A LAGRANGIAN ANALYSIS ON COASTAL DISPERSAL OF
CORAL LARVAE AND SPAWN AROUND OKINAWA ISLAND, JAPANYusuke Uchiyama1*, Tsubasa Miyagawa1, Sachika Odani1, and Satoshi Mitarai2
1

Department of Civil Engineering, Kobe University
1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japanuchiyama@harbor.kobe-u.ac.jp
2

Marine Biology Unit, Okinawa Institute of Science and Technology Graduate University
1919-1 Tancha, Onna, Okinawa, Japansatoshi@oist.jp

ABSTRACT: A JCOPE2-ROMS downscaling oceanic circulation model in a triple nested
configuration coupled with a 3-D Lagrangian particle tracking model was developed forquantifying coastal connectivity of coral larvae and spawn originated from nearshore areas
around Okinawa Island, Japan, located in the East China Sea. Coastal dispersal of neutrally
buoyant Lagrangian particles was extensively examined as a proxy of corals. A Lagrangian
analysis of ~24.3 millions of particles revealed that the along-island residual currents are
responsible for the prevailing clockwise coral transport consisting of the northeastward
residual current on the west coast and the opposing currents on the east coast. Semi-enclosed
coastline topography locally induces residual stagnating circulations, resulting in notableparticle entrainment. In particular, Kin and Nakagusuku bays on the east coast and Cape Hedo
at the northernmost tip of the island serve as nodes, where intensive particles accumulation
provokes. Therefore, the along-island residual currents and topographic constraint jointly
affect the local, short-distance coral connectivity around the island.
INTRODUCTION
Both self-recruitment and remote transport are essential factors to maintain abundantcoral ecosystems in tropical and subtropical marine environments. Coastal connectivity has
widely been exploited to assess biological linkages of species of interest across certain areas,
to deduce geometrical pathways of aquatic fauna, and to determine marine protected areas(MPAs) for preservation of desirable ecosystems. In general, connectivity has been evaluatedbased on population genetics, in which genetic similarity among individual corals sampled at
different locations are carefully diagnosed. In contrast, dispersal of Lagrangian particles
transported by 3-D velocity evaluated by circulation models imparts an alternative measure ofpelagic coral transport that enables us to statistically quantify connectivity.
The Nansei Archipelago, Japan, has unique marine environment for abundant corals
because of the Kuroshio that plays a crucial role in carrying warm water from lower latitude
to maintain favorable temperature for corals inhabited in a meridionally stretched chain of theislands fringing the East China Sea (Fig. 1a). Uchiyama et al. (2018) [1] revealed from adetailed numerical experiment that the northeastward drifting Kuroshio is also responsible forlong-distance transport of coral larvae and spawns by ~1,000 km during a three-week pelagicstage immediately after they spawn, when they are transported passively by ambient currents.
Nevertheless, the short-distance connectivity is found to be much higher than the remoteinterisland connectivity due to long-distance larval transport. Such high connectivity within
an island or a regional archipelago has substantial importance to regional and local biologicallinkages of corals as well as other marine fauna and flora. Therefore, very high-resolution

