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UFL/COEL -2001/002
COMPARISONS OF EROSION MODELS FOR HURRICANES
FLOYD AND IRENE AT FT. PIERCE BEACH, FLORIDA
by
Lisa Dawn Heckman
Thesis
2001
COMPARISONS OF EROSION MODELS FOR HURRICANES FLOYD AND
IRENE AT FT. PIERCE BEACH, FLORIDA
By
LISA DAWN HECKMAN
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
ACKNOWLEDGMENTS
I would first like to express my gratitude to Dr. Robert Dean, my advisor on
this thesis project. To be able to study under someone with his standing in the coastal
engineering field has been unforgettable. The insight, constructive advisement, and
support he has provided are invaluable. I would also like to thank Dr. Daniel Hanes,
Dr. Ashish Mehta, and Dr. Robert Thieke for serving on my committee and for their
guidance in the classroom.
Dr. Bruce Taylor gave me the opportunity to work full-time as a staff engineer
at Taylor Engineering, Inc. while I completed this thesis, and to him I owe my
deepest appreciation. I would also like to thank Dr. Mark Gosselin, Dr. Rajesh
Srinivas, and Mr. Ken Craig, co-workers at Taylor Engineering, who all patiently
took time out of their busy days to advise me on this thesis. All my other co-workers
deserve gratitude as well for having patience with me as I completed this thesis while
working full-time.
Finally, I would like to thank my family and friends, who have always
supported me.
TABLE OF CONTENTS
Page
ACKN OW LEDGM ENTS ..............................................- ---.............. ................ -ii
LIST OF TA BLES ................................................................... .................. vi
LIST OF FIGURES ............................ ....................... -- .......... ...... ......... vii
AB STRA CT .................................................... ........ ............................. xi
1 INTROD U CTION ........................ ............... ........-.. .... .... ................... I1
P u rpose ................................................................ ............................ 1
Report Organization ........................................................ 1
2 BACKGROUND INFORMATION AND LITERATURE REVIEW................. 3
The Ft. Pierce Shore Protection Project........................... .................... 3
Storm D escriptions.................................... .. ........... ... ... ......... 5
Hurricane Floyd..................................................... ... 5
Hurricane Irene....................................... .............. .... 6
Literature R eview .............................................. ........... ................... 6
3 BRIEF MODEL DESCRIPTIONS........................................... 10
The Equilibrium Beach Profile .................................................... 10
SBEACH M odel.................................. ... .......................... 11
EDUNE M odel....................... ...... .......... ..... .................... 15
C R O SS M odel.......................................................... ..................................... 16
4 MODEL CALIBRATION................................................... 18
Beach Profile Data and Profile Input ....................... .. ................ 18
Storm Input .................................................................. 19
W ave and W ater Level D ata ......... .... .......................................... ... 19
W ave Height......................................... ..... ... 21
W ave Period ............................................................ ... 22
W ave Direction. ........................... ...... ....... .. ................... 22
W ater Level..................... ....... .. .................................... 22
W ind D ata .................................. ....................... ... .......... ................... 23
Program Options .................................... ...... .................... 23
SBEA CH M odel................................. .................. ............................. 23
EDUNE and CROSS Models..................... ........................ 23
C alibration Procedure............................... .......................... ..................... 23
SBEACH Model Calibration........................... ................... 28
EDUNE M odel Calibration............................................... ..................... 30
CROSS Model Calibration................................. ............... ... 32
5 MODEL VERIFICATION............................................... 38
Profile Input ............. .......... ........ ....................... ... 38
Storm Input .................................... ................................... 38
W ave D ata............................... ............... .................... 39
W ave H eight.................................. ............................... 39
W ave Period ...................................................... ......................... 39
W ave D irection..................................................................... 39
W ater L evel ................................................................................................. 40
W ind D ata .................................................... ... ................................................ 4 1
V erification Procedure................ ................................................................. 41
6 MODEL PERFORMANCE............................ ......................... 49
Measures of Model Performance ...................................... 49
R esidual Param eter ..................................................................................-....... 49
E roded V olum e............ ........................... ... .................................... 50
Shoreline R etreat ......................................... .............. . .... ....... ............. 50
Contour Change Along Entire Profile ........................................ 52
Relative Model Performance .................... .......................... 53
SB E A C H M odel ......................................................... ................................... 53
EDUNE M odel................................... ...... .....................54
CR O SS M odel........................................ ......... . ............ ................. 55
Model Comparisons ........................................... 55
Mean Sediment Grain Size Sensitivity Analysis ............... ........ .. 59
7 SUMMARY AND CONCLUSIONS ................................................................. 70
Sum m ary .........................................................--.............. ..... .............................. 70
C onclu sio ns................. ................... .......................... ................................ 7 1
APPENDIX A MEASURED AND PREDICTED PROFILES FOR HURRICANE
FL O Y D ......................... ...... ........ ............-. .. ......... ......... .................................. 75
APPENDIX B MEASURED AND PREDICTED PROFILES FOR HURRICANE
IR E N E .................................................................................................................. 10 0
APPENDIX C MEASURED AND PREDICTED CONTOUR CHANGE FOR
HURRICANES FLOYD AND IRENE.......................................................... 119
LIST OF REFERENCES..................... ...... ........... ... 133
BIOGRAPHICAL SKETCH ......................................... .............. ..................... 135
V
LIST OF TABLES
Table Page
3.1 Summary of Recommended A Values (m1r ) (Dean, et al., 1994)..................... 11
4.1 Permissible calibration ranges for the SBEACH model parameters.................. 29
4.2 SBEACH Model Calibration for Hurricane Floyd.............................................. 30
4.3 Calibration ranges for the EDUNE model parameters....................................... 31
4.4 EDUNE Model Calibration for Hurricane Floyd................................................ 32
4.5 Calibration ranges for the CROSS model parameters........................................ 33
4.6 CROSS Model Calibration for Floyd.................................................... 34
6.1 Predicted Residuals, Measured and Predicted Eroded Volume Between +8 and
0 ft-NGVD and Shoreline Retreat at the 6-ft Contour for Hurricane
F loyd ......................................... ................... .... .................. 51
6.2 Predicted Residuals, Measured and Predicted Eroded Volume Between +8 and
0 ft-NGVD and Shoreline Retreat at the 6-ft Contour for Hurricane
Irene ............... ................... ...... .... ............................ 52
6.3 Summaries of Model Performances for Hurricane Floyd Model Calibration.... 56
6.4 Summaries of Model Performances for Hurricane Irene Model Verification ... 56
6.5 Mean Sediment Grain Size Sensitivity Analysis for Profile R-38................... 60
7.1 Summaries of Model Performances for Hurricanes Floyd and Irene ............... 72
LIST OF FIGURES
Figure Page
2.1 Ft. Pierce Shore Protection Project Location Map (Taylor Engineering,
2000) ............................................................. ............ .................. 4
3.1 4-Zone Transport Relationship for SBEACH (Larson, 1989)......................... 13
4.1 M measured Profile Data R-37 .............................................. ........................ 20
4.2 Hurricane Floyd Significant Wave Height and Period........................................ 24
4.3 Hurricane Floyd Wave Direction ............................................................. 25
4.4 Hurricane Floyd W ater Level........................................................................... 26
4.5 Hurricane Floyd Wind Speed.............................. ..................................... 27
4.6 Profile R-37 Measured and Predicted Post-Floyd from SBEACH Model ........... 35
4.7 Profile R-37 Measured and Predicted Post-Floyd from EDUNE Model ......... 36
4.8 Profile R-37 Measured and Predicted Post-Floyd from CROSS Model............ 37
5.1 Hurricane Irene Significant Wave Height and Period...................................... 42
5.2 Hurricane Irene Wind Speed and Direction.................................. ........... ... 43
5.3 Hurricane Irene Wave Direction ............................................................... 44
5.4 H hurricane Irene W ater Level........................................................................ .... 45
5.5 Profile R-37 Measured and Predicted Post-Irene from SBEACH Model............ 46
5.6 Profile R-37 Measured and Predicted Post-Irene from EDUNE Model .............. 47
5.7 Profile R-37 Measured and Predicted Post-Irene from CROSS Model ............ 48
6.1 Profile R-37 Contour Change for Hurricane Floyd.......................................... 61
6.2 Profile R-41 Post-fill, Post-Floyd, and Post-Floyd SBEACH............................. 62
6.3 Profile R-41 Post-fill, Post-Floyd, and Post-Floyd EDUNE ........................... 63
6.4 Profile R-38 Post-fill, Post-Floyd, and Post-Floyd CROSS ............................ 64
6.5 Profile R-37 Measured and Predicted Post-Floyd from Three Models ............. 65
6.6 Profile R-37 Measured and Predicted Post-Irene from Three Models................. 66
6.7 Average Contour Change for Hurricane Floyd................................................. 67
6.8 Average Contour Change for Hurricane Irene................................................ 68
6.9 Profile R-34 Post-fill, Post-Floyd, and Post-Floyd SBEACH............................. 69
A.1 Profile R-34 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH............. 76
A.2 Profile R-35 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH............. 77
A.3 Profile R-36 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH ............ 78
A.4 Profile R-37 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH .............. 79
A.5 Profile R-38 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH ............ 80
A.6 Profile R-39 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH ............ 81
A.7 Profile R-40 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH ............ 82
A.8 Profile R-41 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH ............ 83
A.9 Profile R-34 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd EDUNE................ 84
A. 10 Profile R-35 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd EDUNE ............ 85
A.11 Profile R-36 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd EDUNE ............ 86
A. 12 Profile R-37 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd EDUNE ............ 87
A. 13 Profile R-38 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd EDUNE............. 88
A. 14 Profile R-39 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd EDUNE............. 89
A. 15 Profile R-40 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd EDUNE............. 90
A. 16 Profile R-41 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd EDUNE.............. 91
A.17 Profile R-34 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd CROSS.............. 92
A. 18 Profile R-35 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd CROSS................. 93
A. 19 Profile R-36 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd CROSS................. 94
A.20 Profile R-37 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd CROSS............... 95
A.21 Profile R-38 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd CROSS................ 96
A.22 Profile R-39 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd CROSS.............. 97
A.23 Profile R-40 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd CROSS............... 98
A.24 Profile R-41 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd CROSS................ 99
B.1 Profile R-36 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
