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UNIVERSITY GHENT
UNIVERSITEIT
GENT
INTERUNIVERSITY PROGRAMME
MASTER OF SCIENCE IN
PHYSICAL LAND RESOURCES
Universiteit Gent
Vrije Universiteit Brussel
Belgium
Groundwater Surface Water Interaction
Modelling Using Visual MODFLOW and GIS
June 2008
Promotor: Master dissertation in partial fulfilmentProf. F. De Smedt of the requirements for the Degree of
Master of Science in
Physical Land Resources
by: Jemaneh Shibru Wake
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ACKNOWLEDGMENT
I would like to express my heartfelt gratitude to my brother Y.S. Wake who has had the biggest
influence in my life in being with me throughout my study in Belgium and to support my interestthroughout my stay.
I would like to thank my promoter prof. F. De Smedt for his important suggestions. I am equally
grateful to doctoral students, A. Christian and G. Adem for their support, guidance, suggestions
and data provision.
I like to thank all my class mates and staff members of PHYLARES at Ghent University and the
department of Hydrology and Hydraulic engineering of the Free University of Brussels for theirsupport and services.
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Abstract
Understanding interconnections among the components of the hydrologic cycle is fundamental to
development of effective water resources management and policy. The need to assess the effects
of variability in geology, climate, biota and human activities on water availability and flow
requires the development of models that couple two or more components of the hydrologic cycle.
Groundwater and surface water resources are by no means disjoint, as knowing where surface
water recharges groundwater and where groundwater flows supply surface water is an important
aspect of the hydrologic cycle. As global concerns over water resources and the environment
increase, the importance of considering groundwater and surface water as a single resource has
become increasingly evident.
Ground water and surface water are hydraulically interconnected, but the interactions are
difficult to observe and measure. In many situations, surface-water bodies gain water and solutes
from ground-water systems and in others the surface-water body is a source of ground-water
recharge and causes changes in ground-water quality. As a result, withdrawal of water from
streams can deplete ground water or conversely, pumpage of ground water can deplete water in
streams, lakes, or wetlands. Pollution of surface water can cause degradation of ground-water
quality and conversely pollution of ground water can degrade surface water. Thus, effective land
and water management requires a clear understanding of the linkages between ground water and
surface water as it applies to any given hydrologic setting.
At some reaches water moves from the land surface to the subsurface and in other areas it moves
from the subsurface to the land. Lakes and wetlands can receive groundwater inflow throughout
their entire bed, have outflow throughout their entire bed, or have both inflow and outflow at
different localities. In this thesis, surface water and groundwater interaction model was
developed for a study area located in the Nete Catchment, Belgium.
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Table of contents
Acknowledgment ............................................................................................................................ IAbstract ..........................................................................................................................................II
Table of contents ......................................................................................................................... III
List of figures ................................................................................................................................ V
List of tables................................................................................................................................. VIChapter 1:Introduction ................................................................................................................ 1
1.1 General Overview ....................................................................................................... 1
1.2 Objective ..................................................................................................................... 2
1.3 Structure of the thesis.................................................................................................. 3
Chapter 2:Approach and Methodology ...................................................................................... 42.1 General overview of Models ....................................................................................... 4
2.2 Groundwater models ................................................................................................... 52.3 Model Development.................................................................................................... 7
2.3.1 Model Objectives ................................................................................................... 72.3.2 Hydrogeological Characterization ......................................................................... 7
2.3.3 Model Conceptualization ....................................................................................... 7
2.3.4 Model Design ......................................................................................................... 7
2.3.5 Model Calibration .................................................................................................. 8
2.3.6 Sensitivity Analysis ............................................................................................... 8
2.3.7 Model Verification ................................................................................................. 82.3.8 Predictive Simulations ........................................................................................... 8
2.3.9 Performance monitoring Plan ................................................................................ 9
2.4 Methodology ............................................................................................................... 9Chapter 3:Interaction of groundwater and surface water ...................................................... 10
3.1 General overview ...................................................................................................... 10
3.2 Interaction of groundwater and stream ..................................................................... 12
3.3. Interaction of Groundwater and Lakes ..................................................................... 17
3.4 Interaction of Groundwater and Wetlands ................................................................ 17
3.5 Groundwater and Coastal Environments ................................................................. 18
3.6. Human activity and interaction of groundwater and surface water .......................... 18
Chapter 4:Description of the study area ................................................................................... 19
4.1 Geographical location ............................................................................................... 19
4.2 Study boundaries and previous work ....................................................................... 20
4.3 Topography .............................................................................................................. 224.4 Hydrological setting ................................................................................................. 244.5 Recharge .................................................................................................................. 25
4.6 Land-use and Soil .................................................................................................... 25
4.7 Climate of the study area ......................................................................................... 25
Chapter 5:Modeling tools ........................................................................................................... 275.1 ArcView GIS ............................................................................................................ 27
5.1.1 Introduction ........................................................................................................... 27
5.1.2 Types of data used in ArcView GIS ..................................................................... 27
5.1.3 Geographical data ................................................................................................. 27
5.1.4 Spatial data ............................................................................................................ 28
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5.1.5 Image data ............................................................................................................. 28
5.1.6 Tabular data .......................................................................................................... 285.1.7. Extensions of GIS ................................................................................................. 28
5.2 Visual MODFLOW .................................................................................................. 295.3. Surfer 8...................................................................................................................... 30
5.4 Grapher 7 .................................................................................................................. 30
Chapter 6:Model Setup .............................................................................................................. 316.1 Description of the Groundwater Flow Model ........................................................... 31
6.1.1 Model dimensions ................................................................................................ 32
6.1.2 Layers ................................................................................................................... 33
6.1.3 Elevation limits .................................................................................................... 34
6.1.4 Grid ...................................................................................................................... 346.1.5 Elevation data....................................................................................................... 34
6.1.6 Hydrogeological information ............................................................................... 36
