Volumetric beach and coast erosion due to storm and hurricane impact

State of Florida
Department of Environmental Protection
David B. Struhs, Secretary

Division of Administrative and Technical Services

salterhmidt, a elogist aChief

Dueto S and Aurricane Impact
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,Tallaha orida
S1999
-; "1 Ope Re F~Report No. 78 ,

,Volumetic Beach and Coast Erosion *
'Due to Ston and Hurricane Impact

, ,_ ,by

SJames H. Balsillie

Florida Geological Survey
Tallahassee, Florida
1999

ISSN 1058-1391

CONTENTS

Page
A BST RA C T .... .. .. .............. .. .. .. ................ .. ......... 1
INTRO DUCTIO N .................................................... 1
EXTREME EVENT EROSION AND ITS RELATION TO THE TYPE OF PRE-IMPACT
COASTAL PHYSIOGRAPHY ...................................... 2
D A TA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
ANALYTICAL RESULTS ............... ............................... 4
The Event Longevity Parameter (ELP) ................................. 7
Average Erosion Quantity Above Mean Sea Level and Probability
Density Function (PDF) ..................................... 7
Average Erosion Quantity Above the Peak Storm Tide Level and
Probability Density Function (PDF) ............. ... ............ 12
Design Erosion Quantities ...... ................................. 13
The Offshore Sink Efficiency Parameter (OSEP) ........................ 14
Return Period Volumetric Erosion Events ....................... ......... 18
Post-Storm Recovery .......................................... 20
APPLICATIONS ................................... ................ 21
Post-Storm Beach and Coast Physiography ........................... 22
Encounter Period and Probability .................................. 23
An Erosion Damage Potential Scale ................................ 24
CONCLUSIONS ................................... ............... 25
ACKNOW LEDGEMENTS ............................................. 27
REFERENCES ............. ........................................ 27
APPENDIX ............. .......... .... ... ....................... 35

TABLES

Table 1. Characteristics of storms and hurricanes used in this study. .
Table 2. TYPE I erosion volume above mean sea level ...........
Table 3. TYPE I erosion volume above the combined peak storm tide..
Table 4. Amended Saffir/Simpson Hurricane Damage Potential Scale..

. . . . . . . 5

FIGURES

Figure 1. Idealized pre-storm (solid lines) and eroded (dashed lines) profile scenarios
for the three basic types of coastal physiography .......................... 2
Figure 2. Relationship between the measured TYPE I average erosion volume above mean
sea level and the event longevity parameter............................. 8
Figure 3. Example of water surface hydrograph through an idealized storm tide, and
definition of storm tide rise time measure (after Balsillie, 1986) ............. 11
Figure 4. Relationship between the storm tide rise time and event forward speed,
where the relating coefficient, 0.00175 is in units of hours squared (after
Balsillie, 1986). .................................... ..... ....... 11
Figure 5. Typical examples of density distributions for determination of the slope Q
relating Q, and e3P (event I. D.s refer to Table 2). ..................... 12

Figure 6. Relationship between the event longevity parameter and distribution
coefficients for TYPE I average volumetric erosion above MSL. .............. 13
Figure 7. Relationship between the measured TYPE I average net erosion quantity above
peak combined storm tide and the event longevity parameter. .............. 13
Figure 8. Relationship between the event longevity parameter and distribution
coefficients for the TYPE I average erosion volume above the peak combined
storm tide. ................................................. 14
Figure 9. Tesselated relationship relating nearshore bed slope to the ELP
coefficient, f. ................................................ 16
Figure 10. Comparison between a typical Florida nearshore profile and typical Cancun,
Mexico nearshore profile. ........................................ 17
Figure 11. Relationship between the initial nearshore bed slope, tan a,, and the
power curve fit shape coefficient, a,. ............................... 18
Figure 12. Relationship between exceedence probability, P, return period, T,, and
average TYPE I erosion volume above MSL. .......................... 19
Figure 13. Example of application for determining two-dimensional post-storm
physiography using volumetric data, and design wave conditions ........... 23
Figure 14. Nomograph for relating event return period, encounter period, and
encounter probability............................................ 24
Figure 15. Beach and coast erosion damage potential scale as a function of event
forward speed at landfall and peak storm tide elevation. Erosion volumes are
based on peak storm tide elevation classes of Table 4; even so, results apply
to storm events as well as hurricanes. ............................. 26

VOLUMETRIC BEACH AND COAST EROSION DUE
TO STORM AND HURRICANE IMPACT

by

James H. Balsillie, P. G. No. 167

ABSTRACT

Prior to the initial work of the author during the early 1980s, methods to predict nearshore,
beach, and coastal erosion due to storm and hurricane impact were based on theoretical applications and
estimation. However, with the acquisition of actual field data quantifying storm and hurricane erosive
impacts, it became clear that, in addition to the combined storm tide (commonly termed the storm surge),
the length of time that an event has to erode the beach and coast is a highly significant factor that could
be quantified (i.e., given two events each producing identical storm tide hydrographs, the slower moving
event will result in greater beach and coast erosion). Hence, based on actual field data, the eent
Aargv*y paramtr (BP) was introduced (Balsillie, 1985c, 1986)which incorporates both the combined
storm tide and its rise time, the latter of which can be computed from the event forward speed.

Since the published work of the mid-1980s, additional field data (a three-fold increase) have
become available to further verify the ELP approach, and to introduce new developments. It has, for
instance, become apparent that in addition to the design peak storm tide elevation, the design erosion
event requires attention in many coastal engineering design applications if they are to be successful. In
fact, aside from design soffit elevations which are determined from the peak combined storm tide
elevation and superimposed storm waves propagating upon the storm tide surface, it is the design erosion
event that quantifies the final expression of all other impacts. Hence, probability density functions are
defined for both erosion above mean sea level and peak storm tide level. In addition, it has been found
that the pre-impact offshore bed slope can be used to indicate the "efficiency" or "receptiveness" of the
offshore sediment sink to accept sand eroded from the beach and/or coast (termed the offsham snk
efi~inic parames (OSEP. Incorporation of the new data, and quantification of the two additional
developments and an amended Saffir/Simpson hurricane damage potential scale constitute the subject
matter of this paper.

INTRODUCTION

Although, in the seasonal and
long-term sense, beaches are constantly
being remolded by waves, tides and winds,
the most dramatic changes occur as the
result of extreme event (i.e., short-term
impacts from storms and hurricanes). The
consideration of short-term, seasonal, and
long-term impacts (i.e., force elements such
as astronomical tides, storm tides, waves,
etc.) and the resulting outcomes (i.e.,
response elements such as beach and coast
erosion, longshore bar formation, and
structural damage) are matters of standard

coastal engineering practice. In this paper,
short-term impacts define the subject of
interest.

For many years, only the peak
combined storm tide (also commonly termed
the storm surge) was employed in
determining and assessing nearshore, beach,
and coastal engineering design solutions.
Consideration of the storm tide alone,
however, does not provide a realistic
measure of impact potential. For instance,
given two extreme events with identical
storm tides, the slower moving event will
result in greater beach and coast erosion.

The peak storm tide elevation plus
superimposed storm wave activity
propagating upon the storm tide surface is
useful in determining deck, floor, etc. (termed
"soffit") elevations, provided that any shift or
erosion of the bed is known, since increased
water depth results in higher waves. All
other design solutions are more nearly related
to erosion responses, such as pile tip
penetration, seawall and bulkhead panel
embedment elevations, etc. In addition,
since storms cause nearshore erosion and
bed shifts in response to longshore bar
formation accompanying beach and coast
erosion, resulting increased water depths can
significantly affect both horizontal and
vertical wave impact potentials which require
consideration in design solutions and
assessments.

The need for methodology to predict
beach and coast erosion due to the impact of
storms and hurricanes has been an issue of
ongoing and increasing concern. Moreover,
it is one which, for the majority of the history
of the discipline of coastal science, has
eluded satisfactory quantifying solutions.
The lack of methodology is not surprising
considering the complexities involved in
quantifying littoral processes. Ultimately,
however, only through the acquisition of field
data will confident, successful solutions be
realized. This paper provides a significant
update (in terms of the number of hurricane
and storm events) to previous work by the
author (Balsillie, 1985c, 1986).

EXTREME EVENT EROSION AND
ITS RELATION TO THE TYPE OF
PRE-IMPACT COASTAL
PHYSIOGRAPHY

In this paper erosion is considered to
be the overall term encompassing horizontal
and vertical recession components of beach
and coast response due to storm and/or
hurricane impact. Depending on the type of
coastal physiography, these components can
result in quite different outcomes. Horizontal

recession is important in determining siting of
coastal development activities. It is,
however, the maximum vertical recession
produced during event impact (Balsillie,
1984c, in manuscript) which is needed to
assess structural design constraints (e.g.,
piling tip penetration, "first floor" soffit
elevations, etc.) based on hydraulic forces
such as shore-breaking wave impact
pressures (Balsillie, 1985b). Vertical
recession should include effects due to both
scour, and sediment liquefaction (Zeevaert,
1983, 1984).

It is also important to bear in mind the
differences between the nearshore, beach (or
shore), and coastal subzones of the littoral
environment (Figure 1). Under normal
hydraulic littoral conditions, processes are
clearly different within each subzone
(discussed in detail in later sections).
Whether or not the storm rises above the
beach, or if not, has the longevity to erode

---- *Scol- eauch-4-NTor

FLOODED

-r4

Overwash
/ BREACHED

NON-FLOODED

Figure 1. Idealized pre-storm (solid lines) and
eroded (dashed lines) profile scenarios for the
three basic types of coastal physiography
(STL = peak storm tide level, MSL = mean
sea level).

the beach and begin to erode the coast, and
post-storm beach recovery, are important
issues which shall be addressed later.

