MODELING OF SEASONAL VARIATION OF GROUNDWATER LEVELS USING ARTIFICIAL NEURAL NETWORK – A CASE STUDY (APO/GUDU)
METROPOLIS, ABUJA
CHUKWUEMEKA WILLIAMS ATUMA
BU/18A/3000/ENG
Department of Civil Engineering
Baze University
Abuja, Nigeria
July 2021
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Appendix II
DECLARATION
BAZE UNIVERSITY
DEPARTMENT OF CIVIL ENGINEERING
I, Chukwuemeka Williams Atuma, confirm that this report and the work presented in it are my own achievement.
I have read and do understand the penalties associated with plagiarism.
Signed: .......................................................
Date: ...........................................................
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CERTIFICATION
This is to certify that this thesis is fully adequate in scope and quality as an undergraduate project work for the award of degree of Bachelor of Engineering in Civil Engineering.
----------------------------------------------------- ------------------ Name and Signature of First Supervisor Date
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Name and Signature of Second Supervisor (if applicable) Date
This is to certify that this thesis satisfies the requirements as a graduation project for the award of degree of Bachelor of Engineering in ------------------- Engineering.
----------------------------------------------------- ------------------ Name and Signature of H.O.D, Date Department of -----------------
Engineering
Endorsement of External Examiner:
This is to confirm that this thesis satisfies the requirements as a graduation project for the award of degree of Bachelor of Engineering in -------------------- Engineering.
----------------------------------------------------- ------------------ Name and Signature of External Examiner Date
Approval of the Faculty of Engineering:
----------------------------------------------------- ------------------ Name and Signature of Dean, Date Faculty of Engineering
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Dedication
I dedicate this project to God Almighty my creator, my stronghold, alpha, and omega. He has been
my guidance and my source of strength, wisdom, and understanding. Without him, I would not be
able to carry this project out. I would also like to dedicate the thesis to my Family. Without their
unconditional love and guidance over me, I would not have been able to complete my studies and see
this project through.
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Acknowledgment
I want to thank my family and companions who helped me a great deal in concluding this venture
during the restricted period.
To my father who has been the stronghold of the family, thank you for seeing me through these years,
your guidance and faith in me made me who I am today.
To my mother who never lets me go astray and reminds me where I come from, thank you for all the
love and advice given unto me.
To Victoria and Joshua thank you for being there for me and make living at home pleasant and
enjoyable to live in.
To my friends our countless study sessions will never go in vain, thank you for being such kind souls
to me and helping me when times get rough, we always found a way.
I want to send my extraordinary thanks of appreciation to my instructor Dr. Sani Isah Abba and also
the head of the department Dr. Rotimi who offered me the brilliant chance to do this great undertaking
on the subject Modeling of Seasonal Variation of Groundwater Levels Using Artificial Neural
Network – A Case Study (Apo/Gudu) Metropolis, Abuja, which likewise assisted me with lotting of
Research and I came to think about such countless new things I am truly grateful to them.
Thank you all. My love for you all can never be quantified. God bless you all.
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ABSTRACT
Artificial Neural Networks (ANNs) have been successfully used for predicting and modeling
groundwater levels for a good period. In this paper, I use Artificial Neural Network (ANN) and Multi-
Linear Regression (MLR) to model groundwater levels in Abuja, Nigeria using Apo-Gudu as a case
study. After setting the models with the various parameters that affect groundwater level in Abuja, the
developed ANN and MLR should be able to produce near accurate predictions of the groundwater
level variations using just the input variables that have been identified as maximum and minimum
temperature, rainfall, relative humidity, and wind speed. To accomplish this, the models are first
aligned on a preparation dataset to perform as they should as neural networks to forecasts future
groundwater levels utilizing past noticed groundwater levels and outside inputs. Reproductions are
then delivered on another informational index by iteratively taking care of back the anticipated
ground-water levels, alongside genuine outer information. The outcomes show that the created ANN
and MLR can precisely imitate groundwater levels and accurately model them. With the results
obtained a comparison will be made of which neural network is more accurate. The examination
proposes that such tools can be utilized as a suitable option in contrast to physical-based models to
recreate the reactions of the seasons under conceivable future situations or to remake extensive
stretches of missing perceptions gave past information to the impacting factors is accessible.
VII
Table of Contents CHAPTER ONE ......................................................................................................................................................1
INTRODUCTION ...................................................................................................................................................1
1.1 Background of the Study .....................................................................................................................1
1.2 Statement of the Problem ...................................................................................................................3
1.3 Objectives of the Study .......................................................................................................................4
1.4 Research Questions .............................................................................................................................4
1.5 Significance of the Study .....................................................................................................................4
1.6 Scope of the Study ...............................................................................................................................5
1.7 Limitations of the study .......................................................................................................................5
1.8 Definition of Terms ..............................................................................................................................6
CHAPTER TWO .....................................................................................................................................................7
LITERATURE REVIEW ...........................................................................................................................................7
2.1 Introduction .........................................................................................................................................7
2.2 CONCEPTUAL FRAMEWORK ................................................................................................................7
2.3 Concept of Aquifers ...................................................................................................................................9
2.3.1 Type of aquifers ......................................................................................................................................9
2.3.2 Aquifers Chemical characteristics of groundwater ............................................................................. 10
2.4 Spatial and Seasonal Variation in Groundwater Quality .................................................................. 11
2.5 Application of Artificial Neural Network in GWL .................................................................................... 12
CHAPTER 3 ........................................................................................................................................................ 15
REVIEW OF ARTIFICIAL NEURAL NETWORK AND MULTILINEAR REGRESSION ANALYSIS ................................ 15
3.1 Artificial Neural Network (ANN) ............................................................................................................. 15
3.2 Network Training of ANN ....................................................................................................................... 16
3.3 Process of Learning................................................................................................................................. 17
3.4 Standard of Learning .............................................................................................................................. 17
3.5 Training algorithm .................................................................................................................................. 18
3.6 Learning algorithm ................................................................................................................................. 19
3.7 The Design of neural network ................................................................................................................ 20
3.8 Properties of Neural Networks ............................................................................................................... 23
3.8.1 Input layer ....................................................................................................................................... 23
3.8.2 Output layer .................................................................................................................................... 23
3.8.3 Hidden layer .................................................................................................................................... 23
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3.9 Model development ......................................................................................................................... 24
3.9.1 Data standardization ................................................................................................................ 24
3.9.2 Performance criteria of the model ........................................................................................... 25
3.10 Multi Linear Regression Analysis (MLR) ............................................................................................... 26
CHAPTER FOUR ................................................................................................................................................. 29
RESULTS AND DISCUSSION ............................................................................................................................... 29
4.0 Data Processing and Pre-analysis ........................................................................................................... 29
4.1 Results of ANN, and MLR models ........................................................................................................... 32
CHAPTER FIVE ................................................................................................................................................... 49
SUMMARY, CONCLUSION AND RECOMMENDATIONS .................................................................................... 49
5.1 SUMMARY OF FINDINGS .................................................................................................................. 49
5.2 CONCLUSION .................................................................................................................................... 49
5.3 RECOMMENDATION ......................................................................................................................... 50
References ........................................................................................................................................................ 51
1
CHAPTER ONE
INTRODUCTION 1.1 Background of the Study
Water is a universal solvent and natural resource tapped by man, animals, and plants to meet their
need on the earth, either in vapor, liquid, or solid form. Water is one of the essential compounds for
all forms of plants and animals, thus its pollution is generally considered more important than soil.