SB E A C H .................................................... ...................................... 10 1
B.2 Profile R-37 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
SB E A C H ............................................................................................. 102
B.3 Profile R-38 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
SB E A C H ............................................................................................. 103
B.4 Profile R-39 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
SB E A C H ........................................ ................................................... 104
B.5 Profile R-40 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
SB E A C H ............................................................................................. 105
B.6 Profile R-41 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
SB E A C H ............................................................................................. 106
B.7 Profile R-36 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
EDUNE ............................................................. .................... 107
B.8 Profile R-37 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
E D U N E ............................................................................................... 108
B.9 Profile R-38 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
ED U N E ..................................................... ............................... 109
B.10 Profile R-39 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
ED U N E ........................... .......................................................... 110
B. 11 Profile R-40 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
ED U N E ............................................................................ 111
B.12 Profile R-41 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
ED U N E ......................................... .. .... .. 112
B.13 Profile R-36 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
C R O SS ...................................................................... 113
B.14 Profile R-37 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
C R O SS ................................................. ........................ ........... 114
B.15 Profile R-38 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
C R O S S ................................................................................................ 115
B.16 Profile R-39 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
C R O S S .............................................................. ........... 116
B.17 Profile R-40 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
CR O SS ............................................................... 117
B. 18 Profile R-41 Pre-fill, Post-fill, Post-Floyd, Post-Irene, and Post-Irene
CROSS ......................................... 118
C.1 Profile R-34 Contour Change for Hurricane Floyd ........................................ 120
C.2 Profile R-35 Contour Change for Hurricane Floyd ........................................ 121
C.3 Profile R-36 Contour Change for Hurricane Floyd ................................... 122
C.4 Profile R-38 Contour Change for Hurricane Floyd ........................................ 123
C.5 Profile R-39 Contour Change for Hurricane Floyd ........................................ 124
C.6 Profile R-40 Contour Change for Hurricane Floyd ................................... 125
C.7 Profile R-41 Contour Change for Hurricane Floyd ........................................ 126
C.8 Profile R-36 Contour Change for Hurricane Irene ......................................... 127
C.9 Profile R-37 Contour Change for Hurricane Irene ....................................... 128
C. 10 Profile R-38 Contour Change for Hurricane Irene .................................... 129
C. 11 Profile R-39 Contour Change for Hurricane Irene ................................... 130
C. 12 Profile R-40 Contour Change for Hurricane Irene ....................................... 131
C. 13 Profile R-41 Contour Change for Hurricane Irene ........................................ 132
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
COMPARISONS OF EROSION MODELS FOR HURRICANES FLOYD AND
IRENE AT FT. PIERCE BEACH, FLORIDA
By
Lisa Dawn Heckman
May 2001
Chairman: Dr. Robert G. Dean
Major Department: Civil and Coastal Engineering
This thesis presents a comparison of three cross-shore sediment transport
models applied to predict erosion at the Ft. Pierce Shore Protection Project area in
Florida during Hurricanes Floyd and Irene of 1999. Post-fill, post-Hurricane Floyd,
and post-Hurricane Irene survey data were available for Florida Department of
Environmental Protection reference monuments R-34 to R-41. The models were
calibrated with post-fill and post-Hurricane Floyd survey data, and Hurricane Floyd
storm data taken at a wave gage located offJensen Beach, Florida. The calibration
procedure was to vary the calibration parameters of each model, and determine which
set of parameters provided the least average root mean square error of measured to
predicted beach erosion for all profile lines. The models were then verified with post-
Hurricane Floyd and post-Hurricane Irene survey data, and Hurricane Irene storm
data taken from the NOAA buoy located offshore Cape Canaveral, Florida. The
calibrated parameters that were previously determined with Hurricane Floyd were
used in the verification procedure for the Hurricane Irene model runs.
The performances of the three models were evaluated and compared using
several methods including the residual parameter, eroded volume of sand, beach
retreat, and contour change. All three models provided reasonable predictions for
beach erosion for both Hurricanes Floyd and Irene. For Hurricane Floyd, the average
residual was between 0.47 and 0.51 for the three models, the average ratio of
predicted eroded volume to measured eroded volume was between 0.44 and 0.49, and
the average ratio of predicted retreat to measured retreat was between 0.46 and 0.52.
For Hurricane Irene, the average residual was between 0.47 and 0.74 for the three
models, the average ratio of predicted eroded volume to measured eroded volume was
between 0.67 and 2.50, and the average ratio of predicted retreat to measured retreat
was between 0.53 and 2.77. All three models underpredicted the average volume of
erosion during Hurricane Floyd, while for Hurricane Irene, the SBEACH and
EDUNE models overpredicted and the CROSS model underpredicted. The SBEACH
and EDUNE models incorporate dune overwash processes, but only the SBEACH
model predicts some very slight overwash during Hurricane Floyd. The SBEACH
model predicts the upper part of the beach face better than the EDUNE or CROSS
models, while the EDUNE and CROSS models provide better predictions of the
lower beach face. The SBEACH model allows non-monotonic profile input, while
the EDUNE and CROSS models allow only monotonic profile input at every contour.
The pre-storm profiles were therefore most accurately represented in the SBEACH
model, which led to a slightly better prediction of the overall post-storm profiles.
CHAPTER 1
INTRODUCTION
Purpose
Beaches are constantly evolving in response to waves, tides, sea level rise,
winds, and currents. While the time scale of a beach fill adjustment can take from
months to years, storm induced beach erosion can occur on time scales of only hours
to days and can have significant impact on coastal communities. The increasing use
of the coastal zone makes accurate predictions of beach profile evolution in response
to storm conditions very important in coastal engineering.
This thesis evaluates and compares the predictions of three cross-shore
sediment transport models with two sets of measured post-storm data at the Ft. Pierce
Shore Protection Project area. The three models are SBEACH (Larson and Kraus,
1989, Larson et al., 1989), EDUNE (Kriebel, 1986, 1989), and CROSS (Zheng, 1996,
Zheng and Dean, 1997).
Report Organization
This thesis is organized in the following manner. Chapter 2 provides
background information on the Ft. Pierce Shore Protection Project area and
Hurricanes Floyd and Irene. It also contains a brief review of a similar study
evaluating the predictions of the three models during two storm events at Ocean City,
Maryland. Brief descriptions of the equilibrium beach profile concept and the three
models are provided in Chapter 3. Chapter 4 discusses the model calibration
2
procedure and results. It includes detailed descriptions of the beach profile data,
profile input, storm input, and program options. The model verification procedure
and results are detailed in Chapter 5, which also includes detailed descriptions of the
program inputs. Chapter 6 evaluates and compares the performances of the calibrated
models using several methods and contains a mean grain size sensitivity analysis.
Finally, Chapter 7 presents a summary of this thesis as well as conclusions on the
performances of the three cross-shore sediment transport models.
CHAPTER 2
BACKGROUND INFORMATION AND LITERATURE REVIEW
This chapter presents background information on the Ft. Pierce Shore
Protection Project and brief descriptions of the storms that impacted the project area
shortly after construction. A review of the relevant literature is also presented.
The Ft. Pierce Shore Protection Project
The Ft. Pierce Shore Protection Project is located on the barrier island
shoreline of Hutchinson Island in St. Lucie County, Florida. The project area is
located immediately south of Ft. Pierce Inlet between Florida Department of
Environmental Protection (FDEP) reference monuments R-34 and R-41. Figure 2.1
provides a location map of the project area. The property adjacent to the project area
includes three St. Lucie County parks (South Jetty Park, South Beach Boardwalk, and
Surfside Beach State Park) and a number of private residential lots consisting of
condominiums and single-family homes (Taylor Engineering, June 1997).
The Ft. Pierce Shore Protection Project provides for nourishment of 1.3 miles
of shoreline between FDEP monuments R-34 and R-41. The Ft. Pierce Shore
Protection Project was completed in May 1999 with the placement of approximately
900,000 cubic yards of sand from Capron Shoal. Capron Shoal is located
approximately 3 miles offshore and 2.5 miles south of Ft. Pierce Inlet (Taylor
Engineering, June 1997). The mean sediment grain size of the native beach material
Figure 2.1 Ft. Pierce Shore Protection Project Location Map (Taylor Engineering,
2000)
was 0.30 mm (Taylor Engineering, 1997). The mean sediment grain size of the fill
material placed on the beach was 0.41 mm (Taylor Engineering, 2000).
The 1.3 mile project area contains extensive areas ofhardbottom. The
nearshore hardbottom occurs in nearshore parallel bands. The bands appear from
approximately 400 ft to 2,000 ft offshore, are denser in the northern project area, and
are less dense in the southern project area. Taylor Engineering, Inc. estimated that
the Ft. Pierce Shore Protection Project would cover approximately nine acres of the
hardbottom (Taylor Engineering, July 1997).
The construction profile template was one vertical to ten horizontal until
intersection with the existing bottom. The construction template was intended to
naturally evolve to a milder sloped equilibrium profile under the effects of waves and
water levels over a period of approximately one year (Taylor Engineering, June
1997).
Storm Descriptions
After construction of the Ft. Pierce Shore Protection Project in May 1999, two
hurricanes impacted the project area the following summer. Hurricanes Floyd and
Irene impacted the project area in mid-September and mid-October, respectively.
Hurricane Floyd
Hurricane Floyd originated from a tropical wave, which moved off the coast
of Africa and became a hurricane on September 11, 1999. Floyd became a strong
Category IV hurricane on the Saffir/Simpson scale on September 13, with winds of
155 miles per hour (mph), and it ravaged portions of the central and northwest
Bahamas on September 13-14. Floyd posed a serious threat of landfall to the East
Coast of Florida, but it took a turn to the northwest while slowly weakening.
Hurricane Floyd stayed approximately 100 miles off the coast of Florida as it moved
to the north as a Category 4 hurricane (Unisys, 2000). Hurricane Floyd impacted the
Ft. Pierce area during the period of September 12-17, 1999 as a Category 4 hurricane.
A PUV wave gage, located offshore of Jensen Beach, Florida (approximately 10 *
miles north of Ft. Pierce, Florida), in 26 ft of water, recorded a peak significant wave
height of 12.8 ft and a peak wave period of 14.2 s on September 15.
Hurricane Irene
Hurricane Irene originated from a broad area of low pressure in the southwest
Caribbean and became a tropical depression on October 13, 1999. Irene became a
Category 1 hurricane on October 14, and the center passed over Key West, Florida,
early on October 15. The storm moved offshore near Jupiter, Florida, later that day.
Irene retained her hurricane strength and moved northward parallel to the Florida
coast (Unisys, 2000). Hurricane Irene impacted the Ft. Pierce area during the period
of October 13-18, 1999, as a Category 1 hurricane. National Data Buoy Center
(NDBC) Buoy #41009, located east of Cape Canaveral, Florida, in 42 m of water,
recorded a peak significant wave height of 23.3 ft and a peak wave period of 8.0 s on
October 16.
Literature Review
A beach nourishment project can provide substantial storm protection and
erosion control for beach communities. Several researchers have documented the
responses of natural and nourished beaches to storms in order to improve beach fill
design, monitoring procedures, and cross-shore sediment transport models.
