Review of solutions for 3D hydrodynamic modeling applied to aquaculture in South Pacific atoll lagoons.

Abstract

A workshop organized in French Polynesia in November 2004 allowed reviewing the current methods to model the three-dimensional hydrodynamic circulation in semi-enclosed atoll lagoons for aquaculture applications. Mollusk (e.g. pearl oyster, clam) aquaculture is a major source of income for South Pacific countries such as French Polynesia or Cook Islands. This aquaculture now requires a better understanding of circulation patterns to improve the spatial use of the lagoons, especially to define the best area to set larvae collectors. The pelagic larval duration of the relevant species (<20 days) and the size of the semi-closed lagoons (few hundreds of km2) drive the specifications of the model in terms of the spatial and temporal scale. It is considered that, in contrast with fish, mollusk larvae movements are limited and that their cycle occurs completely in the lagoon, without an oceanic stage. Atolls where aquaculture is productive are generally well-bounded, or semi-closed, without significant large and deep openings to the ocean. Nevertheless part of the lagoon circulation is driven by oceanic water inputs through the rim, ocean swells, tides and winds. Therefore, boundary conditions of the lagoon system are defined by the spatial structure of a very shallow rim (exposition and number of hoas), the deep ocean swell climate, tides and wind regimes. To obtain a realistic 3D numerical model of lagoon circulation with adequate forcing, it is thus necessary to connect in an interdisciplinary way a variety of methods (models, remote sensing and in situ data collection) to accurately represent the different components of the lagoon system and its specific boundary conditions. We review here the current methods and tools used to address these different components for a hypothetical atoll of the Tuamotu Archipelago (French Polynesia), representative of the semi-closed lagoons of the South Pacific Ocean. We hope this paper will serve as a guide for similar studies elsewhere and we provide guidelines in terms of costs for all the different stages involved.

Full text

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Review
Review of solutions for 3D hydrodynamic modeling applied
to aquaculture in South Pacific atoll lagoons
S. Andre ´foue ¨ta,*, S. Ouillona, R. Brinkmanb, J. Falterc, P. Douilleta, F. Wolkd, R. Smithe,
P. Garenf, E. Martinezg, V. Laurenth, C. Loi, G. Remoissenetj, B. Scourzick,
A. Gilberta, E. Deleersnijderl, C. Steinbergb, S. Choukrounb, D. Buestelf
aInstitut de Recherche pour le De ´veloppement, B.P. A5 98848 Noumea Cedex, New Caledonia
bAIMS@JCU, Australian Institute of Marine Science and School of Mathematical and Physical Sciences, James Cook University, Townsville, Australia
cHawaiian Institute of Marine Biology, University of Hawaii, Kaneohe, Hawaii 96744, USA
dInstitute of Astronomy and Geophysics, Universite catholique de Louvain, 2 Chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgium
eSouth Pacific Applied Geoscience Commission, Private Mail Bag, GPO, Suva, Fiji
fInstitut Franc ¸ais de Recherche et Exploitation de la Mer, Centre Oce ´anologique du Pacifique, BP 7004, 98719 Taravao, Tahiti, French Polynesia
gObservatoire Ge ´ode ´sique de Tahiti, Universite ´ de la Polyne ´sie Franc ¸aise, BP 6570, 98702 FAAA, Tahiti, French Polynesia
hMe ´te ´o France, Direction Inter-re ´gionale de la Polyne ´sie Franc ¸aise, BP 6005 98702 Faa’a Tahiti, French Polynesia
iDe ´partement Recherche et De ´veloppement, Service de la Perliculture, B.P. 9047, Motu Uta, 98715 Tahiti, French Polynesia
jProgrammes Aquaculture Cellule De ´veloppement, Service de la Pe ˆche, BP 20 Papeete Tahiti, French Polynesia
kMission Oce ´anographique du Pacifique, Service Hydrographique et Oce ´anographique de la Marine, SP 9164700260 Arme ´es-Tahiti, French Polynesia
lInstitute of Astronomy and Geophysics and Centre for Systems Engineering and Applied Mechanics, Universite catholique de Louvain, 4 Avenue G. Lemaitre,
B-1348 Louvain-la-Neuve, Belgium
Abstract
A workshop organized in French Polynesia in November 2004 allowed reviewing the current methods to model the three-dimensional
hydrodynamic circulation in semi-enclosed atoll lagoons for aquaculture applications. Mollusk (e.g. pearl oyster, clam) aquaculture is a
major source of income for South Pacific countries such as French Polynesia or Cook Islands. This aquaculture now requires a better
understanding of circulation patterns to improve the spatial use of the lagoons, especially to define the best area to set larvae collectors.
The pelagic larval duration of the relevant species (<20 days) and the size of the semi-closed lagoons (few hundreds of km2) drive the
specifications of the model in terms of the spatial and temporal scale. It is considered that, in contrast with fish, mollusk larvae move-
ments are limited and that their cycle occurs completely in the lagoon, without an oceanic stage. Atolls where aquaculture is productive
are generally well-bounded, or semi-closed, without significant large and deep openings to the ocean. Nevertheless part of the lagoon
circulation is driven by oceanic water inputs through the rim, ocean swells, tides and winds. Therefore, boundary conditions of the
lagoon system are defined by the spatial structure of a very shallow rim (exposition and number of hoas), the deep ocean swell climate,
tides and wind regimes. To obtain a realistic 3D numerical model of lagoon circulation with adequate forcing, it is thus necessary to
connect in an interdisciplinary way a variety of methods (models, remote sensing and in situ data collection) to accurately represent
the different components of the lagoon system and its specific boundary conditions. We review here the current methods and tools used
to address these different components for a hypothetical atoll of the Tuamotu Archipelago (French Polynesia), representative of the semi-
closed lagoons of the South Pacific Ocean. We hope this paper will serve as a guide for similar studies elsewhere and we provide guide-
lines in terms of costs for all the different stages involved.
? 2006 Elsevier Ltd. All rights reserved.
Keywords: Coral reef; Hoa; Tuamotu; Pearl oyster; Remote sensing; ADCP; Multi-beam; Bathymetry; Residence time; Larval propagation
0025-326X/$ - see front matter ? 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.marpolbul.2006.07.014
*Corresponding author.
E-mail address: andrefou@noumea.ird.nc (S. Andre ´foue ¨t).
www.elsevier.com/locate/marpolbul
Marine Pollution Bulletin 52 (2006) 1138–1155

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1. Introduction
South Pacific atolls have been used for experimental
small-scale aquaculture applications for decades, but a real
explosion in activities came in the 1980s with the black
pearl industry. In a few years, tens of lagoons were used
to collect wild animals, capture spats and raise the black
pearl oyster Pinctada margaritifera. The core of the activi-
ties lies in the Tuamotu Archipelago (French Polynesia),
but it has also spread to the Society Islands (French Poly-
nesia), Cook Islands and Fiji. In addition, Marshall
Islands, Federate States of Micronesia, Tonga, Papua
New Guinea, Solomon Islands and Kiribati are all in vary-
ing stages of commercialization of cultured pearls (SPC,
2005). The farming of black pearls provides the second
largest source of income to French Polynesia, with ?100
millions of US$ per year. In 2004, there were ?600 farms
in French Polynesia, occupying ?10,000 hectares of lagoo-
nal surfaces. Some atolls, such as those of the Western Tua-
motu (Fig. 1) are covered by farm structures between the
surface and 10 m deep (Fig. 2). These lagoons are typically
between 80 and 300 km2, and registered farm structures
may cover up to 10% of the area (Fig. 2). It is estimated
that 7000 people were employed in pearl farm activities
in 2004 (out of a total of 250,000 people living in French
Polynesia). In the Cook Islands, 95% of the activity comes
from Manihiki atoll which harbored 205 farms in 2003.