6.1.7 Aquifer characteristics data.................................................................................. 386.1.8. Hydraulic conductivity......................................................................................... 41
6.1.9 River ..................................................................................................................... 416.2 Input to the model ..................................................................................................... 42
6.2.1 Recharge ............................................................................................................... 42
6.2.2 River ...................................................................................................................... 436.2.3 Constant Head boundary ....................................................................................... 44
6.3 Output from the model .............................................................................................. 44
Chapter 7:Model calibration ..................................................................................................... 467.1 Calibration water levels ........................................................................................... 47
7.2 Calibrated Aquifer Parameters ................................................................................. 49
7.2.1 Hydraulic conductivity.......................................................................................... 497.2.2 Water levels .......................................................................................................... 49
Chapter 8:Results and discussion .............................................................................................. 528.1 Output from the model .............................................................................................. 52
8.1.1 Model Water balance ............................................................................................ 52
8.1.2. Zonebudget ........................................................................................................... 55
8.3 Groundwater head ..................................................................................................... 568.3 Groundwater - Surface Water Interactions ............................................................... 58
Chapter 9:Conclusions and Recommendations ....................................................................... 63
9.1 Conclusions ............................................................................................................... 63
9.2. Recommendations and future considerations ........................................................... 64
References .................................................................................................................................... 65Annex ........................................................................................................................................... 68
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List of figures
Figure 3.1 Flow through a Hypothetical aquifer system ........................................................ 11Figure 3. 2 Interaction of streams and ground water. .............................................................. 13
Figure 3. 3 Effects of pumping from a hypothetical aquifer discharging to a stream ............ 15
Figure 3. 4 The dynamic interface between ground water and streams. ................................. 16
Figure 4. 1 Geographical Location of Belgium ...................................................................... 19
Figure 4. 2 The study area and its location in the Nete Basin. ................................................ 21Figure 4. 3 Two dimensional view and elevation of the study area. .................................... 22
Figure 4. 4 3D of Topography ................................................................................................. 24Figure 4. 5 Slope map of the study area .................................................................................. 24
Figure 6. 1 Model domain and units of measurement. ............................................................ 33Figure 6. 2 Bottom elevation for layer 1 ................................................................................. 35
Figure 6. 3 Bottom elevation of layer 2 ................................................................................... 35
Figure 6. 4 Bottom elevation of layer 3 ................................................................................... 36
Figure 6. 5 Stratigraphy of the different aquifer units of the model. ...................................... 38
Figure 6. 6 Geologic cross section along the middle points of the model. .......................... 39
Figure 6. 7 Geologic cross section along the river flow route ............................................. 40
Figure 6. 8 Two- dimensional view of the river segment in the model domain. .................... 41
Figure 6. 9 Spatially distributed recharge ............................................................................... 42
Figure 6. 10 Reclassified recharge zones and their values ....................................................... 43Figure 6. 11 Head values of layer 1 used for constant head boundary. .................................... 44
Figure 6. 12 Location of the pumping wells ............................................................................. 45Figure 7. 1 Location of observation wells ............................................................................... 48
Figure 7. 2 simulated versus field measured water levels ....................................................... 50
Figure 7. 3 Scattergram for the measured versus simulated values ........................................ 51
Figure 8. 1 The Volumetric water balance of the model. ........................................................ 53
Figure8. 2 Volumetric water balance of the model in percentage of components. ................ 54Figure 8. 2 Zone 2 water balance ............................................................................................ 55
Figure 8. 3 Ground water heads and flow directions in Layer 1 ............................................. 56
Figure 8. 4 Equipotential head distribution of layer 2 ............................................................. 57
Figure 8. 5 Equipotential head for layer 3 ............................................................................... 58Figure 8. 6 Cross section along column 328, groundwater flows to the river......................... 59
Figure 8. 7 Cross- section along row 185. Groundwater flows away from the river .............. 60
Figure 8. 8 Position of the river water level and the groundwater level ................................ 61
Figure 8. 9 North- South water table cross section along column 222. .................................. 62Figure 8. 10 General flow direction of groundwater within the model domain ........................ 62
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List of tables
Table 6. 1 Geographic extent of the model. ........................................................................... 32
Table 6. 2 Model Configuration ............................................................................................. 33
Table 6. 3 Main units of the HCOV hydrogeological code .................................................. 37
Table 6. 4 Overview of aquifers on the HCOV classification for Flanders ........................... 37
Table 6. 5 The ground-water model recharge and the annual recharge rate per zone. .......... 43Table 6. 6 Location and pumping rate of the wells in the model domain. ............................. 45
Table 7. 1 Water level and location of piezometers. .............................................................. 47
Table 7. 2 Calibrated Hydraulic conductivity values for the three layers.............................. 49
Table 8.1 Input and output of the model in terms of volume................................................ 53
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Chapter 1
Introduction
1.1 General Overview
Water covers two-thirds of the Earths surface and surrounds the planet in vapor form. Chemical
and density stratification during and immediately following accretionary heating of the Earths
primordial planetary body resulted in its present layered configuration. Internal heat and
chemical reactions caused water, which was originally bound as oxygen and hydroxide in
minerals, to diffuse from the Earths interior towards its surface. This degassing (still an on-
going process) of both water and other volatile species resulted in the accumulation and eventual
condensation of the fluid envelope of the Earth. Of course, water was also delivered to our planet
by infalling comets and other H2O bearing planetesimals.
The hydrologic cycle describes the complex system whereby water circulates among its variousreservoirs at and near the surface of the Earth. These reservoirs include the oceans, the
atmosphere, underground water (including both soil water and groundwater), surface water
(lakes, rivers and wetlands), glaciers and the polar ice caps. The Hydrologic cycle is directly
coupled to the Earths energy cycle, because solar radiation combines with gravity to drive the
global circulation of water. This circulation, in turn, plays an important role in the heat balance
of the Earths surface. The hydrologic cycle is also closely linked to the geosphere and its rock
cycle. Water erodes geologic materials, and the breakdown of these materials releases many
chemical constituents that in turn define the chemical nature of the water. Water can also build
geologic formations, through both chemical and mechanical depositional processes. Water is
essential to all life forms in the planetary biosphere. (Mauricie, et.al, 2001).
Only a small portion (3 %) of the water covering the earths surface is fresh. Of the fresh water
77.5% is locked in ice fields and glaciers. Surface water and underground water are the utilizable
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fresh water resources of which groundwater water accounts for 95%; lakes, reservoirs, swamps
and river channels 3.5%; and soil moisture comprises 1.5% (Freeze & Cherry, 1979).
Understanding interconnections among the components of the hydrologic cycle is fundamental to
development of effective water resources management and policy. Ground water and surface
water are hydraulically interconnected, but the interactions are difficult to observe and measure.
