JOURNAL
OF GEOPHYSICAL
RESEARCH, VOL. 94, NO. C1, PAGES 995-1011, JANUARY
15, 1989
Quantificationof SandBar Morphology:
A Video TechniqueBasedonWave Dissipation
T. C. LIPPMANN AND R. A. HOLMAN
College of Oceanography,Oregon State University, Corvallis
A techniqueis presentedto remotelymeasurethe scalesand morphologyof natural sandbars based
on the preferentialdissipationof wind waves and swell over the crestsof the bar. Photographicor
video images are recorded and statistical uncertaintiesassociatedwith incident wave height modulations removedby averaging(time exposures).Ground truth testing of the techniquewas carried out as
part of the SUPERDUCK experimentin October 1986. The time exposuresgenerallyprovideda good
mappingof underlyingmorphology,allowing detectionof the bar and determinationof cross-shore
and longshorelength scales.However, during high waves, persistentsurfacefoam obscuresthe relationship of image intensityto local dissipation(modeledtheoreticallyby dissipationof a random
wave field), and an enhancementtechniqueof image differencingmust be done to remove the bias.
Errors in the estimateof bar crest distancefrom the shorelineare generally less than 35%, but this
value dependson the geometryof the particularbar. Logistic simplicityand quantitativecapabilities
make this techniquevery attractive.
INTRODUCTION
thought, it is now feasible [Huntley et al., 1981; O ltrnanShay and Guza, 1987].
Measuring the morphology over large enough spatial
coastlines. The accumulation of sediment into large-scale
features makes them an important, as well as interesting, scales and short enough time scalesremains a major diffisediment transport region. They are also very dynamic. culty, exacerbated by the scientific emphasis on storm
While annual cycles in sedimentdepositionare observedon periods when bar evolution is occurringmost rapidly. Traditionally, bar measurements are made using in situ field
most coastlines (with offshore transport tending to form
techniquesthat, due to hostile conditions in the surf zone
bars during higher energy wave conditions in winter
environment, are not always easily applied. Also, the large
months), significant morphological changesalso occur on a
scale of most bar forms requires extensive surveying both
much shorter time scale, especially in responseto storms.
cross-shoreand alongshore,typically on the order of many
The physicalprocessesthat contributeto the dynamicsof
hundredsof meters. Nonstationaritymay lead to errors if the
barred beaches are clearly not as simple as for plane
beaches. Yet the new information available from studying bar moves significantly during the surveying period.
these more complicatedenvironmentsmay provide valuable Hastening the surveying process can eliminate bar
clues into the nature of the fluid-sediment
interaction.
In
stationarityproblems,but not without the inevitable loss in
particular, cross-shoreand longshore length scales of bars spatial resolution and the potential introduction of spatial
may potentially be related to fluid parametersif appropriate aliasing.
dynamicalmodels are available.
We have developeda remote sensingtechniquethat allows
The literature containsa numberof models for bar genera- the visualization and subsequentquantificationof nearshore
tion by fluid motions. It has been hypothesizedthat linear morphology based on the patterns of incident wave breakbars are formed at the breaker location of plunging incident ing. The premise of the techniqueis that more waves break
waves [Keulegan, 1948; Shepard, 1950; Miller, 1976], or over the shallows of the bar than surrounding areas. The
under nodes or antinodes of waves standing against the sharp contrast between breaking and nonbreaking regions
shoreline [Carter et al., 1973; Lau and Travis, 1973; Short,
may be imaged photographically;however, instead of using
1975; Bowen, 1980]. Hypothesesexist for the formation of
an instantaneous"snapshot,"we employ a long time expothree-dimensional crescentic [Bowen and lnman, 1971],
sure, thereby averagingout fluctuationsdue to incident wave
welded, and apparentlyaperiodicsandbars, based,for exam- modulations and giving a statistically stable image of the
ple, on the interactionof phase-locked
edgewaves[Holman wave breaking pattern. Figure 1 illustrates the technique.
and Bowen, 1982]. Yet, surprisingly, these models are The breaking wave pattern in Figure la suggeststhe preslargely untestedunder natural conditions.
ence of a sand bar, but the poor spatial coverage provided
There are several reasons why field tests have not been by breaking crests and the statistical uncertainty associated
accomplished.Propermeasurementof the low frequency"surf with natural modulationsin wave height render the details of
beat," invoked by several of the models, requires sophisti- the bar morphology uncertain. In Figure lb the breaking
cated analysistechniquesto resolve particular trapped (edge pattern has been averagedover a 10-min period in a time
waves) and leaky modes. Though this techniquerequires a exposure.This image yields a much clearer view of the bar.
more extensive array of instrumentation than originally
Spatial coverage is both extensive and of high resolution.
Nonstationarity problems are avoided, since the sampling
Copyright 1989 by the American GeophysicalUnion.
interval (10 min) is substantially less than the observed
time scales of appreciablebar movement [Sallenger et al.,
Paper number 88JC03642.
1984]. Finally, the logistics of the remote measurement
0148-0227/89/88JC-0 3642505.00
technique are not constrainedby high-energy surf zone conOffshore
sand bars are common
features
of the world's
995
996
LIPP•
AND HOLMAN: QUANTIFICATIONOF SAND BAR MORPHOLOGY
Fig. la
':
ß
.{ -....i:.!;;½•:
7'*--...
-..,....:.;•
.
....
.......
Fig. 1b
Fig. 1. (a) Oblique snapshotof wave breakingon October 10, 1986, at low tide duringthe SUPERDUCK experiment.
(b) A 10-min time exposurefrom the samedate and tide. The white band at the shorelineis the dissipationmaximum
corresponding
to the shorebreak, while the band offshoreindicatesthe presenceof a sandbar.
ditions and can be utilized wherever an adequate vantage
point is accessible.
There has been some work on this problem as early as the
1940s using aerial photography [e.g., Wiegel, 1947;
Lundall, 1948; Harris and Urnbach, 1972], however with
large uncertaintiesresultingfrom the small numberof infre-
light intensity patterns observed in time exposure images
and the underlying morphology, we make a working
assumptionthat light intensity will vary as the dissipation
of the incident waves. Modeling of dissipation over arbitrary topographyusing the random wave model of Thornton
and Guza [1983] then gives guidanceto the expectedperforquent observationsand limited knowledge of the precise mance of the technique (while measured light intensity
connection between instantaneous visual wave breaking profiles turn out to be very similar to calculated profiles of
patterns and underlying topography. Our approach will dissipation, lending support to our assumption,we do not
greatly improve these estimatesand allow for quantitative actually test this hypothesis by measuring wave dissipation).
evaluation of the technique.
Following the theory is a section on the photogrammetry
Our discussionof the techniquewill start with the theoretical background.To understandthe relationshipbetween the involved in the transformation of oblique images. The theo-
LIPP•
ANDHOLMAN:QUANTIFICATION
OFSANDBARMORPHOLOGY
retical resolution and accuracyof the techniqueare then
discussed,
followed by a descriptionof our field methodsand
laboratory digitization techniquesusing a computerized
image processor.Finally, we will discussfield tests based
on field data from the 1986 SUPERDUCK experiment
[Crowson et al., 1988].
TiIEORY
sity signal to determine the location of the bar crest, not
the break point. However, this problem, which also occurs
in the theory of longshore currents [Thornton and Guza,
1986], can be correctedby consideringa random wave model
where wave energy is consideredcomposedof a distribution
of waves with heights that are described statistically
[Thornton and Guza, 1983]. For the remainder of the paper
we will
The patterns of light intensity that are recorded in the
time exposurephotographsare a result of the bubbles and
foam of breakingwaves.To relate this visible signalto the
fluid motions (and hence the underlyingbar morphology),
we must make some assumptionabout the mechanism of
bubble formation. For the purposesof this paper we will
hypothesize that the light intensity recorded on the film,
I(x,y), is simply proportional to the local incident wave
energy dissipation l•(x,y),
997
Random
focus on the random
Wave
wave model.