Pearl exports represent 12 millions US$ in 2000, or in other
terms, 90% of the Cook Island export revenue and 20% of
the gross domestic product (GDP). Other atolls take
advantage of other natural resources, such as clams or tro-
chus, but the economic importance of these cultures/
harvests is still several orders of magnitude lower than
the pearl industry.
Pearl farming is a difficult activity which is no longer
growing in most atolls, and even declining, due to diseases
(Cook Islands) or overproduction or poor quality pearls
and drop in market sales (French Polynesia). In Tuamotu,
pearl farming relies entirely on the ability to collect larvae
of P. margaritifera (spat collecting) since the natural stock
is not exploited, for its preservation. Many farms actually
do not grow pearls, but just collect and grow oysters that
are sold to other farmers. The success of spat collection
appears highly variable in space and time (Fig. 3) even in
these small lagoons which are partially closed by a shallow
reef rim with numerous emergent islands thus limiting
their connectivity with the surrounding ocean. It is there-
fore a high priority for the management of the black pearl
Fig. 1. The Tuamotu archipelago with location of the atolls quoted in the paper: Ahe, Fangataufa, Manihi, Moruroa, Takapoto, Tikehau, Takaroa,
Rangiroa, Raroia.
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industry to enhance the understanding of larval propaga-
tion within a lagoon, understand the physical factors
explaining the spatial and temporal variability of larval
recruitment, locate the best collecting sites, and identify
the best periods for spat collecting. It is timely to apply
well-constrained 3D numerical circulation models, and
not just rely on the past experience and empirical knowl-
edge of farmers who often got unpredictable and sporadic
Fig. 2. Pearl farm leases in Ahe atoll (Western Tuamotu, French Polynesia) as in September 2005 showing the high density of pearl farms and larvae
collectors throughout the lagoon.
0
200
400
600
800
1000
1200
1400
1600
1800
11/9/198812/7/1988
1/4/19892/1/19893/1/1989
3/29/19894/26/1989 5/24/1989 6/21/19897/19/1989 8/28/1989
10/23/1989 11/20/198912/19/1989
1/17/1990 2/28/19903/28/19904/25/19905/23/1990 6/20/19907/18/1990 8/16/19909/12/1990
10/12/1990
11/7/199012/5/1990
12/31/1990
1/30/19912/27/1991 3/27/19914/24/19915/22/1991
Date (month/day/year)
Number of collected spats
Fig. 3. Time-series of spat collecting in one location of the lagoon of Takapoto atoll (Western Tuamotu) over a three-year period (from Brie ´, 1999).
1140
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success rates from one year to another. Indeed, numerical
models can account for many of the important forces driv-
ing lagoonal circulation and exchange (i.e. bathymetry,
wind, waves, tides, and stratification), and identify which
are the most important variables governing the dynamics
of a given lagoon (e.g. Nihoul, 1984; Blumberg and Mellor,
1987; Lazure and Salomon, 1991; Davies and Lynch, 2005).
This review describes the current state-of-the-art to
design well constrained 3D model useful for aquaculture
applications. The information comes from a workshop
organized in Tahiti (French Polynesia) in November 2004
to discuss these issues. We focused on the type of atolls that
are encountered in the South Pacific (specifically the Cook
Islands and Tuamotu archipelago) and where black pearl
farming is the most developed. We reviewed the physical
processes that drive lagoonal circulation and how these
processes have been modeled and measured in a variety
of places. Then, we estimated the costs of implementing a
3D numerical model, calibrate and validate it for an atoll
representative of the Tuamotu archipelago.
This paper digests the information provided during the
workshop to raise managers’ awareness of the benefits,
technology involved and associated costs to conduct a
3D modeling exercise in their atoll lagoons.
2. Overview of a Tuamotu atoll
A Tuamotu archipelago atoll is made of three seascapes:
the lagoon, which is bounded by a shallow rim, which is
itself surrounded by the deep Pacific Ocean (Fig. 4). On
top of the marine systems, we need to consider the atmo-
spheric forcing for circulation and for air–sea energy trans-
fer purposes.
The main object of interest are atoll lagoons, where
aquaculture activities take place. They are generally sau-
cer-shaped basins, reaching ?70 m in its maximum depth,
but average depth is closer to 20–30 m (Andre ´foue ¨t et al.,
2001a). They are frequently dotted by coral patches that
reach vertically to the surface (pinnacles), thus the fine-
scale topography may be complex in places. Lagoon bot-
toms are generally dominated by fine carbonate sediment,
but areas with significant coral and algal cover (carpets
and massive patches) are frequent, especially on the shal-
low inner slopes. A narrow inner reef flat of coralline algae
and coral may bound the lagoon. Sediments get coarser in
the shallows, with rubble and boulders in the vicinity of the
channels that connect the lagoon with the ocean through
the rim of the atoll.
These channels (called hoa in Polynesian) are narrow
spillways (a few tens to hundreds of meters wide) or large
reef flats (up to few kilometers wide) that interrupt and
cut the ‘‘land’’ or motu in Polynesian. Motus are few meters
high carbonate deposits over fossile terraces of coral con-
glomerates that are frequently colonized by vegetation.
The result is a landscape made of small islands and hoas
along the atoll rim. Deeper passes through the rim may
exist in Tuamotu and Cook Island atolls. They are gener-
ally narrow (few tens of meters) with a few meters depth
in its shallowest part. Areas with frequent strong current
(passes, functional exposed hoas) may be free of any living
Fig. 4. Ahe, an atoll of the Western Tuamotu archipelago showing its lagoon bounded by a semi-closed rim with numerous hoas and motus. Images of the
entire atoll is a Landsat 7 ETM+ image at 30 m-resolution, the image of the rim is a merged panchromatic-multispectral IKONOS image at 1 m-resolution
(? Space Imaging). Details in distribution of different facies and bottoms along the rim are readily visible including erosion areas (Cong: conglomerate),
deposits (Rub: rubbles), smooth pavement areas (Pav.), and coralline crests (Cor.).
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cover, with only a bare carbonate pavement. In addition,
some atolls of the western Tuamotu have been locally
uplifted by tectonic processes (lithospheric flexure due to
Tahiti island mass), from few centimeters to few meters
(Pirazzoli et al., 1988). Exchanges of water through these
uplifted rims are less efficient than elsewhere.
3. General circulation features of semi-closed atoll
The renewal of lagoon waters can be described generi-
cally, but what is really happening along the rim of any
given atoll depends on its rim morphology, orientation,
swell regimes, tides, and presence of passes or not (Tartin-
ville et al., 1997; Kraines et al., 1999; Andre ´foue ¨t et al.,
2001a; Callaghan et al., 2006). The generic mechanisms
are: (1) waves due to wind or swell break at the reef edge
(crest) and bring water to the exposed outer rim reef flat.
The basic physics is that when waves break at the crest, a
radiation stress gradient (set-up on the reef flat) is created
that forces water across the reef lagoon-ward (Longuet-
Higgins and Stewart, 1964; Tait, 1972); (2) this water also
crosses the hoas towards the lagoon; (3) lagoon water in
excess gets evaporated, or may be evacuated by the passes
during low tides, or may be evacuated by gravity draining
water through the hoas opposite to incoming swell direc-
tion if the lagoon set-up is high enough (Callaghan et al.,
2006), and if there is no pass.