In many situations, surface-water bodies gain water and solutes from ground-water systems and
in others the surface-water body is a source of ground-water recharge and causes changes in
ground-water quality. As a result, withdrawal of water from streams can deplete ground water or
conversely, pumpage of ground water can deplete water in streams, lakes, or wetlands. Pollutionof surface water can cause degradation of ground-water quality and conversely pollution of
ground water can degrade surface water. Thus, effective land and water management requires a
clear understanding of the linkages between ground water and surface water as it applies to any
given hydrologic setting.
In this work Visual MODFLOW 3.0 groundwater modeling package is utilized to quantify
groundwater surface water interaction. Visual MODFLOW 3.0 package is an integrated
modeling environment for applications in three dimensional groundwater flow and
contaminant transport simulations based on the finite-difference method.
ArcView GIS has been used to store analyze and display the spatial data on topography, recharge,
and in making the base map for the visual MODFLOW. Thus visual MODFLOW and ArcView
GIS have been used to simulate the ground water flow and consequently the flux between the
ground water and surface water.
1.2 Objective
The main objectives of this thesis work are to:
Develop a steady state model and calculate the water balance of the area
Quantify the flux exchange between the ground water and the river in the study area
( groundwater surface water interaction)
Identify the loosing and gaining sections of the river
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Specific objectives of this thesis are:
Calibration and validation of the model
Development of a model to simulate groundwater flow in the study area and interpret the
flow system using the developed model.
1.3 Structure of the thesis
This thesis is organized into three major parts: literature review, methodology and discussion of
the results and conclusion & recommendations. Chapter 1 is the introductory part which deals
mainly with the importance of the topic and the associated research questions. Chapters 2 and 3
deal with literature review on past and existing knowledge about the topic of groundwater-
surface water interaction and its importance in the study of hydrologic systems. Chapter 4
focuses on the detailed description of the study area and available data for the modeling work.
Chapter 5 8 discuss the modeling tools, procedure, calibration of the model and the results
obtained. Conclusion and recommendation is presented in Chapter 9 on the ideas and issues for
further work in the focus area.
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Chapter 2
Approach and Methodology
2.1 General overview of Models
Models are a substitute for a real system. Models are used when it is easier to work with a
substitute than with the actual system. Domenico (1972) defined a model as a representation of
reality that attempts to explain the behavior of some aspect of it and is always less complex than
the system it represents. Wang & Anderson (1982) defined a model as a tool designed to
represent a simplified version of reality. Banks (1993) defines two types of models (1)
consolidative: Consolidates facts regarding the system into a single model used as a surrogate to
the real system and (2) exploratory: a series of computational experiments to explore cause and
effect. Bredehoft et.al. Further subdivided ground water models into (1) Data driven exploratory
models or history matching (2) policy question driven models and (3) conceptually driven
models.
In studying a groundwater flow model we first develop a conceptual model descriptive of the
present condition of a system. At this stage we identify relevant processes and physical elements
controlling groundwater flow in the aquifer, namely: the Geologic framework, the Hydrologic
framework, the Hydraulic properties, and the Sources & sinks (water budget) and determine data
deficiencies. Conceptual model dictates how we translate the real world to a mathematical Model.
To make predictions of future behavior, a dynamic model is needed that is capable ofmanipulation. Mathematical models are one type of dynamic models and use equations to
represent the interconnections in a system. The simplest mathematical model of groundwater
flow is Darcys law. To apply Darcys law we need to have a conceptual model of the aquifer
and to develop data on the physical properties of the aquifer system, the potential field and the
fluid properties. The process of formulating and solving a mathematical model is referred to as
mathematical modeling. The methods of obtaining the solution to a mathematical model can be
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broadly divided into two classes, analytical and numerical, even though the hybrid of these two
classes is not uncommon. Analytical methods yield exact solutions to the governing differential
equations. Darcys law is an example of an analytical model. To solve an analytical model, one
must know the initial and boundary conditions of the flow problem. These conditions must be
simple enough that the flow equation can be solved directly by using calculus.
Numerical methods approximate the differential equations with a set of algebraic equations.
These recast equations are numerical approximations and the answers obtained are also
approximations. The equations are most commonly in matrix form and they are solved on a
digital computer, unlike analytical models which can be solved rapidly, accurately andinexpensively with a programmable calculator or a spread sheet on a personal computer.
Generally, analytical solutions can be obtained under many simplifying assumptions, such as a
unidirectional velocity field, a set of uniform transport properties, a simple flow domain
geometry, and a simple pattern of sink and source distribution. For this reasons, numerical
solutions which are capable of approximating more general conditions, are more widely used in
field applications (Zheng & Bennett, 2002). This thesis is a numerical model to approximate
steady state water balance and interaction of surface and groundwater.
2.2 Groundwater models
Groundwater models are computer programs of groundwater flow systems for the calculation of
groundwater flux and head. Because of the simplifying assumptions embedded in the
mathematical equations and the many uncertainties in the values of data required by the model, a
model must be viewed as an approximation and not an exact duplication of field conditions.
Groundwater models, however, even as approximations are a useful investigation tool.
For the calculations one needs (hydrological) inputs, (hydraulic) parameters, initial and boundary
conditions.The input is usually the inflow into the aquifer or the recharge, which varies
temporally and spatially.
Important parameters are the topography, thicknesses of soil and aquifer layers and their
horizontal and vertical hydraulic condustivity, porosity and storage coefficient, capillarity of the
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unsaturated zone.Initial conditions and boundary conditions can be related to levels, pressures,
and hydraulic heads on the one hand (head conditions), or to recharge, discharge, inflow and
outflow on the other hand (flow conditions).
In general, groundwater models are conceptual descriptions or approximations that describe the
given flow system using mathematical equations; they are an approximate descriptions of the
physical system or process. By mathematically representing a simplified version of a
hydrogeological system, reasonable alternative scenarios can be predicted, tested, and compared.
The applicability or usefulness of a model depends on how closely the mathematical equations
approximate the physical system being modeled (model calibration).
Application of existing groundwater models include water balance (in terms of water quantity),
assessing the impact of changes of the groundwater regime on the environment, setting
up/optimizing monitoring networks, setting up groundwater protection zones and understanding
the quantitative aspects of the unsaturated zone, simulating water flow and chemical migration in
the saturated zone including groundwater Surface water interactions.
