UFL/COEL2001/012
DEVELOPMENT OF EROSIONAL INDICES AND A SHORELINE
CHANGE RATE EQUATION FOR APPLICATION TO EXTREME
EVENT IMPACTS
by
Jonathan K. Miller
Thesis
2001
DEVELOPMENT OF EROSIONAL INDICES AND A SHORELINE CHANGE RATE
EQUATION FOR APPLICATION TO EXTREME EVENT IMPACTS
By
JONATHAN K. MILLER
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
2001
This thesis is dedicated to all of those who have believed in me along the way as well as
those who have not. Without the influence of both I would not have possessed the desire
and dedication required to get to this point.
ACKNOWLEDGMENTS
First of all, I would like to thank my advisor, Dr. Robert Dean, for his inspiration
and guidance. His knowledge and enthusiasm truly are contagious. Our Saturday and
Sunday morning "breakfast" meetings have been invaluable. Many were the times I
came to him frustrated and dejected, only to be reinvigorated by an enlightening Saturday
morning marathon meeting.
I would like to thank the other members of my supervisory committee, Dr. Daniel
Hanes and Dr. Robert Thieke, for their insightful comments and thought provoking
lectures. I would also like to thank the rest of the faculty and staff, particularly Becky
Hudson, for making these past two years as rewarding as possible. I also feel it is
necessary to thank several of the students who made my transition to Gainesville and
graduate school much easier. The help of Jamie MacMahan, Sean Mulcahy, David
Altman, Cris Weber and especially Al Browder was much appreciated.
I would be remiss in not thanking both the Florida Sea Grant and the American
Society for Engineering Education for providing financial support for this project. Their
contributions have been greatly appreciated.
Several teachers I have met along the way have played an integral role in my
development as a student and as a person. First of all, I would like to thank Br. Paul
Joseph who first instilled in me a desire to become a teacher. His enthusiasm and love
for his students shined through every day. Next, I need to thank Dr. K.Y. Billah and Dr.
Michael Bruno. Dr. Billah believed in me always and encouraged me to learn as much as
possible. He made me want to learn for the sake of learning, not for a grade. He is the
true epitome of a teacher. I need to thank Dr. Bruno for encouraging me to follow my
heart and pursue the field of coastal engineering when others told me I would be better
off doing something more "practical."
Without the continued support and assistance of my family this would not have
been possible. They have always been there to back me and encourage me in whatever I
have chosen to do.
Last and most importantly, I need to thank my wonderful wife Diana. Without
her emotional support and encouragement over the past 2 years this would not have been
possible. She has always been there for me even when I was not there for her. I can
never thank her enough for her infinite love and patience.
TABLE OF CONTENTS
page
ACKNOW LEDGM ENTS..................................................................... ... ..................... .. iii
LIST OF TABLES .......................................................................................................... vii
LIST OF FIGURES ...................................... ......................... viii
ABSTRACT ..................................................................................................................... xi
INTRODUCTION.................................................................................................. 1
Coastal Erosion Processes ..................... ...... ........................................................... 1
Objectives and Scope .................................................................. .............................. 5
LITERATURE REVIEW ........................... ................................. .................................. 7
M odel Hurricane ........................................................................................ .. .......... 7
Bathystrophic Storm Surge ............................... ........................... ......................... 10
Erosion M models ................................................................................. ...................... 11
Shoreline Recovery M odel................................................. ............ .......... 14
Seasonal Shoreline Change ........................................................................................... 14
SHORELINE CHANGE ANALYSIS .................................................... .................... 16
Site Descriptions ................................................................................. ............ .............. 18
Volusia County............................................................................ ............ ........... 18
St. Johns County................................................................. .............................. 18
M martin County .............................................. ....................................................... 19
Sources and Analysis Techniques .................................................... 19
Results and Conclusions.................................................... .................................... 21
EROSION INDICES ........................................................ ........................................... 28
Event Longevity Parameter Index (ELP) ....... ... ................................... ................... 31
Theory ....................................................................................................................... 31
W inter Storm Related SurgeReconstructed Hydrographs ..................... ............ 33
Hurricane Related SurgeBathystrophic Storm Surge Model............................. 34
Results.......................................................................... .....................................39
Hurricane Erosion Index (HEI) ................................................... .......................... 49
v
Theory ................................................................................................................. 49
Results ....................................................................................................................... 50
M odified Hurricane Erosion Index (M HEI).......................................... ........ ..... 53
Theory ................................................................................................................. 53
Results ................................................................................................................. 55
SH ORELINE RESPON SE RATE .................................................. .......................... 58
Rate Equation .......................................................................................................... 59
Theory ................................................................................................................. 59
Results....................................................................................................................... 60
D eterm nation of Equilibrium Shoreline Position................................... ........... ... 65
Theory ................................................................................................................. 65
Results ....................................................................................................................... 70
CONCLUSIONS AND RECOMMENDATIONS ....................................... .......... .. 88
Erosion Indices.............................................................................................................. 88
Sum m ary and Conclusions................................................ ................................ 88
Recom m endations for Future Study.............................. .................................. 90
Shoreline Response Rate Equation ............................................... ........................ 92
Sum m ary and Conclusions................................................ ................................ 92
Recom m endations for Future Study.............................. ................................. 93
LIST OF REFEREN CES ........................................................................................... 97
BIOGRAPH ICAL SKETCH ....................................................... ............................. 99
LIST OF TABLES
Table Page
4.1 Rsquared values indicating the correlation between the observed erosion and the
ELP Index for the case of no setup and no winter storms............................... 40
4.2 Rsquared values resulting from the removal of the 1989 data set and the cumulative
data point where the interval of application is greater than 10 years ................ 44
4.3 Rsquared values indicating the correlation between the observed erosion and the
ELP Index for the case of no setup, including winter storms............................ 45
4.4 Rsquared values indicating the correlation between the observed erosion and the
ELP Index for the case of including setup and no winter storms.................... 47
4.5 Rsquared values indicating the correlation between the observed erosion and the
H E I. ..................................................................................................................... 50
4.6 Rsquared values resulting from the removal of the 1989 data set and the cumulative
data point where the interval of application is greater than 10 years .............. 52
4.7 Rsquared values indicating the correlation between the observed erosion and the
M H E I.................................................................................................................. 56
5.1 Relevant site characteristics ........................................ ................ .............................. 68
5.2 Maximum and minimum average monthly potential shoreline change values
calculated from Eq. (4.19) using the WIS data set. Values are reported in feet. 73
5.3 Maximum and minimum average monthly potential shoreline change values
calculated from Eq. (4.19) using buoy data. Values are reported in feet............ 78
5.4 Range of potential shoreline change values based on individual extreme values.
Values are reported in feet...................................................... .................... 87
LIST OF FIGURES
Figure Page
1.1 Storm surge and high water marks for Hurricane Opal. Calculation of the setup
utilizing associated wave conditions indicates a large portion of the increase in
the mean high water marks with respect to the measured surge can be
attributed to setup................................................................................................ 4
2.1 Definition sketch of the model hurricane................................................ ................ 7
2.2 Plan view of the pressure field associated with the model hurricane............................ 8
2.3 Plan view of the gradient wind field associated with the model hurricane................... 9
2.4 Illustration of the determination of trfrom a typical storm surge hydrograph................ 12
2.5 Variation of hei with nondimensional distance from the hurricane center ................ 14
3.1 Sites selected for aerial photograph analysis............................................ ............ ... 17
3.2 Example of the aerial photograph analysis technique .............................................. 20
3.3 Shoreline positions at the St. Augustine Site ........................................... ............ ... 22
3.4 Shoreline positions at the St. Johns Site................................................................ 23
3.5 Shoreline positions at the Volusia North Site .................................... ............ 23
3.6 Shoreline positions at the Volusia South Site .................................... ................ 24
3.7 Shoreline positions at the Martin County Site ..................................... ............... 24
3.8 Comparison of the average shoreline positions at each of the five Sites ........................ 25
4.1 D definition sketch of a, 0, and ............................................ .............................. 30
4.2 D definition sketch of sin_rotwvect ................................ .................................................. 30
4.3 D definition sketch of o and ................................................................ ..................... 31
4.4 Example of a recreated storm surge hydrograph using the Mayport, Florida data. In
this case two distinct surge events are observed. ............................................ 34
4.5 Plot of ELP Index versus erosion at the St. Augustine Site. Setup and winter storms
are not included. ............................................................................................. 40
4.6 Plot of ELP Index versus erosion at St. Johns Site. Setup and winter storms are not
included. ........... ...................................................... ..................................... 41
4.7 Effect of removing all four points associated with the 1989 erosional event from
Figure 4.5. ............................................................... .................................... 41
4.8 Effect of removing all four points associated with the 1989 erosional event and the
cumulative point associated with the period 19601971 from Figure 4.6........... 42
4.9 Plot of ELP Index versus erosion at Martin County Site. Winter storms are included,
setup is not..................................................................................................... 45
4.10 Plot of ELP Index versus erosion at the Volusia North Site. Setup is included,
winter storm s are not......................................... ................ .......................... 48
4.11 Plot of ELP Index versus erosion at the Volusia South Site. Setup is included,
winter storm s are not. ...................................................... ....................... 48
4.12 Plot of HEI versus erosion at the St. Johns Site....................................... ............ 51
4.13 Effect of removing all four points associated with the 1989 erosional event and the
cumulative point associated with the period 19601971 from Figure 4.12......... 53
4.14 Definition sketch for the calculation of the change in shoreline position resulting
from an increased water level, S, and wave setup, ....................................... .. 54
4.15 Plot of MHEI versus erosion at the Volusia South Site .............................................. 56
4.16 Plot of MHEI versus erosion at the Volusia North Site .............................................. 57
5.1 Graphical depiction of the effect of storm sequencing on the perceived effectiveness
of the erosion indices. In both cases the value of the erosion index will be the
same however the final position of the shoreline will be much different. ......... 59
5.2 Application of Eq. (5.3) for the case ke=ka=l and no external forcing ....................... 62
5.3 Application of Eq. (5.3) for the case of ke=ka=l with external forcing applied at t=0
and t= 10 ............................................................................................. ............ 63
5.4 Application of Eq. (5.3) for the case of ka=ke=5 and no external forcing................... 63
5.5 Application of Eq. (5.3) for the case ke=1, ka=0.2 and no external forcing ................ 64
5.6 Application of Eq. (5.3) for the case of ke=1, ka=0.2 with external forcing applied at
t=0 and t= 10 ...................................................................................................... 64
5.7 Site and data station location map................................................ .......................... 67
5.8 Average shoreline positions at Jupiter and Westhampton as reported in Dewall (1977)
and D ew all (1979).............................................................. ....................... 72
5.9 Average monthly potential shoreline change values. S represents the measured tide.
Eta is the wave induced setup effect. ......................................... ............ ... 72
5.10 Envelope of average monthly potential shoreline change values at Jupiter Island
calculated from Eq. (4.19) using the WIS data set, assuming the setup is
included implicitly. Each line represents a single year of the 20 years with
available data....................................................................................................... 74
5.11 Envelope of average monthly potential shoreline change values at Jupiter Island
calculated from Eq. (4.19) using the WIS data set, including the setup
explicitly. Each line represents a single year of the 20 years with available
data. ................. ................................................. ... .. ................................ 74
5.12 Envelope of average monthly potential shoreline change values at Westhampton
calculated from Eq. (4.19) using the WIS data set, assuming the setup is
included implicitly. Each line represents a single year of the 20 years with
available data ................................................................................................ 75
5.13 Envelope of average monthly potential shoreline change values at Westhampton
calculated from Eq. (4.19) using the WIS data set, including the setup
explicitly. Each line represents a single year of the 20 years with available
data. ..................................................................................................................... 75
5.14 Envelope of average monthly potential shoreline change values at Jupiter Island
calculated from Eq. (4.19) using buoy data, assuming the setup is included
implicitly. Each line represents a single year of the 11 years with available
data............................................................................................................... 76
5.15 Envelope of average monthly potential shoreline change values at Jupiter Island
calculated from Eq. (4.19) using buoy data, including the setup explicitly.
Each line represents a single year of the 11 years with available data .............. 76
5.16 Envelope of average monthly potential shoreline change values at Westhampton
calculated from Eq. (4.19) using buoy data, assuming the setup is included
implicitly. Each line represents a single year of the 9 years with available data. 77
5.17 Envelope of average monthly potential shoreline change values at Westhampton
calculated from Eq. (4.19) using buoy data, including the setup explicitly.
Each line represents a single year of the 9 years with available data........... 77
5.18 Potential shoreline change at Jupiter Island calculated using buoy data, assuming the
setup is im plicitly included ................................... ......................................... 81
5.19 Potential shoreline change at Jupiter Island calculated using buoy data, explicitly
calculating the setup............................................................. ...................... 82
5.20 Potential shoreline change at Westhampton calculated using buoy data assuming the
setup is implicitly included ................................................... ................. 82
5.21 Potential shoreline change at Westhampton calculated using buoy data, explicitly
calculating the setup. ........................................................................................... 83
5.22 Potential shoreline change at Jupiter Island calculated using WIS data, assuming the
setup is implicitly included. ...................................................................... 83
5.23 Potential shoreline change at Jupiter Island calculated using WIS data, explicitly
calculating the setup...................................................... .... .................. 84
5.24 Potential shoreline change at Westhampton calculated using WIS data assuming the
setup is implicitly included ................................... .................................. 84
5.25 Potential shoreline change at Westhampton calculated using WIS data, explicitly
calculating the setup. .............................................................. .................. .. 85
6.1 Illustration of the potential application of the shoreline change rate equation for
determination of the appropriate rate constants. In this case ka=0.2 and
ke= 1.0. .................................................................... ............................... 94
6.2 Determination of error at a single point ............................................... .............. 95
6.3 Potential results of trial and error solution for determining ka and ke............................. 96
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
DEVELOPMENT OF EROSIONAL INDICES AND A SHORELINE CHANGE RATE
EQUATION FOR APPLICATION TO EXTREME EVENT IMPACTS
By
Jonathan K. Miller
August 2001
Chairman: Robert G. Dean
Major Department: Civil and Coastal Engineering
Several indices are developed for the prediction of the erosive potential associated
with extreme events. The indices utilize readily available storm parameters. The
proposed indices are compared with historical shoreline changes as determined from
aerial photographs. Analysis of the results obtained from applying the indices to predict
the historical shoreline changes leads to the proposal of a shoreline change rate equation.
The shoreline change rate equation is a function of the displacement from the equilibrium
shoreline position and rate constants with different values for erosion and accretion.
Seasonal shoreline changes are investigated in an effort to determine the unknown
parameters of the rate equation.
CHAPTER 1
INTRODUCTION
The population of America, and indeed the world, is in love with the beach.
Although true throughout the world, nowhere is this more true than in the United States.
The thirty coastal states (including those bordering the Great Lakes) contain 62 percent of
the U.S. population and twelve of the thirteen largest cities. In all, 53 percent of the U.S.
population lives within 50 miles of the shore (Edwards, 1989). It has been reported that
the United States largest trade surplus is the tourism industry with beaches accounting for
a large percentage of this surplus. Several states, Florida, California, and New Jersey
among them, list tourism among their fastest growing industries (Douglass, Scott L.,
University of South Alabama, personal communication, 2001). More people visit Miami
Beach per year than the three largest national parks combined (Douglass, Scott L.,
University of South Alabama, personal communication, 2001). With such a large social
and economic stake in the health of our nations shorelines, beach protection and
preservation are a national concern.
