Post on 17-Feb-2019
To Whom It May Concern:
We submit this manuscript entitled “Understanding long-term shoreline change through integration of historical aerial photographic, sedimentological, and computer modeling techniques: Lanikai and Bellows Beaches, Oahu, Hawaii” for publication in your journal, Marine Geology. We feel this work is an original and relevant contribution to our knowledge of coastal sediment transport and a case study in integrating multiple diverse analysis techniques. The results of this study have great applicability to beach renourishment projects, shoreline sediment management, and to our understanding of the strengths and limitations inherent in common coastal analysis techniques. Thank you for your time. Sincerely, Christopher Bochicchio Charles Fletcher
Draft 04/06/09 1
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Title:
Understanding long-term shoreline change through integration of historical aerial
photographic, sedimentological, and computer modeling techniques: Lanikai and Bellows
Beaches, Oahu, Hawaii
Author names and affiliations:
1) Christopher Bochicchio – Dept. of Geology and Geophysics, University of 9
Hawaii at Manoa
2) Charles Fletcher – Dept. of Geology and Geophysics, University of Hawaii at
Manoa
3) Sean Vitousek – Dept. of Geology and Geophysics, University of Hawaii at
Manoa
4) Bradley Romine – Dept. of Geology and Geophysics, University of Hawaii at
Manoa
5) Tomas Smith – United States Army Corp of Engineers, Honolulu Engineering
District
Corresponding author:
Charles Fletcher: fletcher@soest.hawaii.edu
Present/permanent address:
Department of Geology and Geophysics
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University of Hawaii at Manoa
1680 East-West Rd., POST 721
Honolulu, HI 96822, USA
Abstract:
Beach loss is significant to the economy, environment, and quality of life of many coastal
regions, particularly in Hawaii. Understanding multi-decadal trends in shoreline change
is a difficult and complex problem that benefits from the integration of multiple analysis
techniques. Lanikai and Bellows beaches are located on the windward coast of Oahu
Island, Hawaii, and separated by Alala Point. This shoreline has experienced long-term
poorly understood changes in shoreline position ranging 70 meters of width over the last
80 years. In an effort to better understand long-term coastal sediment transport at this site
and provide information for successful management, we integrate three commonly used
techniques for studying shoreline change: 1) grain-size sediment trend analysis (GSTA),
2) hydrodynamic computer modeling (Delph 3D), and 3) historical aerial photoanalysis.
Results of GSTA and hydrodynamic modeling are generally consistent with shoreline
change observed in historical aerial photographs. It is shown that sediment has been
shared between Lanikai and Bellows and that decadal-scale changes in the dominant
trade wind direction are closely tied to shoreline change.
Keywords:
coastal erosion, Hawaii, grain size trend analysis, historical shoreline analysis, Delph 3D
model, trade wind direction
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1. INTRODUCTION
Beach loss poses a serious threat to the economy, ecology, and safety of many coastal
regions. Over the latter part of the 20th century nearly 70% of the world’s beaches have
experienced net erosion (Bird, 1985). Much of this is attributed to the combined
influence on coastal sediment budgets of rising sea level and increasing shoreline
development (NRC, 1995). On the island of Oahu, Hawaii, historical analysis of beach
length shows 24% of all beaches have either narrowed or disappeared over a ~60 year
interval (Fletcher et al, 1997; Coyne et al., 1999). The impact of this beach loss is
particularly profound in Hawaii as sandy beaches drive a multi-billion dollar tourism
industry that accounts for 60% the jobs in the state and represents an important element
of cultural identity.
Beach volume and shoreline position are largely governed by locally unique
trends in longshore and cross-shore sediment transport. These are difficult to observe and
predict over the long time scales needed to develop sustainable coastal management
plans. Hence, where historical observations are available, it is important to investigate
the processes driving shoreline change on poorly understood beaches.
Lanikai Beach on windward (east-facing) Oahu is a developed shoreline
threatened by long-term erosion that is poorly understood. Lanikai has experienced a
series of decadal-scale erosion and accretion events producing >50 m changes in beach
width over a 60-year period. The net trend has been erosional and consequently the total
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beach length has decreased from 2.3 km to 800 m over the period from 1950 to 2007.
Discussion regarding appropriate management of Lanikai Beach has continued for over
30-years without resolution. Central to this debate is the source and fate of beach sand,
and specifically whether sand is exchanged around a rocky headland marking the
southern littoral cell boundary of Lanikai Beach with Bellows Beach (Figure 1).
In this study, we test the hypothesis that littoral sediment transport occurring
between Bellows and Lanikai beaches controls historical shoreline change at Lanikai.
We examine the direction of this exchange and assess factors that have potentially altered
sand transport over time. We integrate grain size trend analysis and hydrodynamic
modeling (Delft 3D) and compare the results with a detailed review of historical
shoreline change (derived from aerial photographs) to evaluate littoral sediment transport
across the Lanikai-Bellows boundary and greater shoreline. We expand our analysis to
include historical shifts in wind direction as a driving factor in shoreline change.
Results indicate that sediment transport does occur around Wailea Point linking
Bellows and Lanikai Beach and hardening of the Bellows shoreline has starved Lanikai
Beach by impounding an apparently important sediment supply. We also find evidence
that historical changes in wind direction have had a significant influence on sediment
transport. These results also indicate that future integration of sediment grain-trend
analysis into shoreline change studies could be beneficial to coastal authorities tasked
with managing poorly understood shorelines. This study is the first major reconstruction
of shoreline dynamics along the Lanikai-Bellows Beach and represents the first
application of sediment grain size trend analysis (GSTA) to studying shoreline change.
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2. REGIONAL SETTING 93
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The Lanikai-Bellows region encompasses roughly 4.3 km of coastline along a broad,
embayed headland marking the boundary between Kailua and Waimanalo Bays. The
study area extends to rocky Alala Point in the north, and the mouth of Waimanalo Stream
in the south. Basaltic Wailea Point, in the center of the study area, marks the boundary
between northeast facing Lanikai Beach and southeast facing Bellows Beach. Northeast
trade winds are dominant with an average speed of 10-20 kts over 90% of the summer
season (April-September) and 50-80% of the winter season (October-March) (Harney et
al., 2000). Trade wind waves dominate during summer months, with average deepwater
significant wave heights of 1-3 m and periods of 6-9 s. During the winter, refracted swell
from the North Pacific reach significant wave heights of 4 m with periods of 10-20 s.
Breaking face heights at the beach are substantially lower (<0.5 m) as a shallow reef crest
and the twin Mokulua Islands dissipate most incoming energy. Typical tidal range in
Hawaii is <1 m.