Model
Models for the shoaling and breaking of random wave
fields have been publishedby a number of authors[Collins,
1970; Battjes, 1972; Kuo and Kuo, 1974; Goda, 1975;
Battjes and Janssen,1978; Thornton and Guza, 1983]. These
models considerthe wave energy to be composedof a distribution of waves of varying height. The analysis is then
carried out statistically, representingthe waves in terms of
probability distributions whose bulk properties may be
(1)
found by integration. Many of these models invoke depthwhere the angled brackets indicate time averaged. Since limited breaking to determine dissipation (equation (2)).
modelsof dissipationover a barredprofile suggesta strong However, the latter two [Battjes and Janssen, 1978;
dependenceof local dissipationon underlyingmorphology, Thornton and Guza, 1983] specify dissipationand use (2) in
dissipationmay serve as a proxy measureof the nearshore the opposite direction to find wave height. We will follow
topography.
the analysisof Thornton and Guza [1983] (hereafterTG83).
We will approachthe problemthroughthe energy flux
Using the extensivedata set from the NearshoreSediment
balance,
TransportStudy (NSTS), TG83 showedthat the wave heights
H of a randomincidentwave field were well describedby a
a'-•'
(Ecg)
=•
PgH c = <e>
(2) Rayleigh probability distribution,
where p is density,g is the accelerationdue to gravity,E is
p(/_/)=2// exp-
thewaveenergydensity,
andcgis thegroupvelocity.
(4)
The simplestrepresentation
of wavesshoalingon a beach
assumesthat the incident energy is narrow banded and can which is an implied function of local depth, and hence of
be represented
by a singlefrequency
f andwaveheightHrms. cross-shoredistance. Surprisingly, this result was found to
Outside the surf zone, dissipationis throughbottom fric- be valid throughout the entire nearshore region, including
tion. This is small comparedwith the dissipationdue to surf the surf zone where the underlying assumptionsof linearity
zone breaking[Thorntonand Guza, 1983] and providesno are clearly violated.
As the wave field shoals, some portion of the waves
surfacesignalfor imaging.Thus we take wave energyflux
begin
to break, modifying the distribution.The form of this
Ecgto be conserved
outsidethebreakerline.Insidethesurf
zone, wave height is assumeddepth limited, similar to soli- modification is the main distinguishingfeature of the abovetary wave theory [McCowan, 1891] or monochromaticlab listed random wave models. TG83 are unique in that their
results[Galvin and Eagleson,1965] and supportedby field model for the shoaling of the wave height distribution is
based on field data from a barred beach (Soldier's Beach,
tests [Thornton and Guza, 1982],
Hrms(X
) = •[h(x) x < xb
(3)
where xt, is the position of the breaker line and h is the still
water depth.Thus wave energyflux is strictly a functionof
depth, and local dissipationis simply determinedfrom the
flux gradient(equation(2)). Dissipationover an arbitrary
beachprofile can easilybe calculatedusing(2) and (3).
This monochromatic representation of the wave field,
while simple, has several distinct disadvantages.
First, if
taken strictly, wave heights should actually increase as
wavespropagatefrom the bar crest into the deeperwater of
the trough.However,this nonphysicalresult can be simply
avoided if, as a wave is numerically shoaled,the criterion
for whetherit is breakingis basedon a "local" wave height,
calculatedby inviscid shoalingfrom the point immediately
offshore. The second problem with the monochromatic
model (more severefor our application)is that the maximum
dissipationwill generally be at the initial break point. This
is, again, a nonphysicalresult, as well as an unfommate one
for our technique,sincewe are interestedin using the inten-
California) wherein the wave height time series were augmentedwith a record of which waveswere actuallybreaking.
They expressthe probability distributionof breaking waves
pb(H) as a weightingof the distributionof all waves,
pb(H) = W(H) p(H)
(5)
where, from the data, they determine the best form of the
weighting function to be
They then model the dissipationof a breakingwave based
on a periodicbore model [Stoker, 1957;Hwang and Divolcy,
1970],
3
l•= f-pg(B/-/)
4
h
(7)
whereB is an empiricalbreakercoefficient,roughlyrepresenting the fraction of the bore face that is covered with
foam. The mean dissipation(1•) is then the integral through
the breaking wave height distribution,
998
LIPPMANNAND HOLMAN: QUANTIFICATIONOFSANDBARMORPHOLOGY
Plane
0
Beach
Case
i
-2'
-6
0
20
4'0
6'0
80
1;0
120
x (m)
Random
Wave
Model
1.2
200
1.0
'•--ø
Hrms
150
0.8
0.6
100 •:
0.4
A
50
0.0
,
E
,
0
20
,
,
40
60
1;o
8'0
V
o
12o
piest beach profile and provides a good illustration of the
behavior of wave dissipation over unperturbedtopography.
The second, Torrey Pines beach (the site of the NSTS
results) was used first to check the model results against
TG83 (an error check of the programming) and, second,to
show the sensitivity of dissipation to minor perturbations
in an otherwisesimple profile. Finally, a barred profile from
the SUPERDUCK experimentwas usedto show the ability of
dissipation(and hence the time exposuretechnique)to highlight the bar crest location. The latter case was also used to
provide an understandingof the ground truth studies,conductedduringSUPERDUCK, that will be discussed
later.
Figure 2 showsthe behaviorof the random wave model on
a plane beach profile, shown in the top panel. The model
shows a single broad dissipation maximum offshore, resulting from the distribution of wave heights with some
dissipationarising offshore due to the more energeticwaves
while most waves break near a finite break point. There is a
dissipationmaximum (albeit broad) despite the fact that the
beach profile is plane. The area under the curve must equal
the deep water energy flux.
Figure 3 shows the model results for Torrey Pines beach
on October 20, 1978, during the NSTS experiment.This day
was chosen as one of the two data runs analyzed in TG83
againstwhich we could check the functioningof our model.
Again, the beach profile is shown in the top panel, with
associatedHrms and (1•) curvesfor and randomwave model
shown in the lower panel. Since the distribution of dissipation is dependenton local water depth, peaks of dissipation
xi'm)
Fig. 2. Model results as waves are shoaled over a plane beach
profile (top panel). The behaviorof Hrms and (e), plotted against
offshore distance, is shown for the random wave model in the
Torrey Pines 20 OCT 78
bottom panel.
3rem
5
Hnns
_
(•>
='-• pgB
3ey2h
3
1
H
(8)
-1
-2-
Application of the Model
Numerical implementationof the randomwave model was
carried out to determine the behavior of dissipation over
variousprofiles, and to provide a comparisonfor field tests,
to be discussedlater in the paper. The energy flux balance
(2) forms the basisfor the model. TG83 note that in testing
a variety of numerical schemes,the simplestforward stepping techniquewas foundto be sufficientlyaccurate.We will
-4
100
1•0
2;0
2,,
x (m)
Random
Wave
Model
0.8
use this same algorithm,
ecv,
l--gq,,I +
ax
Starting from the deepest grid point (assuming a wave
height that has been linearly shoaledfrom deep water), the
wave energy flux is steppedlandward.For the randomwave
model, the flux at any shorewardpoint, labeled 2, is calculated using the flux and dissipation(equation(8)) found at
the next seaward point, labeled 1. Note that the shallow
water assumption
is valid for all casesexamined.Valuesused
for B and ? are 1.54 and 0.42, respectively,taken as repr•.sentative of field data [TG83].
