Citation
Equilibrium beach profiles

Material Information

Title:
Equilibrium beach profiles concepts and evaluation
Series Title:
UFLCOEL-94013
Creator:
Dean, Robert G ( Robert George ), 1930-
Charles, Lynda L., 1962-
Florida Sea Grant College
University of Florida -- Coastal and Oceanographic Engineering Dept
Place of Publication:
Gainesville Fla
Publisher:
Dept. of Coastal and Oceanographic Engineering, University of Florida
Publication Date:
Language:
English
Physical Description:
v, 22, 14 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Coast changes -- Mathematical models ( lcsh )
Beach erosion -- Mathematical models ( lcsh )
Beach nourishment -- Mathematical models ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 20-22).
General Note:
"August 30, 1994."
Funding:
This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
Statement of Responsibility:
prepared for Florida Sea Grant College Program, University of Florida ; prepared by Robert G. Dean, Lynda Charles.

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University of Florida
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University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
31795612 ( OCLC )

Full Text
UFL/COEL-94/013

EQUILIBRIUM BEACH PROFILES: CONCEPTS AND EVALUATION
by
Robert G. Dean Lynda Charles

August 30, 1994
Prepared for: Florida Sea Grant College Program University of Florida Gainesville, FL 32611




UFL/COEL-94/013

EQUILIBRIUM BEACH PROFILES:
CONCEPTS AND EVALUATION
August 30, 1994
Prepared for: Florida Sea Grant College Program
University of Florida Gainesville, Florida
Prepared by: Robert G. Dean Lynda Charles
Department of Coastal and Oceanographic Engineering
University of Florida Gainesville, Florida




TABLE OF CONTENTS

LIST' OF FIGURES .
LIST OF TABLES .
INTRODUCTION .
BACKGROUND .
OBJECTIVES .
FIELD PROCEDURES .
ANALYSIS AND RESULTS . . . . . . . .
Variation of Beach Slope With Sediment Size .
Comparisons of Measured and Predicted Profiles SUMMARY AND INTERPRETATION . . . . . .
CONCLUSIONS AND RECOMMENDATIONS . . . . . ACKNOWLEDGEMENTS . . . . . . . . .
REFERENCES .

v
6 7 7 7
17 19
20

20

APPENDIX

GRAPHICAL PRESENTATIONS OF FLORIDA EAST COAST AND COUNTY BY COUNTY CROSS-SHORE DISTRIBUTIONS OF SEDIMENT AND PROFILE CHARACTERISTICS . . . A-1




LIST OF FIGURES

FIGURE PAGE
1 Variation of Sediment Scale Parameter, A, With Sediment
Size, D, and Fall Velocity, wf. From Dean (1987) . . 4
2 Numbers of DNR Monuments Along Florida's Predominantly
Sandy Shoreline Counties . . . . . . . . 8
3 Variation of Average Profile Slope with Average
Median Diameter, Both to Approximately 2 m, Depth.
Comparison of County Averages (Points) and Equilibrium
Beach Profile Theory (Line) . . . . . . . 10
4 Blindfolded Comparison of Average Measured and Predicted
Profiles. Based on Moore's Relationship. All Twelve
Florida East Coast Counties . . . . . . . 12
5 Blindfolded Comparison of Average and Predicted Profiles.
Based on Kriebel et al. (1991) Relationship. All Twelve
Florida East Coast Counties . . . . . . . 15
6 Comparison of Average Measured and Computed Profiles.
Based on A = 0. 1 m1/3. All Twelve Florida East Coast
Counties 16
A-1 All Counties. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . ... . . . . . A-2
A-2 Nassau County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . . . . . . . A-3
A-3 Duval County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . . . . . . . A-4
A-4 St. Johns County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . . . . . . . A-5

iii




A-5 Flagler County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . . . . . . . A-6
A-6 Volusia County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average ... . . . . . . . A-7
A-7 Brevard County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . . . . . . . A-8
A-8 Indian River County. a) Cross-Shore Distribution of
Average Median Sediment Size. b) Blindfolded Comparison
of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of
Profiles Contributing to Average . . . . . . A-9
A-9 St. Lucie County. a) Cross-Shore Distribution of
Average Median Sediment Size. b) Blindfolded Comparison
of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of
Profiles Contributing to Average . . . . . A-10
A-10 Martin County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . . . . . . A-11
A-11 Palm Beach County. a) Cross-Shore Distribution of
Average Median Sediment Size. b) Blindfolded Comparison
of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of
Profiles Contributing to Average . . . . . A-12
A-12 Broward County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . . . . . . A-13
A-13 Dade County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . . . . . . A-14




LIST OF TABLES

TABLE PAGE
1 Summary of Recommended Sediment Scale Parameter (A)
Values (From Dean, 1994) 5
2 Summary of Data Characteristics . . . . . . 9
3 Comparison of Measured and Computed Depths . . . 14
4 Standard Deviations for Various Depths and Sediment
Scale Parameter, A, Relationships . . . . . 18




EQUILIBRIUM BEACH PROFILES:
CONCEPTS AND EVALUATION
INTRODUCTION
Equilibrium beach profile (EBP) methodology is useful for a variety of engineering applications, including beach nourishment with materials different than the native and incorporation as an
element of some cross-shore sediment transport models. EBP's are also an essential stepping stone to the understanding of the behavior of profile dynamics. Sediment particles forming all
profiles are acted on by a number of forces, some of which act seaward and others act landward. By definition, for EBP's, these
forces are in balance. An equilibrium beach profile might be considered as one which would occur if the forcing (dominantly waves and water levels) were held constant for a sufficiently long
time for the sediment transport resulting from the force imbalance to mold the profile to one in which the forces are in balance. In
nature, profiles may never achieve equilibrium under the constantly changing tides and waves, a complicating factor in studies of this type. In some locations, the average seasonal shoreline fluctuations may amount to more than 30 meters, however, in Florida, these fluctuations are generally less than 10 m. The time scales associated with the equilibration process vary with water
depth, being shorter in the more dynamic environment of the shallow nearshore waters and much longer where waves may break on the order of once annually or so. These characteristics raise questions as to whether or not studies of natural profiles can contribute to the understanding of the subject of equilibrium beach profiles.
Attempts, to predict the quantitative characteristics of equilibrium beach profiles based on sediment characteristics are fairly recent and there have been no comprehensive studies to evaluate existing methodology and, if necessary, to carry out the necessary refinements. This study was conducted to address this question.
BACKGROUND
EBP's have been a subject of considerable interest to Coastal
Engineers and Marine Geologists for many years. Several features of EBP's are known based on observations: (1) They tend to be concave
upward, (2) Their slopes are greater for coarser materials, and (3) Higher waves result in milder slopes.
Keulegan and Krumbein (1919) investigated the characteristics of mild bottom slopes such that the waves never break but rather are continually dissipated by energy loss due to bottom friction. Bruun (1954) examined a number of beach profiles from the Danish
North Sea and Monterey Bay, California and concluded that they could be represented reasonably well by the simple relationship




