Citation
Application of equilibrium beach profile concepts to Florida's east coast

Material Information

Title:
Application of equilibrium beach profile concepts to Florida's east coast
Series Title:
UFLCOEL-94016
Creator:
Charles, Lynda L., 1962-
Florida Sea Grant College
University of Florida -- Coastal and Oceanographic Engineering Dept
Place of Publication:
Gainesville Fla
Publisher:
Coastal & Oceanographic Engineering Dept., University of Florida
Publication Date:
Language:
English
Physical Description:
xii, 103 p. : ill., map ; 28 cm.

Subjects

Subjects / Keywords:
Coast changes -- Mathematical models -- Florida ( lcsh )
Beach erosion -- Mathematical models -- Florida ( lcsh )
Beach nourishment -- Mathematical models -- Florida ( lcsh )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF ( lcsh )
Coastal and Oceanographic Engineering thesis, M.S ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (M.S.)--University of Florida, 1994.
Bibliography:
Includes bibliographical references (p. 100-102).
Funding:
Funded by Florida Sea Grant.
Statement of Responsibility:
by Lynda L. Charles.

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Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
34548766 ( OCLC )

Full Text
UFL/COEL-94/016

APPLICATION OF EQUILIBRIUM BEACH PROFILE CONCEPTS TO FLORIDA'S EAST COAST by
Lynda L. Charles Thesis

1994




APPLICATION OF EQUILIBRIUM BEACH PROFILE CONCEPTS
TO FLORIDA'S EAST COAST
By
LYNDA L. CHARLES
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




ACKNOWLEDGEMENTS

First and foremost, I wish to express a great deal of thanks to my advisor and.supervisory committee chairman, Dr. Robert G. Dean, who provided much more than support and guidance. Thanks also go to Florida Sea Grant for providing the financial support which made this project possible and to the Department of Coastal and Oceanographic Engineering for providing matching funds. I would also like to thank Dr. Daniel M. Hanes and Dr. Robert J. Thieke for their participation as supervisory committee members.
The contribution of many people made the completion of this project possible. I am especially indebted to those who at various times allowed me to drag them up and down the state in quest of the ultimate data set. They include Rajesh Srinivas, Emre OtayPaul Work, Mark Pirello, Victoria Jones, Chris Jette, David St. John, Suna Birsen, Mark and Scott who participated in the onshore work and Mark Sutherland, Vic Adams, Don Mueller, Lee Townsend, and Jon Grant for the offshore work.
Another group I must thank, are those who participated in the design, construction, calibration, and operation of the rapid sediment analyzer (RSA). They include Sidney Schofield; Chuck Broward, Vernon Sparkman, Danny Brown, Jim Joiner, and George Chappell.
Finally, I would like to thank Subarna Malakar for his assistance in the graphics reduction of the, at times, almost unmanageable data set. As well, I would like to express appreciation for the help of the office staff: Becky Hudson, Sandra Bivens, Lucy Hamm, Sonya Brooks, Ilen Twedell, and John Davis.




TABLE OF CONTENTS
Rne
ACKNOWLEDGEMENTS ........................................ ii
LIST OF TABLES .............................................. v
LIST OF FIGURES ............................................ vi
" STRACT ................................................. xi
CHAPTERS
1 INTRODUCTION .......................................... 1
1. 1 The Power Law Form of the Equation for an Equilibrium Beach Profile (EBP I 1.2 Scope of This Thesis .......................... -!--, ........ 4
2 BACKGROUND AND REVIEW ................................. 6
2.1 Curve fitting h =Ay' and h =Ay" for invariant A ........ S .......... 6
2.2 Varying A Along the Profile ............................ ....... 9
2.3 The Gravity Term ...................................... 12
2.4 Application Beyond the Surf Zone ............................. 13
2.5 Motivation for Different m Values ............................ 13
2.6 Fitting Two Curves to the Non-monotonic Beach Profile .............. 14
2.7 Time Varying A ....................................... 15
3 DATA COLLECTION AND STUDY AREA ......................... 21
3.1 Study Area ............................. .... 21
3.2 Field Data Collection: Beach Profiles and Sediment Samples ........... 12
3.3 Lab Methods for Sediment Size Analysis ....................... 25
4 PROCEDURES FOLLOWED IN DATA ANALYSIS .................... 2 8
5 RESULTS AND DISCUSSION .................... .............. 29
5. Sediment Size Data ............ : ........................ 29
5.2 Results from the "Blindfolded" Test on -Beach Profile Predictability
using Sediment Size Data ............................... 30
5.3 Comparison Between EBP Calculations Performed With and Without the
Gravity Term ....................................... 34




5.4 Results from the Curve Fit Analysis of h =Ay' and h =Ay' for Invariant A . 35 5.5 Motivation for Different m Values ............................ 37
5.6 Relationship Between A and Sediment Size ...................... 37
5.7 Application Beyond the Surf Zone and Dependence on Profile Depth ...... 38 5.8 Non-monotonic Beach Profiles .............................. 40
5.9 Time Varying Beach Profiles ............................... 40
CHAPTER 6 SUMMARY AND CONCLUSIONS ......................... 90
6.1 Sum m ary ............................................... 90
6.2 Conclusions ............................................. 91
APPENDIX DATA COLLECTION DATES FOR EACH PROFILE LOCATION ..... 92
REFERENCES .............................................. 100
BIOGRAPHICAL SKETCH ....................................... 103




LIST OF TABLES

Table pge
3-1 Data Summary by County ...................................... 23
3-2 Data Collection Dates for each Field Location Identified by the FDEP Range
Number -- Nassau County, Florida ............................... 24
5-1 Median diameter of sediment samples collected at depths of 0.0, 0.9, 1.8,
3.7, 5.5, 7.3, and 9.1 meters averaged over the entire east coast of Florida
and averaged for each of the 12 east-coast counties .................... 30
5-2 Root Mean Square (RMS) deviations of predicted equilibrium beach profiles
(EBP) from the measured beach profile for each measured profile extending out
to depths of 1.8, 3.7, 5.5, 7.3, and 9.1 meters; these individual RMS values
for each profile are averaged over the entire east coast of Florida and
averaged for each of the 12 east-coast counties; EBP predictions based on
calculations (1) without the gravity term and (2) with the gravity term ........ ..31
5-3 Root Mean Square (RMS) deviations of the average predicted equilibrium beach
profile (EBP) from the average measured beach profile extending out to depths
of 1.8, 3.7, 5.5, 7.3, and 9.1 meters; EBP predictions based on calculations
(1) without the gravity term and (2) with the gravity term ................. 33
5-4 Averages, for the entire east coast of Florida and county-by-county, of bestfit
A and m parameters from curve fit analysis of h =Ay" to measured beach profiles
out to depths of 1.8, 3.7, 5.5, 7.3, and 9.1 meters .................... 36
5-5 Averages, for the entire east coast of Florida and county-by-county, of bestfit
A parameter for m=213 from curve fit analysis of h=Ay' to measured beach
profiles out to depths of 1.8, 3.7, 5.5, 7.3, and 9.1 meters ...............36




LIST OF FIGURES

Figure e
1-1 Map of Florida showing the 12 coastal counties on the east coast shaded ....... 5
2-1 Moore's Curve: scale parameter, A, versus sediment diameter, D, and fall
velocity, w, in EBP relationship h =Ay/3 ........................... 17
2-2 Definition sketch showing Inman's compound curve fitting scheme where crosses
denote the origin for the bar-berm profile (dotted) and for the shorerise profile (dashed) ................................................. 18
2-3 Seasonal beach changes as observed with Inman's compound curve approach comparing
mean summer (solid) with mean winter (dotted) profiles ................ 18
2-4 Fitted A and m parameters for Inman's bar-berm profiles plotted against available
beach face sediment size ......................................19
2-5 Schematic illustrating the decomposition of Pruszak's time-varying A parameter in
h = Ay23 . ..... .. . . . .. . . . . .. . . . ..... . . . 20
2-6 Long term variation in A parameter for Pruszak's Baltic Sea data............20
2-7 Short term variation of A parameter for Pruszak's Black Sea data ........... 20
3-1 Median sediment diameter from sieve analysis versus sediment median diameter
calculated from settling velocities using Gibbs' equation, all in phi units,
solid straight line is bestfit line defining calibration equation also shown at
the top of the graph ......................................... 27
5-1 Variation in median sediment diameter, in millimeters, along the east coast of
Florida for all of the sediment samples analyzed ...................... 42
5-2 Variation in median sediment diameter, in millimeters, along the east coast of
Flbrida for all of the sediment samples collected at the waterline ............ 43
5-3 Variation in median sediment diameter, in millimeters, along the east coast of
Florida for all of the sediment samples collected at 0.9 meters depth ......... 44
5-4 Variation in median sediment diameter, in millimeters, along the east coast of




Florida for all of the sediment samples collected at 1.8 meters depth. .. .. .. ...45
5-5 Variation in median sediment diameter, in millimeters, along the east coast of
Florida for all of the sediment samples collected at 3.7 meters depth. .. .. .. ...46
5-6 Variation in median sediment diameter, in millimeters, along the east coast of
Florida for all of the sediment samples collected at 5.5 meters depth. .. .. .. ...47
5-7 Variation in median sediment diameter, in millimeters, along the east coast of
Florida for all of the sediment samples collected at 7.3 meters depth...........48
5-8 Variation in median sediment diameter, in millimeters, along the east coast of
Florida for all of the sediment samples collected at 9.1 meters depth...........49
5-9 Best performance of predicted profiles: (A) cross-shore variation in sediment
median diameter, in mm; and (B) measured beach profile (solid line),
calculated equilibrium beach profile: (1) without the gravity term (dotted),
and (2) with the gravity term (dashed) for Range number 27 in Duval County,
Florida.................................................. 50
5-10 Worst performance of predicted profiles: (A) cross-shore variation in sediment
median diameter, in mm; and (B) measured beach profile (solid line),
calculated equilibrium beach profile: (1) without the gravity term (dotted),
and (2) with the gravity termn (dashed) for Range number 1 in Broward
County, Florida............................................ 51
5-11 Longshore distribution of RMS values based on cumulative deviations of the
calculated equilibrium beach profile: (1) without the gravity term (solid)
and (2) with the gravity term (dotted) from the measured profile out to 1.8
meters depth .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ....52
5-12 Longshore distribution of RMS values based on cumulative deviations of the
calculated equilibrium beach profile: (1) without the gravity term (solid)
and (2) with the gravity term (dotted) from the measured profile out to 3.7
meters depth............................................. 5
5-13 Longshore distribution of RMS values based on cumulative deviations of the
calculated equilibrium beach profile: (1) without the gravity term (solid) and (2) with the gravity term (dotted) from the measured profile out to
5.5 meters depth........................................... 54
5-14 Longshore distribution of RMS values based on cumulative deviations of the
calculated equilibrium beach profile: (1) without the gravity term (solid)
and (2) with the gravity term (dotted) from the measured profile out to
7. meters depth............................................ 55
5-15 Longshore distribution of RMS values based- on cumulative deviations of the
calculated equilibrium beach profile: (1) without the gravity term (solid)
and (2) with the gravity term (dotted) from the measured profile out to
9.1 meters depth............................................ 56