Studies show that about 80% of communicable diseases are either water-borne or water-related. Water
is an indispensable resource for the existence of man, animals, and plants. Demand for groundwater
has been on the increase due to rapid growth in population as well as the accelerated pace of
industrialization and urbanization in the last few decades especially in developing countries like
Nigeria (Abimbola, A. P. and Odukoya, Abiodun M. and Olatunji, 2012). The inadequate supply of
pipe-borne water and the paucity of surface water has led to an increase in demand for groundwater
in Abuja. People around the world have used groundwater as a source of drinking water and even
today more than half the world’s population depends on groundwater for survival.
Groundwater has long been considered as one of the purest forms of water available in nature and
meets the overall demand for rural and semi-rural people (Amadi et al., 2012). The increase in
groundwater demand for various human activities has placed great importance on water science and
management practice worldwide. (UNESCO, 2003) estimates that globally, groundwater provides
about 50% of current potable water supplies, 40% of the demand of the self-supplied industry, and
20% of water use in irrigated agriculture. Over much of Africa, groundwater is the most realistic water
supply option for meeting water demand.
However, increasing demand and withdrawal, significant changes in land-use patterns, vast industrial
and agricultural effluents entering the hydrological cycle as well as seasonal variation, affect the
quality and quantity of groundwater (O. M. Idoko, 2010). The determination of groundwater quality
for human consumption is important for the wellbeing of the ever-increasing population. Groundwater
quality depends, to some extent, on its chemical composition (Al-Ariqi & Ghaleb, 2010; M. Idoko &
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Oklo, 2012) which may be affected by natural and anthropogenic factors. Changes in groundwater
recharge, due to seasonal variation, also affect the concentration of the water parameters. Rapid
urbanization, especially in developing countries like Nigeria, has affected the availability and quality
of groundwater due to waste and effluent disposal practices, especially in urban areas. Once
groundwater is contaminated, its quality cannot be restored by just stopping the pollutants from the
source, this is because groundwater contamination may continue years after the waste source is in
place (Ramakrishnaiah et al., 2009; Water & For, 2012).
As groundwater has a huge potential to ensure the supply of future demand for water, it is important
that human activities on the surface do not negatively affect the precious resource. Agricultural
activities, especially abattoir operations, produce a characteristic highly organic waste with relatively
high levels of suspended solid, liquid, and fat. The improper disposal of these wastes onto lands and
into water bodies leads to the contamination of the environment, one of which is the impairment of
water quality (Abdul-Gafar, 2016). There is a high possibility that the effluents from the abattoir will
percolate into the ground and pollute the groundwater. This study, therefore, seeks to determine the
extent of pollution of the groundwater from the abattoir effluents through the qualitative analysis of
groundwater samples taken from different existing wells at various distances from the abattoir. It also
evaluates the influence of seasonal variation on the concentrations of the parameters.
The groundwater level is a key parameter for evaluating spatial and temporal changes in groundwater
environments (Iwasaki et al., 2013). The groundwater level is governed by various factors. Climate
change, as reflected in precipitation and evaporation rates, influences the groundwater level
fluctuation. (Z. Chen et al., 2002). (Z. Chen et al., 2004) also found that climate trends have high
correlations with groundwater level variations in southern Manitoba (Z. Chen et al., 2004). In plain
areas, precipitation infiltration and evapotranspiration in the vertical direction are the major recharge
and discharge processes of the water cycle. In the study area, most of the rainfall falls between July
and October. Seasonal variation in climate is obvious. So, the focus is on the influence of short-term
seasonal variation in climate on groundwater level in this place. The impact of climate variability on
groundwater levels can be investigated by analyzing the relationship between climate records and
groundwater level fluctuations. Hence, the study aims to investigate the modeling of seasonal
variation of groundwater levels using artificial neural networks across Abuja using Apo and Gudu
District of Abuja metropolis as a case study.
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1.2 Statement of the Problem
Abuja is underlain by crystalline basement rocks with rocks that include different textures
of granites, coarse to fine, consisting essentially of biotite, feldspars, and quartz. In most cases, the
rock has weathered into reddish micaceous sandy clay to clay materials capped by laterites. Generally,
only a small amount of water can be obtained in the freshly un-weathered bedrock below the
weathered layers. Groundwater is found mainly in the variable weathered/transition zone and in
fractures, joints, and cracks of the crystalline basement. Fissure systems in Nigeria rarely extend
beyond 50m, as evidenced by the available drilling data. The local water table depth is controlled by
textural and compositional changes within the regolith vertical profile and the bedrock topography.
However, the poor management of waste arising from industrialization and urbanization has led to
contamination of groundwater hence the need for the present study. It, therefore, becomes imperative
to evaluate the quality of groundwater from shallow aquifers in Abuja, to prevent the occurrence of
water-borne diseases such as typhoid, cholera, diarrhea, and dysentery as well as cancer-related
diseases due to contamination by heavy metals.
Figure 1.1: Aerial map of the specified location.
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1.3 Objectives of the Study
The main objective of this study is to examine the high-resolution spatial modeling of seasonal
variation of groundwater levels across Abuja using the Apo-Gudu metropolis as a case study.
The specific objectives include;
i. To perform the sensitivity analysis to determine the most dominant GW parameters.
ii. To determine the performance of ANN and MLR model in modeling GWL
iii. To develop an independent model for the prediction of GWL at APO/GUDU
iv. To detect the dynamic of GWL in both wet and dry season
v. To compare the performance linear model (MLR) and Nonlinear model (ANN) for the
simulation of GWL
1.4 Research Questions
i. What are the dynamics of groundwater level and salinity in the wet and dry seasons?
ii. Is there any relationship between the groundwater level, maximum and minimum
temperature, rainfall, relative humidity, wind speed in the Apo and Gudu metropolis in
Abuja?
iii. What is the relationship between the geophysical survey on Apo-Gudu metropolis and its
results with drilling data for better resistivity interpretations for productive and effective
borehole construction?
1.5 Significance of the Study
This study will benefit the management of groundwater level companies in Nigeria, especially in the
Abuja metropolis to understand the importance of using artificial intelligence such as artificial neural
networks in modeling seasonal variation of groundwater levels in Nigeria.
This study will be of immense benefit to other researchers who intend to know more about this study
and can also be used by non-researchers to build more on their research work. This study contributes
to knowledge and could serve as a guide for another study.
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1.6 Scope of the Study This study is on the modeling of seasonal variation of groundwater levels using an artificial neural
network across Abuja using Apo and Gudu metropolis as a case study.
Gudu is an established district in phase 2 of Abuja city. It is also sometimes known as Apo-Gudu. The
district occupies a strategic location just outside Abuja’s city center. Gudu is residential but has quite
an extensive commercial part to it. Although well-populated it is not as dense or as busy as
neighboring areas like Garki. Gudu sits close to Garki in the north, Guzape in the northeast, Apo
Dutse in the southeast, Gaduwa in the southwest, and Durumi to the west.
Being a developed neighborhood, the infrastructure is good. The road network is extensive, giving
easy access to most parts of the Abuja metropolis. The main roads are Oladipo Diya Street, Ahmadu
Bello Way, and the Nnamdi Azikiwe Expressway. An excellent location (away from the hustle and
bustle of the inner city) and a high level of development have attracted many people to the
neighborhood. Residents include civil servants, politicians, traders, and other middle-class citizens.
The research study will cover the Apo/Gudu metropolises in Abuja.
1.7 Limitations of the study The demanding schedule of respondents at work made it very difficult to get the respondents to
participate in the survey. As a result, retrieving copies of a questionnaire in a timely fashion was very
challenging. Also, the researcher is a student and therefore has limited time as well as resources in
covering extensive literature available in conducting this research.
Financial constraint: Insufficient fund tends to impede the efficiency of the researcher in sourcing
for the relevant materials, literature, or information and in the process of data collection (internet,
questionnaire, and interview).
Time constraint: The researcher will simultaneously engage in this study with other academic work.
This consequently will cut down on the time devoted to the research work.