Examples
Theoretical dissipationprofiles have been calculatedfor
three beach profiles. The first, a plane beach, is the sire-
0.6
,,,,,'
Hrms
0.4
40
0.2
20
¾
0.0
100
0
150
200
250
x {m.)
Fig. 3. Model test resultsfor wave shoalingand dissipationover a
surveyedprofile (top panel)from TorreyPinesbeachon October20,
1978. The cross-shore
behaviorof Hrms and (e) are shownfor the
randomwave model in the lower panel.
LIPP•N
SUPERDUCK
999
ANDHOLMAN:QUANTIFICATION
OFSANDBARMORPHOLOGY
poorlyreproduced,
sinceour dissipation
modelartificially
11 OCT 86
forceswave height to zero at the shoreline(we allow no
standingwave component).
The influenceof deep-water
significant
waveheightH 0 on
the randomwave model is shownin Figure 5. For any off-
shoreposition,
it appears
thatan increase
in H0 will result
-2
in an increasein local RMS wave heightHrmsup to a maximumvaluewhichdepends
on depth.Furtherincreases
in H0
have no effect, and the local wave field is said to saturate.
This behaviorshowsthe mergingof the dissipation-based
model of shoalingused here with earlier depth-limited
-5
100
modelsfor depthsthat are "shallow"with respectto the
waveheight,a point that was alsomadetheoretically
in
500
TG83.
x(m)
Variation of wave period T will affect the modelin two
Random
Wave Model
ways.The deepwaterenergyflux (henceareaunderthedis-
lOO
1.0
-
0.8
..--"
rms
80
,
•6o
SUPERDUCK
E
11 OCT 86
o
J
0.4'
-40 •
v
1
A
0.2'
•
20 •V
0
0.0
O0
200
300
400
500
x (m)
Fig.4. Model resultsfor wave shoalingand dissipationover a
barredbeachprofile(toppanel)fromSUPERDUCK
on October11,
1986. The cross-shore
behaviorof Hrmsand(t) are shownfor the
5
100
randomwave model in the lower panel.
i
200
ß
i
300
ß
i
ß
400
500
100
will reflect positivechangesof slope ("bumps"in the
E 8o-
perturbation
profile).Themodelindeed
yieldsa well-defined
dissipation
peakoverthelargeoffshore
bumplocated
at x =
ß""
60-
perturbations
(sandbars,terraces)
in thebathymetry.
v
40
Figure4 shows
waveshoaling
anddissipation
for a barred
beachprofile (actuallya linearstormbar whichformed
duringtheSUPERDUCK
experiment).
A second
perturbation
r.O 20
200 m. Thusit appears
thatthe imagingof dissipation
may
proveusefulin determining
thehorizontal
lengthscales
of
375 m offshoreis the residualof a semipermanent
second
linear bar. Three featuresare apparentin the dissipation
curves. Offshore, the presence of the second bar
H 0 = 1.50
v
o
lOO
200
300
400
500
1.5
(perturbation)
is indicated
by therandom
wavecurveby a
smalldissipation
peak,shoreward
of whichdissipation
is
H 0 = 1.50
lower but not zero. This is similar to the resultsfor the low-
tideterraceon TorreyPinesbeach.The well-developed
inner
bar is clearlyhighlighted
by thedissipation
curve.However,
the locationof maximumdissipationis displacedseaward
from the measured
bar erest(locationof minimumdepth)by
20 m, a resultof weightingthe dissipation
towardthe larger
waves.Continuinglandward,the troughis indicatedby a
ß
.•0.5
•
o.5o
0.0
,
regionof essentially
zerodissipation.
Thiscontrast
between
100
200
300
400
500
thelargedissipation
overthebar andzerooverthetrough
x (ml
distinguishes
(at leastqualitatively)
the signaldueto sand
barmorphology
fromthatof a terraceor moreminorperturFig.5. Influence
of deep-water
rmswaveheightH0 overa barred
bation.Finally,we seea narrowdissipation
maximumnear beach
profile(toppanel)fromSUPERDUCK
onOctober
11, 1986.
the shoreline,a featurethat alsoshowsup in the field tests The effect of increasingH0 on dissipation,(t), and local wave
locations
is shownin themiddleandlower
discussedlater. While the presenceof this shorebreak heightHrms at offshore
maximum is reasonable,the details of its location may be
panels,respectively.
1000
LIPPMANNAND HOLMAN: QUANTWICATIONOFSAND BARMORPHOLOGY
Theoretical Error vs. Non-dimensional Wave Height
0.40
noted that this value is just from one sample geometry and
would be different for different beach profiles. For instance,
the value of Xc does not enter into the dimensionalerror Ax,
so that for bars that are farther
offshore
the error would
be
smaller, and vice-versa.Similarly, for larger hc (suchas for
higher
tides),
Hc*wouldbesmaller,
andfor highertides,xc
0.30
would be larger. Both would tend to yield smaller relative
errors. Again, the opposite is also true, so that for lower
fides and smaller he, estimateswill tend to be worse.
x
0.20
PHOTOGRAMMETRY
We wish to use oblique images to quantify the offshore
and longshorelength scalesof the sand bar (and potentially
other variables). Although photogrammetric equations for
transformingimages have been developed[e.g., Okamoto,
0.00
1982], the necessaryequationswill be derived here for com1'o
15
20
pleteness.
H
c
The location of any object in the image is a function of
the spatial orientation of the camera in relation to ground
Fig. 6. Fractional error in locating the bar crest from theoretical topography and can be determined by a simple analysis of
dissipationmaxima plotted againstnondimensional
wave height/-/•c.
the geometry. We will outline the equations that define the
transformation between image coordinates and ground
coordinates. When transforming from ground to image
sipation curve) dependslinearly on T. Also, the dissipation
coordinatesthe equationsare fully defined. However, since
(equation (8)) is inversely proportional to T. The net result
the image is two-dimensional while the ground is threeis that dissipation profiles for different wave periods have
dimensional, the opposite process (called rectification) is
different magnitudes but the same structure, including locaunderdetermined. This is overcome by assuming one
tion and shape of peaks.
dimension to be known. For example, in rectifying images
The saturationbehavior of dissipationis beneficial to our of waves the vertical coordinate is assumed to be at sea
objective of locating sand bar features,since the location of
level; errors of the order of the wave amplitudeare assumed
the offshore dissipationmaximum is only weakly sensitive
negligible comparedto the height of the camera.
to offshore wave parameters.This is quantified in Figure 6,
The geometry and labeling conventionsused in the rectiwhich shows the fractional error in locating the bar crest
fication process are shown in Figure 7. Image coordinates
(difference between the location of the offshore dissipation
will be denoted with small letters (x,y), and ground coordimaximum and the measuredbar crest position Ax, divided by
nates will be denoted with capital letters (X,Y). The optic
the offshore distanceto the bar crest at mean tide xc) versus
center of the camera is located at point O, a distanceZc
the nondimensional wave height,
above the x-y (ground) plane. The camera nadir line intersectsthe ground at the nadir N. The image points lie in the
focal plane, which for our purposeswill be consideredthe
1'1 positive, consistent with traditional photogrammetry
The variables hc and kc refer to the depth and local wave conventions. The focal plane is separated from O by the
number at the bar crest, and k0 is the deep-waterwave num- focal length fc, determined by the camera lens. The optic
ber.Hc*is derivedby shoaling
thedeep-water
energyfluxto axis intersects the center of the focal plane at point p,
the bar crest, if wave breaking were not allowed (note that
the secondterm in (10) is the shoalingcoefficient).Figure 6
shows that the fractional error in locating the bar crest
0
prinmpal line
varies from 0% for small waves that just break over the bar
0.10
i
(Hc*= 0.5-1.0)to about35%for a saturated
wavefield.