The actual dynamics and equilibrium of all these pro-
cesses depend on the magnitude (significant wave height)
and direction of the swell, tide magnitude, number of hoas
(degree of aperture of the rim), and size of the passes. For
instance, during high swell and high lagoon set-up, the pass
flows can be only directed outward even during incoming
tides. Furthermore, tidal flow through small passes have
little effect on circulation because the incoming water does
not penetrate far on the flood before the tide changes to an
ebb. Lenhardt (1991) showed that oceanic water remained
only within a 1 km-radius zone around the pass of the
Tikehau atoll lagoon which covers an area of 394 km2.
Mixing between ocean and lagoon waters is thus only very
limited, except for atolls with very large passes (e.g. Moru-
roa atoll studied in Tartinville et al., 1997). Further, we will
consider that our hypothetical targeted atoll has a narrow
pass, but the real specificity of semi-closed atoll hydrody-
namic functioning is the control exerted by the hoas (see
Section 7).
Circulation within deep lagoons is usually dominated by
wind stress at the surface, which generates a downwind
flow at a few percent of wind speed (2–3% in Von Arx,
1948; Atkinson et al., 1981; Tartinville et al., 1997) in a
10–20 m depth layer with slower reverse flows in the deeper
water that is directed to the pass if there is one. In the case
of Moruroa lagoon, using an idealized simplified model
and a 3D model, Mathieu et al. (2002) have studied how
wind stress, pressure gradient and bathymetry combine to
shape the vertical distribution of velocities, i.e. when veloc-
ities is maximum, minimum and reverse. However, in very
shallow lagoons, the two-layer system may not develop,
and in extreme cases circulation can be driven entirely by
inflow over the reef flat from wave-overtopping and flow
out through reef gaps, with little wind or tidal influence.
For small and shallow lagoons, density differences due to
evaporation and precipitation may induce density-driven
circulation between ocean and lagoon. Within a given
lagoon, similar processes may occur, however thermal
and salinity differences are small on most large lagoons,
with limited diurnal variation (see review in Andrews and
Pickard, 1990). Vertical stratification is generally weak in
atolls, with small gradients in temperature and salinity
(Atkinson et al., 1981; Kraines et al., 1999), but very calm
oceanic and atmospheric conditions may lead to stratifica-
tion and even anoxia and mass mortalities of lagoon organ-
isms (Adjeroud et al., 2001). Under normal forcing,
differences in temperature have reached 0.5 ?C for the
60 m deep Eniwetok atoll (Atkinson et al., 1981). Short
term, local thermoclines can develop in the vicinity of the
passes due to the entrance of cold waters during incoming
tides as reported by Farrow and Brander (1971) for the
shallow Aldabra atoll in the Indian Ocean. In this case,
the water is brought from below the oceanic thermocline
during the early flood, but the waters are then quickly
mixed afterward.
According to studies published from other sites, the
moderate depth and semi-closed status of Western Tua-
motu atolls suggest that circulation forcing can be domi-
nated by either winds or waves. Lagoon stratification,
albeit weak, needs to be captured for an optimal model,
which means that sea surface temperature (SST) needs to
be known at the external boundary limit. Therefore, proper
modeling of lagoon dynamics requires precise characteriza-
tion of the atoll rim structure, lagoon and hoa bathymetry,
wind direction and speed, swell direction and height, and
oceanic and lagoon SST.
4. Aquaculture constraints on circulation modeling
In our case, the necessities of black pearl aquaculture
drive the specifications of the circulation model. The model
needs to be parameterized to capture the spatial–temporal
variation of larval propagation and settlement. If we con-
sider the black pearl oyster problem, current studies in
Takapoto atoll (see Fig. 1) allows defining these scales.
An experiment conducted on undifferentiated bivalve lar-
vae including two species of oysters (P. margaritifera and
P. maculata) in 2004 provided maps of lagoon larval densi-
ties throughout a spawning event (Fig. 5). Larvae were
monitored in situ. These maps suggest that a spatial resolu-
tion of 100–200 m is required to capture the spatial vari-
ability in larval distributions. In addition the pelagic
larval duration (PLD) for these species are typically 20–
21 days. Thus, the model needs to accurately simulate the
path of passive drifters released from the bottom (natural
oysters) or from the water column (farmed oysters hang-
ing on lines) at time scales no longer than one day. A
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parameterization of the oceanic forcing integrated over
three-days or one week would be inadequate. Forcing fac-
tors (swell, SST, wind and flows through hoas and passes)
need to be characterized at least daily, and preferably at
higher rates. For instance, the tradewinds that are domi-
nant in this area show diurnal/nocturnal variations, and
the tides can significantly modulate the wave-driven flows
across the atoll rim in case of moderate swell (Laurent
et al., 2004).
P. margaritifera spawning periods are variable in Wes-
tern Tuamotu. It is acknowledged that oysters spawn
throughout the year in Takapoto atoll, but there are signif-
icantly more spawning events in February–March and
September–October, during the change of seasons (Pouv-
reau et al., 2000). The black-pearl oyster is the target of
choice for aquaculture, however, other benthic resources
are now considered for farming, including giant clams
(Tridacna maxima for Tuamotu) and trochus (Trochus nil-
oticus). Giant clams are in high demand not only for their
meat but also for the aquarium trade. On-going experi-
ments for giant clam collecting seem to be very successful,
but in atolls that are different than those that well-suited
for oyster farming. Shallow (average ?10 m deep) and
small (<50 km2) atolls in the Eastern Tuamotu are the most
interesting because of their impressive clam densities
(Andre ´foue ¨t et al., 2005; Gilbert et al., 2005). Knowledge
of circulation is for the moment less of an issue for the
management of clam resources in small atolls. Neverthe-
less, it could be more of a priority if other atolls launch
aquaculture activity with a more limited natural stock to
start with. The PLD for giant clams is 7–10 days while
the PLD for trochus is even shorter – from 3 to 5 days.
(Jameson, 1976). Spawning of giant clams also occur
throughout the year, but seems to be triggered by thermal
stress due to colder oceanic water inputs into the lagoon.
5. Bathymetry
Accurate
required to build a model. However, in situ discrete sound-
ing from occasional ships are generally too spatially sparse
to obtain after interpolation a useful grid for a model,
except near the area where detailed hydrographic surveys
may exist (passes, navigation channels). To achieve high
resolution bathymetry at the model scale of interest, two
options are recommended. First, interpretation of optical
remote sensing images may provide a first cut on the
bathymetry with reasonable accuracy. However, this tech-
nique is limited to shallow clear waters. Since the late
80s, the French hydrographic survey office of the Navy
(SHOM) has released atoll spacemaps where bathymetric
information derived from SPOT satellite is provided in 4
classes of depth, with 5 m intervals. The theoretical limit
for super clear waters over a bright bottom is ?40 m for
nadir viewing satellites (Philpot, 1989). In atoll lagoon
waters that have higher diffuse attenuation coefficients
(Maritorena and Guillocheau, 1996), the technique still
works to a depth of ?25 m, but provides only a relative
bathymetry. More severe limitations occur if the bottom
is dark (coral, algae) (Philpot, 1989). If ground-truth data
exits, it is possible to calibrate the optical models (empirical
or semi-analytical) more accurately to obtain actual depth
bathymetryistheprimaryinformation
Fig. 5. First data on larval propagation of undifferentiated pool of two oyster species from in situ monitoring around a spawning event in the Takapoto
atoll lagoon. The left panel shows census just before the spawning which occurred in the north of the lagoon. The second panel shows where the larvae
have accumulated after three days. Data for D-larvae development stage (70 lm). Census were achieved along a 1 km-grid size. Patterns of accumulations
are clear at the scale of the lagoon, but the 1 km resolution is too coarse to capture the fine distribution of the larvae. Workshop discussion suggested that a
resolution of 100–200 m would be optimum.
