monthly variation in recharge in2013
are shown in graph:
Model Parameters Unit Value
Longitudinal dispersivity αL m 2.5
Transverse
dispersivity αTH, αTV
m 0.5
Porosity n For filling material
layer
- 0.35
For layer silty clay 0.28
For layer fine sand 0.3
For layer clayey sand 0.04
Hydraulic Conductivity For
filling material layer
m/s 1.26 × 10−4
For layer silty clay m/s 1.26 × 10−5
For layer fine sand m/s 7.17 × 10−4
For layer clayey sand m/s 7.17 × 10−7
Figure: Transient variation of recharge in 2013
Table: Model Parameters

7/3/2023 119
Borehole No. N1 (m) N2 (m) N3 (m)
N4
(m)
Average
(m)
Date
26-01-2013 1.9 1.706 2.216 2.198 2.005
26-02-2013 1.76 1.986 2.016 2.048 1.9525
26-03-2013 1.27 1.516 1.436 1.518 1.435
26-04-2013 2.19 2.446 2.426 2.358 2.355
27-05-2013 2.76 2.886 2.906 2.908 2.865
26-06-2013 3.16 3.416 3.386 3.288 3.3125
26-07-2013 3.36 3.586 3.566 3.498 3.5025
26-08-2013 3.38 3.786 3.756 3.698 3.655
30-09-2013 4.03 4.286 4.276 4.208 4.2
25-10-2013 2.82 3.346 3.256 3.218 3.16
30-11-2013 2.66 3.046 3.016 2.968 2.9225
24-12-2013 2.545 2.956 2.861 2.813 2.79375
Table: hydraulic head in 2013 from each borehole
Figure: Model with grid details
Time
Step
Source flux (g/s)
S1 S2 S3 S4
1 15.49 21.21 10.60 8.73
2 2.2 1.50 3.20 0.88
Table: Source flux at different locations

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Observed and Simulated head

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1095 Days
180 Days 365 Days 540 Days 730 days 910 days
1277 Days 1460 Days 1642 Days 1825 Days
Contaminant Transport Prediction

7/3/2023 122
2737 Days
3650 Days
Contaminant Transport Prediction

7/3/2023
•A total of 150 input-output patterns were generated, of which 105 were used for training,
and 45 were used for testing.
•Four type of models were generated using three different modelling approaches i.e ANN,
SVM and Hybrid (ANN-SVM) .
•Six different standard performance statistics were employed for these model development.
These are root mean square error (RMSE), Nash-Sutcliffe efficiency (MENash), coefficient
of correlation (R), average percentage error (APE), percent bias (PBIAS), and normalized
error (NE)
124
Model Description

7/3/2023
Models No. of
models
Input characterization (BTC characterization) Output
characterization
Type 1 4 Twenty temporal simulated concentration (no
characterization of BTC)
Magnitude of source
fluxes at S1, S2,S3 and
S4 (8 outputs)
Type 9 1 Thirty two input values from the predicted source flux from 4
wells (8 predicted output from each metamodels) from Type
1 models
Magnitude of source
S4 (8 outputs)
Type 10 1 Eight average values from thirty two input values of Type 9
models.
Magnitude of source
S4 (8 outputs)
Type 11 1 Eight predicted output from type 9 models Magnitude of source
S4 (8 outputs)
125

7/3/2023
Errors / Type
of model
APE (%) Correlation
coefficient (R)
Normalised error
(NE)
ANN type 1 28.36 26.8 0.5 0.85 0.25 0.22 -0.01 0.793 0.25 0.34 2.15 1.99
SVM type 1 27.37 27.82 0.57 0.7 0.24 0.23 0.0615 1.26 0.31 0.3 2.08 2.05
ANN type 9 23.26 22.87 0.56 0.81 0.22 0.2 1.45 4.94 0.4 0.59 1.78 1.85
SVM type 9 20.19 20.77 0.67 0.78 0.16 0.17 0.96 1.83 0.52 0.54 1.81 1.72
Hybrid type 9 18.97 19.08 0.66 0.89 0.15 0.16 1.86 1.15 0.53 0.62 1.86 1.55
ANN type 10 23.66 19.08 0.55 0.86 0.21 0.16 -0.24 -0.094 0.35 0.63 2.01 1.49
SVM type 10 22.98 22.36 0.59 0.78 0.20 0.19 -5E-10 1.14 0.42 0.52 1.91 1.69
Hybrid type 10 24.41 21.11 0.55 0.88 0.22 0.17 -5E-10 0.73 0.37 0.58 1.98 1.6
ANN type 11 25.7 22.37 0.49 0.78 0.23 0.19 0.04 0.5862 0.31 0.51 2.07 1.69
SVM type 11 22.15 22.58 0.63 0.74 0.197 0.19 -6E-08 0.87 0.46 0.51 1.85 1.72
Hybrid type 11 25.25 22.7 0.51 0.77 0.22 0.19 -2E-09 0.52 0.33 0.49 2.04 1.75
2 Stage Hybrid
type 11
23.39 17.69 0.56 0.85 0.21 0.15 0.439 0.89 0.36 0.67 1.99 1.44
126

