UFL/COEL 92/001
SHORT COURSE ON
PRINCIPLES AND APPLICATIONS
OF BEACH NOURISHMENT
FEBRUARY 11 -12,1992
INSTRUCTORS
THOMAS CAMPBELL
ROBERT G. DEAN
HSIANG WANG
ORGANIZED BY
FLORIDA SHORE AND BEACH PRESERVATION ASSOCIATION
AND
COASTAL ANDOCEANOGRAPHIC ENGINEERING DEPARTMENT
UNIVERSITY OF FLORIDA
....:....
'
SHORT COURSE
ON
PRINCIPLES AND APPLICATIONS
OF
BEACH NOURISHMENT
S-. Instructors .
Thomas Campbell
Robert G. Dean
Hsiang Wang
... Organized by ...
Coastal and Oceanographic Engineering Department
University of Florida
Gainesville, Florida 32611
TABLE OF CONTENTS
CHAPTER
1 OVERVIEW
AIM OF BEACH NOURISHMENT
HISTORY AND OUTLOOK
MAJOR STEPS IN PROJECT PLANNING
REFERENCES
2 ENGINEERING DESIGN PRINCIPLES
PART I DESIGN
INTRODUCTION
CROSS-SHORE RESPONSE
Beach Width Gained vs. Sediment Quality
Effects of Sea Level Rise on Beach Nourishment
Quantities
Case I Nourishment Quantities for the Case
of No Onshore Sediment Transport
Case II Nourishment Quantities for the Case
of Onshore Sediment Transport
PLANFORM EVOLUTION OF BEACH NOURISHMENT PROJECTS
The Linearized Equation of Beach Planform Evolution
Governing Equations
Transport Equation
Equation of Sediment Conservation
Combined Equation for Beach Planform Evolution
Analytical Solutions for Beach Planform Evolution
(1). A Narrow Strip of Sand Extending into the
Ocean
(2). Initial Shoreline of Rectangular Planform
Effect of Retention on Setting Back the Fill Ends from
Project Boundaries
Effect of Ends on a Beach Fill
A Case Example Bethune Beach
Project Downdrift of a Partial or Complete Littoral
Barrier
DAMAGE REDUCTION DUE TO BEACH NOURISHMENT
REFERENCES
3 ENGINEERING DESIGN PRINCIPLES
PART II BOUNDARY CONDITIONS
HISTORICAL SHORELINE INFORMATION
COMPUTATION OF SHORELINE CHANGES
A. Estimation of closure depth
B. Errors induced by survey inaccuracy
C. Seasonal variations
LONG-TERM AND EXTREME SEA CONDITIONS
A. Summary of Synoptic Meteorological
Observations (SSMO)
B. Measured Wave Data
C. Wave Hindcasting Information
NEARSHORE WAVE INFORMATION
STORM SURGE AND WATER LEVEL CHANGES
MORPHOLOGICAL AND SEDIMENTARY CONDITIONS
HYDROGRAPHIC SURVEY
LITTORAL DRIFT ENVIRONMENT
SAND SOURCES
BIOLOGICAL CONDITIONS AND WATER QUALITY
NATURE AND MAN-MADE STRUCTURES
REFERENCES
4 SEDIMENT STORAGE AT TIDAL INLETS
INTRODUCTION
INLET HYDRAULICS
SEDIMENT BYPASSING
Natural Bypassing
Artificial Bypassing
SEDIMENT VOLUMES NEAR AN INLET
EVOLUTION OF EBB AND FLOOD SHOALS
SAND TRAPPING
Selected Inlets and Physical Environment
Volumetric Calculation
iii
Summary of Results
EBB SHOALS
Florida Inlets
Georgia Inlets
Ebb Shoal and Nearshore Environment
ROLE OF JETTY STRUCTURES
REFERENCES
5 THE BEACH RESTORATION PROCESS
INTRODUCTION
DESIGN
Silt & Clay
Rock in Fill
Beach Design
Initial Fill
Design Cross-section
Storm Benefits
Recreation Benefits
Optimizing the Design
Advanced Fill
Construction Profile
Permits & Approvals
Chapter 1
OVERVIEW
Hsiang Wang
Coastal & Oceanographic Engineering Department
University of Florida, Gainesville
AIM OF BEACH NOURISHMENT
At present, there are only three alternatives to shoreline recession; retreat as shoreline
regresses, harden the shoreline with protective structures and replenish the beach. One
should not, however, confuse them as three coastal protective alternatives as the primary
goal served by each alternative is different. Retreat from shoreline achieves the main purpose
of seeking harmony with nature, it offers little or no help to coastal protection in the usual
sense. Harden the shoreline with protective structures, on the other hand, is meant to
protect upland; seeking harmony with nature, at best, is a constraint but not the goal.
The primary aim of beach nourishment is to maintain a beach, although its benefit is often
measured in terms of recreation, coastal protection or other social and economic factors.
Once communities have settled on the coast, coast and beaches become part of the
utility system much the same as highways and power supplies that the community relies
upon. If society wants to use them, it must be prepared to pay to maintain and preserve
them. Therefore, beach nourishment is a means to maintain the community utility at a
cost.
Case review reveals that the decision to select beach nourishment over other alternatives
is often based upon one or more of the following reasons:
1. Maintain a beach at a designated location.
2. Soften the impact on adjacent coast.
3. Offer a certain degree of upland protection.
4. Spread the cost.
5. Can be reversed to natural state with minimal effort.
Many people perceive beach nourishment as a simple task of dumping sand on the
beach. This simplistic view is similar to claiming that a highway is simply the pouring of
asphalt over cowpath. In reality, beach nourishment, like any engineering work, in a harsh
environment, it is a complicated task. Our present technology, however, is at its infancy.
The intent of the short course is to review the state of art and to present the essential
elements of beach nourishment design.
HISTORY AND OUTLOOK
Americans were the pioneers in beach nourishment practice. The earliest documented
beach nourishment work can be traced back to 1922, at Coney Island, New York. It was
actually a fairly large scale operation at the time. Approximately 1.7 million cubic yards
of material from New York Harbor was transferred to the 0.7 miles beach at Coney Island
through hydraulic dredging, at a cost of about 21 cents per cubic yard. Numerous projects
were carried out afterwards.
Hall (1951) complied a list of 72 beach nourishment projects in the United States dur-
ing the period of 1922 to 1950 (a number of them were actually one project of different
segments). The majority of these projects were for the purpose of beach restoration and
shore nourishment; 12 of these 72 projects were actually carried out for the primary purpose
of dredge disposal. During this period, most of the nourishment projects were along the
southern California coast and mid-Atlantic coast of New York and New Jersey. Only a
handful of projects were along the southeast Atlantic coast and Gulf coast.
In this early stage, there was really no basic criterion pertaining to artificial beach
nourishment. Hall did propose a set of design criteria suggesting some simple rules on
nourishment configuration and required quantity of material. Since there was no follow-up
study on any of these projects, little knowledge was gained.
In the last three decades, the number of beach nourishment projects increased consider-
ably, particularly along the east coast and the coast of Florida. Tonya and Pilkey (1988), for
instance, identified more than 90 documented cases of replenishment in over 200 separate
pumping operations along the U.S. Atlantic barrier shore (Long Island, New York to Key
Biscayne, Florida) alone. Table 1.1 shows the number of locations in each state along the
barrier shore than beach nourishment projects have been identified. Of the 75 locations, 31
were in Florida, or more than 40%.
Table 1.1: Locations in Each State Along the East Coast Barrier Shore with Nourishment
Projects
State NY NJ DE MD VA NC SC GA FL Total
Number of
Locations 5 17 1 1 2 13 4 2 31 75
In terms of expenditure, Florida was also the highest. Under the Florida Beach Erosion
Control Program, a total of 67.3 miles of beach has been restored or renourished during the
period from 1965 to 1984 with a total cost of some 115.6 million (Florida DNR report, 1984).
Figure 1.1 shows funds spent for restoration/renourishment projects during 1965-1984 in 5
year intervals. The trend of increased spending was clear. According to the data compiled
by the Florida Department of Natural Resources 92.7 million were spent to restore 51.12
miles of shoreline and 22.9 million have been used to renourish (maintenance) 16.18 miles
of beaches. Table 1.2 shows the actual expenditures of each individual beach nourishment
FLORIDA DEPARTMENT OF NATURAL RESOURCES
Division of Beaches and Shores
Funds Spent for Restoration/Renourishment Projects
1965 1984
In Five Year Intervals
- State Cost
[ l Federal/Local Cost
$77,597,758.
$115,6321,597.
$33.390.650.
$2,491,137.
1965-1970
No. Projects -3
MIes Restored/
Nourished 6.45
1971-1975 *
No. Projects- 12
Mies Restored/
Nourished- 17.12
1975-1980 '
No. Projects -6
Miles Restored/
Nourished- 13.35
1981-1984
No. Projects -7
MIes Restored/
Nourished- 30.38
19Jb-1V8 4 '
Total
No. Projects -28
Miles Restored/
Nourished- 67.30
PERIOD OF TIME
Figure 1.1 Funds Spent for Restoration/Renourishment Projects in Florida from
1965 1986 (DNR, 1984).
100r-
801-
6 0-
40 -
20o-
$557,920
Total Cost
Name of Project Of Project
Mexico Beach Restoration $ 40,625
Mexico Bch Renourishment ---
Pompano/Lauderdale ny-The-Sea
Restoration 1,873,437
Pompano Beach Renotlrishment ---
Virgina Key/Key Biscayne Rest. 577,075
Virginia Key Renourishment --
Cape Canaveral Beach Restoration 1,050,000
Hallandale Beach Restoration 779,977
Delray Beach Restoration 3,015,383
Delray Beach Nourishment---
Delray Beach Renourishment ---
St. Petersburg Beach Restoration 682,716
Venice Beach Restoration 49,700
Ft. Pierce Beach Restoration 621,208
Ft. Pierce Renourishment ---
Bal Harbour Restoration 4,962,420
Indialantic/Melbourne Restoration 3,582,000
John U. Lloyd Restoration 2,945,262
llollywood/HIallandale Restoration 7,743,376
Lido Key Restoration 360,000
Ln Miami Beach Restoration 49,892,000
North Redington Beach Restoration 369,000
Jacksonville Beach Restoration 9,757,900
Mullet Key Restoration 649,878
Jupiter Island Restoration 3,574,221
Treasure Island Restoration 216,000
Treasure Island Renourishmont ---
Treasure Island Renourishnent ---
Total Restoration Projects $92,742,258
Total Renourishment Projects ---
Project
State Share Length
Of Cost (miles)
$ 20,312 .65
468,359
69,249
241,055
292,491
976,044
305,109
36, 668
150,041
819,154
1,162,911
784,340
2,825,513
150,000
14,530,114
247,125
2,267,086
97,483
716,332
44, 650
$26,204,036
3.30
2.50
2.80
.78
2. 67
.50
.17
1.30
.85
2.10
1.50
4.73
.62
9.65
.30
10.50
1.20
4. 60
.40
S-.-2
Total Cost
Of Project
$ 41,155
10,273,340
2,381,742
1,660,584
3,949,117
1,559,431
1,228,000
1,796,970
State Share
Of Cost
20,000
3,549.,453
262,516
564,423
1,408,713
493,259
7---
314,500
573,750
$22,890,339 $7,186,614
Note: Total Restoration
Ronourishment $115,632,597 $33,390,650 67.12
Cost per mile 1,718,166 Renourishment
1,944,214 Restoration
Total Number of Projects 28 Restoration
Table 1.2. Expenditure on Individual Beach Restoration/Renourishment Projects, 1965-1984
(DNR, 1984).
Project
Length
(miles)
.55
5.20
1.30
2.70
2. 63
1.30
1.70
.80
16.18
project during this period. As you can see, Miami Beach restoration project was far the
largest, with a listed cost of $49,892,000. The actual cost up to date probably exceeded 54
million. 14.4 million cubic yards of sand were placed on a stretch of beach about 10 miles
long. More detailed information on beach restoration projects in the State of Florida can
be found in literature compiled by Walton (1977) and Wang (1988).
During this period, technology of beach nourishment began to develop. The concept
of overfill ratio was first proposed by Krumbein (1957) and Krumbein and James (1965)
which allows rational estimation of the required volume of borrow material to retain a unit
volume of beach material after nourishment and sorting by natural forces. The method of
computation was further refined by Dean (1974), James (1975) and Hobson (1977). The
ideal of equilibrium beach profile (Bruun, 1954; Dean, 1977; Moore, 1982) was applied to
beach nourishment to determine the shape of original and nourished beaches. Since the
1970's computer modelings on shoreline changes were developed and were being applied to
beach nourishment design. These models include one-line models, two-line models, N-line
models, the GENESIS ( Generalized Shoreline Change Numerical Model for Engineering
Use, Hanson, 1987), dune erosion models, etc. Methods of beach nourishment have also ex-
panded. In addition to the conventional approach of placing sand on the beach face through
hydraulic dredging, feeder beach, inlet sand by- passing, perched beach, sub-aqueous nour-
ishment, beach scraping, stock piling, and other means were all experimented. There was
also a growing awareness of environmental concern. Environmental impact assessment now
becomes an integral part of beach nourishment design. We also begin to see some effort in
performance monitoring.
