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# Movement of Salt and Hazardous Contaminants in Groundwater Systems

## Material Information

Title:
Movement of Salt and Hazardous Contaminants in Groundwater Systems
Series Title:
Florida Water Resources Research Center Publication Number 71
Physical Description:
Book
Creator:
Benedict, Barry A.
Rubin, Hillel
Means, Stephen A.
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

## Notes

Abstract:
Efforts have been directed toward finding ways of reducing computer resources and expertise required for modeling movement of contaminants through the groundwater system. An approach has been developed which simplifies the basic equations. To test the method, it has been applied to the stratified flow problem associated with the upward seepage of saline water into freshwater aquifers overlying semiconfining formations. This seepage in response to pumpage is particularly of concern in northeastern Florida, which obtains the majority of its potable water from the freshwater zone of the Floridan aquifer. This region is being subjected to increasing rates of pumpage. Traditional attempts to simulate the mineralization process in a stratified aquifer arose by applying a sharp interface assumption or by a complete solution of the equations of motion and solute transport through the aquifer. The sharp interface approach suffers from a lack of coherence with the physical phenomena while the complete solution approach involves sets of highly nonlinear differential equations, the solution of which is subject to serious problems of stability and convergence. This study attempts to simplify the basic model by the application of the Dupuit approximation in conjunction with the boundary layer theory to a flow field divided into three zones as follows: (a) the freshwater zone, (b) the saltwater zone, and (c) the transition zone. The equations of continuity, motion, and solute transport are solved simultaneously subject to the conditions found in the simplified flow field. The result is the development of three partial differential

## Record Information

Source Institution:
University of Florida Institutional Repository
Holding Location:
University of Florida
Rights Management:
System ID:
AA00001552:00001

Full Text

BY

BARRY A. BENEDICT, HILLEL RUBIN,
AND STEPHEN A. MEANS

PUBLICATION NO. 71

FLORIDA WATER RESOURCES RESEARCH CENTER
RESEARCH PROJECT TECHNICAL COMPLETION REPORT

ACKNOWLEDGEMENTS

This project was sponsored by the Florida Water Resources Research

Center with funds provided by the United States Department of the Inter-

ior, Office of Water Research and Technology. Additional funds were

provided by the Engineering and Industrial Experiment Station, Univer-

sity of Florida. The assistance of Dr. James Heaney and Mary Robinson

of the Water Resources Center is appreciated.

The computer facilities of the Northeast Regional Data Center of

the State University System of Florida were used for this work.

The material presented in this report is substantially the same as

presented by Mr. Means in partial fulfillment of the requirements for

the Master of Engineering degree under the title "Numerical Simulation

of Aquifer Mineralization in Northeastern Florida."

ACKNOWLEDGEMENTS . . . . .
LIST OF TABLES . . . . .
LIST OF FIGURES . . . . .
LIST OF SYMBOLS . . . . .
ABSTRACT.. . . . . . .
CHAPTER

1 INTRODUCTION . . . . . .

1.1 Objectives and Possible Approaches . . .
1.2 General Scope of Study . . . .
1.3 Methodology . . . . .

2 THE FLORIDAN AQUIFER IN NORTHEASTERN FLORIDA . .

Introduction . . . .
Geology . . . .
The Availability of Potable Groundwater
Mineralization . . .
Current Assessment . . .
Summary . . . .

3 STUDIES LEADING TO THE QUANTITATIVE ANALYSIS OF AQUIFER
MINERALIZATION . . . . .

3.1
3.2
3.3
3.4
3.5
3.6

Introduction . . .
Early Studies . . .
Current Approaches . . .
Analytical Techniques . .
Numerical Techniques . . .
Summary . . . .

4 THE APPROXIMATE METHOD OF STRATIFICATION ANALYSIS ..

4.1 Introduction . . . . .
4.2 Description of the Flow Field . . .
4.3 Basic Equations . . . .
4.4 The Integral Method of Boundary Layer
Approximation . . . . .
4.5 Summary . . . . . .

j :

CHAPTER Page

5 NUMERICAL SIMULATION . . . .... .50

5.1 Introduction . . . .... .. 50
5.2 The Numerical Model . . . .... 51
5.3 Model Execution . . . . ... .56
5.4 Numerical Results . . . . 59
5.5 Discussion and Conclusions . . .. 96
5.6 Summary . . . . ... . 102

6 CONCLUSIONS . . . . ... ... .104

APPENDIX A

APPENDIX B

THE DEVELOPMENT OF THE FINITE DIFFERENCE SCHEMES
REPRESENTING EQUATION (4.22) . . .... 107

COMPUTER PROGRAM . . . .... 112

REFERENCES . . . . . . .

LIST OF TABLES

Table Page

2.1 Historical groundwater withdrawals for irrigated crops
in the Tri-County area . . ........... 13

2.2 Aquifer test data . . . . . 18

5.1 Parameter values for the execution of the preliminary
simulation ............................. 60

5.2 Summary of experiments . . . .... 73

LIST OF FIGURES

Figure Page

2.1 Delineation of the study area . ....... 5

2.2 Geologic column showing rock units in the Tri-County
area . . . ... . . . 7

2.3 Diagram showing the generalized hydrologic conditions
in Northeastern Florida . . . ... .10

2.4 Physiographic features of the Tri-County area . .. .11

2.5 Piezometric level and generalized direction of groundwater
movement in the Tri-County area, March, 1975 ...... 15

2.6 Location of the areas of intensive agriculture within
the Tri-County area. . . .. . 16

2.7 Location of aquifer test sites in the Tri-County area 17

2.8 Location of the freshwater zone and the saline water
zone within the Floridan Aquifer . . .... 21

2.9 Schematic diagram of saltwater coning as related to the
Tri-County area . . . . ... .. 22

2.10 Piezometric map of the Floridan Aquifer, March, 1975 24

2.11 Isochlor map of the Floridan Aquifer, March,1975 .. 25

2.12 Piezometric map of the Floridan Aquifer, September, 1975 .26

2.13 Isochlor map of the Floridan Aquifer, September, 1975 27

4.1 Schematic description of the development of a transition
zone in a stratified aquifer . . . .. 41

4.2 Control volume for the development of equation (4.22) 47

5.1 Flow chart . . . ... .. .. .. 57

5.2 Map of pumpage. Pumpage rate = 0.1 m/day . ... 62

5.3a Map of drawdowns. T = 2.0 days, maximal ordinate
= 20.01 m . . . .. .... .. .. 63

Figure

5.3b Map of saltwater mound.
ordinate = 0.88 m .

5.3c Map of transition zone.
ordinate = 5.03 m .

5.4a Map of drawdowns. T =
ordinate = 20.12 m .

5.4b Map of saltwater mound.
ordinate = 2.83 m .

5.4c Map of transition zone.
ordinate = 9.03 m .

5.5a Map of drawdowns. T
ordinate = 20.22 m .

5.5b Map of saltwater mound.
ordinate = 4.69 m .

5.5c Map of transition zone.
ordinate = 11.70 m .

T = 2.0 days, maximal

T 2.0 days, maximal

T = 2.0 days, maximal

T = 6.0 days, maximal

T6.0 days, maximal

10.0 days, maximal

T = 1.0 days, maximal

T 10.0 days, maximal .
T = 6.0 days, maximal
. . .

10.0 days, maximal
. . . .

T = 10.0 days, maximal
. . .

T = 10.0 days, maximal

5.6 Rate of growth of the maximal value of the drawdown,
the height of the saltwater mound, and the thickness
of the transition zone . . . .

5.7a Map of drawdowns. DT = 0.2 days, T = 2.0 days,
maximal ordinate = 20.01 m . . . .

5.7b Map of saltwater mound. DT = 0.2 days, T = 2.0 days,
maximal ordinate = 0.88 m . . . .

5.7c Map of transition zone. DT = 0.2 days, T = 2.0 days,
maximal ordinate = 4.96 m . . . .

5.8a Map of drawdowns. a = 0.05 m, T = 2.0 days, maximal
ordinate = 19.99 m . . . . .

5.8b Map of saltwater mound. a = 0.05 m, T = 2.0 days,
maximal ordinate = 0.88 m . . . .

5.8c Map of transition zone. a = 0.05 m, T = 2.0 days,
maximal ordinate = 1.58 m . . . .

5.9a Map of drawdowns. a = 0.05 m, T = 6.0 days,
maximal ordinate = 20.08 m . . . .

Page

. . 64

. . 65

. . 66

. . 67

. . 68

. . 69

. . 70

. . 71

Figure Page

5.9b Map of saltwater mound. a = 0.05 m, T = 6.0 days,
maximal ordinate = 2.83 m . . . . 81

5.9c Map of transition zone. a = 0.05 m, T = 6.0 days,
maximal ordinate = 2.84 m . . . . 82

5.10a Map of drawdowns. a = 0.05 m, T = 10.0 days, maximal
ordinate = 20.17 m . . . . . 83

5.10b Map of saltwater mound. a = 0.05 m, T = 10.0 days,
maximal ordinate = 4.69 . . . . 84

5.10c Map of transition zone. a = 0.05 m, T = 10.0 days,
maximal ordinate = 3.67 m . . . . 85

5.11a Map of drawdowns. N = 0.01 m/day, T = 2.0 days,
maximal ordinate = 2.00 m . . . .. 86

5.11b Map of saltwater mound. N = 0.01 m/day, T = 2.0 days,
maximal ordinate = 0.09 m . . . . 87

5.11c Map of transition zone. N = 0.01 m/day, T = 2.0 days,
maximal ordinate = 1.50 m . . . . 88

5.12a Map of drawdowns. N = 0.01 m/day, T = 6.0 days,
maximal ordinate = 2.01 m . . . . 89

5.12b Map of saltwater mound. N = 0.01 m/day, T = 6.0 days,
maximal ordinate = 0.28 m . . . . 90

5.12c Map of transition zone. N = 0.01 m/day, T = 6.0 days,
maximal ordinate = 2.82 m . . . . 91

5.13a Map of drawdowns. N = 0.01 m/day, T = 10.0 days,
maximal ordinate = 2.02 m . . . . 92

5.13b Map of saltwater mound. N = 0.01 m/day, T = 10.0 days,
maximal ordinate = 0.47 m . . . . 93

5.13c Map of transition zone. N = 0.01 m/day, T = 10.0 days,
maximal ordinate = 3.63 m . . . . 94

5.14 Rate of growth of the maximal values of the drawdown, the
height of the saltwater mound, and the thickness of the
transition zone for experiment numbers 2 and 3 . .. 95

viii

LIST OF SYMBOLS

a dispersivity

B thickness of freshwater zone

Bo thickness of freshwater zone at the edge of the transition zone

B1 thickness of semiconfining formation

C solute concentration

Co characteristic solute concentration

Cf solute concentration of freshwater

C solute concentration of mineral water
s
D coefficient of dispersion

D dispersion tensor

F distribution function of specific discharges

t unit vertical vector

K hydraulic conductivity of the aquifer

Kf hydraulic conductivity of a porous medium containing freshwater

K1 hydraulic conductivity of the semiconfining formation

Ks hydraulic conductivity of a porous medium containing saltwater

L distribution function of solute concentration

m time index used in finite difference equations

n porosity

N pumpage or recharge per unit area

p pressure

q specific discharge vector

s drawdown of the piezometric head

S coefficient of storage

t time

u specific discharge in the transition zone in the x direction

U characteristic specific discharge in the x direction

v specific discharge in the transition zone in the y direction

V characteristic specific discharge in the y direction

x horizontal coordinate

y horizontal coordinate

z elevation

zb elevation of the bottom of the transition zone

zt elevation of the top of the transition zone

Greek Letters

a coefficient relating concentration with specific weight

y specific weight

YO specific weight of reference

Yf specific weight of freshwater

Ys specific weight of mineral water

6 thickness of the transition zone

r dimensionless coordinate defined in equation (4.11)

C buoyancy coefficient defined in equation (4.14)

if piezometric head at freshwater zone

ffo original piezometric head at freshwater zone

?ft piezometric head at the top of the transition zone

es piezometric head at mineral water zone

!so original piezometric head at mineral water zone

*sb piezometric head at the bottom of the transition zone

ABSTRACT

Efforts have been directed toward finding ways of reducing computer

resources and expertise required for modeling movement of contaminants

through the groundwater system. An approach has been developed which sim-

plifies the basic equations. To test the method, it has been applied to

the stratified flow problem associated with the upward seepage of saline

water into freshwater aquifers overlying semiconfining formations. This

seepage in response to pumpage is particularly of concern in north-

eastern Florida, which obtains the majority of its potable water from

the freshwater zone of the Floridan aquifer. This region is being subjected

to increasing rates of pumpage.

Traditional attempts to simulate the mineralization process in a

stratified aquifer arose by applying a sharp interface assumption or by

a complete solution of the equations of motion and solute transport

through the aquifer. The sharp interface approach suffers from a lack

of coherence with the physical phenomena while the complete solution

approach involves sets of highly nonlinear differential equations, the

solution of which is subject to serious problems of stability and

convergence.

This study attempts to simplify the basic model by the application

of the Dupuit approximation in conjunction with the boundary layer

theory to a flow field divided into three zones as follows: (a) the

freshwater zone, (b) the saltwater zone, and (c) the transition zone.

The equations of continuity, motion, and solute transport are solved

simultaneously subject to the conditions found in the simplified flow

field. The result is the development of three partial differential

equations describing in three dimensions the distribution of the drawdowns

in the flow field, the growth of the saltwater mound, and the development

of the transition zone. These equations are formulated into a numerical

model by utilizing an iterative alternating direction implicit (ADI)

method and the appropriate linear finite difference representation.

The results of the execution of the numerical model indicate that

a highly stable, convergent numerical scheme is developed in this study.

The model is capable of describing the three-dimensional effects asso-

ciated with the transient nature of stratified flow in an aquifer.

While the specific example treated salt movement, other contaminants,

including hazardous wastes, could easily be modeled in the same way in a

stratified conditions or occur in a saline-stratified region, the same

basic procedure can be utilized by removing contaminant influence on the

flow field in the equation of motion.

xiii

CHAPTER 1

INTRODUCTION

1.1 Ojectives and Possible Approaches

The primary project objective is the development of simplified,

yet physically correct, mathematical models to describe groundwater

systems, reducing needed computer resources. Two basic approaches can

be taken to achieve this goal: (1) use analytical solutions to perti-

nent equations, or (2) simplify the basic equations in such a way as to

enable development of numerical models using reduced computer resources.

A number of published analytical solutions exist, including those by

Wilson and Miller [1978], Sagar [1982], Hunt [1978], and Prakash [1982].

In addition, several solutions based on perturbation techniques have

been presented [see section 3.4]. In addition, numerous solutions to

problems. A review of these is given by Benedict [1981].

The above analytical models are perceived to have much utility,

but the major focus of this study was to be on density-stratified

fluids. Handling such effects in analytical solutions can be partially

accounted for by using modified dispersion coefficients, but this cannot

account for density influences on the flow field, changing density in-

fluences through the flow field, and non-unidirectional flows. In addi-

tion, use of perturbation techniques for three-dimensional flows would

become very complicated. For these reasons, and due to the great

interest in the saltwater intrusion problem in Florida, this problem

was selected for the main thrust of the work.

2

1.2 General Scope of the Study

The Floridan Aquifer is the primary source of potable water for

the northeastern Florida area. The aquifer is extremely productive and

supplies freshwater for domestic, municipal, industrial, and agri-

cultural purposes. In most areas semiconfining formations containing

saline water underlie the freshwater aquifer.

The inland areas of northeastern Florida are predominantly rural

and highlyagriculturalized. The demand for irrigation water is intense

during the growing season and heavily taxes the freshwater supply found

within the Floridan Aquifer. Where the rates of pumpage of this aquifer

are high, the saline water found in underlying formations is subject to

upward migration. This process leads to the formation of stratified

flow conditions within the aquifer and is termed mineralization. The

mineralization process is typical to the highly agriculturalized areas

of northeastern Florida and is known to cause a gradual increase in the

chloride content of freshwater derived from wells penetrating the

artesian aquifer. The understanding of the physical phenomena asso-

ciated with the mineralization process is essential to sound groundwater

management programs.

1.3 Methodology

The quantitative analysis of an aquifer system subject to stratified

flow conditions involves the solution of highly nonlinear partial dif-

ferential equations. This study seeks to simplify these nonlinear

equations, and thus the basic model, by the application of appropriate

quantitative tools while still maintaining a three-dimensional simulation.

This model will specifically relate to mineralization phenomena in the

Floridan Aquifer in inland areas of northeastern Florida.

Contemporary groundwater flow problems are generally solved by a

variety of analytical and numerical techniques. For aquifers subject to

steady state conditions and simple boundary conditions, analytical

solution techniques have been proven to work well. On the other hand,

numerical solution techniques are usually superior when analyzing aquifers

subject to transient flow conditions, heterogeneous soil conditions, and

complicated boundary conditions.

Because of the complicated nature of the transient stratified flow

conditions in the aquifer system, a numerical solution technique is chosen

for simulation purposes. The nonlinear nature of the basic model presents

problems with stability and convergence in a numerical scheme. With an

appropriate selection of simplifying steps, a highly stable and convergent

numerical scheme describing the transient effects of stratified flow

conditions within an aquifer is possible. The numerical results, being

coherent with the physical phenomena, could then be used as a tool for the

design and implementation of groundwater programs associated with ground-

water management in the area.

The remaining chapters will describe an application of this modeling

system to a particular set of conditions peculiar to the salt water

intrusion problem in northeastern Florida. The area will be described and

the model features and typical results described in detail. It is important

to realize that contaminants other than salt can also be modeled using the

same integral formulation, thereby enabling analysis of hazardous waste

movement. Extension to other geometries and pumping patterns is also

possible, although it is not included in the following work.

CHAPTER 2

THE FLORIDAN AQUIFER
IN NORTHEASTERN FLORIDA

2.1 Introduction

Florida is underlain by extensive limestone deposits which form

some of the most productive aquifers in the United States. Known as the

Floridan Aquifer, this system is the major geologic unit underlying north-

eastern Florida. Confined by the Hawthorn Formation in most areas of

northeastern Florida, the Floridan Aquifer is artesian and supplies the

majority of potable water to this area. Domestic, municipal, and ir-

rigational needs constitute the majority of demand for potable water.

Freshwater is supplied to the Floridan Aquifer primarily in the

form of infiltrated precipitation. Recharge occurs where the upper

portion of the aquifer outcrops in the middle areas of Georgia and through

local sites such as sinkholes and other breaches in the Hawthorn Formation.

This recharge helps maintain the freshwater balance in the aquifer system.

Underlying the freshwater zone of the Floridan Aquifer in north-

eastern Florida are deposits saturated with mineralized water of varying

quality and origin. This condition creates the potential for well con-

tamination due to the upward migration of the mineralized water.

Of special interest to this study is the area located in north-

eastern Florida comprised of Flagler, Putnam, and St. Johns counties

(Figure 2.1). Known as the Tri-County area, this area is extremely agri-

culturalized. A lack of precipitation during the growing season forces

WATER MIrAItanENT r dIMCTnCr

G EJORGaIItN
~STUOD AtEA
'. / T-

^-a^ ^ *:i '
"^.^ ~ ~ 1 '^s-.
*;~~ ~ r ... ^ ^ _______

N

-- ;\j K-i .
<_*- 0 *'.

. I '.
~ ~ ~ ~ \ ; 1.3 < jI '

Figure 2.1 Delineation of the study area. Figure from Munch et al.
[1979].

the agriculturalists to obtain their irrigation water directly from the

Floridan Aquifer. Excessive pumpage of this aquifer since the turn of

the century has caused a general decline in its piezometric surface in

the vicinity of the agriculturalized areas. This decline was accompanied

by a noticeable increase in the salt content of the freshwater pumped

from certain wells, and prompted the Florida State Legislature to appro-

priate funds for an investigation. The investigation began in 1955 as

part of the statewide cooperative program between the United States

Geological Survey and the Florida Geological Survey.

Major investigative studies into well contamination in the Tri-

County area are few but in most cases well documented. The November,

1955 investigation resulted in an extremely thorough and informative

report by Bermes et al. [1963]. Two subsequent well studies were con-

ducted in the area but went unpublished. It should be noted that even

though these investigations recognized the mineralization problem, no

remedial programs were specified. A report by Munch et al. [1979] con-

tains the most recent developments and data concerning well contamination

in the area. Prepared in cooperation with the St. Johns Water Management

District, this report outlines recommendations for safe well use in the

area.

2.2 Geology

An inspection of a geologic column from the Tri-County area reveals

several distinct rock units. In ascending order these units are as

follows: the Lake City Limestone, the Avon Park Limestone, the Ocala

Group, the Hawthorn Formation, and a surficial unit. The geologic column

is represented in Figure 2.2. Bermes et al. [1963], Chen [1965], and

Munch et al. [1979] provide thorough descriptions of these units.

Figure 2.2 Geologic column showing rock units in the Tri-County area.
Figure from Munch et al. [1979].

The Lake City Limestone and the Avon Park Limestone units are both

of Middle Eocene Age and are comprised of alternating beds of limestone

and dolomite. Peat beds are found scattered throughout these two units.

Johnson [1979] characterized the top of the Avon Park Limestone as the

"Avon Park low porosity zone" which consists of hard, low permeability

dolomite. This distinguishing feature of the Avon Park Limestone can be

seen as a semi-impervious barrier to vertical groundwater flow.

The Ocala Group of late Eocene Age consists predominantly of pure

soft limestone and shows a lower average resistivity than does the Avon

Park Limestone [Munch et al., 1979]. The Ocala Group contains principally

freshwater and supplies large quantities of potable water to the Tri-

County area.

The Hawthorn Formation of Miocene Age consists of clays and sands

with some interbedded limestones and dolomites and serves as a confinin-

formation for the underlying limestone units. The base of the formation

consists predominately of hard dolomite and in most cases is impermeable.

A distinguishing feature of the formation is its high phosphate content

relative to the Ocala Group. This feature provides for very accurate

logging of the contact between these two units.

The Hawthorn Formation underlies the entire Tri-County area except

for portions of southeastern Putnam County and most of southern Flagler

County. The formation is breached locally by sinkholes, faults, and

general erosional processes.

The surficial unit of recent to Miocene Age consists of interbedded

lenses of marine sediments, fine to medium sands, shell, and green cal-

careous silty clay. Thin beds of limestone can be found in certain areas.

Small volumes of artesian and nonartesian waters are found in this unit.

2.3 The Availability of Potable Groundwater

Large quantities of potable groundwater are available from the per-

meable formations underlying northeastern Florida. The hydrologic regime

of these formations is commonly divided into two units termed the non-

artesian surficiall) aquifer and the artesian (Floridan) aquifer (Figure

2.3). Although the majority of potable water is obtained from the

artesian aquifer, small quantities of water are pumped from the nonartesian

aquifer for a domestic use. Seasonal irrigation provides the heaviest

demand for freshwater derived from the artesian aquifer.

Recharge and withdrawal rates from both aquifers along with the

respective aquifer characteristics determine the availability of potable

groundwater in the Tri-County area. Recharge rates to the two aquifers

have a direct influence on the safe yield from wells in the area. There-

fore, a thorough knowledge of the physiography and climatic conditions of

the area is essential to a groundwater survey.

The climate of the Tri-County area is classified as humid subtropic

with a mean annual rainfall of 135 cm (54 in.). Normally over 50 percent

of the total annual rainfall occurs during the months of June through

September, with the driest months being November through May. Because

the dry season coincides with the area's growing season, large quantities

of irrigation water are needed to perpetuate the crops.

The topography of the Tri-County area is generally flat with the

majority of land area located in the Eastern Valley. The area is bounded

to the west by the Palatka Hill and the Crescent City Ridge and to the

east by the Atlantic Coastal Ridge. Figure 2.4 illustrates the physio-

graphy of the area. Recharge to the surficial aquifer occurs over the

entire area. Recharge to the Floridan Aquifer occurs primarily in the

western portions of the area (Figure 2.3).

.as

S/I

I I i P
i \ I .. ",

-i ---..~~' ^ -
I

2 ''" 'K' -
: ^ \
,
^ ^ -
= \ "--
1 ,0 _

I-O Y ^^

W !m

Figure 2.3

- Diagram showing the generalized hydrologic conditions in
Northeastern Florida. Figure from Bermes et al. [1963].

/ I

IYV

a

I

c~~r~

11

San Mateo Hi"ll
r +

1 .. ST ., -STIN_
Florahore Valley Te olC

fl 5*0 10 --
Sana Il n

KIOMETERC N

SFLALuER

Welaka Hill F- aV oaRITA

MILES Crescent City Ridge
0 5 10 -T -l-" -
SEspanola Hill
0 5 10 15
KILOMETERS

Figure 2.4 Physiographic features of the Tri-County area. Figure from
Munch et al. [1979].
Munch et al. [1979].

Although the surficial aquifer supplies only a small amount of

potable water to the Tri-County area, this aquifer is nevertheless an

important source of groundwater. The aquifer grades from deposits of

high average permeability at the surface to very low average permeable

deposits as the Hawthorn Formation is encountered. The aquifer underlies

the entire area attaining its maximum thickness of about 46 m (154 ft)

in inland areas and gradually thinning as the Atlantic Ocean is approached.

The piezometric head in the aquifer is generally sufficient to bring the

top of the water table to within 1 to 3 meters of the ground surface.

In the inland areas, withdrawals from the nonartesian aquifer are

generally limited to domestic use. This is due to the small amounts of

water and to the high degree of inhomogeneity found within the aquifer.

Municipal well fields tapping the nonartesian aquifer can be found in the

immediate coastal areas where the underlying artesian aquifers contain

saline water.

The artesian aquifer underlying the Tri-County area consists of a

principal aquiclude, secondary aquifers, and the Floridan Aquifer. The

principal aquiclude is the Hawthorn Formation, which serves to restrict

vertical groundwater movement to and from the artesian aquifers. The

secondary aquifers consist of lenses of sand, shell, and limestone and

occur within the Hawthorn Formation. These aquifers are recharged by the

overlying nonartesian aquifer and the underlying Floridan Aquifer. They

are important sources of potable groundwater in some coastal areas where

the underlying Floridan Aquifer contains saline water.

The Floridan Aquifer is the principal freshwater zone for irrigational,

municipal, and industrial uses. Irrigation demands constitute the

majority of withdrawal from the aquifer. Table 2.1 summarizes irrigation

13

Table 2.1 Historical groundwater withdrawals for irrigated crops in
the Tri-County area.

1956

IRRIGATED ACRES

No Report

4,000

16,000

1965

13,000

6,500

22,000

1970

11,200

8,230

19,000

1975

11,380

4,500

20,120

GROUND WATER
WITHDRAWAL (MGD)

5

6

26

11.6

3.5

13.9

7.6

9.0

22.1

15.8

6.7

28.57

Table from Munch et al. [1979]

COUNTIES

Putnam

Flagler

St. Johns

Putnam

Flagler

St. Johns

Putnam

Flagler

St. Johns

Putnam

Flagler

St. Johns

withdrawals ov'e the ast 25 years for the area. Withdrawals for 4rri-

gation purposes have generally increased over the past 26 years while the

land area under irrigation has remained relatively constant.

Figures 2.5 and 2.6 illustrate a piezometric map of the area and the

locations of intensive agriculture in the area, respectively. The impact

of irrigation withdrawal upon the piezometric map of the Floridan

Aquifer is seen when these two figures are compared. The piezometric sinks

roughly coincide with the heavily agriculturalized areas.

Recharge to the aquifer principally occurs in the western and south-

eastern portions of Putnam County where the aquiclude is breached by

sinkholes, in Flagler County where the aquiclude is either thin or absent,

and to a smaller extent by downward leakage through the aquiclude.

Groundwater is discharge in spring areas, wells, and to some of the over-

lying secondary aquifers.

At the turn of the century, artesian pressure in the Floridan Aquifer

was sufficient to produce free-flowing wells. By the 1950's,artesian

water levels dropped, and free-flowing wells could no longer supply enough

water for irrigation [Munch et al., 1979]. In response to this condition,

several well studies were prepared to determine aquifer characteristics

and the potential impact on the Floridan Aquifer due to heavy seasonal

withdrawals [Bermes et al., 1963; Bentley, 1977; lunch et al., 197S].

Bentley's study in 1977 consisted of two types of aquifer tests performed

on eighteen well sites (Figure 2.7). The results of the individual well

test are given in Table 2.2. Based on the aquifer tests, Bentley [1977]

concluded that on a regional scale the hydraulic characteristics through-

out the Tri-County area were relatively homogeneous with local variations

to be expected.

Figure 2.5 Piezometric level and generalized direction of groundwater
movement in the Tri-County area, March, 1975. Figure from
Munch et al. [1979].

Figure 2.6 Location of the areas of intensive agriculture within the
Tri-County area. Figure from Munch et al. [1979].

Figure 2.7 Location of aquifer test sites in the Tri-County area.
Figure from Bentley [1977].

Table 2.2 Aquifer test data.

Well
Location Nouber

3 ml southeast 1
ol Ilastings IA

1.2 ml east of 2
East Palatka 2A
2B

2 ml south of 3
Hastings 3A
3B

1.5 mi northeast 4
of East Palatka 4A
4B

2 mi west of 5
Iastlings 5A

3 mi northwest of 6
Armstrong 6A
611

7 mt northl.,tt of 7
I'1 o .la1 ti l7A

USGS ID Number

2939580812842.01
2939500812842.01

2939300813436.01
2939330813420.01
2939320813458.01

2940490812944.01
2940490812952.01
2940530812927.01

2940330813502.01
2940320813455.01
294045081J515.01

2942570813247.01
2942550813240.01

2947480812906.01
2947520812905.01
2947480812924.01

29572'0812910.01
2951100 ) 129 10.01

Spuds 8 2941430812H33.01
BA 29434308122840.01

0.5 ml south of 9 2945400813833.01
llotwuick

Well Thicknes s
depth of aiulufer
(ft) (ft)

200 41)
450 250

Observed Ij ydiolIyoic character Is stlcs
Tr.ansmil s; I v It y Storage Leakalnce
(It 2/d) m ll Icl vut, ~-1

8UI.(,ll) 0.0006

46,000

56,000

24,000

300 150
300 I50

525 12'.
57i 127'

2801
28(0

260

5').0110 t.
60, 01OO

25 ,000

51. ,0)l

17.000

17,000

.001

.0006

.0008

. 100 1
11001

.000)
.1100 1

0.019

.021

.0011

Table 2.2 continued.

Well
Location Number

10 mi south of 10
Palatka

Roy 11

4 mi northeast 12
Riverdale

1.5 mi north of 13
Riverdale

10 ml south of 14
Greencove Springs

St. Augustine 15
Beach

4 ml soutlhwet of 16,
Iurb in

9 mi north of 17
St. Augustine

1.5 mi northeast 18
Armstrong

Well
USCS 10 Number depth
(ft)

2932340814241.01

2937160812936.01

2951060812909.01

2950280813309.01

2951440813717.01

2951320811648.01

3003540813012.01

3000480812333.01

2946120812534.01

Thicknessn
of aqulfrr
(ft)

240(

250

200

70

80

55

4f

10

150

Observed [ yd oogi tc characteristics
Transinl'usilvty, Storage Leakance
(Wt /d) coefficlelit, d-1

'i I, (1)0

126 1(1(0

(data not used In analysis)

8, 700
H.71)0

7,800

1 J3, 000

hi, HiOi

1,600

15,000

Table adapted from Bentley [1977, Table 2]

2.4 Mineralization

The Floridan Aquifer in northeastern Florida contains zones of

saline water which underlie the freshwater artesian aquifer. The origin

of the saline water was probably due to the infiltration of sea water

during the Pleistocene Epoch when the sea stood above its present ele-

vation. As the sea level subsequently receded, recharge to the mineralized

aquifer flushed out the saline water in the upper portions of the aquifer.

This flushing action is a continuous process and will occur as long as

the inland piezometric heads are above sea level.

Currently, the Floridan Aquifer in the area consists of a freshwater

aquifer and a saline water aquifer (Figure 2.8). The freshwater aquifer

extends from the bottom of the Hawthorn Formation, through the Ocala

Group, and ends at or near the "low porosity zone" marking the top of the

Avon Park Limestone. The saline water aquifer underlies the freshwater

aquifer. Because fresh and saline waters are miscible fluids, there

exists a small zone of transition between the fresh and saline aquifers.

Contaimination of the freshwater aquifer occurs from downward leakage

through the Hawthorn Formation and from the upward migration of saline

water from deep semiconfining formations. Large differences between the

values of the piezometric heads of the freshwater aquifer and the overlying

phreatic aquifer suggest minimal leakage through the Hawthorn Formation.

This would imply that the majority of leakage occurs from deep semi-

confining formations. In this study the contamination of the freshwater

aquifer from underlying saline water is termed mineralizationn". The

mineralization process is shown schematically in Figure 2.9.

The mineralization of the freshwater aquifer in the Tri-County area

stems from heavy seasonal pumpage in the highly agriculturalized areas

Figure 2.8 -

Location of the freshwater zone and the saline water zone
within the Floridan Aquifer. Figure adapted from Munch
et al. [1979, Figure 32].

'
r

e
--
~-~-.:-P

~-

'~~-"
,. -.. c
.o~~.~
,-~i---
'
~ -''-~=--r.- ~ "'

.- r.

~ "~"~"'

GROUND SURFACE

Cv

SUNCONSOLIDATED
- '' ... SANDS

-CONFINING UNIT -
OF
FLORIDAN AQUIFER -

Figure 2.9 Schematic diagram of saltwater coning as related to the

Tri-County area. Figure from Munch et al. [1979].

(Figure 2.6). Irrigation of crops begins in late September and continues

through May. At the beginning of the growing season the piezometric

surface of the freshwater aquifer is sufficiently high to produce many

free-flowing wells. Intense groundwater withdrawals during the season in

the agriculturalized areas produce cones of depressions that may exceed

6 m (20 ft) below the land surface, and water quality deteriorates

rapidly. Partial to total recovery of the original piezometric surface

occurs due to natural recharge during the summer months when little to no

pumpage occurs. The recovery process is illustrated in Figures 2.10 and

2.12. These piezometric maps are accompanied by their respective isochlor

maps in Figures 2.11 and 2.13. Note the correspondence between the agri-

culturalized areas, the piezometric sinks, and the areas of higher chloride

content. This correspondence again suggests that the mineralization

process occurs due to upward leakage of saline water into the freshwater

aquifer in response to heavy pumpage.

Two major mineralization studies [Bermes et al., 1963; Munch et al.,

1979] have been performed in the Tri-County area. The most recent study,

completed in 1979, thoroughly reviews the mineralization process and reflects

the current policy in the area. In general, this study has found that

in the area: (1) a gradual decline in the piezometric surface of the

Floridan Aquifer has occurred due to increasing groundwater withdrawals

during this centuryand (2) the areas and amounts of saltwater contami-

nation have increased from 1956 to 1975.

2.5 Current Assessment

Current assessments concerning the problems of groundwater mineral-

ization in the Tri-County area are presented in the study [Munch et al.,

1979] prepared by the St. Johns Water Management District. A portion of

EXPLANATION

L

Figure 2.10- Piezometric map of the Floridan Aquifer, March,1975. Figure
from Munch et al. [1979].

Figure 2.11 Isochlor map of the Floridan Aquifer, March, 1975. Figure
from Munch et al. [1979].

Figure 2.12 Piezometric map of the Floridan Aquifer, September,1975.
Figure from Munch et al. [1979].