•.•,
fc focal
plane
The above analysis suggeststhat if the visible intensity
signal recorded in time exposure photographsdoes depend
on incident wave dissipation, then the time exposuretechnique should work. Best resultswill occur for waves which
just break over the bar, but even for larger waves the error
in bar location identification
35%
will reach a maximum value,
for the above case. If the results are to be used to test
bar generation models based on standing wave motions,
wherein the bar location Xc scales as
C•2x
c
Zc--•
g[•
J. / / / •Ground
(11)
Plane
where• is the effective
beach
slope
ando = 2Kfisthe
radian frequency,then errorsof less than 18% will occur in
the predicted frequencyf of the standingwave. It shouldbe
Fig. 7. Geometry and labeling conventionsused for photogrammerry.
LIPPMANNANDHOLMAN:QUANTIFICATION
OFSANDBARMORPHOLOGY
called the principal point, and forms an angle x (the camera
tilt) with the vertical nadir line. The principal line passes
through the principal point and bisectsthe focal plane. The
principal point is also the origin for the image coordinate
systemwith the principal line as the y axis. The nadir point
acts as the origin for the camera coordinatesystem with the
principal line in the ground plane defining the positive y
axis.
The ground location of any point Q is determinedfrom its
imagecoordinates
(Xq,yq)
by
Xa =
sec + a) tan
(12)
1001
The unknowns •c, x, and • can be determined quite
accurately by making use of targets at known locations in
the image. By knowing both the ground and image coordinates of particular points, (12), (13), and (14) can be solved
iteratively to calculate the unknowns. If one known point
and the horizon are used, the solution will be unique. If two
or more known points are used, the problem is overdetermined and can be solved by m'mimizing an appropriateerror
term. Using this techniquein analyzing the images discussed
later in the paper, we find typical errors in the estimatesof
x, •, and f• to be less than 0.25ø, 0.5', and 0.5%,
respectively,
roughly consistent with theoretical
expectationsdiscussedbelow.
¾• = Z• tan(z + a)
TI-IEORETICAL RESOLUTION AND ACCURACY
The photogrammetric measurementsoutlined in the last
where the angles ot and •/are defined as
section are based on estimates of one distance (the camera
height) and two angles (vertical and azimuthal). The precision of the techniquethen relies on the precisionof each of
and
(13)
these
estimates.
While there may be errors associated with estimating
camera height above some surface, there is no inherent
limitation on that measurement.On the contrary, there is a
discrete resolution associatedwith our estimates of angle.
Transformation in the opposite direction, from ground to For image quantificationwe use an image processingsystem
image points, is done by simply inverting and combining (describedlater) which breaks the image into a 512 x 512
(12) and (13) to yield
array of pixels. Since we can resolveto no better than + 1/2
pixel, we find a fundamentallimit on angularresolutionto
yq=f½tantan
4
and
_x
be Aot = AT = 15/1024 (assuming tan 15/2• 15/2). For our
typicalwide-anglelens, 15= 40', so Aot= 0.04'= 7 X 10-4
(14)
radians.
From(12) we seethat theprecisionof estimates
in YI2is
given by
AYe2 AHc 2A(x+el)
Y•2 Hc sin2(x+ o•)
Several complications arise in applying these relationshipsin the field. First, theseequationsare a functionof the
camera tilt and focal length. Field measurementof tilt may
be awkward and inaccurate, and the focal length of a zoom
lens may be hard to estimate. Second, we do not generally
work from a 1:1 positive, but instead either read distances
on a photographicenlargementor count picture elements
(pixels) on a television screen. In doing so we will have
altered the apparent focal length of the image by an unknown amount. We can solve for the "magnified" focal
length analytically using
Xe
where xe is the measureddistancefrom the principal point to
the right-handedge of the enlargedimage and 15is the horizontal field of view of the lens. Unfortunately, for most
cases,15itself is not accuratelyknown. Third, the direction
of aim of a camera in the field is generally chosen to give
the best view. Thus the ground coordinatesystemdefined by
the principal line may not be particularly convenient.The
transformedground points can be easily rotated into a more
traditional coordinate system, for example with the x axis
directedoffshore, if the angle • between the two coordinate
systems is known. Unfortunately, accurate estimation of •
in the field is again difficult.
2A(x
+ o•) 1.4x 10-z
sin 2(x + o•)
(16)
sin 2(x + o•)
Sensibly, resolution degrades as (x + e•) approaches•/2, or
as the point of view approachesthe horizon. If we take the
maximum useful vertical angle to be 85ø (5 ø from the horizon), the resolution in Y will be 0.8%. Note that the fractional errors also increase as the view approachesnadir.
However, this is simply a result of normalizingby Y•2,
which goes to zero at the nadir; absolute errors will actually
be a minimum.
The error in X estimates(normalizedby Y•2, roughly
representingthe distancefrom the camera) is given by
AXQ={A"
4 tan•/ tan
TA(x
+el)
Y12 [-•-c
] sin(x+a)+ cos
(x+a)
+
1
AT
sin (x + a) cos27
(17)
For typical camera views, sin (x + or)= 1; hence the theoretical resolution is again limited by angular resolution
through the last two terms. Using representativevalues, we
find a worst case resolution of 0.3%, a smaller value than
for Y, partly due to the choice of normalization. Since the
camera coordinate system is not usually aligned with the
survey system, we chose a conservativeestimate that spatial
1002
LIPP•
ANDHOLMAN:QUANTE•CATION
OFSANDBAllMORPHOLOGY
600
I
•.
E
500
z
400
m
300
'
o
03 200
CERC
frf Pier
i i iii
iiiiiiii
iiiii
• I CERC
Tower
O
100
.i:i:5:!:i:i:5:i;i:i:i.:5:i:i:i:i:i:i:!:;:5:!:!:i:i:i:i:;:!:i:i:5:i
............................................
..,:....
...............
...................................................
:.:.:
..............
:.:.:.:.:.:..:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:
........
i:.i•"•
[ i
i
i400
i
i
i200
i
I
iOO0
I I
i
800
i
600
400
LONGSHORE DISTANCE (m)
Fig. 8. Map of the field site during the October portion of SUPERDUCK. The stippled area indicatesthe ground
coveragein the field of view of the camera.Cross-shoretransectSD200 is the location of some example profiles in
the text, while SD210 is the locationclosestto the main instrumentline in SUPERDUCK. Longshorespacingfor the
CRAB surveylines was 20 m (there existsan intermediateline, SD205, betweenthe two lines indicated).
resolution
distance
in either
from
axis will
be of the order of 0.8%
of the
the camera.
While fundamental limits on precision depend, for our
system, simply on the angular size of the pixels, the absolute accuracy of our measurement depends on cumulative
errors
from
a number
of
geometry, then solve for the maximum vertical angle for
which
estimates.
If
the location
of
the
camera is well known, the error in the first term of (16) and
(17) results largely from errors in determining sea level
(assumingthat the ocean surface is being imaged). For the
data discussed later, this will be of the order + 0.25 m with a
camera height of 40 m, so that the relative error contribution is 0.65%. This error could be substantiallylarger for
lower camera heights. Estimation of the vertical and horizontal angles actually incorporatesparameterssuch as x,j ø,
and q•,each of which has associatederrors.If we assumethat
the parametersthemselveswere estimatedbased on the location of two known points (as outlined in the previous
discussion),then they will collectively incorporatethe error
of four separate angle measures, 4Act. Including the error
associatedwith estimating the angle of interest, the total
angularerrorcouldbe 5Ac•= 0.20*= 3.5 x 10-3 radians.