5-16 Average measured profile (solid line), and average calculated equilibrium
beach profile: (1) without the gravity term (dotted) and (2) with the gravity
term (dashed) for the entire east coast of Florida . . . . . . . . . . . 57
5-17 Average measured profile (solid line), and average calculated equilibrium
beach profile: (1) without the gravity term (dotted) and (2) with the gravity
term (dashed), and maximum and minimum measured depths (thick solid line)
for Nassau County, Florida .................................... 58
5-18 Average measured profile (solid line), and average calculated equilibrium
beach profile: (1) without the gravity term (dotted) and (2) with the gravity
term (dashed), and maximum and minimum measured depths (thick solid line)
for Duval County, Florida ..................................... 59
5-19 Average measured profile (solid line), and average calculated equilibrium
beach profile: (1) without the gravity term (dotted) and (2) with the gravity
term (dashed), and maximum and minimum measured depths (thick solid line)
for St. Johns County, Florida .................................. 60
5-20 Average measured profile (solid line), and average calculated. equilibrium
beach profile: (1) without the gravity term (dotted) and (2) with the gravity
term (dashed), and maximum and minimum measured depths (thick solid line)
for Flagler County, Florida ................................... 61
5-21 Average measured profile (solid line), and average calculated equilibrium beach
profile: (1) without the gravity term (dotted) and (2) with the gravity term
(dashed), and maximum and minimum measured depths (thick solid line) for
Volusia County, Florida ..................................... 62
5-22 Average measured profile (solid line), and average calculated equilibrium
beach profile: (1) without the gravity term (dotted) and (2)7 with the gravity
term (dashed), and maximum and minimum measured depths (thick solid line)
for Brevard County, Florida .................................. 63
5-23 Average measured profile (solid line), and average calculated equilibrium
beach profile: (1) without the gravity term (dotted) and (2) with the gravity
term (dashed), and maximum and minimum measured depths (thick solid line)
for Indian River County, Florida ................................ (A
5-24 Average measured profile (solid line), and average calculated equilibrium
beach profile: (1) without the gravity term (dotted) and (2) with the gravity
term (dashed), and maximum and minimum measured depths (thick solid line)
for St. Lucie County, Florida ................................... 05
5-25 A*erage measured profile (solid line), and average calculated equilibrium
be ch profile: (1) without the gravity term (dotted) and (2) with the gravity
term (dashed), and maximum and minimum measured depths (thick solid line)
for M artin County, Florida ................................... 66
5-26 Average measured profile (solid line), and average calculated equilibrium




beach profile: (1) without the gravity term (dotted) and (2) with the gravity
term (dashed), and maximum and minimum measured depths (thick solid line)
for Palm Beach County, Florida ................................ .67
5-27 Average measured profile (solid line), and average calculated equilibrium
beach profile: (1) without the gravity term (dotted) and (2) with the gravity
term (dashed), and maximum and minimum measured depths (thick solid line)
for Broward County, Florida ................................... 68
5-28 Average measured profile (solid line), and average calculated equilibrium
beach profile: (1) without the gravity term (dotted) and (2) with the gravity
term (dashed), and maximum and minimum measured depths (thick solid line)
for Dade County, Florida ..................................... 69
5-29 Generalized representation of the relationship between the EBP calculation:
(1) without the gravity term (dotted), and (2) with the gravity term (dashed);
the gravity term alone is also shown (solid) ......................... 70
5-30 Longshore variation in bestfit A (solid line) and m (solid line with symbols)
parameters as well as A (dotted line) for m = 2/3 from curve fit analysis of h =Ay,
to measured beach profiles out to a depth of 1.8 meters ................. 71
5-31 Longshore variation in best fit A (solid line) and m (solid line with symbols)
parameters as well as A (dotted line) for m = 2/3 from curve fit analysis of h =Ay"
to measured beach profiles out to a depth of 3.7 meters ................. 72
5-32 Longshore variation in bestfit A (solid line) and m (solid line with symbols)
parameters as well as A (dotted line) for m =2/3 from curve fit analysis of h =Ay"
to measured beach profiles out to a depth of 5.5 meters ................... 73
5-33 Longshore variation in bestfit A (solid line) and m (solid line with symbols)
parameters as well as A (dotted line) for m =2/3 from curve fit analysis of h=A/
to measured beach profiles out to a depth of 7.3 meters ................. 74
5-34 Longshore variation in bestfit A (solid line) and m (solid line with symbols)
parameters as well as A (dotted line) for m = 2/3 from curve fit analysis of h =AY"
to measured beach profiles out to a depth of 9.1 meters ................. 75
5-35 Variation of A parameter with median sediment size. A parameter is bestfit
value to depths of 1.8,3.7, 5.5, 7.3, and 9.1 meters. Sediment size is average
of all samples which extend from the waterline to each of the designated depths 76
5-36 Scatter plot of average county A values out to 1.8 meters depth versus sediment
si.e averaged over all profiles in county and over all landward samples in each profile .................................................77
5-37 Scatter plot of average county A values out to 3.7 meters depth versus sediment
size averaged over all profiles in county and over all landward samples in each profile . .. .. .. . . . ... . . . .... . . . . .. ... . . . 78




5-38 Scatter plot of average county A values out to 5.5 meters depth versus sediment
size averaged over all profiles in county and over all landward samples in
each profile 79
5-39 Scatter plot of average county A values out to 7.3 meters depth versus sediment
size averaged over all profiles in county and over all landward samples in
each profile ............................................. 80
5-40 Scatter plot of average county A values out to 9.1 meters depth versus sediment
size averaged over all profiles in county and over all landward samples in
each profile ............................................. 81
5-41 Plots of average county A values out to 1.8 meters depth and sediment sizes
averaged out to that depth. County code denotes the county sequence
commencing from the north on Florida's east coast . . . . . . . . . . 82
5-42 Plots of average county A values out to 3.7 meters depth and sediment sizes
averaged out to that depth. County code denotes the county sequence
commencing from the north on Florida's east coast .................... 83
5-43 Plots of average county A values out to 5.5 meters depth and sediment sizes
averaged out to that depth. County code denotes the county sequence
commencing from the north on Florida's east coast .................... 84
5-44 Plots of average county A values out to 7.3 meters depth and sediment sizes
averaged out to that depth. County code denotes the county sequence
commencing from the north on Florida's east coast ..................... 85
5-45 Plots of average county A values out to 9. 1 meters depth and sediment sizes.
averaged out to that depth. County code denotes the county sequence
commencing from the north on Florida's east coast . ... . . . . . . . 86
5-46 Illustration of effect of a seaward displacement of the equilibrium profile,
possibly by an offshore reef . . . . . . . . . . . . . . . . . 87
5-47 Comparison of measured and predicted profiles for Range R-15 in Indian
River County. Note that the measured profile appears to be displaced seaward
by a distance of approximately 200 meters .......................... 88
5-48 Comparison of measured and predicted profiles for Range R-15 in St. Lucie
County. Note that the measured profile appears to be displaced seaward by
a distance of approximately 600 meters .......................... 89




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 APPLICATION OF
EQUILIBRIUM BEACH PROFILE CONCEPTS TO FLORIDA'S EAST COAST By
Lynda L. Charles
December 1994
Chairman: Dr. Robert G. Dean Major Department: Coastal and Oceanographic Engineering
This thesis aims to test and evaluate the latest modifications to Dean's' equlibrium beach profile concept and to evaluate Moore's empirical relationship between grain size and A. Toward this end the data set collected, analyzed, compiled, and examined in this report is considerably more extensive than those employed in previous works.
This report examines data from Florida's sandy east coast which is comprised of 12 counties and encompasses 531 kilometers of coastline. A total of 1834 sediment samples was collected for this study. Where possible, 9 surface-sediment samples were collected along each of 207 profiles at depths of 0.0, 0.9, 1.8, 3.7, 5.5, 7.3, and 9.1 meters as well as a dune and berm saniple. The spacing between these 207 profiles averages 2.7 kilometers. The profile locations extend from the St. Marys River on the Georgia-Florida border (Nassau County) to Government Cut in Miami (Dade County).




Results indicate that, on average, Dean's equilibrium beach profile equation of the form h=Ay', which is computed solely from sediment size information, adequately predicts the measured beach profile from the east coast of Florida out to a depth of approximately 4 meters. The depths of the computed profile between 4 and 9 meters depths, however, are under predicted by this method. As this methodology was based on Moore's empirical relationship between the A parameter and sediment size, no change was recommended for this relationship in the sand size range. Also, the results indicate a regional dependence in the relationship between sediment size and A.




CHAPTER 1
INTRODUCTION
1.1 The Power Law Form of the Equation for an Equilibrium Beach Profile (EBP)
Modelling of nearshore processes, and profile or shoreline response to these processes, generally requires some quantitative depiction of beach profile shape. Specifically, shoreline position and sand volume calculations for beach nourishment purposes have been found to be rather sensitive to the profile shape selected for these computations. Although various equations have been proposed, the most widely used in numerous aspects of coastal engineering research and project design is a power law form of the equation for an equilibrium beach profile (EBP) empirically developed and then theoretically motivated by Bruun (1954), Dean (1977), and Kaihatu (1990). This equation, in its simplest and most familiar form, is h=Aym(1 .1)
h =Ay '
where h is water depth at a seaward distance y from the shoreline, and m and A are coefficients related to wave climate and sediment stability characteristics', respectively. Both of these coefficients have been determined by empirical, as well as by various theoretical, means. The empirical method (Dean, 1977) involves application of least squares, to find the A and m values of the EBP which provide the best fit to the actual measured profile. The theoretical development which has been the most popular was proposed by Dean (1977) and is based on the consideration of uniform wave energy dissipation per unit water volume across the surf zone for a beach profile in equilibrium.
1. Sediment stability characteristics include grain size, density, shape, and surface texture, or fall velocity which is a measure which incorporates all of these properties.
1




2
In this particular development by Dean, the governing equation in terms of energy conservation is
__ hDq (1.2)
where, Deq, is the wave energy dissipation per unit water volume for the equilibrium case and the energy flux, F, is obtained from shallow water linear wave theory as F= pgi (1.3)
Assuming a spilling breaker characterized by wave height, H= rih, Dean (1977) obtained a value of 2/3 for m, so that (1.1) becomes h=Ay, (1.4)
and A is given by
[ 24 D j I(1.5)
A 5p g3/2K 2
where g is gravitational acceleration, p is the density of water, K is the breaking index2, and Dq can be expressed as
D eq= [ gPI9h (1.6
From (1.5) note that A is related to wave energy dissipation, D., which in turn is related to profile'slope as shown in (1.6).
Dean develops this concept further, introducing sediment size into these relationships by postulating that Deq represents the wave energy dissipation rate per unit water volume under

2. The breaking index is taken as a constant, usually 0.78 (see McCowan, 1891).




3
which a sediment particle of a certain size? is stable. The utility associated with this particular relationship is that it provides this equation with a predictive capability if grain size data are available. Later, using data compiled from the existing literature, Moore (1982) developed an empirical relationship between A and grain size, which allows profile shape to be determined simply by grain size, thereby avoiding the complexities of wave energy dissipation.
Originally, the relationship between grain-size and the A parameter allowed for only a single grain size for the entire profile. Most recently, however, attempts have been made to account for the natural cross-shore variation in sediment size along the profile (Work and Dean, 1991; Larson, 1991; Dean et al., 1993; Duncan, 1993).
In response to these recent modifications to the EBP concept, some studies have indicated a need to revise Moore's empirical relationship (Stockberger, 1989; Madalon, 1990; Kriebel et al., 1991). Others have contended that a relationship between the A parame~ter and grain size does not exist (Pilkey et al., 1993). Whatever the case, evaluating the relationship between the A parameter and grain-size is not a trivial task. This is primarily due to the fact that the data collection process necessary to evaluate such a relationship (including beach profile surveying, sediment sample collecting, and grain-size analysis) is extremely labor intensive.
Although published profile and sediment size data are available, they are rarely bolh available for the same location and time. When they do occur together, there is generally no standard method of representing sediment data, thus, making the compiled data sets difficult to compare and therefore unsuitable for testing, evaluating, and if necessary, revising Moore's empirical relationship.