h =Ay 2/3 (1)
in which h is the depth at a distance y from the shoreline, and A is a sediment scale parameter. Eagleson, Glenne and Dracup (1963)
developed a complex characterization of the wave and gravity f orces acting on a particle located outside the zone of "appreciable breaker influence" and developed expressions for the seaward limit of motion and f or the beach slope for which a sand particle would be in equilibrium.
Swart (1974) carried out a series of wave tank tests and developed empirical relationships relating prof ile geometry and transport characteristics to the wave and sediment conditions. The active profile was considered as four zones and empirical expressions were developed for each zone. Vellinga (1983) investigated dune erosion using wave tank tests and developed the
following "erosion profile" which included the effect of deep water significant wave height, Hos and sediment fall velocity, wf,
7-6) h=0. 47 [(- )1.28 ( ) 0.56 y+18]0-5 -2. 0 (2)
H., H,, 0.0268
in which all of the values are expressed in the metric system. It can be shown that Eqs. (1) and (2) are in reasonable agreement for wave heights on the order of 1 m; however, for large wave heights, increased slopes are predicted by Eq. (2) for water depths inside the breaking zone which is contrary to nature.
Two of the disadvantages of Eq. (1) are that the slope of the
profile at the shoreline is infinite and the scale parameter, A, is not non-dimensional but rather has dimensions of length to the onethird power. Dean (1977) considered EBP's to be the result of (unknown) constructive forces and several candidate destructive forces: (1) Wave energy dissipation per unit volume, (2) Wave energy dissipation per unit surface area and (3) Uniform bottom shear stress due to oblique waves. It was found that for all three
destructive forces, the EBP could be represented by an equation of the form
h=Aym (3)
in which the exponent m was found to be 2/3 for the case of wave
energy dissipation per unit volume and 2/5 for the other two destructive forces. Dean (1977) examined over 500 profiles
collected by Hayden et al. (1975) extending from the eastern end of Long Island, NY south around the Florida peninsula to the Texas/Mexico Border. Best least squares fits were carried out for these profiles for the scale parameter, A, and the exponent, m. A histogram of the 500+ m values showed a reasonably wide range with a clear peak at a value of 2/3, In an attempt to provide a basis
for extending Eq. (1) in a prognostic manner, Moore (1982) examined




a number of beach profiles from nature and laboratory conditions and expressed the values of the sediment scale parameter, A, as a function of sediment size, D. This is shown in a slightly modified f orm (by Dean, 1987) in Figure 1. Dean has shown that if the A versus D relationship is transformed to an A versus fall velocity relationship, the result is
A=0 067 w24 (4)
thereby potentially allowing calculation of profiles composed of
other shapes than are typical for sands, f or example, shell. Because the material comprising most beaches lies within a fairly
narrow size range, say 0. 1 mm to 1. 0 mm, and because of the dif ficulty of reading this range from Figure 1, Dean (1994) has developed the tabulation presented in Table 1 which ranges from a
sediment size, D, of 0.1 mm to 1.09 mm. As noted in the footnote to the table, although the tabulated values are presented to f our significant figures in some cases, this does not imply that the values are known to this accuracy, but merely ensures that two individuals carrying out calculations involving EBP's would obtain the same results. Figure 1 will be referred to as "Moore's curve".
To remove the infinite slope at the shoreline inherent in Eq. (1), Dean (1991) has shown that consideration of gravity as a destructive force yields
y h +h3"2 (5)
m A312
which can be shown to approximate a linear slope, m, in shallow water and Eq. (1) in deep water. Larson (1988) and Larson and Kraus (1989,1990) have shown that Eq. (5) can also be obtained alternatively by considering the more complete breaking wave model
of Dally et al. (1985). Exponential EDP's having the following form have been proposed by Bodge (1992) and Komar and McDougal (1993).
h = h0(i-e-ky) (6)
Neither Bodge nor Komar and McDougal present a basis for applying their EBP's in design.
Inman et al. (1993) analyzed 23 historical profiles from the San Diego region and have recommended a form for equilibrium beach profiles that consists of two independent segments (for the inner
and outer portions of the profile) each f it by the form of Eq.
(3), generalized as
h-h0 = A(y-y0)m (7)
The inner segment is allowed a vertical offset relative to mean sea level (thus avoiding the infinite slope at the waterline) and the outer segment is allowed a horizontal offset. Fits to each profile
required determination of 7 parameters. It was found that this




SEDIMENT FALL VELOCITY, wf (cm/s)
1.0 10.0

Suggested Empirica Relationship A vs D
From Hughes' Field Results From Individual Field Profiles where a Range of Sand Sizes was Given

7 r
From Swan's / Laboratory Results

1.8
0.10

__ _ _ __ _ _I I__ _ __ _ _

31

I
(Moore)

.7

Based on Transforming A vs D Curve using Fall Velocity Relationship

10.0

100.0

A = 0.067 w10.44

100.0

SEDIMENT SIZE D (mm)

Figure 1. Variation of Sediment Scale Parameter, A, With Sediment Size, D, and Fall velocity, wf. From Dean (1987).

I1

0

0.01I
0.C




Table 1
Summary of Recommended Sediment Scale Parameter (A) Values (From Dean, 1994)

rD(mm) 0.00 ( 0.01 I 0.02 I 0.03 I 0.04 1 0.05 I 0.06 0.07 0.08 T 0.09
0.1 0.063 0.0672 0.07 14 0.0756 0.0798 0.084 0.0872 0.0904 0.0936 0.0968
0.2 0.100 0.103 0.106 0.109 0.112 0.115 .0.117 0.119 0.121 0.123
0.3. 0.125 0.127 0.129 0.131 0.133 0.135 0.137 0.139 0.141 0.143
0.4 0.145 0.1466 0.1482 0.1498 0.1514 0.153 0.1546 0.1562 0.1578 0.1594
0.5 0.161 0.1622 0.1634 0.1646 0.1658 0.167 0.1682 0.1694 0.1706 0.1718
0.6 0.173 0.1742 0.1754 0.1766 0.1778 0.179 0.1802 0.1814 0.1826 0.1838
0.7 0.185 0.1859 0.1868 0.1877 0.1886 0.1895 0.1904 0.1913 0.1922 0.1931
0.8 0.194 0.1948 0.1956 0.1964 0.1972 0.198 0.1988 0.1996 0.2004 0.2012
0.9 0.202 0.2028 0.2036 0.2044 0.2052 0.206 0.2068 0.2076 0.2084 0.2092
1.0 0.210 0.2108 10.2116 0.2124 0.2132 0.2140 0.2148 0.2156 0.2164 0.2172
Notes:
(1) The A values above, some to four places, are not intended to suggest that they are known to that accuracy, but rather are presented for consistency
and sensitivity tests of the effects of variation in grain size.
(2) As an example of use' of the values in the table, the A value for a median sand size of 0.24 mm is: A = 0. 112 mn"3. To convert A values to feet
units, multiply by 1.5.