For
a maximum vertical angle of 85', and including the error for
cameraheight, the theoreticalworst case accuracyshouldbe
this resolution
is achievable.
Fla.13 TECHNIQUES
The time exposure technique for estimating the incident
wave dissipationdistributionand hence large-scalenearshore
morphology was tested as part of the DUCK85 and
SUPERDUCK experimentsin September1985 and October
1986, respectively, at the Army Corps of Engineers Field
Research Facility (FRF) in Duck, North Carolina. The
DUCK85 experiment [Mason et al., 1987] was used to
perform initial testing primarily with standard 35-mm
cameras and simple photographictime exposuretechniques.
The images acquired were projected onto an x-y digitizer
table, and the location of the intensity maximum determined
visually [Holman and Lippmann, 1987]. Results from that
experimentwere encouragingbut indicateda need for further
quantification and for more sophisticated digitization
methods.
During SUPERDUCK the use of video imagerywas implemented as an improvement to the photographictechnique.A
Panasonic
black-and-white
television
camera
was mounted
on top of a 40-m-high tower erected on the dune crest.
Figure 8 is a map of the field site during the Octoberportion
of the SUPERDUCK experiment showing the location of the
AXQ AyQ
•
<
= 0.65% + (5 x 0.8%) < 5%
(18)
study area, referred to as the minigrid, in relation to the FRF
YQ
YQ
tower and the groundcoverageassociatedwith the camera.
As shown, the accuracy and resolutionof the systemdeHourly video recordsof 20-min length were acquiredfrom
pendson the angularfield of view 15and the verticalangle October 6-16. Time exposures were created digitally by
(x + or). The value of 15used here is for a wide-anglelens mathematicallyaveragingsuccessivevideo frames over a 10and gives a worst case result. Clearly, a telephoto lens, min period using an Imaging Technology image processing
zoomed in on the subject at hand, will yield improved esti- system in a DEC LSI 11/73 host computer (Figure lb is an
mates. The vertical angle becomes critical as (x + or) example time exposureimage from October 10). Using the
approachesthe horizon.While 85ø is a reasonablevalue for photogrammetry results, the time exposure image can be
a maximum angle, a better approachto experimentaldesign rectified to produce a map view with known scaling. The
would be to determine the required resolution and camera rectification process involves mapping the oblique image
LIPPMANNAND HOLMAN: QUANTIFICATIONOFSANDBARMORPHOLOGY
1003
Fig. 9. Rectified time exposureimage obtainedat low tide on October 16, 1986, encompassing
the minigrid area.
The longshoreand cross-shore
distancesare scaledequally with tic mark spacingof 50 m. The thin white band indicates the shore break, while the broader offshore band showsbreaking over the bar. The relative size in raster width
reflects the pixel resolutionin the original time exposure.
intensities, pixel by pixel, onto the scaled grid. From the
rectified view, cross-shore intensity profiles at prescribed
longshoredistancesare easily found. Figure 9 is the rectified
image of the minigrid area outlined in Figure lb. Figure 10
shows an example cross-shoreintensity profile and the local
bathymetry. Clearly, there are local maxima in the intensity
distribution in the vicinity of the shoreline and the bar,
which appear very similar to the model results presented
earlier (Figure 4). Note that only relative magnitudes of
intensity are relevant within an image; absolutemagnitudes
vary with ambient light and camera aperature.
Quantification of images is accomplishedusing an image
processingsystem. Extracting information with this system
is objective and allows for minimum handling of raw data.
Furthermore, with the aid of the image processor we may
digitally enhance the images to best reveal the information
available. For example, though some video records do not
yield high-contrastraw images, the image processorallows
5.0
:•.....Bathymetry
-
%•
Intensity
_
-o
Cross-Shore
Profile16Oct.86 .......................
SD200
-5.0
us to increase the dynamic range of the image by stretching
the contrastto as many as 256 gray shades.
Ground truth bathymetry data during SUPERDUCK were
collected by the FRF staff using the CERC Coastal Research
Amphibious Buggy, or CRAB [Birkemeier and Mason,
1984]. Figure 8 shows the location of the intensive survey
region referred to as the minigrid. The bathymetry was
sampled once per day (October 6, 9-16) along preset crossshore profile lines spaced approximately 20 m apart alongshore. Each survey went beyond the first (and most prominent) sand bar, with the exception of the tenth, when
adverse conditions prevented survey completion. Figure 11
shows three-dimensional oblique views of the minigrid
survey for October 6, 9, 11, 13, 15, and 16 [Birkemeier et
at., 1988].
A maximum of 20 shore-normal image intensity profiles
within the minigrid area were analyzed for each data run. As
in Figure 10, each profile contained a maximum intensity
(or peak) in the vicinity of the shoreline and the bar,
provided the waves were breaking offshore. Given the large
amount of data, 464 cross-shore comparisons, not all the
profile plots are included. Instead most of the data are
summarized in the following analysis using two-dimensional
plan view maps indicating the surveyed bar location and
digitized intensity maximum location at different stages of
the tide. With this sampling scheme we are able to determine the behavior of the cross-shore intensity distribution
in relation to the bathymetry under varying wave conditions, water levels, and beach state. Table 1 summarizes the
sampling times, wave conditions,.and video quality for each
data run.
1142 rn
I
I
I
I
50
I00
150
200
i
250
RESULTS
I
300
Cross-Shore Distance (m)
Fig. 10. Example cross-shoreintensity profile and bathymetry for
October 16, 1986, during SUPERDUCK. The intensity values are
nondimensionalwith absolute magnitudesthat are not related to the
bathymetry.
Time Exposures
The researchobjectivesof the time exposuretechniqueare
threefold. The first is to infer the presence of a sand bar
from an offshore intensity maximum correspondingto the
maximum time-averaged incident wave dissipation. The
1004
LIPP•
AND HOLMAN: QUANTIFICATION
OFSANDBARMORPHOLOGY
SUPERDUCK
OCT
s
11 OCT
BATHYMETRY
OCT 86
86
86
s•__..__ 13OCT86
.............
? F_.
•... '
d.
•
15 OCT
-
86
16 OCT
86
.
Fig.11. Three-dimensional
obliqueviewsof theminigridsurveyduringSUPERDUCK
[Birkemeier
et al., 1988].
second is to determine the cross-shorelength scale of the
bar from the locationof the intensitymaximum.The third is
to detect the presenceof any longshorevariability in the
The theoretical dissipation model suggeststhat best
resultswill be obtainedfor small waves that just break over
thebar(H*c valuesof 0.5 to 1.0). For October6 an average
bar and determineappropriatelongshorelengthscales.We
value of H* c was approximately 0.85, and while the
will examine each objectivein turn.
bathymetrywas complex,therewere local regionsof good
LIPPMANNAND HOLMAN: QUANTIFICATIONOF SAND BAR MORPHOLOGY
TABLE
1.