Outside the United States, the Netherlands and Germany are among the more active
ones in beach nourishment engineering. Australia, Belgium and Singapore have also seen
some limited activities.
In the Netherlands, beach nourishment was experimented as early as 1953 when 70,000
m3 of sand was placed on the beach at Scheveningen (Edelman, 1960). Since then nour-
ishment projects were carried out at numerous locations covering the entire coast of the
country. Roelse (1986) compiled a list of 32 projects completed between 1952-1985. Fig-
ure 1.2 shows the locations of artificial beach nourishment along the Dutch Coast. Of
these projects, the Hoek Van Holland project was the largest. During the years of 1971- 72,
18.94 million m3 (24.92 million ydS) were dredged from the entrance channel of Europort
via hopper dredgers to create a beach 3300 m long and 900 m wide. This project serves
the dual purposes of dredge spoil disposal and land reclamation. The cost of the project
was at an amazingly low figure of 7.4 million DFL (approximately 3.9 million U.S. dol-
lars). Even when converted to 1987 cost, it came to approximately 11 million dollars, or,
$0.46/yd3. This was an exceptional case. In general, the cost of dredging and placement in
the Netherlands is about half that of a comparable job in the United States.
Since land reclamation and shore protection is a national priority in the Netherlands,
considerable advances have been made there in beach nourishment technology even though
they are a late comer on the scene. In fact, the first and, at present, the only artificial
beach nourishment design manual was published by the Dutches (Manual, 1986).
In Germany, the major beach nourishment effort is along the 40 km shoreline of Island
of Sylt. Sylt is the popular resort island in northern Germany. It is under heavy ero-
sional stress with dune recession in excess of 1 m per year along the entire coast. Various
nourishment projects were carried out since 1972 (Kramer, 1972; Fuhrboter, 1974; Gartner
and Dette, 1987). On a per unit length basis, the stretch of beach is probably the most
frequently nourished coast in the world. It is also the location where various nourishment
schemes were tested on a prototype scale including various planforms a unique sand groyne
configuration, multiple sand groynes, rectangular shapes of different length to width ratios
as well as various profile geometries different proportions and slopes at different elevations.
A performance monitoring program has been instituted since 1972. Therefore, it is one of
the few nourishment projects, systematic monitoring and documentation were carried out
on a long term basis.
Figure 1.2. Locations of Artificial Nourishment Along the Dutch Coast
(Dutch Manual, 1986).
8
Since the first project in the early 1920's, beach nourishment practice has developed
from a simple sand dumping exercise into a multi-facet engineering work. We also witnessed
significant increases in project activities in the last two decades. The trend is most certainly
to continue perhaps at an accelerated rate. The reasons behind the projected increase in
activities are:
1. Shorelines are deteriorating at a national scale.
2. Shoreline hardening practice becomes increasingly undesirable and, at certain in-
stances, is no longer permitted.
3. Spreading the coast over a period is politically more palatable than one-time large
expenditure.
In the State of Florida, a coastal restoration task force was organized by the Governor
in 1985 to examine the existing coastal condition and to provide guidance in the long term
strategy of coastal restoration. Of the 800 miles of sandy shoreline around Florida, 543 miles
were identified as erosional, again of which 140 miles (224 Km) were considered critically
eroding, (Figure 1.3). A ten-year program for the restoration and maintenance of Florida's
critically-eroded beaches was proposed by the Florida Department of Natural Resources
(DNR) at an initial estimated cost of $362 million with an additional $110 million during
that ten-year period to be used for periodic renourishment of restored beaches (DNR, 1985,
1986). Similar programs are also expected in other coastal states and in other countries.
Germany, for instance, has a five-year program to preserve the beach and dunes for the island
of Sylt requiring 20 million m3 of material at a cost of $80 million. Japan, where coastal
protection is of national priority but presently has no or very limited beach nourishment
programs, is also aggressively looking into the soft structure approach as the future solution.
Region I
Miles Completed 1.20
Region II
Miles Completed
5.69
Federal/Local
Percent of
Total Cost
51%
67%
77%
73%
71%
71%
State Percent
Of Total Cost
49%
33%
23%
27%
29%
29%
Regional
Percent of
Air Cost
.1%
4.9%
8.0%
9.0%
78%
100.9%
Region III
Miles Completed 10.50
_" Region IV
Miles Completed
12.10
,r Region V
Miles Completed
37.81
REGIONS
(Southeast) V
(East Central)
IV
21.8
(Northeast) III /.
21.9
(Southwest) II
(Panhandle) I
.9 46.2
1 Total 103.7
53.0 51.5
I Total 137.0
53.3 62.5
NI Total 137.6
Critical Erosion
22Non-Critical Erosion
0r Stable or Accreting
Shoreline
112.5
STotal 177.4
Total 219.2
100
SHORELINE (Miles)
Figure 1.3. Present Erosional Condition Along Florida Coast (DNR, 1985).
Reaion
II
III
IV
V
Total
.6 58.1
200
.U
MAJOR STEPS IN PROJECT PLANNING
Beach nourishment project planning is still by and large a trial and error process requiring
numerous iterations. It is complex and time consuming and it is not uncommon that a
project from its incipiency to its implementation could take 5 to 10 years. Planning is,
however, critical to the success or even the survival of the project.
In the State of Florida, dredge and fill operations, such as beach restoration which are
conducted on the sovereignty lands of the State must be authorized by various regulatory
agencies including the Department of Natural Resources, Department of Environmental
Regulations, Department of State, Board of Trustees of the Internal Improvement Trust
Fund and the U.S. Army Corps of Engineers. If the beach is in the county or city jurisdiction
local permits have to be obtained as well. The process of obtaining all the various approval
and the collecting and providing of the necessary information to obtain these approvals is
time consuming. If the project is to be coast shared by the Federal dollars, a feasibility
study must be conducted to show justifiable cost/benefit from the Federal level for project
authorization. Projects needing State and Federal funding can then be submitted to the
State Legislature or to the Congress for appropriation. During the process, if excessive
funds are expended for project preparation, cost overruns could dissuade the Legislators for
project funding. Furthermore, certain aspects of the project such as shoreline position and
sand sources could change or become outdated requiring costly restudy. Therefore, timely
and controlled project planning is essential to insure successful project implementation.
The major steps involved in a beach nourishment project are illustrated by the following
block diagram:
Elements required to accomplish each step are given as follows:
1. Problem Proposal
A). Problem Evaluation
Existing erosion problem
History of efforts and their effectiveness
B). Alternative Solutions
C.) Project Definition
Requirements storm protection, recreation, shoreline restoration
Alternative sand sources offshore borrow areas, inlet by-passing, etc.
D). Preliminary Cost Analysis
E). Beach Access Analysis
F). Cost/Benefit Analysis
G). Environmental Statement
2. Project Preparation
A). Engineering
B). Environmental Impact Study
C). Cost Estimation
D). Financing
E). Permitting
F). Project Authorization and Documentation
3. Project Implementation
A). Bidding and Tendering
B). Pre-Construction Survey
C). Construction Management and Monitoring
D). Acceptance
E). Post-Project Monitoring and Evaluation
F). Maintenance
The elements listed in each step are usually not independent of each other. Therefore,
iterations are expected within each step and sometimes across the steps.
Of course, the tangible product of the whole exercise is the engineering work of a nour-
ished beach. This is also the main topic of the short course. An engineering design is
influenced by many factors, such as environmental effects, cost, sand sources, delivery sys-
tems, etc. The intent of the course is to provide an overview of a complete engineering
design practice. A flow chart such as presented in the Dutch Manual on Beach Nourish-
ment (1986) can be used to aid in the design process. Figure 1. 4 presents a flow chart for
beach nourishment engineering.
TOOL
o Fill Factor
o Equilibrium Profile
o Survey
TOOL
o Shoreline Response Models
o Dune Erosion Model
o Wave and Storm Surge Models
o Inlet Models
o Data
CONSTRAINTS
o Storm Protection
o Recreation
o Beach Access
o Environment
SEcoomy
Coastal and Sediment Process
CONSTRAINTS
o Sand Sources
o Nourishment Method
o Cost
Modification
I Modification |
PROJECT EVALUATION
o Longevity
o Updrift-Downdrift Impact
o Interactions (Inlet, Existing Engr. Works)
o Effectiveness
o Environmental Impact
CONSTRAINTS
Implementation a Cost
o Delivering System
o Time
Beach Nourishment Design Flow Chart.
BOUNDARY CONDITION
o Coastal Condition
o Environmental Forces
o Sediment Properties
o Geometry and Structures
TOOL
o Historical Information
o Wave Models
o Littoral Environment
o On/Off Shore Transport
PROJECT DEFINITION
o Geometry
o Volumetric Requirement
o Material Specification
o Auxiliary Structures
Figure 1.4.
REFERENCES
Bruun, P. (1954) Coast Erosion and the Development of Beach Profiles, U.S. Army Beach
Erosion Board Tech. Memo. No. 44.
Dean, R. G. (1974) Compatibility of Borrow Material for Beach Fills, Proc. 14th Coastal
Engineering Conf., ASCE, Copenhagen, Denmark.
Dean, R. G. (1977) Equilibrium Beach Profiles: U.S. Atlantic and Gulf Coasts, Tech. Rep.
No. 12, University of Delaware, Newark.
DNR (1984) Beach Restoration: A State Initiative, Florida Department of Natural Re-
sources Tallahassee, FL.
DNR (1986) A Proposed Comprehensive Beach Management Program for the State of
Florida, Florida Department of Natural Resources, Tallahassee, FL.
Dutch Manual (1986) Manual on Artificial Beach Nourishment, Rijkswaterstaat (Dutch
Public Works Department) Delft, The Netherlands.
Fuhrboter, A. (1974) A Refraction Groin Built by Sand, Proc. 147th Coastal Engineering
Conf., Copenhagen, Denmark.
Gartner, J., and Dette, H. H. (1987) Design and Performance of Large Scale Nourishments,
Proc. Coastal & Engineering in Developing Countries, Beijing, China, pp 181-196.
Hall, Jr., J.V. (1952) Artificially Nourished and Constructed Beaches Beach Erosion Board,
Tech. Memo, No. 29.
Hanson, H. (1987) GENESIS, A Generalized Shoreline Change Numerical Model for En-
gineering Use, Lund Univ., Pep. No. 1007, Lund, Sweden.
Hobson, R. D. (1977) Sediment Handling and Beach Fill Design, Coastal Sediments 77,
ASCE, Charleston, S.C.
James, W. R. (1975) Techniques in Evaluating Suitability of Borrow Material for Beach
Nourishment, U.S. Army Coast al Engineering Research Ctr., Tech. Memo, No. 60.
Kramer, J. (1972) Artificial Beach Nourishment on the German North Sea Coast, Proc.
137th Coastal Eng. Conf., Vancouver, B.C., Canada.
Krumbein, W. C. (1975) A Method for Specification of Sand for Beach Fills, Beach Erosion
Board, Tech. Memo, No. 102.
Krumbein, W. C., and James, W. R. (1965) A Log-Normal Size Distribution Model for
Estimating Stability of Beach Fill Material, U.S. Army, Coastal Eng. Res. Ctr., Tech.
Memo. No. 16.
Moore, B. (1982) Beach Profile Evolution in Response to Changes in Water Level and
Wave Height, M.S. Thesis, Dept. of Civil Engr., Univ. of Del., Newark, DE.
Roelse, P. (1986) Artificial Nourishment as Coastal Defense in the Netherlands Previous
Fills, Future Development, Amex IV Artificial Beach Nourishment Manual, Ministry
of Transport and Public Work, The Netherlands.
Wang, W. C. (1988) List of Literature Related to the Beach Restoration Projects in the
State of Florida. Technical Rep., Coastal Engr. Dept., Univ. of Florida, Gainesville,
FL (in preparation).
Walton, Jr., T. L. (1977) Beach Nourishments in Florida and on the Lower-Atlantic and
Gulf Coasts. UFL/COEL-77/081, Coastal and Oceano. Engr. Dept., Univ. of
Florida, Gainesville, FL.
Tonya, C. and Pilkey, 0. (1988) An Historical Survey of Beach Replenishment on the U.S.
Atlantic Barrier Coast: Good News for Florida, Beach Preservation Technology Conf.,
Gainesville, FL.