Information provided by the researcher may not hold true for all businesses or organizations but is
restricted to the selected organization used as a study in this research especially in the locality where
this study is being conducted. Finally, the researcher is restricted only to the evidence provided by the
participants in the research and therefore cannot determine the reliability and accuracy of the
information provided.
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1.8 Definition of Terms
Artificial Neural Network: An artificial neural network (ANN) is the piece of a figuring framework
intended to mimic the manner in which the human mind investigates and
measures data. It is the establishment of man-made reasoning (AI) and tackles
issues that would demonstrate outlandish or troublesome by human or factual
guidelines.
Modeling: Modeling involves making a representation of something.
Seasonal Variation: Seasonal variation is variation in a time series within one year that is repeated
more or less regularly. The seasonal variation may be caused by the
temperature, rainfall, public holidays, cycles of seasons, or holidays.
Groundwater: Groundwater is water that exists underground in saturated zones beneath the
land surface. The upper surface of the saturated zone is called the water table.
It fills the pores and fractures in underground materials such as sand, gravel,
and other rock, much the same way that water fills a sponge.
Metropolis: An urban area that has a name, defined boundaries, and local government, and
that is larger than a village and generally smaller than a city.
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CHAPTER TWO
LITERATURE REVIEW 2.1 Introduction This chapter tries to present a brief continuation of research findings related to the modeling of
seasonal variation of groundwater levels using artificial neural networks across Abuja, Apo-Gudu
metropolis. In the present context, the interest of the researcher is to review the findings of past
research. The previous research helps the researchers to theorize and assume occurrence and do critical
appraisal which may contribute regarding design appropriate methodology. Keeping in mind these
objectives, the researcher reviewed the literature to obtain information and the status of work being
done in this area. Therefore, literature from various sources was extensively reviewed in the light of
the present investigation.
2.2 CONCEPTUAL FRAMEWORK
Groundwater accounts for about 98% of the world’s fresh water and it is fairly well distributed
throughout the world (Bouwer, 2002). The exploration and exploitation of groundwater as a major
resource to meet the growing population in some urban cities in Nigeria located on basement complex
rocks has been a subject of discussion (Woakes, M, Rahaman, M.A. and Ajibade, 2013). Those works
involved a combination of hydrogeological and geoelectrical parameters to delineate aquifer
characteristics in the Nigerian crystalline basement rocks in Akure, Gusa, and Lokoja. However, this
work is concerned with the exploration and exploitation of groundwater resources in the basement
complex terrain in parts of Abuja, northcentral, Nigeria. Abuja, the Federal Capital Territory of
Nigeria, has witnessed exponential growth in physical infrastructures and human development. The
major surface water scheme in use within the city has been the ‘Lower Usman Dam’. A smaller dam
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built at the Apo-Gudu metropolis serves its immediate community also within the territory. Another
dam, the ‘Gurara Dam’, constructed from a distance of about 56 km from the metropolis has been
reticulated to serve the city. In the meantime, government, private establishments, and individuals
have had to drill boreholes to supplement discharge from the dam for both domestic and industrial
uses.
Groundwater may be defined as the subsurface water in soils and rocks that are fully saturated. Due
to precipitation surplus, part of the infiltrated rainwater flows through the soil and reaches the
saturated zone, where it becomes groundwater (Ward R.C. & Robinson M., 2012). The increasing
demands for freshwater, on the one hand, and the decrease in availability, on the other, have become
matters of serious concern. In general, fresh groundwater flows in the direction of the lowest
groundwater heads, usually the lower elements in the landscape, where it finally exfiltrates as surface
water. The flow speed depends on the gradient (slope) in the groundwater table and the permeability
of the soil.
Groundwater is the water present beneath Earth's surface in soil pore spaces and in
the fractures of rock formations. A unit of rock or an unconsolidated deposit is called an aquifer when
it can yield a usable quantity of water. The depth at which soil pore spaces or fractures and voids in
rock become completely saturated with water is called the water table. Groundwater is recharged from
the surface; it may discharge from the surface naturally at aquifers and seeps and can
form oases or wetlands. Groundwater is also often withdrawn for agricultural, municipal,
and industrial use by constructing and operating extraction wells. The study of the distribution and
movement of groundwater is hydrogeology, also called groundwater hydrology.
Typically, groundwater is thought of like water flowing through shallow aquifers, but, in the technical
sense, it can also contain soil moisture, permafrost (frozen soil), immobile water in very low
permeability bedrock, and deep geothermal or oil formation water. Groundwater is hypothesized to
provide lubrication that can possibly influence the movement of faults. It is likely that much of Earth's
subsurface contains some water, which may be mixed with other fluids in some instances.
Groundwater may not be confined only to Earth. The formation of some of the landforms observed
on Mars may have been influenced by groundwater. There is also evidence that liquid water may also
exist in the subsurface of Jupiter's moon Europa Richard Greenburg ( 2015).
Groundwater is often cheaper, more convenient, and less vulnerable to pollution than surface water.
Therefore, it is commonly used for public water supplies. For example, groundwater provides the
9
largest source of usable water storage in the United States, and California annually withdraws the
largest amount of groundwater of all the states (Geographic, 2013). Underground reservoirs contain
far more water than the capacity of all surface reservoirs and lakes in the US, including the Great
Lakes. Many municipal water supplies are derived solely from groundwater (National Geographic,
2015).
The use of groundwater has related environmental issues. For example, polluted groundwater is less
visible and more difficult to clean up than pollution in rivers and lakes. Groundwater pollution most
often results from improper disposal of wastes on land. Major sources include industrial and
household chemicals and garbage landfills, excessive fertilizers and pesticides used in agriculture,
industrial waste lagoons, tailings and process wastewater from mines, industrial fracking, oil field
brine pits, leaking underground oil storage tanks and pipelines, sewage sludge, and septic systems.
Additionally, groundwater is susceptible to saltwater intrusion in coastal areas and can cause land
subsidence when extracted unsustainably, leading to sinking cities (like Bangkok)) and loss in
elevation (such as the multiple meters lost in the Central Valley of California). These issues are made
more complicated by sea-level rise and other changes caused by climate changes which will change
precipitation and water scarcity globally.
2.3 Concept of Aquifers
An aquifer is an assortment of permeable stone or residue filled with groundwater. Groundwater enters
the aquifer as precipitation leaks through the earth’s surface. It can travel through the aquifer and
reemerge through aquifers and wells.
2.3.1 Type of aquifers
There are two general sorts of aquifers: confined and unconfined. Confined aquifers have a layer of
impervious stone or earth above them, while unconfined aquifers lie under a porous layer of soil. A
typical confusion about aquifers is that they are underground waterways or lakes. While groundwater
can saturate or out of aquifers because of its permeable nature, it cannot move adequately quickly to
stream like a waterway. The rate at which groundwater travels through an aquifer fluctuates relying
upon the rocks' porousness. A large part of the water we use for homegrown, modern, or agrarian
intentions is groundwater. Most groundwater, including a lot of our drinking water, comes from
10
aquifers. To get to this water, a well should be made by boring an opening that arrives at the spring.
While wells are synthetic purposes of release for aquifers, they additionally release normally at
aquifers and in wetlands.
Aquifers normally channel groundwater by constraining it to go through little pores and between silt,
which assists with eliminating substances from the water. This characteristic filtration measure, in any
case, may not be sufficient to eliminate the entirety of the impurities.