Models Evaluation
modelling approach.
7/3/2023 127

7/3/2023 128
0
0
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6
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101
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111
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121
126
131
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141
146
151
Flux
(gm/sec)
No. of datasets
Source-1 observed [365 days] Simulated [365]
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21
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36
41
46
51
56
61
66
71
76
81
86
91
96
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106
111
116
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126
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Flux
(gm/sec)
No. of datasets
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0
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46
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56
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71
76
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91
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101
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121
126
131
136
141
146
151
Flux
(gm/sec)
No. of datasets
0
5
0
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1
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21
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36
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56
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66
71
76
81
86
91
96
101
106
111
116
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126
131
136
141
146
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Flux
(gm/sec)
No. of datasets
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0
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26
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61
66
71
76
81
86
91
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101
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111
116
121
126
131
136
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146
151
Flux
(gm/sec)
No. of datasets
0
5
0
5
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
151
Flux
(gm/sec)
No. of datasets
0
0
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
151
Flux
(gm/sec)
No. of datasets
0
0
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
151
Flux
(gm/sec)
No. of datasets
Graph between observed and simulated datasets

7/3/2023 129
Parameter or
source
duration and
location
Actual
value
Estimated
value
NE(%)
S1, T1 15.49 15.36
29.16%
S1, T2 2.2 2.23
S2, T1 21.21 17.39
S2, T2 1.50 2.81
S3,T1 10.60 13.69
S3,T2 3.20 1.816
S4,T1 8.73 16.18
S4,T2 0.88 2.277
ANN model 9
Comparison of actual and predicted source fluxes from Type 9
Model
Parameter or
source
duration and
location
Actual
value
Estimated
value
NE(%)
S1, T1 15.49 18.34
34.79%
S1, T2 2.2 2.79
S2, T1 21.21 13.62
S2, T2 1.50 1.88
S3,T1 10.60 11.58
S3,T2 3.20 1.49
S4,T1 8.73 15.48
S4,T2 0.88 2.24
SVM model 9

7/3/2023 130
and predicted source
fluxes for 1 stage
Hybrid Model 9
Parameter or
source
duration and
location
Actual
value
Estimated
value
NE(%)
S1, T1 15.49 13.98
24.54%
S1, T2 2.2 1.95
S2, T1 21.21 20.27
S2, T2 1.50 2.20
S3,T1 10.60 15.65
S3,T2 3.20 2.27
S4,T1 8.73 13.97
S4,T2 0.88 1.95
Hybrid
(ANN-SVM)
model 9

Comparison of actual and predicted flux
Comparison of actual and predicted source flux for each source at each time
intervals are compared by ANN type 9, SVM type 9 and hybrid (ANN+SVM)
type 9
It is revealed from NE values (29.16% from ANN model, 34.79% from SVM
Model and 25.54% from hybrid model ) that hybrid type 9 Model (i.e., first
stage generation of source fluxes using ANN and second stage prediction using
SVM) give better results than ANN and SVM models.
7/3/2023 131

Comparison of Actual and Predicted
Concentration
Using type 9 models, the temporal concentration values are simulated for all 4
observation wells.
 The Actual and predicted concentration are compared for each observation
wells and are graphically represented in fig.
The graphical evaluation of concentration curve reveals that predicted values
are very close to observed values and able to form same the same pattern.
7/3/2023 132

7/3/2023 133

Conclusions
Different type of BTC characterization techniques have been adopted for source
identification model. Data mining is performed to characterize the BTC to reduce
the total no of inputs for ANN models. Statistical characterization of BTC was
also performed.
Three stage models were developed viz initial models, intermediate model, final
model.
Three different modelling approaches were used viz. ANN models, SVM
models, Hybrid model (utilizing ANN and SVM both).
7/3/2023 134

