UFL/COEL86/019
SEDIMENT BUDGET
PRINCIPALS AND APPLICATIONS
By
Robert G. Dean
November, 1996
SEDIMENT BUDGET
PRINCIPLES AND APPLICATIONS
BY
R.G. DEAN
PUBLISHED IN DYNAMICS OF SAND BEACHES, INTERNATIONAL
CONFERENCE ON COASTAL ENGINEERING (ICCE) 20th TAIPEL,
R.O.C. NOV., 1986.
TABLE OF CONTENTS
CHAPTER PAGE
SEDIMENT BUDGET PRINCIPLES AND APPLICATIONS..................... 3
INTRODUCTION................................................. 3
GOVERNING EQUATIONS.......................................... 3
Integrated Form of the Governing Equation................. 4
Application..... ......................................... 6
EQUILIBRIUM BEACH PROFILES........... ...................... 11
Introduction.............................................. 11
Equilibrium Beach Profile Characteristics................. 11
Applications of Equilibrium Beach Profiles................ 19
Required Beach Nourishment Volumes..................... 19
Response to Sea Level Rise................................ 22
Volume of Sediment Transported Offshore to Various
Depths Due to Sea Level Rise........................... 22
Additional Applications of Equilibrium Beach Profiles..... 26
ADDITIONAL USEFUL APPROXIMATIONS IN SEDIMENT BUDGET
CALCULATIONS............................................... 26
Volumetric Changes Associated with Shoreline Changes...... 26
APPLICATIONS... .......................... .................. 27
South Shore of Long Island. .............................. 27
Brevard County, Florida................................... 30
Ocean City Inlet, Maryland................................ 37
CrossShore Distribution of Longshore Sediment Transport.. 40
Entrance to St. Andrews Bay, Florida...................... 44
Rudee Inlet, Virginia..................................... 48
SUMMARY ................................................ ..... 48
REFERENCES................................................... 51
CHAPTER
SEDIMENT BUDGET
PRINCIPLES AND APPLICATIONS
by
R. G. Dean
INTRODUCTION
The framework of sediment budget concepts provides a formalized procedure
to account for the various components of sediment flux and the changes of
volume that occur within a given region. Sediment budget methodology can be
useful in a number of coastal engineering and research applications,
including: inferring the amount of onshore sediment transport for a nearshore
system that contains an "excess of sediment", determining sediment deficits to
downdrift beaches as a result of engineering works at navigational entrances,
evaluating the performance of a beach nourishment project, inferring the
distribution of longshore sediment transport across the surf zone, etc.
This chapter reviews briefly the governing equations for sediment budget
calculations, considers various measurement and other bases for determining
the sediment flux components necessary to apply the sediment budget concept
and finally for illustration purposes, applies the sediment budget concept to
several examples.
GOVERNING EQUATIONS
The governing differential equation for a sediment budget expresses
conservation of sediment volume as
+ j q S (1)
CHAPTER
SEDIMENT BUDGET
PRINCIPLES AND APPLICATIONS
by
R. G. Dean
INTRODUCTION
The framework of sediment budget concepts provides a formalized procedure
to account for the various components of sediment flux and the changes of
volume that occur within a given region. Sediment budget methodology can be
useful in a number of coastal engineering and research applications,
including: inferring the amount of onshore sediment transport for a nearshore
system that contains an "excess of sediment", determining sediment deficits to
downdrift beaches as a result of engineering works at navigational entrances,
evaluating the performance of a beach nourishment project, inferring the
distribution of longshore sediment transport across the surf zone, etc.
This chapter reviews briefly the governing equations for sediment budget
calculations, considers various measurement and other bases for determining
the sediment flux components necessary to apply the sediment budget concept
and finally for illustration purposes, applies the sediment budget concept to
several examples.
GOVERNING EQUATIONS
The governing differential equation for a sediment budget expresses
conservation of sediment volume as
+ j q S (1)
in which z is the vertical coordinate of the bottom, q is the sediment
transport vector with components (qx, qy) and S represents a source of sand
per unit area, see Figure 1. Eq. (1) can also be expressed in terms of the
water depth, h, referenced to a fixed datum,
h S (2)
or in expanded form
ah x q+ S (3)
3t ax Sy
Integrated Form of the Governing Equation
In some cases, it is possible to apply Eq. (2) directly; however, usually
the data available for use in the conservation equation or information
required from application of the equation are such that an integrated form is
more useful. Integrating Eq. (2) across the beach from xl to x2,
x2 x2 x2
f h dx = q x +x qy dx f S dx (4)
X 1 1 ax x1
in which qx x2 and qx Ix represent the transport per unit width in the
offshore direction at the seaward and shoreward ends of the control volume
respectively. The first integral term represents the water area, A, between
the sand level and the vertical datum, z=0. If onshore transport occurs at
the seaward limit of the control volume, then qx x2 < 0 and if landward
transport of sand occurs due to overwash processes or wind blown sand,
then qxxl < 0. If fill were added to the profile, then S > 0. Equation (4)
may be useful to apply in this form. However, in some applications, it is
helpful to integrate Eq. (4) in an alongshore direction between coordinates yl
and y2; the result is
Figure 1. Definition Sketch for Sediment Transport Considerations.
S(Y2 1 y x xI x x2 y y + (5)
in which Qy(y2) and Qy(Y1) represent the total longshore fluxes of sediment
passing through the control volume boundaries at y = yl and y y2. The
quantity represents the total sand volume (referenced to some vertical
datum) within the control volume and *A is the amount of volume added.
Finally, since volume changes are usually observed over some time period
At(= t2 tl), in these applications it is appropriate to integrate Eq. (5)
over time interval, At, which yields
= (Y2 y1) At [q xx2 qx xl] [Q(Y2) (y1)] At + AVA (6)
Application
Prior to proceeding further it may be useful to illustrate an immediate
application of Eq. (6).