Groundwater modeling begins with a conceptual understanding of the physical problem. The
next step in modeling is translating the physical system into mathematical terms. Most models
solve the general form of the three-dimensional groundwater flow equation which is a
combination of the water balance equation and Darcys law:
t
hSsW
z
hKz
zy
hKy
yx
hKx
x
=
+
+
(1)
Where,
Kx, Ky, Kz are hydraulic conductivity values along the x, y, z axes [LT-1
]
h = hydraulic head [L]
W= source/sink terms [T-1
]
Ss= specific storage coefficient [L-1]
tis time [T].
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2.3 Model Development
A groundwater model application can be considered to be two distinct processes. The firstprocess is model development resulting in a software product, and the second process is
application of that product for a specific purpose.
2.3.1 Model Objectives
Model objectives should be defined which explain the purpose of using a groundwater model.
The modeling objectives will profoundly impact the modeling effort required.
2.3.2 Hydrogeological Characterization
Proper characterization of the hydrogeological conditions at a site is necessary in order to
understand the importance of relevant flow or solute transport processes. Without proper site
characterization, it is not possible to select an appropriate model or develop a reliably calibrated
model.
2.3.3 Model Conceptualization
Model conceptualization is the process in which data describing field conditions are assembled
in a systematic way to describe groundwater flow and contaminant transport processes at a site.
The model conceptualization aids in determining the modeling approach and which model
software to use.
2.3.4 Model Design
To successfully transform a conceptual model into a mathematical model, it is necessary to have
a database that provides adequate information to apply the requisite equations. All models start
with a groundwater flow model. For this, one needs to know the physical configuration of the
aquifer. This includes the location, areal extent, and thickness of all the aquifers and confining
layers; the location of the surface water bodies and streams; and the boundary conditions of all
aquifers.
Important hydraulic properties include the variation of transmissivity or permeability and storage
coefficient of the aquifers, the variations of permeability and specific storage of the confining
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layers, and the hydraulic connection between the aquifer and surface- water bodies. Hydraulic
energy as indicated by the water table or potentiometric surface maps and the amounts of natural
aquifer recharge and natural stream flow are also needed. (Fetter, 2001).To model stresses on the
natural ground-water flow system, the modeler must know the locations, types, and amounts,
through time, of any artificial recharge, such as results from recharge basins and wells or return
flow from irrigation, as well as the amounts and locations through time of ground-water
withdrawals from wells. Changes in the amounts of water flowing in the streams and changes in
the water levels of surface-water bodies should also be known.
2.3.5 Model Calibration
Model calibration consists of changing values of model input parameters in an attempt to match
field conditions within some acceptable criteria. Model calibration requires that field conditions
at a site be properly characterized. Lack of proper site characterization may result in a model
calibrated to a set of conditions that are not representative of actual field conditions.
2.3.6 Sensitivity Analysis
A sensitivity analysis is the process of varying model input parameters over a reasonable range
(range of uncertainty in value of model parameter) and observing the relative change in model
response. Typically, the observed change in hydraulic head, flow rate or contaminant transport
are noted. Data for which the model is relatively sensitive would require future characterization,
as opposed to data for which the model is relatively insensitive.
2.3.7 Model Verification
A calibrated model uses selected values of hydrogeologic parameters, sources and sinks and
boundary conditions to match historical field conditions. The process of model verification may
result in further calibration or refinement of the model. After the model has successfully
reproduced measured changes in field conditions, it is ready for predictive simulations.
2.3.8 Predictive Simulations
A model may be used to predict some future groundwater flow or contaminant transport
condition. The model may also be used to evaluate different remediation alternatives. However,
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errors and uncertainties in a groundwater flow analysis and solute transport analysis make any
model prediction no better than an approximation. For this reason, all model predictions should
be expressed as a range of possible outcomes that reflect the assumptions involved and
uncertainty in model input data and parameter values.
2.3.9 Performance monitoring Plan
Groundwater models can be used to predict the migration pathway and concentrations of
contaminants in groundwater. Errors in the predictive model, even though small, can result in
gross errors in solutions projected forwarded in time. Performance monitoring is required to
compare future field conditions with model predictions.
2.4 Methodology
The model construction is done by using the Visual MODFLOW 3.0 interface. To construct the
model, the study area was divided up into finite difference cells, which have a constant size of 5
meter by 5 meter. In the vertical dimension, 3 groundwater layers were represented. Parameters
representing physical characteristics and flow conditions were attributed to each cell. Visual
MODFLOW stores all of the data in a set of files. Most of the input files are stored in ASCII text
format. As a result, the input files can be manipulated using a text editor or even generated using
a FORTRAN or Visual Basic program. Visual MODFLOW then translates these data files to the
required format prior to running the models. By constructing the model, Visual MODFLOW
creates the modules, basic pieces of the program code, needed by the numeric engine.
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Chapter 3
Interaction of Groundwater and Surface water
3.1 General overview
Each component of the hydrologic system is in continuing interaction with other components.
Groundwater and surface water interact throughout all landscapes. As global concerns over waterresources and the environment increase, the importance of considering groundwater and surface
water as a single resource has become increasingly evident and the interactions of ground water
and surface water have been shown to be a significant concern in water supply, water quality,
and degradation of aquatic environments. (USGS, circular 1139).
At some reaches water moves from the land surface to the subsurface and in other areas it moves
from the subsurface to the land. Lakes and wetlands can receive groundwater inflow throughout
their entire bed, have outflow throughout their entire bed, or have both inflow and outflow at
different localities.
In order to fully understand the interaction between surface and ground-water flows, a detailed
description of the budgets of all hydrologic components is necessary. Ground water is a major
contributor to flow in many streams and rivers and has a strong influence on river and wetland
habitats for plants and animals.
The groundwater system as a whole is a three dimensional flow field; therefore, it is important
to understand how the vertical components of groundwater movement affect the interaction of
groundwater and surface water. A vertical component of a flow field indicates how the potential
energy is distributed beneath the water table in the groundwater system and how the energy
distribution can be used to determine vertical components of flow near a surface water body. The
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potential energy is also described as the hydraulic head which is the sum of elevation and water
pressure divided by the weight density of water.
The geology of an area governs movement and availability of surface and ground waters. The
permeability of geologic materials and the intensity of precipitation determine the water flows
above and below the land surface. Each geologic material exhibits its own permeability based
upon its chemical and structural composition.
Much groundwater discharge into surface water is from local flow systems. Local flow systems
are the most dynamic and the shallowest flow systems; therefore, they have the greatestinterchange with surface water. Local flow system can be underlain by intermediate and regional
flow systems. Water in deeper flow systems have longer flow paths, but eventually discharge to
surface water and they can have a great effect on the chemistry of the receiving water.
