• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 Abstract
 Introduction
 Review of literature
 Study area
 Methodology
 Analysis and results
 Summary and conclusions
 Appendix A
 Appendix B
 Appendix C
 Appendix D
 Appendix E
 References
 Biographical sketch






Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 94/015
Title: Field evaluation of equilibrium beach profile concepts southwest Florida
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Permanent Link: http://ufdc.ufl.edu/UF00085006/00001
 Material Information
Title: Field evaluation of equilibrium beach profile concepts southwest Florida
Series Title: UFLCOEL-94015
Physical Description: xiv, 182 leaves : ill. ; 29 cm.
Language: English
Creator: Jones, Victoria Lly
University of Florida -- Coastal and Oceanographic Engineering Dept
Publication Date: 1994
 Subjects
Subject: Coastal and Oceanographic Engineering thesis, M.S   ( lcsh )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF   ( lcsh )
Genre: bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (M.S.)--University of Florida, 1994.
Bibliography: Includes bibliographical references (leaves 177-181).
Statement of Responsibility: Victoria Lly Jones.
General Note: Typescript.
General Note: Vita.
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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Volume ID: VID00001
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Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 33315002

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
    Dedication
        Page ii
    Acknowledgement
        Page iii
    Table of Contents
        Page iv
        Page v
        Page vii
        Page ix
        Page x
        Page xi
        Page xii
        Page xiii
        Page xiv
    Abstract
        Page xv
        Page xvi
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
    Review of literature
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
    Study area
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
    Methodology
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
    Analysis and results
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
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        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
    Summary and conclusions
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
    Appendix A
        Page 123
        Page 124
        Page 125
        Page 126
        Page 127
        Page 128
        Page 129
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        Page 138
        Page 139
        Page 140
        Page 141
        Page 142
        Page 143
    Appendix B
        Page 144
        Page 145
        Page 146
    Appendix C
        Page 147
        Page 148
        Page 149
        Page 150
        Page 151
        Page 152
    Appendix D
        Page 153
        Page 154
        Page 155
        Page 156
        Page 157
    Appendix E
        Page 158
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    References
        Page 171
        Page 172
        Page 173
        Page 174
        Page 175
        Page 176
        Page 177
        Page 178
        Page 179
        Page 180
        Page 181
    Biographical sketch
        Page 182
Full Text



UFL/COEL-94/015


FIELD EVALUATION OF EQUILIBRIUM BEACH
PROFILE CONCEPT: SOUTHWEST FLORIDA






by




Victoria Lly Jones






Thesis


1994















FIELD EVALUATION OF EQUILIBRIUM BEACH
PROFILE CONCEPTS: SOUTHWEST FLORIDA














By

VICTORIA LLY JONES


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


1994


I




















This Study is Dedicated to

H. Kenneth Jones









ACKNOWLEDGMENTS

I wish to thank my junior college counselor who told me that I was not smart

enough to be an engineer.

There are many people in both Florida and Texas who have helped me in

numerous ways throughout my graduate career. At the University of Florida I want to

thank Dr. Robert G. Dean for his patience and support. Additionally, special thanks go

to Lynda Charles, John Davis, Becky Hudson, Tim Mason, Don Mueller, Emre Otay,

Mark Sutherland, Peter Thompson, Helen Twedell, Paul Work, and to Mark and Scott.

At Texas A&M University I want to thank Dr. Ted Chang, Kevin Colston,

Lorraine Devallier, Dr. Emie Estes, Dr. John Herbich, Dr. Xiaoyu Liu, and Dr. Peter

Santschi. Special thanks go to Dr. Ted Chang, Engineering Department Head, for the

use of the Engineering Wave Tank Facility; and, to Mr. Kevin Colston, Engineering

Laboratory Technician, for his expertise, aid, and support.

Additional thanks go to Joe Larkin, Rollie Smith, and Harold Stone.

Special thanks go to my newest friends, and co-workers, Rich Lukens and Kevin

Colston who made me laugh, especially when I wanted to cry.

To my family, particularly my parents, who by lesson, and by example, have

instilled in me honesty, independence, hard work-ethics and, most importantly, a healthy

sense of humor.

And to my dear friend Ann Larkin, through whose love and support I am

continually reminded that it is not 'what I know' but rather 'who I am' that is truly

important.

Support for this study was provided by the Florida Sea Grant Program under

Contract No. R/C-5-31 and matching funds were provided by the Department of Coastal

and Oceanographic Engineering. Funding for this effort by these two entities is

gratefully acknowledged.















TABLE OF CONTENTS


ACKNOWLEDGMENTS ................................... iii

LIST OF TABLES ....................................... vi

LIST OF FIGURES ..................... ..................... vii

ABSTRACT ..................... ....................... xiii

CHAPTERS

1 INTRODUCTION ................................. 1

2 REVIEW OF LITERATURE ......................... 13

3 STUDY AREA ................................... 29

3.1 Pinellas County ........................... 29
3.2 Manatee County .............................. 31
3.3 Sarasota County .............................. 33
3.4 Charlotte County ........................... 35
3.5 Lee County ................... ........... 37
3.6 Collier County ............................... 39

4 METHODOLOGY ........................ ......... 41

4.1 Beach Profiles ........................ ...... 41
4.2 Sediment Samples .......................... 42
4.3 Equilibrium Beach Profile (EBP) Model ............. 48

5 ANALYSIS AND RESULTS ........................... 54

5.1 Individual Profiles ............................ 54
5.2 Grouped Profiles ............................. 56
5.3 Best-Fit Profiles .............................. 57

6 SUMMARY AND CONCLUSIONS ..................... 118

iv









APPENDICES

A


B

C

D

E


S

ADDITIONAL PROFILES AND SEDIMENT
DISTRIBUTIONS ..............................

COMPUTER PROGRAM OUTPUTS ..................

LOCATIONS OF DNR MONUMENTS ................

OFFSHORE SEDIMENT SAMPLES ..................

SEDIMENT SAMPLE ANALYSIS ...................


REFERENCES ........................

BIOGRAPHICAL SKETCH .................


124

145

148

154

159

171

182















LIST OF TABLES


Table Page


1.1 Summary of Recommended A Values (from Dean [1994])
(Units of A Parameter are in m"3) ....................... 9

4.1 DNR Profile Dates for Current Study ....................... 41

4.2 Coordinates, Elevations, Beach Face Slopes, and Azimuths for DNR
Monuments in Pinellas County, FL. ...... ................. 43

4.3 Locations and Depths of Offshore Sediment Samples: Pinellas County,
FL. ... ....................... .................. 45

4.4 Sieve Sizes for Sediment Analysis ......................... 46

4.5 Sediment Sample Analysis: Charlotte County ................. 47














LIST OF FIGURES


Figure


Page


1.1 Forces Affecting Beach Profile Evolution (from Work [1992]) ....... 3

1.2 Variation of Sediment Scale Parameter, A, with Sediment Size and Fall
Velocity. (Dean [1987], modified from Moore [1982], from Dean et al.
[1993]) . . . . . . . . . .. 5

1.3 Comparison of Equilibrium Beach Profiles With and Without Gravitational Ef-
fects Included. A = 0.1 m1"3 Corresponding to a Sand Size of 0.2 mm. .. 11

3.1 Pinellas County .................................... 30

3.2 M anatee County ................................... 32

3.3 Sarasota County ..................................... 34

3.4: Charlotte County ................................... 36

3.5: Lee County ...................................... 38

3.6: Collier County .................................... 40

5.1: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 21, Pinellas County, Florida. ............. 59

5.2: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 33, Pinellas County, Florida. ............. 60

5.3: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 42, Pinellas County, Florida ... ........... 61

5.4: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 57, Pinellas County, Florida. ............. 62









Figure


5.5: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 69, Pinellas County, Florida .

5.6: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 138, Pinellas County, Florida. ..

5.7: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 159, Pinellas County, Florida. ..

5.8: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 9, Manatee County, Florida. .

5.9: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 18, Manatee County, Florida. ..

5.10: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 27, Manatee County, Florida. ..

5.11: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 36, Manatee County, Florida. ..

5.12: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 45, Manatee County, Florida. ..

5.13: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 51, Manatee County, Florida. ..

5.14: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 60, Manatee County, Florida. ..

5.15: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 66, Manatee County, Florida. ..

5.16: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 3, Sarasota County, Florida. ...

5.17: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 12, Sarasota County, Florida. ..

5.18: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 21, Sarasota County, Florida. ..


median grain


median grain


median grain


median grain


median grain


median grain

median grain .

median grain


median grain


median grain

median grain .

median grain


median grain


median grain
median grain


median grain













. . . .


Page









Figure


5.19: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 27, Sarasota County, Florida. . . ... 77

5.20: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 36, Sarasota County, Florida. ........... 78

5.21: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 54, Sarasota County, Florida. . . ... 79

5.22a: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 72, Sarasota County, Florida. ........... 80

5.22b: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution with -8 m sample removed, Range 72, Sarasota County,
Florida. ................... ...................... 81

5.23: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 90, Sarasota County, Florida. . . ... 82

5.24: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 99, Sarasota County, Florida. ........... 83

5.25: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 108, Sarasota County, Florida. ........... 84

5.26: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 171, Sarasota County, Florida. . . ... 85

5.27: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 180, Sarasota County, Florida. . . ... 86

5.28: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 1, Charlotte County, Florida. . . ... 87

5.29: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 9, Charlotte County, Florida. . . ... 88

5.30: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 30, Charlotte County, Florida. . . ... 89


Page










Figure


5.31: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 36, Charlotte County, Florida. ..

5.32: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 54, Charlotte County, Florida. ..

5.33: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 1, Lee County, Florida. . .

5.34: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 12, Lee County, Florida. . .

5.35: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 21, Lee County, Florida. . .

5.36: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 126, Lee County, Florida ....

5.37: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 135, Lee County, Florida ....

5.38: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 144, Lee County, Florida ....

5.39: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 156, Lee County, Florida ....

5.40: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 162, Lee County, Florida ....

5.41: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 168, Lee County, Florida ....

5.42: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 189, Lee County, Florida ....

5.43: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 198, Lee County, Florida .....

