We investigated the connectivity properties of an
idealized western boundary current system separating two ocean gyres, where
the flow is characterized by a well-defined mean circulation as well as
energetic fine-scale features (i.e., mesoscale and submesoscale currents).
We used a time-evolving 3D flow field from a high-resolution (HR-3D) ocean
model of this system. In order to evaluate the role of the fine scales in
connectivity estimates, we computed Lagrangian trajectories in three
different ways: using the HR-3D flow, using the same flow but filtered on a
coarse-resolution grid (CR-3D), and using the surface layer flow only
(HR-SL). We examined connectivity between the two gyres along the western
boundary current and across it by using and comparing different metrics, such
as minimum and averaged values of transit time between 16 key sites, arrival
depths, and probability density functions of transit times. We find that
when the fine-scale flow is resolved, the numerical particles connect pairs
of sites faster (between 100 to 300 d) than when it is absent. This
is particularly true for sites that are along and near the jets separating
the two gyres. Moreover, the connectivity is facilitated when 3D instead of
surface currents are resolved. Finally, our results emphasize that ocean
connectivity is 3D and not 2D and that assessing connectivity properties
using climatologies or low-resolution velocity fields yields strongly biased
estimates.
Agence Nationale de la RechercheANR-11-BTBR-0008Introduction
Solutions to a number of problems important to the marine environment
require knowledge of connectivity, i.e., how distant ocean sites are
connected to one other through transport by currents. Connectivity is
important, for example, to understand the persistence of isolated
populations and the flow of genetic information (Treml et al., 2008;
Roughgarden et al., 1988; Gaylord and Gaines, 2000; James et al., 2002;
Palumbi, 2003; Trakhtenbrot et al., 2005). This is all the more important
given that spatial and temporal patterns in the distribution of marine organisms
are strongly influenced by differences or changes in population connectivity
(Treml et al., 2008; Levin, 1992; Warner, 1997). Quantifying connectivity is
therefore essential for managing marine ecosystem protection. But
connectivity is also useful for assessing pollutant dispersion from
sources to other regions, for managing water quality, for planning pollutant
release to coastal or offshore waters, and for assessing the evolution of
oil spills (Mitarai et al., 2009; Fischer et al., 1979; Grant et al., 2005).
In recent years, connectivity analysis has become a dynamic and rapidly
evolving field of research in marine science and oceanography, partly
because there is an increasing demand to inform effective assessment and
management of marine resources (e.g., Hariri et al., 2022; Drouet et al.,
2021; Bharti et al., 2022; Ward et al., 2021; Richter et al., 2022). Thus
connectivity is usually understood as the exchange of individuals between
remote marine populations, the transport of plastic, or more generally the
exchange of water masses and water properties (Froyland et al., 2014;
Ser-Giacomi et al., 2015). In this work, we will evaluate connectivity in terms of
its most general definition of the exchange of particles between different
sites.
Estimating connectivity from Lagrangian analysis requires knowledge of
Eulerian velocity fields. In the ocean, such velocities are either derived
from satellite altimetry, from ocean general circulation models, or from
ocean reanalyses, which combine the two (e.g., Poulain and Niiler, 1989;
Swenson and Niiler, 1996; Dever et al., 1998; Blanke and Raynaud, 1997;
LaCasce, 2008; Alberto et al., 2011; Watson et al., 2011; Mora et al., 2012;
van Sebille et al., 2012; Hariri et al., 2015; van Sebille et al., 2018;
Hariri, 2020, 2022). The resolution of such products is often
insufficient to fully capture the highly dynamical fine-scale portion of the
ocean circulation. Also, many studies have limited the implementation of the
Lagrangian approach to the surface layer (e.g., Treml et al., 2008; Mitarai
et al., 2009; Jönsson and Watson, 2016; Dever et al., 1998; LaCasce, 2008;
van Sebille et al., 2012; Poulain and Hariri, 2013; Drouet et al., 2021;
Hariri, 2022). This can potentially induce a strong bias in the estimates of
connectivity to the intense horizontal and vertical circulation associated
with ocean mesoscale eddies and jets as well as with submesoscale features such as
filaments and fronts.
Recent studies demonstrate the breadth of techniques and applications
employed in ocean connectivity analysis and underscore the importance of
this field in advancing our understanding of ocean dynamics; a variety of
tools have been used, such as ocean circulation models, in situ measurements,
and numerical models, to examine the connectivity of diverse marine
populations, identify subpopulations from connectivity matrices, and analyze
biogeographical patterns along large-scale oceanic currents (e.g., Wang et
al., 2019; Drouet et al., 2021; Novi et al., 2021; Ward et al., 2021;
Cotroneo et al., 2022; Ser-Giacomi et al., 2021b; Hariri et al., 2022;
Richter et al., 2022; Kot et al., 2022).
In this study, we assess how connectivity properties of typical ocean flows
are affected by the fine-scale circulation and highlight the challenges we
face in estimating ocean connectivity due to lack of spatial resolution
(both horizontal and vertical) of the flow field. We focus on midlatitude
open-ocean gyres that are typical of the subtropical and subpolar oceanic gyres of
the North Atlantic, separated by the western boundary current Gulf
Stream–North Atlantic drift system, and of the North Pacific, separated by
the Kuroshio–Oyashio, which are regions where fine scales are particularly
intense. Our results highlight the need for high-resolution velocity fields
(i.e., mesoscale and submesoscale currents) to derive reliable connectivity
estimates. In order to study the transport of numerical particles in a
specific area, we conducted offline Lagrangian transport simulations. The
study involved the release of these particles from regularly distributed
sites in the region, and the simulations were run for a period of 5 years. To perform these simulations, we used the ARIANE quantitative
Lagrangian approach (Blanke and Raynaud, 1997; Blanke et al., 2012), which
integrates all spatial scales of the modeled velocity. In the published
literature, marine connectivity has often been assessed by defining metrics
based on Lagrangian integrations and “connectivity time” (e.g., Cowen et
al., 2007; Froyland et al., 2009; Mitarai et al., 2009; Rossi et al., 2014;
Jönsson and Watson, 2016; Ser-Giacomi et al., 2021).