method provided a significantly improved fit over the EBP form being tested here in which only one free parameter existed. No basis was presented for applying this method to engineering problems or to test it in a "blindfolded" manner.
Most applications and evaluations of the EBP concepts have been conducted considering a single sediment size across the
profile. Exceptions include Larson (1991), Work and Dean (1991) and Dean, et al (1993) who carried out evaluations of the equilibrium beach profile theory considering variations of sediment size over the profile. Larson, noting the sediment sorting that occurs over
most profiles, developed an analytical form of the wave energy dissipation per unit volume that varied exponentially across the
prof ile. Additionally, he f it a f orm, of the prof ile with a unif orm A value and allowed for a shift in the shoreline position. It was
found, based on fits to profiles at three locations, that the exponential relationship provided the best fit. Although these evaluations were based on best fit approaches rather than
blindfolded, Larson did comment on the relationship between the best fit values and those based on the Moore relationship. It was
found in two cases that the agreement was reasonable and that significant differences existed in the third case. Work and Dean
(1991) carried out both blindfolded and best fit tests for profiles at four locations. It was found that the blindfolded tests agreed reasonably well with the measured profiles out to depths of approximately 1.5 to 6 m in three of the cases, but underpredicted
the depth by a factor of approximately two in the fourth case. Dean et al. (1993) carried out blindfolded comparisons for ten profiles on the north island of New Zealand. In this study, the A vs D relationship of Moore (1982) was used with the EBP form that includes a finite slope at the water line (Eq. 5) Thus, although these comparisons were not entirely consistent as the Moore relationship was determined based on the EBP relationship without
the slope term, it was found that reasonably good agreement was obtained in nine of the ten cases for which blindfolded comparisons were carried out. It was shown that the blindfolded profiles agreed better with the measured profiles than the average of the measured profiles.
Finally, EBP approaches presented and evaluated here are not
meant to apply to three dimensional situations or extraneous influences such as near inlets where other agents are operative or where rock outcrops and reefs are present.
OBJECTIVES
The general objectives of the present study were, through comprehensive field data collection and analysis efforts, to evaluate existing EBP methodology and, as appropriate, to develop improvements. Specifically, the intent was to compare some of the
basic tenets of the EBP theory, one of which is that the beach profile slope depends on the sediment size. Secondly, calculated
profiles based on the cross-shore distribution of sediment sizes




and existing EBP theory (Eq. I and Moore's curve) will be compared with the measured and the applicability of the theory will be evaluated. Based on the results of this comparison, the theory may be modified as appropriate. Finally, potentially productive approaches for future efforts will be identified.
FIELD PROCEDURES
The field data utilized here were collected along the twelve
sandy beach counties of the east coast of Florida ranging from Nassau County on the north through Dade County to the south. The
data were collected along selected Department of Natural Resources (DNR) now the Department of Environmental Protection (DEP) profile lines which are spaced nominally at 1000 feet (approximately 328 meters) DNR surveyed every third profile to a nominal depth of 30 feet (9 meters) whereas the intermediate profiles were measured to wading depths (less than 2 meters). Figure 2 presents the twenty four CCCL Counties, twelve along each of the east and west coast counties. The numbers adjacent to each county indicates the number of profiles within that county. Our sediment and other data were collected along the "long" DNR lines and where possible, at every
ninth profile resulting in an approximate spacing of 9000 feet (2.7 km) In some counties this objective was not achieved due to restricted beach access or other reasons. An attempt was made to collect 10 sediment samples across the profile at the following nominal depths: 1 m, 2 m, 4 m, 6 m, 8 m and 9 m depths.
In total, data from 165 profiles and 986 sediment samples were collected and will form the basis of the analysis to be presented in this report. The numbers of profiles and sediment samples for each east coast county are presented in Table 2.
ANALYSIS AND RESULTS
I
Variation of Beach Slope With Sediment Size
One of the basic tenets of EBP methodology is that the equilibrium beach slope increases with sediment size as reflected
in Figure 1 and Table 1. To evaluate this concept, the average profiles for each county were averaged and the average slope out to the approximate 2 m contour was calculated and compared with the average sediment size out to the same contour. The points,
representing county averages in Figure 3 show a clear but somewhat scattered relationship between average beach slope and average sediment size.
Based on Figure 3, it is concluded that there is a correlation between sediment size and profile slope. To test the relationships in Figure 1 and Table 1, the average slope associated with a particular sediment size, D (or equivalently A) was determined from Eq. 1 as




Nassau
(82)
Duval
S(80)
St. Johns
(209)
Flagler (100)
Volusla
(234)

Franklin (239)

Brevard (219) Indian River

Pinellas (193)

(67) %.Sarasota V)l
(183) (12)
Charlotte Palm Beech
(68) (227)
(239) Broward
Cole -(128) (148) 6.b ,,,
Dade
N 0 (113)
Figure 2. Numbers of DNR Monuments Along Florida's Predominantly Sandy Shoreline
Counties.




TABLE 2

SUMMARY OF DATA CHARACTERISTICS
County Number of Number of
Profiles Sediment Samples
Nassau 7 31
Duval 8 44
St Johns 22 138
Flagler 11 75
Volusia 23 153
Brevard 23 143
Indian River 12 66
St Lucie 13 68
Martin 2 12
Palm Beach 23 159
Broward 13 60
Dade 8 37
[ Totals 165 986




0.05
00.04
0 .
0
1.0.03
0
164
04
~0.02
0.01
0.001
0.

. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
............. !............. ............ : ... .... .. ..... .. .. !D D .. ..
............. ............ ............-" i i i i i i i i i i i ii ... .... !.... ....... !.............
.. ........... ............ .... .......... ...................... . . .
. .. ... ... . .. .. .. ...... :. ....... .. .. ... . ....: .... ..... ... 4, ) D .. .. .
............. ............ ... !:. ........ ..... ........ !............ .............
.. . . .:. . .............. . . i . .......... .. ........ ........ . ..... I .. ............ ............s : . . . . . . : . . .
....... ....... ...............on s.
.. . . . . . . . . . . . . .. . . .
o. . . . . . . . .. . . . . . .
. . . . . . . . . . I . . . I . . . . . .