After rainfall events, materials with low permeability will cause water to pond whenever the
water input (recharge) exceeds the capacity of the materials to hold the water. Ponding of water
will then cause water movement across the land surface and/or into the subsurface. Surface
movement of water will follow elevation differences on the land surface, thus water will
eventually spill into lakes, streams, rivers, etc. (Figure 3.1)
Figure 3.1 Flow through a Hypothetical aquifer system (GSFLOW model based on integration of
PRMS and MODFLOW 2005, Steven.L et.al USGS Techniques and methods 6-D1, 2008)
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3.2 Interaction of groundwater and stream
The interaction between groundwater and streams takes place in three basic ways: streams gain
water from inflow of groundwater through the streambed (gaining stream), they lose water to
groundwater (losing stream) or they do both, gaining in some reaches and losing in other reaches
Woesner (2000) classified four types of interactions between a stream and groundwater: (1)
gaining, where the groundwater flows into the stream; (2) losing, where the water in the stream
drains into the aquifer; (3) flow through, where the groundwater flows into the stream on one
side of the channel and out of the stream on the other side of the channel; and (4) parallel, where
the groundwater flows in the aquifer beneath the stream and in the same direction as the stream
without entering or leaving the stream. (Fetter, 2001)
Generally, Streams either gain water from inflow of ground water (gaining stream; Figure 3.2A)
or lose water by outflow to ground water (losing stream; Figure 3.2 B). Many streams do both,
gaining in some reaches and losing in other reaches. Furthermore, the flow directions between
ground water and surface water can change seasonally as the altitude of the ground-water table
changes with respect to the stream-surface altitude or can change over shorter timeframes when
rises in stream surfaces during storms cause recharge to the stream bank. Under natural
conditions, ground water makes some contribution to stream flow in most physiographic and
climatic settings. Thus, even in settings where streams are primarily losing water to ground water,
certain reaches may receive ground-water inflow during some seasons.
Losing streams can be connected to the ground-water system by a continuous saturated zone
(Figure 3.2A,B) or can be disconnected from the ground-water system by an unsaturated zone
(Figure 3.2C). An important feature of streams that are disconnected from ground water is that
pumping of ground water near the stream does not affect the flow of the stream near the pumped
well.
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Figure 3. 2 Interaction of streams and ground water. (Winter et.al, 1998.)
In Figure 3.2, (A) represents gaining streams that receive water from the ground-water system,
whereas losing streams (B) lose water to the ground-water system. For ground water to discharge
to a stream channel, the altitude of the ground water table in the vicinity of the stream must be
higher than the altitude of the stream-water surface. Conversely, for surface water to seep to
ground water, the altitude of the water table in the vicinity of the stream must be lower than the
altitude of the stream surface. Some losing streams (C) are separated from the saturated ground-
water system by an unsaturated zone.
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A pumping well can change the quantity and direction of flow between an aquifer and stream in
response to different rates of pumping. Figure 4 illustrates a simple case in which equilibrium is
attained for a hypothetical stream-aquifer system and a single pumping well. The adjustments to
pumping of an actual hydrologic system may take place over many years, depending upon the
physical characteristics of the aquifer, degree of hydraulic connection between the stream and
aquifer, and locations and pumping history of wells. Reductions of stream flow as a result of
ground-water pumping are likely to be of greatest concern during periods of low flow,
particularly when the reliability of surface-water supplies is threatened during droughts.
At the start of pumping, 100 percent of the water supplied to a well comes from ground-water
storage. Over time, the dominant source of water to a well, particularly wells that are completed
in an unconfined aquifer, commonly changes from ground-water storage to surface water. The
surface-water source for purposes of discussion here is a river, but it may be another surface-
water body such as a lake or wetland. The source of water to a well from a stream can be either
decreased discharge to the stream or increased recharge from the stream to the ground-water
system. The streamflow reduction in either case is referred to as streamflow capture.
In the long term, the cumulative stream- flow capture for many ground-water systems canapproach the quantity of water pumped from the ground-water system. This is illustrated in
Figure 14, which shows the time-varying percentage of ground-water pumpage derived from
ground-water storage and the percentage derived from streamflow capture for the hypothetical
stream-aquifer system shown in Figure 13. The time for the change from the dominance of
withdrawal from ground-water storage to the dominance of streamflow capture can range from
weeks to years to decades or longer.
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Figure 3. 3 Effects of pumping from a hypothetical aquifer discharging to a stream (Heath, 1983, cited
by USGS, Circular 1186)
Under natural conditions Figure 3.3A, recharge at the water table is equal to ground-water
discharge to the stream. Assume a well is installed and is pumped continuously at a rate, Q1, as
in Figure 3.3B. After a new state of dynamic equilibrium is achieved, inflow to the ground-water
system from recharge will equal outflow to the stream plus the withdrawal from the well. In this
new equilibrium, some of the ground water that would have discharged to the stream is
intercepted by the well, and a ground-water divide, which is a line separating directions of flow,
is established locally between the well and the stream. If the well is pumped at a higher rate, Q 2,
a different equilibrium is reached, as shown in Figure 3.3C. Under this condition, the ground-
water divide between the well and the stream is no longer present, and withdrawals from the well
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induce movement of water from the stream into the aquifer. Thus, pumping reverses the
hydrologic condition of the stream in this reach from ground-water discharge to ground-water
recharge. In the hydrologic system depicted in Figure 3.3 (A) and (B), the quality of the stream
water generally will have little effect on the quality of ground water. In the case of the well
pumping at the higher rate in Figure 3.3 (C), however, the quality of the stream water can affect
the quality of ground water between the well and the stream, as well as the quality of the water
withdrawn from the well. Although a stream is used in this example, the general concepts apply
to all surface-water bodies, including lakes, reservoirs, wetlands, and estuaries.
In gaining and in losing streams, water and dissolved chemicals can move repeatedly over short
distances between the stream and the shallow subsurface below the streambed. The resulting
subsurface environments, which contain variable proportions of water from ground water and
surface water, are referred to as hyporheic zones (see Figure 3.4). Hyporheic zones can be active
sites for aquatic life. For example, the spawning success of fish may be greater where flow from
the stream brings oxygen into contact with eggs that were deposited within the coarse bottom
sediment or where stream temperatures are modulated by ground-water inflow. The effects of
ground-water pumping on hyporheic zones and the resulting effects on aquatic life are not well
known.
