21

Comparison between Longshore Sediment Transport Due toWaves and Long-term Shoreline Change in Majuro Atoll,
Marshall Islands
Hiromune YOKOKI,1 Hiroya YAMANO,2 Hajime KAYANNE,3 Daisaku SATO,4
Yosuke MINAMI,4 Soya ANDO,4 Hiroto SHIMAZAKI,2 Toru YAMAGUCHI,5
Masashi CHIKAMORI,6 Albon ISHODA,7 Hiroshi TAKAGI8
1

Center for Water Environment Studies, Ibaraki University,
4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japane-mail: yokoki@mx.ibaraki.ac.jp
2Social and Environmental Systems Division, National Institute for Environmental Studies, Japan3
Department of Earth and Planetary Science, The University of Tokyo, Japan
4
Graduate School of Science and Engineering, Ibaraki University, Japan
5
Department of Ethnology and Archaeology, Keio University, Japan
6
Faculty of Informatics, Teikyo Heisei University, Japan
7
Coastal Management Officer, Environmental Protection Authority, Republic of the Marshall Islands
8
Environmental System Center, Fuyo Ocean Development and Engineering Co. Ltd., Japan

Abstract
Topographic changes in Majuro Atoll, Marshall Islands, are caused by various natural and artificial
processes, for example, sediment transport induced by waves and currents, sediment supply from coral
reefs, and the existence of constructed structures along the shoreline. For the present paper, numericalcalculations of wave transformations of the lagoon of Majuro were carried out, and wave energy fluxes,
which are the potentials of alongshore sediment transport, were also estimated. The waves in the lagoon
were assumed to be generated in two ways: wind waves and diffracted waves from swells. The contribution of waves to topographic changes in Majuro were estimated by comparison with the process of past
topographic change, which was obtained by satellite imagery.
Key words: diffracted waves, lagoon-side coast, Majuro topographic change, wave energy flux,
wind waves

1. Introduction
In the Pacific Ocean there are many atolls on
which often appear very low and narrow islands,
which are called atoll islands. Coastal sediments ofatoll islands consist mostly of dead foraminifers andcoral and shell fragments since the coasts of atoll
islands have no rich sources of sands such as rivers.
On such coasts of atoll islands, there should exist asediment supply process from the reef edge to theshoreline due to biological sediment production ofreef-building organisms, in addition to cross-shore andalongshore sediment transportation processes due tonearshore waves and currents. Since the biologicalsediment supply process is too complicated to bemeasured quantitatively, the biological process andGlobal Environmental Research9(1)/2005: 21-26
printed in Japanthe interaction between the biological and the physicalprocesses have not been analyzed quantitatively so far.
These processes play a crucial role in the morphological changes of atoll islands over the long term. In particular, the rising sea-level will be one of the mostnotable impacts of global climate change on atoll
coasts in the near future (Letherman, 1977). Thus wehave to take this into account in developing strategies
for adaptation to future environmental changes onatoll islands.
In the present study, field measurements andnumerical calculations were carried out at Majuro
atoll in the Marshall Islands, in order to investigate theinteractions between the wave field in the lagoon andshoreline changes on the lagoon-side coast. Majuro
atoll is located at 171°22'E, 7°6'N, and is the capital of©2005 AIRIES22

H. YOKOKI et al.

the Republic of the Marshall Islands is located (Fig. 1).
In field measurements, we carried out inspections ofcoastal sediments and beach profile surveys, as well as
continuous observations of bottom velocities along thelagoon-side coast using self-recording velocimeters.