Leadon (1999) studied profile data collected along the Panhandle Coast of
Florida before and after Hurricane Opal in 1995. The extensive data set provided an
excellent opportunity to study beach and dune erosion and offshore sand transport
during a severe storm event. As expected with a hurricane, higher erosion occurred
near and to the right of Hurricane Opal's landfall, and decreasing erosion occurred
with increased distance from the point of landfall. The flattest post-storm beach
slopes also occurred nearest to Hurricane Opal's landfall, with increasing slopes seen
with increasing distance from the point of landfall. Survey data collected within two
to three years after Hurricane Opal indicate a very slow natural dune recovery and
very slow landward recovery of sand deposited in deep water during the hurricane.
Stauble (1993) studied three beach fill projects that were impacted by severe
storm events, including two major storms at the Ocean City, Maryland, project area.
He concluded that the storms eroded the beach fill from above the water line and
deposited a majority of the beach fill adjacent to the project between the water line
and the depth of closure. Stauble recommends analyzing pre- and post-storm profiles
at the project area, as well as updrift and downdrift of the project area to analyze the
alongshore sand movement and the variation in the beach responses of the nourished
beach versus the natural beach. The profiles should extend sufficiently far offshore in
order to estimate both the cross-shore and long-shore movement of sand. At the three
project sites, recovery of the sand back onto the subaerial beach took between 4 and
14 months, with between 68% and 100% of the pre-storm subaerial beach volume
returning.
Stauble and Grosskopf(1993) also analyzed the two storms impacting the
Ocean City, Maryland, project. A systematic monitoring program, with special
emphasis on response to major storms, provided an excellent set of profile, sediment,
and storm data. The authors found that the first storm, the 1991 Halloween storm,
had little effect on the constructed storm dune, but did remove sections of the
subaerial beach. Much of the beach fill did remain in the active nearshore area. The
second storm, in early January 1992, removed some sections of the storm dune and
most of the berm along the project area. As with the first storm, nearly all of the
eroded volume of sand remained in the nearshore area, as a low-tide terrace. As early
as the March 1992 survey, sand had been transported back onto the subaerial portions
of the beach at most survey locations.
Kraus and Wise (1993) made use of the extensive profile and storm data at the
Ocean City, Maryland, project area as well to test and improve the cross-shore
sediment transport model, SBEACH. With the first program simulation results, the
authors concluded that overwash occurred at the project area because the wave run-up
was exceeding the dune elevation, and they incorporated overwash into the SBEACH
model. The SBEACH model simulations indicated that the beach fill design had
functioned as predicted.
Zheng and Dean (1997) also made use of the Ocean City, Maryland, data set
to compare the predictions of their new cross-shore sediment transport model with
three existing models. The authors developed a modified non-linear cross-shore
sediment transport model, CROSS, based on equilibrium beach profile concepts and
scaling relationships. The CROSS model was calibrated and compared with the
linear transport relationship based on laboratory experiments. They concluded that
the nonlinear transport model yielded better overall predictions than the linear
transport equation. The models CROSS, EDUNE, and SBEACH were applied along
seven profile lines with the two storms at Ocean City, Maryland. The authors used a
non-dimensional mean square residual parameter to compare the predictions of the
models with the measured data, with smaller residual values indicating better model
performance. The authors found that while all three models underpredict the average
dune erosion, they all provide reasonable predictions for dune erosion and the entire
profile response. The predictions of the CROSS model were the best for an entire
profile and yielded the least average residual. In terms of errors of eroded volume of
sand and beach retreat, all three models provided comparable predictions. They
concluded that by incorporating dune overwash processes in the CROSS model,
which are included in the EDUNE and SBEACH models, the underprediction
associated with the CROSS model could be improved.
CHAPTER 3
BRIEF MODEL DESCRIPTIONS
The three models used in this thesis project are three of the most common
models used to predict cross-shore erosion in the United States. The models include
SBEACH, EDUNE, and CROSS, and all three are based on the equilibrium beach
profile concept discussed next.
The Equilibrium Beach Profile
A beach profile is considered to be in equilibrium when there is a balance
between the constructive and destructive forces. Dean (1977) proposed the following
equation for an equilibrium beach profile assuming that D., the wave energy
dissipation per unit water volume, is the dominant destructive force:
D.(d) (EC,) (3.1)
h dy
where h is the water depth at distance y offshore, E is the local wave energy density,
and Co is the local wave group velocity. Assuming shallow water and spilling wave
breaker assumptions, Equation 3.1 can be integrated to give
2
h(y)= A(d)y (3.2)
where A is defined as the sediment scale parameter in units of m13, which depends on
the sediment size, d, or equivalently, the sediment fall velocity (Dean, 1987). Table
3.1 presents A values for sand in 0.01 mm increments (Dean et al., 1994). Based on
equations 3.1 and 3.2, the sediment scale parameter is given by
A(d)
where K is the breaker index. Dean (1977) analyzed approximately 500 beach
profiles along the Atlantic and Gulf coasts that provide reasonable agreement with
this equilibrium form.
Table 3.1 Summary of Recommended A Values (m"3)
d
d 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
mm
0.1 0.063 0.0672 0.0714 0.0756 0.0798 0.084 0.0872 0.0904 0.0936 0.0968
0.2 0.100 0.103 0.106 0.109 0.112 0.115 0.117 0.119 0.121 0.123
0.3 0.125 0.127 0.129 0.131 0.133 0.135 0.137 0.139 0.141 0.143
0.4 0.145 0.1466 0.1482 0.1498 0.1514 0.153 0.1546 0.1562 0.1578 0.1594
0.5 0.161 0.1622 0.1634 0.1646 0.1658 0.167 0.1682 0.1694 0.1706 0.1718
0.6 0.173 0.1742 0.1754 0.1766 0.1778 0.179 0.1802 0.1814 0.1826 0.1838
0.7 0.185 0.1859 0.1868 0.1877 0.1886 0.1895 0.1904 0.1913 0.1922 0.1931
0.8 0.194 0.1948 0.1956 0.1964 0.1972 0.198 0.1988 0.1996 0.2004 0.2012
0.9 0.202 0.2028 0.2036 0.2044 0.2052 0.206 0.2068 0.2076 0.2084 0.2092
1.0 0.210 0.2108 0.2116 0.2124 0.2132 0.2140 0.2148 0.2156 0.2164 0.2172
(Dean et al., 1994)
SBEACH Model
The SBEACH model incorporates an extension of the breaking wave model
developed by Dally et al. (1985) to compute wave height and energy flux
distributions across the subaqueous beach profile. Four distinct zones with different
sediment transport expressions are identified across the active nearshore zone and are
as follows:
Zone 1: Pre-breaking zone
Zone 2: Transition zone
Zone 3: Broken wave zone
(3.3)
Zone 4: Swash zone
Figure 3.1 presents a summary of the transport relationship used in the four
zones. In all four zones, the direction of transport is determined by the following
criterion, specifying offshore transport when
H< 0.0007 (3.4)
Lo wT
and onshore transport when
Ho >_ 0.0007 HO (3.5)
where Ho is the deep water wave height, Lo is the deep water wave length, w is the
sediment fall velocity, and T is the wave period.
Zone 1, the pre-breaking zone, extends offshore from the break point, and the
sediment transport rate is assumed to decay exponentially with distance from the
break point as expressed by
Q=QBp exp[-A(y0-yB,)] (3.6)
where QBP is the sediment transport at the break point, %1 is the spatial decay
coefficient, and yeB is the break point location. The parameter X1 is expressed by
0.47
= 0.4 do (3.7)
where dso is the median grain size in mm, Hb is the breaking wave height in m, and 1i
is in m1.
Bfeakina Wave Ihalah ht
pl Average Slope Over
One-Thlrd Local
Wave Length Seawrd
ol Break Point
flun tjlalhtg. ,z
IA7lt!.!Slope
[I = IitialSlope
Wavit Of akha aIA2"
ay- R-IECQ) -(E CoMj
1, aIIM, K'" 0.17
I'm 0.40
Figure 3.1 4-Zone Transport Relationship for SBEACH (Larson, 1989)
Zone 2, the transition zone, is the region between the break point and the
plunge point with a transport rate similar to that in Zone 1 given by
Q = Qpp exp[- (y- ypp)] (3.8)
where Qpp is the transport rate at the plunge point located at ypp. The decay rate, X2, is
expressed by
22 =0.21 (3.9)
Zone 3, the broken wave zone, extends from the plunge point to the seaward
limit of the swash zone, and the sediment transport in this region controls the
sediment transport of the other zones. The sediment transport rate is determined by
Q = +K D. + ,D > D. -- (3.10)
Q O,D< D.--- (3.11)
K
where E is an empirical constant (about 0.0006 m2/s) and K is the transport rate
coefficient.
Zone 4, the swash zone, extends from the seaward swash zone limit to the run-
up limit, where the transport is assumed to decay linearly up to the run-up limit such
as
Q=Q y"YRU (3.12)
YW -YRU
where the subscript RU denotes the run-up limit and WR the landward end of the surf
zone.
The continuity equation,
8h SQ
ah (3.13)
at ay
is combined with the transport relationships for Zones 1 through 4 to solve for the
beach profile evolution.
EDUNE Model
The cross-shore sediment transport rate, Q, in the surf zone is determined
directly from the degree of disequilibrium by
Q = K(D D.) (3.14)
where K is the transport rate coefficient, D is the actual value of the local wave
energy dissipation per unit volume, and D. is the equilibrium value of the wave
energy dissipation per unit volume. The parameter D is defined by
D = pg g h (3.15)
24 By
where K is taken to be 0.78. The parameter D is only dependent on the local water
depth and the bottom slope. During a storm, the water level increase causes the
degree of disequilibrium, and therefore the offshore transport to increase. The sand in
the profile will erode until the wave energy dissipation level decreases to that of the
equilibrium value of the wave energy dissipation.
As in the SBEACH model, the continuity equation, given by
Ox O
(3.16)
at Sh
is combined with the transport rate equation to solve for the beach profile evolution.
The wave break point offshore and the wave run-up limit onshore bound the profile
change.
CROSS Model
The equilibrium concept applied in the EDUNE model is also applied in the
CROSS model. The cross-shore sediment transport rate is determined directly from
the degree of disequilibrium, or the deviation of the actual wave energy dissipation
from the equilibrium wave energy dissipation. However, the transport equation in the
CROSS model is given by
Q =K(D-D.)' (3.17)
where the exponent in the transport relationship is set to three, not one as in the
SBEACH and EDUNE models.