Coastal Erosion Processes
Coastal erosion is the result of numerous processes, some of them yet to be fully
understood. In the most general sense, erosion is the result of sand being removed from
the beach either by man or nature. Although many natural processes tend to erode the
beaches, they usually restore them as well. In many cases, the single largest cause of
beach erosion is man made structures that interrupt the dynamic natural processes. By
removing sand from the natural system whether directly through sand mining/dredging,
or indirectly through inlet stabilization, breakwater construction or any number of other
construction activities, the result is often chronic erosion. As coastal engineers, we are
too often faced with the task of attempting to reintroduce sediment into a system in which
we are the primary cause of the sediment deficit.
Aside from anthropogenic effects, there are many natural processes that induce
erosion. Numerous studies have been undertaken on the shoreline changes resulting from
various natural processes. Everything from wind speed, ground water table, and sea
temperature, to more intuitive processes such as wave action and sea level rise has been
studied. The most damaging erosion however is caused by extreme storm events. Long
term erosional trends can be addressed by a number of coastal engineering remedies. The
sudden, catastrophic erosion associated with hurricanes and winter storms however, is
difficult to predict and even more difficult to prepare for. Extreme event induced erosion,
and methods to quantify it through the development of a predictive erosion index,
comprise the main focus of this thesis.
Much of the coastal damage associated with hurricanes can be attributed to the
massive storm surges they produce. In many cases, surges of over 15 feet have been
reported with the maximum being 22.4 feet at Pass Christian, Mississippi caused by
Hurricane Camille in 1969 (Dean and Dalrymple 2001). In addition to causing beach
erosion, storm surge often leads to substantial inland flooding which is the primary cause
of associated with hurricanes. This deadly surge can be decomposed into four separate
components that combine during a hurricane to form a massive wall of water. Extreme
low barometric pressure at the hurricane's center acts to "suck up" the water surface with
respect to water around it. The enormous winds associated with hurricanes create a shear
stress on the water surface, in effect pushing the water ahead of it until it is forced to pile
up at a boundary, the beach. The strong winds also create large longshore currents that,
combined with the Coriolis force, either reinforce (in the case of southerly currents on the
east coast in the Northern hemisphere) or negate the previous two effects. The fourth
component is an increase in the mean water level caused by increased wave action and
termed the wave setup. In general the wind shear stress is the dominant term, although in
some cases such as Hurricane Opal in 1995 and in the case of winter storms, the wave
setup can actually dominate. Figure 1.1 illustrates the important contribution of wave
setup during Hurricane Opal. Nielsen (1988) has shown that wave induced setup values
of 40 percent of the deepwater Hn value for waves between 2 and 8.5 feet is not
unusual.
When investigating extreme event induced erosion and the subsequent shoreline
recovery, the different time scales of the processes involved must be considered. In
general, erosion occurs at a much faster rate than accretion, hence it can take a beach a
substantial amount of time to recover from a relatively short duration storm event.
Several models exist that predict erosion rates under different conditions with various
degrees of success, but to the author's knowledge, an adequate shoreline recovery model
has yet to be developed. There are vast complexities governing the dynamics of the
fluidparticle interactions, however as with most dynamic processes, a quasiequilibrium
state is presumed to exist. How quickly a shoreline reaches this equilibrium state
depends on both the time scale of the processes involved, and the magnitude of its
displacement from the equilibrium position. An equation expressing the shoreline
4
response as a function of the equilibrium position and the time scales of the governing
processes will be proposed later in this thesis.
OPAL Ir 
STORM SURGE
HYDROGRAPH "*' '9 mm,
Peak Storm
i .. ...; .r ; srg .hy fl:fr ;a : .... .
HURR OPA L Hgh at rMr
0 W 2 24 h .2' ,
II
10a3 1014 1015 1016
TIME (hr#,UTC);ala flng 0:00 on 10/03/95
Figure 5. Storm surge hydrograph for Opal at Panama City Beach
HURRICANE OPAL High Water Marks
Cr.
4 0* 16 20 oMNLES
S OJ ^n
Figure 6. Surveyed high water marks after Opal long the Panhandle Coast
Figure 1.1 Storm surge and high water marks for Hurricane Opal. Calculation of the
setup utilizing associated wave conditions indicates a large portion of the increase in the
mean high water marks with respect to the measured surge can be attributed to setup
(Leadon et al. 1998).
As if this problem were not complex enough, the equilibrium state itself is
unsteady. Any attempt to sufficiently define shoreline response rates must first
5
sufficiently define the equilibrium position. Even the casual beachgoer knows that the
beach tends to be narrowest in the winter and widest during the summer. This is part of
the beach's natural defense mechanism to help dissipate the increased winter wave
energy more efficiently. The second objective of this thesis is to examine these seasonal
shoreline fluctuations with the goal of developing an expression for the equilibrium
shoreline position for input into the proposed rate equation.
Objectives and Scope
The main objective of this project is to develop an index capable of correlating
storm characteristics to potential shoreline changes. To achieve this, several previously
defined indices have been modified and applied to historical events in an effort to predict
the observed shoreline changes. The results obtained during the investigation of the
primary objective led to the development of a secondary objective. The secondary
objective is to develop an equation that accurately predicts the rate of shoreline response
to nonequilibrium conditions, while accounting for the different time scales of the
processes involved. Seasonal shoreline changes were investigated for potential
application to the rate equation model.
The scope of the investigation varies. The spatial scope of the erosion index
portion of the project is limited to five sites located in three counties within Florida. The
initial phase of the hurricane index investigation addresses the time period from 1950
1995, while the second phase dealing with the modified erosion indices is limited by the
available data to 19761995.
The spatial scope of the secondary objective is limited to two sites: Westhampton,
New York and Jupiter Island, Florida. In both cases the maximum time period of
analysis is limited by the available wave data to19761995.
The scope of the primary objective is limited to attempts at correlating historical
events to the observed shoreline changes though the application of several existing
hurricane erosion indices. Based on the data available and the results achieved,
expansion to statistical parameters and predicted events is not warranted at this time.
The scope of the secondary objective is limited to the suggestion of an equation to
describe the varying rates of erosion and accretion. An attempt is made to define a
seasonally varying equilibrium shoreline position for use in this rate equation. Further
analysis and more data are needed to determine the appropriate constants for application
in the shoreline change rate equation.
CHAPTER 2
LITERATURE REVIEW
Model Hurricane
Of intrinsic importance to this study is the characterization of a model hurricane.
Wilson (1957) provides the characterization of the model hurricane utilized throughout
this thesis. Figure 2.1 provides a definition sketch.
yvt
Figure 2.1 Definition sketch of the model hurricane
The model hurricane has both a characteristic pressure field and wind field associated
with it. The pressure field is composed of concentric isobars and is defined by the
equation
p(r) = po + ApeR/r (2.1)
where po is the central pressure, R is the radius to maximum winds, r is the distance from
the location of interest to the hurricane center, and Ap is the central pressure deficit
defined by
Ap = p. po (2.2)
in which po is the ambient pressure at a location sufficiently far as to be free from the
influence of the hurricane. Figure 2.2 provides a plan view of the pressure field
associated with the model hurricane.
10"
8 .
4 "
2
S0
.Z 2 I
4 '
10
10 8 6 4 2 0 2 4 6 8 10
NonDimensional Distance, x/R
Figure 2.2 Plan view of the pressure field associated with the model hurricane
The wind field associated with the model hurricane is more complex. Three
related wind speeds are defined: cyclostrophic, geostrophic, and gradient. The
cyclostrophic wind speed, Uc, is a balance between the pressure field gradients and the
centripetal force, neglecting the effects of friction and the Coriolis force. The
cyclostrophic wind field is composed of concentric isovels and is given by
U /AP Re (2.3)
Pa r
where pa is the mass density of air. The geostrophic wind speed, Ug, is the speed that
would occur if the pressure field were in balance with the Coriolis force and is defined as
Ap R2 
U = Par (2.4)
g= 2o)R sin <
where to and 0 are the rotational speed of the earth in radians per second and the latitude
of the location of interest respectively. The gradient wind speed, W, is the speed of
interest in most calculations, and is the wind speed measured approximately 30 feet
above the water surface. The gradient wind speed is related to the cyclostrophic and
geostrophic wind speed through the parameter y
1 Vf sin p U
Y= + c (2.5)
2 U U
S c g)
where Vf is the event forward speed and 1 is the angle defined in Figure 2.1. The
gradient wind speed is then defined in terms of y and Uc as
W= 0.83U,( y+ ) (2.6)
where the gradient wind vectors are rotated inward by approximately 180. The gradient
wind speed is the speed utilized in all of the models. Figure 2.3 represents a plan view of
the gradient wind speed associated with the model hurricane.
10. '
10 8 4 4 2 0 2 4 6 8 10
I r) f
8u
0 2
Z 8 I
10 8 6 4 2 0 2 4 6 8 10
NonDimensional Distance, x/R
Figure 2.3 Plan view of the gradient wind field associated with the model hurricane
Bathystrophic Storm Surge
Freeman, Baer, and Jung (1957) developed a simple method for calculating the
onedimensional storm surge due to a translating atmospheric disturbance. They made
use of the following assumptions to reduce the problem to onedimension.
1. Minimal crossshore transport takes place.
2. Divergence of the velocity field does not significantly affect the height of
the water surface.
3. Change in height in the alongshore direction is assumed negligible.
4. Space derivatives of the current are assumed negligible when compared to
the Coriolis force.
Assumption one necessitates the existence of a compensating alongshore current termed
the bathystrophic current. Assumption two is a result of the fact that any "bumps"
created by a diverging velocity field spread out at a faster rate than the velocity field can
build them up. Assumption three is a common assumption in many models. The final
assumption is justified by the small magnitude of the currents involved relative to the vast
spatial scales.
Applying the above assumptions to the depth integrated equations of motion
results in the following differential equations
81 1 [Tw x 1 1 8p
x gD p, Pg x(2.7)
dq 1 ( _by) (2.8)
dt p,
where x and y represent the crossshore and longshore directions respectively, g is
gravity, ri is the water surface elevation, D is the total local depth, Tw and Tb are the
surface wind and bottom shear stresses respectively, e is the Coriolis parameter, pw is the
density of water, p is the atmospheric pressure, and q is the volumetric flow per unit
width. Chiu and Dean (1984) used the bathystrophic surge model as the basis for a one
dimensional model against which a larger twodimensional model was calibrated.
Rewriting Eqs. (2.7) and (2.8) in finite difference form yields
1 At 1
q n+I q + Pw (2.9)
qy, BB. p, I
axI n+I Pi pi+l
Ix+lI Ax Ii 1 p (2.10)
gDi L Pw Pwg1
fAt qy
BB = 1.0+ (2.11)
Di2
where the boundary conditions include initiation from rest (qy=0 & T=0) and Ir due to
barometric pressure alone at the seaward edge of the grid.
A= (2.12)
Pwg
Erosion Models
Balsillie (1985, 1986, 1999) utilizes empirical methods to determine the
volumetric erosion due to 14 erosional events associated with 11 major hurricanes, and
22 erosional events associated with other severe storms, with good success. Balsillie's
equation incorporates a measure of the event longevity, tr, and gives the volume per unit
length eroded above MSL as
Qe = 1 6 t,S2 (2.13)
1622
where tr is the storm tide rise time, and S is the combined peak storm tide elevation
including both the astronomical tide and the dynamic wave setup. The storm tide rise
time is defined as "the final continuous surge of the storm tide representing impact of the
event at landfall" (Balsillie 1999, p.8), and does not include prestorm setup. Figure 2.4
illustrates the definition of rise time as determined from a storm surge hydrograph.
Balsillie also parameterized the storm tide rise time in terms of a more readily available
quantity, the event forward speed as
t, = 0.00175 g (2.14)
V,
where g has units of length per hour squared, the coefficient has units of hours squared,
and Vf has units of length per hour and is measured at the time the radius of maximum
winds makes landfall.
7*3y1 '  i *i :~
Storm Tide
4 Pre*Storm
Elevation Lo S tup
Above MSL 3
(m)
2 Normal ProStorm
Tidal Conditions
o a ~ ,~ ,
20 4 0 60 0s
Time cours)
Figure 2.4 Illustration of the determination of tr from a typical storm surge hydrograph
(Balsillie, 1999)
Dean (1999) presents a different method for calculating the erosive potential of a
storm. He calculates a Hurricane Erosion Index (HEI) based primarily upon the Bruun
Rule given by Eq. (2.15).
Ay = S (2.15)
(h. +B)
Here the shoreline change Ay is dependent on the change in water level, S, the berm
height, B, and the width and depth of the active profile, W* and h* respectively. Relating
h* and W* through equilibrium beach profile concepts, Eq. (2.14) can be rewritten
h^
Ay = S (2.16)
AY(I1+ h
where A is the sediment scale parameter and has units of length to the onethird power.
Dean argues that the storm surge is dominated by three primary factors: onshore
wind stress, pressure reduction, and wave setup. Recognizing that two of the three
effects are proportional to the wind speed squared (wind stress and pressure reduction),
and that the other is directly proportional to the wind speed, Dean proposes
S(x) o W2 cosOdy (2.17)
Y1
where 0 is defined as the angle between the rotated wind vector and the shoreline normal.
Recognizing that the quantity h* is also proportional to the wind speed, Dean defined the
Hurricane Erosion Index (HEI) as
T1 T1 W (xy)cos~dxdy To ,
HEI=' T W (xy)cosdxdy= hei(x)dx (2.18)
0 0 Vf 0
where R is the radius to maximum winds, and Vf is included as a measure of the time a
given storm acts upon the adjacent shoreline. Lower case hei is a local erosion index,
which can be integrated alongshore to obtain the global hurricane erosion index, HEI.
Figure 2.4 depicts the variation of hei with distance from the storm's center.
1.6
1.4
1.0
:1 0.8
o.08
0.4
0.2
0.0, 24 ,i
0 1 2 3 4 5 6 7 8 9 10
NonDimensional Distance, x/R
Figure 2.5 Variation of hei with nondimensional distance from the hurricane center
Shoreline Recovery Model
Kriebel and Dean (1993) present a method of calculating the time varying beach
profile response to a given forcing function. Based upon laboratory observations, an
approximate equation for the time dependent beach response to a steady state forcing
function can be written as
R(t) = Rj 1e/t (2.19)
where Ro represents the maximum or equilibrium response, and Ts is the representative
time scale of the response. It then follows from the differential equation that the rate of
recovery is proportional to the difference between the instantaneous and equilibrium
profile responses
dR(t) 1 (R.(t)R(t)) (2.20)
dt T,
which can be integrated analytically for constant Ts and various Ro(t).
Seasonal Shoreline Change
Dewall (1977, 1979) studied seasonal shoreline fluctuations at Jupiter Island,
Florida and Westhampton, Long Island. Dewall observed the beach at both locations
tended to advance seaward during the summer, and retreat shoreward during the winter in
response to the fluctuations in local wave energy. Unfortunately, Dewall's study may
have been biased by several factors:
1. The construction of groins and beach nourishment projects during the study.
2. The insufficient spatial density of the surveys (2 Jupiter profile lines separated
by only 250 feet).