Figure 1 – (a) Left: the triple nested JCOPE2-ROMS model domains bounded by black
rectangles representing the outermost ROMS-L1 with a lateral grid resolution of 3 km, theintermediate L2 at 1 km, and the innermost L3 at 250 m. (b) Right: the enlarged ROMS-L3
domain squeezed to encompass Okinawa Island, Japan. The background colors indicate
bathymetry in m. Colored circles in (b) are the 133 source and sink patches with a 2-km
radius defined in the nearshore areas around the island for the Lagrangian particle tracking
experiment. A total of 12 areas are further defined by grouping all the 133 patches by
topographic features using the same color. Five hundred particles are released once a dayfrom each patch for a period of one year; hence, approximately 24.3 million particles (500particles × 133 patches × 365 times) are analyzed.
circulation modeling is inevitable for investigating effects of complicated nearshore
topography such as laterally semi-enclosed embayment, fringing reefs, or steep slopes aroundreef edges on dynamics and associated dispersal. Nevertheless, such a high-resolution model
assessment has never been conducted previously as far as the authors are aware.
In the present study, we conducted a triple nested high-resolution synoptic oceanmodeling based on the JCOPE2-ROMS downscaling system (e.g., Uchiyama et al., 2017a [2];2017b [3]; 2018 [1]; Kamidaira et al., 2017 [4]) coupled with a 3-D Lagrangian particletracking model (e.g., Carr et al., 2008 [5]; Romero et al., 2013 [6]) that enables us to quantify
coral connectivity near Okinawa Island (Fig. 1b) at a lateral spatial resolution of 250 m withaccounting for the realistic mesoscale oceanic condition of the East China Sea including thenorthward drifting Kuroshio. A comprehensive Lagrangian analysis was then performed toquantify the nearshore connectivity to determine the areas to be preserved (MPAs), based on amassive amount of particles mimicking coral larvae and spawn released from a total of 133
source patches mostly located near reef edge regions around the island (Fig. 1b). Our primary
focus is on effects of the detailed nearshore topography depicted by the very high-resolution
model on coastal, local, short-distance connectivity of coral spawn and larvae.
THE TRIPLE NESTED JCOPE2-ROMS MODEL
We developed a downscaling regional circulation model based on the JCOPE2-ROMS
system (e.g., Uchiyama et al., 2017a [2]) in a triple nested configuration embedded in theJapan Coastal Ocean Predictability Experiment version 2 (JCOPE2; Miyazawa et al., 2009[7]) domain. Trilinear spatiotemporal projection of the parent model solution was carried out

to force embedded child ROMS models through the corresponding open boundary conditionsas prescribed in Mason et al. 2010 [8], with successively decreasing grid spacing from ~10km (JCOPE2), to 3 km (ROMS-L1), to 1 km (ROMS-L2; Uchiyama et al., 2018 [1];Kamidaira et al., 2017 [4]), and further down to 250 m (ROMS-L3). The innermost ROMSL3 model is our test bed here, which was designed to encompass Okinawa Island with 1280 ×1120 horizontal grid cells and 32 vertically stretched terrain-following and surface-followings-layers, covering an approximately 320 km × 280 km lateral area (Fig. 1).
Surface wind stresses were imposed from the GPV-MSM operational atmosphericproduct of Japan Meteorological Agency (JMA) at horizontal resolution of 0.05° × 0.0625°.
Net heat, fresh water, and radiation fluxes at the ocean surface were obtained from the NOAACOADS monthly climatology with the flux correction described in Uchiyama et al. (2017a)[2]. Ten principal tidal constituents from the TPXO7.0 global tidal reanalysis were imposedon the sea surface elevations along the perimeter of ROMS-L2 model to include barotropic
tides and resultant intrinsic baroclinic tides excited in the L2 domain. Therefore, internal andbarotropic tides were spontaneously propagated in and out through the perimeter of the L3model with two-hourly update of the open boundary conditions. We conducted an annual
reanalysis for the entire one-year period of 2013 excluding a model spin-up time of several
months in prior to the main computation. Extensive model-data comparison was performed toensure the present L3 model has a good reproducibility against the observations (not shown).
LAGRANGIAN PARTICLE TRACKING MODEL
Coastal connectivity around Okinawa Island was estimated from Lagrangian
probability functions (PDFs) of an enormous amount of Lagrangian particles originating fromthe nearshore sites, where spawn and larvae are released (Fig. 1b). We exploited the offline 3D Lagrangian particle tracking model developed in Carr et al. (2008) [5] and used previously,e.g., in Mitarai et al. (2009) [9] and Romero et al. (2013) [6] with the ROMS model outputs.
In the present study, we did not introduce any ad hoc behavior models, such as random walk
subgrid-scale diffusivity or diel vertical migration, to avoid further complexity anduncertainty. These factors should be examined in future works. Released particles weretracked for up to 30 days, or until they crossed the boundaries of the L3 model domain, orwere beached on land cells. Because coral spawn and larvae are fully passive to the ambient
currents for 21 days before they settle down, the following analysis was made for theadvection time of no more than 21 days to be consistent with the life cycle of corals. Although
the coral spawning occurs in late May, we conducted the release of the particles repeatedly
every 24 hours for the entire one year period, in order to extend the present model results forconnectivity of other marine flora and fauna. Five hundred particles were released from a totalof 133 source patches at the depth of 2 m below the mean surface (Fig. 1b). Hence, the total
number of Lagrangian particles released is 500 particles × 133 patches × 365 times ≈ 24.3
millions.
LAGRANGIAN ANALYSIS
To quantify the dispersal of Lagrangian particles released from source patches, wecalculated Lagrangian PDFs following the methodology described in Mitarai et al. (2009) [9]from the results of the 3-D particle tracking model. A Lagrangian PDF represents theprobability density function of particle displacement for a given elapsed time τ, which is often
refereed to as an advection time (Ta). Its discrete representation is:Figure 2 – Connectivity matrices around Okinawa Island for the advection times Ta of 7,14, and 21 days. Colors indicate the joint probability Cji defined by Eq. (4). The abscissashows the grouped source sites (origins) #1–12, while the ordinate is the grouped sink sites(destinations) #1–12 (see Fig. 1b for the grouped patches consisting of each site).
!