The explanation for the exponent in the transport relationship being set to
three is as follows. The scale relationship of the term (D-D.) is length /2. If the
Froude relationship is applied, the scale relationship is given by
L'2 =
Q- = L, (3.18)
-r
where L, is the length scale and Tr is the time scale, the square root of the length
scale. Therefore, by scaling the transport relationship according to the Froude model,
the exponent of the transport relationship is three.
Once again, the continuity equation, given by
ax (3.19)
at ah
17
is combined with the transport rate equation to solve for the beach profile evolution.
CHAPTER 4
MODEL CALIBRATION
The three models SBEACH, EDUNE, and CROSS were run and calibrated
with data from Hurricane Floyd. The following sections describe the beach profile
data and profile input, storm input, program options specific to each model, and the
calibration procedure and results.
Beach Profile Data and Profile Input
Four sets of beach profile data were used for model calibration, model
verification, and model comparison purposes. The beach profile data sets represent
the project area at pre-fill, post-fill, post Hurricane Floyd (post-Floyd), and post
Hurricane Irene (post-Irene). The pre-fill survey, taken between February 19 and
March 20, 1999, by the Jacksonville District U.S. Army Corps of Engineers
(USACE), represents the project area before the beach fill was in place and is used for
comparison with the post-fill survey. The post-fill survey, taken between June 25 and
July 1,1999, by the USACE, represents the project area immediately after the beach
fill was in place and before the hurricanes influenced the area. For both the pre-fill
and post-fill surveys, profile lines R-34 to R-41 were surveyed to depths of
approximately -25 ft-NGVD.
On October 3, 1999, immediately following Hurricane Floyd, lidar data were
collected along Hutchinson Island by the Department of Environmental Protection,
including along profile lines R-34 to R-41 in the project area. These data were
filtered for buildings and vegetation, and are only accurate to the water line
(approximately 0 ft-NGVD). In November 1999, following Hurricane Irene, Morgan
and Eklund, Inc. performed wading depth surveys for St. Lucie County for profile
lines R-34 to R-41. The depths of these surveys are between 0 and -8 ft-NGVD.
Figure 4.1 illustrates the pre-fill, post-fill, post-Floyd, and post-Irene conditions for
profile line R-37.
The SBEACH model allows non-monotonic profile input, and therefore the
profile data were input exactly from the post-fill survey, including the dune features
and offshore features. The models EDUNE and CROSS allow only monotonic
profile data input at every contour. The post-fill profile data were interpolated at
every contour from the top of the dune to the offshore for input into the EDUNE and
CROSS models.
Storm Input
The three models require storm inputs of some or all of the following: wave
height, wave period, wave direction, water level, and wind speed.
Wave and Water Level Data
A PUV wave gage offshore Jensen Beach, Martin County, Florida, provided
significant wave height, peak wave period, peak wave direction, and water level data
during Hurricane Floyd. The wave gage is located offshore of the Jensen Beach
Holiday Inn at an average water depth of approximately 26 ft. The wave gage
collects wave data for the first 17 minutes of every hour and collects tide data every 7
minutes. After examining the wave data, it was determined that Hurricane Floyd
- *- Pre-fill - - Post-fill --- Post-Floyd - Post-Irene
Distance from Monument (ft)
Figure 4.1 Measured Profile Data R-37
affected the Ft. Pierce area for 60 hours from September 13 at 4 pm until September
16 at 4 am.
Wave Height
The SBEACH model allows the input of a significant wave height time series.
The significant wave height time series used for the SBEACH model is taken directly
from the wave gage data and is shown in Figure 4.2.
The EDUNE and CROSS models allow the input of a root-mean-square
(RMS) breaking wave height time series. The significant wave height time series
shown in Figure 4.2 was converted to an RMS breaking wave height time series using
the following procedure. The significant wave heights were first changed to RMS
wave heights according to
H,. (4.1)
1.416
where HFIs is the RMS wave height and Hsig is the significant wave height (Dean and
Dalrymple, 1991). The RMS wave height was then changed to a RMS breaking wave
height using linear wave theory. The deep water wave heights were shoaled into
shallow water wave heights using Snell's Law and the Conservation of Energy.
Snell's Law states that
sin O sin b (4.2)
(4.2)
CO Cb
where 0o is the deep water wave direction, Ob is the breaking wave direction, and c is
the wave velocity. The Conservation of Energy is given by
Ho C o coso = Hb2CGb cosOb (4.3)
for straight and parallel contours where Ho is the deep water wave height, Hb is the
breaking wave height, Co is the group velocity, 60 is the deep water wave direction,
and Ob is the breaking wave direction (Dean and Dalrymple, 1991).
McCowan (1984) defines the breaking wave height, Hb, as
Hb = .78x hb (4.4)
where hb is the breaking water depth.
Wave Period
The SBEACH model is the only model to allow the input of a wave period
time series. The wave period time series used for the SBEACH model is taken
directly from the wave gage data and is shown in Figure 4.2.
Wave Direction
The SBEACH model is the only model to allow the input of a wave direction
time series. The wave direction time series used for the SBEACH model is taken
directly from the wave gage data and is shown in Figure 4.3.
Water Level
All three models, SBEACH, EDUNE, and CROSS, allow the input of a water
level time series. The water level time series taken by the wave gage does not include
the effects of barometric pressure, which is added back into the water level according
to
P P = pgAh (4.5)
where P2 is the ambient pressure, P1 is local barometric pressure, p is the density of
water, g is gravity, and h describes the increase or decrease of the water level due to
the pressure difference. The adjusted water level time series is shown in Figure 4.4.
Wind Data
A National Climatic Data Center (NCDC) weather station located at the Ft.
Pierce St. Lucie County Airport, just west of the Ft. Pierce Inlet, collected wind speed
and barometric pressure data during Hurricane Floyd. Data were taken at
approximate one-hour intervals.
The SBEACH model is the only model to allow the input of wind speed time
series. The wind speed time series used for the SBEACH model is taken directly
from the weather station and is shown in Figure 4.5.
Program Options
The following paragraphs describe the options specific to each model.
SBEACH Model
The input wave water depth is set to 26 ft, the depth at which the wave gage
collected the data. The option of irregular waves, which requires an input of a
significant wave height time series, is chosen. The option that all the sand remains on
the grid is chosen, as the post-fill profiles extend sufficiently offshore. The effective
grain size is entered at 0.41 mm. The USACE took post-fill beach samples in
September 1999 and determined the mean grain size diameter was 0.41 mm.
EDUNE and CROSS Models
The sediment scale parameter, A, is entered as 0.1466 mI', corresponding to
the mean grain size of 0.41 mm.
Calibration Procedure
Each model was run with several combinations of the calibration parameters
specific to that model for Hurricane Floyd. The predicted post-Floyd profile was
o-+-Wave Height - Wave Period
14 16
12 14
]12
S10
S* V
10
*m p -. -o
"1 . r M m 8
6 C
I-~
4 4
2 2
0 0
0 10 20 30 40 50 60
Hour
Figure 4.2 Hurricane Floyd Wave Height and Period
50
40
E
L- 30 -
0
O
S20
E
Hoo
0
( 0
0
e -20
-30
-40
0 10 20 30 40 50 60
Hour
Figure 4.3 Hurricane Floyd Wave Direction
3.5
3
2.5
2
(9 1.5
z
-J,
7@
3 0.5
0
-0.5
-1 -
-1.5 -
0 10 20 30 40 50 60
Hour
Figure 4.4 Hurricane Floyd Water Level
40
35
30
' 25
0 20
C
15
10
5
0
!0 30 4
Hour
Figure 4.5 Hurricane Floyd Wind Speed
60
M /V
A V,
V
compared with the measured post-Floyd profile by using a mean square error
analysis. The mean square error across the entire length of the measured profile, L, is
defined as
C = (hm -hp)2d (4.6)
L L
where hm and hp are the measured and predicted elevations at cross-shore distance x.
The cross-shore distances are taken between consecutively measured post-storm data
points and are relatively evenly spaced. The sum of the cross-shore distances equals
the entire length of the profile. The cross-shore distances were taken at each post-fill
survey data point. A root mean square error was calculated for each profile line for
each run. The average of the root mean square errors for all profiles lines for each
run was used to estimate that run's goodness of fit with the measured data. The
calibrated model was determined by the run with the least average root mean square
error.
SBEACH Model Calibration
The SBEACH model allows for the calibration of four parameters. The
transport rate parameter, K, determines the magnitude of sediment transport and
influences the response time of the profile. Larger values of K result in faster
response times to equilibrium, whereas smaller values of K result in slower response
times. The slope-related transport parameter, s, influences bar formation, with
smaller values resulting in more enhanced bars and larger values resulting in more
subdued bars. The spatial decay factor, X, influences the rate of decay of transport
seaward of the break point, with smaller values of X resulting in slower rates of decay
and wider bars. The angle of advent of avalanching, (, influences the maximum
slope that the eroded profile is allowed to achieve, with larger values resulting in
steeper profiles. The values of the calibration parameters can only be specified within
a particular range of values, detailed in Table 4.1.
Table 4.1 Permissible calibration ranges for the SBEACH model parameters
Parameter Range
K 0.5 x 10 2.5 x 10 m4/N
s 0.001 0.003 m2/s
X 0.1 0.5 m-
150 450
The model was run twelve times, with varying combinations of the calibration
parameters. Table 4.2 details the calibration parameters and average root mean
square error for each run of the SBEACH model. The model was first run with the
default values for the calibration parameters: a K value of 1.75x10.6 m4/N, e value of
0.002 m2/s, X value of 0.5 m"1, and 4 value of 450, producing a root mean square error
of 1.49 ft. A K value of0.50x10-6 m4/N, value of 0.003 m2/s, value of 0.1 m1,
and 4 value of 150 produced the least average root mean square error of 1.42 ft. The
calibrated SBEACH model for this study consisted of these parameter values as
highlighted in Table 4.2. The average residual for each model run is included in the
table for comparison purposes only. The average residual will be discussed further in
Chapter 6, Model Performance.
Table 4.2 SBEACH Model Calibration for Hurricane Floyd
Run Calibration Parameters Average Root Mean Average
K (m4/N) (m2/s) X (m) ) Square Error (ft) Residual
1 1.75 x 10-6 0.002 0.5 45 1.4906 0.5373
2 2.50 x 10-6 0.002 0.5 30 1.6608 0.6541
3 1.75 x 10-6 0.002 0.5 30 1.5017 0.5487
4 1.00 x 10-6 0.002 0.5 30 1.4596 0.5145
5 0.50 x 10-6 0.002 0.5 30 1.4595 0.5030
6 0.50 x 10-6 0.002 0.1 30 1.4557 0.5022
7 0.50 x 10-6 0.002 0.3 30 1.4585 0.5024
8 0.50 x 10-6 0.002 0.2 30 1.4584 0.5036
9 0.50 x 10-6 0.001 0.1 30 1.4615 0.5063
10 0.50 x 10-6 0.003 0.1 30 1.4508 0.4982
~ rX;IiO"4 001 O-T, )A LA J- jj V13j I
12 0.50 x 10-6 0.003 0.1 23 1.4498 0.4977
Figure 4.6 illustrates the post-fill profile, measured post-Floyd profile, and the
SBEACH model's predicted post-Floyd profile at R-37 in the project area. Figures
A. 1 through A.8 in Appendix A present the pre-fill profiles, post-fill profiles,
measured post-Floyd profiles, and the predicted post-Floyd profiles for the SBEACH
model for profiles R-34 through R-41.