3. The insufficient temporal density of the surveys (3 data points in 10 years
defines July average position at Westhampton).
4. An admitted biasing of the surveys towards winter poststorm events
(particularly Westhampton).
In spite of this less than perfect data set, a significant correlation was observed
between the breaking wave conditions and the observed shoreline fluctuations.
Shoreline advance tended to be associated with the mild wave conditions more
prevalent during the summer months, and retreat with more energetic winter
conditions. Dewall's study encompassed both long and shortterm behavior. In
general, an inverse relationship between the magnitude of the fluctuations and their
associated time scales was observed. The largest shoreline changes occurred on the
smallest time scales as a result of individual storms, while the smallest changes were
observed over the longest time scales, and were associated with changes in the yearly
mean shoreline position. Within these extremes, Dewall also observed large cyclical
fluctuations of up to 90 feet in one year at Westhampton and 70 feet in one year at
Jupiter. A later study of several New Jersey beaches by Everts and Czeriak (1977)
supports Dewall's results.
CHAPTER 3
SHORELINE CHANGE ANALYSIS
Dean, Cheng, and Malakar (1998) have shown that on average, Florida's east
coast beaches are accreting at a longterm, prenourishment rate of approximately 4
inches per year. This conclusion is based on the analysis of shoreline data obtained from
a database maintained by the Florida Department of Environmental Protection, Office of
Beaches and Coastal Systems (OBCS). The OBCS data consists of surveys referenced to
fixed monuments located approximately every 1000 feet along Florida's sandy
shorelines. Because the OBCS data set is too sparse temporally to capture the shortterm
dynamic behavior of the beaches needed for this study, aerial photographs from several
sources are analyzed to obtain a more temporally dense coverage over the study period.
Considerable photographic data exists; however, the use of many of these photographs
was precluded by their cost.
Five sites within three counties were selected as locations representative of typical
Florida East coast conditions. Site selection was based on three primary criteria. First
and foremost, locations representative of the entire east coast were desired. In order to
achieve this, an attempt was made to include widely spaced locations. Secondly, the sites
should be as free from anthropogenic effects as possible. This criterion eliminates areas
within the limits of nourishment projects or within the influence of inlets, and
consequently makes the fulfillment of the first criteria much more difficult. This is
particularly true in the case of south Florida. Photograph availability and suitability was
the final criterion. Suitability incorporates, photo quality, scale, and the location of a
sufficient number of control structures within the available photographs. Figure 3.1
depicts the five selected sites based on fulfillment of the above criteria. Within each site
several locations were selected for analysis to ensure accuracy and to eliminate any
anomalous trends. In order to make the analysis easier to follow, an attempt has been
made to consistently refer to the locations within each county as Sites, and to refer to the
individual locations within each Site as Locations.
Figure 3.1 Sites selected for aerial photograph analysis
Site Descriptions
Volusia County
As indicated in Figure 3.1, two sites in Volusia County were selected. The
northernmost site is located in Daytona Beach and is centered about DNRBS Monument
R76. Three locations, A, X, and O, over a several mile stretch were analyzed. Location
X is near the intersection of Route A1A and Driftwood Avenue. Locations O and A are
approximately one mile north and one mile south of Location X respectively. At all three
locations, buildings were utilized as control structures. This site is referred to as the
Volusia North Site.
The second Volusia County site is located south of Ponce De Leon Inlet in New
Smyrna Beach, and consists of three locations, X, O, and *. This site is centered about
Monument R172 and is referred to as the Volusia South Site. Location X is at the
intersection of East 7h Street and Route A1A. Location O is approximately 1 mile south
of Location X, near the intersection of East 24h Street and Route A1A. Location is
approximately 3000 feet north of Location X, near the intersection of Ocean Avenue and
Route A1A. The centerlines of nearby roads were utilized as reference points at all three
locations.
St. Johns County
Two sites were also selected in St. Johns County. The northernmost site, located
north of St. Augustine Inlet and centered about Monument R117, is referred to as the St.
Augustine Site. Three locations, A, B, and C were analyzed at this site. Location C is
the southernmost location, and is situated near the intersection of Meadow Avenue and
Route A1A in St. Augustine. Locations B and A are located 2000 and 6000 feet north of
Location A respectively. The control structure at all three locations is the centerline of
Route A1A.
The second St. Johns County site is located approximately five miles north of
Mantanzas Inlet near Monument R170. Two locations, A and B, are analyzed at this site
which is referred to as the St. Johns Site. Location B is situated at the intersection of
Mantanzas Avenue and Atlantic Boulevard in Crescent Beach. Location A is also located
in Crescent Beach, approximately 2 miles south of Location B near the intersection of
Route 206 and Route A1A. The centerlines of nearby streets were used as control
structures at both locations.
Martin County
Martin County is the least well documented of the five selected sites. In Martin
County only one site was selected due to the scarcity of control structures and the limited
availability of the photographs. The Martin Site is located one mile north of St. Lucie
Inlet on Hutchinson Island and is centered about Monument R26. The Site spans
approximately 3.5 miles encompassing locations, A, X, and Z. Location X is adjacent to
the entrance to the Elliot Museum on Hutchinson Island. Location Z is approximately 1
mile south of Location X and less than 1 mile north of St. Lucie Inlet. Location A is
approximately 3000 feet north of Location X near the entrance to the Little Ocean Club
on Hutchinson Island. Buildings, roadway centerlines, and an inland marina were
utilized as control structures at the Martin Site.
Sources and Analysis Techniques
Aerial photographs were obtained from several sources. Most of the photographs
were obtained from the Florida Department of Transportation and the United States
Department of Agriculture, with several being obtained from other sources. Photographs
range in scale from 1:2,400 to 1:40,000. The extent of photographic documentation
varies from county to county. Photographs for Volusia County and St. Johns County are
available for the periods 19431992 and 19421998 respectively. In many cases the older
photographs for both counties were not utilized due to poor photograph quality and a lack
of suitable control structures. In Martin County, photographs were only available for the
thirty year period from 1966 to 1996. In general there is a marked increase in the
frequency of the aerial surveys in all three counties between 1980 and the present.
The photographic analysis is performed utilizing a Hewlett Packard Scanjet to
digitally capture the images. Standard photo editing software is utilized to pinpoint and
enlarge areas of interest. Shoreline location is measured from an established reference
point to the wetted sand line using the initial shoreline position as a reference. Permanent
structures such as roadway centerlines, and buildings are utilized as reference points, and
are considered fixed from photograph to photograph. In rare cases, the photoediting
software is utilized to clarify the distinction between wet and dry sand. This is avoided
wherever possible. Due to the accuracy requirements for the current study, no attempt is
made to rectify the images.
Figure 3.2 Example of the aerial photograph analysis technique
Results and Conclusions
Figures 3.33.7 depict the shoreline positions at each location within each site.
Shoreline position is with respect to the shoreline location in the earliest photograph. In
examining Figures 3.33.7, it should be noted that the period from 19401950 was the
most active for Category 3 hurricanes in Florida's history (Hebert and Case 1990). Data
points obtained immediately after this decade reflect an initially eroded state, therefore
care should be taken when comparing two sets of shoreline position data. For example,
the St. Johns Site data indicates a longterm accretional trend while the St. Augustine Site
data indicates an erosive trend. A significant portion of this difference can be attributed
to the fact that the first St. Augustine data point in 1942 is prior to or near the very
beginning of this active period and may reflect a more normal beach width, whereas the
first St. Johns data point is immediately after this period and will reflect an initially
eroded state. As previously indicated, all future shoreline positions are recorded with
respect to this initial condition, leading to the difference in the longterm trends observed
in Figures 3.3 and 3.4.
In general the major shoreline trends are similar at all 5 sites, however the
magnitude of the major trends varies from site to site in response to the different local
conditions. Superimposed on these major trends are smaller more localized trends.
Examining the two sites within each county together yields some insight into the
major shoreline trends. At the St. Augustine Site and the St. Johns Site, the observed
shoreline trends are very similar. As previously mentioned, the effects of the active
hurricane period from 1941 to 1950 are reflected in the erosion indicated by the first two
St. Augustine data points. Both sites exhibit an accretional trend during the 1950's,
indicating the gradual recovery from the previous decade's erosion. The effects of two
major storm events, the Ash Wednesday Storm in 1962 and Hurricane Dora in 1964, are
reflected in the erosion indicated at both sites by the first post storm data points.
Comparison of the magnitudes of the erosional events is made difficult because the first
post storm data point at the St. Johns Site is in 1971, and reflects 7 years of recovery from
the storms. Another erosional event occurs between 1971 and 1974, and is followed
immediately by an accretional trend between 1974 and 1975. The erosion indicated by
the 1975 and 1980 data points is most likely the result of Hurricane David in 1979. The
most recent data points indicate a more naturally dynamic shoreline. This is reflective of
both the increased temporal density of the photographs and the lack of a singular severe
hurricane impact during the period. The erosion caused by two major events, the 1984
Thanksgiving Storm and the passage of Hurricanes Dean, Gabrielle, and Hugo offshore
in 1989, is indicated at both sites by the data points immediately following their
occurrence.
ST. AUGUSTINE
SHORELINE POSITION
60
30
+ 
30
0.
120 __
150
1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Year
Figure 3.3 Shoreline positions at the St. Augustine Site
ST. JOHNS
SHORELINE POSITION
300 
270 B B
240  A
210
S180
o 150
U)
0
a. 120 1
90 
60____ ___
30
0
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Year
Figure 3.4 Shoreline positions at the St. Johns Site
VOLUSIA NORTH
SHORELINE POSITION
180
 A
150 
r 0
120
120  O
90 ______
.' 60
0
60
60 *       
1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995
Year
Figure 3.5 Shoreline positions at the Volusia North Site
VOLUSIA SOUTH
SHORELINE POSITION
A/ _____,______ ___
,AAst
 ~ X~
Z0
__
_
120
90
60
30
0
30
60
90
120
150
180
210
1!
1990 1995
Figure 3.6 Shoreline positions at the Volusia South Site
MARTIN COUNTY
SHORELINE POSITION
e
+.'
,
....... ............ 
^.^\N. N l\__ ___ __ __
1980 Year
Year
1990
1995
2000
Figure 3.7 Shoreline positions at the Martin County Site
1945 1950 1955 1960 1965 1970 1975 1980 1985
940
90
60
30
0
30
60
90
120
150
180
210
240
1
965
COMPARISON OF AVERAGE SHORELINE POSITION
AT THE FIVE SITES
270
240 Martin U St. Johns
210 St. Augustine 0Volusia North 
180 Volusia South
120 
30
60 
90 30
120
150
1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Year
Figure 3.8 Comparison of the average shoreline positions at each of the five Sites
Both sites within Volusia County also exhibit similar trends. The erosion caused
by the Ash Wednesday Storm and Hurricane Dora is reflected in the first post 1964 data
point at both sites. This erosional trend is followed by an accretional trend as both sites
recover from the Ash Wednesday and Hurricane Dora induced erosion, and accrete to
maximum seaward positions by 1978. The effects of Hurricane David are reflected in the
erosion indicated by the 1979 data points at each site. Again the most recent data points
indicate a more naturally dynamic shoreline position. The major trend indicated by the
most recent 20 years of photographs is the erosion related to the passage of Hurricanes
Dean, Gabrielle, and Hugo in 1989, and the subsequent recovery. In this case,
comparison between the two sites is made more difficult due to the different time periods
between photographs.
In Martin County only one site was analyzed due to the scarcity of photographs
containing suitable control structures. The shoreline at Locations A and X exhibit similar
behavior. The deviation of the trends observed at Location Z from those observed at
Locations A and X is likely due to the fact that Location Z is too close to St. Lucie Inlet.
It appears likely that Location Z is more affected by the inlet dynamics than the local
shoreline change trends, particularly in the case of small shortterm trends. Locations A
and X experience an erosional trend between 1971 and 1974, but recover and accrete to
maximum seaward positions in 1976. Once again, the effects of Hurricane David are
observed in the erosion indicated by the 1980 data points. Between 1980 and 1996 the
shoreline changes are much milder than in the preceding decade with all three locations
exhibiting an erosional trend between 1983 and 1986 followed by an accretional trend
between 1986 and 1992. It should be noted that the 1992 data points are based upon
photographs taken in January and thus do not reflect the impact of Hurricane Andrew.
Averaging the several locations at each site and plotting the average shoreline
positions at each site as in Figure 3.8 yields some interesting results. Several major
trends are be observed. The erosion indicated by the data points in the early 1940's and
the early 1950's reflects the impact of the abnormally large number of Category 3
hurricanes making landfall during the 1940's. The erosion caused by Hurricane Dora and
the Ash Wednesday Storm is reflected in most of the post 1964 data points. The
relatively calm period between 1964 (Dora) and 1979 (David) is indicated by the
accretional trends exhibited at all five sites. Most sites accrete to a maximum beach
width between 19751978. The influence of Hurricane David at all five sites is exhibited
in the erosion indicated by the first post 1979 data points. In all cases, the most recent
data appears to indicate a more dynamic shoreline due to closer spacing of the
photographs and the lack of a large number of extreme storm events. The only major
trend exhibited at all 5 sites in the last 20 years is the erosion resulting from the passage
offshore of Hurricanes Dean, Gabrielle and Hugo in 1989.
Based on Figures 3.33.7 shoreline change rates may be calculated. Individual
shoreline change rates range from 6.5 feet per year at Location Z of the Martin Site to
+4.6 feet per year at Location B of the St. Johns Site. Based on the individual trends, an
average shoreline change rate of 0.05 feet per year is calculated. Removing Location Z
of the Martin Site (due to the expected influence of St. Lucie Inlet) from the average
calculation results in an average shoreline change rate of +0.41 feet per year, or
approximately 5 inches per year. This number agrees well with what Dean has reported.
In analyzing these results, it is interesting to note that shoreline trends are largely
dependent on the initial position chosen for comparison. Choosing an initially eroded
state will most likely yield an accretional trend while choosing an initially accreted state
will most likely result in the calculation of an erosional trend. In general the layperson
does not appreciate the magnitude of these naturally dynamic conditions. The shoreline
change data presented here indicates natural shoreline fluctuations of over 200 feet in the
past 50 years at several locations. It is interesting to note that the beginning of the coastal
construction boom in Florida, during the mid to late 1970's, coincided with the period of
maximum beach width.
CHAPTER 4
EROSION INDICES
As discussed in the introduction, the primary objective of this thesis is to correlate
observed shoreline fluctuations with readily available storm parameters. The goal is to
develop an index capable of accurately predicting the erosive potential associated with
extreme storms. Dean's hurricane erosion index and Balsillie's equation for calculating
volumetric erosion are modified and applied in an attempt to develop an index capable of
predicting the observed shoreline changes caused by historical storms.