5.44: Measured profile, blindfolded prediction, and cross-shore
size distribution, Range 234, Lee County, Florida ....


median grain
. . 90

median grain
. . . 91

median grain
. . 92

median grain
. .. ... 93

median grain
. . . 94

median grain
. . .95

median grain
. . 96

median grain
. . 97

median grain
. . 98

median grain
. . 99

median grain
. . 100

median grain
. . 101

median grain
. . 102

median grain
. . . 103


Page









Figure


5.45 Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 3, Collier County, Florida. . . ... 104

5.46a: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 18, Collier County, Florida. . . .... 105

5.46b: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution with -1 m sample removed, Range 18, Collier County,
Florida ....... .. .. .... .. ......... ... .. ... 106

5.47: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 30, Collier County, Florida. . . .... 107

5.48: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 72, Collier County, Florida. . . .... 108

5.49: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 84, Collier County, Florida. . . .... 109

5.50: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 139, Collier County, Florida. . . ... 110

5.51: Averaged profiles for DNR ranges R-30 and R-36, Charlotte County,
Florida . . . . . . . . . . 111

5.52: Averaged profiles for DNR ranges R-21 and R-27, Sarasota
County, Florida. ................... ................. 112

5.53: Averaged profiles for DNR ranges R-153, R-162, and R-171, Sarasota
County, Florida. .................................... 113

5.54: Averaged profiles for DNR ranges R-180, R-189, and R-198, Lee Coun-
ty, Florida ..................................... 114

5.55: Measured profile, blindfolded prediction, and best-fit profiles, Range R-l,
Charlotte County, Florida. Best fit parameters: Blindfolded: RMS
err.=e=0.45m; Average: A=0.16m"3, e=0.98m; Constant:
A=0.12m1u3, e=0.37m; Exponential: A,=0.09, A =0.11, k=0.012,
e=0.35m; Polynomial: B,=0.006m, B1=0.019, B2=1.35E-5m1,
e= 0.29m .......................................115


Page









Figure


Page


5.56: Measured profile, blindfolded prediction, and best-fit profiles, Range R-
135, Lee County, Florida. Best fit parameters: Blindfolded: RMS
err.=e=0.17m; Average: A=0.09m13, e=0.33m; Constant:
A=0.075m13, e=0.17m; Exponential: Ao=0.07, Ai=0.075, k=0.011,
e=0.17m; Polynomial: Bo=0.004m, B =0.018, B2=5.63E-5m-,
e= .11m . . . .... . . . .. ..... 116

5.57: Measured profile, blindfolded prediction, and best-fit profiles, Range R-3,
Collier County, Florida. Best fit parameters: Blindfolded: RMS
err.=e=0.31m; Average: A=0.14mu/, e= 1.04m; Constant:
A=O.llm"3, e=0.31m; Exponential: Ao=0.11, A1=0.09, k=0.007,
e=0.43m; Polynomial: Bo=0.004m, B, =0.023, B2=3.61E-5m1,
e= 0.19m ........................................117














Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

FIELD EVALUATION OF EQUILIBRIUM BEACH
PROFILE CONCEPTS: SOUTHWEST FLORIDA

By

Victoria Lly Jones

December 1994



Chairman: Dr. Robert G. Dean
Major Department: Coastal and Oceanographic Engineering

Sixty-nine beach profiles from corresponding field sites and accompanying sedi-

ment data are used for the partial development of a comprehensive data base to describe

the cross-shore distribution of sediment characteristics on the beaches of southwest

Florida. This data base includes beach profiles and cross-shore sediment characteristics

from Pinellas, Manatee, Sarasota, Charlotte, Lee, and Collier counties. Field collection

of sediment samples was conducted over a one year period; and, the measured profiles

were obtained from the Florida Department of Natural Resources' "Coastal Construction

Control Line" profiles.

Using the known spatial distribution of sediment sizes, a "blindfolded" test is

described and used to compare the measured profiles to calculated profiles at selected

field sites. In addition, four best-fit analyses are described and employed to further

xiii









examine the existing relationships between the sediment scale parameter, A, and sedi-

ment diameter, D, and/or sediment fall velocity, w, for varying cross-shore sediment

attributes. Comparison is made to both the measured and blindfolded (predicted) pro-

files for several locations. Further evaluation of these relationships includes averages of

both measured and predicted profiles for several successive sites in an effort to deter-

mine whether these averages may better represent the equilibrium beach profile than the

predicted profile method.

Results indicate that inclusion of the cross-shore distribution of sediment size

(and hence the variation of the A parameter), and additional parameters, does not signif-

icantly enhance the goodness-of-fit to the measured profile compared to the simpler,

empirical approach with A held constant. The "blindfolded" tests show a general trend

of under-predicting the measured profiles near the shoreline and over-predicting further

offshore. Additionally, the equilibrium beach profile model used for the blindfolded

tests is extremely sensitive to cross-shore sediment grain sizes, and even one anomalous

sample was found to drastically alter the predicted profile.














CHAPTER 1
INTRODUCTION

The general characteristics of the actual two dimensional beach profile, the varia-

tion of water depth with distance offshore from the shoreline, can be described by the

concept of an equilibrium beach profile. This concept can be most useful for the inter-

pretation of nearshore processes and for the design of many coastal engineering projects.

'The effects of relative sea rise, beach erosion due to storm events, and beach nourish-

ment with sand different from the native are examples of these processes and projects,

respectively.

In an overall manner, beaches (sand particles) are acted upon by a complex set

of both constructive and destructive forces which act to displace the sediment seaward

in the case of destructive forces, and vice versa. The equilibrium profile is the result of

the balance of these forces. That is, if the system of these forces could be maintained

in steady state for a sufficient time period, it seems reasonable to conclude that, given

enough time, the beach system will tend toward an equilibrium with a corresponding

profile (Dean et al. [1993]).

Several characteristics of beach profiles are well known at this time (from Dean

[1991]): (1) they tend to be concave upwards, (2) the slope of the beach face is approxi-

mately planar, (3) milder and steeper beach face slopes are associated with smaller and








2

larger sediment diameters, respectively, and (4) steep waves result in milder slopes and

tendencies for bar formation, or what is known as winter (storm) profiles.

Fully descriptive, physics-based models for the prediction of equilibrium beach

profiles are, to date, considered ineffective when the complex processes dominant in the

surf zone (e.g. turbulence, bottom friction, streaming velocities in the bottom boundary

layer, shoaling, energy dissipation due to wave breaking, seaward directed bottom

undertow currents, etc.) are considered (Work and Dean [1991]). Some of the agents

acting to alter beach profiles are shown in Figure 1.1. Indeed, as this is only a partial

listing of the complex forces which act upon sediment particles in the surf zone, an

empirical description of beach profiles is considered here since it is a simpler approach,

purely descriptive in nature, and represents an attempt to describe the beach profiles in

forms which are characteristic of those found in nature.

The empirical approach applied here is from Bruun [1954] who analyzed beach

profiles from the Danish North Sea coast and Mission Bay, CA, and found that they

followed the simple relationship represented by


h(y) =Ay2/3 (1.1)

in which h is the water depth some distance, y, offshore and A is a scale parameter

which depends primarily on sediment characteristics. Dean [1977] later analyzed 504

beach profiles from the Gulf and Atlantic coasts of the United States. He employed the

least squares approach to determine the best fit between each measured profile and the

following relationship












































Figure 1.1: Forces Affecting Beach Profile Evolution (from Work [1992])













h(y) =Ay (1.2)

His results showed the value of n to lie between 0.6 and 0.7 (with a central value of

0.66) consistent with Bruun's earlier finding.

The sediment scale parameter, A, in equations (1.1) and (1.2) is size dependent

and was determined by Moore [1982] who collected and analyzed a number of published

beach profiles, and developed the relationship between A and D shown as the solid line

in Figure 1.2. As might be expected, this relationship shows that the larger the sedi-

ment size, D, the greater the A parameter and, in turn, the steeper the corresponding

beach slope.

Dean [1987] later transformed the A vs. D relationship to an A vs. W relationship,

where w is the particle fall velocity. This relationship is linear on the log-log plot of

Figure 1.2 and is represented by the dashed line. In addition, Dean showed this A vs.

0w relationship to be well-represented by


A=0.067(044 (1.3)

in which w is in units of cm/sec and A is in meters13.

Using a value of 0.67 for n in equation (1.2) is appealing because the resulting

.profile shape is representative of the equilibrium wave energy dissipation per unit vol-

ume of water throughout the surf zone from linear wave theory as follows (Dean and

Dalrymple [1984, 1993]).
















SEDIMENT FALL VELOCITY, w (cm/s)


S1.0-





rc
Ic
ci:
< 0.10 -


(0
-I



atC
C/)


0 0.01 -
0.01
0a


Figure 1.2:


0.1 1.0 10.0 100.0
SEDIMENT SIZE, D (mm)


Variation of Sediment Scale Parameter, A, with Sediment Size and Fall Velocity. (Dean [1987],
modified from Moore [1982], from Dean et al. [1993]).









6

A wave propagating shoreward, upon entering the surf zone, will break resulting

in a steady state solution in which a portion of the wave energy continues shoreward into

the nearshore region of interest. The remainder of the energy flux results in a local

dissipation of energy. This energy flux due to the breaking wave can be represented as


Yr=ECg (1.4)

where E is the sum of the potential and kinetic energy contained within the wave and C,

represents the group velocity of the wave, or the speed at which the energy is transport-

ed shoreward. Based on linear, shallow water wave theory (Dean and Dalrymple

[1984]) and substituting


c=gi (1.5)

and


E= yH (1.6)
8


into equation (1.4), where y is the specific weight of sea water, H is the wave height,

h is the water depth, and g is the gravitational constant, the expression for energy flux

becomes


9jr=_YHVi (1.7)
8


If the wave height is assumed proportional to the water depth throughout the surf zone,

i.e.













H=Kh (1.8)

where K is a dimensionless breaking wave parameter = 0.8 (McGowan [1891]), the

expression for energy flux is now


= K2 h /2 (1.9)
8

More specifically, a constant energy dissipation per unit volume for a given grain

size can be expressed as D., and can be written in terms of energy conservation by


a -hD, (1.10)
ayl


in which y' is the shore normal coordinate directed onshore. Equation (1.10) states that

any change in .-over a given distance divided by the water depth, h, must be equal to

the average wave energy dissipation per unit volume for which the sediment is stable.

If the allowable wave energy dissipation per unit volume for an equilibrium beach pro-

file is now considered to be a function of sediment size, D, only and not a function of

the distance, y, offshore, then from equation (1.10)


8a pg2h 2V ) (1.11)
ay =hD*
ay

The dissipation per unit volume is found by taking the derivative and simplifying equa-

tion (1.11) as











D.= 5 pg3/2K12h/2 ah (1.12)
16 dy
This relationship shows that the wave energy dissipation is proportional to the product

of the square root of the water depth and the beach slope. Additionally, since the depth

h in equation (1.12) is the only variable that changes with distance y, this equation can

be integrated for h into a final form

S24D \2/3
h(y) =( p---24* y2/3=Ay2/ (1.13)
5 p g,!- K2

where y is now oriented offshore with an origin at the water line. The parameter A is

now defined as a proportionality constant depending on the wave energy dissipation per

unit volume or, more directly, sediment size. Values for A as a function of sediment

size, D, used in this study are based on Table 1.1.

This power law formula for equilibrium beach profiles has the advantage of

producing profiles that are concave upwards, similar to those found in nature. One

disadvantage, however, is that the formula predicts an infinite slope at y = 0, i.e. at the

shoreline. One reason previously suggested for this is the exclusion of the gravitational

forces which are induced by large beach face slopes. A well-documented modification

of equation (1.1) (Dean [1991] and Dally et al. [1985], from Larson [1988]; Larson and

Kraus [1989], and Dean et al. [1993]) to include gravitational effects is given by


D. ah 1 (ECg) =D. (1.14)
m 9y h ay

in which the first term on the left-hand side represents destabilizing forces due to gravi-

ty, and the second term represents turbulent fluctuations due to wave energy dissipation.












Table 1.1: Summary of Recommended A Values (from Dean [1994])
(Units of A Parameter are in m"3)


Notes:


(1) The A values above, some to four place, are not intended to suggest that they are known to that accura-
cy, but rather are presented for consistency and sensitivity tests of the effects of variation in grain size.

(2) As an example of use of the values in the table, the A value for a median sand size of 0.24 mm is:
A = 0.112 mu3. To covert A values to feet units, multiply by 1.5.


D(mm) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.1 0.063 0.0672 0.0714 0.0756 0.0798 0.084 0.0872 0.0904 0.0936 0.0968
0.2 0.100 0.103 0.106 0.109 0.112 0.315 0.117 0.119 0.121 0.123
0.3 0.125 0.127 0.129 0.131 0.133 0.135 0.137 0.139 0.141 0.143
0.4 0.145 0.1466 0.1482 0.1498 0.1514 0.153 0.1546 0.1562 0.1578 0.1594
0.5 0.161 0.1622 0.1634 0.1646 0.1658 0.167 0.1682 0.1694 0.1706 0.1718
0.6 0.173 0.1742 0.1754 0.1766 0.1778 0.179 0.1802 0.1814 0.1826 0.1838
0.7 0.185 0.1859 0.1868 0.1877 0.1886 0.1895 0.1904 0.1913 0.1922 0.1931
0.8 0.194 0.1948 0.1956 0.1964 0.1972 0.198 0.1988 0.1996 0.2004 0.2012
0.9 0.202 0.2028 0.2036 0.2044 0.2052 0.206 0.2068 0.2076 0.2084 0.2092
1.0 0.210 0.2108 0.2116 0.2124 0.2132 0.2140 0.2148 0.2156 0.2164 0.2172








10

In equation (1.14), m is the beach face slope and D. still represents the stability charac-

teristics of the sediment but is now 'expanded' to include gravity as an additional desta-

bilizing force.