- ----------------- ----

CHLORIDE CONCENTRATION r// /
~~~~~, o ////.
______ 0* 050-/
S0,o 50 b / //,
5I 5r 250 /
S251 "500 ,//
t
501 1000 / / / ," -.
S1C.O0 / 2/V//,

-. ........ .. ..&: \$ '""" .. N
/ 7 / ^. 71 /' / / ,'T \ ^/. .* -*
.----- -Li ^ .. '//// / ^ /// ^ //.- i -*_ --

/ 7 /. l /0 '//// l~/7 l/ // 7 r. I
/ l / '/ ( > /11 1 I I / IIIII ."*i "/ '', .. -

..// / 7/ /'0 / ..// 7/ / 7///// / / /
'7 7;-'. '777 //7/i// 7/////// -:.
//*//,' ~/ /~, /////// // // /' / /'* /y^ .
-/l/ll// 1// .t i///l//7/1/7/ l/ .7 ."*
'/i i- 7/ 77 7/ 7liili illl.77 /i7 '.'.. .
'.. "i'i* / ilT//^"/'llii I l o,.li '+/l ll I l//lll /'/,.; i;; \ *
i///// l I/// /// ia/lt/// l/ A ...........
///////l ///////i /// /l/l/* A : "u;_:.'.
i////////// 7/'//// //^l / /., .. ...
// 7/// // i L // .:"" .;..."".,.' .
iilll' "ll / r / ;'#' // #11 / /^ "' *-'* ** *: -.;,,'
~/ l //i/ // I/llilr,^' ll / -.^^ y/ '' '** "L++' .. ... *- .'+ "
/i////l77 7 //77 77 ... .. ....

/71!111 7I/ 77777/7li7,27 41L-.. i ",1 ': */ .
............ .r' /^/ '- *il l l ... Il l l i l '" *../ '.' '..'. '..'./ f "

.,,, .; ,. 7 /7..7. ./,,,,. .', ./.. ,. .. .. ," ,,- ** \' .
/. ./ ,/ /////,///./ /////<' //7 :I: .. "
// / / i -. / l //l ///l/i // //// .... \ ... }
//./. ..... ////... /////.77././ ..'.. 7 ....
lil i t7i/// llil 7l.7,',7^.-j- .. a* **- -
/ l l '..7 7, 7// 7l// 11, */'.i /'.,' X ^/ ig ;";-;/ .B .-. 0.
'.' -'1 -- < ,;//./ ::0 /, \'\ "1 \
-/' 11"*--.r:^ ",\: <* .^-". I \ "\

^ / ** ** .. ... *, -..* \l/': #/ ^ i -/ /. \' *, ,~- tl ir \
'/'// *^ ,/, .* **. / '/ // I, ,-. I.. j- *^ l Y w f i

^...... .- ... .
*,,// 7 7 ,,'// 7 7. ..... ..... .
u'>' 7 7 7 / / : "'. 1 7: 7\\
7.////0/.777// // 77////. // A ,\
/.* 1////1/.1//,*T ^//// //'/* / ^V *l// :I\'\ *
*^/ 7,.77 **/.77777.''.' 'L- / / 77 /* 7\7 77
7// //,//// /7V7.'.///.//7,'/7 :\
'.'///^.// /////.^ ^//ri' ,/ /, ^^ i
'y///-^ /I////,./ ^ ? \ .- -\ \

I /4// ;.777 \ / .
1 I,~ }'i '*'V- \i* \
i ///^/ /- *

I .- i
A. N /7777".0.7 -'

7,,. ^ N ^ -^

...0--1..1 ~~~77r l'^ 's../^- -/ \ ---**

Figure 2.13 Isochlor map of the Floridan Aquifer, September, 1975. Figure
from Munch et al. [1979].

this study attempts to correlate chloride concentration with pumpage

rate, well depth, aquifer penetration, and piezometric level by a re-

gression analysis and polynomial expansion. The compiled data illustrate

that in response to pumpage, piezometric levels decrease and chloride

concentrations increase. The reverse situation prevails during the non-

growing season when pumpage is small and recovery occurs. A statistical

analysis indicated that 50 percent of the wells in the study area may

produce water with a chloride content less than or equal to 210 ppm, and

that 10 percent of the wells may exceed 778 ppm chloride during any time

of the year. At times some of the deeper wells can act as direct con-

duits for the transport of saline water into the freshwater aquifer.

During periods of intense pumpage, local cones of depression are

formed in the areas of Orange Hills, Hastings, Elkton, and Bunnell

(Figure 2.5). Recharge to the aquifer from leakage is insufficient to

stabilize the local cones of depression. The lowest piezometric levels

and the highest chloride concentrations were apparent in the local cones

of depression during the month of March. The greatest variation in water

levels and water quality occurred during the months of March through

September when recovery of the aquifer occurs.

The combination of well construction, well spacing, and overdraft

lead to the upcoming of saline water beneath pumping wells. The study

attempted to calculate safe yields from various theoretical formulas

which might stabilize the local cones of depression during periods of low

piezometric levels. Pumpage rates ranged from 817 m3/d (150 gpm) within

the central portions of the local cones of depression to as much as

1910 m3/d (350 gpm) in areas where the freshwater aquifer thickness ex-

ceeds 61 m (200 ft). According to a statistical analysis, it was

determined that at least 120 wells in the area could benefit from reha-

bilatative construction procedures.

Recommendations available to the agriculturalists and the various

governing agencies are presented at the end of the study.

2.6 Summary

The geologic structure of the Tri-County area consists of rock units

ranging in age from Middle Eocene to recent. These units in ascending

order are the Lake City Limestone, the Avon Park Limestone, the Ocala

Group, the Hawthorn Formation, and a surficial unit. The Lake City

Limestone, the Avon Park Limestone, and the Ocala Group consist predomi-

nately of porous limestone and dolomite. The Hawthorn Formation consists

primarily of sands, clays, and marls and is considered a confining unit.

The hydrologic regime of the area consists of a nonartesian

surficiall) aquifer, a principal (Hawthorn Formation) aquiclude, and an

artesian (Floridan) aquifer. The nonartesian aquifer supplies small

amounts of potable water to the area mainly for domestic use. In the

Floridan Aquifer the Ocala Group contains predominately freshwater while

the underlying units contain saline water. This aquifer supplies the

majority of irrigational, municipal, and industrial waters to the area.

Irrigational needs constitute themajority of withdrawals from the aquifer.

Because of excessive pumpage for irrigational purposes, the chloride

content of the freshwater zone of the Floridan Aquifer has increased

steadily since the turn of the century. It is suggested that this con-

dition is caused by the upward migration of saline water from deep semi-

confining formations. The mineralization problem is most severe in the

vicinity of the highly agriculturalized areas.

30

Two major mineralization studies have been conducted in the Tri-

County area [Sermes et al., 1963; Munch et al., 1979]. Munch's study

in 1979 supplies a thorough overview of the mineralization problem and

presents recommendations for the control and prevention of well contami-

nation.

CHAPTER 3

ANALYSIS OF AQUIFER MINERALIZATION

3.1 Introduction

The intense development of certain coastal regions of the world

in the twentieth century has created a situation where saltwater in-

trusion has jeopardized the quality of freshwater derived from coastal

aquifers. The east and west coasts of Florida pose various problems

associated with salinity intrusion into coastal aquifers. In response

to the problems presented by saltwater intrusion within coastal aquifers,

a great variety of studies have been conducted to better understand and

evaluate these problems.

Many aquifers located quite far from coastal areas are also subject

to the mineralization phenomenon. This has of late begun to attract much

attention. The mineralization phenomenon associated with inland aquifers

is very similar to that experienced by coastal aquifers. Many of the

techniques utilized for the study of the mineralization phenomenon in coastal

aquifers may be applied for the study of inland aquifers. Several studies

pertaining to both types of aquifer mineralization are reviewed within.

In the analysis of flow through porous media, the nomenclature con-

cerning the number of dimensions in which the analysis is conducted is

often confusing. Therefore for the sake of clarity, a two-dimensional

analysis will be defined as representing flow in a plane region while a

three-dimensional analysis will be defined as representing flow in a

spatial region.

3.2 Early Studies

The first analytical relationship relating fresh and saline waters

in a phreatic coastal aquifer was presented by two independent investi-

gators [Ghyben, 1888; Herzberg, 1901]. The Ghyben-Herzberg relationship

states that the depth below sea level at which saltwater can be found in

a coastal aquifer is about forty times that of the corresponding height

of freshwater above sea level. Although this is an approximate relation-

ship for a phreatic aquifer subject to horizontal flow, it can be used

to obtain a rough estimate of the location of the freshwater-saltwater

interface within the aquifer.

Despite the efforts of Ghyben [1888] and Herzberg [1901], investi-

gators working for the oil industry were the first to complete detailed

analytical mineralization studies [Muskat and Wychoff, 1935; Arthur, 1944].

These studies describe the upcoming of saline water into overlying oil

deposits. Their applications were limited due to the simplified geometry

utilized in the development of the analysis. Nevertheless these first

studies provided valuable insight into the physical phenomena associated

with the mineralization process.

Subsequent mineralization studies stemmed primarily from the

groundwater quality problems associated with the intensive development

of the world's coastal regions. These studies attempted to simulate

the flow conditions within an aquifer subject to mineralization by a

variety of physical, analog, and mathematical models.

Before the emergence of high speed digital computers in the late

1950's, physical and analog models were popular in mineralization studies.

The Hele-Shaw model was especially well suited for this purpose. Although

physical and analog models are useful for the understanding of the

physical phenomena associated with aquifer mineralization, a new model

must be constructed for each unique application incurring great time and

expense. With the advent of digital computers came a switch from

physical and analog models to sophisticated analytical and numerical

models. These latter models are the basis for our contemporary knowledge

of the mineralization phenomenon.

3.3 Current Approaches

Two basic approaches can be adopted when applying an analytical or

numerical model to an aquifer mineralization problem. The first approach

assumes the immiscibility of the fresh and saline waters whereby an

assumed sharp interface is found at their mutual boundaries [Bear and

Dagan, 1964; Hantush, 1968; Shamir and Dagan, 1971; Haubold, 1975]. The

second approach simultaneously solves the equations of motion and solute

transport to describe the transient position of a dispersive saltwater

front migrating into the freshwater aquifer.

With the sharp interface approach, potential flow theory can be

applied to both sides of the sharp interface between the fresh and salt

waters. But because fresh and saline waters are miscible fluids, this

approach suffers from a lack of coherence with the physical phenomena.

However, the assumption of a sharp interface sometimes supplies a good

approximation to the transient position of the transition zone between

freshwater and saltwater zones.

The inclusion of the solute transport equation in the second ap-

proach implies the existence of a zone of transition or a dispersive

front either of which migrates through the porous media. The solute

(salt) is dispersed within the flow field due to diffusion and mechanical

dispersion processes and thereby affects the dynamics of the flow. The

mineral distribution in the flow field introduces nonlinear terms into

the equations that should be used in the analysis. For numerical

schemes these nonlinear terrs cause problems with convergence and

stability. Various approaches attempt to linearize the equations to

facilitate analytical solutions.

The analysis of either a transition zone or a dispersive front may

be performed in a variety of ways. If the solute is a neutrally buoyant

material, then various perturbation methods can work extremely well and

generate simplified models that can lead to analytical solutions.

If the solute is not a neutrally buoyant tracer then various combinations

of perturbation approaches can also be used in order to simplify the

mathematical model. Some of these methods are discussed in detail in

subsequent sections.

3.4 Analytical Techniques

The analysis of stratified flow in porous media by analytical

techniques usually involves the application of certain perturbation

methods. When applied to a steady flow field, perturbation methods can

reduce the solute transport equation to an equation of the heat conduction

type. Solutions to the heat conduction equation are well documented in

various texts.

Dagan [1971] analyzed the migration of neutrally buoyant tracers.

He considered both longitudinal and lateral hydrodynamic dispersion in

the porous medium. The analysis derives an inner boundary layer

solution for a transition zone in a steady flow field by utilizing the

stream function and the velocity potential function as coordinates. In

this analysis it is required that the stream function and the velocity

potential function be defined for every Doint in the flow field prior

to the calculation of the solute dispersion. This is true only when a

neutrally buoyant material is introduced into the flow field. Only

problems with constant hydraulic conductivity and a constant coefficient

of dispersion can be solved by this analysis. Eldor and Dagan [1972]

later extended their analysis to include radioactive decay and

Gelhar and Collins [1971] applied a second perturbation method to

analyze dispersive flow in porous media. The study develops an approxi-

mate analytical technique for the description of longitudinal dispersion

in unidirectional steady flow with variations along a streamline. The

governing equation is reduced to a simple diffusion equation, and a

general solution is obtained. Results are obtained by evaluating two

integrals in the velocity field. Lateral dispersion is not treated in

the analysis. Thus, a solution is not found for a boundary layer which

develops along a streamline.

Hunt [1978] introduced a perturbation method that can be used for

The solution, while being very general, is most accurate when the boundary

layer is relatively thin and accurate numerical solutions are difficult

to obtain due to numerical dispersion. The study suggests that the

perturbation solution initially be used until the size of the boundary

layer approaches a predetermined limiting value where a numerical solution

is then employed to finish the analysis.

The above perturbation methods are based in part upon the assumption

of the existence of potential flow at every point in the flow field.

In the case of saltwater intrusion problems, this assumption fails due

to the density differences between the fresh and salt waters whereby

nonpotential flow conditions exist in the boundary layer. Dagan [1971]

addressed a saltwater intrusion problem but assumed that the minerals

within the saltwater act as ideal tracers.

Rubin and Pinder [1977] solved the nonpotential flow problem in

the boundary layer by the utilization of the integral method of boundary

layer approximation ["zisik, 1980] in conjunction with a perturbation

method. The dispersion process is described as a migration of a sharp

interface perturbed by small disturbances due to salinity dispersion.

Salinity dispersion creates a mixing zone in which boundary layer

similarity exists. Although this study gives only steady state solutions,

the boundary layer integral method supplied a means by which transient

mineralization problems may be analyzed, usually by a numerical scheme.

While perturbation methods yield good two-dimensional analyses,

the extension of these methods to three dimensions would be extremely

difficult. For example, following Dagan [1971] a solution in three

dimensions would necessitate the use of stream function planes and

velocity potential function planes.

3.5 Numerical Techniques

Numerical techniques have several advantages over analytical tech-

niques when applied to aquifer mineralization problems. Numerical tech-

niques are able to handle complex geometries and boundary conditions,

heterogeneous and anisotropic porous media, and time dependent problems

whereas most analytical techniques can not. On the other hand, ana-

lytical solutions are often easier to apply and can be used to check the

accuracy of the numerical solution.

Both finite element and finite difference schemes are used when

analyzing aquifer mineralization problems. Pinder and Cooper [1970]

utilized a finite difference numerical scheme to simulate saltwater

intrusion within a coastal aquifer. The method of characteristics is

used to solve the solute transport equation and the alternating direction

implicit (ADI) method is used to solve the equation of motion for a

two-dimensional problem. The method is applicable to heterogeneous,

anisotropic porous media with irregular geometry, constant head, and

constant flux boundary conditions.

Segol et al. [1975] applied a Galerkin-finite element technique

for the two-dimensional simulation of saltwater intrusion within a

.coastal aquifer. The Galerkin-finite element theory is used to formulate

approximations to the nonlinear equations for velocity and pressure.

With this information the solute transport equation is solved separately.

Iteration between the solute transport equation and the flow equations

continues until convergence is reached.

Rubin and Christensen [1982] and Rubin [1982] developed numerical

schemes for the two-dimensional simulation of stratified flow in a coastal

aquifer and an inland aquifer, respectively. Both studies utilize the

integral boundary layer method where the solute transport equation is

integrated over the thickness of the boundary layer subject to certain

similarity conditions. The resulting equation is then solved simulta-

neously with the equations of continuity and motion by an implicit-

explicit finite difference numerical scheme. The study presented herein

extends Rubin's work [1982] to obtain a three-dimensional analysis.

3.6 Summary

The problems associated with the mineralization of coastal aquifers

have generated a large number of studies attempting to describe the

phenomenon. Few studies have dealt with the mineralization problems

found in inland aquifers. However, some of the analytical and numerical

concepts developed for coastal aquifers can be applied to inland

aquifers.

Two common approaches can be applied to the flow field for the

description of the mineralization phenomenon. The first approach assumes

a sharp interface which exists between the fresh and saltwater zones.

This approach suffers from a lack of physical coherence. The second

approach solves the equations of motion and solute transport simulta-

neously. Perturbation methods as well as numerical schemes can be used

for this purpose. Boundary layer methods can be applied in order to

generate analytical as well as numerical approaches for the description

of the dispersive freshwater-saltwater interface. Various studies

utilize all three methods.

CHAPTER 4

THE APPROXIMATE METHOD
OF STRATIFICATION ANALYSIS

4.1 Introduction

Stratified flow in an aquifer stems from the contact between fresh

and saline waters in the aquifer. Flow within the aquifer creates a

zone of transition separating the fresh and saline waters. The mineral

(salt concentration) distribution within the transition zone affects

the dynamics of the flow field. On the other hand, the transport of

the minerals within the flow field depends on the structure of the flow

field. It is clear that complicated flow conditions exist within an

aquifer subject to mineralization.

To simulate stratified flow within an aquifer the equations of

continuity, motion, and solute transport are solved simultaneously

subject to a given set of boundary conditions. This procedure leads to

a set of highly nonlinear equations which cause problems associated with

stability and convergence in the numerical solution.

This study presents an approach whereby the equations describing

stratified flow within an aquifer are simplified. The Dupuit approxi-

mation and the integral boundary layer method are used for this purpose.

The result is a highly stable, convergent numerical scheme describing

the mineralization process in three dimensions.

4.2 Description of the Flow Field

Figure 4.1 shows a schematic description of a flow field typical

to an inland aquifer. According to this figure the flow field is divided

into three zones as follows: (a) the upper zone of freshwater, (b) the

transition zone, and (c) the lower zone of saltwater. By applying the

Dupuit approximation to the flow field, certain simplifying assumptions

are made. The flow in the freshwater zone is mainly horizontal and

potential. The flow in the transition zone is mainly horizontal and is

nonpotential due to the mineral distribution within this zone. The flow.

in the saltwater zone is vertical and potential. For the purposes of

this study, this flow field description will be extended in the remaining

horizontal dimension to yield a two-dimensional flow field.

4.3 Basic Equations

The basic equations used for the simulation of stratified flow in

an aquifer are the equations of continuity, motion, solute transport, and

state represented respectively as follows

S q + = 0 (4.1)

Vp + y k + q = 0 (4.2)

n C + V (qC) = V7 (D vC) (4.3)
3t

Y = Y (1 + aC) (4.4)

where, q = specific discharge; n = porosity; t = time; p = pressure;

y = specific weight; k = unit vertical vector; K = hydraulic conductivity;

C = mineral concentration; D = dispersion tensor; Y = specific weight

Pumpage N
&t t' Confining Formation

B
B K Freshwater Zone
0

Transition Zone

z=O
S Saltwater
b Mound

B1 K Saltwater with Constant Semiconfining Formation

Figure 4.1 Schematic description of the development of a transition
zone in a stratified aquifer.

of reference; a = constant relating changes in mineral concentration with

specific weight.

Equations (4.1), (4.2), (4.3), and (4.4) are solved simultaneously

utilizing a finite difference numerical scheme as shown in the following

sections.

4.4 The Integral Method of Boundary Layer Approximation

The integral method of boundary layer approximation is an analytical

tool first introduced by von Karman. The method is applicable to both

linear and nonlinear transient.value problems for certain boundary con-

ditions. Basically, the method simplifies the appropriate equations by

integrating over a phenomenological distance thereby creating a boundary

layer. The distribution of the desired parameters within the boundary

layer is given for example by a polynomial profile that satisfies simi-

larity conditions. Thus, the parameter distribution is given as a

function of time and position in the medium. In this study, the phenomeno-

logical distance is the thickness of the transition zone and the desired

parameters are the solute concentration and the specific discharge.

This study applies the integral method of boundary layer approxi-

mation for the simplification of the simultaneous solution of the basic

equations (4.1), (4.2), (.4.3), and (4.4) in the three-dimensional simu-

lation of the stratified flow process. The analysis is based upon the

work of Rubin [1982] and represents an extension of his approach for the

simulation of the mineralization process in the two-dimensional flow

field.

In Figure 4.1 the upper zone includes freshwater whose specific

density is constant. Therefore,in this zone equation (4.2) yields

= -Kf 7f (4.5)

where

f = P/Yf + z (4.6)

Here, Of = piezometric head at the freshwater zone; Kf = hydraulic con-

ductivity of the porous medium containing freshwater; Yf = specific weight

of the freshwater; z = elevation with respect to an arbitrary datum.

The lower zone includes mineral water whose specific density is

constant. Therefore, in this zone equation (4.2) yields

q = Ks v (4.7)

where, K = hydraulic conductivity of the porous medium containing salt-

water.

s P/Ys + z (4.8)

Here, Os = piezometric head at the mineral water zone; ys = specific

weight of the mineral water.

We may assume K = K = K.

Assuming the flow in the transition zone is mainly horizontal, then

an integration of equation (4.2) between the bottom and the top of the

transition zone yields

Ssb Zb)- Y ft dz (4.9)
o o zb o

where, b,t = indices referring to the bottom and the top of the transition

zone, respectively.

It is assumed that the transition zone is represented by a boundary

layer where the specific discharge and the solute concentration profiles

satisfy the following similarity conditions

u = UF(n) v = VF(n) C = C L(n) (4.10)

where, u,v = components of the specific discharge in the transition zone

in the horizontal x and y directions, respectively; U,V = character-

istic specific discharge in the horizontal x and y directions, respectively;

C = characteristic concentration; F,L = distribution functions;
o
n = dimensionless coordinate of the transition zone defined as follows

n = (z Zb)/6 6 = zt zb (4.11)

Here, 6 = thickness of the transition zone.

Introducing equations (4.4), (4.10), and (4.11) into equation

(4.9) yields

(1 + aCs) sb (1 + aCf) ft + aCf6 a(Cs Cf) zb

1
= aC 6 Ldn (4.12)

Assuming C = 0 and C = Co yields

ft (1 + s) sb Zb 0 Ldn (4.13)

where

E = aCs = (y5 Yf)/Yf

(4.14)

Referring to Figure 4.1, it is assumed that beneath the semiconfining

layer the piezometric head is not affected by pumpage and has a constant

value so. Initially, the freshwater-saltwater interface is assumed to

be a sharp interface and is horizontal. Therfore, continuity of the

pressure yields

Yf 4fo = Ys so (4.15)

where, o = subscript referring to initial conditions.

The piezometric head at the bottom of the transition zone is given

as follows

az B z
b so n 1 bb ) (4.16)
sb so at K 1 K

where, B1 = thickness of the semiconfining layer; K,K1 = hydraulic con-
ductivities of the aquifer and the semiconfining formation, respectively.
Combining equations (4.13) and (4.16) yields

a zb B zz
ft= 4fo n (1 + 5) at zb
ft fo at K K b
1

1
I6 Ldn (4.17)
0

Reference to the drawdown, s, instead of the freshwater piezometric

head, and an application of equations (4.1) and (4.2) yield for a two-

dimensional flow field

1
[K(B + o Fd) -] + [K(B + I i Fd) 2
Jx F ax ay d -

SZb
-n + N s (4.18)
at at

where, S = coefficient of storage; N = rate of pumpage per unit area.

Rearranging (4.17) yields

a z K K
at n(B1 K + zb K1) (1 + E) b

1
E6 Ldn) (4.19)

The equation describing the growth of the transition zone is

developed with reference to Figure 4.2. In this figure a portion of the

transition zone is considered as a control volume. The application of

the equation of solute transport to this control volume and an integration

over the thickness of the transition zone yields

Zb+6 zb+6
a ( nCdz)dx + ( uCdz)dx = D acl dx (4.20)
tax ) az
Zb Zb Zb

where, n = porosity of the porous medium.

Introducing the similarity conditions given in equation (4.10) into

(4.20) and rearranging yields

1 2 U a2
S(n Ldn) -- + [ ax + 62 LFdn = DL'(0) (4.21)
t- J^ dL C d d j,-

where, L'(0) = (dL/dn)0.=O
n~=U

aC
ac 0
az

Flow

. dx

zb+6

Zb

uCdz +
ax

zb+6
(I uCdz) dx
Zb

aC
- D dx
3Z

Figure 4.2 Control volume for the development of equation (4.22).

Z +6

zb

uCdz --

Equation (4.21) represents the growth of the transition zone for a

unidirectional flow. The application of the same approach to a two-

dimensional horizontal flow field yields

c 62 2 au v 1 3 2
(1 oLdn) + [62 ( + -) + (U
2 J0 at ax ay 2 ax

2 1
+ V _6] FLdn = DL'(O) (4.22)
dY." 0

This analysis considers that the bottom of the transition zone is

represented by zb and is stationary. However, zb is a function of time

thereby generating one additional term in equation (4.22). However,

this term is canceled by the convection term generated by the vertical

specific discharge in the saltwater zone.

In general the coefficient of dispersion, D, is proportional to

the absolute value of the specific discharge. Therefore, it is assumed

that
2 21/2
D = a(U2 + V2) (4.23)

where, a = constant almost identical to the transverse dispersivity of

the aquifer.

According to Figure 4.1, it is evident that

B = Bo zb (4.24)

Equation (4.18) is a parabolic second order equation and describes

the distribution of the drawdown in the flow field. Equation (4.19)

describes the rate of growth of the saltwater mound. Equation (4.22)

is a hyperbolic first order equation describing the development and pro-

pagation of the transition zone in the aquifer.

For the simulation of flow conditions in the two-dimensional flow

field, an implicit-explicit finite difference scheme for equations

(4.18), (4.19), and (4.22) is developed in the next chapter. This

numerical scheme results in a three-dimensional simulation of the miner-

alization process in the aquifer.

4.5 Summary

Stratified flow in an aquifer is associated with quite complicated

flow conditions. The mineral transport within the flow field depends

upon the structure of the flow field. On the other hand, the mineral

distribution affects the dynamics of the flow.

A two-dimensional flow field is described where a freshwater zone,

a transition zone, and a saltwater zone are found. By the application

of the Dupuit approximation and the integral method of boundary layer

approximation to the two-dimensional flow field, the simultaneous

solution of the equations of continuity, motion, and solute transport

yields three partial differential equations describing a three-dimensional

stratified flow process. Originally these equations are highly nonlinear

and create problems with stability and convergence within a numerical

scheme. By applying the boundary layer approach the complexity of the

system is reduced and its susceptibility to numerical problems of con-

vergence and stability is diminished.

CHAPTER 5

NUMERICAL SIMULATION

5.1 Introduction

The governing equations, (4.18), (4.19), and (4.22), developed in

the last chapter have the unique ability to completely describe the

mineralization phenomenon in an inland aquifer. The objective of this

chapter is to formulate a solution for these equations that is coherent

with the actual mineralization process. Because the equations are non-

linear and expressed in two independent space variables and one

independent time variable, a numerical scheme is the only practical

means by which a solution may be obtained. Most groundwater flow prob-

lems are numerically approached by a variety of finite difference,

finite element, and boundary element methods. Satisfactory groundwater

flow models have been developed utilizing each of the above methods.

Several finite difference methods offer approaches leading to ap-

proximate solutions to partial differential equations. Implicit schemes

with their exceptional stability properties are almost always used.for

the solution of initial value problems in two space variables. A variety

of solution techniques are offered in the literature [Mitchell, 1976]

and include the alternating direction implicit (ADI) method, the

locally one-dimensional (LOD) method, and the successive overrelaxation

(SOR) method, among others.

In selecting the appropriate numerical solution technique for un-

steady groundwater flow problems, the ease of application and the ability

to utilize the resulting model in various geographical regions is of

considerable importance. Finite element and boundary element models are

generally specific to one application and are not easily adapted to a

distinctly separate region. On the other hand, a finite difference model

utilizing an ADI solution method can in most cases analyze a variety of

applications, often only with a simple change in parameters. Also,

groundwater flow modelers generally accept the ADI method and its vari-

ations as the most efficient technique for the simulation of two-

dimensional unsteady groundwater flow problems. It is for these reasons

that it was decided to adopt the ADI method as a solution technique in

this study.

5.2 The Numerical Model

The numerical model developed in this section is based on the

linearization of equations (4.18), (4.19), and (4.22) and the application

of an iterative ADI method. The equations are linearized by appropriate

finite difference representations. The result is a highly stable, con-

vergent numerical scheme capable of completely simulating three-dimensional

stratified flow conditions found in an inland aquifer.

The ADI method was first introduced by Peaceman and Rachford [1955]

and is especially well suited for the solution of time dependent, linear

parabolic systems. The application of the ADI method to a parabolic

system involves the solution of tridiagonal sets of equations along lines

parallel to the x and y coordinate axes. The appropriate finite difference

equations are formulated into two subsets in the horizontal x-y plane.

First, the unknowns in the x direction are calculated at the time level

(n+l) utilizing known values in the y direction from time level (m). Second,

the unknowns in the y direction are calculated at the time level (m+2)

utilizing known values in the x direction from time level (m+l). The method

alternates between the two directions for the desired time sequence.

When utilizing an ADI method it is important to realize that a
solution can only be found when the tridiagonal matrix contains a set of
linear equations. Because equations (4.18) and (4.22) are highly non-

linear, extreme care must be taken when formulating their linear finite
difference representations. These equations must be linearized correctly
for the ADI method to be of any practical use.
The linearization of equations (4.18) and (4.22) is accomplished by
referring to certain parameters at different time levels. It is common
to use half-time intervals, (m), (m+1/2), (m+l), etc. In this manner non-
linear terms may be linearized to accommodate their solution.
The finite difference representation of equations (4.18), (4.19),
and (4.22) is now presented. These finite difference equations comprise
the numerical model.

An implicit scheme for the calculation of the drawdown in the x

direction for time level (m+l) is obtained from equation (4.18) as
follows

S[(B ) 1 F K t (m+/2) m+l)(+[B
i-,j [( + -- + s {S + [B
S (Ax) i-/2,j

16 F A (m+1/2) +1 K (m+1/2)
+ 0 Fdn) --,] + [(B + 6 Fdn) tKJ_}
0 (Ax) i+1/2,j 0 (Ax) i-1/2,j

s(+l [( + 6j Fdn) At (+/ S, ()
i+,j 10 (Ax)2 i+1/2,j ,

a zb (m+1/2)
-n ( )
at

1 K (m+I1/2)
+ 6 Fdn) K--
0 (Ay) i,j+1/2

1 d K At (m+1/2)
+ 6 Fdn) K A,
f0 (Ay) i,j-/2

(m) ) [( B
At + Nij At + (s ) [(B
1,3 ij+1 i,j

+ (sim) s m) [(B
Sij i- 1,

(5.1)

An implicit scheme for the calculation of the squared thickness of the
transition zone in the x direction for the time level (m+l) is obtained
from equation (4.22) as follows

2( ) n 1d + At (s (m+1/2) (m+1/2)) FLdn]
6 Ldn 2 K (5 s.. ) Fdn]
1,j [2 0 4(Ax)2 ,j i+1,j i-iJ 0

2(m) n IL 2(m+1/2)
= 62 0 Ldn {6i

At i (s(m+1/2)
(x)2 i+1/2,j i+,j

S(m+1/2 (m+/2) s(m+1/2))
i,j -1/2,j i-1 -,j I,.

2(m+l) At K (m+1/2) (m+1/2) f1
i-lj 4(Ax) Kij si+l,j -i0 FL

At2(m) At (m+1/2) (m+1/2)
ij (Ay)2 [Ki+ (s 1s. )+K (s (m1-/2)
{,j i,j+1/2 i,j+l ,j ,j-1/2 i,j-

(m+1/2))]+ At K ((m+1/2)
i,j 4(Ay)2 i,j ,j+

S(m+1/2 2(m)
i'j-1 i,jtl

(m) 1s(m+l/2) s(m+1/2)
- m )} FLd a t K. [(i+l,j i-1, )2
-1 J0 2 1 ,j AX

(m+1/2) -(m+1/2)
+ (,j+l si-1 )2 1/2 L'(O)
Ay

(5.2)

An implicit scheme for the calculation of the drawdowns in the y
direction for time level (m+2) is obtained from equation (4.18) as
follows

_s12- (m+l
-s(m2) [(B + 6 Fdn) JK At(
ij-1 0 (Ay) i,j-

1 K At (m+l 1/2)
+ [(B + 6 Fdn) i2j] +
jo (Ay) i,j+1/2
(m+2).r, KI1 (m+

- s j [(B + 6 1 Fdn) KAt
S1 (Ay) i1j

+ 5(m+2) {S
1 ,J

K At (m+1 1/2)
+ [(B + 6 Fdn) -K A
0 (Ay) i,j-1/2

= ss
ij

a z (m+1 1/2)
- n ( ) /2)t + N At + (s l [(B
at -ij t i,j 't i+,j ij

1 Fd K A (m+1 1/2)
0 (Ax) i+1/2,j

1 K At (m+l 1/2)
+ 6 Fdn) 1 i-]
0 (AX) i-1/2,j

+ (s1m+1 (m+l)) [(B

(5.3)

An implicit scheme for the calculation of the squared thickness of the
transition zone in the y direction for the time level (m+2) is obtained
from equation (4.22) as follows

[C Ldn
2- f0

1
o Ldn -
0

At (m+ 1/2)
4(Ay) (i ,j+l

2(m+l
{,j

1/2)

- (m+l 1/2)) f1 FLdr
- sij- 0 FLdn]

At K (m+1 1/2)
(y)2 i,j+/2 ,j+l

- (m+l 1/2) (m+ 1/2) (m+l 1/2)
J /2) + -1/2 j- ,)
S,Jij-/ i,j-I,

At K
4(Ay)2 ij

s(m+1 1/2)
(i j+l

- s 12)) } FLdn
0,- JQ

2(m+l)
- {6.
1,J

At
(x)2 [Ki+l
1/2)

+K /(m+1 1/2)
i-/2,j(Si-l,j -

(m+l 1/2) 2(m+l)
- si-,j i+l,j

a At K
2 1,3

_(m+l 1/2)
[(si+1,j

S(m+l 1/2) (m+l 1/2)
/2,j i+lj i,j

(m+l 1/2)+ At K
i,'J 4(AX) 2i'

(s(m+l 1/2)
i+1,j

2(m+l) )I I FLd
i 6 j f

- sM~l 1/2))
i-

s(m+l 1/2)
+ ( ij+l

s(m+1 1/2)
Sij- )2 1/2 L'(0)

(5.4)

2(m+2)

= 'i6
1 i ,J

2(m+2)
- '6-l

Although an implicit approach was adopted for the development of equation
(5.3) and (5.4), it is conceivable to also apply an explicit approach.
These two approaches are developed in the Appendix.

Equations (4.19) and (4.24) yield, respectively

SZb (m+1/2) K K
at n (Bl K + Zb K1)(1 + S (s b

f1 (m+1/2)
Ldn)] (5.5)
0 i,j

and
(m+1/2)
B(1/2) = B ( + 6) (5.6)
i ,j o b i,j

These finite difference equations are solved numerically by the
application of an iterative ADI method. The details of the application

are presented in the next section.

5.3 Model Execution
The numerical model developed in the previous section is executed
with the aid of a high speed digital computer. Following the flow chart

given in Figure 5.1, a computer program is written for this purpose.

The flow chart illustrates the application of an iterative ADI method in

conjunction with a print scheme for the solution of the numerical model.

Before the computer program is written a finite difference grid

is constructed which represents an aquifer's flow field. The grid is
formulated in a horizontal x-y plane. The grid spacing is chosen as an

example to be uniform in both the x and y directions, and for com-

putational convenience ax equals Ay. A field of pumpage is superimposed

Initialize Para-
meters & Boundary
Conditions

i
Calculate Values
of s, 6, and zb
for time steps
(m+1/2) & (m+l)

Calculate values
of s, 6, and zb
for time steps
(m+1/2) & (m+l)

Print Results
For Time Step

Figure 5.1 Flow chart.

upon the grid and is located in its center. The size of the pumpage

field can be varied according to the application.

Following the flow chart, all parameters are initialized and the

boundary conditions stipulated according to the application. From here

the iterative procedure begins in the x direction. In the first

iteration it is assumed that the parameter values at the time level

(m+1/2) are identical to their values at the time level (m). Aftercalcu-

lating the parameter values at the time level(m+l)their values are cal-

culated for the intermediate time level(m+1/2). For each row analyzed a

tridiagonal matrix of linear equations is generated using equation (5.1).

The solution vector is calculated by the application of the Thomas

Algorithm. In this manner the drawdown values for the time level(m+l)

are calculated for the entire grid. With this information the values of

the squared thickness of the transition zone and the height of the

saltwater mound are calculated for each node from equations (5.3) and

(5.5), respectively. Intermediate parameter values at the time level

(m+1/2) are calculated by an arithmetic average between the respective

parameters at the time levels(m)and(m+l). This ends the first iteration.

The iterative procedure stops when the difference between the drawdown

values at each node for two successive iterations is less than some

predetermined value. Divergence of the scheme is checked by specifying a

maximum number of iterations.

Once convergence is obtained in the x direction the results are

printed on a line printer by utilizing subprograms written specifically

for this purpose. The computer printout supplies a three-dimensional

representation of the distributions within the aquifer of the drawdown,

the thickness of the transition zone, and the height of the saltwater

mound. Various examples are presented in the next section.

Finally, the time is incremented by a predetermined amount and the

parameter values at time level(m+l)are reset to the time level(m).

The procedure for the calculation of the unknown parameter values