Input data common to both models includes shoreline position data obtained from
the OBCS database and hurricane data obtained from the Colorado State University
hurricane database. Additional storm parameters are obtained from the National
Hurricane Center website and NOAA Technical Report NWS 15 (Ho, Schwerdt, and
Goodyear, 1975). Hurricane track information is first translated from latitudelongitude
coordinates to Florida State Plane East coordinates using the US Army Corps of
Engineers' Corpscon program. Once the hurricane tracks are converted, all hurricane
positions with negative coordinates, indicating locations well south and west of the study
area, are eliminated. This procedure limits the hurricane data set to 337 hurricanes and
major tropical storms occurring during the study period from 1950 to 1997. Of the
required hurricane parameters including: location, forward velocity, maximum winds,
radius to maximum winds, and central pressure, only the radius to maximum winds and
central pressure are not consistently recorded. In the case of central pressure, a sufficient
number of records exist, such that linear interpolation to determine the missing values is
valid. The missing radius to maximum wind data is more problematic. A large number
of records are missing this vital parameter. The statistical analysis presented in Ho,
Schwerdt, and Goodyear is utilized to assign all hurricanes lacking a recorded radius to
maximum winds a value of 23.5 miles, corresponding to the approximate median radius
of landfalling hurricanes along Florida's East coast. It is recognized that this assumption
limits the index accuracy; however, lacking more complete data, it is required.
A brief review of the geometry utilized in the development and application of the
indices will facilitate future discussions. The base coordinate system is the Florida State
Plane East coordinate system with the East axis corresponding to the xaxis and positive
offshore, and the North axis corresponding to the yaxis and positive north. Most angles
are defined with respect to the xaxis and are positive counterclockwise, although
exceptions exist and will be noted. The shoreline orientation defined by the angle a is
one such exception. The angle a is defined as the angle between the shoreline and the y
axis and is clockwise positive. Several angles defined in the conventional manner and
used throughout include 0, sin, Osrotwvect, and P. The angle 0 defines the hurricane
location with respect to the base coordinate system. Oin is the angle between the radius
and shoreline normal and is defined in terms of 0 and a as
0,, =0+a (4.1)
The angle of interest is the angle of the gradient wind vector with respect to the shoreline
normal. In terms of Osin, this angle, Osin_rotwvect, is defined as
rotwv = Os, 90 +18" (4.2)
The 18 accounts for the inward rotation of the gradient wind vectors due to frictional
effects. The angle 3 is defined as the angle between the velocity vector and the radius,
and is given in terms of o and 0 as
3 = 180 o0+ (4.3)
Here o defines the direction of the velocity vector. Figures 4.14.3 provide definition
sketches of the problem geometry.
.N (delE.delN)
Shore
R Normal
E
Figure 4.1 Definition sketch of a, 0, and %in
irmal
Rotated
Wind
Vector
Figure 4.2 Definition sketch of 0sin_rotwvect
Figure 4.3 Definition sketch of ( and 13
Event Longevity Parameter Index (ELP)
Theory
The Event Longevity Parameter (ELP) Index is an application of Eq. (2.13). The
index name refers to the inclusion of a measure of the event longevity, the storm tide rise
time, which led Balsillie to originally refer to the parameter raised to the fourfifths
power in Eq. (2.13) as the "event longevity parameter". Required input parameters for
the ELP Index are the maximum storm surge and the associated storm surge rise time.
Ideally the surge and rise time can be determined from storm surge hydrographs as
indicated in Figure 2.4. Due to the large scope of the project (337 hurricanes), and the
scarcity of available storm surge hydrographs, alternative methods of determining the
required parameters are employed. The maximum surge associated with each hurricane
is determined from a onedimensional storm surge model. The associated rise time is
calculated from the event forward speed according to Eq. (2.14).
Because most winter storm related surge is caused by wave induced setup, an
alternate method of determining the surge related to winter storms is required. The local
wind conditions utilized in the storm surge model often give little indication of winter
storm related surge. Artificial hydrographs are created for the winter storms based on the
difference between the observed and predicted water levels. Both methods of
determining the surge are described in detail in the next section.
Once the storm surge and rise time have been determined, the ELP Index is
defined as
ELP= 2 (S jtg'5 (4.4)
1622
where S is in feet, tr is in hours, and g is in feet per hour squared. In order to more
accurately represent the dynamic conditions associated with a hurricane, the tracks are
interpolated to hourly intervals, prior to the application of the ELP Index.
There are several minor differences between the ELP Index and Balsillie's
original equation. Balsillie defines S as the maximum storm tide including astronomical
effects. Here, S is taken as the maximum storm surge in absence of astronomical effects.
The storm surge is used in place of the storm tide because most of the surge values are
calculated from a storm surge model. Since Eq. (4.4) is intended to be an index,
obtaining the astronomical tides and synchronizing the results of the surge model to the
astronomical tides is thought to be unnecessary at this stage. Another difference between
the index and the original equation is in the determination of the event rise time. Balsillie
defines the forward velocity, Vf, in Eq. (2.14) as that corresponding to the time at which
the radius to maximum winds makes landfall. Since in the ELP Index the surge data are
calculated from a model, it is possible that the radius to maximum winds never makes
landfall. Here, the instantaneous velocity corresponding to the time at which the
maximum surge occurs is used in the calculation of the storm surge rise time.
The ELP Index is applied for a total of three cases. In the first case a one
dimensional storm surge model is applied without including the effects of setup. In the
second case, the same model is applied but several winter storms are introduced. The
third and final case considers only hurricanes and utilizes the same surge model but
includes wave setup.
Winter Storm Related SurgeReconstructed Hvdrographs
The main component of the surge generated by winter storms is the wave induced
setup. A storm surge model based upon local conditions, as applied to the hurricane data,
cannot capture the effects of remotely generated swell. Reconstructed hydrographs are
developed for all 25 included winter storms, utilizing observed water level data and
predicted tidal elevations. The reconstructed surge hydrograph is simply the observed
minus the predicted water level. Figure 4.4 is an example of a hydrograph created using
this technique. Maximum surge elevations and rise times are obtained directly from the
reconstructed hydrographs as indicated in Figure 4.4.
Tide predictions are obtained from National Oceanic and Atmospheric
Administration (NOAA) tide tables and the Mote Marine Laboratory website. (The
website data are comparable to the NOAA tables but are electronically formatted, making
them easier to analyze.) Observed water levels are obtained from the NOAA Center for
Operational Oceanographic Products and Services (COOPS) database. Unfortunately,
the COOPS data are incomplete for many of the Florida stations. Mayport is the station
nearest to all three sites that contains a complete data set; therefore the artificial
hydrographs are created based upon conditions at Mayport. It is recognized this will
introduce some error into the indices particularly at the Martin County Site, however
because the indices are only intended to compare the effects of various storms at a single
location and are not intended to compare the effects of individual storms between
locations, it is hoped that any error will be reasonably small.
Ash Wednesday Storm
March 1962
18
16
14
12
t
F 10
I 8
m 6
4
2
0
2
1 4 7 10 13 16 19
Day
Figure 4.4 Example of a recreated storm surge hydrograph using the Mayport, Florida
data. In this case two distinct surge events are observed.
Hurricane Related SurgeBathystrophic Storm Surge Model
In order to calculate the storm surge associated with passing hurricanes, a one
dimensional storm surge model is employed. The storm surge created by a hurricane can
be considered as the sum of four individual components: wind stress, barometric pressure
reduction, Coriolis contribution, and wave setup. Generally the Coriolis and pressure
effects are small compared to the wind stress and wave setup components. The one
dimensional model employed here does not include the effects of wave setup, therefore it
is calculated explicitly utilizing WIS hindcast data. Unfortunately, the WIS data prior to
Observed+10'
Surge=2.04' Surge=1.9'  Predicted+10'
t6hrs 111 84hr_Surge (ObsPred)
1976 do not include the effects of hurricanes and tropical storms. Because of this
limitation, the storm surge model was applied for the full study period from 19501997
excluding the setup, and also for the reduced period from 19761995 including the setup.
The onedimensional storm surge model is based upon the bathystrophic surge
model originally proposed by Freeman, Baer, and Jung (1957), and later applied by Chiu
and Dean (1984). Applying the assumptions of Freeman, Baer, and Jung, as described in
Chapter 2, and writing the simplified equations of motion in finite difference form results
in
q n+ = 1 F +At y, (4.5)
qi_ BB y + tw" (4.5)
n+1 n+1 Ax w1 n+1 n++
4T =f +  q I + P P (4.6)
gDi I p, y p0g
BB = 1.0+ f (4.7)
Di2
where the previously undefined f is a bottom friction factor taken as 0.01. The subscripts
i and n refer to the grid location and time step respectively. Reviewing the coordinate
system, x represents the crossshore direction and is positive onshore, and y represents
the longshore direction and is positive North. At this point it is convenient to break the
surge into its constituent parts and describe each component individually.
The surge generated by the atmospheric pressure gradient associated with a
hurricane is given by
n+I n+I
Pi Pi+i (4.8)
Pwg
The pressure at each location along the grid is calculated from Eq. (2.1) and is based
upon the exponential pressure distribution associated with the model hurricane. As
evidenced by Figure 2.2, the magnitude of the pressure reduction associated with a
hurricane dies out rapidly. Close examination of Figure 2.2 and Eq. (2.1) reveals that
unless the hurricane passes within several radii of the coastline, the barometric induced
surge is not expected to be a dominant contributor to the total surge.
The contribution of the Coriolis force to the total surge is given by the second
term inside the brackets of Eq. (4.6).
Ax Eq +1] (4.9)
gDi
The Coriolis parameter E is defined as 2osino, where 0 is the latitude of the location of
interest, and o is the angular frequency of the earth's rotation. Due to the large length
scales, and significant longshore currents, a hydrostatic gradient (surge) is developed to
compensate for the Coriolis effect. The negative sign indicates that a negative longshore
current, directed south in this case, results in a positive contribution to the surge. As was
the case with the barometric contribution, the contribution of the Coriolis effect is small
when compared to the contributions of wave setup and wind stress.
The wind stresses in both the crossshore and longshore directions are important
components of the storm surge even in this onedimensional model. The crossshore or
xcomponent of the shear stress is included directly in the calculation of the surge
through the first bracketed term in Eq. (4.6).
Axr'i p, (4.10)
gDL Pw J
where Twx is the wind shear stress given by
T = pkW2 (cos 0 Iotwvet ) (4.12)
The previously undefined factor k is the Van Dor airsea friction coefficient given by
1.1x106 W
k = Wc 2 (4.14)
S1.1x106+2.5x106 1 W >WC
We is a critical velocity equal to 16.09 miles per hour. The negative cosine term in Eq.
(4.12) is the result of two different coordinate systems. Eqs. (4.54.7) consider the cross
shore coordinate to be positive onshore, however the Florida State Plane system used as
the base system for calculating the indices, defines the crossshore coordinate as positive
offshore. The negative sign simply reverses the direction of the wind stress term
rendering the systems compatible. The longshore or ycomponent of the wind stress is
included in the surge calculation indirectly through its influence on the volumetric
longshore transport. The longshore component of the wind stress is given by
T, = P kW2 (sins_rotwvc) (4.13)
Eq. (4.5) gives the volumetric longshore transport per unit width as a function of the
longshore wind stress. The effect of the longshore component of the wind stress on the
surge is eventually incorporated into the contribution of the Coriolis term discussed
previously. The direct and indirect contributions of the wind stress, along with the wave
induced setup, are the largest contributors to the total storm surge.
The contribution of the wave setup must be calculated and included explicitly.
Prior to determining the effectiveness of either index, it was determined that calculation
of the wave fields associated with each hurricane to obtain local wave conditions was
beyond the scope of this project. The largest sets of wave data available are the WIS
hindcast data, which are available for the period 19501995. The WIS data are composed
of two sets of hindcasts, the first of which does not include the effects of hurricanes and
therefore is excluded. This reduces the usable range of WIS data to the period from 1976
to 1995. The WIS data report the wave parameters in variable water depths, at 0.25
spacing, on threehour intervals. The WIS data are time synchronized to each individual
hurricane. A filter is applied based upon the wave angle with respect to the shoreline
orientation to eliminate any offshore propagating waves. Linear theory and the
assumption of straight and parallel contours are utilized to refract and shoal the waves to
the breakpoint. Depth limited breaking assuming a breaking index of y=0.78 and the
familiar LonguetHiggins (1964) result ares utilized to calculate the setup at the shoreline
from the breaking conditions.
H 2kh, 3y/8 (4.4
b + hb
16hb sinh(2khb) 1+3 /8
Here k is the wave number and Hb and hb are the breaking wave height and depth
respectively. Recognizing that waves are always present and that a background setup
exists, the average setup over the 25year data set is calculated and subtracted from the
result, isolating the hurricane induced setup. The contribution of the setup is included
only at the shoreline. In order to simplify the calculations, the setup is not assumed to
modify the depth at each location along the profile.
The onedimensional storm surge model, encompassing Eqs. (4.54.7), is solved
over the full time period neglecting the setup, and over the shortened time period
including the setup. The initial and boundary conditions for the model include initiation
from rest and surge due to barometric effects alone at the seaward edge of the grid.
S1=P Pi (4.15)
P g
Here poo is the pressure in the absence of the hurricane and pi is the local pressure at the
seaward edge of the profile.
Results
The ELP Index is calculated for each storm at the monument corresponding to the
center point of the three locations analyzed at each of the 5 sites. In an effort to
determine an optimal interval of application, the index is summed over one, three, and
five years prior to each photograph as well as over the period between photographs. The
ELP Index is then plotted versus the average observed shoreline change at each site.
When the accretion is plotted versus the ELP Index, no trend is observed. This should be
expected, as the index is not intended to predict accretion. When erosion is plotted
versus the ELP Index a minor trend is observed. As expected, larger values of the ELP
Index tend to indicate more erosion, although the correlation is less than expected. A
bestfit line is added based upon the Rsquared value. The Rsquared value is a measure
of the goodness of fit and is defined as
R2 = 1 __ j (4.16)
n
Both exponential and linear trends were fit to the data. In the case of a linear trend, an
attempt was made to force the line through the origin, as ideally an index value of zero
indicates no erosion. In most cases, the bestfit line takes a linear form and is not forced
through zero. The parameters associated with the bestfit lines vary substantially from
location to location, in some cases even indicating a decreasing trend.
Table 4.1 gives the Rsquared values for each case at each site. Underlined values
correspond to trendlines with negative slopes, indicating poor agreement. Table 4.1
40
indicates the best correlation as determined by the Rsquared values occurs when the ELP
Index over the year preceding each photograph is utilized. In general the correlation
between the observed shoreline changes and the ELP Index is not good, with only one R
squared value greater than 0.5. Examining several of the plots allows us to see where and
why the index failed.
Table 4.1 Rsquared values indicating the correlation between the observed erosion and
the ELP Index for the case of no setup and no winter storms.
R SQUARED VALUES
Site 1 year prior 3 years prior 5 years prior Between Photos Data Points
St. Johns 0.039 0.005 0.002 0.044 6
St. Augustine 0.710 0.433 0.455 0.380 6
Volusia North 0.055 0.138 0.014 0.000 4
Volusia South 0.307 0.148 0.265 0.130 6
Martin 0.498 0.285 0.201 0.304 4
Average 0.322 0.202 0.187 0.172
ELP Index vs Erosion
St. Augustine Site
I i I I I I I
25
20
x
O
 15
Lu
J
10
5
0
Cum
3yr
 Linear (lyr)
 Linear (5yr)
S___ 2.7
K9
c
S,
y=0.3797: 1.9187 .
R2 = 0 4551 /
* x 7
0" y =0.4143x 14.305
= 0.3567x 4.7668 R2 = 0.709
R2 = 0.304 of
 M 4
0 10 20 30 40 50 60 70 80 90
Erosion (ft)
Figure 4.5 Plot of ELP Index versus erosion at the St. Augustine Site. Setup and winter
storms are not included.