Considering initial coastal
physiography and responses due to extreme
event impact, three general types of
geomorphic scenarios are suggested:
non-flooded, flooded, and breached profiles
(Figure 1). In assessing these profile types,
several assumptions are made: 1) the beach
and coast are composed of relatively
unconsolidated sand-sized sediment, 2)
onshore-offshore sediment transport
processes prevail and alongshore processes
are assumed static, and 3) "shallow water"
hydraulic processes are approximately
constant for a given water depth, noting that
a change in wave conditions (principally
shore-breaking and broken waves) will cause
a shift in bathymetry which, in turn, will
affect the waves.

Where the coast is higher than the
peak storm tide and is wide enough not to be
breached (i.e., the non-flooded condition),
only the offshore "sink" is available for
deposition of sand eroded from the beach
and coast. A major contributing erosional
mechanism is gravitational mass wasting,
because only a relatively few waves are
required to cause an unstable, steep sand
face to collapse. As the sediment
escarpment increases in height, increasingly
more sediment is potentially available for
introduction to the prevailing littoral hydraulic
environment for redistribution.

The barrier islands of the lower Florida
Gulf Coast may in many places be inundated
by 1 to 2 meters of water due to impact of a
100-year return period peak combined storm
tide event (see Table 1 for definition). This
does not include the added hydraulic
elevation due to shore-breaking wave activity
which propagates upon the storm tide
surface. Therefore, the contribution of
gravitational mass wasting, important to the
non-flooded scenario, may not be of special

consequence for relatively low-lying barriers.
It does, however, introduce the aspect of an
additional "sink" for eroded sand due to
overwash processes (Leatherman, 1976,
1977, 1979, 1981; Leatherman and others,
1977; Schwartz, 1975). Combination of the
preceding two physiographic-hydrographic
scenarios leads to the breached profile
condition illustrated in inset B of Figure 1 in
which the overwash sink again occurs.

It is also apparent from the literature
that the success of grain-by-grain
onshore-offshore sediment transport
mechanics under littoral wave activity as yet
remains to reach the status of satisfactory
quantification (Balsillie, 1984c, 1986). That
existing attempts at quantification may be
fraught with insensitivities is further
exaggerated when dealing with a rising and
falling storm tide and with storm-generated
littoral wave activity. Hence, pursuit of
alternative approaches is desirable. One
such approach is investigation of field data
quantifying actual storm and hurricane
impact upon our shores.

DATA

This subject has received much
attention in previous work, dating back for
about 3 decades. Perhaps the most
compelling work is that of Caldwell (1959)
just preceding the infamous U. S. east coast
Ash Wednesday storm of 1962
(Bretschneider, 1964; Harrison and Wagner,
1964; and O'Brien and Johnson, 1963), with
a resurgence of interest occurring with the
works of Edelman (1968, 1972). There
have, in addition, been many studies reported
in the literature providing descriptive
accounts of the erosive power of extreme
occurrences. However, until this work was
originally published (Balsillie, 1985c, 1986),
there were insufficient types and quantities
of field data on which to quantify beach and
coast erosion due to storm and hurricane
impacts. This work has increased the size of
the field data base by a factor of three.

Fourteen erosion events for 11
hurricanes, and 22 erosion events for 20
storms (Table 1) provides the largest field
data compilation amassed to date for the
purpose of quantifying beach and coast
erosion due to extreme event impact. Seven
events (H4, S17, S18, H7,H8, H9 and H10)
were assessed through field data collection
of the State of Florida, Department of Natural
Resources (DNR, now the Department of
Environmental Protection, DEP), Division of
Beaches and Shores (now the Bureau of
Beaches and Coastal Systems); field data
collection techniques have been discussed
elsewhere (Sensabaugh and others, 1977;
Balsillie, 1985a, 1985c, 1985e, 1986,
1988). Thirteen events (S2 through S11,
S14, S15 and S16) are the direct results of
the efforts of the Coastal Engineering
Research Center (CERC); field data collection
techniques are discussed by Birkemeier
(1979); Birkemeier and others (1988). A
more recent event has been reported by Kana
and Jones (1988) and Jones and Kana
(1988). Hurricane Hugo (H11) information is
presented by Birkemeier and others (1991)
and Stauble and others (1991). A tropical
storm (S20) was reported by Beumel and
Campbell (1990). Ferriero (1994) reported
erosion from a Portuguese storm event that
occurred in 1989. Remaining events are
from independent studies (references are
listed in Table 1) that were previously
analyzed by the author (Balsillie, 1985c,
1986).

Of the aspects concerning the data, it
is important to note for management
purposes that there are two types of erosion
(Balsillie, 1985a, 1985e). One is the
measure which represents those sampled
profiles where erosion only occurred (TYPE I
erosion measure). The other (TYPE II) is that
which includes all profiles regardless of gain
or loss. TYPE II erosion is important in
assessing actual beach and coast economic
losses. For design applications, TYPE I
erosion is the better measure, since for
design work we are interested in locations

only where erosion has occurred. Hence, in
this paper, TYPE I erosion volumes are used.
Using the data from events H4, H5, S17,
S18, H7, and H8, Balsillie (1985e, p. 33-34)
found that, on the average, TYPE II erosion is
73% of TYPE I erosion (n = 13, sampled for
over 200 profile pairs, r = 0.9515).

Where possible, profiles were selected
to represent known extreme event impact
magnitudes. For instance, only DNR (now
DEP) ranges R-33 through R-125 in Walton
County, Florida were selected for Hurricane
Eloise, since it was this area that coincided
with the first quadrant of Eloise in terms of
the combined storm tide height (see Balsillie,
1983a). In other cases, one could only
consider what pre- and post-storm profile
data were available; an example is the Ash
Wednesday storm of 1962.

ANALYTICAL RESULTS

Two reference water levels have
commonly been used, above which
volumetric erosion is determined: 1. the
peak storm tide still water level (STL), and 2.
mean sea level (MSL).

The first water level (STL) is
considered here because it has been used in
other work. It is particularly accurate for
non-flooded profiles since erosion volumes
represent single process losses above the
reference water level due to gravitational
mass wasting, and include none of the
complexities occurring below the reference
level due to interactive hydraulic and
sediment transport processes. It should be
clear, however, that this reference water
level has no applicability in determining
volumetric erosion for breached or flooded
profiles and, therefore, its use results in only
partial success in volumetric erosion
determination.

The mean sea level reference will, on
the other hand, provide for volumetric
erosion determination for all three

Table 1. Characteristics of storms and hurricanes used in this study.

Peak Event Storm
Tide
Storm Forward
Event and Location Ti Rise Information Sources
I Tide (Im Speed Tim
MSL) (km/hr)
(hs)
H Hurricane Audrey, June
H1 1957, Louisiana Gulf Coast 3.66 19.0 11.7 Morgan and others, 1958

Hurricane Cara, Sep. Reid and others, 977; Neumann
H2 Hurrc1961, Texas Gulf Coast 2.30 6.3 51.0' and others, 1981; Schwerdt and
1961, Texs Gf C t others, 1979; U. S. Army, 1962
Ash Wednesday Storm, Bretschneider, 1964; Harrison and
S1 Mar. 1972, U. S. East 3,05 --- 28.0' Wagner, 1964; O'Brien and
Coast Johnson, 1963
S2 Nov. 1962 Storm, U. S. 1.50 7.5
East Coast
6 Nov. 1973 Storm, U. S.
3 Coast 1.40 --- 18.6' Birkemeier and others, 1988
East Coast

S4 13 Jan. 1964 Storm, U. S. 1.50 --- 12.4
East Coast
Hurricane Betsy, Sep. Wanstrath, 1978; Neumann and
H3 1965, Mississippi Gulf 2.26 16.0 18.0' others, 1981; Schwerdt and
Coast others, 1979; U. S. Army 1979

S5 16 Sep. 1967 Storm, U. S. 1.40 -- 12.4
East Coast

S6 12 Mar. 1968 Storm, U.S. 1.20 --- 6.1
East Coast
S 12 Nov. 1968 Storm, U. S. 1.60
East Coast
S 2 Feb. 1970 Storm, U. S. 10 6.
S8 1.10 --- 6.1
East Coast

S9 17 Dec. 1970 Storm, U. S. 1.60 -- 12.4 Birkemeier and others, 1988
East Coast
S10 19 Feb. 1972 Storm, U. S.
East Coast
SlOa New Jersey 1.80 --- 6.1'
SlOb New York 2.00 --- 6.1'
S11 17-22 Mar. 1973 Storm,
U. S. East Coast
Sla New York 1.40 --- 12.2'
S11b New Jersey 1.30 --- 12.2'

S12 Nov-Dec. 1973 Events --- --- Erchinger, 1974
German North Sea Coast

S13 23 Sep. 1974 Storm, U. S. 1.45 --- 9.0 Kana, 1977
East Coast

Hurricane Eloise, Sep. Balsillie, 1983a; Burdin, 1977;
H4 1975, N.W. Florida Gulf 3.15 42.6 5.0' C 197; U. 1976
CoastChiu, 1977; U. S. A 1976
Coast

Table 1. Characteristics of storms and hurricanes used in this study (cont.).

