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 Report documentation page
 Title Page
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction
 Concepts
 Methodology
 Results
 Summary and conclusions
 Acknowledgements and reference...






Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 88/009
Title: Realistic economic benefits from beach nourishment
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Permanent Link: http://ufdc.ufl.edu/UF00076123/00001
 Material Information
Title: Realistic economic benefits from beach nourishment
Series Title: UFLCOEL
Physical Description: 29 p. : ill. ; 28 cm.
Language: English
Creator: Dean, Robert G ( Robert George ), 1930-
University of Florida -- Coastal and Oceanographic Engineering Laboratory
Publisher: Coastal & Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1988?
 Subjects
Subject: Shore protection -- Economic aspects   ( lcsh )
Beaches -- Protection -- Economic aspects   ( lcsh )
Coastal engineering   ( lcsh )
Coastal and Oceanographic Engineering thesis M.S
Coastal and Oceanographic Engineering -- Dissertations, Academic -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Bibliography: p. 29.
Statement of Responsibility: by Robert G. Dean.
General Note: Cover title.
Funding: This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
 Record Information
Bibliographic ID: UF00076123
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: oclc - 19476437

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Table of Contents
    Report documentation page
        Unnumbered ( 1 )
        Unnumbered ( 2 )
    Title Page
        Page 1
    Table of Contents
        Page 2
    List of Tables
        Page 3
    List of Figures
        Page 4
        Page 5
    Abstract
        Page 6
    Introduction
        Page 7
    Concepts
        Page 7
        Page 9
        Page 8
        Page 10
        Page 11
    Methodology
        Page 12
        Page 13
        Page 14
        Page 11
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
    Results
        Page 24
        Page 25
        Page 26
        Page 27
    Summary and conclusions
        Page 28
        Page 29
    Acknowledgements and references
        Page 29
Full Text


REPORT DOCUMENTATION PAGE
1. Report No. 2. 3. Recipient's Accession No.


4. Title and Subtitle 5. Report Date
REALISTIC ECONOMIC BENEFITS FROM September 1988
BEACH NOURISHMENT 6.

7. Author(s) 8. Performing Organization Report No.
Robert G. Dean UFL/COEL-88/009
9. Performing Organization Name and Address 10. Project/Task/Work Unit No.
Coastal and Oceanographic Engineering Dept.
University of Florida
336 Weil Hal 11. Contract or Grant No.
336 Well Hall
Gainesville, FL 32611 1. Te o
13. Type of Report
12. Sponsoring Organization Name and Address
Miscellaneous


14.
15. Supplementary Notes



16. Abstract

A method is presented and illustrated with examples to establish
appropriate storm damage reduction and recreational benefits from
beach nourishment projects. Unlike previous methods, benefits to
project adjacent areas are recognized due to sand transport out of the
project area and deposition on adjacent beaches. Assuming homogeniety
along the shoreline, the character of storm damage reduction and
recreational benefit relationships are such that sand transported from
a project area and deposited on adjacent beaches always results in an
increase rather than a reduction in benefits. A central element in
calculating storm damage reduction benefits is the establishment of a
proportional damage curve for upland structures as a function of beach
width and storm return period. To illustrate the method, limiting
cases are presented in which (A) all sediment remains within the area
placed, and (B) all sediment spreads out immediately over a long
segment of shoreline. Using Monte Carlo simulation to represent the
random character of the storms, the method is applied to 15 realistic
cases with varying project lengths, representative wave heights, added
beach widths and interest rates. The present worth storm damage

continued -

17. Originator's Key Words 18. Availability Statement
Beach nourishment
Damage reduction
Nourishment benefits
Recreational benefits
Storm damage
19. U. S. Security Classif. of the Report 20. U. S. Security Classif. of This Page 21. No. of Pages 22. Price
Unclassified Unclassified 29










reduction and recreational benefits are calculated to demonstrate the
effects of the various parameters. It is found that for short project
lengths and relatively large wave heights, the benefits from project
adjacent areas exceed those in the project area where the sand is
placed. Although no littoral control structures, such as jetties are
included in the present application, the method could be extended
readily to include their effects.