in the y direction are exactly the same as for the x direction except

that equations (5.2) and (5.4) are now used. Thus, the scheme alternates

between the x and y directions for the desired time sequence.

The application of the ADI method to the numerical model in con-

junction with proper programming yields a highly stable, convergent

solution scheme. This was found to be true under a variety of parameter

changes. Examples and results are presented in the next section.

The model is executed by utilizing the facilities of the Northeast

Regional Data Center of the State University System of Florida, located

on the campus of the University of Florida in Gainesville. The model is

executed by an IBM 3033N12 utilizing a WATFIV compiler. Memory require-

ments and execution time are approximately 300 K byte and 1100 CPU

seconds, respectively.

5.4 Numerical Results

The numerical results presented in this study are based upon a

preliminary simulation and a subsequent series of numerical experiments

whereby the values of selected parameters are altered in order to

observe the behavior of the numerical model. The parameter values

utilized throughout the simulation process are representative of the

Floridan Aquifer in northeastern Florida.

The parameter values used in the preliminary simulation are sum-

marized in Table 5.1.

A twenty by twenty k.m grid is selected with the grid spacing in

both principal directions equalling 0.5 km. The rate of pumpage occurs

Table 5.1 Parameter values for the execution of the preliminary
simulation.

Parameter Description Value

K hydraulic conductivity of the 40 m/day
freshwater zone
K hydraulic conductivity of the 0.1 m/day
1 semiconfining formation
B initial thickness of the freshwater 50 m
o zone
B thickness of the semiconfining 20 m
1 formation
n porosity 0.2

S coefficient of storage 10-3

a dispersivity 0.5 m

F distribution function of the 2 2
specific discharge
L distribution function of the 1- 2n + 2
solute concentrationn
DT time step 0.1 day

buoyancy coefficient 0.025
defined by equation (4.14)

N rate of pumpageper unit area 0.1 m/day

over a 25 Km2 area centered within the grid (Figure 5.2). Transient

conditions are simulated for a period of 10 days at a constant rate of

pumpage. Figures 5.3a through 5.5c show three-dimensional maps repre-

senting the drawdown, the saltwater mound, and the thickness of the

transition zone for the selected times, T, of 2, 6, and 10 days. These

maps are photographically reduced versions of the actual computer print-

out. A comparison of Figure 5.3a and Figure 5.3b demonstrates the two

print schemes which are utilized for reporting results. The first

print scheme, for example Figure 5.3a,reports ordinate values at each

grid point only when these values are between 0.5 and 50 m. These

values are rounded to the nearest meter to save space on the computer

printout. The second print scheme, for example Figure 5.3b, reports

ordinate values between 0.05 and 0.5 m. These values are rounded to the

nearest tenth of a meter. Both schemes illustrate the development of

the various zones within the aquifer. Figure 5.4 illustrates the rate

of growth of the maximal values of the drawdown, the height of the

saltwater mound, and the thickness of the transition zone.

Four subsequent experiments were performed to observe the behavior

of the numerical model. In each of the four experiments one parameter

was altered by an order of magnitude. Table 5.2 summarizes the experi-

mental procedure leading to the numerical results shown in Figures 5.7a

through 5.13c. Figure 5.14 illustrates the rate of growth of the

maximal values of the drawdown, the height of the saltwater mound, and

the thickness of the transition zone for experiment numbers 2 and 3.

el t .1 .1 *I *I .1 .1 I t t
*II. .1 .1I .1 I t el I t
*I 1 .1 t el 1 .1 .1 l It
(~. t *I .) It .I 1 .) .5 I ,S
( .1 *I st *I al el at *I .1 *I .1
*1 .1 *I.It *I I .l *I .t *I at
.1 *3 at *I .I at .I .1 *3 .1 .1
3I .4 .I *I *3 .1 .1 .l .I .t el

*I l .1 t at I st *I *I al et
.1 I t .1 .1 .1 .1 l el l el
(~a l l el *I)I. at .1 *I1 *i
el .t l el1 .1 I. .1 .1 .1 at *
*I st .1 *I al el el .1 *I I et
( *1 *I .1 .1 *I l .1 .1 *I *I t
l I *1 of .1 *I I l t .5 .5

*1 al *I .t *I .I rl .1 *I .1 I
l at l el *I .1 .1 *I .1 I t
at .1 .1 .1 *I .1 .L at *S I 1 t
4 4

4**

4O4
4
4 4

3

4 .3.3 .3 3 .33 .13.3.
4)~tl~( ~ ~~~~tt~ .3.1..1 ~.3..I.4.31.3~(.3ll 4~~*~~)11.(~t~t.
..3.33 .3..3.33.3.

Figure 5.2 Map of pumpage. Pumpage rate = 0.1 m/day.

* *

** lit t **It*I **Il
* i *nI l .l..l**ltl l lttl* lt
**t+ *+ ( *. i et* + **I+ it *e it
*l J tlf
1**+1 + 2 I t + 6 6 6 6 6 : 2 : |t* 1
# t* 10 12 13 1I I 1* tl13 I2 4 2 t +
2 7 4 0 12 13 14 14 1 3 1 0 4 2 + l
Si 2 0 5 12* 1 11 4 I l1 *It117I*|I07* 1025 2 i
t +I12+ 17 J t *1 l *I tI *I | 715 12**l* 2 *t

l l. P; ]17 1 2 2.0 2 9tlt9 1 t o t3 l +i
Stl + Jt 6 1 i 1**t91 20 20 20*19it 1tII 14 6 #3 tl:1
ltt1 ++ 6 2 2ltl 2 20 20, 20* 1 18 1j 6 2 trt t l c
tl*I**1t 6 1t171019 260 20 2 0 20191? 1 26 rl
+ +l t*62 +3 6 *1 1*147 20 20 20 20 20+196I1 16 466 2 *ttl
2 4 101213 14 14 14 14 14132104 2 1
S*tl9 20 2 0 20 20*19#71 14 6 2 35l.t( *
*l**I*.J* 6 13.11tl 20 19 20 20 20t1 917 14:1 6 +3::!.l,
*ilt**11 lI01*tl1 11 90 20 00 20 I0.19 .l7 146 3**lt*l,
* tl ,.ltJ1 6 1I4 17*1 20 20 20 2Otl0l2* 117 14 6 *t3 I*l*ti *
StlI** 4 Ji. 6 4lJ 1l7 20qtl 2l0 2 20 019*1 7 1 1 1 6 *3**lt* l,

S*1 3* 1 20 2 0 201 20 9r 1 1 613 1 +0 3 t k
** 20 20 200*19 *19 7 14 6 I

tl*- 1 661t l |9* 1 9 1

6 0 12*13 14 1 4 14 2 4.13 20 2 1 0 4 6 *
12 2 1* 13 .14 14 4 14 14*13 12 10 4 2 1*I
t *l l* 61 2 4*7+ 6 0 2 6 6 6 6 2 ***

+l. :]: ::I
*1 4 *1 6 7 .3* 13 1 9* I+** 7* .| 6

t 1

Figure 5.3a Map of drawdown. T =2.0 days, maximal ordinate = 20.01 m.

* I .3 I .3 I I I .I .3 .I .1 .I 3 I .I .I .I .1 1 .I .3 .1 .I .1 .I .I .I .I 1 .I
3 *l .1 i 1 .I .I I .I . . . .
* .3.3 .3 .3 .3 *t .! *I .3 1 .3 .' .1 *I .I .I .I .1 .3 I .3 .i .2 .3.3 .3 .3 1. 1 1 1 1
.3 .3 .l 3 .3 .3 .3 .3 .3 .3 *3 ~ .4 .1 I . .

S I I 3 I .I . *
I iI *I T I l. I 9 l

.2 .3
I I l .l I I *) I *1 .I I I 9l I i I :t .l *2 I

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..2. .6 .3 .3 .3 .39 .9 .0 .
S 1 i l l.2i .1 .I 1 1 1 1 1l 1 -l

a 3 I .3 .I 2 I *

*6 :2 *3 .3i | .3 .333. 6 .3 7 .7 . I .3 i 3 I 3 .3 .3. .
3 *.3 *| I .I .3 .3 | I *. .2 .1 I 9 9 ..* .l .6 .3 .3 .3 .3 .3 .3 .3 .3 .3 .3 .3
* .3 .3 .3 .3 : .3 :l 3 ." : .1 .6 ,.6 .1 .9 .9 .3 .3 .2 .3 .3 .3 .3 .3 .3 .3 .

......... .. ........ ...J .. ... .. ... ." .*.. .3 .. 3 .....

Fiur 5pt m= a xt 0.88m
.| : ::
...*. .. .. *, ,' 3. ..3 ,. q 9 >6 **(.. .A 3. 3 3 3 .l .*I I 3 3

*igr 3 ig M of 3. .satae mo d T = 2. das maia 3 .. .88
I 3 .3 .3 .i .3 :91 .2 .3 .3
: .3 :3 .3 :. i. .3 :l .3 | .: .6 .6 9 :.6 :! .3 7 .3 .3 .3 .3 :. .3 .3 .,: .3 .3 :| "| .3 3 ,
. 3...': :: :: "3 3 3.3 :3:.:e:."I : : : : : : : :3:: : : : : :3
* .3.3.3.3.3 .3.33 I .3.| .1 3 ,|.3 .|.3.2.3 .3 .3 *| 3. .3 .3 I 3 *3 .3 .3 .

e3. r x 3333 = .
3' ~ 33333333i~ii i r
: : 3 3 3 3 3 3 3 3 3
~ I 3 3 3 3 3 3

I 1 I ~ I IJ I d OOP YO 333 33*,3.3.3 33 .3 3333333 *.3**3.33333333.3*3333.3,, 33
t .II II I1 I 1 ~ I Y c .
Figure~~ 5.3 -P Map of satwte mond T) 2.0 days ma ima orint =I 0.8 m. I

*t *Itl* *I> I 2 2 2 2 2 2 2 2 Z lt *
* 3****** **4** t**t1****.***,**

II *3t*++1 **It*I** **lttlE ***s*3 l1*3 *l* **l**

** *tl**t 2 2 2 ? 2 2 2 2 2 2 2 *+lI* l*#** t
**i*tl f*I* 2 2 2 2 2 2 2 2 2 2 *I. tl** t*It
S* 13 2 *3**J** 1 *it ,j,*,Jt ** 3,*tJ 1* 2 2* ,I**I 2

S** I** 5* .. 2 2 1 *3**3**J t* t*5 t t* *2 I* t
2 +,. 5 ..5. 7. 2 ,2 2 2 2 1 ... ... .. t*,2*,..,
I**lt 2, 4 st*]* ** S*1**1**| ]5** t5* 4t3* 2 lt** I*

***t* + tIt..I 2 3 ** ** t *S .5** 5**I 5 3, *5*Jt 2 *I **,I**
H*3** 2* 3t **S**5**5**5* I 5*,t *S**5,*95 *i* 2 tltti

t* I **Itl* 2 ** 1*45* 1 4 ,1 ,, **.t t3ttjtt, i lS*tt l
*.*I*I* 2, i, 5.5,. 4.*.3.. 3*3'1* 3 3 3 J 4*5**5*,I 2 *I2 t

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*t*t *I+* 2 l t.*5I5t** 3t 2 2 ? 2 *3***t*5*t* 2 *I**It*It

l*l Sl.** 2 t3*S* S+* 4 t2l* t3** **3t* *.I 4 %*I*St* 3* *I *I**It

.* ti .*t.S**5* *t.t*. ....t* 5..*.**.*t *. . ...
I* **** *3**5**5**i* 2 *** t t
I ***3, A *3**t+5,3* 2 *I**I* *5**I5 2 *5 +5 ** *** 2 9 *3 **

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2*34*t IS** 2 2 A 2 2 2 2 3.*5**S**] 2 *I+tI**1
S*I**I**** 2 *S****,*t.**.**3,*3**3,**.tlI 4+***'**3* 2 *Ittl *I*
+ *3*t *I >* S **5**S I* 91*5 .t9*, **5* 9 **T 22 l**It
fI *|*| 2 13 5**S ** 5**5*t* |*5*S *In

Fig .te. 2 o3* 4t s t o n z5*e T di*5**5** 4 ti**5**. m
...9 1 .. ..3 2 A *3** ** 1 .3* ..3*J**3. e*** .2 2*I* *I*

F 5 3 M pt*oI*ra *I o**It*l e.T*,*l I mt*tmtl*5*I**It

3*I***t*l,***,,I*l3i1*t3 *

I**I+***I**t**t*,*** 114*,*W**** I **II t* tt,.t******ltI**,I,IIII* I* *t+* ***** ****** t ****

Figure 5.3c. Map of transition zone. T = 2.0 days, maximal ordinate = 5.03 m.

'"- 6 ...... '" "" "
+1* *I* 2 2 *J* l Il I ** l), *l*lti* *2 2 1 *1*

.l. ** 12*. 1* 7l*l7. I 7H ,*7 5 2* 2 st*

*1,*I* L. 14*5 7*), *o 6s 7 elf 6.I 124 *s*I
1* .2 14 12*. l i 14* 14 i0 *I
1** 14 .19I 1 ) I I, ) ( I I ** 4 *

1l 2 *5 12 10'* 1 1 1 ,t,.) 1 1 Y- 2 r 1 6 l
I I*--I tI 1 9 0 5 0 -). i3 ) *J:l* SIt1
1 l** I4 lt 6 2 2 2 0 20 *I t ? 1 **1*1

*1 ***)* lI *l*I ) 0 2' 0**IV* 2 I 6 t*s *

+ 1**1 1 3. 1* 1 a9*20 2 *7 14* 6 *
t* *l*)** 7 f10 1 I *l1 22 23 i *2 r) *s *a i Iil* l
I5. 3 .6 12.117)rII .10 I0 el 2 l.0 .17 It 6 l ..I
0 2.* 1} 4 14 1 4 2 i ) o t *1 .

t* *I** I** I** I** I** I** .I Qi*1*** 1** 1***I*
** ** 1*2** 7* *7 1* 7 7 *1 1 2* 2 *l
4 10 I-? I I 1 3 1 4 14 .a3 0 II

**I **| ** I+* i* ** t**|

Figure 5.4a Map of drawdowns. T = 6.0 days,maximal ordinate = 20.12 m.

ol ,I I I I I I I I 1t l It .2 a, I I j l ,I .I 1 1- I I l l .

2 2 2
1 1 .1 .. 5 5I ..1 ..1A 1 .1 .2 .! 5 2... .5 2 1 2 1-. .5. 4.2. .1 5 1.1

1 2 1
2 2. 1:. 5: 9 *
2 2 2 2 2 2 1
.I .l o ,I .I .I ,t .I .I ,I 92, ,I I .I .I ,I .. ,i ,8;!.82.? I +I I I ,I ,

2 2 2 2 1' I
S1 .I I .I .5 .5 .5 2 .5 .I l. 5 2 .5 .8 .7 .5 .5 .5 .I 5 5
~ .5 I. I i I 5. s I. .5. I.5. . .5.5.5.5.5 ...1.] .9 ..92. .. .2
-I .1 1 .5.5 .l 1.1.1.1.. .5 .s s .1 5Z.5 .2 .9 2 8.
S 5 5 5 5 5 .5 .9 .5 a .1 I 9 .5 .8 .5 .9 .2 .5 *

2 2 2 8
.? ? 2 9 5 5 92. 82.5. .5.
.92. 2.U.5 2 .5 ...2 5..5 .2.5.5.5. .9.. .
555 .5. 15 5 5 91 92.5 4.5 2.5 ?.5 7.5 ?2. T2. 6 .41.9 .9 . .45. .5.5 5 5
a ..051.0.2..5 .5 .5. .. 2 2 2 S2I.% 2 .21. 5 .2 .2 1 2. ,
.5. .5 5.5 5. .5.~5 .5. .5 5.5 5. .52.5S.52.5.2t.8 5. .5 1. 5 5 1 .5 5 5 5
'I.5.5 .5 .5 5 .I 5 .5 5 .I 9 2 2 222. 2. .1 .. 5 1 5 .. .i I
I .8 .5 .5 .5 5 .5 2 2 .2 .2 2 5 .. 6 .5 ..
S. .5 5 .2 5 .5 .2 .4 .4 4 4 4 .9 5 4 .9 .. .5 .. 1

Z4 6 99 9
.I .5 .I .5 5 .5 .I .Z .5 2 4 .2.9 .4 .. 2 2 .. .
5 .5 .I .5 5 1 .. 22. .2.3 65 5. 5. I2 2. 2 2 2 5 2 . .

*iur *5..55..bsMap ofsalwae .mou.nd4. .2.T22.69.0 d5.5.6.3 rdnae 225555...~ .83 m.
* .5 .5 .5 .5 .5 .5 .I .5 .5 .5 .2 .4 I. I, I. I. .858 24 25 25 24 ss .2. .5 .5 .5 .5 .5 5 .5 .5 5 .5
* .5 .I5 I5 .5 o.5 .5 5 .5 .5 .2.4 .4 .42.22.4 I.52.52.52.5 -5.42.z oi5.sI .4.I2 .5 .5 .5 .5 .5 .5 .5 .5 .5
* .5 .5 .5 .5 .5 I I I .5 5 .5 .I. .95.92.42u2.72. I2?2. z.22.2,45.g ,I .4 .2. 5 .5 .5 5 .5 5 .5 5 5 .I5I
* .5 .5 .5 .5 .5 .5 .5 I, .5 .5 .5 .2. .9.2 .42..2 2 .72.7,2 12 e z.4 .2 9.i 2.5I .5 .5 .5 5 .5 .5 .5 5 .5 5 I
* .5 .I .5 .5 .I .5 oi .5 .5 .5 I I .2 2 2522 .42 .82.8 2.8 2 .2.7 2.z 9 .4 .2 .5 .5 .5 .I .5 .5 .5 .5 .5 .5 .I5
* .5 .5 .5 .5 .5 .5 .5 .5 .5 .5 .2 .4 .92 2.iZ.22.92.4 2. 24 ,.42.?z .9 .4 .2. .5 .5 .5 .5 5 5 5 .5 .5 .I5,
* .5 .5 .5 .i .5 .I .5 .5 .5 .5 .2, ? l 4.4 .92 2128 29 .92 .8z .5'. 2 .9.4.2 .5.5 .5 .5 .5 .5 .5 .5 .5 .5 .5 I
* .5 .5 .5 .5 .5 .5 .5 .5 .5 .5 .2 4 ,6 ,2 2. 2 '2.92. *92. 2. 2. zvz529 Q 4 .2 .5 .5 .5 .I 5 .I .5 .5 .I .5 ,I 4I
4 I5 .5 .5 .5 .5 .5 .5 .i .5 .5 .2 .4 .92,S. I. 2 ,5 ). 292.92, .92.92 ,nI5 .9.4. 2. .I .5 ,I ,I 5 .I .5 5 .I .I 5
* I5 ,5 .5 .I .5 .5 .5 .5 ,I 5 .2, .4, .9, 2.b2.2I, 42.9, 2, .9 2.82 .22s .9 4 .3 2 .5 .5 .5 .5 .5 .I .5 .5 .5 .5 .5
* .5 .5 .5 .5 .5 .I .5 .5 .5 .I .2.,4 .42I. ?.2 72 .42, 92.92.922. 24z 2.3|g .9 .4 .2. .5 5 .5 .5 .5 .5 .I .5 .5 .5
* 5 5 oi .5, .5 .5 5 I 5 5 .2 4 92.l 2ii 92i.2 I 2.4 2.92 2.92,82.?2.521. .9.4 .2 .5. 5 .5 ,I 5 .5 .5 .5 .5 5
* .5 .5 .5.5 I. .5. 5 2.I ; 4 .91-2. I2.52 .2 2.4 .2.8. 2.5 2.42 .22 152 .9 .4 .2. .I5, .I .5 .I. .I .5 5.5.5I
4 .5 .5 .5 .I .5 .5 .5 .5 .5 .I .2.,4 -92, 2.42.? ,2.8 2.f2.2.42, .9 2 ,?~z .l 9 .4 .2.52 .5 .5 .5 .5 .5 .5 .I ,I 5 .5
4 .5 I I .5 .5 I5 I5 .5 ,I ,I ,.2.4 ,952, 42 .'2, .?f2.I2,?2.?z.2 .62 ..52. ,9 .9.4.2. .5 .5 ,I ,I .5 .I ,I ,I 5 .5 .5
* .5 .5 .5 .I .5 .5 .5 .5 .5 .5 .2 .4 .15.92,42.6?2, 2.7t.2 .72 .?2,1 62.4s.9 .9 .4 .2. .5 .5 .5 .5 .I .5 .5 .5 5 .5
* .5 .5 .5 .5 .5 .5 .5 .5 .5 .5 .2.,4 .85.2 .222. 52, 5.% 2 .12.92 .42 .z25.s .8.4 .2 .5 .5 .5 .I .5 .5 .5 .5 .5 .5 .5
* .5 .5 .5 .5 .I .I .I .5 .5 .5 ,2 .4 .95.2 22 .42.5 2.S .2.42.52.42. 25. .4 .4 .2 .5 .5 .5 .I .5 .5 .5 .5 .5 .5 .5
* .5 .5 .5 .5 .5 .5 .5 .5 .I .5 .' .3 2 2.5.5 92, 2. 2 .9 2. 2.t2 5.95.45.5.6.3.2. .5 .5 .5 .5 .5 .5 .5 .5 .5. 4
4 II .5.5. .5. .5. 5,I, .5.5.2. 65.15.85 .12. 2.92. 2. 2. .4 5...3.1S. q, 2 5 I.5.5.5.5.5.5.5 .5.5.54
4 .5 5 .5 .5 .5 .5 .5 .5 .5 .5 .2 .4.6.5.9S,/2 1.9. 2v.9.9 29.92,42 \$ 4 2 5 .5 ,I .5 .5 .5 .5 ,5 .5 .5 .5 .5
4 I, .5.5 I 5 I5 I5o5 5 i .4 ,2 .\$,;.2.4.9.8 9.5. .9 2.9q.9 2.5 .9 i.. ? ,I5 I ,I I 555 .5.5.5.54
* .5 .5I .5 .5 .5 .5 .5 .5 .t5 ,I5 .5 4.5 I2. ,324t4.42o4.4.4,\$2 .4.4 .3.21o .5[ e .5. .5 .5 .5 .5 .5 .5 .5 .5 .5 .
* :: :: :: :: :: 2" .,,.2..2. 2.2..,.2.? 2. ,.,...,. .,.z. 2.2.2.. 5.. .,:5" : ; 5::: 5 5 5 5 5 54: : :

* .55. .5 *.5. 5. 5 5 .5. 5. 5..... .. ... 5 5.5: :, 555555: : .5.5.5.5.5.5.5: :
4 .5.5.5.5.s.5.s,4 4 5 5 554 .5.,.5.54

~ i I I I I I I I oi I I ,I I I I I i o i i

I i II I I I I I I I o I
~~ I *I I I I I *I I I I I i I I i I I I I o I
*~~~ . 5. . ..5.5.5.>. 5.5.5. 5 51 5, .5...I 5.. 5.5. .5.5.5.5.5 54,..

Figure 5.4b Map of saltwater mound. T = 6.0 days, maximal ordinate = 2.83 m.

S l **9 4 *** ** 9****** ** *** ** ** I el l
S 1 :. : .: : : : :: :

Sl | l .*1* 4*: 2 A 2 2 2 2 2 .2 3 6 *5 : :
1*1t*1 1* 2 *3. 4 1 52 3 6 *6 1 3 6 6 '* 1 1 3**,* *

31 1 1,1I 4 4 *4 4 4,.,* *. 9 .
2:. I: : i !

1 2 .. .1 ... .. 1 2. 65 3.
..34.. 3Z... 14, ...s a **** *** 9 .5. 4 ....,...

6 11 i 7 4,51 : '911: 1 14 4 6 1 1 A :A 9 : 3 H : 2 3
i**I**Il 211*4 191194 4 4 4 4 4 449*9* 6 4*5, 2*3*13. l3
3*AI**3. 2*1 A ~eg46 4 4 4 4 4 4 >*49 ,*61 4 I3A 2 43**l3 l

4 i3* 2 1 4 4 6 49 49, 6* 4 .3. 2 2 t 3 6 4 6 t 91191 *34 2 4t. 2* A
3 i.3*,3. 1 4 6 1 *4 4 4 ** 2 2 2* 446 6 9 6 01 4132 1 *li 3 A3 2

t* ** *t t *** **2. t*3*1 t*1** t ***1*t* *t**** 9 *t t t* t*** t** ** t*
Figure 5.4c Map of transition zone. T = 6.0 daysmaximal ordinate = 9.03 m.
.3* l3.? 2 4 *5 2 24.944746 6 e9 6 6 6 (* 4 2 ,4 542 2 1

Figure 5.4c ap of transition zone. T = 6.0 days, maximal ordinate = 9.03 m.

** ** ** I6** **** *** I** ** I** **

*1* 2 2 i33** ** +3* 33. 2 2 *l** *
+11.* 2 2 +* J *3* 3 3 .J* 2 2 +t *|* .
I t* l 2 4 *St 6 6 6 6 6 6 *5 & 2 *l* *I
4 6 4 +
+ 1 2 2 24 2 + 1 6 6 3 ..1+.1+
+1* 4 1.,i 1: 1 4 2 4 4 23 2 4 20 10 t 2 s 6
a* 2 + 5*1 t r 1 1 14 1 : 1 0 *
2 45++13 n TIF I 18 I 23 7* 7 16*P35 92 *I
+. 2 3 5* 6 1i 1 a *1 I Id 0 I 91*7 162 *+1 9 3*I e
*+ 4 1 14*|7 1 O 192 0 209 190 19 to917 14 6 +3*. l a
S*1 *3* 6 14 1 *8+ 20 20 20 2 0 19 17 14 6 131*%* *
1* 4t* *3 1 17.19 20 20 20 2 0 20*1 9 17 t 6 j3 1t**
S*tl 6 146 1 *1 20 o 23 !0 0+t 19 T8 14 6 +3**l +
9 1 *1.3* 6 14 1 R 231 20 2. 0 9 299. 9 1+ 14 J4t t*1
*t+ J 6 14 1919 3 20 20 20 20 19 18 14 6 +3+9 l *
S* *I *3 6 14 1 19 20 20 20 20 20 19 10 14 + *3t 2 21
*44*9* 2 24 4 36* 33 2 30 20 7*3 204 ]9 2 4 6 t494**9
4lt l 3t} 6 14* I 9 231 20 20 21 20t19 7 14 6 +3**1t 2
*I *l tU 6 14*1*I.9 29 70 23 20 20 *9tl r 14 6 +3*1** 1 *l

2 4 10t*3 14 4 14 14 14 |4 14 13 1 0 2 t
*t*9 4 0411 4 14 9 1 14 14 14 14413 10 4 2 t 9
**14 2 4 *St 6 6 6 f, 6 6 *965 4 Z *I-
*|9*I 2 4 *97 6 *964t9l694 040 s 2 9 6 3* 9t
*l**l. 2 2 3 2*3 3 J*t*3* lf3t 2 9 *l 4l *

+ +1* 1 k + It** +*t e ** I** I+*t* ****t ** **

*F g 5.5a3 4ap 20 20ow s 2 2 200d9ay m a *3*e*********************

Figure 5.5a Map of drawdowns. T = 10.0 days, maximal ordinate = 20.22 m.

S I *l i I f *I I i I I .* *. .2 2 I 2 :I *1 *i *I I

1' 23 2 2 .
O~~~~~ ~ ~ ~ I. *I* I I I I I *l* *I* I -I I! l. l* l* l* l* l* l

:3 :3 :3 :3 :3:2:
j 3 2 2
3 .5 .6 .I
6. 3 2
.1 1 3 51
2 l I l i 3 .61.I 'I *I 1.41 1 51..i 3 1.l 5 I .4 .i 3 1.. *3 .*l *1. 1. 1 1l *l 5 1l 1I *l 3l 6

k I .1 I I .1 1 I .2 l .6 2. 3 6 3I 94.I 4. 14. 1 1 *. 11 99 1: I.I2: .9 : '1 *I *i 1* I I I .

1 9 34 4 4 54 5 4. I I 4 1
.3 .I 6 1 i i 1 .3l 1 .l 1 1 6i : 6 1: 1 : *6 *1 *1, It I 5 ? 1 .2 1 1 l 1 1 1 1 1i 1 *1

4
1, 9 .2 .37. 3 4I 3 : 2 1 1 1 1
.7 .5 .14.3.11?
.2 J1 *l l l I 1 I .1 *i 3. *4. 14 3 .7 4 14. 74 1 54 13. *l *i 1 *1 2 1, 1 1 l 1 *l ,

3 | l 1. 3 l l 1 *? 1 1 .l* 131 1 .* 1.3 2 .1 .1
S o I i I I I I I *l *I Z 5 Z J. J% 14 3 .6 4 1' 4. ? 6 412 3 .Z ?I :l I *I I 1 *i I. l *1 oi .1 *l 1
1 1 1 1 .1 1 *1 7 l 2 *1 14 1 .6 4 4. ?4 6 4 1. 1., .i *l 1 ,1 ,I .1 .1 .1 1l o

22 1
II '1 2 I 1 3 6 I. ? 64. 6 1 5
. *l *l *l 5* *i *Z ,3 **, *T t 5 1 *. 3 *. *i ,1 *S I
F ,igure 5.5b -i ap ,5 of s41*ta e 3 3n .2 3 :2 :1 a .1 .m a*l ,1 .6
1, 1i 1, *l 1. 1i 1 .I I 2l .'3 .12. 2 .....lS 13. 93 64 .1.3l .6 .3 .2 1 1i .I *I : i l .1 :l I
1, 1 1| 1 .i .l .l l Z 61.3 :93.61.94.14.1i4.1 2.13 9|6 ,9 6 *1 I *l l I l l l
i* i*l. l, Z* 61] 36 9 l ~1~l~ ]6 .g 3 .6 *] .2 i* l le 1 ,
.l *1 .l .I *l *l *l .2 .3 .* *61*4 :* :9 .4*.*44 14 14 .13.44 J93 ,2 6 Z l i l i o
.1 1 1 1 .i .3 .612 21 3 .23 .I* *l .Z SJ 1 J 4 4 6 4 41. l 11 .1 .2| 31. *l l .2 e1 1 l

2 e *l 2l *3 .l I '1 el *2 *3 3Fe ] ] e S e ? 4 4 S 3t 3] 22 2 1 1 '1 .1 1 1 1 1t *
*l *l~ ~ ~ 1 l *. 1l '1 .l 2l 12 23 612223 q *4. 5 .244o391, 3* l l* l* |e l
f~I 51 1, 12 3 l,3]\$.3 i,3., 12 1 ,\$ 1. 1,

.. . .. . .. ... ...... :1

Figure 5.5b -Map of saltwater mound. T = 10.0 days, maximal ordinate =4.69 m.

.. .................. ... t............................. ................ ............... .................,

*7* .1 1 1 t 1

7

*7 4 >
*11 2 6 2 1 I
7 .

7177777 I I7777777777 777777777 7

7771717l 7*71 77777 2 2 2 2 8 t *ll*7l 7*17 *77
**1 7 177777777 7 2 2 2 2 27 7 1

1*777777 7 3 5 3. 3 7 737 3 2 I.7..777+..7. .5 575

7.l i..i 2.777 0 3 '57 157 .5 t t 1 11* ,I l
5 7 a l a' 1 2 1 1
*1 7 777 77 2 7 *7 0 6 8 I t7* 77 6 7577737 2* 7 77 17777
*l 7777I*7 7 7 6 77, 7. 0 77 7 1 1.a 7
I I I7*71 2 I K01 1 7 7 7 7 7 7.77 3l7 77 2 1 7 .i 1
+ I.,fI

*l~~~tlt~ I + I # 1 I fl 5 ] J 4 35 1 4 l t l ? *~ 1 ll l
7 777777777 2 + 6 77 + I I7 72 706 S A 73 2 777777777

'' 2
l7777777 2 777757 77717l 7 8l 0 8' 0"5*5.5 6 87*117117777677772777l17717l7
71 7777777772737.6.777 l777777 8 7 7 8 8 8 8 l7717717777577 77 2717717717

Sl* l** 7 71 5 27 6 .7 7711 7 i 1 7 4 5 8 7 *l 51 2 11..1 7
*l 777 2 7 7 5 7 7 7 7 1 8 75,l 44l *3 7 7 3 7 7 7 4l 8 1 0 1, 2 2 7 717

2 2 5* 7 7 5 7 7 3712 2 2 7 3 7 7 5 7 8 7 0 5*3 2 2 7 7 7 7 77t7
t* I 2
7 7777772l 2I377 570 75 I2 i .1l l t lt l 77'7 I75 7 a7 2 277777II.
7 7 7 77 7 0 5 7 7 7 3 7 7 5 7 8 7 7 7 I71 1 3 2 '1 7 7
7 3 t5 I 2 2 1 1 7*77777
7 77777*7 73 17777 1 8 7 7.71 0 15 1 107.5. 27 77
0

7 77777777 7 6 7 7 7* *' 7. 75 77 77 75 7757 6 8 7 7 7 2 75 7 'l 77771l 777
*31 2 737757777777777*t I 8 it 8 82
7 7 7 7 7 7 1 58 7 5 2 7 7

*... .. . ... ........ ,.. ... ..
7i*777 777* 737 2 6 7 2 7 77 1 7 7 7 77 2 7 7 7 70 2 8.337 2 7 7 7 7
77 7 7 7 .7 7 2* ? 2 7 2 7 7 2 5 27 2 Z 777777777 7
7 777777777 273775777* 7777777771177 2 7 2 2 777777777?
7*7777 7 *777 2 *2 3 71. 3* 3 2 7 2 3 773 *3 ++* ..[*77 3**7***
7 *I7l7 2 2 2 2 2 2 2 2 2 2 77 77777 777 t ,
*l* * ** >* **l* l

H II>1 t.> ,, ... .. ...... ..l...., ............,,, .. .... ..,, ,. ,.,.... .. ......,... .... ^.. ,

Figure 5.5c Map of transition zone. T = 10.0 days, maximal ordinate = 11.70 m.

N = 0.1 m/day
s[m] zm] .-- 6 without convective terms A = 0.5 m
smax DT = 0.1 day
20 15 max

15 -10 .max

10

S/ zb max

0 2 4 6 8 10
t(days)

Figure 5.6 Rate of growth of the maximal value of the drawdown, the height of the saltwater mound,
and the thickness of the transition zone.

Table 5.2 Summary of experiments.

Experiment Altered Original Altered Applicable
Number Parameter Value Value Figures

5.7a
1 DT 0.1 day 0.2 day 5.7b
5.7c
5.8a
2 a 0.1 m 0.05 m through
5.10c
5.11a
3 N 0.1 m/day 0.01 m/day through
5.13c

4 K1 0.5 m/day 0.05 m/day None

******* ******* 23+ * ** ** ****
*1 **I .* i *t i* it 1i**j* *1i* 1*

S* I 1* 14 1, 1 I |J a 6C "1 a
**1* 1- 1 2 .I**I, M1 1I 1 ,1 1 .1 4* I I *
*1* .* ". *< *1 ** 4 j .I' i t l t 1 4 *I**I

*I* *J 'II ? 1* :0 O *I t 4 is > | *I I
I j? *I o o'a *II** *J* l *l

I I 2 *l ll1 I. 0 ,J 1, 'I l i 1 7 4 2, 2t*T **It

*.*......... .*7 t .. .) .J .'... .... 4 **

i*uir 5I M *1T1 of 1d 0| 110 =* 01 1')s t = 4 2. *J** **y
*l* I '* aj all l I l ll 4 | l J I 07 14 JO *.t1
*I.* 2 0 14,*,72 a a 3 6l ri b, 1 9a1a 1 .5, 2 II*.**

1l** 1 t 2 l 6 O i 0 p i 6 *| t al
>*I+ aI ** *I J IJ **a l a )*tJ*, lt J I a *I
t l t** t 1 *I. t* *t Il ( t t is l l l 11 i t 1

el, U l la1 tI *f I t1 **1 1 1t| It| I

*F ***r** *** ** *5 7 aa of dta*wd wn D .* **T* *0.* *da s ** 2.0 days*, maximaa ordinate =a 20.0t ,.

Figure 5.7a Map of drawdowns. DT = 0.2 days, T = 2.0 days, maximal ordinate = 20.01 m.

2*2*22 -I222 *. t**.*-* -222 22* 22#.2 2.- ,.* 2...- 2 2 2 *2 >-t 1e 2* 22*2 2 2 .#2 .,,. ,. .
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.. .2 .2 .2. .. .+ .2 .. I . .2 .o .2 I .I .I I I .i .2 . . .
I I

.6
I
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:3
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16 2
.7 .- .. .2.2.2 .2 .2 .2.2 .s mound'. .9.2)T 0.02 a 1. .6 2.2.0 .d .s .2.2 m .2 .2 .2 .2 .0 .2
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F ig .2 57 .2 .2 p of .altwa .. .7 .D T2 .0..9.9.0 .a.6. T =. 2.0 .2 .2 .r .i na te .2 .m .U
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2 .2 I.|2.2. . . . .2.2.2.2.2.I. I I i 2.2 I I I 2.2 ioi.2.2.2 I2 I.2 I2 I. 2 i i.2.2

2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2. .2 .2 .2 .2 .2 .2.2 .2 .22 .2 .
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22 .I .2 .2.- 2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .I .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2.2.. .I2
0 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .I
JIo .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .i2o .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .i .2 .2 .2 .2 2
i oio 2 .2 .i .2 .i 2 .2 .2 .2 2 .2 2 .2 .2 .2 2 .I .2 2 2 2 .2 .2 .2 .i .2 .2 .2 .I 2

Fiur 5 ol o- Map1oi of satwter io I i= io moun. O 0.02 days, T o 2.0 days, maximaloordinate oi0.88.m

***e ***** ******* ***** t ,* ***** ** ***fr**tf***t *tt t ****tt, *** ***,,*, *t o o D*Q ***

.......... .. . ., ... ..2 .. .
1 . . .2 .

SI 1

..2 .. .1.1.1.1. .1.1 2 ..

S.2i .. .4 i. .J.1.2. 7.. 14. 4. 04.J4. 0. 5. 94.9| 24. 4.3 .l l. .4 ..

9.I9. .2.l' 2.14.14 .J .94, 5,4.* 4 .*4.84., ]o2 .2.1, 9 4 .

I ) 1 ..2 .JI 4 .5l 5..4 1.1o .y ll ..7 ..z.r.1.d l. .s ss i .
:1 :

l. .4 ,574.u.8.j4.9.9.9. 9. ,.9.4 4.1, 6 .41 3 2 1

*1 92. 1.4. 1.41.41. 2.92.91.91.91.91.12. .9.4.8.41..i .4.1. 21. 2 .9
9 .41, .4. 9 9. .9)4. 4 3.4. 4.99 .9 49 .39. .1 .6 .0 ..1 .62 .
9 2 3 .4 .0 J 48. .~ .49.49.41.41.49.49., ,.29. .4 .0.9 .2

: ::! .....:' 1.. I : "
S. 1.9 1. .1 .1 .1

*i u e 5 7 ap .4o9 .5ns o n T.3.9.9.21.4.21.y. T.2.0 d m x ao.d.n 9...4 .J4 9 m
.. I 2., ,a2 2 I

.4 2 2
: ".9" ";39.4" "" 9. :.
j .9 2 4 .5i 344. 2.19.1 .4 3

S3.4. 4.

11 1 .- of ti 14 11 1 .2 0.59 a. I A = 2.4. 12.. .5d y m
4 .I2 1 52 I 2 34
*9 J.42.9 4 :?1 .5t .4 ;.122.23.14.89944 2 1 4 3' 1

9i 4 8 4 1 2 91 4
I 1 3 6 4
.1 A 4.14..b1.13 '3 9 12 34 "3 .9

*d9 2 .4 9 2 .4 4 .9.. .4 23.. 14.

Figure 5.7c Map of transition zone. DT 0.2 days, T 2.0 days, maximal ordinate 4.96 m.

+ +

+ +

*1***l Ittt1**I**t**l*
*I*+ 2 2 <* 3**3******3*l*** 2 t t tl |t

1 2 2 *2*3 ** ** *** 2 2 t1| 1*|*
1 6
I* 2 4 .5. 6 4 6 6 4 6 *so 2 *1t
+ 2 o 12 14 14 It 1 4 13 12 10 4 2 1+
610 it + 14 1 4 1 6 1| 2 13 4 |Q
Sel 2 ** 12* I1 t i ll7+1 \$?*7 16'I 125 2 *1
+ 6 12 is ir 1r* 7 +1 r 1 6 2: *
+16#:1+ 230*6 -13 166 1 1 19*13 t | |0 | |+
>tetl** I t **l9*l0 0tlg 0*19*I* 1 **1 4 t
I 6* 19 20 20 70t9*1 1 14's
1.-1itte 1 9 20 20 + 10 '+'*19 1, 1. 6 +3++ i+. I

9 1 o 0 20 0 20 #20191 9 1 f
Fgue 5.8a6Map1 ftdf19 20 20 20 20 20..9+1 1. A m3tl a l d t 1 9
9+l 1.i 3: 1 I4+17?: 20 20 20 20 20*19*11 1.
+ 4+ 1 26 2 4 6 6 63: e"*
1 3+ 1 9 20. 20 20 20 20 91 1
l 3663 6 14 317* 19. 20 20 20 1 9*19*1 12 636
68+612. 6 12*179.9 20 20 24 419*19* 14 238*l 6
.*1 I 6 1g#1 #19#19 1629 19 1 1 I 1
19 .*I J I 1 9 1 9 9 1 9 9 1 a 1 6 1 3 6 3 s i l t l
*8 2 6 15. 2+15 ?61741 7 17 17 3126* 2 *1
S6*1 2 3 5* 12*15 *IT IT 37 7 36635 3 12-56 2 6# 6

I 2 10 |2 I I* 1+ It |41|4 I| 6O2 to 2 .l#
*1 61 1 6 6 10 16 It 1:6 16 4 | t41* 3 12 106 4 2 3 1
I *86 *I 4* 6 6 2 6 6 6 6 65 3 6 4
2 6 6 6 6 646 66 9 6 6 6 3.* 6 2 *1*8*
*3*663 2 2 2 23 0 0 20**2**3 2 6 6* 8
S*68663 *3 6 2 3 *8 3 320 30 t2 3*2 30 8 2 4 6.1 +*

Figure 5.8a Map of drawdowns a = 0.05 m, T 2.0 days, maximal ordinate = 19.99 m.
63 636 36 846 2*8 20 20 0 20 206 963 34 +3 686 36
6 6866363673690003698863668
63663* 3678692222*9367863668
6 3665683 08698.83 663 3668
6 68663 3 63668693693 63 3663
6 63 2 5* 3*85 86636378768263 8665 3656 *3
68 5 23 63,7867m 63 29 3
63 203633 6864 363 334 23
6 63 2 0288 43 8 43184 28

6 836662 465 6 6 6 656 2**63

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~ ~~~~~~~~~~ ~~~~~ .l l* lo I* l* 1. l. l* l* io l* I* I, I* I I I tl I I| 1 oi
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t *1 l I *1 .i 1,* .1 21 9 l i 9 9 .9 1l i i 1 1 1 i I 1 .

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.l ,I I *l l .1 *l *I *l 1 92 9 '9 .9 : 9 9 *27 1 I I l l I *
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l .3 .3 .3 .3 .3 .3 .i .3 .3 .3 .3 .S 6 .7 .5 .0 .5 .5 .9 .8 .8 .7 .6 .3 .3 .3 I .3 .3 .3 .3 .3 .3 .3 .3 .3 .3

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CO
Fiue58* apo atae mound*333..333.. a= .053,3 T 2.0day, mxial rdiate 0.83m

,. 666*............6........ ..........636. .... .... ........................ *6** 66*6** *646*~*6

6 * *
6 *

I 1 2 2 2 2 2 2I
6

2 2 2
3

SI I
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.2 I
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.2 9 .3 .3 '1 1 69 .3 .3

91 61 1 I ,I I Ii ll l l, l61
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Figure. 5.4 .2p of trnito zn.7 a = 0.05 m, T7 .77. 2.0 da4 s maxma or2.at 1.5 m.

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Figure 5.9a Map of drawdowns. a = 0.05 m, T = 6.0 days, maximal ordinate = 20.08 m.
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6 4642 4 1010412 66 14 64 64 14 6112 604 244
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Fgure 5.9b Map of saltwater mound. a 0.05 m, T .6.0 days, maximal ordinate 2.83 m.

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Figure 5.9c Map of transition zone. a = 0.05 m, T = 6.0 days, maximal ordinate = 2.84 m.

l*l Il Il*lt* |lsIle. l 1

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l+ 2 12t5l# t7+Il7 IB1T |2l + 1.

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Figure 5.10a Map of drawdowns. a = 0.05 m, T = 10.0 days, maximal ordinate = 20.17 m.

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Ul
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Fiur 5.12b2-2Map2of.saltwatermound.I.N. = 2222 .2.2.2.2.=2.6.. .ay.2.2.2.2.2.2. te=20.9.m

Full Text

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," BY BARRY A. BENEDICT, HILLEL RUBIN, AND STEPHEN A. MEANS NO. 71 FLORIDA WATER RESOURCES RESEARCH CENTER RESEARCH PROJECT TECHNICAL COMPLETION REPORT \

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'ACKNOWLEDGEMENTS This project was sponsored by the Florida Water Resources Research Center with funds provided by the United States Department of the Interior, Office of Water Research and Technology. Additional funds were provided by the Engineering and Industrial Experiment Station, Univer sity of Florida. The assistance of Dr. James Heaney and Mary Robinson of the Water Resources Center is appreciated. The computer facilities of the Northeast Regional Data Center of the State University System of Florida were used for this work. The material presented in this report is substantially the same as presented by Mr. in partial fulfillment of the requirements for the of Engineering degree under the title "Numerical Simulation of Aquifer Mineralization in Northeastern Florida." i i

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TABLE OF CONTENTS ACKNOWLEDGEMENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS ABSTRACT ..... CHAPTER 1 INTRODUCTION 2 3 4 1.1 Objectives and Possible Approaches 1.2 General Scope of Study ..... 1.3 Methodology ....... THE FLORI DAN AQUI FER IN NORTHEASTERN FLORI DA 2.1 Introduction ............. 2 2 Geo logy . . . . 2.3 The Availability of Potable Groundwater 2.4 Mineralization .. 2.5 Current Assessment .......... 2.6 Summary ............... STUDIES LEADING TO THE QUANTITATIVE ANALYSIS OF AQUIFER MI NERALI ZA TI ON 3.1 Introduction .... 3.2 Early Studies ... 3.3 Current Approaches .. 3.4 Analytical Techniques 3.5 Numerical Techniques. 3.6 Summary ...... THE APPROXIMATE METHOD OF STRATIFICATION ANALYSIS 4.1 Introduction ............ 4.2 Description of the Flow Field ... 4.3 Basic Equations .......... 4.4 The Integral Method of Boundary Layer Approximation 4.5 Summary .............. iii i i v vi ix xii 1 1 2 2 4 4 6 9 20 23 29 31 "31 32 33 34 36 37 39 39 40 40 42 49

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CHAPTER Page 5 NUMERICAL SIMULATION 50 5.1 Introduction 50 5.2 The Numerical Model 51 5.3 Model Execution 56 5.4 Numerical Results 59 5.5 Discussion and Conclusions 96 5.6 Summary . 102 6 CONCLUSIONS . 104 APPENDIX A THE DEVELOPMENT OF THE FINITE DIFFERENCE SCHEMES REPRESENTING EQUATION (4.22) . . 107 APPENDIX B COMPUTER PROGRAM . . . 112 REFERENCES 125 iv

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Table 2.1 2.2 5.1 5.2 LIST OF TABLES Historical groundwater withdrawals for irrigated crops in the Tri-County area Aquifer test data Parameter values for the execution of the preliminary simulation. . .. Summary of experiments v Page 13 18 60 73

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LIST OF FIGURES Figure Page 2.1 Delineation of the study area 5 2.2 Geologic column showing rock units in the Tri-County area .............. 7 2.3 Diagram showing the generalized hydrologic conditions in Northeastern Flori da . . 10 2.4 Physiographic features of the Tri-County area 11 2.5 Piezometric level and generalized direction of ground\'Jater movement in the Tri-County area, March, 1975 . 15 2.6 location of the areas of intensive agriculture within the Tri-County area ....... ........ 16 2.7 location of aquifer test sites in the Tri-County area 17 2.8 Location of the freshwater zone and the saline water zone within the Floridan Aquifer. . 21 2.9 Schematic diagram of saltwater coning as related to the Tri-County area . . . 22 2.10 Piezometric map of the Floridan Aquifer, March, 1975 24 2.11 Isochlor map of the Floridan Aquifer, March,1975 25 2.12 Piezometric map of the Floridan Aquifer, September, 1975 26 2.13 Isochlor map of the Floridan Aquifer, September, 1975 27 4.1 Schematic description of the development of a transition zone in a stratified aquifer. . . . 41 4.2 Control volume for the development of equation (4.22) 47 5.1 5.2 5.3a Flow chart .. tap of pumpage. Pumpage rate = 0.1 m/day Map of drawdowns. = 20.01 m .... T = 2.0 days, maximal ordinate vi 57 62 63

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Figure 5.3b 5.3c 5.4a 5.4b 5.4c 5.5a 5.5b 5.5c 5.6 5.7a 5.7b 5.7c 5.8a 5.8b 5.8c 5.9a Map of saltwater mound. T = 2.0 days, maximal ordinate = 0.88 m t1ap of transition zone. T = 2.0 days, maximal ordinate ::: 5.03 m of drawdowns. T = 6.0 days, maximal ordinate = 20.12 m of saltwater mound. T = 6.0 days, maximal ordinate = 2.83 r'l . Map of transition zone. T = 6.0 days, maximal ordinate = 9.03 r'l nap of drawdowns. T = 10.0 days, maximal ordinate = 20.22 m Map of saltwater mound. T = 10.0 days, maximal ordinate = 4.69 m . Map of transition zone. T = 10.0 days, maximal ordinate = 11. 70 m Rate of growth of the maximal value of the drawdown, the height of the saltwater mound, and the thickness of the transition zone ... of drawdowns. DT = 0.2 days, T = 2.0 days, maximal ordinate = 20.01 m r"1ap of saltv/ater mound. DT = 0.2 days, T = 2.0 days, maximal ordinate = 0.R8 m Map of transition zone. DT = 0.2 days, T = 2.0 days, maximal ordinate = 4.96 m Map of drawdowns. ordinate = 19.99 m a = 0.05 m, T = 2.0 days, maximal Map of saltwater mound. a = 0.05 m, T = 2.0 days, maximal ordinate = 0.88 m ........... .. of transition zone. a = 0.05 m, T = 2.0 days, maxima 1 ordi nate = 1. 58 m . t1ap of drawdowns. a = 0.05 m, T = 6; 0 days, maximal ordinate = 20.08 m ........ vii Page 64 65 66 67 68 69 70 71 72 74 75 76 77 78 79 80

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Figure Page 5.9b Map of saltwater mound. a = 0.05 m, T = 6.0 days, maximal ordinate = 2.83 m ............ 81 5.9c Map of transition zone. a = 0.05 m, T = 6.0 days, maximal ordinate = 2.84 m . 82 5.10a Map of drawdowns. a = 0.05 m, T = 10.0 days, maximal ordinate = 20.17 m . . . 83 5.10b 5.10c 5.11 a r1ap of sal b/ater mound. maximal ordinate = 4.69 a = 0.05 m, T = 10.0 days, ........... Map of transition zone. a = 0.05 m, T = 10.0 days, maximal ordinate = 3.67 m ........... Map of drawdowns. N = 0.01 m/day, T = 2.0 days, maximal ordinate = 2.00 m ........... .... 84 85 86 5.11b rap of salt\"/ater mound. N = 0.01 m/day, T = 2.0 days, maximal ordinate = 0.09 m . . . 87 5.11c Map of transition zone. N = 0.01 m/day, T = 2.0 days, maxima 1 ordinate = 1.50 m . . 88 5.12a Map of drawdowns. N = 0.01 m/day, T = 6.0 days, maximal ordinate = 2.01 m . . . 89 5.12b Map of saltwater mound. N = 0.01 m/day, T = 6.0 days, maximal ordinate = 0.28 m . . . 90 5.l2c Map of transition zone. N = 0.01 m/day, T = 6:0 days, maximal ordinate = 2.82 m . 91 5.13a Map of drawdowns. N = 0.01 m/day, T = 10.0 days, maximal ordinate = 2.02 m . . . 92 5.13b Map of salt\'/ater mound. N = 0.01 m/day, T = 10.0 days, maximal ordinate = 0.47 m . . . 93 5.13c Map of transition zone. N = 0.01 m/day, T = 10.0 days, maximal ordinate = 3.63 m . . . 94 5.14 Rate of growth of the maximal values of the drawdown, the height of the saltwater mound, and the thickness of the transition zone for experiment numbers 2 and 3 .. 95 viii

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LIST OF SYMBOLS a dispersivity 8 thickness of freshwater zone 80 thickness of freshwater zone at the edge of the transition zone 8 1 thickness of semiconfining formation C solute concentration Co characteristic solute concentration C f solute concentration of freshwater C s solute concentration of mineral water o coefficient of dispersion o dispersion tensor F distribution function of specific discharges f unit vertical vector K hydraulic conductivity of the aquifer K f hydraulic conductivity of a porous medium containing freshwater Kl hydraulic conductivity of the.semiconfining formation Ks hydraulic conductivity of a porous medium containing saltwater L distribution function of solute concentration m time index used in finite difference equations n porosity N pumpage or recharge per unit area p pressure ix

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q specific discharge vector s drawdown of the piezometric head S coefficient of storage t time u specific discharge in the transition zone in the x direction U characteristic specific discharge in the x direction v specific discharge in the transition zone in the y direction V characteristic specific discharge in the y direction x horizontal coordinate y horizontal coordinate z elevation Zb elevation of the bottom of the transition zone Zt elevation of the top of the transition zone Greek Letters a coefficient relating concentration with specific weight Y specific weight Yo specific weight of reference Yf specific weight of freshwater Y s weight of mineral water o thickness of the transition zone n dimensionless coordinate defined in equation (4.11) buoyancy coefficient defined in equation (4.14) piezometric head f piezometric head at freshwater zone fo original piezometric head at freshwater zone 9ft piezometric head at the top of the transition zone x

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?s piezometric head at mineral water zone original piezometric head at mineral water zone piezometric head at the bottom of the transition zone xi

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ABSTRACT Efforts have been directed toward finding ways of reducing computer resources and expertise required for modeling movement of contaminants through the groundwater system. An approach has been developed which simplifies the basic equations. To test the method, it has been applied to the stratified flow problem associated with the upward seepage of saline water into freshwater aquifers overlying semiconfining formations. This seepage in response to pumpage is particularly of concern in north eastern Florida, which obtains the majority of its potable water from the freshwater zone of the Floridan aquifer. This region is being subjected to increasing rates of pumpage. Traditional attempts to simulate the mineralization process in a stratified aquifer arose by applying a sharp interface assumption or by a complete solution of the equations of motion and solute transport through the aquifer. The sharp interface approach suffers from a lack of coherenGe with the physical phenomena while the complete solution approach involves sets of highly nonlinear differential equations, the solution of which is subject to serious problems of stabflity and convergence. This study attempts to simplify the basic model by the application of the Dupuit approximation in conjunction with the boundary layer theory to a flow field divided into three zones as follows: (a) the freshwater zone, (b) the saltwater zone, and (c) the transition zone. The equations of continuity. motion. and solute transport are solved simultaneously subject to the conditions found in the simplified flow field. The result is the development of three partial differential xii

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CHAPTER 1 INTRODUCTION 1.1 Ojectives and Possible Approaches The primary project objective is the development of simplified, yet physically correct, mathematical models to describe groundwater systems, reducing needed computer resources. Two basic can be taken to achieve this goal: (1) use analytical solutions to pertinent equations, or (2) simplify the basic equations in such a way as to enable development of numerical models using reduced computer resources. A number of published analytical solutions exist, including those by Wilson and Miller [1978], Sagar [1982], Hunt [1978], and Prakash [1982]. In addition, several solutions based on perturbation techniques have been presented [see section 3.4]. In addition, numerous solutions to the diffusion equation can readily be adapted to groundwater transport problems. A review of these is given by Benedict [1981]. The above analytical models are perceived to have much utility, but the major focus of this study was to be on density-stratified fluids. Handling such effects in analytical solutions can be partially accounted for by using modified dispersion coefficients, but this cannot account for density influences on the flow field, changing density influences through the flow field, and non-unidirectional flows. In addition, use of perturbation techniques for three-dimensional flows would become very complicated. For these reasons, and due to the great interest in the saltwater intrusion problem in Florida, this problem was selected for the main thrust of the work.