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in meters. Even if published papers have advertised excel-
lent results in controlled situations (small area, clear
waters, homogeneous bottom-types), as a rule of thumb,
it is necessary to consider a RMS error of 10% of the max-
imum depth (Andre ´foue ¨t et al., unpublished data, based on
Great Barrier Reef data).
The second option of choice for measuring bathymetry
is by acoustic survey. This technique can not be applied
in very shallow waters, but optical data can fill the gap
to obtain a complete image. Several atolls of the Cook
Islands have been recently mapped with high-resolution
swath mapping, using multi-beam echo sounders (Fig. 6).
Those are able to map a complete underwater landscape
in a fraction of the time than is currently required by a sin-
gle beam echo sounder, and with much greater accuracy.
Computer-processing of swath mapping data reduces com-
plex data sets to three-dimensional visualisation images
that represent, in fine detail, the morphology of the sea-
floor, as well as occasional wrecks and other peculiar fea-
tures. Range is frequency dependant and the precision is
tremendous, with for instance individual lines of pear-oys-
ters hanging on their stations visible on the data.
6. Characterization of oceanic and atmospheric forcing
at the day scale
Aquaculture applications call for high temporal resolu-
tion forcing data to track the dispersal of larvae from
spawning to settlement. The forcing factors are primarily
the wave regime around the island, due to local wind and
oceanic swell generated in higher latitude seas. Then, the
filter due to the structure of hoas and presence of passes
needs to be described (next section). Oceanic SST is
required to correctly solve lagoonal stratification. Finally
wind is a key forcing factor for lagoon surface drift and cir-
culation. Climatology of in situ or remotely sensed weather
measurements is available and useful to predict an average
picture of the lagoon circulation. Although there are many
sources available, here we refer only to the products and
software used in French Polynesia institutions. The World
Ocean Atlas provides a monthly climatological coarse 1
degree resolution compilation of in situ data such as tem-
perature, salinity, nutrients and geostrophic (large-scale)
velocities. They can be complemented by higher resolution
regional circulation model data, such as the Regional
Ocean Model System (ROMS, http://marine.rutgers.edu/
po/index.php?model=roms) (Fig. 7). This model allows
to focus on a small area and to reach a very high spatial
and temporal resolution. For instance Marchesiello et al.
(2003) worked at 3.5 km resolution. Other model products
used in French Polynesia include wind field products
(provided at 10 m altitude, which is standard require-
ment in oceanography) from the European Centre for
Medium-RangeWeatherForecasts
http://www.ecmwf.int/) and the Me ´te ´o-France numerical
weather prediction model ARPEGE v1.5. One drawback
of all these models is that they lack calibration around
coastlines, including oceanic atolls.
Swell Significant Wave Height (SWH) can be provided
regionally by altimetry space missions (ERS-1, Topex,
Jason), and wind speed and direction can be obtained by
spaceborn scatterometers (e.g. NSCAT, Quickscat). They
also provide sea surface currents and anomalies. These
are primary and convenient sources of information since
data are available for anywhere on the tropical belt
through different web-accessible data centers. Individual
altimetry satellites have poor temporal resolutions, but dif-
ferent sources can be combined to fill the gaps. In addition,
(ECMWF v1.5,
Fig. 6. 3D output of a 5 m-resolution bathymetric model from a SeaBat 8101 Multibeam Echosounder survey of Manihiki (Cook Island), overlaid on
satellite image. The sounder had 101 beams operating at 240 kHz, with a swath width at 150? or 7.4· the water depth.
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by considering a large neighborhood (500 km radius)
around one point of interest, it is possible to obtain daily
remote sensing measurements. These spatially integrated
measurements prove to be useful to establish relationships
between SWH and water velocities and fluxes at a daily
time scale in exposed hoas from a variety of Tuamotu
atolls (Tartinville and Rancher, 2000; Andre ´foue ¨t et al.,
2001a). Altimeter data are able to capture short-term
weather events (high swell or high winds, not to mention
hurricanes) which can last only few days (see the abrupt
passage of a southern 3 m swell in the time series of altim-
etry data in Andre ´foue ¨t et al., 2001a). Such short-terms
events are most likely to be extremely relevant to explain-
ing the variability of spat collecting success across time.
Ocean–atmosphere interactions are investigated in dif-
ferent areas of the Pacific Ocean using the Weather
Research and Forecasting model (WRF, http://wrf-mode-
l.org/index.php). Combined with models such as ECMWF,
they allow modeling the atmospheric circulation at the
kilometer-resolution. Wind and exchanges and the air–sea
interface can thus be taken into account in the ocean, but
also in the lagoons given the spatial resolution.
In both French Polynesia (FP) and the Cook Islands,
the availability of weather data from models and remote
sensing information is completed by an array of in situ
observations, which is still the primary source of informa-
tion for local weather forecasters. Shipborne observations
are compiled in FP to quantify sea state and swell direc-
tion. There are a number of meteorological stations,
including two in Western Tuamotu (Takaroa and Rangiroa
atolls, Fig. 1) which provide a time-series of wind observa-
tions since 1951. Given the minimal impact of relief on the
wind regime in atolls, these observations would be more
than adequate to constrain at high temporal resolution
the circulation model. In situ data are scarce but nonethe-
less help validate the model output, or point to model lim-
itations and errors close to coastlines. For instance, models
seem to overestimate the western swell when compared to
ship data.
The Cook Islands opted for buoys to monitor their
lagoons. In Manihiki lagoon, it measures air temperature,
barometric pressure, wind direction and speed, and also
sea-surface temperature, and salinity as well as dissolved
oxygen, chlorophyll and pH. It is instrumented with a mul-
tichannel cosine irradiance and a profiling spectroradiome-
ter. Data is transmitted in a daily report via satellite phone
to the offices of the South Pacific Applied Geoscience Com-
mission (SOPAC) in Fiji where a monthly report is com-
piled and sent back to Cook Island. These sensors are
expensive (see Section 10.8) and require maintenance, but
their use goes beyond just circulation modeling. They are
used to monitor potential stresses and anomalies in the
water column, and send warning signals to the community
ofpearl farmers (http://www.sopac.org/tiki/tiki-index.
php?page=Cook+Islands+Manihiki+Buoy).
7. Wave-driven flows across the reef flats and hoas
The geomorphology of the rim is the most defining char-
acteristic of atolls. A ‘‘typical’’ Western Tuamotu atoll rim
will have an outer reef flat that follows almost the entire
periphery of an atoll (Fig. 4). The hoas oriented perpendic-
ular to the rim crest allows the exchange of waters from the
exposed outer reef flat to the lagoon. Variations on this
theme have been conceptualized by Chevalier (1972) who
proposed a typology of hoa and hoa development. The
Fig. 7. Example of SST and current velocities output from ROMS model for French Polynesia.
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number of hoas, their width, their depth, their degree of
uplifting (relative to mean sea level) and their bottom
types, are all factors that need to be quantified in order
to accurately estimate flows within the hoas under varying
swell and tide. One of the difficulties in modeling hoa flows
is that the entire system is dynamic. Hoa’s width and depth
are not stable and vary constantly and quickly with the
wave set-up of the exposed outer reef flat. At low tide, dur-
ing low swell, and depending on the level of sediments
accumulated (Kench and McLean, 2004), most of these
hoas may not be functional while the rim may be almost
entirely submerged during high swell events. The ratio of
opened sections between low swell and high swell condi-
tions can be as much as ten (Andre ´foue ¨t unpublished data)
in some Tuamotu atolls. It is possible to define an average
flooding situation useful for classifying atolls in term of
renewal rates regimes (Andre ´foue ¨t et al., 2001a), but fine
descriptions are required to accurately estimates the fluxes
on a daily basis.