UFL/COEL-88/009


REALISTIC ECONOMIC BENEFITS FROM BEACH NOURISHMENT

by


Robert G. Dean










TABLE OF CONTENTS

PAGE

LIST OF TABLES.............................................. 3

LIST OF FIGURES ............. ....... ....... ..... ............. 4

ABSTRACT. .............................. .. ................... 6

INTRODUCTION.................................... .......... 7

CONCEPTS ... .............. ....... .......................... 7

METHODOLOGY ...... ................ ......................... 11

Shoreline Evolution Model............................. .. 15

Storm Damage Reduction Benefits........................ 15

Idealized Cases.......................... ............... 20

Case (A). ... ......... ............. .............. ...... 22

Case (B) ...... ......... .... ..... ... ............... .... 22

Case (A) ................... ........ .................... 22

Case (B) ..................................... .......... 22

RESULTS .................................................... 24

SUMMARY AND CONCLUSIONS..... .............................. 28

ACKNOWLEDGEMENTS. ............... ......... .. ................ 29

REFERENCES.... ........... ..... .................. ........... 29










LIST OF TABLES


TABLE


PAGE


I. PRESENT WORTH DAMAGE FUNCTION, PWDF(w,-) VERSUS
BEACH WIDTH, w, FOR ALL FUTURE DAMAGE ..................

II. PRESENT WORTH STORM DAMAGE AND RECREATIONAL BENEFITS
FOR VARIOUS WAVE AND PROJECT CONDITIONS ................










LIST OF FIGURES


FIGURE PAGE

1. Structural Damages Due to Hurricane Eloise (1975)
and Example of Reduced Damages by Beach
Nourishment Advancing the Shoreline Seaward by
Fifty Feet ........................................ 9

2. Damage Reduction Per Structure Resulting from a
One Foot Wide Additional Beach, as a Function of
Structure Location Relative to Control Line. Based
on Hurricane Eloise Data........................... 10

3. Hypothetical Usage and Recreational Benefits of
Sandy Beaches....................................... 12

4. Annual Recreational Benefits Per Additional Foot of
Beach Width as a Function of Initial Beach Width,
Per Foot of Beach Length. Developed from
Figure 3b........................................... 13

5. Schematic of Erosion of Nourished Area and Deposition
in Project Adjacent Areas........................... 14

6. Example Solution of Evolution of Initially
Rectangular Beach Planform. Pelnard Considere
Method. Wave Height, Hb = 2.0 ft, Initial
Nourished Beach Width = 100 ft, Fill Length,
X = 4 miles, t = time............................... 16

7. Hypothetical Proportional Storm Damage, D, as a
Function of Storm Return Period, TR, and Beach
Width, w.................. .............. ............ 17

8. Flow Chart of Methodology........................... 18

9. Expected Damage D(w) Due to a Single Storm as a
Function of Beach Width, w.......................... 21

10. Interpretation of Damage Reduction Benefits if
Sand Remains Where Placed (Case A) and if Sand
Spreads Out Immediately (Case B).................... 21

11. Ratio of Storm Damage Benefits, RSD, vs Initial
Beach Width, wo, and Additional Beach Width, Aw.
RSD is Ratio of Storm Damage Benefits for Sand Which
Spreads Out Immediately to Those for Which Sand
Remains Where Placed............................... 23









PAGE


12. Ratio of Recreational Benefits, RRB, vs Initial
Beach Width, wo, and Additional Beach Width, Aw.
RRB is Ratio of Recreational Benefits for Sand
Which Spreads Out Immediately to Those for Which
Sand Remains Where Placed........................... 23

13. Present Worth Storm Damage Reduction and Recreational
Benefits. Hb = 2.0 ft, A = 2.0 miles, wo = 0.0,
Aw = 100.0 ft., Interest Rate = 8%, Run No. 5....... 26

14. Present Worth Storm Damage Reduction and Recreational
Benefits. Hb = 1.0 ft, = 4.0 Miles, wo = 0.0,
Aw = 100.0 ft, Interest Rate = 8%, Run No. 7........ 26









REALISTIC ECONOMIC BENEFITS FROM BEACH NOURISHMENT
by
Robert G. Dean


ABSTRACT


A method is presented and illustrated with examples to
establish appropriate storm damage reduction and recreational
benefits from beach nourishment projects. Unlike previous
methods, benefits to project adjacent areas are recognized due to
sand transport out of the project area and deposition on adjacent
beaches. Assuming homogeniety along the shoreline, the character
of storm damage reduction and recreational benefit relationships
are such that sand transported from a project area and deposited
on adjacent beaches always results in an increase rather than a
reduction in benefits. A central element in calculating storm
damage reduction benefits is the establishment of a proportional
damage curve for upland structures as a function of beach width
and storm return period. To illustrate the method, limiting
cases are presented in which (A) all sediment remains within the
area placed, and (B) all sediment spreads out immediately over a
long segment of shoreline. Using Monte Carlo simulation to
represent the random character of the storms, the method is
applied to 15 realistic cases with varying project lengths,
representative wave heights, added beach widths and interest
rates. The present worth storm damage reduction and recreational
benefits are calculated to demonstrate the effects of the various
parameters. It is found that for short project lengths and
relatively large wave heights, the benefits from project adjacent
areas exceed those in the project area where the sand is
placed. Although no littoral control structures, such as jetties
are included in the present application, the method could be
extended readily to include their effects.









