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Field evaluation of equilibrium beach profile concepts southwest Florida

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Field evaluation of equilibrium beach profile concepts southwest Florida
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UFLCOEL-94015
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Jones, Victoria Lly
University of Florida -- Coastal and Oceanographic Engineering Dept
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English
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xiv, 182 leaves : ill. ; 29 cm.

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Coastal and Oceanographic Engineering thesis, M.S ( lcsh )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (M.S.)--University of Florida, 1994.
Bibliography:
Includes bibliographical references (leaves 177-181).
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Typescript.
General Note:
Vita.
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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.
Statement of Responsibility:
Victoria Lly Jones.

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University of Florida
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UFL/COEL-94/015

FIELD EVALUATION OF EQUILIBRIUM BEACH PROFILE CONCEPT: SOUTHWEST FLORIDA by
Victoria Lly Jones Thesis

1994




I

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




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. Ernie 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
ABSTRA CT .......................................... xiii
C HAPTERS
1 INTRODUCTION ................................ 1
2 REVIEW OF LITERATURE .......................... 13
3 STUDY AREA .................................. 29
3.1 Pinellas County ............................ 29
3.2 M anatee 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 ............. 49
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 ........................
3IOGRAPI-CAL SKETCH .................

124 145 148 154 159 171 182




LIST OF TABLES

Table Pge
1.1 Summary of Recommended A Values (from Dean [19941)
(Units of A Parameter are in rn"')............................ 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 (19871, modified from Moore [1982], from Dean et al.
[1993]) . . . . . . . . . . . . . . . . . . . . . 5
1.3 Comparison of Equilibrium Beach Profiles With and Without Gravitational Effects Included. A = 0. 1 in"' Corresponding to a Sand Size of 0.2 min ... 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




:112UreP

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 meia grain .. median grain meia grain .. median grain meia grain .. median grain meia grain .. median grain meia grain .. median grain meia grain .. median grain
median grain

Page




ia=

Page

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. 2 1: 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 in 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




Fiore

Rue

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




Figre P

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 County, Florida .......................................... 114
5.55: Measured profile, blindfolded prediction, and best-fit profiles, Range R-1,
Charlotte County, Florida. Best fit parameters: Blindfolded: RMS err.=e=0.45m; Average: A=0.16mI/3, g=0.98m; Constant: A=0.12mI13, s=0.37m; Exponential: Ao=0.09, A1=0.11, k=0.012, e=0.35m; Polynomial: Bo=0.006m, B1=0.019, B2=1.35E-5mt,
e=0.29m ........................................... 115

Page




Figure

Page

5.56: Measured profile, blindfolded prediction, and best-fit profiles, Range R135, 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, At=0.075, k=0.011, e=0.17m; Polynomial: Bo=0.004m, BI=0.018, B2=5.63E-5m',
e= 0.11m 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=0.14m3, e= 1.04m; Constant: A=0.1lm "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 sedimient 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 xii




examine the existing relationships between the sediment scale parameter, A, and sediment diameter, D, and/or sediment fall velocity, w, for varying cross-shore sediment attributes. Comparison is made to both the measured and blindfolded (predicted) profiles for several locations. Further evaluation of these relationships includes averages of both measured and predicted profiles for several successive sites in an effort to determine 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 significantly 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 variation 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 interpretation 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 [19911): (1) they tend to be concave upwards, (2) the slope of the beach face is approximately 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 bo om 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) =Ay213
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 sediment 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. WJ relationship, where wi 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. relationship to be well-represented by
A=0.067(01.44 (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 volume of water throughout the surf zone from linear wave theory as follows (Dean and Dalrymple [1984, 1993]).