EDUNE Model Calibration
The EDUNE model allows for the calibration of four parameters. The
transport rate parameter, K, determines the magnitude of sediment transport. The
dune slope, d, determines the equilibrium eroded profile slope above the run-up limit,
where the larger the value, the steeper the slope. The shoreline slope, b, determines
the equilibrium eroded profile slope below the run-up limit, where the larger the
value, the steeper the slope. The run-up limit, R, controls the location of the dune
scarp above the peak still water flood level, with higher values indicating a higher
run-up limit along the profile. Table 4.3 details the range of values used for the
calibration parameters.
Table 4.3 Calibration ranges for the EDUNE model parameters
Parameter Range
K 0.0001 0.0045 ft4/lb
d 1-5
b 0.05 -0.20
R 1-4ft
The model was run fourteen times, with varying combinations of the
calibration parameters. Table 4.4 details the calibration parameters and average root
mean square error for each run of the EDUNE model. The model was first run with
the default values for the calibration parameters: a K value of 0.0045 ft4/lb, d value of
1.0, b value of 0.05, and R value of 1.0 ft, producing a root mean square error of 2.75
ft. A K value of 0.0003 ft4/lb, d value of 5.0, b value of 0.1, and R value of 3.0 ft
produced the least average root mean square error of 1.46 ft. The calibrated EDUNE
model for this study consisted of these parameter values and as highlighted in Table
4.4. The average residual for each model run is included in the table for comparison
purposes only. The average residual will be discussed further in Chapter 6, Model
Performance.
Table 4.4 EDUNE Model Calibration for Hurricane Floyd
Run Calibration Parameters Average Root Mean Average
K (ft4/lb) d B R (ft) Square Error (ft) Residual
1 0.0045 1 0.05 1 2.7541 1.6070
2 0.0045 2 0.10 2 2.4473 1.2679
3 0.0020 2 0.10 2 2.2628 1.0164
4 0.0010 2 0.10 2 1.9773 0.7338
5 0.0005 2 0.10 2 1.5730 0.5237
6 0.0003 2 0.10 2 1.4819 0.5021
7 0.0001 2 0.10 2 1.8320 0.7021
8 0.0002 2 0.10 2 1.5875 0.5464
9 0.0003 2 0.10 4 1.4798 0.4963
10 0.0003 2 0.10 3 1.4646 0.4925
I:M I L.464t 042
12 0.0003 4 0.10 3 1.4642 0.4923
13 0.0003 5 0.0625 3 1.4714 0.4924
14 0.0003 5 0.20 3 1.5172 0.5140
Figure 4.7 illustrates the post-fill profile, measured post-Floyd profile, and the
EDUNE model's predicted post-Floyd profile at R-37 in the project area. Figures
A.9 through A. 16 in Appendix A present the pre-fill profiles, post-fill profiles,
measured post-Floyd profiles, and the predicted post-Floyd profiles for the EDUNE
model for profiles R-34 through R-41.
CROSS Model Calibration
The CROSS model allows for the calibration of four parameters. The
transport parameter, K, determines the magnitude of sediment transport. The dune
slope is the maximum slope that the profile is allowed to achieve. The shoreline
slope controls the profile evolution between the shoreline and the run-up limit. The
offshore slope controls the slope at the end of the deposited volume of sand offshore.
Table 4.5 details the range of values used for the calibration parameters.
Table 4.5 Calibration ranges for the CROSS model parameters
Parameter Range
K 8.00 xl104 8.00x10-7 ftgs2/lb3
Offshore slope 0.15 0.50
Dune slope 0.5 3.0
Shoreline Slope 0.05 0.20
The model was run twelve times, with varying combinations of the calibration
parameters. Table 4.6 details the calibration parameters and average root mean
square error for each run of the CROSS model. The model was first run with the
default values for the calibration parameters: a K value of 8.0x104 ft8s2/1b3, offshore
slope of 0.15, dune slope of 1.0, and shoreline slope of 0.05, producing a root mean
square error of 3.45 ft. AK value of 7.0x 107 ft8s2/lb3, offshore slope of 0.5, dune
slope of 1.5, and shoreline slope of 0.13 produced the least average root mean square
error of 1.56 ft. The calibrated CROSS model for this study consisted of these
parameter values and as highlighted in Table 4.6. The average residual for each
model run is included in the table for comparison purposes only. The average
residual will be discussed further in Chapter 6, Model Performance.
Table 4.6 CROSS Model Calibration for Floyd
Run Calibration Parameters Average Root Mean Average
K offshore dune shoreline Square Error (ft) Residual
(ft8s2/lb3) slope slope slope
1 8.00x104 0.15 1.0 0.05 3.4524 2.4091
2 3.68x10'7 0.5 3.0 0.2 1.5893 0.5264
3 4.41x10'7 0.5 3.0 0.2 1.5770 0.5181
4 6.00x10'7 0.5 3.0 0.2 1.5649 0.5100
5 8.00x10-7 0.5 3.0 0.2 1.5666 0.5100
6 7.00x10'7 0.5 3.0 0.2 1.5610 0.5074
7 7.00x10-7 0.15 3.0 0.2 1.5679 0.5117
8 7.00x10'7 0.3 3.0 0.2 1.5625 0.5083
9 7.00x107 0.5 0.5 0.2 1.5620 0.5081
10 7.00x10'7 0.5 1.5 0.2 1.5609 0.5073
12 7.00x10.7 0.5 1.5 0.05 1.5598 0.5065
Figure 4.8 illustrates the post-fill profile, measured post-Floyd profile, and the
CROSS model's predicted post-Floyd profile at R-37 in the project area. Figures
A. 17 through A.24 in Appendix A present the pre-fill profiles, post-fill profiles,
measured post-Floyd profiles, and the predicted post-Floyd profiles for the CROSS
model for profiles R-34 through R-41.
- Post-fill -A- Post-Floyd *- Post-Floyd SBEACH
15
5
0
Z 0
S100 200 300 40 1 500 600 700 800 910
0
=C -5
w \
-10
-15
-20
Distance from Monument (ft)
Figure 4.6 Profile R-37 Measured and Predicted Post-Floyd from SBEACH Model
- - Post-fill --- Post-Floyd - Post-Floyd EDUNE
Distance from Monument (ft)
Figure 4.7 Profile R-37 Measured and Predicted Post-Floyd from EDUNE Model
- - Post-fill --- Post-Floyd - Post-Floyd CROSS
15
10
5 M
Z 0 100 200 300 400% 500 600 700 800 90
10
5 X,
C)
Z 0
-10
-15
-20
Distance from Monument (ft)
Figure 4.8 Profile R-37 Measured and Predicted Post-Floyd from CROSS Model
CHAPTER 5
MODEL VERIFICATION
The three calibrated models were next run for verification purposes with
Hurricane Irene. The following sections describe the profile input, storm input, and
model verification procedure and results.
Profile Input
The post-Floyd profile data were used as the profile input data for the
Hurricane Irene model runs. The actual post-Floyd data are only available to the
water line, and therefore the profile data are a combination of the actual post-Floyd
data and the predicted post-Floyd data. For each profile in each of the three models,
the actual post-Floyd data to approximately 0 ft-NGVD were spliced with the
predicted post-Floyd data below 0 ft-NGVD. For example, the R-36 profile input in
the EDUNE model consisted of the actual R-36 post-Floyd data down to 0 ft-NGVD
and the predicted (from EDUNE) R-34 post-Floyd data below 0-ft NGVD. Only
profiles R-36 through R-41 were used for the Hurricane Irene analysis because the
spliced profiles for R-34 and R-35 appeared to be anomalous.
Storm Input
As stated in the model calibration chapter, the three models require storm
inputs of some or all of the following: wave height, wave period, wave direction,
water level, and wind speed.
Wave Data
NDBC Buoy #41009, located 20 nautical miles east of Cape Canaveral,
Florida, in an approximate water depth of 42 m, recorded significant wave height and
dominant wave period during Hurricane Irene. The buoy collects data every hour.
After examining the wave data, it was determined that Hurricane Irene affected the
Ft. Pierce area for 42 hours from October 15 at 7 pm until October 17 at 1 pm.
Wave Height
The SBEACH model allows the input of a significant wave height time series.
The significant wave height time series used for the SBEACH model is taken directly
from the buoy data and is shown in Figure 5.1. The significant wave height time
series was converted to an RMS breaking wave height time series using the same
procedure outlined in Chapter 4 for input into the EDUNE and CROSS models.
Wave Period
The SBEACH model is the only model to allow the input of a wave period
time series. The wave period time series used for the SBEACH model is taken
directly from the buoy data and is shown in Figure 5.1.
Wave Direction
The SBEACH model is the only model to allow the input of a wave direction
time series. No wave direction data were available during Hurricane Irene in the Ft.
Pierce area. Therefore, the following procedure was used to produce a wave direction
time series. The wave direction during Hurricane Floyd shows a linear trend (see
Figure 4.3), with the wave direction coming from approximately -200 at the
beginning of the storm, from shore normal at the peak of the storm, and from
approximately + 200 towards the end of the storm. This is consistent with the storm
passing the Ft. Pierce area offshore from south to north. Hurricane Irene took a
similar offshore south to north track as it passed the Ft. Pierce area. The wind
direction time series shown in Figure 5.2 for Hurricane Irene illustrates the south to
north shift of the hurricane, with wind coming off the water as the storm approached
and off the land as it passed by. Therefore, the wave direction time series shown in
Figure 5.3 was approximated using the wind direction and then a linear trend
continuation of the wind direction. The wave direction for the first half of the storm
was taken as the corresponding wind direction. A linear trend was then fit to
correspond to a zero wave direction at the peak of the storm, and at the end of the
storm the wave direction was the opposite of what it was at the beginning of the
storm.
Water Level
As stated earlier, all three models allow the input of a water level time series.
No water level data were available during Hurricane Irene in the Ft. Pierce area.