Date
SamplingTime, Wave Conditionsand Video Qualityfor
MorphologyImagesDiscussedin Text
Tide,m
(October)
Time,
Hrm•, m
f, Hz
Video Quality
•
6
6
9
9
9
10
10
10
11
11
11
low -0.11
mid 0.25
high 0.80
mid 0.27
low -0.27
low -0.08
mid 0.55
high 1.10
low 0.09
mid 0.56
high 1.06
1400
1730
1130
1445
1800
0600
0915
1230
0720
1040
1400
0.82
0.56
0.43
0.44
0.38
0.33
1.35
1.58
2.06
2.13
2.06
0.1680
0.1719
0.1641
0.1641
0.1641
0.2656
0.1484
0.1406
0.1094
0.1563
0.1016
good
good
good
good
good
good
poor (rain)
poor (rain)
good
good
good
12
12
low
mid
0830
1145
1.65
1.85
0.0938
0.0859
excellent
excellent
!2
13
13
13
14
high 0.93
low -0.22
mid 0.15
high 0.73
low -0.36
mid 0.17
high 0.70
low -0.22
mid 0.30
high 0.76
high 0.91
mid 0.40
low -0.30
1500
1000
1230
1600
1100
1.77
1.20
1.25
1.25
0.75
0.0859
0.0820
0.0977
0.0977
0.0977
excellent
good
good
good
poor (noisy)
1400
1700
0.69
0.61
0.1055
0.0938
poor (noisy)
poor (noisy)
1130
1445
1800
0600
0915
1230
0.77
0.64
0.54
0.49
0.68
0.72
0.1719
0.1719
0.1641
0.2349
0.1992
0.2031
good
good
good
good
good
good
14
14
15
15
15
16
16
16
0.03
0.45
1005
stippled area whose bounds correspond to a deepening by
5% of the bar crestdepthhc, usually 5-10 cm.)
The shape and trend of the bar in Figure 14 appearsto be
preserved at all stages of the tide. However, the offshore
location of the intensity peaks does not fall over the bar,
and in fact lies inside the crest well into the trough. This
result cannot be reproduced in any way by our model and
shows that our assumption that the average visual wave
breaking signal represents incident wave dissipation is
invalid
under
these conditions.
Investigation of the original video images reveals two
apparentsourcesfor the error. The firrite distancerequiredfor
wave reformation after passing the bar crest appears to
provide a minor landward offset. Most of the error appears
to stem from preferential persistenceof foam in the trough
Simple Time Exposure 6 OCT 86
140
y=1187m
120
100
Int.
80
60
-2
•, Bathy.
-3
40
20
-4
lOO
150
200
300
250
bar definition (Figure 11a). Figure 12 shows the midtide
intensity transects for the three best defined sand bar
profiles (determined from minigrid bathymetry). The inten-
12o
y = 938 rn
sit3' maxima clearly indicate the presence of the sand bar,
althoughthe peak definition is somewhatsubfie for the y =
-lOO
1187 wansect, consistent with the subtle nature of the bar.
There is excellent agreement between the locations of the
intensity maxima and bar crest, well within the resolutionof
the image. This supportsthe validity of the model and the
potential of the technique for imaging morphology under
optimal conditions.
Figure 13 is the rectified time exposureimage obtained at
low tide on October 11, a day when model performancewas
expected to be poorer due to the larger wave heights
Int.
-1
-80
c:
-(30
--
-2
-3
-4
40
lOO
150
200
250
300
(average
He*= 4.3, 2.6, and2.4 for low, middleandhigh
tide, respectively). The bathymetric survey (Figure 11c)
showed the bar to be linear with no longshore variability.
The intensity distribution in Figure 13 confirms this, showhag a clearly linear pattern and providing a good qualitative
descriptionof the sand bar.
While the qualitative descriptionis good, the quantitative
behavior of the technique breaks down in an unexpected
way. Figure 14 showsthe location of the intensitypeak for
low, middle, and high tide over the minigrid area. Also
shown
are the locations
of the mean shoreline
t
y = 777 rn
'
112o
- 100
-
-8O
Int.
-2
-6O
-3
and bar crest.
-4
i
ß
i
ß
i
ß
;40
The latter is depictedby a central line (the best estimateof
100
150
200
250
300
bar crest position) surroundedby a stippled area, reflecting
the fact that the bar itself may not be well defined. (From
Cross-shore distance (m)
Figures 12 and 17, it is clear that bar definition is typically
based on three CRAB survey points with a typical spacing Fig. 12. Local bathymetry and cross-shoreintensity profiles from
of 15 m and whoselocationsare subjectto operatorsubjec- a simpletime exposureobtainedat midtideon October6, 1986. The
tivity. To parameterize this uncertainty, we have added the three transectswere chosenas having the best defined bars.
1006
LIPPMANNANDHOLMAN:QUANTIFICATION
OFSANDBAll MORPHOLOGY
Fig. 13. Rectified time exposureimage encompassingthe minigrid area obtainedat low tide on October 11, 1986.
The longshore
andcross-shore
distances
are scaled•quallywith tic markspacingof 50 m. The imagecontrasthasbeen
stretchedto better reveal the bar location. The weak offshoreintensitymaximumcorresponds
to a poorly defined
second bar.
region. This differential in foam persistence weights the
intensitymaximum shorewardfrom the location of maximum
wave dissipation. We know of no testable physics to
describe
this
behavior
and hence
allow
us to remove
the
The two transectsdiffer by 10 m in offshore location and are
centered about the mean bar position. The intensity and
bathymetry profiles for this day and for all others tested
from SUPERDUCK showedsimilar structure.The presenceof
bias. By examining those records for which a well-defined
bar is present, we find that approximately 42% of the
intensity maxima were located shoreward of bar crest and
that these were generally associatedwith high waves and
strong onshore winds. This latter observation suggests a
potential mechanismwhich would need considerablefurther
testing, though it should be noted that moderate-to-strong
onshore winds could blow spray from the active wave
breaking regions (especially for plunging breakers)
shoreward
to
cause
an
inshore
bias
in
the
Longshore Transects 16 OCT 86
' 250
x=60
rn
200
t.
150
maximum
intensity location. In addition, high winds could cause
whitecapsin regions of little or no incident wave breaking,
also biasing the intensity distribution.
The capabilitiesof the techniquefor detectingand quantifying longshore variability are illustrated in Figure 15, a
comparison of shore-parallel transects of intensity and
•r'•Bathy
'
lOO
-4
-1500
-1•00
-11'00
ß
-9•)0
50
-700
bathymetry
forOctober
16,a dayof lowerwaves
(H•*= 1.7).
225
1
SimpleTime ExposureData
250
x=70rn
October 11
-200
o
lnt.•,
-175
low
tide
•
-1
mid tide •
150-
- 150 •
hightide
-2
mean shoreline
• Bathy.
125
100
1500
1400
•
1300
1200
1100
1000
900
800
700
-3
-1500
-1;•00
-1•00
ß
-9'00
100
-700
Longshoredistance(m)
Longshore distance (m)
Fig. 14. Location of the mean shoreline, measuredbar crest (solid
squares),and intensitymaxima from simpletime exposuresobtained Fig. 15. Shore-paralleltransectscenteredover the mean bar disat low, middle, and high tide on October11, 1986. The stippledarea tance, 60 m (upper panel) and 70 m (lower panel) offshore,from a
indicates the area around the crest for which the water depth is simple time exposure obtained at low tide on October 16, 1986.
Variationsof intensity correspondto the underlyingbathymetry.
within5% of he
LIPPMANN
ANDHOLMAN:QUAN'rlFICATION
OFSANDBARMORPHOLOGY
1007
Fig. 16. Rectified differencingtime exposureobtainedat low tide on October 12, 1986. The bright white band offshoreindicatesthe presenceof a sandbar, whereasthe shorelineis indicatedby a relative darknesswithin the shorebreakregion.The longshoreand cross-shore
distancesare scaledequallywith tic mark spacingof 50 m.
dips in the shore-parallelbathymetry (caused possibly by
topographicallytrapped rip currents), originally a concern,
does not appear to cause a problem, since the relative
"darkness"above the deeper channel is imaged in a consistent manner with the darknessdue to reducedbreaking in the
same region. Several other examplesof rhythmic morphology from other times of year confu-mthe robustnessof the
technique for this purpose, indicating that the time exposures can in fact be used to detect and measure dominant
breaking pattern is indicated again by the high-intensity
band offshore.