2. Coasts at Majuro Atoll
Field measurements were carried out from September 14 to 26, 2003, at Majuro atoll. Figure 1 shows anoutline of the atoll. It is 40 km long in the longitudinal
direction and 9.7 km wide in the latitudinal direction.
The area of the lagoon is 324 km2, with an average
depth of 46 m. The lagoon is surrounded by reefs,
except for the north passage as shown in Fig. 1 (Xue,
2001).
In the southern part, one atoll island, Long Island,
stretches from Rita, on the eastern end in Fig. 1, to
Laura, on the western end, while small islets stud thenorthern part. Rita and Uliga are densely populated
and highly urbanized districts of the atoll. Ports andharbors have been constructed on the coasts of those
districts. On the other hand, Laura is a less urbanized
district, where the traditional life-style seems to continue.
When we saw the coast along Long Island, artificial vertical seawalls seemed to cover almost all thecoast around Rita and Uliga. Ships and boats weremoored in the ports and harbors, and no sandy
beaches could be seen, as shown in Fig. 2. Approaching Laura along Long Island, we could see
sandy beaches, the width of which became broader
and broader as shown in Figs. 3 and 4.
We carried out beach profile surveys at lines No. 1
through 5 shown in Fig. 1. The profile survey ranged
from shoreline areas to reef edges on both lagoon-side
and ocean-side coasts. The results of the survey showthat the reef area where water depth is less than 1 m
extends offshore for 200-400 m, and that the water
depth suddenly increases beyond the reef edge. The
measured profile at line No. 2 in Fig. 1 is shown in
Fig. 5. Water depths near the shoreline up to 200 m on
the horizontal axis were obtained using the ordinary
surveying equipment (Fig. 6). In deeper areas, weused a fish-finder attached to a boat to detect the sea
bottom. Sandy beaches and sandy sediments on thereef were found on the lagoon-side coasts, while there
were few sandy sediments on the ocean-side. Thissuggested the existence of alongshore sediment transport due to waves and nearshore currents.
According to Xue (2001), coastal erosion damaging Majuro for 50 years since World War II has
brought about shoreline regression by about 10 m on
both lagoon-side and ocean-side coasts. In particular,

Fig. 1 Majuro atoll, Marshall Islands.

Fig. 2 Lagoon-side coast of Rita.

Fig. 3 Lagoon-side coast of Long Island.

Longshore Sediment Transport and Shoreline Change

23

severe erosion was found on the lagoon-side coast of
Uliga and the tip of Laura islet. Xue (2001) pointed
out that the construction of artificial coastal structures
such as vertical seawalls and dredging of the reefs
were the main causes of coastal erosion, and thatblocking the flow across the island due to constructionof causeways was also a cause of erosion. The existence of alongshore sediment transport from Uliga to
Laura is also indicated in Xue (2001).

3. Detection of Coastal Changes
Fig. 4 Coast at the tip of Laura.

Fig. 5 Surveyed profile at Line 2 (of Fig. 1).

Fig. 6 Surveying at Line 2.

A map surveyed in 1944, in aerial photos taken in
1983, and a satellite image (IKONOS) taken in
October 2000 were used in detecting long-term coastalchanges in Majuro over the last several decades.
Changes in shoreline positions between 1944 and1983 were based on 1:25,000 maps prepared by
Manoa Mapworks (1989) who revealed shorelines atmean sea level using aerial photographs in 1944 and1983. The maps were scanned at 300 dpi resolution
and were georeferenced to the 2000 IKONOS image
using ERDAS Imagein version 8.7. We used a 4-m
resolution IKONOS multispectral image to detect theshorelines in 2000. Using values of the near infrared(NIR) band of the IKONOS data, we excluded water
areas and estimated the shoreline positions at the
IKONOS image acquisition time, as wavelengths in
the NIR region are strongly absorbed by the watercolumn. Then we performed contextual editing to exclude areas of subaerially exposed reef flats that hadhigh NIR values. Finally, considering the slope angles
of beaches estimated by the field survey, we obtained
the shoreline positions at mean sea level. The areas
bounded by the shorelines were converted to polygon
data and were overlayed using ArcView version 3.2 todetect changes over time. Yamano et al. (submitted)
describes these processes in detail.
Figure 7 shows the eroded and accreted areas detected by comparing the IKONOS image in 2000 andthe map in 1944. This figure indicates that the tip of
Laura islet has been eroded and the lagoon-side coastof Laura has accreted during the period. The coasts ofLong Island are dotted with both eroded and accreted

Fig. 7 Areas of erosion and deposition detected around Long Island and Laura (1944-2000).