INTRODUCTION

Policies and methodologies should evolve continuously to
remain consistent with modern understanding of coastal processes
and the true equities of those residing along the shoreline.
Several changes have occurred in the last few decades that argue
for an examination and modifications of present economic analysis
procedures relating to beach nourishment: (1) It is now clear
that on a long, uninterrupted shoreline, good quality sand placed
in a beach nourishment project will eventually be transported out
of the region placed, but will remain within the active nearshore
system, (2) Sand transported from a project area and deposited on
project adjacent areas provides not only continuing damage
reduction and recreational benefits, but provides enhanced
benefits, and (3) With increasing concern over the use of "hard
structures" as a means of shoreline control, beach nourishment
will play an increasing future role.

This paper considers the economic consequences of sand
eroded from a beach nourishment project area and deposited on
project adjacent areas. Realistic damage reduction relationships
and recreational benefits for a widened beach are utilized to
demonstrate that this evolution process actually results in a net
increase in project benefits. Benefits from simple limiting cases
are examined in which (1) the sand remains in the area placed,
and (2) the sand spreads out immediately. A direct procedure is
presented to account for total present worth project benefits.
The procedure utilizes Monte Carlo simulation to faithfully
represent the probability of storm occurrences.

Although the methodology presented here is not applicable to
shorelines which include features which would cause longshore
sediment transport interruptions, the concepts could be extended
readily for such cases.


CONCEPTS

There are two simple concepts which are critical to the
methodology presented here:









INTRODUCTION

Policies and methodologies should evolve continuously to
remain consistent with modern understanding of coastal processes
and the true equities of those residing along the shoreline.
Several changes have occurred in the last few decades that argue
for an examination and modifications of present economic analysis
procedures relating to beach nourishment: (1) It is now clear
that on a long, uninterrupted shoreline, good quality sand placed
in a beach nourishment project will eventually be transported out
of the region placed, but will remain within the active nearshore
system, (2) Sand transported from a project area and deposited on
project adjacent areas provides not only continuing damage
reduction and recreational benefits, but provides enhanced
benefits, and (3) With increasing concern over the use of "hard
structures" as a means of shoreline control, beach nourishment
will play an increasing future role.

This paper considers the economic consequences of sand
eroded from a beach nourishment project area and deposited on
project adjacent areas. Realistic damage reduction relationships
and recreational benefits for a widened beach are utilized to
demonstrate that this evolution process actually results in a net
increase in project benefits. Benefits from simple limiting cases
are examined in which (1) the sand remains in the area placed,
and (2) the sand spreads out immediately. A direct procedure is
presented to account for total present worth project benefits.
The procedure utilizes Monte Carlo simulation to faithfully
represent the probability of storm occurrences.

Although the methodology presented here is not applicable to
shorelines which include features which would cause longshore
sediment transport interruptions, the concepts could be extended
readily for such cases.


CONCEPTS

There are two simple concepts which are critical to the
methodology presented here:









S200
00

WL" 160


< 120-


4- 80- CL


0 II

-150 -100 -50 0 50 100 150

Seaward 1 Landward
DISTANCE FROM CONTROL LINE (ft)
a) Damage to Structures in Relation to their Location with
Control Line (Resulting from Study of 540 Structures in Bay
County after Hurricane Eloise, by Shows, 1978).

0 200

W -
o 160


L 120
wU Reduced Damages
c D Damage Curve
W M Shifted by 50 ft
> !- 40
40

0 00-
150 100 50 0 50 100 150

Seaward Landward
DISTANCE FROM CONTROL LINE (ft)
b) Damage Reduction Due to Beach Nourishment Advancing the
Profile Fifty Feet Seaward.

Figure 1. Structural Damages Due to Hurricane Eloise (1975) and
Example of Reduced Damages by Beach Nourishment Advancing the
Shoreline Seaward by Fifty Feet.









(1) Good quality sand placed in a beach nourishment project will
be eroded from the area placed but will remain indefinitely
in the active nearshore region, and


(2) The greatest storm damage and recreational benefits are
generally realized for the initially narrower beaches.


The first concept will be considered as valid without much
discussion. Although "good quality sand" is a matter of degree,
here it refers to sand that is greater than 0.14 mm or so in
diameter and that is coarser than or as coarse as the material
originally present on the beach. For those nourishment materials
in which the above is not the case, this paper refers to that
sand fraction which is compatible. Monitoring results from a
number of beach nourishment projects have demonstrated the first
concept, for example at Port Canaveral, FL (Dean, 1988) and
Captiva Island, FL (Tackney and Associates, 1983).