𝑓!! 𝝃; 𝜏, 𝒂 = !

!
!!! 𝛿 𝑿! 𝜏, 𝒂−𝝃 ,(1)where N is the total number of Lagrangian particles, δ is the Dirac delta function, Xn is theposition of the nth Lagrangian particle, a is the initial position of the particle of interest, and ξ
is the sample space variable for X. Discrete Lagrangian PDFs are evaluated from the center
location of the release sites defined later, averaged over each site. Hence,!

𝑓!! 𝝃; 𝜏, 𝒂 ≈ !!!

𝑓 ! 𝜉; 𝜏, 𝒂 + 𝒓 𝑑𝒓,! !! !

(2)

where R is the radius of each release site a. The final form of discrete Lagrangian PDF isobtained after applying an isotropic spatial Gaussian filter G with standard deviation of 3 km:!

𝑓! 𝝃; 𝜏, 𝒂 ≈ !! 𝐺 𝒙 − 𝝃 𝑓!! 𝝃; 𝜏, 𝒂 𝑑𝒙.

(3)Figure 3 – An example of temporal evolution of the Lagrangian PDF distributions (colors).
This particular example exhibits Lagrangian PDF of the particles released for the one-year
period from a total of 11 source patches (black circles) that form site #5 representing thenorthern half of Nago Bay on the west coast of Okinawa Island, at the labeled advection
times Ta (days). The areas with higher (lower) PDFs depicted by warm (cold) colors at thegiven Ta days after repeating releases correspond to statistically larger (smaller) numbers ofthe particles positioned there at Ta. Note that although the particle tracking was conducted
three-dimensionally, the PDFs are plotted after the vertical summation. This operation
implies that vertical displacement of the particles is not explicitly illustrated. In thisexample, many particles are transported northward along the western shore, then pass thenorthern tip of the island to further be brought to the eastern shore at Ta = 7 days. Later at Ta= 14 and 21 days, non-trivial PDFs are observed along the east coast. These sequences
demonstrate that nearshore clockwise particle transport is prevailed, whereas the modest
southward transport from site #5 manifests that counter-clockwise transport is rather minor.
Coastal connectivity Cji (τ) is defined as the probability of Lagrangian fluid particles
transported from a source site j to a sink site i over a time interval τ (viz., an advection time).
𝐶!" 𝜏 = 𝑓! 𝝃 = 𝒙! ; 𝜏, 𝒂 = 𝒙! 𝜋𝑅! ,(4)where xj and xi are source and sink patch locations, and the normalization by πR2 converts thePDFs to probabilities.
CONNECTIVITY AND LAGRANGIAN PDF
Figure 2 represents the L3 model-derived connectivity matrices Cji around Okinawa
Island for the advection times Ta of 7, 14, and 21 days. The abscissa and ordinate show thegrouped source and sink sites, respectively (see Fig. 1b for the definition). For instance, forthe particular combination of the abscissa #7 and the ordinate #11, Cji (=C7, 11) at Ta = 14 days
is found to be ~10-3, which is interpreted that one coral spawn out of 1000 released from site
#7 can be transported to site #11 (viz., the probability of 10-3) in 14 days to settle down there.
Overall, high connectivity manifests on and around the straight line with a slope of 1:1 (viz.,45°) depicted by reddish colors, exhibiting that these particles mostly remain near the released
sites after the given advection time. This is true for the initial stage (Ta = 7 days), whereas theparticles are diluted and dispersed to other sites surrounding the island in later times (Ta = 14and 21 days).
Influences of coastal currents on particle transport manifest in a complicated manner;particle dispersal occurs neither isotropically nor unidirectionally. If the northeastward
