• TABLE OF CONTENTS
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 Front Cover
 Report documentation page
 Title Page
 Table of Contents
 List of Tables
 List of Figures
 Introduction
 Laboratory studies
 Data analysis
 Results and discussion
 Conclusions
 References
 Data reduction






Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 92/004
Title: Beach face dynamics as affected by ground water table elevations
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 Material Information
Title: Beach face dynamics as affected by ground water table elevations
Series Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 92/004
Physical Description: Book
Creator: Oh, Tae-Myoung
Dean, Robert G.
Publisher: Coastal and Oceanographic Engineering Department
Publication Date: 1992
 Subjects
Subject: Ground water
Beach erosion
 Notes
Funding: This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
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Bibliographic ID: UF00080459
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
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Table of Contents
    Front Cover
        Front Cover
    Report documentation page
        Unnumbered ( 2 )
    Title Page
        Title Page
    Table of Contents
        Page I
    List of Tables
        Page II
    List of Figures
        Page III
    Introduction
        Page 1
        Page 2
    Laboratory studies
        Page 2
        Page 3
        Page 4
    Data analysis
        Page 5
        Page 4
        Page 6
        Page 7
    Results and discussion
        Page 8
        Page 9
        Page 7
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
    Conclusions
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 14
        Page 21
    References
        Page 22
        Page 21
    Data reduction
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
Full Text



UFL/COEL-92/004


BEACH FACE DYNAMICS AS AFFECTED BY
GROUND WATER TABLE ELEVATIONS






by




Tae-Myoung Oh
and
Robert G. Dean


May, 1992





REPORT DOCUMENTATION PAGE
1. Report No. 2. 3. Recipient aC ccession No.


4. Title and Subtitle i. Report Date
May, 1992
BEACH FACE DYNAMICS AS AFFECTED BY GROUND
WATER TABLE ELEVATIONS 6.

7. Author() Tae-Myoung Oh a. Pertorulns Oranization report No.
Robert G. Dean UFL/COEL-92/004

9. Performing Organization Jame and Address 10. Project/Task/Uork Unit No.
Coastal and Oceanographical Engineering Department
University of Florida 11. contract or crant No.
336 Weil Hall
Gainesville, FL 32611 13. T of epet
12. Sponsoring Orgnization Name and Address Miscellaneous



14.
15. Supplementary Notes



16. Abstract

This report presents the results of laboratory studies which were carried out in the Coastal
and Oceanographical Engineering Laboratory to investigate the effects of ground water table
elevations on the beach profile changes over the swash zone. The experiment was conducted at
three different water table levels while the other experimental conditions were fixed to constant
values with regular waves. The water table levels included (1) normal water table level which
is the same as mean sea level, (2) a higher level and (3) a lower level than the mean sea
level. Special attention was given to the higher water level to investigate whether this level
enhances erosion of the beach face and also to methods of interpreting the experimental data.
The experiment described herein was carried out with a fairly fine sand and has demonstrated
the significance of beach water table on profile dynamics. The increased water table level
caused distinct effects in three definite zones. First, erosion occurred at the base of the beach
face and the sand eroded was carried up and deposited on the upper portion of the beach
face. Secondly, the bar trough deepened considerably and rapidly and the eroded sand was
deposited immediately landward. This depositional area changed from mildly erosional to
strongly depositional. Third, the area seaward of the bar eroded with a substantial deepening.
The lowered water table appeared to result in a much more stable beach and the resulting
effects were much less. The only noticeable trend was a limited deposition in the scour area at
the base of the beach face.

17. Orginator's Key Uords 18. Availability Statment
Beach Face Dynamics
Ground Water Table Elevations
Experimental Data Analysis


19. U. S. Security Classif. of the Report 20. U. S. Security Classif. of This Page 21. No. of Peges 22. Price
Unclassified Unclassified 35















Beach Face Dynamics
as Affected by
Ground Water Table Elevations






by
Tae-Myoung Oh
and
Robert G. Dean


May, 1992











TABLE OF CONTENTS


Table of Contents i

List of Tables ii

List of Figures iii

1 Introduction 1

2 Laboratory Studies 2
2.1 Facilities . . . . . . . . .. 2
2.2 Procedures . . . . . . . . . 3
2.3 M easurem ents ................................... 3

3 Data Analysis 4
3.1 Compilation of Data ............................... 4
3.2 Equilibrium Criteria ............................... 6

4 Results and Discussions 7

5 Conclusions 14

6 References 21

Appendix A 23









LIST OF TABLES


A.1 Volume Errors and Mismatch ................. ....... 25
A.1 Calibration Factors at Each Time Step . . . ... .. 26











LIST OF FIGURES


1 Schematic Diagram of Initial Profile and Experimental Details . 5
2 Profiles at 0.0 hrs and 0.5, 1.0 and 1.5 hrs with Normal Water Table Level 8
3 Profiles at 0.0 hrs and 1.5 hrs at Normal Level and at 2.0, 2.5, 3.0 and 3.5
hrs with Higher Water Table Level ................... .. 9
4 Profiles at 0.0 hrs and 3.5 hrs at Higher Level and 4.0, 4.5 and 5.0 hrs with
Lower Water Table Level ................... ...... 10
5 Distributions of Squared Profile Change Rate (el) at 0.0-0.5, 0.5-1.0 and
1.0-1.5 hrs associated with Normal Water Table Level . . ... 11
6 Distributions of Squared Profile Change Rate (el) at 1.5-2.0, 2.0-2.5, 2.5-
3.0 and 3.0-3.5 hrs associated with Higher Water Table Level ....... .. 12
7 Distributions of Squared Profile Change Rate (el) at 3.5-4.0, 4.0-4.5 and
4.5-5.0 hrs associated with Lower Water Table Level . .... 13
8 Profiles, Profile Differences and Transport Rate Curves during Normal,
Higher and Lower Water Table Levels. . . . . 15
9 Definitions of Berm Height, Onshore Scour Depth, Onshore Deposition
Height, Bar Trough Depth, Bar Crest Height and Offshore Scour Depth 16
10 Time Variations of Berm Height, Onshore Scour Depth, Onshore Depo-
sition Height, Bar Trough Depth, Bar Crest Height and Offshore Scour
Depth ................. ................... 17
11 Time Variations of Root Mean Square Value of the Profile Change Rate, E1 18
12 Time Variations of Root Mean Square Value of the Profile Deviations from
the Initial Profile, E2 ................... ......... 19
13 Time Variations of Average Absolute Transport Rate, E3 . ... 20
A.1 Filter Response Function versus Wave Number . . . .. 28
A.2 Unfiltered and Filtered Data for 3.5 hrs . . . .... 29
A.3 Wave Number Spectrum of the Unfiltered, Filtered and Removed Ripples
for 3.5 hrs . . . . . . . . .. .. 30
A.4 Time Signal of Removed Ripples for 3.5 hrs . . . ... 31