SEDIMENT FALL VELOCITY, w (cm/s)

21.0-.
rc
Ic cc: < 0.10 a.
C)
/)
o0.1
cc 0.01
IL

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 Y-ECg (1.4)
where E is the sum of the potential and kinetic energy contained within the wave and Cg represents the group velocity of the wave, or the speed at which the energy is transported shoreward. Based on linear, shallow water wave theory (Dean and Dalrymple [1984]) and substituting
C=(1.5)
and
E= 8H2 (1.6)
into equation (1.4), where -y is the specific weight of sea water, H is the wave height, It is the water depth, and g is the gravitational constant, the expression for energy flux becomes
jr=. y V-g~i(1.7)
8
If the wave height is assumed proportional to the water depth throughout the surf zone, i.e.




H=ich (1.8)
where x is a dimensionless breaking wave parameter = 0.8 (McGowan [1891]), the expression for energy flux is now
_=_ h/ (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 ay" -hm (1.10)
ayl
in which y' is the shore normal coordinate directed onshore. Equation (1.10) states that any change in -9-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 profile 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) a pgK2h 2v/5)
ay
The dissipation per unit volume is found by taking the derivative and simplifying equation (1.11) as




D.=..!pg/2 K2h1/2 ah (1.2)
16 ay
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
I24Db 2/3
h(y) =( --g |2/3 y2/3=Ay2/3 (1.13)
5 p g,!- :,2
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 -h+ 1 a (ECg)=D. (1.14)
mf a3y hay
in which the first term on the left-hand side represents destabilizing forces due to gravity, 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 accuracy, 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 m3. To covert A values to feet units, multiply by 1.5.

D(mm) I .01 0.02 0.03 0.04 0.05 10.6 0.07 .08 0.091
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 0.115 0.117 0.119 0.121 0.123
0.3 0.325 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 0.3546 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 0.379 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 0.2316 0.23.24 0.2132 0.2140 0.2148 0.2156 0.2164 0.2372




10
In equation (1. 14), m is the beach face slope and D. still represents the stability characteristics of the sediment but is now 'expanded' to include gravity as an additional destabilizing force.
Further, Larson [1988] and Larson and Kraus*[1989] have shown that use of the more realistic wave breaking model of Daily et al. [1985], along with the use of a specified uniform wave energy dissipation per unit water volume, results in an equilibrium profile of the form
Y12h h3"2
-=+- (1.15)
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=Ay2l3 (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 (n

2 LU

Figure 1. 3:

Comparison of Equilibrium Beach Profiles With and Without Gravitational Effects Included. A = 0.1 rn"' 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 [19801, Kriebel [1982] (see also Kriebel and Dean [1985] and Kriebel [1986]), Seymour and King [19821, Dally and Dean (1984], and Larson and Kraus [1989]) have been proposed due to the difficulty and uncertainty of describing nearshore flows, and are stiff 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) win 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 'bestfit' 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 equilibrium 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=Ay13, 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 proriles.
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
Recto r [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 material 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."
Edelmnan [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 "sufficient" duration, the upper par of the profile would attain an equilibrium shape and that .1he 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, Veulinga [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/oaT for bar formation and, based on laboratory data, established that bars would occur for H/oaT > 0.85. Because most previous studies had related bar occurrence to wave steepness, this relationship was also expressed in terms of the wave steepness (H/L) and the ratio of sediinent fall velocity to the wave period and to gravitational acceleration (ow/Tg). Kriebel et al. [1986] later examined only large scale wave tank data and showed that the critical value of H/T 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 experiments 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 includes investigations by Iwagaki and Noda [1962], Nayak [1970], Noda [1972], Collins and Chestnutt [1975], Dalrymple and Thompson [1976] and Hughes [1983]. Paul et al.