drifting Kuroshio were most influential, dispersal would have to appear also in thenortheastward direction. However, the computed connectivity manifests that site #12 at thenorthernmost tip and #8–9 on the east coast behave as nodes, around which particles tend toaccumulate notably. As depicted by the example of temporal evolution of Lagrangian PDFs
originated from site #5 (Fig. 3), the particles released from the west coast are mostlytransported in the clockwise direction around the island with passing site #12 and drifting
upstream toward the east coast. These particles barely pass the southernmost tip (#6–7) toform counter-clockwise transport around the island. In contrast, the particles released from theeast coast (not shown as PDFs, but as connectivity matrices in Fig. 2) are largely accumulated
in sites #8–9 even at later times, where semi-enclosed coastal geometry and resultant local
lateral circulations act to entrain particles in there. While sites #8–9 provoke relatively
stagnant environment for particles, the northeastward residual currents on the west coast andsouthwestward residual current on the east coast influence site #12, which concurrently
induce a clockwise circulating local whirl that promotes particle accumulation near #12.
These features are apparent in Figs. 2 and 3 in particular in earlier time, whereas LangangianPDFs decreases with time and eventually majority of the particles exit the L3 model domain.
CONCLUDING REMARKS
Long-distance larval transport due to the northeastward drifting Kuroshio (Uchiyamaet al., 2018 [1]) and short-distance, local entrainment associated with coastal topographies(the present study) coincidently contribute to formation of the local and remote biologicalnetwork across the Nansei Archipelago in the East China Sea. Around Okinawa Island, thelatter mechanism is characterized by the transport associated with residual coastal currents
along the island that bifurcates at the southernmost tip (sites #6–7, Tokashiki Strait; Fig. 1b)
to provoke northeastward transport on the east coast while weak southwestward transport on
the west coast of the island, and then form a clockwise residual circulation. The Lagrangianparticles mimicking corals were released from the nearshore areas, drifted seaward at about
several km from the shore, and subsequently advected by the along-island clockwisecirculating residual current. During the northeastward transport, some portions of the particles
are trapped in semi-enclosed topographies due to localized lateral circulations and residual
whirls, in particular around sites #8–9 (Kin and Nakagusuku Bays) on the east coast whereparticles become notably stagnant. A similar particle entrainment occurs at the northernmost
tip (site #12, Cape Hedo) due to a highly localized clockwise whirl. These results clearly
indicate that very high-resolution circulation modeling is essential to quantitatively accountfor nearhore behavior of corals under strong topographic constraint in shallow nearshore areas,
where the particles mostly remain even for several weeks after the releases.
ACKNOWLEDGEMENTS
The present research was financially supported by Japan Society for the Promotion of Science(JSPS) Grants-in-Aid for Scientific Research 15KK0207, 15H04049, and 18H03798 (PI: Y.
Uchiyama) at Kobe University.
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