Landward of the shoreline at both Lanikai and Bellows are unconsolidated
carbonate marine and dune sands (Grossman and Fletcher, 1998; Harney and Fletcher,
2003). A 0.5 to 1.0 km wide reef flat fronts the majority of the site in water generally 1.5
to 3.5 m deep. Three large sand fields extend from the beach to the reef crest, containing
a total of 130 x 103 m3 of sediment with average thicknesses of 0.7-1.3 m (Bochicchio et
al., 2009). A thin veneer of sediment, occasionally observed with ripple marks, is found
over parts of the reef flat. Seaward of the Mokulua Islands the fore-reef slopes to >20 m
depth.
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Beaches at Lanikai and Bellows are narrow with gentle slopes and made up of
poorly sorted medium to fine-grained calcareous sand (Noda, 1989). Changes in beach
volume tend to be related to chronic fluctuations in alongshore sand transport and
sediment deficiencies, rather than event-based erosion because the offshore reef platform
diminishes incoming swell (Fletcher et al., 1997). Currently, the northern and southern
regions of Lanikai as well as northern Bellows Beach are without a beach and protected
by seawalls.
Noda (1989) investigated transport processes at Lanikai and stated that longshore
transport is responsible for substantial historical shoreline change at Lanikai Beach
despite a relatively mild wave climate. Noda found no evidence of sediment transport
occurring around Alala Pt. to the north, indicating that the Kailua-Lanikai cell boundary
is closed. Two sandbars on the southern Lanikai shoreline, located 15 and 30 m offshore
of the sea walled coast, corresponds with the node and anti-node of the mean incoming
wave (Lipp, 1995). Lipp concluded that strong wave reflection off the Lanikai seawalls
is, to some degree, preventing the accretion of a beach.
3. MATERIALS AND METHODS
To test the hypothesis that sand transport between Bellows and Lanikai cells controls
shoreline change, we use grain size trend analysis (GSTA), hydrodynamic modeling, and
historical shoreline change analysis.
3.1 Sediment grain size trend analysis
3.1.1 Sample collection and analysis
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A total of 214 sediment samples were collected on a grid surrounding Wailea Point
(Figure 2). Spacing between sample sites varied from 37.5 m near Wailea Point, to 75 m
within sand fields, and 150 m between sand fields. Samples were recovered from the
ocean bottom using a sediment dredge, which removed between 10 and 30 cm of the
surface sediment. Between 1000 and 2000 g of sediment were recovered in each sample.
The upper 5 cm layer of sample within the dredge was discarded to reduce error caused
by fine sediment potentially billowing out of the dredge mouth as it was pulled to the
surface. Samples were GPS positioned within 4 m. Grain size distributions of each
sample were based on the weight percent of each size fraction from standard sieve
analysis method ASTM C 136 (ASTM, 2006). Sieve openings ranging between -2 and 5
Ø at 0.5 Ø intervals. Mean size, sorting, and skewness were calculated for use as
parameters in the trend analysis.
3.1.2 General background on method
Spatial trends in the grain size of surficial sediments are a direct result of natural
sediment transport processes (Russell, 1939; McCave, 1978; Swift et al., 1972; Harris et
al., 1990). These trends are primarily the effect of transport processes selectively sorting
and abrading sediment in the direction of transport (McLaren and Bowles, 1985; Gao and
Collins, 1992; Le Roux and Rojas, 2007). Using mean size, sorting, and skewness, four
trends have been found to be reliable indicators of transport direction (McLaren and
Bowles, 1985; Gao and Collins, 1992; Gao et al., 1994; Le Roux 1994b).
Trend 1: finer, better sorted, and more negatively skewed
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Trend 2: coarser, better sorted, and more positively skewed
Trend 3: coarser, better sorted, and more negatively skewed
Trend 4: finer, better sorted, and more positively skewed
Accordingly, transport pathways can be identified if a series of sediment samples follows
one of these. Type 2 and 3 trends show distinctive coarsening along the direction of
transport that at first appear counterintuitive. Type 2 and 3 trends are interpreted as
indicators of more energetic transport processes in which a majority of fine-grained
sediment is removed, thus creating a thin and coarse lag deposit that “shields” underlying
deposits that have not been winnowed. This coarse upper layer may be mixed with
underlying fine sediments during sampling, which results in an overall finer-grained
texture upstream of the transport direction (McLaren and Bowles, 1985).
GSTA encompasses a range of techniques for recovering net transport direction
from naturally sorted seafloor sediments by identifying grain size trends in sediment
samples collected around an area of interest. McLaren and Bowles (1985) first proposed
a one-dimensional methodology to accomplish this task. This was followed by a number
of two-dimensional approaches (e.g. Gao and Collins, 1992; Le Roux, 1994b,c;
Asselman, 1999; Rojas et al., 2000; Rojas, 2003). These methods have been used to
characterize sediment transport for a variety of engineering, environmental, and
sedimentological investigations.
In this study we apply two separate methods put forth by Gao and Collins (1992)
and Le Roux (1992) to a dataset collected offshore of Lanikai and Bellows beaches.
These two methodologies use significantly different mathematical approaches for
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locating trends in sediment size data, yet are shown to detect sediment transport at similar
spatial scales (Rios et al., 2002). An overview of each method is provided below to
highlight the differences, provide an instructive reference, and aid in discussion of the
results. Likewise, the respective authors of each method provide full descriptions in Gao
and Collins (1992) and Le Roux (1994b). The Gao-Collins method is described in more
detail using practical examples (Appendix A), because current publications on this
method are limited to theoretical application.
3.1.3 Gao-Collins and Le Roux methodologies
The method put forth in Gao and Collins (1992) determines sediment transport direction
by comparing grain size parameters among a group of sampling sites. Parameters at each
site are compared with those of neighboring sites within a predefined characteristic
distance. The characteristic distance is defined as the spatial scale over which transport is
expected to occur in the study area, generally given as the maximum interval between
any two adjacent sampling sites. This study uses a characteristic distance of 200 m,
which reflects the spatial scale of transport processes anticipated for this region and
maximum distance between potentially related sites. In every case where either Trend 1
or Trend 2 is identified, component vectors with the unit length (i.e. equal to 1) are drawn
in the direction of the neighboring site (Figure 3A). Summing all component vectors at
each site produces a single vector referred to as a transport vector (large arrow in Figure
3A and 3B). Component vectors are relevant only in terms of direction. Their lengths do
not reflect differences in grain size parameters or distance between points. As all
component vector lengths are equal, the number and direction of neighboring sites
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showing a positive transport trend determine both the direction and length of the resulting
transport vector. Determining transport vectors for every point produces a field of
transport vectors (Figure 3B), which can be filtered to reduce noise and reveal the
dominant trends, by averaging the vector at each site with surrounding transport vectors
(Figure 3C). Details of the steps and calculations used in Figure 3 are included in
Appendix A.