Further, Larson [1988] and Larson and Kraus'[1989] have shown that use of the

more realistic wave breaking model of Dally et al. [1985], along with the use of a speci-

fied uniform wave energy dissipation per unit water volume, results in an equilibrium

profile of the form

h h3"2
y=- 3- (1.15)
m A 3/2

which is the same form as equation (1.14). This equation is more appealing in that it

has a non-zero uniform slope in shallow water of the form

h=my (1.16)

In deeper water the second term in equation (1.15) dominates and can be simplified to

h=Ay2/3 (1.17)

as presented earlier. Figure 1.3 presents a comparison of equation (1.1) which has an

infinite slope at the water line, and equation (1.15) which includes the planar portion

near the water line.

For the most part the above concept of an equilibrium beach profile is based on

a beach of specific, constant grain size and exposed to constant forcing functions. The

validity of this concept has been verified through many laboratory experiments on beach

profile change (e.g. Rector [1954], Saville [1957], Iwagaki and Sawaragi [1959], Swart









11





DISTANCE OFFSHORE (m)


E


LU
0


Figure 1.3:


Comparison of Equilibrium Beach Profiles With and Without Gravita-
tional Effects Included. A = 0.1 m"3 Corresponding to a Sand Size of
0.2 mm. (from Dean [1991])








12

1[1976], and Kajima et al. [1982]). The forcing conditions on a natural beach however

are never constant and changes in topography occur at all times. Regardless, most

beach profiles in the field have shown persistent concave upwards configurations on the

overall 'main' profile.

Aside from this fundamental approach, many models for beach profile evolution

(Dally [1980], Kriebel [1982] (see also Kriebel and Dean [1985] and Kriebel [1986]),

Seymour and King [1982], Dally and Dean [1984], and Larson and Kraus [1989]) have

been proposed due to the difficulty and uncertainty of describing nearshore flows, and

are still the subject of research studies. Presently, however, none are considered reliable

for the "quantitative prediction of beach profile evolution" (Work, p. 165).

For this study, the empirical relationship between A and D (Table 1.1) will be

used for a number of comparisons of measured beach profiles against the equilibrium

beach profile concept. Both the scaling parameter, A, and the sediment size, D, will be

allowed to vary along the profile, i.e. A=A(y) and D=D(y). In addition, several 'best-

fit' tests for selected profiles will be conducted assuming a cross-shore distribution of the

A parameter. An attempt will be made to find the parameters which yield the equilibri-

um profiles that best approximates the measured profile. These procedures will be

discussed in detail in Chapter 4.














CHAPTER 2
REVIEW OF LITERATURE

Since the early 1900's several approaches have been pursued to characterize

equilibrium beach profiles with related studies in cross-shore sediment transport and

nearshore processes. Keulegan and Krumbein [1919] investigated mild bottom slope

characteristics whereby wave energy is continually dissipated from losses due to bottom

friction rather than from breaking. Bruun [1954] analyzed beach profiles from the

Danish Coast and Mission Bay, CA, and found that they followed a simple relationship

of the form h=Ay2/3, where h is the water depth, y is the distance offshore (with an

origin at the water line), and A is a scaling parameter primarily dependent on sediment

characteristics. Many field and laboratory investigations have followed in attempts to

prove, disprove, and/or modify this 2/3-power law formula for equilibrium beach pro-

files.

Ippen and Eagleson [1955] conducted wave tank experiments investigating the

mechanics of the processes shoaling waves have on selectively sorting beach sediments.

Their study of discreet, spherical sediment particles (2-6 mm in dia.) concluded that the

net sediment motion was due essentially to the inequality of hydrodynamic drag and

particle weight, with an "equality position" separating zones of net onshore and offshore

motion. Additionally, they found that the net sediment transport rate was governed by

wave action in the shoreward transport, and by gravity in the transport offshore.









14

Rector [1954], Saville [1957], and Noda [1972] performed numerous laboratory

experiments to investigate the relevance of deep water wave characteristics (with nearly

constant wave heights) on the formation of beach profiles. Their results showed that

deep water wave steepness had significant effects on the resulting beach profiles. In

addition, the study by Rector concluded that the initial slope of the beach had little effect

on the final profile shape, and the presence of a sorting effect whereby the larger materi-

al showed a tendency to move shoreward.

Iwagaki and Sawaragi [1959] compared natural and model profiles and found

reasonable agreement between the two landward of a critical point defined as the point

on the profile seaward of which the profile is unaffected by wave action. This is not the

same as the point of incipient motion which is seaward of their critical point.

Eagleson et al. [1963] developed expressions for the seaward limit of motion and

for the beach slope for which sand particles would be in equilibrium. These expressions

were developed using a complex characterization of the gravity and wave forces acting

on a particle outside the zone of "appreciable breaker influence."

Edelman [1968,1972] applied the equilibrium profile concept to predict erosion

during a severe storm. This was based on the hypothesis that during a storm of "suffi-

cient" duration, the upper par of the profile would attain an equilibrium shape and that

.he vertical position of the profile would be related to the storm surge level. Horizontal

position and total eroded area were obtained by shifting the equilibrium profile such that

no sediment was lost from it. From many scale experiments, Vellinga [1982], (using









15

theoretical considerations), derived scale relations for the assessment of erosion for a

particular profile and storm.

Dean [1973] proposed the significance of the parameter H/oT for bar formation

and, based on laboratory data, established that bars would occur for H/wT > 0.85.

Because most previous studies had related bar occurrence to wave steepness, this rela-

tionship was also expressed in terms of the wave steepness (H/L) and the ratio of sedi-

ment fall velocity to the wave period and to gravitational acceleration (oo/Tg). Kriebel

et al. [1986] later examined only large scale wave tank data and showed that the critical

value of H/oT should be about 2.8.

Swart [1974] utilized a series of wave tank tests to develop empirical expressions

relating transport characteristics and profile geometry (equilibrium beach profiles) to

wave and sediment conditions. These expressions were developed for each of four

different zones considered within the active beach profile.

Sunamura and Horikawa [1974] examined and characterized beach profiles for

two sizes of sediments. In addition, several ranges of wave heights, wave periods, and

initial slopes of planar beaches were investigated. The results of their laboratory experi-

ments included three beach profile types, one erosional and two accretional. This same

problem was later investigated by Suh and Dalrymple [1988] who applied equilibrium

beach profile concepts and identified one accretional profile type and one erosional type.

The numerous problems in sediment scale effects in beach profile models in-

cludes investigations by Iwagaki and Noda [1962], Nayak [1970], Noda [1972], Collins

and Chestnutt [1975], Dalrymple and Thompson [1976] and Hughes [1983]. Paul et al.


'L









16

[1972] indicated that exact similarity between a prototype sand beach and its correspond-

ing light-weight sediment model is impossible to attain. They concluded that a general-

ized criterion (in this instance for bar formations) for all materials would be impossible

and that a separate criteria must exist for each material due to the differences in porosi-

ty, angularity, and specific gravity.

Krumbein and James [1974] examined foreshore properties and behavior in terms

of maps rather than by discrete profiles stating that maps have the advantage of bringing

out changes that may occur at an angle to the shoreline by using contours drawn through

a field of numbers. Their findings, as measured by shear vane and/or penetrometer,

indicated that particular foreshore subareas could be subjected to erosion or accretion

based on beach (bed) firmness.

Miller [1976] investigated the shape of breaking waves on sediments in three

applications: (1) bedforms in the surf zone, (2) impact pressures due to breaking waves,

and (3) the interaction of post breaking bore and foreshore. Using optical laboratory

techniques, analysis of the internal components of motion in breaking waves on sedi-

ments was investigated. Conclusions included that the erosion-deposition balance on the

foreshore can be gained through analysis of initial bore strength.

Smith et al. [1976] investigated characteristics of a two dimensional model beach,

subjected to wave action, with varying initial slopes to test the hypothesis that the beach

profile reaches a repeatable equilibrium. Their findings showed that the entire profile

did not have a repeatable equilibrium shape possibly due to minor uncontrollable water

level fluctuations. While the maximum height of the offshore bar reached an oscillatory









17

equilibrium, the maximum depth of the nearshore trough and the sand level at the profile

midpoint showed absence of both stability and repeatability.

As a method of characterizing beach profile changes both in nature and in labora-

tory models, Hayden et al. [1975] applied empirical orthogonal functions (EOF). This

statistical analysis can be used to analyze temporal beach profile variations from a set of

profile data; however, it is purely descriptive and does not address the processes or

causes of profile changes.

A data set of 504 beach profiles along the Atlantic and Gulf coasts of the U.S.

assembled by Hayden et al. [1975] was later analyzed by Dean [1977] who used a least

squares procedure to fit an equation of the form h =Ay" to the data. Dean found a cen-

tral value of n=2/3 as Bruun had earlier.

This equilibrium profile model first presented by Bruun [1954] and later charac-

terized by Dean [1977,1991] is, according to Kriebel et al. [1991], probably the most

widely used in coastal engineering today. It has been used in numerous recent studies,

Seymour and Castel [1988], Larson [1988], Larson and Kraus [1989], Work and Dean

[1991], Moutzouris [1991], and Dean et al. [1993]; and, with modifications (Larson

[1988] and Larson and Kraus [1989]) among others with varying results.

Seymour and King [1982] used profiles measured during the 1978 Nearshore

Sediment Transport Study (NSTS) at Torrey Pines, CA, in an effort to predict the cross-

shore transport of sand. Eight models, from previous investigators, included the catego-

ries of winds, tides, sediment size sorting, rip currents, wave steepness, wave height,

energy dissipation, wave power, and velocity asymmetry. Their findings concluded that









18

while several of the models were capable of predicting major changes, none was capable

of predicting more than one-third of the total beach volume variability.

Hallermeier [1981] developed a three-zone model to divide the shore-normal

profile. This model was based on two Froude numbers which gave "distinct thresholds"

in sand mobilization by waves to the shoal zone. This zonation development used linear

wave theory and an exponential distribution of cumulative wave heights. Results showed

that wave period, standard deviation of significant wave height, and sediment diameter

were the primary factors that shoal-zone boundaries depend on in addition to mean

wave height. In addition, the model appeared to predict the seaward limit of significant

wave effects on the nearshore profile.

Allen [1985] evaluated Dean's [1973] model of shore-normal sediment transport,

which included the use of wave steepness, using field data (including daily beach pro-

files) with mixed results. He found that 98% of the erosional events were correctly

predicted by the model, but only 45 % of the depositional events were correctly predict-

ed. Several of the beach profiles displayed essentially no change.

Dally and Dean [1984] investigated local suspended sediment transport in the

cross-shore mode by a simplified analytical model, which was then adopted for computer

solution to model beach profile evolution. Their transport scheme involved first-order

wave induced and mean return flow currents coupled with an exponentially-shaped

sediment concentration profile. They considered their results promising due to the close

qualitative agreement with both natural and laboratory profiles, but recommended that








19

the model features of sediment concentration profiles and lateral fluid momentum receive

further development.