The Nearshore Sediment Transport Study (NSTS) included a field program at
Santa Barbara, California to provide data to calibrate the total longshore
transport equation,
Qy K P2s (7)
in which PIs is the socalled longshore energy flux factor at the wave
breaking line and Qy is the associated total longshore sediment transport.
The field site including the location of the directional wave gage used
in the correlation and the survey lines are presented in Figure 2. In this
example, the survey lines extended sufficient distances offshore and upland to
East Beach
S 50 meter Nominal Spacing
+ = Sxy Wave Array
0 250 500
scale in m
Santa Barbara Survey Plan and Location of Sxy Wave Gages.
xy
Figure 2.
encompass the entire limit of profile change; thus qx xl x qx x2 0.
Additionally, the navigational channel at the east end of the spit was
considered (and believed to be) a complete barrier to longshore sediment
transport (Qy(Y2) = 0) and there were no sediment additions or removals to the
system (AVA) = 0. Therefore Eq. (6) simplifies to
A = Q(yl)At (8)
which simply expresses that the change in volume is due to the influx of
sediment at an average rate Qy(y1), where yl is the location of the wave
gage. Thus, the coefficient K can be determined by combining Eqs. (7) and
(8).
t2 t2
I Qydt = f K Psdt
t t
1 1
t2
J Qydt
K =2 (9)
t2 t
SPsdt f Psdt
t t
such that the numerator is determined from the field surveys and the
denominator from the directional wave gage. The results from this study are
presented in Table I and Figure 3.
Prior to presenting more examples, it may be useful to review various
approaches to augmenting limited data to provide the necessary components in
the sediment budget expressions. Because so many useful results can be
obtained from equilibrium beach profile concepts, a summary will be presented
in the next section.
Santa Barbara Field Results
Net Onshore
Immersed Net Longshore Flux of
Weight Component of Longshore K* I/Sxy
No. Total Transport Wave Energy K It/Pts Component of
Intersurvey of Dredging Volume Rate Flux at Breaking Momentum (m/s)
Perioo Days Event Change(m3) I (N/s) P.s (N/s) Sxy (N/m)
Oct. 13, 1979 48 No 32,820 85.3 52.2 1.63 27.8 3.06
Nov. 30, 1979
Dec. 1, 1979 31 Yes, 65,070 159.1 101.4 1.57 45.4 3.50
Jan. 20, 1980 Major
Jan. 21, 1980 35 Yes, 82,810 295.0 352.4 0.84 119.6 2.47
Feb. 25, 1980 Minor
Apr. 11, 1980 53 No 10,290 24.2 76.6 0.32 37.9 0.64
June 3, 1980
June 4, 1980 82 No 22,220 33.8 31.7 1.07 17.6 1.91
Aug. 25, 1980
Aug. 26, 1980 57 No 38,760 84.8 63.8 1.33 32.6 2.60
Oct. .23, 1980
Oct. 24, 1980 54 Yes, 35,640 84.6 64.4 1.31 34.2 2.47
Dec. 17, 1980 Major
Table I
 Summary of
100
P (N/S)
1000
Data from Santa Barbara (*) and Rudee Inlet (o) Field Experiments.
I, vs Pts, Present and Past Correlations.
Figure 3.
EQUILIBRIUM BEACH PROFILES
Introduction
Beach profiles in nature are continuously evolving under the varying
action of waves, currents, tides and sediment supply which here will be termed
the "forcing functions". If the "forcing functions" were maintained constant,
the profile would stabilize into a socalled "equilibrium beach profile",
although the equilibration time could be very long. A knowledge of
equilibrium beach profiles is useful both in interpreting natural beach
conditions and in engineering applications. Problems which can be addressed
through equilibrium beach profiles include: beach restoration with a sand of
arbitrary size, response of natural or seawalled shorelines to storms and
tides, the effects of changes in wave characteristics and thus the seasonal
variations in beach profiles, response to sea level rise, and finally through
a knowledge of equilibrium beach profiles, it is possible to formulate and
test hypotheses on the response of profiles out of equilibrium. One
limitation of most presently available equilibrium profile forms is that they
are monotonic whereas many profiles in nature are seasonally or perennially
barred.
Equilibrium Beach Profile Characteristics
Studies, encompassing several thousand beach profiles from nature and
laboratory (with by far a predominance from nature) have demonstrated that
most beach profiles can be represented well by the monotonic form
h(x) Ax2/3 (10)
in which h(x) is the water depth at a distance, x, offshore and A is a so
called "scale parameter". It is noted that the parameter A has dimensions of
length to the onethird power (i.e., ft1/3 or m1/3). It can be shown from
linear wave theory that Eq. (10) is consistent with uniform wave energy
dissipation per unit water volume in the surf zone. Figure 4 shows the origin
of one set of field profiles exceeding 500 in number. This set extended from
the eastern end of Long Island to the TexasMexico border.
Figures 5, 6, 7 and 8 present examples of the fits to various averaged
and individual profiles that were used in an assessment to determine the scale
parameter. Figure 7 is of special interest in that the sizes of the "sand
grains" ranged from 10 to 30 cm in diameter, approximately the size of bowling
balls!
Most engineering applications require knowledge of the scale parameter
"A" in Eq. (10). The analyses carried out have shown that A depends primarily
on the sediment size and only secondarily on wave conditions. Figure 9
presents A vs D which was the first relationship developed and is recommended
if no information is available describing the particular wave height
characteristics. It is evident from this figure that beaches composed of
larger diameter sediments are steeper, i.e., characterized by larger A values
whereas finer grained beaches are characterized by smaller A values and thus
are milder in slope. The second representation of A is presented in Figure 10
and includes effects of both sediment size, here represented as the fall
velocity, w, and waves, i.e., the breaking wave height, Hb, and wave period
T. Examination of Figure 10 will demonstrate the following variation of beach
slope with various parameters.