3. Or other stability characteristic.




1.2 Scope of This Thesis
This thesis aims to test and evaluate the latest modifications to the EBP concept, and to evaluate Moore's empirical relationship between grain size and A. Toward this end the data set collected, analyzed, compiled, and examined in this report is considerably more extensive than those employed in previous works.
This report examines data from Florida's sandy east coast which is comprised of 12 counties and encompasses 531 kilometers of coastline, see Figure 1-1. The Florida Department of Natural Resources (DNR) maintains 1753 monuments in this area for which extensive profile data are available. At each of these monument locations, both long- and short-term shoreline change rates have been established by Grant (1992). Shoreline stability information is useful to any field study involving equilibrium beach concepts. In addition to the DNR survey data, which extends out to a depth of at least 10 meters, 155 profiles were surveyed to del~ths of approximately 4 meters specifically for this study to correspond with the sediment sampling efforts.
A total of 1834 sediment samples was collected for this study. Where possible, 9 surfacesediment samples were collected along each of 207 profiles at depths of 0.0, 0.9, 1.8, 3.7, 5.5, 7.3, and 9.1 meters as well as a dune and berm sample. The spacing between these 207 profiles averages 2.7 kilometers. The profile locations extend from the St. Marys River on the Georgia' Florida border (Nassau County) to Government Cut in Miami (Dade County). The particular DNR monuments studied in this thesis are presented by county in the Appendix along with tfie dates the profiles were surveyed and the dates each sediment sample was collected. DNR provides maps of all their monument locations for all 12 east-coast counties (Penquite et al., 1983). Sediment size analyses were performed using both the sieving and settling techniques.




St Johns S Flagler Volusia
---- Bard

~SLLucie
Pam Beach
Broward

Dade

Figure 1-1. Map of Florida showing the 12 coastal counties on the east coast shaded.




CHAPTER 2
BACKGROUND AND REVIEW
2. 1 Curve fitting h =AVf and h =A)!!! for invariant A The original empirical studies determined the m and A parameters which provided the best fit to the measured beach profile data. The earliest of these studies include a study by Bruun' (1954) and a study by Dean2 (1977). Bruun found that the best fit to the data was obtained with m = 2/3 for profiles extending out to at least a 30 foot depth, but that for profiles extending to depths greater than 40 or 50 feet, a better approximation of the data occurs if m =1/2. Dean obtained as an average value, m = 0. 66, for all of the 502 profiles he examined; his group averages, however, ranged from 0.52 to 0.82.
Currently, the most widely used value is m =2/3. Boone and Green (1988), however; proposed m = 0. 5 as a more appropriate choice for the typical carbonate beaches 6f the Caribbean as it provides a better fit to that particular data.
A straightforward least squares method can be applied to determine the m and A parameters which provide the best approximation to the measured data. Equation (1. 1) is first linearized by taking the log of each side of the equation logh = logA + m logy (2. 1).
and then substituting H = log h
C =logA
Y = log Y
1. Bruun (1954) examined 25 profiles from Mission Bay, CA, and 30 profiles from the Danish North Sea Coast.
2. Dean (1977) examined 502 profiles along the U.S. Atlantic and Gulf coasts from Long Island, NY, to Galveston, TX.




to obtain
H=C+mY
which is linear in H and Y. For (2.2) the normal equations are
N N
NC+m, (Y)=E (H,)
i=1 il
N N N
CE (Y)+m (Y2) i (YH) i=I i=l i=1

where

(2.2)

(2.3) (2.4)

N = number of data points

Solving (2.3) and (2.4) for C and m and replacing C with log A yields the following expressions forA and m

N N N N
H,E (Y,) (Yi) (YHi) A =exp l t=1 ii i=1
N N
NE ( Y ) E(Y)

N N N
NE (YHi)- (Y.i) (Hi)
i=1 i=1 i-1 2 NN
NF, (Y') (Y)
" I It I -

(2.5)

(2.6)




For the case with, m = 0. 67, the calculation simplifies and A becomes
N N
N
Following the above procedure for m = 0. 67, Moore (1982) compiled and analyzed data from the available literature. He located data from 38 profiles' with known sediment sizes ranging from 0. 1 to 300 millimeters. He plotted the resulting A value for each profile against its corresponding sediment size and drew a smooth curve through the data points. Moore's empirical relationship between A and sediment size is commonly referred to as Moore's curve which is presented as the solid line in Figure 2-1.
Moore's curve has been used extensively as it provides a predictive capability to the EBP calculation. Dean (1987) converted the grain-size values in Moore's curve to fall velocities and found the data could be well described by the log-linear relationship A=O.067w'0" (2.8)
where w is the fall velocity in centimeters per second and the dimensions of A are meters to the one-third power. This relationship is shown as the dashed line in Figure 2-1. Since sediment data are usually presented as grain size, Dean's relationship is not as commonly used as Moore's unless the data are converted to settling velocities.
3. Of the, 1 38 profiles Moore studied, 10 came from lab experiments and 28 from field investigations. The size data were given usually as a: median diameter but occasionally as a size range for each profile.
4. Even if sediment is analyzed using a settling tube or rapid sediment analyzer (RSA) which directly provides the distribution of sediment settling velocities, as a matter of convention, the data is almost always converted to size data which is representative of the data obtained directly from the standard sieving technique.




9
Thus, for a beach of known sediment size, the relationships presented in Figure 2.1 provide an A value which can then be used in equation (1.2) to calculate a predicted EBP. Then, if profile data are available, this calculated EBP can be compared to the actual measured profile. Interpretations of these comparisons involve discussions on the state of equilibrium (or disequilibriumn) of the actual profile and whether there may be an excess or deficit of sand in the profile (Dean et al., 1993). In the case of beach nourishment, this method is applied in volumetric calculations and is especially useful when the fill material has a grain-size distribution (GSD) which differs from that of the native beach which is to be filled. Also, in the case of modeling dynamic profile response to various nearshore conditions, this EBP concept has been found useful in providing either a target profile for which to aspire or a control profile with which to base comparisons.
At this point, the methodology thus explained allows only one vatiie of grain-size to represent the sediment characteristics for the entire profile. Usually the median diameter (D50) is used however the mean diameter has also been used as well as an equivalent value (either mean or median) of settling velocity. It is well known, however, that the GSD varies in the cross-shore direction along the profile on natural beaches. If grain-size data are available from several sample locations along the profile, an averaging technique (Hughes, 1978) may be used to obtain a single composite GSD for the entire profile from which the composite D50 may be obtained. This procedure, however, has not been widely used.
2.2 Varving A Along the Profile
Recently, there have been attempts to account for the variations in sediment characteristics which naturally occur along the profile by allowing A also to vary along the profile.




Referring to the original derivation by Dean (1977), the governing equation is d( PgK2h2fig) (2
dy =hDeq
Taking the derivative of (2.9) yields the common differential form of (1.2) as follows a h3/2 24 Deq A312 (2.
ay 5 pg 2g
Work and Dean (1991) examined a linear and exponential form for A given respectively as

A(y)=A0-+ ny

A(y) = Aoe -Y

-.9)

10)

(2.11)

(2.12)

By separately substituting (2.11) and (2.12) into (2.10) and integrating, respectively, the following EBP equations are obtained: h 3) -n [A~Or- (A.o-nYya] (2. 13

h(y) =A, [2A3]Ii e2

(2.14)

where n and k are the coefficients which provide the bestfit to the actual measured profile using an iterative scheme (Work and Dean, 1991). This technique is not predictive, however, unless n and k are known quantities.




11
The relationship between A and D50 (or w50) here again provides the method with predictive capability. With D50 (or w50) data from samples collected at various locations along the profile, A values along the profile can be determined using the relationships presented in Figure 2-1.
By considering A to be locally constant, say between y, < y < y,+,, we can integrate (2.10) to obtain
h3r2 = A3/2y + c (2.15)
for which the constant of integration can be found by using the condition that at y,, h =h,. This results in the final equation
h(y) =[h 3/2 +A 3(y_y.)12 (2.16)
where A, is the constant A value between yn and y,,+,.
This particular method, which allows A to vary with grain size, was introduced by Dean (1991) and is applied to data from Florida and the Caribbean by Work and Dean (1991) A modified version of this method was also used by Dean et al. (1993)6 and Duncan (19937) t6 examine data from New Zealand. Another modified approach, which also incorporates a varying sediment size along the profile, was introduced by Larson (1991) using the same data as Work and Dean (1991).
5. Work et al. (1991) examined data from four profiles in Florida (two from Escambia County on the westernmost Panhandle; one from Pinellas County on the peninsular Gulf coast; and one from Martin County on the Atlantic Coast) and two profiles in the Caribbean (one from Mullet Bay, Sint Maarten, and one from Baie Rouge, St. Martin).
6. Dean et al. (1993) examined 10 profiles from New Zealand.
7. Duncan (1993) studied one profile from New Zealand for which sediment data from 22 locations along the profile were available.




2.3 The Gravity Term
This most recent modification to the EBP concept, introduced by Dean et al. (1993), is basically the addition of a second term into the equation. It corrects a problem inherent in the original equation which is the prediction of a vertical slope at the shoreline where y = 0. This added term is referred to as the gravity term.
Dean hypothesizes that gravity acts through the beach slope as a destructive force in addition to wave energy dissipation. Thus, the governing equation in terms of energy conservation is expressed as
d _9gI hl (2.17)
Deq dy 2V + Bg dh
D h = dy
where B is an unknown constant.
Taking the derivative of (2.16) yields the following differential form,5 K-'-h3g2 a ah (2.18)
integrating and substituting for A yields = hBg + h3t2 (2. 19-)
Deq A3/2
In their application, Dean et al. (1993) substituted the measured beach face slope, BSL, for D/Bg in (2.18) and obtained the following differential form
A
dh= [ I +h12] (2.20)
y BSL 2Aj-3J




13
which was then applied using the following simple Euler forward difference scheme to calculate the predicted beach profile:
h(y,,1) =h(y,) + TAY (2.21)
2.4 Application Beyond the Surf Zone
In most engineering design applications, information regarding the total profile extending from the shoreline to the limiting depth of motion is required. Although the original theoretical developments are applicable only within the surf zone, the EBP equation in various modified forms as discussed above has been applied out to these depths when profile shape information is necessary. Hughes (1978) applied equation (1.2) to both long and shortened profiles fr om Florida's northeastern coast .and the southeastern shoreline of Lake Michigan and found significant differences in the A values obtained. One exception in Hughes study was in Brevard County, Florida; he suggests the closure depth may extend out further for this particular county.
2.5 Motivation for Different m Values
The theoretical basis by Dean (1977) for m = 2/3 in (1. 1) was briefly reviewed in Chapter 1 of this thesis. As well, it was pointed out that empirical fits to the data yield a similar value for m on average; although group averages may range from 0.52 to 0.82 (Dean, 1977). Dean (1977) also discusses two additional theoretical motivations for a value of 2/S for m. In these two theoretical developments, Dean considers the primary destructive force involved in molding the beach profile to be due to (1) uniform alongshore shear stress, and (2) uniform wave energy