1yr
5yr
 Linear (3yr)
 Linear (Cum)
2 = 0.4327
I


ELP Index vs Erosion
St. Johns Site
0 10 20 30 40 50 60 70 80 90
Erosion (ft)
Figure 4.6 Plot of ELP Index versus erosion at St. Johns Site.
are not included.
ELP Index vs Erosion
St. Augustine Site
35
Cum lyr
30 A 3yr X 5yr
 Linear (lyr)  Linear (yr) X
 Linear (5yr)  Linear (Cum)
25
y = 0.4204x 19293
S15 ^ 
10 to A 
= 0.3628x 2.8005 0 0
'02_n ,  =O. 46
2 5 .y=0.
0 i
Setup and winter storms
0 10 20 30 40 50 60 70 80 90
Erosion (ft)
Figure 4.7 Effect of removing all four points associated with the 1989 erosional event
from Figure 4.5.
42
ELP Index vs Erosion
St. Johns Site
35
30
25
x
c 20
Si15
10
5
n
0 10 20 30 40 50 60
Erosion (ft)
Figure 4.8 Effect of removing all four points associated with the 1989 erosional event and
the cumulative point associated with the period 19601971 from Figure 4.6.
The St. Augustine Site, represented by Figure 4.5, is the case where the index
appears to work the best. The trend is clear and the Rsquared values for the bestfit lines
are reasonably high. Figure 4.6, representing the St. Johns Site, is an example of a case
where the index appears to fail. The St. Johns data appear to indicate larger values of the
ELP Index are associated with less erosion. Not only are the Rsquared values low, the
bestfit lines indicate a trend completely opposite of what was expected. Closer
examination reveals one or two data sets responsible for the poor agreement at the St.
Johns Site. Examination of these data sets indicates why the index fails. The data points
in Figure 4.6 associated with over 80 feet of erosion and low values of the ELP Index
cause the bestfit lines to slope in the wrong direction. This data set corresponds to
shoreline change over the period 19881989. Extensive analysis of the local conditions
during this period revealed extreme wave conditions associated with the three offshore
Cum N lyr
A 3yr X 5yr
S Linear (3yr) Linear (1yr)
 Linear (5yr)  Linear (Cum)
y = 0.5431x+ 1.935
R = 0.5307 01 a 0 __ "0
O
= 0.485x+ 1.131 _______
R2=0.5046 o O
R2 = 0.9874
Hurricanes Dean, Gabrielle, and Hugo. The surge model does not predict large surges
associated with these storms due to their distance offshore. These storms behave much
like winter storms in that a large proportion of the storm surge will be due to wave
induced setup. As is the case with winter storms, an alternate method of analysis is
required to capture the setup effect.
The data point corresponding to an index value of over 150 feet in Figure 4.6 also
appears to be distorting the results. This data point corresponds to the cumulative ELP
Index between a photograph in 1960 and the next available photograph in 1971. Here the
long interval of application is questioned. Examination of the ELP Index associated with
each individual storm occurring between the available photographs indicates that nearly
75% of the index value is associated with Hurricane Donna in 1960, and Hurricane Dora
in 1964. In this case, the interval of application is believed to be too long. The 28 feet of
erosion indicated by the two available photographs reflects both the erosion caused by the
storms, and 8 years of subsequent recovery. Very few storms impacted St. Johns County
between 1964 and 1971, therefore it is likely that the shoreline recovered substantially
prior to the second photograph. Here the index fails because the photographs taken over
10 years apart do not capture the true erosional effect of the storm. Figure 4.8 illustrates
the improvement observed in the correlation between the ELP Index and the erosion at
the St. Johns Site when the cumulative data point and all four data points corresponding
to 1989 are removed. Although the correlation at the St. Augustine Site was good to
begin with, Figure 4.7 shows additional improvement resulting from the removal of the
1989 data set. No cumulative data point is removed at St. Augustine due to the higher
density of photographs, including one in 1963.
The substantial increases in Rsquared values at the St. Johns and St. Augustine
Sites are observed at all locations when the 1989 data set and any cumulative data points
calculated by summing the ELP Index over 10 or more years are eliminated. Table 4.2
gives the Rsquared values resulting from the removal of these data points. It should be
noted that the value of 1.0 reported for the cumulative data point at the Volusia North
Site reflects the fact that after removing the 1989 data set and the cumulative point for the
period 19581969 only two data points remain.
Table 4.2 Rsquared values resulting from the removal of the 1989 data set and the
cumulative data point where the interval of application is greater than 10 years.
R SQUARED VALUES
Site 1 year prior 3 years prior 5 years prior Between Photos Data Points
St. Johns 0.723 0.504 0.531 0.987 5 (4 cum)
St. Augustine 0.870 0.716 0.621 0.752 5
Volusia North 0.453 0.000 0.405 1.000 3 (2 cum)
Volusia South 0.640 0.586 0.821 0.712 5
Martin 0.498 0.285 0.201 0.304 4
Average 0.637 0.418 0.516 0.751
A second set of plots is generated by adding 25 severe winter storms to the
analysis. The procedure for analyzing the results is the same as in the first case. Again
the bestfit line, as determined from the Rsquared value, is linear in all cases. Table 4.3
presents the Rsquared values from these plots. Comparing the values in Table 4.3 with
those in Table 4.1, it is observed that inclusion of the winter storms drastically reduces
any correlation between the ELP Index and the observed erosion. Table 4.3 indicates that
nearly half of the bestfit lines have negative slopes as indicated by the underlined values.
Only the St. Augustine Site produces results that follow the expected trend. Although all
four trendlines at the St. Augustine Site have positive slopes, the small Rsquared values
are indicative of the large amount of deviation from the trendline. Excluding cumulative
data points calculated over 10 years or more and the 19881989 data set, as done in the
previous case, has a negligible effect on these results. An example of the results obtained
by including winter storms is given in Figure 4.9.
ELP Index vs Erosion
_ Martin Site (Winter Storms Included)
t3yr, ,
300
250
e 200
1 150
100
50
0
Cum
t5yr
 Linear (t5yr)
 Linear (t1vrt
t3yr
t1yr
 Linear (Cum)
 Linear ft3vr
y = .4384x + 494.39
2 0.200721
4* A
y=02079x+130.2 
2 = 0.0012
y = 0.6687x 27.764
R2=0.4 84
I ..XV
10 20 30 Erosion (ft) 40 50 60
0 10 20 30 Erosion (ft)40 50 60
Figure 4.9 Plot of ELP Index versus erosion at Martin County Site. Winter storms are
included, setup is not.
Table 4.3 Rsquared values indicating the correlation between the observed erosion and
the ELP Index for the case of no setup, including winter storms.
R SQUARED VALUES
Site 1 year prior 3 years prior 5 years prior Between Photos Data Points
St. Johns 0.312 0.055 0.001 0.263 6
St. Augustine 0.001 0.008 0.000 0.002 6
Volusia North 0.203 0.464 0.500 0.018 4
Volusia South 0.065 0.382 0.202 0.121 6
Martin 0.498 0.607 0.499 0.001 4
Average 0.216 0.303 0.240 0.081
y = 6.2481 x
2 ,
+ 559.74
0n
Several possible explanations are given for the reduction in the index's
effectiveness. Although in general the magnitudes of the winter storm related surge is on
the order of the hurricane related surge, the rise times are five to ten times larger.
Although not surprising physically, this results in ELP Index values for winter storms that
are four to eight times larger than those associated with even the strongest hurricane. The
analysis of seasonal shoreline changes presented in Chapter 5 indicates that in selecting
only 25 storms, numerous other important winter storms are excluded. The winter season
is characterized by a large number of severe storms, both named and unnamed, that cause
substantial erosion. Without representing the background effect of all of these storms,
the index will not work. The summer season on the other hand, is characterized by more
predictable, mild conditions. In 90% of the cases, extreme summer erosion is associated
with the 337 analyzed hurricanes. The background effect is much less important in the
summer, allowing for a better application of the ELP Index.
As mentioned in the discussion of the results from Case 1, excluding the effect of
wave setup appears to be limiting the index's effectiveness. Although this is particularly
true in the case of the 19881989 data, it is assumed the exclusion of the wave setup
affects other data sets as well. A third case was examined explicitly including the wave
setup in the storm surge model, however, as previously mentioned, this has the
consequence of limiting the scope of analysis. The duration of the analysis is limited to
19761995 by the available wave data and produces inconclusive results. In the previous
analyses, the bestfit lines were based upon a maximum of six data points. Reducing the
study period reduces the number of data points on which the trendlines are calculated,
thereby reducing the amount of confidence that can be placed in the results.
The method of analysis is the same as in the previous two cases. The results are
plotted and the linear bestfit trendline is added. Table 4.4 gives the Rsquared values
associated with the best fit lines. As in the previous two cases, underlined values
indicate negatively sloped trendlines. The large variability in both the Rsquared values
and the slope directions within each site is a direct consequence of calculating the
trendlines based on only three data points. The best agreement is observed at the Volusia
North Site, which is presented as Figure 4.10. Here, three of the four bestfit lines
indicate increasing trends, and the Rsquared value for both the threeyear and the
cumulative trendlines is nearly one. Figure 4.11 is an example of a case where little
correlation between the ELP Index and the historical erosion is observed. In this case
two of the four trendlines are sloping in the wrong direction and of the two positively
sloping trendlines only one has an Rsquared value greater than 0.5. Theoretically,
including the setup should improve the correlation between the ELP Index and the
observed erosion, however with only three data points on which to base the results no
definitive conclusion can be made.
Table 4.4 Rsquared values indicating the correlation between the observed erosion and
the ELP Index for the case of including setup and no winter storms.
R SQUARED VALUES
Site 1 year prior 3 years prior 5 years prior Between Photos Data Points
St. Johns 0.976 0.773 1.000 0.995 3 (5yr2)
St. Augustine 0.248 0.437 1.000 0.083 3 (5yr2)
Volusia North 0.846 0.949 0.134 0.960 3
Volusia South 0.737 0.004 0.538 0.992 3
Martin 0.177 0.144 1.000 0.047 3 (5yr2)
Average 0.597 0.461 0.734 0.615
48
ELP Index vs Erosion
Volusia North Site
15 25 35 45 55 65 75 85 95 105
Erosion (ft)
Figure 4.10 Plot of ELP Index versus erosion at the Volusia
included, winter storms are not.
North Site. Setup is
ELP Index vs Erosion
Volusia South Site
Cum y = 4.0669x +331.43
1yr R = 0.92 y = C.4586x+230.7
RA = 0.538
A 3yr R  ,
5 yr .....
S Linear (1 yr)
 Linear (Cum) _
Linear (3 yr)
Linear (5yr)   
'=0.0761 +118.8l
R2 = 0.003'
Sy = 2.012x40.45
S S R2=0.7367
0 10 20 30 Ersion () 40 50 60 71
Erosion (ft)
Figure 4.11 Plot of ELP Index versus erosion at the Volusia South Site. Setup is
included, winter storms are not.
300
250
200
_ 150
a.
J
100
50
0
Hurricane Erosion Index (HEI)
Theory
The HEI is very similar to Dean's original index discussed in Chapter 2, with
several minor modifications made. In the new index, the forward velocity in the
denominator of the original HEI, is eliminated. Here, the forward speed is accounted for
directly when integrating over a hurricane track recorded at a constant time interval (6
hours). Density and friction factor terms are also added to the original index, resulting in
an equation more closely resembling the dominant wind stress component of the storm
surge.
10R
HEI= J pkW (cosO rtwvt)dr (4.17)
0
As described previously, the negative sign preceding the cosine term is the result of the
two different coordinate systems. The negative sign reverses the direction of the cross
shore coordinate, making the onshore direction positive. Reversing the direction of the
crossshore coordinate results in positive index values corresponding to an onshore wind
stress. Based on Figure 2.5, the limits of integration are kept the same.
In applying Eq. (4.17), two geometrical approximations are employed. The first
assumption is that the shoreline is located at the monument location. In reality, the
monuments are not located at the shoreline, however the large spatial scales involved in
calculating the HEI justify this simplification. An approximation is also employed for the
shoreline orientation angle, a. The shoreline orientation is taken as 17.80, north of state
plane coordinate 833,400.0 (approximately West Palm Beach), and +6.7 to the south.
Both of these angles are approximate and are determined graphically.
Results
The results obtained from the application of the HEI are very similar to those
obtained with the ELP Index. The methodology applied in analyzing the results is the
same. The HEI associated with each hurricane is calculated at the center of each site and
then summed between each photograph, and one, three, and five years prior to each
photograph. The results are plotted versus the average observed shoreline change over
each interval at each site. As expected, periods of accretion are characterized by small
values of HEI. Trendlines are added to the plots of HEI versus erosion, with the bestfit
lines determined from the Rsquared values. In all cases, the bestfit lines are linear,
although the slopes and intercepts exhibit significant scatter. Table 4.5 presents the R
squared values for each case at each site, where underlined values indicate trendlines with
a negative slope. Again the correlation between the observed erosion and the HEI is less
than expected. Several of the trendlines slope in the wrong direction, and only three of
the twenty Rsquared values are greater than 0.5. Examination of the results obtained at
the St. Johns Site as presented in Figures 4.12 and 4.13, yields some insight into the
apparent failure of the index.
Table 4.5 Rsquared values indicating the correlation between the observed erosion and
the HEI.
R SQUARED VALUES
Site 1 year prior 3 years prior 5 years prior Between Photos Data Points
St. Johns 0.006 0.067 0.046 0.081 6
St. Augustine 0.514 0.180 0.197 0.173 6
Volusia North 0.027 0.717 0.367 0.012 4
Volusia South 0.311 0.003 0.293 0.270 6
Martin 0.556 0.454 0.066 0.140 4
Average 0.283 0.284 0.194 0.135
HEI vs Erosion
St. Johns Site
12
1 Cum lyr
10 A 3yr X 5yr
 Linear (3yr) Linear (1yr)
S Linear (5yr) Linear (Cum)
8 ______
W 6 00445X4 5474 
R= 0.0E 08
R2= (.0669 " R2= 00462
"'" ,, ,'.'.'' = =.
= 0.0058 0.696.6 ... .       
R2 = 0. 055
0 10 20 30 40 50 60 70 80 90
Erosion (ft)
Figure 4.12 Plot of HEI versus erosion at the St. Johns Site.
Upon examination of Figure 4.12, it is apparent that problems similar to those
affecting the application of the ELP Index affect the application of the HEI. Contrary to
what was expected, Figure 4.12 indicates larger HEI values correlated with smaller
amounts of erosion. Similar to the problem with ELP Index, this can be attributed to the
data set indicating over 80 feet of erosion, corresponding to the shoreline changes
between 1988 and 1989. As discussed previously, three hurricanes producing substantial
storm surges, passed offshore of Florida during 1989. The effects of these hurricanes are
not captured because they fall outside the limit of integration placed on the HEI.
Increasing the limits of integration has little effect due to the rapid decay of the wind field
with distance. Similar to winter storms, the erosion caused by these offshore hurricanes
is likely the result of an increased water level due to the setup resulting from hurricane
waves generated well offshore.