Peak Event Storm
Tide
Storm Forward
Event and Location Rise Information Sources
Tide (m Speed
1. D. Time
i. D. MSL) (km/hr) T
(hrs)

S14 14 Oct. 1977 Storm, U. S. 1.80 --- 17.0
East Coast
19 Dec. 1977 Storm, U. S.
S15 9 Dec 177 tor, 1.40 --- 35.0 Birkemeier and others, 1988
East Coast

$16 6 Feb. 1978 Storm, U. S. 1.70 19.9
East Coast
Balsillie and Clark, 1979; Parker
H5 Hurricane Frederic, Sep. 3.66 24.1 11.. and others, 1981; Penland and
1979 Alabama Gulf Coast others, 1980; Schramm and
others, 1980

H6 Hurricane Allen, Aug. 2.74 32.2 6.0. Dahl and others, 1983; U. S.
1980, Texas Gulf Coast Army,1980
No Name Storm, 17-18
517 June 1982, Lower Florida 1.68 40.2 8.0' Galvin, 1983; Trescott, 1983
Gulf Coast

H7 Hurricane Alicia, Aug. 3.86 12.0 18.0. Dupre, 1985; Garcia and Flor,
1983, Texas Gulf Coast 1984
Thanksgiving Holiday
S18 Storm, 21-24 Nov. 1984, 1.83 --- 21.0' Balsillie, 1985a
Florida East Coast
H8 Hurricane Elena, Sep.
1985, Florida Gulf Coast
H8a Pinellas County 1.37 14,5 20,0' Balsillie, 19e
H8b Franklin County 2.32 16.1 13.4
H8c Gulf County 2.10 16.1 13.4
H8d Escambia County 2.29 25.7 8.0'

H9 Hurricane Kate, Nov. 198 2.60 --- 9.2 Balsillie, 1986
N. W. Florida Gulf Coast
S19 1 Jan. 1987 Storm, U.. S 1.50 12.0 Kana and Jones, 1988; Jones and
East Coast Kana, 1988
O Hurricane Gilbert, Sep. 31 Unpublished Florida Department of
1988, Cancun, Mexico Natural Resources data.

S20 Feb. 1989 Storm, 3.53 --- 45.0 Ferreira, 1994
Portuguese Atlantic Coast
Birkemeier and others, 1991;
H11 Hurricane Hugo.. Sep 3.80 32.2 5.0 Nelson, 1991; Stauble and others,
1989, U. S. East Coast 1991
1991
Tropical Storm Marco, Oct
S21 10-11, 1990, Lower 1.13 16.1 9.0 Beumel and Campbell, 1990
Florida Gulf Coast __

Notes: Peak storm tide is the combined peak storm tide level above NGVD including the astronomical tide and
dynamic wave setup; Peak storm tide for event S12 was measured from the local datum; indicates the measure
storm tide rise time, all other are predicted using equation (2).

physiographic scenarios of Figure 1 (except,
perhaps, for extreme cases such as inlet
formation where erosion occurs below MSL).
For breached or flooded profiles, overwash is
eliminated from erosion volumes, so that
volumetric erosion for non-flooded profiles
(where only the seaward sink is available for
deposition) and for flooded and breached
(where the seaward and upland sinks are
available, but eliminated) profiles are
comparable. Elimination of upland and
seaward sinks is desirable since, on the
average, the sum should be equivalent to the
amount eroded. While at the seaward
extremity of the post-storm profile, some
material of the seaward sink (also including
some degree of post-storm beach recovery)
may reside above MSL (determined to be about
6% of the seaward sink volume from 245
analyzed profile pairs from Balsillie, 1985c),
the analytical method is fairly unbiased since
it is applied equally to all profiles investigated.

For erosion volume determinations and
applications, any datum other than MSL (i.e.,
mean lower low water (MLLW), mean low
water (MLW), mean high water (MHW), and
mean higher high water (MHHL)) is not to be
employed. Their departure from MSL is not
constant from locality to locality (Balsillie and
others, 1998). Hence, volumes will not be
comparable.

It should be noted that volumetric
changes were investigated which included
offshore profile data. The results, however,
introduced significant scatter. It is to be
understood that offshore profiling requires
considerable time and resources (Sensabaugh
and others, 1977; Balsillie, 1985a, 1985e).
Post-storm field measurements are most useful
when the response time is swift, since any
delay increases the possibility of post-storm
beach recovery which can be faster than
previously thought. Based on the preliminary
analysis alluded to above, the inclusion of
offshore profile bathymetry does not yet
appear to be justifiable.

There have been a number of extreme
event erosion studies in which volumetric
erosion calculations are based on single
averaged or composite pre-storm and
post-storm profiles, even though multiple
profiles were measured. In this study,
however, pre- and post-storm profiles are
surveyed from precisely located coastal
monuments, along azimuths established for
each monument. Hence, volumetric changes
have been calculated for each profile pair, and
resulting data have been then statistically
treated to obtain point estimators and
probability density functions (PDFs).

The Event Longevity
Parameter (ELP)

Average Ersion Quantty Above Mean Sea
Level and Probabty Density Function
(PDF)

The most complete set of field data
amassed to date is now available to quantify
beach and coast response due to extreme
event impact. However, such data have little
value if there does not exist a methodology for
predicting future occurrences of erosion. In
fact, until recently, there has been no
consolidated methodology by which to realize
such prognostication. Recognizing that the
amount of erosion is significantly dependent
upon the length of time that an extreme event
affects the beach and coast (Hayes, 1967;
Hayes and Boothroyd, 1969), the author
(Balsillie, 1985c, 1986) developed the event
longevity parameter (ELP). In terms of the
average TYPE I erosion quantity above MSL,
Q avg, the relationship is given by:

,, = 1622-1 (11 S2)45 (1)

where g is the acceleration of gravity, S is the
combined peak storm tide elevation (see note
of Table 1 for definition), and tr is the storm
tide rise time. The relationship and data on
which equation (1) is based are plotted in
Figure 2 and listed in Table 2. The data

I ldO

e avg
(m3/m)

0 50000 100000 150000 200000 250000 300000

(gl92 t, s 2)45 (mn m)
Figure 2. Relationship between the measured TYPE I average erosion volume above
mean sea level and the event longevity parameter (n = number of events; r = Pearson
product-moment correlation coefficient).

sample on which equation (1) is founded is
three times larger than that available to
Balsillie (1985c, 1986) in the original
development of the relationship, which
allowed for refinement of the dimensionless
constant. The coefficient of equation (1) is,
however, but 2.5% smaller than that
reported in the earlier work.

The storm tide rise time, t,, is the final
continuous surge of the storm tide
representing impact of the event at landfall.
In some cases, pre-storm setdown (e.g.,
particularly for alongshore hurricanes not
considered here) and pre-storm setup can
occur. These should be eliminated in
determining the value of tr, whose graphical
determination is illustrated in Figure 3.

Values of the storm tide rise time are
from measured storm tide hydrographs
(references are given in Table 1). Such
records are not always simple to interpret,
depending on gauge siting, distance of
gauges from event landfall, and relationship
of the storm generated tide and the
astronomical tidal cycle. Consideration of the
combined storm tide rise time rather than
the total tide history does, however,
eliminate uncertainty, which may be

introduced, when trying to interpret when the
storm tide ends. The total value of tr for a
storm produced tide, maintained over
multiple astronomical tides, is determined by
adding the rise time components of each
additional cycle.

For analytical purposes, tr is an
excellent quantitative measure of event
longevity. However, for applied predictive
purposes, for an approaching event, the
measure is not useful because it is available
only after event impact. However, it was
found (Balsillie, 1985c) that the storm tide
rise time and event forward speed, vf
(measured at the point when the radius of
maximum winds, or a facsimile thereof for
extratropical storms, makes landfall), are
related (Figure 4) according to:

t = 0.00175 g (2)

where g is in units of km/hr2 (i.e., g = 9.8
m/s2 = 127008 km/hr2), vf is in units of
km/hr, and the coefficient 0.00175 is in units
of hr2.

The role of pre-storm setup as an

Table 2. TYPE I erosion volume above mean sea level.