14
dissipation per unit surface area. Another theoretical development proposed by Kaihatu (1990) yields a value of 14/17 (or 0.82) for m.
Kaihatu (1990) follows Deans' theoretical development of uniform wave energy dissipation per unit water volume, but incorporates a spectral breaking model instead of Dean's fixed break point assumption. Kaihatu employed the simple random wave dissipation model of Thornton and Guza (1983, equation 27).
Based on field evidence in Australia8, Kotvojs and Fried (1991) divided beaches into 3 groups: (1) reflective, (2) dissipative, and (3) intermediate. They obtained the following average values for m from a best fit analysis: (1) m=0.49 for reflective, (2) m=0.83 for dissipative, and
(3) m=0.65 for intermediate.
2.6 Fitting Two Curves to the Non-monotonic Beach Profile
Using an iterative technique, Inman et al. (1993) fit field data9 with two curves of the form h =Aym. One curve, the bar-berm profile extends from the berm crest to the breakpoint-bar. The other profile, the shorerise profile extends from the breakpoint-bar to at least a 12 meter depth. Figure 2-2 shows both curves fitted to a typical profile; notice that the origin of th& shorerise profile is at mean sea level (MSL) whereas the origin of the bar-berm profile averages 1.4 meters above MSL. This particular compound-curve fitting approach removes the monotonic restriction of the single curve fit as well as removing the vertical slope at the water line. In the case of multiple offshore bars, the shorerise profile begins at the outer bar.
8. Kotvojs and Fried (1991) studied 25 profiles from reflective beaches in New South Wales, 957 profiles (9 transects over a nine year period) from intermediate beaches in the Narrabeen, and 12 profiles from dissipative beaches around Goolwa in South Australia.
9. Inman et al. (1993) examined 51 profiles obtained from 8 range lines in San Diego, CA, collected over a 40-year period. This data was also supplemented with a number of profiles from Torrey Pines, CA; Duck, NC; and the Nile Delta, Egypt.




15
In this study by Inman et al. (1993), the best fit to the data yields an m value generally around 2/5 for both profiles. Distinct seasonal variations in the profiles were observed as simple displacements of the two curves as the offshore bar moved farther offshore in the winter (Figure 2-3); the A value also tended to increase in winter.
One of the most interesting findings in this study was the relationship with A in the shorerise profile and average beach-face sand size (Figure 2-4). Unfortunately, sediment size information was limited for this particular data set. Figure 2-4 clearly shows, however, that a relationship exists at least for this particular data set using Inman's approach.
2.7 Time Varying A
An interesting field study by Pruszak (1993) proposed a time-varying A expressed as A(t) =A+A+ A2 +Al ..(2.22)
where
,i = 5(sediment size, shoreline geomorphology)
Al = .9O(long-term cyclic changes, e.g., in sea level, sediment supply, etc.)
A2 = .F(meso-term cyclic changes, e.g., seasonal changes in wave conditions, etc.)
Al = 9(short-term random changes, e.g., single storm events, etc.)
10. Pruszak studied profile data collected from Lubiatowo, Poland, on the Baltic Sea and data from Gold Beach, Bulgaria, on the Black Sea. The Baltic Sea data includes 20 range lines spaced 150 meters apart for which data was collected periodically from 1964 to 1991. The Black Sea data consists of monthly surveys of one range line from September of 1972 through June of 1978.




Pruszak specified A (t) more specifically as
A(t)=A+alcos 27r i+k1 +a2cos 27r+02 +A1 (2.23)
where a,, T1, ', a2, T2, 02 in the Fourier series correspond to the amplitude, period, and phase of the longterm, A,, and mesoterm, A2, cyclic changes, respectively. Figure 2-5 illustrates this decomposition of A (t).
Pruszak fit h =A (t)y13 to data from the Baltic Sea after simplifying A (t) as
A(t) = A + A1 = A + a, cos (wit+k 1) (2.24)
where t is time in years. For this data set, which ranged from 1964 to 1991, Pruszak obtained the following values for the parameters in (2.24) Ai = 0.075 [m"3]
a, = 0.022 [in3]
w= 0.230 [yr']
Thus, the longterm profile changes have a period of approximately 25 to 30 years. The associated long term variation in A is presented in Figure 2-6.
Figure 2-7 shows the time variation in A which Pruszak obtained after fitting h =A/'3 to profile data from the Black Sea. The Black Sea data were collected at a higher frequency (monthly) and over a smaller duration (5 years) than the Baltic Sea data. Figure 2-7 shows' that for this data, the A2 component can be identified. For this Black Sea data, Pruszak does not give any calculated values for each component.




SEDIMENT FALL VELOCITY, w (cm/s)

SEDIMENT SIZE, D (mm)

Figure 2-1. Moore's Curve: scale parameter, A, versus sediment diameter, D, and fall velocity, w, in EBP relationship h =Ay13 (Dean, 1987, modified from Moore, 1982).
k'




Figure 2-2. Definition sketch showing Inman's compound curve fitting scheme where crosses denote the origin for the bar-berm profile (dotted) and for the shorerise profile (dashed) (Inman et al., 1993).
p I p I
4 2W 7
Basic Data Set 2s-
_____ MSL o
/1 AX1

Distance, meters

Figure 2-3. Seasonal beach changes as observed with Inman's compound curve approach comparing mean summer (solid) with mean winter (dotted) profiles (Inman et al., 1993).




3I I
2
D
I**
0I
TP .5
* .4
*N .3
).2

0.5
0.3 L

100

Diameter, Um

Figure 2-4. Fitted A and m parameters for Inman's bar-berm profiles plotted against available beach face sediment size (Inman et al., 1993).

Sqq
III
TP **4
I N
I I I

V i "




A(t) 20
A, A, *
time
t
Figure 2-5. Schematic illustrating the decomposition of Pruszak's time-varying A parameter in h=Aym (Pruszak, 1993).
Alt)
A(tA *A, a cossUzt
0.12 y=A(,x2/ =0.075+0.022 cos(0.23-.t)
0.10
00O6 0.075
1960 1964 1968 1972 1976 1980 1984 1988 1992 t
Figure 2-6. Long term variation in A parameter for Pruszak's Baltic Sea data (Pruszak, 1993).
0.25 AA
020
0.15
0,10.
010,5- ,.
0 x I x Mi 0 ixix a l Ix
)4r72 1973 1974 1975 1976 1977 1978
/Figure 2-7. Short term variation of A parameter for Pruszak's Black Sea data (Pruszak, 1993)./
Figure 2-7. Short term variation of A parameter for Pruszak's Black Sea data (Pruszak, 1993).




CHAPTER 3
DATA COLLECTION AND STUDY AREA
3.1 Study Area
The study area includes all 12 coastal counties on the east coast of Florida (Table 3-1), spanning some 531 kilometers from the St. Marys River entrance at the Georgia-Florida border to Government Cut in Miami, Florida (Figure 1-1). This segment of the Atlantic Coastline is exposed to moderate to high wave energy levels and is characterized by numerous sandy barrier islands separated by 17 tidal inlets. Fringing coral reefs occur in shallow water along the coastline in various areas primarily south of Cape Canaveral. In the northeast, linear shoreparallel shoals have been documented as well as arcuate cape-associated shoals just offshore fron! Cape Canaveral (Meisburger and Field, 1975).
For the most part, the sediment forming the east-coast beaches is merely a thin veneer (geologically speaking) spread over a Pleistocene limestone core (the Anastasia Formation). This type of barrier island is called a "perched" barrier island by some coastal geologists. The limestone core which parallels the Florida coastline is believed to have been a carbonate ridge at one time during the Pleistocene (Tanner, 1964). This Pleistocene core acts to stabilize the shoreline with a smooth rather than irregular configuration. It is exposed in various places along the coast, especially in Flagler and Palm Beach Counties.
The northeastern beaches are made up of relatively fine siliceous sand and are primarily rather wid6 and gently sloping. Flagler county is an exception, however. In many areas of this county, the beach is relatively narrow and steep while the sediment exhibits an increase in coquina shell material derived from the outcropping Anastasia Formation. Similar to the Flagler




22
County beaches, the southeastern beaches are generally narrow and steep. In this region, as well, the beach sediment is dominated by highly permeable shell mixtures.
In the Southeast, tidal inlets are more numerous than in the northeast. Stabilization of these inlets for navigational purposes has resulted in severe erosion at some downdrift locations.
3.2 Field Data Collection: Beach Profiles and Sediment Samples
Along Florida's entire coastline there exists a series of permanently located baseline monuments which serve as benchmarks for beach profile surveys. These monuments are spaced 305 meters apart on average and are referenced with the state's grid system'. The monuments were installed and are maintained by the Florida Department of Natural Resources (DNR) as an integral part of their effort to establish and regulate a Coastal Construction Control Line (CCCL) for the sandy beaches in Florida. Since the 1970's, when the first CCCL line was established, the DNR has periodically surveyed the beaches and offshore regions of Florida on a county-bycounty basis. The DNR records survey data and benchmark elevations in feet relative to NGVD2 and profile azimuths in degrees relative to magnetic North. From each benchmark, beach profiles are surveyed using a standard rod-and-level procedure out to "wading" depths averaging 1.5 meters. On every third monument, the DNR extends the surveys out to at least 1000 meters offshore which corresponds to-depths greater than 10 meters on the east coat. These offshore surveys are performed using a survey vessel equipped with a fathometer and electronic positioning system. Currently, this is the most widely used method of surveying the beach pro ile. This type of surveying yields beach profile data with a vertical accuracy of 2 to
1. This grid system is the Florida State Plane Coordinate System.
2. NGVD represents the National Geodetic Vertical Datum which was formerly called the 1929 Mean Sea Level (MSL) Datum and currently corresponds to a level somewhere between MSL and MLW (mean low water) due to the modern trend of rising sea level.