0

0.1 0.2 0.3 0.4 0.5
Average Median Diameter, Dso%, (mm)

0.6

Figure 3. Variation of Average Profile Slope with Average Median Diameter, Both to
Approximately 2 m Depth. Comparison of County Averages (Points) and
Equilibrium Beach Profile Theory (Line).




h A312(8)
The solid line in Figure 3 presents the results of Eq. (8). It is
seen that the relationship correctly portrays the trend, but may be somewhat high.
Comparisons of Measured and Predicted Profiles
The most basic evaluation of the existing EBP theory is founded on a blindfolded comparison of measured and predicted profiles. The "blindfolded" profiles are those based entirely on existing relationships and do not entail any curve fitting or any
other subjective elements. For this purpose, the sediment scale parameter, A, was determined from Table 1 based on the median sediment size and it was assumed that the A value varied linearly
between adjacent sampling locations. This allowed establishment of the equilibrium profile between the two points at offshore
distances, y(n) and y(n+1) in accordance with the following relationship
h(n+1) =[h(n) 3/2 2 (A(n+l) -5/2 -A(n) 5/2) 2/3 (9) 5BB
in which BB is the slope of the A vs y relationship between the two points of interest, ie
BB= A(n+1) -A(n) (10)
y(n+1) -y(n)
This process was repeated to the last point in the profile and various comparisons were carried out between predicted and measured profiles.
The comparison to be presented first is the average of the 165 measured and predicted profiles as shown in Figure 4. The upper panel in this figure presents the distribution of the average grain size across the profile and the numbers in parentheses indicate the number of profiles that contributed to the sediment size at that
location. The lower panel presents a comparison between the average measured and calculated profiles. It is emphasized that the
calculated profiles were determined in a "blindfolded" manner, that is they are based only on knowledge of the measured grain size distribution across the profile and the EBP methods described earlier. It is seen from the lower panel of Figure 3 that the average profiles agree quite well for water depths out to 4 meters, then deviate for greater depths with the measured depths being progressively greater than the calculated. The reason/ interpretation for this deviation will be explored later.
The same type of comparisons as presented in Figure 3 was carried out for the twelve individual counties on the east coat of




0 100 200 300 400 500 600 700
Offshore Distance (in)
a) Measured Sediment Sizes, D50%, (mm)
Averages for 165 Florida East Coast Profiles
............... easured.......................... ..
......Calculated
.. . .. .. .. . . -- - -

0 100

200 300 400 500 600
Offshore Distance (in)

700

b) Comparison of Measured and Predicted Profiles Averages for 165 Florida East Coast Profiles
Figure 4. Blindfolded Comparison of Average Measured and Predicted Profiles. Based on
Moore's Relationship. All Twelve Florida East Coast Counties.

0.7
0.6 0.5
0.4 0.3
0.2 0.1 0.0

I I I I I I
.. ... . . . I .. . . . . .
61):..~.....(t7 ................
I*16 ........

0
-5
-10




Florida: these comparisons along with a repeat presentation of the
results in Figure 4 are presented in Appendix A as Figures A-1 A13 and are discussed as follows. A general result supported by the comparisons was that the county wide average measured and
calculated profiles agreed reasonably well out to 3 or 4 meters and then deviated in the manner shown in Figure 4. This finding is similar to that for the aggregate of all 165 profiles. Table 3 summarizes the average deviation for the twelve counties at approximate depths of 2 and 4 meters.
A second blindfolded test was carried using a sediment scale parameter, A, representation proposed by Kriebel, et al (1991)
2
A=2.25 ( f ) 1/3
9
in which the fall velocity is in m/s and g is the gravitational constant. This form has the advantage of dimensional consistency. To apply Eq.(11), the sediment sizes were converted to fall
velocities using a standard empirical relationship (Rouse, 1937) considering a water temperature of 20' Centigrade. The comparison between the same 165 measured profile averages with those computed based on Eq. (11) is presented in Figure 5. It is seen that this
representation fits reasonably well in water depths less than 2 m, but does not fit as well as Moore's relationship as shown in Figure
4.
An additional evaluation was carried out to determine whether the "All value versus D representation should differ from that shown in Figure 1. Some results from Hughes (1978) suggest that perhaps
the A value is independent of grain size whereas other results from this author suggest that data from the Brevard County area, vary in a manner qualitatively consistent with Figure 1. Several tests were carried out to address this question. The first was to determine whether a single value of the A parameter could provide as good a fit as that based on the measured grain sizes. First, the standard deviations at the various depths were calculated for the
blindfolded calculations. Secondly, the standard deviations were calculated for various constant values of the A parameters. It was found that an A value of 0.1 m113 yielded a particularly good fit, in fact better than that for the blindfolded test (Figure 4) especially in water depths greater than 4 m. The comparison between the measured and calculated profiles for the entire Florida east coast is shown in Figure 6 for a fixed value A = 0.1 nP.
Based on the results shown in Figures 4 and 6, an attempt was
made to determine whether altered values of the A vs D relationship would yield an improved blindfolded test. Since a constant A value
of 0. 1 mY3 had yielded a high quality fit, several tests with the values of A were conducted




TABLE 3

COMPARISON OF MEASURED AND COMPUTED DEPTHS
Nominal Depth Nominal Depth
of 2 to 3 meters of 3 to 4 meters
County
Average Average Average Average
Measured Calculated Measured Calculated
Depth (m) Depth (m) Depth (m) Depth (m)
Nassau 2.61 2.83 4.57 3.68
Duval 1.83 1.94 3.66 3.55
St Johns 1.91 2.02 3.74 3.61
Flagler 1.83 1.64 3.66 3.07
Volusia 2.15 2.42 3.98 3.97
Brevard 2.63 2.50 4.46 3.43
Indian River 1.83 2.00 3.99 5.00
St Lucie 1.83 1.42 4.65 4.76
Martin 1.83 1.94 3.66 3.72
Palm Beach 1.83 1.94 3.66 3.74
Broward 1.83 1.49 3.99 3.69
Dade 1.83 2.12 3.66 2.74
Overall 2.03 2.05 3.99 3.76
Average I I




0.7 0.6 0.5
0.4 0.3 0.2
0.1 0.0

200 300 400
Offshore Distance (r

500 600 700

a) Measured Sediment Sizes, D50%, (mm)
Averages for 165 Florida East Coast Profiles

0 100

200 300 400 500 600
Offshore Distance (m)

b) Comparison of Measured and Predicted Profiles Averages for 165 Florida East Coast Profiles
Figure 5. Blindfolded Comparison of Average and Predicted Profiles. Based on
Kriebel, et al (1991) Relationship. All Twelve Florida East Coast Counties.

0 100

I I I I I I
... . . . . .... .. ... .. .% m ) ....
. .......... ........
........... 6 .................(
"( 1 .... i.......... ............ ........... ....... I
... .................. .......... '.... ................
......
........... ........... :............: ........... ........... o........... ...........