The method of Le Roux (1994b) functions by comparing grain size parameters of
a central site with the closest four neighboring sites in all cardinal directions (i.e. one site
is selected from the North, East, South, and West quadrants) (Figure 4A). The Le Roux
method searches for all four trend types individually, producing a vector field of transport
for each trend.
Trend determination begins with the normalization of all three grain size
parameters between all five sites. These values are combined into a single value (E)
representing the strength of transport along that axis. The process of normalizing and
combining the parameters is modified in a manner depending on the trend type. For
example, Equation 1 is used in the case of Trend 3, where all parameters are expected to
decrease along the direction of transport.
( ) ( )
( )minmin
minminmax
minminmax
sksk sk
33.
varvar varvar33.33mnmn
mn 33.33
−
−−
+−−
maxsk33
mn
−+
=E Equation (1)
In this process, sites with the smallest values receive the highest score (E)
indicating stronger transport potential in the direction of that site. Conversely, to achieve
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the same effect with Trend 1, Equation 1 must be modified so that increasing mean grain
size results in a lower value of E. This is done simply by subtracting 33.33 from the
normalized mean size parameter (Equation 2).
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ter for Trend 2 and the 233
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te (Figure 4B) then the value of the central site 236
is subtr237
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). 243
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earchi ns 245
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( ) ( )
milar adjustments are made to the normalized skewness parameSi
normalized variance parameter for Trend 4 to so that increasing values on these
parameters result in higher values of E.
Values (E) are defined for every si
acted from each adjacent site and the relative difference between sites is used to
define the length of component vectors, which are summed to produce a final transport
vector (Figure 4C). This process is repeated at every site to produce a field of transport
vectors for each trend type. Trend 1 results are shown in Figure 4D. Commonly, the
strongest vectors from each trend type are incorporated into a final vector field. The
Watson (1966) non-parametric test is used to ensure that the final transport vectors are
sufficiently non-random before smoothing the data to reduce noise (Le Roux et al., 2002
The Gao-Collins and Le Roux methods both determine transport direction by
s ng for predefined trends between a single site and adjacent sites, but Gao-Colli
uses only Trends 1 and 2, while Le Roux checks for all four trends. The Gao-Collins
method checks a variable number of sites (all those that fall within the characteristic
distance), while Le Roux only uses a central site and four adjacent sites. With Gao-
( )min
minminmax
minminmax
sksk sk sk
33.33
varvar varvar33.33mnmn
mn mn33.3333.33
−−
+
−−
+⎟⎟⎠
⎞⎜⎜⎝
⎛⎥⎦
⎤⎢⎣
⎡−
−−=E
Equation (2)
minmax
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Collins, direction of transport is determined by relative position of all neighboring si
showing a trend to the central site, with transport occurring in the direction of the most
trend positive sites. In contrast, using Le Roux, transport direction and strength is
determined from the calculated difference between the actual grain size parameters
five sites. Both methods have been shown to give comparable and informative results
(Rios et al, 2002).
tes 249
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of all 252
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.2 Computer hydrodynamic model (DELFT 3D) 256
sed here) solves the unsteady shallow-257
water e258
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3
The Delft3D-FLOW module (v. 3.24.03 u
quations with the hydrostatic and Boussinesq assumptions. In 2D mode the model
solves two horizontal momentum equations (see Eq. 3-4), a continuity equation (Eq. 5)
and a transport (advection-diffusion) equation (Eq. 6) shown below:
2 2
2 2( )( ) ( )
bx xe
w w
Fu u u u uu v g fvt x y x h h x y
τη νρ η ρ η
∂ ∂ ∂ ∂ ∂ ∂+ + + − + − − + =
∂ ∂ ∂ ∂ + + ∂ ∂0 (3) 262
2 2
2 2( )( ) ( )
by ye
w w
Fv v v v vu v g fut x y y h h x y
0τη ν
ρ η ρ η∂ ∂ ∂ ∂ ∂ ∂
+ + + − + − − + =∂ ∂ ∂ ∂ + + ∂ ∂
(4) 263
[( ) ] [( ) ] 0h u h vu vt x yη η η∂ ∂ + ∂ ++ +
∂ ∂ ∂= (5) 264
[ ] [ ] [ ]H H
hc huc hvc c ch D Dt x y x x y y
⎡ ⎤⎛ ⎞∂ ∂ ∂ ∂ ∂ ∂ ∂⎛ ⎞+ + = +⎢ ⎥⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠⎣ ⎦ (6) 265
266
here u and v = the horizontal velocities in the x and y directions respectively; t = time; g 267
= gravity;
w
η = free surface height; h = water depth; f = coriolis force; wρ = density of 268
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water; bτ = bed friction; F = external forces due to wind and waves, eν = horizontal eddy
viscosity;
269
HD = horizontal eddy diffusivity; and c = concentration of suspended
sedimen The equations are solved on a staggered finite difference grid using the
Alternating Direction Implicit (ADI) method after Stelling (1984).
In this study the Delft 3D model is employed to examine the potential for
different transport regimes developing under changing forcing cond
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i s. This element 274
of the ahu’s 275
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wind 285
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th 2005 on the 288
southe289
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taset 291
t.
s
r
tion
ber, 12
tudy focuses on trade winds, as it is the most persistent type of forcing on O
windward shore and most likely to determine equilibrium shoreline conditions. Figure 5
shows a 58-year time series of trade wind direction recorded at Kaneohe Marine Corps,
located on the coastline approximately 9 kilometers north of the study area. These data
show periodic shifts in trade wind direction that persist over decadal-scale time periods
and are in some cases rapid (e.g. 1964, 1974, and 1987). Changes in trade wind direction
were first documented by Wentworth (1949) and implicated as a possible factor in
shoreline change in Lanikai in a report by Noda (1988). This study is the first to extend
the directional dataset presented by Wentworth (1949). The exact cause of these
directional shifts is not currently understood. Using the range of observed wind
directions, this study uses Delft 3D to model the potential influence that changing
direction could have on sediment transport in the Lanikai region.