The cumulative data point corresponding to a HEI of approximately 11 also
appears to be distorting the results. This data point corresponds to the cumulative HEI
between a photograph in 1960 and the next available photograph in 1971. As discussed
in the ELP Index section, the interval of application is too long. Analysis of the HEI
values attributed to individual storms during this period reveals over half of the index
value can be attributed to Hurricane Donna in 1960. It is likely that the shoreline changes
indicated by the 1971 photograph reflect not only the erosion caused by Hurricane
Donna, but also a substantial amount of poststorm recovery.
Figure 4.13 illustrates the effects of removing the 1989 data points, and the
cumulative data point from the ST. Johns data. In this case, as in all cases, the Rsquared
values increase substantially. The Rsquared values resulting from the removal of
cumulative data points calculated over periods of ten or more years, and the entire 1989
data set, are illustrated in Table 4.6. Upon removal of the questionable data points, more
than half of the Rsquared values increase to greater than 0.5, a substantial improvement.
Summing the HEI between each photograph and over the 5 years prior to each
photograph results in the best correlation.
Table 4.6 Rsquared values resulting from the removal of the 1989 data set and the
cumulative data point where the interval of application is greater than 10 years.
R SQUARED VALUES
Site 1 year prior 3 years prior 5 years prior Between Photos Data Points
St. Johns 0.428 0.825 0.881 0.896 5 (4 cum)
St. Augustine 0.647 0.425 0.436 0.434 5
Volusia North 0.216 0.592 0.518 1.000 3 (2 cum)
Volusia South 0.643 0.019 0.791 0.793 5
Martin 0.556 0.454 0.066 0.140 4
Average 0.498 0.463 0.538 0.653
HEI vs Erosion
St. Johns Site
5
4 
y = 0.0802x + (.7099 A 
3 0.811 y 0931x1.2557
2 x + F 2 = 0.4275
Sy = 0.0784x + 0.6466
R=0.8254 Cum I lyr
S0 A 3yr X 5yr
1 y = U.U084x 4 .4614 0  Linear (3yr)  Linear (lyr)
R2=0.8 58 Linear (5yr)  Linear(Cum)
010 20 30 40 50 60
Erosion (ft)
Figure 4.13 Effect of removing all four points associated with the 1989 erosional event
and the cumulative point associated with the period 19601971 from Figure 4.12.
Modified Hurricane Erosion Index (MHEI)
Theory
As discussed in the previous section, two major factors limit the HEI's
effectiveness. The first factor is the excessive time period between applications of the
index, particularly during the early period of the study. Errors resulting from attempts at
applying the HEI over intervals greater than the limits of its effectiveness can only be
fixed by obtaining more, better data, eliminating data points where the HEI is pushed
beyond its limits, or developing a method to account for the amount of recovery between
storms. The second factor hindering the effectiveness of the HEI, the exclusion of wave
effects, is somewhat easier to correct. A more detailed index for calculating the erosive
potential of a given storm including the effects of increased wave heights is developed
and termed the Modified Hurricane Erosion Index or MHEI.
w.
Ay<0
Figure 4.14 Definition sketch for the calculation of the change in shoreline position
resulting from an increased water level, S, and wave setup, Tj (Dean and Dalrymple
2001).
Once again, the Bruun Rule provides the basis for the MHEI. In addition to an
elevated water level, S, we introduce the wave induced setup, rl. Figure 4.14 graphically
depicts the problem setup. Equating the volume eroded from the foreshore and deposited
offshore utilizing equilibrium beach profile methodology results in
0 W.+Ay
I(BS1I(y))y+ A(yAy)2/3dy=
Ay Ay
W.+Ay W.+Ay
J Ay2/3dy + J+ i(y))y (4.18)
0 0
where A is the sediment scale parameter in units of length to the one third. All other
variables are defined in Figure 4.13. Integrating Eq. (4.18) and simplifying for the case
of small relative shoreline displacement results in
0.068Hb +S" .
Ay = W. .68Hb j (4.19)
(y BB+1.28Hb
where W* is the distance to the breakpoint and is calculated from the breaking depth
assuming an equilibrium beach profile. Writing W* in terms of Hb and dividing both the
numerator and denominator by 1.28 Hb results in
1.28Hb (S + 0.068Hb)
Ay = A B(4.20)
Y A3/2 B +12H
1 1.28Hb
Now we will define the numerator as the Modified Hurricane Erosion Index
MHEI= (S + 0.068Hb )1.28HbdA (4.21)
hurricane
Here the surge, S, is calculated from the previously described onedimensional storm
surge model. The integral is taken over the sea surface area affected by the hurricane.
The contribution of the wave setup is included through the breaking wave height, which
is calculated from the WIS data. As with the setup term in the surge model, a
background breaking wave height is subtracted from the storm related breaking wave
heights. The background wave height is obtained by averaging the longterm breaking
wave heights at each site, which are calculated by applying the shoaling routine to the
WIS data. Again the dependence on WIS data limits the period of analysis to 19761995.
Results
The shorter period of analysis imposed by the availability of the wave data allows
only a limited analysis. The same procedure as described previously is utilized to
compare the observed shoreline changes with the MHEI. Unfortunately, the reduced
study period leaves only three erosional trends for analysis. It is difficult to draw
conclusions from trendlines fit to only three points. The Rsquared values for each case
at each site are presented in Table 4.7, where the underlined values indicate decreasing
trends. It is obvious from Table 4.7 that the MHEI does not appear to improve the
results. Aside from the Volusia South Site, only one trendline has an Rsquared value
greater than 0.5 and a positive slope. Figures 4.15 and 4.16 represent cases where the
index appears to succeed and fail respectively. In viewing the results, the lack of
sufficient data must be kept in mind. A more complete data set is required before a
definitive judgment on the effectiveness of the MHEI can be made.
Table 4.7 Rsquared values indicating the correlation between the observed erosion and
the MHEI.
R SQUARED VALUES
Site 1 year prior 3 years prior 5 years prior Between Photos Data Points
St. Johns 0.731 0.017 1.000 0.046 3 (5yr2)
St. Augustine 0.095 0.865 1.000 0.799 3 (5yr2)
Volusia North 0.291 0.102 0.103 0.098 3
Volusia South 0.824 0.943 0.778 0.101 3
Martin 0.015 0.270 1.000 0.015 3 (5yr2)
Average 0.391 0.439 0.776 0.212
MHEI vs Erosion
Volusia South Site
600
Cum U 1 yr
A 3 yr X 5 yr y = 4. 585x + 230.49 X
500  Linear (5yr)  Linear (3 yr) R = 0.7782
 Linear (lyr)  Linear(Cum) ,
400 .
 . x J.
300 y=8094x 26943  
R2=0.1008 0 4 e "
200 ,
y =4.4021x 84.379 A *
R2 = 0.9429 I0
100
S y=7.63 7x 152.31
0 R2 = 0.8238
0 10 20 30 Erosion (ft) 40 50 60 70
Figure 4.15 Plot of MHEI versus erosion at the Volusia South Site
MHEI vs Erosion
Volusia North Site
700
CUM 1 yr
A 3 yr X 5 yr
600 y .342x+ . I Linear (1 yr) Linear (3 yr)
SR2= 0.0981
300 ..... 
300 x y= 1.0685x+220.
200
100 y = 1.983x + 260.87 
R = 0.2908
0
0 20 40 60 80 100 120
Erosion (ft)
Figure 4.16 Plot of MHEI versus erosion at the Volusia North Site
CHAPTER 5
SHORELINE RESPONSE RATE
The results presented in Chapter 4 suggest that at least a portion of the failure of
the erosion indices is due to the different time scales governing the erosion and accretion
processes. Ideally the indices should be compared with changes observed immediately
after each storm event, however in many cases they are applied over periods of a decade
or longer, as dictated by the photograph spacing. In this case, storm sequencing plays an
important role in determining the index's effectiveness as illustrated in Figure 5.1. If we
assume the index is perfectly correlated with the observed shoreline changes, the
following two scenarios are proposed. In Case 1, a large erosional event and
corresponding large index value occur at the beginning of a fixed time period. In Case 2,
the same event occurs at the end of an equal time period. The value of the erosion index
will be the same for both cases. In Case 1 the shoreline will gradually recover over the
remainder of the period. In Case 2, because the erosional event occurs immediately
before the end of the period, the beach will not have time to recover. Depending upon
the length of the period, and the rates of the erosion and accretion processes, the
perceived effectiveness of the index can vary substantially. In Case 2 the erosion index
performs admirably; in Case 1 it fails.
There are many models able to predict erosion adequately, but few if any, that
predict the recovery accurately. A satisfactory equation representing the rate of shoreline
response is needed to help describe the longterm evolution of the beach, particularly the
recovery phase. Potential applications of such an equation are numerous.
Effect of Storm Sequencing
on Perceived Erosion Index Effectiveness
0 1 2 3 4 5 6 7 8 9 10
Time
Figure 5.1 Graphical depiction of the effect of storm sequencing on the perceived
effectiveness of the erosion indices. In both cases the value of the erosion index will be
the same however the final position of the shoreline will be much different.
Rate Equation
Theory
An effective shoreline change rate equation should incorporate two key concepts.
First, the shoreline response should be related to its displacement from an equilibrium
position; the farther the shoreline is displaced from equilibrium, the faster it should
respond. Secondly, the equation should allow for the different time scales governing the
erosion and accretion processes to be represented. An equation similar to Eq. (2.20) is
proposed based upon these criteria.
Sk (t) y(t)) (5.1)
Here ka is a rate constant with different values for erosion and accretion, and yeq is the
equilibrium shoreline position, which is also a function of time. Eq. (5.1) can be solved
analytically for constant ka resulting in
y(t)= yoekat + kJek,(tt y(t)dt (5.2)
0
where yo represents the shoreline location at some initial time to. The contribution due to
yo approaches zero for steady state conditions and long time intervals. Analytic solutions
to Eq. (5.1) exist for a limited number of functions. A more direct application of Eq.
(5.1) is made by numerically solving the finite difference form of the equation.
Syln k1 At2 ++kAty.q
y =+ kAt (5.3)
The difficulty in solving Eq. (5.3) lies in the fact that both rate constants (erosion and
accretion) are unknown, as well as yeq. As discussed in Chapter 2, yq is a also a function
of time, varying in response to the different seasonal conditions throughout the year.
Results
Shoreline changes predicted by Eq. (5.3) are presented for several idealized cases
to illustrate the effect of changing the rate constants. In all cases, the seasonal
equilibrium shoreline position is approximated by a sinusoidal function. Artificial
erosional and accretional events are applied to help illustrate the effect of different rate
constants on the shoreline response.
Figure 5.2 illustrates the shoreline response assuming both rate constants are
equal to one, although in reality the erosion constant is larger than the accretion constant.
The shoreline response is a sinusoidal function, damped and phase lagged by nearly 900
with respect to the equilibrium shoreline position. Figure 5.3 illustrates the shoreline
response under the same conditions to both an erosional and accretional forcing. Because
the rate constants are equal, the shoreline requires the same amount of time to "recover"
from both events. Figure 5.4 illustrates the effect of increasing the rate constants. Notice
the shoreline fluctuations approach those of the equilibrium shoreline, and the phase lag
exhibited in Figure 5.2 is reduced as the shoreline responds at a faster rate.
Figures 5.5 and 5.6 illustrate the effect of reducing the accretional rate constant to
onefifth the erosional constant. Reducing the accretion constant has the effect of
reducing the amount of recovery that is achieved in a given time. When compared with
Figure 5.2, Figure 5.5 exhibits two critical differences. First a new quasiequilibrium
position is established for the given rate constants. Initially, the erosion and accretion
cycles occur over the same time period, but because the erosion proceeds at a faster rate,
the entire response curve shifts downwards. As the curve shifts down, the shoreline
spends a longer period of time in an accreted state with respect to ye. A quasi
equilibrium state is reached when the accretion time is sufficient for the amount of
accretion to equal the amount of erosion over one period of the equilibrium function. The
second difference is that the shape is no longer sinusoidal. The larger value of the
erosion constant results in a steeper slope during the erosional phase, which contributes to
the response curve shifting to the quasiequilibrium position.
Figure 5.6 examines the effects of introducing both an erosional and an
accretional forcing event while keeping the accretional constant at onefifth the value of
the erosional constant. As described in the previous paragraph, a new quasiequilibrium
state develops for the chosen values of the rate constants. From Figure 5.6 it is observed
that for events of the same magnitude, the recovery from the erosional event takes much
longer. This is a direct result of reducing the magnitude of ka with respect to ke. Ten
years after the erosional event, the shoreline has not reached a quasiequilibrium state.
Due to the larger value of the erosional constant, the shoreline reaches a quasi
equilibrium state within approximately seven years after the accretional event. This
behavior is similar to what is observed in nature. For events of the same magnitude, a
shoreline will erode to its equilibrium state from an artificially accreted state much faster
than it will accrete to its equilibrium state from an initially eroded state. The exact time
scales of the processes will be determined by the relative magnitudes of the rate
constants.
RATE EQUATION (Ka=Ke=1)
1.25 
0.75
t
S0.25
1.25
0
0
0.75
1.25
0 2 4 6 8 10 12 14 16 18 20
Time (yrs)
Figure 5.2 Application of Eq. (5.3) for the case ke=ka=1 and no external forcing
AI 01 ii iI 1A I l I, I, I, I, It I' 11 _ II_ I I
IC IA I I A I A I Al IA I'A IA I, IA I A IA I I
IVIVIV VI IYV IV IV V ' 9 1 I I IV IV
H Hy \ 1 IH
RATE EQUATION (KaK.=1)
Yeq
2
A 0
a. I \ L I I l II &ly \ I I
CO
2
3 ____ ____ ____ _____________
0 2 4 6 8 10
Time (yrs)
12 14 16 18 20
Figure 5.3 Application of Eq. (5.3) for the case of ke=ka=1 with external forcing applied
at t=0 and t=10
RATE EQUATION (Ka=Ke=5)
AI IA I 11 I
A I
1111
I
In Il
111 11
i IIR II
A l
'I Ii
fII l 1 '~ II III II
SIIRi AI
i'BII
I I
IAI
~IA Ii
' I Ill II
R IIUI
f18i~i!
Iill IIll liii 11111i 111(i111 1 1111
I Il t il il I I I
I 1 I
I I I I I I I I I1I I
  Yeq Y
0 2 4 6 8 10
Time (yrs)
ii 'I
1IA
12 14 16 18 20
Figure 5.4 Application of Eq. (5.3) for the case of ka=ke=5 and no external forcing
1.25
0.75
, 0.25
0
0.25
0
0 0.25
C
0.75
1.25
RATE EQUATION (KaKe5)
I
ml
A ;, A
I It I 111
64
RATE EQUATION (Ka=0.2,Ke=1)
I
!
[ l I A I II AI A I I A I A !I A A
Il I 1 11 11 II II 11 I1_I I i I i i II I I i I I
Tl I, I i i11, i1i1 i 1i i i11i i i i i i ii 1 i ii i i II 1 1 ii
  Yeq  Y
0 2 4 6 8 10
Time (yrs)
12 14 16 18 20
Figure 5.5 Application of Eq. (5.3) for the case ke=1, ka=0.2 and no external forcing
RATE EQUATION (Ka=0.2,Ke=1)
0 2 4 6 8 10 12 14 16 18 20
Time (yrs)
Figure 5.6 Application of Eq. (5.3) for the case of ke=1, ka=0.2 with external forcing
applied at t=0 and t=10
1.25
0.75
t
0.