24

H. YOKOKI et al.

areas, thus no apparent erosion or accretion area weredetected. The some small accreted areas along Long
Island may be due to the causeway.
The other comparisons between the map and theaerial photos, and between the aerial photos and thesatellite image yielded no apparent areas of erosion or
accretion. The results shown in Fig. 7 may include
errors due to the geometric correction of each image
and the shoreline determination (Yamano et al., submitted). Thus it is quite difficult to determine precisely the magnitude of the shoreline retreat and advance. However, trends in erosion and accretion werereasonably detected through the comparison.

4. Calculation of the Wave Field in the
LagoonWe calculated wave transformations numericallyin the lagoon of Majuro, in order to verify whether
lagoon-side coastal changes had been due to waves
incident from the lagoon. In this study, waves in the
lagoon were assumed to be generated by the windblowing in the lagoon or by diffracted swells entering
through the northern passage. These two kinds ofwaves were simulated with wave and wind climate
data by appropriate numerical models.

4.1 Wave and wind climate data at Majuro
Figures 8 and 9 show wind speed and direction
data at 12 hour intervals, which were extracted fromhourly data observed at Majuro Weather Station fromJanuary 2002 to September 2003. The wind direction
was measured in degrees clockwise from true north.
These figures indicate that northeastern or eastern
trade winds blowing at a speed of 4 to 5 m/s are predominant in winter, around January, and that no dominant wind direction is found in summer, around
September, since the trade winds become weaker.
Figures 10 and 11 show monthly-averaged significant wave heights and mean wave directions of wind
waves and swells, respectively, around Majuro from1990 to 1999, which were obtained from the ECMWF(European Centre for Medium-Range Weather Forecasts). These figures indicate that both the heights ofwind waves and swells become larger in winter when
the trade winds predominate and the directions are
south for the wind waves and northeast for the swells.
On the other hand, the height of both waves becomes
smaller in summer.
4.2 Wave height and direction of wind waves
The waves generated in the lagoon were simulatedby the SMB (Sverdrup, Munk, Bretschneider) method

Fig. 8 Wind speeds observed at Majuro.

Fig. 10Significant wave height and mean direction of wind
waves around Majuro.

Fig. 9 Wind directions observed at Majuro.

Fig. 11Significant wave height and mean direction of swells
around Majuro.

Longshore Sediment Transport and Shoreline Change(Bretschneider, 1958). In the SMB method, significant
wave height, H1/3, and significant wave period, T1/3,
are estimated according to wind speed at 10 m above
sea level, U10, and the fetch, F, using the following
equations (Wilson, 1965).

Three cases of wind speed on the lagoon were assumed as 6, 4 and 2 m/s, since the average wind speed
at Majuro was about 4 m/s as shown in Fig. 8. For
each case, three cases of wind direction were assumed
as eastern, northeastern, and northern, since the dominant direction measured at Majuro was northeastern as
shown in Fig. 9. The effective fetches for each winddirection at points along the lagoon-side coast were
measured using a nautical chart.
Figure 12 shows the distributions of significant
wave heights along the lagoon-side coast, calculated
for the three wind directions and for a wind speed of
4 m/s on the lagoon. The horizontal axis ranges from
Uliga to the tip of Laura islet along the lagoon-side
coast. The numbers put on the axis correspond to
those of the surveying lines shown in Fig. 1. Figure 12
shows that the wave height at Laura becomes maximum when waves in the lagoon are generated by aneastern wind and minimum for a northern wind. However, the wave height at Uliga becomes maximum fora northeastern wind because the shape of Majuro atoll
gives rise to a sheltered area around Uliga. The reason
wave heights are relatively low on the coast between
Nos. 3 and 4 is that a shallow water area and two
groins located on the coast, as shown in Fig. 1, act as
breakwaters for the coast.
4.3 Wave height and direction of diffracted waves
The average water depth in the lagoon is about
46 m and the lagoon is surrounded by a sheer cliff ofcoral reefs. Thus, the dominant transformation of the
waves incoming through the northern passage can be

Fig. 12Significant wave height distributions by the SMB
method.