1 Introduction


The swash zone is defined as that region on the beach face delineated at the upper
level by the maximun uprush of the waves and at its lower extremity by the maximun
downrush. This region becomes alternately wet and dry, as the waves move up and
down until they disappear into the beach or return to the sea. Knowledge of the swash
zone is very important because not only does it provide the boundary condition for
beach profile evolution models but sediment transport in this zone is directly related
to the shoreline position. Additionally, a significant portion of the longshore sediment
transport may occur in the swash zone. Hence, considerable research has been directed
toward understanding and predicting swash mechanisms and related processes.
Studies by Bagnold (1940) and Bascom (1951) found that the dynamic sediment
distribution in the swash zone is a function of the characteristics of the incoming waves
and the sand size. The effects of incoming waves are obvious; they provide the mass
and momentum of the water in the swash zone. On the other hand, the sand size of the
beach face is related to its stability and will influence the water motion through the bed
roughness and the porosity. If we change the point of view from individual factors to the
forces induced by them, then we can say that the sediment transport in the swash zone
is a function of several forces (e.g., friction, gravity, inertia and pressure gradient forces)
acting on a water element within the swash zone.
With the combination of these forces, the waves rush up the foreshore until they lose
all their forward momentum, at which time the velocity of the leading edge of the waves
or the mass of uprush flow is zero. During that time, most of the sediment transported
is deposited on the foreshore. As the foreshore slope is increased by sediment deposition,
backrush velocities are increased thereby limiting further net acceretion. Finally, the
equilibrium slope of the swash zone is reached. However, if there are any changes in
these forces, the system will again be put into disequilibrium.
Grant (1948) noted by observations that the aggradation or degradation of a beach,
and the value of the beach slope are functions of several variables, one of which is the
position of the ground water table within the beach. A high water table accelerates
beach erosion, and conversely, a low water table may result in pronounced aggradation
of the foreshore. This concept has been supported by various researchers. Most of their
studies have focused on tidal cycle response (Emery and Foster, 1948; Duncan, 1964) or
on high frequency response to individual waves (Emery and Gale, 1951; Waddel, 1973
and 1976; Sallenger and Richmond, 1984). The results of these studies not only support
Grant's idea very strongly but try to provide additional physical reasoning. If we have a
low water table, water percolates rapidly into the sand and reduces the uprush mass as
well as velocity and this facilitates deposition of sand over the swash zone. Conversely
for a saturated beach, water escapes through the sand and increases mass and velocity
of the backrush flow and this enhances erosion of the swash zone. Most of the available
studies are based on field measurements and have not been carried out with controlled
laboratory experiments.










Based on possibilities of beach stabilization, test installations of the beach drain
system have been conducted; this approach consists of burying a pipeline along the
beach to lower the water table level on the beach face by pumping (Machemehl, French
and Huang, 1975; Chappell, Eliot, Bradshaw and Lonsdale, 1979; Danish Geotechnical
Institute, 1986; Terchunian, 1989). Successful demonstrations have been carried out in
the laboratory and apparently in the field, although the field data are more ambiguous.
Most of these studies argued that beach dewatering stabilizes beaches by enhancing
deposition on wave uprush and retarding erosion on wave backrush and hence, beach
aggradation could be induced by maintaining the beach water table at a low level.
As noted by Dean and Dalrymple (1991), however, it is not obvious how this method
works, which it clearly does in the laboratory. Kawata and Tsuchiya (1986) pointed out
the ratio of the seepage velocities within the sand to the velocities within the jet of fluid
rushing up the beach face are about 1/1000. Bruun (1989) claimed that the method
ought to be more effective in mild conditions than storm conditions as the velocities are
far higher in the surf zone during a storm. It was noted also by Chappel et. al. that,
in the case of beach erosion, more is involved than the simple effect of high water tables
increasing the backrush.
This brief report presents the results of a laboratory study of beach face dynamics
as affected by the variations of ground water table elevations within the beach. To
achieve this goal, an experiment was conducted at three different water table levels while
the other factors (e.g., wave height, wave period, water depth, initial beach slope, etc.)
were fixed to constant values with regular waves. The water table levels included : (a)
normal water table level which is the same as mean sea level, (b) a higher level and (c)
a lower level than the mean sea level. Special attention is given to the higher water level
to investigate whether this level enhances erosion of the beach face or not and also to
methods of interpreting the experimental data.


2 Laboratory Studies

2.1 Facilities
Laboratory studies were carried out in the Coastal and Oceanographical Engineering
Laboratory to investigate the effects of ground water table elevations on the beach profile
changes over the swash zone. The major facility was a wave tank which is 120 ft long, 6
ft wide and 6 ft deep. A long partition has been constructed along the tank centerline
dividing it into two channels each of 3 ft width. A hydraulic driven piston-type wave
maker is located at one end of tank and a sand beach was constructed at the downwave
end of the parallel channel in which the tests were conducted. Regular waves with a
period of 2.0 sec and height of 0.160 m were utilized for this experiment. The initial
beach profile was linear at a slope of 1:18. The water depth at the toe of the beach slope
was 1.5 ft at mean sea level. The beach was composed of well-sorted fine sand with a
median diameter of 0.2 mm (2.32 in 0 unit) and a sorting value of 0.53.










Based on possibilities of beach stabilization, test installations of the beach drain
system have been conducted; this approach consists of burying a pipeline along the
beach to lower the water table level on the beach face by pumping (Machemehl, French
and Huang, 1975; Chappell, Eliot, Bradshaw and Lonsdale, 1979; Danish Geotechnical
Institute, 1986; Terchunian, 1989). Successful demonstrations have been carried out in
the laboratory and apparently in the field, although the field data are more ambiguous.
Most of these studies argued that beach dewatering stabilizes beaches by enhancing
deposition on wave uprush and retarding erosion on wave backrush and hence, beach
aggradation could be induced by maintaining the beach water table at a low level.
As noted by Dean and Dalrymple (1991), however, it is not obvious how this method
works, which it clearly does in the laboratory. Kawata and Tsuchiya (1986) pointed out
the ratio of the seepage velocities within the sand to the velocities within the jet of fluid
rushing up the beach face are about 1/1000. Bruun (1989) claimed that the method
ought to be more effective in mild conditions than storm conditions as the velocities are
far higher in the surf zone during a storm. It was noted also by Chappel et. al. that,
in the case of beach erosion, more is involved than the simple effect of high water tables
increasing the backrush.
This brief report presents the results of a laboratory study of beach face dynamics
as affected by the variations of ground water table elevations within the beach. To
achieve this goal, an experiment was conducted at three different water table levels while
the other factors (e.g., wave height, wave period, water depth, initial beach slope, etc.)
were fixed to constant values with regular waves. The water table levels included : (a)
normal water table level which is the same as mean sea level, (b) a higher level and (c)
a lower level than the mean sea level. Special attention is given to the higher water level
to investigate whether this level enhances erosion of the beach face or not and also to
methods of interpreting the experimental data.