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2 1.2 General Scope of the Study The Floridan Aquifer is the primary source of potable water for the northeastern Florida area. The aquifer is extremely productive and supplies freshwater for domestic, municipal, industrial, and agricultural purposes. In most areas semiconfining formations containing saline water underlie the freshwater aquifer. The inland areas of northeastern Florida are predominantly rural and highly,agriculturalized. The demand for irrigation water is intense during the growing season and heavily taxes the freshwater supply found within the Floridan Aquifer. Where the rates of pumpage of this aquifer are high, the saline water found in underlying formations is subject to upward migration. This process leads to the formation of stratified flow conditions within the aquifer and is termed mineralization. The mineralization process is typical to the highly agriculturalized areas of northeastern and is known to cause a gradual increase in the chloride content of freshwater derived from wells penetrating the artesian aquifer. The understanding of the physical phenomena associated with the mineralization process is essential to sound groundwater management programs. 1.3 Methodology The quantitative analysis of an aquifer system subject to stratified flow conditions involves the solution of highly nonlinear partial differential equations. This study seeks to simplify these nonlinear equations, and thus the basic model, by the application of appropriate quantitative tools while still maintaining a three-dimensional simulation. This model will specifically relate to mineralization phenomena in the Floridan Aquifer in inland areas of northeastern Florida.

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3 Contemporary groundwater flow problems are generally solved by a variety of analytical and numerical techniques. For aquifers subject to steady state conditions and simple boundary conditions, analytical solution techniques have been proven to work well. On the other hand, numerical solution techniques are usually superior when analyzing aquifers subject to transient flow conditions, heterogeneous soil conditions, and complicated boundary conditions. Because of the complicated nature of the transient stratified flow conditions in the aquifer system, a numerical solution technique is chosen for simulation purposes. The nonlinear nature of the basic model presents problems with stability and convergence in a numerical scheme. With an appropriate selection of simplifying steps, a highly stable and convergent numerical scheme describing the transient effects of stratified flow conditions within an aquifer is possible. The numerical results, being coherent with the physical phenomena, could then be used as a tool for the design and implementation of groundwater programs associated with ground water management in the area. The remaining chapters will describe an application of this modeling system to a particular set of conditions peculiar to the salt water intrusion problem in northeastern Florida. The area will be described and the model features and typical results'described in detail. It is important to realize that contaminants other than salt can also be modeled using the same integral formulation, thereby enabling analysis of hazardous waste movement. Extension to other geometries and pumping patterns is also possible, although it is not included in the following work.

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CHAPTER 2 THE FLORIDAN AQUIFER IN NORTHEASTERN FLORIDA 2.1 Introduction Florida is underlain by extensive limestone deposits which form some of the most productive aquifers in the United States. Known as the Floridan Aquifer, this system is the major geologic unit underlying northeastern Florida. Confined by the Hawthorn Formation in most areas of northeastern Florida, the Floridan Aquifer is artesian and supplies the majority of potable water to this area. Domestic, municipal, and ir-rigational needs constitute the majority of demand for potable water. Freshwater is supplied to the Floridan Aquifer primarily in the form of infiltrated precipitation. Recharge occurs where the upper portion of the aquifer outcrops in the middle areas of Georgia and through local sites such as sinkholes and other breaches in the Hawthorn Formation. This recharge helps maintain the freshwater balance in the aquifer system. Underlying the freshwater zone of the Floridan Aquifer in north-eastern Florida are deposits saturated with mineralized water of varying quality and origin. This condition creates the potential for well contamination due to the upward migration of the mineralized water. Of special interest to this study is the area located in north-eastern Florida comprised of Flagler, Putnam, and St. Johns counties (Figure 2.1). Known as the Tri-County area, this area is extremely agri-culturalized. A lack of precipitation during the growing season forces 4

PAGE 17

Figure 2.1 -.. _._j ,-Delineation of the study area. [1979J. !IT. .I0I-l""8 RN WATaA MANAaaM.NT CUl'TRICT _____ .. --eou_n STUDY .UE. N I 5 Figure from Munch et a1.

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6 the agriculturalists to obtain their irrigation water directly from the Floridan Aquifer. Excessive pumpage of this aquifer since the turn of the century has caused a general decline in its piezometric surface in the vicinity of the agriculturalized areas. This decline vias accompanied by a noticeable increase in the salt content of the freshwater pumped from certain wells, and prompted the Florida State Legislature to appropriate funds for an investigation. The investigation began in 1955 as part of the statewide cooperative program between the United States Geological Survey and the Florida Geological Survey. Major investigative studies into well contamination in the TriCounty area are few but in most cases well documented. The November, 1955 investigation resulted in an extremely thorough and informative report by Bermes et al. [1963J. Two subsequent well studies were con ducted in the area but went unpublished. It should be noted that even thouSh these investigations recognized the mineralization problem, no remedial programs were specified. A report by Munch et al. [1979] contains the most recent developments and data concerning well contamination in the area. Prepared in cooperation with the St. Johns Water Management District, this report outlines recorrmendations for safe \vell use in the area. 2."2 Geology An inspection of a geologic column from the Tri-County area reveals several distinct rock units. In ascending order these units are as follows: the Lake City Limestone, the Avon Park Limestone, the Ocala Group, the Hawthorn Formation, and a surficial unit. The geologic column is represented in Figure 2.2. Bermes et al.[1963], Chen [1965], and Munch et al [1979J provide thorough descriptions of these units.

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AGE FORMATION CLASTICS w z -w ---U 0 :::E -------OCAl..A GROUP I AVON !'ARK W Z W U 0 W / LAKE CITY :.r:IESTONE THICKNESS o to 100 ft o to 30m 3 to 180 it 1 to 55 m 90 to 250 ft 30 to 75 m 150 to :50 ft 45 to 75 m .. 00 to 500 ft 1:0 to 150 m 7 DESCRIP"'ICN Sand, Clay, and of che Two Clay, wich Sana, Sandy C:.:lY and Sandy Soit. Pure Limestone Alternating Li:nestone and Dolomite 3cds ;"rich some Disseminat.!d ?e.:lt: and some Thin ?eat Beds Altarn.:1ting, Limestone and Dolomic" B"ds with Dissemin;lced P=ac ;lnd Distinct: Peat 3"ds Figure 2.2 Geologic column showing rock units in the Tri-County area. Figure from Munch et a1. [1979J.

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8 The Lake City Limestone and the Avon Park Limestone units are of Middle Eocene Age and are comprised of alternating beds of limestone and dolomite. Peat beds are found scattered throughout these two units. Johnson [1979J characterized the top of the Avon Park Limestone as the "Avon Park 10\'1 porosity zone" which consists of hard, low permeability dolomite. This distinguishing feature of the Avon Park Limestone can be seen as a semi-impervious barrier to vertical groundwater flow. The Ocala Group of late Eocene Age consists predominantly of pure soft 1 inestone and shm'ls a lower average resi sti vity than does the Avon Park Limestone [Munch et al., 1979J. The Ocala Group contains principally freshwater and supplies large quantities of potable water to the Tri County a rea. The Hawthorn Formation of Miocene Age consists of clays and sands with some interbedded limestones and dolomites and serves as a formation for the underlying limestone units. The base of the formation consists predominately of hard dolomite and in most cases is impermeable. A distinguishing feature of the formation is its high phosphate content relative to the Ocala Group. This feature provides for very accurate logging of the contact between these two units. The Hawthorn Formation underlies the entire Tri-County area except for portions of southeastern Putnam County and most of southern Flagler County. The formation is breached locally by sinkholes, faults, and general erosional processes. The surficial unit of recent to Miocene Age consists of 'interbedded lenses of marine sediments, fine to medium sands, shell, and green calcareous silty clay. Thin beds of limestone can be found in certain areas. Small volumes of and nonartesian waters are found in this unit.

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9 2.3 The Availability of Potable Groundwater Large quantities of potable groundwater are available from the permeable formations underlying northeastern Florida. The hydrologic regime of these formations is commonly divided into two units termed the nonartesian (surficial) aquifer and the artesian (Floridan) aquifer (Figure 2.3). Although the majority of potable water is obtained from the artesian aquifer, small quantities of water are pumped from the nonartesian aquifer for a domestic use. Seasonal irrigation provides the heaviest demand for freshwater derived from the artesian aquifer. Recharge and withdrawal rates from both aquifers along with the respective aquifer characteristics determine the availability of potable groundwater in the Tri-County area. Recharge rates to the two aquifers have a direct influence on the safe yield from wells in the area. There fore, a thorough knowledge of the physiography and climatic conditions of the area is essential to a groundwater survey. The climate of the Tri-County area is classified as humid subtropic with a mean annual rainfall of 135 cm (54 in.). Normally over 50 percent of the total annual rainfall occurs during the months of June through September, with the driest months being November through May. Because the dry season coincides with the area's growing season, large quantities of ; rrigation water are needed to perpetuate the crops. The topography of the Tri-County area is generally flat with the majority of land area located in the Eastern Valley. The area is bounded to the westby the Palatka Hill and the Crescent City Ridge and to the east by the Atlantic Coastal Ridge. Figure 2.4 illustrates the physio graphy of the area. Recharge to the surficial aquifer occurs over the entire area. Recharge to the Floridan Aquifer occurs primarily in the western portions of the area (Figure 2.3).

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Figure 2.3 :;; 1 J \ r { (' I I' i 1 --Diagram showing the generalized hydrologic conditions in Northeastern Florida. Figure from Bermes et al. [1963J.

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San Mateo Welaka Hill MILES 0 5 10 i M a8' 01 o 5 10 15 KILOMETERS Creseenl City Ridge Espanola Hili FI..ACLER :.';'. I o Cl '" .. ,\ ( I i \ I 11 CCR\NCR =, 'l...."'-"" L._ ...;.--._._._. __ ._ ..l 11 Figure 2.4 Physiographic features of the Tri-County area. Figure from Munch et a1. [1979J.

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12 Although the surficial aquifer supplies only a small amount of potable water to the Tri-County area, this aquifer is nevertheless an important source of groundwater. The aquifer grades from deposits of high average permeability at the surface to very low average permeable deposits as the Hawthorn Formation is encountered. The aquifer underlies the entire area attaining its maximum thickness of about 46 m (154 ft) in inland areas and gradually thinning as the Atlantic Ocean is approached. The piezometric head in the aquifer is generally sufficient to bring the top of the water table to within 1 to 3 meters of the ground surface. In the inland areas, withdrawals from the nonartesian aquifer are generally limited to domestic use. This is due to the small amounts of water and to the high degree of inhomogeneity found within the aquifer. Municipal well fields tapping the nonartesian aquifer can be found in the immediate coastal areas where the underlying artesian aquifers contain saline water. The artesian aquifer underlying the Tri-County area consists of a principal aquiclude, secondary aquifers, and the Floridan Aquifer. The principal aquiclude is the Hawthorn Formation, which serves to restrict vertical groundwater movement to and from the artesian aquifers. The secondary aquifers consist of lenses of sand, shell, and limestone and occur within the Hawthorn Formation. These aquifers are recharged by the overlying nonartesian aquifer and the underlying Floridan Aquifer. They are important sources of potable groundwater in some coastal areas where the underlying Floridan Aquifer contains saline water. The Floridan Aquifer is the principal freshwater zone for irrigational, municipal, and industrial uses. Irrigation demands constitute the majority of withdra\'/al from the aquifer. Table 2.1 sunmarizes irrigation

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1 J Table 2.1 -Historical groundwater withdrawals for irrigated crops in the Tri-County area. 1956 COUNTIES IRRIGATED ACRES Putnam No Report Flagler 4,000 St. Johns 16,000 1965 Putnam 13,000 Flagler 6,500 St. Johns 22,000 1970 Putnam 11,200 Flagler 8,230 St. Johns 19,000 1975 Putnam 11,380 Flagler 4,500 St. Jolms 20,120 Table from Munch et al. [1979J GROUND I.JATER IHTHDRAllr\L 5 6 26 11.6 3.5 13.9 7.6 9.0 22.1 15.8 6.7 28.57

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14 oyer the past 25 area. for gation have generally increased over the past 26 years while the ldnd area under irrigation has remai:led re1atlvely C8nstart. Figures 2.5 and 2.6 illustrate a piezometric map of the area and the locations of intensive agriculture in the area, respectively. The impact of irrigation withdrawal upon the piezometric map of the Floridan Aquiferis seen when these two figures are compared. The piezometric sinks roughly coincide with the heavily areas. Recharge to the aquifer principally occurs in the western and southeastern porti ons of Putnam County It/here the aqui cl ude is breached by sinkholes, in Flagler County where the aquiclude is either thin or absent, and to a smaller extent by dOIt/nward 1 eakage through the aqui cl ude. Groundwater is in spring areas, wells, and to some of the over lying secondary aquifers. At the turn of the century, artesian pressure in the Floridan Aquifer was sufficient to produce free-flowing wells. By the 1950's, artesian water levels dropped, and free-flowing wells could no longer supply enough water for irrigation [Munch et al., 1979J. In to this condition, several well studies were prepared to determine aquifer characteristics and the potential impact on the Floridan Aquifer due to heavy seasonal withdrawals [Bermes et al., 1963; Bentley, 1977; :lunch et al., 1978J. Bentley's study in 1977 consisted of two types of aquifer tests performed on eighteen It/ell sites (Figure 2.7). The results of the individual \'Ie11 test are given in Table 2.2. Based on the aquifer tests, Bentley [1977J concluded that on a regional scale the hydraulic characteristics through out the Tri-County area \'Iere relatively homogeneous with local variations to be expected.

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-50 LINE OF EaUAL POTENTIOMETRIC LEVEL OF THE FLORIDAN AQUIFER INFERRED POTENTIOMETRIC LEVEL DIRECTION OF MILES o 5 10 IME.M. e o 5 10 15 KILOMETERS Figure 2.5 Piezometric level and generalized direction of movement in the Tri-County area, 1975. Munch et al. [1979J. 15 ground\'/ater Figure from

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INTENSIVE AGRICULTURE AREAS o MILES 5 10 !. 8M o 5 10 15 KILOMETERS 1 G Figure 2.6 Location of the areas of intensive agriculture within the Tri -County a rea. Fi gure from Munch et .a 1. [1979].

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JO o I o .,. .,. EXPLANATION Figure 2.7 Location of aquifer test sites in the Tri-County area. Figure from Bentley [1977J. 17

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Table 2.2 Aquifer test data. Well Wdl Thlckness J.ocat Jon Nuolber USGS ID N ..... ber depth or "tluJ rer TrallRnlts:;'vlty. Slt)rnue (ft ) (fl) (I t 2/<.1) ,0, fJdt'nt. ,,-I --_. ----"_. ---------1 ml southeast 291'1580812842.01 20n I,ll IIII.UIIII 0.0001> 0.019 uf lIast I"gs lA 2919500812842.01 1)0 1.2 OIl east of 29)9)0081)4 )6.01 JOO 1110 l,b,OnO .001 .016 East I'aldtka 2A 2'1)9)1081)420.01 541 411, 211 293"9 1208U4 58.01 2 OIl south of .) 29404908129104.01 4)0 51>,000 .0006 .0051 Hastlngs 1A 2940490812952.01 610 480 38 29405)0812921.01 568 420 1.5 .. 1 northeast 4 2940))0813502.01 250 UO H,OnO .0008 .010 of East 4A 2940)2081)455.01 48 294045081 J515. 01 122 'Ill 2 mt \.Icst uf 5 294Hl081 )241.01 )00 ISO t-.1101 .021 lIastlngs 5A 2942550813240.01 100 I So flll,Ullll ) OIl northwest of 6 2941480812906.01 )02 1)11 .11001' .0011 Armstrung flA 2941520812905.01 '115 I SO 611 2'141480812924.01 12S 7 ml uf 2951250812910.01 5H 12 '. V"OUlI .011111 .lIn .. o l'll:olalil 1A 10.111 S;lr, Spuds 8 294]41081281).01 J81l lUll l'J.IIIIII .(11111) .111111'11. 8A 294)4 )08f28I,O. 01 2M 511 0.5 OIt south of 9 2945400813833.01 lllO 71) 17,000 CD

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Table 2.2 continued. Well Well 11,ickneR!l ties Location Number llSGS lU Number del,th of aqulft'r Storage Leakance (f t) (ft) (ft7./d) l-u('fflcieflt, d-1 --------_._----------_ .. __ +--_.-. -----+ ---.- _---10 mi south of 10 29323408142',1.01 295 I,I,UOO Palatka Roy 11 2937160812936.01 250 2b,Olln 4 III northeast 12 2951060812909.01 400 200 (data not used in analysis) Riverdale 1.5 .. I north of 1) 295028081lJ09.01 JOO 70 1I,7!,0 Riverdale 10 ml south of 14 29514408lJ717.01 340 80 7,800 Greencove Springs St. Augustine 15 2951120811648.01 248 55 I J,nOO 8l'8eh I, .. I southw"ut of If> 300J5,.1I111 JU12.01 )(,2 I,ll (',HIIII 'It"bln 9 .1 north of 17 )000480812))3.01 258 10 1,60n St. lIogus tine 1.5 ml northeast 1ft )06 150 15,000 IIrmstrong Table adapted from Bentley [1977, Table 2] <0

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equations describing in three dimensions the distribution of the drawdowns in the flow field, the growth of the saltwater mound, and the development of the transition zone. These equations are formulated into a numerical model by utilizing an iterative alternating direction implicit (ADI) method and the appropriate finite difference representation. The results of the execution of the numerical model indicate that a highly stable, convergent numerical scheme is developed in this study. The model is capable of describing the three-dimensional effects associated with the transient nature of stratified flow in an aquifer. While the specific example treated salt movement, other contaminants, including hazardous wastes. could easily be modeled in the same way in a stratified flow. In addition, if the contaminant did not bring about stratified conditions or occur in a saline-stratified region, the same basic procedure can be utilized by removing contaminant influence on the flow field in the equation of motion. xiii

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20 2.4 Mineralization The Floridan Aquifer in northeastern Florida contains zones of saline water which underlie the artesian aquifer. The origin of the saline water was prObably due to the infiltration of sea water during the Pleistocene Epoch when the sea stood above its present elevation. As the sea level subsequently receded, recharge to the mineralized aquifer flushed out the saline water in the upper portions tif the aquifer. This flushing action is a continuous process and will occur as long as the inland piezometric heads are above sea level. Currently, the Floridan Aquifer in the area consists of a freshwater aquifer and a saline water aquifer (Figure 2.8). The freshwater aquifer extends from the bottom of the Hawthorn Formation, through the Ocala Group, and ends at or near the "low porosity zone" marking the top of the Avon Park Limestone. The saline water aquifer underlies the freshwater aquifer. Because fresh and saline waters are miscible fluids, there exists a small zone of transition between the fresh and saline aquifers. Contaimination of the freshwater aquifer occurs from downward leakage through the Hawthorn Formation and from the upward migration of saline water from deep semiconfining formations. Large differences between the values of the piezometric heads of the freshwater aquifer and the overlying phreatic aquifer suggest minimal leakage through the Hawthorn Fonnation. This would imply that the majority of leakage occurs from deep semi confining formations. In this study the contamination of the freshwater aquifer from underlying saline water is termed "mineralization". The mineralization process is shown schematically in Figure 2.9. The mineralization of the freshwater aquifer in the Tri-County area stems from heavy seasonal pumpage in the highly agriculturalized areas

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GROUND SURFACE UN CONSOLIDATED SANDS AND CLAYS __ HAWTHORN FM. CONFINING UNIT __ OF -FLORIDAN AQUIFER HAWTHORN FM. ROCK AQUIFER OCALA GROUP FLORIDAN AQUIFER SALINE ZONE 21 Figure 2.8 Location of the freshwater zone and the saline water zone within the Floridan Aquifer. Figure adapated from Munch et al. [1979, Figure 32J.

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r GROUND SURFACE ---------------------------------------. HAWTHORN FM. ---------------------CONFINING UNIT ---. OF --.---FLORIDAN AOUIFER __ ---------------':::,: -----------------------------------------... -, ,-HAWTHORN 'FM. ; I"" ==::::J ROCK AOUIFER \-i i: i I. '.:,1 OCALA GROUP FRESH WATER SALT WATER INTERFACE ..... -.-= -22 Figure 2.9 Schematic diagram of saltwater coning as related to the Tri-Countyarea. Figure from et a1. [1979J.

PAGE 36

23 (Figure 2.6). Irrigation of crops begins in late September and continues through May. At the beginning of the growing season the piezometric surface of the freshwater aquifer is sufficiently high to produce many free-flowing wells. Intense groundwater withdrawals during the season in the agriculturalized areas produce cones of depressions that may exceed 6 m (20 ft) below the land surface, and water quality deteriorates rapidly. Partial to total recovery of the original piezometric surface occurs due to natural recharge during the summer months when little to no pumpage occurs. The recovery process is illustrated in Figures 2.10 and 2.12. These piezometric maps are accompanied by their respective isochlor maps in Figures 2.11 and 2.13. Note the correspondence between the agriculturalized areas, the piezometric sinks, and the areas of higher chloride content. Thls correspondence again suggests that the mineralization process occurs due to upward leakage of saline water into the freshwater aquifer in response to heavy pumpage. Two major mineralization studies [Bermes et al., 1963; Munch et al., 1979J have been performed in the Tri-County area. The most recent study, completed in 1979, thoroughly reviews the mineralization process and reflects the current policy in the area. In general, this study has found that in the area: (1) a gradual decline in the piezometric surface of the Floridan Aquifer has occurred due to increasing groundwater withdrawals during this centurY"and (2) the areas and amounts of saltwater contami nation have increased from 1956 to 1975. 2.5 Current Assessment Current assessments concerning the problems of groundwater mineral-ization in the Tri-County area are presented in the study [Munch et al., 1979J prepared by the St. Johns Water Management District. A portion of

PAGE 37

24 EXPLANATION -'-'-: .... i \., J' '._.-._._.':'-._._-----_._._-_ .. Figure 2.10 -Piezometric map of the Floridan Aquifer, narch,1975. Figure from Munch et a1. [1979J.

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c::=::::l 0 N 50 c=J 2.51.0500 c:::=J 501 1000 c==:: 1000+ ...... .. ,.... u;u ... 111. ... N Figure 2.11 Isochlor map of the Floridan Aquifer, March, 1975. from Munch et al. [1979J. 25 Figure

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EX Pt,.AHAnOH ___ 30_... N 70 Figure 2.12 Piezometric map of the Floridan Aquifer, September, 1975. Figure from Munch et al. [1979J.

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CHlORIOE' CONCENTRATION === 0 '050 c:::== 51 '0250 === SOO 501'::11000 ==== 1000. N o 27 Figure 2.13 -Isochlor map of the Floridan J\quifer, September,-1975. from et a1. [1979]. Figure

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28 this study attempts to correlate chloride concentration with pumpage rate, well depth, aquifer penetration, and piezometric level by a re-gression analysis and polynomial expansion. The compiled data illustrqte that in response to pumpage, piezometric levels decrease and chloride concentrations increase. The reverse situation prevails during the non-growing season I'/hen pumpage is small and recovery occurs. A statistical analysis indicated that 50 percent of the wells in the study area may produce water with a chloride content less than or equal to 210 ppm, and that 10 percent of the wells may exceed 778 ppm chloride during any time of the year. At times some of the deeper wells can act as direct con-duits for the transport of saline water into the freshwater aquifer. During periods of intense pumpage, local cones of depression are formed in the areas of Orange Hills, Hastings, Elkton, and Bunnell (Figure 2.5). Recharge to the aquifer from leakage is insufficient to stabilize the local cones of depression. The lowest piezometric levels and the highest chloride concentrations were apparent in the local cones of depression during the month of March. The greatest variation in water levels and water quality occurred during the months of March through September when recovery of the aquifer occurs. The combination of loJell construction, well spacing, and overdraft lead to the upconing of saline water beneath pumping wells. The study attempted to calcillate safe yields from various theoretical formulas which might stabilize the local cones of depression during periods of low piezometric levels. Pumpage rates ranged from 817 m3jd (150 gpm) within the central portions of the local cones of depression to as much as 1910 m 3 /d '(350 gpm) in areas where the freshwater aquifer thickness ex ceeds 61 m (200 ft). According to a statistical analysis, it was

PAGE 42

29 determined that at least 120 wells in the area could benefit from rehabilatative construction procedures. Recommendations available to the agriculturalists and the various governing agencies are presented at the end of the study. 2 .6 Surruna ry The geologic structure of the Tri-County area consists of rock units ranging in age from Middle Eocene to recent. These units in ascending order are the Lake City Limestone, the Avon Park Limestone, the Ocala Group, the Hawthorn Formation, and a surficial unit. The Lake City Limestone, the Avon Park Limestone, and the Ocala Group consist predominately of porous limestone and dolomite. The Hawthorn Formation consists primarily of sands, clays, and marls and is considered a confining unit. The hydrologic regime of the area consists of a nonartesian (surficial) aquifer, a principal (Hawthorn Formation) aquiclude, and an artesian (Floridan) aquifer. The nonartesian aquifer supplies small amounts of potable water to the area mainly for domestic use. In the Floridan Aquifer the Ocala Group contains predominately freshwater while the underlying units contain saline water. This aquifer supplies the majority of irrigational, municipal, and industrial waters to the area. Irrigational needs constitute the majority of withdrawals from the aquifer. Because of excessi ve pumpage for i rri gati onal purposes, the ch 1 ori de content of the freshwater zone of the Floridan Aquifer has increased steadily since the turn of the century_ It is suggested that this condition is caused by the up\
PAGE 43

30 Two mineralization studies have been conducted in the Tri County area [Sermes et a 1., 1963; et a 1., 1979J. 1>lunch I s study in 1979 supplies a thorough overview of the mineralization problem and presents recommenda ti ons for the control and preventi on of \'Iell contamination.

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CHAPTER 3 STUDIES LEADING TO THE QUANTITATIVE ANALYSIS OF AQUIFER MINERALIZATION 3.1 Introduction The intense development of certain coastal regions of the world in the b/entieth century has created a situation \'/here salt\'/ater in-trusion hac; jeopardized the quality of freshwater derived from coastal aquifers. The east and west coasts of Florida pose various problems associated with salinity intrusion into coastal aquifers. In response to the problems presented by saltwater intrusion within coastal aquifers, a great variety of studies have been conducted to better understand and evaluate these problems. Many aquifers located quite far from coastal areas are also subject to the mineralization phenomenon. This has of late begun to attract much attention. The mineralization phenomenon associated with inland aquifers is very similar to that experienced by coastal aquifers. of the techniques utilized for the study of the mineralization phenomenon in coastal aquifers may be applied for the study of inland aquifers. Several studies pertaining to both types of aquifer m"ineralization are reviewed within. In the analysis of flow through porous media, the nomenclature con cerning the number of dimensions in which the analysis is conducted is often confusing. Therefore for the sake of clarity, a two-dimensional analysis will be defined as representing flow in a plane region while a three-dimensional analysis will be defined as representing flow in a spatial region. 31

PAGE 45

32 3.2 Early Studies The first analytical relationship relating fresh and saline waters in a phreatic coastal aquifer was presented by two independent investigators [Ghyben, 1838; Herzberg, 1901J. The Ghyben-Herzberg relationship states that the depth below sea level at which saltwater can be found in a coastal aquifer is about forty times that of the corresponding height of freshwater above sea level. Although this is an approximate relationship for a phreatic aquifer subject to horizontal flow, it can be used to obtain a rough estimate of the location of the freshwater-ialtwater interface within the aquifer. Despite the efforts of Ghyben [1888J and Herzberg [1901J, investigators vlorking for the oil industry were the first to complete detailed analytical mineralization studies [Muskat and Wychoff, 1935; Arthur, 1944J. These studies describe the 'upconing of saline water into overlying oil deposits. Their applications were limited due to the simplified geometry utilized in the development of the analysis. Nevertheless these first studies provided valuable insight into the physical phenomena associated with the mineralization process. Subsequent mineralization studies stemmed primarily from the groundwater quality problems associated with the intensive development of the world's coastal regions. These studies attempted to simulate the flow conditions within an aquifer subject to mineralization by a variety of physical, analog, and mathematical models. Before the emergence of high speed digital computers in the late 1950's, physical and analog models were popular in mineralization studies. The Hele-Shaw model was especially well suited for this purpose. Although physical and analog models are useful for the understanding of the

PAGE 46

33 physical phenomena associated with aquifer mineralization, a new model must be constructed for each unique application incurring great time and expense. With the advent of digital computers came a switch from physical and analog models to sophisticated analytical and numerical models. These latter models are the basis for our contemporary knowledge of the mineralization phenomenon. 3.3 Current Approaches Two basic approaches can be adopted when applying an analytical or numerical model to an aquifer mineralization problem. The first approach assumes the immiscibility of the fresh and saline waters whereby an assumed sharp interface is found at their mutual boundaries [Bear and Dagan, 1964; Hantush, 1968; Shamir and Dagan, 1971; Haubold, 1975J. The second approach simultaneously solves the equations of motion and solute transport to describe the transient position of a dispersive saltwater front migrating into the freshwater aquifer. With the sharp interface approach, potential flow theory can be applied to both sides of the sharp interface between the fresh and salt waters. But because fresh and saline waters are miscible fluids, this approach suffers from a lack of coherence with the physical phenomena. However, the assumption of a sharp interface sometimes supplies a good approximation to the transient position of the transition zone between freshwater and saltwater zones. The inclusion of the solute transport equation in the second ap proach implies the existence of a zone of transition or a dispersive front either of which migrates through the porous media. The solute (salt) is dispersed within the flow field due to diffusion and mechanical dispersion processes and thereby affects the dynamics of the flow. The

PAGE 47

34 distribution in the flow field introduces nonlinear terms into the equations that should be used in the analysis. For numerical these non1ir.ear cause problems with convergence and stability. Various approaches attempt to linearize the equations to facilitate analytical solutions. The analysis of either a transition zone or a dispersive front may be performed in a variety of ways. If the solute is a neutrally buoyant material, then various perturbation methods can work extremely well and generate simplified models that can lead to analytical If the solute is not a neutrally buoyant tracer then various combinations of perturbation approaches can also be used in order to simplify the mathematical model. Some of these methods are discussed in detail in subsequent sections. 3.4 Analytical Techniques The analysis of stratified flow in porous media by analytical techniques usually involves the application of certain perturbation methods. When applied to a steady flow field, perturbation methods can reduce the solute transport equation to an equation of the conduction type. Solutions to the heat conduction equatjon are well documented in various texts. Dagan [1971J analyzed the migration of neutrally buoyant tracers. He considered both longitudinal and lateral hydrodynamic dispersion in the porous medium. The analysis derives an inner boundary layer solution for a transition zone in a steady flow field by utilizing the stream function and the velocity potential function as coordinates. In this analysis it is required that the stream function and the velocity potential function be defined for every Doint in the flow field prior

PAGE 48

35 to the calculation of the solute dispersion. This is true only when a neutrally buoyant material is introduced into the flow field. Only problems with constant hydraulic conductivity and a constant coefficient of dispersion can be solved by this analysis. Eldor and Dagan [1972J later extended their analysis to include radioactive decay and adsorption. Gelhar and Collins [1971J applied a second perturbation method to analyze dispersive flow in porous media. The study develops an approximate analytical technique for the description of longitudinal dispersion in unidirectional steady flow with variations along a streamline. The governing equation is reduced to a simple diffusion equation, and a general solution is obtained. Results are obtained by evaluating two integrals in the velocity field. Lateral dispersion is not treated in the analysis. Thus, a solution is not found for a boundary layer which develops along 3. streaml ine. Hunt [1978J introduced a perturbation method that can be used for nonuniform, steady and unsteady flow through heterogeneous porous media. The solution, while being very general, is most accurate when the boundary layer is relatively thin and accurate numerical solutions are difficult to obtain due to numerical dispersion. The study suggests that the perturbation solution initially be used until the size of the boundary layer approaches a predetermined limiting value where a numerical solution is then employed to finish the analysis. The above perturbation methods are based in part upon the assumption of the existence of potential flow at every point in the flow field. In the case of saltwater intrusion problems, this assumption fails due to the density differences between the fresh and salt waters whereby

PAGE 49

36 nonpotential flow conditions exist in the boundary layer. Dagan [1971J addressed a saltwater intrusion problem but assumed that the minerals within the saltwater act as ideal tracers. Rubin and Pinder [1977] solved the nonpotential flow problem in the boundary layer by the utilization of the integral method of boundary layer approximation [nzisik, 1980] in conjunction with a rerturbation nethod. The dispersion process is described as a migration of a sharp interface perturbed by small disturbances due to salinity dispersion. Salinity dispersion creates a mixing zone in which boundary layer similarity exists. Although this study gives only steady state solutions, the boundary layer integral method supplied a means by which transient mineralization problems may be analyzed, usually by a numerical scheme. While perturbation methods yield good two-dimensional analyses, the extension of these methods to three dimensions would be extremely difficult. For example, following Dagan [1971] a solution in three dimensions would necessitate the use of stream function planes and velocity potential function planes. 3.5 Numerical Technigues Numerical techniques have several advantages over analytical tech niques when applied to aquifer mineralization problems. Numerical tech niques are able to handle complex geometries and boundary conditions, heterogeneous and anisotropic porous media, and time dependent problems whereas most analytical techniques can not. On the other hand, analytical solutions are often easier to apply and can be used to check the accuracy of the numerical solution. Both finite element and finite difference schemes are used when analyzing aquifer mineralization problems. Pinder and Cooper [1970J

PAGE 50

37 utilized a finite difference numerical scheme to simulate saltwater intrusion within a coastal aquifer. The method of characteristics is used to solve the solute transport equation and the alternating direction implicit (ADI) method is used to solve the equation of motion for a two-dimensional problem. The m'ethod is applicable to heterogeneous, anisotropic porous media with irregular geometry, constant head, and constant flux boundary conditions. Segal et a1. [1975J applied a Ga1erkin-finite technique for the two-dimensional simulation of saltwater intrusion within a coastal aquifer. The Galerkin-finite element theory is used to formulate approximations to the nonlinear equations for velocity and pressure. With this information the solute transport equation is solved separately. Iteration between the solute transport equation and the flow equations continues until convergence is reached. Rubin and Christensen [1982J. and Rubin [1982J developed numerical schemes for the two-dimensional simulation of stratified flow in a coastal aquifer and an inland aquifer, respectively. Both studies utilize the integral boundary layer method where the solute transport equation is integrated over the thickness of the boundary layer subject to certain similarity conditions. The resulting equation is then solved simulta neously with the equations of continuity and motion by an imp1icitexplicit finite difference numerical scheme. The study presented herein extends Rubin's work [1982J to obtain a three-dimensional analysis. 3.6 Summary The problems associated with the mineralization of coastal aquifers have generated a large number of studies attempting to describe the phenomenon. Few studies have dealt with the mineralization problems