Figure 3. 4 The dynamic interface between ground water and streams. (Winter et.al, 1998.)
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3.3. Interaction of Groundwater and Lakes
Lakes, both natural and human made, are present in many different parts of landscapes and can
have complex ground-water-flow systems associated with them. Lakes interact with ground
water in one of three basic ways: some receive ground-water inflow throughout their entire bed;
some have seepage loss to ground water throughout their entire bed; and others, perhaps most
lakes, receive ground-water inflow through part of their bed and have seepage loss to ground
water through other parts. Lowering of lake levels as a result of ground-water pumping can affect
the ecosystems supported by the lake diminish lakefront esthetics, and have negative effects on
shoreline structures such as docks.
The chemistry of ground water and the direction and magnitude of exchange with surface water
significantly affect the input of dissolved chemicals to lakes. In fact, ground water can be the
principal source of dissolved chemicals to a lake, even in cases where ground-water discharge is
a small component of a lake's water budget. Changes in flow patterns to lakes as a result of
pumping may alter the natural fluxes to lakes of key constituents such as nutrients and dissolved
oxygen, in turn altering lake biota, their environment, and the interaction of both.
3.4 Interaction of Groundwater and Wetlands
Wetlands occur in widely diverse settings from coastal margins to flood plains to mountain
valleys. Similar to streams and lakes, wetlands can receive ground-water inflow, recharge ground
water, or do both. Public and scientific views of wetlands have changed greatly over time.
Wetlands generally were considered to be of little or no value. It is now recognized that wetlands
have beneficial functions such as wildlife habitat, floodwater retention, protection of the land
from erosion, shoreline protection in coastal areas, and water-quality improvement by filtering of
contaminants.
The persistence, size, and function of wetlands are controlled by hydrologic processes (Carter,
1996). Characterizing ground-water discharge to wetlands and its relation to environmental
factors such as moisture content and chemistry in the root zone of wetland plants is a critical
aspect of wetlands hydrology (Hunt et.al, 1999).Wetlands can be quite sensitive to the effects of
ground-water pumping. Ground-water pumping can affect wetlands not only as a result of
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progressive lowering of the water table, but also by increased seasonal changes in the altitude of
the water table.
3.5 Groundwater and Coastal Environments
Coastal areas are a highly dynamic interface between the continents and the ocean. The physical
and chemical processes in these areas are quite complex and commonly are poorly understood.
Historically, concern about ground water in coastal regions has focused on seawater intrusion
into coastal aquifers. More recently, ground water has been recognized as an important
contributor of nutrients and contaminants to coastal waters. Likewise, plant and wildlife
communities adapted to particular environmental conditions in coastal areas can be affected by
changes in the flow and quality of ground-water discharges to the marine environment.
3.6. Human activity and interaction of groundwater and surface water
Many natural and human activities affect the interaction of groundwater and surface water. These
include agricultural development, urban and industrial development, and drainage of the land
surface, modification to river valleys and modification to the Atmosphere.
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Chapter 4
Description of the study area
4.1 Geographical location
Belgium is a small country in Western Europe bordering the North Sea, between France and the
Netherlands (Figure 4.1) with a total area of 30,528 sq km (CIA world fact) covers a land area of
30,278 sq km and water covers 250 sq km of the area. The geography of Belgium, with the
geographic coordinate of 50 50'N, 4 00E, shows to have three different areas: lower Belgium
(up to 100 m above sea level), Central Belgium (between 100 and 200 m above sea level) and
Upper Belgium (from 200 to over 500m above sea level, with the highest point at an elevation of
694 meters above sea level..
Flanders is one of the three regions of Belgium and it is situated on the Northern part of Belgium
and covers an area of 13.524 km2
(44% of Belgium), bordered by Netherlands and France.
Among the major rivers of Flanders, Nete is one of them. Nete Basin covers an area of 1672.6
km2.
The area used for the modeling in this thesis is found at the Eastern part of the Nete area,
NE of Antwerp, Belgium.
Figure 4. 1 Geographical Location of Belgium (from the World Atlas Map)
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Figure 4. 2 The study area and its location in the Nete Basin.
Kleine Nete
basin
Study area
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4.3 Topography
Figure 4.3 shows the contour of the Topographic elevations in the area. The highest points are
found at the Southeastern part and reach 21.88 meters while the lowest elevation point is located
in the Southwestern part of the model and reaches 4.85 meters above the datum of the model.
Three dimensional view of the slope is shown in Figure 4.4 The slope of the elevation of the
topography is shown in figure 4.5.
181200 181400 181600 181800 182000 182200 182400 182600 182800
X - Lambert (m)
210400
210600
210800
211000
211200
211400
211600
Y
-lambert(m)
0 100 200 300 400
m
LEGEND
14 Elevation contour
Observation well
Figure 4. 3 Two dimensional view and elevation of the study area.
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Figure 4. 4 3D of Topography
Figure 4. 5 Slope map of the study area
4.4 Hydrologicalsetting
Surface water
A 2.4 Km segment of the Aa river occurs in the study area. It flows through the study area from
the North - Eastern to the South Western ends. This river segment is gaining from ground
water in its upstream part and loosing in its downstream section (This is discussed in detail in
chapter 8). The main Aa river has a total length of 36.7 Km with a drainage area of 23.7 km2
.
The average discharge is 1.74m3
/s and average water depth is 1.15m and an average width of
7.5m.
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Ground water
The regional aquifer underlying the area is preliminary the tertiary and Quaternary sands. The
dominant sources of recharge to the model area are precipitation in the winter, river leakage and
constant heads. Dominant mechanisms of discharge from the groundwater are drains, river
leakages and pumping wells.
4.5 Recharge
Spatially distributed recharge over the entire first layer of the model (in mm/y) was used in the
modeling process. There were six reclassified recharge zones.
4.6 Land-use and Soil
In general, the texture of the soil can be described as sandy loam, clay, loamy sand, and
sand .The main land use types of the area are agriculture (50%), Meadow (17.29%), build up
(1.98%) and coniferous forest (11.29%).
4.7 Climate of the study area
Flanders has a temperate, oceanic climate. The average annual rainfall is 780 mm and the
average temperature is 9.8 degree centigrade. Statistical analysis of the observed temperature
data indicates January being the coldest month of the year with the average temperature of 5.8 C
and august as the warmest month of the year with an average temperature of 18C. However, the
study area has a moderate average winter and summer temperatures of 5C and 14C, with wind
speed of 3.27 and 3.84 m/s respectively.