Chapter 2
ENGINEERING DESIGN
PRINCIPLES: PART I DESIGN
Robert G. Dean
Coastal & Oceanographic Engineering Department
University of Florida, Gainesville
INTRODUCTION
It is convenient to discuss the physical performance of beach nourishment projects in
terms of the cross-shore response (or profile adjustment) and longshore response, i.e. trans-
port of sand out of the area placed. it is also convenient in exploring performance at the
conceptual level to utilize idealized considerations and simplified linearizedd) equations in
some cases. This allows one to obtain a grasp or overview of the importance of the different
variables without the problem of being clouded by complications which may be significant
at the 10% 20% level. To simplify our cross-shore considerations, we will use the so- called
equilibrium beach profile concept in which the depth h(y) is related to the distance offshore,
y, by the scale parameter, A, in the form
h(y) = Ay2/3 (2.1)
Although this is not a universally valid form, it serves to capture many of the important
characteristics of equilibrated beach profiles. To assist in providing an overview of transport
in the longshore direction, we will utilize the linearized combined form of the transport and
continuity equations first developed by Pelnard ConsiderB
ay a2Y
= Ga2y (2.2)
at X2
where x is the longshore distance, t is time, G is a longshoree diffusivity" which depends
strongly on the wave height mobilizing the sediment and Eq. (2.2) is recognized as the
"heat conduction equation".
CROSS-SHORE RESPONSE
Beach Width Gained vs. Sediment Quality
From Fig. 2.1, it is seen that the scale parameter, A, in Eq. (2.1) increases with increasing
sediment size. Thus, as presented in Fig. 2.2, a finer sediment will be associated with a
milder sloped profile than one composed of coarse sediment. We will denote the native and
fill profile scale parameters as AN and Ap, respectively. The consequence of sand size to
beach nourishment is that the coarser the nourishment material, the greater the dry beach
width per unit volume placed.
Nourished beach profiles can be designated as "intersecting", "non-intersecting", and
"submerged" profiles. Figure 2.3 presents examples of these. Referring to the top panel in
this figure of intersecting profiles, a necessary but not sufficient requirement for intersecting
profiles is that the fill material be coarser than the native material. One can see that an
advantage of such a profile is that the nourished profile "toes in" to the native profile thereby
negating the need for material to extend out to the closure depth. The second type of profile
is one that would usually occur in most beach nourishment projects. Nonintersecting profiles
occur if the nourished material grain size is equal to or less than the native grain size.
Additionally, this profile always extends out to the closure depth, h.. The third type of
profile that can occur is the submerged profile (Fig. 2.3c) the characteristics of which are
shown in greater detail in Fig. 2.4. This profile type requires the nourished material to be
finer than the native. It can be shown that if only a small amount of material is used then
all of this material will be mobilized by the breaking waves and moved offshore to form a
CIE 1.0 1
w Suggested Empirical
hI- Relationship
< From Hughes'
Field Results7 / From Individual Field Prol
C Where a Range of Sand S
c" Was Given
E. 0.10
I F-rom Swart's
W Laboratory Results
w 0.011
0.01 0.1 1.0 10.0 100.0
SEDIMENT SIZE, D (mm)
Figure 2.1. Beach Profile Factor, A, vs. Sediment Diameter, D, in Relationship
h = Ay23(Modlfied from Moore, 1982).
DISTANCE OFFSHORE (m)
0
0
IL
10-
a
Figure 2.2 Equilibrium Beach Profiles for Sand Sizes of 0.3 mm and 0.6 mm
A(D = 0.3 mm) = 0.12 m11/ A(D = 0.6 mm) = 0.20 m13.
200
Added Sand
Intersecting Profile AF>AN
Added Sand ~
b) Non-Intersecting Profile
Virtual Origin of
Nourished Profile
Added Sand
c) Submerged Profile AF
Figure 2.3. Three Generic Types of Nourished Profiles.
DISTANCE (m)
100
200
300
400
B = 1.5m
b) Added Volume = 490 mS Im
c) Added Volume
d) Added Volume = 1660 m3 /m
Case of Incipient Dry Beach
Figure 2.4 Effect of Increasing Volume of Sand Added on Resulting
Beach Profile. A = 0.1 m1/ A = 0.2 m/3 h,= 6 m, B = 1.5 m.
500
+4 -
Z 0
O-
U 10
L-
_
OFFSHORE
small portion of the equilibrium profile associated with this grain size as shown in the upper
panel. With increasing amounts of fill material, the intersection between the nourished and
the original profile moves landward until the intersection point is at the water line. For
greater quantities of material, there will be an increase in the dry beach width, Ay, resulting
in a profile of the second type described.
Figure 2.5 illustrates the effect of placing the same volume of four different sized sands.
In Fig. 2.5a, sand coarser than the native is used and a relatively wide beach Ay is obtained.
In Fig. 2.5b, the same volume of sand of the same size as the native is used and the dry
beach width gained is less. More of the same volume is required to fill out the milder
sloped underwater profile. In Fig. 2.5c, the placed sand is finer than the native and much
of the sand is utilized in satisfying the milder sloped underwater profile requirements. In a
limiting case, shown in Fig. 2.5d, no dry beach is yielded with all the sand being used to
satisfy the underwater requirements.
We can quantify the results presented in Fig. 2.5 for beach widening through nour-
ishment by utilizing equilibrium profile concepts. It is necessary to distinguish two cases.
The first is with intersecting profiles such as indicated in Fig. 2.3a and requires AF > AN.
For this case, the volume placed per unit shoreline length, -V associated with a shoreline
advancement, Ay, is presented in non-dimensional form as
V1 Ay 3 h /Ay\5/ 1
K + (2.3)
BW. W. 5 WB W [1- (A) 3/2] 2/3
in which B is the berm height, W, is a reference offshore distance associated with the
breaking depth, he, on the original (unnourished) profile, i.e.
(h \3/2
W = (2.4)
and the breaking depth, h, and breaking wave height, Hb are related by
h, = Hb/nC
with n(; 0.78), the spilling breaking wave proportionality factor. Figure 2.6 presents an
estimate of h* around the Florida shoreline.
S92.4m
a) Intersecting Profiles,
AN= 0.1ml3AF = 0.14m113
45.3m
b) Non-Intersecting Profiles
AN= AF= 0.1m1/3
c) Non-intersecting Profiles
AN= 0.1m 3,AF = 0.09m1/3
d) Limiting Case
Non-intersecting
100
h,= 6m
h.= 6m
of Nourishment Advancement.
Profiles, AN= O.lm 3,AF = 0.088m/13
200
300
400
500
600
OFFSHORE DISTANCE (m)
Figure 2.5. Effect of Nourishment Material Scale Parameter, AF, on Width of
Resulting Dry Beach. Four Examples of Decreasing AF.
24
20
1-
16
.c
MA
ST
_cc
CC
CL
VB
VE WP
MI
12 16 20 24
h, (Feet) ,
,. "-
Figure 2.6 Recommended Distribtuion of hAlong the Sandy Shoreline
of Florida.
h* (Feet)
12 16 20 24
For non-intersecting profiles, Figures 2.3b and 2.5b,c and d, the corresponding volume
V2 in non-dimensional form is
WBV2 Ay 3 h* ay +( AN3/2 5/3 AN 3/2
+= + + (2.5)
W.B W.5*B W. Ap Ap
It can be shown that the critical value (Ay/W,), for intersection/non-intersection of
profiles is given by
(W,* )AF ( ) (2.6)
with intersection occurring if Ay/W* is less than the critical value.
The critical volume associated with intersecting/non- intersecting profiles is
(IV )c=(1() 3 h [ (A) 3/2] (2.7)
BW, -1 5 B Ap
and applies only for (AF/AN) > 1. Also of interest, the critical volume of sand that will
just yield a finite shoreline displacement for non-intersecting profiles (AF/AN < 1), is
SV 3 h AN\ 3/2 AN (2.8)
[BW-), 2 -5B AB p3 A
Figure 2.7 presents these two critical volumes versus the scale parameter ratio AF/AN for
the special case h,/B = 4.0.
The results from Eqs. (2.3), (2.5) and (2.6) are presented in graphical form in Figs. 2.8
and 2.9 for cases of (h,/B) = 2 and 4 respectively. Plotted is the non-dimensional shoreline
advancement (Ay/W,) versus the ratio of fill to native sediment scale parameters, AF/AN,
for various isolines of dimensionless fill volume V' (= W per unit length of beach. It is
interesting that the shoreline advancement remains more or less constant for AF/AN > 1;
for smaller values the additional shoreline width decreases rapidly. For AF/AN values
slightly smaller than plotted, there is no beach width gain, i.e. as in Fig. 2.5d.
Effects of Sea Level Rise on Beach Nourishment Quantities
Recently developed future sea level scenarios developed based on assumed fossil fuel
consumption and other relevant factors have led to concern over the viability of the beach
15 1 1 3
w LL
O 2
LU I --
Z- / z
o 1 < /
IC- _
0 0
0 1 2 3
cFn > 7) cn >
AF /(2)
Figure 2.7. (1) Volumetric Requirement for Finite Shoreline Advancement
(Eq. 2.8); (2) Volumetric Criterion for Intersecting Profiles
(Eq. 2.7). Variation with AF/AN. Results Presented for h,/B = 4.0
0 --
0 1 2 3
Figure 2.7. (1) Volumetric Requirement for Finite Shoreline Advancement
(Eq. 2.8); (2) Volumetric Criterion for Intersecting Profiles
(Eq. 2.7). Variation with Ap'AN. Results Presented for h,/B = 4.0
10.0
1.0 o \ te -
1 _... re--I .
S/ i tv' = 0.5
11-1l1,V- = 0.2
0.10 I V = 0.1
I V' = 0.05
f o
-Asymptotes -1V' = 0.02
for Ay0 -" ""T-7-"-- "
V0.01 = 0.01
0.01 L I
W.
~ Ay! -' = 0.005
:;, y! ^ r .-- -- L
AFI V = V/BW, = 0.002
A* ------ h.- ---,
0.001 -Definition Sketch
0 1.0 2.0 2.8
A' = AF/AN
Figure 2.8. Variation of Non-Dimensional Shoreline Advancement
Ay/W, With A' and VW. Results Shown for h, /B = 2.0
1.0
0.1 1 I 1 F
11 I F = 0.05
Asymptotes
for Ay =0
I < | ,'= --- ---
0.010
0.01 = 0.01
Ii I VA' 0.00
.00 = 0.002
S .~~ h,.
.--.- -Y- ---
A'=AF/AN
Figure 2.9. Varnitionation of Non-Dimensional Shoreline Advancementketch
AyWWith A'and Results Shown for h AF V= 4.0
W, -B AN B ,W'
0 1.0 2.0 2.8
A' = A,/AN
Figure 2.9. Variation of Non-Dimensional Shoreline Advancement
Ay/W, With A' and V'. Results Shown for h, /B = 4.0
nourishment option. First, in the interest of objectivity, it must be said that the most
extreme of the scenarios published by the Environmental Protection Agency (EPA) which
amounts to over 11 ft. by the year 2100 are extremely unlikely. While it is clear that
worldwide sea level has been rising over the past century and is highly likely to increase in the
future, the future rate is very poorly known. Moreover, probably at least 20 to 40 years will
be required before our confidence level of future sea level rise rates will improve substantially.
Within this period, it will be necessary to assess the viability of beach restoration on a
project-by-project basis in recognition of possible future sea level increases. Presented below
is a basis for estimating nourishment needs for the scenario in which there is no sediment
supply across the continental shelf and there is a more-or-less well-defined seaward limit of
sediment motion; in the second case the possibility of onshore sediment transport will be
discussed.
Case I Nourishment Quantities for the Case of No Onshore Sediment Transport
Bruun's Rule (1962) is based on the consideration that there is a well-defined depth limit
of sediment transport. With this assumption, the only response possible to sea level rise is
seaward sediment transport. Considering the shoreline change Ay, to be the superposition
of recession due to sea level rise Ays and the advancement due to beach nourishment, AyN,
Ay = Ays + AYN (2.9)
and, from Bruun's Rule
W.
Ays = -S (2.10)
h, +B
in which S is the sea level rise, W, is the distance from the shoreline to the depth, h,,
associated with the seaward limit of sediment motion and B is the berm height. Assuming
that compatible sand is used for nourishment (i.e. AF = AN)
AYN h B
h,+B
and V is the beach nourishment volume per unit length of beach. Therefore
1
AyN = [(h V -SW.]