0
-5
-10

0
0
-41

.. Kriebels iMetd ForDetermining.A..
.......... ........... .. . ... ....... ..... . % ....... ...........
...... ............. ......... 0- Measured
*A .. Calculated

700




0.7 0.6 0.5
0.4 0.3
0.2 0.1
0.0

0 Constant A.Value:
-5........
-10 I I I I
0 100 200 300 400
Offshore Distance

500
(M)

600 700

b) Comparison of Measured and Predicted Profiles
Averages for 165 Florida East Coast Profiles
Figure 6. Comparison of Average Measured and Computed Profiles. Based on A = 0.1 in.
All Twelve Florida East Coast Counties.

I I I I I I
. . . . : . . .: . . . ... . . . . . ..... . . . ..-- -. .. ..C-m [. . .
.. .... ..... ........... .. ......... ..........
.-q i6 .!.......... ........... !........... : ......... D 50% ... .. .. ----.. ..
. ......... . ( 4... . ...........
... ...,,- ... .. ..: ... 'T......... . .. .. ... 1..'... ..... ... ....
.. . .. -.. . ..'. . .. ........... :............ -. .. .............
....... (161):..........47) .. ...(118) .....
. ......... .......... . .......... ..... ....... . .... . .i .........
. ........... .......... ........... ........... ........... .......... ...........
, I I I I
) 100 200 300 400 500 600 700
Offshore Distance (m)
a) Measured Sediment Sizes, D50%, (mm) Averages for 165 Florida East Coast Profiles




ANEW= 0. 1 +F (AMOORE-0 1) (12)
such that if the f actor, F, is unity, the value of the new A is the same as that from Moore's curve (Figure 1 and Table 1) and if the factor, F, is zero, the value of the new A is always 0.1 m 1/3. The standard deviations for these tests are presented in Table 4 for F values of 0, 0.1, 0.2 ...... 1.0. In general, it is seen that for
the shallower depths, the standard deviations are smallest for a F
value of approximately 0.5 whereas for greater depths, a F value of zero, corresponding to a constant A value of 0.1 m 1/3 yields the smallest standard deviation. These results will be interpreted in the following section.
SUMMARY AND INTERPRETATION
In summary, although it is not known whether the profiles being examined are in equilibrium, because of the shorter response times, it is reasonable to consider the shallower portions of the profiles to be in equilibrium, at least on the average. Although
there are considerable differences between the county wide measured and calculated profile averages, for depths less than 4 m, these
differences appear to be unbiased (Table 2) based on Moore"s relationship.
Comparisons were carried out to determine whether there was a clear dependency of the beach slope with grain size. For this purpose, the data were organized by county and the average profile slope to the nominal 2 meter depth was compared with the average
grain size to this depth. The results are presented in Figure 3 where it is shown that, indeed there is a correlation between grain size and average slope.
It was found, based on blindfolded comparisons of profiles that, particularly in those depths greater than 4 meters, a constant value of A = 0.1 m 1/3 yields a somewhat improved fit over that based on Moore's curve. In interpreting these results, it is
important to consider that the shallower and deeper portions of the profile experience different forces. Inside the breaking zone the effects of breaking waves are to cause an additional destructive
force acting on the bottom and thus a milder beach slope. Of course, at any point along the east coast of Florida, there is a
range of wave heights affecting the profile. The percentage of time that waves are breaking decreases from approximately loot at the
shoreline to a very small percentage for water depths greater than 3 to 4 meters. Thus, at any given water depth, the profile slope
reflects the percentages of times that waves are breaking versus not breaking. Since the form of the EBP being evaluated herein is




Standard Deviations Between Measured and Calculated Depths (m) Factor For the Following Measured Water Depths (m)
F 0.94 2.03 3.99 5.85 7.60 9. 1=4
0.0 0.39 0.60 1.06 1.23 1.47 1.90
0.1 0.38 0.57 1.04 1.24 1.53 2.00
0.2 0.38 0.56 1.08 1.26 1.61 2.11
0.3 0.37 0.55 1.03 1.30 1.71 2.24
0.4 0.37 0.54 1.05 1.36 1.83 2.37
0.5 0.37 0.55 1.07 1.44 1.95 2.52
0.6 0.37 0.56 1.11 1.53 2.08 2.67
0.7 0.38 0.58 1.16 1.63 2.22 2.82
0.8 0.39 0.60 1.21 1.74 1 2.37 2.98
0.9 0.40 0.63 1.27 1.86 2.51 114 1
1.0 0.41 0.66 1.34 1.98 2.67 3.30 _] I

TABLE 4

STANDARD DEVIATIONS FOR VARIOUS DEPTHS AND SEDIMENT SCALE PARAMETER, A, RELATIONSHIPS




based on a breaking wave regime, it may be appropriate to limit the comparison to water depths of 2 to 3 meters.
It is of interest to note that a depth of about 4 m
corresponding to the approximate depth to which the profiles agreed using Moore's relationship is also a reasonable depth to which the sand.is activated by breaking waves along the Florida east coast. Dean and Grant (1989) have estimated that the so-called "depth of
closure" ranges from approximately 5.8 m at the north end of Nassau County to 4.3 m at the south end of Dade County. The findings that the profile shapes differ within and outside the zone of reasonably active breaking are consist with our understanding of the forces forming EBP's and provide the basis for the following interpretation. Within the generally active surf zone, there are
both constructive an destructive forces acting. Seaward of this region, one of the destructive forces, the equivalent offshore bottom shear stress drive by the gradient of the momentum flux is
not active. This changes the force balance, with the onshore bottom forces larger that the offshore forces relative to the breaking zone. This, in turn results in a steeper beach profile.
CONCLUSIONS AND RECOMMENDATIONS
The following conclusions are based on the evaluation of equilibrium beach profile methodology using an extensive data set from the east coast of Florida which encompasses approximately 600 kilometers.
It is concluded that there are two distinct zones operative
that govern the shape of the beach profiles. The inner zone is subjected to and shaped by the action of breaking waves on a somewhat regular basis. As is well known, the breaking waves cause
destructive forces to be exerted on the beach profile and result in a characteristic shape that has been found to be well represented
by a simple equation of the f orm. of Equation (1) For data from the east coast of Florida, the depth which separates these two zones is approximately 3 to 4 meters. In the outer zone, the destructive forces due to breaking waves are present only rarely and there is
a relative predominance of constructive forces resulting in a steeper equilibrium slope for the same sediment size.
For the inner zone (3 to 4 meters), it was f ound, based on "blindfolded" tests, that the existing equilibrium beach profile methods provide reasonably good agreement with the measured profile characteristics. For the outer zone, an A value of 0. 1 m1/3 provided an improved fit to the average data. Slightly improved representations within the breaking zone could be pro vided by decreasing slightly the variation of the sediment scale parameter, A, with sediment size, D.It is recommended that the A values in Table 1 be modified in accordance with Eq. (12) with a proportionality factor, F, of 0.5 over the range of sediment sizes encompassed in this study, ie approximately 0.1 mm < D < 0.6 mm.
I