The second concept is illustrated by Figure la which
represents a survey (by Shows, 1978) of the structural damage
caused by Hurricane Eloise (1975) in Bay County, FL as a func-
tion of proximity of the structures relative to a jurisdictional
control line which is generally parallel to the shoreline. Of
particular significance in Figure la is the steeply sloped por-
tion of the damage curve near its seaward end and the relatively
mild slope near its landward end. It is instructive to consider
the effect of a beach nourishment project which displaces the
beach seaward by a certain amount such as 50 ft as shown in
Figure lb. It is seen that due to the slope characteristics
discussed above, the greatest damage reductions occur for those
structures which initially have very little beach in front of
them. Figure 2 presents the damage reduction per structure
associated with an additional one foot of beach width. For the
narrower initial beach widths, the reduction is approximately
$3,000 per structure whereas for greater initial beach widths,
the damage reduction per structure is less than $500. In
summary, the damage reduction benefits are greater for beaches
which are initially much narrower.
8





















3



2



1



0 100
150 100


50 0 50 100 150


Seaward I Landward
DISTANCE FROM CONTROL LINE (ft)




Figure 2. Damage Reduction Per Structure Resulting from a One
Foot Wide Additional Beach, as a Function of Structure Location
Relative to Control Line. Based on Hurricane Eloise Data.


SE
0
o
O-





UO


i-
Q/









The same concepts demonstrated above for damage reduction
benefits apply for recreational benefits. Figure 3 presents the
hypothetical usage and associated recreational benefits for
beaches of varying widths. The number of people using the beach
will increase with beach width; however, the rate of increase
decreases for the greater widths. The results in Figure 3b are
based on a visitation value of $6.00 per visitor per day and a
plan area visitation requirement of 200 square feet. The annual
recreational benefits associated with an additional foot of beach
width versus initial beach width, based on Figure 3, are
presented in Figure 4. As before, it is seen that the greatest
benefits occur for the initially narrower beaches.

Referring to Figure 5, the significance of greater benefits
for initially narrower beaches is that as a beach nourishment
project evolves with the beach fronting the project area
narrowing and the project adjacent beaches widening, benefits are
lost in the initially wider project area. This loss of benefits
is small compared to the gain of relatively large benefits in the
initially narrow project adjacent areas. Assuming that the value
of the upland structures protected by the project and the initial
beach widths in project adjacent areas are uniform along the
beach, there is always a net gain in storm reduction benefits as
a result of project evolution. Similarly with respect to
recreational benefits, assuming that the need for and access to
recreational beaches are uniform, etc., the net effect of project
evolution is a gain in recreational benefits.


METHODOLOGY

The methodology will be described and illustrated for
idealized cases of no project evolution and rapid project
evolution and general cases of benefits due to project evolution
over realistic time frames.




















300

200

100

0
0


Weekend
Visitation
4 -410


100


150


BEACH WIDTH, w(ft)

a) Number of Days Per Year that Full Beach Width Is Used


z 500
2
(n 400

5L) 300
-u 200

S100
z
z 0
<1 I


50 100 150
BEACH WIDTH, w(ft)


b) Annual Recreational Benefits vs Beach
Foot of Beach Length


Figure 3.
Beaches.


Hypothetical Usage and Recreational Benefits of Sandy


Width Per






















S10
Cv

CO
t-
uL
z
w
-J

z 5
0

U-
oc
0
-J
-=


z
z 0
< I


100


150


INITIAL BEACH WIDTH (ft)






Figure 4. Annual Recreational Benefits Per Additional Foot of
Beach Width as a Function of Initial Beach Width, Per Foot of
Beach Length. Developed from Figure 3b.


I I I I I


I I I I I I


I I I I I I I I I .. .



















Benefits Gained








Benefits Lost







Benefits Gained


a) Initial Nourished Planform


b) Eroded Nourished Planform
with Material Deposited on
Adjacent Beaches


Figure 5. Schematic of Erosion of Nourished Area and Deposition
in Project Adjacent Areas.









The same concepts demonstrated above for damage reduction
benefits apply for recreational benefits. Figure 3 presents the
hypothetical usage and associated recreational benefits for
beaches of varying widths. The number of people using the beach
will increase with beach width; however, the rate of increase
decreases for the greater widths. The results in Figure 3b are
based on a visitation value of $6.00 per visitor per day and a
plan area visitation requirement of 200 square feet. The annual
recreational benefits associated with an additional foot of beach
width versus initial beach width, based on Figure 3, are
presented in Figure 4. As before, it is seen that the greatest
benefits occur for the initially narrower beaches.