High resolution satellite imagery such as those provided
by IKONOS (4 m resolution), and Quickbird (2.5 m) sen-
sors would be adequate to quantify rim geomorphometrics.
Those sensors, and the SPOT 5 sensor as well, also offer
products that merge panchromatic and multispectral spec-
tral bands providing visually impressive 1, 0.6 and 2.5 m
resolution for IKONOS, Quickbird and SPOT respectively.
Merged panchromatic-multispectral data are not recom-
mended for mapping at depth (5–20 m), but for shallow
(<3 m) hoas and rims these products are useful. Images
actually provide the only feasible way to obtain rim
bathymetry since most hoas would be too shallow for
acoustic surveys. To our knowledge, only Yamano et al.
(in press) have characterized atoll rim geomorphology with
IKONOS data, but focusing on waterline extraction only.
Coarser space-borne data have been used to characterize
rim types (Andre ´foue ¨t et al., 2001b, 2003), but we suggest
that excellent characterization of the variation of water lev-
els, bottom-types, conglomerates and sediments loca-
tions can be done using the new high resolution images
(Fig. 4). The merit of image-based rim quantification and
interpretation would be to identify the variety of hoas pres-
ent in one atoll in order to obtain in situ measurements for
all the different hoa configurations, and measure their effi-
ciency in terms of water transport, or sediment transport
(Kench and McLean, 2004). Then, images will help in gen-
eralizing spatially in situ current velocities data for each
type of hoa present to up-scale local flow measurements
at rim-scale. It is worth noting that if no images are avail-
able, it is also possible to apply labor-intensive and low-
tech survey techniques, that local inhabitants could even
learn to help out in the surveys.
To our knowledge, there are no time-series of in situ cur-
rent measurements in Western Tuamotu hoas except in
Tikehau atoll (Lenhardt, 1991). Current meter data exist
for Eniwetak in Marshall Islands (Atkinson et al., 1981),
Fangataufa and Moruroa (Delesalle, 1990; Tartinville
and Rancher, 2000) in the south-east Tuamotu, Cocos
(Keeling) Island in the Indian Ocean (Kench and McLean,
2004). However, there are more studies on barrier reef flats,
which may be considered as very wide unbounded hoas
between the ocean and lagoon (e.g. Hardy and Young,
1996; Lugo-Ferna ´ndez et al., 1998; Lowe et al., 2005;
Kench and Brander, 2006). Symonds et al. (1995) provide
for a schematic reef flat a formulation of the cross-reef
velocity u following:
u ¼ bHðhb? HÞ
u ¼ 0
if H < hb
if H > hb
where H is the depth over the reef flat, hbis the total water
depth at the wave breaking point, b is a function of the
geometry of the reef flat (outer slope, flat width, coefficient
friction. b = 0.5 for Moruroa atoll in Tartinville et al.,
1997). This definition of u is important because it provides
a link with Significant Wave Height (SWH) from satellite
measurements at daily scale. Indeed, Hbis proportional
to wave height with Hb= SWH/c, (c = 0.35 in Symonds
et al., 1995). Using some reef geometry-dependant tuning,
it is possible to develop from altimetric SWH the flows of
current on reef flat (Tartinville and Rancher, 2000; Andre ´-
foue ¨t et al., 2001a). The Symonds et al. (1995) model was
confirmed in atoll hoas by Tartinville and Rancher
(2000). Other wave-driven flows models have also been
proposed to include more types of reef configurations
(Hearn, 1999; Massel and Brinkman, 2001), including for
steep reef faces (Gourlay and Colleter, 2005). The reef flat
model by Kraines et al. (1998) was able to include wave
refraction behavior, and was implemented to model the
boundary conditions of Majuro atoll (Kraines et al., 1999).
Symonds et al. (1995) model is satisfactory for atolls for
day-scale previsions, but b is dependant on reef flat geom-
etry (slope and width) and cover type (friction). For fine
predictions in time and space, it will require local calibra-
tion around the part of the atoll exposed to waves. Reef flat
width can be easily computed for any point of the rim
(from high resolution satellite images), outer slope profiles
could be also estimated using high resolution images and
combined with the models linking outer slopes geometry
and reef set-up (Gourlay, 1996). Coefficient friction Cfis
a factor controlling wave energy dissipation across reef
flats. Friction due to bottom roughness can be as important
as the turbulent breaking wave process for energy dissipa-
tion (Lowe et al., 2005). As in Tartinville and Rancher
(2000) or Kraines et al. (1999) friction can be assumed
and set empirically to study wave-driven currents. Hoa-
scale integrated measurements of flows would be adequate
for questions regarding the net flows of water entering the
lagoon, but understanding the relative role of wave break-
ing and friction on energy dissipation would be also rele-
vant for biogeochemical studies on nutrients uptakes and
productivity of the different living communities across the
flat. Using a series of pressure sensors and current meters
deployed along several cross-reef transects on Kaneohe
Bay Barrier Reef flat in Hawaii, Falter et al. (2004)
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obtained an average Cf= 0.22 ± 0.03 over coral-algal reef
flats. Similar magnitudes were previously reported by
Gerritsen (1981) for Ala Moana reef flat in Hawaii
(Cf= 0.28 ± 0.05), and by Nelson (1996) for John Brewer
Reef in Australia (Cf= 0.15 ± 0.04).
Observing in Manihiki atoll, an atoll without pass, that
water level gradients were generally sloping down from the
lagoon into the ocean at all tidal phases during three weeks
of observations, Callaghan et al. (2006) proposed for Man-
ihiki atoll a wave-pumping analytical model (Nielsen et al.,
1999) considering lagoon-scale wave-driven flushing in the
case of closed lagoons (no passes). Integration of flows
around the part of the atoll exposed to waves explained
lagoon-levels variations for two tidal cycles and thus
inflows estimated with this approach could be used at smal-
ler time-scales than days. The main deficiency with this
model is involved with defining the wave pump efficiency
(or wave energy flux), but in contrast with Symonds et al.
(1995) it avoids partially the nearshore geometrical com-
plexities, the assumption of a saturated surf zone and
applying linear wave theory were it breaks down. Thus
far, the atoll wave-pumping model is only validated consid-
ering lagoon-scale measurements (i.e. prediction of lagoon
level variance). Though not yet demonstrated, we suggest
that for lagoon circulation modeling which require spa-
tially explicit input along the rims, the wave-pumping
model will provide, at day scale, a correct estimate of
inflows per hoa mouth if the model is applied on the rim
section drained by the hoa. In the case of closed atoll with-
out passes, or if the passes sections are too small to effi-
ciently drain the excess lagoon water, Callaghan et al.
(2006) suggest that two different boundaries are required
within the 3D model. First, a wave driven inflow boundary
where water is driven into the lagoon by waves (models dis-
cussed above). Second, a gravity driven outflow boundary
is required to account for flows from the lagoon towards
the ocean though hoas leeward of incoming wave, when
lagoon levels are higher than ocean levels.
8. Flows through the Tuamotu passes
Modeling studies have been conducted in both Majuro
and Moruroa atolls (Kraines et al., 1999, 2001; Tartinville
et al., 1997), both containing passes. However, Moru-
roa’pass is atypical of Tuamotu’s due to its great width
(5 km). The narrower passes of Majuro make it more rep-
resentative of Western Tuamotu atolls despite its location
in the Marshall Islands, although Majuro’s passes are
much deeper. If swell wave-driven flows are totally absent
due to very calm oceanic and atmospheric conditions (an
unusual situation in the Tuamotu), the tide is the main
forcing factor of water exchanges through the pass. All
in situ observations worldwide confirm this (Farrow and
Brander, 1971; Michel et al., 1971; Smith and Jokiel,
1975; Atkinson et al., 1981). In Western Tuamotu region
the tide amplitude is small, about 15 cm, with the M2 mode
(principal lunar) being the major tidal constituent (Len-
hardt, 1991).