i




16
[1972] indicated that exact similarity between a prototype sand beach and its corresponding light-weight sediment model is impossible to attain. They concluded that a generalized 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 porosity, 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 sediments 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 laboratory 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 =Ay1 to the data. Dean found a central value of n=2/3 as Bruun had earlier.
This equilibrium profile model first presented by Bruun [1954] and later characterized 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.
Sey mour and King [1982] used profiles measured during the 1978 Nearshore Sediment Transport Study (NSTS) at Torrey Pines, CA, in an effort to predict the crossshore transport of sand. Eight models, from previous investigators, included the categories 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 profiles) 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 predicted. Several of the beach profiles displayed essentially no change.
Daily 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 favorably 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 investigators 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. Observations 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 morphology 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/1wT. 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 differences 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 offshore 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 equilibrium profile was used to describe the representative profile at three different beaches with varying grain size along the profiles. The classical equilibrium shape of Bmuun [1954] and Dean [1977] was used for comparison. All of the theoretical profile equations 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 Bniun 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 increased, 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=Ayn 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 monochromatic 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 investigators 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 geometrical 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 recommended 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 relationships.




23
Daily [1991] studied the effects of long waves on cross-shore transport in laboratory tests using random waves in short (5 min.) and long (30 min.) bursts and corresponding 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. Daily 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 longwave 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 erosion potential in response to water level rise, and also presented a new method for incorporating 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 characteristics 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/coT, 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: inclusion 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 in 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.
Naim 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
zation, and lateral spatial schemnatization of the processes included) was considered sufficient to provide relatively accurate predictions of alongshore transport and profile change for "short to medium scale" (<1I year) problems.
Dean et al. [1993] extended previous methodology for calculating equilibrium beach profiles of uniform sand size to include arbitrary distribution of sediment characteristics 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 N',ew Zealand. The "blindfolded" tests showed that although individual measured vs. predicted profiles did not show consistently good agreement, the averages of the measured profiles were in good agreement particularly close to shore ( <5 in). They concluded 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 interactions vary greatly. As a result, the use of sediment texture to define or identify environments 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 currents move from place to place in the nearshore zone as a result of water level fluctuation.
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 laminations 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 characteristics 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 10ft 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 projects 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 during the winter months (Doyle et al. [1984]). Data from the U.S. Army Corps of Engineers', 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 periods (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

Honeymoon Is.
' Honeymoon Is

GULF OF MEXICO Sand Key

R-90 R--110
Indian Rocks

R- 1 1)

GULF OF MEXICO

R-170 F-180
Mullet Key Mullet Key

0 a 3 MIS
- I-_ IM

Figure 3.1: Pinellas County

[1L I I AI

LJ




31
extensively developed. Most of the beaches in this county are considered critical erosion areas (Clark [1992]); and, several areas Honeymoon Island, Redington Shores Redington 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 Longboat Key varies from about 915 m at the north end to approximately 240 m in the middle of the Manatee County portion.
The beach sediments are probably derived from the offshore and nearshore bottom of the Gulf, and from the island itself (Doyle et al. [1984]). Currents are predomi-




Tampa Bay

Anna Maria Key

GULF
OF
MEXICO

Figure 3.2: Manatee County

MANATEE

3 4
-6 Mli [S

0 1 2
!,CALE




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 A [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, revetments 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 "ido 1 -.10
P 20 Lido Siesta Key
Key Big
R-1 Longboat Sarasota Midni
Key Pass Pass
GULF

SARA' 1A

i I P- 180
80 R 100 R 120 R 1-10 R 160
Casey Key Venice Manasota Peninsula
ght Inlel
OF MEXICO ,,,
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 fime 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 Gasparifla Island. Of these 22 km of shoreline, only portions of south Manasota Key and north Gasparilla Island are accessible 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




CHARLO1 TE

Sarasota County
R-1 Peace River
Manasota
Key R-o10
R 20
Knight R Charlotte
Is. Bocilla Harbor
Is. Pedro R-40' Is.
Little R 50. Gasparillals R-60)I
GULF Is. Gasparilla
OF IS. Lee County
0 1 2 3 MEXICO I J.I.."L
SCALE

Figure 3.4: Charlotte County




37
[1972, 1974a]) although many property owners have placed numerous groins, revetments, 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 shoreline 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 engineering 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 L I Island

R-I1
R-20

R-40 Cayo Costa
Island

GULF

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

'Estero R- 160 Island

I -- 1I )

Sanibel Island

MEXICO

R 240 Lovers
Key
. C ALL"

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 northem 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]).