Referring to Figure 5, the significance of greater benefits
for initially narrower beaches is that as a beach nourishment
project evolves with the beach fronting the project area
narrowing and the project adjacent beaches widening, benefits are
lost in the initially wider project area. This loss of benefits
is small compared to the gain of relatively large benefits in the
initially narrow project adjacent areas. Assuming that the value
of the upland structures protected by the project and the initial
beach widths in project adjacent areas are uniform along the
beach, there is always a net gain in storm reduction benefits as
a result of project evolution. Similarly with respect to
recreational benefits, assuming that the need for and access to
recreational beaches are uniform, etc., the net effect of project
evolution is a gain in recreational benefits.


METHODOLOGY

The methodology will be described and illustrated for
idealized cases of no project evolution and rapid project
evolution and general cases of benefits due to project evolution
over realistic time frames.









Shoreline Evolution Model


The shoreline evolution model adopted here will be that due
to Pelnard-Considere for an initially rectangular planform as
presented in Figure 6. The factor G is the so-called longshoree
diffusivity" and for small angles of wave incidence is

K H 5/2IK
G K Hb
G = 8(s-1)(l-p)(h*+ B)

in which K is the sediment transport factor usually taken as
0.77, Hb is the representative breaking wave height, g is
gravity, K is the spilling breaker ratio (on the order of 0.8), s
is the ratio of sediment specific gravity to that of the water in
which transport is occurring, p is the in situ porosity and (h*+
B) is the vertical extent of beach profile response.


Storm Damage Reduction Benefits

Development of storm damage reduction benefits commences
with the establishment of the relationship of a proportional
storm damage factor, D, as a function of beach width fronting the
structure, w, and storm return period, TR. Figure 7 presents one
example of such a relationship which has been used in the state
of Florida Beach Management Plan. Development of this
relationship is by no means trivial and should be based on an
analysis of the expected damage to a range of representative
structures as well as calibration with available storm results if
such data are available. The proportional storm damage factor,
D, depends on the foundation and structural and elevation
characteristics of the buildings as well as the beach morphology,
and presence and integrity of coastal protection structures, etc.

With the availability of D(w,TR) it is possible to predict
the present worth damage reduction benefits PWDRB(N) during N
years by the general procedure described in Figure 8 and the
following equation















DISTANCE FROM ORIGINAL
SHORELINE, y (ft)


Original Nourished Beach Planform
Planform After 3 Months
10 Months
-7 Years
,-30 Years
. -130 Years Pre-Nourished
\-- ../ Shoreline


6 4 2 0 2 4 6 8


ALONGSHORE DISTANCE, x (miles)








Figure 6. Example Solution of Evolution of Initially Rectangular Beach Planform. Pelnard
Consider Method. Wave Height, Hb = 2.0 ft, Initial Nourished Beach Width = 100 ft, Fill
Length, k = 4 miles, t = time.













1.0


LL.
0



LL
0
<
U-

C<
Q


1 10 100


1000


RETURN PERIOD, TR (Years)




Figure 7. Hypothetical Proportional Storm Damage, D, as a Function of Storm Return
Period, TR, and Beach Width, w.






FLOW CHART OF


Damage Reduction Benefits
(a) In Project Area
(b) In Project Adjacent Areas
Initial Nourished Beach Ranform Evolution
Planform Evolution
Planform (Pelnard-Considered)
(Rectangular) (Pelnard-Considered) Recreational Benefits
(1) (2) (a) In Project Area
(b) In Project Adjacent Areas

(3)
m --m--m-m m-m----------------------------------------m


Damaae Reduction Benefits


x
Y



y


X



I.


y- {erf[A(1 + )] + erf [A(1 2)]

A-
4VGt


(a) Random Storm Magnitudes in Accordance
with Actual Distribution
(b) Damage Reduction vs. Storm Return Period
and Beach Width
(c) Present Worth Damage Reduction Benefits


Recreational Benefits

(a) Recreational Benefits vs. Beach Width


Present Worth Recreational Benefits


Figure 8. Flow Chart of Methodology.


METHODOLOGY









PWDRB(N) =


N
I n V(x,n)[D(w(x,n)TR(n))-D(w ,TR(n))]dx
n=1 (1+I) Project
Area
(1)
N 1
+ I n f V(x,n)[D(w(x,n),TR(n))-D(wo,TR(n))]dx
n=1 (1+I) Project
Adjacent
Areas
in which I is the interest rate and V(x,n) represents the
structure value at a location, x, at a time n years into the
future. The two integrals differ only in their respective
intervals of integration and are written separately here to
illustrate the contributions from the two areas.