The model was calibrated using current and sea-level data collected by two
acoustic doppler velocimeters deployed from August 10th to Septem
n and northern bounds of the study area (Figure 6). The model parameters
included wind driven currents, tidal forcing, open ocean waves, and wave-driven
currents. Ocean swell direction and height was simulated using a representative da
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from a deepwater directional wave buoy located 2 km north-east of the study area
Kailua Bay (National Data Buoy Center number 51001). Tidal forces were modeled
using standard harmonic components. Separate model runs used directional extremes
from the historical dataset to simulate time periods when north-east (51°), east-north-e
(71°), and east (85°) wind conditions dominated.
3.3. Shoreline change analysis
in 292
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ast 295
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nalysis of shoreline change draws from data collected by Romine et al. (in press). 299
ere hand digitized from survey quality aerial photos and 300
988, 301
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. 304
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a 306
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.1. Textual and transport trend analyses 311
re over much of the study area is characterized by distinct, isolated zones 312
shore of Lanikai tend to be coarser (Figure 7), 313
more poorly sorted (Figure 8), and positively skewed (Figure 9) than those at Bellows. 314
A
Historical shoreline positions w
T-sheets acquired in: 1911, 1928, 1949, 1951, 1959, 1963, 1967, 1971, 1975, 1982, 1
1989, 1996, and 2005. Distortion errors from scanning the photos were corrected
(Thieler and Danforth, 1994), and following the methodology of Fletcher et al. (2003), all
photos were orthorectified and mosaicked using software from PCI Geomatics, Inc
Seaward and landward boundaries of the sub-aerial beach were defined as the position of
mean lower low water (MLLW, using the toe of the beach, or base of the foreshore as
proxy) (Bauer and Allen, 1995) and the vegetation line. Horizontal error in shoreline
position was ± 4.49 – 10.78 m.
4. RESULTS
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Sediment textu
of varying size. As a whole, sediments off
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While sediment textures directly adjacent to shore tend to be finer and more negatively
skewed along the entire sample area. Offshore of Wailea Point, in the central portion of
the study area, sediments are generally finer, better sorted, and more negatively skewed
towards the tip of the point. However, closer examination of the entire study area shows
a close juxtaposition of alternating sediment textures indicative of lag and lead deposits.
Results of the Gao-Collins (Figure 10) and Le Roux (Figure 11) methods indicate
the direction and relative probability of sediment transport. A fundamental difference
between the two methodologies is well illustrated by the smooth appearance of the Gao-
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Collins323
nd 324
325
” 326
327
lts show 328
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331
ecoming better 332
sorted to the north (box B). Results from the Le Roux method show a majority of 333
transpo t to 334
335
r, 336
better-sorted, and more negatively skewed toward the north, which is the signature of 337
results and the noisier appearance of the Le Roux results. As described in the
methodology, the Le Roux method is more sensitive to small differences in grain size a
to small-scale isolated trends than the Gao-Collins method. Results of the two
methodologies generally agree, with the only major exception being the box labeled “A
in the southern part of the study area, where results differ considerably. In A, the Gao-
Collins results show primarily north-to-northeast trends, while the Le Roux resu
an opposing southeast trend converging with a north-to-northwest trend.
Within 100 m of the Bellows shoreline, sediment textures alternate between
coarse-positively skewed and fine-negatively skewed with all sediments b
rt to the north and Gao-Collins also shows a consistent northern trend adjacen
Bellows Beach.
Offshore sediment immediately south of Wailea Point (box C) becomes fine
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Type 1 transport. Gao-Collins results indicate uniform northern transport of sediment
from Bellows tow
338
ard Wailea Point. Similarly, Le Roux results show northwesterly 339
transpo340
341
ux 342
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nt 344
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transport 347
vectors f 348
ent at 349
. 350
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et 357
representing major shifts in 358
position are overlain on a modern (2005) aerial photograph in Figures 12 and 13. Plots 359
rt toward Wailea Point where it meets an opposing transport trend. This is
mirrored to the north in box D, where sediment becomes finer, better-sorted, and more
negatively skewed toward the south. Resulting transport vectors in D from both Le Ro
and Gao-Collins methods are southeasterly and directly oppose transport in B.
Near the northern slightly embayed portion of Wailea Point (box E), sedime
within 250 m of southern Lanikai Beach shows two distinct textures. Nearshore
sediments are finer, better-sorted, and more negatively skewed than sediment farther
offshore. This contrast in sediment texture produces onshore and southeasterly
in the both Gao-Collins and Le Roux methodologies. To the north, both sets o
results show an opposite northwesterly trend in box F along Lanikai Beach. Sedim
F tends to be coarse, poorly sorted, and positively skewed relative to areas to the south
In general, transport trends in F and E show divergence between northerly and southerly
transport. Similar divergence occurs between A and B, while both results show
convergence near Wailea Point between C and D. Le Roux transport vectors seem to
indicate a gyre-like circulation pattern across C and D.
4.2. Shoreline change analysis
Changes in shoreline position are visible in historical aerial photography (e.g. Fletcher
al., 1997, Romine et al., in press). Historical shorelines
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show relative shoreline position over time along transects A through G centered on sites
with the greatest shoreline movement.
Lanikai Beach (Figure 12) shows multi-decadal trends of either accretion or
erosion, indicated on transects B, C, and D. Shoreline position appears relatively stable
between 1912 and 1949, although this c
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ould be due to under sampling (only 3 364
shorelin d 365
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7, 367
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369
has 370
t 371
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ct 374
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followed by erosion until 1961 resulting in 376
the loss377
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4.3. Hydrodynamic modeling results 382
es). In southern Lanikai (transect D) from 1949 to 1967 the shoreline accrete
significantly, adding approximately 60 m of new land. Beach to the north (transects C,
B, and A) was either stable or lightly accreting over the same period. After 196
accretion turned to erosion until halted by seawalls in 1990. To the north, accretion
intensified and central Lanikai (transect C) added approximately 30 m of new land. This
ended by 1987 and the beach has chronically eroded since. At transect B accretion
persisted and accelerated. At transect A the shoreline was relatively stable throughou
much of the 20th Century until 1975 and has subsequently eroded, culminating with the
construction of seawalls in the early 1980’s.
Figure 13 summarizes chronic erosion at Bellows south of Wailea Point (transe
E) persisting since the beginning of the dataset in 1916. To the south, transect F reveals
an accretionary trend between 1916 and 1928,
of approximately 40 m of land. At transect G, shorelines remain stable until a
general erosional trend developed during the 1961 to 1962 time period. This continued
until seawall construction in 1998. Erosional trends at transects E and F were also halted
by seawalls.