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4.8 Available data
1) Digital Elevation Model:
The DEM with 5m by 5m grid size covering the whole study area was created by digitizing the
topographic contour map of the area.
2) Meteorological data:
The basic meteorological data requirement for running the model is recharge. These data was
collected from the previous works and the measurements on the Aa river.
3) Flow data:
Observed daily discharge data are taken from the measurement points of the Aa river. The flow
data is used for model calibration.
4) Hydrogeologic and Geologic data:
The geologic and hydrogeologic characteristics and parameters of the study area including the
hydraulic conductivity ranges, bottom elevation of the layers is collected from previous works by
Solomon T, 2006.
5) Well data:
Three pumping wells and 5 observation wells are identified in the area. Their location (X-Y
coordinate), average pumping rate and depth of the filter is available from the previous studies
and recent measurements from the study area.
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Chapter 5
Modeling tools
In this chapter, the tools used for modeling of the study area are described. The first part deals
with ArcView GIS and in the second part, the three-dimensional groundwater modeling
environment of waterloo hydrogeologic Inc, Visual MODFLOW is discussed.
5.1 ArcView GIS
5.1.1 Introduction
Geographical Information System (GIS) is a tool used to gather, transform, manipulate, analyze,
and produce information related to the surface of the Earth, i.e. geographically referenced data.
GIS is an information system where the database consists of observations on spatially distributed
features, activities or events which are definable in space. ArcView is a GIS software that allows
creating maps, and adding information. Using Arc Views visualization tools, records from
existing databases can be accessed and displayed on maps. ArcView GIS 3.2 is the revised
version of 3.1.
5.1.2 Types of data used in ArcView GIS
ArcView GIS comes with a full set of ready-to-use general purpose data. For many applications,the data are used to create maps or are used as a base where data can be added.
5.1.3 Geographical data
Data that describes any part of the earths surface or the features found on it can be called
geographic data. Geographic data from a variety of sources are used in ArcView. This includes
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not only cartographic and scientific data, but also land records, photographs, real estate listings,
videos, etc. In fact a surprisingly large amount of information is geographic.
5.1.4 Spatial data
Spatial data is the heart of every ArcView application. Spatial data is geographic data that stores
the geometric location of particular features, along with attribute information describing what
these features represent. Spatial data is also known as digital map or digital cartographic data.
5.1.5 Image data
Image data includes satellite images, Air photographs and other remotely sensed or scanned data.
5.1.6 Tabular data
Tabular data includes almost any data set, whether or not it contains geographic data. Some
views are displayed are displayed directly on a view directly; others provide additional attributes
that can be joined to existing spatial data. ArcView supports the following formats: i) Data from
database servers such as Oracle, Ingres, Sybase, Informix, etc. ii) dBase III files iii) INFO tables
v) Text files with fields separated by tabs or commas. XY event tables are used in this project.
5.1.7. Extensions of GIS
Some extensions of GIS used in the project re as follows:
i) 3D Analyst
3D Analyst is an extension that adds support for 3D shapes, surface modeling, and real timeperspective viewing to ArcView. Spatial data can be created and visualized with 3D analyst
by using a third dimension to provide insight, reveal trends, and solve problems.
ii) Geoprocessing
The Geoprocessing is an extension which performs spatial analysis function in ArcView. The
wizard makes to walk through the desired theme to select for processing and allows selecting
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the name and location of the resulting output shape file. The following functions are provided
in the wizard: a) Dissolve features based on an attribute b) Merge themes together c) Clip one
theme based on another d) Intersect two themes f)Assign data by location.
iii) Grid analyst extension
It is used to transform data from one form to another. This extension is used here to convert
image to grid theme, convert grid theme to x, y, z text file, and extract X, Y and Z values for
point theme from grid theme.
iv) Spatial Analyst
The ArcView Spatial analyst is an extension used to discover and understand spatial
relationship within a data. The main component of the spatial is the grid theme. The grid
theme is the raster equivalent of the feature theme. The spatial Analyst also represents
generic spatial analysis functionality on grid and feature themes that is added to ArcView as
an extension that is loaded with Extensions in the file menu when the project window is
active. The user interface components of the spatial analyst are loaded into the interface for
views.
5.2 Visual MODFLOW
Visual MODFLOW is the most complete and easy-to-use modeling environment for practical
applications in three dimensional groundwater flow and contaminant transport simulations.
This fully- integrated package combines MODFLOW, MODPATH, zone budget,
MT3Dxx/RT3D, and WinPEST with graphical interface. Visual MODFLOW is designed with a
modular structure each dealing with a specified feature of the hydrologic system. Visual
MODFLOW provides professional 3D groundwater flow and contaminant transport modeling
using MODFLOW-2000, MODPATH, MT3DMS and RT3D.Visual MODFLOW Pro seamlessly
combines the standard Visual MODFLOW package with WinPEST and the Visual MODFLOW
3D-Explorer to give the most complete and powerful graphical modeling environment available.
This fully-integrated groundwater modeling environment allows to:
Graphically design the model grid, properties and boundary conditions,
Visualize the model input parameters in two or three dimensions,
Run the groundwater flow, path line and contaminant transport simulations,
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Automatically calibrate the model using WinPEST or manual methods, and
Display and interpret the modeling results in three-dimensional space using the Visual
MODFLOW 3D-Explorer
5.3. Surfer 8
Surfer is contouring software which easily and quickly converts grid data to contours and 3D
surfaces, wireframe, vectors, image, shaded relief and post map. Contours of the topography and
3D views of the geological cross sections in this report were produced with surfer 8.
5.4 Grapher 7
Grapher 7 is an easy-to-use technical graphing package to generate graphs quickly and
easily. With Grapher, creating a graph is as easy. One can change tick mark spacing, tick labels,
axis labels, axis length, grid lines, line colors, symbol styles, and more. It is also possible to add
legends, bitmaps, fit curves, and drawing objects to the graph. The 2D geologic cross- sections in
this study were generated using Grapher 7
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Chapter 6Model Setup
6.1 Description of the Groundwater Flow Model
The steps of model construction can be summarized as follows (Pinder, 2002):
1. Establish the minimum area to be represented by the model.
2. Determine the hydrological features that can serve as boundaries to the model.
3. Compile the geological information.
4. Compile the hydrological information.
5. Determine the number of physical dimension needed for the model.
6. Define the size of the model.
7. Define the model descritization.
8. Input the model boundary conditions.
9. Input the model parameters.
10. Input the model stresses.
11. Run the model.
12. Output the calculated hydraulic heads.
13. Calibrate the model.
14. Make the production runs.
The groundwater model boundary areal extent must be such as to incorporate all locations where
model heads are expected to change in response to stresses imposed on the model, incorporate
the area of interest to the client and to the extent possible coincide with an area defined by
distinct and easily evaluated hydrological boundary conditions.