2.3.2 Aquifers Chemical characteristics of groundwater
Since groundwater often occurs in association with geological materials containing soluble minerals,
higher concentrations of dissolved salts are normally expected in groundwater relative to surface
water. The type and concentration of salts depend on the geological environment and the source and
movement of the water. A simple hydro-chemical classification divides groundwater into meteoric,
connate, and juvenile. Meteoric groundwater, easily the most important, is derived from rainfall and
infiltration within the normal hydrological cycle and is subjected to the type of hydro-chemical
evolution. Groundwater originating as seawater that has been entrapped in the pores of marine
sediments since their time of deposition is generally referred to as connate water. The term has usually
been applied to saline water encountered at great depths in old sedimentary formations. It is now
accepted that meteoric groundwater can eventually become equally saline, and that entrapped
seawater can become modified and moved from its original place of entrapment. It is doubtful whether
groundwater exists that meets the original definition of connate water, and the non-generic term
formation water is preferred by many authors. Connate Water is, perhaps, useful to describe
groundwater that has been removed from atmospheric circulation for a significant period of geological
time. Formation waters are not usually developed for water supplies because of their high salinity.
However, they may become involved in the assessment of saline intrusions caused by the over-
pumping of overlying aquifers.
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Figure 2.1
Generalized distribution of hydrocarbon phases down a groundwater gradient following a surface
spillage.
Juvenile groundwater describes the relatively small amounts of water which have not previously been
involved in the circulating system of the hydrological cycle but are derived from igneous processes
within the earth. However, juvenile groundwater often cannot be distinguished geochemically from
meteoric groundwater that has circulated to great depths and becomes involved in igneous processes.
True juvenile waters unmixed with meteoric water are rare and of a very localized extent and are not
normally associated with the development and assessment of fresh groundwater resources.
2.4 Spatial and Seasonal Variation in Groundwater Quality
Knowledge of hydrological processes (change of groundwater level, groundwater quality, and tidal
level) in coastal aquifers is important because approximately 50 percent of the world population live
12
in coastal zones, particularly in low-lying deltaic areas within 60 km of the shoreline (Nickson et al.,
2005).
An understanding of the spatial variation and processes affecting water quality is essential in
sustaining usable water supplies under changing climate and local environmental pressures. Temporal
changes of recharged water composition, hydrologic and human factors, may cause periodic changes
in groundwater quality (Vasanthavigar et al., 2010). The quality of alluvial groundwater in rural areas
is sensitive to contaminants originating from agricultural chemicals, such as fertilizers, pesticides, and
lime (Kelly, 1997). The use of nitrogen fertilizers frequently leads to extremely high nitrate
concentrations in groundwater and may cause serious health problems. In such circumstances, the
knowledge of temporal and spatial trends of water quality should help in the decision-making process,
particularly in developing countries, where there are insufficient data.
2.5 Application of Artificial Neural Network in GWL
Trichakis et al. (2011) tested a proposed ANN to measure data from Edward’s aquifer in Texas USA
by simulating the hydraulic head change at an observation well in the area (Trichakis et al., 2011). All
the input factors are directly or indirectly connected to the aquatic equilibrium and the ANN will be
regarded as a sophisticated analog to empirical models of the past. Nourani et al. (2011) used a hybrid,
the artificial neural network-geostatistics study is offered for spatiotemporal prediction for
groundwater level (Nourani et al., 2011). The proposal contains two separate stages for the prediction
of GWL and is applied in the Shabetar plain. Taormina et al. (2012) employed the ANN model using
FFNN to predict the GWL in a coastal unconfined aquifer sited in the Lagoon of Venice, Italy
(Taormina et al., 2012). the study used different input variables combinations, and the obtained results
showed that ANN with FFNN algorithms can produce reliable simulation outcomes. Reza and
Mohammad (2012) employed four different neural networks for GWL predictions in the Shiraz plane
(Reza & Mohammad, 2012). The results were put up against each other by means of statistical
measures of mean square error and square of a correlation coefficient. They found out the best overall
performance was attained by the feed-forward neural network, which was seconded by Elman neural
network. Sahoo and Jha (2013) compared multiple linear regression (MLR)and artificial neural
network (ANN) techniques in predicting GWL (Sahoo & Jha, 2013). The modeling was carried out
in 17 different sites in Japan and they considered all influential factors such as rainfall, temperature,
13
etc. Their results were that ANN is better than MLR. Mohanty et al. (2013) appraised the execution
of finite difference-based numerical model MODFLOW and ANN model developed in this research
in simulating GWL in an alluvial aquifer system (Mohanty et al., 2013). Groundwater levels were
observed at 18 different wells and were simulated in a specific period. ANN was made to predict the
GWL of those 18 wells. The results of the MODFLOW and ANN were compared, and ANN is of a
higher caliber than MODFLOW. Emamgholizadeh and Moslemi (2014) researched the potential of
the intelligent models named Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference
System (ANFIS) in predicting GWL in the Bastam Plain, Iran (Emamgholizadeh & Moslemi, 2014).
The result showed that both ANN and ANFIS predict GWL accurately. Taylor et al. (2014) used ANN
to predict the hydraulic head in well locations (Taylor et al., 2014). In the present work, the particle
swarm optimization algorithm was used to train a feed-forward multi-layer ANN for the simulation
of hydraulic head change at an observation well in the region of Agia, Chania, Greece. ANN was
ultimately used for midterm prediction of the hydraulic head, as well as for the research of three
climate change scenarios. Data time series were created using a stochastic weather generator, and the
scenarios were examined for a period of ten years (2010-2020). Juan et al. (2015) developed two ANN
models, one with three input variables and another with two input variables, were developed to
simulate and predict the site-specific suprapermafrost groundwater level on the slope scale (Juan et
al., 2015). The results indicate that the three-input variable ANN model has superior real-time site-
specific prediction capability and produces excellent accuracy performance in the simulation and
forecasting of the variation in the suprapermafrost groundwater level. Manouchehr Chitsazan (2015)
used the feed-forward back propagation neural network (FNN) to predict the groundwater level of the
Aghili plain in Iran (MANOUCHEHR CHITSAZAN, 2015). The achieved results of ANN model was
different to the results of finite difference model and showed a very high accuracy of artificial neural
network in calculating groundwater level. Yoon et al. (2016) Utilized a weighted error approach to
enhance the output of ANN and SVM using recursive prediction models for long-term prediction of
GWL in relation to rainfall. The results shows in comparison that the SVM was better than ANN
(Yoon et al., 2016). Okeechobee (2015) Carried out a research to test authenticity of three nonlinear
time-series intelligence models, artificial neural networks (ANN), support vector machines (SVM)
and adaptive neuro fuzzy inference system (ANFIS) in the prediction of the GWL when taking the
interaction between surface water and groundwater into consideration (Okeechobee, 2015). The
attained results from this study would be valuable to the water resources management, it proved to be
14
necessary and effective, considering the surface water-ground water. Ostad-ali-askari et al. (2017)
investigated and represented nitrate pollution in groundwater of marginal area of Zayandeh-rood
River, Isfahan, Iran using water quality and ANN (Ostad-ali-askari et al., 2017). The results were
successful and determined that ANN models can be used in investigating water quality parameters. S.
Sahoo and Jha (2013) developed a new modeling outline using spectral analysis, machine learning,
and uncertainty analysis, as a second choice to complex and computationally expensive physical
models(Sahoo & Jha, 2013). It was concluded that the modeling outline can serve as an alternative
approach to simulating groundwater level change and water availability, especially in regions where
subsurface properties are not available. Ngoie et al. (2018) studied a review process in the field of
GWL, water management, and hydrology using ANN application (Ngoie et al., 2018). Kaya et al.