2 Laboratory Studies

2.1 Facilities
Laboratory studies were carried out in the Coastal and Oceanographical Engineering
Laboratory to investigate the effects of ground water table elevations on the beach profile
changes over the swash zone. The major facility was a wave tank which is 120 ft long, 6
ft wide and 6 ft deep. A long partition has been constructed along the tank centerline
dividing it into two channels each of 3 ft width. A hydraulic driven piston-type wave
maker is located at one end of tank and a sand beach was constructed at the downwave
end of the parallel channel in which the tests were conducted. Regular waves with a
period of 2.0 sec and height of 0.160 m were utilized for this experiment. The initial
beach profile was linear at a slope of 1:18. The water depth at the toe of the beach slope
was 1.5 ft at mean sea level. The beach was composed of well-sorted fine sand with a
median diameter of 0.2 mm (2.32 in 0 unit) and a sorting value of 0.53.










2.2 Procedures


The experiment was conducted over a duration of 4.5 hrs to examine the changes of
an initially linear beach profile subject to a regular wave at three different water table
levels. The duration of each test with the same water table level was determined based on
an assessment that the beach profiles were near equilibrium and would not significantly
change beyond this test duration. Throughout the test program, the beach profiles were
monitored at one-half hour intervals.

The test procedures are as followings:

1. Measure the initial beach profile.

2. Run waves for 1.5 hrs with normal water table level.

3. Establish a new water table level which is 0.36 ft higher than normal.

4. Run waves for 2.0 hrs while maintaining the higher water table level.

5. Establish a new water table level which is 0.36 ft lower than normal.

6. Run waves for 1.5 hrs while maintaining the lower water table level.

The raised water table (at 1.5 hrs) was established by raising the entire water level in
the wave tank and allowing the ground water table to equilibrate with no waves acting.
The tank water level was then lowered and the water table was maintained by excavating
a small depression in the berm below the desired water level, which was then maintained
by filling periodically with a hose. For the lower water table, the procedure described
above was followed except that water was siphoned out of the excavated hole in the beach
berm to maintain the desired level.

2.3 Measurements
For two-dimensional laboratory experiments, sand should be conserved between a land-
ward position of profile closure, where no changes in profile occurred, and a seaward
depth of closure, where no sand transport occurred; this implies that the profile data
measurements should cover the length between these two positions.
During the experiment, the landward closure could be defined easily by observation.
However, defining the seaward depth of closure was more difficult since a small quantity
of sand was transported beyond the toe of the beach slope and was spread in a thin layer
over the horizontal section of the tank. Hence, the seaward closure was assumed to be
located at 1 ft seaward from the toe of beach. These allowances of the small seaward
transport could cause transport volume errors, which will be discussed later.










In this study, the origin is taken at the landward position of profile closure and at
still water level, with the x-axis oriented seaward and the z-axis upward. For this origin,
the seaward depth of closure was found to be approximately 30 ft and this length is
designated as Fig.1 shows the schematic diagram of initial profile and experimental
details.
Beach profiles over a 30.0 ft portion of the active profiles were documented by a
combination of automatic bed profiler which only functions over submerged profiles and
manual measurements at time intervals of 0.5 hrs. The profiler mounted on the carriage
was used for measuring the beach profiles from 7.0 ft to 30.0 ft. The beach profile
from 0.0 ft to 7.0 ft was measured manually since the water depth in this region was
too small for accurate readings. Exceptions are the profiles at 0.0 and 1.5 hrs. For
the initial profile, the whole profile over the measurement length was measured by using
profiler after increasing the mean sea level. The profile at 1.5 hrs was documented by
using the profiler except for the landward 1.0 ft portion. These two parts of bed profile
data were combined later for subsequent processing. In addition, three profiles across the
tank were measured over the whole measurement length to document three-dimensional
effects; these three profiles were averaged to represent the mean profile. It is noted that
the profiler did not operate properly during the profile measurements at 3.0 and 3.5 hrs
and only one profile was taken at these times. It should be noted also that the offset
of profiler changed approximately 0.04 volt after 3.0 hrs, which could cause the shift of
bed profile as much as 0.03 ft. The effects of these errors in the measurements will be
discussed in the next section.


3 Data Analysis

3.1 Compilation of Data
Sand conservation can be checked easily by calculating the time-averaged change in sed-
iment volume per unit width of tank, which is obtained by integrating the profile differ-
ences from the initial profile over the portion of the active profiles as :

V(t)= [z(x,t) z(x,0)] d (1)

here z(x, t) is the profile elevation at a given point x and time t and z(x, 0) is the initial
profile.
For complete conservation of sand, if the bulk density is unchanged, the integrated
value V(t) should be zero. However, as expected, the errors in transport volumes were
found to be non-zero. To satisfy the condition of sand conservation the mean profile at
each time step was adjusted. The details of this adjustment and a filtering procedure to
remove the ripples are summarized in Appendix A.

