There are several series of current measurements inside
Tuamotu passes, mostly performed by SHOM. A Raroia
atoll (Fig. 1) example is provided in Page `s and Andre ´foue ¨t
(2001). It shows well that outgoing flows are most of the
time positive, and only calm seas let the tide control the pro-
cess with oceanic water going lagoonward. The outgoing
flux during high seas reached 4 m s?1in Raroia. Lenhardt
(1991) also recorded currents in the northwest oriented pass
of Tikehau atoll but the mechanical device used to perform
the measurements was judged unreliable above 1 m s?1.
To our knowledge, atoll passes have not been specifi-
cally modeled at high spatial resolution. Instead, they have
been integrated in coarse resolution 3D circulation models
as in Kraines et al. (1999) or as part of the model boundary
(Tartinville et al., 1997). However, similar features found
along continental barrier-island coasts have been modeled
using high-resolution (down to 50 m) finite-element models
(Hench and Luettich Jr, 2003), in an idealized situation
first, and then for an actual inlet of North Carolina,
USA, with similar proportions as Tuamotu atoll passes
(5 m depth, 0.5 km length, 1 km width). The high resolu-
tion model show many topography-dependant local
processes (e.g. flow separation zones). Similarly as for
cross-reef current along the hoas, the pass can be included
in the general model and be part of the boundary of the
lagoon system, or, passes and lagoon-ward vicinity of the
pass can be an object of focus in itself. The sub-kilometer
variability observed around inlets call for a fine modeling
of atoll passes to be able to predict small-scale features that
may be critical for larval propagation or retention.
9. Types of 3D models and review of past and present atoll
applications
The number of available 3D models is actually quite
high and numerous options are available to the practitio-
ners. Table 1 lists some of them, with their main character-
istics. More details can be found for each model on web
sites and users forums, and we highlight below the 3D
models previously used for reefs and atolls.
The review of existing 3D circulation models applied to
true atolls is brief. Only, Moruroa and Majuro atolls have
been studied with finite-difference models (Tartinville et al.,
1997; Kraines et al., 1999), and one finite-element model
for Rongelap atoll in Marshall Islands is currently under
development (Peterson et al., 2006). Moruroa has been
the target of many nuclear tests since the 60s and the pri-
mary application of the model was to predict the fate of
potential dissolvedradioactive
et al., 1997). Residence times and particles trajectories were
computed under different forcing conditions (Fig. 8).
Another atoll targeted for nuclear testing, Fangataufa
has been also investigated but the results have remained
largely unpublished. In Majuro, the model was used to
assess how the artificial closing of the southern part of
pollutants(Tartinville
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the atoll with roads and walls have changed the renewal
rates of the lagoon (Kraines et al., 1999). Abaiang atoll
(Kiribati) was studied with Mike21, a 2D model, to inves-
tigate the impact of a seaweed culture project (Lelaurin,
2000). Application-wise, several platform reef (i.e. no sig-
nificant lagoon completely bounded by a shallow reef flat)
and continental lagoons bounded by barrier reefs have
been investigated using 2D or 3D model for circulation,
productivity (coupling with biological models), mapping
of residence time field, sediment transport, larval transport,
pollutant transport and coral bleaching (Douillet et al.,
2001; Carleton et al., 2001; Pinazo et al., 2004; Fernandez
et al., 2006; Jouon et al., 2006).
GETM is the 3D model currently applied on Moruroa.
GETM uses a finite-volume, finite-difference approach on
Arakawa’s C-grid with 15 r-levels for each of the 250 m
resolution mesh (Blumberg and Mellor, 1987). The r-levels
scheme is better than the traditional z-level scheme since
the later can not handle well the surface or boundary layers
in case of large bathymetric variations. The (x,y,z) grid
transformation into a (x,y,r) system allows to better han-
dle topographic variation since in a r-coordinate system,
the number of vertical levels in the water column is the
same everywhere in the domain irrespective of the depth
of the water column. Details on the numerical techniques
used in the Moruroa hydrodynamic module and parame-
terization are in Tartinville et al. (1997) and references
within. This study investigated the sensitivity of residence
time to wind and hoa flows. Only the lagoon was modeled
and the pass appeared as an open boundary. Passes and
hoas were not explicitly represented. Hoa inflow was
included as a boundary steady state process.
The model used in Majuro atoll is a 10 z-levels finite-dif-
ference 3D model (Guo and Yanagi, 1997; Kraines et al.,
1999 and references within). Its spatial resolution is
500 m. It integrates density-driven current, tidal-stress cur-
rent, wind-driven current and the radiation-stress driven
cross-reef transport. It includes the Longuet-Higgins and
Stewart (1964) radiation stress tensor to parameterize wave
refraction along the atoll rim. The rim is explicitly included
in the model (with at least two z-levels at 50 cm and 1 m
depth). In contrast with the lagoon where constant eddy
viscosities coefficients were used (from Bikini atoll in Munk
et al., 1949), specific eddy viscosities were assigned to reef
flat meshes to account for higher turbulent viscosity due
to wave actions. Finally, specific drag coefficients were
computed for reef flats and meshes with water depth <5 m.
Other models currently used in coral reef lagoons (not
just atolls) may also provide interesting numerical tech-
niques which have been locally validated with in situ data.
For instance, Mars3D is a r-coordinate finite-difference
model used in New-Caledonia lagoon that have benefited
from a wide array of in situ measurements for its calibra-
tion (Blumberg and Mellor, 1987; Douillet, 1998; Douillet
et al., 2001). This model is also currently under develop-
ment to integrate inflows through the barrier reef flats.
10. Options and guidelines for a case-study
The Tahiti workshop aimed at developing a model spe-
cifically for a biological/economic application so our stan-
dards for model performance are particular to the life-
history of oysters and clams. During the workshop, local
technical services have prioritized three of the French Poly-
nesia main pearl-oyster industry atolls if a model could be
implemented. These are Ahe, Manihi and Takaroa, all in
the Western Tuamotu (Fig. 1). Thus, this narrows the
scope of the options. We realize that the discussion below
is fairly specific to one environment and case study, but
we also believe it will provide to funding organizations
(government, NGOs, managers) a general indication of
what this type of work costs and the necessary items to
account for.
Lagoon and inner slopes cover 140, 160 and 85 km2for
Ahe, Manihi and Takaroa respectively. Maximum reported
depth on nautical charts are 60 and 40 m for Ahe and
Table 1
Main characteristics for existing 3D models
Vertical discretisation Horizontal discretisationHigh-order turbulence closures Drying/floodingPublic domain
MOM-4
POM
ROMS
POL3DB
GHER-M
COHERENS
TRIM-3D
MIKE-3
TELEMAC-3D
ECOM
MOHID
GETM
MARS3D
SHOC
z
s
s
s
2–r
r
z
z
r
s
s
s
r
s
CU
CU
CU
CA
CA
CA
CA
CA
FE
CU
CA
CU
CA, CU
OCU, CA
N
Y
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
N
N
N
N
N
N
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
N
N
Y
Y
Y
Y
N
Extended from http://www.bolding-burchard.com/html/GETM/history_and_outlook.htm which also provides links to other oceanic models. Abbrevi-
ations used: z = z-level, s = general vertical coordinates, r = sigma coordinates, CU = curvilinear, CA = cartesian, FE = finite elements, OCU orthogonal
curvilinear.