(2018) researched GWL by using methods such as ANN and M5T in the Reyhanl region in Turkey
(Kaya et al., 2018). The study was carried out efficiently and the result demonstrated that ANN and
M5T models were close to one another. Rajaee et al. (2019) reviewed the special issue on artificial
intelligence approaches for GWL modeling and predictions (Rajaee et al., 2019). This study also
provides a short but effective overview of the most popular AI methods. Many of the results were
attained by reviewing various papers in this area. Roshni et al. (2019) developed the Feedforward
Artificial Neural Network (FFANN) and the hybrid WANN model and later put with Gamma and M-
tests (GT) method for predicting Spatio-temporal groundwater fluctuations in a complex alluvial
aquifer system (Roshni et al., 2019). From the research, the results are that the GTWANN method can
be an effective predictive tool for modeling Spatio-temporal fluctuations of groundwater levels. Y.
Chen et al. (2020) conducted an extensive investigation and analysis on ANN-based water quality
prediction from three aspects, namely feedforward, recurrent, and hybrid architectures (Y. Chen et al.,
2020). The results of many of the review articles are useful to researchers in prediction and similar
fields. Several new architectures shown in the study like recurrent and hybrid structures, can improve
the modeling quality of any development in the future. Khaledian and Pham (2020) used this research
to estimate the water level of Caspian sea using support vector machine and artificial neural network
(Khaledian & Pham, 2020). The results show that the SVM simulated better than ANN.
15
CHAPTER 3
REVIEW OF ARTIFICIAL NEURAL NETWORK AND MULTILINEAR REGRESSION ANALYSIS
3.1 Artificial Neural Network (ANN)
Artificial Neural Network (ANN) as an artificial intelligence model, is a numerical model expected
to deal with non-linear relationships of information yield dataset. ANN has been used effectively,
over the previous decade, in the field of design, drafting, and science. Additionally, ANN has shown
to be efficient in handling complex functions in different fields. Some of which include design
acknowledgment, prediction, arrangement, forecasting, and simulation of control energy.(S &
Jayalekshmi, 2015). Notwithstanding, ANN can be ordered in terms of various capacities, among
the groupings, Levenberg Marquart (LM), Scaled Conjugate Gradient (SCG), and Conjugate
Gradient with Powell/Beale Restarts (CGB) are the most normal and generally utilized strategies
in different written works (Leung et al., 2006). In LM, each input training data is intended to stream
by means of the framework and therefore go through the yield layer by including it in the cycle.
The error is arrived at which is alluded to as a training error. This error is then proliferated back to
the underlying interaction until the ideal yield of the reaction is reached. Meanwhile, the layer
consists of interconnected neurons by weight and enactment work (Isa & Elkiran, 2018). The
organic neuron related with computational neuron is introduced in Fig. 3.1
Figure 3.1: A portrayal of the likeness between a human and an artificial neuron(Can et al., 2004)
16
ANN has ascended as a significant thought from the field of artificial intelligence and has been
used adequately over the earlier decade in exhibiting designing issues in expansive, and especially
those relating to the system direct of composite materials.
3.2 Network Training of ANN In a large portion of the figuring tools, accurate and exact recipes are not accessible while picking
the incredible ANN structure, also the training algorithm that will deal with a specific issue, rather
results are acquired by experimentation or strategies. This is because of the way that they are
characterized to be discovery models. In this situation, figuring out how to choose the best preparing
capacity, concealed layer, shrouded neuron, and other related components are central significant
for reproduction and demonstrating the ANNs. The essential and basic boundary should be seen
from the outset and avoid the unhelpful boundary in the model (Dogan et al., 2008; Nourani &
Sayyah, 2012). (Isa & Elkiran, 2018).
The underlying loads are haphazardly allotted to the concealed neurons. To acquire the best
outcome, the processing data should be free from noise; both as far as quality and amount, data
sourcing and processing ought to at first be embraced, while then again, deficient data, absence of
data sourcing, and insufficiency of information could prompt terrible outcome, overfitting or
underfitting (Isa & Elkiran, 2018; Woodford, 2017). Under each situation, a singular layer is made
of up neurons and loads associated together. The activated function existed in every neuron and
considering a definitive objective of progress by means of the immediate capacity to nonlinear
capacity which is computational capacity. This abundancy applies to neuronal arrangement and
portrayal of how this neuron is run; it additionally perceives contributions from previous layers and
produces yields for the succeeding layers (Nourani et al., 2015). Figure 3.2 present a three-layered
feed-forward neural organization.
17
Figure 3.2: Three-layer feed-forward neural network (Nourani et al., 2015)
3.3 Process of Learning Learning is characterized as the limit of the neural organization to gain from its current
circumstance and to improve its presentation through learning (Mendel & Mclaren, 1970). Adapting
in a general sense suggests obtaining/getting data and rules from a circumstance. The Neural
Network is mimicking/copying the human model, moreover acquiring from an intelligent network
of changing its synaptic loads and predisposition stages notwithstanding upgrading following
progressive cycle according to suggested measures (Haykin, 1999, 2001)
3.4 Standard of Learning There are five essential standards of learning, which are as follows;
• Error-Correction Learning
At the point when data is inputted into the framework in the midst of training and goes through the
framework creating a set of characteristics on the output units, then, the noticed yield is
differentiated while the anticipated yield and a match are figured. In case the yield shifts from the
evenhanded, a change should be made to the amendments. One of the instances of error correction
is the Least Mean Square analytical process (Belciug & Gorunescu, 2016).
18
• Memory-Based Learning
A memory-based learning network is an extended memory organization network that different the
data space into sub-areas either statically or progressively to store and recuperate practical
information. The guideline theory techniques utilized by memory-based learning networks are the
nearest neighbor search, space decay methodology, and clustering (Haykin, 1999).
• Hebbian Learning
It is an unaided learning algorithm that is fit for getting sorted out itself to arranging contributions
to a completely new way it has not been instructed. In Hebb's words, Hebbian learning is when two
associated neurons are initiated all the while, the association fortifies, which makes them bound to
be enacted together later. This interaction assumed a critical part in the learning cycle and
arrangement of living creatures, including people (Guo et al., 2015; Morris, 1999)
• Competitive Learning
This can also be illustrated as an unaided neural organization. The point of emphasis here is to
decrease error while increasing entropy. It changes the organization loads to oblige a new set in
another example that will influence the centroid of the set (Haykin, 1999).
• Boltzmann Learning
Boltzmann learning resembles error-correction learning and is applied in the midst of regulated
learning. In this estimation, the state of each and every neuron and yield are thought of. In such a
manner, the mistake remedy learning is quicker than Boltzmann learning. It is likewise used to
prepare the organization for each emphasis. Notwithstanding, rather than examination between the
anticipated value and the noticed worth, the distinction is between the odds of the conveyance of
the organization (Haykin, 1999).
3.5 Training algorithm There are a few algorithms of training received while preparing an organization in neural networks.
Be that as it may, in this examination Levenberg–Marquardt backpropagation (trainlm) and scale
form angle (trainscg) work are utilized.
19
Backpropagation is the name given to the algorithm used for this. Subsequent to giving the
organization information, it will deliver a yield, the following stage is to show the organization
what ought to have been the right yield for that input (the ideal yield). The organization will take
this ideal yield and begin changing the loads to deliver a more precise yield sometime later,
beginning from the yield layer and going in reverse until arriving at the information layer. So next
time a similar it will show that equivalent contribution to the organization, it will give a yield nearer
to that ideal one that was prepared. This cycle is rehashed for some emphasis until we consider the
mistake between the ideal yield and the one yield by the network or organization to be adequately
little.
This training work finds the base of a multivariate potential that can be conveyed as the total of
squares of non-straight originally-regarded limits. It is an iterative method that works such that the
presentation limit will be diminished in each algorithm cycle. Trainlm is the fastest training
algorithm as a result of it having this component (Khademi et al., 2017).
• Scaled conjugate gradient (trainscg)
This is a second-order algorithm that is faster than any other second-order algorithms. The trainscg
work needs more iteration to assemble than the other conjugate gradient algorithms, however, the
number of calculations in each iteration is significantly less because no line search is carried out.