25

assumed to be wave diffraction, where wave refraction and shoaling are relatively neglected. In the present study, the wave height distribution along thelagoon-side coast was calculated by the boundary integral method (Lee, 1971), applying the Green’s theorem to the Helmholtz equation, which was the governing equation.
The boundary elements were set along thelagoon-side coast and across the northern passage.
The length of the boundary elements were set at
500 m for the passage and 1,000 m for the coast,
respectively. Since the length of elements had to be
set longer than desirable due to numerical restrictions,the period of incoming swells also had to be set longer
than the observed one, so that the wave direction
along the coast could be estimated accurately. The
height and period of incoming swells were set 1 m and20 s respectively. The calculations were carried out
for the three cases of incoming wave direction, eastern,northeastern, and northern. The boundary condition
along the lagoon-side coast was set as a vertical seawall with no water exchange across the boundary,whether or not an atoll islet existed on the reef.
Figure 13 shows the calculated wave heights anddirections on the lagoon-side coast for a northeastern
incoming swell. In the figure, the angle of wave direction of 90 degrees indicates waves entering normal tothe coast: a direction angle of less than 90 degrees
indicates waves going toward Luara, and of more than
90 degrees, toward Uliga. The wave heights becomelarger between Nos. 3 and 4 because the area islocated in front of the northern passage. The wave
directions on the Laura coast are toward the tip of
Laura but those on the Uliga coast are the opposite.
4.4 Wave energy flux along the coast
Wave energy flux at the breaking point is an important quantity since it can be proportional to thealongshore sediment transport rate for general conditions (e.g., Inman & Bagnold, 1963; Komar & Inman,1970). In this study, wave energy fluxes were calculated according to wave heights and directions estimated on the coast. Figure 14 shows the alongshore

Fig. 13 Wave height and direction of diffracted waves.

26

H. YOKOKI et al.

equilibrium profile and its modifications adjusted tocoaral reef beaches (Cowell & Kench, 2001; Kench &Cowell, 2001). Also, estimation of the biological sediment production rate was not dealt with in this study.
Future research will need to address these in order todevelop a long-term model to simulate maintenancesystems of atoll islands.

Acknowledgments
Fig. 14 Alongshore component of wave energy fluxes.

component of wave energy fluxes on the lagoon-side
coast: the solid line indicates fluxes based on wind
waves generated by a 6 m/s northeastern wind, and thebroken line, those based on diffracted waves of thenortheastern swells. The positive value of the energy
flux component indicates that the direction of the flux
is from Uliga to Laura.
In Fig. 14, the energy fluxes toward Laura, calculated for diffracted waves become larger in the area
between Nos. 3 and 4. The magnitude of wave energy
fluxes of diffracted waves is larger than that of wind
waves in the area, but, the area is limited in scope to
only in front of the passage. On the other hand, theenergy fluxes calculated for wind waves change theirdirection around No. 4. This may correspond to theaccreted area on the lagoon-side coast of Laura shownin Fig. 7. The eroded areas along Long Island shownin the figure are also explained by the energy fluxes of
the wind waves.
The energy fluxe results indicate that waves generated by winds are more effective at producing topographic changes in Majuro atoll, comparing the eroded
and accreted areas in Fig. 7, even though the magnitude of fluxes are larger for the diffracted waves.

5. Concluding Remarks
In the present study, a field investigation andnumerical calculations were carried out in order toclarify the relationship between waves in the lagoon
and topographic changes on the coast of Majuro atoll.
The discussions lead to the following conclusions:• Comparions of the map and the IKONOS satellite
image indicate that the tip of Laura islet has been
eroding and the lagoon-side coast has been accreting for about 50 years.
• Numerical simulations of the wave field in the
lagoon indicate that the distribution of wave
energy fluxes based on wind waves agree with the
distribution of eroded and accreted areas better
than those based on the diffracted waves of swells.
In order to estimate the shoreline change due towaves and currents more accurately, cross-shore
topographic changes should be considered: Dean’s

The authors deeply appreciate SOPAC (South
Pacific Applied Geoscience Commission) for providing the IKONOS satellite image. This research was
supported by the Global Environmental Research
Fund of the Ministry of the Environment, Japan (Project No. B15, Principal investigator: HK), and partially funded by Grant-in-Aid for Scientific Research(A), Japan Society for the Promotion of Science(JSPS) (Project No. 14209003, Principal investigator:
Prof. Nobuo Mimura, Ibaraki University). Ross
Togashi provided valuable information on maps ofMajuro Atoll.
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