Dally et al. [1985] developed an "intuitive" expression for the spatial change in

energy flux associated with breaking waves in the surf zone. Their study included the

effects of both beach slope and wave steepness on wave decay, and derived analytical

solutions for wave transformation due to breaking and shoaling on a plane slope, a flat

shelf, and an "equilibrium" beach profile. These solutions were then compared favor-

ably to laboratory data. In addition, from calculations based on a study by Kamphuis

[1975], they concluded that bottom friction plays a negligible role in the surf zone when

compared to the effects of breaking and shoaling. Larson [1988] and Larson and Kraus

[1989] showed that the use of the more realistic wave breaking model of these investiga-

tors resulted in an equilibrium profile equation form that has both shallow and deeper

water components.

Niedoroda et al. [1985] discuss general dynamics within the shoreface. Obser-

vations and empirical data suggested that the shoreface of open ocean sandy coasts is a

dynamic feature where gravitational and fluid forces from waves and currents adjust the

shape of the shoreface sediments into a time-averaged equilibrium. Further, the mor-

phology of the shoreface should result from this balance of forces, and differences in

width, depth, slope and shape of various shorefaces should be explainable in terms of

the local oceanographic environment.

Suh and Dalrymple [1988] developed a semi-empirical model that expressed

shoreline advancement of an initially plane beach in terms of known parameters specif-









20

ically that for an initial plane beach, and for what they termed the "Dean number",

H/wT. Their results showed different trends for both short- and long-duration tests,

suggesting that an equilibrium may never have been reached in the short-duration tests;

and, they concluded that this model may be primarily suited to long-duration tests.

Seymour [1985] applied simple transport model relationships to show the effects

of the initiation of motion for a broad range of conditions for both cross-shore and

longshore sediment transport. This study produced these findings: (1) initiation of

motion effects can be included in analytical sediment transport models, (2) large differ-

ences occur in the net transport resulting from broad-band and monochromatic waves of

the same energy, (3) threshold effects significantly alter transport estimates under certain

surf zone conditions, and (4) low frequency oscillations may be expected to decrease the

impact of the threshold phenomenon on observed transport.

Kobayashi and DeSilva [1987] developed a Lagrangian model for predicting the

movement of individual sand particles in the swash zone and found good prediction for

erosional trends but not for accretional trends. They concluded that the model may be

used to predict the velocity of sediment particles moving cross-shore, and that it would

clarify the causes of scale effects in two-dimensional beach studies.

Seymour [1989] studied cross-shore transport data from four U.S. locations and

compared the variations of the sites. Two of these sites with low slope beaches and

small breaker angles showed a principle variation mode to be a change in concavity,

while the other two sites, of steeper slope and larger breaker angles, displayed principle

variation by horizontal retreat.









21

Kriebel [1982], Kriebel and Dean [1984,1985] and Kriebel [1986] considered

profiles out of equilibrium hypothesizing that the difference between the actual and

equilibrium wave energy dissipation per unit water volume is proportional to the off-

shore transport. A sand conservation relationship was incorporated into a numerical

model of sediment transport with relatively good agreement between field results and

laboratory profiles. This model is limited to monotonic profiles.

Larson [1991] has suggested that although the proposed 2/3-power law provides

a good fit to many beaches, significant changes in overall shape may occur if the grain

size varies "markedly" along the profile. He further suggests that significant sediment

sorting across the profile may result in an equilibrium profile that is steep near the

shoreline but slopes more gently in the seaward portion. In his study, a modified equi-

librium profile was used to describe the representative profile at three different beaches

with varying grain size along the profiles. The classical equilibrium shape of Bruun

[1954] and Dean [1977] was used for comparison. All of the theoretical profile equa-

tions were least-square fitted to the data with Larson's modified equation allowing a

better fit than the 2/3 power curve.

In addition, Boon and Green [1988] argue that the equilibrium profile should be

governed by h=Ay" as n may differ from the 2/3 value used in the Bruun and Dean

studies. Their findings, based on profiles in the Caribbean, generally showed that the

n value providing a best fit was approximately equal to 0.55. They suggest that the use

of a different exponent in the power law equation could lead to better overall agreements

between measured and predicted profiles.









22

Work and Dean [1991] however suggest that the exponential value of n be in-

creased, rather than decreased. This also presents an additional problem in selecting an

appropriate scale parameter, A, for a given sediment size since the empirical curve by

Moore [1982], who developed the A vs. D relationship, is based on a best fit between

h=Ay" and measured profiles, with n=2/3.

Kraus et al. [1991] examined a simple criteria to predict whether a beach would

accrete or erode due to wave-induced cross-shore sediment transport. Their criteria,

originally developed based on data from small and large wave tank studies, and mono-

chromatic waves, correctly predicted most accretion and erosion events from a data set

of beaches from around the world. Eight criteria, including several introduced in the

study, were evaluated; and, due to the correct prediction of most events, the investiga-

tors questioned previous studies which determined these criteria unsuccessful.

Moutzouris [1991] reported on field results from various non-tidal beaches in

Greece with mixed sedimentary environments and correlated various characteristic geo-

metrical parameters to the two 'classical' beach profiles in terms of varying the grain

size distributions across-shore. His results showed similarities between the field data

and previous laboratory tests with uniform cross-shore distributions, though he recom-

mended that non-uniformity of grain-size distribution should not be ignored in nearshore

process models. With regard to wave characteristics on beach profiles he found that,

unlike laboratory tests, field conditions were not suitable for deriving quantitative rela-

tionships.









23

Dally [1991] studied the effects of long waves on cross-shore transport in labora-

tory tests using random waves in short (5 min.) and long (30 min.) bursts and corre-

sponding profile evolution. Results showed that seiching induced by long-duration tests

has a distinct influence on beach profile evolution as it tends to smooth the bar\trough

formation and shift the position of the bar landward. Additionally, the rate of profile

evolution was shown not to be influenced by seiching. Dally also states that seiching

had little influence on wave statistics in the nearshore region indicating that the sand

carried by long-wave motion may be more significant to profile evolution than the long-

wave influence on shoaling and breaking behavior in shallow water.

Kriebel et al. [1991] conducted an investigation on beach profile changes using

three equilibrium profile forms, two of which accounted for realistic beach face slopes.

They then used these profile forms to obtain analytical solutions for the maximum ero-

sion potential in response to water level rise, and also presented a new method for incor-

porating time-dependent erosion based on a convolution integral. When expressed in the

form of this integral, it was found that analytical solutions for time-dependent erosion

could be related to the maximum erosion potential and the characteristic erosion time

scale (rate parameter).

Dalrymple [1992], in turn, rearranged the large wave tank tests of Larson and

Kraus [1989] and introduced a profile parameter, P, which uses deep-water wave char-

acteristics to distinguish between storm (barred) and normal (non-barred) equilibrium

beach profiles. He also showed that the use of the shallow-water Dean number, H/wT,

would serve the same purpose in shallow water. This investigation also showed a









24

Froude number representation of the sediment fall velocity to be an important parameter

for equilibrium profiles.

Roelvink and Broker [1993] discuss various classes of cross-shore profile models

concepts and compared transport concepts used in process-based models to the dominant

processes to be modelled as well as an intercomparison of several morphodynamic

models. Some of the recommendations for future modelling studies cited were: inclu-

sion of long wave effects on sediment transport, inclusion of swash zone processes and

dune erosion, and detailed comparison verifications of sediment transport models.

Inman et al. [1993] developed an equilibrium model that treats the outer portion

of the profile independently from that of the inner portion. The two portions are

matched at the break-point bar. Using beach profile data not previously available, it was

shown that both portions were well-fitted by curves of the form h=Ay" with a value of

mn 0.4 nearly the same for both portions. In addition, m was found not to change

significantly with seasonal beach changes, and that changes in seasonal equilibria were

a consequence of changes in surf zone width and 0(1) variations in the scale factor A.

Nairn and Southgate [1993] in a two part paper describe computational models

of beach profile response, first concentrating on wave and current modelling and then on

sediment transport and profile development predictions. In the first model, using an

approach described by Halcrow [1991], generally good predictions for wave height,

wave bottom velocity moments, wave-induced longshore current velocities, and fraction

of broken waves were obtained for beaches with monotonically decreasing depths. The

second model, due to selected schematization (time-averaging in the temporal schemati-









25

nation, and lateral spatial schematization of the processes included) was considered

sufficient to provide relatively accurate predictions of alongshore transport and profile

change for "short to medium scale" (< 1 year) problems.

Dean et al. [1993] extended previous methodology for calculating equilibrium

beach profiles of uniform sand size to include arbitrary distribution of sediment charac-

teristics across the profile. Their methodology, using measured profiles, sediment sizes,

and beach face slopes, was applied to data from ten field sites on the northern island of

New Zealand. The "blindfolded" tests showed that although individual measured vs.

predicted profiles did not show consistently good agreement, the averages of the mea-

sured profiles were in good agreement particularly close to shore (<5 m). They con-

cluded that it was difficult to predict whether the differences shown between measured

and predicted profiles for this study were due to profile disequilibrium or to limitations

in the present knowledge of equilibrium beach profiles.

In other studies relative to the current study, Davis [1983] described barrier

sediments as typically coarsest and least sorted at the surf "plunge point." Fines were

found both seaward and landward of this point. In addition, generally finer and better

sorted sediments were found on the longshore bar compared to the trough, though the

reverse has also been found. He suggests that the apparent disagreements are due to

complex interactions between currents, waves, and bottom sediments as these interac-

tions vary greatly. As a result, the use of sediment texture to define or identify environ-

ments can be problematic.









26

Davis also describes the processes in barrier island environments as due to the

complex interactions between wind, waves, and currents. Waves dominate primarily in

the nearshore and foreshore zones, wind in the backshore, and wave-generated currents

in the surf zone.

Davis and Fox [1981] found that tidal currents typically are of significance only

very near and inside inlets where they move sediments. And Davis et al. [1972] state

that away from inlets tidal range plays an indirect role as the effects of waves and cur-

rents move from place to place in the nearshore zone as a result of water level fluctua-

tion.

Boothroyd [1985] considered wave energy as the dominant process on microtidal

coasts, such as those found in the current study. The term microtidal from this study is

from Hayes [1979] who compared mean wave height vs. mean tidal range for a number

of selected coastal-plain shorelines and developed a tidal classification scheme. Along

with being wave dominant, microtidal inlets have proportionally smaller ebb-tidal deltas

than do mesotidal inlets. Boothroyd states that microtidal areas are also thought to have

relatively larger flood-tidal deltas due to the dominance of wave energy flux over the

small tidal prism.

Davis [1985] discussed the general relationships between groundwater level, tidal

fluctuations and foreshore processes which showed the direct influence of tides on beach

sedimentation. In addition, a discussion on tidal causes in altering longshore current

velocity, and the migration and morphologic modification of ridge/runnel systems was

included. Davis further points to studies by Ingle [1966] in which local currents were








27

observed to cause sediments on either side of the breaker zone to move toward the

breaking wave.

Leeder [1983] summarized barrier island migration seaward under conditions of

net sediment supply in which an upward-coarsening sequence is produced that may be

broken by fining-upwards tidal-inlet channel forces. In addition, as with "normal beach"

environments, offshore bars tended to show variably dipping internal sets of tabular

cross stratification directed landward; and, the troughs showed small-scale cross lamina-

tions produced by landward-migrating wave-current ripples. Smaller amplitude ridge

and runnel topography, similar in structure, occurred in the foreshore zone of broad

sandy tidal flats and beaches.

Davis et al. [1985] describe the coastal morphodynamics of the barrier island

environment from Egmont Key to Anclote Key in Pinellas County, Florida. This study

includes the geologies of a "recently" formed, emergent barrier island, an example of a

classic "drumstick" barrier island, as well as local geology and quaternary sea-level

fluctuations for this area.