Therefore, a predictive model was run to produce a time series for water level during
the storm. The model is based on the theory ofa bathystrophic storm tide (Dean,
1991). Longshore currents generated by wind during a hurricane are influenced by
the Coriolis forces. The Coriolis forces require balancing hydrostatic gradients that
will either add to or reduce the surface gradient induced by the wind. A hurricane's
circular wind patterns induce longshore currents in both directions.
The predictive model requires beach profile and storm data for the area and
storm of interest as input. The beach profile data include the range and elevation data
for each of the profile lines R-34 to R-41. The storm data include time series of
location nothingg and eatingg, center (latitude) location, forward velocity, maximum
wind velocity, radius to the maximum wind, and central pressure for Hurricane Irene.
This information was taken from the unisys website (www.weather.unisys.com). The
time series for water level produced by the model was then increased by 60% to
account for wave set-up. The predicted water level time series is shown in Figure 5.4
for Hurricane Irene at the Ft. Pierce Shore Protection Project.
Wind Data
The NCDC weather station located at the Ft. Pierce St. Lucie County Airport
provided wind speed and wind direction data during Hurricane Irene. Data were
taken at approximate one-hour intervals.
The SBEACH model is the only model to allow the input of wind speed time
series. The wind speed time series used for the SBEACH model is taken directly
from the weather station and is shown in Figure 5.2. The wind direction time series
used to estimate the wave direction time series is also shown in Figure 5.2.
Verification Procedure
Each of three calibrated models was run with the profile and storm input
described above. Figures 5.5 through 5.7 illustrate the post-fill profile, measured
post-Floyd profile, measured post-Irene profile, and the model's predicted post-Irene
profile at R-37 in the project area for the SBEACH, EDUNE, and CROSS models.
Figures B.1 through B.6, B.7 through B. 12, and B. 13 through B18 in Appendix B
illustrate the pre-fill profiles, post-fill profiles, measured post-Floyd profiles,
measured post-Irene profiles, and the predicted post-Irene profiles for the SBEACH,
EDUNE, and CROSS models, respectively for R-34 through R-41.
-- Wave Height - -Wave Period
25
8
20 ---------. 7
. 6
S15
10 3V
> 2
S 101
5
0 i 0
0 6 12 18 24 30 36 42
Hour
Figure 5.1 Hurricane Irene Wave Height and Period
-I- Wind Speed - -Wind Direction
ir *i i
*~~~ ------f-----------------------* *-'
V*-* "
---m-m- - 1n n. n--n-nm- --" ----
0 6 12 18 24 30 36 42
150
0
0
100 I
In
50 .2
0)
50 S)
0 )
-50 .|
-100
Hour
Figure 5.2 Hurricane Irene Wind Speed and Direction
20
E
0
C 10
0
a-
0
E
0
-10
S-20
S-30
TO
40
-50
-50
0 6 12 18 24 30 36 42
Hour
Figure 5.3 Hurricane Irene Wave Direction
2
1.8
1.6
1.4
C11
>. 1 2
C) L I U"
J.
S0.8
0.6
0.4
0.2
0
0 6 12 18 24 30 36 42
Hour
Figure 5.4 Hurricane Irene Water Level
- - Post-fill -A- Post-Floyd -x- Post-Irene .-- Post-Irene EDUNE
Distance from Monument (ft)
Figure 5.6 Profile R-37 Measured and Predicted Post-Irene from EDUNE Model
- Post-fill Post-Floyd -x- Post-Irene - Post-Irene SBEACH
15
5-------^----------
0 \
5
z 0
b, 100 200 300 500 600 700 800 9
C
-10
-15
-20
Distance from Monument (ft)
Figure 5.5 Profile R-37 Measured and Predicted Post-Irene from SBEACH Model
- -- Post-fill --- Post-Floyd -x-- Post-Irene -- Post-Irene CROSS
Distance from Monument (ft)
Figure 5.7 Profile R-37 Measured and Predicted Post-Irene from CROSS Model
CHAPTER 6
MODEL PERFORMANCE
This chapter evaluates and compares the performances of calibrated
SBEACH, EDUNE, and CROSS models using several methods. These methods
include the residual parameter, eroded volume of sand, beach retreat, and contour
change. The models are evaluated individually as well as in comparison to each
other.
Measures of Model Performance
Several methods were used to compare the predicted post-storm profiles with
the measured post-storm profiles. The residual parameter, eroded beach volume,
shoreline retreat at the 6-ft contour, and contour change along the entire profile were
used to evaluate the accuracy of the model predictions.
Residual Parameter
The residual parameter, Res, provides a meaningful comparison of the
measured and predicted profile change. The Res is defined in non-dimensional form
as:
n
S(hp,, hma, )
Res= '=- (6.1)
C(h, h,,)2
where h is the elevation from 0-ft NGVD, the subscripts p and m describe predicted
and measured, the subscripts b and a describe before and after the storm, and the sum
of all the ith locations describes the entire profile. In a perfect model simulation, the
residual parameter would equal zero. The residual parameters are shown in Tables
6.1 and 6.2 for all predicted post-Floyd and post-Irene profiles.
Eroded Volume
The eroded volume of sand in the profile between +8 and 0 ft-NGVD also
provide a valid comparison of the measured and predicted profiles. The upper limit
for the erosion calculations was chosen because the berm height of the post-fill
profile is approximately +8-ft NGVD. Although the overwash experienced from
Hurricane Floyd extends well above +8 ft-NGVD, SBEACH predicts only a very
slight overwash on a few profiles, while EDUNE and CROSS do not predict any
overwash. There will not be an accurate comparison of eroded volume if this
accreted volume of sand is used to compare the measured to predicted eroded
volumes of sand because the net erosion will be quite small. The lower limit for the
erosion calculation was chosen because the post-Floyd survey data only extend to
approximately 0 ft-NGVD. Eroded volumes of sand are shown in Tables 6.1 and 6.2
for all measured and predicted post-Floyd and post-Irene profiles.
Shoreline Retreat
Shoreline retreat at the 6-ft contour was also used to compare the measured
and predicted profiles. The retreat at the 6-ft contour is representative of the erosion
along the beach face between the berm and 0-ft NGVD. The shoreline retreats at the
6-ft contour are shown in Tables 6.1 and 6.2 for all measured and predicted post-
Floyd and post-Irene profiles.
Table 6.1 Predicted Residuals, Measured and Predicted Eroded Volume Between +8
and 0 ft-NGVD and Shoreline Retreat at the 6-ft Contour for Hurricane Floyd
Profile Model Residual Eroded Volume Retreat at 6-ft
Between +8 and 0 ft- Contour (ft)
NGVD (ft2)
R-34 Measured -1150.62 -127.05
SBEACH 1.001 -42.58 -2.77
EDUNE 0.858 -20.43 -3.06
CROSS 0.858 -26.64 -10.32
R-35 Measured -642.86 -71.93
SBEACH 0.653 -395.59 -32.70
EDUNE 0.880 -371.71 -27.12
CROSS 0.878 -356.98 -27.86
R-36 Measured -343.79 -44.20
SBEACH 0.121 -249.06 -36.20
EDUNE 0.075 -245.25 -29.38
CROSS 0.109 -215.69 -30.49
R-37 Measured -179.68 -22.58
SBEACH 0.673 -235.51 -31.99
EDUNE 0.641 -195.87 -23.86
CROSS 0.619 -179.07 -28.50
R-38 Measured -243.88 -28.53
SBEACH 0.335 -197.36 -21.43
EDUNE 0.460 -183.79 -20.21
CROSS 0.464 -169.77 -21.76
R-39 Measured -230.54 -27.48
SBEACH 0.342 -189.03 -30.13
EDUNE 0.394 -203.45 -28.82
CROSS 0.418 -189.44 -29.88
R-40 Measured -347.80 -48.47
SBEACH 0.295 -185.07 -27.38
EDUNE 0.232 -205.51 -28.81
CROSS 0.240 -189.10 -29.71
R-41 Measured -282.46 -35.02
SBEACH 0.371 -194.12 -28.34
EDUNE 0.398 -197.18 -26.63
CROSS 0.457 -177.07 -27.55
Average of Measured -427.70 -50.66
All Profiles SBEACH 0.474 -211.04 -26.37
R-34 to R- EDUNE 0.492 -197.79 -23.49
41 CROSS 0.505 -187.97 -25.76
Table 6.2 Predicted Residuals, Measured and Predicted Eroded Volume Between +8
and 0 ft-NGVD and Shoreline Retreat at the 6-ft Contour for Hurricane Irene
Profile Model Residual Eroded Volume Retreat at 6-ft
Between +8 and 0 ft- Contour (ft)
NGVD (ft2)
R-36 Measured -128.27 -13.33
SBEACH 0.274 -190.55 -21.11
EDUNE 0.312 -117.05 -19.89
CROSS 0.293 -44.70 -1.39
R-37 Measured -72.09 -13.44
SBEACH 0.596 -162.38 -14.62
EDUNE 0.406 -127.12 -23.65
CROSS 0.249 -60.21 -5.88
R-38 Measured -14.52 -2.67
SBEACH 0.568 -194.90 -23.83
EDUNE 0.423 -77.22 -15.65
CROSS 0.305 -38.37 0.11
R-39 Measured -245.88 -17.97
SBEACH 0.612 -117.57 -11.62
EDUNE 0.399 -62.95 -2.12
CROSS 0.566 -47.22 -7.31
R-40 Measured 5.33 6.55
SBEACH 0.774 -163.93 -20.26
EDUNE 0.567 -30.36 -8.43
CROSS 0.449 -23.21 0.46
R-41 Measured 83.58 5.68
SBEACH 1.601 -100.99 -6.08
EDUNE 1.145 -81.07 -16.32
CROSS 0.974 -33.91 -4.52
Average of Measured -61.98 -5.86
All Profiles SBEACH 0.738 -155.05 -16.25
R-36 to R- EDUNE 0.542 -82.63 -14.34
41 CROSS 0.473 -41.27 -3.09
Contour Change Along Entire Profile
Another method of comparison between the measured and predicted profiles
is a contour change analysis. The pre-storm to post-storm contour change is
calculated at every contour along the entire profile. Graphs of the contour change as
a function of the contour illustrate well where sand is eroded from and accreted to
along the profile as well as compare the accuracy of the predicted profiles to the
measured profiles. Figure 6.1 illustrates the contour change as a function of the
contour for the measured and predicted profile data at R-37 for Hurricane Floyd.
Appendix C contains the contour change as a function of the contour for the measured
and predicted post-Floyd and post-Irene profile lines. Figures C. 1 through C.7
compare the measured and predicted post-Floyd contour changes and Figures C.8
through C. 13 compare the measured and predicted post-Irene contour changes. The
measured and predicted post-Floyd to post-Irene contour changes only extend to 0 ft-
NGVD because the measured post-Floyd data only extend to that depth.