17
A hydrodynamic model is useful for envisioning nearshore currents that develop
under various forcing co
383
nditions. In Figures 14-16 we use a scale along the shoreline to 384
define locations for discussion. Results show substantially different nearshore current 385
th-east (51°), east-north-east (71°), and east (90°) 386
winds a 387
388
389
390
391
392
0 393
394
onable 395
396
397
398
399
ange in the study area is presented in 400
igure 17. The color grid is interpolated from historical shoreline position data with 401
rate of shoreline change (m/yr) during a time period (horizontal axis) 402
al-scale erosion and accretion 403
events 404
405
configurations in the region when nor
re used to force the model. The most noticeable effect of changing wind direction
is the shifting location of longshore current convergence and divergence. Eastern winds
(Figure 14) induce northward transport along the entire study area. East-North-East
winds (Figure 15) create a divergence point in longshore flow near location 40 along the
Bellows shoreline and induce a distinct gyre to the north of Wailea Point. Under
northeast winds (Figure 16) the divergence point shifts to the north along the Bellows
coast to location 10 and divergence develops in southern Lanikai between locations 9
and 100. In general, southern transport becomes more common along both shorelines as
the northern component of wind direction becomes more prominent, which is reas
considering the geometry of the shoreline.
5. DISCUSSION
5.1. Comparing Historical Shoreline Data with Results
A reconstruction of historical shoreline ch
F
color indicating the
over a length of beach (vertical axis). A number of decad
are visible in this data. The most prominent pattern is the aforementioned
expansion and erosion of south Lanikai, followed by central Lanikai. From these
18
changes in shoreline position we can derive an empirical analog for historical littoral
sediment transport direction. Arrows on Figure 17 show the direction of longshore
sediment transport inferred from changes in shoreline position.
It is apparent that there are coinciding system-wide shifts in sediment trans
certain times throughout the dataset. Figure 18 shows major shifts in wind direction
delineated into eight periods (periods II through VIII). These same periods are over
on Figure 17. The good agreement between changes in wind dire
406
407
408
port at 409
410
lain 411
ction and shoreline 412
change413
414
415
416
417
tructure would have a notable effect on shoreline 418
position d in 419
420
atch, 421
422
423
424
425
atterns are overwritten or mixed 426
with ne427
428
suggests that wind direction plays a significant role in driving sediment transport
along the Lanikai-Bellows shoreline.
The relationship between shoreline position and wind direction supports the
results of the hydrodynamic modeling experiments, in which different wind directions
showed the formation of different nearshore currents (Figures 14, 15, and 16).
Presumably, these changes in current s
, however in some cases the currents predicted in the model are not expresse
shoreline positions or are at odds with the observed shoreline history. This pairing of
datasets allows evaluation of the model performance and, where observations m
provides insight to processes driving shoreline change.
Gao (1992) suggests that the time period represented by GSTA is related to the
deposition rate of sediment but the issue is still poorly understood. In coastal settings,
transport patterns can shift on time scales ranging from days to decades, during which
grain size distributions representing previous transport p
w transport. Figure 19 summarizes both Le Roux and Gao-Collins results. The
nearshore vectors show divergence near Lanikai transect 90 and Bellows transect 30.
19
Convergence occurs near Lanikai transect 70 and in the vicinity of Wailea Point, as wel
as an overall northerly transport trend. This pattern is typical of trends observed since
Period IV (Figure 17), suggesting the GSTA results are valid back to the mid-1960’s,
coinciding with the onset of the modern erosive trend on south Lanikai.
5.2. Analysis of Historical Transport Trends
This section takes the form of a timeline detailing observed shoreline changes i
the context of wind direction, model predictions, and GSTA results. A g
l 429
430
431
432
433
434
n 435
eneralized 436
mmary of historical sediment transport trends (Figure 17) and dominant wind direction 437
VIII in Figure 20. The goal for these data 438
is to cre439
440
441
442
443
ave come from erosion in south Lanikai. 444
445
Period 446
447
ng from Bellows was likely transported 448
round Wailea Point into south Lanikai, which shows accretion during this time. 449
ng Lanikai Beach supported the supported the stable or accreting 450
shoreline during this period. 451
su
(Figure 18) is presented for periods II through
ate a predictive, empirical model relating shoreline change to wind direction.
Period I. 1910 – 1928
Southern Lanikai eroded over the first half of this period (1911 to 1928), while
the remainder of Lanikai and Bellows both accreted. Source material for accretion may
h
II. 1928 – 1953
Wind records during period II show that eastern winds dominated (Figures 18 and
20). Modeling indicates that sediment erodi
a
Northward transport alo
20
Modeling under east winds (Figure 14) indicate northward longshore currents
developed along Bellows and Lanikai Beaches and around Wailea Point. Current
intensities are greatest in North Bellows corresponding to with the highest observed
erosion rates during this period. Modeling also shows a slackened current in south
Lanikai thus accounting for sa
452
453
454
455
nd deposition. During this period Lanikai Beach volume 456
was lik et 457
458
459
460
461
462
was interrupted as erosion slowed previously uniform in central 463
Bellows and turned to accretion in south Bellows. However, erosion accelerated in north 464
evelopment of a divergent current. Current divergence also 465
466
e 467
468
469
470
471
ar 472
appear in aerial 473
photos where erosion rates were highest, and expand in later decades. These revetments 474
ely dependant on the delivery of Bellows sediment to balance the sediment budg
in south Lanikai.
Period III. 1953 – 1964
Wind direction during this period shifted to the northeast, which resulted in a
more complex system of littoral transport. The previously uniform transport from
Bellows to Lanikai
Bellows indicating the d
developed in central Lanikai, which eroded substantially during this period. South
Lanikai experienced accretion rates in excess of 3 m/yr over this entire period as larg
volumes of sediment arrived from central Lanikai and north Bellows.
Modeling using 71-degree winds fails to capture converging currents in south
Lanikai or diverging currents in central Lanikai. It does however capture divergence
centered on Bellows transect 35 near the observed erosion hotspot.
Bellows Air Force Base underwent substantial development during and after World W
II (1941-1945) as the shoreline eroded. A series of coastal revetments
21
effectively impounded landward sediment reducing sources to down-drift littoral cells.
South Lanikai especially reflects this event as some part of the source material for the
large accretion event was likely provided by erosion in north Bellows
475
476
. 477
478
479
480
481
482
zone has 483
shifted north. Slight accretion on both sides of Wailea Point suggests the divergence 484
ows has shifted to the south. A convergence zone seems to have also 485
rmed486
ear 487
lso 488
489
as 490
s 491
ere accretion is observed. 492
493
494
495
496
IV. 1964 – 1972
Wind during this period shifts further to the northeast causing a relocation of
convergence and divergence zones. Accreting and eroding areas essentially reversed
during this period marking the start of long erosive trend in south Lanikai. Central
Lanikai experiences accretion during this time, , suggesting the convergence
zone in north Bell
fo in south Bellows where the beach undergoes accretion.