Balsillie [1982] tabulated offshore profile descriptions for the Florida coast using

the power curve fit. Fits were conducted for all 1579 Florida Department of Natural

Resources profiles using both fixed and free exponents. In addition, Clark [1992] lists

and categorizes beach erosion problem areas for the state of Florida by county; and

Hubertz and Brooks [1989] tabulated Gulf of Mexico hindcast wave information from

the wave information studies (WIS) of U.S. coastlines.









28

Machemehl et al. [1991] evaluated inlet stability based on hydraulic characteris-

tics for 51 U.S. tidal inlets. This research concentrated on developing relationships

between inlet length, width, and stability using aerial photography data sets collected

over a thirty year period.

A sediment sampling study by the Beach Erosion Board [1956b] found that all

samples taken from only one profile line within a 300-ft beach section had approximately

twice the error, in mean sediment size, than did samples taken across the profiles at 10-

ft intervals. In addition, it was shown that taking pairs of samples at each location

across a profile only gained a slight improvement (0.6%) in the error and, therefore was

not considered time or cost effective.

Numerous studies on beach erosion, inlet stability, and beach nourishment pro-

jects throughout the six-county study area (Chiu [1979], Doyle et al. [1984], Foster and

Savage [1989], Lin and Dean [1990(a,b)], Clark [1992], and Inglin and Davis [1993]

among others) have also been conducted.














CHAPTER 3
STUDY AREA

There are approximately 275 km of sandy beaches in the six-county study area -

most of which lie on a long series of barrier islands. The beach sediments primarily

consist of fine quartz sand and shell fragments [Neale et al., 1983] and with a few

exceptions have low- to moderately-sloping offshore profiles. In addition, most barrier

island elevations are low, between 1.2 and 2.75 m; and, the coast is categorized as low

microtidal (as defined by Hayes [1979]) with tides ranging between 0.67 to 0.85 m (Reid

[1991] and Doyle et al. [1984]).

Wind and wave climates are considered "moderate" with shoreline approaches

predominantly from the southwest, and changes to the northwest to north-northwest dur-

ing the winter months (Doyle et al. [1984]). Data from the U.S. Army Corps of Engin-

eers', Wave Information Studies (WIS) Stations 39-43, give mean significant wave

heights (H,) for this region ranging from 0.8 to 1.0 meters, with mean peak wave peri-

ods (Tp) from 4.3 to 4.8 seconds (Hubertz and Brooks [1989]).

3.1 Pinellas County

Pinellas County has approximately 56 km of beaches on barrier islands extending

'from the southern-most tip of Anclote Island in the north to Mullet Key (which lies at

the northern end of Tampa Bay) in the south (Figure 3.1). With the exception of the

north-west end of Honeymoon Island and Caladesi Island, these barrier islands are























I


I
I Honeymoon Is.

R-1


GULF OF MEXICO Sand Key


R-90 R--110

Indian Rocks


R- 1 ')


GULF OF MEXICO


R-170 R-18

Mullet Key


0 -f 3 MIUES
SCAIE


Figure 3.1: Pinellas County


FILL I I AI-


bJ
z
-1

I)-
,
<









31

extensively developed. Most of the beaches in this county are considered critical erosion

areas (Clark [1992]); and, several areas Honeymoon Island, Redington Shores Redin-

gton Beach, and the majority of the shoreline from Indian Rocks Beach south to the end

of Long Key have either been restored or nourished, or are authorized for restoration

(Lin and Dean [1990(a,b)], Sayre [1987], Creaser et al. [1993] and Inglin and Davis

[1993]).

The Indian Rocks area, a natural headland which has historically been subjected

to high erosion rates, supplies sediment both to the north and south (Doyle et al. [1984])

and is aptly named due to the large percentage of rock which extends far offshore. In

addition, there are five tidal inlets (passes) Hurricane, Dunedin, Clearwater, Johns,

and Blind Pass which either directly or indirectly affect erosion/accretion rates on their

respective adjacent beaches (Clark [1992]).

4.2 Manatee County

The 19 km of Gulf shoreline in Manatee County consist of 2 barrier islands, 12

km-long Anna Maria Key and the northern 7.2-km section of Longboat Key. The two

are separated by Longboat Pass (Figure 3.2). Elevations of these islands are generally

1.5 to 2.75 m. Widths vary from about 2.0 km near the northern end of Anna Maria

Key to approximately 122 m at the southern end of the same island; and, that of Long-

boat Key varies from about 915 m at the north end to approximately 240 m in the mid-

dle of the Manatee County portion.

The beach sediments are probably derived from the offshore and nearshore bot-

tom of the Gulf, and from the island itself (Doyle et al. [1984]). Currents are predomi-


I
































Tampa Bay
c/\^^


GULF

OF

MEXICO


Figure 3.2: Manatee County


R-1


MANATEE


Anna
Maria
Key


0 1 2

S-ALE
!.,(CALE


3 4
-6 Mi ES


e\\OS_
,,









33

nately tidal in nature and, historically, the longshore transport diverges near the center

of Anna Maria Key with a net littoral drift northerly in the area of Holmes Beach, and

southerly south of Holmes Beach (Doyle et al. [1984]).

The shoreline has a history of advancement and retreat and numerous beach

stabilization, re-nourishment, and restoration projects have been implemented

(Demirpolat et al. [1987] and Walton [1977a,b]). Much of this historical shoreline

change has been due to natural events. Since 1900, a total of 30 known hurricane and

tropical disturbances have passed within a 80-km radius of Manatee County; and, the

relative frequency of such storms is estimated at approximately 1 in 2.5 years (Doyle et

al. [1984]).

3.3 Sarasota County

Sarasota County (Figure 3.3) has approximately 55 km of barrier island beach

from the southern half of Longboat Key in the north to the northern portion of Manasota

Peninsula (Key) in the south. Most of the coastline is heavily developed. With the

exception of the public beaches at Lido Key, Siesta Key, and Casey Key where beach

nourishment (Truitt et al. [1993]) or jetty construction has occurred, most beaches are

generally narrow and steep. In addition, the offshore 3-, 4-, and 6 meter depth contours

have advanced and retreated; and, in some instances coastal emplacement of seawalls,

Srevetments and groins has accentuated erosional problems by steepening offshore profiles

(Doyle et al. [1984]). In a few cases, inlet instability (Midnight Pass, Venice Inlet, and

Big Sarasota Pass) has worsened these problems (Machemehl et al. [1991], Chiu [1979],

Foster and Savage [1989], and Walton [1979]).




































k Lido R-.O10
R ? Lido Siesta Key
Key Big
R-1 Longboat Sarasota Midni
Key Pass Pass








GULF


SARA'OIA


80 R 100 R. 120 R 1-10 R-'160 1
Casey Key nice Manasota Peninsula
Venice
ght Inlel
ghf









OF MEXICO 1 ,,
SCALE


Figure 3.3: Sarasota County









35

Of the four inlets (passes) in Sarasota County, the three mentioned above and

New Pass which separates Longboat Key from Lido Key, only Big Sarasota Pass and

Venice Inlet are considered stable (Machemehl et al. [1991], and Clark [1992]) as they

are dredged periodically and maintained by the U.S. Army Corps of Engineers for

navigation purposes. Although the beach sediments in Sarasota County are typically

composed of fine quartz sand and shell fragments (Doyle et al. [1984]), some of the

coarsest sediments retrieved in this study were found at the waterline and 1- and 2 meter

contours, particularly in the region between monuments R-90 and R-117.

3.4 Charlotte County

There are approximately 22 km of barrier islands and spits in Charlotte County

(Figure 3.4) including the southern 6 km of Manasota Key; Knight, Bocilla, Pedro, and

Little Gasparilla Islands 13 km of barrier islands separated by Bocilla Pass, Blind Pass,

and Little Gasparilla Pass; and, the northern 3 km of Gasparilla Island. Of these 22 km

of shoreline, only portions of south Manasota Key and north Gasparilla Island are acces-

sible by automobile. As a result, much of the county shoreline is undeveloped.

Between Stump Pass (north of Knight Island) and Gasparilla Pass (south of Little

Gasparilla Island) the beaches are very dynamic due to the presence and influence of at

least 5 different inlets which have opened and closed at various times between 1883 and

1982 (Foster and Savage [1989] and Doyle et al. [1984]).

State and federal nourishment and restoration projects have historically centered

around the Charlotte Beach State Park area on Manasota Key (Corps of Engineers





















CHARLOI TE


Sarasota County

R-1 Peace River
Manasota
Key R-10

Knight Charlotte
Is. Bocilla Harbor
Is. Pedro R-40 '
Is.
Little R 1
Gasparilla R-60_ -
Is. -
GULF Gasparilla
OF Is. Lee County
0 I 2 :3 1
MEXICO I ---:Jf -- "L
SCALE
. .. . . .. .


Figure 3.4: Charlotte County









37

[1972, 1974a]) although many property owners have placed numerous groins, revet-

ments, and seawalls on the northern 6-7 km of the county's beaches.

3.5 Lee County

The 71-km coastline of Lee County (Figure 3.5), the longest sandy beach shore-

line county in this study, is comprised of a group of low barrier islands that generally

follow a south south-easterly trend. The one exception is Sanibel Island (the largest of

the group) trending in an easterly northeasterly direction. From Gasparilla Island in

the north to the northern half of Little Hickory Island (also known as Bonita Beach) in

the south, there are 9 inlets Boca Grande Pass, Captiva Pass, Redfish Pass, Blind Pass,

San Carlos Bay and Matanzas Pass. Big Carlos Pass, New Pass, Little Carlos Pass, and

Big Hickory Pass bordering the barrier islands. Of these, Captiva, Redfish, Blind, and

Little Hickory passes are natural inlets while the remaining are dredged and maintained

by the U.S. Army Corps of Engineers (Doyle et al. [1984]). With the exceptions of

Cayo Costa (La Costa) Island, North Captiva Island, and Lovers Key, the beach front

is heavily developed with homesites and vacation resorts.

A number of studies of the stability of various inlets in Lee County (including

Jones [1980] and Machemehl et al. [1991]) have been conducted in the past. However,

the primary focus since the 1960's has been the restoration and various coastal engineer-

ing solutions to the erosional problems on Captiva Island (Coastal and Oceanographic

Engineering Laboratory [1974], Silberman [1979], Olsen [1982], Barnett and Stevens

[1988], and Coastal Engineering Consultants, Inc. [1990]) where over the last 30+ years
































Gasparilla
SIN Island


R-1

R-20


R-40
Cayo Costa
Island


GULF


H --60 /
N. Captiva R 80
Island
Captiva R() 120
Island


Estero
- 160 Island


I 1 .


Sanibel Island


MEXICO


R 240
Lovers
Key







.'CALt"


Figure 3.5: Lee County









39

state, county, and local agencies have implemented a series of seawalls, groins, and

renourishment projects.

Most recently, the Captiva Erosion Prevention District (CEPD) has proposed a

1995 three-component nourishment project which includes placing approximately

954,500 cubic yards of sediment along the entire length of Captiva Island and the north-

ern few kilometers of Sanibel Island. In addition, two inlet management projects, one

at Blind Pass, and one at Redfish Pass (which includes a terminal groin) are also under

consideration (Ruediger [1994]).

3.6 Collier County

Collier County has approximately 56 km of sandy beaches and another 24 km of

coastline south of Marco Island which are generally mangrove islands, although a few

small "pocket" beaches are present (Figure 3.6). The northern 30 km of beaches consist

of Bonita Beach Island, bounded by Wiggins Pass, and the remainder is part of the

mainland cut by Clam Pass, Doctors Pass, and Gordon Pass. South of Gordon Pass a

series of barrier islands is present including Keewaydin Island (bounded by Little

Marco Pass), the Little Marco Island group (bounded by Big Marco (or Hurricane)

Pass), and Marco Island (bounded by Caxambas Pass).