7/3/2023 135
• For study area 1, 11 type of ANN models, 4 type of SVM models and 4 type of
hybrid models were developed for identification of source flux. And there
performance indices are evaluated, from which type 9 models shows least normalized
Error.
• 4 type of ANN models, SVM models and hybrid models were developed for
simultaneous identification of source flux and flow and/or transport parameters.
Again type 9 model performed best in both cases.
• ANN and SVM both performed well, especially the SVM had very high accuracy for
training data but not for testing. Hybrid models performed comparatively better than
ANN and SVM alone. The NE value was least for Hybrid type 9 models.

7/3/2023 136
• The best type (type 9) of models in every case (source identification and
simultaneous identification) were used to compare the actual source flux and
concentrations at each observation wells using all three approaches (ANN, SVM,
Hybrid). Hybrid model (initial prediction using ANN and Final prediction using
SVM), was found to be best compared to ANN and SVM models in terms of both NE
and graphical representation of concentration curve.
• Different cases of uncertain parameters are considered. Uncertainty characterization
results show that with 50% uncertainty in hydraulic conductivity, average uncertainty
is 11.84. As the number of uncertain parameters increases, uncertainty
characterization become more and more complex. For the most complex case of
uncertainty in four parameters (flow and transport parameters) the uncertainty in
identification was found maximum.

7/3/2023 137
• For study area 2, 4 type of ANN models, SVM models and hybrid models were
developed for identification of source flux. There performance indices shows Hybrid
type 9 (NEtraining= 15% and NEtesting= 16%)again gave the comparative results.
• Type 9 model (ANN, SVM and Hybrid) are used to predict actual flux for the
validation of model. The result shows that the type 9 model can be used in real area
source identification problem as well. Again the hybrid type 9 model (NE=24.54%)
performed better.
• For more realistic area, the performance evaluation of the model shows that the error
increase may be due to the heterogeneity of the aquifer.

7/3/2023 138
Future Scope
• The proposed methodology may be extended for the multiple reactive and
radioactive pollution sources in the real world groundwater aquifer.
• Parameter uncertainties in the flow and transport parameters as extension of the
developed methodologies would be the incorporation of reactive and radioactive
pollutant transport.
• The consideration of economic aspects (e.g. cost of source identification) with
varying number of observation locations may be an interesting extension.
• Finally, this methodology used static monitoring network available in the aquifer.
The methodology can be extended incorporating optimal dynamic monitoring
network design algorithm.

7/3/2023 139
Publications
1. Singh P. and Singh R. M. (2018) “Identification of pollution sources using artificial neural
network (ANN) and multilevel breakthrough curve (BTC) characterization.”
Environmental Forensics, Taylor & Francis. (communicated)
2. Singh P. and Singh R. M. (2017) “Groundwater Contaminant Transport Modelling and
Source Identification Using ANN and Data Mining”. Proceedings of International
Conference on modeling of environmental and water resources systems (ICMEWRS-2017),
March 24 - 26th , 2017, HBTU Kanpur, India. Page 63, ISSN: 978-93-85926-53-2.
3. Singh, P. and Singh R.M., (2016) Groundwater Quality Mapping And Salinity Prediction
In Irrigated Alluvial Plain. 21st International Conference on Hydraulics, Water Resources
and Coastal Engineering (HYDRO-2016), 8th -10th Dec. 2016, CWPRS Pune, India

7/3/2023 140
4. Singh P. and Singh R. M. (2016).,“Geospatial Mapping of Groundwater Quality
Using GIS” Environmental Science and Technology 2016 Vol. 2. American Science
Press, 2016, Houston, USA. (ISBN 978-1-5323-2260-0)
5. Singh P. and Singh R. M. (2016).,“Spatiotemporal Mapping And Prediction of
Groundwater Quality” India Water Week (IWW-2016), Ministry of Water Resources,
Govt. of India, New Delhi, April 4-8, 2016
6. Singh R. M. and Singh P. (2016).,“Groundwater quality mapping and predictions
using geospatial and soft computing techniques” Application of Soft Computing
Techniques in Civil Engineering (ASCTC 2016), Viva Book Publications, ISBN 978-
93-87692-99-2

7/3/2023 142
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