(h, + B)
(2.11)
(2.12)
The above equation can be expressed in rates by,
dy 1 F dV dS 1
dy 1 W. d (2.13)
ddt (h- + B) -t (2.13)
where a now represents the rate of sea level rise and is the rate at which nourishment
material is provided. It is seen from Eq. (2.13) that in order to maintain the shoreline stable
due to the effect of sea level rise the nourishment rate is related to the rate of sea level
rise S by
dV dS
S= W (2.14)
dt dt
Of course, this equation only applies to cross-shore mechanisms and therefore does not
recognize any background erosion, or longshore transport (so-called "end losses"). It is seen
that W, behaves as an amplifier of material required. Therefore, it is instructive to explore
the nature of W, and it will be useful for this purpose to consider an equilibrium profile
given by
h = Ay2/3
in which A is the scale parameter presented in Fig. 2.1. Using the spilling breaking wave
approximation
A, =A /3
h, = = A W,
then
W = (2.15)
i.e. W, increases with breaking wave height and with decreasing A (or sediment size).
Case II Nourishment Quantities for the Case of Onshore Sediment Transport
Evidence is accumulating that in some locations there is a substantial amount of
onshore sediment transport. Dean (1987) has noted the consequences of the assumption
of a "depth of limiting motion" in allowing only offshore transport and proposed instead
that if this assumption is relaxed, onshore transport can occur leading to a significantly
different response to sea level rise. Recognizing that there is a range of sediment sizes in
the active profile and adopting the hypothesis that a sediment particle of given hydraulic
characteristics is in equilibrium under certain wave conditions and at a particular water
depth, if sea level rises, then our reference particle will seek equilibrium which requires
landward rather than seaward transport as resulting from the Bruun Rule. Figure 2.10
summarizes some of the elements of this hypothesis.
Turning now to nourishment requirements in the presence of onshore sediment transport,
the conservation of cross-shore sediment yields
+ sources sinks (2.16)
ay at
in which h is the water depth referenced to a fixed vertical datum and the sources could
include natural contributions such as hydrogenous or biogenous components, and suspended
deposition or human related contributions, i.e. beach nourishment. Sinks could include
removal of sediment through suspension processes. Eq. (2.16) can be integrated seaward
from a landward limit of no transport to any location, y
rv ry Bh
q(y) (sources sinks)dy = -dy (2.17)
If only natural processes are involved and there are no gradients of longshore sediment
transport, the terms on the left hand side of Eq. (2.17) represent the net rate of increase of
sediment deficit as a function of offshore distance, y. For y values greater than the normal
width, W., of the zone of active motion, the left hand side can be considered as representing
the "ambient" deficit rate due to cross-shore sediment transport resulting from long-term
disequilibrium of the profile and source and sink terms.
In attempting to apply Eq. (2.17) to the prediction of profile change and/or nourishment
needs under a scenario of increased sea level rise, it is reasonable to assume that over the
next several decades the ambient deficit rate (or surplus) of sediment within the active zone
will remain constant. However, an increased rate of sea level rise will cause an augmented
demand which can be quantified as W. [() (-S)] in which (-) is the reference
sea level change rate during which time the ambient demand rate is established. Thus the
POSSIBLE MECHANISM OF SEDIMENTARY EQUILIBRIUM
SIncreased Sea Level
JS -Originial Sea Level
Sediment .
Particle
"Subjected to a Given Statistical Wave Climate, A Sediment
Particle of a Particular Diameter is in Statistical Equilibrium
When in a Given Water Depth"
Thus When Sea Level Increases, Particle Moves Landward
Figure 2.10. Possible Mechanism of Sedimentary Equilibrium (After Dean, 1987).
active zone sediment deficit rate will be
.B [ h d]. [^ )-(dS\) dV
+ .t Y]dt dt ( 21dt8)
in which represents the nourishment rate and the subscript "0" on the bracket represents
the reference period before increased sea level rise. In order to decrease the deficit rate to
zero, the required nourishment rate is
dV [fW- ah ] [(dS) (dS) ] (2.19)
dt 0 at fdt dt
These models may assist in evaluating the vulnerability of various shoreline systems to
increased rates of sea level rise. For Florida, long-term trend estimates of over the last
60 or so years are 0.01 ft./year although there is considerable variability in the year-to-year
values of sea level changes, including interannual increases and changes which can amount
of 40 times the annual trend value.
PLANFORM EVOLUTION OF BEACH NOURISHMENT
PROJECTS
To a community that has allocated substantial economic resources to nourish their beach,
there is considerable interest in determining how long those beaches can be expected to last.
Prior to addressing this question, we will develop some tools.
The Linearized Equation of Beach Planform Evolution
The linearized equations for beach planform evolution were first combined and applied by
Pelnard Consider6 in 1956. The combined equation is the result of the sediment transport
equation and the equation of continuity.
Governing Equations
Transport Equation Utilizing the spilling breaker assumption, the equation for long-
shore sediment transport has been presented as
K HSI2v t sin20 (2.20)
8 (1 p)(s 1) 2
in which p is the sediment porosity (; 0.35-0.40) and s is the sediment specific gravity (=
2.65). Equation (2.20) will later be linearized by considering the deviation of the shoreline
planform from the general shoreline alignment to be small. Referring to Fig. 2.11, denoting
p as the azimuth of the general alignment of the shoreline as defined by a baseline, / as
the azimuth of an outward normal to the shoreline, ab as the azimuth of the direction
from which the breaking wave originates, then
K H 12 Vgll sin 2(/ ab)
2= (2.21)
Q- 8(1-p)(s-1) 2 (2.21)
where = p tan- ()
Equation of Sediment Conservation The one-dimensional equation of sediment
conservation is
ay 1 8Q
+ Q= 0 (2.22)
at (h+ + B) 8z
Combined Equation of Beach Planform Evolution
Differentiating with respect to x, the equation of longshore sediment transport, Eq.
(2.21), we find
8Q K H5/2
Q= cos 2(8 ab) (2.23)
a- 8(1 p)(s 1) a-
Recalling the definition of 3 and linearizing
X 1 ay r ay
=-i- tan- ; a- (2.24)
2 2 ax
and considering the wave approach angle (/P ab) to be small such that cos 2(/ cab) ; 1,
the final result is
QQ K H 8/2V f 2y
8( K (2.25)
ax 8(1 p)(s 1) ax2
Combining Eqs. (2.22) and (2.25), a single equation describing the planform evolution
for a shoreline which is initially out of equilibrium is obtained as
ay _y
= G a2 (2.26)
at ax2
where
K H
G )(-p B) (2.27)
8(s 1)(1 p)(h. + B)
C.
0
a-
Ioreline
Reference
Base Line
1Q
+Qs
Figure 2.11. Definition Sketch.
The parameter G may be considered as a "shoreline diffusivity" with dimensions of
(length)2/time. Field studies have documented the variation of K with sediment size, D, as
presented in Fig. 2.12. A more detailed evaluation demonstrates that a more appropriate
expression for G can be developed and expressed in terms of deep water conditions
K 2.4f-A.2 0.4 1.2 0 to) cos 2(po a.)
K Go os o) cos2(lo a) (2.28)
8(s 1)(1 p)C. .04(h. + B) cos(po a,)
where the subscript "0" denotes deep water conditions and C. is the wave celerity in water
depth, h,. Figure 2.13 presents estimates of G around the Florida peninsula and Figs. 2.14
and 2.15 present estimates of effective deep water wave height and period.
It is recognized that the form of Eq. (2.26) is the heat conduction or diffusion equation
for which a number of analytical solutions are available. Several of these will be explored
in the next section.
It is of interest to know approximate values of the shoreline diffusivity, G. It is seen that
G depends strongly on Hb, and secondarily on Hb, (h, + B) and n. Table 2.1 presents values
of G for various wave heights in several unit systems where it is noted that the reference
wave height is the breaking wave height.
Table 2.1: Values of G for Representative Wave Heights
Hb Value of G in
(ft.) ft2/s miz/yr m /s km"/yr
1 0.0214 0.0242 0.00199 0.0626
2 0.121 0.137 0.0112 0.354
5 1.194 1.350 0.111 3.50
10 6.753 7.638 0.628 19.79
20 38.2 43.2 3.55 111.9
Note: In this table the following values have been employed: K = 0.77,
= 0.78, g = 32.2 ft/s2, s = 2.65, p = 0.35, h, + B = 27 ft.
Analytical Solutions for Beach Planform Evolution
Examples which will be presented and discussed include: (1) the case of a narrow strip of
sand protruding a distance, Y, from the general shoreline alignment, and (2) a rectangular
I I I I
Result From This Study,
S Santa Barbara
\ Relationship Suggested
Previously
I I *
IIII
N.
0.5
1.0
DIAMETER, D (mm)
Plot of K vs. D. Results of Present and Previous
Studies (Modified From Dean, 1978).
d 1.0[-
Figure 2.12.
2.0
0.02 0.06 0.10 0.14
G(ft2/s)
G(ft2/s)
0.02 .0 0.10
_^V---
It
Figure 2.13. Approximate Estimates of G(ft2/s) Around the Sandy
Beach Shoreline of the State of Florida. Based on
the Following Values: K = 0.77, g = 32.2 ft/sec2,
S = 2.65, p = 0.35, = 0.78, h, From Fig. 8., B Estimates
Ranging from 6 to 9 ft, Ho from Fig. 23, T from Fig. 24.
1 35
H eff2(feet)
H eff2(feet)
1 35 8
T I I
!l
1 .
Figure 2.14. Recommended Values of Effective Deep Water Wave Height,
Ho, Along Florida's Sandy Shoreline.
8
05
c3
. 14
i-
0
S6
S2
cc
2 6 10 14
Wave Period, T(sec)
-1
Figure 2.15. Recommended Values of Effective Wave Period, T, Along
Florida's Sandy Shoreline.
Wave Period, T(sec)
2 6 10 14
L I +--
,1 _
||1
distribution of sand extending into the ocean which could provide a reasonably realistic
representation of a beach nourishment project.
(1). A Narrow Strip of Sand Extending into the Ocean
Consider the case of a narrow strip of sand extending a distance, Y into the ocean and
of width Ax such that m = YAx, Fig. 2.16. The total area of the sand is designated m and
the solution for this initial condition and the differential equation described by Eq. (2.26)
is the following
(x, t) exp (2.29)
which is recognized as a normal distribution with increasing standard deviation or "spread"
as a function of time. Figure 2.17 shows the evolution originating from the initial strip
configuration. Examining Eq. (2.29), it is seen that the important time parameter is Gt.
The quantity, G, which is the constant in Eq. (2.27) serves to hasten the evolution toward
an unperturbed shoreline. In Eq. (2.29) it is seen that the quantity, G, is proportional to
the wave height to the 5/2 power which provides some insight into the significance of wave
height in remolding beach planforms which are initially out of equilibrium.
It is interesting that, contrary to intuition, as the planform evolves it remains symmetric
and centered about the point of the initial shoreline perturbation even though waves may
arrive obliquely. Intuition would suggest that sediment would accumulate on the updrift
side and perhaps erosion would occur on the downdrift side of the perturbation. It is recalled
that the solution described in Fig. 2.17 applies only for the case of small deviations of the
shoreline from the original alignment and may be responsible for the difference between the
linear solution and intuition.
For purposes of the following discussion, we recover one of the nonlinearities removed
from the definition of the "constant" G from Eqs. (2.23) and (2.26)
G = co s 2(p ea) (2.30)
8(s 1)(1 p)(h, + B) co
and it is seen that if the difference between the wave direction and the shoreline orientation
exceeds 450, then the quantity, G, will be negative. Examining the results presented earlier,
T-
Y
I
- m = YAx
I ~L
Figure 2.16. Initial Beach Planform. Narrow Strip of Sand
Extending From Unperturbed Shoreline.
y
1.0
Gt = 0.1
m -x2 /4Gt
0 y(x,t)= m 4Gt
0.5
2.0 .--
5.0
-10 -5 0 5
x/ T4
Figure 2.17. Evolution of an Initially Narrow Shoreline Protuberence.
it is clear that if this should occur then it is equivalent to "running the equation backwards"
in time. That is, if we were to commence with a shoreline which had a perturbation
represented by a normal distribution then rather than smoothing out, the perturbation
would tend to grow, with the ultimate planform being a very narrow distribution exactly as
was our initial planform! In fact, regardless of the initial distribution one would expect the
shoreline to grow into one or more accentuated features. Shorelines of this type (cos 2(P6 -
ab) less than zero) can be termed "unstable" shorelines and may provide one possible
explanation for certain shoreline features including cuspate forelands.
(2). Initial Shoreline of Rectangular Planform
Consider the initial planform presented in Fig. 2.18 with a longshore length, e, and
extending into the ocean a distance, Y. This planform might represent an idealized config-
uration for a beach restoration program and thus its evolution is of considerable interest to
coastal engineers, especially in interpreting and predicting the behavior of such projects.