PAGE 51

38 found in inland aquifers. However, some of the analytical and numerical concepts developed for coastal aquifers can be applied to inland aqui fers. Two common approaches can be applied to the flow field for the description of the mineralization phenomenon. The first approach assumes a sharp interface \.o.fhi ch exi sts between the fresh and saltwater zones. This approach suffers from a lack of physical coherence. The second approach solves the equations of motion and solute transport simulta neously. Perturbation methods as well as numerical schemes can be used for this purpose. Boundary layer methods can be applied in order to generate analytical as well as numerical approaches for the description of the dispersive freshwater-saltwater interface. Various studies utilize all three methods.

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CHAPTER 4 THE APPROXIMATE METHOD OF STRATIFICATION ANALYSIS 4.1 Introduction Strati fi ed flow in an aqui fer stems from the contact between fresh and saline waters in the aquifer. Flow within the aquifer creates a zone of transition separating the fresh and saline waters. The mineral (salt concentration) distribution within the transition zone affects the dynamics of the flow field. On the other hand, the transport of the minerals within the flow field depends on the structure of the flow field. It is clear that complicated flow conditions exist within an aquifer subject to mineralization. To simulate stratified flow within an aquifer the equations of continuity, motion, and solute transport are solved simultaneously subject to a given set of boundary conditions. This procedure leads to a set of highly nonlinear equations which cause problems associ.ated with stability and convergence in the numerical solution. This. study pre.sents an approach whereby the equations describing stratified flow within an aquifer are simplified. The Dupuit approxi mation and the integral boundary layer method are used for this purpose. The result is a highly stable, convergent numerical scheme describing the mineralization process in three dimensions. 39

PAGE 53

40 4.2 Description of the Flow Field Figure 4.1 shows a schematic description of a flow field typical to an inland aquifer. According to this figure the flow field is divided into three zones as follows: (a) the upper zone of freshwater, (b) the transition zone, and (c) the lower zone of saltwater. By applying the Dupuit approximation to the flow field, certain simplifying assumptions are made. The flow in the freshwater zone is mainly horizontal and potential. The flow in the transition zone is mainly horizontal and is due to the mineral distribution within this zone. The flow, in the saltwater zone is vertical and potential. For the purposes of this study, this flow field description will be extended in the remaining horizontal dimension to yield a two-dimensional flow field. 4.3 Basic Equations The basic equations used for the simulation of stratified flow in an aquifer are the equations of continuity, motion, solute transport, and state represented as follows -+ an (4.1) 'V q + -= 0 at -+ 1.-+ 'Vp + y k + K q = 0 (4.2) 'V (qC) 'V (0 'VC) (4.3) n at + = y = Yo (1 + aC) (4.4) -+ where, q = discharge; n = porosity; t = time; p = pressure; -+ y = specific weight; k = unit vertical vector; K = hydraulic conductivity; C = mineral concentration; B = dispersion tensor; Yo = specific weight

PAGE 54

Pumpage N Confining Formation B K Freshwater Zone Transiti on Zone Sa 1 twater with Con.stant Piezometric Head Semiconfining Formation 41 Figure 4.1 Schematic description of the development of a transition zone in a stratified aquifer.

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42 of reference; 0::1. = constant re 1 at; ng changes ; n m; nera 1 concentrati on wi th specific weight. Equations (4.1), (4.2), (4.3), and (4.4) are solved simultaneously utilizing a finite difference numerical scheme as shown in the following sections. 4.4 The Integral Method of Boundary Layer Approximation The integral method of boundary layer approximation is an analytical tool first introduced by von Karman. The method is applicable to both linear and nonlinear transient. value problems for certain boundary conditions. Basically, the method simplifies the appropriate equations by integrating over a phenomenological distance thereby creating a boundary layer. The distribution of the desired parameters within the boundary layer is given for example by a polynomial profile that satisfies similarity conditions. Thus, the parameter distribution is given as a function of time and position in the medium. In this study, the phenomenological distance is the thickness of the transition zone and the desired parameters are the solute concentration and the specific discharge. This study applies the integral method of boundary layer approxi mation for the simplification of the simultaneous solution of the basic equations (4.1), (4.2), ('4.3), and (4.4) in the three-dimensional simulation of the stratified flow process. The analysis is based upon the work of Rubin [1982J and represents an extension of his approach for the simulation of the mineralization process in the two-dimensional flO\'1 field. In Figure 4.1 the upper zone includes freshwater whose specific density is constant. Therefore, in this zone equation (4.2) yields

PAGE 56

43 (4.5) where 4>f = P/Yf + z (4.6) Here, 4>f = piezometric head at the freshwater zone; K f = hydraulic conductivity of the porous medium containing freshwater; Yf = specific v/eight of the freshwater; z = elevation with respect to an arbitrary datum. The lower zone includes mineral water whose specific density is constant. Therefore, in this zone equation (4.2) yields -+ q = -K V4> s s (4.7) where, Ks = hydraulic conductivity of the porous medium containing salt v-Iater. Here, 4>s = piezometric head at the mineral water zone; Y s = specific weight of the mineral water. We may assume K f = Ks = K. Assuming the flow in the transition zone is mainly horizontal, then an integration of equation (4.2) between the bottom and the top of the transition zone yields Zt f 'i' Z ) = --dz t Z Yo b (4.9) where, b,t = indices referring to the bottom and the top of the transition zone, respectively.

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44 It is assumed that the transition zone is represented by a boundary layer where the specific discharge and the solute concentration profiles satisfy the following similarity conditions u = UF(n) v = VF(n) (4.10) where, u,v = components of the specific discharge in the transition zone in the horizontal x and y directions, respectively; U,V = character-istic specific discharge in the horizontal x and y directions, respectively; Co = characteristic concentration; F,L = distribution functions; n = dimensionless coordinate of the transition zone defined as follo'tls n = (z Z b)/ 0 (4.11) Here, 0 = thickness of the transition zone. Introducing equations (4.4), (4.10), and (4.11) into equation (4.9) yields = aeoo J: Ldn (4.12) Assuming C f :: 0 and C s = C o yields
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45 Referring to Figure 4.1, it is assumed that beneath the semiconfining layer the piezometric head is not affected by pumpage and has a constant value Initially, the freshwater-saltwater interface is assumed to be a sharp interface and is horizontal. Therfore, continuity of the pressure yi e 1 ds (4.15) where, 0 = subscript referring to initial conditions. The piezometric head at the bottom of the transition zone is given as follows \.:-. I (4.16) where, Bl = thickness of the semiconfining layer; K,Kl = hydraul ic conductivities of the aquifer and the semiconfi ning formation, respectively. Combining equations (4.13} and (4.16) yields a z B z = -n (l + __ b (_1 + i) zb ft fo at Kl K 1 f Ldn a (4.17) Reference to the drawdown, s, instead of the freshwater piezometric head, and an application of equations (4.1) and (4.2) yield for a twodimensional flow field

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_ ( 1 '\ _0 rK(B + 6 + _0 [K(B +3 ax l ,. jon ax ay at (1 Fd ) as] Jon 3y 46 (4.18) where, S = coefficient of storage; N = rate of pumpage per unit area. Rearranging (4.17) yields (4.19) The equation describing the growth of the transition zone is developed with reference to Figure 4.2. In this figure a portion of the transition zone is considered as a control volume. The application of the equation of solute transport to this control volume and an integration over the tnickness of the transition zone yields acl -D -dx az z b (4.20) where, n = porosity of the porous medium. Introducing the similarity conditions given in equation (4.10-) into (4.20) and rearranging yields Ld).LL + + 02 LFdn = J 2 2 Jl 2 0 n at 2 ax -ax 0 -DL I (0) (4.21) where, L'(O) = (dL/dn)n=O'

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1-----dx -D If dx az Zb+O uCdz + (J uCdz) dx ax z b Figure 4.2 Control volume for the development of equation (4.22).

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48 Equation (4.21) represents the growth of the transition zone for a unidirectional flow. The application of the same approach to a twodimensional horizontal flow field yields (-2n fol Ldn) d + [02 + 1 (u d at ax ay 2 ax + V FLdn = 2 fol ay. OL 1(0) (4.22) This analysis considers that the bottom of the transition zone is represented by zb and is stationary. However, zb is a function of time thereby generating one additional term in equation (4.22). However, this term is canceled by the convection term generated by the vertical specific discharge in the saltwater zone. In general the coefficient of dispersion, 0, is proportional to the absolute value of the specific discharge. Therefore, it is assumed that (4.23) where, a = constant almost identical to the transverse dispersivity of the aquifer. According to Figure 4.1, it is evident that (4.24) Equation (4.18) is a parabolic second order equation and describes the distribution of the drawdown in the flow field. Equation (4.19) describes the rate of growth of the saltwater mound. Equation (4.22)

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49 is a hyperbolic first order equation describing the development and pro. pagation of the transition zone in the aquifer. For the simulation of flow conditions in the two-dimensional flow field, an implicit-explicit finite difference scheme for equations {4.19}, and (4.22) is developed in the next chapter. This numerical scheme results in a three-dimensional simulation of the miner-alization process in the aquifer. 4.5 Sumnary Stratified flow in an aquifer is associated with quite complicated flow conditions. The mineral transport within the flow field depends upon the structure of the flow field. On the other hand, the mineral distribution affects the dynamics of the flow. A two-dimensional flow field is described where a freshwater zone, a transition zone, and a saltwater zone are found. By the application of the Dupuit approximation and the integral method of boundary layer approximation to the two-dimensional flow field, the simultaneous solution of the equations of continuity, motion, and solute transport yields three partial differential equations describing a three-dimensional stratified flow process. Originally these equations are highly nonlinear and create problems with stability and convergence within a numerical scheme. By applying the boundary layer approach the complexity of the system is reduced and its susceptibility to numerical problems of con vergence and stability is diminished. r\ d

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CHAPTER 5 NUMERICAL SIMULATION 5.1 Introduction The governing equations, (4.18), (4.19), and (4.22), developed in the last chapter have the unique ability to completely describe the mineralization phenomenon in an inland aquifer. The objective of this chapter is to formulate a solution for these equations that is coherent with the actual mineralization process. Because the equations are nonlinear and expressed in two independent space variables and one independent time variable, a numerical scheme is the only practical means by which a solution may be obtained. Most groundwater flow prob lems are numerically approached by a variety of finite difference, finite element, and boundary element methods. Satisfactory groundwater flow models have been developed utilizing each of the above methods. Several finite difference methods offer approaches leading to ap proximate solutions to partial differential equations. Implicit schemes with their exceptional stability properties are almost all'Jays used.for the solution of initial value problems in two space variables. A variety of solution techniques are offered in the literature [Mitchell, 1976J and include the alternating direction implicit (ADI) method, the locally one-dimensional (LOD) method, and the successive overrelaxation (SOR) method, among others. In selecting the appropriate numerical solution technique for unsteady groundwater flow problems, the ease of application and the abi:ity 50

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51 to utilize the resulting model in various geographical regions is of considerable importance. Finite element and boundary element models are generally specific to one application and are not easily adapted to a distinctly separate region. On the other hand, a finite difference model utilizing an ADI solution method can in most cases analyze a variety of applications, often only with a simple change in parameters. Also, groundwater flow modelers generally accept the ADI method and its variations as the most efficient technique for the simulation of two dimensional unsteady groundwater flow problems. It is for these reasons that it was decided to adopt the AD! method as a solution technique in this study. 5.2 The Numerical Model The numerical model developed in this section is based on the linearization of equations (4.18), (4.19), and (4.22) and the application of an iterative ADI method. The equations are linearized by appropriate finite difference representations. The result is a highly stable, con vergent numerical scheme capable of completely simulating three-dimensional stratified flow conditions found in an inland aquifer. The ADI method was first introduced by Peaceman and Rachford [1955J and is especially well suited for the solution of time dependent, linear parabolic systems. The application of the ADI method to a parabolic system involves the solution of tridiagonal sets of equations along lines parallel to the x and y coordinate axes. The appropriate finite difference equations are formulated into two subsets in the horizontal x-y plane. First, the unknowns in the x direction are calculated at the time level (r.1+1) utilizingknownv3luesin the y direction from time level (m). Second, the unknowns in the y direction are calculated at the time level

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52 utilizing known values in the x direction from time level (m+l). Themethod alternates between the two directions for the desired time sequence. When utilizing an ADI method it is important to realize that a solution can only be found when the tridiagonal matrix contains a set of linear equations. Because equations (4.18) and (4.22) are highly non-linear, extreme care must be taken when formulating their linear finite difference representations. These equations must be linearized correctly for the ADI method to be of any practical use. The linearization of equations (4.18) and (4.22) is accomplished by referring to certain parameters at different time levels. It is common to use half-time intervals, (m), (m+l/2), (m+1), etc. In this manner non-linear terms may be linearized to accommodate their solution. The finite difference representation of equations (4.18), (4.19), and (4.22) is now presented. These finite difference equations comprise the numerical model. An implicit scheme for the calculation of the drawdown in the x direction for time level (m+l) is obtained from equation (4.18) as fo 11 ows (m+l) Jl K t (m+l/2) (+1) -si-l,J' [(B + 0 Fdn) ] + s.m. {S + [B 0 (llX ) i -1 /2, j 1 J Jl K llt (m+l/2) fl (m+l/2) + 0 Fdn) -:--:2J + [(B + 0 Fdn) f4J } o (llX) i+l/2,j 0 (llX) i-l/2,j fl (m+l/2) s m; 1 [( 8 + 0 F d n ) K II t J = 1+ ,J 0 i+l/2,j s s J

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53 a zb (m+l/2) (m) [(8 -n (---at).. ilt + Ni,j ilt + (si ,j+l ',J ,J J 1 (m+1/2) ( ( + 0 Fdn) + 1 [(8 o (ily)L i ,j+l/2 l,J-1,J J1 K ilt (m+l/2) + 0 Fdn) --2J o (ilY) i,j-l/2 (5. 1 ) An implicit scheme for the calculation of the thickness of the transition zone in the x direction for the time level (m+1) is' obtained from equation (4.22) as follows 2(m+l) n f1 l:It (m+l/2) ( +1/2) J1 0.. [-2 Ldn + 2 K .. (s. s.m1 .) FLdnJ 1,J 0 4(l:Ix) 1,J l+l,J l-,J 0 2(m) n f1 2(m+1/2) ilt ( 1/2) = 0,. -2 0 Ldn {o.. --2 [K. 1/2 (s.m+ l,J (l:Ix) 1+ ,J 1+1,J 2(m) ilt (1/2) (1/2) () {c .. --2 [K. '+1/2 s.m: )+K.. l,J (l:IY) l,J 1,J+l l,J 1,J-l/21,J-l

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2(m) 1 s(m+l/2) (m+l/2) 0, 'l)} f FLdn a2 tlt K, ,[( i+l,j Si_l,j )2 1,J-)0 1,J M s(m+l/2) (m+1/2) + (i,j+1 -Si,j_l )2Jl/2 L'(O) llY 54 (5.2) An implicit scheme for the calculation of the drawdowns in the y direction for time level (m+2) is obtained from equation (4.18) as follows _s(m+2) J1 K t::.t (m+l 1/2) + s(.m+,2) [(B + <5 0 Fdn) {S i,j-1 i.j-1/2 1,J Jl (m+ll/2) J1 K H (m+l 1/2) + [(B + 0 Fdn) K + [(B + 0 Fdn) --2J } o (lly) i,j+1/2 0 (llY) i,j-l/2 + 6 Fdn) K lit] = S ( Jl (m+l 1/2) 1.J+l 0 (lly)2 i ,j-l/2 1,J -n a Zb (m+l 1/2) (m+l) (+1' () t N t ( _s,m,')[(B at, II + ,t. + s'+l 1 J 1 J 1,J 1 ,J + <5 Jl Fdn) K ll2t]{m+l 1/2) + [(B o (M) i+l/2,j 1-,J 1,J fl K lit (m+l 1/2) + 6 Fdn) o (t.x) i-1/2,j (5.3)

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55 An implicit scheme for the calculation of the squaredthic'kness of the transition zone in. the y direction for the time level (m+2) is obtained from equation (4.22) as follows 2(m+2) n fl At ( +1 1/2) (+1 1/2) fl 0.. [ -2 Ldn + .... 2 K. (s. m -s. m. 1 ) FLdn] 1,J 0 4 (6.y) 1,J 1,J+l 1,J0 2{m+l) n fl 2{m+l 1/2) 6.t (s(.m+.l 1/2) -Oi,j 2" oLdn-{oi,j 1,J+l 1/2)) + K.. 1/2) 1/2))] 1,J 1,J-l/2 1,J-l 1,J (m+l) {o2 ( (m+l 1/2) (m+l 1/2)) i,j (6.x)2 i+l/2,jsi+l,j Si,j + K. 1/2 1/2)] + 6.\ K .1/2) 1-,J 1-,J 1,J 4(6.X) 1,J 1+1,J (m+1 1/2):J2(m+1) 2(m+1) fl -Si_1,j ) (oi+1,j i_1,j )} 0 FLdn s(m+1 1/2) 2 = a 6. t K [( i+ 1 ,j 1 -,J ) 2 i,j 6.X s(m+l 1/2) (m+l 1/2) + ( i,j+1 -Si,j_l )2]1/2 L'(O) t,y (5.4)

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56 Although an implicit approach was adopted for the development of equation (5.3) and (5.4), it is conceivable to also apply an explicit approach. These two approaches are developed in the Arpendix. and Equations (4.19) and (4.24) yield, respectively K Kl = [n ( 8 1 K + zb Kl )( 1 + d (s I; zb fl (m+l/2) I; 6 Ldn)] a i ,j = Bo 1 J (m+l/2) (zb + 6). 1 ,J (5.5) (5.6) These finite difference equations are solved numerically by the application of an iterative ADI method. The details of the application are presented in the next section. 5.3 Model Execution The numerical model developed in the previous section is executed with the aid of a high speed digital computer. Following the flow chart given in Figure 5.1, a computer is for this purpose. The flow chart illustrates the application of an iterative ADI method in conjunction with a print scheme for the solution of the numerical model. Before the computer program is written a finite difference grid is constructed which represents an aquifer's flow field. The grid is formulated in a horizontal x-y plane. The grid spacing is chosen as an example to be uniform in both the x and y directions, and for com-putational convenience 6X equals 6y. A field of pumpage is superimposed

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Initialize Para meters & Bounda ry Conditions Calculate Values of s, 0, and zb time steps (m+l/2) & (m+l) No Yes Print Results For Time Step No Calculate values of s, 0, and zb for time steps (m+l/2) & (m+l) Yes Stop Increment Time = l,J 1,J Yes 'No Figure 5.1 -Flow chart. 57 No

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58 upon the grid and is located in its center. The size of the pumpage field can be varied according to the application. Following the flow chart, all parameters are initialized and the boundary conditions stipulated according to the application. From here the iterative procedure begins in the x direction. In the first iteration it is assumed that the parameter values at the time level (171+1/2) are identical to their values at the time level (m). Aftercalculating the parameter values at the time level (m+l) their values are calculated for the intermediate time level (m+l/2). For each row analyzed a tridiagonal matrix of linear equations is generated using equation (5.1). The solution vector is calculated by the application of the Thomas Algorithm. In this manner the drawdown values for the time level (m+l) are calculated for the entire grid. With this information the values of the squared thickness of the transition zone and the height of the saltwater mound are calculated for each node from equations (5.3) and (5.5), respectively. Intennediate parameter values at the time level (m+l/2) are calculated by an arithmetic average between the respective parameters at the time levels (m)and(m+1). This ends the first iteration. The iterative procedure stops when the difference between the drawdown values at each node for two successive iterations is less than some predetermined value. Divergence of the scheme is checked by specifying a maximum number of iterations. Once convergence is obtained in the x direction the results are printed on a line printer by utilizing subprograms written specifically for this purpose. The computer printout supplies a three-dimensional representati on of the di st ri buti ons wi thi n the aquifer of the drawdown, the thickness of the transition zone, and the height of the saltwater mound. Various examples are presented in the next section.

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59 Finally, the time is incremented by a predetermined amount and the parameter values at time level (m+l) are reset to the time level (m). The procedure for the calculation of the unknown parameter values in the y direction are exactly the same as for the x direction except that equations (5.2) and (5.4) are now used. Thus, the scheme alternates between the. x and y di rections for the desi red time sequence. The application of the ADI method to the numerical model in con junction with proper programming yields a highly stable, convergent solution scheme. This was found to be true under a variety of parameter changes. Examples and results are presented in the next section. The model is executed by utilizing the facilities of the Northeast Regional Data Center of the State University System of Florida, located on the campus of the University of Florida in Gainesville. The model is executed by an IBM 3033N12 utilizing a WATFIV compiler. Memory requirements and execution time are approximately 300 K byte and 1100 CPU seconds, respectively. 5.4 Numerical Results The numerical results presented in this study are based upon a preliminary simulation and a subsequent series of numerical experiments whereby the values of selected parameters are altered in o.rder to observe the behavior of the nUmerical model. The parameter values utilized throughout the simulation process are representative of the Floridan Aquifer in northeastern Florida. The parameter values used in the preliminary simulation are summarized in Table 5.1. A twenty by twenty k'.m grid is selected with the grid spacing in both principal directions equalling 0.5 km. The rate of pumpage occurs

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60 Table 5.1 Parameter values for the execution of the preliminary simulation. Parameter Description Value K hydraulic conductivity of the 40 m/day freshwater zone K, hydraulic conductivity of the 0.1 m/day semi confini ng fonnati on B initial thickness of the freshwater 50 m 0 zone B1 thickness of the semiconfining 20 m formation n porosity 0.2 S coefficient of storage 103 a dispersivity 0.5 m F distribution function of the 2n -n 2 specific discharge L distribution function of the 1 2n + 2 solute concentration -n DT time step 0.1 day buoyancy coefficient defined by equation (4.14) 0.025 N ra te of pumpage per un; t a rea 0.1 m/day

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61 over a 25 Km2 area centered within the grid (Figure 5.2). Transient conditions are simulated for a period of 10 days at a constant rate of pumpage. Figures 5.3a through 5.5c show three-dimensional maps repre senting the drawdown, the saltwater mound, and the thickness of the transition zone for the selected times, T, of 2, 6, and 10 days. These maps are photographically reduced versions of the actual computer printout. A comparison of Figure S.3a and Figure S.3b demonstrates the two print schemes which are utilized for reporting results. The first print scheme, for example Figure S.3a, reports ordinate values at each grid point only when these values are between 0.5 and 50 m. These values are rounded to the nearest meter to save space on the computer printout. The second print scheme, for example Figure S.3b, reports ordinate values between 0.05 and 0.5 m. These values are rounded to the nearest tenth of a meter. Both schemes illustrate the development of the various zones within the aquifer. Figure 5.4 illustrates the rate of growth of the maximal values of the drawdown, the height of the saltwater mound, and the thickness of the transition zone. Four subsequent experiments were performed to observe the behavior of the numerical model. In each of the four experiments one parameter was altered by an order of magnitude. Table 5.2 summarizes the experi mental procedure leading to the numerical results shown in Figures S.7a through S.13c. Figure 5.14 illustrates the rate of growth of the maximal values of the drawdown, the height of the saltwater mound, and the thickness of the transition zone for experiment numbers 2 and 3.

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t .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 ., .\ \ .1 .1 \ 01 1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 1 .. .1 .1 .1 .1 .1 1 .1 .. 1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .. ., .1 .1 .1 .1 .1 ., .1 .1 .1 .. .1 1 .1 .1 .1 .I .1 .1 1 .1 .. .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .. .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .. .1 1 .1 .. .1 .1 .! .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 01 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 1 .1 .1 .1 .1 .. ., .1 .1 1 .1 .. ., .1 ., .1 .1 .1 .1 .1 \ .1 .1 .. .. ., 1 .. .1 .. .1 .1 .1 .. .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .................................................................................................. .................. Figure 5.2 of pumpage. Pumpage rate = 0.1 m/day.

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.t +t ........................................................................................................ t t t. ..... 1.. ....... tI." '.'I'+' '.'" .a .t'I.'." ,+" .1' ".'.+' ,. ., ................... ++,+ .... ,.+ +,++, .. +.,+ 2 2 fJ.+J".l".]"".]'+]' 2 2 + .... ,. 2 2 +1 )."] 3 ) 3.'3' 2 2 .,.tlt ".',t 2 S. 6 6 6 6 6 6 6 .. S 2 tI "t.,. 2 '6.6 6 6 6 6 .,." 2 ....... ... l 4 0 '2.13 .. '" I" '.'1 J '2 0" 2 fl' ? '0 12Ul .. 14 .4 ." ,,,"1 ,2 10" Z .,+ 2 '5+ 12 5+"+""'.1' .. 7'1,. .2.5.2 'I. .,. +S+ 12 ,,1, .. ,+,7.,'5 '2 .. 5. 2 .. """+.1.6 .. ] 7 .8.,7+136 11 ,., ....... 1. It "1+11 .8',Q+,9.JC,UI9.19 Ilhl").] 6 .J"I .... ""''''J' 6 1"." Q'19 20 20 20119.,9.'7 '4 Il',"." "'."'J' 6 ,,,.,,.,9.'Q 20 10 '4 6 +l.".t.* ....... ,1. 6 ,hI9 20 .zt) 20 20 20tl9." ." f. ,1.'".,+ J .. 20 20"9',, ." 6 .J ".,t '''''''It 6 '."".9 20 20 20 20 20'19." .] ,. """.J. t 't.ll.,9 2U lO 20 20t ... .4 6 .1 t f.J. 6 '.""'9 ZO 20 ZO 20"9 .t 6 .1 u .... .. 920 20 20 20 2,".9t.7 14 6 .]''' '' t l. 6 '''.19.,9 202020'19119'" ." to '3.e, ,. .".".J' 6 ,7*.0,,9 20 20 10"9 9'" '4 '1 1. 6 .8 7."6 .3 J. 6 tll'.7 '8""') 6 '1.',.,,+ 2 .5' 12'15 ., ,.,., ,+., ., 5 .,.,. Z 2 .St '2t"+" "'5 .2 + a 10 ".1] '4 ." '2 10" Z ... 2 au .2'll .4 ." a "'.3.2: 10' 2 tI. ,. 2: s. 6 6 f\ 6 6 6 .S+" 2 t,e.,. ., .... 2 'i. 6 6 b 6 ,. 6 .,." 2 ....... .2 iZ .) 1 ) .1 ) ) )+ 2' .2 .,.+,. ., 2 .2 .] .] 3 .] 3 1. 2 2 .... ..... .............. .. ..... ... +I"'t.' ,.,, ."'.' 1'.".,. .......... ........ ..................... t t t t .................................................................................................. ..................... Figure 5.3a -Map of drawdown. T =2.0 days, maximal ordinate = 20.01 m. 0'1 v-J

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J .... 1 .J .J .2 .. 1 .. 1 .\ .\ .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 2 J .J .J .J J ) .J .J .J .. .1 .1 I .1 I .1 .1 .1 .1 I .1 .1 .1 I .1 .1 ., .1 .1 .1 .1 .1 I .1 .1 .1 .. .1 .. .l .2 .2 .1 .1 .1 1 .1 I I .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 \ .1 .1 .1 .1 .l .. > .2 .. .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 I .1 .1 .1 .1 .1 .\ \ .1 .. .1 1 \ .\ \ .1 .1 .1 .\ I .1 .1 .1 .1 .1 .1 .1 I .1 .1 1 .1 .1 .1 1 .1 .\ .1 .1 .1 .1 .1 .. 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .1 .. .1 I .1 .1 .. .1 .1 .1 ., ., ., .1 .\ ., .. ., .1 .1 ., 1 .1 ., .1 ., .1 .1 I I .1 ., .1 .1 .1 .1 ., .1 I .. .1 .1 .1 ., .1 ., .1 .1 .1 .1 .1 ., ., .. .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .\ .1 ., .1 .1 .1 .1 .1 .1 .1 .1 1 .1 ., .1 .1 ., .1 .1 .. .1 .1 .1 I .1 .1 .. .1 .. .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 ., .1 I .1 .1 .1 .1 .. ., ., .1 ., .1 ., I .1 .1 I I .1 .1 .1 .\ .\ .\ I .\ .1 .1 .1 I ., .1 ., ., .1 I .1 .1 .1 ., .1 ., .1 .1 ., ., ., ., ., .1 .1 .1 .1 ., ., ., ., .1 ., ., .1 .1 .1 ., ., ., ., .1 ., .1 ., ., .1 .1 1 .1 ., .. ., ., ., .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 ., ., .1 .. 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I .1 .1 .1 .1 .1 .1 .1 .1 .1 ., 1 ., .1 .1 .1 ., .1 .1 .1 I .. .1 .1 .1 ., .1 .. .1 .1 .1 .1 ., .\ .1 ., ., ., ., ., .1 .1 ., ., ., I .1 ., 1 .1 ., ., ., ., .1 .1 .1 .1 .. .1 I ., .1 .1 .1 .1 .1 .1 .1 .1 ., 1 .1 ., .1 .1 .1 .1 .1 .I .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 ., .1 .1 ., .1 .1 I .1 .1 .1 .1 .1 ., ., ., ., ., ., ., ., I .1 I ., .1 .1 I .1 .1 .1 I .1 .1 ., .1 ., .1 1 .1 .1 .. .1 .1 .1 .1 ., ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., ., .1 .1 .1 .1 .1 ., .1 ., ., .1 ., I ., ., .1 ., ., ., ., .1 ., ., ., ., .1 .1 .. .. .1 : I .1 .1 .1 .1 I .1, .1 I .1 .1 .1 .1 .1 .1 .1 .1 ., I .1 ., .1 .1 I .. 1 .1 .1 .1 I .1 I ., .. 1 ., .1 .1 .1 ., ., ., I .\ .1 ., .1 ., ., .1 .1 .. .. .1 .1 .1 .1 .1 ., ., .. .1 .. I .1 .1 .1 .1 .. .1 .1 ., ., ., .1 ., .1 ., ., ., .1 .1 .\ ., .1 1 .1 ., .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 I .1 .1 .1 .1 .1 I .1 ., ., .1 ., ., .1 .1 .1 I ., ., .. .. .1 ., ., ., ., .1 .1 .. 1 ., .1 .1 .1 .1 .1 ., .1 ., .1 .1 .1 ., ., .1 .1 ., I ., I .1 ., .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .. I .1 .1 .1 I ., .1 .1 .1 .1 .1 .1 .1 .1 ., .. .1 I ...................................................................................................................... 0'1 -I';> Figure 5.3b -Map of saltwater mound. T = 2.0 days, maximal ordinate = 0.88 m.

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t t ....... ........... ...... .... .. .. .. ............ ... ................... ........ ........ ... ...... "1 a .'1 t 't ,t ... 'tl ....................................... .. ....... f ...... ,,). 1 2 ;" 2 2 2 2 Z .z .......... .. ., .... 2 2 l 2 2 2 2 l 2 2 ? f".".I." ,.f'f.'.? Z .J J ..... h.J ] J jt.1 J l. 2 2 fl ,. 2 .1 ] j J ] 1 J J 1 ] I. ....... Z '1. 4 .'\$ ... 'i .. -:. ...... 5 5 '5 'l .1. 2 ., ..... .. .j ... '5 5 5 5 5 5 .... J' l., 't tj. ."" -:; r) e: 5 5 5 .... It 1 ...... l .It" .5 '5 5 "j S S.'S 5 5 2 .1 ..... l .J 5 J. tl. Z ., ,.,. 2 2 .J .I' 2., ,t., ? ..... 5'.5 ,' i! I ,. I 2 .] '\ l. 2 ., ,. ''.".2 .1 'H.'.'J. 2 ............... 2 .) -;,.5.,]+ l., .. l .... 'i S l. l ., 2 .) Ojt."!' .... l ., ... '].'5 0; ). 2 2 '1 5 Jt Z ., ......... l .)t.5 o; ), 2 ..... 1 .l "j .. J. 2 .".'.'1' ., 1. .1f.'S ,. ? 1 ........ ,. 2 .J -; ]. 2 .... 2. 'J 5'."i 1. Z ,. ? .] 0; 0; .... 1. ....... 2 .. S '. '1 ./. ., 1 I .] "'i l. 2 ., ''''''.2 'J." o:i ':'.? I l 2. .J S.t"\ )t 2. ........ .. Z .J !\'.S J. 2 2 I l I 2. I .1 '\$.",,]. l Z .... 5 5 ,. l Z 2 2 2. 2 2 .J o; .... l. 2. 2: .' .... ,. .... ] 3 l ,..,." '!' J. l ,., 2. ']'.".'5. ." .I'.J 1 ) ".)' 4 .-; ""'.3. Z l .,. '5 ""i 1, l l '5 5.'O;.'S.t5 5.'IS.'''i. 4 .11 :- ,. I .J '5.'5'.5'.;; "i'.5'.5'.5 ,.".tt O! ,. l .l. 4 .5.'5 5 0; 0;.'5 5,.'5.'5. 4 .}. 1 2. t! 'l'.l.'J"J'.J..'J ,'. JI.J Jt.l'? 2 t 2. 4. .1 1 1 ) J ] J ) ,. l 1 ......... .. ............ l 2 l Z. 2. Z I 1 2. l .,., ....... ........... ,. l Z 2 Z l 2 Z Z l J 2 ........... ....... ..' ... ... 1 ........ .. ........ ........ ............ ,.,." tt ,."1.' ... ...... ... .. .... ,. "." .. .. ,." .. .. ,., ....... 1 "'1'.' ... .... .... ......... .............. ......... ...................... ............ ..... ...................................... Figure 5.3c. Map of transition zone. T = 2.0 days, maximal ordinate = 5.03 m. ()) (]l

PAGE 79

t I I f" f'" ..... I t t I t t t I', t t t 1' 1 1 1 1 f" I"" t I". ,.1 1 I" I" I "1 '.1 ,.tI.,2 O! .J"I"l")"}'.l I. Z 2 '1"1' '1"" 1. 1 J J l' I ., ,. 2 '!.i., c. h 6 f> to ,. ,5" 1 '1"" .1 .... 2 ..... 0 60 h 6 f. to to ., l '1"" '1' Z '0 12. I 1 .. ,. ,. It ... 11 I Z I I)' :!., ,. l .. 10 '4 '4 I' .. "'11 IZ I)' 2 _I' .,. Z .5. Il'ls.,r'I'''' 1"'1"1"'''1512'''' 2 ... 2 '5' ,hili. 2 .,. '1""')' 6 '1)'" ,1\'11.1'111"')'19'1(\ IP""IJ to 'J"I"" 'I"I"H '.h" 1 1".16 .1 ...... '1""']' .. 1ttQ'I'1 10 2,) Z"'lfl.,Q." ,. .,] ..... ]. to """I'.Jtlv 10 20 6 .,. ..... ""'tI"'" ,.,t;?l.!u 2lJ 2) ,e" ." ..... """'J.", '"t",,10 ;!.) ..!Q .l.l ,_ 6 ').t .It.). Co '4 Z) lO 2 20'19 11 '.6 '1""", .,ltl.tl' It f' .'t.,qI Z,) 1.0 21,) 20 2\)1''1 I' ._ ,. .) ..... I'" tl' to I""" 2" In '/'0 20', 9. I 1 I 4 .. "., I '1"",.", '.'I"'lJ 211 "oJ Z,) ?1 2,"19." I' f ']"1"', '1""')' t. "'I"I?'IC',/,I) 20 1hlll'19.,' '4 '1""'" ""1")" '.""'-)'IQ!O 1" l)""'fQ'I' I. "",,'1. ""1"" I'J '1.11, 1 I .... q Q. h" 1-). t Q 18' I ,.,) r.. I '1"1")1 b '11'1' ''''10;'19''9'''1'14 ".1"1) 6 .) ,. tI. 12,,'"10""'''17 ...... ,.1' "1512 .... 2 '1' .,. 1 '5' 12 ..... 1' lZ'" 2 ... l 10 "ZlI) '4 .4 .' .... l 12 10, '1' .1 ....... 10 12.11 ., ., ., .t "'IJ 12 10. Z ) 1 ,. 5' b 6 ... I\. ,. bit. 5.. 2', t I' ., ... "!.o. 6 ,... 6 6 6 t f')' 5. t l" ...... 2 Z .:1 .. ).,) J""']I'." 2 1. ., ... 1. Z l """'1""')"J")" Z I I" I" I.', t ,., I"" It ....... tt I t .. f ""'1"1"1' '1" I """" "'1 I 1 '1' .............................................. ..................................................................... 5.4a -Map of drawdowns. T = 6.0 days,maxima1 ordinate = 20.12 m.

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t f ........................................... f f .1 1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 ., ., ., ., ., .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 ., ., .1 .1 .1 .1 .1 .1 .1 .1 .1 ., ., .1 .1 .1 .1 ., .1 .1 .1 .1 .1 ., .1 .1 ., .1 .1 .1 ., .1 .1 ., .1 ., .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 ., .1 .1 .1 .1 .1 .1 ., ., ., ., .1 .1 ., ., .1 ., ., ., .1 ., ., ., .1 ., .1 .1 .1 .1 .1 ., .1 .1 ., .1 ., ., ., .1 .1 ., .1 .1 .1 .1 .1 .1 ., .1 ., .1 .1 ., ., .1 .1 ., .1 .1 .1 .1 ., ., ., ., ., ., ., .1 ., .1 ., ., .1 ., ., ., ., ., ., ., ., .1 ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., J ., .1 .1 .1 J .1 .1 .1 ., ., .1 .1 .1 .1 .1 .1 .1 ., ., .1 .. 1 .1 .1 ., ., .1 .1 ., ., ., ., ., .1 ., .J ., ., ., .1 ., ., .1 J .1 .1 .1 .1 .1 .1 .1 J .1 .1 ., ., .J ., ., .1 ., ., ., ., .1 ., ., J ., ., ., .1 ., ., ., ., ., ., ., ., ., ., ., ., ., ., , .1 ., .1 ., ., .J ., ., ., , J ., , ., .1 .1 ., .1 .1 .1 ., ., ., ., .1 ., ., .1 ., .1 J .J .1 ., .1 .J ., .1 .1 .1 ., ., ., .J J ., ., .1 .1 .1 ., .1 ., ., .1 ., .J ., ., ., ., .1 .J .1 .1 .. ., .1 .J .1 .1 ., .1 ., ., ., .1 .1 ., .1 ., ., ., ., ., .1 ., ., ., ., ., .J .1 .1 .1 .J .1 ., ., ., ., .1 .1 ., ., .1 .J ., .1 ., .1 ., ., .1 ., .1 ., ., ., ., ., ., .1 .1 ., ., .J .1 .1 .J .1 .1 ., .1 ., ., ., ., ., ., .1 .1 .J .1 .1 ., .1 ., ., .1 ., .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .1 ., .1 J .1 ., ., ., ., ., ., ., ., ., ., ., .1 ., ., .J .2 ., .2 d .2 .2 .2 .2 2 .. .2 .1 ., ., ., ., ., ., ., ., .J ., ., ., ., ., .1 ., ., ., ., J ., ., .2 oJ .' .' .' .' .' .' .. oJ .. ., .J ., ., ., .1 ., ., .1 ., ., ., ., .1 .1 ., ., ., ., ., ., ., .. J .. .. .' .. .. .. .. .. ] .2 .1 ., .1 ., ., ., ., ., ., ., .1 ., .1 ., ., ., ., ., ., .1 .1 .2 .' .6 .9 .9 d .. 9 .. 8 .6 .2 .1 .1 ., ., ., ., .1 ., .1 .1 ., ., .1 .1 ., ., .1 .1 .1 .1 ., ., .1 .1 .. .6 .8 .9 .9 .. .' .9 .. 9 .8 6 .2 .1 .1 ., ., .1 ., .1 ., .1 .1 ., ., .1 ., .1 .1 ., ., ., ., .2 .] Z. Z. Z. 2. oJ .Z .1 .1 .1 .1 .1 ., .1 .1 .1 ., .1 .1 ., .1 ., .1 .J .1 ., .2 .l 2. 2. 2. l. 1.91.'U.5 .6 .l .. .1 ., .1 ., ., ., ., .1 ., .1 ., ., ., ., ., ., .1 .. .. 8 .. .. ., ., ., ., ., J .1 ., ., ., ., ., ., ., ., ., ., ., ., .2 .. .. .. .. J .1 ., ., ., ., ., ., .1 .1 ., ., ., ., ., ., ., .. .91.'12. &l.6l. r2. 12. '2. 12.12.62.'1.9 .. .. .. ., ., ., ., ., ., ., ., .J .J ., ., ., ., .1 .1 ., .2 .. .91.92. '2.6 ... 12.12. I Z. 12. 'it. 6l. 4' .. .. .2 .1 .1 ., .1 J ., ., ., .1 .1 .1 .1 ., .1 .. .q2. 2. '2. 12:. "2. 82 2. 12.8Z. ll. 52. .. .r .1 ., .1 .1 ., .1 .1 ., .1 .1 J .1 ., .1 .1 ., .1 ., .. .. ..,2. l.ftZ.12.57 .. .. .2 .1 ., ., .J .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 ., .1 .1 .. .' IIZ. 2.52.1 C!. 92. 92. 92.12. 72. .9 .. .2 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .J 1 .1 .1 .1 .1 ., .>. "2. .. .. .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .Q2. .. .. .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 ., .1 .1 .:! .. .(,12. 2.12.52. .. .. .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .? .. .92. I. S2. 17. 9l. ",.92. lIZ. 72.52. ., .. .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .. .92. 2. '\$1. 72.82.92'. CJ2. 9l. az. ll. 52. .. .' .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 2 .' 2.52.12.82."2.82.'2.82.12.52. .. .. .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .. .'i2. Z. 17. 8Z. fl2. 82.12. 12.52. .9 .. r .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 ., .1 ., .2 .. .9 .. 92. 42. 12.12. 2.12.72.62.41.9 .9 .. .2 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., ., .1 .1 ., .1 .. .. 1.9 ." .. .2 .1 ., .1 ., .1 .1 ., .1 ., .1 .1 .. .1 .1 .1 .1 .1 ., .1 ., .:! .. .81 .. .2 .1 .1 .1 .1 .1 .1 ., ., .1 .1 .1 .1 .1 .1 .1 .1 ., .1 ., .1 .' .. .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 ., .1 .1 ., .>.J .01.'1.81.91. 2. 2. 2. .. l.ct 'I.S .6 .J .2 .1 ., .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .! J "I. 'II. 81 2 .. .. >. J.QI.fll.5 .6 oJ .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 ., .1 .1 .. 1 I ., .2 .. .6 .s .. .9 .Y .9 .. .. d .4 .6 .. ., I .1 .1 .1 .1 ., ., ., ., .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 ., .. 6 .9 .' .. .. .. ... .9 .. .6 .. ., .1 ., .1 .1 ., ., ., .1 ., .1 .1 ., .1 .1 .1 .1 I .1 .1 I .1 .1 .. J .. .' .. .. .. .. ., .' 03 .>. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 ., .1 .1 .1 .1 l 1 .' .' .. .. .' .. .' .' .l .1 .1 .1 .1 ., ., ., .1 .1 .1 ., .1 .1 .1 .1 ., .1 .1 ., .1 ., .1 .1 ., .1 .1 .1 .2 .2 .Z .1 .2 .2 .1 .. .2 .2 .2 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .2 .. 2 .. .2 .2 2 .2 .. ., ., .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 ., .1 ., ., ., .1 .1 ., .1 .1 .. .1 .1 .1 .1 .1 .1 .1 ., .1 .1 ., .1 .1 .1 .1 .1 .1 ., .1 .1 ., ., .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 ., ., ., .1 .1 ., .1 .1 ., .1 ., ., .1 .1 .1 .1 .1 ., ., .1 .1 .1 .1 .1 .1 ., ., .1 ., .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 ., ., ., ., ., ., .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 ., ., .1 .1 .1 .1 .1 ., .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 ., .1 .1 .1 .1 ., ., .1 .1 .1 .1 .1 .1 ., .1 .1 .1 ., .1 .1 .1 J .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 ., .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 ., .1 ., .1 ., ., .1 .1 .1 .1 ., .1 .1 ., .1 ., ., ., .1 .1 ., ., ., .1 .1 .1 .1 .1 ., ., .1 .1 .1 .1 .1 .1 .1 ., ., .1 ., ., ., .1 .1 .1 ., ., .1 .1 ., ., .1 .1 .1 .1 .1 ., .1 .1 .1 .1 ., .1 ., .1 .1 .1 ., ., ., .1 .1 .1 ., ., .1 .1 ., .1 .1 ., ., .1 ., ., ., ., ., ., ., .1 ., .1 .1 ., .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 ., .1 ., ., ., .1 ., ., .1 .1 .1 .1 ., .1 ., .1 .1 .1 .1 ., .1 .1 ., .1 .1 .1 ., .1 .1 .1 .1 ., ., .1 .1 ., .1 ., ., .1 .1 ., .1 ., ., ., .1 ., .1 ., ., .1 .1 .1 ., .1 .1 .1 .1 .1 ., ., .1 .1 ., .1 ., .1 .1 ., .1 .1 ., .1 .1 .1 .1 ., .1 .1 ., .1 ., .1 ., .1 ., .1 .1 ., ., ., .1 ;, .1 .1 ., .1 .1 ., .. .1 .1 ., .1 .1 .1 ., .1 ., .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 ., ., .1 .1 .1 .1 .1 .1 .1 .1 ., .. ., .1 .1 ., .1 .1 .1 .1 .1 ., ., .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 J .1 .1 .1 ., ., .1 ., ., .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., ., .1 .1 .1 .. .1 ., ., ., ., ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 ., ., ., .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .' .1 ., .1 .1 ., ., .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 ., .1 .1 ., .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 ., ., .1 ., ., .. .1 .1 ., ., .1 .1 ., .1 .1 .1 ., ., ., .1 ., ., .1 ., ., I .1 .1 .1 .1 .1 .1 .1 ., .1 ., .1 ., ., .1 ., .t ., ., ., .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 ., ., .1 ., .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 ., .1 .1 .1 .1 ., ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 ., ., ., ., .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., ., .1 .1 ., .1 .1 .1 .1 .1 .1 ., f f f 0) '-J Fi gure 5.4b of saltwater mound. T = 6.0 days, maximal ordinate = 2.83 m.