Eq. (1) accomplishes the objective of providing methodology
for quantifying storm damage reduction. However, it is
instructive to develop concepts further. Referring to Figure 7
which presents the proportional storm damage factor, D, the
expected damage by a single storm D(w) as a function of beach
width, w, is

1
D(w) = f D(w,TR)p(D)dD (2)
0

in which p is the probability density function and is related to
the cumulative probability distribution P by

dP
p(D) dP (3)

and noting that

TR = (4)

Eq. (2) simplifies to
-1 dP 1
D(w) = f D(w,TR) dD = f D(w,TR)dP (5)
0 0









Figure 9 presents D as a function of beach width as developed
from Eq. (5). It is noted that this distribution is
qualitatively similar to damages experienced in Hurricane Eloise
(Figure 1) which was approximately a 70 year storm.

Assuming that the value of the upland structures remain
constant with time and that damaged structures are rebuilt to the
same standards (both considerable assumptions), the present worth
damage factor, PWDF(w) as a function of beach width for N years
into the future is

N -
PWDF(w,N) = D(w) [1 ] D(w) (6)
n=1 (1+I)n (1+1)

and again, I is the interest. The bracketed factor in Eq. (6)
approaches unity with large N. Table I presents values of
PWDF(w,-) for several beach widths interest rates. It is noted
that the present worth damage factor can range as high as 1.31
for the case of zero beach width and an interest rate of 8%.

TABLE I

PRESENT WORTH DAMAGE FUNCTION, PWDF(w,-)
VERSUS BEACH WIDTH, w, FOR ALL FUTURE DAMAGE

Present Worth Damage Function, PWDF(w,m)
Interest For Beach Width, w
Rate 0 ft 50 ft 100 ft 150 ft

6% 1.75 0.67 0.47 0.35
8% 1.31 0.50 0.35 0.26
12% 0.88 0.33 0.23 0.18


Idealized Cases

In contrasting project benefits realized within the project
area to those outside the project area, it is instructive to
consider two simple cases:














0.10


5 LU



o(3 0.05
z
w
.1 G


F-

0
lw >-
n- fn
X
x
UJ


50 100 150

BEACH WIDTH, w(ft)


Figure 9. Expected Damage D(w) Due to a Single Storm
Function of Beach Width, w.


0.1


uwO






00
w

a>-



LU


0.05 -


0 -


0 wo 50 wo+AW 100


150


as a


BEACH WIDTH, w(ft)



Figure 10. Interpretation of Damage Reduction Benefits if Sand
Remains Where Placed (Case A) and if Sand Spreads Out Immediately
(Case B).


,Damage Reduction if
Sand Remains Where Placed (Case A)

Damage Reduction if Sand
SSpreads Out Immediately
(Case B)

Additional Damage Reduction
Due to Sand Spreading
Out Immediately









Case (A). All sediment remains within the area placed, and


Case (B). The sediment placed spreads out immediately over a
long segment of shoreline.


Case (A).

The expected storm damage reduction benefits due to a single
storm are


(SDRB)A = [D(wo + Aw) D(wo)]a (7)


Case (B).

Denoting the (long) distance over which the sediment has
been distributed as V' and the associated additional width as
Aw', we have


(SDRB)B = ()w Aw'' (8)
o
and since sediment is conserved Aw2 = Aw'a',


(SDRB)B = ()w Awk (9)
0

The ratio, RSD, of storm damage reduction benefits for the
case of sand spreading out immediately to the case in which sand
remains where placed is

/D
(w)w Aw
aw w
RSD = -- (10)
[D(wo + Aw) D(wo)]

It is noted that the ratio RSD is always greater than
unity. As shown in Figure 10, the interpretation is simple with
the numerator representing the tangent of the damage curve
at wo and the denominator the secant slope between wo and
Wo + Aw. Due to the character of the curve, the ratio will
always exceed unity. Figure 11 presents the ratio RSD vs wo for
several values of Aw.














cc c
0 M

SI-w
O i


SLUW


ca


5.0

4.0

3.0

2.0

1.0


100


150


INITIAL BEACH WIDTH, wo (ft)

Figure 11. Ratio of Storm Damage Benefits, RSD, vs Initial Beach
Width, Wo, and Additional Beach Width, Aw. RSD is Ratio of Storm
Damage Benefits for Sand Which Spreads Out Immediately to Those
for Which Sand Remains Where Placed.


-J
z




Om
o
-LL

0
<,
cca


2.0




1.0


50 100 150


INITIAL BEACH WIDTH, wo (ft)
Figure 12. Ratio of Recreational Benefits, RRB, vs Initial Beach
Width, Wo, and Additional Beach Width, Aw. RRB is Ratio of
Recreational Benefits for Sand Which Spreads Out Immediately to
Those for Which Sand Remains Where Placed.