It is seen that in a conceptual sense it would be possible to consider the problem of
interest to be a summation of the narrow small strip planforms presented in the previous
example. In fact, this is the case and since Eq. (2.26) is linear, the results are simply
a summation or linear superposition of a number of normal distributions. The analytic
solution for this initial planform can be expressed in terms of two error functions as
(,t) = erf [ ( + )] erf ( 1)] (2.31)
where the error function "erf{}" is defined as
erf(z) = 2 f e-udu (2.32)
and here u is a dummy variable of integration. This solution is examined in Fig. 2.18 where
it is seen that initially the two ends of the planform commence spreading out and as the
effects from the ends move towards the center, the planform distribution becomes more like
a normal distribution. There are a number of interesting and valuable results that can be
1.0 t 16 Gt
t' = 0.04 2
t' = 1.0
-1'1.0 't' = 0.11
0.8 -
0.6- t = 4.0
Note:
04 Shoreline Positions
0.4 Symmetric About x/(./2) = 0
t' = 16.0 "
0.2 \- --:, ,
0 2 -, **rl
0 L I .T
0 1 2 3 4
x/(1 /2)
Figure 2.18. Evolution of an Initally Rectangular Beach Planform on an
Otherwise Straight Beach. Only One-Half of Project is
Shown.
obtained by examining Eq. (2.31). First, it is seen that the important parameter is
t (2.33)
where e is the length of the rectangle and G is the parameter in the diffusion equation
as discussed earlier. If the quantity ( ) is the same for two different situations, then
it is clear that the planform evolutions are also the same. Examining this requirement
somewhat further, if two nourishment projects are exposed to the same wave climate but
have different lengths, then the project with the greater length would tend to last longer.
In fact, the longevity of a project varies as the square of the length, thus if Project A with a
shoreline length of one mile "losses" 50 percent of its material in a period of 2 years, Project
B subjected to the same wave climate but with a length of 4 miles would be expected to
lose 50 percent of its material from the region where it was placed in a period of 32 years.
Thus the project length is very significant to its performance.
Considering next the case where two projects are of the same length but located in
different wave climates, it is seen that the G factor varies with the wave height to the 5/2
power. Thus if Project A is located where the wave height is 4 ft and loses 50 percent of its
material in a period of 2 years then Project B with a similarly configured beach planform
located where the wave height is 1 foot would be expected to lose 50 percent of its material
in 64 years.
Figure 2.19 presents a specific example of beach evolution and Fig. 2.20 presents results
in terms of the proportion of sediment remaining in front of the beach segment where
it was placed as a function of time. These results are presented for several examples of
combinations of wave height and project lengths. As an example of the application of Fig.
2.20, a project of 4 miles length in a location where the wave height is 4 feet would lose 60
percent of its material in 7 years and a second project in a location where the wave height is
2 ft and the project length is 16 miles would lose only 10 percent of its material in a period
of 40 years. Figure 2.20 was developed based on the solution presented in Eq. (2.31).
It is possible to develop an analytical expression for the proportion of sand, M(t),
DISTANCE FROM ORIGINAL
SHORELINE, y (ft)
Nourished Beach Planform
Months
7 Years
30 Years
Pre-Nourished
Shoreline
6 4 2 0 2 4 6 8
ALONGSHORE DISTANCE, X (miles)
Figure 2.19.
Example of Evolution of Initially rectangular Nourished Beach Planform.
Example for Project Length, P, of 4 Miles and Effective Wave Height, H,
of 2 feet and Initial Nourished Beach Width of 100 Feet.
-H = 1.0, = 16 miles
H = 2.0, = 16 miles
\H = 1.0,1 = 4 miles
H= 4.0, = 16 miles
S .0, miles
v < ^' ^ -^ o................................................................. .
z
0
(f w
ZC)
_J
U Z
o
2
z
< U
-J
-00
LL
10 20 30
TIME IN YEARS FROM TIME OF FILL PLACEMENT
Figure 2.20.
Fraction of Material Remaining in Front of Location Placed for
Several Wave Height, H, and Project Lengths, Effect of
Longshore Transport.
l ires
2-0-., M=1 ile
HC- 2H 4.0, -., 1 mile
1.0
0.8
0.6
0.4
0.2
0
remaining in the location placed, as defined by
1 1l/2
M(t) = -J 2 y(x,t)dx (2.34)
to yield
M(t) = 2/ (e-( 2-2 1) + erf (2.35)
which is plotted in Fig. 2.21 along with the asymptote for small times
2
M() 1 (2.36)
which appears to fit reasonably well for
Vft/ < 0.5 (2.37)
A useful approximation for estimating the "half-life" of a project is obtained by noting
that M = 0.5 for VGt/e 0.46. Thus the half-life, ts5, is
il t2
t50 = (0.46)2- = 0.21- (2.38)
in which all variables are in consistent units. A more readily applied form is developed from
Eq. (2.27) as
tso = 8.7 (2.39)
where tso is in years, in miles and Hb is the breaking wave height in ft.
Effect on Retention of Setting Back the Fill Ends from Project Boundaries
As noted earlier, there is an understandable interest by a community or other entity
which is funding a project in retaining the sand within their boundaries as long as practical.
One approach to this concern would be to install retaining or stabilization structures near
the ends of the fill. A second would be to simply set-back the limits of the fill from the project
boundaries with the understanding that the sand would soon "spread out". Omitting the
details, Fig. 2.22 presents results for relative end set-backs A/ = 0, 0.2 and 0.5. It is seen
that the effects are greatest early in the project life (say V/G-t = 0.6 or 0.8) where a set
back A/f = 0.5 would increase the percent material retained from 42% to 73%.
0 1. 0.5 1.0
[Z W t = Time After Placement
-1 0' .. G= Alongshore DIffuslvity Initial ,
ULL. Asymptote Planform-
OZ 0O.5- 1 -
O 0 -VI
C n -10 .0
Ow 0 1 2 3 4 5 6
ar-
Figure 2.21. Percentage of Material Remaining In Region Placed vs. the
Parameter .
0.5 -
0
0
Figure 2.22.
-aJ
C..
-z
LU Z
C)
LLJ
wZ
M Cr
Percentage of Material Remaining in Designated Area of Length,
I + 2A. Rectangular Beach Fill of Length,-.
1.0 2.0 3.0 4.0 5.0
Effect of Ends on a Beach Fill
It is somewhat interesting to evaluate the effect on longevity of providing a fillet at the
two ends of a fill which is otherwise rectangular in planform. Basing the longevity on the
retention of sand within the placed planform, it is interesting that tapered- end planforms
have a substantially greater longevity than rectangular planforms. The reasons is apparent
by examining Fig. 2.19. The loss rates of a rectangular planform fill are higher over the
first increment of time than over the same increment of time but later in the project history.
It is seen from Fig. 2.19 that the evolution of the planform occurs with the early changes
occurring where the planform changes are the most extreme. This is not surprising when
one recalls that the governing equation (Eq. (2.26)) is the heat conduction equation and
that the fill planform is equivalent to a temperature distribution above background of the
same form in an infinitely long rod. Returning again to the tapered end planform, which
approximates the evolved rectangular planform at a later stage, the evolution of the tapered
end fill at an early stage approximates that of a rectangular fill at a later stage.
Figures 2.23 and 2.24 present calculated evolutions for rectangular and tapered end
planforms, respectively and Table 2.2 summarizes the cumulative losses from the region
placed over the first five years. It is seen that the tapered end fills have reduced the end
losses by about 33%.
Table 2.2: Comparison of Cumulative Percentage Losses from Rectangular and Tapered Fill
Planforms (G = 0.02 ft2/sec; e = 3 miles; Y = 55 ft)
Cumulative Percentage Losses With
Years After Rectangular Rectangular Planform
Placement Planform With Triangular Fillets
1 5.7 2.4
2 9.5 4.6
3 11.8 6.6
4 13.8 8.3
5 15.5 9.8
A Case Example Bethune Beach
In 1985, shorefront property owners in Bethune Beach, Volusia County, FL applied
0
:0
=o
VU
-2.0 -1.0 0 1.0 2.0
ALONGSHORE DISTANCE (miles)
Figure 2.23.
Calculated Evolution of a Rectangular Planform Beach Nourishment
Project. Planforms Presented for Initial Conditions and 1,2 and 5
Years After Placement.
Figure 2.24.
Z *~ =r
(DO(D
(D(D(D0
7W 0
-2.0 -1.0 0 1.0 2.0
Calculated Evolution of a Rectangular Planform with Triangular End
Fillets. Planforms Presented for Initial Conditions and 1,2 and 5
Years After Placement.
for a permit to construct two segments of armoring. The Governor and Cabinet initially
deferred a decision requesting that consideration be given to utilizing the same funds for
beach nourishment. The two segment lengths were 925 ft and 3,850 ft, as presented in
Fig. 2.25. The designation beside each segment (e.g. VO 353) is the identifier given by
the Division of Beaches and Shores to the permit application. The cost of the revetments
was about $200 per foot which at a nourishment cost of $6 per cubic yard would purchase
approximately 33 cubic yards per front foot or a total of 160,000 cubic yards for the two
segments combined.
Rather simple numerical modeling was carried out using Eqs. (2.26) and (2.27) with
monthly averaged wave heights as determined by the University of Florida's wave gage at
nearby Marineland, FL. The results of this numerical modeling are presented in Figs. 2.25
and 2.26. Figure 2.25 presents the planform evolution after one month and one year. It is
seen in accordance with earlier discussions, that due to the relative short lengths of these
segments, the sand spreads out rapidly in an alongshore direction. Figure 2.26 presents, as
a function of time, the volume of sand remaining in front of the two segments where the
nourishment would have been placed.
Project Downdrift of a Partial or Complete Littoral Barrier
In this case the project is located downdrift of a partial or complete littoral barrier,
such as a jettied inlet. We will denote the net longshore transport as Qo and the bypassed
quantities as FQo(0 < F < 1), see Fig. 2.27. In this case, the fraction remaining, M2(t), is
t V(xt)dz
M2(t) = (2.40)
and can be shown to be
M2(t) = erf ( ) + 1v'G (e-(//T -) ( 2-4
in which Vo is the volume placed. Eq. (2.41) is presented vs G/t/e in Fig. 2.27 for various
values of (1 F)Qoe/VoG. This latter parameter presents the ratio of longshore
8000
VO353
(925')
7000
6000
5000
4000
3000
VO370
(3850')
2000
1000
0
OFFSHORE
DISTANCE (ft)
0 50
I I I 1 I I
wInitial
SNourished
,. Shoreline
-4
.t
Shoreline
i-" After Two
I Months
II
I
- .. Nourished
Shoreline
SShoreline
After
I One Year
I
I
I
Figure 2.25. Initial and Subsequent Planforms of Nourished
Beach. Bethune Beach, Florida, Example.
100
I-
u. 80
z
44 60
I I
w
u.. 40
o
OQ \
,< V0370
LU
0 I I I I
0
0 5 10 15 20 25
TIME (Months After Fill Placement)
Figure 2.26. "Loss" of Beach Fill From Infront of Area Placed as a Result
of Longshore Transport. Bethune Beach, Florida, Example.
1.0
I-
z
LU
Oz 0
OZ
W.
z
0-3
51
SLUL
0
0
0:
-3.0
Figure 2.27.
1.0 2.0 3.0 4.0 5.0
\Gt/.e
Proportional Volumes of Beach Nourishment Remaining After
Placement vs, /Gt/~ and (1-F)Qo/Vo G.
transport losses due to a bypassing deficit to those losses resulting from the anomalous
planform.
DAMAGE REDUCTION DUE TO BEACH NOURISHMENT
The concept of reduction in storm damage by beach nourishment will be illustrated by
two approaches. First, data collected and summarized by Shows (1978) documented the
relationship between average damage costs suffered by a structure as a function of the
proximity of that structure to the shoreline set-back line in Bay County. The set-back
line is approximately parallel to the shoreline. Figure 2.28 presents these results for
540 structures in Bay County following Hurricane Eloise in 1975. The horizontal axis is the
structure location relative to the set-back line which is more or less parallel to the shoreline.
Relative to beach nourishment, the two most significant features of Fig. 2.28 are: (1) the
steeply rising damage function with proximity to the set-back line (or shoreline), and (2) the
possibility of displacing the damage function seaward by beach nourishment which would
translate the curve in Fig. 2.28 horizontally to the left by the width of beach added. As a
second illustration consider the situation in Fig. 2.28 which corresponds to a profile off Sand
Key, Florida. A peak storm tide of 11 ft and an offshore breaking wave height of 20 ft will
be assumed for purposes of this example. These conditions are believed to be reasonably
representative of a 100 year return period. Considering the pre-nourishment condition and
utilizing the breaking wave model reported by Dally, Dean and Dalrymple (1985), the wave
height distribution is presented in Fig. 2.29. Considering now a beach nourishment project
which advances the shoreline gulfward a distance of 40 ft, the wave height distribution is as
presented in Fig. 2.29. Table 2.3 summarizes the wave height at the seawall for the original
and nourished conditions and also presents a measure of the damage potential for the two
cases with and without nourishment. In these results the damage potential is considered to
be proportional to the cube of the wave height. The presence of the nourishment project
reduces the damage potential by nearly a factor of four!