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...................................................................................................................... '1'" ........... .......... .. ...... t I 1 I I' ... 1 t t "'1""" I ,., """"1""""1' ., .;! 1. 2. 2 2 z z l ""1'"""", .,.t ? .,. '-' 2. 1 1. 2. 2 ., ..1.2 2. l '.1 j ].tj")"]"1_ 2. 2. l: 'I",tt"'" """""" 2 2 2 .) ) ] ) ] ) j. Z Z !! .1 1 .......... 1 ",'1' 4 .. ,. 1 """"H' l 'j'''J'. ) ). 2 ........... .......... Z 'l' !.. t f, ,. 6 .5 5' l. 2 'I.t"", 2 'l' 6 6 III ,. 6 t, 6 .'S ........ ;\. J. ,.t" 2 ., !.t ..... 9 9 .., 9 9 r;l 9. (I '" _, '1' 2. """'1. """", l 'l' PI! .r ... ;Jt'9 9 C) ", I!II It ]t z ,"""" l 'j ", ., f"9""'.9 ., q V 9 9." .0; ,. 2. ",,'11', '1"'"" 1. ']"5' f' '9"V.tch .., a ,. l ","1 1. 2 '5' fJ 6 6 b 6 CI ,. ""9' A I 2 '1"" 2 ? ...... '9""" 6 6 6" & "'.9t 1 '1"" 2 .,., t .9"9'" ,. .I) r '" 2 ee ,. .". 6 .."ea CIo ,. ,,, fOo." 'l' 1 .,.t"", '1"1"1' J ., ,. .", q., "'1.1 :" ,. to '9 9. t Z '1""", """", ? to ''''''9' 6 ')'.J"l"J'.J' ). 6 ... ,. 1 "".",1 'If""" 6.9"9' tt ]. 2. I l'l. 6 .(h'Ii' ti 'l' '2 Z 'l'. ,., .Q ..... b 'l' '? Z 2. 'J. .9 .. 9." 11. 2 """"t ......... 2 .If. It '9"9' .. '1' l 2. .l' 6 .9"9' Co l. 1 """"t ......... 2", 6 ''i,'9' h ,. 2 2." e .0 9' f. 'l' 2 """"1 '''I.?1t f .4 9'" '1' l. 2. ? 6'."9' 1\ 'l. 2 .... .c .,. ... .11;. ..,. t .. 'l. l 2 1 'J' .. 9.,. j. l """'.1 ""1"" 2'" ,.00 .rU,. '.1""'1"J.')' 6 .. 0. 6 ". 2 ........ 2 1. f. 119"9' 6 'l"l*'l")"l. 0 0. f. 'l' 2 .1 '. J' ,. ...... 9. (. ,q 6 ). 2 '1"1"1' ? '" 6 '9"9* f ........ 6 ..... 9. 6 '1' Z :::::: : : ; : : : : : : :::::: ......... 1 .j ...... It .9 Q ...... 9 9 9 9 9 .,. a .5"J. l ......... 1. .H .... PI II ."Iit.]. 2 ...... 1. .) !\o. a ,. .q 9"" 9 y 9 !I ." II. .'1.'"" 2 .J. ..... III .. '9"9 t1 2. It ..... 1. .)1 '5 !".. f 6 6 to b 6 Co .5 'J. l .,." 't "t'I"" 2 .)t ""!Io' 6 ,. to 6-tI ,. o; '1' 2 """'1' """1"'" 2 ., ] ........... ']",. 1 ""'tt','" ,. 1 ']"j' .......... ".) ,. l 1 '. I. ..... ;t 1 l 'J"l',JIIJ ] ],.). 2 2 '1 ,. """''''1' '1 '1 l J j.: l 2 ....... .. ,. """"""'1' 2 2 1 2 2 l l 2 """."'Itt., """""1"" 2 2 2 2 2 1. 2 I I '." .. .' 1 1. 1 1 1 "1" "" "1 I""'" t t 1""'1""', """"1""""., I" 1'1' ,_ .,., .. '1"""" I' ... t. "1" I'" ""1".""'1""'" f.' f t Figure 5.4c -Map of transition zone. T = 6.0 ordinate = 9.03 m. CJ) (X)

PAGE 82

................................................................................................................ ... H 1 1 1 1 1 ..... .. 1 1 1 1.+1 ........ 1 .. .. .. .. .. It., ........ f.', ...... 2 2 '.l ] )t')"J'f] 3' 2 2 '1'", '1"" 2 2 'J""'3"J")"J")' 2 2 ,,'.1. ""1' 2 4 .5. 6 6 6 6 6 .S. 4 2 ., ,. '1"" 2 .. '5.6 6 to IISc 6 6 6 +5' 4 Z '1' 1 ... rUI,,4 14 I 4 '4'11104 2 tI. 2 10' t 1 '4 I. .. I" 14 14 I J a.. '1. Z '5"ll 16."'" 1111 18 16'1]'5' 2.1t '1. Z '5"1] 16'11'1' 18 Id ,'HI7'11 16'11'5' 1. '1' ....... ].,. ''''1' 111J'11#"9'I9'lchI9 .,,.,, ,. 6 'J ,.t,+ """')' 6 '4." le'I' .4 e ']"1'", """+)'6 ""'flc;. 20?O 20 20 20'10;'" ,. 6 'l"I"" '1"1"]' '4'1"19 20 20 20 20'19'.' ,4,. 'J"I"I' ]. 6 '4 23 !O 20"9 Ie '46 .) 'I't, ,. 6 I' IA"? 20 10 2) 20 1'0'19 I" '4 b 'l"ltt't t"'I'+l' 6 ,_ "'19 2020 71 16 14 f 'l ,. 'I""'J' 6 ,4 18'19 2' 20 20 20 20'19 18 ']""'1' """']' 6 ,. 18"9 20 20 20 2020'19 Ie 14 .]+ '1"1"1' 1&'192') :!o 2'0 71 20"9 'tj '4 b')")"" .... ]. 6 '4'11"" 1) ZO 20 21) 20'19'11 146 .j""'I' '1"lt'I' 6 '4'11"9 2? 10 2J 20'19." '46 ')"1"1' """'3' 6 .... ''''19.19'.>i',9'19 18.,7 14 (. .J I"I"J+ 6 '.'11 lB." 14 .) + '1' 2' ''5 ... 3 Il""" I" 1ft 1 '1+1' 1(.11.5' 2' ." 16+,1+" 18.'1 19 H., '6'13'5' 2 '1' 2 I Q.,) '4 '6 '6 1. 14 14., J .0. 2. I ,.? to' I] '4 '6 .4 '6 4 .4 14"1 10. 2'. ,. 2 6 6 6 6 6 b '5'. 2 ., I ,. 2 ..5. 6 6 6 f. 60 Co b'!I' 4 2' + I ., l 'l"J"]'.)"]"]"]' 2 2 ., .( 2 'J")"3"J")")"). 2 ",,'.1. '1""""I.'I..++, tt. ... tI ...... ,. tt "1"1 t'I"1 ")"'+'1""""" .... ..... ..... .. ,. '.+"""'1"1"1"', t t .................... ....................................................... Figure 5.5a -Map of drawdowns. T = 10.0 days, maximal ordinate = 20.22 m.

PAGE 83

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I I .1 ., I I I I .1 1.1.. .1 ,.1.1 1.1.1.1.1.1.,.1.1.1., 1.1.. ,.1.1.1.1.1.1., 1.1.1.1 1., 1.,.1,., 1.1.1.1 1.1 1.1.1 .1.1.1 1.1.1 1 .1 1.1 .1.1.1.1 1.1.1 1 1 .1 l t.I.I.I.,.I I .1 .. 1.. .1.1 1.1.1 ,.2.2.2.1.2 .i .2.2.2 .'.).1 .'.1.1 .. 1.1.1.1.1 1 .1 .1 .1 ., ,.1 1 2.2.2.2.2.2.2.2.2 1.1.1 1.,.1.1.1.,.,.1.1.1 .1., 1 .1 I.I ,z.2.].l.1.1.1.1.1.1.J.2.2 ,.I I.I I I.1 ,I .1 1.' .1.,.a.I.I.I.2 .2 .J .J .1 .1 .J .1 .) .] .J .2 .2 .1.. 1.1 1.1.,.1.1' .1 .a .1 .'.1 1.1.1.2.1 .5 .6 .6 .7 .1 ., .1 ., .6 .6 .5 .1 .2.1 1.1.1.1.1 1 .. I .1 .1 I.I I.I.2.l.S.6.6.J.'.7.1.1.6.6.5.J.2.1 .t.I.I a.1 ,I .1 .1 ., .1 1., ,.1.2.1.61 11.41.'1.51.5 51., 4 ] 6.).2 .1.1.1 1.1.1.1 1 1 .1 .t .1.1 .1.1.1.,.2.l .6 1.11 I.,t.51.'5I., 41.]I 6.].2 1 1.1.,.1.1.1.1., 1.1 I.t .1.1.,.,.2.151. 2.9).2J.]].]].).1.J).J].2a.92 5.2.1.1.1.1.).1.1.1.1 .1 .1 .1.. .1 1.1.2 .51. Z 2.91.2.l.1] .J'.Jl.J.J.l1.ZZ.92 I 5.2.1 .... 1.1.1 1.1.1 .1 .1.1.1 1.1.1.2.J .61.JZ.9J.6J.9 4 4.1 I ll.QJ.62.91.].6.J.a ,I .1 .1 .1.1.1 .t .1 1 .1 .1 .1 .1 .1.1.1.2.J .61.12.9J.6J.9 14., 11.9J.62.91.1.6.1.1.1 .1 .1 .1.1 1 .t ., .1 1 .1 .. I .1 .1 .1 1 .2 .1 .61 1.21.9 J4.4 4.Jl.9l.ll 6 .] .1 ., .1 .1 .1 1 .1 1 .1 .1 1.1.1.1 1.1 .61 ... 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J.al.9 l 5 !1 ll.9l.2 ..... 6 .J .2 .1.1.1 .1.1.1 .1 .1 .,.1.1.1 1.,.1.2.1 .01.J2.93.61.9 I ,.91.62.' J.6.].2 1 ., .1 1 .1.1.1.1.1.1.1.1 2.3 .t.I.J2.9l.6J.94 4.14 ..... I ll.'J.62.91.].6.].!.1 .1 .1 .1 .1 1 ., .1.1 .'.1.1.1 ,'.1.1 .2.'5'. Z.4Z.9].Zl.JJ.Jl.JJ.]1.l].zz.va 5.2.1.,.1.1.1.1 1.1.1 .1 .1 .1 .1 .t .1 .1 .1 .1 .2 .,t. z a.9J.21.]1.1].],.)].]].!2.".41 S.2.,.I.I.I.I.I.t., I.I' ., 1 .1 .1 ., .1 .2.J .61.1.11 5 51., '1 ]1 6.).2.1.'.1.1.1.1.1.1.1.1.1 .1 .1 1 .1 .1.' .1 .2 .1 .61. 1.'I I.'1.51.51.!51.51 ,.JI 6.).2.1 ,.,.t.I.1 .1 .1 1 .1 t .1 .1 .1 .1 .2 .] .5 .6 .6 ., .7 ., .1 .1 .6 .6 .s .1 .2 .1 .1 1 .1 t .1 .1 .1 .1 .1 1 .1.1.1 .t .1 .1.1.1.1.2.1.,.6.6.'.f.1.7.1.6.6.S.J.2.1.1 1 1 1 .a ., 1 .a .1 .1 .1 .1 .1 .1 .1 .1 .1 .2.2.1.1 .J .) .J .] .l .1 .) .2 .a .1 .1 .1 .1 .1 1 .1 ., .1 1 .1 .1 .1 1 1 1 .1 .2., .] .1 .] .1.1.1.1.1 .J .2 .2 1 .1 1 .1 .1 1 .1 ., 1 1 .1 t .1 .1 .1 .1.1.2.2.2.2.2.2.2.2.1.1.1.1.1 1 1 .1 .1 1 1., .1 1 1.1.1.1 2.1 .2.2.2 .2 .2 .2 .2 .1 1 .1 1 1 1 1 .1.1.1.1 .t I I.I.I.I.I.I.I I.I.,.I.I.I.I.I.,.I I.I I.I ., .1 .1.1 .1.1 I.I.I.I.I I.I I.t.I.1 .1., 1.1 1.1.", .'.1 I I I I I I I ., I I I I I I .1 .1 t .1 I t I I I .1 .1 .1.1 1.1 1.1.1 1.'.1 '.1.1.1.1.. 1.1.1.1 1.... .1.1 .1 I .'.1 I .1 I I .1 I I I I I I I I ,. I I .1 I ., I I I .1.1.'.1 .1.1.1.1 I.I I.I I I I t I.I.I.I.I.I.t 1 I 1.1 .,. I I I I ., I I .1 I I I I I I I I I I .1 I I I .... I I I I I I I I. I I I I I .. I I I I I I.. t 1.1.1.1 .1.'.I.t.I.I.l.I.I.I.I I I.I I.I I.I.I.t I 1 1 .1 I I I I I I I I I I 1. I I 1 I .1 1 I I I 1.1.1.1 .1.1 I.I.I.I I.I.I.I.I I.t.I.1 .1.1 '.1 ,.1 1 1 1.1 ".1 1.1.1.1.1.1.,.1.1.,.1.1 1.1.... .,.I.I.I.t.I I.I.,.1 .1.' I I I I I I I I I .1 .1 I I I ., I I I I I 1.1 I I 1 1 1.1 1 1 1.1.1.1.1 ,.1.1.. .1 1.1 ,.1.1.1 1 I .1 I I I I I ., .1 I I I. I I I I t .1 I I .1 I I .1 I. I 1.1.1 t I.I.I I.I.I.I I.a I 1.1.1.1.1.1.,.,.1.1 ,.1.1 .1.1.1.1.1.1.1., .1 ., .1 .1 ., .1.1.1.1.1 1.1.1.,.I I.I.I.I a.I 1 .1.', .1 I I I I .1 I I I I I I I I I I I I I I 1 .. I I 1 1.1.1.(.1.1.'.1.1 ) 1 .1.1.1.1.I.t I I I.I.I.1 1 f .1. I ., .1 I .. I 1 I .1 I I I. 1 I .1 .1 I I 1 I I I I. I + Figure 5.5b -Map of saltwater mound. T 10.0 days, maximal ordinate 4.69 m. '-.J o

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f f .' .. 1... .... ................. 1 .......................... ..... ... 1 .1 "1' ""1""" 1 1 2 2: 1 2 ., ............ 1 ............. 2 2 l l 2 """""1"",."" I,,'t"t." l ? 2 1 Z '-l 2 1 2 2 l .'t ....... .... Z 2 Z 2 Z Z 2 2 2 Z Z 2 Z ., I t.,. 2 1 '1".]") "tJ")""'J ] 1 ]. Z ....... I""""".! 2 ')"1 J.,J"3 1"J"J"J"J")' 1 ,. 2 .... l. 4 ''5.'5''5''''''''5''5''5 5' ... J"l' 1 '1""'1"1' Z 'J j .... H.'\ 5 '\ 5 ,. 4 'l".]' 2 ., ,. .1 .2 'l' 4 '.5' 6 "",,'7. A e e., ,." .... ). 1 ,. ""1"" ; jt ... ':". ., ,. 8 8 fi ., '1 ,. !J ... ,). Z ., .... .,. 7' Z ""5.'" .0.11.11.".11 .......... 1 .o.,..c; ,. 2 ......... l :! .j ,. IQ.I I,tl ".' .... II'''.'' Z ........ ,. 7 t,. .. ,. 10 12"' ... .... 1'11'11'''.'' 12 10' "._,. l ....... 1. ,. 'l." fJ 10 17 ............. 11 .. 1 .... 11 .... 2106 4 .). l ....... ... ....... .t. .... fI e e It 8 e It .. ,."., 4\ 1 ........ .... 2 +J'.!\'.'.'"'II A e .. .. II ., ..... 5 2 .... ,. ".'1'.'.2')"'5"'.'11'.1'1 6 5 5.'5. 6 e ."."., 7 .. .. I. '.ttS'."."t" ft 6 5.'5"5. 1.1 e .1".Ultt5"J.:! .... 1. 2.) 5, ,. ...... H .'U" '.h.] ] '5' 8 hll.' s :t. 2 l .! 1 .U.s "e" It .5 .... ) J ..... '"le. tI.''''''.5 1. Z ,. l 2 .]'.5. !II ...... 8 '5'.). Z Z it 'l.e,. II .... I. a t' 't Z 2. t ,.t'.:'! 2 "'.5' II ...... II .-;ttjt 2 2 ')*.5. t.lt .... ''5 't 2 ., "t + 2 ''''5+ e .... 8 +5.'], 1 7.) 5. 8.' .... III .5 1 .. Z 7. ...... ? l 'l"'S' .... "t" II .,.t't Z il tJ'tS. 8 ." ... e .St.]t 2 ...... :::::: : !n:n : : :::::: : ; :::::: ........ Z '1'.".' 1.'11 e .'S' .J.'J .J' .. 8 .11 .... 5 ]. 1: 2 e...... ? .".!U.' ...... II e .5' .Ju, ] ... '5. e 1t".' 5"" Z ..... ".,. 1 t'.s "."" 6 '5 5"5."'5 5. 1\ It ''''''*' .. 5 j. Z ........ "'.,tt,. 2 .j .. ,. ...... 'I ,. "'.5 5"5"-;, 6 .... tt'.' 5'.3. ....... ,t "." ... t l ')"5.1'.''''11 II B a It tt II IJ .... ltll., \$ ]. 1 .'.'1.'" '1'."'. I '''.S.'''' .... I'' II II II II 8 .. 'l1'"""S'.JI 2 .... 'l ., ... 6 to 12 1t.1'1I''''''.'''''' .... 1 .2 't) (I. '.2 ".".'1. t'."'I' Z .)., 6 10 12"'."'"""I"'''."t",,, 12 10 h ,. .... ......... 2 .l. ')"5 '. 10.11 .......... ............. 10.".5 ). l ? ""'.'1' .... .... 2 J.'St.7 0 .... \1.11 .................. 10.7 :, )t l. 2 ......... .! .J' .. _5. 6 .7 ,. 8 fI ".,.1' ,." .5' ). Z .t.".'I' ....... ,.? 'l' .5." ., ,. .. PI 7." '.6.5 ... 'l. ., ,. ""."1'." 2. .... l .... 5 5 S .. 5 5 ....... 5 .... ] _1. l ........... .. I ..... j. ."i s s 'i 'S :i ...... 'i !t .... J j. 1 .......
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I,[m s[mJ -zJm 20 lS lS 10 10 S S o a ._. 0 without convective tenns max 2 4 6 s max 8 N = 0.1 m/day A = O.S m DT = 0.1 day 10 t(days) Figure S.6 -Rate of growth of the maximal value of the drawdown, the height of the saltwater mound, and the thickness of the transition zone.

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73 Table 5.2 -Summary of experiments. Experiment Altered Original Altered Applicable Number Parameter Value Va lue Figures S.7a 1 DT 0.1 day 0.2 day S.7b S.7c S.8a 2 a 0.1 m 0.05 m through S.lOc 5.11 a 3 N 0.1 m/day 0.01 m/day through S.13c 4 K1 0.5 m/day 0.05 m/day None

PAGE 87

I -I I. I I '1"'" 1 1 1 '. '1"1 "'1" I" I" I 1,,1"'" I.t, I' I "1' tI ,'1",."", I 1t"'1 ,,1' t I' ., :! "".l"J" "'J.']""..! .! ...... .:. .)+h.' .. ,..,. .... J. l .! ,1 1 ....... &: 0 ., t.. r, .s." .! ,1"1' I' 1':0 ". '.i' ... .. '. ... -.I ".i" C:.,. I I' tI ... I .. I!'I' l\'4 It" 1"'IJ 12 Ie" : ... II'..! J, 1.!'IJ,t .\ ''''11 to" .: .1. '1' 1 .... I.I'.lr.I'.I'.I'.I'.I!t 12.;1 .! '1' '!.J!' 1;:'I";'lr'.""'I"I"I"I"'''S Il.'')' .1. '1""'1. u HI' J.'ul?1 1I11t1" ....... '.1 .:! I .... '1"1 1. '11'1' 1 II '.t? li'll'l] '1"",1' I' '."', I I II I I ltl _") l'" 1'1"", I" I" I'" ""I"J". H"I"lltl' ..!}'IU" 't H.IIII' .1 1 1 ..... I "",.!, l.J..!) I" '., .Jttl ,. t"'I"J' .,.,7t.t!" lO !).!I) .!O., ,.,7 '4 til 'J""'I. "''''.J. ,ul',".!,) .. ') !o !t; .!C,'lhl' I' ....... ,. I" I'" .!) 11) 2:, 1,).,7 I' I I I .. ... u If ." ,..',.!) lO !();.:Il oil., 'H'I'''' ""I"J. to .... ,., 1) .!) .!J "!J .;!:J"("I' ...... 1'.1 1. '1"I lt (.t .",".'"'I.!O !,) .10 ... '.46 'H.I'.I' '1'''" It r., l.a."" ) It) ..!J ,. r;. .; ..... 1 .1.1t.' 1 1,.11.1',.,,,,, 1.ltlltl1 'l .J"I"I. '1""')'" "J.', 1,.I j"".I)'11 I')"'.I.!,.. ., '";111117"1"'''1''''''',':'; ,l.)t l '1' t, .......... ,"! .,. 'I .! .. II I"!"J .... 14 14 .UIJ 13" J'I' I.:. Il'I' ,-,. ,4 ,. ".11 IZ ,I) 4 ;! '1, '1 1 ..... oJ' ., ':' ,. {, fr '-(t ''"i'" ,! '1"1" ., .... 2 ''i'.' .. 6 ': 'i ... t, .i ... '1"1' '1,'1' l l .4'.J.I"')I'''')''J .! .! ""1' '1"" o! .J"J"J Jt'J tJ. J Z 1 1 1 1.' ,.+, .. 1 ''' 1 ..... 11 1 1 .... .. .. 1 1. .......................................................................................................... ............ Figure S.7a of dra\oJdowns. DT = 0.2 days, T = 2.0 days, maximal ordinate = 20.01 m.

PAGE 88

...................................................................................................................... 1 .1 .1 .1 .1 .1.1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .. .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .1 .1 .1 .1 .\ .1 .1 .. 1 .1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .. 1 .. .1 .1 .1 .1 .. 1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .. .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 oJ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 oJ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .\ .\ oJ .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .. 1 .. .. .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 oJ .1 .. .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .1 .1 .. .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .. .1 .. .1 .1 .1 .1 .. .1 .1 .1 .1 oJ .1 .1 .1 .!! .2 .2 .2 .2 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .. 1 .1 .1 .1 .1 .1 .1 .. 1 .1 U .2 .2 .2 .. .2 .. .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ... .1 .1 .J .J ol .J J .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .1 .1 .1 .1 .1 .1 .1 .1 oJ .1 .1 .J' .1 .1 .1 .1 .J .J .1 J ol .J .J .J .J .2 .1 .. 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 . j ... ., .7 r r .7 .7 .6 .5 .2 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .l .:i .', .7 .r .7 .r r .r .6 .5 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .J ." .r .u .1 .8 .d .u .1 .8 .r .6 .J .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .2 J r .. .J .u .8 .8 .8 .r .6 .. .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 oJ .1 .1 .1 .1 .1 .1 .. 1 .1 .. 1 .. .1 .1 ... .d ._1 .-' .9 -J .. .. 6 .1 .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 2 oJ .'. .11 .9 ." .'J .'1 .11 .. .6 .J .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .J ., .u ." ." .1 .. .'1 o'J .'J .s .r .J .l .1 .1 .1 .1 .1 1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .1 .7 .& .'J .'1 .9 .1 .'1 .9 .9 .8 .r .J .2 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .J .7 .. ." ." 9 .9 .'J ... ... .. r .J .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 ) of .'J .'J ." .'J .9 ." ... .ft r .J .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .J .'1 ... .' .J .'1 .9 .'J .9 ... r .1 .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .: .1 .1 .1 .1 .1 .2 .1 .9 ." .> .-1 .'1 .9 ., .. .r .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .. 1 oJ .1 .1 .1 .. .J ., .-1 ." .. ." .9 ." ... 9 .8 .7 .J .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .. .r .-' 1 .. .'J ... .9 .8 r .J .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .J .8 .. .-' 9 ." .9 ... ., .7 .J .2 .1 .1 .1 .1 .1 .1 .1 .. .1 oJ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .J ." I J. ." ... .9 r oJ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 01 .1 .. \ 01 ... .-J ... .J .'J .J 6 .J .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .. .1 oJ .1 .1 .1 .1 .1 .1 .l 1 .u .0 .,J '1 ... .9 .-J .. .4 .6 .1 .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .\ .J ... .r oJ .1 ./1 .11 .0 8 .r ... J .2 .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .J .1, r -J .8 .8 .. .7 ... .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .7 .1 .r .r .r .Ii .5 .2 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .5 u .r .' .r .r .7 .r r .6 .5 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 oJ .1 .1 .J .J J .1 .1 ol ._1 .J .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 :i .1 1 .1 J .J .J ol .J .J .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .! .2 .2 .2 o! .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., ., .2 .2 .l .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .a .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .\ .1 .\ .\ .1 .1 .1 .1 .\ .\ .1 .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .\ .\ .1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .. .1 .1 .1 .1 .1 ,I .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 oJ .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .a .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .. .1 .. 1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .a .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .a .1 .1 .1 .1 01 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 01 .1 .1 .1 .1 .1 .1 .1 oJ .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1' .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ....................................................................................................................... '-I In Figure 5.7b -Map of saltwater mound. DT = 0.02 days, T = 2.0 days, maximal ordinate 0.88 m.

PAGE 89

f, f t t t t t t tt ft t f f" t f .t t.f f f I f ,. f' ff I f I t I. I t ,.t t t.t I ,., t I Figure 5.le -Map of transition zone. DT = 0.2 days, T = 2.0 days, maximal ordinate = 4.96 m. ....j 0)

PAGE 90

................................................................... .. '.u.......... ....... .......... 1 .. 1....... ""1""" ...................... .... .1 1 ...... 1.. 1 '............. '1"1' 2 2 'l"3 ] 3 ) ] ,. Z 2 .1.... .... It 2 I 'J ] ... J"l".lttJ"]' Z 2 '1"" '1.1' 2' ".!O. 6 6 ,. 6 r. 6 6 'S" Z ., ,. .. .1. Z '5'" f\ ,. 6 (I 6 ,. '5'. 2 ,. '1. 2 10 12'IJ '4 t "'.3 ., .1. 2 '1' '1' Z 10 .2'll I 4 '4 .4 '4'.l 12 10' 2.1t '1' 2 .\$. 16""""""'I? '6'15 2 tI. 2 211'5 """""'.''''.7 16"5 'Z,5' 2 '1' ., ..... ). 6 '1:' 16 1.,.19'19.19'19.19 .8 16t1' .' 1. '1", 6 '1' ,f 18'19'19'19'19'19 ., '6'1' 6 """'1, ""1")' t"17'IO.19 20 10 20"9"."7 14 6 """'1' ""1"]' 6 '.""19"9 20 ZO 10"9"9'" 6 ""1".' ., ,. 6 '.""1920 20 20 20"9'" ,. ""1"1. '1""", 6 9 20 20 20 20 20.,9"7 6 .3....... '1"1"1' 6 "'1"'9 20 10 ZO ZO'I"" 6 .,....... 6 1""'1920 ZO 20 20 20'19'" 14 """"'1' ., ,.,1'. """19 20 20 20 10 1.6 .] ,. '1""'" 6 ,.,. 20 20 20 20 20'19'17 6 .3 '.... .1 3. 6 .4"".9.,9 20 20 20"9'19'17 +]"1"" '1"1"]' '."7".'19 20 'I 6 .1....... .... 1 1. f '.3 Ie 18'19.19"9""19 .8 '.'.lI ,. ')""'1' '1"1"" ,., '6 IA'19'.9.19'19 e 16"'6 .3 1.... 2 '2'15 le'.7.t, ,6.'5 2 tI. 2 '5+ '2'15 .f-'17+17""'"'' 1e.'15 '2'5' 2 fl' 2 4 .0 .2'llI '1 I' 3 10' Z .,. '1' 4 .e .,.,.1 '4 '4 '4 ... .2 ,04 2 '" ""1' 2 .. '5'" 6 6 6 6 6 '5" 2 ""1' .1 2 4 6 6 6 6 6 6 6 '5' 4 2 .... ,. 2 2 ,;",],'.1,'1 ) ) ). Z Z Z 2 """']")")"J"" 2 Z '''''1' '1""" 'fl""" ..... ,.... "++"'1""""1" 1 ... '1""""1"1'"'''' .1 ..... 1............. 9 ................................................................................. ......................................... Figure 5. 8a -Map of drawdowns. a = 0.05 m, T = 2.0 days, maximal ordinate = 19.99 m.

PAGE 91

........................................................................................................... ........... .1 .1 .1 1 .1 .1 .1 .1 .1 .1 1 .. 1 .. .1 .. .1 ., .. .1 .1 I I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 1 .1 .1 .1 .1 .. .. .1 .1 ., .1 1 ., .1 .. 1 .1 .1 .1 I .1 .. .1 .1 ., .1 .1 .. I I .1 .1 .. I I .1 .1 I .1 .. .. .1 ., .1 .. .1 1 .. .1 .. .1 .1 .1 .1 I .1 1 .. .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 ., I .. 1 .1 ., .. .1 .1 .1 .1 .. .1 .1 1 .1 .1 .1 .1 I I .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1' .1 I .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .. .1 .1 .1 .1 .. .. .. .1 .1 1 .1 .1 .1 .. I 1 .1 .1 .1 .1 I I .1 I .1 .. 1 .1 1 .1 1 .1 .1 1 .1 .1 I .1 .1 .1 .1 I I .1 .1 .1 1 .1 .1 .1 I .1 .1 .. 1 .1 .1 .1 .1 .1 1 .. .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 1 1 I I .1 I .1 .1 .. 1 .. .1 .1 .1 .1 .1 .1 1 .1 1 I I .1 .1 I .1 .1 .1 .1 .1 .1 .1 I 1 .. .. .1 .1 1 .1 I .1 .1 .1 I .1 .1 .1 .. .1 .1 .1 1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 I .1 .1 .1 .. .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 1 .1 .1 .. .1 I I 1 I .1 .1 .1 I .1 .1 .1 .. ., .1 .1 .1 .1 .1 ., .. ., I .1 I .. 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. ., ., ., .. .. .. .1 .1 .1 .1 .1 .1 .. .1 .1 .1 ., .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 1 .1 .1 .1 .. 1 1 .1 .. .1 .1 ., .1 .1 .1 .1 .. 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., ., .1 ., .. .1 I 1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 ., .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 I ., .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 oJ .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 I .1 .1 .1 .1 I I .1 .1 I .1 1 .1 .1 I .1 .1 ., .1 .1 .1 I I .1 .1 I I .1 .1 .1 .. 1 .1 .1 I .1 .1 .1 .1 ., .1 ., .. .. .1 .1 .1 .1 .1 .. .1 ., .1 .1 ., .. .1 .. 1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .2 .2 .2 .2 ., .2 .2 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I I .1 .1 I .1 .1 .1 .1 I 1 .. .1 .2 .2 .2 .2 .2 .2 .2 .1 .1 .1 .1 I .. .1 .1 .1 .. I .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .2 .J oJ .J .J .. .1 .J .J oJ ., I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 ., .J .J .J .J J .J 03 .J .J .2 I I .1 .1 .1 .1 .1 .1 .. ., .1 .1 .1 I .1 .1 .1 .. 1 .1 .1 .1 .1 .1 .. .5 .6 .r .r .' .' .r .6 .6 .1 .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .. .1 .1 .1 .1 .1 .1 .1 .1 .1 2 .. .6 .r r r r .r .6 .6 .1 .2 .1 .1 1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 I .1 .1 .1 .1 I .1 .1 .1 .J .6 .7 .. .. ., .6 .. 7 .6 J .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .. .. .1 .1 ., .1 .1 .J .. .7 .ft .. .ft .ft .7 .6 .J .1 .. 1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 J .. .. .ft .. 9 .9 9 .. .. .J .2 .1 I I I I .1 I .1 .1 I .1 .1 I .1 .1 .1 ., ., .1 .1 .1 .1 .2 .. .. .. .. 9 .9 .9 .. .. .1 .2 .1 I .1 .. 1 .1 .. t .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .2 oJ .7 .ft .9 .9 .9 .9 .9 .9 .. .7 .J .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 1 I ., .1 .1 I .1 I .2 .J .r .. .9 .9 .9 .9 .9 .9 .J .J .2 .1 .1 1 .1 1 .1 .1 .. .. 1 .. .1 .1 I .1 .1 .1 I .. .1 .2 .J .r .9 9 .9 .9 .' .r .J .2 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 ., .1 .2 .J .r .. .. .9 .. 9 .9 .9 .7 .J .2 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .. .1 .1 1 .. .1 I .. 1 .2 ., .7 .. .9 .9 .9 .9 .9 .9 .. .. .r .J ., .1 .1 1 .1 .1 .1 .1 I .1 I .. .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .2 oJ .r .0 .9 .9 .9 .9 .. r .J .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .. .1 .1 .1 I 1 .1 .2 ol .r .ft .9 .. 9 .9 .9 .9 ., r .J .2 .1 1 .1 .. 1 .1 .1 .1 .1 .1 .1 .1 .2 .J .J .. 9 .9 .. 9 .9 .9 .9 .7 .1 .2 .1 .1 .1 .1 .1 .. 1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .J .r .9 .9 .9 .9 .. .9 .9 .... .J ., .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 I .1 .1 .1 .1 .1 .2 .J .r .. 9 .9 .9 .9 .. .9 .9 .s .7 .J .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .J .f .. .. 9 .9 .9 .9 .9 .. .. .J .2 .1 .1 .1 .1 1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .2 .J .6 .. 9 .9 .9 .9 .9 ._ .6 ., .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .1 1 .1 .1 .1 .1 .. 1 .1 .J .. .7 .. .. .. .. ., .6 .J .1 .. .1 .1 .1 .. .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ol .. .r .. .ft .. .r .6 .J .1 .1 .1 .1 I .1 .1 .1 .1 .1 .. .1 1 .1 I .1 .1 1 .1 .1 .1 ., .2 5 .. .. .' .r .r .r .r .0 .5 ., 1 I .1 .1 .1 .1 .1 .. 1 .. i 1 .1 .. .1 .1 .1 .1 .1 .1 .2 .5 .. .. .r .J .r r .r .. .S .2 .1 .. .1 .. ., 1 .1 .1 .. .. .1 .. .1 .1 .1 .1 .1 .. .1 .1 .1 .2 .J .J .J .J .J J .J .J .3 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .r .J .1 .J ., .1 .J .J .:1 ., .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .2 .2 ., .2 ., ., .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .2 .2 .2 .2 .2 ., .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. I .1 .1 .. 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 ., 1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .. .1 .. .1 .1 1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I ., .1 I .1 I I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .. 1 .1 .1 .1 .1 .1 .1 I .1 I .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 ., .1 ., .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .. .1 .. 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .. 1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .. .. .. .1 .. 1 1 .1 1 1 .1 .1 I .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 1 1 1 1 .1 .. 1 .1 .1 .1 .1 1 .. .1 .1 .1 .1 .. .. .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 ., .1 .1 .1 I .1 .1 1 .1 I .. .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I 1 .1 .1 .1 1 .1 1 .. 1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 1 .1 .1 .1 .. .. .1 .1 .1 .1 I .. 1 .1 .1 .1 .1 .1 .. .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .. .1 .1 .1 ,.1 .1 .1 1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 I .1 .1 .1 1 .. 1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 ., .1 .1 .. 1 .1 .1 .1 .1 I .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 it .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I I .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 I .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 1 1 .1 .1 .1 .. 1 1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .. .. .1 ., .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .. ., .1 .1 .1 .1 .1 .1 .1 .. 1 .1 .1 .. 1 .1 .1 .1 .. ., 1 .1 .1 I ., .1 .1 .1 .1 .1 .1 .1 ., .1 '._ .1 .1 .1 .1 .. 1 .. 1 .. .1 .. .1 ., 1 t"'" t CO Fi gure 5.8b of sal tl'iater mound. a = 0.05 m, T = 2.0 days, maximal ordinate = 0.88 m.

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............................................................................................................... .1 .1 .1 .1 .1 .1 .1 I .1 I .1 I .1 .1 .1 .1 I .1 t .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 I .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .2 .2 .2 .2 .2 .2 .1 .2 .2 I .1 .1 .1 I I I .1 .1 .1 .1 .1 .2 .2 .2 .2 .2 .2 .1 .2 .z .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .z .2 .1 .1 .2 .2 .Z .z .2 .2 .1 .1 .1 .2 .2 .1 .1 .1 .1 .1 I .1 .1 .1 .2 .1 .1 .2 .2 .2 .l .2 .2 .2 .2 .2 .2 .2 .1 .1 .1 .1 .1 .1 .1 .1 .2 .r .1 ., ] .3 .J .J .J .J .J .J .J .] .2 .2 .1 .1 .1 .1 .\ .1 .1 .1 ., .Z .J .3 .3 .J .J J .. .J .J .J .J .J .3 .. .2 I I I .1 .1 I .1 .1 .2 .2 .J .0 .0 .5 .5 .5 .5 .5 .S .5 .5 .0 .0 .l .2 .z .1 .1 .1 .1 .1 .1 .1 .1 .2 .2 .J 0 .0 ... .5 ... .s .5 .5 .5 ... .5 .0 .0 .J .2 .2 .1 .1 .1 .1 .1 .1 .1 .2 .2 .J .0 .6 .r .r .r .r r .r .r .r .r .6 .5 .0 .J .1 .2 .1 .1 .1 .1 I .1 .2 .? .] .0 ." .r .1 .r .r .r .r .r .r .r .6 .5 .0 ., .2 .2 .1 .1 .1 .1 .1 .1 .2 .2 J .-... .7 .411. I. 1.11.11.11.11.11. 10 .9 .7 .5 .0 .J .2 .2 .1 .1 .1 I \ I .2 .. -.. .91. I. I. II. I I. II. II .11_ I .9 .' .5 .0 .] .. 1 .1 \ .1 I .1 .2 .3 .. .5 .11. 1.41. 5 .. !'t1.61.61. 61.61.t. I .51.51.41. .r .5 .0 .] .>. .1 .1 .1 .1 .1 .1 .. J .. .s '1. 1.4'. 51.' 61.61.5 .. .. 41 .1 .5 .0 .J .2 .1 .1 .1 .1 I .1 .2 .J .- f .91 .9 .. 0 .J .2 .1 .1 .1 .1 .1 .1 .2 .J .' .11 1.41.61 .t,l. &1.61.61.61 ...... 1.61.61.6 ... .9 .6 .0 .] .2 .1 .1 .1 .1 .\ .1 ? .2 J ... .71. .r .5 .J .2 .2 .1 .1 .1 .1 .1 .1 .2 .2 .] 5 '1. I .51.61. ?, II I I. II. I I. II. II. 11.2'.61.51 .1 .. .] .. .1 .1 .1 .1 .1 I .2 1 .. .'I.II.fll.61.1 .6 .8 .1 .1 .8 .'U.II.61.61.' .1 .5 .l 2 .1 I .1 .1 .1 .1 2 .. .] ... '1.11." .. 61.1 .- 1 .1 .r .8 11 1.61.1 r .s ., .2 .2 .1 .1 .1 .1 .1 I .2 .. .J .11.11.&I.fl.I.1 .5 .5 .s .6 ." .. 1 .. 61.61 7 1 .2 .2 .1 .1 .1 I .1 I .l .2 .] .5 .71.11.f-I.ftl.1 .ft .6 .s .s .. 6 .41.11.61.6 .. 1 .7 .s .J .2 .1 .1 .1 .1 .1 .1 .2 .2 ..5 .11.11.f.1.61.1 r .5 .0 J .0 .5 .11.11.61.61.1 .1 .S .0 .1 .2 .1 .1 .1 .1 .1 .1 ., .2 .- 5 .71.11.61.6 .. .r .s .0 ] .0 .s .rt.II.61.61.1 .1 S .2 .2 .1 .1 .1 .1 1 .1 .. .. .0 .71.11.61.61.1 .1 ... .] .1 .J .5 ."'.11.61.61.1 .1 .5 .0 .:! .z .1 .1 .1 .1 .1 .1 .2 .. .5 .71.11.61.61.1 .r .3 I .J .5 .'t.1 .. 61.61.1 .1 .s .0 .2 .2 .1 .1 .1 I I \ .1 .. .0 .5 .71.11.61.61.1 .7 .5 .0 J .' .71.11.61.61 1 .5 .0 .2 .z .1 .1 .1 .1 .1 I .2 .-.rl.II.ft.I."'.1 .1 .5 .0 .J .0 .5 ."1.11.61.61.1 .7 .s .0 .2 .2 .1 .1 .1 .1 .1 .1 ., .2 .J .' .,..1 .. 61.61.1 .' .6 .5 .s .6.e ..... 61.,. ... .7 ., .1 .2 .2 .1 .1 .1 .1 .1 .1 .l .2 .J .'5 .71.11.61.61.1 .11 .f, .s .5 .6 .11.11.61.61.1 .r .5 .1 .2 .2 .1 I .1 .1 .1 .1 .! .2 .1 .! .71.II.tl.61.1 .11 .ft r .7 .7 ..7 .s .1 .2 .z .1 .1 .1 .1 .1 .1 .z .2 .J .'I.II.f-I.C.lel .8 .1 .7 .r .el.II.61.61.1 .7 .3 .2 .2 .1 .1 .1 .1 .1 .1 .l .2 .l .5 .11. 1.51." .. 21.11. I .. 1I.11.11.11.II.ZI.el.SI. .' .5 .J .2 .1 .1 .1 .1 1 .1 .. .2 1 .., .. hi 1.11.1, 11. II. 11.2" .1 .J .2 .2 .1 .1 I .1 .1 I .2 ..6 .lI 1.41.61.61.61.61.61. 61. 61.61.61 .61.61.' .9 .6 ., .1 .2 .1 .1 .1 .1 .1 .1 .2 oJ 0 .. .91 61.t. .. f I. 61. 61.61.fIol.I!tI.61. 6, .0 ... .0 .] .1 .1 .1 .1 .1 .1 .2 ] .' 5 .'1. I. '1. I. ftl. 61. 61.61. 'il. 51. tl .1 .. .J .2 .1 .1 .1 I .1 .1 .2 .J .0 .71 1. 'SI. "'.fI.61 .f'I 41. .7 .. .0 .J .2 .1 .1 .1 .1 .1 .1 .2 .2 .] .. ., .7 .ql. I. 1.11.11.11.11.11. I. .9 .1 .5 .0 J .2 .2 .1 I .1 I I I .2 .r .] .0 .1 .91. I. '.11.11.11.11.11. I. .9 .1 .5 .0 .J .? .2 .1 .1 .1 .1 .1 .z .2 .0 .5 ." 1 .1 .r .7 ., .r r .' .6 .0 .J .2 .2 .1 .1 .1 .1 I .1 .? .? .3 .0 .. .7 .7 .r r ., .1 .7 .1 .6 .5 ] .2 .2 I .1 .1 ., .1 .1 I .2 .o. .3 .0 .0 .5 .5 .5 .S .5 .s .5 .5 .0 .. .J .2 .2 .1 .1 .1 .1 .1 I .1 1 .. .1. .3 .. 0 .s .S .S .S .5 .5 .5 .0 .J .2 .2 .1 .1 .1 .1 .1 .1 .1 .1 .. .? .J .J .J .1 .3 .] ..J .] .J .J .J .J .2 .2 .1 .1 .1 .1 .1 .1 .1 .1 .2 .2 .J .J .] oJ .3 .3 .0 ] .3 .J .J .J .] .2 .2 .1 .1 .1 .1 .1 .1 .1 .1 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .1 .1 .1 .1 .1 .1 .1 I .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .-.2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .2 .2 .2 .2 .2 .2 .2 .2 I I .1 .1 I .1 .1 .1 .1 .1 .1 .1 .. .2 .2 .2 .z .2 .2 .2 .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 I I .1 .1 I .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 I I .1 .1 I I .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I I .1 .1 I .1 I .\ .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I I I .1 .1 .1 .1 .1 ................................................................................. '..J \? Figure S.8e -Map of transition zone. a = 0.05 m, T = 2.0 days, maximal ordinate = 1 .58 m.

PAGE 93

......................................................................................................... .. """""""", .. ,, """'It"""""" ., ",t., ""'1""""""""'" """""" ..... ... """""""" .... ,. z Z ')"""""')")"]' a Z """ ., ,. 2 2 """']""']"]"" Z I ., 't ., ,. 2 'S. 6 6 6 6 6 6 6 .S.. 2 """ ., ,. I !H 6 6 6 6 ,. ., 2 ., ,. .,. z '0 12." ,. ,. I. ,. 12 '0' 2 '" .,. 2 10 ",,3 ,. I. ,. ,. '2 '0' Z .,. z '1'5. Z .,. .,. Z 'S' 12"'.,'t",'1." .. ".,.,,.,, 12'S' Z .,. ]. 6 ,,1'" '."9".',V"."9 '8"""6 ']1"'", ....... u 6 ."tI, '."9"9".".'19 1 ,Ft'l f, 'J""'" """'3' a ".'9".201020+19+19." ,. 6 .H .... '. "."'+], 6 """,0"9 20 20 10"."9'" ,. 6 .) ,. ., ).6 ",. 21t 20 '0 23 20".'" I .... J ,. + f """'" 6 ,7.,9.0 20 20 23 ZO"9'" '4 e ,]",t", """,), 6 '4""'9 10 20 '0 20 20.'0." ,.6 """'" .... ]. a, ".,. ao 20 '0 10 20".'" ,.6 ., ,. ] t"""9 2D 20 20 20 lO"."? 6 ,]""", ]. 6 I "". 20 20 23 zo.,.", I. 6 .l "." ,,*.)* 6 ".,9"9 20 20 20., ,. 6 ']""'" ). 6 """"9"9 20 2020'19.'9." ,. 6 ., ,. ,. 6 ,." '.'I.t.o.,o.,q.,o '."""6 ., ,.... ,. 6 ,., '."""6 .l '.... ... 2 12"5""'1"1+"""'1"'''5 'I'" Z .,. z +s. 12"5tI7.,,""""".""+" '2'" Z .,. .,. 2: '0 'Z." .4 ,. ,t.', '2 '0 .2 .,. .. z. 10"'.3,4""""'.1.210. I.,. + Z +S' 6 I 6 6 6 ., t"." ., 2 'S.. 6 6 a ft 6 6 'S" Z .,.... 2 2 .J""']""'].'3 .2 2 ...... ,. z Z """""]"]"]")' r z ., ,. ....... ........ .. .. "., ..... .. ,.... """"""."",."""""'+".". II ,......... ....... ., .. .. .. """"", .. t Figure 5.9a -Map of drawdowns. a = 0.05 m, T = 6.0 days, maximal ordinate = 20.08 m. OJ o

PAGE 94

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I. 2. 2. I.IJI.SI.4 .6 .l .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .a .1.1.1.1.1,1.1.1.1.1.2.J .."."1.92. 2. 2. 1.2. 1.91.!!I1.4.6.l.2.1.1 .1 .1 .1.1.1.1.1.1.1 .. .1.1.1.1.1.I.l.I.I.I.2.t .81.82.22 ... 2 Z.2 8 ._ .2.1.1 .a .1 .1 .1 .1 .1 .1 .a t .1.1.1.1.1.1.1.1.1.1.2.t 2.1.1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ,1.1 I.I.I.I.'.I ,.t .91.CJlZ.t,.6Z.1Z.7Z.72.72,'Z.62.'1.9 .9 Z ,a .1 .1 .1 .1 .1 ,I .a .1 .a .1.1.1.1.1 .1 .1 .1 .1 .1 .2 .t .9 ... 2.42,62.11.,'.,72.72.72.62.1,.9 ,9 .11 .2 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 ,I .1 .a .1 .1 .1 .1 .1 .1 .2 .t .92. Z.!li2"Z,8Z.81.81.12.ft2,7Z.IIZ ,1.1.1.1.1.1.1.1.1.1.2 92:. 2.52.7Z.82.82 2."2.82.72.52 9,11.2.1.1 ,a 1 .1 1 .1 .1 .1 .1.1.1.1.1.1.1.1.1.1.2.5 .9Z. 2.52.72.11,.92.92.92.82,".", ,9.S.2.1.1.1.1.1.1.1.I.t.I.I .. .1.1.1.1.1.,.1 .1 .1 .1 .2.5.92. 2.S2.72.fltZ.QZ.9Z.92.82.7,z.52 9.S.2.1.1 I.I.I.a.I.I.I.I. .1.1.1.1.1.1.I.t.I.I.2'.1 ,92. Z."Z.7,.82.92.92 2.82.'Z,52 9.5.1.1,1.1.I.a ,1.1.1.1.1.1. .a.I.I.I.I.I.I.1 1 ,,2 .0Z. Z.7Z.52 9.5.2.1.1.1.1.1.1.1.1.1.1 .1.1.1.1.1.1.1.1.1.1.2,5 .92:. 9.5.2.1.1 ,I .1 .1 .1 .1 .1 .1 .a .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .? .'i2. 2.52.'7. ... 2.92.92.92.12.'2.52 tt.5.2.1.1.1.1.I.a.I.I.I.I .1.1.1.1.1.1.1.1.1.1.2.11 .02. Z.!Z.72.1Z.ftZ.Il2.ez.ez.7z.5Z 9.4.2.I.I.I.I.I.I.I.I.t.I.I. .1.1.1.1.1.1.1 a.1 ,? ._ .92. t: ,,z .1 .1 .1 ,I .1 .1 .1 ,I .1 .1 .1 .1.1.1.1.1.1.1.1.1.1.2 91.92 2.,.Z.72.72.72.72.72.62,41.9.9.11 .Z .t .a .1 .1 .1 ., .1 .1 ., .1.1 .1.1.1,1.1.1.1.1 ,I .1 .2 91.92.42.6,.12.72.'1.72.7,.62.4'.9.9 1 .1 .a .1 .1 .1 .1 ., .1 .1 .1 .1 .1.1.1.1.1.1.1.1.1.1.1. ,A ._ .2 .1 .1 .1 .1 .1 .1 ., .1 .t .1 .1 .1.1.1.1.I.t.I.I.I.1 I:! .it. .. e.e._ ,2,1 1 .1 .1 ., .1 .1 .1 .1.1 .1.1.1 ,I .1 .1 .1 .1 .1 .1 .l '''1,41,,,,.91. 2. 2. Z. 2. 1.91."1.1 .6 .] .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1.1.1.1.1.1.1.1 .1 .1 ...... 1 .... ... '.9? 2. 2. 2. 2. 1.91.01.4 .f .3 .2 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1.1.1.1.1.1.I.t.I.I.a.1. 6.e.9.1l.9.9.9.9.9.e.6._.2.1 ,I .1 .1 .1 .1.1 .1 .1.1 .1 .a ,1.1 ,I .1 .1 .1 .1 .1 .1 .1 .1 1\.8.Q 9.9 .9.9.9 ... ,6 .4 .2 .1 .1 .1 .1 .1 .1 .a .1 .1 .1 .1 .1 .1.I.I.I.I.I.I.I.I.I.I.I.2.J.e.e 5.I.t ...... l.2.'.t.I.I.I.I.a.I.I.I.I.I.I .. .1.1.1.1.1,1.1.1 .1 .1 .1 .1 .2 .l .-.t .t 5 .' 1 .1. .1 .1,1.1 .t .1 .1 .1.1 .1 .1 .1 .1 .1.1 I.I.I.I I.I.I.2.z.2.?..2.2.2.2.2.2.2 I.I.I.I.I.I,'.I.I.1 ,I .1 .1 : .1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.'.I.t.I.I.I.I.I.I.I.I.I.I.1 ,,1.1.1 .1.1.1.1 .1 1.1 1.1.1.1.1.1.1.1.1.1.1.&.1.1.1.1.1.1.1.1.1 ,I .1 .1 ,I .1 .1 .1 .1 ,I .1 1 .. ,1.I.I.I.I.I.I.I.I.I.I a.I.I.a.I.I.I.I.I.I.I.I.I.a.I.I.I.I.I.1 ,I .1 .1 .1 .1 : :::: :1 :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: : 1.1.1.1 1.1.1.1 1.1.1.1.1.1.1.1.1.1 1 1 ,I .a ,I .1 1 .1 .1.1 .1 .1 .1 .1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 ,I .1 .1.1 .1 .1 .1 .1.1 .1 .1 .1 .1 .1 1 .1 .1 .1.1.1.1.1.1.1.1 .1 .1 .1 .1 .t .t .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 1 .1 .1 .1 .1.1.1.1.1,1.1 1.1.1 1.1,1.1 .t .1.1.1.1.1.1.1 ,t .1.1.1.1.1.1 1,1.1.1.1.1 .1.1.1 .1 .1.1 .1 .1 .1.1.1,1 1 .1 .1 .1 .1 .1.1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1.1.1.1.1 .1 .1 .1 .1.1 .1 .1 .1.1.' .1 .1 .1 .1 .1.1.1.1.1.1.1 .1 .1 .1 .t .1 -.1 .1 .1 .1 .1 .1.1 ,1.I.a I.I.I.I.I.I.I.I.I.I.I.1 ,I .1 .1 .t .1 .1 .1 .1 .1 .1 ,1,1.1 .1 .1.1.1.1 .1 1 .1 .1.1.1.1.1.1.1.1.1 1.1 .1 .1 .a ,t .1 .1 .1 .a .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1, 1 .1.1 .t ., .1.1.1.1 .1 .1 .1 .1 .1 .1 .1 1.1.1,1 .1 .1 .1 .1 .1 .1 .1 .1 1 ,1.1.1,1.1.1.1 1 .1 .1 .1 .1 I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.'.I.I.I.I.I.I.J.1 ,I ,I .1 .1 .1 1 .1 .1 .1 .1.1.1.1.1.1.1.1.1.1.1.1.1.1.'., ,I .1 .1 .1 .1 .1 .1 .1,1.1 .1 .1.1.1 .1 .1 .1 .1 .1 .1.1.1 .. 1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.I.t.I ,.I.I.,.I I.I.I.I.I.I.I.I' t .1.1 ,I .1 .1 ,I ,I .1 .1 .1 .1 .1 .1.1.1 .1 .1 .a .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .a ., 1 .1 .1.1 .1.1 ,.1.1.1 .t 1 1 .1.1 .1 ,I .1 ., .1 1 .1 .1 .1 .1 .1 .1.1.1.1.1 .1 1 .1 .1.1.' .1.1.1.1.1.1.1.1., .1 .1 .1.1.1.1.1.1.1 1.1.1.1.1.1 1.1.1.1.1.1.1.1.1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .a .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1.1 .............................................................................................................. Figure 5.9b -Map of saltwater mound. a = 0.05 m, T = 6.0 days, maximal ordinate = 2.83 m.