Conjugate gradient backpropagation (Ascione et al., 2017).
More iteration is required for the training function to amass than the other form of gradient
algorithms, in any case, the quantity of figuring in every cycle is altogether less on the grounds that
no line search is done. Form angle backpropagation (Ascione et al., 2017).
3.6 Learning algorithm Artificial neural networks are equipped for gaining from the exhibition of tests, which shows the
conduct of the framework. Along these lines, ensuing to the framework to gain proficiency with
the relationship among information sources and yields, in which the framework organization could
make an objective yield that, is nearer to the foreseen consequence of predefined input factors.
Accordingly, the preparation phases of neural organizations incorporate the presentation of
utilizing a few stages of changing the neurons and loads so that the neural total will deliver the
yield (Haykin, 1999; Wilson, 1993).
20
The framework is observed to be reacting until the existing varieties in the synaptic weight are
exhausted and when this is achieved, the framework is thought to have stopped learning and is to
suggest as organization consolidating (Kasabov, 1996).
Two algorithms of learning are inspected hereunder;
a. Supervised Learning System
In the learning framework, the required information and target yield are organized and fed into
the organization accordingly and the weight and inclination are refreshed forward which is
called the feed-forward cycle while it goes through the training with engendered error till the
objective worth is reach. This learning cycle happens with the predefined information and yield
values by the software engineer (Haykin, 2001).
b. Unsupervised or solo Learning System
The interaction of the solo learning framework happens when just the required inputs factors are
set and inputted into the organizations for the training purpose. The neurotransmitter is
consequently changed once the factors are inputted, this cycle is called learning with no
developer and has the ability to get sorted out the data with the least mistake values. It is a self-
assenting method where just info information is used. This calculation uses no data of the
potential yields and is otherwise called learning without educator (Haykin, 1999). This algorithm
uses no data of the potential yields to grasp its assignment by identifying the information data
(Becker & Plumbley, 1996).
3.7 The Design of neural network Artificial neural networks principle designs, the dissemination of nodes, layers course, and
interconnections are briefly analyzed underneath:
• Single-layered feedforward network
Is a kind of artificial neural network that includes just one layer referred to as the input layer and
the next layer called the output or yield layer of the network.
21
Figure 3.3: Single-layered feedforward neural network (Haykin, 1999)
• Multi-layered feedforward neural network
These are networks that incorporate three layers to be specific: input, hidden,
and output layer.
22
Figure 3.4: A typical three-layer Feedforward Network (Journal et al., 2008)
• Repetitive networks
These networks can be utilized for determining time arrangement investigation, control
framework, streamlining, and identification e.t.c
Figure 3.5: Illustration of a repetitive network
Input Layer Content
unit
Hidden Layer
Output Layer
23
• Mesh networks
This organization considers the spatial underlying of modes and plan utilized for design
acknowledgment and expulsion purposes. This organization is most and broadly applied in a
few fields of streamlining, grouping, neural organization design acknowledgment, etc.
Figure 3.6: Structure of a mesh network
3.8 Properties of Neural Networks 3.8.1 Input layer
This is the accepting layer, where data like images, unprocessed data, signals, and so on from any
acknowledged source are inputted into the organization for training purposes. These data sources
are typically standardized inside the breaking point values in order to scale the data.
3.8.2 Output layer Following the input layer in the organization is the output layer where the information is gotten to
deliver the last and wanted objective. The layer interacts with the inputs introduced by the input
layer with weight and predisposition.
3.8.3 Hidden layer
The hidden layers contain nodes that are in control of taking out patterns related to the technique
that is assessed. This layer executes the most extreme inward interactions from an organization
(Haykin, 1999)
24
3.9 Model development Model advancement is viewed as a proficient examination strategy. It helps the researcher in
depicting, foreseeing, testing, or understanding troublesome frameworks. Subsequently, models
typically present a structure for directing an examination and can comprise of synopses like
drawings, conditions, or figures for the investigation of a framework. It incorporates
fundamental outlines of what is the issue here. A few phrases and steps which were undergone
during model development are shown in Fig. 3.7. for both the ANN and MLR models.
Figure 3.7: Model development process (Khademi et al., 2017)
3.9.1 Data standardization The training algorithm is very sensitive in scaling data, Thus, the input and output values of the
data set should be standardized. For the most part, input and output data was set up to the scale
scopes of either (– 1, 1), (0.1, 0.9), or (0, 1) (Khademi et al., 2016).
Standardization is the method of figuring out and laying out a data model capable of storing data
in a data set. The eventual outcome is that inconsequential data is eliminated, and just data
Identify inputs & Data collection
&
Conduct descriptive data &
Model Design
Select computer development
Determine network architecture
Train the designed
Find the optimal set of
Model Testing Evaluate performance
Model Execution
Run the model for future
Model Training
25
applicable to the attributes are placed in a table. Unimportant data waste circle space and make
maintenance issues. In the event that the data that exists much of the time should have fluctuated,
the data should be varied similarly in all areas. The condition underneath was embraced for the
standardization (Nourani et al., 2015):
𝑆𝑆𝑇𝑇 = 𝑆𝑆𝑖𝑖−𝑆𝑆𝑚𝑚𝑆𝑆𝑀𝑀−𝑆𝑆𝑚𝑚
(3.1)
Where;
SM = maximum
Si = actual values to be used.
ST = normalized
Sm = minimum
3.9.2 Performance criteria of the model Distinctive statistical parameters, like the mean square error (MSE) and correlation coefficient (R)
are adopted when exploring the presentation of the ANN model. Conditions (3.2) and (3.3) show
the R and the MSE separately.
𝑹𝑹 = 𝟏𝟏 − ∑ (𝑺𝑺𝒊𝒊−𝑺𝑺𝒊𝒊′)𝑵𝑵
𝒊𝒊=𝟏𝟏∑ (𝑺𝑺𝒊𝒊−𝑵𝑵𝒊𝒊=𝟐𝟐 𝑺𝑺�)𝟐𝟐
(3.2)
𝑴𝑴𝑺𝑺𝑴𝑴 = �∑ (𝑺𝑺𝒊𝒊−𝑵𝑵𝒊𝒊=𝟏𝟏 𝑺𝑺𝒊𝒊
′)𝟐𝟐
𝑵𝑵 (3.3)
Where;
26
N = number of data used
Si = Observed value
Si’= model computed value
𝑆𝑆̅= average observed data
The conditions applied to obtain the effectiveness and functioning of the model development are
dependent upon particular difficulties, and the statistical performance assessment applied to arrive
at the correlation coefficient (R) and the mean square error (MSE). Both MSE and R show the
variation between the two instances, i.e. measured and calculated values. To obtain the excellent
model, the higher the R and MSE values in the training and validation the better, and the higher the
R-value, the lesser the MSE value under normal circumstances (Nourani & Sayyah, 2012).
The standard MSE strategy is employed to value the productivity and adequacy of the model and
its capacity to acquire a precise expectation and decision, also to give out the best match among
estimated and determined qualities when MSE is zero way of its qualities. Spanning from zero to
best gauge, indicate that the contrasts among expected and estimated values are progressively more
noteworthy.
3.10 Multi Linear Regression Analysis (MLR) A few designing issues comprise of a decision for the connection between at least two variables.
Regression analysis is a valuable statistical tool for researchers in this field of study. Considering
a linear Regression model, that is explicit to this sort of regression model, linear prediction abilities
will be utilized for information demonstrating, and the objective boundaries of the information are
assessed. It is important to note that, in numerous employments of regression examination, more
than one information factor is viewed as that would bring about a "multi-linear regression". For
this situation, MLR assesses the connection between at least two input factors, by introducing a
linear equation to control the processed data (Khademi et al., 2016; Sadrmomtazi et al., 2013).