-100
-50 0 50 100 150
Seaward Landward
DISTANCE FROM CONTROL LINE (ft)
Damage to Structure in Relation to its Location
with Control Line (Resulting From Study of 540
Structures in Bay County After Hurricane Eloise,
by Shows, 1978).
S200
00
O.o
I--o
LL 160
g: 120
LU
W Jr
80
>4- 40
Un
I',I
U
-150
CL
I
Figure 2.28.
I B I I
15-
Wave Height,
IOriginal Profile-
(0 1 0 -
10 --wave Height,
/ Nourished Profile
> 5 .f /
\2.9ft
0 I !I
0 100 200 300
DISTANCE GULFWARD FROM SEAWALL (ft)
-100 Year Storm Surge Z 12 ft
-*4 40ft Oe
S-----% Nourished Beach,
: Displaced 40 ft Gulfward
Original Be ach"-"
Figure 2.29. Wave Height Reduction at Seawall Due to Presence
of a Beach Nourishment Project.
| +10
O 0
e2
!-io
>u
W
Table 2.3: Summary of Wave Height and Damage Potential Reduction at Seawall with
Beach Nourishment Project*
*Refer to Fig. 2.29.
Table 2.4: Present Worth Damage Factor, F(w, I) as a Function of Interval Considered and
Beach Width
Interest Present Worth Damage Factor, F(w, I), for Various Beach Widths, w
Rate, w = 0 ft w = 50 ft w = 100 ft w = 150 ft
I
6% 1.84 0.89 0.59 0.37
8% 1.39 0.56 0.44 0.27
10% 1.07 0.49 0.44 0.27
There are various general approaches to developing estimates of damage reduction due
to beach nourishment. One approach is to attempt to carry out a structure-by-structure
damage analysis due to a storm of a certain severity as characterized by a storm tide, wave
height and duration. The damage due to many such storms weighted by their probability
of occurrence can then be combined to yield the total expected damage. A second approach
and that which will be employed here is to recognize that during a particular storm, it
is appropriate to consider (1) relative alongshore uniformity of wave attack, and (2) a
representative proportional damage as a function of storm severity and beach width, W.
Having demonstrated qualitatively the damage reduction due to beach nourishment, we
will proceed to a formalized procedure, making assumptions and simplifying as necessary.
The methodology will assume that a proportional structural damage curve is available
as a function of storm return period, TR, and additional beach width, w. Curves of this
type would be site specific depending on the location of the existing structure relative to the
shoreline, and the design and quality of the structures. Figure 2.29 presents one example
of such a set of relationships. The cumulative probability, P(TR) of encountering a storm
of return period TR in any given year is
1
P(TR) = (2.42)
TR
The information presented in Fig. 2.30 can be developed with varying degrees of realism
through Monte Carlo simulation methodology such that the result is applied directly and
easily. One approach is to assume that the damage from one storm is repaired prior to the
occurrence of a succeeding storm. The present worth damage factor, F(w, I, J) in a period
of J years, depends on the interest rate, I, the maintained beach width, w, and represents
the ratio of present worth of all damage values over the J year to the present structure
value.
This method obviously embodies many approximations, but does provide a rational
framework for a very complex problem. One realization of the present worth damage factor
for storms over the next J years if the beach width is maintained constant can be shown to
L
1.0
0 0.8-
z 7
L 0.4 -
O 0.2
0.0 I I
1 10 100 1000
RETURN PERIOD,TR (Years)
Figure 2.30. Assumed Damage Function, D, for Various Beach Widths, w, and
Storm Return Periods, TR.
J
FK(w, I,J) = D(w,TR) (2.43)
i=11
Hear the superscript K denotes the Kth realization and the selection of the J storms is
carried out through Monte Carlo simulation in accordance with the cumulative probability
distribution, P (= -). Thus, in addition to the most probable damage, it is possible to
develop probability distributions of the present worth damage factor.
Table 2.4 presents the values of the average present worth damage factor F(w, I, oo) for
all future damages and constant beach width, w. As expected, for the higher interest rates,
the present worth values are less. Of relevance is that the greatest incremental benefits
occur for the beaches that are initially the most narrow, i.e. for the situation in which
the structures are in greatest jeopardy. This reinforces the earlier statement that sand
transported from a nourishment project that widens adjacent beaches should be recognized
as a financial benefit of not loss to that project.
A somewhat more realistic approach would be to recognize that due to erosional pro-
cesses, it would be necessary to renourish every j3 years during which the beach would
narrow from we to w' at an annual recession rate, r,
Wo WI
r = (2.44)
For this case, one realization of the present worth damage function, F(wo,j.,r,I,J), is
determined as
oo (n+l)ji
FKto,",,, )= E D w()-r nj,+ -. T2 (2.45)
n=o K+nj,+l -r (1 (2.45)
Each of the inner summations represents the contributions to the present worth damage
factor during one nourishment interval. Damage reductions employing Eq. (2.42) can assist
in identifying the optimal renourishment interval, j,.
REFERENCES
Bruun, P. (1962) "Sea Level Rise as a Cause of Shore Erosion", ASCE Journal of Water-
ways and Harbors Division, Vol. 1, p. 116-130.
Dally, W.R., R.G. Dean and R.A. Dalrymple (1985) "Wave Height Variation Across
Beaches of Arbitrary Profile", Journal of Geophysical Research, Vol. 90, No. C6,
pp. 11917-11927.
Dean, R.G. (1987) "Additional Sediment Input to the Nearshore Region", Shore and Beach,
Vol. 55, Nos. 3- 4, p. 76-81.
Shows, E.W. (1978) "Florida's Coastal Setback Line An Effort to Regulate Beachfront
Development", Vol. 4, Nos. 1/2, Coastal Zone Management Journal, p. 151-164.
Chapter 3
ENGINEERING DESIGN
PRINCIPLES: PART II-
BOUNDARY CONDITIONS
Hsiang Wang
HISTORICAL SHORELINE INFORMATION
In beach nourishment engineering, historical shoreline change information is needed to
assess the dynamics of the sediment process and the effects of man-made structures and
constructions such as inlet improvement, jetties, groins, harbors, etc.This information is also
needed for the prediction of the performance of a beach nourishment project and estimating
the quantity and frequency of renourishment.
Historical shoreline changes can be deduced from three sources: hydrographic and beach
surveys, maps and charts and aerial photographs. In the state of Florida, shoreline maps
from the U.S. Coastal and Geodetic Survey (U.S. C&GS.) of reliable quality can be found as
early as 1850s. The so-called T-sheet map series is available at varying scales from 1:10000
to 1:40000. One set of these T-sheet maps, the 7. 5 minute series of Standard Topographic
Quadrangle Maps (scale 1:24000), is the most complete one. The shorelines are expressed
as the Mean High Waterline (MHW).
Another map source is the TP-sheet series of Coastal Zone Ortho Maps (scale 1:10000),
produced by the National Ocean Survey. This series of maps was constructed from aerial
photos and covered the period of the 1970's only. These maps were rectified for both the
horizontal and vertical distortions and the shorelines were rectified for both the horizontal
and vertical distortions and the shorelines were given as Mean High Waterline also.
The second source of shoreline information is the aerial photos. Usually only vertically
controlled photographs should be used. In the state of Florida, the most complete set was
collected by the Florida Department of Natural Resources (DNR) from 1970s on.
They were at scale of 1:1200 and/or 1:2400 and were used to produce the states' Coastal
Construction Control Line maps.
The third and perhaps the most reliable source of shoreline information is the actual
ground truth survey. The sources of this type of information are quite scattered from, for
instance, U.S. C&GS, U.S. Corps of Engineers (C.O.E.), state, county and city agencies and
engineering consulting firms. The most systematic beach surveys are conducted by DNR.
They are available since mid 1970s at approximately six year intervals. These data consists
of beach face surveys to wading depth at 1000 ft intervals and hydrographic surveys to 3000
ft offshore at 3000 ft intervals.
DNR has just completed an effort to digitize and map historical shoreline changes for
the entire coast of Florida. These data set should consists of the following information
(Wang and Wang, 1987).
a. Digitized shoreline and offshore bathymetry at 6 ft, 12 ft, 18 ft, 24 ft, and 30 ft contours
whenever available. All the data are referred to DNR monuments which, in turn, are
referenced to State Plane Coordinates.
b. Composite historical shoreline change maps at a scale of 1:24000 and 1:24000.
c. Composite historical offshore depth-contour change maps at a 1:24000 scale.
Figure 3.1 is an example of the data file of the digitized shoreline information stored in
DNR. Based upon our experience, the digitization error is within 0. 01 inch if done properly,
which translates to 20 ft at 1:24000 scale.
9. 99W0OW~O
bi., 999 9t
i00000000 0
ioo~oor~r Pd
9a a
99 .9O Owe
Li9nw00W0O
*r 9** 9
000 00000 0
uN
0 qVVO cupo
~ 09 09- 00s2
.99 999~ .- 99IY
COOCOOCO 0
gss8 0. ~
0040rwr 09d P
NEldP4Cd9 Pd .
99 94Y OWOI~
2 22@4 Ma9
00000000 0
Pd
I 5 E00 m-4M 91999 99; 4)499
Is 1* 0 9 *90@S*S*09 9999999990 *.09 0
u~k~~~94 990P99949)009- 999 99. 4994
-I.. wewwftfdwpm =%P;4
-CIL
.129WF= S2l222ro =swum SUSSM80
0 09 0. 00 !!--2 49
-r .-)
3040%004
*9 *r 999 OWO
000000042 0
4pO.M wn4I"
*OqD41"001"
v O99999k9
000000
*999*699099
4444.44444
'---9
'-9---~-
;tl I'
'U
zw".- a
Iu
Z~U. a%49
EiIZ a-us
za aL~ oinae*@ ..m
W4.wrwlrwr)~~r
=wJ I
EI C)000000000
90L'U 000006 X000)
'Ju. a
*~ Fnmoo
94=
>Z-
5-
L.
z.
00.
2322223132
I~i~iiiI
Ir004~)nH
0000000000
00~0~000000
r.9m.9.9mmm
4.44444444
0400000.0000
909999* 0999
:.044.a 44:3
4444444044
-.9 --
I 0W)99/9*-4'PW9
'oino 0-ino>o0
00<4)<03>00
NMeIIV
0000000000
opo9oooo9 oo
00C 040 000
OOCQ )COOO
?***-9---*9
9999949949
0 000
ooco00 000
*494 .e-'r44
--99'a oow--
i~rr~nftwxruu
>ftA..900
9-C
as a gml,545
0 0
5- 4. 9'
04.CO4WSn~Y
0r~r~Q
a o' lu-iu-uuC-C'
'--9-u---u
9- .1 '
eu-u
NN'4APrN,~
III silts IIur
~C~~~(~LO
rr.C 94(-9-~
IOblu- suC-u u-
9-4.4w~r
0 0' C'
Isis ilI~
XMX222R3221 22333233213
en 000000000
0 0006C O00QO
000000000 C
44.4444.44.44.
- 0-.4@..9400
*4099V20-PWre
-00 @~m90-.d
.04 Q0.9Pd0-Pd
0000000000
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*49 9999 9999
0444444444-
.94. .d*.4 44 4
9@'Pdm9.."Mwp9
09990-O Q')
.44d999
NNNNNNYNN 0
44444444 C
C.oJC1~00000 L
949999999~
X.-
.95999.9.
NIINP4NNNftN
.94.49*94.
*tx0c O0
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00'40'440W
luVI fVI u .C' C'
P- -4 .0
oo a- -p
-9-.-.1 -o
0 --
F'- W 9-tY~
i~Oc-lus -0O) -
- ..' .'940.9n.jVJ9L~
1115511 ~~ill
0 )-co
1010. '-%u-4
,-~O9-u-C)
'-.4.4O
)1111511
949 *4 9~ 6=
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-'99.9.99
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Iiw
19
For beach nourishment design, two kinds of information are useful-shoreline changes
and volumetric changes. The problems associated with the computations of shoreline and
volumetric changes are discussed in the following sections.
COMPUTATION OF SHORELINE CHANGES
For beach nourishment design shoreline change information are useful to assess back-
ground erosion or accretion rate and the effects of structure on updrift and downdrift
shorelines. An example is used here to illustrate the procedures.
The example used here is the stretch of shoreline centered around Sebastian Inlet which
is located at the Brevard/Indian River County line on the east coast of Florida (Fig.3.2).
Attempts to open the inlet by hand labor started in 1886 but the inlet was never remained
open for any extended period until 1948 when the inlet was stabilized by the construction
of permanent jetties. Therefore, it serves as an good example as how the structure effects
the shoreline change through examining historical data.