Numerous studies on the dynamics of various inlets in Collier County (including

.Coastal and Oceanographic Engineering Laboratory [1970 a,b] and Bushey [1984]) have

been conducted along with various coastal engineering projects (including Stephen

[1981]).














































i 120 0
I.' IO 2
ea sa
Keewaydin Island


x
a
) 30
3
I'In
R 1-10) -

Marco Island "


GULF OF MEXICO




Figure 3.6: Collier County


R-1


0 1 34
SCALE














CHAPTER 4
METHODOLOGY

4.1 Beach Profiles


The beach profiles used in this study are from the Florida Department of Natural

Resources (DNR) files which periodically update cross-shore beach profiles for the

Florida coastline. Since these data sets (profiles) are measured only every few years,

the measured profiles used in this study pre-date the sediment samples from 4 to 18

years. Table 4.1 indicates the dates of the DNR profiles by county used in this study.



Table 4.1: DNR Profile Dates for Current Study


County Date Measured (mo/yr)

Pinellas Sept.-Oct. /1974
Manatee Aug.-Sept. /1986
Sarasota Apr.-Aug. /1987
Charlotte December /1982
Lee June-Oct. /1982
Collier March /1988



Only "long" profiles (nominally every third line extending beyond the breaker

zone out to about 30 ft depth) were used here. Sediment sampling and profile analysis

was primarily conducted at every third, long profile, or approximately every nine thou-

sand feet. Exceptions to this nine thousand foot separation are due primarily to "site









42

availability" as some monuments were disturbed, some could not be located, and others

are accessible only by boat.

4.2 Sediment Samples

Approximately 320 surface sediment samples were collected, to document the

spatial variability in sediment size, throughout the six county study area. The number

of samples collected at each profile varied from three to nine including samples taken in

the dunes, at the berm, on the beachface, and at the -1 m, -2 m, -4 m, -6 m, and -8 m

contours. Table 4.2 gives the coordinates, elevations, beach face slopes, and azimuths

for the DNR profile locations where samples were collected for Pinellas County. Loca-

tions for the remaining counties are presented in Appendix C.

One deviation from this particular methodology includes samples from Longboat

Key in Manatee and Sarasota counties. The sediment data for these profiles (Manatee

R-45, R-51, R-60, and R-66, and Sarasota T-3, R-12, R-21, and R-27) were collected

and analyzed by Applied Technology and Management, Inc., of Gainesville, Florida, for

use in another study. The offshore sampling depths for these sediments included the -5

ft, -10 ft, and -15 ft contours.

Samples from the -1 m and -2 m contours were collected by a swimmer using a

small can as a scoop. The -4 m, -6 m, and -8 m were collected from a boat using a

metal container which was lowered over the side to the seafloor and dragged until suffi-

ciently full. The horizontal positions for these offshore sampling points were established

using a Loran navigation system. Once located, the boat operator followed the profile

line and indicated the appropriate depth locations to the sample collector. Depths for


1


























Coordinates, Elevations, Beach Face Slopes, and Azimuths for DNR
Monuments in Pinellas County, FL.


(1) Monument coordinates are in units of feet for consistency with
standard information sources.
(2) Azimuths are measured clockwise from magnetic North.
(3) From Balsillie et al. [1987].


Table 4.2:


Notes:


Monument Northing' Easting Range Elevation Beach
No. (ft) (ft) Azimuth2 (m,NGVD) Face
(degrees) Slope3

R-21 1347453.600 235282.120 285 1.96 0.0312
R-33 1336351.000 232881.790 270 1.60 0.0276
R-42 1327243.800 232748.930 275 2.51 0.0346
R-57 1314305.177 230331.453 295 2.03 0.0848
R-69 1303124.200 226817.070 280 2.53 0.1281
R-81 1291401.642 224983.776 270 2.65 0.0572
R-93 1279589.600 226708.180 250 1.91 0.1343
R-108 1266287.600 234582.270 225 2.10 0.0366
R-138 1242885.200 253152.070 250 1.74 0.0745
R-159 1224528.800 261332.720 270 2.00 0.0428
R-177 1195339.000 261809.470 280 2.10 0.0722









44

these samples were not corrected for tidal stage. Table 4.3 indicates the DNR ranges,

and the sediment samples collected at each profile for Pinellas County. Sample collec-

tion for the remaining counties are presented in Appendix D. (Note: no offshore samples

were collected for Lee or Collier counties).

All samples were placed in labeled cloth sacks, and then dried in a 40*C oven

before sieve analysis. Salt and other organic material content in the samples was consid-

ered negligible though no analysis was conducted to quantify the percentage of this

material. Most samples consisted of quartz sand and shell fragments, with the percent-

age of shell increasing between the berm and -1 m contour. However, many of the

offshore samples consisted of a mud-like ooze which became hard-packed during drying

and needed to be crushed prior to sieve analysis.

Twelve sieves were used to determine the grain size distribution of each sample.

Table 4.4 lists the sieve sizes and numbers.

Following sieve analysis, the mean and median grain sizes, skewness, kurtosis,

and sorting index for each sample was computed using a FORTRAN computer program

at Texas A&M University @ Galveston in Galveston, Texas (Sampson [1985]). This

program uses the method of Folk [1965] and a "seven-magic-phi-point" analysis to

calculate (using a cubic spline fit) these values in phi units. Conversion from phi units

to millimeters was done following computer analysis. An example of the output from

this program is given in Appendix B. An example of the results of this analysis, for

Charlotte County, are shown in Table 4.5. The sediment analysis results for the remain-

ing samples are presented by county in Appendix E.


i



















and Depths of Offshore Sediment Samples: Pinellas County, FL.


Range Latitude Longitude Nominal Depth
No. (Deg.,Min.) (Deg.,Min) Depth(m) (m)

R-21 2802.18 8249.14 4 3.4
6

R-33 28 00.27 82 49.40 4 4.2
6

R-42 27 58.57 82 49.41 4 3.7
6

R-57 27 56.49 82 50.07 4 4.4
6 6.3

R-69 27 54.58 82 50.45 4 3.5
6 5.6

R-81 2753.22 8251.05 4 3.6
6 5.9

R-93 2751.00 8250.00 4 4.6
6

R-108 2748.54 8249.16 4 3.6
6

R-138 27 45.03 82 45.47 4 4.3
6 5.7

R-159 27 42.02 82 44.15 4 4.2
6


Table 4.3:


Locations























Table 4.4: Sieve Sizes for Sediment Analysis

I .1


Standard
Sieve No.


10
14
18
25
35
45
60
80
120
170
230
PAN


Opening
(in mm)


2.000
1.410
1.000
0.710
0.500
0.350
0.250
0.170
0.125
0.088
0.0625


L ________________________________________________________________










Table 4.5: Sediment Sample Analysis: Charlotte County

Sample Total D50 Dmean S.I. Elevation Distance
(g) (mm) (mm) (m) (m)

R01DUNE.CHA 60.350 0.215 0.252 0.558 3.00 -50.00
R01BERM.CHA 76.660 0.889 0.780 0.900 1.00 -15.00
R01WL.CHA 72.780 0.774 0.793 0.868 0.00 00.00
R011M.CHA 73.040 0.470 0.580 1.526 -1.00 40.00
R012M.CHA 80.720 0.121 0.122 0.326 -2.00 120.00
:R014M.CHA 74.720 0.342 0.312 0.889 -4.60 260.00
R016M.CHA 72.610 0.163 0.207 1.161 -5.40 600.00
R018M.CHA 74.860 0.168 0.200 1.036 -7.50 900.00
R09DUNE.CHA 74.700 0.195 0.198 0.409 3.50 -80.00
R09BERM.CHA 30.190 0.330 0.330 0.573 1.00 -20.00
R09WL.CHA 84.540 0.876 0.945 1.234 0.00 00.00
R091M.CHA 73.270 0.243 0.250 0.684 -1.00 120.00
R092M.CHA 72.260 0.191 0.224 1.024 -2.00 260.00
R094M.CHA 75.600 0.114 0.134 0.765 -4.20 600.00
R096M.CHA 69.110 0.257 0.257 0.715 -6.10 900.00
R18DUNE.CHA 82.210 0.354 0.339 0.692 2.00 -35.00
R18WL.CHA 78.350 0.512 0.526 0.667 0.00 00.00
R181M.CHA 74.970 0.497 0.590 1.640 -1.00 60.00
R182M.CHA 81.500 0.146 0.157 0.614 -2.00 170.00
R184M.CHA 73.270 0.114 0.167 1.315 -3.90 420.00
R186M.CHA 70.740 0.117 0.126 0.738 -6.20 660.00
R188M.CHA 69.660 0.968 0.899 1.509 -7.40 900.00
R302M.CHA 70.820 0.154 0.176 0.709 -2.00 80.00
R304M.CHA 71.620 0.119 0.123 0.501 -4.50 400.00
R306M.CHA 88.810 0.111 0.113 0.405 -6.20 825.00
R362M.CHA 76.710 0.124 0.123 0.314 -2.00 85.00
R364M.CHA 85.900 0.115 0.121 0.653 -3.70 350.00
R366M.CHA 67.740 0.015 0.145 2.153 -6.30 850.00
R45WL.CHA 76.130 0.332 0.429 1.470 0.0 00.00
R451M.CHA 70.720 0.180 0.216 1.018 -1.00 50.00
R452M.CHA 76.870 0.154 0.177 0.907 -2.00 70.00
R456M.CHA 38.790 -0.672 0.003 1.532 -5.50 780.00
R458M.CHA 75.520 1.638 1.416 1.117 -7.60 1000.00
R54WL.CHA 77.740 0.255 0.328 1.318 0.0 00.00
R541M.CHA 75.400 0.110 0.113 0.366 -1.00 30.00
R542M.CHA 71.840 0.127 0.130 0.533 -2.00 160.00
R544M.CHA 72.490 0.114 0.120 0.540 -4.40 1000.00









48

In most instances, the sediment distributions show an expected decrease in size

across the profile, with some fining evident offshore and the coarsest sediments located

near the water line, though this is not always the situation. In some rare cases, anoma-

lies or "jumps" in the sediment distributions were noted and may be attributed as possi-

ble relict sediments. In the majority of these instances, either the sample was omitted

from the overall profile data set, or the entire profile was deemed inappropriate for use

in the current study.

The median grain size was used in the equilibrium model for all considered

profiles. In most cases the mean and median sizes were close enough to consider their

differences negligible. When these values were not close, however, the median size was

still used as it was considered a better quantitative, physical representation of the local

sedimentary environment.

4.3 Equilibrium Beach Profile (EBP) Model

It is important to note that while sediment sampling analysis was conducted for

the profiles noted in Table 4.3 (and in Appendix D), not all of these measured profiles

were considered suitable for inclusion in the EBP model analysis. Examples of excluded

profiles are (1) those near inlets and passes where current forces exist that are not repre-

sentative of a long straight beach, (2) profiles with large percentages of rock and/or shell

fragments offshore, such as is found near the Indian Rocks area of Pinellas County, and

(3) profiles in or near areas of previous beach re-nourishment (such as Honeymoon

Island and the Redington Shores/Beach areas of Pinellas County and Captiva Island in

Lee County) since often the placed sediment is of a different grain size (diameter) than









49

the "natural", local sediments. However, plots of the measured DNR profiles and cross-

shore sediment distributions for locations of this nature may be found in Appendix A.

These profiles have been excluded as the intent of this study is to provide an unbiased

and objective evaluation of the equilibrium beach profile model.