K
0
N 120 0
N 1UU
Keewaydin Island Keewaydin Island

X x a
) 3
In1
k 160 R 1-10 60
Marco Island

GULF OF MEXICO
Figure 3.6: Collier County

R-1

f IS
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. 11974
Manatee Aug.-Sept. /1986
Sarasota Apr.-Aug. /1987
ChrOtte December /1982
Lee June-Oct. /1982
Collier March /1988
Only "long"t 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 thousand 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 mn, -2 m, -4 m, -6 mn, 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. Locations 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 mn and -2 mn 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 sufficiently 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




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
L 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 collection 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 considered negligible though no analysis was conducted to quantify the percentage of this material. Most samples consisted of quartz sand and shell fragments, with the percentage of shell increasing between the berm and -1 mn 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 ait 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 remaining samples are presented by county in Appendix E.




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 1. .1

Standard Sieve No.

Opening (in mm)

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

2.000 1.410 1.000 0.710 0.500
0.350 0.250 0.170 0.125 0.088 0.0625




Table 4.5: Sediment Sample Analysis: Charlotte County
Sample Total D50 Dmean S.I. Elevation Distance
(g) (mm) (mm) (m) (m)
R01DUJNE.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
RO9DUNE.CHA 74.700 0.195 0.198 0.409 3.50 -80.00
RO9BERM.CHA 30.190 0.330 0.330 0.573 1.00 -20.00
RO9WL.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, anomalies or "jumps" in the sediment distributions were noted and may be attributed as possible 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 representative 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 crossshore 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. [11993]):
h1/2dh-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




d12 h .112 (4 .2 )
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 continuous (and hence A is piece-wise continuous) between two points along the profile, y, and n+p. In this case it was shown that h can be represented by y= h-hn h3/2-h/2 (4.3)
m An2
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 transformed 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/.1 =h( ) 1+ i (4.4)
h(Yi+I) =h2 X3m+ /2 (Yi +I -Yi)
where
N sA Andh-An (4 5)
= -yn +1 yn)\ 2 Y)
Note that in this case y,, < y, and y,,+, < 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, mn, were obtained from Balsiffie 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 L-arson [ 199 1] found profiles more accurately described "; Work and Dean [ 199 1] 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 diescribed, 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 constant A fit, (2) an exponential fit, and (3) a polynomial fit. For these schemes, a functional 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:
hp (y) =Ayfi3 (4.6)
where y, is some measured distance offshore and h(y) represents the predicted depth at location y,. Further, if hJy.) is used to represent the measured depth at y,, then the mean square error between the measured and predicted depths is given by 2= 1l (i ]2
--! [hp (j) -h,( (4.7)
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 aCl2. 2N ahP (Y (4.8)
a [hp (Yi h(Yi)] aA 0
A 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) =A1+ (AO-A,) 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,, A1, 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+Bly+B2y 2 .. +B. n (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, 5.3 1, and 5.32) which cannot be represented




55
1:y 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 [19911).
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 goodness-of-fit is present. Cross-shore variations in median grain size range from approximately 0.01 mmn 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-offit 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 continuity) 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 corresponding 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/rn + 3/2(h121A3/2)]dlzldy = 1). ThS 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 conducted using profile averages. This comparison was -employed to determine whether the IEBP 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 overpredicted 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 Figtire 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 measurements 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 seaward 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, although the presence of the bar/trough system represents difficulty for analysis. Nevertheless, 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 previously. 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 inspection, 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 .......................................................................................................................
0.2 . .......................................................................................................................
0.15 ...... ..................................................................................................................

100 200 300 400 500 600 700 800
y, Distance Offshore (m) MEASURED ..... PREDICTED

6 160 2 60 300 46o 560 60'0 700 800 900
y, Distance Offshore (m)
. ....... ............................... ............................................................................