Several potentially rewarding areas for future research were identified in this study. It would appear that considerable opportunity exists for investigating the profiles of equilibrium for waters in the seaward zone that are not affected predominantly by breaking. Secondly, the differences between the profiles of the inner and outer zones contain quantitative information concerning the relative magnitudes of the constructive and destructive forces and could contribute to an improved understanding of the dynamics of the profile system.
It is hoped that this report will stimulate other comparisons with extensive data sets and will provide direction for future research.
ACKnOWLEDGEMENTS
Support for this study was provided by the Florida Sea Grant Program under Contract No. R/C-S-31 and matching funds were provided by the Department of Coastal and Oceanographic Engineering. Funding for this effort by these two entities is hereby gratefully acknowledged.
REFERENCES
Bodge, K.R. 1992. "Representing equilibrium beach profiles with an exponential expression," Journal of Coastal Research, Vol 8, No. 1, pp 47-55.
Bruun, P. 1954. "Coast erosion and the development of beach profiles," U. S. Army Beach Erosion Board Technical Memorandum No. 44.
Dally, W.R., R.G. Dean and R.A. Dalrymple, 1985. "Wave height variation across beaches of arbitrary profile," Journal of Geophysical Research, Vol. 90, No. C6, pp.11917-11927.
Dean, R.G. 1977. "Equilibrium beach profiles: U. S. Atlantic and Gulf coasts," Department of Civil Engineering, Ocean Engineering Report No. 12, University of Delaware, Newark, Delaware.
Dean, R.G. 1987. "Coastal sediment processes: Toward engineering solutions," Coastal Sediments '87, Specialty Conference on Advances in Understanding of Coastal Sediment Processes, ASCE, Vol. 1, New Orleans, Louisiana, pp 1-24.
Dean, R.G. 1991. "Equilibrium beach profiles: Characteristics and applications," Journal of Coastal Research, Vol 7, No. 1, pp 53-84.
Dean, R.G. 1994. "Cross-shore sediment transport processes," (in Draft Form), Prepared for the Coastal Engineering Research Center as a Chapter in the Forthcoming Coastal Engineering Manual.




Dean, R.G. and J. Grant, 1989. Development of methodology for thirty-year shoreline projections in the vicinity of beach nourishment projects," Department of Coastal and Oceanographic Engineering Report No. UFL/COEL-89/026, University of Florida, Gainesville, FL.
Dean, R.G., T. Healy and A. Dommerholt, 1993. "A Blind-folded test of equilibrium beach profile concepts with New Zealand data," Marine Geology, Vol. 109, pp. 253-266.
Eagleson, P.S, B. Glenne and J.A. Dracup, 1963. "Equilibrium characteristics of sand beaches," Journal of Hydraulics Division, American Society of Civil Engineers, Vol. 89, No. 1, pp. 35-57.
Hayden, B., W. Felder, J. Fisher, D. Resio, L. Vincent, and R. Dolan, 1975. "Systematic variations in inshore bathymetry," Report No. 10, Department of Environmental Sciences, University of Virginia, Charlottesville, VA
Hughes, S.A. 1978. "The variation of beach profiles when
approximated by a theoretical curve," Masters Thesis, Department of Coastal and Oceanographic Engineering, University of Florida, Gainesville, FL.
Inman, D.L., M.H.S. Elwany and S.A. Jenkins, 1993. "Shorerise and Bar-Berm Profiles on Ocean Beaches", Journal of Geophysical Research, Vol. 98, No. C10, pp. 18,181 18,199.
Keulegan, G.H. and W.C. Krumbein, 1919. "Stable configuration of bottom slope in a shallow sea and its bearing on geological processes,"Transactions, American Geophysical Union, Vol. 30, No. 6, pp. 855-861.
Komar, P.D., and McDougal, W.G., 1993. "The analysis of exponential beach profiles", Journal of Coastal Research, Vol. 10, No. 1, pp. 59-69.
Kriebel, D.L., N.C. Kraus and M. Larson, 1991. "Engineering methods for predicting beach profile response," Proceedings, ASCE Conference on Coastal Sediments '91, pp. 557-571.
Larson, M., 1988. "Quantification of beach profile change", Report No. .1008, Department of Water Resources and Engineering, University of Lund, Lund, Sweden.
Larson, M., 1991. "Equilibrium profile of a beach with varying grain size," Proceedings, ASCE Conference on Coastal Sediments '91, pp. 905-919.
Larson, M., and N.C. Kraus, 1989. "SBEACH: Numerical model for simulating storm-induced beach change, Report 1: Empirical foundation and model development," Technical Report CERC-89-9 U.S.




Army Coastal Engineering Research Center, U.S. Army Waterways Experiment Station.
Larson, M., and N.C. Kraus, 1990. "SBEACH: Numerical model for simulating storm-induced beach change, Report 2: Numerical formulation and model tests," Technical Report CERC-89-9, U.S. Army Coastal Engineering Research Center, Waterways Experiment Station.
Moore, B.D. 1982. "Beach profile evolution in response to changes in water level and wave height," Masters Thesis, Department of Civil Engineering, University of Delaware, Newark, DE.
Rouse, H. 1937. "Nomogram for the settling velocity of spheres," Division of Geology and Geography Exhibit D, Report of the Commission on Sedimentation, 1936-1937, National Research Council, Washington, D. C., pp. 57-64.
Swart, D.H. 1974. A schematization of onshore-offshore transport," Proceedings, Fourteenth International Conference on Coastal Engineering, ASCE, pp. 884-890.
Vellinga, P. 1983. "Predictive computational model for beach and dune erosion during storm surges," Proceedings, ASCE Specialty Conference on Coastal Structures '83, pp. 806-819.
Work, P.A. and R.G. Dean, 1991. "Effect of varying grain size on equilibrium beach profiles," Proceedings, ASCE Conference on Coastal Sediments '91, pp. 890-904.




APPENDIX A
GRAPHICAL PRESENTATIONS OF
FLORIDA EAST COAST AND COUNTY BY COUNTY
CROSS-SHORE DISTRIBUTIONS OF
SEDIMENT AND PROFILE CHARACTERISTICS




INTRODUCTION

The graphs on the following pages present the cross-shore distributions of median sediment size (Upper Panel) and a blindfolded comparison of the average calculated and measured beach profiles (Lower Panel). The calculated beach profiles are based solely on the measured sediment size distributions and Moore's relationship (Figure 1 and Table 1) and not on any curve fitting to obtain a best-fit, ie the calculated profiles are obtained in a blindfolded manner. The values in parentheses in the upper panel represent the number of profiles for which data were available and contributed to the average at this particular cross-shore location.
Figure A-1 presents the averages for the entire east coast of Florida and is based on 165 profiles and 986 sediment samples and is a representation of Figure 3 for sake of completeness. Figures A-2 through A-13 present the same type of information commencing with Nassau County on Florida's east coast to Dade County at the south.