Average Maximum Event
Erosion Erosion Longevity Elapsed profile
(m2m) (m/m Profile
Event and Location Volume Volume n Parameter r,me Type
(mr/m) (m'/m) (m'/m) (months)

Hurricane Audrey,
H1 Jun. 1957, Louisiana 51.7 89.0 6 99,461 5.55 0.8449 29-48 F
Gulf Coast
Hurricane Carla, Sep.
H2 1961, Texas Gulf 89.8 -- 8 153,710 --- --- 5.3 NF,F
Coast
Ash Wednesday
S1 Storm, Mr. 1962, U. 93.0 --- 5 149,327 --- -- 60-96 NF
S. East Coast

S2 Nov. 1962 Storm, U. 12.9 28.9 31 16,724 1.80 0.9721 0.36 NF
S. East Coast
S3 6 Nov. 1963 Storm, 20.5 47.3 28 30,970 2.95 0.9634 0.60 NF
U. S. East Coast

4 12 Jan. 1964 Storm, 25.0 56.9 21 25,037 3.55 0.9703 0.50 NF,
U. S. East Coast MS
Hurricane Betsy, Sep.
H3 1965, Mississippi Gulf 46.5 99.0 9 64,912 6.17 0.9939 4 F,B
Coast

S5 16 Sep. 1967 Storm, 16.6 43.6 18 22,420 2.72 0.9637 0.16 NF
U. S. East Coast

6 12 Mar. 1968 Storm, 9.7 24.9 18 9,919 1.55 0.9787 0.16 NF
U. S. East Coast

7 12 Nov. 1968 Storm, 26.2 55.8 41 32,285 3.48 0.9610 0.72 NF,
U. S. East Coast MS

S8 2 Feb. 1970 Storm, U. 11.1 19.1 29 8,630 1.19 0.9404 0.52 NF
S. East Coast

9 17 Dec. 1970 Storm, 17.7 43.5 37 27,724 2.71 0.9906 0.41 NF
U. S. East Coast
S10 19 Feb. 1972 Storm,
U. S. East Coast
SlOa New Jersey 9.5 18.8 34 18,977 1.17 0.9572 0.76 NF
SlOb New York 20.2 41.7 23 22,462 2.60 0.9630 0.82 NF
S11 17-22 Mar. 1973
Storm, U. S. East
Coast
S11a New York 23.6 52.9 16 22,102 3.30 0.8923 0.69 NF,
MS
S11b New Jersey 10.3 25.3 17 19,630 1.58 0.9768 0.66 NF,
MS

Nov.-Dec. 1973 Event,
S12 German North Sea 200.0 --. --- --- -- --- --- NF
Coast

S13 23 Sep. 1974 Storm, 12.0 .-- 10 18,328 --- --- 0.07 NF
U. S. East Coast

Hurricane Eloise, Sep.
H4 1975, N.W. Florida 20.0 50.7 62 39,628 3.16 0.9735 24 NF
Gulf Coast

Table 2. TYPE I erosion volume above mean sea level (cont.).

Average Maximum Event
Erosion Erosion Longevity Elapsed Profile
.D. Event and Location Volume Volume Parameter ) r. Time Type
(m3/m) (m3/m) (mW/m) (months)

S14 14 Oct. 1977 Storm, 18.5 34.8 22 43,085 2.17 0.9710 0.23 NF
U. S. East Coast
15 19 Dec. 1978 Storm, 11.6 37.9 17 42,979 2.36 0.9800 3.25 NF
U. S. East Coast

$16 6 Feb. 1978 Storm, U. 11.6 37.9 17 42,979 2.36 0.9800 3.25 NF
S. East Coast
Hurricane Frederic, Sep.
H5 1979, Alabama Gulf 52.0 121.1 32 94,671 7.55 0.9738 6 F,B
Coast

H6 Hurricane Allen, Aug, 28.0 --- 3 36,682 --- --- 30 NF,B
1980, Texas Gulf Coast
No Name Storm, 17-18
S17 Jun. 1982, Lower 14.0 25.8 24 21,111 1.61 0.9917 3 NF
Florida Gulf Coast

H7 Hurricane Alicia, Aug. 92.4 1 152,259 --- -- 36 NF
1983, Texas Gulf Coast
Thanksgiving Holiday
8 Storm, 21-24 Nov. 27.0 70.0 127 52,388 4.30 0.9077 3-20 NF
1984, Florida East
Coast
H8 Hurricane Elena, Sep.
1985, Florida Gulf
Coast
H8a Pinellas County 21.0 48.3 44 31,704 3.01 0.9622 130 NF
H8b Franklin County 40.0 75.4 35 54,456 4.70 0.9585 49 NF
H8c Gulf County 24.0 44.1 54 45,579 2.75 0.9753 13-21 NF
H8d Escambia County 19.0 38.3 112 34,653 2.39 0.9875 10 NF
Hurricane Kate, Nov.
H9 1985, N. W. Florida 22.0 51.2 18 47,481 3.19 0.9617 2 F,NF
Gulf Coast

S19 1 Jan. 1987 Storm, U. 19.4 --- 4 25,669 -- --- 0.3 NF
S. East Coast
Feb. 1989 Storm,
$20 Portuguese Atlantic 164.0 341.0 4 276,390 .
Coast
Hurricane Gilbert, Sep. 144.7 2970 8 89,782 18.52 0.9842 60 NF
1986, Cancun, Mexico 231,462_

H11 Hurricane Hugo, Sep. 28.0 52.5 19 53,501 3.98 0.9691 4 NF
1989, U. S. East Coast

Tropical Storm Marco,
S21 Oct. 10-11, 1990, 3.9 11.4 28 9,317 0.57 0.9755 1 NF
Lower Florida Gulf
Coast

Notes: Elapsed time is the time between pre- and post-storm surveys; Profile types are: F = Flooded, B = Breached,
NF = Non-flooded, MS = Multiple Storms; adjusted value to account for increased offshore sediment sink efficiency,
see text for discussion; data sources are listed in Table 1.

erosive agent deserves
additional comment. If
the general onshore
physiographic scenario
can be described as a
beach that is backed by
a coast comprised of a
dune or bluff (see Figure
1 for graphical
definition), then the
elevation relative to MSL
which identifies where
the coast begins (i.e.,
the beach-coast
inflection point, or
nickpoint), becomes an
important measure.
That is, if the storm tide
is less than the
beach-coast nickpoint
elevation, then more
time will be required to
erode the beach before
the coast is affected,
relative to the case
where the storm tide is
higher than the
beach-coast nickpoint
elevation, so that both
the beach and coast will
be affected within time
constraints of the event.
Experience with

Elevation
Above MSL
(m)

0 20 40 60 so
Time (hours)
Fligure 3. Example of water surface hydrograph through an
idealized storm tide, and definition of storm tide rise time
measure (after Balsillie, 1986).

100
so
tr 60
(hrs) 40

0 10 20 30 40 50 60
Vf (km/hr)
Figure 4. Relationship between the storm tide rise time and event
forward speed, where the relating coefficient, 0.00175 is in units
of hours squared (after Balsillie, 1986).

identification of the
beach-coast intersection for Florida beaches
(i.e., those for beaches preceding events
listed in Table 1), tells us that it is the latter
scenario which usually defines the design
erosion condition. Current examples of
average nickpoint elevations are +2.19 m
MSL for Florida's upper East Coast (St.
Johns County), + 2.25 m MSL for the lower
Gulf Coast (Charlotte County), and +2.1 m
MSL for the northwestern panhandle Gulf
Coast (Walton County). It is significant that
of the events of Table 1 and those
graphically reported by Harris (1963), none
resulted in a pre-storm setup in excess of
about + 1.5 m MSL, well below the
beach-coast nickpoint elevation for Florida.
Hence, in combination with the observation

that pre-storm setup is an anomalous feature,
the above further substantiates that it should
be deleted from consideration in erosion
prediction.

It is to be noted that the ELP contains
both the peak storm tide, S, and the storm
tide rise time, tr. It is the introduction of the
latter which prompted the name event
longevity parameter. Utilizing stepwise
regression (Krumbein and Graybill, 1965;
Balsillie, in press; Balsillie and Tanner, in
press), it has been determined that S results
in a relative net contribution in predicting
Qe av of 76%, and tr provides a net relative
contriution of 24%. Even so, both are
required in order to obtain the success of

equation (1) evident in Figure 2.

There are 29 events that
provide information on which to
investigate an erosional probability
density function (PDF). From 6 to
127 profiles represent each of the
events (Table 2), and result in the
following equation:

0,= (e3P) (gIt t, S2 (3)

in which Qe is the volumetric
coastal erosion quantity occurring
above mean sea level
corresponding to the erosion Oe
probability, P, which is the
probability of erosion less than or (mJm)
equal to that stated, and f is a
relating coefficient. Values of (
(examples are plotted in Figure 5,
results and correlation
coefficients are listed in Table 2)
are plotted against the ELP in
Figure 6, showing remarkable
agreement. The relating
coefficient f becomes 12344-t.

Correlation coefficients
associated with P are all
significantly large. Note that if we
were to consider, say, median and
larger erosion values in the PDFs
(see Figure 5), rather than all Figure 5.
values available, correlation determine
coefficients would be even larger. I.D.s refer

Average Erosion Quantity Above the
Peak Storm Tide Level and Probabity
Density Function (PDF)

The preceding has dealt with
volumetric erosion occurring above mean sea
level. While it has been noted that
consideration of erosion above the peak
storm tide elevation has no applicability for
flooded or breached profiles, such a
consideration does have validity for
non-flooded profiles. Based on available
data listed in Table 3, the following
relationship based on 24 events, illustrated in

STypical examples of density distributions for
ation of the slope Q relating Q, and e3" (event
er to Table 2).

Figure 7, surfaces:

,,', = 3299-' (g/2 tS2) 4

where Q'e avg is the TYPE I average erosion
quantity occurring above the peak storm tide
level.

Using data from 22 events (Table 3) a
PDF may be proposed according to:

o, = (' e P) (gl2 t, S2)4/5

50000 100000 150000 200000

(11/2 tr S2)45
Figure 6. Relationship between the event longevity parameter and
distribution coefficients for TYPE I average volumetric erosion above
MSL.

50000 100000
(g112 tr g245

150000

Figure 7. Relationship between the measured TYPE I average net
erosion quantity above peak combined storm tide level and the event
longevity parameter.

where the relating coefficient f from Figure
is 23630'1.

It is evident from results presented in
Figure 8, that the correlation between
variables is significantly less than those
statistical assessments for analyses
presented in Figures 2, 6, and 7. Even so,
the probability that a random sample of this
size could result in sample correlations so
large, is very small.