23
3 centimeters for the rod-and-level procedure and a vertical accuracy in the range of 15 t0 20 centimeters for the offshore portion (Otay et. al, 1994).
As mentioned previously, this report examines data from Florida's east coast which is comprised of 12 counties and encompasses 531 kilometers of coastline. DNR maintains 1753 monuments in this area for which extensive profile data are available. In addition to DNR survey data, 155 profiles were surveyed to "swimming" depths of approximately 4 meters specifically for this study. Sediment samples were also collected from 207 monument locations corresponding to approximately every ninth DNR survey. This information is summarized in Table 3-1.
Table 3-1. Data Summary by County.
kilometers total number of number of number of profiles County of coastline FDEP profiles UF profiles with sediment data
Nassau 21 82 0 7
Duval 26 80 0 9
St. Johns 66 209 23 23
Flagler 29 100 11 11
Volusia 74 234 0 26
Brevard 64 219 14 24
Indian River 35 119 12 12
St. Lucie 35 115 13 13
Martin 35 127 34 34
Palm Beach 72 227 26 26
Broward 39 128 13 13
, Dade 34 113 9 9
total: 12 530 1753 155 207




24
A total of 1834 samples were collected for this study. Nine surface-sediment sampJes were collected along each profile at depths of 0.0, 0.9, 1.8, 3.7, 5.5, 7.3, and 9.1 meters as well as a dune and berm sample. The dune, berm, waterline (or 0.0 meter), 0.91, and usually the 1.8 meter samples were collected using a coffee can as a scoop during the "swimming" profile surveys when possible. The offshore samples were collected using a drag sampler from a boat equipped with a fathometer for depth determination and a loran for profile positioning. Depths were not corrected for tidal fluctuations at the time of sampling. On average, these sampling techniques produced 500 gram samples which were placed in labelled cloth sample bags. Table 3-2 presents sampling and survey dates for the Nassau County data; this table is reproduced in the Appendix along with similar tables for each of the remaining 11 counties.
Table 3-2. Data Collection Dates for each Field Location Identified by the FDEP Range Number
-- Nassau County, Florida.
NASSAU COUNTY:
beach proUile survey dates sediment sampling dates
FDEP UF PDEP FDEP Om 1d91m -L83m -3.66m -.49m .7.32m -9.14m
Benchmark Survey Oshoe Offsbore dune berm WL -3ft .6t -12ft -18t -24ft -30ft
R-S15 N/A (10/28/81) (12/16/81) (8/20/92) (8/20/92) (8/20/92) (8/292) (8/20/92) (8/20/92) (2) (820/92) (80/92)
R-27 N/A (10/27/81) (12/16/81) (8/2092) (8/2092) (8/2092) (8/20/92) N/A (8/20/92) (8/2092) (820/92) (820/92)
R-36 N/A (1/27/81) (1216/81) (8/2/92) (8/20/92) (8/20/92) (8/2/92) (8/2/92) (8/20) (2 ) (8/20/92) (820/92)
R-45 N/A (1022/81) (12/16/81) (8/20/92) (8/20/92) (8/20/92) (8/20/92) N/A (8/20/92) (8/20/92) (8/20/92) (820/92)
R-57 N/A (10/14/81) (12/17/81) (8/20/92) (8/20/92) (8/20/92) (8/20/92) N/A (8/20/92) (8/20/92) (8M20/92) (82092)
R-66 N/A (10/07/81) (12/17/81) (8/20/92) (8/20/92) (8/20/92) (8/20/92) (8/20/92) (8/2092) (&MM9) (/M) (/20/)
R-72 N/A (10/07/81) (12/17/81) (8/20/92) (8/20/92) (8/20/92) (820/92) N/A (8/20/92) (8/20/92) (8/20/92) (8/20/92)
TOTAL7 p(ofiles subtotals: 7 7 7 7 3 7 7 7 7
Sto sp: 59
NOTE: N/A = not available or not attempted.




3.3 Lab Methods for Sediment Size Analysis
Initially a somewhat random selection of 500 samples was prepared for grain-size analysis. These 500 samples were first dried in an oven at 50' centigrade afterwhich a subsample weighing approximately 100 grams was obtained using a Jones-type splitter. These subsamples were then placed in the top of a stack of sieves which was in turn secured to a Rotap' mechanical shaking device with a runtime set at 15 minutes. Each subsample was sieved through at least 12 different sieves with different screen sizes which varied depending on the bulk characteristics of the sample. The median diameter of each sediment sample was calculated from the resulting grain-size distribution.
The standard sieving technique proved infeasible for the number of samples requiring analysis, so an alternative method was devised. A settling tube apparatus was constructed and the 500 sieved samples were used specifically for calibration of the samples collected in this study. The remainder of the samples were analyzed using this settling tube apparatus, also called a rapid sediment analyzer (RSA).
For the RSA, subsamples weighing approximately 40 grams were obtained again using the Jones-type splitter. These subsamples were placed in a plastic cup containing enough water to saturate the sample. The saturated sample was then placed into the release mechanism at tie top of the RSA by first scooping with a spoon and then rinsing the remaining sample out of the cup using a wash bottle. The electronically triggered sample-release mechanism at the top of t~e RSA is controlled through an IBMAT computer. After the sample is released, it falls 246 centimeters to an aluminum pan which is suspended from a load cell above the plexiglass settling tube. This load cell continuously measures the total pan weight as the sediment particles fall while the computer accesses this information at quarter-second intervals. Thus, the raw data file consists of a time series of cumulative weights sampled at a frequency of 4 hertz. The raw data




26
-ire then reduced to an effective grain-size distribution using the following empirical formula (Gibbs et al., 1971):
-3v /V9p2 +gd2(s-1)(0.003869+0.02480d) (3.1)
0.011607+ 0.07440d
where settling velocity, w., is in cm/s, grain diameter, d, in centimeters, and the fluid viscosity, v, in cm/s. Median diameters were obtained from these calculated distributions and corrected with the following calibration formula: sieve size[O] = -0.1252 + 1.232135 (RSA size[5]) (3.2)
where the size is given in phi-units.
By expressing the sediment size in phi-units, the calibration procedure was reduced to a simple linear regression of the size data from both measurements. Figure 3-1 is a plot of the sieve size versus the RSA size, both in phi units, as well as the bestfit calibration line defined by (3.2). The conversion from phi units to millimeters is written size[ram] = 2"-sfr4i (3.3)




SIEVE [phi] = -0.125 + 1.232 RSA[phi]

0.5 1 1.5
RSA median diameter [phi-units]

Figure 3-1. Sediment median diameter from sieve analysis versus sediment median diameter calculated from settling velocities using Gibbs equation, all in phi units, solid straight line is best fit line defining calibration equation also shown at the top of the graph.




CHAPTER 4
PROCEDURES FOLLOWED IN DATA ANALYSIS This study applies (1.4) and (2.18) in a predictive or "blindfolded" manner using Moore's relationship between sediment median diameter and the A parameter. The A parameter was allowed to vary along the profile in accordance with the corresponding variation in sediment size. Sediment size, and therefore the associated A value, was considered to vary linearly between each sample location. As mentioned in the previous chapter, Work and Dean (1990) applied (1.4) in this way and Dean et al. (1993) applied (2.18) in the same "blindfolded" manner.
After calculating predicted profiles using both of the abovementioned techniques, the root mean square difference (RMS) was calculated for each profile in an attempt to quantify the quality of the "fit" to the actual measured profiles. The RMS error was calculated by
RMS= E (hm,-hc)2
1
where N is the number of data points, hmi and hc are the measured and calculated depths at the i' location, respectively.
To further investigate the validity of the A versus D50 relationship, least squares was applied in the manner discussed in Section 2.1 in order to determine the A and m values which provided the best approximation to the measured profile. This was done for m=2/3 using (2.7) as well as m= best fit using (2.5) and (2.6).
Insight of the discussion on the applicability of the EBP equation beyond the surf zone, all of the above analyses were performed out to 5 specified depths for each profile. These depths correspond to the sediment sample locations, i.e., depths of 1.8, 3.7, 5.5, 7.3, and 9.1 meters.




CHAPTER 5
RESULTS AND DISCUSSION
5.1 Sediment Size Data
The variation of the sediment median diameter along the east coast of Florida is plotted, ini Figure 5-1 for all of the sediment samples analyzed in this study. Figures 5-2 through 5-8 present similar plots of the sediment size variation at each of the following depths used in the EBP calculations: 0.0, 0.9, 1.8, 3.7, 5.5, 7.3, and 9.1 meters.
Much of the scatter in the data presented in Figures 5-1 through 5-8 is due to the shell content of the sediment samples. Increased amounts of shell material in the sediment yields a larger sediment size for those sample locations which occurred around reefs or shell pockets. IiR, general, the 0.0 and 0.9 meter samples contained the greatest amount of shell material. As well, south of Brevard County, all of the sediment s amples tended to contain more shell material than the samples from the counties to the north. Specifically, Indian River and Broward counties may be identified in Figures 5-4 through 5-6 by the scatter in their respective size data. These counties were especially characterized by offshore reef systems.
Table 5-1 lists the average median diameters for the sediment samples collected at each of the 7 sampling depths mentioned above. These averages were done over the entire east coast as well as for each individual county. The average median diameter for all of the sediment samples is 0.24 millimeters. Two notable trends in this data are that generally the sediment size becomes finer in the offshore direction and that the southernmost counties, i.e., Dade and JBroward counties, comprise the coarsest sediment.




Table 5-1. Median diameter of sediment samples collected at depths of 0.0, 0.9, 1.8, 3.7, 5.5, 7.3, and 9.1 meters averaged over the entire east coast of Florida and averaged for each of the 12 east-coast counties.
averaging average sediment sample median diameters [mm]
spatial
domain depth of sediment samples [m]
0.0 0.9 1.8 3.7 5.5 7.3 9.1
east coast 0.3792 0.3153 0.1972 0.1563 0.2018 0.1826 0.2561
Nassau 0.3456 0.1985 0.2903 0.1678 0.3379 0.1032 NA
Duval 0.1723 0.1770 0.1400 0.1301 0.1196 0.1119 NA
St. Johns 0.2142 0.1912 0.1603 0.1218 0.1590 0.1093 0.1564 Flagler 0.5858 0.2016 0.1719 0.1396 0.1259 0.1281 0.1301
Volusia 0.2279 0.2527 0.1454 0.1382 0.1264 0.1378 0.1573
Brevard 0.3303 0.4894 0.3727 0.0898 0.0849. 0.1384 0.3518
Indian River 0.4929 0.3910 0.2493 0.3061 0.3630 "0.3128 0.6078
St. Lucie 0.3872 0.1314 0.1412 0.2500 0.3867 0.3917 0.5291 Martin 0.3030 0.3094 0.1495 0.1123 0.1010 0.1019 0.8464
Palm Beach 0.5154 0.3680 0.1924 0.1598 0.1692 0.1786 0.1933
Broward 0.4644 0.3611 0.2225 0.3067 0.5027 0.4902 0.2782
Dade 0.6663 0.6586 0.2305 0.1429 0.4491 0.3440 NA
NOTE: NA = not available

.5.2 Results from the "Blindfolded" Test on Beach Profile Predictability using Sediment Size Data
Initially, for each profile the measured profile (solid line) was plotted with both calculated profiles; one without the gravity term (dotted line) and the other with the gravity term (dashed line). Above these graphs, the cross shore variation in sediment median diameter for the measured profile was plotted. These figures have been omitted from this thesis to reduce its bulk, however, they are presented in Charles (1994). Figure 5-9 and 5-10 present two examples of these figures showing the best and worst fit to the measured profiles, respectively.