0.1
E
d
>
0
-2
0
M
4
LLI

E
E

Figure 5. 1: Measured profile, blindfolded prediction, and cross-shore median grain
size distribution, Range 21, Pinellas County, Florida.




60
Pinellas R-33

0 100 200 300 400 500 600 700 86o 90o 1
y, Distance Offshore (mn)

200 300 400 500 600 700 y, Distance Offshore (in)

I- 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
.2 ...... .. .... .. ... .... ........ ... .. ....... ... .. ... ..... ... ..
9 .. .... ... .. .. .. .. ......... ........ .. .. ..... .. .. ... ..... .
is ...... .... .. .. ..........................................
7 1 ... .. .... .. .. .. ... ......... ........... ...... ......... ...
6 ..... .. .. .... .. ... ....... ..... ... .... ...... .... ........... .

0.15-'~

-200 -100 0

100 200 300 400 500 600 700 860 9o y, Distance Offshore (in)

3 0 100 200 300 400 500 600 700 800 900
y, Distance Offshore (in)
-MEASURED ---IPREDICTED

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

A:
..................... ................. .................................................................................
..................... ................... .........................................................................




62
Pinellas R-57

E
-U,
E E 0
E
0
0
z
C_.
(U
IDo
o

-10o 0 16o 200 360 400 500 600 760 80 900 iV
y, Distance Offshore (m)

100 260 360 400 560 600 760 860 90
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 (mn)

200 300 400 500 600 70 y, Distance Offshore (mn)

I- MEASURED ...PREDICTE

Figure 5.5:

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




64
Pinellas R-138
......... ............................................................................................................
........ ...........................................................................................................
........ .. ..........................................................................................................
. .........................................................................................................
.. ........................................................................................................
....... ... ... .......................................................................................................
.... ......................................................................................................
...........
........... k
.. ............ ............ ........
................. .... _--

U.4"
E
E 0.40.35
E 0.35 0.250.2
0.15
0.1
-1
2
1"
E 0.
0-1"
(D -2z
.2 -4
> -5.
-a)
_7-

30 0

160 260 300 460 500 660 760 86o 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
Pineilas R-1 59

75
0.17 .................. ... ........................................... I ...........................................
0.165 .................. ...... .......................................................................................
0.16 ............ ........ ......................................................................................
0.155 .................. ......... .....................................................................................
0.15 .................. .......... .....................................................................................
0.145 .................. t ........... ...................................................................................
01
n id .................... .......... ...............................................................................

I MEASURED ..... PREDICTED I

00

0.1350.13
_2

............
.................. 7 .......................................... .................................................

20;0 400 600
y, Distance Offshore (m)

1000

y, Distance Offshore (m)

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




66
Manatee R-9

200 400 600 800 1000 1200 1400 1V
y, Distance Offshore (m)

6 260 460 660 860 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.

0
0
E 0
z
C
as 0
a) 0U




Manatee R-1 8

200 40o 60 0 800 10 1 0 1261 0 14 100 16
y, Distance Offshore (in)

200 400 600 800 1000
y, Distance Offshore (in)

I- MEASURED ...PHREIE

Figure 5.9:

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

0 7 1 ...............................................................
0 67 ...... .......................................................
0 4 1....... ........................................................
0 3 1......................................................




68
Manatee R-27

2 6 j...... ......................................................
2 4 ...... ................................... ................. ..
22 ...... ........................................................

0.161...
0.14
.200

0 260 460 660 800 10'00 12'00 1400 1600 1800
y, Distance Offshore (in)

200 400 600 800 1000 1200 140
y, Distance Offshore (mn)
- MEASURED ...PREICTED

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 (in)

400 600 800 1000 y, Distance Offshore (in)

I- MEASURED --- PHREITE

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 o
E
0
0 0
E
z
C
w

100 200 300 400 500 600 700
y, Distance Offshore (m)

2-i
31S

0 100

200 300 400 500 600 (00
Distance Offshore (m)

I- MEASURED .... PREDICTED I

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
0.21....................... ..................
0 20 40 60 80 100 120 140 160 180 200
y, Distance Offshore (in)

y, Distance Offshore (mn)

I- MEASURED ---PR EDITED_

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




Manatee R-60
(ATM, 1991)
I. ..........................................................................................................................