Design Erosion Quantities

Now that we have established
successful relationships that quantitatively
predict average erosion volumes for events

relative to MSL and the peak storm tide
elevations, we can broaden our quantitative
expectations. We know that for engineering
design purposes, using TYPE I erosion
volumes, an average measure is not
responsible. For engineering design purposes
it is always prudent to consider some upper
measure of a destructive force, or response
element. A highly useful measure from
substitution of equations (1), (3), (4), and
(5), where PDF linearity prevails, is given by:

a,
00 Avg

0.1314 e3 P
0. A

in which Qe and Q'e are erosion volumes for

100
80

40
20
0

I

250000

10
a Q = e3 P, where
6 =23630-1 (g12 t, 2
4 r = 0.5797
4
n=22
2
0
0 20000 40000

60000

(g/2 tr S2) 4S
Figure 8. Relationship between the event longevity parameter and
distribution coefficients for the TYPE I average erosion volume above the
peak combined storm tide.

a specified exceedence probability P above
MSL and peak storm tide, respectively.
Hence, the TYPE I median erosion volume
(i.e., P = 0.5) is about 61% less than the
TYPE I average erosion volume (for the
average erosion volume P = 2/3), the third
quartile TYPE I erosion volume (i.e., P =
0.75) is 130% greater than the average
TYPE I erosion volume, etc.

Noting that pre-storm profiles are
seldom measured just prior to storm or
hurricane impact, some physiographic
deviation might be reasonable to levy on a
PDF in assessing a design maximum erosion
volume. This and purely random,
anomalously high erosion volumes suggest
that, perhaps, a probability P of between 0.9
and 0.95 would not seem inordinate to
apply. Using a value of 0.925 and
coefficients from equations (1) and (4), the
application of equation (6) yields the
following design relationships:

,, = 770-1 (g11 t, S2)4/5 (7)

for the TYPE I erosion volume above MSL,
and:

= 1473-1 (gl12 S2)4/5 (8)

for the TYPE I
combined peak
equations result

erosion volume above the
storm tide level. Both
in erosion volumes close to

twice (i.e., 2.1) the average erosion volume.

It is to be noted that coefficients of
equations (7) and (8) precisely agree with
fitted coefficients describing the graphically
estimated maximum erosion quantities of
Tables 2 and 3.

The Offshore Sink Eficiency
Parameter (OSEP)

The form of the event longevity
parameter has invoked some controversy.
While the combined peak storm tide height
and storm tide rise time components have
generally been well received, the appearance
of the acceleration of gravity and the
dimensionless proportionality constant have
not.

If one compares erosion quantities
above the combined storm tide to those
above mean sea level, it is apparent that
about half the eroded sand volume originates
from above the peak storm tide level (50% if
one compares coefficients from equations (1)
and(4), and (3) and (5), and 55% from the
data). This should not be surprising from a
geomorphic viewpoint, considering that our
beaches and coasts have certain constraining
dimensions physiographically. It is
recognized that the efficiency of gravitational
acceleration is not only greater for steeper
slopes when dealing with sand transport, but

Table 3. TYPE I erosion volume above combined peak storm tide.

Average Maximum Event
1.. Event and Location Erosion Erosion Longevity
I. 0. Event and Location n
Volume Volume Parameter q) r,
(m'/m) (m/m) (m/m)

S1 Ash Wednesday Storm, Mar. 1962, 53.0 --- 4 149,327 ...
U. S. East Coast
S2 Nov. 1962 Storm, U. S. East Coast 6.3 18.6 32 16,724 1.16 0.9953
S3 6 Nov. 1963 Storm, U. S. East Coast 6.9 24.2 26 30,970 1.51 0.9552
S4 13 Jan. 1964 Storm, U. S. East Coast 11.7 26.1 37 25,037 1.63 0.9841
S55 16 Sep. 1967 Storm, U. S. East Coast 3.9 7.1 19 22,420 0.44 0.8918
12 Mar. 1968 Storm, U. S. East 5.8 18.6 9919 590
S6 Coast 5.8 18.6 37 9,919 1.16 0.9590
Coast

7 2 Nov. 1968 Storm, U.S. East 14.8 28.7 43 32,285 1.79 0.9879
Coast
58 2 Feb. 1970 Storm, U. S. East Coast 6.9 15.6 31 8,630 0.97 0.9559
17 Dec. 1970 Storm, U. S. East
S9 1970toEast 5.8 15.1 42 27,724 0.94 0.9316
Coast
S10 19 Feb. 1972 Storm, U. S. East Coast
SlOa New Jersey 12.0 22.8 23 18,977 1.42 0.9815
SlOb New York 7.6 15.7 38 22,462 0.98 0.9831
S11 17-22 Mar. 1973 Storm, U. S. East
Coast
Slla New York 7.5 16.4 17 22,102 1.02 0.9758
Sllb New Jersey 5.3 12.5 16 19,630 0.78 0.9909

S12 Nov-Dec. 1973 Events, German 31.0 92944
North Sea Coast

4 Huricane Eloise Sep. 1975, N. W. 16.0 29.8 72 39,628 1.86 0.9557
Florida Gulf Coast
S14 14 Oct. 1977 Storm, U. S. East Coast 15.5 31.6 22 43,085 1.97 0.9890
19 Dec. 1977 Storm, U. S. East
515 1977toEast 11.8 23.4 20 51,356 1.46 0.9890
Coast
316 6 Feb. 1978 Storm, U. S. East Coast 12.3 30.5 17 42,979 1.90 0.9940

517 No Name Storm, 17-18 Jun. 1982, 14.0 25.8 24 21,111 1.61 0.9917
Lower Florida Gulf Coast

S18 Thanksgiving Holiday Storm, 21-24 14.6 32.4 128 52,388 2.02 0.9807
Nov. 1984, Florida East Coast
H8 Hurricane Elena, Sep. 1985, Florida
Gulf Coast
H8b Franklin County 10.3 31.6 34 54,456 1.97 0.9661
H8c Gulf County 7.1 18.9 30 45,579 1.18 0.9958
H8d Escambia County 4.2 11.4 58 34,653 0.71 0.9459
H9 Hurricane Kate, Nov. 1985, N. W. 8.7 22.0 13 47,481 1.37 0.9247
Florida Gulf Coast
Note: The time between pre-storm and post-storm surveys, and comments are given in Table 2; data sources
are listed in Table 1.

due to inertial effects is less
response oriented under lower slope
subaqueous than steeper slope subaerial
littoral conditions. The result is a partitioning
of sediment transport between kinetic energy
(i.e., by virtue of low-slope, near horizontal
motion due to shore-normal subaqueous
sediment transport mechanics) and potential
energy (i.e., by virtue of subaerial elevation
of dunes and bluffs and potential
gravitational mass wasting due to wave
impacts propagating upon an elevated water
level). Based upon this logic, it would appear
that the diminished effect of the acceleration
of gravity is not unwarranted, because it
probably relates more to spreading rates
across the nearshore than to dune or bluff
mass wasting. The latter is essentially
instantaneous, while the former is time-
consuming. In fact, the prototype wave tank
results of Dette and Uliczka (1987) appear to
provide some elucidating information. First,
their results show that the pre-impact
nearshore bed slope correlates with the
magnitude of beach and coast erosion
volumes and the rate of erosion.
Specifically, the steeper the pre-storm
nearshore bed slope, both the greater the
erosion volume above SWL, and the faster
the removal rate. Second, regular and

irregular waves appear to erode
and coast at different rates.

Dette and Uliczka (1987)
report prototype results for initial
nearshore bed slopes of 0.25 and
0.05, and Saville (1957) for a
slope of 0.0667. U. S. East and
Gulf Coast natural nearshore
slopes (i.e., 300 to 800 m
offshore) are, however,
characteristically less than 0.02,
averaging about 0.016 for
Florida. Application of these data
relative to f the PDF coefficient
of equation (3), yields a
dimensionless proportionality
constant Y termed the offshore
sink efficiencyparameter (OSEP),

the beach

6
5
4
$3
2
1

according to:

T = -1 (tan a,)

where tan ai is the initial or pre-impact
nearshore bed slope, and:

0 = 2.07 + 13.2 tan a,

(10)

Data and fitted relationship leading to
equations (9) and (19) are plotted in Figure 9.
Results from equation (9) apply only where
the initial or pre-impact nearshore bed slope
is greater than 0.01638; where the initial bed
slope is less than 0.01638 the value of Y is
unity (i.e., 1.0). The final form of equation
(3) now becomes:

0, = ( (e31 (g112 t, S2)5

(11)

The validity of YJ can be tested using
data obtained from Hurricane Gilbert which
struck Cancun, Mexico in September, 1986.
While the accuracy of data for Hurricane
Gilbert is not touted to be of the standard for
the remainder of the data base presented
here (and in particular for the Florida data),
the magnitude of the event was so
overwhelming that it cannot be neglected;
best known data are listed in Tables 1 and 2.
A significantly important factor associated
with the Gilbert data are the very steep

h

o00l 005 O.I 0.5
tan ai
Figure 9. Tesselated relationship relating nearshore bed
slope (tanai which occurs from 300 to 800 m offshore of
the MSL shoreline) to the ELP coefficient .