Several schemes are presented for comparison of the EBP theory to the measured

profile data available from the DNR field sites. The first is termed a "blindfolded" test

as it involves a simple prediction of beach profiles which are not based on fitting to the

measured profiles (aside from the beach face slope) but which uses known cross-shore

sediment size distribution based on a methodology to be described. Several additional

approaches, involving comparisons of best-fit profiles to the measured profile, modeled

after Work and Dean [1991] and Dean [1990] are also presented.

4.3.1 "Blindfolded" Tests

The fundamental equilibrium beach profile (EBP) model (i.e. h(y) = A(y)w)

presented by Bruun [1954] and later documented by Dean [1977,1991], as described in

the introduction of this study, is the basis for this methodology. To expand on this basic

profile model scheme, this equation can be applied to the case of uniform sediment size

across the surf zone and results from integration of the following equation (Dean et al.

[1993]):

h/2 dh =2A3/2 (4.1)
dy 3

This equation provides a basis more often found in nature one in which there is a

cross-shore variation in sediment characteristics (e.g. D=D(y) and A=A(y)). Inclusion

of the gravity term in equation (4.1) yields











dhai 2 A /2 (4.2)
dy m 2 A312

Larson [1991], Dean [1991], Work and Dean [1991] and Dean et al. [1993]

describe various approaches for predicting the EBP for the case of non-uniform sediment

size and, therefore, a non-uniform A parameter. The simplest of these approaches is the

instance when the cross-shore sediment size distribution is considered piece-wise contin-

uous (and hence A is piece-wise continuous) between two points along the profile, y, and

y'.. In this case it was shown that h can be represented by

h-h+ h3/2-h3/2 (3
y=yn + +- n (4.3)
m A3/2

which applies for y, < y < y,+,. In the approach here, sediment characteristics were

obtained at various points, y, across the profile. The median diameters were then trans-

formed to A values (from Figure 1.2 and Table 1.1). These A values were considered

to vary linearly between two adjacent, known points, y,, and y,,,. From Dean et al.

[1993] the predicted equilibrium profile can then be obtained by numerical integration

as follows:


h(y.)=h(y)1 +3 hi (4.4)
h (yI) =h (yM) + X+32 (Y+I2i+ -Yi)

where


StA An Yi-AnI(yi+yl -y (4.5)
= -Yn+yn +-ynA 2 Y)

Note that in this case y., < y, and yn+, < Y,+,. This approach has the advantage in that









51

it can be "marched step-by-step" linearly between the two known adjacent profile points.

In this case the "step", y,,, y,, was taken as 1 m; and, the values for the beach face

slope, m, were obtained from Balsillie et al. [1987] who tabulated a "6-point moving

average foreshore slope" for DNR ranges in this study area (Table 4.2 and Appendix C).

The above mentioned researchers employed similar methods to determine the

significance of incorporating cross-shore sediment size variation with varying results -

Larson [1991] found profiles "more accurately described"; Work and Dean [1991] found

results "not drastically improved"; and Dean et al. [1993] recommended that further

study be conducted before the results of apparent (dis-)equilibrium "can be interpreted

with confidence."

In essence, providing that the cross-shore distribution of the A parameter is sufficiently

described, and this modified version of the fundamental equilibrium beach profile theory

is realistic, good agreement between the predicted and measured profiles should be

obtained for this "blindfolded" approach.

4.3.2 Best-Fit Tests

Following the blindfolded tests for equilibrium profiles, a series of best-fit tests

were conducted on select profiles. These three best-fit approaches include: (1) a con-

stant A fit, (2) an exponential fit, and (3) a polynomial fit. For these schemes, a func-

tional form for the cross-shore distribution of the A parameter was first assumed. Each

test then uses an iterative scheme; or, more specifically, a least squares fit method using

a computer graphics software program (Abelbeck, no date).









52

First considered was a form of equation (1.1) as follows:


h,(y,) =Ayf/3 (4.6)

where y, is some measured distance offshore and hP(y) represents the predicted depth at

location y,. Further, if h,,,(y) is used to represent the measured depth at y,, then the

mean square error between the measured and predicted depths is given by
2= 1 N (y]2

eC2= [hp ( Yi- -hYi)12 (4.7)
Ni -1

where N is the total number of measured data points. In addition, for the error to be

minimized its derivative with respect to the shape parameter (A=A(y)) should be equal

to zero.

4.3.2.1 Constant A

For this test the value of A was held constant over the entire profile; and, a

minimized error function (with respect to A the only adjustable parameter) is defined

by Work and Dean [1991] as


=C2 =( 2 h(y) =0 (4.8)
S[hp(Yi) -h,(Yi)] aA 0
i-3

where ahp(y/laA =y 3 for this case.

An initial guess (in this case the average value over the entire profile) was made

for A and, in this instance, could be solved for explicitly (using trial and error) to an

accuracy of 0.01.











4.3.2.2 Exponential variation

Another possible form for the cross-shore distribution of the A parameter (again

described by Dean [1990] and Work and Dean [1991]) is to assume that:

A(y)=Aoexp(-ky) (4.9)

This format allows for a simple analytical expression for the predicted depth, but also

yields the result that A 0 as y oo which is not realistic. Work and Dean [1991]

assumed a more realistic version of equation (4.12), to avoid this problem, of the form

A(y) =A+ (Ao-Ai) exp (-ky) (4.10)

The solution for hp(y) is approximated numerically by the same method used for the

blindfolded tests; and, the best-fit values of A,, A,, and k are found from the graphics

program. Again, the error is as defined in equation (4.7).

4.3.2.3 Polynomial fit

The final best-fit scheme considered is to assume that the cross-shore distribution

of the scale parameter, A, may be of the form


h (y) =Bo+B+ByB2y2 .. +B. (4.11)

This solution is attractive due to its relative simplicity and is easily obtainable via the

graphics program employed.














CHAPTER 5
ANALYSIS AND RESULTS

Fifty field sites from the six-county study area were compared for agreement

between measured and predicted profiles as described by equation (1.15). Although the

basis for the equilibrium profile theory described by this equation implies applicability

only within the surf zone out to the depth of incipient motion, profiles were calculated

to the seaward limit of either the measured DNR profile or the sediment data. Attempts

were made to select sites away from structures, tidal inlets, and previously nourished

locations such that strong gradients in the longshore sediment transport rate would be

minimal (Work and Dean [1991]). All figures are presented at the end of this chapter.

5.1 Individual Profiles

The comparison of measured profiles and blindfolded predictions, as well as the

cross-shore sediment distributions of median grain size, are presented in Figures 5.1

through 5.50. Inspection of these figures indicates that the general trend of the model

under-predicts the measured profiles close to shore and over-predicts the same further

offshore. The depth of this transition occurs between approximately 2.5 to 3.0m.

Reasonable agreement was found in several cases for water depths less than two meters

.(e.g. Figures 5.17, 5.20, 5.26, and 5.29). In some instances, substantial bar/trough

systems are present (e.g. Figures 5.9, 5.15, 5.31, and 5.32) which cannot be represented









55

by the EBP theory. Additionally, the calculated profiles generally tend to deviate with

increasing distance offshore.

Two feasible explanations of the inability of the EBP theory to explain the outer

portions of the profile are (1) a possible excess of sediment in the profile that, given

adequate time and onshore stress (due to waves), may eventually be driven onshore, and

(2) that these areas are outside the dominant sediment zone of motion (i.e. seaward of

the depth of limiting motion) (Work and Dean [1991]).

Although the number of sediment samples (from the waterline seaward) ranged

from two to six, no apparent correlation between the number of samples and the good-

ness-of-fit is present. Cross-shore variations in median grain size range from approxi-

mately 0.01 mm to 1.1 mm. As can be seen from Figures 5.23, 5.30 and 5.28, 5.26

which represent small and large variations in cross-shore grain size, respectively, no

apparent correlation is present between sediment variation and goodness-of-fit in these

instances. In addition, single anomalies in the cross-shore median grain size (possibly

due to recent 'events' or relict sediments) may produce predicted profiles which vary

greatly from the measured. Examples of this case are presented in Figures 5.22a, and

5.46a. As an indication of the sensitivity of the equilibrium model, with respect to grain

size, these same profiles were re-calculated without the anomalous samples and are

presented in Figures 5.22b and 5.46b.

In most instances the profiles here transition to milder slopes offshore, though

transitions to steeper slopes are evident in a few cases. Dean et al. [1993] describe this

characteristic form of disequilibrium as possibly representative of: (1) a profile likely









56

constructed by onshore sediment transport (with long-term shoreward transport continu-

ity) in the case of a gradual transition, or (2) a profile likely constructed by seaward

transport from sediment sources in the shore zone into water which is shallower than the

equilibrium, in the case of an abrupt transition. This latter interpretation requires that

the sediment in the advancing profile be larger (coarser) than that in the underlying

profile (Dean [1991]).

Dean et al. [1993] also describe a local equilibrium concept in which correspond-

ing depths on the measured and predicted profiles have the same shape but need not be

located at the same offshore distance. This concept requires that the derivative of h with

respect to y for equation (1.15) equal one (i.e. [1/m + 3/2(h"l/A3/2)]dlh/dy = 1). This

consideration is included here as a possible explanation for the goodness-of-fit between

portions of the measured and predicted profiles in Figures 5.22a, 5.26, and 5.28.

5.2 Grouped Profiles

An additional comparison between measured and predicted profiles was conduct-

ed using profile averages. This comparison was employed to determine whether the

EBP theory could provide a reasonable representation of the actual profile shape, based

solely on cross-shore sediment size distribution or, if the average of several measured

profiles is a better representative. Four separate averages employing ten individual

measured and predicted profiles were implemented.

For the comparisons to be viable, it was first necessary to establish predicted

depths at the same locations of the measured depths for each profile. Depths at either

ten- or twenty meter cross-shore intervals were then interpolated from the points where









57

measured data were available. These interpolated, measured and predicted depths (both

obtained in the same manner) were then averaged and compared.

Figures 5.51 through 5.54 present the results of the averaged tests. In Figure

5.51, the profile is under-predicted close to shore and over-predicted further offshore,

similar to results found for individual profiles. One interpretation of this result may be

that this area has an excess of sand, and investigation of the individual profiles (Figures

5.30 and 5.31) reveals that this may be true.

The averaged, predicted profile in Figure 5.52 is indicative of what one might

expect had a best-fit approach been employed. The measured profile is slightly over-

predicted near the shoreline and under-predicted seaward of the 3 m contour, yet the

average depths of the two profiles differ by less than 1 m at any point.

Perhaps the best agreement between profiles in this comparison is found in Fig-

ure 5.53. Goodness-of-fit is evident to a depth of 6 m, at which point the measured

profile is over-predicted to the end of the line (EOL). Again, this could be interpreted

as an excess of sediment in the region, a situation which may also be noted by inspection

of the individual profiles.

The results found in the comparison presented in Figure 5.54 parity those found

in many instances in this study that is, an under-prediction of the computed profile

shoreward of the 2 m contour, with the measured profile transitioning to milder slopes

in the seaward direction resulting in an over-prediction of the calculated profile.









58

5.3 Best-Fit Profiles

Figures 5.55 through 5.57 compare the various best-fit profiles to the measure-

ments for the same profiles, respectively. Locations in which measured and blindfolded,

predicted profiles exhibit relatively good agreement were selected.

Although none of the calculated methods show good agreement to the measure

profile shoreward of the 2m contour in Figure 5.55, the profile is better-described sea-

ward of the terminal bar. While the best-fit profiles are slightly over-predicted, the

profile is well-described by the simple A =constant method, such that little difference is

seen between this and the other best-fit methods. The general functional form describing

the equilibrium profile is therefore supported, but differs in regard to the magnitude of

the A parameter.

The profile in Figure 5.56 is fairly well described by the best-fit methods, al-

though the presence of the bar/trough system represents difficulty for analysis. Never-

theless, the deviation between the measured profile and the best-fit methods is quite

small less than 0.20m.