Location Map of the 502 Profiles Used in the Analysis (From Hayden,
et al.).
Figure 4.
DISTANCE OFFSHORE (ft)
400 600 800
Data Group I
N =35
h = 0.398 x0533
Data Group II
N =43
h = 0.079xO822
Data Group I
N = 38 0762
h = 0.095 x
O0 Data Group "Z
h = 0.128 XO709
10 
Data Group Z
N=14
h = 0.243 x.523
Average Profile for Group
Reference Profile (Average of All 502 Profiles)
& A Computed Profile from Given Equation of Form: h= Axm
Figure 5. Comparison of Beach Profiles .for Data Groups IV (From Dean, 1977).
DISTANCE OFFSHORE (ft)
400 600 800
1000
1200
U II III
Data Group I
N =234
h =0.255x0.594
0
0(O I^ ^ ^c '^
Data Group 3II
N= 10
Data Group =3ZI
N=34
h = 0.277x0.554
Data Group IK
N =38
Data Group I
N = 27
Average Profile for Group
 Reference Profile (Average of All 502 Profiles)
A a Computed Profile from Given Equation of Form: h= Ax
Figure 6. Comparison of Beach Profiles for Data Groups VIX (From Dean,
1977).
I
I
a
w
0
LJ
Q
f
200
DISTANCE OFFSHORE(m)
25.00
 Least Squares Fit
Actual Profile
Profile P4 (From Zenkovich, 1967).
Kamchatka. Sand Diameter: 150 mm 
of A = 0.82 m1/3 (From Moore, 1982),
A Boulder Coast in Eastern
300 mm. Least Squares Value
DISTANCE OFFSHORE (m)
60.00
Least Squares Fit
Actual Profile
Profile P10 (From Zenkovich, 1967). Near the End of a Stit in
Western Black Sea. Whole and Broken Shells. A = 0.25 m173
(From Moore, 1982).
50.00
Figure 7.
Q,
E
w
w
!LJ
3.5
Figure 8.
E
i
Ln
_J
U
1
z
0
Beach Profile Factor, A, vs Sediment Diameter, D, in Relationship h = Ax2/3 (Modified From Moore,
1982).
1.0
0.10
0.01
0.01
0.1 1.0 10.0 100.0
SEDIMENT SIZE, D(mm)
Figure 9.
,Normal Profile I Storm Profile,
cr
w
H
0
U
_1
<
6
LIJ
w
Co
0.5
SHb= Breaking Wave
Height
T = Wave Period
Sw = Sediment Fall
Velocity
0.10
0.05
0.01
.01
(No Bar)
 V ..........N
I I I I III
Bar Present
I I I I lI II* _
Recommended
Relationship
From Hughes'
Field Results
___________________________________ 4
I I
I u I sI ll
From Swart's
Laboratory Results
I I
I I I j l ,
I I I I 'I I l l
.10 1.0 10.0
FALL VELOCITY/ WAVE CHARACTERISTICS
(Hb/wT)
Figure 10.
PARAMETER,
Correlation of Equilibrium Beach Profile Scale Parameter, A, with Combined Sediment/Wave
Parameter, Hb/wT.
h(x)= Ax/3
(2) A < AN
In this case, with a finer sand placed in the nourishment process than is
naturally present on the beaches, the nourished profile will be characterized
by a milder slope than the native. The required volume per unit length of
beach is
[AN (Ax + W,513 AB (W,)5/3] + B Ax (12)
it is seen that Eq. (A3) reduces to Eq. (A2) for the case of AN = AB.
(3) AB > AN
In this case, with the placed material being coarser than the native, the
two profiles may or may not intersect, depending on the geometry. Thus
consideration of two subcases is required.
In the first subcase, the two profiles do not intersect. In this case,
the volume required per unit length of beach is the same as for Case 2, in
which the profiles do not intersect, i.e.,
S=I [AN (Ax + W,)5/3 A (W,)5/3] + B Ax (13)
In the second subcase, the profiles intersect at h', so sand is only required
shoreward of this location, see Figure 11.
The required volume is
V 3 h'W' + B Ax (14)
5
where h' is determined by solving the following equation, first for W'
h' AN (Ax +W')2/3 '2/3 (15)
which yields
1 Ax (16)
A 2/3
) 1
AN
20
Large fall velocities (large diameter sediment)
Steep Slopes Small wave heights
Long wave periods
Small fall velocities (small diameter sediment)
Mild Slopes Large wave heights
Short wave periods
It is noted that all of the above interrelationships are in accord with
observations in nature of the variation of wave profiles with wave and
sediment characteristics.
Applications of Equilibrium Beach Profiles
Some of the applications of equilibrium beach profiles will be developed
below.
Required Beach Nourishment Volumes This problem must be considered for three
separate cases: (1) AB = AN, (2) AB < AN and (3) AB > AN, where the subscripts
"B" and "N" denote "borrow" and "native", respectively and A is the profile
scale parameter discussed earlier.
(1) AB=AN
For this case, the native and nourished profiles would be of the same
form. The required volume, I, per unit length of beach would be
3A [(Ax + W,5/3 5/3
S=  [(x + W)53 3] + B Ax (11)
in which Ax = shoreline advancement
h, = effective depth of limiting motion
B = berm height
W, = width of the nourished surf zone (i.e., out to h*).
h6x
a) SubCase in which Two Profiles do not Intersect, h* > h'.
W i
b) SubCase in which Two Profiles Intersect, h' < h*.