S I.... . . . I I ,. .
Saville (1957) /
o Dette and Uliczka (1987)
Present study ,
-= --
.------- Y' = (tanai,) where
0 = 2.07 + 13.2 tanai for tanai> 0.016
= 12344-1 for tanai 0.016
0 ,I a

nearshore slopes off of Cancun as illustrated
in Figure 10. In fact, the nearshore slope is
over twice Vie., 222%) as steep as slopes
commonly found off U. S. East and Gulf
Coast nearshores. Such a slope is steep
enough that sand is not able to be
transported back onshore during post-storm
conditions. Hence, the steep offshore slope
becomes, for all practical purposes, a
sediment sink. Given the following data for
Hurricane Gilbert:

tan ai = 0.0363,

tr = 9.5 hours,
S = 3.81 m,

P = 0.68 (average erosion volume),
P = 0.925 (maximum erosion volume),

then:

and:

ELP = 89,782 m3/m,
OSEP = 2.578,

e3P = e3(/3) = 7.3891,

and,

e3P = e3(0.92) = 16.0386.

The adjusted ELP due to the effect of the

steeper nearshore and increased value of the
offshore sink efficiency parameter is the
product of the ELP and OSEP, resulting in a
value of 231,462 m3/m. The goodness of fit
of this result is illustrated in Figure 2.
Moreover, equation (11) results in an average
erosion volume (i.e., P = 2/3) of 144.5 m3/m
which is very close to the measured amount
of 144.7 m3/m, and a maximum erosion
volume (i.e., P = 0.925) of 313.6 m3/m
which is within 5.6% of the measured value
of 297 m3/m.

The final form of equation (5) for
volumetric erosion above the peak storm tide
level becomes:

O = (e ) 2 (gl t, s2

(12)

where by similitude, it is assumed that the
OSEP applies straightforwardly as in equation
(11) (field data are needed, however, for
confirmation).

Nearshore geometry is now commonly
quantified by a power curve (Dean, 1977;
Hughes, 1978; Balsillie, 1982a, 1987) given
by:

d= a, X4

(n MSL)

10 -- '--------

a 200 4W0 6410 lo0 w
Distance (M)
Figure 10. Comparison between a typical Florida
nearshore profile and a typical Cancun, Mexico nearshore
profile.

(13)

in which d is the water depth, and
x is the distance offshore. Using
the data of Saville (1957), Dette
and Uliczka (1987), and average
data for Florida, tan ai may be
approximately related to the shape
coefficient (Dean, 1977), as,
according to:

tana, = 0.5 aS52

(14)

illustrated in Figure 11 (as in
equations (11) and (12) has units
of m/3; if as is in units of ft/3
multiply the value by 0.673 to
obtain consistent S. I. units).

1 16 C.

Retum Period Volumeric
Erosion Events

The incidence of extreme phenomena
may require site-specific treatment. Such is
the case with the determination of the return
period storm tide which is dependent not
only on historical storm/hurricane
characteristics and water levels, but also,
importantly, on local conditions such as
offshore and nearshore bathymetries. A
major problem in following such an approach
for erosion responses is that site-specific
quantitative erosion data are historically
deficient. However, since uncertainties
about erosion make simplified considerations
the most appropriate (Hallermeier and
Rhodes, 1986), and because of the apparent
success of foregoing quantitative results, it is
assumed that physiographic responses to
storm attack need not be held to a
site-specific treatment.

Further, it has been a major tenet of
this and other works (Balsillie, 1985c, 1986)
that the storm tide return period event and
the storm erosion return period event are
seldom coincident. Until now there has been
insufficient information on which to specify
the probabilistic erosion event.

The frequency Pe used in plotting the
distribution is found (Gumbel, 1954) by
ranking the erosion volumes from smallest to
largest and then dividing the rank of each of
the sample size plus one, i.e.:

P, = 1 (15)
n+ 1

where m is the ranked value. If the theory
does hold, the points should plot as a
straight line on probability paper. The return
period Te is then given by:

r 1 (16)
1 P,

Using equations (15) and (16), the

0.1

tan ai 0os
i aos

W.,I

0 01

0.2 03 0.4 0.5 0h 0.7 OA

as (m1s)
Figure 11. Relationship between the initial
nearshore bed slope (tan ai occurring 300 to
800 m offshore of the MSL shoreline) and
the power curve fit shape coefficient, a,.

plot of Figure 12 is constructed using data
from Table 2. Only Atlantic Ocean events
are considered in this analysis. There are 35
events listed in Table 2 which apply. These
events occupy a 34-year period from 1957
through 1990. During this period some 324
tropical storms and hurricanes formed in the
Atlantic. Of these, about 104 (or 32% of the
total) landfalling or exiting events affected
the Americas along the U. S. East Coast, and
Gulf of Mexico coasts of the U. S. and
Mexico. It is assumed that the applicable 35
events of Table 2 represent a random sample
of erosion conditions. The 35 events,
however, represent only one-third of the
actual number of events that affected
coastal reaches. Therefore, for analytical
purposes, the 35-event sample is
triplicatedd" to yield 105 events (i.e., tripled
in size to more nearly represent the 104
events that actually occurred); only the mid-
point of each 'triplicate" is plotted to

J ------- ,--' ----- --! -

o1

Jo 0 I J j o.s as
/
I

I

-a or oe and Ulicka (1987)
/
/
/
/

I
/

P s 3u2
/
/I
/

/ Saville (1957)
a o Dette and Uliczka (1987)
p s Present Study

I, .

Segment A:
1.25
1 + 0.006 ev
eaVg

Segment C:
6 G.85
8.5 x 10. Q6 .5
(r 0.9629) To -

1000
500
200
100
50
20

To 10
Ta

(years) S

2

1.25

0 e avg
Figure 12. Relationship between exceedence
TYPE I erosion volume above MSL.

represent the associated probability and
return period. It is noted that three
straight-line segments are apparent for which
possible explanations have been suggested
(see Figure 12). Equations of immediate
interest for coastal construction design
purposes are:

1 + 0.0060 (17
aaq9 (17)

for segment A which describes extreme
events with a frequency less than about a 4-
year return period, where Qe avg is specified
in cubic meters per alongshore meter of
beach or coast (note: m3/m = 2.508
(yd3/ft)). Utilizing, by substitution, equation
(6) the corresponding probability of equation
(17) is given by:

(18)

P, = 1 (I 0.006

(m'/m)
probability P, return

0, =60 [(In 7,) -1]o.-

period T,, and average

(19)

By incorporating results from equation (6),
the design maximum erosion volume (i.e., for
P = 0.925) results in a factor of 2.1 and:

Oen= = 126 [(In T,) -1]

(20)

For segment B of Figure 12, which
describes events between about 1.25- and 4-
year return occurrences, the return period is
given by:

0.00033 02.,
r= e

(21)

for which equations corresponding to (18),
(19), and (20), become:

S1 (e1 0*00 o (22)
\

Further, by rearranging equation (17), the
return period erosion quantity in m3/m may
be determined according to:

Segment 8: -
0.00033 00 a
7 S (r a 0.9786) *
A
e e The peak stuona tide rose above theme rc/cosst npckpoint
elevetion o nd the prollie was 61hwr nonwallded or
breached, resuliag kI both besch and coast rosion.
Th pea* storrm did not rise abore the beach/lcomet nctkpnat
eslovatloa but purelAted to result la both beach sed cost
eroslon or the promise wan oIOdm. -

C The peak stelonn nti Oe not rile ebov* the beach/el*st niekpait
elevation end dM not peraslt. eswun las beachn eroon only.
I I I I I I I I I j

(r 0.9905)-

I 1

1] 0.A16

and:

(23)

5 1 1 1 1 1 1 1 1 11 I I

1 50 100 1

0.999
0.998
0.995
0.99
0.98
0.95
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.05
0.02
i0

I!

0,,., = 25 [(In T,)

0 a, =53.5 [(In T.)

1 ]0.4016

Following this methodology, similar
equations may be developed for segment C
that represent events occurring more often
than the 1.25-year return period (see Figure
12).

There is simply not yet sufficient field
data to reliably determine return period
volumetric erosion events for erosion above
the peak combined storm tide level (in
particular for that portion corresponding to
segment A of Figure 12). However,
statistics indicate that erosion volumes above
the peak storm tide level, on the average are
about one-half those above MSL. Hence, in
the interim, a reasonable estimation may be
determined by doubling the value of
Q'e avg and using equations (17) through
(24).

The quantifying equations developed
in this section are of special consequence.
Past return period damage elements have
been assessed in terms of forces, specifically
the combined storm tide elevation and wave
heights. Now, for the first time, a return
period response element in terms of erosion
is provided which accounts for all the force
elements, including longevity of the event. It
is envisioned that these equations will be
highly valuable in design and coastal
management activities.

One might be inclined to believe that
the developed approach is based upon broad
assumptions (e.g., global continuity in littoral
physiography) and a limited sample size.
Recognize, however, that errors creep into
design computations due to assumptions
about convoluted littoral processes. At
present, and at a minimum, equations (17)
through (24) would seem to provide
information as a valuable check for the more
involved design computations (methodology
for application of volumetric erosion volumes
is discussed in the conclusions).

It is, however, notable that Figures 11
and 12 support the significance of
physiographic zonation between the beach
and coast.

Post-Storm Recovery

There seems to be considerable
interest among coastal scientists and
engineers in post-storm littoral recovery,
even though we are just now quantifying
details about magnitudes of physiographic
responses during the "height" of extreme
event impact. While there exists some
quantifiable representation of such recovery
(Balsillie, 1985d, in manuscript), additional
work remains. Generally, based on what is
known about littoral processes, we can
endeavor to find discernible and logical
conclusions about such recovery. Again, it
becomes of importance to delineate littoral
subzones (see Figure 1), namely, ... 1. the
nearshore, 2. the beach, and 3. the coast. It
is these three subzones which interactively
define the extent of both extreme event
impacts and what are discernibly "normal" or
"day-to-day' littoral processes.