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Takaroa respectively, and unknown for Manihi. They all
have a unique narrow pass. These passes have a least
charted depth of about 3–4 m though deeper channels
occur. Each pass also differs in morphology and exposure
from one atoll to another. According to the atoll rim typol-
ogy from Andre ´foue ¨t et al. (2001b), their rims are mostly
made of rim types Rim 1 or 8 in the north (completely
closed and vegetated), and Rim 2, 5 and 7 in the south
(semi-closed to semi-opened with succession of hoas and
motus). Thus they are asymmetrical atolls, more open in
the south than the north.
Following these basic morphometrics information, it is
necessary to discuss the different options if a model is imple-
mented in one of these atolls. First, only technical criteria
wereconsideredasifanidealsamplingandmodelingscheme
couldbeachievedwithoutcostconstraints.Theseoptionsset
an obviously upper limit that is further put in perspective by
the evaluation of the induced costs (Table 2) that are dis-
cussed in Section 10.8.
10.1. Lagoon spatial resolution, horizontal and vertical
discretisations
A fine spatial resolution of 100–200 m for the lagoon
would be satisfactory for larval propagation applications,
however the need for better representation of rim and
passes points to several options:
1. a finite-difference model throughout the entire domain,
but at very high resolution (10–50 m),
2. a finite-element model with variable mesh size (Hench
and Luettich Jr, 2003; Pietrzak et al., 2005),
Fig. 8. Examples of 2D products from Moruroa 3D model: atoll residence time and particle tracking sensitivity study to different forcing factors such as
wind, tide, hoa inflows and stratification (from Tartinville et al., 1997).
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3. high resolution rim and passes nested models within the
coarser atoll model.
The choice of option 1, and the choice of the spatial res-
olution, is a question of balancing computational costs and
the availability of adequate bathymetry. For Ahe atoll
(140 km2), a 10-m regular mesh grid involves 1.4 million
cells and would require very high computation costs. A
100 m-resolution would mean a more manageable 14,000
cells model. Current computer technology allows building
and tuning a powerful cluster of personal computers for
?KUS$20 (as at 2006). The Mars3d finite-difference model
at 500 m resolution running in New Caledonia lagoon is an
18,700 cells model, running on a PC or, for long-term sim-
ulations, on a 20 processor pc-cluster.
The choice of option 2 allows increasing the spatial res-
olution where it is needed. However, the set-up of a high
resolution, unstructured mesh may not be trivial and the
complexity of the network depends on the complexity of
the topography (Legrand et al., 2006). This technique is
currently applied to Rongelap atoll (Peterson et al., 2006).
Regarding option 3, no nesting models have been used
in atolls thus far, but this technique is now frequently used
elsewhere. It allows increasing grid resolution in a sub-
region of the whole domain, without the cost of running
a high resolution everywhere. Several levels of nested mod-
els have been implemented. For instance, Tang et al. (2006)
uses three levels of nesting. The two-ways interaction
between the fine and coarse model can be achieved in dif-
ferent ways depending on the type of nesting: through a
dynamic boundary if the models do not overlap or through
substitution if domains overlap (Sheng et al., 2005 and ref-
erences therein). Nesting is applied in New-Caledonia
lagoon using Mars3d and the AGRIF library (Debreu
and Blayo, 2002), in the Belize barrier reef system using
the 3D CANDIE model (Sheng and Tang, 2004; Tang
Table 2
Itemization of the main costs for a 3D atoll modeling project
ItemTime and salary OthersComments
Expertise
Ocean modeling
Rim modeling
3D lagoon model and
integration of
boundary models
We assumed experienced scientists
(postdocs) immediately operational
who do not need to learn the tools
and the theory. The 3D model is
assumed from-the-shelf (Table 1)
12 months
12 months
24 months
60 KUS$
60 KUS$
120 KUS$
240 KUS$
Computers 3 months15 KUS$
15 KUS$
>10 processors-cluster
20 KUS$
One IT technician to install,
maintain and tune the system
Satellite imagery 6 months30 KUS$ High resolution
(<4 m) satellite image
3 KUS$
A 170 km2atoll is assumed.
Cost is 18 US$/km2. The image and
the 6-months post-doc provide the rim structure
30 KUS$
Field work
Bathymetry
(multi-beam survey)
2 · 1 months on siteBoat rental
Freight (600 kg)
Transport
Post-processing
20 KUS$
On site costs are estimated
considering a 150US$/day per-diem rate
10 KUS$ For bathymetry, we assumed a 170 km2
atoll implying a 3-weeks survey for
2 people + transfer
For circulation instruments, we assumed
data acquired during two one-month
periods by 4 technicians
Circulation (incl. 3 ADCPs, pressure
sensors, tide-gauge, 2 ADVs, 1 CTD,
and moorings)
4 · 2 months on site Boat rental
Freight
Transport
100 KUS$
40 KUS$
Instruments
Bathymetry (multi-beam sensor)One month rental
Post-processing
120 KUS$
We assume that the multibeam
sensor can be rented with DGPS,
motion sensor, gyros, survey and
post processing software and data
logging computer
Instruments are priced based on
list prices available from the web from
a variety of providers. Full options
were considered (e.g. 6 sensor-CTD,
transect mode for ADCP, etc.)
Circulation
3 ADCPs
4 pressure sensors
2 ADVs
CTD
Moorings
Initial capital cost
120 KUS$
5 KUS$
40 KUS$
25 KUS$
5 KUS$
195 KUS$
Salaries, transport boat rentals, freight and perdiems are highly variable between locations and institutions. Here, we have considered salaries with benefits
corresponding to an experienced US or French overseas-based post-doc. The targeted site is a 170 km2atoll of Western Tuamotu which is accessible by
plane or ship cargos. Total cost is ?800 KUS$ for a project that could be staged in a 3 year-period.
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et al., 2006) and is currently under development for the
Capricorn-Bunker group of the Great Barrier Reef in
Australia using the Sparse Hydrodynamic Ocean Code
(SHOC) model (Walker and Waring, 1998). SHOC is a
finite difference general purpose model applicable to scales
ranging from estuaries to regional ocean domains.
Topography variations in atolls due to large pinnacles
call for the use of r-coordinates. Even if r-coordinates have
been introduced to better represent complex topography,
sharp depth variations pose other problems, and careful
vertical discretisation is required (Deleersnijder and Bec-
kers, 1992).
10.2. Rim modeling
The rim could be separately modeled at high resolution
to define the boundary conditions of the lagoon model. The
rim could be also fully included in the lagoon model like in
Kraines et al. (1999), with a specific parameterization.
Rims could be also processed within a nested-model. The
resolution achieved by Kraines et al. (1999) at 500 m is here
judged too coarse to accurately model the Western Tua-
motu rim morphology since hoas widths are of the order
of few tens to hundred meters at best (Fig. 4). For a
finite-difference model, a spatial resolution on the rim coar-
ser than hoas width would imply a parameterization of an
aperture factor (e.g. ratio of land and hoas) for each cell of
the rim. This can be easily computed with high resolution
satellite images (Fig. 4). Furthermore, it should be possible
to modify dynamically this aperture for different levels of
wave energy and set-up. It would be possible to calculate
volumetric flux as a function of dynamic sea-level for differ-
ent rim zones and use these calculations to define the rim
computationally as a permeable boundary.
Hoas also require a model able to handle drying/flood-
ing conditions (Table 1), which can take into account the
change in computation domain when some cells become
dry following sea level variations. For such a model, hoas
also require a dynamic shift from a 3D model towards a
2D model when the depth is too low to accommodate
too many r-levels. Indeed, very small vertical discretisation
leads to computational instability that can be handled only
using a very short time-step inducing excessive computa-
tion costs.
10.3. Oceanic boundary conditions
Nesting the atoll model within an oceanic model (e.g.