The differencing techniquerequires the selection of two
free parametersto yield an optimal image. The first is the
time interval betweenimagesto be subtracted.The secondis
a threshold
value
below
which
contrast
differences
are con-
siderednegligible (and are mapped to zero). This threshold
serves the double purpose of eliminating minor values of
difference
that result
from
camera
shake
or the inevitable
longshorelength scalesof a sandbar system[Holman and
video noise, as well as eliminating the negative values of
Sallenger, 1986].
difference (since time averaging allowing both positive and
Overall, the time exposure technique appearsto be a very negative differences must always be zero). While resulting
useful tool for determiningthe presenceof a bar systemas image quality is influenced by the particular values of these
well as the presence and length scales of longshorevari- parameters, the conclusions about sand bar morphology
ability. Cross-shorescalesare well reproducedunder certain (intensity peak locations) are not overly sensitive. Fixed
conditions, but an observer hoping to use photographic values have been used throughout this paper to eliminate
time exposures,for example,would have to bear in mind the selective bias.
potentialfoam bias and make a qualitativeassessment
of the
We start our examination of the differencing time expoproblem before quantifying any sample (residual foam is sure technique by again looking at the limiting case where
visible, so at least an assessment can be made). This
waves just begin to break over well-defined bar crests.
problemseemsto reducethe effectivenessof the time expo- Figure 17 is a bar location map for October 9 indicating the
sures. However, if an image processingsystem is available, estimated
bar locationandintensity
maximaat low (H*c•
more powerful techniquesare availableto improve the situation. We have developed a modification to the technique,
DifferencingTime ExposureData
called differencing time exposure, that eliminates this
25O
October 09
problem.
Differencing Time Exposures
One way to altogetheravoid the dynamicsof residualfoam
accumulation is to eliminate unwanted, persistent signals
that do not pertain to active breaking (thus energy dissipation). This elimination can be accomplishedby subtracting
video frames, separated in time by a given interval
(commonly0.5-1.0 s) to yield a differenceimage. Regions
of little or no contrast change, such as areas of persistent
foam, will show zero difference. Areas of active breaking
will show large intensity changes,hence large difference
signals.A time exposurecan be made by averaginga set of
thesedifferenceimagesover a suitableperiod, again 10 min
for our case. Figure 16 is an examplerectified differencing
time exposure image from October 12. The offshore
lowtide
mid tide
150-
mean shoreline
'
1500
'
1400
I
1300
'
I
1200
'
I
1100
'
I
'
1000
I
900
'
I
800
700
Longshoredistance(m)
Fig. 17. Location of mean shoreline, measured bar crest (solid
squares),and intensity maxima from differencedtime exposuresobtained at low and midtide on October 9, 1986. The stippled area
indicates the area around the crest for which the water depth is
within 5% of he.
1008
LIPPMANN
ANDHOLMAN:QUANTIFICATION
OFSANDBARMORPHOLOGY
Differencing
TimeExposure
Data
OifferencingTime Exposure 09 OCT 86
250
lowtide•
35
2
mid tide •
y = 1328 rn
>
25 •,
•
15 (n
'•
5
-2
(•
'•
C:
•
•oo.hightide•
.
150
-
!
•c•Bathy.
mean shoreline
-5
-3
100
1500
1400
1300
1200
1100
1000
900
800
-15
-4
100
150
200
250
Longshoredistance(m)
300
Fig. 19. Location of mean shoreline, measuredbar crest (solid
squares),
and intensitymaximafrom differenced
time exposures
obtained at low, middle, and high tide on October 11, 1986. The
stippledarea indicatesthe area aroundthe crestfor which the water
depthis within5% of hc.
40
2
1
y=1187m
-30
0
Int.
-1
-20
estimate for most of the data. At lower tide levels the inten-
=
sity moved offshore, consistentwith greater dissipation
-2
10
offshore.
Forlowtide(He*•- 4.3)themeanvalueof Ax/xc•
--
39%, somewhat above the same range for the model
-3
calculations(Figure 6) but not unreasonable.
-4
100
ß
i
150
i
[
200
i
250
ß
o
Figure 20 showsthe performanceof the techniquefor
October16 when the bathymetrywas quite variable in the
300
longshore.
At hightide(H*c • 0.4) thewaveswerebarely
2
breakingover the bar, and the intensitymaximumprovided
an excellent mapping of even this complicated bar
6O
morphology
' However,for low tide (H*C •
o
•
1.7), the
differencingtime exposuremaximum is further offshoreand
correspondsto the location of the more continuousslope
.o.Z' breakat about1.75-mdepth.TheH* valuefor the slope
c
-3
10
-4
100
0
150
200
250
300
Cross-shore distance (m)
Fig. 18. Local bathymetryand cross-shoreintensityprofiles from
a differencedtime exposureobtainedat midtideon October9, 1986,
break was approximately 1.0, large enough to allow
significantbreakingthere. This may explain the "selection"
by the techniqueof the straighterslopebreak insteadof the
complicatedand more poorly definedbar crest.
The above discussionsupportsthe hypothesisthat our
time exposuretechnique(modifiedby a differencingalgorithm) is representativeof energy dissipationof incident
wave breaking. Continuingthe comparison,we attemptto
characterizethe discrepanciesin bar location Ax as a func-
for the three best defined sand bar locations.
0.8) andmidtide(H* • 0.6) for the differencing
algorithm
c
DifferencingTime ExposureData
250
(He*= 0.45 at hightide andno waveswerebreaking
October 16
lowtide•
offshore). At midtide the intensity maximum location falls
mid tide •
200-high
tide•
'
";'-•'::•':•:'•
within the survey error of the position of the bar crest,
indicatinga good estimateat all longshorelocations.Crossshore profiles correspondingto several regions with well150definedbar crestsare shownin Figure 18. Not surprisingly
the offshore intensity maximum shows excellent agreement
- mean shoreline
with the bar crest location. Furthermore, the intensity
maximum has moved offshore at lower water level,
1500
1400
1300
1200
1100
1000
900
800
consistentwith the results of the dissipationmodel (Figure
6; equation (10)).
Longshoredistance(m)
Figure 19 showsthe resultsof the differencingtechnique
for October11, when the bar was linear but the simpletime Fig. 20. Location of mean shoreline, measured bar crest, and
exposure results were their worst. The improvement is intensitymaximafrom differencedtime exposuresobtainedat low,
middle,and high tide on October16, 1986. The stippledareaindi.
ß
100' I ' • ' • ' •
immediately
evident;
at hightide(H*c= 2.4) the intensity catesthe area aroundthe crestfor which the water depthis within
locations lie quite near the crest within the range of bar
5% of hc.
LIPP•
AND HOLMAN: QUANTIFICATIONOF SAND BAR MORPHOLOGY
DISCUSSION
Differencing Time Exposure Data
Both the simple time exposure and the differencing time
exposure techniques seem to provide a valuable tool for
studying nearshoremorphology. Both detect the presenceof
a bar system and allow measurementof any dominant longshore length scales of rhythmicity. Both can be used to
estimate cross-shorelength scales, a necessaryprerequisite
for testing bar generationmodels. The results from the differencing technique are quite similar to the model, which is
based on sound physics, so relative errors are better understood and, fortunately, are constrained by incident wave
saturation. The simple time exposure technique may be
biased by problems associatedwith residual foam accumula-
0.30
0.20
0.10
tion,so thatfor nondimensional
waveheights
H* greater
o.oo-I
-0.10
0
1009
,
5
!