The role played by regression analysis is of utmost importance to researchers in the field. Generally,
regression analysis can be considered as the route toward fitting models to data. In a linear
regression model which is a specific sort of regression model, the linear indicator limits would be
utilized to show the data, and target boundaries are assessed from the data (Akbari & Jamal, 2015;
27
Khademi et al., 2017). It justifies indicating that in various usages of regression analysis, more than
one input factor is incorporated which would trigger the "multilinear regression" work. The goal of
MLR is to find a condition that can anticipate the dependent variable as a part of a couple of
independent variables. Various linear regressions incorporate instructions data and furthermore
investigating the association between factors (Sobhani et al., 2010). The MLR condition is given
by:
𝒚𝒚 = 𝒃𝒃𝒄𝒄 + 𝒃𝒃𝟏𝟏𝒙𝒙𝟏𝟏 + 𝒃𝒃𝟐𝟐𝒙𝒙𝟐𝟐 + ⋯𝒃𝒃𝒊𝒊𝒙𝒙𝒊𝒊 (3.4)
Where;
x1 is the ith predictor value
bc is the constant of regression
bi is the ith predictor coefficient
29
CHAPTER FOUR
RESULTS AND DISCUSSION
4.0 Data Processing and Pre-analysis
Data pre-processing and pre-analysis are very important prior to the modeling procedure. Data
mining is the process of turning the raw data into appropriate and meaningful information, for the
purpose of this work, the available daily data were obtained from two different places including
NASA, and NHA. The estimation of the chosen parameters was based on a different set of inputs and
outputs variables as shown in statistical Table 4.1. Every data analysis concerning AI base models
relies normally on historical data. Therefore, the mathematical and data modeling of the input-output
is important as it describes the nature and strength of the relationship between inputs and outputs. To
efficiently train AI base model, these data need to be clean and filtered properly, because the raw data
is often comprised of missing records, outliers, noise, discrepancies of codes and names, or was
infected by all kinds of error including human and instrumental. The descriptive statistical analysis
used to explain the data trend series are smoothing and normalization, the former was carried out by
fitting the data into regression function to eliminate the noise from the data and the latter was to ensure
the uniformity of the input-output value (scaling to fall within a small, specified range). At the initial
phase, all input and output data were standardized within the range between 0 and 1 prior to model
training. Normalization is performed to reduce data redundancy and improve data credibility. The
descriptive statistic of the selected parameter can be presented in Table 4., as stated above.
30
Table 4.1: Descriptive statistic between the parameters
Parameters T.MAX T.MIN R (mm) RH (%) WS (m/s) GWL Mean 0.4812 0.4678 0.2591 0.6501 0.3827 0.4139 Median 0.5319 0.4474 0.2035 0.7542 0.4143 0.4148 Standard Deviation 0.2843 0.2309 0.2758 0.3043 0.2253 0.1054 Sample Variance 0.0808 0.0533 0.0761 0.0926 0.0508 0.0111 Kurtosis -1.1411 -0.4694 -0.1592 -0.8364 0.0581 -1.1857 Skewness 0.1231 -0.0808 0.7845 -0.7276 0.2075 -0.1882 Minimum 0.0000 0.0000 0.0000 0.0000 0.0000 0.2214 Maximum 1.0000 1.0000 1.0000 1.0000 1.0000 0.5797
In this research work, descriptive statistical analysis and correlation matrix was applied to explore the
degree, type, and extent of the relation between the input-output parameters. The correlation
coefficient (R) was evaluated to measure the extent of linear interaction between the two variables.
The concept of R is to classified a variable using a linear function that acts as a tentative indicator of
a possible correlation between the set of variables. As presented in Table 4.2 the R-value with bold
marked is stationary and significant variables with probability less than 0.05 (P<0.05) that indicates
high strength of linear correlations. Also, the negatives R-values indicate an inverse interaction
between the two variables. Therefore, the weakness observed by R-value showed that the use of
conventional approaches in modeling complex interactions is insignificant and it is crucial to
implement a more robustness method. The major importance of this correlation is to determine the
linear input variable selection as indicated in the objective sections. As mentioned above, three
different models based on dominant factors were generated to classify the GWL. This could be better
understood by considering the newly adopted visualized correlation matrix between the parameter as
indicated in Fig. 4.1.
31
Table 4.2: Correlation analysis between the input and output variables
Parameters T.MAX T.MIN R (mm) RH (%) WS
(mtrs./s) GWL T.MAX 1 T.MIN 0.373604 1 R(mm) -0.71785 0.04151 1 RH (%) -0.69133 0.25756 0.773566 1 WS (m./s) 0.233262 0.386059 0.11881 0.040017 1 GWL 0.725675 0.022414 -0.61478 -0.75147 -0.1119 1
Fig. 4.1: Visualized correlation matrix between the parameters
Correlation Matrix
0.2 0.4 0.6
GWL1 0 0.5 1
WS 0 0.5 1 1.5
RH 0 0.5 1
R 0 0.5 1
TMIN10 0.5 1
TMAX1
0.2
0.4
0.6
GW
L1
0
0.5
1
WS
0
0.5
1
1.5
RH
0
0.5
1
R
0
0.5
1
TMIN
1
0
0.5
1
TMAX
1
0.37 -0.72 -0.69 0.23 0.73
0.37 0.04 0.26 0.39 0.02
-0.72 0.04 0.77 0.12 -0.61
-0.69 0.26 0.77 0.04 -0.75
0.23 0.39 0.12 0.04 -0.11
0.73 0.02 -0.61 -0.75 -0.11
32
From Fig. 4.1, the Spearman Pearson Correlation demonstrates how effectively a linear function
can be used to explain the relationship between the GWL variables. The direction or the sign does not
affect the strength of the correlation. In other words, a positive correlation implies that an increase in
the first parameter is proportional to an increase in the second parameter, whereas a negative
coefficient implies an inverse relationship, in which as one parameter increases, the second parameter
decreases(S. I. Abba et al., 2020; Eisinga et al., 2013; Ghali et al., 2020; Selin & Abba, 2020; USMAN
et al., 2020).
4.1 Results of ANN, and MLR models
As stated above the ANN, and MLR models were used in this study for the prediction of GWL using
different input parameters.
For ANN the optimum model architecture was optimized and selected using the trial-and-error
technique based on hyper-turning parameters, such as hidden neurons, activation function, learning
algorithms, etc. A qualified model is one that fits the requirements of most statistical evaluation
criteria, according to the literature (Abdullahi et al., 2020; Pham et al., 2019; USMAN et al., 2020).
In both calibration and verification, the model simulation was assessed using the most commonly used
performance metrics, such as R2, MSE, RMSE, and R. Table 2 shows the simulated outcomes in terms
of evaluation assessment based on model combinations (M1-M5) for ANN models. It is worth
mentioning that, for all the model development the simulation was done in MATLAB 9.3 (R2020a).
meanwhile, the MLR models were carried out in excel software based on the above model
combination (M1-M5).
33
Table 2: Modeling Results of ANN models
Training Phase Testing Phase R2 R MSE RMSE R2 R MSE RMSE ANN-M1 0.6120 0.7823 0.0038 0.0614 0.6241 0.7900 0.0045 0.0668 ANN-M2 0.5286 0.7271 0.0046 0.0677 0.5723 0.7565 0.0051 0.0712 ANN-M3 0.6414 0.8008 0.0035 0.0590 0.5552 0.7451 0.0053 0.0726 ANN-M4 0.7134 0.8446 0.0028 0.0528 0.8700 0.9327 0.0015 0.0393 ANN-M5 0.6624 0.8139 0.0033 0.0573 0.9170 0.9576 0.0010 0.0314
From the results in Table 2, the level of precision of all the models in terms of statistical criteria
was attained within the range of marginal to good (M4) by almost all the combinations. According to
the obtained results, these algorithms are known to be capable of handling models with multiple free
parameters, reducing the error function, solving data fitting problems, and have become a standard
approach for highly chaotic non-linear problems. Besides, the overall single ANN results
demonstrated that ANN-M4 served as the best simulation in terms of R2, MSE, RMSE, and R.