- ..... MEASURED
u-

0.36 FT HIGHER WATER TABLE


i 0.0 --N -......................................------------------------
SNORMAL HATER TABLE ORIGIN
C


Z 0.36 FT LOHER HATER TABLE
C

I
.-J

-1.0 INITIAL SLOPE = 1:18
-1.0

SAND SIZE = 0.2 (MM)


WATER DEPTH = 1.542 (FT)
TANK BOTTOM' TANK BOTTOM



-2.0 I I I I I I
-15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0

DISTANCE ( FT )



Fig.1 Schematic Diagram of Initial Profile and Experimental Details










In this study, the origin is taken at the landward position of profile closure and at
still water level, with the x-axis oriented seaward and the z-axis upward. For this origin,
the seaward depth of closure was found to be approximately 30 ft and this length is
designated as Fig.1 shows the schematic diagram of initial profile and experimental
details.
Beach profiles over a 30.0 ft portion of the active profiles were documented by a
combination of automatic bed profiler which only functions over submerged profiles and
manual measurements at time intervals of 0.5 hrs. The profiler mounted on the carriage
was used for measuring the beach profiles from 7.0 ft to 30.0 ft. The beach profile
from 0.0 ft to 7.0 ft was measured manually since the water depth in this region was
too small for accurate readings. Exceptions are the profiles at 0.0 and 1.5 hrs. For
the initial profile, the whole profile over the measurement length was measured by using
profiler after increasing the mean sea level. The profile at 1.5 hrs was documented by
using the profiler except for the landward 1.0 ft portion. These two parts of bed profile
data were combined later for subsequent processing. In addition, three profiles across the
tank were measured over the whole measurement length to document three-dimensional
effects; these three profiles were averaged to represent the mean profile. It is noted that
the profiler did not operate properly during the profile measurements at 3.0 and 3.5 hrs
and only one profile was taken at these times. It should be noted also that the offset
of profiler changed approximately 0.04 volt after 3.0 hrs, which could cause the shift of
bed profile as much as 0.03 ft. The effects of these errors in the measurements will be
discussed in the next section.


3 Data Analysis

3.1 Compilation of Data
Sand conservation can be checked easily by calculating the time-averaged change in sed-
iment volume per unit width of tank, which is obtained by integrating the profile differ-
ences from the initial profile over the portion of the active profiles as :

V(t)= [z(x,t) z(x,0)] d (1)

here z(x, t) is the profile elevation at a given point x and time t and z(x, 0) is the initial
profile.
For complete conservation of sand, if the bulk density is unchanged, the integrated
value V(t) should be zero. However, as expected, the errors in transport volumes were
found to be non-zero. To satisfy the condition of sand conservation the mean profile at
each time step was adjusted. The details of this adjustment and a filtering procedure to
remove the ripples are summarized in Appendix A.










3.2 Equilibrium Criteria
For analyzing the data, it is helpful to define what is meant by 'equilibrium' profile
and also to determine whether or not equilibrium has been reached. In the field, the
equilibrium profile is considered to be 'dynamic' as the tide and incident wave field change
continuously in nature and therefore the profile changes shape as well. In the laboratory
it is relatively easy to establish an equilibrium profile, by running a steady wave train onto
a beach for a long time. After the remolding of the initial profile, a 'final' profile results,
which changes little with time. This is the equilibrium profile for that beach material
and wave conditions. Hence, as a beach profile approaches an equilibrium, the incident
wave energy is dissipated without any significant profile changes and the time-averaged
sediment transport rate converges to zero at all points along the profile.
From this definition of equilibrium, we can develop criteria to indicate the approach
of the profile to an equilibrium. In this study, three criteria are suggested as follows :

(1) Root mean square (RMS) profile change rate, E1


E1 el(x, t) d (2)

where,
el(,t) = (AZ)2
Az = z(x,t) z(x,t At) (3)
At = the profiling interval ( 0.5 hrs )

E1 has dimensions of velocity and indicates the rate of profile change during consecutive
times.

(2) RMS profile deviations from initial profile, E2


E2 = e2(x,t) dx (4)

where,
e2(x,t) = [z(x,t) z(x, 0)2 (5)

E2 has dimensions of length and indicates the overall profile changes relative to the
initial profile. As the profile approaches equilibrium, E2 approaches a constant value,
which implies that the decrease in slope of the E2 curve is a measure of the rate at
which the equilibrium is approached. This criterion may be misleading as a measure of
equilibrium as it can be seen that a profile shifting along an initially planar slope would
cause no change in E2. Hence, it may not be a good measure.










(3) Average of the absolute transport rate, E3


1
E3 = e3(x,t) dx (6)

where,
e3(x,t) = Iq(x,t)l
q(x, t) = time-averaged sediment transport rate (7)
= -o dx

E3 has dimensions of transport rate per unit width of tank. This criteria is equal to the
averaged sediment transport rate over the interval of change. Also, E3 approaches zero
with equilibrium conditions.

Smaller values of criteria E1 and E3 and steady values of criteria E2 indicate that
the profile is more stable and approaches an equilibrium. If there are any changes in
experimental conditions such as variations in water table level, then we would expect the
three criteria to reflect these changes.


4 Results and Discussions

The profile evolutions with three water levels are presented in Fig.2 through Fig.4. Fig.2
shows the profiles at 0.0, 0.5, 1.0 and 1.5 hrs measured during normal water table level.
Fig.3 and Fig.4 show the profiles measured during higher and lower level, respectively,
together with the initial profile and the last profile of the previous water table level. In
general, the bar moved seaward with normal level, and the profiles were approaching an
equilibrium. After changing to the higher level, the bar started to move landward rapidly
at the initial stages and stayed stationary at the later times. Also at the higher water
table, the trough deepened and the profile aggraded substantially in a zone immediately
landward of the trough. The bar position remained almost fixed even after lowering the
water table level. Profile changes in the swash zone were small during the normal and
lower water table levels. However, the berm built up very rapidly during the higher level.
These general trends can be confirmed more clearly by examining Fig.5 through Fig.7,
which represent the distributions of the squared profile change rate over the measurement
length with the fixed water table level. Fig.5 shows the squared values at 0.0-0.5, 0.5-1.0
and 1.0-1.5 hrs with normal level while Fig.6 and Fig.7 show the distributions with the
higher and lower level. During the first wave run, shown in Fig.5, significant changes
occurred as the profile shape varied from a nearly planar slope to a barred profile. As
the profile approached equilibrium, the values of the distributions approached zero at all
points. As soon as the higher level was established, however, very large changes occurred
at the bar crest with relatively smaller changes at the bar trough.





















1.0 I


1.5 (HR)
1.0 (HR)
LL 0.5
S------- 0.5 (HR)

j ------------- 0.0 (HR)


20.0










.0.0 :-----------------------------------------------------------------------------------------------------------
cr
z




















DISTANCE ( FT ]
Fig.2 Profiles at 0.0 hrs and 0.5, 1.0 and 1.5 hrs with Normal Water Table Level
I-

._J






-1.5




-2.0 I I I I
0.0 5.0 10.0 15.0 20.0 25.0 30.0

DISTANCE ( FT I


Fig.2 Profiles at 0.0 hrs and 0.5, 1.0 and 1.5 hrs with Normal Water Table Level


I



















1.0 I
3.5 (HR)
-- -- 3.0 (HR)
.- --- 2.5 (HR)
L.. 0.5
2.0 (HR)
_ --- -- 1.5 (HR)
-- -.....-----..- 0.0 (HR)
000.0 (R]

0 O 0 -- M-L
S0.0



2 -0.5


-j
-1.0




-1.5




-2.0 I I
0.0 5.0 10.0 15.0 20.0 25.0 30.0

DISTANCE ( FT


Fig.3 Profiles at 0.0 hrs and 1.5 hrs at Normal Level and 2.0, 2.5, 3.0 and 3.5 hrs with
Higher Water Table Level. Note the rapid build-up above the mean water level
(MWL) and scour below MWL.