ROMS) is also an attractive option to account for oceanic
SST and current. There is no need to include very deep
atoll slopes, in order to avoid vertical digitization problem,
but it is necessary to set the depth limit of the model in the
ocean to below the average thermocline to account for
possible temporary drains of cold water through the pass
during flood.
The oceanic boundary conditions set by Kraines et al.
(1999) is a 10 km domain around the island. Here, if the
wave field is estimated through altimetry data or models,
the boundary domain needs to be temporarily set around
?500 km at least (Tartinville and Rancher, 2000) to include
enough satellite tracks. Then, the oceanic wave field can be
reduced to a 2D model near the coastline and the Kraines
et al. (1999) scheme could be used to adequately account
for wave-driven processes.
After the 1997/1998 El Nin ˜o transition to La Nin ˜a,
mean sea level increased up to 40 cm in Samoa. Given that
other regions of the Pacific Ocean would experience a sim-
ilar signal it is necessary to consider the affect of this low-
frequency sea-level variation on long term atoll flushing.
10.4. Bathymetry
The required precision of the topography depends on
the spatial resolution of the model. Eventually, the model
resolution is driven by the scale of flow or feature that
needs to be captured by the model and by the computing
power. The potential need of creating nested model at
higher resolution than 100 m for the passes or dense pinna-
cles areas justifies the collection of high-range data similar
in quality than those obtained for Manihiki atoll, at 5 m
resolution using a multi-beam system (Fig. 6). Very shallow
water bathymetry can be estimated from optical satellite
images to fill the gaps.
In addition, fine-scale bathymetry offers the possibility
to estimate the bathymetric variation within each mesh.
This provides a way to quantify a roughness coefficient
for each mesh. This requires a model domain in which
the friction coefficient is spatially variable. This is not typ-
ically done in hydrodynamic models over coral reefs. In
practice, there is no established scheme to define this coef-
ficient. Bottom roughness needs to be empirically tuned by
in situ velocities measurements, for instance on both-sides
of a pinnacle-rich areas.
10.5. Tracking module
A tracking module is mandatory to study larval propa-
gation under different forcing. Lagrangian models of
advection–diffusion such as Hunter et al. (1993) are now
common in most 3D models (Table 1). They may also tend
to accumulate particles in region where depth or diffusivity
are the smallest. However, this is a numerical artifact that
can be corrected with proper numerical solutions (e.g.
Spagnol et al., 2002 for a 2D model).
The modeling of larvae is not as simple as modeling a
dissolved tracer. Buoyancy needs to be parameterized,
and in some cases, larvae may have behaviors which
require specific developments. This is obviously true for
fish larvae with swimming abilities, but mollusk larvae,
though passive during a good part of their PLD, have
the capacity to avoid settling in unsuitable areas, and
bounce from the bottom. This warrants further investiga-
tions in terms of coupling physics and biology, like this is
increasingly done for fish larvae connectivity modeling. A
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first-order model where larvae are considered passive
throughout their PLD and bottoms equally suitable would
be a useful decision-support tool. However, substrate suit-
ability could be considered as a secondary product of the
model and explicitly included in it.
10.6. Tide model
A global oceanic tide model such as FES99 or FES2004
provide a useful source for forcing at the deep ocean
boundary (Le Provost et al., 1994; Lefe `vre et al., 2002).
The FES (Finite Element Solution) model is based on the
resolution of the tidal barotropic equations on a global
finite element grid without any open boundary conditions
and no assimilation, which leads to solutions independent
of in situ data. The accuracy of these ‘‘free’’ solutions is
improved by assimilating tide gauge and TOPEX/Poseidon
(T/P) altimeter information through an assimilation
method. For the eight main constituents of the tidal spec-
trum (M2, S2, N2, K2, 2N2, K1, O1, and Q1), about 700 tide
gauges and 687 T/P altimetric measurements are assimi-
lated. FES2004 gives heights of tidal constituents on a 1/
8? · 1/8? grid for a global coverage. Data files in NETCDF
format can be downloaded through the web portal of
FES2004 (http://www.legos.obs-mip.fr/en/soa/).
10.7. In situ data collection
Climatology data clearly shows two different seasons for
wave and wind regimes. From November to March, there
is a north swell which is absent the rest of the year. It would
be optimal to collect data during the two seasons.
Existing meteorological stations should provide wind
direction and speed (at least for Western Tuamotu), in
addition to irradiance, cloud cover, humidity, evaporation
and rain. The buoy used in Cook Island atolls would be an
ideal sensor to monitor at the lagoon level atmospheric
parameters, and sea surface parameters as well.
In addition to conductivity-temperature-depth (CTD)
casts to measure temperature and salinity, several types
of sensors can be deployed to calibrate the model: tide
gauge, pressure sensors, current meters, Acoustic Doppler
Velocimeters (ADVs) and Acoustic Doppler Currentmeter
Profilers (ADCPs). Current meter measures speed velocity
of flowing water and can be capable of measuring direc-
tional waves. The three most common types of modern
current meters are mechanical (rotor and vane), electro-
magnetic, and acoustic Doppler. Current profilers provide
current simultaneously over a range of depths and gener-
ally have a pressure sensor as well. Acoustic sensors uses
the Doppler effect (change in frequency) on backscattered
echo from plankton, suspended sediment, bubbles and
waves all assumed to be moving with the speed of the
water. Doppler instruments are now the industry standard
for current measurements. Indeed, measurements are made
in a remote sampling volume free from flow distortion
from the sensor itself. Doppler technology has no inherent
minimum detectable velocity, giving excellent performance
at low flows, however care must be taken in stratified
waters as density differences can refract sound waves. In
addition, ADCP can be used mounted on a boat, to pro-
vide large coverage instead of being used in one single spot.
We do not advertise or recommend any particular brand
here, but readers may refer to detailed tests for evaluating
new and developing coastal sensor technologies made by
third-party scientists independent from manufacturers.
For instance, the Alliance for Coastal Technologies is a
consortium of academic groups who publish detailed
instrument fact-sheets on www.actonline.ws.
The use of an ADCP on transect mode would be an
ideal configuration to characterize the flows in passes and
lagoons under different forcing. The lagoon and passes
can be also instrumented with fixed ADCP either bottom
mounted or downward looking off a buoy. Lagoon loca-
tion may be difficult to select, but south lagoon and rim
are likely the most interesting areas due to presence of hoas
where cross-rim exchange between the lagoon and ocean is
most dynamic. Finally, to characterize hoa currents, the
best configuration would be to deploy two pressure sen-
sors, one upstream the entrance the hoa, and one close to
the mouth. Between them, an ADV would measure current
velocities. This set-up should be used on different hoa
types, during different wave regimes. Finally, one tide-
gauge and wave-gauge should be deployed on the fore-reef,
before the hoa sensors.
All depths, ocean and lagoon levels should be measured
against the same vertical datum, such as the Mean Sea
Level (Callaghan et al., 2006).
10.8. Costs
The various options described above all have pros and
cons. The final factor that needs to be accounted for is
obviously the costs induced. Options need to be selected
depending on the funds available for the modeling exercise.
Costs can be itemized based on 6 main categories:
• expertise,
• computers and software,
• high resolution satellite images,
• field work for acquisition of observations,
• instruments for acquisition of observations,
• administration.
Table 2 itemizes the costs for the ideal implementation
of a Western Tuamotu atoll model if they were part of a
hypothetical grant proposal. We have not included over-
heads administration costs which vary widely. Administra-
tion also includes all the costs related to organizing
purchases, trips, meeting, provide information to locals,
etc. Some variables are the same for any sites worldwide
(time for expertise), but salary costs, surface area, remote-
ness, shipping costs and field trip costs are fairly specific to
each region. Also, costs may decrease or increase with time.
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