' 1.25
S0.25
0
CO
0.75
1.25
Potential applications of Eq. (5.3) are numerous. The key is describing both the
equilibrium shoreline position function and the appropriate rate constants accurately.
Unfortunately, these parameters are themselves functions of numerous complex
variables, among them sediment characteristics, beach conditions, and local wave
environment. For use as an aid in assessing the accuracy of a hurricane erosion index, a
shoreline response equation could provide guidance in determining a maximum time
period of applicability, as well as a method for calculating shoreline recovery between
individual storm events.
Determination of Equilibrium Shoreline Position
Theory
As discussed in Chapter 2, Dewall found substantial seasonal shoreline
fluctuations in his studies at Westhampton and Jupiter Island. A clear relationship was
found between the average beach width and the average breaking wave conditions. In
general the more energetic winter wave conditions were correlated with the narrowest
beach width. Associated with these more energetic wave conditions is an increase in the
mean water elevation as a result of wave setup. A simple equation based upon the Bruun
Rule is applied in an attempt to reproduce Dewall's results, and develop an expression for
the equilibrium shoreline position as a function of time
For purposes of this study, the shoreline recession or advancement is assumed to
be in response to an increase in local water elevation. The equation utilized to define the
MHEI, Eq. (4.19), is reapplied to calculate potential shoreline changes. Figure 4.14
illustrates the problem setup, and Eq. (4.19) defines the potential shoreline change Ay.
Again W* is taken as the width of the surfzone and is calculated from the breaking depth,
assuming an equilibrium beach profile. Here S is the observed water level taken from the
COOPS database and the wave setup effect is represented by the breaking wave height
Hb. The potential shoreline changes are calculated and compared to the seasonal changes
observed by Dewall.
The shoreline changes calculated by Eq. (4.19) are referred to as potential changes
because the conditions causing the change may not persist long enough for the shoreline
to reach an equilibrium state. Values calculated from Eq. (4.19) assume that a new
equilibrium state is reached, however in nature the conditions are so dynamic that often
the shoreline is not able to respond completely to the local conditions before they change
and a new equilibrium results. Here, Eq. (4.19) is applied on either an hourly or three
hourly basis as dictated by the wave data set. Due to the frequency with which Eq. (4.19)
is applied, the shoreline will rarely reach an equilibrium state; therefore, the results
obtained represent only the potential shoreline response, assuming the beach has
sufficient time to evolve to a new equilibrium state.
The required inputs for Eq. (4.19) are the local wave conditions and water surface
elevations. Offshore wave data were obtained from two sources. Both WIS (Stations 13
& 78) and NDBC (Buoys 41009 & 44025) data were utilized. Each data set has some
advantages as well as disadvantages. Advantages of the WIS data set include: proximity
to the sites of interest, length of the data set, and inclusion of wave direction. The main
disadvantage of the WIS data set is the fact that it is a statistical hindcast based on wind
data, and often excludes important local effects. Although the NDBC data consist of
actual wave measurements, this data set also has some disadvantages. These include:
distance from the site, lack of wave direction data, and the frequent malfunctioning of the
equipment. Both data sources provide significant wave heights, Hs, and the associated
wave periods. For application to Eq. (4.19), the significant wave heights are converted to
average wave heights using the relation Havg=0.626Hs. A filter based upon the wave
direction (assumed to be the same as the wind direction in the case of buoy data) is
applied to eliminate offshore propagating waves.
17 4BP0
: 17 00A
S15 Locations 7 80
s 1 *1**** 1
11 7 72 25
0 .Data
/9 70 Locations
/ 7 .
Figure 5.7 Site and data station location map
Water level data are obtained from the NOAA COOPS database. Due to the
length of the study and the incomplete nature of the NOAA COOPS data sets, conditions
at representative stations are utilized and converted to approximate equivalent local
conditions. The representative stations for Westhampton and Jupiter Island are Montauk
and Mayport respectively. The time offset of the high and low tides is under one hour
between the representative and local stations allowing for a direct correlation with the
hourly and three hourly wave data once the tidal amplitudes have been adjusted.
Amplitude modification factors as reported in the NOAA tide tables are applied to
account for the difference in the magnitude of the tidal fluctuations between the sites and
the representative locations. The amplitude modification factors for low and high tide are
applied to all water level observations falling below and above the uncorrected average
tidal elevations respectively. Table 5.1 lists these factors and other pertinent site
characteristics. The astronomical tides were not removed from the water level data,
which results in the astronomical tides being considered as erosional and accretional
events. Since we are most interested in obtaining the maximum range of shoreline
positions and are calculating the potential shoreline changes, inclusion of the
astronomical tide in the water level observations is allowable.
Table 5.1 Relevant site characteristics
'.V S ? Westhampton, Jupiter Island,
S New York Florida
Surge Data .. .
Mean Tidal Range 2.90 ft 2.46 ft
Spring Tidal Range 3.50 ft 2.95 ft
Representative Station Montauk Mayport
Maximum time difference 51 min 17 min
High Tide Modification Factor 1.22 0.58
Low Tide Modification Factor 1.09 0.75
Wave Data
WIS Station 78 13
Recording Depth 89 ft 148 ft
Average Hb 3.21 ft 3.02 ft
Buoy Number 44025 41009
Recording Depth 131 ft 138 ft
Average H2.60 ft 2.97 ft
Site Conditions
Berm Height 9.5 ft 6.9 ft
Sediment Diameter 0.45 mm 0.30 mm
Sediment Scale Parameter 0.230 ft/3 0.188 ft1/3
Subaerial Beach Slope 1 on 10 1 on 10
Shoreline Azimuth 67 15
The site conditions recorded in Table 5.1 are from either the aforementioned
sources, or directly from Dewall's reports, with the exception of sediment size. Dewall
briefly mentions the sediment size at Westhampton as being in the range of 0.3 to 1.2
millimeters. A sediment size of 0.45 millimeters was assumed for the calculations at
Westhampton based upon previous experience. Sediment sample data is included in
Dewall's report for the Jupiter Island site, however the maximum sample depth is only 6
feet. The average sediment size of the samples collected between the MLW line and the
6 foot contour was approximately 0.35 millimeters. Previous experience indicates this
value is too large. Dean and Dalrymple (2001) and Charles, Malakar, and Dean (1994)
show the sediment size at Jupiter Island drops sharply at approximately the 6 foot
contour, due in part to a nearby Coquina rock outcropping. Since we need a median
sediment size applicable across the entire active profile, a more representative sediment
size of 0.3 millimeters was chosen. A sensitivity test was performed on the results to
examine the effects of changing the sediment scale parameter. Decreasing the sediment
size at Westhampton to 0.3 millimeters results in increasing the average range of
shoreline change values by approximately 2 feet. Increasing the sediment size at Jupiter
Island to 0.45 millimeters has the opposite result, decreasing the average range this time
by approximately 2 feet. This result is not surprising as the sediment scale parameter
only enters into Eq. (4.19) through the calculation of W*, which simply acts as a
multiplier, modifying the magnitude of any trends, but not changing them.
A question that arises in the analysis of the data is whether the setup is already
captured in the water level observations recorded at the gauges. Both representative
stations are somewhat sheltered compared to the open coast; therefore it is assumed these
stations capture only a small fraction of the setup occurring on the open coast.
Nonetheless, calculations are performed for both cases; assuming the setup is implicit in
the water level observations, as well as calculating and including the set up explicitly.
Two sets of calculations are performed at each site for each data set resulting in a total of
eight distinct cases.
Results
Dewall's observations of the average shoreline position at each location during
each month are reproduced in Figure 5.8. Clear seasonal trends are observed at both
sites, with maximum ranges of approximately 35 feet in both cases. Dewall's results are
compared with the potential shoreline changes predicted by Eq (4.19). Figure 5.9
displays the results of averaging the potential shoreline change values for each month
throughout the study period, and plotting the average values. As can be expected from
inspection of Eq. (4.19), including the setup explicitly shifts the curves towards a more
erosional value and increases the range of values. Surprisingly, Figure 5.9 indicates a
greater range of average potential shoreline change for Jupiter Island. This result is
contrary to what was found by Dewall. Although both sites appear to exhibit some
seasonal fluctuations, the trends do not coincide with those observed by Dewall. The
Jupiter Island curves mimic the observed trend from August to December, but predict a
maximum accreted or only slightly eroded state (depending on the method of including
the setup), from January to April, the most eroded months according to Dewall's
observations. The Westhampton curves predict only slight variations in the average
potential monthly shoreline position, and are slightly out of phase with Dewall's results.
Figure 5.9 also reveals that the average potential shoreline changes for each
month at Westhampton indicate erosion, while the Jupiter Island data indicate both
erosion and accretion. This is primarily due to the relative magnitudes of the predicted
potential shoreline changes. As discussed later in the chapter, the magnitudes of the
erosional changes are generally much larger than the magnitudes of the accretional
changes at Westhampton, skewing the average potential shoreline changes towards
negative values.
A somewhat surprising feature of Figure 5.9 is the minimal effect explicitly
including the wave setup has during the summer months, at Jupiter Island. This indicates
very mild wave conditions even though July may be considered as the beginning of
hurricane season. At both Westhampton and Jupiter Island, the effect of including the
setup explicitly is more substantial during the winter months which is expected due to the
larger wave heights at both locations during the winter months.
The maximum range in the monthly average potential shoreline changes at
Westhampton and Jupiter Island are 3.32 and 7.92 feet respectively. In comparing these
results to Dewall's, it should be noted that the averaging technique employed here does
not incorporate any measure of the time scales of the erosion and accretion processes as
will be discussed in Chapter 6. Also, Dewall's averages are admittedly biased towards
post storm surveys.
Another useful method of analyzing the data is to examine the average potential
shoreline positions on a monthly basis within each year. Table 5.2 presents the maximum
and minimum average potential monthly shoreline change values calculated using Eq.
(4.19) and the WIS data. The range column is simply the maximum monthly average
potential shoreline change minus the minimum monthly average potential shoreline
change as presented in the table. The average range over the entire period of the study is
calculated as the average of the yearly range values, excluding years containing
incomplete data sets. In Figures 5.105.13, the average monthly potential shoreline
change for each month during the study period is plotted. Each line represents a single
72
year of the study. Table 5.3 and Figures 5.145.17 present the same information
calculated using buoy data in place of the WIS data.
AVERAGE SHORELINE POSITION AT JUPITER AND WESTHAMPTON
AS OBSERVED BY DEWALL
9_ ,,
* Jupiter Island
 I Westhampton
__II~~2
0 ^ 1
10 I I I I
15 I
20
35m
1 2 3 4 5 6 7 8 9 10 11 12
Month
Figure 5.8 Average shoreline positions at Jupiter and Westhampton as reported in Dewall
(1977) and Dewall (1979)
AVERAGE CALCULATED AY VALUES
(BOTH LOCATIONS, BOTH DATA SOURCES)
1 2 3 4 5 6 7 8 9 10 11 12
Month
Figure 5.9 Average monthly potential shoreline change values. S represents the
measured tide. Eta is the wave induced setup effect.
(
73
Table 5.2 Maximum and minimum average monthly potential shoreline change values
calculated from Eq. (4.19) using the WIS data set. Values are reported in feet.
Jupiter Island ISetup Implicit) Westhampton (Setup Implicit)
Year Max Min Range Year Max Min Range
1976 5.684 2.761 8.445 1976 2.377 2.140 4.517
1977 6.685 2.903 9.588 1977 1.842 5.159 7.001
1978 4.506 6.097 10.603 1978 0.103 8.642 8.745
1979 8.454 2.221 10.675 1979 0.000 5.265 5.265
1980 3.564 0.280 3.284 1980 0.000 0.000 0.000
1981 6.831 2.375 9.207 1981 0.699 2.873 3.572
1982 5.252 4.910 10.162 1982 1.793 2.299 4.092
1983 1.599 5.108 6.707 1983 0.885 6.349 5.465
1984 3.710 6.507 10.217 1984 0.295 8.191 7.896
1985 5.308 7.344 12.651 1985 0.160 6.018 6.178
1986 3.005 3.119 6.125 1986 2.263 3.679 5.941
1987 2.531 3.482 6.013 1987 0.330 4.351 4.021
1988 2.980 4.360 7.340 1988 0.987 2.368 3.354
1989 1.795 3.791 5.586 1989 0.640 2.864 3.504
1990 3.197 1.632 4.829 1990 1.248 2.555 3.803
1991 1.998 6.784 8.782 1991 0.000 3.612 3.612
1992 1.634 4.589 6.223 1992 0.634 8.171 7.537
1993 2.253 3.681 5.934 1993 0.560 4.447 3.888
1994 2.737 7.247 9.985 1994 0.026 4.825 4.799
1995 3.076 6.653 9.730 1995 0.533 5.143 4.610
Average 3.840 4.264 8.104 Average 0.479 4.754 5.233
Jupiter Island Setup Explicit) Westhampton (Setup Explicit)
Year Max Min Range Year Max Min Range
1976 3.039 7.849 10.888 1976 0.053 4.900 4.847
1977 2.426 7.111 9.537 1977 0.591 8.905 9.496
1978 1.858 11.802 13.660 1978 1.398 10.956 9.558
1979 2.247 5.423 7.670 1979 0.468 11.285 10.817
1980 0.817 6.215 7.032 1980 0.738 5.679 4.941
1981 1.562 6.332 7.894 1981 0.616 7.990 7.374
1982 2.268 9.755 12.023 1982 0.210 3.412 3.201
1983 0.101 9.553 9.653 1983 1.332 11.992 10.660
1984 0.874 12.722 13.596 1984 1.387 13.193 11.806
1985 0.877 12.188 13.065 1985 1.322 8.716 7.394
1986 0.324 7.008 7.331 1986 1.237 7.909 6.673
1987 0.510 10.723 11.233 1987 1.242 6.646 5.404
1988 0.342 7.167 7.509 1988 0.685 3.529 2.844
1989 1.146 7.134 8.280 1989 1.172 6.688 5.516
1990 1.758 3.449 5.207 1990 0.746 4.728 3.982
1991 0.155 10.518 10.672 1991 1.020 6.534 5.514
1992 0.409 7.288 7.696 1992 1.374 11.064 9.691
1993 0.736 6.991 7.728 1993 1.209 7.421 6.213
1994 0.802 11.992 12.794 1994 1.206 6.781 5.575
1995 1.561 8.346 9.907 1995 1.717 8.158 6.441
Average 1.191 8.478 9.669 Average 0.983 7.737 6.754
ENVELOPE OF AY VALUES JUPITER ISLAND
(WIS DATA SETUP IMPLICIT)
10
2 2
4
o 2
6
8
10
1 2 3 4 5 6 7 8 9 10 11 12
Month
Figure 5.10 Envelope of average monthly potential shoreline change values at Jupiter
Island calculated from Eq. (4.19) using the WIS data set, assuming the setup is included
implicitly. Each line represents a single year of the 20 years with available data.
ENVELOPE OF AY VALUES JUPITER ISLAND
(WIS DATA SETUP EXPLICIT)
4
0
2
4
6
8
*10
12 '
.AA
2 3 4 5 6
7 8 9 10 11 12
Month
Figure 5.11 Envelope of average monthly potential shoreline change values at Jupiter
Island calculated from Eq. (4.19) using the WIS data set, including the setup explicitly.
Each line represents a single year of the 20 years with available data.