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.............................................................................................................. ., ., ., .1 ., ., ., ., ., .1 .\ ., .\ ., ., ., .1 ., .1 .\ .1 .1 .\ .1 .1 .1 ., .1 ., .1 ., .1 ., .\ ., ., .\ .\ .\ .1 .1 .\ .1 .\ ., .\ .\ ., ., ., ., ., ., .1 .1 .\ .\ \ .\ ., .1 .. ., ., .\ ., ., .1 .1 .1 ., .\ .1 .\ .. ., .\ .. ., ., ., .\ .\ .\ .\ ., ., .\ .1 .1 .1 .1 ., .2 .2 .2 .2 .2 .2 .1 ., .\ .\ .\ '., ., .1 .\ ., .\ .1 .1 .1 .2 .2 .2 .2 .2 .2 .1 .1 .1 .1 .1 .1 ., .1 ., .1 1 1 .1 .2 .. .2 .2 .. 2 .. .2 .2 .2 .. .. .1 .2 .1 .1 .1 .1 .1 .1 .1 ., ., .2 .1 2 .. .1 .2 .2 .2 .. .2 .. .. .. .2 .2 .1 .1 .1 .1 .1 ., .1 .1 .1 ., .. .. .. .' .J ) oJ .J oJ oJ .J .J .J 03 2 .2 I ., ., .1 .1 .1 .1 .1 .. .. .2 .2 .1 oJ .J .J ol J J .J ) oJ ,] .2 .2 .2 I .1 .1 .1 .1 ., .1 .1 .1 .2 .. .J ol .. .. .. .. .. .J .J .2 .2 .2 .1 .1 .1 .1 .1 .1 1 1 .1 .. .1 .) .J .. .. .. .. .. .. .. .. .J .] .2 .2 .1 .1 .1 .1 .1 .1 .1 .2 .> .> .' .. .. .. .. .. .. .. .. .t .5 .. .. .] .2 .> .> .1 .1 ., .1 1 ... .1 ., .J .. .. .f .. .f .. .. 6 .. .( .5 .. .. .J .2 .. .1 .1 .1 .. .. 1 .. ., .2 .. .5 .( 1 .. .. .9 .9 .. .' .s r .. .. .] .2 .z .1 .1 .1 .1 .. .1 .1 .1 .2 .' .. ., .. .1 .. .. .. .. .' .. .. r .. .. oJ .2 .> .1 .1 .1 .1 1 .1 .. .1 .2 oJ .. -01 .91. 1,.21., Ja. 11. ]'.11.] I. 11. 2' I. I .' .7 .5 .. .1 ., ., .1 .1 .1 .1 I .1 ., .1 .z .J .r .91.II.Zl.ll.ll.JI. :U. 11.11.31.21.1 .' .1 J .2 .. .1 .1 .1 .1 .1 .1 1 .z .. .J .' .1 91.11.(1.1 91.91.91.91.91.91.91."1.61. .. 1 .5 .. .J .2 .2 .1 .1 .1 .1 .1 .1 1 .. .J .' ., .1 91.11.61. "'I.ql. 91. VI. 91. 'H. 91. 91 .1\1. 61.] .. ? .. .1 .2 .> .1 .1 .\ .1 1 .1 .. ." 1 .. .f QI.ll. 12. 52. 12. eO! .82. ."2.12'. '2. 51 ." l 6 .. .J ., .2 .1 .1 .1 .1 .1 .1 ., .z .J .. ."1. J I. III? 52.12. ". 82. 82.1)2. 1'12.12.11..51 tI.l 6 oJ .2 .2 .1 .1 .1 I .1 .1 .) .. 1 I.!. 2.0;2. 9'."2''''''''2. 81.",.lIl.el. ez. "2.92.51.61.1 .? .s .' .] .2 .1 .1 .1 .1 .1 ., .1 .2 1 .. ., .' 1.11.62. -;2. 92.8,.82. 82. 82. 82. '2. 1Z.IIZ. r .' .. .] .. 1 .. .\ .1 I I .1 .1 .1 .. .' 81.?, .82. 12'''2. 11.9, .91. 91. 91. 91.91.9 .... 12.82.11.81.2 .. .J .. 1 .1 .1 1 1 .2 .. .. ., ." l.ll.! Z. 12.8:1'.11.91.91.91.9 I.", .91.9!.ll. 41. 'I.e,. 2 .. f> .. .1 .1 .1 .1 .. .1 .l 2 .. .. .f 91.51.11.11. '1.11.11. 51.02.12."I ..... I.J .9 .' ., .> .. 1 .1 .1 .. .1 .> .. .1 .' .' '11. 'I. 9l. 82.fll. 91.",.11. It. J I. )1.". -;1. "12. 1111. 91.] .' .J .. .. .1 .1 .\ .1 .1 .1 > 1 .' .1. e.I. JI.Q?.12.fll.t),.11 .0 .' .91. l.lI.?l.fI.!,e ", .3 .9 .' .J .2 ., .1 .1 .1 .1 .. .1 .> .. .. .. .01. l' .91..Hl.8 I. 91.l1. .' q I. 1.11. .. ? "2. ft I. ql.l .1 .. .. 1 .1 I .1 1 I .. .l J .. .f .91.11 .oz .,Z.II. 91.] 6 .h .. .'U. JI.9l ... Z.ftl.91. J .. .J .. .2 I I .1 .1 .1 2 .. .. .eu. ,1.92. fl2.11. 91.1 .9 .6 .. 6 91.l'.9'!. 82." 91.J .9 .. .. .J .2 ., 1 .1 1 .1 .z J .. .f .91.11.'= Z. "2. fl "I.] .6 .1 .6 .QI. ]1. ';2.12. ,.,. 91. J .9 .. .. .J .2 .. 1 .1 .1 .1 1 1 .. ;. ., f. .QI. '1.92.tl2."1.91.] .9 .' .1 .. .91.:U .-11 .,?" 1.91. J .] .2 .1 .1 .1 .1 1 .1 .. .2 J .. .f qa.ll.0Z.III.e c;,I.] .6 .6 .. ql. 11. 92. ez. JI 91.l .9 .J .2 .1 .1 ., I 1 .1 .. .. .. .f. .. .. .41. J .. iz.a2.el.VI.' .. .] .2 .. 1 .1 .1 .1 I .1 .' .1 .. .. .9 .. )1. 1.II.Ql.f&?IIiI., l .. .. .' .] .2 .1 .1 .1 .1 .1 II > .. oJ .. .C;I. J' .92.82.11. "1. ]1. .91. 1.11 .;;!.1?", 1.] ., f .J .2 .2 .1 .1 .1 .1 .1 .1 .! ., oJ .. .91.ll.97. ,,.. 8 9t.! 1.11. ll. 11. JI. 11.51. Q?. fIIZ.I 91 .l .9 .f .. .J .. .. 1 .1 .1 .. 1 .. .. .2 ., .. .-.QI "I. 11. 11.11.11.1" ",. "'Z. 117. 'II. 91.1 -. .. .J 2 1 .1 .1 I ., .. oJ .f. .'u .ll.fIIl. 1'-.82.11.9, .91. "'1. 91.', .91.91..1 ""1. 71.11.2 .f .J .. 1 .1 .1 .1 .1 1 .1 .. 1 .. .. .III.? 1.8 2. J'?. ql. 91. 91. H. 9 I. 9?,.t r ... Z.11 1.2 .S .. .. .' .2 .1 .1 .1 .1 I .1 .1 .l J .. .!; '1. 1 I. !'to l. '\$2. 92. "Z.I';o. IIIZ. '12." Z. Ill. "Z. 12. ('12.92. !III. 61. I ? .. .] .2 .1 .1 .1 1 .1 '. .' .. ., I 1. I\? "t2. 02. J2. It,. "2. e1'. II 2.U .ft2. 12. It,. ,1.!' I. 61 I .? .' .. .] .2 .1 .1 .1 .1 .1 .1 I .z .1 .' .. ...),.),. "'2. IS:? 12. 11 ... 2. '2. 7?. 51. It .. ] .. .. J .2 .. I .. .1 .1 .1 I .. .. J .. .. ; I.:" l.e2.52. J'Z. !i!."'. ". 14.51."I.l .6 .. ] I .1 .1 .1 .1 .1 .> .J .r, .r .Q 1I.61.1t, ."1.91. 91. 91. 9'.-11 .'w 81.l 1.1 .9 .' .' .J .. .. 1 .1 .1 ., 1 ., ., .. .1 .' .. .1 .",1. "1.9 t. ql. QI. fP I. 91.91. '-1. 61.) .. r .S .. 03 .2 .. I .1 .1 1 .1 .. .1 .2 .1 .' .' .r .91 1 I. ?I ] I .ll. II 11. 11 JI It 11 2 I. I .v .r .5 .' .2 .. .1 .1 .1 .1 ., .1 1 .1 .. .1 .1 .. .1 .91. II. I'. ]1.]I.ll. JI. ".ll.1I.11. I .r .. .. .J .. .2 .1 .1 .1 ., .1 1 .1 1 ., .1 0) .. ., .r .r .. .9 .' .. .. .9 .0 .9 .. .5 ., ] .. .. .1 I .1 .1 1 1 .. .. .. .. .. .. r .. .. .' .. .Q .9 ., .. .' .. oJ .2 .. .1 .1 .1 ., .. .. 1 .2 .' .. .. .. 5 .f 6 .. .. .. .. .f> .. ., .J .2 .2 .1 .1 .1 ., .1 ., .2 ., .2 .1 .. .. -.f> .b .. .. .6 h .. .. .1 .2 .:! 1 .1 .1 .. .1 .. .. .. .2' J .. .. .. .' .. .. .. .. J .2 .2 .. 1 .1 .1 .1 1 .1 .1 .1 .1 .. 2 .1 oJ .. ., .. .. .. .. .. .. .' 01 .1 .2 .2 1 .1 .1 ., 1 ., .1 .. .1 ., .1 .2 ol J .1 01 .1 1 .1 .. oJ .J .2 .2 .. .. .1 .1 .1 .1 .. .. .1 .1 .. .1 .2 .J ol J .3 J .1 3 .1 oJ .1 .1 .2 .1 1 .1 .1 .1 1 .. .1 .1 .2 .2 .2 .2 .2 .,. .l .l .2 ., .2 .2 .2 .2 .1 .1 .1 .1 .1 .1 1 .1 ., .. .. .2 ., .2 .2 .. .. .2 .2 ., .2 .1 .1 .1 1 .. .1 .. .. .1 .> .2 .2 .> 2 .. .2 .1 .. I I .1 I 1 .. .1 .1 ., .1 .. .1 ., 2 .2 .. .2 .. .2 .1 1 .1 .1 .. 1 .. ., .1 ., .1 .1 .1 I I .1 .1 .1 .. .1 .1 .1 .1 .1 ., .1 .. .1 ., .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 1 1 .1 .1 .1 .1 .1 .1 .1 1 .\ .1 .1 .1 .. .. .. .1 .1 .1 ,I I .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .. 1 .1 .1 .. .. ., .1 ...................................................................................................................... CO 1') Figure 5.9c -Map of transiti on zone. a = 0.05 m, T = 6.0 days, maximal ordinate = 2.84 m.

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't '1""""""""'" .......... + .1.. .... 1 ........ t """ 2 2 '3 ,.+] ,. Z t ., ,. .,t.,. 2 2 .l 1 ] 3 l. 2 2 2 4 6 6 6 6 6 6 6 .,. 6 Z ""1' '1"" 2 6 6 6 6 6 6 t,. 4 Z "",t '1' 2 4 ,0 11.,3 ,4 '4 .4 '6 ,] .2 '0. 2 '1' ... 2 .0 ,2.13 '4 '4 16 '4" J .2 10 4 2 +.+ t,' 2 '5' '2"5"""'1' 18""1""'15 2' U' 2 _5' 1""''''_'''15 II'" 2 .'t ,. 6 '11'" 18'14.10.19.19'19 .8 ] 6 ,] .I ..... J. f '11'" 18.,9"9"9"9"9 18."", 6 ., ,t.,. "'.1'.3. 6 '4'."19'19202020""'9""66 ., ., ,. 6 .,.,7"9"9 20 20 20"9"9'" '4 ']""'1' """'3' ,4""19 20 20 20 20'19'" '4 6 '1 ,. """.1+ 6 """'9 20 20'19'11 .t 6 .' 1 1 3. 6 .' 11 9 20 20 20 20 '0'.9 .e .t 6 .] +.1. ., ). 6 I" 20 20 20.,9 II '" 6 ., ,. ., ,. 6 ,4""'9 20 20 20 20 20'19'" ." 6 -I'""" ., ,6""19 20 20 20 20 20'19"7 ." 6 '3"1',., '1''''']' 6 '"'17''9''''' 202020"9'19." '4 e.] ,. ., ]. 6 """'9"9 20 20 20"9"9'" 6 """'1' +1"1"]' 'll'17 Ift'19'.9""'9.,9 .e .. ,.I, 6 .] ., ,. ( ,.,.,7 '8'",,] 6 'J""'" .,. Z .5. 12'15"7'1"'7 ,,,,,,,,,,,,,.5 12'5' 2 '1' .,. 2 '5' "'1"17"7'" 1"1""'1"'5 IZ'5' Z .,. .,. Z 4 10 IZ'" I' '4 '4 .,." 12 10" 2 .,. .,. 2 0 'l") '4 ." '4 '4 .".,J ,Z 10' ,. .,. '1"'. 2 6 6 6 6 ,6 6 .,." Z ,. '1"1' 4 6 6 6 6 6 6 6 _,." Z ., 2 2 ,]""",."""",], 2 I """ z ""]"l"]")""'" Z Z ""1' '1"1'" "1""" ,., "1' ., 1 .... """""1""""1' .1 .......... ...... .......... .......... ... ... .... ........ .... ..... ..... .... .... .......................... .... ...... ... ...... ........ ... .. Figure 5.10a -Map of drawdowns. a = 0.05 m, T = 10.0 days, maximal ordinate = 20.17 m. ();) W

PAGE 97

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I.I.' .1 .1 .1 .1 .a .1 .1 .1 .1 .1 .1 .1 1.'.Z.,.1'.2.2.2.2.2.1.1.1.1.1.1.1 .1 .1 .1.1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1.1 .1.I.a.I.I.I.I.I.I.'.I.1 .1.1.1.1.1.1.1.1 1 .1 1' .1 .t .1 .1 .1 .a .1.1.1.1.,.1 1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1,'.1 .1 1 .1 1 .1 .1 .1 .1 .1 .1 .1., 1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 1.1.1.1 1 1.1.1.1.1.1 1.1.1.1.1 .1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 .1 1 .1.1 .1 .1 .1 .1 .1 1 .,.1 .1.1.1.1.1.1.1.1., I.I.I.I.I.I.t.I.I.t.I.I.1 1.1., .1 .1 .1 .1 .1 1 1 .1.I,I.I.a.I '.a.I.I.I.I.t.t.I.I.I.I.I.I.I.1 .1' .1.1 1 .t 1 1.1 .a.. .1.1.1.1.1 I.t.I.I.I.I.I.I.I.I.,.I.I.,.l.I.. .1 1 .1 .1 .1 .1 .a .1 .1 .1 .1.1.1 I.I.I I.I.a.I.I.I.I.I.'.I.'.I.I.'.I.I.I.1 .1' .1 .1 .1 .1 .1 .1 .1.1 .1 .1 .1 1.1.1.I.t.I I.I.I.I.I.I.I.I.I.I.t.t.I.I.I.1 .1' 1 .1 .1 ., .a .1 .1 .1 .1 .1 .1 1.1.1.1.1.1.1.1.1.1.1.1.1.1.I.t.t.I.I.I.I.I.1 .1. .I.I.I.I.'.I.I.I.I.!.I.'.I.I.I.I I.I.I I.I.I.'.I.I.I.I.I.I.I.I.I.I.I 1' .1.1.1.1.1.1.1.1.I.t.I.I 1.1.1.1.1.1.,.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 .1, .1.I.t.l.t.I.I.1 .1 .1 .1.1 .1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 1 1. .1.1.1.I.a.I.I.I.I.t.I.I 1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 1. .1.1.1 I.I.t.I.1 .1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 1.1 .1.1.1.1.1 1. .1.1, 1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1. .1.1.1.1.1.1.1.1.1.1.1.1.1.,.1 1.1 1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 .1. .1.1.1.1.1.1 I.I.I.I.I.,.I.I.I.I.I.I.I.I.I.I.I.a.I.I.I.I.I.I.I.I.I.I.1 .1' .1.,.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.,.I.I.I.I.I.I.I.I.I.I.I.I.a .1' .1.1.1.1 I.I.I ,.I.I.I.I.I.I I.I.I.t.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I 1' f Figure 5.10b -Map of saltwater mound. a = 0.05 m, T = 10.0 days, maximal ordinate = 4.69 m. 0:> -t:>

PAGE 98

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Pl. ,.1 2.11. 51 .' .J .2 .z .\ .\ .\ .\ 0 \ I I .l ,-. .J ,. 71. h :"2:.13. 4]. 62. 12. 5;::. 52. "2. 52. 52. 52. 52.'", 63. 42. "1.51. .1 .J .2 .. .1 .1 .1 .1 .1 I .\ .z J .. ,5 .11.11.62. 4].5J.62. 'U. 91.11. '1. 7 I. '1.71.92.53. 6J .52.4 1.6,., .1 .5 .. .J .2 .1 .\ .\ .1 I .1 .\ .2 .] .. .5 .11.' I.' 2 '.53. 62. 51.9'. 71. ", ., I. 'It 7" 92. 53. el. 52 '.61 .1 .5 .' .J .\ .1 .\ .\ .1 .1 .\ .\ .2 J .. ."1,. 11,.,02. 4.".63.62. '1. 31. I' .11.11.31. 72.53. 63.62.' 61. I .5 .' .3 .2 .\ .1 .1 .1 .\ .\ .1 .\ .z .J .. .5 .a 1.11.62.43.63.62.51. 7a. ,1.11. ''''1.31. 7Z.SJ.fl.6Z.4 1.61.1 ..'5 .' .] .:! .1 1 .\ .1 .1 .\ .2 .l .J .. ,5 '\1.".1 .ft .r 71.62.41.' .. .. .5 .' ., .2 .2 .\ .\ .1 0 ., .1 .1 2 .' .' .. .. ."1. II. J'!.43.tl.e 2. 51. 71.1 ., '1'.11. 72.'53. 7l.fl2.4 71. I .5 J ... .z .1 .\ .1 .1 .. .1 2 ... .3 I '1.11. 72.1i1. 7l.f.2.41.".a .R .' .3 .2 .z .1 .1 .1 1 \ I 2 .. 01 .. al .11. 12.43.63. 7f. "".71. I .1 \ .11.11.12'.5]. 73.62.41.n.1 .-.5 ..J .2 .2 .\ .\ .1 .1 .\ .2 .? .J .. ,5 ." ..... 1,.4l.63.t-,. '51."'" .. .1 .11.11.72.53.7].62.41.71.' .5 .' .] .2 .2 ., .\ .1 1 .1 1 .2 .2 J .. ., .el.I' .72.4 J.t 3.4\2. 5,. '11. I .8 'I'. 11.7'.53.73. f 2. 41. ll. I .5 .5 .. .1 .2 .. .\ .1 .1 .1 .\ \ .\ .1- 1 ,.1.11. 62.4 J.61.t!lZ. 51.71.] I., 1.11. '1.11. 12.51.6l.t-2."'.61. I .ft .5 .. .] .' .\ .. .\ \ .' .\ .\ .\ .\ .2 J .. .81.' I.' !'.4 l.ft]. ef. '1. 31 .... I hi I. ll. 72. 53. 6J.fl.tl.oS'.1 .-.5 .J .z ., .1 .1 ., .\ \ .2 .. .11 I 51.91.11.11.' I. 71.71. 92."l.63.152. 41.61.1 .' .5 .' .J .2 ., ., .1 0 ., I .. .' .. .5 '1. II. "'2. 43.5J.'-2. '51. cH. 71.11. '1. '1.11. 92.53.f3.52.4, .61.1 .1 .5 .4 .J .. 1 .\ .\ .1 .1 .1 .2 .. .J .5 .71. a. 3.62.77. '5? 52. 52. 52.52.52. fl. 63 2. ll. !il. .' .2 .2 ., .1 .\ \ .\ .1 1 2 2 .1 .5 .71 2.]I.'I .1 .] .2 .. .1 .\ .\ .1 0 .1 .1 .\ 2 .1 .. .1 .91.42.13.2'. 7,. 7l. 11.?Z.I'.4 .9 J .2 .> ., .1 I .1 .1 .. 2: .1 .. .. .'i I." 2.13. ZJ. 7 J. 3.1,3. 71.63. "3.63. 7J.22.11.' .9 .. .. .3 .2 .z .\ .\ .1 0 I .1 .l 2 oJ .. AI.' 1.(,2.21.23.41. t;1.ftl.6l.6l.61.6J.153.'J. 22.2,.61.' .1 .' .J .z .? .1 .1 .. 0 .1 .1 .1 .. 2 d ,. .. .8 .3 .2 .2 .\ .\ .1 .\ \ \ \ .>. .>. oJ .s ., 2 2 .9 .6 .5 .1 .2 .2 \ ., .1 .1 ., .\ ., .z .J .. J I. 2 1.62. I Z. 32. 4Z." 2. '2.42.42'.42.42. J2. II .t 1.2' .q .6 .-. .2 .2 .1 \ .1 ., .1 .\ ., ., .' .J .' ." .' .t;, I. 11.41.51."1.61. ",., i. 11.61. ftl. 51.4 1 .9 .1 .5 .' .J .2 .2 .1 .\ .1 .. .\ .! .J .. .. .. f"I 1 11.4' '51.61 I. 1.1 61 '--I .51. 4 I. I .9 .r ., .' ., .! \ ., .1 0 .1 .1 .1 .1 .>. .2 oJ .' .< .91. 1.11.11.11.11.11.11.11. .9 .e .6 .5 .4 .J .. 2 .1 \ .\ .1 .1 .1 .1 ., l .7 .J .. .-.91. 1 t.II.II I.II.II.II .9 .. .. ., 1 .2 .2 .1 .\ .. ., 0 .1 .1 .\ 1 2 .2 ., .5 .. .. .r .f .8 .-... .r .r .6 .. .5 .' J .2 .. 1 .\ .1 .. .1 I \ .2 .2 J .. .5 11 .1 .7 .1 s .7 .7 .6 .. 5 .J .z .z .\ \ ., .1 .1 I .1 .. .2 .2 .1 .' .. .5 .5 .5 ., 5 .5 .5 .. .. 1 J .2 1 .\ .1 .\ .\ .1 .1 .\ .2 .. .. .J .J .' .' ., .5 .5 .5 .' .5 .5 .1 .3 .J .2 .z .2 1 I ., ., .1 .1 .1 .. .? .2 J .J .J .. .. .. ., .' .. 3 .J 03 .2 .2 .1 ., .\ .\ ., .1 1 .1 1 .\ .2 .2 .' .1 .J J .. .. .. .. .. .J J .J .2 .2 .2 .1 .\ .\ ., .\ .\ .\ .\ .\ .. 2 .2 .3 .1 .J .1 .J .J .J .2 .2 2 .. .2 .1 .1 .\ 1 0 ., .\ I .1 .2 .z .J ., .J .J J .3 .J .2 .2 .2 .2 .2 .\ .1 .\ .\ .\ 0 1 1 .. ., .1 .\ .. .2 .2 .o. .2 .2 .. .2 .2 .2 .2 .2 ., ., \ .. .. .1 .1 .1 .1 .1 .\ 2 .2 .2 .2 .2 .2 .2 .2 .2 .. \ .\ .1 .1 .\ .. ., .1 .1 .1 .1 .\ .1 .. 1 .2 .. .2 .\ .\ .1 .\ .\ .\ .\ .1 .\ .1 .1 ., ., .1 .\ \ .. 1 .1 \ .2 .2 .2 .1 .1 I .1 \ .\ \ .1 I .. \ \ .1 .\ .\ .1 .1 .\ .\ .. \ .\ .1 .\ .1 .\ .\ ,I 0 .. .1 .1 ., .\ .1 .1 \ .\ I \ .1 .1 .\ .1 I I .\ .1 .0 .\ .1 .1 I .\ 1 I \ ., .1 .1 \ .\ .1 .\ .1 .1 .1 I I \ .1 .1 .1 .\ .\ .\ .\ 0 I .. \ .\ I .1 \ \ 0 I .1 .1 .1 .1 .1 .\ .1 .. ....................................................................................................................... CO UI Figure 5,lOc of transition zone. a = 0.05 m, T = 10.0 days, maximal ordinate = 3.67 m.

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t.t t. .......... 1. ...... ... 1. .... ..................... 1 1 ........ 1. ............. ,tI 1 ,tI. ...... I I I I I I I ..... "' I I I I I I .... + I I a I I I ". "t I I a I .... .. .... ,.. I I 2 ... tI. .1 2. '2' '1"" a I I I ., ....... I I I .... ,. I I I .... .. t I I I I J '."'t ....... I I tt I '2' .... ,. ., I a I I I t ., I I I I I ., I I I I Z I ...... I I I I t ,. I I I I I I' ""1' '1"1" I I I .......... tt II' ................... ............ ................ 1 It I ........ I. t I I ,.t fl ff t t f Fi gure 5.11 a Hap of dra\'1downs. N = 0.01 m/day, T = 2.0 days, maximal ordinate = 2.00 m. CO 0)

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t ................... t ..... tt .......... t t ..................... ................ .............. t ............. f .... t ............... 4o ...... f ff404o .......... .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., ., ., ., ., ., .1 .. ., ., ., .. ., ., ., ., ., ., ., ., ., .1 ., ., .. ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., .. ., ., ., ., ., .1 ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., .1 ., ., ., ., ., ., ., ., .1 ., ., ., ., ., ., ., ., ., ., .1 ., ., ., ., ., ., ., .1 ., ., ., .. ., ., ., ., ., , ., ., ., ., ., ., ., ., .. .. 1 .. ., ., ., ., ., ., .. ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., .. ., ., ., ., ., ., ., ., ., .1 ., ., ., ., ., ., ., ., ., ., ., .1 ., ., ., ., ., .. 1 .1 .1 ., ., ., .. .1 ., ., .. ., ., .1 ., ., ., .1 ., ., ., ., ., ., ., ., ., ., ., ., .1 .1 ., ., ., ., .. ., ., ., ., .1 ., ., ., ., ., ., ., ., ., ., .1 ., ., .. 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., ., ., .1 ., ., ., ., .1 ., .. ., .0 ., ., .. .. .. ., .1 ., .1 .1 ., .1 .1 1 .1 .1 .1 .. ., .1 ., ., ., ., ., .. ., .1 ., ., ., ., ., .. 1 ., .1 ., ., ., .. ., ., ., .1 .. 1 ., 1 .. ., ., ., .1 ., .. ., .. .1 .. ., ., .1 ., .. .. .1 .1 .1 .. .1 ., ., ., .1 1 .1 .1 ., ., ., ., ., .. .. ., .1 .1 .. ., ., .. ., ., ., ., ., ., ., .1 ., .1 ., ., .. .1 ., ., ., .. ., 1 ., .1 .1 ., .1 ., 1 ., .. ., ., .1 ., ., .. ., ., .. .. .. .. 1 ., ., ., ., ., ., ., ., .. ., ., ., ., .. .. .. ., ., ., .. 1 ., ., .. ., .. ., .. ., .1 ., ., .. ., ., .. ., ., ., ., ., ., ., ., ., .. ., ., ., .1 ., ., ., ., ., ., ., ., .. ., ., ., ., ., ., ., ., ., ., .1 .. .1 ., .. 1 ., ., ., ., ., ., ., ., ., ., ., ., .. ., .. 1 ., ., .. ., ., .. ., .. ., ., ., ., ., ., ., ., ., .1 ., ., ., .. .. .. ., ., .. ., ., ., ., ., ., ., ., ., .1 ., .1 ., ., ., ., ., .. ., ., ., .. .1 ., .1 ., .. ., ., .. .. ., ., ., .. ., ., ., .. 1 ., .1 ., .. ., 1 ., ., .. ., .. .. ., .1 ., .. ., ., ., .1 ., ., ., .. ., .. ., ., ., ., ., ., ., 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.1 .1 .1 ., ., ., ., .1 ., .. ., .. .. ., ., .1 ., .1 ., ., ., ., ., .1 ., ., ., ., .1 ., .. ., ., ., .1 ., ., .. ., .1 1 .. ., ., .1 ., .. .. .. .. .. .. ., .0 ., ., .. ., .. ., .. ., .. ., .1 ., .1 ., ., .1 ., .. ., ., ., ., ., ., ., .1 ., ., .1 .1 .. 1 ., ., .1 .1 .. ., ., 1 ., .1 ., ., ., ., .. .. .. ., .. .. .1 ., .1 .. .1 ., ., .. .. ., ., .. ., .. ., ., .. ., ., .. ., ., ., ., .. ., ., ., ., .1 .. .1 .1 .. 1 .1 .1 ., .1 .1 ., ., ., .. ., .. .1 ., ., ., ., ., ., ., ., ., ., .1 ., ., .1 ., .1 ., ., .1 ., .1 ., .. ., ., ., ., .. ., ., ., ., ., .1 .. ., ., .. .. ., .. .. ., .1 ., ., .. .. ., .1 ., .1 ., ., ., .1 .. ., .1 .. .. ., ., .1 .. ., ., 1 .. .1 ., .1 .1 .1 ., .. ., .1 ., ., ., ., ., .. ., ., ., ., ., ., 1 .1 ., .. .. ., .. ., 1 ., ., ., .1 .1 .. .1 ., ., .. ., .. ., .. .1 ., .1 .1 ., ., .. ., ., .1 ., ., .. ., .. ., ., ., ., .1 ., ., .1 ., ., .1 .1 .1 ., ., ., .1 ., .1 .1 ., .1 ., .. .. ., ., ., ., .0 ., ., ., ., .. .1 .1 .1 .1 ., .1 ., .1 .1 .1 ., ., .1 ., ., ., .. .1 .. ., ., ., ., ., .. ., ., ., .. ., ., .. ., ., ., .1 ., .1 .. ., ., ., .1 .' ., ., .1 .. ., .. .. .1 ., .. .. ., .. ., ., .. .. ., .1 ., ., ., ., ., .. .. ., ., ., .1 .1 ., ., ., .. 1 .1 ., .. ., ., ., .. .. .1 ., ., .. .. ., ., ., ., ., ., .. ., .. ., ., ., .' ., ., .1 ., ., ., ., ., .1 .1 ., .1 ., ., ., .1 ., ., ., .1 ., .1 ., ., ., ., ., ., .. ., .. ., ., ., ., ., ., 1 ., .. ., .. ., ., ., .. ., .. ., ., .. .. ., .. ., ., ., ., ., ., .1 .1 .1 ., ., .1 ., ., ., ., ., ., ., ., .. .. ., ., ., ., ., ., ., .. ., ., .. ., .1 .. ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., .1 ., .. ., .1 ., ., .1 ., ., ., .' ., ., ., ., .1 .1 .. .1 ., .. .1 ., .1 .. ., ., ., .1 .. .! .1 ., ., ., ., ., .1 ., ., ., ., ., ., ., ., .1 ., ., .1 .1 ., .1 ., ., ., ., ., ., ., ., .1 .1 ., ., ., .. ., .1 ., .1 ., .1 .1 ., ., ., .. ., .1 ., ., .1 ., ., .1 ., .1 ., .1 .1 .1 ., .1 .1 ., ., ., ., ., ., ., ., .. 1 .1 .. ., .1 ., ., ., ........................................ f .......... 4o ......................... t f f ..... f f ........ 4o" ft f. CO '-l Fi gure 5.l1b -Map of saltwater mound. N = 0.01 m/day, T = 2.0 days, maximal ordinate = 0.09 m.

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...................................................................................................................... 1.1.1.1.1.1.1.1.1 .1.1.,.1.1.1.1.1.1,1.1 .1 .1 .a .J .2 .Z .2 .2 .2 .2 .2 ., .2 .1 .1 .1 .1 .2., .2 .1 .2 .2 .2 .1 .2 .1 .1' .1 .1 .1 .1 .2 .2 .lI .J ., .lI .1 .lI .J .1 .lI .lI .11 .1 .1 .1 .1 .1.1 .2 .2 .3.1., .J ., .l .1 .1 .lI .lI .J .1 .1 .1 .1 1 .1 .2 .l .lI .4 .... 5 .5 ., .5 .5 .5 .4 .t .lI ., .2 .1 .1 1 .1 .2 .1 .1 .' 5 .5 .S .5 .S .5 .5 .lI .2 .1 .1 1 .? .J '5.6.7.1.7.7.1.1.7.7 .r .6 .S .4 .1 .2 .1 1 .2 .J 5 .6 .1 .7 .1 .r .1 .1 .1 .r .1 .a .5 l .2 .1 .1 .2 .1 .4 .5 .r .91. I. 1.11 ....... 11.11. I 9.r.5.4.l.,.1 .1 .2,1 '5 .7 ,91. I. 1.11.11.11,11.11, I 7.5 ,2 2 .] "1. 1 51.51.0 ... I .l .2 .) .5 .11. 1 1,5 51.61.61.111.01.61.51.51 1 r.".1.2.1 .1 .1 .,J .4 .6 .91 .. 61 6 .' .1 ,2 .1 .1 .l .1 .4 .6 ,QI.fI,.01.61.61.61.61.6h61.61.61.61.61 9 .6 .4 .1.2 .1 .1 .2 .l ..... "1. 1.51.61.21.11,11.11.11.11.11 ,21.61.51 ,.'5.1.2.1 ,I ,2 .1 .5.11 51,AI.21.11.1I.1I I.II.tl.II.21.61.5, 7, J.2., .1 ,2 .l .5.11. 1.61.61 a .r .r .1 .' ., ....... 61.61 r.5.1.2.1 .1 .2 .l .'5 .11. 1.6 61.1 ,.7., .r .7 .e 11.61.elt .1.'5.:1.2.1 2 .3.'5.11.11.61.61.1 .11 .6 .S.5 .'1 .6 .el 1.61 ...... r .'.1 .l .1 .1.2 .J .00; .71.11.61.61.1 .a.6 .'.5 ., .1.,II ,.el.1 .1 .'5 .J .2 .1 .1 .2 .J .5 .11.1 61.61.1 ,r .5 1 .11.11.01.e.1.1 .1.5.1.2 .1 .1 .2 .3 .' .11.1 61.61 .... t .J 5 .?I .... 61.lol.1 .7 ., ., .2 .1 .1 .2 .,J .'5 .11.11.61.61.1 .r ."1.1.1.1.'5 ,71.1I,61.el,1 .7.5.1 .2 .1 .1 .2 .' .,!'II .11.11.61.61.1 .7.5.] .1.1 .S .' .. 11.61 1t r.'5 .1,.2.1 .1 .2 .J ,;, .,I.II.el.e 1 .' .5.' ., .e .5 .7I.1I.61.f 1 .r .'5 .J ., .1 .1.2 .l ."1 ,'I.II.61.AI.1 .r .5 ,4 ,J .... .'1.11 ....... 1 .r .S.l.2 .1 .1 .2 .J .5 .11.11.61,61.1.8.0., .5 .'5 .4 .11,11.61.61., .r .5.1 .2 .1 .1 .2 ., ."" .71.11.61.61.1.8.6.5.5., .6 .8 1I.61.t'1.1 .7., .1 .2 .1 .t .2 .J ."" ,71. 1.61,61.1 r .1 .1 .1 ., 1.5.J.2.1 .1 .2 .:t ,,,,, .11. l.fl.61.1 .ft .7 .r ., .1 .r 1.11.61.61 1 J ,2 .1 .1 .2 .1 .5 .11. 1.51.61.21.11.11 .... 11 .... 11.11.21.61." ... r.s .2 .1 .1 .2 .1 .'!I .n ... 51.61.ZI .... II.II.II.II.II.II.2I I.' r"".7.1 .1 ., .1 ..6 .91 I 1.61.61.61.61.e I.AI 9 .6 .' .1 .2 .1 .1 .2 .J .4 .'a .91 '.61.61.61.61 1.61 61 .... '1.61 '''., .' .2 .1 .1 .2 .J .'5 ,'I. 1.41.'\1 ..... ,.'.61.61.61.,.1.'1.51 7.'5.1.2 .1 .2 .l ., .11. 1 1.51.51.61.61.el.61.61.51.51 I r."I.,.2 :: :: :; :; :: .1 .l .1 5 ," .r .r .' .7 .r .r .r .1 .r .6 .5 1 .1 .1 .t .J .1 .4 ., .6 .7 .1 .1 .r .r .r .r .r .1 .a .5 ._ .J .2 .1 .1 .2' .1 .J .t '5 ."S .'" .5 ., .5.5.4.4.1 .J .z .1 .1 .1 :: :; :; :; :: :: :: :: .'. .1 .1 .l .2 .1 .1 .:1 .J.J.J.J.l.,.l.).2 .2 .1 .1 .1 .1 .il .2 .1 .2: .a .1 .z .z .a .2 .2 .1 ,I .1 .1 .il .2 .2 .Z ., .J .Z .il .a .il ., .1 .1 .1.1 .1 .1 .1 .1 .1 .1 .1 .1.1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ff Figure 5.11c -Map of transition zone. N = 0.01 m/day, T = 2.0 day, maximal ordinate = 1.50 m. 0) W

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f ................................................................................................................. .. .... ........... .......... ,.. .. .1 ............ ,......... ....... .............. I.",., .. ,. ., .. .. .. .. .. .. .. .. .. ,.... .. ., ,. 2 a 2 Z Z Z I Z 2 .... '. ...... 2 Z Z Z I Z Z ...... J Z Z I I Z I., ,. ,. Z Z Z I 2. Z 2 Z ...... .. .,.... Z I Z 2 Z Z 2 r .1.... ., It Z I Z I 2 Z 2 I ,. f .,tt,f Z Z 2 Z Z I I I .'f.'. f' ,. I: Z Z Z Z Z 2 ,...... .... ,. Z 2 2 2: I Z Z I .... ,. ,. I I 2 I Z 2. Z Z ,. ...... I Z Z 2 2 Z Z I .... ,. .,.... I 2 Z Z 2 Z ,.,.... ....... I Z 2: Z Z I Z I ...... ...... Z 2 2 Z 2 Z 2 Z .'tt,t ., ,.. Z I Z Z Z Z Z Z .,., ... .... ,. Z Z Z Z Z 2 Z Z ...... .... ,. 2 Z 2 Z Z Z Z Z ., .. .. ,. Z Z Z I Z I Z I ., f' ttl ..... It .. f ., ........................ tI.tI. ............. .......... +,+ .... ........ ........ ... ................................................................ ...................................................... Figure 5.12a -Map of drawdowns. N = 0.01 m/day,T 6.0 days, maximal ordinate = 2.01 m. 00 'D

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...................................................................................................................... .1 .1 .. 1 .1 .1 .. .. 1 .. .1 1 1 .. .. 1 .. 1 .. .1 .. .. .1 .1 I .1 .. .1 .. .. .. .. .. 1 .. .. .1 .. 1 .. .1 .. .. .. .. .. .. .. .. .. .1 .. .. .. .. .. .1-.' .. .. ., .. .. .1 .1 I .. 1 .. .. .. .. .. .. .. .. .1 .. .. .. .1 f f .. 1 .1 .. 1 .1 .1 .. '.' .1 .1 .1 .. I .1 1 .. 1 f .. .1 1 .. .. 1 .. .1 1 I I .1 1 .. .1 1 .1 .. ., I f I ., .. .1 .1 .1 .. .. .. .. 1 I I .1 .. .. .. .1 .1 .. 1 .1 .. .1 I f .1 ., ., .. ., .. .1 ., ., .. .. ., .. ., .. .. .1 .1 .1 .. .. . .1 .. .. f .. .. I .. .. .. .. .. .. .. .. .. .. 1 .. .. 1 .1 I .1 .1 .1 .1 .1 .. .. I ., .. .. 1 .. .1 .1 .1 .1 .. 1 1 .1 .l .1 1 .. .. .1 .. 1 ., .1 .1 .. .. .1 .1 .1 .. 1 .1 .1 .. ., .. 1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 1 .. .1 .. .. 1 .. 1 ., .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 I .. .1 ., .1 .. ,. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .. .1 oJ .1 I .1 .1 .. .1 .. .. .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 I .1 I .. 1 I .1 .1 .1 .1 .1 .1 .. f f .1 .. .. .1 .1 .. .. .. I .1 .1 .. 1 1 .1 .1 1 .1 .1 I .. .1 .1 f .1 .. .1 .1 .1 .1 .1 .. .. .1 .1 .1 .1 .. 1 .. 1 .. 1 .. .1 .. .. .1 1 .1 .1 .. 1 .. .. .. .1 .. .. .. .. .. 1 1 I .. .. .1 I .1 f .. .. .. .1 .. .1 .1 .1 .1 1 I .1 1 .. .. .. 1 .1 .1 .. 1 .. .1 .1 .1 .1 .1 .. .1 f .1 I .1 .1 .. .. .1 1 .. .. .1 .1 .1 .1 .1 .. 1 I .1 .1 .. .1 .1 I 1 I ..1 I .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .. .1 .1 I .1 1 .1 .1 .1 oJ .1 .1 1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 1 .1 I .1 I .1 .1 I I I .1 .1 I .1 .. .1 .1 .1 f .. .. I .. .1 .1 .1 .1 .. .. ., .1 1 .1 I .1 .1 .. 1 .1 .. .. ., 1 .1 .. .. .1 .1 .1 .1 .1 1 1 .1 .. .. .. 1 .. .. .. .. .1 .. .1 .. I .. .. I I .1 .. .. ., .. .1 .. f .. ., .. .. .. .. 1 .1 .1 ., 1 .. .. .1 f .. .. .1 .1 1 .1 .. .1 .. 1 ., .. ., .1 .1 .1 .. .1 .. 1 .. .1 1 .1 I .1 .1 .. .1 .1 .1 .. 1 .1 2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 I .. .. 1 .. .. f .1 .. I I 1 .1 .. 1 .1 .1 .. .. .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .1 .1 .1 .. I .. .. f 1 .1 .1 .. .1 .. 1 .1 .. .1 .1 .1 .. J .3 .J J .1 .J oJ .J .2 .1 .1 .1 .. .1 .1 .1 .. .. .1 .1 .. f 1 .. .. .. .. 1 .1 .. .. .. .2 .J .J d .J .J .2 .. .. .. .. 1 .. .. .. .. .. .. I .. .. .. .1 .. 2 .J .J .J .1 .1 .. .J oJ .2 .. .. . .. .. 1 .. .. f .1 .. .. .. .. .. .. .1 1 .1 .. .2 .J .J .1 J .J .2 .. 1 .. I .. I f .. I I I .. 1 .. 1 .1 .1 .2 .3 .J .1 .1 oJ .J .J .3 .2 .1 .. 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .2 .J .J .J oJ .J o'J .3 .J .3 .2 .. .. ., .1 .1 1 .1 .1 1 .1 .1 .1 .1 1 .1 .. .1 .1 .1 1 .. .1 .2 .J .J .3 .J ol .3 .2 .1 .1 I .1 .1 -I 1 .. .1 f .1 .1 .1 .1 .1 .1 I .1 .1 .1 .2 .1 .1 .1 J .J .3 .J .1 .1 .1 1 .. .1 .. 1 .. .2 .3 ,J .J .J .1 .J .J .2 .1 .. 1 .1 1 .1 1 I 1 .1 .1 .1 .1 I .2 .3 .3 .J .1 .J .J .1 .1 .J .1 .1 .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. 1 .. .2 .J .J .J .J .J J .1 .1 .J .2 .1 .. .. .. .. .. 1 .1 1 .. .1 .1 .1 .1 .3 .J .1 .J .J .J .J .J .J .1 .1 .1 I .. 1 .. .. .1 1 .. .1 2 .J .3 .J .J .J oJ .J .1 .2 1 .. .1 .. .. .. .. .. .1 .1 .1 .3 .1 .1 01 .3 01 .J .1 .1 .1 1 1 .1 .1 .1 .1 .1 .. I .1 .. 1 .2 .J .J .J .3 ol .1 .3 .J .1 .2 .1 .1 .1 I .1 .1 .1 1 .. .1 .1 .. 1 .1 .. .1 .. .2 .J .J ol .J J ol .J .3 .2 .1 .1 .. .1 .1 .. .. .. .. .. I .1 .. .. .2 .J .J .J .J J 01 .1 .J .J .1 1 I .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .. 1 .1 .J .J .3 .J .J .J .J .J .3 .1 1 1 1 .1 .1 .1 .. .. .. .1 .. 1 .1 .. .. 1 .1 .2 .? .2 .2 .2 .2 .2 .2 .2 .2 .2 .. I .. 1 .. 1 .1 .1 1 .. I .1 ... .. I 1 .1 .. .1 1 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .1 .1 I .1 .1 .. .1 .. .. 1 1 .. .. 1 .. 1 .1 .1 .. .. .. .. .1 .. 1 .. .. .. .. .. .. 1 1 .. .. I .. .. .. .1 .1 .. .. .1 1 .1 .1 .1 .. 1 .. .1 .. 1 .. .1 .1 .1 .. .. ., .1 .1 .. .1 .1 .1 I .1 .. 1 .1 .1 .1 .. I I I .1 .. 1 .1 .. .1 .. .. .1 .1 I .1 .. .1 .1 .1 .. 1 1 .1 .1 .1 1 .1 .. .1 .1 1 .1 .. .. .. .1 .1 1 .. .1 .1 .. .. .. .. .. .. .. .1 .1 .1 .. 1 .1 .1 .. .. .1 .. .1 .J . .1 .. I .1 .. I .1 .1 .1 .1 .1 .1 .. .. .1 .. I 1 I .1 .1 1 1 .. .. oJ .1 1 .1 .. .1 .1 I oJ .1 .1 .1 .1 .. .. I .. I I .1 .1 I 1 .1 .1 .1 .. 1 .. .1 I .1 ,I .1 .1 .. 1 1 .1 .. .. .. 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .. .1 ., .. .. .1 .. .1 .. .1 1 1 .1 .. .1 .1 .. .1 I .1 1 .1 .. .. .1 1 .. .1 .1 .. .. .. .. 1 .. 1 .1 f .1 .. .. .. .. .1 .1 .1 .1 1 I 1 .1 I 1 .1 .1 .1 .1 .. .1 .1 .1 1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 .1 1 I .1 .1 .1 .J I 1 1 .1 .. 1 I .1 1 .1 .1 1 .1 .1 .1 .1 .. .1 .1 .. 1 .1 1 .1 .1 .. .. .. .1 .1 1 .1 .1 .1 1 1 I .. .1 1 .. ., I .1 .1 .. .1 .1 .1 .1 1 1 .1 .1 .1 .1 .1 ,I -.1 .. .1 I .. f ,.1 .. .. .. .1 .. 1 .l .1 .1 1 1 .1 .. .1 .1 I 1 1 1 I .1 .. .. .. .1 .. .1 .1 .1 1 1 .1 .1 .1 .. I .. .1 .. .1 .1 .. 1 .' .1 .. .1 .1 .1 f .. 1 1 1 .. .1 .1 .1 .1 1 .1 .1 I 1 .1 .1 .1 f f I .. 1 .1 .. 1 .. 1 .. .1 .1 .. .1 .1 f f .. 1 .. .. .. .. .1 .1 .1 .1 .. .. .1 f f .. I .. .1 .. .. .1 .. 1 .. .1 .1 I I .1 .1 I I 1 1 .1 .. .. .. .1 .. .. 1 .1 .. .. .1 .1 .1 .1 .1 .. I .. 1 I .1 I .1 .1 .1 .. .1 1 .1 .1 .1 .1 1 .1 I 1 I t .t t Figure 5.12b Map.of saltwater mound. N = 0.01 m/day, T = 6.0 days, maximal ordinate = 0.28 m. \.0 a

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'. .................................................................. .1.1.1.1.1.1.1.1.1.1.1.1.1 f t .1,1.1.1.I.t.I.I.I.I,I,I.1 .1 .1 .2 .2 .2 .2' .,2 .2 .2 .2 .2 .2 .2 .2.2 .1 .1 .1 ,I .2 .2 .2 .2 .Z .2 .2 .2 .2 .1.2.2.2,1 .1 .1 .2 .2 .2 .3 .J .l .J ., .1 ., .1 .11 .3 .3 .2 .2 .2.1 .1 .2 .2 .2 .1 .1 .1 .l .J .] .J .l ., .1 .1 .2 .2 .2 .1 .1.2.2.'.' .. 4 .. 3.'.2.2.1 t ,I .l .2 .J .l 4 4 .6 .4 .4 .4 .e ._ .4 .1 .1 .z .2.1 .1 .2 .2 ,3 .4 .4 .5,6 .f\ .6 .6 .6 .6 .6 .6 .6 .S .4.4 .J .2 .2 .1 .a .2.1 .4 .4 .6 .6 .6 .6 .6 ,6 .6 .6 .6 .S .4 .4 .l .2 ,2 .1 .1 .2 .J ..5 .lo .7 .a .9 .9 .9 .9 .9 .'9 .9 .8 .1 .6 .5 .ot .J .2 .2 .1 .1 .2 .2 .1 .4 ., .e .2 .1 .1 .2 .2 .1 .... .7 .91.11.21.]1.31.31.31.11.]1.11.ZI.1 .9 .7 .5 .t .1 .'1 .2 .1 .1 .2.2 .1 .1 .iJ ,7 .91.11,21.11.U .11.1t.U.11.JI.21,1 ,9.7.5,' .J .2 .2 ,I .1 ,2.] 5 .7 .91.'1,61.81.91.91,9 91.91.91,91.81.61.J .9 ,f .5 1 .2 .1 .1 .2 .1 .4 .-.; .7 .91.11.61.81.91 .. ?t.91.91.91,'l,91.81.tl,l ,9 ,7 .'S J .2 .1 .1 .2 .2 .1 .(-, ."lI.ll,ftZ.S2.7Z,ft2.",.IIZ.aZ.IIZ.aZ.8Z.7Z.51.fI,.3 ., .6 .4 .J .2 .2 .1 .. 1 .2 .2 .J ... ,6 .91 .. ll.BZ.'!IZ.77.8,!,82.ftZ.eZ,.Z,82.IZ.7Z."I.I!I,3 .9.6 .t .3 .2 .2 .1 1 .2 .1 .4 .5 .11.11.62.52.92.12.82.112,82,82.82,82,12.7Z.92,51.61.1 .7.5 .' .1 .2 .1 1 .2 .1 .t .'5 .11.11.62.52.92.72.82.&2.82.82.82.82.82.72.'92.51.61.1 .7., .4 .J .2 .1 1 .2.1.4 .6 .8 .f .t .] .2 .1 1 .2 .] .t .,. ''I.''2.12.12.71.fll.Z .8.1'11 .4 .1 .2 .1 .1.1. .1 .4 .t. .QI.11.9Z.aZ.el.91.51.11.11.JI.JI.'I.'1.9Z.8',ftl,91.1 .9.1\ .4 .3.2.1 .1 .2 .1 .' .t .QI.11,92.8Z.81.91.51.31.JI.JI.'I .J1.51.92.et2.81.91.1 .9 .6 l .2 .1 .1 ,2 ., .4 If: .'::11 ..... '2.82 1.111.11. ,9.9 .el. 1 .11.92,.Z.RI.91., .9 .6 .4 ., .2 .1 .1 .2 .) .t .1I 9.9 .91. 1.11.9l."2.81.'II., .9 .(!! .t .3 .2.1 .1 ,2 .1 .t ,6 .CJI.11.92.BZ.81.91.' .9 .& .iJ .6 .91.ll.92.fl2.",.91.3 .9 .6 ., .3 .2 .1 .1 .2 .J .' .Q .6 .5.6 .91.11.9Z.SZ.PI.'I., .9 .4 .3 .2 .1 ,I .2 .J .4 ." .'9I.'1,92.8Z.81.91., .9 .5 .1 .S .91.31.92.a2.el.91,' .9.6 .4 ." .2 .1 .1 .2 .3 .4 .6 ,91.31.9z.eZ.".QI.3 .9 .5 .1 .9.6.4 .l .2.1 .1 .2 ,1 .t .6 .91.11.9z.e2.1I1.91., .9 .ft; .6 .91 .11.92.ft2.81.91., .9 .6 .4 ., .2 .1 .1 .2 .J .4 .f" .91.ll.92.fH!'.IU.91.l .q ,6 .S .6 .91,'1.92.8Z.81.91.' .9 .6 .t .l .2 .1 .1 .2.1 .4 .f .QI.'1.9z.ez.el.91.11 9.9.'1. l.ll.9Z.RZ.fH."." .9 .f. .t .1 .2 .1 .1 .2 .1 6 .QI.'1.9Z.12.ftl.91.11 9.9.91. 1.31.92.82.81.91,' .0 .11 .4 .3 .2 .1 .1 .7 .J .t .f. .OI.31.9Z.!lZ.81.9'.5 JI.31.ll.1,.11.SI.92,12.fll.91.3 .e .6 .4 .3 .2 .1 ,1.2:.J.4 .6 .91.3 ... 2.82.81.91.51,31.31.31.11.11.51.9Z.82.8 91.' .9.6.4 ,1 .2 .1 .1 .2 .1 6 .1!I1.21,eZ,12.l'Z.J1.91.91.91.9 t.91.9Z.12.7z.11,al.z .e .f .4 ., .2 .1 .1 .=' ." ., .f .8.6.4.1 .2.1 .1 .z .1 .4 .5 .11,11.62.'52.92.'Z.82.12.82.ft2.82."2.12.7Z.92.51.61.1 .7 .4 .3 .2 .1 .1 .;0 .1 .t .! .11,11.6Z.S2.92.72.If'Z.ftZ.ftZ,82.II?.ez.fl2.'Z.9l.51.61, 1.5.' .3 .2 .1 .1 .2.2: .l .4 ." .91.l .9 ,6 .4 .1 .2., .1 .li! .2 .l .4 .6 .(n.3 .9 .6 1 .2 .2.1 .1 .2 .1 .4 ., .9 .f 5 .t .1 .2 .1 .1 .l. .l ,4 .'5 .1' .91.JI.61.15I.91.91.91.91.9 91.91.1 61.3 .9 .1 .5 .t .1 .2' .1 .1 ,2 .2 .l .4 ., .91.1I.21.31.11.31 .11.3 'I.3I.21.1.9.f .S .t .3 .2 .2 .1 .1 .2 .l .t ., .91.II.ZI,JI.11.31.31.31.31.31.21.1 .9.1.5.4.3 .Z .2 ., .1 .2 .2 ., .4 .5 .f ., .e .9 .9 .9 .9 .9 .9 .9 .1 .7 .eo .5 .4 ,J .? .2 .1 .1.2 .:! .1 .4 ,5 .f-.1 .ft .1) .9 .9 .11 .9 .9 .9 .8.7.6.5.t .l.7. .2 .1 .1 .;! .2 .4 .4.5.6.6 .6 .6 .6 ,6 .6 .6 .6 .s ] .2 .2 .1 .2 .l .l .' .t .5 .6 .6 .6 .6 .f .6 .6 .6 .6 ,5 .' .4 .3 .2 .2.1 .1 .z .1 .l .) .4 .4 ,t .4 t .t .4 .t .4 .l .1 .1 .2 .1 .1 .2 .1 .1 4 .4 .t 4 .t t .4 .] .l .2 .2 .1 .1 .2 .2 .2 .] .1 ,3 .1 .1 .1 .J .,.J .3.1.2.2.2.1 .1 .2 .2 .2.3 .l .J ,1 ., .1 .3 .3 ., .] .J .2 .2 .2 .1 .1 .1 .2 .2 .Z .2 .2 .2 .2 .2 .2.2.2.2.2.1 .1 I I .2' .2 .2' Z .2 ,2 .2 Z .2 ,2 .2 Z .2' I I .1 .1 .1 .1 .1 .1 .1 .1 .1 .t .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .t .1 .1 .t .1 .1 ........................................................................................ Figure 5.12c -Map of transition zone. N = 0.01 m/day, T = 6.0 days, maximal ordinate = 2.82 m.

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t ., ., ..... .. ............... .......... ............... ......................... ...... ....... .. .............. ...... t t 2 2 2 2 2 Z 2 Z 2 "'t,t ... 2 Z 2 2 Z Z 2 2 2 .... It ., Z Z 2 Z 2 Z Z 2 ... t,. ., ,. 2 Z Z Z I 2 Z Z 2 t, ,. .' ... t, 2 2 2 Z 2 2 Z 2 ., ,. ., I 2 2 Z Z 2 Z 2 Z ., ,. :::::: = t = = : = : = = :::::: z Z Z I 2: 2 I J I ,. "",1 Z Z I 2 Z 2 2 Z J ,. t',,'1 2 I 2 Z Z I Z .'.t,. Z Z Z Z Z 2 2 Z I ., ., ,. 2 Z I 2 2 2 Z I .,.t'l ., ,. 2 Z Z 2 2 Z 2 Z Z .... ,. ., ,. I 2 Z 2 Z Z Z t't.,. .... ,. 2 Z J Z 2 2 Zit, ., ,t Z Z 2 2 z 2 2 2 t"'" ...... 2 Z Z 2 Z J 2 2 ,t t ,. ., """",ft"'""",I.,1 ., 1 ........... ........... ,. .... ""'.' .. '.I ... ,.t , t Figure 5.13a -Map of drawdowns. N = 0.01 m/day, T = 10.0 days, maximal ordinate = 2.02 m.

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f. t ..................... i .................... + ................. + .......... t ...... t .......................................................... .1 .1 .1 .1 .1 .1 t .1 .1 .1 .1 I .1 I .1 .1 .\ .1 I .1 I .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 I I I .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ,I .\ .\ .\ .\ .\ .\ .1 .\ .\ .\ .\ .1 .1 .\ .1 .\ .1 .1 I I .1 .1 .1 .1 .1 ., .1 .1 .1 ., ., ., ., ., ., .1 ., .1 I ., ., ., ., ., ., ., .1 ., ., ., I ., .1 I I .1 I .1 .1 .1 .1 .1 I I .1 .1 .1 .1 .1 ., I ., ., .1-.1 .1 .1 .1 I .1 .1 .1 .\ .\ .1 ., ., .\ ., .1 .1 ., I .1 ., ., .1 .1 .1 .1 ., ., .\ ., .1 .\ ., ., ., ., .1 .1 .1 ., .1 ., .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., ., ., ., ., ., .1 .1 ., ., ., ., .1 I .1 \ .1 I .1 .1 .1 .1 .1 .1 .1 .1 ., I .1 .1 .1 I I I .1 I .1 .1 .1 .1 I .1 I I I .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 I I I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. 1 .1 I ., .1 .1 .1 .1 .1 .1 .1 .1 .\ I \ .\ .1 \ .1 I .\ .1 I ., .1 ., I ., ., .1 ., ., .1 .1 I ., ., ., ., .1 I .. ., ., .\ .. .\ .1 ., .\ ., .1 .1 .\ .\ .1 .\ .1 .1 .1 .1 .1 .\ \ .1 .\ .\ .\ .\ ., ., .\ ., .1 .1 ., .1 .1 .. .. 1 I .1 ., .1 ., ., .1 ., ., .1 ., ., ., ., .1 ., ., ., .1 .1 ., ., .. ., ., .1 ., ., ., ., ., ., .1 .1 ., .1 ., .1 .1 .1 I I ., ., ., .1 ., .1 ., ., ., .1 .\ .\ .1 .1 .\ .\ .. 1 I .1 .1 I .1 .1 .\ .1 .\ .1 .1 .1 .1 .\ .\ .1 .1 .1 .\ .1 .\ .1 .1 .\ .1 .1 ., .1 .\ .\ .1 ., \ .1 I .1 .1 .1 ., .\ .1 .\ .\ I .1 .1 \ .1 I .\ ., .1 .1 .1 .1 ., ., .1 ., \ .\ .1 .1 .1 .1 .1 .1 .1 .1 ., ., .1 .1 .1 .1 .\ .1 .1 ., .\ .1 .1 .1 .1 I .1 .1 .\ \ \ .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .\ ., .1 .1 .1 .1 1 .1 I .1 .. 1 .1 .1 .\ .\ .1 \ \ .1 .1 \ \ .\ .1 .\ .\ .1" I .1 .1 .\ \ .1 .\ .1 ., .\ .1 ., I .1 .\ .1 .1 ., \ \ .\ I .1 \ I I .\ .\ ., .1 \ ., \ \ .\ .1 \ .1 .\ ., ., .1 .\ .. .. .. 1 .1 .. .1 .1 .1 .1 .1 .. ., ., .. .. .. .. .. ., .\ .\ .1 .1 \ .. .1 .. ., .\ .1 .\ .1 .1 I I .. .1 .1 I \ .. .\ ., ., ., ., ., .1 .1 ., ., .1 \ ., 1 .. .. I .1 .\ ., ., .1 .\ .\ .1 .1 .1 .\ .\ .1 .\ .1 .\ .\ .\ ., ., ., ., .1 .1 .\ ., ., .\ .1 .\ .\ .' .1 ., .\ ., ., .\ .\ .1 I ., ., ., ., ., ., ., .1 .1 ., ., ., .\ ., ., ., \ I .1 .1 ., ., .1 ., ., ., ., \ .1 ., .1 ., .1 ., .1 I ., ., I ., ., \ .1 .1 .1 ., .1 ., .\ .1 .\ .\ .\ .\ .1 .1 .\ .\ ., ., .1 .1 ., ., ., ., .\ .1 ., .1 .\ ., ., .\ ., ., ., ., ., ., .1 ., ., .. ., .1 ., ., ., ., ., .1 ., ., ., ., ., ., .. ., ., .\ .1 .1 .1 I ., ., ., ., ., .1 ., ., ., ., .1 ., I \ ., .. ., ., ., ., .1 I .1 .. .. .. .. .. .. .. ., ., ., .1 I .. ., .1 ., ., .1 .1 .\ ., ., ., ., .1 .1 .1 ., ., .1 ., .1 .1 .1 ., .\ .. .2 .. .. .' .! .2 .. .\ ., ., .. ., ., ., ., ., ., ., ., ., ., .\ ., .\ ., .\ ., ., ., .\ ., \ ., ., ., .J .J .4 .4 .4 .4 .. .. .' .J J ., ., .1 \ .\ ., .1 .1 ., ., .1 ., ., ., .. \ .1 ., ., ., .\ ., ., ., \ .J .J .4 ., .. .. .. ., ol ) ., ., ., ., ., ., ., ., .. ., ., .1 ., ., .\ ., .1 .1 ., .1 ., .1 .. ., .. J .4 ., .. .. .. .s ., .' J .. ., ., ., ., .1 .\ ., ., ., ., ., ., ., ., .1 1 .1 .1 .1 .1 .1 .1 .. J .4 .. .. .s .S .1 .. .. .. .J .. .1 ., .1 ., ., .1 .1 .1 ., ., .1 .1 .1 .. ., .1 .1 .1 .. .. .. .. .S .. S .s .. .s .. .. .. .1 ., ., ., ., .1 .1 ., ., ., ., ., ., 1 .1 .1 1 ., .\ ., ., ., .1 ., .1 .. .. .. .5 .. .. .. .s .5 .. .. .1 ., .1 .1 .1 .1 .1 ., ., ., .1 ., ., ., ., .1 ., ., ., .1 .1 .2 .' .5 .5 .5 .5 .. ., .1 ., .1 .1 .1 .1 .1 .1 ., .1 .1 .1 ., .1 ., .1 .1 ., .1 .1 ., .1 1 .2 .. .. .5 ." .5 5, ... .' .. .. .1 .1 .1 .1 .1 .1 .1 ., ., ., .1 .1 ., 1 I I I ., I .1 ., ., ., ., .. .. .. .. .5 .5 .' .2 .1 .1 .1 .1 ., .1 .1 I ., I ., .1 .\ ., .1 ., .. 1 ., .1 .\ .1 .. .. 5 .5 .5 .. .. .. .S 5 .' .. ., ., ., .\ .1 ., .1 .1 ., .1 ., ., .1 .1 .1 1 .1 ., ., .1 .1 .1 ., .1 .. .. .. .5 .S .1 .. .5 .1 .1 .1 .1 .1 .1 .1 I I .1 .1 .1 .1 .1 ., 1 .1 I .1 .1 .1 ., .1 .1 .' S .. .s .1 .5 .. .. .1 .1 .1 .1 .1 ., ., .1 I I .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 ., .1 .1 .1 .. .5 .5 .5 S .. .2 .1 .1 I .1 .1 .1 .1 .1 ., .1 .1 ., .1 1 .1 .1 .1 I I .1 .1 .1 1 I .1 .. .5 .5 .5 .5 .1 .5 .5 5 .1 .1 .1 .1 .1 ., ., ., .1 .1 .1 I I 1 .1 .1 .1 .1 1 .1 .1 I .1 .1 .1 .. 4 .. .. 5 .5 .5 .5 .5 .. .. .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. \ I .. .. .\ .. .. 1 .1 .2 .. .. .5 .1 .5 .. .5 .5 ., .1 .1 .1 .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 I .1 I .1 .1 .1 .1 .1 ., .1 .1 .' .. .5 .. ." .5 5 .. .2 .1 .1 ., .1 .1 .1 .\ I .\ .1 .1 I I .1 .1 .1 1 .1 .1 .1 .1 .1 .1 .1 .1 .. .. .. .. ." .. .5 .. .5 .. .. .1 .1 .1 .1 .1 .1 .1 .1 ., .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. ., .. ., .. .5 .5 ., .J .1 .1 .1 I I ., .1 .1 .1 .1 .1 .1 .1 .1 1 .1 .1 .1 I I I .1 ., .1 .1 .. .J .' .' .. S .5 .1 .. .. .J .. .1 .1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 1 1 .1 .1 .1 .1 I .1 .1 .1 .1 .J .J .' .' ., ., .J J .1 I .1 .\ .\ .\ .1 .\ .1 .\ .\ .1 .\ .\ .1 \ 1 I .1 .1 I \ .1 I .1 .\ .1 .J .J .. .. .. .. ., ., ., .J .J .1 .\ .\ ., .1 ., .1 .1 .\ .\ .1 .1 .\ .\ .1 \ .\ .\ .\ I .1 .1 .\ .1 .\ \ 1 .1 .. .2 .. 2 .2 .. .. .1 .. ., .. .. .\ .1 .\ ., .\ .. ., \ 1 .. 1 .. ., .. .. .. .1 .1 .1 .1 .. 2 .. .2 .. .2 .. .2 I .. . .. .1 .1 .1 .1 .. .. 1 .1 .. .. I .. 1 I .1 .. 1 1 .1 .. ., 1 .1 .1 .1 .. .1 .. .. 1 .1 .1 .1 .. .1 .. .1 .1 .1 .1 .1 I .1 .1 \ .1 .. .1 1 .1 .. .1 I I .1 I .1 ., I .1 .1 ., ., .1 ., ., ., .1 .1 .1 .1 1 I .1 ., .. .1 I I .1 .1 .1 .1 .1 ., .1 .1 I .1 .1 .1 .1 .1 I .1 I .1 .1 .1 .1 .1 .1 .1 I .1 .. .1 .\ \ .1 .1 .1 .1 .1 .1 .1 .1 .1 .\ .1 .\ .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 ., .1 .\ .1 ., .\ .1 ., .1 .1 .1 ., .1 .1 .1 .1 .\ .1 ., ., .1 .1 .1 .1 .1 .\ .1 .\ .1 .1 I .\ .\ .\ .\ .1 \ I .1 .1 ., .\ I I ., .1 ., .1 .1 .1 .\ .1 .1 .1 I ., I .1 I .1 .1 .1 I .1 .1 .1 .1 .\ .1 .1 .1 .1 .1 .1 .1 .1 ., I ., .1 .1 .1 ., ., .1 .1 .1 .1 .1 .1 .\ .1 .1 .1 .1 .1 .. .. .1 .1 .1 .1 .\ .\ I .1 I I .\ .1 .1 .1 .\ .1 .1 .1 .1 .1 ., .\ .1 .1 .1 .1 .1 I .1 .1 I .1 .1 ., 1 .1 .1 .. .1 I I .1 .\ .1 .1 I I .1 ., .1 .1 .1 .1 .1 I .1 _I I .. I .1 .1 I .1 ., I .1 .. .1 .1 .. .1 .1 I \ .1 .\ ., .1 .1 .1 .1 ., .1 .1 .1 .1 ., .\ ., .1 .1 I .1 .1 .. 1 .1 .1 .1 .1 .1 .1 .. 1 .1 .1 .1 .1 .1 I ., .1 .1 .1 .\ I .1 \ I .\ .\ .\ .\ \ \ .\ \ .\ ., \ .1 .1 I I I .1 .1 ., .1 .1 .1 .1 .1 I .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 ., I ., .1 ., .1 ., .1 .1 ., .1 ., ., ., .1 .1 ., .\ .\ \ .\ \ ., \ \ .\ .\ .\ .\ ., .\ .1 .. .\ ., .\ .\ .\ .\ .\ .\ .1 .1 .1 .\ .1 .1 .1 I I .1 .1 .1 ., .\ .1 .\ ., .\ I I I .1 I .1 .1 I I \ I I .\ I I \ .1 .1 .1 .1 .1 .1 .1 .1 .1 ., I .\ ., ., .1 .1 I .1 I .1 .\ ., .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 ., ., ., .1 .1 ., ., .1 .1 .\ I .\ .1 .1 .1 .\ .1 .1 .1 .\ .1 .1 .1 .1 .\ I .\ .1 .\ .1 .\ .1 .1 .1 .1 .1 ., .1 ., I .1 .1 I .1 I I ., I ., ., ., .1 .1 ., .1 .1 ., .\ ., ., ., .1 ., ., .\ ., ., ., .1 1 I .1 .1 ., .1 .1 ; I .1 .1 .1 ., .1 .1 ., .1 .1 .1 .\ .1 ., .1 ., ., ., I .1 .1 .1 .1 ., .1 ., ., .1 .\ ., .1 .1 ., .\ .1 .1 .1 .1 .1 1 .1 ., .1 .1 .1 .1 .1 .1 .1 .1 I .1 ., ., I .1 .1 .\ .\ .1 ., I .1 I .1 .1 ., ., .1 ., .1 ., .1 .1 .1 .1 ., ., ., .1 .1 ., .1 .1 I .1 ., .1 ., .1 ., .1 ., .1 .1 .1 ., .1 ., .1 .1 .1 .1 .1 .1 .1 .1 .1 ., .1 .\ .1 .\ .1 .\ .\ .1 .1 ., .\ .\ .1 .1 .1 .1 I I I .1 .1 .1 .1 .1 .. I .1 .1 .1 .1 .1 .1 .1 ., .1 .1 .1 .1 .1 -. .1 I I .1 I .1 .1 I I .1 .1 .1 ., .\ .1 .1 .1 I I .1 .\ .1 I \ .1 .1 .1 ., .1 .1 .1 .1 .1 I .1 I .1 .1 I .1 .1 .1 .1 .\ .1 I .1 .1 .1 ., ., ., ., .1 I I .1 .1 .\ ., ., ., ., ., ., ., ., .1 ., .1 .1 ., ., .1 I .1 .\ ., ., ., .1 ., ., ., .1 .1 .\ .1 .1 ., ., ., ., .1 .1 .1 .1 .1 .1 ., ., I I ., ., .1 I .1 .1 ., .1 .1 .1 .1 ., ., ., .\ .1 .1 ., ., ., .1 .1 .\ .1 ., ., ., ., .1 ., ., .1 I .1 ., ., .1 ., .1 ., ., .1 ., ., .1 .1 ., I .1 ., ., I .1 ., ., .1 ., .1 .1 .1 .\ .1 .1 ., ., I ., .1 ., .1 I .1 .1 ., ., .1 ., .1 ., .1 .1 .1 ., .1 .1 .1 .1 I .1 .1 ., .1 ., ., ., ., .1 I .1 t. f ..................................... f f" ....................................... t t t ....................... '" 1..0 (.0.) Fi gure S.13b of sal twater mound. N = 0.01 mjday, T = 10.0 days, maximal ordinate = 0.47 m.