15
2O
than about 1, estimates of bar position can be subject to
error for which we have little understanding. Nonetheless,
our results show that the simple time exposure will
generallyyield good bar positionestimates.This is due to a
fortuitous case of compensatingerrors; dissipationof larger
waves tends to give errors in the offshore direction, while
foam tends to compensate toward the onshore. Unfortunately, we have only a qualitative understandingof the
process.When residual foam is apparent,the techniquewill
be
Fig. 21. Results from differencing time exposureson October 9, workbestat lowtidewhenH*cis low, andwill generally
11-13, 15-16, showing the fractional error in locating the bar crest worse
for highertides(higher
H'c).Correcting
theoffshore
plotted against nondimensionalwave height H*c. Negative Ax/xbar discrepancy between intensity maximum and bar crest
values indicate a landward offset in intensity bar location estimate.
locations
usingH* wouldbe difficult;detailsin thebeach
profile, as well as surfacefoam biasing,may causeerrorsin
the location of intensity maxima which are unrelated or not
easilyrelatedto theH* parameter.
Thus,we stopshortof
tion of nondimensional
wave heightH* The Ax values calculatingcorrectionequationsfor the bias.
The relevanceof H* in understanding
errorsin the
arisingin the differencingtechniquefor October9, 11-13,
½.
technique is reassuring from a theoretical point of view.
15-16 are normalized by the mean distanceto the bar crest
However, it is of dubious practical value, since we do not
(different along each profile for each day) and plotted know hc, the depth at the bar crest. Instead, a user of the
against
H* in Figure21. The results,whilenoisy,arenot
inconsistentwith the model behavior shown in Figure 6.
Shoreline Agreement
Shoreline Agreement
A further feature in time exposuresis the representationof
a shore break which shows up 'as higher intensity values
along the beach face. The cross-shoreprofiles shown in
Figures 12 and 18 have well-definedpeaksin the vicinity of
the shoreline. This intensity maxima for all cross-shore
profiles (from simpletime exposures)are comparedquantitatively with the calculated shoreline location in Figure 22.
The
calculated
shoreline
location
was
determined
as the
intersectionof the linearly interpolated profile and the still
water level at the time of the survey. The correlationis very
good (r = 0.92); however,the slopeof the line throughthe
data is slightly greater than unity, potentially a result of
setup or other swash dynamics. For individual days the
agreementis excellent; for example, on October 12 when
image quality was best the interceptis -2.0 and the slope
150
140
o
130
0
120
11o
lOO
90
1.02 (r = 0.97).
The persistenceof foam near the mean run-up location
generatesan unusual result for the differencing technique.
Since foam intensity appears fairly constant, the contrast
differencewill always be low; hence the mean shorelinefor
the differencing image often shows an intensity minimum
that correspondsto the location of the maximum for the
simple time exposure.Shorelinelocation appearsbest done
with the simple time exposure.
80
80
90
100
110
120
130
140
150
Survey measurement (m)
Fig. 22. All shoreline intensity maxima locations from simple
time exposuresobtainedat low, middle, and high tide on October6,
9-16, plotted against measured shoreline location. The regression
line is given by y = -14.8 + 1.15x (r = 0.92).
1010
LIPP•
AND HOLMAN: QUANTIFICATIONOF SANDBARMORPHOLOGY
techniquemust refer back to the qualitative wave parameterizations. Both simple and differencing techniqueswork well
when the waves are "just breaking" over the bar. The simple
techniquestartsto break down when the presenceof foam no
longer seemsdirectly related to the amount of local dissipation. Both of these limits are of a type that may be visually
assessedprior to analysis.
The calibration of the time exposure technique discussed
in this paper assumesthat the appropriatemeasureof a sand
bar location is the point of minimum depth. This may not
always be true. For example, .for the bar generationmechanism presentedby Holman and Bowen [1982] the sandbar is
treated as a perturbationto an underlyingbeach profile. The
point of maximum perturbationwill always be offshore from
the point of minimum depth, on the seaward slope of the
typical bar where the local slope equals a representative
mean slope. Thus the errors in the time exposuretechnique
will probably be less for this application. Holman and
theoretical dissipation modeling. Relative errors may be
assessed
usingH'c, but adjustment
corrections
maynot be
reliably made using this parameterdue to unknown profile
characteristics and a breakdown in understanding the
physical behavior of surface foam accumulation.
Acknowledgments. We would like to thank the entire FRF staff
for their tirelessefforts during SUPERDUCK, particularlyCurt Mason
(who made it all happen), Bill Birkemeier, and Ronbo. COL Grum
was instrumental in approval and constructionof the FRF tower.
Much credit and personal thanks are owed to Paul O'Neill, whose
engineering skills and programming contributionsmade this work
possible. Funding for the developmentof the image processing
systemand time exposuretechniquewas provided by the Office of
Naval Research,Coastal SciencesProgram, under contractN0001484-0218. The groundtruth studyduringSUPERDUCK was fundedby
the U.S. Army Corps of Engineers,Coastal EngineeringResearch
Center under the Barrier Island Sedimentation work unit (thanks,
Suzette). The analysis was carried out while the authors were on
temporary leave at Dalhousie University, and we thank them for
their hospitality.Finally, thanksto Marcia for the care packages.
Bowenalsopointoutthatin •heirtheorya low-tideterrace
can be thought of as a small-amplitude bar. Again, the appropriate location of the maximum perturbation would be at
the slope break, just the point imaged by the time exposure
technique.
Batties,J. A., andJ.P. F. M. Janssen,
Energylossand set-updueto
CONCLUSIONS
We have developed a technique to measure the scales and
morphology of natural sand bars based on the preferential
dissipation of wind waves and swell over the shallows of the
bar. We do not actually measure dissipation, but instead
record the visual signal created by breaking incident waves
and assume that this is proportional to dissipation. The
visual wave breaking patterns are imaged photographically,
with statisticaluncertaintyreducedby the use of time exposures (essentially averaging over a length of time long
compared with modulation time scales for incident wave
height). Analysis of the photogrammetryshows that positional information in the resulting images can be quantified
to an accuracyof 5% of the distanceto the camera.
Theoretical modeling shows the sensitivity of incident
wave dissipation to perturbations in bottom slope; hence
the potential for using dissipationto locate bars. An impor-
tant parameter
is the nondimensional
waveheightH* (Ho/?hc)(kc/2ko)
1/2,whereH0 is thedeep-water
RMS wave
C
--
height, hc and kc are the depth and wave number at the bar
crest, k0 is the deep-water wave number, and y is a breaker
constant,
takenas0.42for thisstudy.ForH* = 0.5-1.0the
c
waves are just breaking and the dissipation maximum
corresponds
well to thebar crestposition.
LargerH* result
c
in weighting the dissipationmaximum farther offshoreup to
a maximum location beyond which the local wave field is
saturated.The maximum discrepanciesbasedon a reasonable
example are 35% of the true bar crest distance.
Ground truth testing,conductedduring SUPERDUCK, confirms the capabilities of the time exposure technique for
detecting the presence of a sand bar system as well as
detecting longshore variability and rhythmicity and quantifying length scales. Cross-shorescale estimatesare good for
smallH* but for higherwaves,persistent
foambiasesthe
C'
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