-4--Aw=150 ft


Aw=100 ft



-AwI __ IO_

- - - - -









The same general discussion presented above applies to
recreational benefits relationships. The ratio of benefits RRB
for a project that spreads out immediately to one that remains in
place is

aR
aw w
RRB = (11)
[R(w + Aw) R(w )]


and this ratio will always exceed unity by the same argument as
for the damage reduction benefits. For the recreational benefits
shown in Figure 3, values of the ratio, RRB, are presented in
Figure 12.


RESULTS

Prior to presenting results for the general case, in which
the beach planform evolves with time, it is worthwhile to
consider the variables which will tend to favor Case A (sand
remains in place) or Case B (sand spreads out immediately). Case
A conditions would tend to dominate for:


Large Beach Fill Lengths, z
Low Wave Height, Hb
Small Transport Coefficient, K
Small Additional Beach Widths, Aw
High Interest Rates, I


and vice versa for Case B.

The methodology described in the previous section was
incorporated into a computer program which was "exercised" for
the variable values shown in Table II. Results will be presented
in two different forms. A schematic of the methodology has been
presented as Figure 8.

Figures 13 and 14 present variations of storm damage and
recreational benefits with time for Runs 5 and 7, respectively.
The relatively large wave height and short beach fill associated










TABLE II. PRESENT WORTH STORM DAMAGE AND RECREATIONAL BENEFITS FOR VARIOUS
CONDITIONS


WAVE AND PROJECT


Characteristics Storm Damage Reduction* Recreational Benefits**

In In
Initial Added In Project In Project
Project Wave Beach Beach Interest Project Adjacent Total Project Adjacent Total
Run Length, Height Width Width Rate Area Area Area Area
i, (miles) Hb (ft) wo (ft) Aw (ft) I

1 1.0 1.0 0 100 0.08 0.368 1.037 1.405 4.4 12.7 17.1
2 1.0 2.0 0 100 0.08 0.176 1.434 1.610 2.1 17.8 19.9
3 1.0 4.0 0 100 0.08 0.072 1.561 1.633 0.9 19.7 20.6
4 2.0 1.0 0 100 0.08 0.592 0.532 1.124 15.4 13.0 28.4
5 2.0 2.0 0 100 0.08 0.323 1.136 1.459 7.6 27.9 35.5
6 2.0 4.0 0 100 0.08 0.148 1.470 1.618 3.6 36.7 40.3
7 4.0 1.0 0 100 0.08 !.009 0.084 1.093 55.9 4.2 60.1
8 4.0 2.0 0 100 0.08 0.525 0.672 1.197 26.6 32.7 59.3
9 4.0 4.0 0 100 0.08 0.280 1.234 1.514 13.0 60.7 73.7
10 2.0 2.0 0 150 0.08 0.388 .679 2.067 10.1 38.5 48.6
11 2.0 2.0 50 100 0.08 0.066 0.178 0.244 4.9 14.5 19.4
12 2.0 2.0 100 150 0.08 0.057 0.144 0.201 7.4 21.7 29.1
13 2.0 2.0 0 100 0.12 0.240 0.697 0.937 5.7 17.0 22.7
14 2.0 2.0 0 100 0.04 0.506 2.413 2.919 11.7 60.0 71.7
15 16.0 2.0 0 100 0.08 1.733 0.002 1.735 392.4 0.5 392.9


*Relative to immediately adjacent upland
**Expressed in millions of dollars


property values within project area












CV)
l 1.5
au Total
M LU
0- y Adjacent Areas
Cn z 1.0-
-Jo
S1.0 1...-- ---

.JO -
Zc LU /
O M 0.5- / Project Area
O..W / **


0 1 I I3I4
0 10 20 30 40 50

YEARS INTO FUTURE

a) Proportional Present Worth Storm Damage Reduction
Components vs. Years Into Future.


<
-J



0 o
LU

LU w


Co




LU
L:
(1)


60



Benefit


10 20 30 40 50

YEARS INTO FUTURE


b) Present Worth Recreational Benefits vs. Years Into Future.



Figure 13. Present Worth Storm Damage Reduction and Recreational
Benefits. Hb = 2.0 ft, a = 2.0 miles, wo = 0.0, Aw = 100.0 ft.,
Interest Rate = 8%, Run No. 5.

















Total
-- -**
"Project Area
/

- /

/ Adjacent Areas

10 20 30 40 -.-- ------
1 10 20 30 40 50


YEARS INTO FUTURE


a) Proportional
Components


Present Worth Storm Damage Reduction Benefit
vs. Years Into Future.