(3) Average of the absolute transport rate, E3


1
E3 = e3(x,t) dx (6)

where,
e3(x,t) = Iq(x,t)l
q(x, t) = time-averaged sediment transport rate (7)
= -o dx

E3 has dimensions of transport rate per unit width of tank. This criteria is equal to the
averaged sediment transport rate over the interval of change. Also, E3 approaches zero
with equilibrium conditions.

Smaller values of criteria E1 and E3 and steady values of criteria E2 indicate that
the profile is more stable and approaches an equilibrium. If there are any changes in
experimental conditions such as variations in water table level, then we would expect the
three criteria to reflect these changes.


4 Results and Discussions

The profile evolutions with three water levels are presented in Fig.2 through Fig.4. Fig.2
shows the profiles at 0.0, 0.5, 1.0 and 1.5 hrs measured during normal water table level.
Fig.3 and Fig.4 show the profiles measured during higher and lower level, respectively,
together with the initial profile and the last profile of the previous water table level. In
general, the bar moved seaward with normal level, and the profiles were approaching an
equilibrium. After changing to the higher level, the bar started to move landward rapidly
at the initial stages and stayed stationary at the later times. Also at the higher water
table, the trough deepened and the profile aggraded substantially in a zone immediately
landward of the trough. The bar position remained almost fixed even after lowering the
water table level. Profile changes in the swash zone were small during the normal and
lower water table levels. However, the berm built up very rapidly during the higher level.
These general trends can be confirmed more clearly by examining Fig.5 through Fig.7,
which represent the distributions of the squared profile change rate over the measurement
length with the fixed water table level. Fig.5 shows the squared values at 0.0-0.5, 0.5-1.0
and 1.0-1.5 hrs with normal level while Fig.6 and Fig.7 show the distributions with the
higher and lower level. During the first wave run, shown in Fig.5, significant changes
occurred as the profile shape varied from a nearly planar slope to a barred profile. As
the profile approached equilibrium, the values of the distributions approached zero at all
points. As soon as the higher level was established, however, very large changes occurred
at the bar crest with relatively smaller changes at the bar trough.





















1.0 I


5.0 (HR]
-- -- 4.5 (HR)
L. 0.54.5 (fIR)
L- 0.5
4.0 (HR)
S---- 3.5 (HR)
-I
S--- .--- ----- 0.0 (HR)
S0.0 -------- -----------------------------------
O ) HWL
z
cI-

O -0.5


_J

-i.S
-1.0




-1.5




-2.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0

DISTANCE ( FT



Fig.4 Profiles at 0.0 hrs and 3.5 hrs at Higher Level and 4.0, 4.5, and 5.0 hrs with
Lower Water Table Level. Note the relatively small changes.




















0.30 I
1.0 TO 1.5 (HR)
S----- 0.5 TO 1.0 (HR)

S----- 0.0 TO 0.5 (HR)
S0.25


I-
U-




(L



C3
I


-J
L 0.10













DISTANCE ( FT
a-
LU

c. o; o
C 0.05 0 ; "





0.0 5.0 10.0 15.0 20.0 25.0 30.0

DISTANCE ( FT )



Fig.5 Distributions of Squared Profile Change Rate (el) at 0.0-0.5, 0.5-1.0 and 1.0-1.5
hrs associated with Normal Water Table Level





















0.30


J -, -
0.--- 2.0 TO 2.5 (HR)
- 0.25 -
S--------------- 1.5 TO 2.0 (HR)

I-
4-

Ll 0.20 -
1-



S0.15 .
cI'


-J


C 0.05 i
LLJ











S0.00
0.0 5.0 10.0 15.0 20.0 25.0 30.0

DISTANCE ( FT )



Fig.6 Distributions of Squared Profile Change Rate (el) at 1.5-2.0, 2.0-2.5, 2.5-3.0 and
3.0-3.5 hrs associated with Higher Water Table Level























4.5 TO 5.0 (HR)
--- 4.0 TO 4.5 (HR)

----- 3.5 TO 4.0 (HR)


4" ~
- S


20.0


25.0


30.0


DISTANCE ( FT )



Fig.7 Distributions of Squared Profile Change Rate (el) at 3.5-4.0, 4.0-4.5 and 4.5-5.0
hrs associated with Lower Water Table Level


0.30


0.25





0.20





0.15





0.10





0.05


0.00


10.0


- ---- --~


-3C_ --C--IC-l










Also, significant deposition commenced within the upper portion of the swash zone.
During the experiment with the higher water level, the peak of the berm moved landward
continuously, which meant deposition over the swash zone. This is contradictory to pre-
vious studies that higher water table level enhances erosion. However, there was erosion
immediately seaward. It appears that this eroded material was deposited landward in
the berm. As shown in Fig.7, little changes occurred with lower water table level.
Fig.8 shows the profiles, profile differences and transport rates during normal, higher
and lower water table levels. We can see easily from the transport rate curves that
during normal water level, sand was transported both onshore and offshore resulting in
deposition at the berm and at the bar. During higher water table, sand was transported
onshore and deposited at the berm and at the depositional area located immediately
landward of the bar trough. Also it can be seen that relative small changes occurred
with lower water table level.
Fig.9 shows the definition of berm height, onshore scour depth, onshore deposition
height, bar trough depth, bar crest height and offshore scour depth. All these variables
are relative to the initial profile. A negative sign denotes erosion while a positive signifies
deposition. The time variations of these variables are shown in Fig.10, which clearly
demonstrates the features mentioned above.
The time variations of the three criteria, El, E2 and E3, are shown in Fig.11 through
Fig.13, respectively. El is the integrated value of the squared profile change rate, shown in
Fig.5 to Fig.7. The value of El increases by approximately a factor of three immediately
after changing to a higher water table level. During higher water level, another peak
value appears. This is because only one profile was measured at 3.0 and 3.5 hrs and the
measured one represents the highest part across the tank. During lower water table level,
the variation shows that the profile remains in approximate equilibrium. The plots of E2
and E3 are in general agreement with the interpretation derived from E1.