Relative Model Performance
The predictions of the three models, SBEACH, EDUNE, and CROSS are
discussed next.
SBEACH Model
On average, the SBEACH model underpredicts the volume of erosion
between +8 and 0 ft-NGVD experienced during Hurricane Floyd, but overpredicts the
erosion during Hurricane Irene. The model performs better, on average, for
Hurricane Floyd than Irene. The average residual for Hurricane Floyd is 0.474, and
for Hurricane Irene is 0.738. Several of the profiles experienced significant overwash
from Hurricane Floyd. The SBEACH model does predict some slight overwash for
profile R-41 from Hurricane Floyd, and predicts the upper beach face better than the
lower beach face for several of the profiles. In several of the post-storm profiles for
both Hurricanes Floyd and Irene, the SBEACH model predicts an offshore bar at
approximately -5 ft to -10 ft-NGVD. Figure 6.2 illustrates a good example of the
slight overwash, the agreement in the upper beach face, and the offshore bar predicted
by the SBEACH model at profile R-41.
The SBEACH model predicts retreat at the 6-ft contour quite well for
Hurricane Floyd. The average retreat for profiles R-36 through R-41 is -34.38 ft, and
the average retreat predicted by the SBEACH model for these profiles is -26.37 ft.
The prediction is not quite as good for Hurricane Irene. The average retreat for
profiles R-36 through R-41 is -5.86 ft, and the average retreat predicted by the
SBEACH model is -16.25 ft.
EDUNE Model
On average, the EDUNE model underpredicts the volume of erosion between
+8 and 0 ft-NGVD experienced during Hurricane Floyd, but overpredicts the erosion
during Hurricane Irene. The model performs slightly better for Hurricane Floyd than
Irene. The average residual for Hurricane Floyd is 0.492, and for Hurricane Irene is
0.542. Although the EDUNE incorporates dune overwash processes, none of the
predicted profiles show any overwash. One explanation for this may be that the dune
is located so far back on the post-fill profile that the predicted erosion did not extend
that far back, and thus there was not overwash of the dune. The EDUNE model
predicts the lower beach face better than the upper beach face and does not predict
any sort of offshore bar feature. Figure 6.3 presents the measured and predicted post-
Floyd profiles at R-41, and provides a representative example.
The EDUNE model predicts retreat at the 6-ft contour reasonably well for
both Hurricanes Floyd and Irene. For Hurricane Floyd, the average retreat for
profiles R-36 through R-41 is -34.38 ft, and the average retreat predicted by the
EDUNE model for these profiles is -23.49 ft. For Hurricane Irene, the average
retreat for profiles R-36 through R-41 is -5.86 ft, and the average retreat predicted by
the EDUNE model is -14.34 ft.
CROSS Model
On average, the CROSS model underpredicts the volume of erosion between
+8 and 0 ft-NGVD experienced during both Hurricanes Floyd and Irene. For
Hurricane Irene, the model predicts very close to the measured eroded volume of
sand. The model performs slightly better for Hurricane Irene than Floyd. The
average residual for Hurricane Floyd is 0.505, and for Hurricane Irene is 0.473. The
CROSS model does not incorporate dune overwash processes, and therefore does not
predict any of the overwash experienced during either hurricane. The CROSS model
predicts the lower beach face better than the upper beach face and does not predict
any sort of offshore bar feature. Figure 6.4 provides a good example of these
predictions at profile R-38.
The CROSS model predicts retreat at the 6-ft contour reasonably well for
Hurricane Floyd and very well for Irene. For Hurricane Floyd, the average retreat for
profiles R-36 through R-41 is -34.38 ft, and the average retreat predicted by the
CROSS model for these profiles is -25.76 ft. For Hurricane Irene, the average retreat
for profiles R-36 through R-41 is -5.86 ft, and the average retreat predicted by the
EDUNE model is -3.09 ft.
Model Comparisons
Tables 6.3 and 6.4 provide summaries of the performances of the three models
for Hurricanes Floyd and Irene. The tables detail the average residuals, the ratio of
the average predicted eroded volume of sand to measured eroded volume of sand
between +8 and 0 ft-NGVD, and the ratio of the average predicted beach retreat to
measured beach retreat at the 6-ft contour. Figure 6.5 illustrates the post-fill profile,
measured post-Floyd profile, and each of the three model's predicted post-Floyd
profiles at R-37 in the project area. Figure 6.6 illustrates the measured post-Floyd
profile, measured post-Irene profile, and each of the three model's predicted post-
Irene profiles at R-37 in the project area.
Table 6.3 Summaries of Model Performances for Hurricane Floyd Model
Calibration
Average Model Residual Ratio of Predicted Eroded Ratio of Predicted
of All Volume to Measured Retreat to
Profiles Eroded Volume Measured Retreat
R-34 to R- SBEACH 0.474 0.493 0.521
41 EDUNE 0.492 0.463 0.464
_CROSS 0.505 0.440 0.509
Table 6.4 Summaries of Model Performances for Hurricane Irene Model
Verification
Average Model Residual Ratio of Predicted Eroded Ratio of Predicted
of All Volume to Measured Retreat to
Profiles Eroded Volume Measured Retreat
R-36 to R- SBEACH 0.738 2.502 2.773
41 EDUNE 0.542 1.333 2.447
CROSS 0.473 0.666 0.527
For Hurricane Floyd, the SBEACH model provided the smallest average
residual, the closest prediction for the average eroded volume of sand, and the closest
prediction for the average beach retreat. From Table 6.1, the SBEACH model's
residual was the smallest for four of the profiles, the EDUNE model's for two of the
profiles, and the CROSS model's for one of the profiles. For eroded volume of sand,
the SBEACH model predicted four of the profiles the closest, the EDUNE model
three of the profiles the closest, and the CROSS model one of the profiles the closest.
The CROSS model predicted the beach retreat the closest for four of the profiles,
while the SBEACH and EDUNE models each predicted the beach retreat the closest
for two of the profiles.
For Hurricane Irene, the CROSS model provided the smallest average
residual, the EDUNE and CROSS models provided the closest predictions for the
average eroded volume of sand, and the CROSS model provided the closest
prediction for the average beach retreat. From Table 6.2, the CROSS model's
residual was the smallest for four of the profiles, while each of the SBEACH and
EDUNE model's residual was the smallest for one of the profiles. For eroded volume
of sand, the CROSS model predicted four of the profiles the closest, while the
SBEACH and EDUNE models each predicted one of the profiles the closest. The
CROSS model predicted the beach retreat the closest for three of the profiles, the
SBEACH model for two of the profiles, and the EDUNE model for one of the
profiles.
The contour change as a function of the contour for the measured and
predicted profile data illustrate well how the models perform along the entire profile.
Figures 6.7 and 6.8 illustrate the average contour changes for Hurricanes Floyd and
Irene. Figure 6.7 illustrates that the models do not predict the overwash experienced
during Hurricane Floyd. Figures 6.7 and 6.8, as well as the individual profile figures,
also illustrate that the SBEACH model predicts the upper part of the beach face better
than the EDUNE or CROSS models, while the EDUNE and CROSS better predict the
lower beach face. The SBEACH model is the only one of the three models to allow
non-monotonic profile input with as many input data points as desired. The EDUNE
and CROSS models allow only monotonic profile input at every contour. Therefore,
the pre-storm profiles were most accurately represented in the SBEACH model. The
profile input for the SBEACH model could describe the irregular shape of the berm,
such as the overwash from Hurricane Floyd. This led to a better prediction of the
overall post-storm profile.
All three of the models fail to predict any erosion for profile R-34, and only
slight erosion for profile R-35 for Hurricane Floyd. Figure 6.9 illustrates the
measured and predicted post-Floyd conditions at R-34 for the SBEACH model, which
is very similar to that predicted in both the EDUNE and CROSS models. These two
profile lines most likely experienced the greatest amount of erosion in the form of
longshore sediment transport due to their proximity to the inlet and jetty (Figure 2.1
in Chapter 2). The only noticeable difference in the post-fill profiles at R-34 and R-
35 compared to the profiles at R-36 though R-41 is their gentler slopes.
Both the SBEACH and EDUNE models overpredict the erosion experienced
during Hurricane Irene. As seen from the measured data, the eroded volumes of sand
from the post-Irene profiles are quite inconsistent. The hurricane caused varied
amounts of erosion at four profiles and accretion at two profiles. At profiles R-37 and
R-38 there was minor erosion, at profiles R-36 and R-39 there was significant
erosion, and at profiles R-40 and R-41 the beach actually saw accretion from
Hurricane Irene. Therefore, on average, Hurricane Irene did not cause a significant
amount of erosion along the project area. The CROSS model consistently predicted
the least amount of erosion of the three models, and therefore, performed the best
overall in terms of beach retreat. It also performed better than the SBEACH model in
terms of eroded volume of sand. The average difference in eroded volume of sand
was comparable for the CROSS and EDUNE models, however, the CROSS model
underpredicted the amount of erosion while the EDUNE model overpredicted.
Mean Sediment Grain Size Sensitivity Analysis
The post-fill mean sediment grain size was 0.41 mm and was used for input
into all three models. The mean sediment grain size is a quantity that is readily
measured in the field. Although the mean sediment grain size of a beach is
representative of the sand on that beach, the beach is actually composed of a range of
sediment grain sizes. In order to test the sensitivity of each model with the grain size,
the following procedure was used. Each of the three calibrated models was run with
varying sediment grain sizes between 0.21 and 0.61 mm at profile R-38 for Hurricane
Floyd.
Table 6.5 provides a listing of the model and the grain size used for each run,
and the corresponding root mean square error and residual for each run. For the
SBEACH model, the post-fill sediment grain size of 0.41 mm provided the least root
mean square and smallest residual in comparison to the finer and coarser sediment
sizes. For the EDUNE and CROSS models, the coarser sediment size of 0.51 mm
provided smaller root mean square errors and residuals than the post-fill sediment
grain size of 0.41 mm. Although a coarser sediment size provided slightly smaller
root mean square errors and residuals in the EDUNE and CROSS models, the
reduction did not justify altering the input sediment size from its measured mean
value.