Figure 11. Two SubCases of AB > AN.
and h' can thus be determined as
h' A [ (17)
() 1
and h' < h*, Profiles do not intersect Eq. (13)
h' > h,, Profiles intersect Eq. (14)
Response to Sea Level Rise
It can be shown that with no additions to or losses of sand from a
profile, a rise of sea level, S, will cause a retreat, R, given by the
implicit equation,
R S 3 h* 5/3
S B B [1 (1 ) ] (18)
W* B 5B W*
It can be shown that for retreat magnitudes, R, which are small compared
to the surf zone width, W*, Eq. (18) simplifies to
W,*
R = S h + B (19)
which is recognized as the socalled "Bruun Rule" presented by Bruun in 1962
to represent this phenomenon.
Volume of Sediment Transported Offshore to Various Depths Due to Sea Level
Rise The case just considered results in an offshore transport of sediment
due to sea level rise. However, if there are no longshore gradients of
sediment transport, there is no loss of sediment along a profile and accurate
consecutive surveys encompassing the entire region of profile change
referenced to the same vertical datum should result in the same total volume.
Of relevance to the present study is the case in which the profiles do
not extend a sufficient distance offshore to encompass the entire region of
profile change. For example, if the surveys extended only out to the profile
intersection point, the apparent volumetric loss would be the hatched area
above the intersection point in Figure 12.
It can be shown that the nondimensional apparent volume loss is
approximately
3/2
VE (B/h, + h /h) h 3/2
= (B/h + ) ( (20)
WS (B/h, + 1) h
in which hS is the offshore depths to which the surveys are conducted. The
profile intersection depth, hl, referenced to the datum before the sea level
rise is approximately
hi 4 1 (21)
h2 9(21)
h* 9 (1 + B/h)2
In Eq. (20), the quantity W*S is the nominal amount usually referenced as the
volumetric erosion due to sea level rise.
To examine Eq. (20) further, Figure 13 presents the nondimensional
apparent volumetric erosion VE/(W*S) vs hS/h* for ratios B/h* of 0 and 0.25.
It is seen that the greatest volume of apparent erosion possible (and only if
the surveys were carried out precisely to the intersection point) are 15% and
20% of the nominal value respectively for B/h* values of 0 and 0.25. The
reason for this can be determined by examining the effects of shifting a
profile vertically upward (due to sea level rise) and landward (to conserve
Portion of Profile
over which Erosion
Occurs
Portion of Profile over
which Deposition Occurs
Figure 12.
Definition Sketch Showing Portions of Profile over which Erosion and Deposition Occue Due to a
Landward and Upward Profile Translation.
___ CS ___
Rwa
(... F W .
"I; ^ _
^T
NONDIMENSIONAL
Figure 13.
SURVEY DEPTH, hs/ h.
Relationship of NonDimensional Apparent Eroded Volume to
NonDimensional Survey Depth.
sediment). The apparent total erosion due to a vertical displacement S is
clearly W*S; however, when the profile is also shifted landward not only is
the net erosion reduced (indeed to zero), but the local erosion (landward of
the limit of offshore motion) is reduced substantially relative to W*S.
Additional Applications of Equilibrium Beach Profiles
Additional applications of equilibrium beach profiles that will only be
mentioned here include: the response of natural and seawalled profiles to
storms and sea level rise and providing a basis for examining the transient
response of profiles, i.e., profiles that are not in equilibrium. The reader
is referred to Dean (1983) for additional information.
ADDITIONAL USEFUL APPROXIMATIONS IN SEDIMENT BUDGET CALCULATIONS
This section presents a number of useful approximations and aids in
supplementing limited data in order to carry out sediment budget calculations.
Volumetric Changes Associated with Shoreline Changes
In many cases, there may be data available for shoreline changes, but not
volumetric changes. If the profile remains unchanged as the profile advances,
the associated volume change, per unit length of beachfront, AV, is
A = (h, + B) Ax (22)
such that an advancement (retreat) of the beach would be associated with a
gain (loss) of volume. In the case in which an entire barrier island is
advancing (retreating) without change of form, then the change of volume is
(Figure 13)
A = (h, h* ) Ax (23)
o b
in which the subscripts "o" and "b" denote ocean and bay, respectively.
APPLICATIONS
One application of the sediment budget concept was presented
previously. This section presents several additional specific examples.
South Shore of Long Island
The south shore of Long Island is 134 km in length and due to the impact
of a number of major storms, several surveys have been conducted since 1933,
although the quality of the more recent data is much better than the earlier
data.
Briefly, referring to Figure 14, the net transport along the shoreline is
from east to west and shoreline surveys indicate that there is not sufficient
erosion to provide the quantity of sediment transport documented at Fire
Island Inlet (approximately 350,000 m3/yr). This strongly suggests an onshore
transport of sediment of considerable magnitude. Two time periods of
reasonably high quality are available: 19401955 and 19551979. The onshore
sediment transport, qx(x2), is inferred from Eq. (6) as
x 2 y) (t2 t) I xl 2 y) + Oyly1 Oyjy A* (24)
Applying the above equation to the data presented in Table II from the two
time periods results in a substantial variation of the onshore sediment
transport, i.e.
sediment). The apparent total erosion due to a vertical displacement S is
clearly W*S; however, when the profile is also shifted landward not only is
the net erosion reduced (indeed to zero), but the local erosion (landward of
the limit of offshore motion) is reduced substantially relative to W*S.
Additional Applications of Equilibrium Beach Profiles
Additional applications of equilibrium beach profiles that will only be
mentioned here include: the response of natural and seawalled profiles to
storms and sea level rise and providing a basis for examining the transient
response of profiles, i.e., profiles that are not in equilibrium. The reader
is referred to Dean (1983) for additional information.
ADDITIONAL USEFUL APPROXIMATIONS IN SEDIMENT BUDGET CALCULATIONS
This section presents a number of useful approximations and aids in
supplementing limited data in order to carry out sediment budget calculations.