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The model area in this study is found within the Nete Catchment. The groundwater model
boundary encloses the main model domain which is part of a larger model domain for the Nete
Catchment; it includes a segment of the Aa river flowing from the North Eastern to the South
western part of the model. It is bounded by constant head boundary along all its four sides.
This ground-water model was developed using Visual MODFLOW 3.0. ArcView GIS 3.2
software was also used for input data preparation and output data. The final model design
follows several model runs to best match field data with model results, also called model
calibration (chapter 7). The conceptual model information is inserted into the mathematical
model and model choices are made to suit the data entered and output required. Visual
MODFLOW requires model data to be entered as consistent units. Selected units are meters and
day, except for recharge where mm/y is used.
Model needs include:
Layers
Elevation limits
Grid
Recharge
Surface elevation
Bottom elevation
Groundwater pumping
Aquifer characteristics
River conductance
River bottom and stage
6.1.1 Model dimensions
The model area has a rectangular geometry and is 1.8 km from East to West and 1.5 km from
North to South (Table.6.1).
Table 6. 1 Geographic extent of the model.
Easting Minimum 0 Easting Maximum 1800
Northing Minimum 0 Northing Maximum 1500
The geographic boundaries of the model domain are given in the Belgian Lambert co-ordinate
system, and have a lower left corner co-ordinate at 181181 and 210274 as X and Y co-ordinate
respectively. These values were used as X min and Y min in the model setup window of Visual
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MODFLOW. Similarly, the upper right model corner is 182981 and 211774 for the X and Y co-
ordinates and these are used as X max and Y max in the model setup window of Visual
MODFLOW (Fig 6.1).
Figure 6. 1 Model domain and units of measurement.
The model framework, given in Figure 6.1 is summarized in Table 6.2.
Table 6. 2 Model Configuration
CHARACTERSTICS VALUE
Maximum model elevation 21.88 m
Minimum model elevation -88.75 m
Layers 3
Grid cell size 5mRows 300
Columns 360
6.1.2 Layers
There are three model layers labeled 1 - 3 from top to bottom. Layer 1 is composed of
Quaternary sediments (HCOV 110 160) which comprise recent alluvium and Pleistocene sand.
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Layer 2 constitutes the HCOV 230 hydrogeologic unit which is a Pleistocene and Pliocene
aquifer system composed mainly of fine sand and clays. Layer 3 is comprised of HCOV 240
(Pliocene clay layer) and HCOV 250 (Miocene sand aquifer). (Solomon T. 2007).
6.1.3 Elevation limits
The datum of the model is located within layer 2 of the model. The maximum model elevation is
21.87 meters above the model datum and represents the highest point of the topography of the
model area. The greatest model depth is 88.75 meters below the datum of the model.
6.1.4 Grid
The model grid is 5 meters by 5 meters, evenly spaced throughout the model area in a North -
South, East-West orientation. The model grid includes 300 rows and 360 columns.
6.1.5 Elevation data
Surface and bottom elevations are entered to give model volume within the model perimeter.
Surface elevations and bottom elevations data of the three layers were exported from ArcView
and imported into Visual MODFLOW.
Importing surface and bottom elevation
Model surface elevation values shown in Figure 4.3 were entered into the model as an xyz data
file. This surface elevation data was derived from an ASCII file by ArcView GIS. Similarly,
Model bottom elevations of the three layers interpolated in ArcView were imported to the visual
MODFLOW using the import elevation command. Figures 6.2 to Figure 6.4 show the elevations
imported.
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Figure 6. 2 Bottom elevation for layer 1
Figure 6. 3 Bottom elevation of layer 2
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local scale of the model of this study, the base of layer 1 is HCOV 160, which is sand. The base
of layer 2 is HCOV 230 and the base of layer 3 is HCOV250. Below HCOV 250, there is a clay
aquitard known as the Boom clay aquitard.
Table 6. 3 Main units of the HCOV hydrogeological code (Cools.et.al, 2006)
Table 6. 4 Overview of aquifers on the HCOV classification for Flanders (Solomon T. 2007)
Aquifer code
(HCOV)
Aquifer name Total Hydraulic conductivity
(m/d)
0100 Quaternary aquifer
/sand/
1-10
0220 Campine clay-sand-
complex
5-15
0230 Pleistocene andPliocene aquifer /sand/ 4-40
0240 Pliocene clay layer 0.04-0.2
0250 Miocene aquifer/sand/ 3-30
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6.1.7 Aquifer characteristics data
The hydrogeologic layers of the model are bounded by clay aquitard at the bottom and recent
alluvial deposits at the top. The steady state model requires the hydraulic conductivity of each
model layer.
Figure 6. 5 Stratigraphy of the different aquifer units of the model.
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Figure 6. 6 Geologic cross section along the middle points of the model in the N S direction.
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Figure 6. 7 Geologic cross section along the river flow route
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6.1.8. Hydraulic conductivity
Hydraulic conductivity zones vary widely in the area. The total hydraulic conductivity of each
HCOV layer is indicated in Table 6.4. (According to Solomon T, 2007), the total conductivity of
the aquifers given in Table 6.4, were taken from a detailed hydro-geological study of the Flemish
underground (Envico 2002a; Envico 2002b; Haecon 2002), and from pumping tests preformed
by Provincial and Intercommunal drinking water society of the Province Antwerp (PIDPA).
6.1.9 River
The river in the model domain is the part of the Aa river (Figure 6.8). The river flows from
North-East to South West direction within the model domain. Aa river has an average discharge
of 1.74 m3/s, a water depth of 1.15 m and width of 7.5 m. Quantifying the amount of water
exchanged between this river and the groundwater of the area is one of the major objectives of
this model. The river stage, river bed bottom elevation, river bed thickness and river conductance
were the data used for the surface water groundwater interaction modeling. The river boundary
condition package was used for data entry into visual MODFLOW.
Figure 6. 8 Two- dimensional view of the river segment in the model domain.
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