The nearshore, which is always
subject to the effects of astronomical tides
and waves, is expanded when a rising storm
tide encompasses the beach, and, under
design conditions, the coast. That longshore
bars are formed during extreme event impact
has been a controversial issue. The problem
is, of course, that nearshore subaqueous
behavior has not been adequately monitored
to yield confident quantification during
extreme event impact. However, based on
additional considerations and tested data
(Balsillie, 1984c, 1985d), and field
observations (Dette, 1980; Birkemeier, 1984;
Sallenger and others, 1985), the formation of
longshore bars during extreme event impact
seems more nearly to be the case.
Ramifications of the concept are not only
essential towards a new understanding of
coastal engineering design constraints that
might be required, but of interactive littoral

forces and responses that could occur during
extreme event impact (bearing in mind that
extreme prospects are probabilistic).

Further, longshore bars are nature's
own protective device. During storm action
they not only are formed but move offshore
(Short, 1979; Birkemeier, 1984; Mason and
others, 1984, Sallenger and others, 1985),
causing storm waves to break further
offshore than would normally occur. By
inducing breaking they cause the greatest
amount of energy dissipation that water
waves can experience and, should wave
reformation occur, significantly reduce the
elevation of destructive wave energy (.e.,
reformed wave heights are attenuated; Carter
and Balsillie, 1983; Balsillie 1984b, 1985b).

During storm impact, the width of the
surf zone dramatically increases. When,
following impact, surf width again attains
"normal' width the bar(s) within the
"normal" surf zone move onshore in a few
days. Outer bars either remain as relict
features or disappear, although the latter
requires months to occur (Birkemeier, 1984;
Mason and others, 1984; Sallenger and
others, 1985).

Beach (or shore) recovery appears to
be considerably more rapid than has been
presupposed by many coastal engineers.
Although complexities occur (e.g., longshore
transport) which can produce a large range in
values, it is now quite clear that beach
recovery often occurs within days.
Birkemeier (1979)found for the 19 December
1977 U. S. east coast storm (event S 15) that
from 38% to 100% beach recovery occurred
within one or two days following event
impact. Bodge and Kriebel (1985)also report
rapid recovery for beaches following impact
of Hurricane Elena in Pinellas County, Florida
(event H7a). Such rapid beach recovery
agrees with response time scales of
post-storm nearshore profile changes.

The coast is of special interest

because it is detrimentally affected only
during extreme event impact (or man's
activity). Where high sandy dunes or bluffs
exist, the coast affords substantive
protection to the upland. It is nature's
physiographic reserve of particulate mass,
drawn upon to replenish the more active
beach subzone, when beach subzone
dimensions are diminished.

Of the three sub-zones, the coast in
its natural state can be expected to
experience no immediate recovery. An
example is Dauphin Island, Alabama struck
by Hurricane Frederic in 1979, destroying
dunes which attained heights of up to +10
m MSL. Average volumetric dune losses
were about 50 m3/m. Assuming the sand
supply is available and that vegetation is
instrumental in natural dune reconstruction,
then based on the data of the U. S. Army
(1984) and Dahl and others (1975), natural
dune reconstruction would require 70 to 75
years for American Beach Grass and Sea
Oats, respectively, and 180 years for
Panicum (Balsillie, 1979a).

APPUCA TONS

The results of this work deal with
volumetric erosion of the beach and coast
due to extreme event impact. This
comprises, however, but one aspect of
interrelated natural processes in terms of
force and response elements that occur
within nearshore, beach, and coast
subenvironments of the littoral zone. Other
aspects include storm wave activity which is
instrumental in causing the erosion,
producing dynamic and impact loads on
exposed structural members, and forming
longshore bars that house sand eroded from
the beach and coast. These various aspects
are quantified and discussed in a series of
papers, the sum total of which actually
describe the entire Multiple Shore-Breaking
Wave Transformation Erosion computer
model (Balsillie, 1984c, 1985d). This
approach allows one to more succinctly

manage research by dealing with discrete or
sets of discrete natural process units, and
also facilitates updating of each manageable
unit as new developments are made. Even
so, it is recognized that some guidance
would be helpful to describe how the
predicted volumetric erosion can be
practically applied.

Post-Storm Beach and Coast
Physiography

The problem in applying volumetric
erosion quantities, is the determination of the
resulting physiography of the profile. For the
two-dimensional case, the following
simplified methodology is suggested as
illustrated in Figure 13 (discussed by Balsillie
1984c, 1985d). Following determination of
the design erosion volume, plot the pre-
impact coast, beach, and nearshore profile.
The nearshore profile shape in Florida can be
determined using the power curve form
according to Balsillie (1982a, 1982b, 1987).
Plot the bar crest envelope, db (i.e., the line
connecting the crests of longshore bars
formed during the event) and the
corresponding bar trough envelope, dbt (.e.,
the line connecting the bar troughs,
according to:

d (S + a, x) (25)

where S is the peak combined storm tide, a,
is the shape coefficient given by Balsillie
(1982b) for Florida, and Xbc is the distance
offshore measured from the pre-storm MSL
shoreline, and:

dt = S + (x + 7 S)2s (26)
5

where xbt is the distance offshore measured
from the pre-storm MSL shoreline.

Inspection of post-storm profiles
indicates that the portion of the eroded
profile above the peak storm tide (segment

AB lying above the nickpoint of Figure 13)
has a 1 on 1 slope. The segment BC is a
slightly curved line smoothly continuing the
bar trough envelope to the nickpoint (where
the coast is flooded only segment BC
applies). Starting at the pre-impact shoreline,
segment ABC (or segment BC where the
coast is flooded) is iteratively moved
landward until the erosion volume is attained
(shaded area of Figure 13).

Nearshore wave heights are
determined using the bar crest envelope to
represent the water depth at breaking, db
(Balsillie, 1983b, 1984b, in press). The
amount of the breaking wave height lying
above the peak storm tide still water level,
Hb', has been determined from field data
(Balsillie, 1983d, 1985b, in press) to be
given by:

H' = 0.84 H,

(27)

in which Hbx is the average height of the
desired moment measure. The breaker
height envelope illustrated in Figure 13,
represents the significant height. Relating
equations developed by Balsillie and Carter,
1984a, 1984b) for other moment measures
commonly used in design work are:

b ,,, = 1.02 Hb

(28)

where Hb rms is root-mean-square breaker
height, and Hb is the average breaker height;

H,, = 1.23 H,

(29)

in which Hbs is the significant breaker height
(i.e., average of the highest two-thirds of the
height record);

Hbo = 1.37 Hb

(30)

where HblO is the average of the highest
10% of the wave record; and:

I I r I A
a011

| I I I I
Measured Data
Pre-Storm Profile
- -- Post-Storm

MSL = Mean Sea Level
PST SWL = Peak Storm Tide Still Water Level

led Volume above MSL

A D Er

1:1 Slope
N: S10po it :, ..:... .---

- Nlckpoint MSL

- -
Prediced Dat

Predicted Data
- Post-Storm Erosion Profile
-Bar Trough Profile
S- Bar Creet Profile
....... Significant Breaker Height Envelope

I a I I I 1

nor attI

1 I I I I

-60 -so -40 -30 -20 -10 0 5 10

15 20 25

Distance from Pre-Storm Shoreline (m)
Figure 13. Example of application for determining two-dimensional post-storm physiography
using volumetric data, and design wave conditions.

H. H,, = 1.57 H, (31)

in which Hbl is the average of the highest
1% waves of record.

Encounter Period and Probabhty

A return period statistic is one
providing a measure of the probability of
annual occurrence. For instance, an event
with a 100-year return period has a
probability of 0.01 or a chance of 1%
occurrence in any given year, an event with
a 5-year return period has a probability of
0.20 or a 20% chance of occurrence in any
given year, etc. Even if the return period
occurrence occurs during an annual period,
its probability of recurrence remains the same
within the current annual framework.

The above often leads to confusion,
particularly when one tries to relate such

statistics to the design life of a project.
What we really wish to do is transform the
return period statistic to one of encounter
probability, based upon a specified encounter
period.

The solution is the use of Figure 14.
The abscissa of Figure 14 gives the
EncsonterPerid which is the period of time
for which a project is to last (i.e., its design
life). In the case of single-family dwelling
design, the encounter period might be 50
years representing a depreciation period for
tax purposes, etc. The ordinate of Figure 14
gives the Erncoeater Probabhity which
represents the assigned return period equaled
or exceeded during the selected Enctouter
Period. Curves internal to the graph are for
various Retun Perids associated with the
design event.

Following is an example of how to use
the figure. Suppose that you would like to

-

i

r

. . .- . . . . ... . . . . . . . . . . . . ...

r~l YIL

1 5 10 50 100 500 1000

Encounter Period (Years)
Figure 14. Nomograph for relating event return period, encounter period, and
encounter probability.

build your single-family beach-fronting
dwelling so that it is relatively safe from the
100-year return period erosion-event. The
probability of a 100-year return period
occurrence being equaled or exceeded during
the above assigned 50-year period (i.e.,
Encounter Period) is 0.4, as illustrated in
Figure 14. Hence, there is a 40% chance
that the 100-year return period erosion event
will occur in the planned life time of the
home. Had the dwelling been designed for
a 500-year return period erosion event, the
structure would have a much better chance
of surviving the critical event ... then only a
10% chance of occurrence during its planned
life.