5 Conclusions

The experiment described herein was carried out with a fairly fine sand and has demon-
strated the significance of beach water table on profile dynamics. Specific effects which
have been clearly demonstrated by this experiment and recommendations for additional
experiments are described below.
The increased water table caused distinct effects in three definite zones. First, erosion
occurred at the base of the beach face and the sand eroded was carried up and deposited
on the upper portion of the beach face. This resulted in a hinge point at about
the mean water line. Secondly, the trough deepened considerably and rapidly and the
eroded sand was deposited immediately landward. This depositional area changed from
mildly erosional to strongly depositional. Third, the area seaward of the bar eroded with
a substantial deepening. These effects are evident through inspection of Fig.2 and Fig.3
(before and after water table increased, respectively).



















-- -- - 0.0 0.0




1 1.0O -1.0



I I -2.0 I I -2.0

0. 10. 20. 30. 0. 10. 20. 30. 0. 10.


s -1.0
I-


U-


-2.0



0.3




0.1
0


U_ -0.1
a:



-0.3



1.0



i-
S0.5
U.
z
C 0.0


c:
o
I-0.5


1.0


0.5


0.0


-0.5


-I


0. 10. 20. 30. 0. 10. 20.

DISTANCE ( FT ) DISTANCE ( FT )

(a) NORMAL WATER TABLE (b) HIGHER WATER


Fig.8 Profiles, Profile Differences and Transport

ans Lower Water Table Levels


3(


0.1




-0.1




-0.3


.0.

1.0


0.5


0.0


-0.5


* fn


20. 30


10. 20. 30















I I I I I


- --i.v --
30. 0. 10. 20. 30

DISTANCE ( FT )

TABLE (c) LOWER WATER TABLE


Rate Curves during Normal, Higher


-0.1








S-0.3 1
30. 0. 10.


0. 10.


I I I I












I i I I


' I I












I I


L


I


i j I


- --- -


- .*
















ZBH


Berm


ZOS


Bar


Initial
Profile


ZBT


ZOF


Fig.9 Definitions of Berm Height, Onshore Scour Depth, Onshore Deposition Height,
Bar Trough Depth, Bar Crest Height and Offshore Scour Depth


I















HIGHER W.T.L.


0.0 0.5


1.0 1.5 2.0 2.5 3.0 3.5 4.0


4.5 5.0


TIME ( HOUR )


Fig.10 Time Variations of Berm Height, Onshore Scour Depth, Onshore Deposition
Height, Bar Trough Depth, Bar Crest Height and Offshore Scour Depth


NORMAL W.T.L.


LOWER W.T.L.



















NORMRL W.T.L. HIGHER W.T.L. LOWER W.T.L.
0.2 1 1 1 11II







C:
I-
U-

U]





S 0.1 -


U-i
C-
U.-
LL





U-
0.1
O \













0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

TIME ( HOUR )



Fig.11 Time Variations of Root Mean Square Profile Change Rate, El
Fig.ll Time Variations of Root Mean Square Profile Change Rate, El


















NORMAL W.T.L. HIGHER W.T.L. LOWER W.T.L.
0.2 I I





I-



bJ

UJ

U-
r 0.1






U-
O
(I






0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

TIME ( HOUR )



Fig.12 Time Variations of Root Mean Square of Profile Deviations from Initial Profile, E2
a_



















Fig.12 Time Variations of Root Mean Square of Profile Deviations from Initial Profile, Ez

















N O M R W L H I H E W L L O E W T L .


0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
TIME ( HOUR


Fig.13 Time Variations of Average Absolute Transport Rate, E3


NORMAL W.T.L.


HIGHER W.T.L.


LOWER W.T.L.










Also, significant deposition commenced within the upper portion of the swash zone.
During the experiment with the higher water level, the peak of the berm moved landward
continuously, which meant deposition over the swash zone. This is contradictory to pre-
vious studies that higher water table level enhances erosion. However, there was erosion
immediately seaward. It appears that this eroded material was deposited landward in
the berm. As shown in Fig.7, little changes occurred with lower water table level.
Fig.8 shows the profiles, profile differences and transport rates during normal, higher
and lower water table levels. We can see easily from the transport rate curves that
during normal water level, sand was transported both onshore and offshore resulting in
deposition at the berm and at the bar. During higher water table, sand was transported
onshore and deposited at the berm and at the depositional area located immediately
landward of the bar trough. Also it can be seen that relative small changes occurred
with lower water table level.
Fig.9 shows the definition of berm height, onshore scour depth, onshore deposition
height, bar trough depth, bar crest height and offshore scour depth. All these variables
are relative to the initial profile. A negative sign denotes erosion while a positive signifies
deposition. The time variations of these variables are shown in Fig.10, which clearly
demonstrates the features mentioned above.
The time variations of the three criteria, El, E2 and E3, are shown in Fig.11 through
Fig.13, respectively. El is the integrated value of the squared profile change rate, shown in
Fig.5 to Fig.7. The value of El increases by approximately a factor of three immediately
after changing to a higher water table level. During higher water level, another peak
value appears. This is because only one profile was measured at 3.0 and 3.5 hrs and the
measured one represents the highest part across the tank. During lower water table level,
the variation shows that the profile remains in approximate equilibrium. The plots of E2
and E3 are in general agreement with the interpretation derived from E1.


5 Conclusions

The experiment described herein was carried out with a fairly fine sand and has demon-
strated the significance of beach water table on profile dynamics. Specific effects which
have been clearly demonstrated by this experiment and recommendations for additional
experiments are described below.
The increased water table caused distinct effects in three definite zones. First, erosion
occurred at the base of the beach face and the sand eroded was carried up and deposited
on the upper portion of the beach face. This resulted in a hinge point at about
the mean water line. Secondly, the trough deepened considerably and rapidly and the
eroded sand was deposited immediately landward. This depositional area changed from
mildly erosional to strongly depositional. Third, the area seaward of the bar eroded with
a substantial deepening. These effects are evident through inspection of Fig.2 and Fig.3
(before and after water table increased, respectively).










It is somewhat surprising that the increased water table was effective so far offshore.
The common effect responsible for the changes in the three zones appears to be a destabi-
lization of the bottom particles in areas of pre-existing marginal stability with the eroded
particles transported to stable areas. The lowered water table appeared to result in a
much more stable beach and the resulting effects were much less. The only noticeable
trend was a limited deposition in the scour hole at the base of the beach face (Fig.4).
There is a substantial need for additional carefully controlled laboratory experiments.
It is anticipated that results may differ substantially with sediment characteristics and
thus experiments should encompass a range of sizes (and thus permeabilities) and sorting.
Improved monitoring of the distribution of the ground water table elevations throughout
the beach berm as well as the piezometric head within the beach across the surf zone
should be considered. The temporal (wave period scale) small scale water table changes
as the wave front rushes up and down the beach face should be documented for a range
of sand size characteristics. Differences for irregular waves and regular waves as investi-
gated here should be investigated. Finally, all comprehensive studies should include at
least limited experiments to document repeatibility and experiments to provide controls
illustrating beach profiles that would have occurred if the water tables had not been
altered.