Figure 3.3 plots the historical shoreline changes for three different period from 1929 to
1947, prior to inlet stabilization, from 1947-70, the initial stage of inlet stabilization and from
1970-1986, the later stage of inlet stabilization. As can be seen, prior to inlet stabilization by
jetty structure, the shoreline overall advanced during this period. During the period of 1947-
70, the effects of the post stabilized inlet was quite pronounced with updrift accretion and
downdrift erosion of approximately 5 miles on each side. The estimated updrift accretion
was about 3 ft/yr. whereas the downdrift erosion was about 5 ft/yr. Clearly, the littoral drift
was not only impounded on the updrift side but also on the ebb tidal shoal and transported
into the inlet. From 1970-86, the rate of shoreline changes slowed down considerably to
approximately 1.5 ft/yr. erosional on the south side and 1.0 ft/yr. accretional on the north
side. This was probably due to the fact that ebb tidal shoal became more matured during
the later stage, thus, impounded less material.
WATERSHED OF THE
Fig. 3.2. Location of Sebastian Inlet, FL., and the watershed of Indian River
Lagoon.
-50000
A..A,A. MA
v vw 1 TY
-50000
50000
70-86
-A Or-^
I Nsr TV
0
DISTANCE (ft)
50000
Fig. 3.3. Historical shoreline changes near Sebastian. Inlet
during three different periods (Inlet stabilized in
1946).
300
200
100
0
-100
-200
-.1uL
-100000
29-47
7
-
-
100(
300.
u 200
z
< 100
0
z
- -100
O -200
()
.~Ut
-100000
100000
-w~-~l"^--*W^~~Uyl**~r\~-~,*
By examining historical data, one can also identify the locations of critical erosion.
In the present case, the most severe erosion occurs immediately on the downdrift of the
downdrift jetty and at three miles downdrift of the inlet.
The data of shoreline change is often quite noisy. Usually some form of smoothing is re-
quired such as running average or harmonic analysis. To separately identify the background
shoreline change and the change due to shore-perpendicular structures, two techniques can
be used; the so-called odd-even analysis proposed recently by Douglas and Dean (1990) and
the well known harmonic analysis.
The odd-even analysis was based on the reasoning that in the absence of structure, the
shoreline change should be more or less spatially uniform, therefore, manifests even function
change. The presence of shore-perpendicular structure, on the other hand, would cause
opposite effects on the updrift and the downdrift shorelines; therefore, the resulting shoreline
change should appear as odd function. Mathematically, the even and odd components of
the shoreline changes can be established by the following equations:
AVe(X) = -[AV(+x) + AVO())] (3.1)
AVo(x) = 2[AV(+x) + AV(V.)] (3.2)
where V can be shoreline position change or volumetric change; the subscripts e and o refer
to even and odd, respectively. The net change is then:
AV = Ve + Vo (3.3)
The results of odd and even analysis for the period of 1947-70 for the Sebastian Inlet region
while the effects of the inlet was most pronounced was illustrated in Fig 3.4.
The harmonic analysis serves similar purpose. The shoreline is expressed as a series of
harmonic functions which contain even and odd functions as follows:
n n
V(x) = ao + an cos kn + bn sin knx (3.4)
1 1
EVEN AND ODD FUNCTION (47-70)
NET
.. .. EVEN
.............. ODD
I I I
DISTANCE (FT)
Fig. 3.4.
Even-odd function analysis near Sebastian Inlet for shoreline changes between
1947-1970 (Inlet location at origin).
300.0
250.0
200.0
150.0
100.0
50.0
0.0
-50.0
U-
L-J
Cr
LU
Z
_J
CE
VI
-100.0
-150.0
-200.0
-250.0
-300.0'
-50000.0
-25000.0
25000.0
50000.0
where ko = 2- with L being the length of the shoreline, and kn = nk. The coefficients a's
and b's can be determined by conventional Fourier analysis. The coefficient ao represents the
mean shoreline movement. All the cosine terms are even functions representing background
shoreline changes whereas all the sine terms are odd functions representing shoreline changes
due to structure effects. This harmonic analysis tends to smooth the data and also brings
out the rhythmic feature, if any, of the shoreline change. This method is, however, not
suitable for short shoreline length.
Other data analysis techniques such as Eigen function analysis are also used to bring
out various features of shoreline changes such as shoreline rotations, etc.
To compute volumetric change requires hydrographic and topographic information in
addition to shoreline position. It is useful to compute the volumetric changes above the
MHW and below the MHW separately. In theory, this can be done simply through inte-
grating the area between measured profiles. In practice, a number of problems are involved
which are discussed here:
A. Estimation of offshore depth limit
There are a number of conventional offshore control depths as defined in Fig. 3.5.: the
breaking depth, db, is where the wave breaks, the depth of active profile, de, is defined as the
seaward depth of littoral zone, the shoaling zone depth, d,, also known as the buffer zone
depth, is the offshore depth of a zone within which the sediment motion is mainly onshore
due to wave induced bottom drift and the closure depth, do, is defined as the limiting water
depth beyond which the sediment motion can be considered to be minimal in a time scale
of engineering interest.
These depths are functions of many variables including, among other, wave and current
environment, tidal range, offshore slope and topography, presence of structures and sediment
characteristics. As just which depth we should select as depth of computation depends on
the purpose.
Tide
Fig. 3.5. Definitions of offshore control depths.
To determine long term volumetric changes the closure depth is the logical choice. For
the Atlantic coast, a depth of 27 ft (9m) measured from the berm elevation has been
suggested as the representative value. Owing to the very mild slope along the Atlantic
coast, this depth could be way offshore (typically from 1000 to 4000 ft offshore but could
be considerably further of offshore rock crops or reefs exist). At such a distance accurate
profile data may not exist. The hydrographic survey by DNR, for instance, was carried out
to approximately 3000 ft offshore at 3000 ft longshore intervals (every fourth monument).
Using Indian River County as an example, Figure 3.6 shows the offshore topographies.
The 30 ft contour line grows wider toward the south partially owing to the existence of
a reef system (shown by hatched area). Therefore, in the northern end, the DNR survey
reached beyond -27 ft but in the southern part of the county, the closure depth was never
reached in either 1972 or 1986 survey series. A number of representative survey profiles in
the county are shown in Figure 3.7.
The effects of choosing different offshore closure depths are further illustrated in Figure
3.8. In this figure, volume changes along the shoreline computed to different elevations were
shown. The solid line marked all means the closure depth was at the end point of the survey
irrespective the depth at this point. This point roughly (but not always) corresponds to the
-30 ft depth. The total volumetric changes for the entire county which is the integration of
volume along the shoreline are tabulated here:
Above NGVD 1.4 x 106 yd3
From NGVD to 5' 0. 6 x 106 yd3
From NGVD to 10' 0. 8 x 106 yd3
From NGVD to 15' 0. 1 x 106 yd3
Total below NGVD -4. 7 x 106 yd3
Therefore, depending upon the selection of offshore boundary, this coast could appear
to be accretional down to -15 NGVD. But this coast is erosional if the closure depth was
used as the offshore boundary by losing about 4.7 x 106 yd 3 of sand during 1972-86.
G= Reef
Figure 3.6.
Offshore Depth Contour of Indian River County (1972
DNR Survey).
40.0 .----- ..------- ----.... R-1 -------........ -......... .. Nov. 72
Juien86
m 20.0
_. -.. .. ......... ...............-
-420.0 ---------------------------------------------***......
O 40.0
R-18
20.0
--20.0 --.-- ----- .---
s -0.0
0 40.0
0r R-18
C 20.0
--
> 0.0
LL40.0
0 20.0 R
-40.0
S *"o-o -----------------------------
-40.0 4 1 1 1 i I I I 1 F I i
-400 0 400 800 1200 1600 2000 2400 2800 3200 3600
(A) Profiles at North End
40.0 R-90
m 20.0
m, 0.0
-20.0
Ll.
.. -40.0
O 40.0
cc R99
20.0
0 0.0
WJ -20.0 ;;
U- -40.0
O
Z 40.0
o R114
20.0
-40.0
I I I I I I II I I I II I I II I I I I II I I I II I I II I I I I I I
-400 0 400 800 1200 1600 2000 2400 2800 3200 3600
HORIZONTAL DISTANCE TO MONUMENT (IN FEET)
(B) Profiles at South End
Figure 3.7. Representative Survey Profiles Along Indian River County Shoreline
(R1, R18, R39 In North) (R90, R99, R114 In South)
q 150.0
ao
O)
100.0
04
o
, 50.0
: -50.0
o -100.0
w
u. -150.0
O
L -200.0
Z
. -250.0
* -300.0
LU
-350.0
0
0
INDIAN RIVER COUNTY
40000 50000 60000 70000 80000
DISTANCE ALONG BASELINE (ft)
Figure 3.8.
Volumetric Changes as Influenced by Different Offshore
Closure Depths (Indian River County).
The selection of beach nourishment offshore depth limit is another important task as
this depth greatly affects the nourishment volumetric requirement computation which, in
turn, affects the project evolution and the performance of the project.
Clearly, it is impractical to use the closure depth as the nourishment limit for it will
require too large a nourishment volume. Furthermore, at such a distance accurate profile
data may not exist as mentioned earlier.
The depth of the active profile can be argued, and certainly is more practical, as a
reasonable choice. This depth can be computed on the concept of critical shear stress, or
as a solution of
U2 = Kc(S 1)gd (3.5)
where Uc is the critical near-bed velocity, S is the ratio of sediment to fluid density, g is
gravitational acceleration and d is the water depth. The coefficient Kc is in the order of
0.03 for median sand. Hallermeier (1983) proposed the following empirical equation
H2
de = 2.9H(S 1)-0s5 110(S (3.6)
(S 1)gT2
For field application it was also suggested that an annual value of de can be established by
using H value exceeded 12 hrs per year, or,the local significant wave height with frequency
of exceedance of 0.137%. Birkermier(1988) found the value from Eq.(3.6) to be too high
and suggested the following modified equation:
(H(137)23.7)
de = 1.75(hs)o.137 57.9H0 (3.7)
For random waves with P-M spectrum and with JONSWAP spectrum, the values of -s
are 0.004 and 0.005, respectively. When these values are used, Eq.(3.6) gives
de = 1.95 to 2.00(H,)0.137 (3.8)
and from Eq.(3.7)
de = 1.45 to 1.51(H8)o.137 (3.9)
A value of de equal to 1.5 to 1.75 (hs)0.137 has been recommended as a practical range.
B. Errors induced by survey inaccuracy
The most serious survey error is the shift of horizontal and vertical datums between
surveys as this error is cumulative. Because of the mild slope and long horizontal distance,
a small shift in either horizontal or vertical datum could translate into thousands cubic feet
of sediment volume per lineal foot of beach front. Thus, the error could be in the same
order of magnitude as the total volumetric change. A sensitivity analysis such as illustrated
in Figure 3.9 would be helpful to establish the confidence level of the results. From this
figure, it can be seen that if the volumetric change is small (mild erosion or accretion), the
survey induced error (relative) could be very large. On the other hand, if the volumetric
change is large (strong erosion or accretion) the survey induced error, relatively speaking,
is usually small. The other source of error which by its nature is less serious is due to the
motion of the survey vessel. Over a long distance the errors of this type tend to compensate
each other as oppose to cumulative.
C. Seasonal variations
The shape of the beach is known to vary seasonally. Therefore, comparisons of beach
profiles surveyed at two different seasons could lead to wrong conclusions. Figure 3.10
shows that from 1972 (winter profile) to 1986 (summer profile), Indian River County had
an apparent shoreline advance. St. Lucie County which is next to the Indian River County
on the south also had two hydrographic surveys by DNR, one in 1972 and the other in
1987. However, the survey in 1972 was carried out in the summer whereas the 1987 survey
was completed in the winter, exactly the opposite to the Indian River County case. Now as
shown in Figure 3.9, the shoreline had an apparent retreat downdrift from the Fort Pierce
Inlet; the volumetric change to the near-closure depth was actually accretional. This is, of
course, exactly opposite to the situation in the Indian River County. These two counties are
adjacent to each other; yet, during the same period the shoreline in one county advanced
while the other retreated. Thus, the possibility of false signals due to seasonal variations
must be examined.
-20 -15 -10 -5 0 5 10
HORIZONTAL DATUM SHIFT (ft)
0
15 20
-20 -15 -10 -5 0 5 10 15 20 25
HORIZONTAL DATUM SHIFT (ft)
Figure 3.9.
Errors Induced by Shifting of Datum (1972 Is used as reference;
Positive Value means 1986 Profile Shifted Seaward).
co
o"
CD
r-
0
CM
Z.
n-
LU
O
co
U
cc
200.0
180.0
160.0
140.0
120.0
100.0
80.0
60.0
40.0
20.0
0.0
-20.0
-40.0
-60.0
-80.0
-100.0
-120.0
-140.0
ST. LUCIE COUNTY
(1972 to 1987)
A
-\V
Ft. Pierce
Inlet
1 iI 2 ?23? 2! !