0 100 200 300 400 5
Offshore Distance (m)

0.7 0.6 0.5
0.4 0.3
0.2 0.1
0.0

700

a) Measured Sediment Sizes, D50%, (mm)
Averages for 165 Florida East Coast Profiles
.......... .., .......... ....... ." .. ........... ............ .......... t...........
. ..........i .......... i........... ..... ..... .. ........: ... .. ..........
... Measured .............. ...... ...
...A.. Calculated
.. .. .. . . . . .. . .... ....

0 100

200 300 400 5
Offshore Distance (m)

)0 600

700

b) Comparison of Measured and Predicted Profiles
Averages for 165 Florida East Coast Profiles

Figure A-1.

All Counties. a) Cross-Shore Distribution of Average Median Sediment Size. b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles. Values in Parentheses in Upper Panel Denote Number of Profiles Contributing to Average.

A-2

SI I I I
. .. .. ... .. ........... ......... ........ ....
. .......... ........................ . .. +, m
_ .. 5..i. . . .. . . ........... ........... i............. (7 )
:'"* *ii * J 50% mm)17
....... ... .1 5 ................1" :.... .. .( .). . .:- II8 .i. . .
' : :.. . .! ....... . ........... .. . .... .... ... .. .... .. .. ............ I: ........... ........... ;........... .......... ...........
-. .15)63.......(147)...
. ,1 5 ,
........... "........... Z........... ........... ........... ........... ...........

O0 600

0
-5
-10




0 100 200 300 400 5
Offshore Distance (in)

0.7 0.6 0.5
0.4 0.3
0.2 0.1 0.0

700

a) Measured Sediment Sizes, D50%, (mm.)
Averages for 7 Nassau County Profiles
-. . ......... .................. %.......... ..
-..-- eaurd........... ...... .....
A..* Calculated
.. .. .. .. .. .. .. .. ... .. .. .

0 100

200 300 400 5
Offshore Distance (mn)

)0600 700

b) Comparison of Measured and Predicted Profiles
Averages for 7 Nassau County Profiles

Figure A-2.

Nassau County. a) Cross-Shore Distribution of Average Median Sediment Size. b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles. Values in Parentheses in Upper Panel Denote Number of Profiles Contributing to Average.

A-3

I I I I I I
.. ...
. .. .. .. ... .. ..... .. .. . ... .. .. ..... . ... .. ..... .. .. .... . .. ...... ... .. .. .
.. .. .. .. .. ... .. ..... .. ... .. .. . ... ... .. ... . ...
....... 0 D 5o% (m m ) I ..............................
................ (4 ) ......
. ......... .......... ........... ........... ............ I .......... I .........
.(7 ) ...... ........... ...........
.. ........................... ..
.......... 7
.... 6 ..... ... ...
..................
7 ) ....................... .......
7 ) .............
.................
........... .......... ... .. .......... ...........
............................
........... .......... ............ ..............................................

)0 600

0
-5
-10




~0.5 ....
.. . . . . . . . . . . .. . . . . . . . .
S02 ((1)8
CA0.1
0 100 200 300 400 500 600 700 Offshore Distance (in) a) Measured Sediment Sizes, D5o%, (mm)
Averages for 8 Duval County Profiles
0
.-0-Meaure ......... ...........
S -- -- ... .. . .. . .. . . . . . . . .
~-0
. . . . . . . . . .
b) omprisn o Measured adPeitdPoie
b) Blindolde CpisnfAvrgCalculated adMaue ec rfls
V)Cmaesn aenhee inUesre Pan Denoedmber Profiles nrbtn
to Average.

A-4




0.7
0.6 0.5
0.4 0.3
0.2 0.1 0.0

0
-5
-1

-J. ~J

0 100 200 300 400 500
Offshore Distance (in)

600

700

a) Measured Sediment Sizes, D5o%, (mm)
Averages for 22 St Johns County Profiles
............... ........... ........... .......
. . . .. . .. . .
............... ......... .. . . . .
...... Measured.......... ..............
A,~. Calculated
.. . . . . . . . . . . . . .

0 100 200 300 400 5
Offshore Distance (in)

0 600

700

Comparison of Measured and Predicted Profiles
Averages for 22 St Johns County Profiles
Figure A-4. St. Johns County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.
A-5

....... ........ .............
... .. .. ... .. ... .. .. .. .. ....... . . ..( )
. . . . . . . . . . . . . . . . . . . . .




0.7 0.6 0.5
0.4 0.3
0.2 0.1 0.0

200 *300 400 5
Offshore Distance (in)

)0 600

700

a) Measured Sediment Sizes, D50% (mm)
Averages for 11 Flagler County Profiles
.. . ..A .. . ... . . .. . . .. . . . . . .
............... ........... ........... .......... .... ....
e.. Measured .................................... Calculated
.. .. .. . .. . .. .. . . .. .. .

0 100

200 300 400 500 600
Offshore Distance (in)

700

b) Comparison of Measured and Predicted Profiles
Averages for 11 Flagler County Profiles
Figure A-5. Flagler County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.

A-6

I I I I I I
... .. .. ........ ....................... ..................
(1...1)..... .......... .......................
...... 0 D50%, (MM) .........................
......................
.......... ....... (11.. .. (11 .: (..................................... .......... ..
..................... ......
Q 1) .. .. .. . .. .IY. .( 1Y .( ). . . .

)

100

0
-5
-10




0.7 0.6 0.5
0.4 0.3
0.2 0.1 0.0

200 300 400 500 600
Offshore Distance (m)

700

a) Measured Sediment Sizes, D5o%, (mm)
Averages for 23 Volusia County Profiles
I I I
" ... Meaure ............. ..........
.. !......... i ........ .. ........... ...... ....ii
........... 1.......... ......... .. ......... . .................... ...........
.. . .. .. .. .. .. ...... ".. .. ..... .. - . . ... .. .... .. .... ...... '... ........
A- Calculated
.. .. .. . .. . . ... .. ..

0 100

200 300 400 5
Offshore Distance (m)

600

700

Comparison of Measured and Predicted Profiles
Averages for 23 Volusia County Profiles

Figure A-6.

Volusia County. a) Cross-Shore Distribution of Average Median Sediment Size. b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles. Values in Parentheses in Upper Panel Denote Number of Profiles Contributing to Average.