Volumetric Changes Associated with Shoreline Changes
In many cases, there may be data available for shoreline changes, but not
volumetric changes. If the profile remains unchanged as the profile advances,
the associated volume change, per unit length of beachfront, AV, is
A = (h, + B) Ax (22)
such that an advancement (retreat) of the beach would be associated with a
gain (loss) of volume. In the case in which an entire barrier island is
advancing (retreating) without change of form, then the change of volume is
(Figure 13)
A = (h, h* ) Ax (23)
o b
in which the subscripts "o" and "b" denote ocean and bay, respectively.
APPLICATIONS
One application of the sediment budget concept was presented
previously. This section presents several additional specific examples.
South Shore of Long Island
The south shore of Long Island is 134 km in length and due to the impact
of a number of major storms, several surveys have been conducted since 1933,
although the quality of the more recent data is much better than the earlier
data.
Briefly, referring to Figure 14, the net transport along the shoreline is
from east to west and shoreline surveys indicate that there is not sufficient
erosion to provide the quantity of sediment transport documented at Fire
Island Inlet (approximately 350,000 m3/yr). This strongly suggests an onshore
transport of sediment of considerable magnitude. Two time periods of
reasonably high quality are available: 19401955 and 19551979. The onshore
sediment transport, qx(x2), is inferred from Eq. (6) as
x 2 y) (t2 t) I xl 2 y) + Oyly1 Oyjy A* (24)
Applying the above equation to the data presented in Table II from the two
time periods results in a substantial variation of the onshore sediment
transport, i.e.
Montouk
Point
Shinnecock
Inlet
Moriches
Inlet
t f %
Fire Island
Inlet
Figure 14.
0 10 20km
I I I I I I I I I I I
The South Shore of Long Island and the Questions of the Magnitude of Net Onshore Sediment
Transport.
Table II
SUMMARY OF SEDIMENT BUDGET ANALYSIS
MONTAUK POINT TO FIRE ISLAND INLET
(4) (5) (6)
STime Span
Number
of Years
Net Change
Change
(yd /yr)
Fill
Additions
(yd3/yr)
Washover
Aeolian
Transport
(yd /yr)
Inferred
Allowance For Transport Transport
Sea Level Rise Past Democrat Onshore.
(yd3/yr) Point (yd3/yr) (yd3/yr)
19401955 15.4 1,356,929 313,032 94,330 64,606 0 1,.359,349
19551979 24.5 7,501 420,444 32,825 64,606 400,000 294,710
19401979 39.9 528,333 378,987 56,564 64,606 245,614 705,622
Inferred Onshore Transport Rate (Column (8)) = Column (3) 0.5 x Column (4) + Column (5)
+ Column (6) + Column (7).
Inferred Onshore
Time Period Sediment Transport
19401955 1,040,000 m3/yr
19551979 225,000 m3/yr
Based on these results, it was concluded that the onshore sediment
transport was episodic and possibly the result of infrequent storm conditions
or highly varying storm seasons. Also, the representative annual onshore
sediment transport, based on a weighted average of the above two values is
540,000 m3.
In applying and interpreting the sediment budget approach, it is always
useful to question the reasonableness of the results and the inferred large
magnitudes of sediment transport at Long Island is no exception. The
continental shelf off Long Island is a glacial outwash plain composed of
poorly sorted sediments. Comparison of a representative profile with two
equilibrium profiles for sediment of the appropriate size (Figure 15)
indicates that indeed the profile is probably "out of equilibrium" with an
excess of sediment which would tend to result in onshore sediment transport
due to the milder bottom slopes (compared to equilibrium). Moreover, the size
of the sediment is such that it tends to be transported only by the larger
waves associated with infrequent storms.
Brevard County, Florida
This example provides a good case study illustrating the application of a
sediment budget analysis to determine the effect of a channel entrance. Port
Canaveral entrance was cut in 1951 and is therefore a relatively young
entrance. Figure 16 presents a location map for this entrance on the east
30
OFFSHORE (m)
00
Actual Profile
\ 17
'0o \
SIdealized
Profiles
Figure 15.
Comparison of Actual and Idealized Profiles.
Sinnecock and Moriches Inlets.
Actual Profile Approximately Midway between
DISTANCE
sO  k
Atlantic
Ocean
Port Canaveral
Entrance
a.*.
.
Location Map of Brevard County and Port Canaveral Entrance.
Gulf of Mexico
Figure 16.
coast of Florida. Shoreline change results are available for this area
commencing in 1855. Table III presents a chronology of events relevant to
changes in the shoreline.
TABLE III
CHRONOLOGY OF SIGNIFICANT EVENTS AT PORT CANAVERAL ENTRANCE
Entrance Cut 1951
Jetties Constructed 19531954
Beach Nourishment Project 1974
The longshore sediment transport is predominantly toward the south at
rates estimated up to 270,000 m3/yr although there is substantial uncertainty
in this estimate. The shoreline changes following construction of the inlet
coupled with a sediment budget analysis provide a basis for improving this
estimate.
Figure 17a presents the preentrance shoreline change rates. The
abscissa represents distance toward the south with the total length shown
representing a distance in excess of 66 km. The ordinate represents shoreline
change rate. It is seen that in the time period 18771951, which is
dominantly preentrance, the shoreline was accreting over more than 80% of the
shoreline. The average shoreline change rate over this 78 year time period is
approximately 0.3 m/yr. During the 19 year period (19551974) subsequent to
the cutting of the entrance, erosion had commenced with the maximum erosion
existing immediately downdrift (south) of the entrance. The maximum erosion
rate was approximately 5 m/yr over this 19 year period and the effect extended
some 5.5 km south of the entrance.
a)Effects of Channel Entrance on Down Drift Beach Stability
SPort Canaveral Entrance
Sebastian Inlet
Entrance I
20 40
DISTANCE SOUTH FROM PORT CANAVERAL
ENTRANCE (km)
Figure 17.
b) Shoreline Changes Following 1974 Nourishment Project
Effects of Establishment of Cape Canaveral Entrance and Subsequent
Nourishment Project on Downdrift Beaches.