The model, when forced with 51 degree winds (Figure 16), shows divergence n
Lanikai transect 80, which is in agreement with historical observations. The model a
indicates a southerly current moving around Wailea Point that could cause the accretion
observed in north Bellows. The model fails to capture convergence in central Lanikai
there is no opposing current moving south from north Lanikai. Similarly, this model doe
not show convergence at the southern edge of the study area wh
This period is the earliest in which GSTA results match observed shoreline
changes. The dominant littoral transport trends in Figure 19 indicate convergence near
Lanikai transect 70 and on the flanks of Wailea Point. GSTA results also show
divergence near Bellows transect 30. These patterns closely match the observed
22
shoreline trends, suggesting that the GSTA results are incorporating grain size
distributions that were established by transport patterns during this period.
497
498
499
500
501
tes in 502
ted, 503
eloped in 504
orth Bellows while sediment in south Bellows was seemingly dispersed to the north and 505
buildup against the jetties stabilizing Waimanalo Stream suggest 506
souther507
508
509
t to 510
511
512
to expect small changes in wind direction to 513
have a 514
n at 515
516
517
o 518
V. 1972 – 1984
Wind direction during this period shifts back to the east (75 degrees), but
shoreline changes show a unique pattern that was not previously seem. Erosion ra
south and north Lanikai increased during this period while central Lanikai accre
likely gaining source material from the north and south. Mild accretion dev
n
south. Sediment
ly transport along the Bellows coast.
We might expect transport under 75 degree winds to be similar to the 71-degree
winds during Period III, but there is no sign of shoreline accretion in south Lanikai.
Possibly: 1) current patterns between 75 and 71 degree winds are sufficiently differen
shift the convergence zone to central Lanikai and/or 2) hardening of both north Bellows
and south Lanikai prevented sand accumulation along the shoreline. With a nearly
perpendicular onshore wind, it is reasonable
disproportional effect on current patterns. The reduced sediment availability from
north Bellows and wave reflection off the hand shoreline may have prevented accretio
this time.
Model results for 71 degrees (Figure 15) are the closest approximation to wind
direction during this time period and match the observations poorly. GSTA results d
23
show sediment transport from south to central Lanikai, but transport patterns in Bellows
are not well represented.
519
520
521
522
d 523
524
ht accretion in southern Lanikai adjacent to Wailea Point as 525
diment moved to the south. This excursion also marks the start of wide-spread erosion 526
, a northward expansion of the eroding area in south Lanikai, and a 527
northw528
529
530
531
rply 532
rodes. Farther evidence of 533
increased northerly currents is the northern shift and general decrease in accretion rate of 534
in central Lanikai. As the accreting area moves north, central Lanikai 535
536
537
i 538
539
540
VI. 1984 – 1987
Wind direction makes a relatively brief northeastern excursion during this perio
causing subtle changes in the shoreline. As in period IV, in which wind was also more
northeasterly, there is slig
se
on Bellows beach
ard shift in the accreting area in central Lanikai.
VII. 1987 – 1995
Wind direction shifts back to an easterly inducing northerly transport along the
entire study area. The slight accretion on the southern edge of Lanikai disappears sha
and sediment accumulated along the Bellows shoreline e
the accreting zone
develops a strong erosive tendency and portions of south Lanikai experience complete
beach loss.
At this point the north Bellows, south Lanikai, and portions of central Lanika
shorelines are completely hardened by seawalls and revetments. This has reduced the
volume of sediment available to the overall system and increased the reflectivity of the
24
shoreline. Sediment eroding from central and south Bellows is likely bypassing south
and central L
541
anikai to accrete in north Lanikai. 542
543
544
545
546
e southern tip of Bellows reveals the 547
ossibility of southward transport, though the sediment volumes involved are relatively 548
ts indicate southerly transport in south Bellows and diverging 549
550
551
552
553
554
555
nd 556
557
s happens there is the chance that more sediment will be transported from 558
e Bellows shoreline into the Lanikai system. However the presence of revetments in 559
limit the amount of sediment available for transport. 560
imilar561
562
563
VIII. 1995 – 2008
Similar to Period VII, north Bellows and south Lanikai continue to erode to the
point of complete beach loss. The accreting zone in north Lanikai narrows by shifting its
border further to the north. A slight accretion at th
p
small. GSTA resul
transport on either side of Wailea Point. This transport might still be occurring, but with
sediment volumes too small to cause notable beach accretion. In general, the modern
trend of shoreline change appears compatible with the results of the GSTA procedure.
5.3 Future coastal change
Since 1987 wind direction has steadily shifted to the east (Figure 18). If this tre
continues, littoral transport along the Lanikai-Bellows shoreline will become increasingly
northern. As thi
th
north Bellows will severely
S ly, seawalls along most of south and central Lanikai might make beach accretion
problematic. A 1995 study of wave energy and shore-perpendicular bottom profiles at
south Lanikai revealed a sand bar offshore containing approximately 10 000 m3 of
25
sediment (Lipp, 1995). The study also showed that height and period of incoming and
outgoing waves was nearly identical due the highly reflective seawalls. The sand
564
bar is 565
566
567
568
569
570
of 571
n to control the occurrence other aspects 572
f Hawaiian weather (e.g. Kona storms). The influence of a decadal scale cycle, such as 573
ecting the North Pacific High and resulting in 574
575
576
577
578
579
580
581
582
the Lanikai-Bellows 583
oreline, windward Oahu. The results show wind direction to be a major controlling 584
sses. Most major accretion and erosion events can be linked to 585
eriodic shifts in the dominant trade wind direction. Hydrodynamic modeling was 586
located at a distance from shore near the exact anti-node between the incoming and
outgoing waves (1/2 x the mean wave length).
5.4 Directional changes in the wind record
The cause of the decadal directional shift in trade winds is not fully understood. An
explanation might lie in small shifts in the North Pacific High pressure system, north
the Hawaii islands. This system is already know
o
the Pacific Decadal Oscillation, could be aff
the directional shifts seen in the data. It is likely that these long-term changes in trade
wind direction have had a similar impact on sediment availability on other windward
shorelines. The primary obstacle to understanding is the relative scarcity of long-term
continuous directional wind records for islands other than Oahu.