0 20000
40000 60000
-""f
- .
80000 100000 120000 140000 160000
DISTANCE ALONG BASELINE (ft)
Figure 3.10. Total Shoreline Change of St. Lucle County.
-160.0
-180.0
-200.0
. A
LONG-TERM AND EXTREME SEA CONDITIONS
Wave is the prime mover of coastal sediment. Long-term wave information is the nec-
essary input for computing littoral drift quantity and shoreline evolution which, in turn,
governs the effectiveness of beach nourishment and the required frequencies of renourish-
ment. The extreme sea conditions are needed to estimate short-term shoreline retreat and
dune erosion due to design storm; both are important boundary conditions for beach nour-
ishment design.
Long-term wave information along the Florida Coast can be derived from a number of
sources:
A. Summary of Synoptic Meteorological Observations (SSMO)
SSMO was prepared under the direction of the U.S. Naval Weather Service Command by
the National Climatic Center. All the data were obtained from Marine surface observations
by ships. It is one of the most commonly cited data sources for surface winds and ocean
waves. Along the Florida coast these marine conditions are divided into five regions -
Jacksonville, Miami, Key West, Fort Myers, Apalachicola and Pensacola. Statistics of
percent frequency of wind speed and direction versus sea height were given on a monthly
basis as were the percent frequency of wave height versus wave period.
Based upon these data, the statistics of wave height versus wave direction in deep water
condition can be inferred. The joint distribution of wave height, wave period and direction
cannot be established with this set of data without further assumptions. Since SSMO data
are biased to calm weather they are not suitable for extreme condition analysis.
B. Measured Wave Data
The National Oceanic and Atmospheric Administration (NOAA) maintained a number
of meteorological buoys along the coast of the United States. The locations of the North
Atlantic and Gulf coast buoys are shown in Figure 3.11. They are all in deep water with
600
1000 800 600
North Atlantic and Gulf of Mexico Buoys.
400
200
400
200
1000
800
Figure 3.11.
water depths ranging from 120 m to 4,000 m (Wilson, 1975-1986). These buoys record wave
height and period as well as wind conditions at the 5-meter level. The wave directions have
to be inferred from wind information.
Along the coast of Florida, the Department of Coastal and Oceanographic Engineering
(COE), University of Florida, maintains a coastal data network (CDN) that contains twelve
gage stations at present. Their water depths range from 5. 8 m to 18. 0 m. These gages
record wave height, wave period and water level variations. A few of the gages also can
provide wave directional information by simultaneously measuring oscillatory current ve-
locities in the horizontal plane. The locations of these gages are also shown in Figure 3.12.
At certain locations, up to 10 years of data have been recorded. All the data are archived
in COE and monthly summary reports are available. Table 3.1 illustrates the format of
the monthly wave information summary and Figure 3.13 shows the graphic display of the
monthly wave information.
A list of information concerning the wave data lengths, types, and mean water depths
and locations where data are being collected by the CDN wave gages and the NOAA buoys
is given in Table 3.2. The CDN wave gages are identified by the names of the nearby cities
or bay systems. The NOAA buoys are identified by the location identification numbers.
Most of the wave data retrieved from the CDN wave gages have data length more than five
years while most of the buoy data have data length longer than ten years.
C. Wave Hindcasting Information
At present, there are a number of operational wave hindcast models for the Atlantic
Ocean along the eastern seaboard of the United States. The Fleet Numerical Oceanography
Center (FNOC), U.S. Navy, for instance, provides routine wave hindcasting based upon their
Global Spectral Ocean Wave Model (GSOWM). The GSOWM is based on a 2. 5 by 2. 5
degree latitude/longitude grid. It provides deepwater wave information in terms of wave
energy- frequencies versus direction. This hindcast information is available on magnetic
COASTAL DATA NETWORK FIELD STATIONS
AND
YEARS OF INSTALLATION
STEINHATCHEE
CLEARWATER 1978
VENICE 1984
PRESSURE GAGE
a P-U-V GAGES
-- TELEPHONE
--- RADIO
IST.MARYt ENTRANCE 1983
JACKSONVILLE 1981
)MARINELAND 1977
CAPE KENNEDY 1977
[ 1983
VERO BEACH 1980
1MIAMI 1977
-...
Figure 3.12. COE Wave Stations.
COASTAL DATA NETWORK
Station: MARIEZLARD
JANUARY, 1988
Time:
Day/Er
/0
/ 6
/12
/18
/0
/ 6
/12
/18
/0
/ 6
/12
/18
/0
/6
/12
/18
/0
/ 6
/12
/18
/ 0
/ 6
/12
/18
/ 0
/6
/12
/18
Rel.
Depth: Es: Ta:
(a) (m) (8eo)
10.8
12.3
10.8
11.8
10.6
12.2
11.0
12.0
11.0
12.4
11.3
11.9
11.0
12.0
11.3
11.6
11.0
11.7
11.5
11.4
11.3
11.5
11.6
11.3
11.5
11.4
11.9
11.2
1.43
1.16
1.18
1.09
0.88
0.84
0.77
1.23
1.47
1.64
1.54
1.68
1.25
1.12
0.82
0.89
0.74
1.45
1.23
1.29
0.93
1.25
1.28
1.22
1.12
1.24
1.38
1.74
12.8
12.8
6.4
5.8
7.1
7.1
8.0
5.3
5.8
8.0
7.1
6.4
8.0
9.1
8.0
9.1
9.1
5.8
6.4
6.4
4.9
8.8
5.3
5.8
8.8
5.3
6.4
7.1
Monthly Wave Data Analysis Report
% Wave Energy Distribution
(Period Bandwidth Limit -in seo)
21+
3.1
2.4
1.3
1.8
1.6
1.6
1.6
1.2
0.7
1.0
1.1
1.1
1.2
1.8
1.4
1.3
1.4
0.6
0.7
0.9
1.1
0.6
0.6
0.7
0.9
0.7
0.7
0.7
16-13 10.7-9.1 8-7.1 5.8-4
21-16 13-10.7 9.1-8 7.1-5.8
2.6
6.8
2.5
1.6
1.6
1.5
2.2
1.1
0.5
0.7
1.1
0.6
0.6
1.4
1.6
1.6
1.6
0.5
0.5
0.6
1.4
1.3
0.8
1.0
0.9
0.5
0.6
0.3
19.8
16.6
11.1
8.4
12.6
5.6
6.2
1.8
0.9
0.8
6.5
4.2
3.0
1.7
2.6
2.4
*2.6
0.7
1.0
1.0
2.6
1.6
2.2
2.3
2.5
1.7
2.0
0.9
9.5
8.0
6.4
9.1
8.2
6.3
8.8
2.8
1.9
2.4
13.8
12.6
12.8
10.8
15.6
8.8
14.6
2.1
3.4
3.9
7.3
4.9
6.3
5.4
6.9
9.5
6.9
7.0
5.3
6.8
7.8
4.7
4.5
8.5
12.1
11.7
13.9
24.2
16.9
20.5
18.0
8.5
7.7
12.8
9.2
9.8
7.6
7.8
11.2 6.7
6.3 8.0
7.6 6.1
3.9 8.1
5.7
6.3
8.9
8.6
9.4
10.0
15.6
8.4
6.7
15.8
12.5
11.2
14.8
15.9
17.3
17.7
15.4
7.8
8.4
9.5
9.2
6.4
7.2
4.4
6.1
3.6
6.4
18.6
4.9 16.
8.3 24.
13.1 33.
14.4 32.
14.5 21.
16.4 29.
11.5 22.
11.7 34.
10.2 36.
14.7 29.
15.1 19.
12.5 30.
10.2 24.
10.8 20.
8.3 19.
9.8 16.
5.6
8.3
8.2
7.6
9.9
7.6
6.9
7.7
7.3
7.4
12.4
28.7
12.
44.
38.
32.
20.
31.
31.
36.
31.
35.
41.
24.
31.
18.
17.
18.
26.
23.
24.
34.
39.
27.
19.
16.
20.
13.
18.
22.
29.
28.
32.
32.
40.
37.
38.
35.
33.
40.
23.
18.
CDN.FORMAT A/Version 1987.1
COEL.University of Florida.Gainesville. Florida 32611
Table 3.1. Format for monthly Wave Data Analysis from Coastal Data Network,
COE, University of Florida.
Marineland
20
-1)
'"-1 0
0
1 5 10 15 20 25 30
JANUARY, 1988
3
2
E
3 .......-..r..... ..........__________ _____________..................
1 --------
JANUARY, 1988
Graphic Display of Monthly Wave Information.
Figure 3.13.
Table 3.2 Summary of wave gage and floating buoy data informations
CDN underwater wave gage data
station data length latitude and water directional
or ID.# (from to) longitude depth(m) data
St. Mary's 11/83- 5/84 30043'N, 81019'W 14.2 yes
entrance 6/86- 7/86 I t1 yes
#4 8/87- 1/88 1i t! yes
11/83- 5/84 30040'N, 81016'W 17.5 yes
St. Mary's 7/84-12/84 It It yes
entrance 3/85- 4/85 II It yes
#5 7/85- 9/85 II yes
8/87- 1/88 yt ti yes
Jacksonville 6/84-12/87 30018'N, 81022'W 10.1 no
Marineland 1/81- 4/86 29040'N, 8112'W 11.4 no
Cape Canaveral 3/82-12/87 28025'N, 80035'W 8.0 no
Cape Canaveral 5/84- 9/84 28020'N, 80025'W 18.0 yes
(offshore) 12/85- 5/86 It it yes
Vero Beach 10/86-12/87 27040'N, 80021'W 7.8 no
West Palm Beach 3/82-12/86 26042'N, 80002'W 9.9 no
Miami Beach 7/83-12/87 25046'N, 80007'W 6.5 no
2/86- 3/87 27004'N, 82027'W 7.5 no
Venice 4/87- 5/87 It it yes
6/87-12/87 I! II no
Clearwater 3/82-12/87 27059'N, 82051'W 5.8 no
Steinhatchee 2/86- 7/86 29042'N, 83046'W 9.2 no
NOAA maintained buoy data
station data length latitude and water directional
or ID.# (from to) longitude depth(m) data
41001 6/76- 4/86 35000'N, 7218'W 4000 no
41002 11/75- 4/86 3218'N, 75012'W 3900 no
41006 5/82- 4/86 29018'N, 7718'W 1200 no
44003 3/79- 4/86 40048'N, 68030'W 150 no
44004 9/75- 4/86 39000'N, 70000'W 1300 no
44005 1/79- 4/86 42042'N, 68018'W 120 no
42001 8/75- 4/86 25054'N, 89042'W 3300 no
42002 3/77- 4/86 26000'N, 93000'W 2400 no
42003 7/77- 4/86 26000'N, 8618'W 3250 no
tape for the period from October 1, 1975 to present (from National Climatic Data Center
in Asheville, N.C.).
The other main operational model is the discrete spectral model developed by the Wave
Information Study (WIS) group of the Waterways Experiment Station (WES), U.S. Army.
The modeling was originally designed to have three separate phases: deepwater wave hind-
casting, wave modification in shelf zone, and finally, transformation into nearshore shallow
water zone. The main intent of the model is to provide hindcast wave information along the
coastal waters on both sides of the continent of the United States. A 20-year hindcast in-
formation was generated at 13 stations along the edge of the continental shelf of the eastern
United States. The hindcast was further extended to shallow water through linear shoaling
and refraction by assuming plane beach (Jensen, 1983). A similar 20-year wave hindcasting
is just becoming available for the Gulf Coast also.
Recently, the Department of COE has just modified the WIS model for the Florida
coast along the Atlantic seaboard (Lin, 1988). The model is more rigorous in shallow water
wave hindcasting and was calibrated using shallow water directional wave data collected
by COE. The model has been applied to hindcasting wind waves along the east coast of
Florida and it performed well for both low- and high-pressure weather systems. Figure
3.14 shows the comparisons between the hindcasted and the measured waves at Marineland
station for a two months period in 1984 (September and October) when three hurricanes
and two northeasters hit the coast. Based upon the actual wave data collected at those
stations with duration of more than four years, extreme wave height analysis was performed
by Lin and Wang (1988). Using monthly maximum waves as data base, they have shown
that Fisher-Tippett Type I distribution, or commonly known as the Gumbel distribution,
to have the best fit for both east coast and west coast waves and in both deep and shallow
water.
By denoting the significant wave height as H,, the Type I distribution of the significant
wave height is expressed as
41(H,) = exp [-exp (- -d) = exp[exp(-y)], c > 0,d > 0 (3.10)
RSS
HIDE