6 References

Bagnold, R.A. (1940), Beach Formation by Waves; Some Model Experiments in a
Wave Tank ", Inst. Civil Engineers Jour., Paper No. 5237, pp 27-53.

Bascom, W.N. (1951), The Relationship between Sand Size and Beach Face Slope ",
American Geophysical Union Transactions, 32(6), pp 866-874.

Bruun, P. (1989), Coastal Drain: What Can It Do or Not Do? ", J. Coastal Research,
5(1), pp 123-125.

Chappell, J., I.G. Eliot, M.P. Bradshaw and E. Lonsdale (1979), Experimental Control
of Beach Face Dynamics by Water-Table Pumping ", Engineering Geology, 14, pp
29-41.

Danish Geotechnical Institute (1986), Coastal Drain System: Full Scale Test-1985
Tormindetangen ", June.

Dean, R.G. and R.A. Dalrymple (1991), Coastal Processes with Emphasis on En-
gineering Applications ", unpublished draft text for Graduate Course EOC 6196:
Littoral Processes, Department of Coastal and Oceanographic Engineering, Uni-
versity of Florida, Gainesville, Florida.










Duncan, J.R. (1964), The Effect of Water Table and Tide Cycle on Swash-Backwash
Sediment Distribution and Beach Profile Development ", Marine Geology, 2, pp
186-197.

Emery, K.O. and J.F. Foster (1948), Water Tables in Marine Beaches ", J. Marine
Research, 7, pp 644-654.

Grant, U.S. (1948), Influence of the Water Table on Beach Aggradation and Degra-
dation ", J. Marine Research, 7, pp 655-660.

Kawata, Y. and Y. Tsuchiya (1986), Application of Sub-Sand System to Beach Erosion
Control ", Proc. International Coastal Engineering Conference, ASCE, Taiwan, pp
1255-1267.

Machemehl, J.L., French, T.J. and Huang, N.E. (1975), New Method for Beach Ero-
sion Control ", Proc. Civil Engineering in the Oceans, III, ASCE, University of
Delaware, pp 142-160.

Sallenger, A.H., Jr. and B.M. Richmond (1984), High- Frequency Sediment-Level
Oscillations in the Swash Zone ", in Hydrodynamics and Sedimentation in Wave-
Dominated Environments, ed. by B. Greenwood and R.A. Davis, Jr., Marine Ge-
ology, 60, pp 155-164.

Terchunian, A.V. (1989), Performance of the STABEACH@ System at Hutchinson
Island, Florida ", Proc. Beach Preservation Technology 89, University of Florida,
Florida Shore and Beach Preservation Association and the American Shore and
Beach Preservation Association, Tampa, Fl., pp 229-238.

Waddel, E. (1973), Dynamics of Swash and Implication to Beach Response ", Coastal
Studies Institute, Louisiana State University, La., Technical Report No. 139, 49
pp.
Waddel, E. (1976), Swash-Groundwater-Beach Profile Interactions ", in Beach and
Nearshore Sedimentation, ed. by Davis, R.A. and R.L. Ethington, Society of Eco-
nomic Paleontologists and Mineralogists, Special Publication No. 24, pp 115-125.










It is somewhat surprising that the increased water table was effective so far offshore.
The common effect responsible for the changes in the three zones appears to be a destabi-
lization of the bottom particles in areas of pre-existing marginal stability with the eroded
particles transported to stable areas. The lowered water table appeared to result in a
much more stable beach and the resulting effects were much less. The only noticeable
trend was a limited deposition in the scour hole at the base of the beach face (Fig.4).
There is a substantial need for additional carefully controlled laboratory experiments.
It is anticipated that results may differ substantially with sediment characteristics and
thus experiments should encompass a range of sizes (and thus permeabilities) and sorting.
Improved monitoring of the distribution of the ground water table elevations throughout
the beach berm as well as the piezometric head within the beach across the surf zone
should be considered. The temporal (wave period scale) small scale water table changes
as the wave front rushes up and down the beach face should be documented for a range
of sand size characteristics. Differences for irregular waves and regular waves as investi-
gated here should be investigated. Finally, all comprehensive studies should include at
least limited experiments to document repeatibility and experiments to provide controls
illustrating beach profiles that would have occurred if the water tables had not been
altered.


6 References

Bagnold, R.A. (1940), Beach Formation by Waves; Some Model Experiments in a
Wave Tank ", Inst. Civil Engineers Jour., Paper No. 5237, pp 27-53.

Bascom, W.N. (1951), The Relationship between Sand Size and Beach Face Slope ",
American Geophysical Union Transactions, 32(6), pp 866-874.

Bruun, P. (1989), Coastal Drain: What Can It Do or Not Do? ", J. Coastal Research,
5(1), pp 123-125.

Chappell, J., I.G. Eliot, M.P. Bradshaw and E. Lonsdale (1979), Experimental Control
of Beach Face Dynamics by Water-Table Pumping ", Engineering Geology, 14, pp
29-41.

Danish Geotechnical Institute (1986), Coastal Drain System: Full Scale Test-1985
Tormindetangen ", June.

Dean, R.G. and R.A. Dalrymple (1991), Coastal Processes with Emphasis on En-
gineering Applications ", unpublished draft text for Graduate Course EOC 6196:
Littoral Processes, Department of Coastal and Oceanographic Engineering, Uni-
versity of Florida, Gainesville, Florida.











APPENDIX A

DATA REDUCTION


In this appendix, the possible causes of errors in transport volumes are discussed
at first in an attempt to provide a reference for future experiments. Next the method
is presented to adjust the experimental data to remedy these errors within reasonable
limits.

The errors in transport volumes and mismatch at the point of manual and profiler
measurement are believed to be caused by combinations of following :

(1) three-dimensional effects

(2) the small amount of sand that was transported seaward of the measurement limit

(3) consolidation of the sand under the beach

(4) change of profiler offset after 3.0 hrs

The errors from (1), (2) and (3) may be inherent in most of movable bed experiments,
while the error (4) is confined to this experiment.