ENVELOPE OF AY VALUES WESTHAMPTON
(WIS DATA SETUP IMPLICIT)
1 2 3 4 5 6 7 8 9 10 11 12
Month
Figure 5.12 Envelope of average monthly potential shoreline change values at
Westhampton calculated from Eq. (4.19) using the WIS data set, assuming the setup is
included implicitly. Each line represents a single year of the 20 years with available data.
ENVELOPE OF AY VALUES WESTHAMPTON
(WIS DATA SETUP EXPLICIT)
.2
4
10
12
.4
14
1 4  I  I  I 
1 2 3 4 5 6 7 8 9 10 11 12
Month
Figure 5.13 Envelope of average monthly potential shoreline change values at
Westhampton calculated from Eq. (4.19) using the WIS data set, including the setup
explicitly. Each line represents a single year of the 20 years with available data.
76
ENVELOPE OF AY VALUES JUPITER ISLAND
(BUOY DATA SETUP IMPLICIT)
12
8 ___ ___
1 2 3 4 5 6 7 8 9 10 11 12
Month
Figure 5.14 Envelope of average monthly potential shoreline change values at Jupiter
Island calculated from Eq. (4.19) using buoy data, assuming the setup is included
implicitly. Each line represents a single year of the 11 years with available data.
ENVELOPE OF AY VALUES JUPITER ISLAND
(BUOY DATA SETUP EXPLICIT)
2
4
6
18
14
16 
18   
1 2 3 4 5 6 7 8 9 10 11 12
Month
Figure 5.15 Envelope of average monthly potential shoreline change values at Jupiter
Island calculated from Eq. (4.19) using buoy data, including the setup explicitly. Each
line represents a single year of the 11 years with available data.
1
0
1
2
7
6
7
8
9
77
ENVELOPE OF AY VALUES WESTHAMPTON
(BUOY DATA SETUP IMPLICIT)
I 2 3 4 5 6 7 8 9 10 11 12
Month
Figure 5.16 Envelope of average monthly potential shoreline change values at
Westhampton calculated from Eq. (4.19) using buoy data, assuming the setup is included
implicitly. Each line represents a single year of the 9 years with available data.
ENVELOPE OF AY VALUES WESTHAMPTON
(BUOY DATA SETUP EXPLICIT)
1
2
3
44
5
0 6
7
8
9
10
11
1 2 3 4 5 6 7 8 9 10 11 12
Month
Figure 5.17 Envelope of average monthly potential shoreline change values at
Westhampton calculated from Eq. (4.19) using buoy data, including the setup explicitly.
Each line represents a single year of the 9 years with available data.
Table 5.3 Maximum and minimum average monthly potential shoreline change values
calculated from Eq. (4.19) using buoy data. Values are reported in feet.
Jupiter Island (Setup Implicit) Westhampton (Setup Implicit)
Year Max Min Range Year Max Min Range
1988 1.809 4.817 6.626 1991 0.000 2.896 2.896
1989 1.930 5.184 7.114 1992 0.924 7.654 6.730
1990 3.661 1.800 5.461 1993 0.537 3.201 2.664
1991 2.787 7.723 10.510 1994 0.082 2.821 2.739
1992 1.949 6.014 7.963 1995 0.743 3.876 3.132
1993 0.690 4.214 4.904 1996 1.221 8.359 7.138
1994 1.790 7.128 8.918 1997 1.152 5.361 4.209
1995 1.634 10.969 12.603 1998 0.660 4.330 3.670
1996 1.609 6.073 7.681 1999 0.236 4.689 4.926
1997 0.558 3.330 3.888 Average 0.635 5.036 4.401
1998 1.214 7.425 8.639
Average 1.782 5.986 7.768_
Jupiter Island (Setup Explicit) Westhampton (Setup Explicit)
Year Max Min Range Year Max Min Range
1988 0.394 8.168 8.563 1991 0.000 4.215 4.215
1989 1.354 9.331 10.685 1992 1.472 10.683 9.211
1990 1.746 4.330 6.076 1993 1.129 5.099 3.970
1991 0.617 12.573 11.956 1994 1.034 4.554 3.520
1992 0.160 11.124 10.964 1995 1.479 4.908 3.430
1993 0.355 7.696 8.051 1996 2.033 10.555 8.522
1994 1.001 10.548 11.549 1997 2.409 7.687 5.278
1995 0.048 16.913 16.961 1998 1.456 6.246 4.790
1996 0.548 10.991 11.539 1999 0.000 6.463 6.463
1997 1.335 5.591 4.256 Average 1.377 7.024 5.648
1998 0.590 12.290 12.880
Average 0.353 10.139 10.492
Tables 5.2 and 5.3, illustrate that slightly "tweaking" the way the average range is
calculated, produces different results. Calculating the average range based on the range
of potential shoreline change values within each year results in an increase of
approximately 3 feet versus the previously defined range. Including the setup explicitly
increases the yearly range values by approximately 2 to 4 feet. It should be noted, that in
no case does the maximum range obtained by including the setup implicitly occur in the
same year as when calculating it explicitly. This supports the previous assumption that
the water level observations do not capture the entire setup.
In general it is observed that the maximum monthly shoreline changes do not vary
substantially, especially when the setup is calculated explicitly. Most of the variation in
the yearly range values results from a decrease in the minimum average monthly
potential shoreline change values. In other words, there is a greater tendency for a large
range of potential shoreline changes to be caused by an extremely erosional month than
an extremely accretional one.
A maximum range of 11.81 feet is calculated at Westhampton in 1984 using the
WIS data. From Figure 5.13, it is observed that the minimum monthly potential shoreline
change for 1984 occurs in March. As would be expected in Long Island, this is most
likely the result of a spring Nor'easter. Using the buoy data, a maximum range of 9.21
feet is calculated at Westhampton in 1992. From Figure 5.17, it is observed that this
event corresponds to a minimum average potential shoreline change occurring in
December of that year. Data presented later in the chapter indicate that a majority of this
minimum average shoreline change can be linked to a single severe storm resulting in
several erosional shoreline change values in excess of 100 feet, with a maximum value of
over 175 feet.
In general the average range of potential shoreline positions at Jupiter Island is 3
to 5 feet more than those at Westhampton. The largest range of average monthly
potential shoreline change values at Jupiter Island is 16.96 feet, and occurs in 1995.
Figure 5.15 indicates that this maximum range is associated with a minimum average
potential shoreline position occurring in August of 1995. Further research reveals that an
incredible 7 hurricanes, including two category 4 hurricanes, passed offshore of Florida
during this month. Comparing the average range calculated from the WIS data with
those calculated from the buoy data for 1995 illustrates one of the disadvantages of the
WIS data set. In this case, significant wave events created by the 7 offshore hurricanes
are not captured in the WIS data set and result in a substantially different range
prediction.
In general the results obtained from the WIS data, Figures 5.105.13, exhibit a
slightly greater range of values than the figures based on the buoy data, Figures 5.14
5.17. Although this is true at both sites, it is most pronounced at Westhampton during the
winter months. This increase in the range of values is due to the difference in breaking
wave height predicted by the two data sets. The average breaking wave height calculated
using the WIS data is larger than that calculated using the buoy data, with a more
pronounced difference at the Westhampton site. The breaking wave height affects the
calculation of W*, which acts as a multiplier in Eq. (4.19). Increasing W* increases the
range of potential shoreline changes predicted regardless of the method of including the
setup.
The variability observed in the average potential shoreline change for each month
is surprising. Due to the method and period of averaging employed, smaller fluctuations
were expected. Figure 5.13 shows the average monthly values fluctuating through more
than 10 feet during 4 of the 12 months. Not only are the ranges of the average potential
monthly shoreline changes surprising, but also the spread within the range. In most
cases, the large range of values in a given month is the result of many values spread
evenly between the two extremes rather than several closely spaced averages with a
single outlier responsible for increasing the range. The envelope plots help illustrate the
substantial variability in the potential shoreline change values predicted during the winter
months as compared to the summer months.
Each individual potential shoreline change value is plotted in Figures 5.18
through 5.25. All of the figures presented previously have depicted the results of various
averaging techniques. Although averaging is oftentimes useful in facilitating
comparisons between large data sets, here it actually obscures the dynamic behavior we
are most interested in. As the period of averaging is decreased, the results become more
interesting. Figure 5.9 indicates very little variability in the average potential shoreline
change values between January and April, however examination of the corresponding
envelope plots reveals a large range of values that is obscured by the averaging
technique. The previously discussed erosional event of December 1992 provides a
convenient platform for discussion.
Potential Shoreline Change
Jupiter island Buoy Data Setu Included mpcity.
40
20 
40
S60
80allow Storm
100 Hunlc nto Dee Gabriel., and H go
120
88 89 90 91 92 93 94 95 96 97 98 99
Year
Figure 5.18 Potential shoreline change at Jupiter Island calculated using buoy data,
assuming the setup is implicitly included
82
Potential Shoreline Change
Jupiter Island Buoy Data (Setup Calculated Explicitly)
1 .. .... I .. .. ... .
S Supersto
4* urrican Gordon
SHal ween St rm I
SLHurricar s Dean, Gabrielle and H lu j arch 199 Storm
___ Janury 1989 storm March 1 96 Stor ______
88 89 90
91 92 93 94 95 96
Year
97 98 99
Figure 5.19 Potential shoreline change at Jupiter Island calculated using buoy data,
explicitly calculating the setup
Potential Shoreline Change
Westhampton Buoy Data (Setup Included Implicitly)
75 ................. .. ..................... ...
50
25
0
25
20 H.u   
0 12
75 D bo
91 92 93 94 95 96 97 98 99 100
Year
0 125 "
150 ; S
17 5 ......................
200 ............................... .............................
91 92 93 94 95 96 97 98 99 100
Year
Figure 5.20 Potential shoreline change at Westhampton calculated using buoy data
assuming the setup is implicitly included
0 
20
40 
Potential Shoreline Change
Westhampton Buoy Data (Setup Calculated Explicitly)
91 92 93 94 95 96 97 98 99 100
Year
Figure 5.21 Potential shoreline change at Westhampton calculated using buoy data,
explicitly calculating the setup.
Potential Shoreline Change
Jupiter Island WIS Data (Setup Included Implicitly)
R L
It*
40  
B. A.^.J^ T
0
( 20
0
* 0
 20
0 40
a
60
80
100
1986
1987 1988 1989 1990 1991
Year
1992 1993 1994 1995 1996
60
Figure 5.22 Potential shoreline change at Jupiter Island calculated using WIS data,
assuming the setup is implicitly included.
84
Potential Shoreline Change
Jupiter Island WIS Data (Setup Calculated Explicitly)
"; l ^t
____ 3~r L I L Z1 I .4 4i U
BO rricane indrew
100anuary Storm hurricane Dean, G brile, & go
V10 Mai :h 1987 S orm M >rch 1989 Storm
120
1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
Year
Figure 5.23 Potential shoreline change at Jupiter Island calculated using WIS data,
explicitly calculating the setup
Potential Shoreline Change
Westhampton WIS Data (Setup Included Implicitly)
100
75
50
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
Year
Figure 5.24 Potential shoreline change at Westhampton calculated using WIS data
assuming the setup is implicitly included
S'Speretorm \
25
0 
6 25
 50
0
, 75 
 100
0
125
150
175
200
1986
~f~'r
I I~
I $
Potential Shoreline Change
Westhampton WIS Data (Setup Calculated Explicitly)
100 
75
00 / Decembr1990 Strm Supe"rst ; 
125
Octol r 1988 St rm Nov1 r 1993 torm  ___ __
150 De ember 19 4 Storm
500
7500 
125
150 Do( ember 199 Storm
7D comber 1! 6 Storm Dec ber 1br992 Storm
1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
Year
Figure 5.25 Potential shoreline change at Westhampton calculated using WIS data,
explicitly calculating the setup.
Close examination of this event depicted in Figure 5.21, reveals 13 potential
shoreline change values greater than 100 feet, occurring over a time period of only 13
hours out of a total of 744 hours in the month of December. The true impact of this large
scale event is masked by the 731 "normal" values throughout the month. The erosion
caused by an event of this magnitude would likely persist throughout the month, a fact
that is lost when the different time scales of the erosion and accretion processes are not
accounted for. A more correct method of averaging the potential shoreline change values
is discussed in the following chapter.
After closely examining the December 1992 storm at Westhampton and the effect
averaging has on its perceived magnitude, it is useful to examine the August 1995 storms
at Jupiter Island. The December 1992 storm and the August 1995 storms contribute to
the maximum range of average potential shoreline changes calculated at each site
utilizing the buoy data. As discussed previously, these maximum ranges are due
primarily to the minimum potential shoreline changes predicted in December of 1992 and
August of 1995. Figure 5.21 indicates that the large average erosional change predicted
for December of 1992 is due primarily to the effects of one severe shortlived storm. In
contrast, examination of Figure 5.19 indicates the large average potential erosional
change predicted in August of 1995, appears to be due to the longer duration of a number
of smaller events. Without including a measure of the time scales of the erosional and
accretional processes, no distinction exists between a singular massive event, and several
smaller, longer duration events.
Several other conclusions may be drawn from Figures 5.18 to 5.25. In general the
magnitudes and the durations of the large erosional events are much greater than those of
the accretional events. This manifests itself in the disproportionate number of potential
erosional changes predicted, particularly at Westhampton, when the results are averaged.
Table 5.4 presents the maximum range of the individual potential shoreline change values
for each year as well as the average of these ranges. The data calculated using both wave
data sets indicate a slightly larger range of values at Westhampton. This is in contrast to
the larger ranges predicted at Jupiter Island when the data are averaged, but in agreement
with what Dewall observed. The averages in Table 5.3 are based upon the potential
shoreline change values and are slightly larger, but of the same order of magnitude as the
90 feet at Westhampton and 70 feet at Jupiter Island reported by Dewall. Considering
that the calculated ranges are based on potential ranges representing the maximum
change, the agreement of the results is considered promising.
87
Figures 5.185.25 also help to distinguish the major causes of erosion at each site.
Keeping in mind the scale difference between the Jupiter Island and Westhampton plots,
it is clear that the Jupiter Island site is more influenced by hurricanes than the
Westhampton site. Although the effects of several hurricanes are observable at the
Westhampton site, most notably, Hurricanes Lilli and Floyd, the magnitude of their
effects and the frequency of their occurrence are small compared to that of the major
winter storms. At Jupiter Island, although the effects of several winter storms are
observed, their magnitude and frequency are less than that of the major hurricanes.
Table 5.4 Range of potential shoreline change values based on individual extreme values.
Values are reported in feet.
WIS DATA BUOY DATA
Westhampton Jupiter Island Westhampton Jupiter Island
Explicit Implicit Explicit Implicit Explicit Implicit Explicit Implicit
186 164 95 100 201 177 121 100
110 88 120 116 142 146 105 94
119 117 160 122 117 117 110 104
91 81 175 153 69 69 95 93
119 114 135 134 112 112 90 83
102 86 170 164 98 98 120 105
205 183 138 125 58 58 96 82
163 164 127 106 89 89 142 107
123 127 166 150 110.75 108.25 73 74
189 163 123 112
118 106 128 107
93 83 122 121
227 208 97 87
173 157 82 81
156 157 97 91
144.38 130.94 100 82
126
127
85
126.55
120
105
83
114.80
98 86
105.00 92.80