Using the figure in another manner, if
a homeowner or prospective home owner is
willing to take a 20% chance that the design
erosion event will occur during the 50-year
design life of the structure, then the Retrn
Period of the erosion event that should be
designed for is 250 years.

The above example uses the return
period erosion event. However, Figure 14

can also be used for any other measure (e.g.,
peak combined storm tide, wave event,
event forward speed, etc.) provided that
return period statistics are quantified.

An Erosion Damage Potential Scale

A beach/coast erosion damage scale
for extreme events has not, here-to-fore,
been proposed. Perhaps the best way in
which to assess an erosion damage potential
scale is to build upon the existing
Saffir/Simpson hurricane damage potential
scale (Table 4). Volumetric erosion is
assessed using equation (1) for average
erosion quantities and equation (7) for
maximum erosion quantities. The
assessment of Table 4 is, therefore,
applicable to the U. S. Atlantic East Coast
and the U. S. Gulf of Mexico Coast which
have relatively low nearshore slopes (i.e.,
where tan ai is characteristically less than
0.02). Equations (1) and (7) were evaluated
using the Saffir/Simpson peak storm tide
(commonly termed the "storm surge")
classes of values. Event forward speed
classes were determined using the historical

Table 4. Amended Saffir/Simpson Hurricane Damage Potential Scale
Peak Storm
Peak Event Storm Average Maximum
Category Prure Spd Eltion Forward Rie Erosion Erosion Damage
Category Pressure Speed Elevation Speed Rise Volume Volume Potential
(mb) (km/hr above Thme (m3/m) (m /m)
MSL (m) (hr)
1 >980 46-59 1.22-1.68 50-90 2.5-4.5 3-8 6.5-17 Minimal
2 965-979 60-68 1.68-2.60 30-50 4.5-7.5 8-25 17-53 Moderate
3 945-964 69-81 2.60-3.81 20-30 7.5-11 25-63 53-132 Extensive
4 920-944 82-96 3.81-5.49 10-20 11-22 63-188 132-395 Extreme
5 <920 >96 > 5.49 <10 >22 >188 >395 Catastrophic

data of Schwerdt and others (1979). Storm
tide rise time was then determined using
equation (2).

The Saffir/Simpsonscale assessed the
damage potential in terms of the wind speed
and peak storm tide. There is, in fact, sound
reasoning for doing so, since both are largely
dependent on event central pressure.

The same is not true of the event
forward speed because the three-dimensional
geometry of surrounding weather systems
and conditions affect steering currents.
Hence, factors other than central pressure
have significant effect on the propagation of
a hurricane.

There are two additional issues to be
considered.

One is that it may be difficult to
envision just what a volumetric erosion value
means in terms of erosion damage for a
specific coastal locality, unless cross-
sections representing pre-storm and post-
storm profiles are assembled. A horizontal
recession value rather than a volumetric
erosion value is an alternative, but this was
found to result in many more problematic
complexities than the volumetric approach
(Balsillie, 1985c, 1986). Hence, while
volumetric erosion values may not obviously
identify the damage potential, they can be
correlated to the Saffir/Simpson hurricane

category and damage potential scale to
provide a pragmatically useful addition to the
scale.

The other issue centers about the fact
that extreme events with much lower
intensities than hurricanes (e.g., tropical
storms, which are here identified under the
collective term "storms') can potentially
result in as much or more erosion than many
hurricanes (see Table 2). An example is a
storm which essentially stalls just offshore
for days. Hence, Figure 15 has been
compiled which, based on event forward
speed and peak storm tide elevation, can be
used to assess erosion damage potential
whether the event is a hurricane or a storm.

Table 4 and Figure 15 are transformed
to British Imperial Units and given in the
Appendix.

CONCLUSIONS

Analyzed information for storms (e.g.,
Birkemeier and others, 1988; Kana and
Jones, 1988; Jones and Kana, 1988; Beumel
and Campbell, 1990; Ferriero, 1994) and
more recent hurricanes (e.g., Birkemeier and
others, 1991; Stauble and others, 1991;
Nelson, 1991) has increased the existing
sample size of Balsillie (1985c, 1986) for
field data quantifying beach and coast
erosion due to extreme event impact. This
addition data allows for testing of a

Rgure 15. Beach and coast erosion damage potential scale as a
function of event forward speed at landfal and peak storm tide
elevation. Erosion volumes are based on peak storm tide
elevation classes of Table 4; even so, results apply to storm
events as wel as hurricanes.

refinement of quantifying relationships.

A most important aspect of being able
to predict beach and coast erosion due to
storm and hurricane impact is the capability
to assess profile geometry during and as a
result of impact. By so doing, coexisting
storm-generated wave activity propagating
upon the storm tide surface can be assessed
for management and design purposes. The
fact remains, regarding waves and their
modifying influence on a mobile bathymetry,
that any change in wave characteristics
induces an alteration in bathymetry but at a

lag-time behind a change in wave
characteristics. Because of the bathymetric
lag-time, bathymetry can in turn impose
significant influential effects on the character
of littoral wave activity. Hence, in addition
to erosive outcomes, it is the destructive
potential of storm-generated wave impacts
that also must be considered if a successful
assessment methodology is to exist.
Determination of profile geometry is then a
matter of modeling interactive littoral
processes, that is, both force (e.g., water
level rise and waves) and response (e.g.,
profile modification) elements. A computer

model exists (Balsillie, 1984c, 1985c,
1985d, 1986) in which a bulk
onshore-offshore sediment transport
mechanism, in terms of bedform movement
has been developed (Balsillie, 1982a, 1982b,
1984b, 1984c), which is dependent on
littoral wave activity (Balsillie, 1983a,
1983b, 1983c, 1983d, 1984a, 1984b,
1984c,1985b; Balsillie and Carter, 1984a,
1984b). It is the volumetric erosion
methodology contained herein which allows
for the real-time calibration of the combined
assessment of combined storm tide, storm
wave impact, horizontal and vertical
physiographic recession force and response
elements due to extreme event impact. In
addition, there now appears to be enough
information to make a statement about the
return period erosion event. Least equivocal
results given by equations (17) through (24)
will, hopefully, be refined by future work. In
the meantime, however, they are valuable as
a check in design applications.

In addition, applications of the
volumetric erosion methodology have been
discussed, including the determination of
post-storm beach and coast physiography,
encounter period and probability, and an
erosion damage potential scale.

ACKNOWLEDGEMENTS

Robert J. Hallermeier with Dewberry
and Davis, Inc., Washington, D. C., identified
several storm erosion events not included in
earlier versions of this work, and reviewed
the manuscript. The review and comments of
William A. Birkemeier, CERC, are gratefully
acknowledged.

An extensive and valuable review of
the manuscript was conducted by the staff
of the Florida Geological Survey. The
contributions of Jon Arthur, Paulette Bond,
Ken Campbell, Ed Lane, Jacqueline M. Lloyd,
Deborah Mekeel, Frank Rupert, Thomas M.
Scott, and Walter Schmidt are gratefully
acknowledged.

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SI0O

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APPENDIX

Table 4 and Figure 15 of main text transformed to British Imperial Units of Measure

Amended Saffir/Simpson Hurricane Damage Potential Scale
Peak
Storm
Central torm Event Average Maximum
ate- Te Foward Erosion Erosion Damage
gory (hes) p Bevation Speed Tie Vokme Volume Potential
above (mph) (hr) (yds3ft) (ydas3/ft)
MSL (ft)

> 28.94
1 > 8 74-95 4-5.5 31-55 2.5-4.5 1.2-3.3 2.5-7 Minimal
(>980)
28.50-28.91
2 .5 .9 96-110 5.5-8.5 18-31 4.5-7.5 3.3-10 7-21 Moderate
(965-979)

27.91-28.47
3 .47 111-130 8.5-12.5 12-18 7.5-11 10-25 21-53 Extensive
(945-964)

27.17-28.88
4 27 -2 131-155 12.5-18 6.5-12 11-21 25-75 53-158 Extreme
(920-944)

<27.17
5 (<920. >155 >18 <6.5 >21 >75 >158 Catastrophic
(<920)

SCentral pressure in parentheses are in millibars.

Beach and coast erosion damage potential scale as a function of event forward speed
and peak storm tide elevation, both at landfall. Erosion volumes are based on peak
storm tide elevation classes of above table; results, however, apply to storm events as
wel as hurricanes.

Peak Storm Tide Elevation (ft MSL)
2 4 6 8 10 12 14 1 6 18 20
55

4s MINIMAL .
S... ....... . . ........ ....... .. ..-.......... ... ..... -- ----- ......... ...... .

I 30 I MODERATE
E .. .................. ... ...... ..... ...... ......... ........ ...... ..........
S......... .. ......... i........ .. .................. ...... ............. ......... ......... ........
L 20
. .......... .A... .... ...
S12 / EXTENSIVE
.... . . ......... . ...... .. ....................... .. ...
u. 10
Iis

.. .M ". ...... .............. ...... ..
4
. . . . . . .... . .... . . ... . .. .7 . . ... .. . . i ... . . - - --

.." T....... ... ........ ... . ....... .....
i 6 ./ i/i EXTREME .-

2 i CATASTROPHIC
........ ......... .... ... . .. ............. ..

	Front Cover
	Table of Contents
	Main
	Reference
	Appendix

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