1974 1986 (Post Nourishment)
 %...  ^ ^
I
*1955 1974 (PostEntrance, PreNourishment)
I
I
/
I I I I I I
_ __
c
~~C~c
50
In order to apply a sediment budget approach to determine the longshore
transport rate, it would be desirable to have available volumetric changes
downdrift of the entrance. However, lacking volumetric data, it is possible
to utilize Eq. (22) which relates volumetric change to plan area change.
Integrating the plan area in Figure 17b to determine the plan area rate of
change between the preentrance and postentrance rate of change yields
approximately 15,000 m2/yr. Considering a vertical dimension of 8 m over
which the profile is shifted landward in the erosion process with the form
remaining unchanged and making the assumption (probably quite true) that there
is no crossshore transport outside the shoreward or seaward limits accounted
for here, Eq. (6) simplifies to
= Qy (y Qy(Y2) (25)
in which Qy(y1) and Qy(Y2) represent the longshore transport at the jetty and
that outside the region affected by the entrance. The quantity Qy(Y2) of
course is the unaffected net longshore sediment transport and is the transport
of interest. If it is assumed that the south jetty is impermeable, then
Qy(Yi) 0, and
Q (y2) = 15,000 m2/yr (8 m)
= 120,000 m3/yr
It is of interest to examine the effect of the south jetty if it were not
impermeable. It is clear that if the jetty is permeable, that sand would be
lost into the entrance through the jetty, i.e. Qy(Yi < 0), and
Y i y(Y1) (26)
Thus a leaky jetty would tend to overemphasize the amount of longshore
sediment transport if it were assumed to be sand tight.
Ideally one would have available other data indicating whether or not the
permeability of a jetty could result in significant transport through the
jetty. In particular the orientation of the shoreline relative to the jetty
can serve as a qualitative indication of permeability. For example, if the
shoreline is aligned perpendicular to the jetty, there is probably little
sediment transport through the jetty. If the shoreline forms an acute angle
with the jetty, the jetty is clearly "leaky" and significant transport over or
through the jetty is probably occurring. In the case of Port Canaveral
Entrance, inspection of the south jetty demonstrates that it is "leaky";
however, the shoreline orientation is such that this transport component is
not considered to be significant.
Having explored the net longshore sediment transport through analysis of
the erosional phase of the shoreline south of Port Canaveral Entrance, it is
useful to examine the shoreline changes subsequent to a relatively substantial
nourishment project. In 1974, a nourishment project consisting of
approximately 2 million cubic meters was placed along a 3,400 m segment of
shoreline immediately south of the south jetty. The shoreline changes from
1972 to 1986 are presented in Figure 17b. This figure is based on an entirely
different data source and over a completely different time period, yet it is
of interest to note that outside the region of influence of the entrance the
shoreline change rates are very similar to those based on the period 1877
1951. This figure clearly shows qualitatively that the erosive "wave" has now
moved some 27 km south of the entrance and that it is being followed by an
accretional wave resulting from the 1974 beach nourishment project. It is of
interest to attempt to separate the erosional and accretional waves. At
present, this can only be accomplished in an approximately manner.
Ocean City Inlet, Maryland
Ocean City Inlet was caused by a hurricane in 1933. Within the next few
years, jetties were constructed to maintain the channel navigable. Major
changes that occurred in the vicinity included impoundment at the north jetty,
severe erosion of the shoreline south of Ocean City Inlet and the development
of a substantial shoal offshore and slightly south of the entrance centerline.
Additionally, substantial erosion of the ocean shoreline occurred with
landward migration. Figure 18 presents map showing the location of Ocean City
Inlet.
This example describes a field effort to explain the cause of erosion to
the northern portion of Assateague Island and also presents the results of an
attempt to compute a sand budget.
The sand budget components were determined by a combination of field and
computational procedures. The net longshore sediment transport was based on a
combination of impoundment measurements against the north jetty after it was
constructed and wave observations. The computational results are presented in
Figure 19 and are to be compared to the impoundment results against the
updrift jetty of 120,000 m3/yr. The computed values based on wave
observations exceed the impoundment values by a factor of 6, however, the
observations were made at a distance of 13 km south of the inlet and it is
known that transport increases to the south. The volumes lost and gained by
migration of the barrier island were based on Eq. (23) and even though the
I *
Approsomote Sector
Sneiterea From
'I
S Northeast waves By
60 1 Deon Contour
I. r
,. ,' ,0o o N
Z TOO' .
' '7500,W
'' : '" Legend
Pa ./I 60 f Contour
~6 tt Contour
o'
0 10 20 30
Scote Inoui. m )
Figure 18. Location of Ocean City Inlet and Influence of Bathymetry in
Reducing Wave Action Along Northern Segment of Shoreline Cape
Henlopen to Fishing Point.
C
.5
/,
II I I I 1 I I I
SNo I: Figures 17 & IS Bosod On The
LorngAhore Tronsport neroy
in The Shore Protection Monuol
I t I I I I I I I I I
J F M A M J J
A SO ND
Month
Figure 19. Averages and Ranges of Net Longshore Transport, Assateague Island,
Based on LEO Data for the Years 1973, 1974 and 1975.
60
400
200
0
200
FIL
'w
island basically retained the original width, the volumes lost exceeded those
gained by 38,000 m3/yr due to ho > hb* of Eq. (23).