Although it is difficult to rank the models in accordance with the achieved accuracies, nevertheless
the ANN-M4 approach relatively showed the best predictions. However, the accuracy of both the three
models (ANN-M1, ANN-M2, and ANN-M3) attained more than 60% in terms of R. However, the
comparative visualization of the three-model combination is presented in scatter plots (see, Fig. 4.2
(a-e)). A scatter plot shows the level of agreement between the observed and predicted load for the
overall goodness-of-fit. It is obvious from the scatter plot that the ANN-M4 model shows higher
accuracy in comparison to the others models.
41
Fig. 4.2: Performance and training stage plots for (a) ANN-M1, (b) ANN-M2 (c) ANN-M3, (c), ANN-M4, and (e) ANN-M5
Regardless of the nonlinear relationship between predictors (inputs variables), and their associated
target objectives, the overall accuracy of single models was good and reported substantial certainty in
terms of error for both MLR and ANN. Essentially, it should be noted that the positive, and promising
estimations occurred during the verification phase, which is generally used to correctly calibrate
models using known input variables and goals. The testing process, on the other hand, is critical in
evaluating a model's performance since it checks the model's accuracy based on unknown goal values.
This benefit does not apply to the calibration phase alone. The section of MLR and ANN models have
generally depicted promising also ability with regards to the single model. This is not surprising as
can be seen in many pieces of literature (S. I. Abba et al., 2020, 2021; S. Abba & Lee, 2014; Alas et
al., 2020; Elkiran et al., 2018; Isa & Elkiran, 2018; Sammen et al., 2021; Sani & Abba, n.d.). The
radar diagram also known as spider chart was introduced in the research to determine the overall
comparison of the single models, and this justified the goodness-of-fit (see, Fig. 4.4).
(e)
42
Table 4.3: Modeling Results of MLR models
Training Phase Testing Phase R2 R MSE RMSE R2 R MSE RMSE MLR-M1 0.625125 0.790648 0.003642 0.06035 0.655661 0.809729 0.004085 0.063914 MLR-M2 0.619209 0.786899 0.0037 0.060825 0.671561 0.819488 0.003896 0.062421 MLR-M3 0.625125 0.790648 0.003642 0.06035 0.674244 0.821124 0.003865 0.062166 MLR-M4 0.651325 0.807047 0.003388 0.058203 0.783258 0.885019 0.002571 0.050708 MLR-M5 0.652627 0.807854 0.003375 0.058094 0.783022 0.884885 0.002574 0.050736
43
Fig. 4.3: Radar Plots for ANN, and MLR Models
0.7
0.75
0.8
0.85
0.9MLR-M1
MLR-M2
MLR-M3MLR-M4
MLR-M5
MLR MODEL
R-Training R-Testing
0
0.2
0.4
0.6
0.8MLR-M1
MLR-M2
MLR-M3MLR-M4
MLR-M5
MLR MODEL
R2-Training R2-Testing
0.00000.20000.40000.60000.80001.0000
ANN-M1
ANN-M2
ANN-M3ANN-M4
ANN-M5
ANN MODEL
R-Training R-Testing
00.20.40.60.8
1ANN-M1
ANN-M2
ANN-M3ANN-M4
ANN-M5
ANN MODEL
R2-Training R2-Testing
44
Fig. 4.4: Error Plots in terms of MSE, and RMSE
0.0000 0.0200 0.0400 0.0600 0.0800
ANN-M1
ANN-M2
ANN-M3
ANN-M4
ANN-M5
RMSE-Testing RMSE-Training
0 0.001 0.002 0.003 0.004 0.005 0.006
ANN-M1
ANN-M2
ANN-M3
ANN-M4
ANN-M5
MSE-Testing MSE-Training
0 0.001 0.002 0.003 0.004 0.005
MLR-M1
MLR-M2
MLR-M3
MLR-M4
MLR-M5
MSE-Testing MSE-Training
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
MLR-M1
MLR-M2
MLR-M3
MLR-M4
MLR-M5
RMSE-Training RMSE-Training
45
0
0.2
0.4
0.6
0.8
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47PRED
ICTE
D AN
N M
ODE
L 1
TIME SERIES
ANN MODEL 1
GWL ANN-M1
0
0.2
0.4
0.6
0.8
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47
PRED
ICTE
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ODE
L 3
TIME SERIES
ANN MODEL 3
GWL ANN-M3
0
0.2
0.4
0.6
0.8
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47PRED
ICTE
D AN
N M
ODE
L 2
TIME SERIES
ANN MODEL 2
GWL ANN-M2
46
Fig. 4.5: Time series Plots in term all the 5 ANN models
0
0.2
0.4
0.6
0.8
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47PRED
ICTE
D M
ODE
L 5
TIME SERIES
ANN MODEL 5GWL ANN-M5
0
0.2
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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47
PRID
ECTE
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LR M
ODE
L 1
TIME SERIES
MLR MODEL 1
GWL MLR-M1
49
CHAPTER FIVE
SUMMARY, CONCLUSION, AND RECOMMENDATIONS
5.1 SUMMARY OF FINDINGS
The purpose of this study was to assess the modeling of seasonal variation of groundwater levels using
an artificial neural network across Abuja using Apo-Gudu metropolis as a case. Two hypotheses were
formulated (generated) to guide the researcher. The first was meant to find out there is a relationship
between the minimum and maximum temperature, rainfall, relative humidity, and wind speed of the
Apo-Gudu metropolis in Abuja.
The objectives of the study were to;
i. To perform the sensitivity analysis to determine the most dominant GW parameters.
ii. To determine the performance of ANN and MLR model in modeling GWL
iii. To develop an independent model for the prediction of GWL at APO/GUDU
iv. To detect the dynamic of GWL in both wet and dry season
v. To compare the performance linear model (MLR) and Nonlinear model (ANN) for the simulation of
GWL
5.2 CONCLUSION
This study has gone a long way to establish the fact that some parts of the Federal Capital Territory
contain a reasonable amount of groundwater which if well tapped will go a long way to alleviate the
water problem in the city. There is a need for a proper understanding of the groundwater condition of
the area, the foundation of which has been laid through this study. This could be achieved by carrying
out comprehensive predrilling hydrogeological studies for the entire area and all boreholes should be
properly designed and properly developed and pump tested. The knowledge of this will reduce
borehole failures and low yield currently experienced in some parts of the project area.
This study assessed the potentials of groundwater using artificial neural networks and multi-linear
regression in basement complex terrain of Apo-Gudu area of Abuja metropolis for the supply of
50
potable water for domestic uses. Results show that ANN model 4 was the best model for groundwater
resources available in both the weathered overburden and fractured zones of the basement complex
rocks in the area. Subsurface fractures in the study area were at depths ranging from 7.0 m to 36.00 m
and they served as good reservoirs for water. Generally, drilling penetrated both the overburden and
the competent basement complex rocks until fractures were encountered.
5.3 RECOMMENDATION
In view of the findings revealed by this study, it is recommended that there is the need for artificial
intelligence in the treatment of the abattoir effluents into a non-toxic state before they are discharged
into the environment.
Efforts should also be made by the regulatory agencies such as National Environmental Standards and
Regulation Enforcement Agency (NESREA) and Abuja Environmental Protection Board (AEPB) to
meet and enforce the international standards and recommendations for the location of abattoirs.
51
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