The best-fit analysis presented in Figure 5.57 is similar to that described previ-

ously. The calculated profiles, though slightly over-predicted, show relatively good

agreement. Again the profile is best-described by the A=constant method. That this

case is well-described by the blindfolded test could be considered somewhat surprising

due to the anomalous sediment sample at the 1 m contour (see Figure 5.45). Further in-

spection, however, reveals that the magnitude of the anomaly is relatively small. This

view will be discussed in more detail in the following chapter.





















Pinellas R-21
0.45

0.4' ......................................................................................................................

0.35 1......................................................................................................................

0.3 ........................................................................................................................


0.25 .......................................................................................................................




0.15 ... ...............................................................................................................
0.4

0.35

0.3

0.25




0.15


0.1









E
d
> -


o
-2
m

LL
-5
aZ


0 100 200 300 400 500 600 700 800 900
y, Distance Offshore (m)















1- *',
3-


100 200 300 400 500 600 700 800
y, Distance Offshore (m)



MEASURED -.... PREDICTED


Figure 5.1: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 21, Pinellas County, Florida.


E
E



(O










60




Pinellas R-33


0 100 200 300 400 500 600 700 800 900 1
y, Distance Offshore (m)


200 300 400 500 600 700
y, Distance Offshore (m)


- MEASURED *... PREDICTED


Figure 5.2: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 33, Pinellas County, Florida.










61






Pinellas R-42
21
.2
19
18-
17
6 i----4------....
I6 4.......................i.............. .................................................................................


0.15-
0.14-


0.12-0 -10
-200 -100 0


100 200 300 400 500 600 700 800 900
y, Distance Offshore (m)


3 0 100 200 300 400 500 600 700 800 900
y, Distance Offshore (m)


-- MEASURED ---** PREDICTED


Figure 5.3: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 42, Pinellas County, Florida.


0.
0
0.1
0.1
0.1
(1


'-:iliiA':^^^^^ ^ ^^^^^^^^^^::::











62






Pinellas R-57


U,
E



0



0
5 0



a


0
0













z



CI)
r-
_>

UJ


-100 0 100 200 300 400 500 600 700 800 900 1(
y, Distance Offshore (m)


100 200 300 400 500 600 700 800 900
y, Distance Offshore (m)



- MEASURED *.... PREDICTED


Figure 5.4: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 57, Pinellas County, Florida.









63




Pinellas R-69


200 300 400 500 600 700 800 900 1
y, Distance Offshore (m)


200 300 400 500 600 70
y, Distance Offshore (m)


- MEASURED -.... PREDICTED


Figure 5.5:


Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 69, Pinellas County, Florida.












64






Pinellas R-138







.. .. . .. . . .. . .. . . .. . .. . .


- U. "
E
E 0.4-
0.35-
E 0.3-

a 0.25-
0.2-
0.15-
0.1
-1





2-
1-

E 0.
S-1
O -1-
(5 -2-
z
-3.
t-
.o -4
> -5.
a)
S -6-
-7


30 0


100 200 300 460 500 600 760 800 900
y, Distance Offshore (m)


100 200 300 400 500 600 700 800 9(
y, Distance Offshore (m)



- MEASURED .... *PREDICTED


Figure 5.6: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 138, Pinellas County, Florida.










65





Pinellas R-159
75-


0n1


0.165-
0.16
0 .15 5 .................. ....... .....................................................................................
0.15 ........................ ........................................
0 .14 5 .................................................................................................................
014............ ...
n i ............... ........................................


0.135-
0.13
-2


30


0 200 400 600
y, Distance Offshore (m)


1000


y, Distance Offshore (m)


- MEASURED .... PREDICTED


Figure 5.7: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 159, Pinellas County, Florida.


....................................iii










66





Manatee R-9


200 400 600 800 1000 1200 1400 V1
y, Distance Offshore (m)


6 260 460 600 800 1000 1200 1400 1
y, Distance Offshore (m)


MEASURED *-- PREDICTED


Figure 5.8: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 9, Manatee County, Florida.


E
E 0


E
0
L5

0










E
0

z
c
0

w
t-

















Manatee R-18


200 400 600 800 1000 1200 1400 16
y, Distance Offshore (m)


200 400 600 800 1000
y, Distance Offshore (m)


- MEASURED ---- PREDICTED


Figure 5.9:


Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 18, Manatee County, Florida.


.5 ........... ...............................................................................................................

0.7
0.7. ........... ...............................................................................................................

0 6.6 .. .. ............................................................................................................
0.6

0.5 ...........

0.4........... ...................

0.3-










68





Manatee R-27


26 ......... ..........................................................................................................

24

22 ...........................

191. .......... ..........................................................................................................


0.16 ......

0.14-
-200


0 200 400 600 800 1000 1200 1400 1600 1800
y, Distance Offshore (m)


200 400 600 800 1000 1200 140
y, Distance Offshore (m)


- MEASURED *.... PREDICTED


Figure 5.10: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 27, Manatee County, Florida.









69




Manatee R-36


400 600 800 1000 1200 1400 1600
y, Distance Offshore (m)


400 600 800 1000
y, Distance Offshore (m)


- MEASURED ----- PREDICTED


Figure 5.11: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 36, Manatee County, Florida.











70






Manatee R-45
(ATM, 1991)


E
0
E
0













E


z
C
0
Q-

Z,


100 200 300 400 500 600 700
y, Distance Offshore (m)


U_





6-
31
41i




7
7-a..


0 100


200 300 400 500 600
Distance Offshore (m)


700 800


-- MEASURED "... PREDICTED


Figure 5.12: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 45, Manatee County, Florida.









71





Manatee R-51
(ATM,1991)
0.222

0.22







0.212-.... ...............

0.21
0 20 40 60 80 100 120 140 160 180 200
y, Distance Offshore (m)


y, Distance Offshore (m)


-- MEASURED ----- PREDICTED


Figure 5.13: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 51, Manatee County, Florida.


















Manatee R-60
(ATM, 1991)


...........................................................................................................................


50 100 150 200 250
y, Distance Offshore (m)


100 150 200 25(
y, Distance Offshore (m)


- MEASURED *... PREDICTED


Figure 5.14: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 60, Manatee County, Florida.


1.1
1i


0.
0.
0.
0.
0.
0.
0.
0.


9
8
. ... .... .............................................. ...



6 ............ ...................................................................................................
5 ...................... .................................................................................................
7





3


0

















Manatee R-66
(ATM, 1991)


E
E 0

E
(3
0
E













0
z
0
0
er,
UJ


y, Distance Offshore (m)


y, Distance Offshore (m)


- MEASURED *-.. PREDICTED


Figure 5.15: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 66, Manatee County, Florida.

















Sarasota R-3
(ATM, 1991)


E
E 0


0
E

0













z


01


y, Distance Offshore (m)


y, Distance Offshore (m)


-- MEASURED -*. PREDICTED


Figure 5.16: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 3, Sarasota County, Florida.




















Sarasota R-12
(ATM, 1991)
1*
9-
9 ............... ...... ................... .
8....... ............... ....................... ... ..... .....................................

7. ................... ................................................................................................

6 ............................. ....... .................................................................................
5. .................................. .............................................................................
4 ........................................ ....................... .........................................

3- \ ..... ..........-...........................................

2 ......................................................... ............................................................
81
7"

6"


4"
3"

2
1


E
> -2-

z
.-3
r-
.0
0 -4-

Uj
a)
wJ


50 100 150 200 250
y, Distance Offshore (m)


100 150 200 250
y, Distance Offshore (m)


300 350


- MEASURED -.... PREDICTED


Figure 5.17: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 12, Sarasota County, Florida.


mA



















Sarasota R-21
(ATM, 1991)


0.18-

0.17>

E 0.16-
E
S 0.15-

.A 0.14-
Q
0.13-

0.12-
(





0

-1
E
> -2
0
z
-3
0
4-
o
(3 -4
ci)
w. _d:;


50 100 150 200 250 300 350 400 450 500
y, Distance Offshore (m)


) 100 150 200 250 300 350 400 450
y, Distance Offshore (m)



MEASURED "... PREDICTED


Figure 5.18: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 21, Sarasota County, Florida.






















Sarasota R-27

(ATM, 1991)
n O'>1 -


0.21

0.2-


U.1
0.1
r 4


aU
8-
7.


W. I
0.16-
0.15-

0.14-

0.13-

0.12
(


100 200 300 400 500
y, Distance Offshore (m)


y, Distance Offshore (m)


-- MEASURED ..... PREDICTED


Figure 5.19: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 27, Sarasota County, Florida.


... ...................................................................................................................

....... ...............................................................................................................

............ ...........................................................................................................
................ .......................................................................................................
.................... ..................................................................................................

......................... .............................................................................................
............................. .........................................................................................

................................
.....................................................................


I






















0.7
0.7-


78





Sarasota R-36
0.9 T ..............
n o .................. ..... T ...............................................................................................


. ................. .... ... ...........................................................................................


0.4

0.3

0.2


0 200 400 600 800
y, Distance Offshore (m)


1000 1200


y, Distance Offshore (m)


- MEASURED ---- PREDICTED


Figure 5.20: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 36, Sarasota County, Florida.


.......


E
E

0
Cu
0










79





Sarasota R-54


.-..Z....... --.. ....
................................................I ........


0 200 400 600 800 1000 1200
y, Distance Offshore (m)


400 600 800 1000
y, Distance Offshore (m)


- MEASURED -.... PREDICTED


Figure 5.21: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 54, Sarasota County, Florida.


0.22-

0.2-

0.18-

0.16-


................................................................. 4 ......................


.-200
-200


1400 1600


...... *. .......


\I\


Vi\ n









80




Sarasota R-72


200 400 600 800 1000 1200 1-
y, Distance Offshore (m)


0 200 400 600 800 1000
y, Distance Offshore (m)


MEASURED ....- PREDICTED


Figure 5.22a: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 72, Sarasota County, Florida.









81




Sarasota R-72


200 400 600 800 1000 1200 1
y, Distance Offshore (m)


0 400 600 800 1000
y, Distance Offshore (m)


- MEASURED ----- PREDICTED


Figure 5.22b:


Measured profile, blindfolded prediction, and cross-shore median grain
size distribution with -8 m sample removed, Range 72, Sarasota County,
Florida.











82





Sarasota R-90
7

6


2 ...... ...... ....... ..... ................ ..... .. ... ...................... ......
2 --------------.-----


0 200 400 600 800
y, Distance Offshore (m)


200 400 600 800
y, Distance Offshore (m)


1000 1200


- MEASURED *... PREDICTED


Figure 5.23: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 90, Sarasota County, Florida.











83






Sarasota R-99


- u
E
E

0
E
S0


0










E


z
C
.2


LUJ


y, Distance Offshore (m)


200 400 600 800
y, Distance Offshore (m)


-- MEASURED **.. PREDICTED


Figure 5.24: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 99, Sarasota County, Florida.

















Sarasota R-108
1.6

1.4 ......................

1.2

1


0.8-




04----------- -- *--i ----- i ---
0.2-

0
-200 0 200 400 600 800 1000 1200
y, Distance Offshore (m)


200 400 600 80(
y, Distance Offshore (m)


- MEASURED -.. PREDICTED


Figure 5.25: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 108, Sarasota County, Florida.










85





Sarasota R-171


o.- .................. .. ..................................................................................................



0 .6 ............... ... ............................. ........ ....... ......................
1.2
0.8





0.2

0


0 200 400 600
y, Distance Offshore (m)


1000


y, Distance Offshore (m)


- MEASURED ..... PREDICTED


Figure 5.26: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 171, Sarasota County, Florida.




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