Table 6.5 Mean Sediment Grain Size Sensitivity Analysis for Profile R-38
Model Mean Sediment Grain Root Mean Square Residual
Size (mm) Error (ft)
SBEACH 0.21 1.4184 0.6160
0.31 1.0691 0.3848
0.41 0.9998 0.3346
0.51 1.3027 0.5057
0.61 1.5720 0.6873
EDUNE 0.21 0.9156 0.4909
0.31 0.8542 0.4613
0.41 0.8449 0.4602
0.51 0.8218 0.4585
0.61 0.8338 0.4623
CROSS 0.21 1.2279 0.4889
0.31 1.2035 0.4668
0.41 1.2039 0.4639
0.51 1.2004 0.4581
__0.61 1.2134 0.4656
--- Post-fill to Post-Floyd
- -- Post-fill to Post-Floyd EDUNE
* Post-fill to Post-Floyd SBEACH
- -x- Post-fill to Post-Floyd CROSS
Contour Change (ft)
Figure 6.1 Profile R-37 Contour Change for Hurricane Floyd
I
-~---
I - Post-fill --A- Post-Floyd -m- Post-Floyd SBEACH
15
10
->
5
__ 100 200 300 400 0O 600 700 800 9 0
-10
-15
-20
Distance from Monument (ft)
Figure 6.2 Profile R-41 Post-fill, Post-Floyd, and Post-Floyd SBEACH
S-. - Post-fill --- Post-Floyd - Post-Floyd EDUNE
Distance from Monument (ft)
Figure 6.3 Profile R-41 Post-fill, Post-Floyd, and Post-Floyd EDUNE
S - Post-fill --- Post-Floyd -x Post-Floyd CROSS
Distance from Monument (ft)
Figure 6.4 Profile R-38 Post-fill, Post-Floyd, and Post-Floyd CROSS
- -A Post-fill - - Post-Floyd -*--Post-Floyd SBEACH -- Post-Floyd EDUNE -. Post-Floyd CROSS
Distance from Monument (ft)
Figure 6.5 Profile R-37 Measured and Predicted Post-Floyd from Three Models
-A Post-Floyd - - Post-Irene - Post-Irene SBEACH C- Post-Irene EDUNE - Post-Irene CROSS
15
10
5
Z0 -
a 20 250 300 350 450 500 550 61
:I -5---- *-
-20
Distance from Monument (ft)
Figure 6.6 Profile R-37 Measured and Predicted Post-Irene from Three Models
-+- Post-fill to Post-Floyd -* - Post-fill to Post-Floyd SBEACH
- -A Post-fill to Post-Floyd EDUNE -x- Post-fill to Post-Floyd CROSS
Contour (ft)
Figure 6.7 Average Contour Change for Hurricane Floyd
I /
o I -i
o
-80 -60 -40 -20 0 20 40
Contour Change (ft)
Figure 6.8 Average Contour Change for Hurricane Irene
S - - Post-fill -*--- Post-Floyd -x- Post-Floyd SBEACH
Distance from Monument (ft)
Figure 6.9 Profile R-34 Post-fill, Post-Floyd, and Post-Floyd SBEACH
CHAPTER 7
SUMMARY AND CONCLUSIONS
Summary
The predictions of three cross-shore sediment transport models, SBEACH,
EDUNE, and CROSS were compared with measured results at the Ft. Pierce Shore
Protection Project due to Hurricanes Floyd and Irene. All three models are based on
the equilibrium beach profile concept and brief descriptions of each model were
provided. The three models were run and calibrated with Hurricane Floyd data in the
project area along the profile lines of the FDEP reference monuments R-34 to R-41.
The profile input consisted of the post-fill survey data and the storm input consisted
of Hurricane Floyd data. The models were each run several times with varying
combinations of their calibration parameters. The calibrated model was established
by the run with the least average root mean square error of the predicted versus the
measured data across the profile. Next, the three models were run for verification
with Hurricane Irene in the project area. The calibrated models were run with the
post-Floyd survey data as profile input and the Hurricane Irene storm data. Finally,
the performances of the models were evaluated and compared using the residual
parameter, eroded volume of sand, beach retreat, and contour change. A grain size
sensitivity analysis was also performed.
Conclusions
The availability of relevant beach surveys as well as measured storm data at
the Ft. Pierce Shore Protection Project area provided a great opportunity to apply the
three most commonly used cross-shore sediment transport models. A limitation of
the survey profile data employed in this study was its shallow offshore extent. The
south jetty at Ft. Pierce Inlet, located just north of the project area, acts as a littoral
barrier. The limited extent of the offshore profile data did not allow determination as
to whether sand was conserved in the project area profiles from pre- to post-storm,
which is assumed in the three models.
The three models all provided reasonable beach erosion predictions during
Hurricanes Floyd and Irene at the project area. Table 7.1 provides a summary of the
performances of each of the three models for Hurricanes Floyd and Irene. For
Hurricane Floyd, the average residual was between 0.47 and 0.51 for the three
models, the average ratio of predicted eroded volume to measured eroded volume was
between 0.44 and 0.49, and the average ratio of predicted retreat to measured retreat
was between 0.46 and 0.52. For Hurricane Irene, the average residual was between
0.47 and 0.74 for the three models, the average ratio of predicted eroded volume to
measured eroded volume was between 0.67 and 2.50, and the average ratio of
predicted retreat to measured retreat was between 0.53 and 2.77.
Table 7.1 Summaries of Model Performances for Hurricanes Floyd and Irene
Hurricane Floyd Model Calibration
Average Model Residual Ratio of Predicted Eroded Ratio of Predicted
of All Volume to Measured Retreat to
Profiles Eroded Volume Measured Retreat
R-34 to R- SBEACH 0.474 0.493 0.521
41 EDUNE 0.492 0.463 0.464
CROSS 0.505 0.440 0.509
Hurricane Irene Model Verification
Average Model Residual Ratio of Predicted Eroded Ratio of Predicted
of All Volume to Measured Retreat to
Profiles Eroded Volume Measured Retreat
R-36 to R- SBEACH 0.738 2.502 2.773
41 EDUNE 0.542 1.333 2.447
CROSS 0.473 0.666 0.527
As indicated by Table 7.1, the average residual indicates that the SBEACH
model performed the best for Hurricane Floyd, while the CROSS model performed
the best for Hurricane Irene. In terms of eroded volume of sand, the SBEACH model
provided the closest prediction for Hurricane Floyd, while the EDUNE and CROSS
models provided the closest predictions for Hurricane Irene. The SBEACH model
provided the best prediction for beach retreat for Hurricane Floyd, while the CROSS
model provided the best prediction for Hurricane Irene.
Overall, the predictions for Hurricane Floyd were better than the predictions
for Hurricane Irene. One reason for this is that the models were calibrated with
Hurricane Floyd, not with Hurricane Irene, and models were considered calibrated
when the comparison of predicted to measured post-Floyd profiles was the best. The
calibrated models were then tested with Hurricane Irene. Had the models instead
been calibrated with Hurricane Irene, they might have performed better for Hurricane
Irene than for Hurricane Floyd. Another reason for the better predictions for
Hurricane Floyd is that for Hurricane Floyd, all the profile and storm input data were
measured, whereas the wave direction and water level for Hurricane Irene were
estimated, and the profile input was a combination of measured and predicted data. A
final reason for the models performing better for Hurricane Floyd than Hurricane
Irene is the inconsistency in behavior of the post-Irene profiles. Some areas
experienced significant erosion, while others experienced accretion, resulting in an
overall trend of relatively minor erosion. Overall, the models underpredicted the
average volume of erosion during Hurricane Floyd, while for Hurricane Irene the
SBEACH and EDUNE models overpredicted, and the CROSS model underpredicted
the volume of erosion.
The overwash experienced during both storms is not accurately predicted by
any of the models, even though the SBEACH and EDUNE models do incorporate
overwash processes. The predictions of the CROSS model would benefit with the
addition of overwash processes. A drawback of both the EDUNE and CROSS
models is that they allow only monotonic profile input at every contour. The
SBEACH model allows non-monotonic profile input that can capture features such as
overwash much better, and can therefore provide better post-storm predictions. For
this reason, SBEACH performed better than the EDUNE or CROSS models along the
upper beach face. However, the models EDUNE and CROSS performed better along
the lower beach face.
The grain size sensitivity analysis indicated that a coarser grain size than the
measured mean resulted in slightly smaller root mean square errors and residuals in
the EDUNE and CROSS models, but the reduction did not justify altering the input
74
sediment size from the measured mean value. In terms of ease of use, the SBEACH
model has a very user-friendly interface that simplifies model input, runs, and output.
The EDUNE and CROSS models are run in Fortran, and organizing the input files
can be somewhat time consuming.
It is beneficial to the coastal engineering community to apply cross-shore
sediment transport models whenever the necessary profile and storm data are
available. The more times the models can be evaluated under different
circumstances, the more improved the models can become.
APPENDIX A
MEASURED AND PREDICTED PROFILES FOR HURRICANE FLOYD
- -- Pre-fill - - Post-fill --- Post-Floyd - Post-Floyd SBEACH
Distance from Monument (ft)
Figure A. 1 Profile R-34 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH
C0
z
0
cc
CU
o\ )
w
- - Pre-fill - - Post-fill --- Post-Floyd -w Post-Floyd SBEACH
Distance from Monument (ft)
Figure A.2 Profile R-35 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH
- -- Pre-fill - - Post-fill --- Post-Floyd - Post-Floyd SBEACH
Distance from Monument (ft)
Figure A.3 Profile R-36 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH
- - Pre-fill - - Post-fill Post-Floyd - Post-Floyd SBEACH
Distance from Monument (ft)
Figure A.4 Profile R-37 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH
- -* Pre-fill - - Post-fill -*- Post-Floyd - Post-Floyd SBEACH
Distance from Monument (ft)
Figure A.5 Profile R-38 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH
- 4- Pre-fill - - Post-fill --- Post-Floyd - Post-Floyd SBEACH
15
10
5
>
0 00
100 200 400 500 600 700 800 90
0
. -5
U1
-10
-15
-20
Distance from Monument (ft)
Figure A.6 Profile R-39 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH
- -- Pre-fill - - Post-fill -A- Post-Floyd - Post-Floyd SBEACH
Distance from Monument (ft)
Figure A.7 Profile R-40 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH
- -*- Pre-fill - - Post-fill -- Post-Floyd - Post-Floyd SBEACH
m
Distance from Monument (ft)
Figure A.8 Profile R-41 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd SBEACH
- -*- Pre-fill - - Post-fill -*- Post-Floyd -x Post-Floyd EDUNE
Distance from Monument (ft)
Figure A.9 Profile R-34 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd EDUNE
- +- Pre-fill - -- Post-fill -A- Post-Floyd -x Post-Floyd EDUNE
Distance from Monument (ft)
Figure A. 10 Profile R-35 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd EDUNE
- +- Pre-fill - - Post-fill --- Post-Floyd -- Post-Floyd EDUNE
Distance from Monument (ft)
Figure A. 11 Profile R-36 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd EDUNE
- --- Pre-fill - - Post-fill --- Post-Floyd -m- Post-Floyd EDUNE
Distance from Monument (ft)
Figure A. 12 Profile R-37 Pre-fill, Post-fill, Post-Floyd, and Post-Floyd EDUNE
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