31
The RMS deviation of the calculated from the measured profile depths was computed for
each profile location in order to quantify the quality of the fit to the measured profile and to
simplify comparisons, see Equation (3.1). For each profile location, RMS values were computed
for the profiles truncated at the following 5 depths: 1.8, 3.7, 5.5, 7.3, and 9.1.meters. The
variation of these RMS values, along the east coast of Florida, is plotted in Figures 5-11 through
5-15 (one plot for each of the 5 depths mentioned above); the solid line is for the calculation
without the gravity term and the dotted line is for the calculation with the gravity term.
Presented in Table 5-2 are the averages of the individual RMS values for each of the two
calculations and for each of the 5 depths. These averages were done over the entire east coast,
as well as for each individual county.
Table 5-2. Root Mean Square (RMS) deviations of predicted equilibrium reach profiles (EBP) from the measured beach profile for each measured profile extending out to depths of 1.8, 3.7, 5.5, 7.3, and 9.1 meters; these individual RMS values for each profile are averaged over the entire east coast of Florida and averaged for each of the 12 east-coast counties; EBP predictions based on calculations (1) without the gravity term and (2) with the gravity term.
averaging average RMS deviations of each predicted profile from measured
spatial profile truncation depth [meters]
domain 1.8 3.7 5.5 7.3 9.1
(1) (2 (1) (2) (1) (2) ((2) (1) 1 (2)
east coast 0.42 0.39 0.65 0.77 0.88 1.08 1.21 1.54 1.58 2.02
Nassau 0.44 0.51 0.48 0.66 0.81 1.39 1.85 2.68 NA NA
Duval 0.33 0.46 0.49 0.98 1.01 1.58 0.39 1.46 NA NA
St. Johns 0.30 0.33 0.39 0.69 0.57 0.96 1.08 1.59 1.74 2.29
Flagler 0.36 0.32 0.78 0.99 0.82 1.08 1.16 1.43 1.73 2.01
Volusia 0.44 0.40 0.43 0.67 0.48 0.98 0.83 1.54 1.24 2.19
Brevard 0.48 0.40 0.70 0.65 0.99 1.04 1.46 1.70 2.07 2.33
Indian River 0.51 0.38 1.41 1.26 1.61 1.35 1.65 1.30 0.62 0.75
St. Lucie 0.41 0.44 0.75 0.78 1.84 1.67 2.26 2.16 1.95 2.16
Martin 0.32 0.32 0.50 0.52 0.64 0.77 1.09 1.31 NA NA
Palm Beach 0.49 0.44 0.74 0.73 0.77 0.87 1.02 1.24 1.35 1.71
Broward 0.42 0.43 0.68 0.82 0.97 0.97 1.43 1.34 NA NA
Dade 0.41 0.26 0.69 0.77 0.75 1.11 NA NA NA NA
NOTE: NA=not available




32
The first set of RMS values, the first two columns in Table 5-2, were calculated for profiles truncated at a 1.8 meter depth. These RMS values range from 0.26 to 0.51 meters indicating that both methods of EBP calculation provide a reasonably good fit to the measured data. For this set of values, the calculation including the gravity term gives a slightly better fit, 0.39 meters on average, than does the other EBP calculation which has an overall average of 0.42 meters. This would be expected since the additional term, the gravity term, includes a measured value for the beach face slope (BSL).
Overall, there are two obvious trends in the data of Table 5-2. The first is that as we include more of the profile in our calculations, the RMS values increase and thus the quality of the EBP fit to the measured profile decreases. The second trend is that except for the profile truncated at 1.8 meters, which was already discussed, the EBP calculation without the gravity term consistently out-performs the EBP calculation including the gravity term. -This second trend is reasonable since Moore's curve, which was used to calculate the A parameter, from the sediment size in both EBP calculations, was derived using the EBP calculation without the gravity term. If the EBP calculation including the gravity term term is, to be judged fairly, a new relationship between A and sediment size should be determined specifically for this calculation.
To provide a reference for discussion, an average measured profile was computed for the entire east coast. As well, an average calculated profile for both techniques was also computed for the entire east coast. These three average profiles are plotted together in Figure 5-16. Examination of this figure shows that the EBP calculation without the gravity term (dotted line) obviously out-performs the EBP calculation including the gravity term (dashed line). For profiles truncated 4t 1.8 meters depth, the RMS values for the EBP calculation (based on profile averages out to a particular depth) with and without the gravity term are 0.30 and 0.08 meters, respectively. For profiles extending out to 3.7 meters depth, the RMS error increases slightly to 0.59 and 0. 11, respectively.




33
To further facilitate analysis of the results, average measured profiles and calculated profiles for both techniques were computed for each of the 12 east-coast counties. An average calculated profile for both techniques was also determined for each of the counties. These group averaged profiles are presented in figures 5-17 through 5-28. Along with the average measured profile and the averaged calculated EBP by two techniques, the maximum and minimum measured depths for all profiles in the group are also plotted versus distance to give an indication of profile variation within the group.
Table 5-3 summarizes the RMS values calculated from these group-averaged profiles. There is great improvement in the quality of the fit of the average measured profiles to the average EBP calculated profiles than was indicated by the individual profiles discussed earlier in this section.

Table 5-3. Root Mean Square (RMS) deviations of the average predicted equilibrium beach profile (EBP) from the average measured beach profile extending out to deptls of 1.8, 3.7, 5.5, 7.3, and 9.1 meters; EBP predictions based on calculations (1) without the gravity term and (2) with the gravity term.
averaging RMS deviations of average predicted profiles from average measured
spatial profile truncation depth [ml
domain 1.8 3.7 5.5 7.3 9.1
(1) (2j (1) (2j (1j (21 (1) 1 (2j (1) (2)
east coast 0.08 030 0.11 0.59 NA NA NA NA NA NA C.
Nassau 0.22 032 0.22 0.62 NA NA NA NA NA NA
Duval 0.29 032 0.20 0.81 NA NA NA NA NA NA
St. Johns 0.09 030 0.26 0.68 0.74 1.04 1.11 1.40 NA NA
Flagler 0.20 0.19 0.75 1.00 034 1.03 0.76 1.56 NA NA
Volusia 0.23 0.44 0.24 0.68 0.63 0.99 NA NA NA NA
Brevard 0.30 0.16 0.28 0.40 NA NA NA NA NA NA
Indian River 0.18 0.16 NA NA NA- NA NA NA NA NA
St. Lucie 0.17 0.24 034 0.66 0.23 0.63 NA NA NA NA
Martin 0.14 0.47 0.25 0.64 0.40 0.66 0.99 1.32 NA NA
Palm Beach 0.05 0.27 0.18 0.40 0.46 0.81 NA NA NA NA
Broward 0.22 0.45 033 0.63 NA NA NA NA NA NA
Dade 0.5 0.14 NA NA NA NA NA NA NA NA
NOTE: NA=not available




34
5.3 Comparison Between EBP Calculations Performed With and Without the Gravity Term.
Examination of Figures 5-9, 5-10, and 5-17 through 5-37 in Section 5.2 shows that there is a consistent relationship between the two EBP calculations, with and without the gravity term. Perusal of these plots shows that the EBP calculation including the gravity term always predicts a shallower depth than the other EBP calculation for any given location, y, along the profile.
This relationship between the 2 calculations can be simply explained by expressing both EBP equations in the same form as follows
y __ (5.1)
Y= [h ]3/2.+ h (5.2)
Inspection of Figure 5-29, makes this effect of the additional term, hIBSL, in (5.2) more obvious.
On average, the EBP calculation without the gravity term out-performs the EBP calculation including the gravity term. As was mentioned in Section 5.2, the A versus sediment size relationship given by Moore's curve was determined using the EBP calculation without th gravity term and for an invariant A along the profile. Thus, Moore's relationship is slightly more appropriate for the EBP equation (5.1) although both applications in this study are for a variable A along the profile. Perhaps Moore's relationship could be re-evaluated for (5.2) at least for the case of an invariant A and then re-applied to (5.2).
Tl1e re-evaluation of the A versus sediment size relationship for (5.2) was not performed in this study. It was felt that the predictive capability of (5.1) using Moore's relationship was quite good and that further study of (5.2) was not justifiable. Thus, the remainder of this chapter considers (5.1) and any additional discussion of (5.2) is omitted




35
5.4 Results from the Curve Fit Analysis of h =Av~' and h =Av21 for-I-nvariant A
In order to investigate further the h =AY" relationship, a curve fit analysis was performed using least squares as was discussed in section 2. 1. The fitting of h =AY" to the measured profile data involved using (2.5) and (2.6) to determine m and A, respectively. The alongshore variation of these A (solid line) and m (solid line with empty square symbols) values are plotted in Figures 5-29 through 5-33 for profiles truncated at each of the following 5 depths: 1.8, 3.7, 5.5, 7.3, and 9. 1 meters. Fitting h =Ay' to the measured data required application of (2.7) to determine the A value. This A value is plotted as the dotted line with asterisk symbols in Figures 5-30 through 5-34.
The most notable feature of the data plotted in Figures 5-30 through 5-34 is the inverse correlation between A and m; as A increases, there is a corresponding decrease in m. This inverse relationship is inherent in the relationship: h =Ayf and may be explained further by returning to the original analysis, that of linear regression. When fitting a straight line (Equation 2.2) through a set of data points, as the slope (the m value) is increased, naturally the y-intercept (the logarithm of A) will decrease and vice versa. As Dean (1977) points out, it is doubtful that this feature in the data has any physical significance.
Table 5-4 presents the average A and m values from (2.5) and (2.6) discussed above, whereas Table 5-5 presents the average A values from (2.7) for m=213. These averages were performed over the entire east coast as well as for each individual county.
It must be mentioned that due to the nature of the log-scaling, the linearized fit to the data using (2.2) is slightly biased toward the portion of the profile closer to the waterline than a direct linear fit of (1. 1) to the data. The added difficulty in curve-fitting (1. 1) is not outweighed, however, by the increased accuracy of the fit.




Table 5-4. Averages, for the entire east coast of Florida and county-by-county, of bestfit A and m parameters from curve fit analysis of h=Af to measured beach profiles out to depths of 1.8,
3.7, 5.5, 7.3, and 9.1 meters.
averaging curve-fit analysis results averaged overall and by county
spatial profile truncation depth meters]
domain 1.8 3.7 1 55 73 9.1
A m A m A Im A m Am
east coast 0.12 0.66 0.13 0.65 0.13 0.65 0.12 0.68 0.11 0.69
Nassau 0.07 0.75 0.07 0.76 0.03 0.89 0.02 0.97 NA NA
Duval 0.05 0.74 0.05 0.79 0.05 0.79 0.04 0.76 NA NA
St. Johns 0.07 0.72 0.08 0.72 0.08 0.73 0.06 0.78 0.06 0.81
Flagler 0.11 0.65 0.11 0.71 0.13 0.66 0.13 0.67 0.12 0.70
Volusia 0.07 0.72 0.07 0.72 0.07 0.74 0.05 0.78 0.05 0.79
Brevard 0.13 0.62 0.13 0.63 0.12 0.65 0.11 0.67 0.10 0.68
Indian River 0.19 0.55 0.26 0.49 0.27 0.48 0.23 0.52 0.19 0.55
St. Lucie 0.15 0.59 0.17 0.57 0.18 0.58 0.17 0.60 0.12 0.67
Martin 0.15 0.59 0.19 0.54 0.17 0.56 0.10 0.66 NA NA
Palm Beach 0.17 0.60 0.22 0.53 0.20 0.56 0.18 0.60 0.16 0.61
Broward 0.19 0.63 0.18 0.65 0.21 0.60 0.26 0.55 NA NA
Dade 0.11 0.71 0.10 0.76 0.13 0.67 NA NA NA NA
NOTE: NA=not available
Table 5-5. Averages, for the entire east coast of Florida and county-by-county,- of best fit A parameter for m = 2/3 from curve fit analysis of h =Af to measured beach profiles out to depths of 1.8, 3.7, 5.5, 7.3, and 9.1 meters.
averaging averaged results of curve-fit analy. m=2/3 spatial profile truncation depth [meters]
domain 1.8 3.7 5.5 7 91
east coast 0.10 0.10 0.10 0.10 0.11
Nassau 0.08 0.08 0.09 0.11 NA
Duval 0.06 0.08 0.09 0.07 NA
St. Johns 0.08 0.09 0.09 0.09 0.09
Flagler 0.10 0.12 0.11 0.12 0.12
Volusia 0.07 0.08 0.08 0.08 0.09
Brevard 0.11 0.10 0.10 0.11 0.11
Indian River 0.13 0.11 0.10 0.10 0.10
St. Lucie 0.11 0.10 0.10- 0.10 0.12
Martin 0.12 0.10 0.10 0.10 NA
Palm Beach 0.13 0.11 0.11 0.11 0.11
Broward 0.16 0.15 0.13 0.13 NA
Dade 0.12 0.13 0.14 NA NA
NOTE: NA=not available