Three-dimensional effects can be removed by measuring several profiles along the
lines parallel to the axis of the tank. In this experiment, three profiles were measured
across the tank, which were averaged to represent the mean profile. However, at 3.0
and 3.5 hrs the profile along only one line was measured. Hence three-dimensional
effects can be important for these two times. Due to the non-zero water particle velocity
over the horizontal section of tank bottom, sand was transported beyond the seaward
measurement limit and was spread over the horizontal-floor of the tank. During the
experiment, no significant sand volumes were observed. Thus it appears that these
errors are negligible. The effect of sand consolidation may be important as the sand
within the beach becomes more compact under continued wave action. At the present
time, however, there are no available means to consider the effects of sand consolidation.
As noted, it was found that in the overlap region in which the profile was obtained by
both the profiler and manually, there was a mismatch of elevations. In this experiment,
the manual measurements were used as one basis for calibrating the profiler. Later
inspection of the data suggested that after 3.0 hrs, the profiler calibration changed
considerably. The basis for post-calibrating the profiler for each run was to match
the profiles in the overlap region to the manual readings and to require that the total
volumetric changes were zero.











The calibration relationship between the elevation, z,, and the output v of the profiler
is

z,(x,t) = a + b v(x,t) WL (A.1)
where,
z(x, t) = calibrated profile elevation (ft)
v(x,t) = profiler data (volt)
a = calibration offset (ft)
b = calibration slope (ft/volt)
WL = water depth to shift the origin from the tank
bottom to the water level (ft)
For this experiment, the profiler was calibrated based on the initial profile and the
results were

a = 3.748362 (ft)
b =- 0.738907 (ft/volt)
With these constants, transport volume errors and mismatch are found as summa-
rized in Table A.1. For each run, the calibration was redetermined so that the profiler
results provided;

(1) agreement over the range of manual profiles, and
(2) zero total volume changes.

If we express the bed profile data as
(t) zm (x,t) ,0 < x < (A.2)
zp (X, t) xz < X < _
where,

z,(x, t) = manual data at x(ft)
zp(x,t) = profiler data at x(ft)
= (a + Aa) + (b + Ab)v(x,t) WL
Aa(t) = correction in calibration offset (ft) (A.3)
Ab(t) = correction in calibration slope (ft/volt)
Xl = x position of a matching point
= total measurement length ( 30 ft )












Table A.1: Volume Errors and Mismatch
Time Transport Volume Mismatch
(hr) (ft2) (ft) Az*(ft)
0.5 -0.0508 7.0 0.0090
1.0 -0.0682 7.0 0.0224
1.5 -0.1060 1.0 0.0088
2.0 -0.0503 7.0 0.0283
2.5 -0.0727 7.0 0.0126
3.0 -0.4238 7.0 -0.0142
3.5 1.3318** 7.0 0.0895
4.0 1.4139 7.0 0.0772
4.5 1.6570 7.0 0.1016
5.0 1.4291 7.0 0.0828
* A positive Az denotes the elevation by the
profiler is below that determined manually.
** After three hours, a significant change in profiler
calibration apparently occurred.


then, we can set up two objective equations.

i) continuity at the matching point xz


ii) zero volume error


Az(xl) = zm(ix,t) Zp(x1,t) = 0



AV(t) = [z(x,t) z(x,0)] dx = 0


z(x, 0) = initial profile data
S c+ dv(x, 0) WL
c = 3.748362 (ft)
d =- 0.738907 (ft/volt)


Based on the above, we can develop simultaneous equations for Aa and Ab as follows:


A1Aa +
A2Aa +


BlAb = C1
B2Ab = C2


(A.7)


(A.4)


(A.5)


(A.6)













Table A.2: Calibration Factors at Each Time Step
Time Slope Offset
(hr) (ft/volt) (ft)
0.0 -0.738907 3.74836
0.5 -0.753827 3.80441
1.0 -0.773760 3.88159
1.5 -0.752734 3.79571
2.0 -0.780490 3.90884
2.5 -0.760062 3.82790
3.0 -0.745610 3.75521
3.5 -0.779667 3.97209
4.0 -0.756362 3.88263
4.5 -0.774138 3.96562
5.0 -0.762894 3.90967


where,


A1 = Xl

B = = v(x,t) dx
1
C1 = C1 + C12 + C13 + C14 + C15
S11= (c WL)xi
S12 = (c a)Ai

C13 = d v(x,0) dx

Cl4 = Zm(x, t) dx
C15 = -bB1
A2 = 1.0
B2 = v(j1,t)
C2 = z,(xi,t) -[(a- WL) + bv(xi,t)]


The final calibration factors are summarized in Table A.2.











These calibrated data are then filtered to remove high frequency bed change. The
filter weighting function for this analysis is linear, symmetric triangular shape which can
be expressed as

(WT)k = K- (WT)o, k = 1,2,..., K (A.8)
K
K
E (WT)k = 1.0 (A.9)
k=-K
where,


2K + 1 = total number of filter weights
1.0
(WT)o =


Fig.A.1 shows the filter response function versus wave number, which has a low-pass
character. The value of K represented in Fig.A.1 and used in this analysis is 10.

Finally, the output data, z,(x, t), can be expressed by finite sum having the form
K
z= E (WT)k Z+k (A.10)
k=-K

Fig.A.2 shows the unfiltered and filtered data for the case of 3.5 hrs, which appears
to contain the greatest ripple contents. The 'unfiltered' data represent the difference
between the calibrated profile at 3.5 hrs and the initial profile, which has the effect
of removing the linear trend from the calibrated data. The wave number spectrum of
the unfiltered and filtered data and removed ripples for 3.5 hrs are shown in Fig.A.3.
Fig.A.4 shows the time signal data of the removed ripples.


















z
0 0.8

I 0.7

& 0.6-

Z 0.5

0.4
00 4 0.3-

0.2-

0.1-

00 0.5 1 1.5 2 2.5

1 / WAVE LENGTH (1/FT)


Fig.A.1 Filter Response Function versus Wave Number
















12


solid line : unfiltered data
0.2 dashed line : filtered data
0.2



U 0.1-






t'. -0.1



-0.2



-0.
0 5 10 15 20 25 30

DISTANCE (FT)


Fig.A.2 Unfiltered and Filtered Data for 3.5 hrs

































0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

1 / WAVE LENGTH (1/FT)




Fig.A.3 Wave Number Spectrum of the Unfiltered and Filtered Data and Removed
Ripples for 3.5 hrs

































DISTANCE (FT)


Fig.A.4 Time Signal of Removed Ripples for 3.5 hrs




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