Field observations of the south jetty demonstrated that it was both low
and porous allowing considerable sediment to flow from north Assateague Island
into the entrance channel from where it was jetted to partially account for
the growth of the offshore shoal. Field measurements were conducted with a
"swash trap" constructed of reinforcing rod and porous plastic mesh, see
Figure 20. Deployment of this trap quantified the flux of sediment through
the south jetty and these results extrapolated to account for the variable
wave and tide conditions resulted in an estimated flux of 31,000 m3/yr over
and through the south jetty. As support for the concept of the low and
permeable south jetty "draining" sand off Assateague Island's north beach,
beach profiles showed a trend of decreasing berm height from the natural
elevation of 2.4 m MSLseveral thousand meters south of the south jetty to the
1.4 m crest elevation of the south jetty, see Figure 21.
Finally, Figure 22 presents a best attempt to account for all the
components of the sediment budget. It is seen that there is a residual or
"mismatch" of 38,000 m3/yr out of a total of 680,000 m3/yr, or a discrepancy
of about 11%
CrossShore Distribution of Longshore Sediment Transport
A knowledge of the crossshore distribution of longshore sediment
transport is important in a number of engineering applications, including weir
jetty design. Several methods have been explored for inferring the cross
shore distribution of longshore sediment transport, including tracers, local
traps and in situ point measurements of suspended sediment, longshore currents
and bed load traps.
^/ Reinforcing Rods
Filter Cloth
Uprush Direction
Figure 20.
Sediment Trap Used in Measurements of Sand Transported by Wave
Swash.
Distance From Boseline (ft)
a) Beach Profiles Approximately 200 ft. South of South Jetty.
w Beach Profile: Sept.,I 1976 (post Belle)
S" Beoch Profile: June I. 1977
4
g6 "~ PProfile of South Jeltty \'
0 Projected on a Line Normal
S2 to Main Beach Alignment
w 0 _J L 1_JL
0 50 100 150 200 250 300 350 400 450
Distance From Baseline (ft)
b) Beach Profiles Approximately 2700 ft. South of South Jetty.
Figure 21.
Comparison of Elevations of South Jetty and Beach Profiles at Two
Locations South of Jetty.
Legend
1972
1931
Boy Shools
(+ 1.0 x 106 yd3)
Total
0 5000
Scale (ft)
:,
,
.*
Upword Growth Of Assoteogue
Island Due To Seo Level Rise
Over A Distance Of 32,000 ft
(+0.8 x 106 yd3)
N
Fillet Impoundment
At North Jetty Over
A 7000 ft Distance
(+ 2.8 x 10 yd )
L Ebb Shoal
/ (+8.0 10 yd5)
;Recession of Eastern
I Shore Of Assoteogue
I Island Over A 32,000 ft
S Distance.
(18.8 x 10 yd )
I
Westward Migration Of
Assoteoge Island Boy
Shoreline Over A Dis
tonce Of 32,000 ft.
(+8.2 x 106 yd )
NET FROM SEDIMENT BUDGET ANALYSIS = +2.0 x 106 yd
Figure 22. Results of Sediment Budget Analysis.
The method described here is based on Eq. (3), rewritten below
ah 9qx + qy
at x ay
in which the source term, S, has been set equal to zero. Consider a barrier
placed instantaneously across the surf zone such that at the barrier,
q E 0. Also, consider that profile measurements are conducted before the
nearbarrier profiles steepen to the degree that crossshore transport is
induced. Thus if the profile is initially in equilibrium and remains so, the
crossshore transport Qx = 0.
Integrating Eq. (3) along a contour from the barrier to a location, y2,
unaffected by the presence of the barrier,
qy(Y2,h) = q y(Ylh) + j Ah(h)dy
Y1
Fulford (1975) has applied this method in the laboratory. Bodge (1986) has
applied this method in the laboratory and field and has presented a method to
remove the firstorder timevarying effects of the tide. Figure 23 presents
an example from Bodge of the crossshore distribution for plunging waves.
Entrance to St. Andrews Bay, Florida
This situation is somewhat similar to Brevard County, Florida. The
entrance was cut across a barrier island in 1934 and thus in geological time
scale is a fairly young inlet.
Shoreline change data are available for the period 18551934 as shown in
Figure 24a. There were areas of erosion and accretion; however, for the 36 km
section presented in Figure 24, the average shoreline change was one of
44
b
IA
Xb
0.01
0
Figure 23. E
T
0.5
x/xb
examples of the CrossShore Distribution of Longshore Sediment
transportt (Bodge, 1986)
5
51 1 1 1
DISTANCE
10
EAST FROM
BAY COUNTY
LINE (km)
a) Shoreline Change Rates
18551934 (79 Years).
5
E
0
z
I
u
z
Li
0
= 1 1
Prior to Cutting Entrance to St. Andrews Bay,
DISTANCE EAST FROM BAY COUNTY LINE (km)
b) Comparison of Shoreline Change Rates Prior to Cutting Entrance to
St. Andrews Bay, 18551934 (79 Years) and Subsequent to Cutting
Entrance, 19341984 (50 Years).
Figure 24. Effect of Cutting Entrance to St. Andrews Bay in 1934 on Downdrift
Shoreline.
0O
accretion, averaging approximately 0.3 m/yr. The average shoreline change for
the period 1934 to 1984 is presented in Figure 24b. It is seen that
immediately downdrift (west) of the entrance, the shoreline change rate had
been altered from one of accretion of approximately 1 m/yr to one of erosion
in excess of 2.5 m/yr, i.e. a differential erosion in excess of 3.5 m/yr. In
this 50 year period, the shoreline immediately downdrift of the inlet eroded
by more than 125 m whereas under natural conditions, the projected accretion
would have been approximately 50 m.
In the case of St. Andrews Bay Entrance, there were three contributing
factors to the downdrift erosion:
(1) Approximately 7.5 million cubic meters of sand was dredged from the
entrance channel and spoiled in deep water,
(2) After the inlet was cut, the ebb tidal shoal developed accumulating
approximately 3,000,000 cubic meters, and
(3) The jetties were extremely leaky which contributed to the necessary
dredging in (1), above.