5.5 Motivation for Different m Values
Inspection of the results from the curve fit analysis indicates that for the east coast of Florida on average, m=O0. 67 is not an unreasonable value. While the group averages range from a low of 0.48 and a high of 0.97, the average m value for the entire east coast is 0.67 for profiles extending out to all 5 depths examined in this study.
As well, there are no major groupings of m values around any of the other values for which theoretical justifications have been made (i. e., m=O0. 4 and m =0. 8).
5.6 Relationship Between A and Sediment Size
The EBP calculation, without the gravity term and allowing A to vary along the profile, proved on-average to be quite a useful approximation of the actual profile (Fiure 5-17), at least out to a depth of 4 meters. Since this calculation was performed using sediment-size data and Moore's empirical relationship between sediment size and A, it would seem that there should be some obvious relationship between A and sediment size in the data set analyzed in this thesis. To investigate the nature of this relationship in the data set at hand, various graphical representations were constructed.
The data selected for this investigation include the average A values calculated from the curve fit analysis of Section 5.4 (Table 5-4) and the average sediment median diameters presented in Table 5- 1. The A values calculated from h =Ay' were selected since this equation is that which was tested in this study. For each of the 5 depths, for which average A values are available, the sediment data represents the average of all of the average sediment size data which are available over the lengths of each of the 5 truncated profiles. So, for instance, the A value calculated from the curve fit to a profile extending to 3.7 meters depth would correspond to the average sediment size of the 0.0, 1.8, and 3.7 meter sediment sizes listed in Table 5-4 as averages for each county.




38
Figure 5-35 is a graph of average A versus average sediment median diameter for the 12 counties and for each of the depths: 1.8, 3.7, 5.5, 7.3, and 9.1 meters; so there are basically 12 data points, one for each county, for each of the 5 depths for which data are available. Inspection of this figure shows a widely scattered but positive relationship between A and average sediment size.
The next step is to examine the same data plotted separately for each individual depth. Thus Figures 5-36 through 5-40 are plots of the same data in Figure 5-35 except they correspond to the data at each depth. There is an obvious positive relationship between A and average sediment size for all of these figures (Figures 5-36 through 5-39) except perhaps for the profiles extending out to 9. 1 meters depth (Figure 5-40).
Finally, the average A values and average sediment median diameters are plotted, by county, north to south; this is plotted for profiles extending out to depths ori.8, 3.7, 5.5, 7.3, and 9.1 meters corresponding to Figures 5-41 through 5-45, respectively. Plotted in this relative spatial scale, the relationship between the average best fit A values and average sediment size becomes more apparent. This would seem to indicate that perhaps'A is also a function of other regional characteristics of the beach profile as Pruszak (1993) indicated for his A
5.7 Application Beyond the Surf Zone and Dependence on Profile Det
The theoretical explanations, applied to the h=Ay" formulation for an EBP, consider breaking-wave and associated dynamics inside the surf zone. Most engineering applications, however, require information regarding the total profile, which extends outside the surf zone and out to the limiting depth of motion. In the absence- of a better method, the EBP equation has been applied out to these closure depths when profile shape information is necessary.




39
A 10 meter closure depth is generally recommended for the east coast of Florida. In an attempt to investigate the depth dependence for the EBP, all calculations in this study were repeated for profiles truncated at depths of 1.8, 3.7, 5.5, 7.3, and 9.1 meters, which correspond to the depths of the sediment samples. All of the data presented so far exhibit marked variation depending on this limiting depth applied to the profile.
The most striking depth dependence is the predictability of the measured profile using h =Ay' where A varies with the cross-shore distribution of sediment median diameter following Moore's empirical relationship. On average, this predictability is quite good out to a depth of around 4.0 meters, see Figure 5-16. In fact, for this east coast average profile, the RMS deviation of the average calculated EBP from the average measured profile out to a depth of 3.7 meters is 0. 11 meters; Otay and Dean (1994) estimate the profile survey error out to this depth is between 0. 15 and 0.20 meters.
Figures 5-17 through 5-27 show the average calculated and the average measured profiles for averages taken over each of the 12 counties; there is generally a marked decrease in quality of the EBP approximation to the measured profile beyond 4 meters, depth. Thus, application of this EBP calculation beyond the 4 meter depth and out to the closure depth is not an ideal method. To remedy this problem, Inman et al. (1993) proposed using 2 profiles of the form' h =Ay-.
Inman pointed out that by combining 2 profiles, one inside and one outside the surf zone, the dynamics associated with shoaling waves outside the surf zone could be handled separately with the second profile. Inman achieved a much better fit to the data using his comipound-curve approach as opposed to the single EBP curve. Interestingly enough, similar values for A, as well as m, for both the shorerise and the bar-berm profiles were obtained from the compound-curve. fitting scheme employed by Inman. Inman's method was not applied to the data in this study.




5.8 Non-monotonic Beach Profiles
Unfortunately, the plots of the measured and calculated individual profiles could not be included in this report due to spatial constraints but they are presented in Charles (1994). Nevertheless, after perusal of these graphs, an unusual trend becomes apparent in-many of the measured profiles. It seems as though there is a consistently sloping profile for most of the length of the profile, but that at the locations of offshore bars and offshore reefs, it is horizontally displaced in the offshore direction; after this displacement, the same sloping profile continues. Figure 5-46 presents this observation in an exaggerated form. Again going back to the original theoretical development of the EBP concept, that of uniform wave energy dissipation per unit volume across the surf zone, we know that Deq is related to depth and slope as h'dh/dy. Conceptually we might expect a plot of D~q across the profile to look something like that which is also plotted for the exaggerated profile in Figure 5-46.
Referring to the graph of the trend in RMS values along the east coast, we see that there
-ire a few noticeably large values. If we examine more carefully the profile plots of the largest of the two, we see something quite interesting. Figures 5-47 and 5-48 show these particular profiles from Indian River and St.Lucie counties, respectively. In both measured profiles, offshore reefs are evident. With a little bit of imagination, one might see the consistent slope of the profile and the horizontal displacement of this sloping profile at the locations of these reefs.
5.9 Time Varying Beach Profiles
It Jis well known that beach profiles are constantly evolving, both under field and lab conditions. For this reason, the EBP concept has always been associated with a sort of dynamic equilibrium. The time varying A parameter proposed by Pruszak (1993), is quite interesting. Unfortunately at the present time, the data set for the east coast of Florida is unsuitable for a test




41
of this approach. With the sediment size data now available, perhaps in the future, profile measurements will be performed at a higher frequency so that the time-varying nature of A can be examined fully. Pruszak's idea of decomposing A does however seem plausible given the results of the data presented in this report.
First, the application of h =Ay"1 for A =A where A is a function of sediment size (here following Moore's empirical relationship) results in a reasonably good fit to the data only on a group average basis. Perhaps some of the variations in the individual profiles which are averaged out could be better explained with a time-varying A as Pruszak proposed. All of the beach profiles were not measured during the same season of the year or during the same general time frame, some profiles were measured 10 years apart, e.g., Dade 1980 and Broward 1979 versus Palm Beach 1990 and Duval 1990. Seasonal shoreline changes in Florida are relatively small however.




Average Sediment Size in mm

River

Figure 5-1. Variation in sediment median diameter, in millimeters, -along the east coast of Florida for all of the sediment samples analyzed.




Average Sediment Size in mm

Nassau Duval St Johns Flagler Volusia
Brevard Indian River St Lucie Martin Palm Beach Broward

Dade

Figure 5-2. Variation in sediment median diameter, in millimeters, along the east coast of Florida for all of the sediment samples collected at the waterline.




Average Sediment Size in mm

Indian River

Figure 5-3. Variation in sediment median diameter, in millimeters, along the east coast of Florida for all of the sediment samples collected at 0.9 meters depth.




Figure 5-4. Variation in sediment median diameter, in millimeters,. along the east coast of Florida for all of the sediment samples collected at .1.8 meters depth.




Average Sediment Size in mm

Figure 5-5. Variation in sediment median diameter, in millimeters, along the east coast of Florida for all of the sediment samples collected at 3.7 meters depth.




Average Sediment Size in mm

Johns

D Indian River
S K St Lucie
Martin
K Palm Beach
RO Broward
DAD Dade
Figure 5-6. Variation in sediment median diameter, in millimeters, along the east coast of Florida for all of the sediment samples collected at 5.5 meters depth.




Average Sediment Size in mm

Johns

River

Figure 5-7. Variation in sediment median diameter, in millimeters, along the east coast of Florida for all of the sediment samples collected at 7.3 meters depth.




Average Sediment Size in mm

Figure 5-8. Variation in sediment median diameter, in millimeters, along the east coast of Florida for all of the sediment samples collected at 9.1 meters depth.




0.155 0.15
.0.145 S0.14 10.135 S0.13
0.125

U.]

.1
Z .
-71
0

0 10 200 300 400 500 600 700 800 90
Distance. from Waterline [mj
B
DUVAL County: Range-027

100 200 S00 400 500 S00 700
Distance from Waterline [ml

800 go0

Figure 5-9. Best performance of predicted profiles: (A) cross-share variation in sediment median diameter, in mm; and (B) measured beach profile (solid line), calculated equilibrium beach profile: (1) without the gravity term (dotted), and (2) with the gravity. term (dashed) for Range number 27 in Duval County, Florida.

* I I I I

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

. . . . . . . . . . . . . . . . . .......... ........... ...................... ;.* .........
............... ........... ....................... .................................. ...........
. . . . . . . . . . .
.................... ........... ...................... ...........
.................................. .......... .......... .... ..........................................
........... .......... ....................... ........... ...........
. . . . . ... . . . . . . . . . . . I . . . . . . . . . . . . . . . . . . . . .........




0.5
-0.
*0.6
E
0.5
C 0.4
*0.
0

70 so go 100

BROWARO County: Range-OSI

10 20 30 40 s0 s0
Distance from Waterline [m]

70 s0 g0 100

Figure 5-10. Worst performance of predicted profiles: (A) cross-shore variation in sediment median diameter, in mm; and (B) measured beach profile (solid line), calculated equilibrium beach profile: (1) without the gravity term (dotted), and (2) with the gravity term (dashed) for Range number 1 in Broward County, Florida.

I I ~ I I I

.......... ................. .......... *...................
. . ~~ . . . . . . . . . . . . . . . . . ... . . . . .

10 20 30 40 so s0
Distance from Waterline [m)

V
-0.5
.1
0
z
5 -2.5
.3
-3.5
.4'
0

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




1.8m
6
4.
3
z#
0'
0 20 40 60 80 100 120 140 160 18(
relative distance from North to South

Figure 5-11. Longshore distribution of RMS values based on cumulative deviations of the calculated equilibrium beach profile: (1) without the gravity term (solid) and (2) with the gravity term (dotted) from the measured profile out to 1.8 meters depth.