6. CONCLUSIONS
This study integrates sedimentological data, hydrodynamic modeling, and historical
shoreline analysis to investigate large-scale enigmatic changes in
sh
factor on littoral proce
p
26
employed to examine the exact mechanism linking wind direction and littoral transpo
Modeled nearshore currents under easterly wind conditions matched observed historica
shoreline change trends, however only portions of the model results matched historical
observations under more northeasterly winds. Two different methods of grain size
sediment trend analysis were applied to samples taken over a portion of the study ar
Roux, 1996 and Gao-Collins 1992). This study represents the first application of GSTA
methods to specifically target coastal change. The results of both methods were in
general agreement. By comparing GSTA results to the observed historical record we
determined that grain size trends reflect the last major shift in sediment transport in
mid-1960’s.
Revealing the relationship between wind direction and coastal change in the
Lanikai-Bellows beach system represents a major step in the creation of a regional
sediment budget and demonstrates the great utility of integrating multiple analysis
techniques. There is strong evidence to support sediment transfer across Wailea Point,
indicating Be
rt. 587
l 588
589
590
ea (le 591
592
593
594
the 595
596
597
598
599
600
llows Beach and Lanikai Beach are dynamically linked. It is also very 601
likely t602
t. 603
hern 604
605
606
ine. 607
608
609
hat coastal hardening in response to erosion in both Lanikai and Bellows has
worsened the over all erosion and further complicated the littoral sediment transpor
Given more recent trends in both wind direction and shoreline position, nort
sediment transport will likely dominate in the immediate future. However, the coastal
armoring in place along both Lanikai and Bellows shorelines will likely negatively
influence sediment availability and the possibility of accretion on the Lanikai shorel
27
7. ACK610
611
612
613
Harold K.L. Castle Foundation. 614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
NOWLEDGEMENTS
Support for this project was provided by the United States Army Corps of Engineers:
regional sediment management program, Hawaii Department of Land and Natural
Resources, United States Geological Survey, University of Hawaii Sea Grant, and the
28
633
. APPENDICES 634
igure 3 illustrates the Gao-Collins method. This appendix details the application of the 635
ao-Collins method to a synthetic dataset. Calculations associated with site 9 are 636
cluded. 637
638
able 1 639
in size data for the calculations used in Figure 3. 640
641
642
pe and component vectors calculated in table for site 9 only. 643
644
etermine which sites are within the characteristic distance from the site of 645
al to two, which 646
ncompasses ten sites: 2, 5, 6, 8, 10, 11, 12, 13, 14, and 16. 647
648
site 9) and the 649
roximal sites listed above. Trend 1: sites 2 and 5. Trend 2: sites 6 and 11. 650
651
652
ed to be equal (i.e. value = 653
When a trend is found the vectors are assigned to the site with the highest sorting 654
8
F
G
in
T
Coordinates and gra
* Trend ty
Step 1. D
consideration (site 9). In the example, the characteristic distance is equ
e
Step 2. Check for the existence of trends 1 or 2 between the central site (
p
Step 3. Define component vectors r(x,y)i between the central site and those showing a
transport trend. All component vector magnitudes are assum
1).
29
655
656
657
658
659
660
coefficient. As an example, calculations to determine the component vector from site 9
to site 5 are below:
45.0118.1
)25.1()()( 95 −=
−=
−=
dXX
xr 5661
662
89.0118.1
)23()()( 95
5 =−
=−
=d
YYyr 663
664
d is the distance between site 2 and the central site 0, given as: 665
666
where
118.15.01)()( 22295
295 =+=−+−= YYXXd 667
668
669
Sum all component vectors r(x,y)i to make a sum vector R(x,y): 670
671
[0.26 3.60] 672
673
tep 5. Repeat steps 1 – 4 on every site in the data set to define sum vectors at every site. 674
675
Step 4.
== ∑=
17
19 ),(),(
iiyxryxR
S
Results of this step are presented in Table 2.
30
676
677
678
Result of the average vector. 679
680
vector with the neighboring sum vectors 681
etermined to be within the characteristic distance (i.e. sites identified in Step 1). This 682
ly serves as a low-pass filter with a search radius of 2. For site 9 this process is 683
xpressed as: 684
685
Table 2
*
Step 6. Remove noise by averaging each sum
d
effective
e
[ ] [ ]( )
[ ]77.009.0
50.803.16.326.0)110(
),(),()1(
),( 99
=
++
=⎥⎦
⎢⎣
++
= ∑ qav yxRyxRk
yxR
where q is a lis
11 ⎤⎡
686
687
t of all sites within the characteristic distance of site 0: 688
689
q = 690
691
and k is the total number of such sites: 692
693
k = 10 694
695
696
[ ]1614131211108652
31
Thus, the final averaged transport vector at site 0 has an x-component of 0.09 and a y-697
omponent of 0.77. 698
699
tep 7. Convert average vector into azimuth direction Θ (exact formula will vary) and 700
ector length VL: 701
702
c
S
v
degrees 709.077.0arctan90 ⎜
⎛−=Θ ≈⎟⎠⎞
⎝ 703
704
( ) ( ) ( ) ( ) 78.09.077.0)()( 2+= iav xRVL 222
=+=iav yR 705
706
707
708
709
710
711
712
713
714
715
716
717
718
32
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720
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ne and O.H. Pilkey, Editors, 845
helf Sediment Transport—Process and Pattern, Dowden, Hutchinson and Ross, 846
sylvania (1972), pp. 195–223. 847
848
849
ving 850
al of Coastal Research, v. 10, no. 3, p. 851
49-563. 852
853
Watson (1966) 854
Watson, G.S., 1966. The statistics of orientation data. Journal 855
Russell, 1939
Russell, 1939. R.D. Russell, Effects of transportation of sedimentary particles. In: P.D.
Trask, Editor, Recent Marine Sediments, Society of Economic Pa
M
Stelling (1984)
Stelling, G.S., 1984. On the construction of computational methods for shallow wat
equations. Rijkswaterstaat communication No. 35/19
Swift et al., 1972
Swift et al., 1972. D.J.P. Swift, J.C. Ludwick and W.R. Boehmer, Shelf sediment
transport: a probability model. In: D.J.P. Swift, D.B. Dua
S
Stroudsburg, Penn
Thieler and Danforth, 1994
Thieler, E.R., and Danforth, W.W., 1994. Historical shoreline mapping (I): impro
techniques and reducing positioning errors. Journ
5
38
of Geology 74 (2), 786–797.
Wentworth
856
857
(1949) 858
entworth, C.K. 1949. Directional shift of tradewinds at Honolulu. Pacific Science 3(1): 859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
W
86-88.