As a verification that the leaky jetties contributed to the required
shoaling (and thus the downdrift erosion), the net longshore sediment
transport is estimated as 60,000 cubic meters per year whereas the downdrift
erosion was in excess of 160,000 cubic meters/yr.
Offshore bathymetry is insufficient to estimate the downdrift volumetric
erosion rate. However, as before, it is possible to estimate this based on
planform changes and Eq. (22). The average annual differential planform
changes are 20,300 m2 erosion which when combined with a profile change of
8 m, yields an annual volumetric erosion rate of 160,000 cubic meters or a
total erosion over the 50 year period of 8,100,000 cubic meters.
Rudee Inlet, Virginia
Rudee Inlet, Virginia was a second field location in the Nearshore
Sediment Transport Study program where transport rates were studied to
investigate the longshore sediment transport equation. The net longshore
sediment transport is toward the north. The south jetty of the inlet includes
a weir section which allows sediment to enter a deposition basin from which
the sediment is dredged and transported by pipeline across the entrance to
Virgin Beach, see Figure 25.
When the experiment was planned, it was assumed that the weir allowed the
net longshore transport to pass over the weir during transport toward the
north and that sediment transported during reversals was relatively small.
Fortunately, the survey plan included a substantial portion of the updrift
beach as shown in Figure 26.
It was found that the net longshore sediment transport toward the north
was a small fraction of the gross transport. During periods of northerly
transport, relatively large volumes of sediment are transported and deposited
updrift of the north jetty whereas only a small quantity enters the deposition
jetty. During periods of sediment reversal, the volumes stored updrift of the
jetty is diminished, but sand continues to be carried across the weir section.
Thus in order to obtain the appropriate volume for correlation with the
longshore wave energy flux factor, it is necessary to include the volume
accumulated in the deposition basin and that either deposited or eroded from
the updrift (south) beach during the intersurvey period.
SUMMARY
The formalized framework provided by a sediment budget analysis is useful
in many general and specific coastal engineering applications, including
Virginia
Beach
I I II I I I I
100
Scale (m)
mber Sheet Pile
Weir Section
Figure 25. Rudee Inlet, Showing Weir Jetty and Impountment Basin (Adapted
From Needham and Johnson, 1972).
200
..
..
..
..
..
..
 Kitt0 tT tl S u.4 ;so t ltt t .
INtItVL
SCALt I' et a o o00 to
Figure 26. Rudee Inlet Survey Plan and Location of SX Wave Gage.
Ky
interpreting natural and altered systems, inferring onshore (or offshore)
sediment transport for a system that is out of equilibrium, determining
sediment transport rates from volumetric measurements, estimating the cross
shore distribution of longshore sediment transport, and many others. This
frameword should be developed and applied by all practicing coastal engineers
confronted by the difficult problems of understanding a system, many times
with inadequate data available.
REFERENCES
Bodge, K. R., "Short Term Impoundment of Longshore Sediment Transport," Ph.D.
Dissertation, Coastal and Oceanographic Engineering Department,
University of Florida, Gainesville, FL, 1986.
Dean, R. G., "Shoreline Erosion Due to Extreme Storms and Sea Level Rise,"
Report No. UF/COEL83/007, Coastal and Oceanographic Engineering
Department, University of Florida, Gainesville, FL, 1983.
Fulford, E. T., "Distribution of Longshore Sediment Transport Across the Surf
Zone," Master's Thesis, Department of Civil Engineering, University of
Delaware, Newark, DE, 1982.
Rudee Inlet, Virginia
Rudee Inlet, Virginia was a second field location in the Nearshore
Sediment Transport Study program where transport rates were studied to
investigate the longshore sediment transport equation. The net longshore
sediment transport is toward the north. The south jetty of the inlet includes
a weir section which allows sediment to enter a deposition basin from which
the sediment is dredged and transported by pipeline across the entrance to
Virgin Beach, see Figure 25.
When the experiment was planned, it was assumed that the weir allowed the
net longshore transport to pass over the weir during transport toward the
north and that sediment transported during reversals was relatively small.
Fortunately, the survey plan included a substantial portion of the updrift
beach as shown in Figure 26.
It was found that the net longshore sediment transport toward the north
was a small fraction of the gross transport. During periods of northerly
transport, relatively large volumes of sediment are transported and deposited
updrift of the north jetty whereas only a small quantity enters the deposition
jetty. During periods of sediment reversal, the volumes stored updrift of the
jetty is diminished, but sand continues to be carried across the weir section.
Thus in order to obtain the appropriate volume for correlation with the
longshore wave energy flux factor, it is necessary to include the volume
accumulated in the deposition basin and that either deposited or eroded from
the updrift (south) beach during the intersurvey period.
SUMMARY
The formalized framework provided by a sediment budget analysis is useful
in many general and specific coastal engineering applications, including
interpreting natural and altered systems, inferring onshore (or offshore)
sediment transport for a system that is out of equilibrium, determining
sediment transport rates from volumetric measurements, estimating the cross
shore distribution of longshore sediment transport, and many others. This
frameword should be developed and applied by all practicing coastal engineers
confronted by the difficult problems of understanding a system, many times
with inadequate data available.
REFERENCES
Bodge, K. R., "Short Term Impoundment of Longshore Sediment Transport," Ph.D.
Dissertation, Coastal and Oceanographic Engineering Department,
University of Florida, Gainesville, FL, 1986.
Dean, R. G., "Shoreline Erosion Due to Extreme Storms and Sea Level Rise,"
Report No. UF/COEL83/007, Coastal and Oceanographic Engineering
Department, University of Florida, Gainesville, FL, 1983.
Fulford, E. T., "Distribution of Longshore Sediment Transport Across the Surf
Zone," Master's Thesis, Department of Civil Engineering, University of
Delaware, Newark, DE, 1982.