3.7m
6
4
3
2
0-
0 20 40 60 80 100 120 140 160 18
relative distance, from North to South

Figure 5-12. Longshore distribution of RMS values based on cumulative deviations of the calculated equilibrium beach profile: (1) without the gravity term (solid) and (2) with the gravity term (dotted) from the measured profile out to 3.7 meters depth.




7.3m
4
3.
0
1.
0 20 40 60 80 100 120 140 160 18
relative distance from North to South

Figure 5-14. Longshore distribution of RMS values based on cumulative deviations of the calculated equilibrium beach profile: (1) without the gravity term (solid) and (2) with the gravity term (dotted) from the measured profile out to 7.3 meters depth.




55
5.5m
6
4
'3
2
1 0
0 20 40 60 80 100 120 140 160 180
relative distance from North to South
Figure 5-13. Longshore distribution of RMS values based on cumulative deviations of the calculated equilibrium beach profile: (1) without the gravity term (solid) and (2) with the gravity term (dotted) from the measured profile out to 5.5 meters depth.




56

9.lm
6,
S.
4

C23
00.
AP" + W" I
o4
0 20 40 60 8 100 120 140 160 18
distance from North to South
Figure 5-15. Longshore distribution of RMS values based on cumulative deviations of the calculated equilibrium beach profile: (1) without the gravity term (solid) and (2) with the gravity term (dotted) from the measured profile out to 9.1 meters depth.




A)1020 1 0
ditnefo hrln m
Fiue51.Aeaemaue4rfl sldlieadaeaecluae qiiru ec
prfl:()wtottegaiytr dte)ad 2 ihtegaiytr dse)frteetr eas costofFlria




.7
A)to2 z 0
ditnefo hrln m
Fiue51.Aeaemaue.rfl sldlieadaeaecluae qiiru ec
prfl:()wtottegaiytr dte) n 2 ihtegaiytr dse) n maiu n iiu esrddph tik oi ie o asuCutFoia




0f
41
0 1;0 U'O 2;0 2;0 300 30 400 40. 300
distance from shoreline [m]
Figure 5-18. Average measured profile (solid line), and average calculated equilibrium beach profile: (1) without the gravity term (dotted) and (2) with the gravity term (dashed), and maximum and minimum measured depths (thick solid line) for Duval County, Florida.




T
0 ; ; S 0
ditnefo hrln m
Fiue51.Aeaemaue0rfl sldlieadaeaecluae qiiru ec prfl:()wtottegaiytr dte) n 2 ihtegaiytr dse) n maiu an.iiu3esrddphs(hc oi ie o S.JhsCutFoia




4
-7
50 100 SO 200 250 300 310 4050 Soo
distance from shoreline [m]
Figure 5-20. Average measured profile (solid line), and average calculated equilibrium beach profile: (1) without the gravity term (dotted) and (2) with the gravity term (dashed), and maximum and minimum measured depths (thick solid line) for Flagler" County, Florida.




.4
d
T
0 200 ;0 400 500
distance from shoreline [im]
Figure 5-21. Average measured profile (solid line), and average calculated equilibrium beach profile: (1) without the gravity term (dotted) and (2) with the gravity term (dashed), and maximum and minimum measured depths (thick solid line) for Volusia County, Florida.




63
-3
z 4
4
0 50 100 ISO 20 0Jo 300 IS 400
disance from shoreline [m]
Figure 5-22. Average measured profile (solid line), and average calculated equilibrium beach profile: (1) without the gravity term (dotted) and (2) with the gravity term (dashed), and maximum and minimum measured depths (thick solid line) for Brevard County, Florida.




04
..02
"U
0 0 0 40 so 60 70 so
distance from shoreline rm]
Figure 5-23. Average measured profile (solid line), and average calculated equilibrium beach profile: (1) without the gravity term (dotted) and (2) with the gravity term (dashed), and maximum and minimum measured depths (thick solid line) for Indian River County, Florida.




65
.
zJ .0
0
distance from shoreline [m]
Figure 5-24. Average measured profile (solid line), and average calculated equilibrium beach profile: (1) without the gravity term (dotted) and (2) with the gravity term (dashed), and maximum and minimum measured depths (thick solid line) for St. Lucie County, Florida.




.4
.7
4"
.10 -- -- - T
0 100 2;0 6 400 300 600 70
distance from shoreline [Im]
Figure 5-25. Average measured profile (solid line), and average calculated equilibrium beach profile: (1) without the gravity term (dotted) and (2) with the gravity term (dashed), and maximum and minimum measured depths (thick solid line) for Martin County, Florida.




67
LI
.
a1 1;0 2; o 4, 5; 6
distance from shoreline [m]
Figure 5-26. Average measured profile (solid line), and average calculated equilibrium beach profile: (1) without the gravity term (dotted) and (2) with the gravity term (dashed), and maximum and minimum measured depths (thick solid line) for Palm Beach County, Florida.




b
.7
0 S 100 11 200 230 300 310 400
distance from shoreline [ml
Figure 5-27. Average measured profile (solid line), and average calculated equilibrium beach profile: (1) without the gravity term (dotted) and (2) with the gravity term (dashed), and
maximum and minimum measured depths (thick solid line) for Broward County, Florida.




0f
z
-3.S
-,
10 2o 30o SO so o a
distance fromshoreine [m]
If
Figure 5-28. Average measured profile (solid line), and average calculated equilibrium beach profile: (1) without the gravity term (dotted) and (2) with the gravity term (dashed), and maximum and minimum measured depths (thick solid line) for Dade County, Florida.




70
equivalent
displacements
y = (h/A)^(3/2) \ y = (h/A)^(3/2) + (hBSL)
." 1 1'% y= (blBSL)
relative distance from shoreline
Figure 5-29. Generalized representation of the relationship between the EBP calculation: (1) without the gravity term (dotted), and (2) with the gravity term (dashed); the gravity term alone
is also shown (solid).




71

1.8m
1'
).9
}.,7.
'.7o
1.1"
Us
0 20 40 60 80 100 120 140 160 1-0
relative distance from North to South
Figure 5-30. Longshore variation in best fit A (solid line) and m (solid line with symbols)
parameters as well as A (dotted line) for m=2/3 from curve fit analysis of h=Ay" to measured beach profiles out to a depth of 1.8 meters.




3.7m
1*
0.9
1.7,
.4o
0 20 40 60 80 100 1 140 160 180
relative distance from North to South
Figure 5-31. Longshore variation in best fit A (solid line) and m (solid line with symbols) parameters as well as A (dotted line) for m=2/3 from curve fit analysis of h=Af to measured beach profiles out to a depth of 3.7 meters.




73.
5.5m
).9
II
.4
0o 20 ;3 k 160 1o 11 1]o 180
relative distance from North to South
Figure 5-32. Longshore variation in best fit A (solid line) and m (solid line with symbols) parameters as well as A (dotted line) for m=213 from curve fit analysis of h=Ayf to measured beach profiles out to a depth of 5.5 meters.




7.3m
I
1.9
.5
.4
).1 ;
0 20 40 60 80 100 120 140 10 180
relative distance from North to South
Figure 5-33. Longshore variation in best fit A (solid line) and m (solid line with symbols) parameters as well as A (dotted line) for m=2/3 from curve fit analysis of h=Ay" to measured beach profiles out to a depth of 7.3 meters.




9.1m
13
20 40 0 80 10 10 10 10 10
bec roie ott deptf. etes
0.6
aD
I 01
C3 13
0U
0! i t I
0 20 40 60 80 160 110 14o 10 180
relative distance from North to South
Figure 5-34. Longshore variation in best fit A (s-lid line) and m (solid line with symbols) parameters as well as A (dotted line) for m=213 from curve fit analysis of h=Ay" to measured beach profiles out to a depth of 9.1 meters.




0.07 0.08 0.09 0.1 o.1 0.12
A parameter [m^ 113]

0.13 0.14 0.15

Figure 5-35. Variation of A parameter with median sediment size. A parameter is bestfit value to depths of 1.8,3.7, 5.5, 7.3, and 9.1 meters. Sediment size is average of all samples which extend from the waterline to each of the designated depths.

0 5.

03
0.45
0.4
-035
030.25
0.2
0.15-

ni S.

0.06

ner
U n




0.07 0.08 0.09 0.1 0.11 0.12
A parameter m ^ 1/3]

Figure 5-36. Scatter plot of average county A values out to 1.8 meters depth versus sediment size averaged over all profiles in county and over all landward samples in each profile.

' 0.4" 0.35'
03
0.5
0.2
015

U
U
U
U
U
U
U
U
U
U
U
U

0.06

0.13 0.14 o.5

9




U.43
0.4
0.35
0.3
0.25 U
0.2"
U
n~t ,

0.07

o. o.9 .1 01 0.12
A parameter [m^ 1/3]

0.13

0.14 0.15

Figure 5-37. Scatter plot of average county A values out to 3.7 meters depth versus sediment size averaged over all profiles in county and over all landward samples in each profile.




0.11
A parameter [m ^ 1/3]

Figure 5-38. Scatter plot of average county A values out to 5.5 meters depth versus sediment size averaged over all profiles in county and over all landward samples in each profile.

79

0.45 .

0.4
033
0.3"
02
0.2-

U
U
a
U
U
U
U
U
U
U U

(1~1*I

0.08




U -"
".U
0.08 0.09 0.1 0.11 0.120.
A parameter [m ^1/3]

Figure 5-39. Scatter plot of average county A values out to 7.3 meters depth versus sediment size averaged over all profiles in county and over all landward samples in each profile.

045 0.4
035"
0.3
40
I!
I
0.2
0.15.
0.1
0.07




0.4

0.35
03*
tlro
"0.250.2
0.15
0.0

9

0.095

0a05p
Aparameter [m^ 1/3]

Figure 5-40. Scatter plot of average county A values out to 9.1 meters depth versus sediment size averaged over all profiles in county and over all landward samples in each profile.

U
U
U
U
U
U
U

0.115




I --F- A parameter -9- cumulative size I

1.8 meters depth

county code

Figure 5-41. Plots of average county A values out to 1.8 meters depth and sediment sizes averaged out to that depth. County code denotes the county sequence commencing from the north on Florida's east coast.




83

3.7 meters depth

county code

--I- A parameter --6- cumulative size I

Figure 5-42. Plots of average county A values out to 3.7 meters depth and sediment sizes averaged out to that depth. County code denotes the county sequence commencing from the north on Florida's east coast.




5.5 meters depth

county code

I-+- A parameter -S--.cumulative size I

Figure 5-43. Plots of average county A values out to 5.5 meters depth and sediment sizes averaged out to that depth. County code denotes the county sequence commencing from the north on Florida's east coast.




1 -4- A parameter --a- cumulative size I

7.3 meters depth

county code

Figure 5-44. Plots of average county A values out to 7.3 meters depth and sediment sizes averaged out to that depth. County code denotes the county sequence commencing from the north on Florida's east coast.




9.1 meters depth

county code

-+- A parameter -E cumulative sizeI

Figure 5-45. Plots of average county A values out to 9.1 meters depth and sediment sizes averaged out to that depth. County code denotes the county sequence commencing from the north on Florida's east coast.




87

I I
profile I
displcmft
I I
relative distance from shoreline

Figure 5-46. Illustration of effect of a seaward displacement of the equilibrium profile, possibly by an offshore reef.