A-7

I I I I I I
. . .. . . . . .. ....:.. . ... .... .. .. .. . .. . . . . .. . .. . . . . . .
....... . . . . .... . . . .... . .__ ,. ... .
. ......... !.......... !........... !........... !........... .......... i. . .
.. .. .. .......... ........... ........... ............-............ ...........
12 .. . .. .. 2 .. .. -2- ..

0 100

0
-5
-10

00




0 100 200 300 400 500
Offshore Distance (m)

600

700

a) Measured Sediment Sizes, D50%, (mm)
Averages for 23 Brevard County Profiles
........... . ...................... ........... ............ .......... t...........
-........... ........ .. .... ................I.......... ..... ..... .. ... .....
. . . . . . . . . . . . . .. . . . . . . .
........... ........... ...... .... ...... .. .. -.... ..... ...-.-..- .........." ...........
.... Measured ...... ......... ......... --A- -Calculated
. .. ... .....
. . . . . . . . .. . .

0 100 200 300 400 500
Offshore Distance (m)

600

700

b) Comparison of Measured and Predicted Profiles
Averages for 23 Brevard County Profiles

Figure A-7.

Brevard County. a) Cross-Shore Distribution of Average Median Sediment Size. b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles. Values in Parentheses in Upper Panel Denote Number of Profiles Contributing to Average.

A-8

0.7 0.6 0.5
0.4 0.3
0.2 0.1 0.0

I I I I I I
_ D 5o% (m m ) ....... .... .... : ...........
- ... .(23) (23 ).
(2 ) * I" . . .:.. . . . . . . . . . . . . . . .
. .......... ... .. ...... ........ ............ ... ....... .... (-. :. .........s .. ...........
(8 ...... (3>..
........... ...................................................... ...........

0
-5
-10




0.7
0.6 0.5
0.4 0.3
0.2 0.1 0.0

200 300 400 500
Offshore Distance (in)

600

a) Measured Sediment Sizes, D5o%, (mm)
Averages for 12 Indian River County Profiles
.......-....-- M measure.
............ Cal..ulated
.. . . . .. . . . .. . . .. . . .

0 100

200 300 400 5
Offshore Distance (in)

)0 600

b) Comparison of Measured and Predicted Profiles
Averages for 12 Indian River County Profiles

Figure A-8.

Indian River County. a) Cross-Shore Distribution of Average Median Sediment Size. b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles. Values in Parentheses in Upper Panel Denote Number of Profiles Contributing to Average.

A-9

I I I I I I
............... ....................... ...
.. .... . . . . %.. . . . .
.. . . .. . . 1) ... .. . (1 . . .

0 100

0
-5
-10

700

700




0.7
0.6 0.5
0.4 0.3
0.2 0.1 0.0

200 300 400 5
Offshore Distance (in)

)0 600

700

a) Measured Sediment Sizes, D5o%, (mm)
Averages for 13 St Lucie County Profiles
'A.
................................
.. .- M asrd. . ...........
A**Calculated
...................................
.. .. .. .. .. .. .. .. .. .. .. .

0 100 200 300 400 500
Offshore Distance (in)

600

700

b) Comparison of Measured and Predicted Profiles
Averages for 13 St Lucie County Profiles
Figure A-9. St. Lucie County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.
A-10

II I I I I
~......................
. . . . . . . . . . . . : . . . . . . . . .

0 100

0
-5
-i n1

-J. 'J




0O.7 1
~0 .6 ............
S0.5. .... -- D50%*, (MM) I......... ..... ....
(2)
.. . . I . . . . . . . . . . . . .
0.
.~ ..... .... ............................................
....... ..........alclate
-10 200.400.6.0..
0. ... ... 100. ............ 300.500.70
Offshore............. Dita c (in
0.) Comparison of........... Measure and.. Predcte .Proile
FiueA-O ari out.a) ros-hredtiuio fAeaeMda Sediment Sizes,.o,(m
b)BidoddCmaio fAveragesfr2Mti ColulatedadMauyec Profiles .
Vausi0aetee nUprPnlDnt ubro rflsCnrbtn
to.. .. Av .. . . . . .

A-11




0 100 200 300 400 5
Offshore Distance (m)

0.7 0.6 0.5
0.4 0.3
0.2 0.1 0.0

a) Measured Sediment Sizes, D50%, (mm)
Averages for 23 Palm Beach County Profiles
....-.----. Measured..
..........Cal..ulated......... .......
... .. .. .. .

0 100

200 300 400 5
Offshore Distance (m)

00 600

700

b) Comparison of Measured and Predicted Profiles
Averages for 23 Palm Beach County Profiles
Figure A-11. Palm Beach County. a) Cross-Shore Distribution of Average Median Sediment
Size. b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles. Values in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average.
A-12

-0-D5ox, (mm) .-....................
(23).. ...........)..
. (2 3 ............................... .............. .... ......

600 700

0
-5
-10

)O




0.7 0.6 0.5
0.4 0.3
0.2 0.1 0.0

200 300 400 5
Offshore Distance (in)

)0600 700

0

a) Measured Sediment Sizes, D5o%, (mm)
Averages for 13 Broward County Profiles
I ........... ................. .................. ....
......................................... I...........
......- 0 M measure. ..... .:........... ........... .......... ...........A.Calculated.
. . . .. . . . . . .. . . . . . .

0 100 200 300 400 500
Offshore Distance (in)

600

700

b) Comparison of Measured and Predicted Profiles
Averages for 13 Broward County Profiles
Figure A- 12. Broward County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.
A-13

0 100

.................
. ...... ... ........... .............. ****" '* .......... ........... .
........... . . . ..........................
: ..... (4 ) .. .......... ...........
. .. .. .. . I .. .. ... ..... .. . ... .. ... .. .. .. .... .. .. . .. ... .. .. ... .. . . ..
. .. .. ... ... . .. .. . .. .. .. ...
................. ... ... ........... ...... .. .
.......... ..... ....................... ............ ......................
. ........ ......... ........... ........... ....................... .........
................... ...................... ........... ....... ... ........
. ......... ....................... ..........
........................................ 0 D 5o% (m m )
...................
. .. ..... .. ... ... .. ..... : .. ... .. .
........... ....................... ........... ........... I .......... I ...........




~0.7 I
o0 I.D5%,(MM)
-4
n .. . . .. . .. . .. . . . . . . .. .. .
0. 10
Offshore Distance (in)
a) Measured Sediment Sizes, DSo%, (mm)
Averages for 8 Dade County Profiles
0 ..................
A
.... ~ ~ . . . . . .. ... .....
*- -~ . . . . ....
Z ........................... .......... ....................... ...S....S ....
.0- eaue
............... ...... ...... Calculated.
b) ComarsoouMaseddn rdctdPoie
-1014