39
879
0. FIGURES LEGENDS 880
igure 1 881
882
tudy area. Bathymetric contours are in meters. 883
884
igure 2 885
886
of surficial sediment sampling sites for sediment grain size trend analysis. 887
set: samples in the vicinity of Wailea Pt. 888
889
igure 3 890
891
ao-Collins method for determining sediment transport. See Appendix for data and 892
893
le). Circles represent sampling sites; those 894
ontaining “x” show either a trend 1 or trend 2 relationship in grain size parameter with 895
shed arrows indicate component unit vectors (length = 1) drawn in the direction 896
f each trend positive site, while the bold arrow is the summation of the component 897
ich 898
899
900 901
902 903
1
F
S
F
Location
In
F
G
calculations used in figure. A) Illustration of transport determination at site 9 with
characteristic distance equal to 2 (dashed circ
c
site 9. Da
o
vectors. B) The process is repeated at each site producing a transport vector field, wh
is filtered (C) by averaging adjacent vectors.
Figure 4
40
Le Roux method for determining sediment transport. Grain size parameters are identical
to those of Figure 3. This method considers each trend type separately, only trend 1
considered in this example. A) The closest site in the northern, eastern, southern, and
western quadrants is selected for used; dotted
904
is 905
906
lines illustrate quadrants and “x” on a site 907
dicates selection. B) All sites are transformed to lie at an equal distance of the central 908
cardinal radials; site 5 is at the position of site 5A, 10 is moved to 10A, etc. 909
910
911
912
913
914
915
916
917
918
-919
920
921
922
ea level and wave energy calibration for ADVs. 923
924
925
ting, and skewness interpolated from seafloor sediment samples. 926
in
site on the
Grain size parameters are modified to reflect the new positions and summed using the
appropriate form of equation (1) for the trend type being investigated. C) The value of
the central site is subtracted from all sites. The resulting values indicate transport
magnitude in each direction, with negative values indicating transport away from the
central site and positive values towards the central point. Summation of component
vectors determines the final transport vector. D) The process is repeated at every site
with available adjacent sites to produce a vector field for that trend type.
Figure 5
Directional wind data from Kaneohe Marine Corps Air Base. Values range between 1
135 degrees.
Figure 6
S
Figure 7
Mean size, sor
41
927
928
trend analysis. 929
930
931
932
igure 10 933
ns sediment grain-size analysis results. 934
935
igure 11 936
ediment grain-size analysis results. 937
938
939
i Beach. Graphs A, B, C, and D show 940
presentative datasets for each corresponding transect location. Positions are given as 941
an offshore baseline, thus positive shifts indicate accretion and negative 942
ent of a sudden accretion trend. Left map 943
ows a period of accretion in southern Lanikai (1949 – 1971). Right map shows erosion 944
south Lanikai and subsequent accretion at central Lanikai. 945
946
947
948
Figure 8
Results of Gao-Collins method for sediment grain
Figure 9
Results of Roux method for sediment grain size trend analysis.
F
Gao-Colli
F
Le Roux s
Figure 12
Summary of historical shoreline position at Lanika
re
meters from
shifts erosion. Gray boxes track the developm
sh
trend in the
Figure 13
42
Summary of historical shoreline position at north Bellows Beach. Graphs A, B, and C
show representative datasets for each corresponding transect location. Posi
949
tions are 950
s meters from an offshore baseline, thus positive shifts indicate accretion and 951
egative shifts erosion. Map shows persistent erosion across region. Arrows mark 952
of seawall construction in response to erosion. 953
954
955
956
957
958
ydrodynamic model result for 71 degree winds. 959
960
961
ydrodynamic model result for 90 degree winds. 962
963
964
istorical Shoreline record for Lanikai-Bellows beach. Red indicates erosion rate, blue 965
cretion rate. 966
967
igure 18 968
ecord showing divisions used to separate periods of sediment transport. 969
970
971
given a
n
beginning
Figure 14
Hydrodynamic model result for 51 degree winds.
Figure 15
H
Figure 16
H
Figure 17
H
indicates ac
F
The wind r
Figure 19
43
44
ombined interpretation of results from Le Roux and Gao-Collins methods. 972
973
974
ach panel shows the generalized sediment transport pattern inferred from changes in 975
h shown on Figure 17 and discussed in section 5.2. The dotted line represents 976
This dotted 977
ne is designed to help the reader track the movement of littoral sand as it is redistributed 978
-to-period. Wind direction from Figure 18 is also displayed on each panel. 979
C
Figure 20
E
beach widt
an exaggerated view of accreting and eroding areas during each time period.
li
from period
Site mean sorting skewness Trend Type*
Component Vector*
I Xi Yi μ σ Sk r(x)i r(y)i
1 1 4.25 -0.5 1 1.2 - - - 2 2 4 0.3 1 0.8 1 0 1 3 3 4 -1 0.8 1.5 - - - 4 0 3 0.2 0.3 0.7 - - - 5 1.5 3 1 0.8 0.9 1 -0.45 0.89 6 3.25 3.25 -0.7 1.1 1.3 2 0.71 0.71 7 4 3 -1.2 0.9 1.8 - - - 8 0 2 -0.1 0.5 1.5 - - - 9* 2 2 -0.3 1.4 1.1 - - - 10 3.2 2 -0.9 1.6 0.7 - - - 11 4 2 -0.9 1.3 1.4 2 1 0 12 1 1.25 -0.8 1.8 1.3 - - - 13 2 0.75 -0.7 1.3 0.5 - - - 14 3.25 1 -0.4 1.7 0.9 - - - 15 1 0 -0.5 1 1 - - - 16 2 0 1 1.7 0.8 - - - 17 4 0 -0.7 1.4 1 - - -
Site Sum Vector Average Vector Azimuth Direction*
Vector Length*
i R(x)i R(y)i RAv(x)i RAv(y)i Θ VL 1 0.72 -1.95 -0.24 0.83 322 0.392 -0.97 1.24 -0.18 0.48 333 0.393 -0.83 -0.55 -0.58 0.3 316 0.834 0 0 0.18 0.85 143 0.35 0 0 0.05 1.05 6 0.486 -1.22 1.01 -0.35 0.82 340 1.057 -0.71 0.71 -0.53 1.12 322 0.858 0 1 0.57 0.85 44 0.829 0.26 3.6 0.09 0.39 7 0.7810 -0.07 1.06 -0.22 0.98 345 0.8511 -0.51 1.86 -0.19 1.18 349 0.9812 2.59 -0.67 0.15 1.59 7 1.1813 0 0 0.57 0.67 30 1.1514 0.42 -0.62 0.07 1.15 2 1.5915 0 0 0.84 1.23 49 1.1216 0.78 3.62 0.47 0.39 45 0.6717 0 1 0.17 1.21 8 1.23