Total --

Project Area





Adjacent Areas
o 10 2I0 30 40 50
0 10 20 30 40 50 6


YEARS INTO FUTURE

b) Present Worth Recreational Benefits vs. Years into Future.


Figure 14. Present
Benefits. Hb = 1.0
Interest Rate = 8%,


Worth Storm Damage Reduction and Recreational
ft, Z = 4.0 Miles, wo = 0.0, Aw = 100.0 ft,
Run No. 7.


I-

CO
oa .


SUJ


OC)
ccz



-.0
o




o-S
<


1.0


0.5



n


-J
<

I La

LUW




a0


ULm


1--------









with Figure 13 favor Case B conditions and it is seen that the
dominant benefits occur within the adjacent project areas. It is
also of interest to note that the benefits in the project
adjacent areas lag those in the project area due to the time
required for sediment transport to these adjacent areas. By
contrast the longer project length and smaller wave height of
Figure 14 favor Case A conditions and the benefits inside the
project area dominate and commence quite early.

Table II summarizes results for all 15 runs conducted.


SUMMARY AND CONCLUSIONS

The methodology and results presented herein support the
following statements.

Wider beaches seaward of structures perform as effective
energy dissipators during storm conditions and, where the demand
exists, also provide recreational benefits. These benefits can be
enhanced through increasing beach widths by nourishment projects.

Beach nourishment projects conducted with good quality sand
will evolve with erosion occurring within the project area and
deposition in the project adjacent areas. Good quality sand will
remain within the active nearshore region and provide continuing
storm damage reduction and recreational benefits.

A simple method is presented for quantifying the benefits in
and adjacent to beach nourishment project areas. Considering
limiting cases in which (a) all sand stays within the area
placed, or (b) all sand placed spreads out rapidly demonstrates
that the potential benefits are greater for the latter. Example
calculations for realistic cases demonstrate that the benefits
for project adjacent areas can be substantial relative to those
in project areas. The relative benefits in project adjacent
areas increase with: short project length, large wave height,
large sediment transport coefficient, low interest rate, and
large additional beach width.










Accounting methodologies for benefits of beach nourishment
projects should be representative of modern understanding of
sediment transport processes and the equities of those residing
along the shoreline and thus should recognize the benefits from
sand transported from the project area and deposited in project
adjacent areas.

Although the method presented here applies to the case of
projects placed on long uninterrupted shorelines, similar
procedures could be applied to situations where littoral controls
exist, such as jetties at a channel entrance.


ACKNOWLEDGEMENTS

The work leading to this paper was carried out under funding
by the Office of Sea Grant and by the Division of Beaches and
Shores of the Florida Department of Natural Resources. This
support is gratefully acknowledged.


REFERENCES


Dean, R.G. (1988) "Sediment Interaction at Modified Coastal
Inlets: Processes and Policies", in Hydrodynamics and
Sediment Dynamics of Tidal Inlets, D. Aubrey, Editor, Woods
Hole Oceanographic Institution, Woods Hole, Mass. (In Press).


Pelnard Considere, R. (1956) "Essai de Theorie de 1'Evolution
des Formes de Rivate en Plages de Sable et de Galets", 4th
Journees de l'Hydraulique, Les Energies de la Mar, Question
III, Rapport No. 1.


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.


Tackney and Associates (1983) "Physical Monitoring Captiva Beach
Restoration Project", Final Report, August.


~










Accounting methodologies for benefits of beach nourishment
projects should be representative of modern understanding of
sediment transport processes and the equities of those residing
along the shoreline and thus should recognize the benefits from
sand transported from the project area and deposited in project
adjacent areas.

Although the method presented here applies to the case of
projects placed on long uninterrupted shorelines, similar
procedures could be applied to situations where littoral controls
exist, such as jetties at a channel entrance.


ACKNOWLEDGEMENTS

The work leading to this paper was carried out under funding
by the Office of Sea Grant and by the Division of Beaches and
Shores of the Florida Department of Natural Resources. This
support is gratefully acknowledged.


REFERENCES


Dean, R.G. (1988) "Sediment Interaction at Modified Coastal
Inlets: Processes and Policies", in Hydrodynamics and
Sediment Dynamics of Tidal Inlets, D. Aubrey, Editor, Woods
Hole Oceanographic Institution, Woods Hole, Mass. (In Press).


Pelnard Considere, R. (1956) "Essai de Theorie de 1'Evolution
des Formes de Rivate en Plages de Sable et de Galets", 4th
Journees de l'Hydraulique, Les Energies de la Mar, Question
III, Rapport No. 1.


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.


Tackney and Associates (1983) "Physical Monitoring Captiva Beach
Restoration Project", Final Report, August.


~




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