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

0.
0.
0.
0.
0.
0.
0.
0.

9
8"
.7 .................................................................................
.6... ...............................................................................
75 ...................................................................................
...................................
3....... ................................................................
n

0




Manatee R-66
(ATM, 1991)

E E,0
0
E
0
z
a 0 0
w

y, Distance Offshore (in)

y, Distance Offshore (in)

I- 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)

E0)
0
z
0
w

y, Distance Offshore (in)

y, Distance Offshore (mn)

I- MEASURED PREDICTED

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




Sarasota R-1 2
(ATM, 1991)
V
9. ..... ... ..... ....................... .
.8..................................................................................
7....................................................................................
6....................................................................................
.5..................................................................................
4....................................................................................
3-\........ _*__.-_*...........................................
2....................................................................................
... .. .

E
0
U 4

50 100 150 200 20
y, Distance Offshore (in)

100 150 200 250 y, Distance Offshore (in)

300 30

I- MEASURED ...*PREDICTEDI

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




Sarasota R-21
(ATM, 1991)

0.18
0.17) 0.16
E
.d 0.15E
.A 0.140.13
0.12
0
E
> -2
z
- -3
0 4
-4
Li
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 131 3-

0.21 0.2-

U.1
0.1 r%4

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.

... ...................................................................................................................
....... ...............................................................................................................
............ ...........................................................................................................
................ .......................................................................................................
.................... ..................................................................................................
......................... .............................................................................................
............................. .........................................................................................
................................
.....................................................................

_L




0.7-

E
0

Sarasota R-36
............T ......................................................

0 .U b ........ .. .. ................................................
0 45 ........... .. ...............................................
0 34 ..........:. .... ...........................................
0 23 ...... ... .............................................
0 .2 ............ ........ ............................................... ..................

0 200 400 600 800
y, Distance Offshore (mn)

1000 12 00

y, Distance Offshore (in)

-7 ME ASURED ---PREDICTED

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

..A...... .. ................................ . ...............




79
Sarasota R-54

.
-. 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

1400 1600

.... - *. ....




6 200 400 600 800 1000
y, Distance Offshore (m)
MEASURED ..... PREDICTED

80
Sarasota R-72

200 400 600 800 1000 1200 1y, Distance Offshore (m)

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 (mn)

0 400 600 800 1000 y, Distance Offshore (in)

I- MEASURED ...PR EIE

Figure 5.22b:

Measured profile, blindfolded prediction, and cross-shore median grain size distribution with -8 mi sample removed, Range 72, Sarasota County, Florida.




82
Sarasota R-90
7
6 ................. ..........................................................................................................
. ................. ........... ...........

................. ...... I ................................................................................................

I MEASURED ..... PR

0 200 400 600 860
y, Distance Offshore (m)

1000 1200

200 400 600 800
y, Distance Offshore (m)

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




83
Sarasota R-99

4-U
E
E
0
z
C
.o
U 0
wL

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-1 08
1.6
.1.4........... 1-1........ 1111*11*11.............. "---,..............
12 ........
0 .1 ........ .. ................................................
-200 0 200 400 66o 800 1000 1200o
y, Distance Offshore (in)

200 400 600 8OC
y, Distance Offshore (in)

I- MEASURED .. CREDITED

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




1.2 ................... ......................................................................................................
. .................. .. ...................................................................................................
0.8 .................. ...... .................................................................................................
0.6 ................ ....... .................................. ........ ..............................................
0.4 ............... ... .......... ........................... ........................................... ...............
0.2 .................... ............ .................... ............. .....................................................
0 i

MEASURED ..... PREZTE

85
Sarasota R-1 71

0 200 460 660
y, Distance Offshore (m)

1000

y, Distance Offshore (m)

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