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...................................................................................................................... .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .2 2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .1 .1 .1 .1 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .1 .1 .1 .1 .2 .2 .2 .2 .J .J .) .1 oJ .J .J .J .2 .2 .2 .z .1 .1 .1 .1 .2 .2 .2 .J .J .J .J .J oJ .J .J .1 .2 .2 .2 .2 .1 .1 .1 1 .. .J .J .J .. ..-.-.-... -.J .J J ., .1 .1 .1 1 .2 .J .J J ... ..-..-.-.-.-.J ., ., ., .1 .1 .1 .1 1 .. J 0 .. ., ., .5 .. .6 .. .s .S .S .-.0 .J .1 .r .1 .1 .1 .1 .. ,] .0 .0 ., ., ., .. .a .. .. .. 5 .S ., .0 .. J .1 .2 .1 .1 1 .1 2 .. ol .0 S .6 .7 .7 .0 .a .. .. .0 .0 .0 .7 .7 .6 .0 .J .2 .2 .1 .1 .1 .1 .2 .2 ., .0 s .a .7 .7 .a .. .. .. .. .0 .. r .. .6 .s .0 .J .2 .2 .1 .1 .1 .1 ., .0 .7 .BI. 1.11 1..1.21.2'.2' 1.11.1 .. .7 ., .2 .2 .1 .1 .2 .2 .J ., .S .r .Sl. 1.11.11.11.21.21.21.11.'1.11. .a .7 .s .' .J .2 ., .1 .1 .2 .2 .. .7 .VI.II.4 1.51.61. p .. 71. PI. 71. U.61. 5,. 41.1 .9 .J oS .0 .1 .2 .2 .1 .1 2 .2 .J .- .91.II.t'.'I.6I.11. 'I. 7 I. PI.71.61.5,. U.I .r .s 1 .r .1 .1 l .J .. .. .r .9, .21.62.11. 32.42. 42. S2. 52. 52.42 2. ]2.,1.61.2 9 .. .. ., .. .1 .1 .2 ., 0 .. .. 9'.21.61.12. 32.4Z. 42. 52 ... ,. 1Z.' 2. 4Z. '2. 11.61. Z .9 s .-.J .& .1 1 .. .. ., .. .6 .11. 11.62.l3. ,l. "1.5J.6,. 61.6 '.6).63.51.43. II. J 1.".1 .. .a .. .J .r .2 .1 1 .2 .. .J .. .6 .111 1 .. 11.6 2.13. 2]. 6 1.6]. 6).6J. 51. 4'. 22. J 1.61. I .0 .. .J .2 .r .1 .1 2 .. .J .s .71 1.42.1'.2J.7'.5'.6'.61.6'.6'.6J.61.61.5'.71.22 .r ., .J .1 .2 .1 .1 .l 2 .J ., 71. .r J .2 .1 .1 .2 .1 .-.- ".11. 52,11. 5J.52. 72.5'. '2. 42 '.42.42.5'. I J. 51. 'Zel'e "' .. .S ..J .2 .1 .1 .J .. .71.11.5,.11.53.5'. ".52 ,. 41. 4 '.'2.41. 5Z."]. ':Is 5 2.1,. 51.t .r ., .' .J .r .1 .1 .2 J .' .. .81.11 ..... 2: ].5l. 62. 51. 91.11.71.1 I. 11.11 ,. 51. I'. 5'.'I.e-I., .0 .s ., .2 .1 .1 .2 .1 .0 .s IJI. II.fI.,.4,. 5l.6Z. 51 .9,. '1. 'I. 71.11.' I. 9'. 5]. Il. "'.4" 61. I .a .s .-.J .2 .1 .1 .2 oJ .6 .11.11.12. ".63.6'.41. 71.11.11.1 I. 11.11. 1l ,. PI.I .a .6 .. .J .2 .1 .1 2 03 .. .. .81.11. ,.71.1 11.11.1'.,11. 7Z.4.1. 6'."'.'1. PI.' .. .. .' ., .1 .1 .1 .2 .J .6 ."1.21.12.5'.6].6'.41.11 1.1 .81.11.12 J.13.&2.51.".' .a .6 .' .1 .2 .1 .1 .J .. .. .fl.21. P2.Sl.61.ft2. 41.1 8 .. .111.'" 43. .3.62. 5 7'.2 .0 .0 ., .1 .1 .1 2 .] .. .6 .el.'I. '2.5J.61.62. 4 ".1 ., .1 ." .11. 1'.4'.61.62.51.' 1.2 .a .0 .' .J .2 .1 .1 2 .J .. .0 .fll.ZI.1'.Sl.6] 2. 41. PI.I .1 p II. 71. ". II.AI.5I.".1 .a .6 .' .] .2 .1 .1 .1 .J .' .. .11.'1.1'.5).6].6'.'1.1 1 .e 1 11.12 3.61.62.5 .. .... 8 .-.' J .:1 .1 .1 2 .J .. .6 .11.21. 7'.5l.61. 62. 41. 71.1 .1 11.1'.".6'.61.51.'1.1 .a .6 .-.J .2 .1 ,I .2 .3 .0 .6 .1' .11.7'.'3.6'.61.41. 'I. 11.11.'1e.1.31. rl :s. .l .. a. 41. 71.' .tI .' .] .1 .1 .1 2 .J .. .6 .SI.II. 71.41.6l.6'. 4'. 7 ll. II. I 1.11.11.7' '.61.61.4 ".1 .8 .6 .. J .2 .1 .1 2 .1 .. ., .81.11.6'.'1. 5].6'. 71. PI.' I. '1.71.91. 1.SI.t t .61.1 .. .s .' .J .f .1 .1 2 .J .. .'111.11.62.4 l.5J.62. 5a.9 .. 71. ". 7" 'a. ,,,9,. 5J. 'J. 51.41.61. I .11 .- .3 .1 .1 .1 .. J .. .. .71. II. 5'.]1.51. 5a. 7a. 51. '2. 41." I. 41.42.51. 'l. til. 51. 1 Shl .. .5 ..J .2 .1 .1 .. .J .. .s ., I., 1.52. )1. 51. 52.12:.52. '2. 42." Z. 42. 4Z. !'I'. 'J. 52.] 1.51. I .r .s .J .2 .1 .1 .. .2 J .s .71 I." 2.11.' l. 73. 51.61.6 J.6l. &l.6l.,6l.6l. 51. fl. 2Z.ll. 4,. .. .11 .J .1 .f .1 .1 .. .2 .J .s .71. '2. I l. '']. ll. 53.6 J. 63. t 3.63.11.,61.61 ,.71.22.11.41. .7 .s ., .1 .1 .1 .1 .2 .J .t .fli. 11.6 Z.ll. Il. "J. SJ. 61. el. 6 3.61.63. 53." Is 12. 1 I .... I It ., .2 .1 .1 .1 .2 .2 .J ..t. .11.11.1 2. 1. "J.Sl. 11.61. 63.61.61. 5J. 4l.2'.1 61.1 .1 .tI .. .J .1 Z .1 .1 .2 .l .. .s ., .9'.1 l.f2.12. 12.42. 42. 5P. 'i2. 41. 4'. :lP.".6 1.1 .. ., ." .-.J ., .1 .1 l J .. .91.2 I .62.1 ,. lZ. 42.42. 52. '51. ,,, 2 2. ll. 11.6 .. a .9 .f .. ., .2 .1 .1 l .. .1 .. .s .r .91. II. 41. 51.61. 71. 71.1 I. PI. 11.1So1. 51."1.1 .9 .7 ..J .2 1 .1 .2 .2 .J .. .r .v 71.11. '1.'1.6,." ..... 1 .. .J .2 .2 .1 .1 z 2 .3 .' .r .". I 1.1I.I .. rl.21.U .11.1 11. .r ., .) .2 .2 .1 .1 2 .2 .) .-.s .r 1. 1.11. II. 11.21. I. 21.11.11.11. .1 .r .s .3 .2 .2 .1 .1 1 .2 .2 .J ... r .r .e .e .0 .1 .-.a .r .' .a .S .. .1 .2-.2 .1 .1 .1 .1 .. .. ol .s .6 .r .r .a .0 .. .. .a .8 .r .r .5 .- J .2 .2 .1 .1 1 .1 .. .. .J .- .. .a .6 .6 .5 ., .. ol .2 1 .1 1 1 .2 .. .. .. .0 s .s .a .. .6 .6 s .-.J .. .2 .1 .1 .1 .1 .2 .2 .J .1 .J .4 '.4 .- .. .' .- J l .J .. .1 .1 .1 1 .1 .2 .1 .J .J .J .' .-.- .. .. .' ..l .'.3 .2 .2 .1 .1 .1 .1 .2 2 .2 .2 J .J .J .J .J .J .J .J .J .2 .2 .2 .1 .1 .1 .1 .. .2 .2 .2 .J .J .J ., .J .J .l ., .J .1 .2 .2 .2 .1 .1 .1 .1 .1 .2 .2 .r .1 .2 .2 .J .2 .J .2 .1 .2 .1 .1 .1 .1 1 .2 .2 .2 .2 .2 .2 .2 .2 .2 .. .2 .1 .. .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .. .1 .1 .1 .1 .1 .1 .1 ., ............................................................................................................... Figure S.13e -Map of transition zone. N = 0.01 m/day, T = 10.0 days, maximal ordinate = 3.63 m.

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s[m] zb[m] (1) a[m] 20 20 (1) smax' a = 0.05 m (2) zb max' a = 0.05 m 15 15 (3) a max' a = 0.01 m/day (4) 15 max' N = 0.01 m/day 10 (5) smax' N = 0.01 m/day 10 (6) zb max; N = 0.01 m/day (2) -5 5 (3) & (4) (51 --(6) o 2 3 4 5 6 7 8 9 10 Time [days] Figure 5.14 -Rate of growth of the maximal values of the dra\,/down, the height of the salb/ater mound, and the thickness of the transition zone for experiment numbers 2 and 3. \.0 Ul

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96 5.5 Discussion and Conclusions By virtue of the results presented in the previous section, the numerical model developed in this study is considered to be highly stable and convergent. The numerical results are coherent with both the physical phenomena associated with the mineralization process and the expected behavior of the governing equations. The preliminary simulation is designed to determine the stability and convergence characteristics of the numerical model and to yield exploratory results. The numerical scheme converges rapidly and yields three-dimensional results similar to Rubin's [1932J two-dimensional results. For the preliminary simulation, Figure 5.6 illustrates a rapid stabilization of the drawdown in the early stages of the simulation period. This phenomenon is quite typical for an aquifer of the type under consideration in this study. Horizontal flow in the freshwater zone and vertical leakage from the semiconfining formation is associated with the establishment of the drawdown within the aquifer. According to equation (4.18) and (4.19), the system approaches steady state conditions with respect to the growth of the saltwater mound where s -( -= z + 0 E; b fol Ldn) (5.7) Given the parameter values in Table 5.1 and a drawdown of 20 m (Figure 5.5a), steady state conditions are reached when the right hand side of equation (5.7) is on the order of 800 m. Assuming this to be true, the aquifer would become completely mineralized before steady

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97 state conditions are reached. However, this vlould rarely be the case in actual field applications since a well will most likely be abandoned when the chloride content of the well water reaches an intolerable level. Nevertheless, the transient simulation provided by the model can serve as a powerful tool when establishing safe yields for well users. When pumpage begins it can be assumed that S C; Therefore, in the initial stages of pumpage (5.8) Equations (4.18) and (5.8) imply that when pumpage begins and the drawdown is small the leakage from the underlying saline formation is not significant. An increase in the drawdown is associated with an increase in the rate of leakage. As the drawdown subsequently stabilizes, the combination of the growth of both the saltwater mound and the transition zone contribute to a decrease in the rate of leakage. Although this is predicted by equation (4.19), the rate of leakage is found to be almost constant (Figure 5.6) for the simulation period. This would imply that for the simulation period the approximation given by equation (5.8) is valid. use of equation (5.8) instead of equation (4.19) during the execution of the model woul d save computer time and memory. The development of the transition zone is described by equation (4.22). The rate of growth of the thickness of the transition zone stems from the relative contributions made by both convective and

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98 dispersive terms. The magnitude of these terms are determined by the horizontal specific discharge in the freshwater zone. Since longitudinal dispersion is neglected in the analysis, it seems reasonable to consider values of the effective dispersivity, a, which are larger than the pre dicted transverse dispersivity. The true profiles of the specific discharge and the solute con-centration wHhin the transition zone are approximated by second order polynomial functions following Rubin [1932b]. Although other functions could be chosen, for example higher order polynomials or sine and cosine functions, a second order polynomial is considered sufficiently accurate for simulation purposes. The of the use of various approximating functions upon the similar profiles is not explored in this study, but it is anticipated that the results would not differ significantly. In order to detennine the relative contribution of the convective and dispersive terms in equation (4.22) toward the development of the transition zone, the preliminary simulation was executed without the \ convective terms. This operation reduces equation (4.22) to the form (5.9) In comparing the results it is found that the development of both the drawdown and the sa ltwa ter mound were i denti ca 1 to that predi cted with convective terms included. Figure 5.6 illustrates the results with regard to the rate of growth of the maximal value of the thickness of the transition zone. The results indicate that the convective terms in equation (4.22) make only minor contributions to the development of the transition zone for the simulation period. This can be deduced

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99 from equation (4.22) in that for the initial stages of pumpage both the squared thickness of the transition zone and its gradient are small. The use of equation (5.9) as an approximation to equation (4.22) in the execution of the model leads to a reduction in computer time and memory of about 18 percent and a more conservative estimate of the thickness of the transition zone when applying the model for recommended safe well yields. As simulation times are increased, the convective te:ms in equation (4.22) will increase in magnitude until steady state conditions are reached. Steady state conditions with respect to the transition zone are reached where 2 Jl [82 + + i (u + V 0 FLdn 2 2 = -a K + Jl / 2 L'(O) ax ay (5.10) For the simulation period the development of the transition zone is attributed primarily to the dispersive term in equation (5.9). Here the rate of growth of the transition zone with respect to the horizontal coordinates is proportional to the dispersion coefficient and the horizontal specific discharge. Figure 5.6 demonstrates that while the rate of growth of the transition zone is initially very rapid, it declines in magnitude during the entire simulation period. This result is coherent with the physical phenomena in that during the initial stage of pumpage the salinity gradient within the transition zone is very large causing rapid growth of this zone. As the transition zone increases in thickness, the salinity gradient within the zone diminishes thereby reducing the rate of growth of the zone.

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100 For the preliminary simulation both the saltwater mound and the transition zone propagate laterally in response to the pumpage. Once again this result is coherent with the physical phenomena. The maximum height of the saltwater mound is located at the center of the pumpage field. The maximum thickness of the transition zone is located where the gradi ent of the drav,down is the greatest. Thi s can be deduced from equation (S.9) where the rate of growth of the transition zone is proportional to the gradient of the drawdown. Referring to Figures S.3c, S.4c, and S.Sc, the thickness of the transition zone vanishes in the vicinity of the center of the pumpage field. This phenomenon is obtained because it is assumed that the coefficient of salinity dispersion is proportional to the horizontal flow in the freshwater zone. However, in the vicinity of the center of the pumpage field vertical flow and longitudinal dispersion in the vertical direction are significant. Therefore, the model seems to underestimate the growth of the transition zone in this region. Experiment number 1 is designed to evaluate the accuracy of the convergence of the numerical model by altering the value of the time step (Table S.2). A comparison of the results obtained in Figures S.3a, S.3b, and S.3c and Figures S.7a, 5.7b, and S.7c demonstrates no significant differences between the respective ordinate values for an alteration in the time step. Therfore, it is found that the numerical model converges to the same values for two different time steps. While this in itself is not a guarantee of numerical accuracy, the results of experiment number 1 indicate that the numerical model converges to the true answer.

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101 Experiment numbers 2, 3, and 4 were designed to observe the distribution of the drawdown, the saltwater mound, and the thickness of the transition 20ne within the flow field under a variety of parameter changes (Table 5.2). Experiment numbers 2 and 3 yield realistic results while the results from experiment number 4 are discarded. Although the numerical model converges for the parameter change in experiment number 4, the results are unrealistic. The decrease in the leakance value by an order of magnitude is associated with drav/down values in excess of 100 m. The system reacts more as a confined aquifer rather than a leaky aquifer. Figure 5.14 illustrates some results with regard to experiment numbers 2 and 3. A reduction in the.value of the dispersivity by an order of magnitude affects only the development of the transition zone. A similar reduction in the rate of pumpage affects the development of both the saltwater mound and the transition zone. These results are to be expected since the development of the saltwater mound depends primarily on the drawdown while the development of the transition zone de pends on both the gradient of the drawdown and the dispersivity. It should be noted here that these results are valid only for the simulation period used in this study. As the simulation period is lengthened the terms in equations (4.19) and (4.22) containing the parameter, 6, play an increasing role in the development of the saltwater mound and the transition zone. At this point the approximation given in equations (5.8) and (5.10) are no longer valid. A consequence of experiment numbers 2 and 3 is demonstrated by examining curves (3) and (4) from Figure 5.14. Here the rate of growth the maximal value of the thickness of the transition zone is almost identical

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102 for both experiments. Although not immediately apparent, this result is explained by referring to equation (5.10) where the coefficient of salinity dispersion, 0, is shown to be proportional to both the dispersivity and the horizontal specific discharge in the freshwater zone. Assuming the validity of equation (5.10) over the simulation period, an alteration in either the dispersivity or the specific discharge by an identical amount will produce the. same effect with regard to the development of the transition zone. The model is not calibrated in this study primarily due to a lack of suitable field data. Although the success of the model when applied to field applications remains to be seen, it is the feeling here that this model can be adapted to a variety of applications. The results should be sufficiently accurate for engineering purposes. In conclusion, the numerical model is found to be highly stable and converges rapidly. The numerical results are coherent with both the physi cal phenomena and the expected behavior of the governing equations. Equations (5.8) and (5.10) are valid as approximations to equations (4.19) and (4.22), respectively, when used for a short simu-' 1ation period. Their use leads to a decrease in the quantities of computer time and memory necessary for the execution of the model. The numerical accuracy of the model is indicated by altering the value of the time step. 5.6 Surrmary The numerical model is formulated by the application of an AD! method and the appropriate linear finite difference representations of equations (4.18), (4.19), and (4.22). The ADI method was chosen as a

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103 solution technique to the parabolic system because of its widespread application to groundwater studies. The model is executed with the aid of a high speed digital computer. Numerical results are presented for a preliminary simulation and a series of experiments. The simulation period is 10 days. The numerical model is found to be highly stable and it converges rapidly. The results are coherent with both the physical phenomena associated with the mineralization process and the expected behavior of the governing equations.

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CHAPTER 6 CONCLUSIONS (1) The problems associated with the mineralizati.on phenomenon typical to northeastern Florida can be simulated by the model developed in this study. (2) The majority of leakage occurs from underlying formations. There fore, the aquifer appears to be a leaky confined aquifer subject to the mineralization process. (3) It is possible to reduce the complexities of the basic model by the application of the Dupuit approximation in conjunction with the boundary layer theory to the flow field. (4) Various numerical experiments indicate that the numerical scheme developed in this study is highly stable, convergent, and accurate. (5) The numerical results generated by the model are coherent \,/ith the physical phenomena associated with the mineralization process as follows: (a) the drawdowns stabilize rapidly while the mineralization process continues throughout the entire simulation period; (b) the thickness of the transition zone is relatively large when compared to the thickness of the freshwater aquifer. This situation is commonly seen in the field where the chloride content of the well water increases gradually. 104

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105 (6) Neglecting the convective terms in the equation describing the development of the transition zone leads to a substantial savings in computer time and memory. (7) The rate of growth of the transition zone depends upon the rate of pumpage and the dispersivity. The rate of growth of the saltwater mound depends only on the rate of pumpage. (8) The success of this model in the present study encourages further use of the basic approach. The model can be used for the improvement of groundwater use in the State of Florida.

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APPENDIX A THE DEVELOPMENT OF THE FINITE DIFFERENCE SCHEMES REPRESENTING EQUATION (4.22)

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APPENDIX A THE DEVELOPMENT OF THE FINITE DIFFERENCE SCHEMES REPRESENTING EQUATION (4.22) Finite difference representations of hyperbolic systems generally arise from either an explicit or an implicit approach. In this Appendix explicit as well as implicit finite difference schemes are developed. However, this study utilizes only the implicit approach due to its superior stability characteristics. Equation (4.22) is considered to be a hyperbolic equation as the dominant terms in this equation are (l:!.. ao_ + '.!.. 2.L) FLd 2 2 Jl 2 ax 2 ay 0 T) Therefore, equation (4.22) may be reduced to the following hyperbol ic fonn (!'!. Il Ld )< ai + (!!. ao2 + y.. ao2 ) .Il = 2 0 T) at 2 ax 2 ay 0 FLdT) Dl' (0) 02 aV) Jl FLd ax ax 0 T) (A.l ) Equation (A.l) assumes that the convective term represented by the product, 02 + in equation (4.22) is very small and that the right hand side of equation (4.22) is approximately constant. An explicit finite difference expression for equation (A.l) inai volves a time difference for the term, and a backward difference 107

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108 U' 382 V, a82 for the term, (2' ax + 2' -ay)' The backwa rd di fference i nvo 1 ves only the time level (m). For this situation,only the time dependent term produces unknown values at the time level (m+l). All constant and minor tenns are formulated for the intennediate time level (m+l/2). The approach used for the development of an implicit finite difference expression for equation (4.22) is identical to that used for the explicit expression except that the backward difference representation U a82 V 302 of the term, (zax+ zay), involves the time level (m+l). Therefore, unknown values at time level (m+l) are generated from two different terms. Following the explicit approach of Mitchell [1976J, an explicit expression for the description of the development of the transition zone in the x direction is obtained from equation (4.22) as follows 2(m) n Jl K, ,t,t ( 1/2) = [ Ld 1,J (m+ 0" 2" 11 -2 s i + 1 ,J' 1 ,J 0 4 (t,x) Jl FLdnJ + {i,j fl FLdn 1-,J ,0 1-,J 4(t.x) 1+1,J 1-,J 0 2(m+l/2) t,t (s(,m+l/,2) s(,m+,1/2)) 0, {--" [K1'+1/2 J' 1 + K 1'-1 / 2,J' 1 J ( t,x ) .::: 1 + J 1 J ( (m+l/2) (m+l/2) t,t ( (m+l/2) (m+l/Z) s' 1 -s. '1 )J + --2 [K, '+1/2 s. '+1 s' 1 -,J 1 ,J -( t,y ) 1 J 1 J 1 ,J 1 K. t,t Z(m) + K, 1 f FLdn -1 IJ [(8. '+1 2 1 ,J-1 ,J-1 ,J 0 8(c,y) 1 ,J

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109 s(m+l/2) s(m+l/2) s(m+l/2) s(m+l/2) [( i+l,j -i-l,j )2 + (i,j+l -i,j-l )2]1/2 L'(O) (A 2) 6.X 6.y I An explicit expression for the description of the development of the transition zone in the y direction is obtained from equation (4.22) as follows 1 1/2) FLdn] + [' ,J 1/2 -( ) Jl (m+ 1) K, 6. t ( ) 1 J -1 0 1 J -1 4 (6.y ) 2 1 J + 1 ( 11/2) Jl 2(m+11/2) 6.t (m+l1/2) )] FLdn a, [Ki J'+1/2 (si J'+l 1,J-l a 1,J (6.y)' [K ( s m+ll ,1 /2) s 1 1 /2)) + K, 1 /2 ( s m+ 1 ,1 /2) i+1/2,j 1+,J 1,J 1-,J 1-1,J ( ) J1 K. 6.t (m+1) (m+l) 1/2 )]} FLdn 1,J ,-o? l' )] 1,J a 8(6.x)2 1+1,J 1+,J J1 FLdn = a K;,j 6.t 1+1,J 1+1,J a 2

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110 (m+l 1/2) (m+l 1/2) (m+l 1/2) (m+l 1/2) -Si_l,j )2 + (Si,j+l -Si,j_l )2Jl/2 6x 6y L I (0) (A.3 ) Following the implicit approach of Mitchell [1976J yields implicit expressions for the description of the development of the transition zone in the x and y directions given by equations (5.2) and (5.4), respectively.

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APPENDIX B COMPUTER PROGRAM

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\$JO;;) c C C C C C C C C C C C C C C 2 3 4 5 u 7 9 10 1 1 1 2 13 14 15 1 is 17 10 5(50,50) ,3N(SO.SO) .SE(S(J,Su) ,2,(50,50) ,ZN(50,50) ,ZE(50,50) ,1)2.(50.50) .XN(50,50) ,XNT(50,50) ,BI(50.S0) ,.. ,A{SO)"D(SO),C(50),D(SO),X(SO) ,D1(50,50) ,D:'N (50,50) ,DLE(50,50) ,02(50,50) ,DN2(SO,50) ... ,. ,. ,. ., AU UIF J BTA I LS --_._-------------------------XK=AQUIFEli'S HYDgi\ULIC CONDUCTIVITY 1K1=HYDRAULIC CONDUCTIVITY OF SEMICONFINING FORMATION BO=AQUIFER'S B1=THICKNESS OF SEMICONfING PN=EPFECTIVE POROSITY ST=STORAGE COEFFICIENT A 1=DISPEBSIVITY XKSI=PARAMETER OF DENSITY RATTO N=NUPlBER OP X NODAL POINTS M= NUftBER OF Y NODAL POINTS NM=NUMBER OF GItID POINTS (=N*M) ID=TYPE Or' PRINT,ING ID=O L1EANS DRAWING ID=O XK=QO. XK1=0.1 80=50. f:ll=20. P N=O. 2 ST=0.001 i\1=O.5 IKSI=0.025 N=40 11=40 N M=N* M Dl3=O. IP=l PRIllT 10,XK,XK1,BO,B1,PN,ST,A1,XBSI.N,M,NM FOHMAT (lli1 ,1/1.51, 1===========================:=============== '/ ,51,'GBOWTH OF SALTWATEH IN A LEAKY ,SX,' TWO DIMENSIONAL ANALYSIS' /,5X,'=======================================', //5X,'AQUIFZR ,---------------'I/,SX,'XK=',F4.0, 5X,'AK1:',F4.1,5X,'BO=',F4.0,5X,'Dl:',F4.0/, 5X,'NODAL AND GRID 112

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c c c c c C 18 1 9 20 2 1 22 23 24 25 'C C C C C C C C C C C 26 27 28 29 30 31 32 33 34 35 20 CHEaCT.E.EtIS'l'ICS OP THE TRANSITlON ZONE ALF=IN'lEGBA1 Of' i:"*DJ:(El'A) AB=INTEGBAL OF F*L*DI(ETA) ALF=2./3 D E'r= 1.13 AB=2./15 AL=-2. AL1=A1*A1 PNL= PN*BET*O. 5 PRINT OF L*DI(TA) AL=L' (0) OF THE TEANSITION ZONE'/ ,. ,5X,'-----------------------------------------,/ ... ,. 5 X, A L1-'=' .F6. 4, 5X, BET=' .. F6. 4" 5!, A B=' F6. 4,,5 X .. A L= .. F6.3, ,. 5X) PAllA:1ETERS ========= S (I, J) S N (I, J) oS E (I J) =1 NIT. Fl. A V E DR A if DOW .!Ii Z (I,J) ,ZN(I,J) ,ZE(I,J)=INIT.,FI.,AVE THICK. OF t'lOiJND DL(I) ,DL1J(I) ,1lLE (I)=INIT.,FI.,AVE.'rHICKl.'iESS CF TRANS.ZC:.E ,DN2{I),nC;2(I)=INIT.,FI.,AVE.SQUAEE THICK. Of 3I(1,J)=AVEHAGE OF THE FRESHWATER ZONE RATE OF GROWTH OF MOUND XN(I"J)=BATE OF PUHGAGE PEB UNIT AREA DO 50 I=1,N DO 40 J= 1, S(I,J)=O. 5N(I,J)=O. SE(.I,J)=O. Z(I,J)=O. ZN(I,J)=O. ZE eI" J) =0. DZ(I,J)=O. BI(I,J)=BO 113

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36 37 Jo 39 '-+U :.t 1 :}.t: 43 40 Ll4 50 (-'" C C 45 0 60 ,J, 7 48 49 50 70 51 80 52 53 S4 82 S5 56 57 do 58 59 GO G 1 :) 2 GJ bit 65 66 67 90 XN (I,J)=O .. i>L(I,J)=O. DLN(.l,J)=O. DI.E(I,J)=O. D2(l,J)=O. D N2 ( I J) =0. DE2(I,J)=O. CONTINUE PIUNT 60 FO B[1 AT (5 X, '2U flPAGE DISTRIBUTION' ,/5X, '====================' /) DO 80 1=15,25 DO 70 J.::15,2S XN(I,J)=O.l CONTINUE conTINUE LF (I D. EQ. 1) GOTO 88 1!HINT 82 FOHMAT(///,10X,'MAP OF CALL DRAW1CXN,IP,DB) GOTO 132 DC 130 1=20,30 DO 120 K= 1,2 a=20+ (K-l) *6 J l=J+ 1 J 2=J+2 JJ=J+3 J 4=J + 4 J5=J+S 1F(K.E;J.2) GOTO 100 PBINT 90,1"J,XN(I,J) ,I,J1,INCI,J1) ,I,J2,XN(I.J2} ,I,J3,XN(I,J3}, ,I,J5,XN(I,J5) FORMAT (3X, 'XN (', 12,',',12, ') =', F4. 2. 3X,' IN C' ,12,',' ,I2.) =' ,F4. 2 ,3X,'XN(',12,',',I2,')=',F4.2,JX,'XNC',12,'.',12,')=',F4.2, 3 X, XN ( 12 , 12 ) =' F 4 .. 2,3 X,, IN (' ,12, ,12 ) = F4.2) 08 GOTO 120 69 100 PRINT 110,I,J,XN(I,J},I,Jl,XN(1,Jl} ,I,J2,XN(I,J2) ,I .. J3,XN(I"J3) ".. ,I"J4 .. XN(I,J4) 70 110 E'Oul:lIl1:(31..,'XN(',I2,,',I2,'}:,P4.2,JX.'XN(',I2,',',I2,')-=:',F4.2, JX.'XN('.12,',',12,')=',.F4.2,3X,'XN(',I2,','.12,')=',Y4.2, 3 X, X N ( 12 , 12, ) =' P 4.2 ) 71 120 SONTINUR 72 130 114

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c c C 73 74 7':: 76 77 7:1, 7'3 dO 8 1 82 C C C gj d4 85 86 d7 dd d 'J 90 ') 1 (U 93 94 ':15 96 97 B .-9 100 10 1 102 GRID INTEBV;a.LS 132 DX=500. P a I NT 1 4 a DX 140 JI,'SRID INTERVALS DY=DX=',F4.J,' Nl=N-l N 2-=.N-2 L'l1=.:1-1 M2=M-2 11 3=[1-3 A(l)=O. INITIAL STEP=DT1 01'1=0.2 P.HN T 150,DT 1 150 STEP DT=',F5.3,' DAYS',/Sl, .* '======'==========:=' I) T-=O. paINT 160,T 160 DAYS'I,SI,'=:==============='/) PRINT 170 170 PORMAT(/I SX,'ALL VANISH'I,sx,'----------------------') DT=D'Il DX2=DX*DX 11J () CJ N'! ll! U E lCKK=Xi\*XK1/(PN* (1. +XKSI lL{=B l*XK DO 200 I=l,N DO 190 XNT(I,J)=XN(I,J)*DT 190 CONTINUE 200 CONTINUE IX=1 210 T=T+DT 115

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103 C C C 104 105 lOb 107 108 109 C C C 11 0 11 1 112 1.1.3 114 115 1Hi 117 118 119 12 U 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 IF(T.GT.2.) GOTO 660 STARTING ITERATION PROCEDUBE XKT=XK*R 220 Ir=-l 222 IT=I'I+ 1 BK=D1*XK IF(IX.EQ.2) GOTO 590 SCHEME IN THE X DIRECTICN SBIG=O. DO 280 J=2,111 DO 230 11=2,N2 1=11+1 A (I 1) =. S>tXKT" (BI (1-1 ,J) +BI (I .J) + (DLE (I-1,J) +DLE (I, J) ) *Al.11) 230 CONTINUE DO 240 I1=l,N2 1=11+1 B(I1)=ST+XKT"O.5*(BI(I+l,J)+2.*BI(I,J)+BI(I-l,J) +(DLE(I+l,J)+2.*DLE(I,J)+DLE(I-1,J*ALF) D(Il)=ST*S(I,J)-PN*DT*DZ(I,J)+XYT(I,J)+XKT*0.5*C(BI(I,J+1)+ ,.. BI(I,J)+(D1E(I,J+l)+DLE(I,J*ALF)*(S(I,J+1)-S(I,J+(BI(I,J) +3 I (I, J-1) + (DLE. (I, J) +DL.E (I, J-l) ) *ALF) (S (I.J-l) S (I, J) 1 ) 24;) CONTINUE DO 250 I1=1,N3 1=11+1 C(I1)=0.5*XKT*(BI(I.J)+BI(I+l.J)+(DLE(I+1,J)+DLE(I,J*ALP) 250 CONTINUE .CALL THOMAS(A,B,C,D,X,N2) DO 2 60 1-=2. N 1 I1=I-1 SN1=X(Il) SB= ABS (S.Nl-S N (I, J) ) IF(SB.GT.5BIG) SBIG=SB IF(SN1.LT.O.) 5N1=0. 5N (I,J) =Sli 1 26 U CONTINUE DO 210 I=2,N1 2 7 0 CON T.IN U.E 280 CONTINUE 116

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133 DO 284 J=2,111 DO 23J I=2,N1. 14u .IF(.6(l,J) .LT.O.OOO1) GOTO 283 141 DEN=PNL+.25*XKT*AB*(SE(I+1,J)-SE(I-l,J 1 4 2 J 2 ( I I J) :: ( D 2 (I J l *" I? N L X K T* A B (D E 2 (I I ,1) (S E (I ... 1 J) ... S E ( I -1 J) 2. *.:; E ( I, J) ) -.25 D ( I-1 J) *" (S E ( 1+ 1 J) 52 (I1 J) ) ... D 2 (I. J) *' (SE (1,..1+1) +52 (1,.J-1)-2.*SE (I,J)) (Ss:n ,J+1) -SE(I,J-l *' (02(I,J+l)-l)2(I,J-1)-.5*DX*AL1*XKT*SQRTSB,{I+l.J)-* 51:; (1-1,J) **2'" (SE (J:,J+ 1) -SE (I,J-1) ) **2) /DEN 143 IF(DN2(I.J} .LT.0.) DN2 (1,J)=O. 144 283 145 284 CONTINUE C ----------------------------------------------------------------C CALCULATION APPLIED TO X AND Y C ----------------------------------------------------------------146 285 DBIG=O. 147 DBI2=O. 148 DO 288 I=2,Nl 149 DO 287 J=2.M1 150 151 DLE(I,J)=.5*(DLN(I,J)+DL(I,J 152 DE2(I,J)=.5*(D2(I,J)+DN2(I,J 153 DB1=ABS(DLN(I,J}-DL(I,J 154 DB2=ABS(DN2(I,J)-D2(I,J 155 IF(DB1.GT.DBIG) D13IG=DB1 156 IF (DB2.GT.DBI2) DBI2=DB2 287 CONTINUE 158 288 CONTINUE 1 5 9 Z 131 G= 0 160 DO 300 161 DO 290 I=2.N1 1b2 DZ(I,J)=XKK/(BK+ZE(I,J)*XK1)*(SE(I,J)-XKSI*(ZE(I,J) +BET*DLE(I,J)) 163 ZN(I,J)=Z(I,J)+DT*DZ(I,J) 1b4 IF(ZN(I,J).LT.O.) ZN(I,J)=O. 165 IF(SN(I,J) .EQ.O.) ZN(I,J)=O. 166 ZE(I,J)=O.5*(ZN(I,J)+Z(I,J 167 BI(I,J)=BO-ZE(I,J)-DLE(I,J) 168 ZB=ABS{ZN(I,J)-Z(I,J 169 IF(ZB.GT.ZBIG) ZBIG=ZB 1]7

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170 290 CONTINUE 171 300 CONTINUE 172 IF(IT/10.NE.O.1*IT) GOTO 312 173 PRINT 310,IT,SBIG,ZBIG,DBIG,DBI2 174 310 FORMAT(//3X,'IT=',I3,3X.'SBIG=',E8.2,3X.'ZBIG:'.E8.2, 3X.'nBIG=I,E8.2,3X.'DBI2=',E8.2) 17 5 312 IF (IT. EQ. 0) GOI'O 222 176 IF(IT.GT.50} GOTO 340 177 IF(SBIG.GT.O.001) GOTO 222 178 IF(IX-2) 320,330,330 17 9 320 I X=2 130 GOTO 380 1;3 1 330 I X= 1 182 GOTO 330 1dJ T=T-DT 134 DT=O.5*DT 185 350 DO 370 J=2,M1 186 DO 360 I=2,Nl 187 5 E (I, J) = 5 (I, J) 188 DLE(I.J)=DL(I,J) 189 DE2(I,J)=D2(I,J) 190 ZE(I.J)=Z(I,J) 191 BI(I,J)=llO-Z(I,J)-DL(I,J) 192 DZ(I,J)=XKK/(BK+ZE(I,J)*XK1)*CSE(I,J)-XKSI*(ZE{I,J) +BET*DLE(I,J) 1jj 36U CONTINUE 194 370 1:15 GOTO 210 19b 380 D5=0. 197 DO 400 J=2,M1 198 DO 390 I=2.Nl DSS=ABS(SN(I.J)-S(I,J 200 IF(DSS.GT.D5) DS=DSS 201 3YO CONTINUE 202 400 CONTINUE 203 IF(DS.LT.O.00001) GOTO 660 204 DB=O. 205 DO 420 J=2,rl1 206 DO 410 I=2,Nl 207 S(I,J)=SN(I,J) 2 () 8 Z (I, J) = Z N (I, J) 20J DL(I,J)=DLN(I,J) 21 0 IF (0 L (I J) Ii'r. L) B) D B= D L ( I, J) 2 1 1 D 2 ( I I .J) = D N 2 ( I ,J ) 212 410 213 420 CONTINUE 118

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c c C 214 21 S 21 G 217 L 1 b ,,2 1 'J 221 222 221 225 430 ,,") ,-L..:. I,) 440 227 228 450 229 230 231 232 23J 234 235 236 237 460 23d 470 239 240 241 480 242 490 243 244 245 246 247 248 TRUNCATION OF THE EDGES K=N/2 DO 480 J-=2,M1 DO 4JJ 1=2,K Ii' (SN (I,J}.EQ. 0.) GOlro 430 1,J*DX .s M-= ::; N (I + 1 J) -.s L GOTO 440 IF(SN{I,J).LT.SM) GOTO 450 SNCI,J)=Si1 S (I,J)=SM GOTO 450 CONTINUE SN (I,J) =0 S (I,J)=O. DO 460 I=K,tn IF(SH(I,J).GT.O.) GOTO 460 SL = ( S N (T -3 J) S (I -2 J) ) D X SM=SN (I-2,J) -SL IF(SN(I-l,J) .1T.SM) GOTO 490 IF (S LT. 0 .) GOT 0 In 0 s ( I -1 J) = S M S(I-l,J)=SM GOTO 490 CONTnHJE SN(I-l,J)=O. S(I-1,J)=O. ::;0 TO CONTINUE K=t'!/2 DO 550 I=2,Nl DO 500 J=2,K IF(SNCI"J).EQ.O.) GOTO 500 SL={SN(I,J+2)-SN(I,J+1*DX SM=SN (I,J+1) -SL IF(SM.LT.O.) GOTO 510 119

PAGE 133

249 H'(:iN(I,J).LT.::iL'i) GOTO 520 250 SN(I,J)=SM 251 S(I,J)=SM 252 GOTO 520 253 500 CON TIN DE 254 510 SN(I,J)=O. 255 S(I,J)=O. 256 DO 530 257 If(SN(I, .. J) .GT.Q.) GOTO 530 258 SL=(SN(I,J-3)-SN(I,J-2*DX 259 Sa=SN(I,J-2)-SL 260 IF{SN(I,J-1).1'.SM) GOTO 560 261 IF(SM.LT.O.) GCiTO 540 262 SN(I,J-1)=SM 263 264 GOTO 560 265 530 CONTINUE 266 540 SN(I.J-1)=O. 267 S(I,J-1)=0. 268 GOTO 560 269 550 CONTINUE 270 560 CONTINUE c ---------------------------------------------------------------C PRINTING RESULTS C ----------------------------------------------------------------271 561 fORMAT(5X,IALL ORDINATES ARE SMALLER THAN 0.05 METER1II) 272 2RIN'I 160.T 1.73 IF(ID .8Q.1) GOTO 508 2"74 562 27S 5i)2 FORl1AT(lII,10X,'l1AP OF DBAVDOWN!j'II) 276 CALL DiAW{S,I2,DB) 277 PRINT 278 564 FORMAT{/II,10X,' MAP OF SALTiiATEB MOUND'II) 27-:J IF(Z(20,20).GE.5.u) CALL DRAW(Z,IP,DB) 2UO CALL 2<31 IF(Z(20,20).LT.O.OS) PRINT 561 282 PRINT 565 283 IP=2 234 565 FORMAT(11110X,'MAP OF TRANSITICN ZCNE'llll 285 IF(DB.GE.5.) CALL DRAW(DL,IP,DB) 206 IF(DB.LT.5.0.AND.DB.GT.O.05) CALL DHAW1(DL,IP,DB) 287 IF'(DB.LT.O.05) PHINT 561 288 IP=l 2d 9 567 GOTu 5t.l6 290 568 570 291 "570 'NODE',SX,'S',11X,'Z',8I,IHODE',5X,'S',11X,'Z'/) 120

PAGE 134

292 ;)0 5 e It 1=1 .. N 293 DO 582 K=1,10 294 J=(K-1) *4+1 295 Jl=J+l 2915 J 2=J + 2 297 J3=J+J .2 9 8 fl R I In 5 a l) I .. J S {I J) Z (I .. J) 1 J 1 .. S (I J 1 ) Z (I J 1) .. ,I,J2,S (I,J2),2. C:,J2) ,I,J3,S(I,JJ) ,Z(I,J3) 29
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321 Jl=J-l 322 SN1=X(Jl) 323 SB=ABS(SN1-SN(I,J 324 SBIG=SB 32 5 IF ( S N 1 LT. 0 .. ) S N 1 = 0 326 SN(I,J)=SNl 327 630 CONTINUE 328 DO 640 J=2,Ml 329 SE(I,J)=O.5*(S(I,J)+SN(I,J 330 640 CONTINUE 331 650 )32 DO 655 I=2,Nl 333 DC 654' J=2,M1 3 J 4 F (Z (I" J) LT. 0 u 00 1) GOT a 65" 335 DEN=PNL+.25*XK1'*AB*(SE(I,J+l)-SE(I,J-l 336 DN2(I,J)=(D2(I,J)*PNL-XKT*AB*(DE2(I,J)*(SE(I,J+l)+SECI,J-l)* 2.*SE(I,J-.25*DN2(I,J-l)*(SE(I,J+l)-SE(I,J-l+D2(I.J)* .. (S.E (I + 1 J) +S E ( 11 J) -2. S.E (I, J) ) +. 25* (SE (I + 1 J) SE (1-1 J) ) .. SE(I-l,J**2+(SE(I,J+1)-SE(I,J-l**2/DEN 337 IF(DN2(I,J).LT.0.) DN2(I,J)=0. 338 654 CONTINUE 339 655 CONTINUE 340 GOTO 285 341 6bO CONTINUE 342 STOP 343 END C ---------------------------------------------------------------C SUBROUTINE SOLVES A SYSTEM OF LINEAR EQUATIOIIS C RE?&ESENTED BY A TRIDIAGONAL !ATTHIX C ----------------------------------------------------------------344 SUBROUTINE THOMAS(A,B,C,D,X,N) 345 DIMENSION A(N) ,B(N) ,C(N) ,D(N) ,leN) ,AL.FA(70) ,5I(70) 346 ALFA(l)=B(l) 347 S1(l)=O(l) 348 DO 20 349 350 ALFAel)=B(I)-E*C(1-1) 351 SIeI)=D(1)+E*SI(I-1) 352 20 CONTINUE 353 X eN} =S1 (N) /ALF A (N) 354 N1=N-1 355 DO 30 I=1.N1 356 J=N-I 357 X(J)={SI(J)+C(J)*X(J+l/ALFA(J) 358 30 CONTINUE 359 RETURN 360 END 122

PAGE 136

] F1 j .') 2 3'.d 3b 4 365 366 367 368 369 370 371 372 373 374 375 376 377 37 U 37 ') J(j 0 J8 1 J83 384 385 386 c c c 10 20 30 40 60 sanSODTINE MA2S VARIABLES BY APPLYING THE SUBROOTINE DRAW(W,I2,DB) *3 ii'(SO,SO) ,JB(50) ,AA(50) ,C(50) D AI':, CC/' '+-9+-',' '* '+-19',' 4< '''29',' *' '+39',' '50'1 ','+1+',' 10','+11',' 20','+21',' 30','+31',' 40' '+ 41 BB(l) =' ..... BB(40)='++ DO 10 1=2,39 HB(I)='+++' CON'l'.INUE 2 -,'+3+',' 12','+13',' 22','+23',' 32','+33',' 42' .. + 4 3' l?RINT 20,(BB(I),I=1,40) (40A3) 8B(1)=' + BB(40) =' + DO 60 J=2,39 DO 40 1=2,39 DO 30 K= 1,50 Xl=K-l.5 A:2=Xl+1 IF(Ii(I,J) .1.T.X2.AND.W(1,J) .GB.Xl) CONTINUE CONTINUE PRINT 20, (BB (I) ,1=1,40) 20, (BB (I) ,1=1,40) CONTINUE BB(l)=' ++' BB(40)='++ I 123 4 ','+5+',' 14','+15',' 24','+25',' 34','+35',' 4u','+45',' BB (1) =CC (K) 6 ','+7+-',' 16','+17',' 26', '+-2.7',' 36','+37',' 46','+47',' 8 18', 28', 36 I 48'

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3H7 388 389 390 391 392 393 394 395 396 J':J 7 39 CI 399 400 401 402 403 404 405 406 407 408 409 410 411 'f 12 L+ 1 3 414 415 416 417 418 419 420 421 422 423 42 + 425 426 427 428 429 430 431 432 433 434 C C C DO 70 1=2,39 BB(I)='''''''' 70 CONTINUE PRINT 20, (Bi3(I) ,1;1,40) IF{IP.EQ.2) GOTO 75 PfiINT RF:TURN 75 PRINT 8D,Dl.l 80 ORDINATE=',F8.3,' RETURN END SUBROUTINE DRAil MAPS PUMPAGE BY APPLYING THE TYPEVRITEB SUBROUTINE DRAWl (W,IP,DB) CHARACTER *3 AA,BB DIMENSION W(50,50),BB{50),AA(50)DATA AA!' ',' .1',' .2',' .3'.' .4',' .5'.' .6',' .7',' .8', .9','1. ','1.1','1.2','1.3','1.4','1.5'.'1.6','1.7','1.8', ,.. '1.9' '2. ',' 2. 1 2.2' 2.3' 2.4' 2.5' 2.6' 2 .. 7', '2.8' '2.9','3. ','3.1','3.2','3.3','3.4'.'3.5','3.6','3.7','3.8', '3.9','4. ','4.1','4.2'.'4.3','4.4','4.5','4.6','4.7','4.8', '4.9'/ BB(l) =' "+' 8B(40)='++ DO 10 1=2,39 BDCI)='"+''' 10 CONTINUE PRINT 20, (BB (I) ,1=1,40) 20 FORM AT (40A3) BB(1)=' + B3(40)=' + DO 60 J=2,39 DO iH) 1=2,39 DO 30 K=1.50 X-=.1*K-O.05 X1=X-O.15 IF(i(I,J) .LT.I.AND.W(I,J) BB(I)=AA(K) )0 CONTINUE 40 CONTINUE PRINT 20,(bB(I),I=1,40) rRINT 20,(EB(I),I=1.40) 60 CONTINUE BB(l)=' ++' BB(40)='++ DO 70 1=2,39 8B(1)='''++' 70 CONTINUE PRINT 20,(BB(I),1=1,40) IF(IP.EQ.2) GOTO 75 PRINT 80,W{20,20) RETU.RN 75 PRINT 80,DB 80 FORMA'IC//5X, 'XA..'{I!1AL ORDINATE=' ,.F8.3, I METE.B'!!) RETOBN END \$ENT Jl Y 124

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REFERENCES Arthur, M.G., Fingering and coning of water and gas in homogeneous oil sand, Trans. Am. Inst. Mining Met. Engrs., 155, 184-201,1944. Bear, J., and G. Dagan, Moving interface in coastal aquifers, J. Hydraul. Div., Amer. Soc. Civil Eng., 90 (HY4), 193-216,1964. Benedict, B.A., Modeling of toxic spills into waterways, Hazard Assess ment of Chemicals, Current Developments, Vol. 1, Ed. by J. Saxena and F. Fisher, Academic Press, New York, 251-301,1981. Bentley, C., Aquifer test analysis of the Floridan Aquifer in Flagler, Putnam, and St. Johns Counties, Florida, U.S. Geo1. Survey Water Resources Investigation Series, WRI 77 (36), 1977. Bermes; B.J., G.W. Leve, and G.R. Tarver, Geology and groundwater resources of Flagler, Putnam, and St. Johns Counties, Florida, Fla. Geol. Survey Rept. Inv. No. 32, 1963. -Chen, C.S., The regional lithostratigraphic analysis of Paleocene and Eocene rocks of Florida, Fla. Bur. of Geo1. Bulletin 45,1965. Dagan, G., Pertubation solutions of the dispersion equation in porous medi a, Resources Res., 7. (1), 135-142, 1971. E1dor, M., and G. ,Dagan, Solutions to hydrodynamic dispersion in porous media, Water Resources Res. ,8 (5), 1316-1331, 1972. Ge1har, L.W., and M.A. Collins, General analysis of longitudinal dis persion in nonuniform flow, Water Resources Res.,7 (6), 1511-1521, 1971. Ghyben, B.W., and J. Drabbe, Nota in verband met de voorgenomen putboring nabij Amsterdam, Tijdscrift von het Koninklujk Institut von Ingeniurs, The Hague, Netherlands, 8-22, 1888. Hantush, M.S., Unsteady movement of freshwater in thick unconfined saline aquifers, Bulletin of the I.A.S.H.,13 (2),40-48, 1968. Haubo1d, R.G., Approximation for steady interface beneath a well pumping freshwater overlying saltwater, Groundwater,13 (3), 254-259, 1975. Herzberg, B., Die Wasserversorgung einiger Nordscebader, Jour. Gasbeleuchtung und Wasserversorgung, 44, 815-819, 842=844, 1901. Hunt, B., Dispersion calculation in nonuniform seepage, J. Hydro1., 36, 261-277, 1 978. 125

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126 Johnson, R.A., Geology of the Oklawaha Basin, St. Johns River Water Management District, Tech. Rept. No.1, 1979. Mitchell, A.R., Computational Methods in Partial Differential Equations. John Wiley and Sons Ltd., London, 50-81, 1976. Munch, D.A., B.J. Ripy, and R.A. Johnson, Saline contamination of a lime stone aquifer by connate intrusion in agricultural areas of St. Johns, Putnam, and Flagl.er Counties, Northeast Florida, St. Johns River Mgmt. Dist. Florida, 2 (1), 1979. Muskat, M., and R.D. Wychoff, An approximate theory of water-coning in oil production, Trans. Am. Inst. Mining Met. Engrs 114, 144-163, 1935. Ozisik. M.N., Heat Conduction, John Wiley and Sons, New York. Chapter 9, 1980. Peaceman, D.W., and H.H. Rachford, The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. App. Math., 3, 28-41, 1955. Pinder, G.F. and H.H. Cooper, A numerical technique for calculating the transient position of the saltwater front, Water Resources Res. 6 (3). 875-882, 1970. Prakash. A Groundwater contamination due to vanishing and finite-size continuous sources, Journal of the Hydraulics Division, American Society of Civil Engineers, 108, No. HY4, 572-590, April, 1982. Rubin. H., On the application of the boundary layer approximation for the simulation of density stratified flows in aquifers, to be pub lished in Advances in Water, Resources, 1982. Rubin, H and B.A. Christensen, Simulation of stratified flow in the Floridan Aquifer, ASCE Irrigation and Drainage Div. Specialty Conference, Orlando, FL, July 21-23, 1982. Rubin, H., and G.F. Pinder, Approximate analysis of upconing, Advances in Water Resources, I, 97-101, 1977. Sagar, B., Dispersion in three dimensions: approximate analytic solutions, Journal of the Hydraulics Division, American Society of Civil Eng ineers, 108, No. HY1, 47-62, January. 1982. Segol, G., G.F. Pinder. and W.G. Gray, A Galerkin finite element technique for calculating the transient position of the saltwater front, Water Resources Res., 11 (2), 343-347, 1975. --Shamir. U., and G. Dagan, Motion of the seawater interface in coastal aquifers: a numerical solution, Water Resources Res. 7, (3), 644657. 1971. Wilson, J.L., and P.J. Miller, Two-dimensional plume in uniform ground water flO\'I, Journal of the Ha-draulics Division. American Society of Civil Engineers, 108, No. HY 503-514, April, 1982.