The paper is organized as follows: the model and methods used to measure
connectivity are described in Sect. 2, the results are presented in
Sect. 3, and the discussion and conclusion are presented in Sect. 4.
Data and methods
The impact of the fine-scale circulation is evaluated by comparing
connectivity estimates derived from a full 3D high-resolution velocity
field, with estimates based on velocity fields where the resolution is
degraded, either horizontally or vertically. The high-resolution (HR)
velocity fields are derived from a HR ocean circulation model. Using this
velocity field, we carry out offline Lagrangian transport of numerical
particles released in a set of regularly distributed sites in the study
region.
Data: the ocean circulation model fields
The ocean circulation was generated with the state-of-the-art ocean general
circulation model Nucleus for European Modelling of the Ocean (NEMO) (Madec et al., 1998). The model domain is a 2000×3000 km rectangle that is 4 km deep and rotated 45∘, with closed boundaries. The
model was forced at its surface by prescribed seasonal buoyancy fluxes and
winds (Lévy et al., 2012a). The model equations were solved on a grid
with a resolution of 1/54∘ in the horizontal. This allows the
simulation of mesoscale and submesoscale dynamical structures with an
effective resolution close to 1/9∘ (the smallest size of the
structures which are captured by the model outside the dissipative range is
less than the grid resolution on which model equations are discretized and
solved) (Lévy et al., 2012b). The model grid consists of 30 vertical
levels, with thicknesses ranging from 10 to 20 m in the upper 100 m,
increasing to 300 m at the bottom. The model equations were integrated for
50 years. In this study we used the last 5 years of model outputs, which
were saved every 2 d at the effective model resolution, i.e., on a
1/9∘ grid.
The time-averaged solution of the model shows two large oceanic gyres, a
subtropical gyre in the south with an anticyclonic circulation, and a
subpolar gyre in the north with a cyclonic circulation separated by a
strong zonal jet and a series of secondary zonal jets. This horizontal
circulation in the surface layers is characteristic of the North Atlantic and
North Pacific, the strong jet being the equivalent of the Gulf Stream or
Kuroshio. It should be noted, however, that our domain is smaller than that
of these two ocean basins. The model velocities are highly turbulent and
show strong variability at the daily scale and on horizontal scales
<1∘. This mesoscale turbulence is characterized by
strong jet oscillations and the formation of secondary jets, eddies, and
filaments between eddies, and it is associated with intense vertical movements.
In order to assess the impact of this fine-scale circulation on
connectivity, we filtered this velocity field on a 1∘ grid to
remove all variations with scales smaller than 1∘ and compared the
connectivity analyses performed with unfiltered (hereafter high-resolution
HR) and filtered (hereafter coarse-resolution CR) velocities. Filtering was
done according to Lévy et al. (2012b) to preserve averaged velocities
and was applied only in space and not in time to conserve seasonal and
higher-frequency variations.
Figure 1 shows a snapshot of the surface vorticity and vertical velocity on
31 March of the first year of the simulation. With full resolution of the
velocity field (HR), the flow is organized with a large number of eddies
covering a wide range of scales, displaying filamentary structures resulting
from their nonlinear interaction. More intense small-scale activity
develops in the vicinity of the two jets, the first one located at around
30∘ N and the second at 35∘ N. Figure 1a illustrates the
importance of mesoscale and submesoscale structures in shaping currents, as well as in
setting scales of spatiotemporal variability and dynamical regimes.
Importantly, these features are associated with intense vertical currents
(Fig. 1c). When these highly turbulent currents are filtered on a coarse-resolution grid, the vorticity is smoother and mainly related to the
position of the main jets (Fig. 1b).
Snapshots on 31 March of (a) surface vorticity at high resolution
(HR), (b) surface vorticity at coarse resolution (CR), (c) vertical velocity
at 40 m at HR, (d) and vertical velocity at 40 m at CR.
MethodsSimulation of trajectories
In this paper, the focus is on the analysis of ocean connectivity from
Lagrangian numerical particles (Figs. 2 and 3a) deployed at different
defined sites across the double-gyre current configuration, located in key
areas of the circulation (Fig. 3b). For this purpose, the positions of the
numerical particles at each time step (1 h) were calculated using the
Lagrangian tool ARIANE (https://ariane-code.cnrs.fr/, last access: 22 May 2021). ARIANE is an open-source, offline, three-dimensional
Lagrangian particle tracking model written in Fortran, and it is compatible
with many ocean general circulation model (OGCM) outputs. It works by interpolating velocity values (bilinear
interpolation in space and linear interpolation in time) to a given particle
position using an analytical scheme (a fourth-order Runge–Kutta scheme) and
advects the particle over a user-defined time step. A description of the
algorithm is given by Blanke and Raynaud (1997) and Blanke et al. (2001).
Sample trajectories deployed from site 1 in HR-3D.
(a) Dispersal of sample trajectories on the surface layer in HR-3D
from site 13. (b) Annual mean speed and location of the sites.
Sites were defined as circular regions of 1∘ radius. This size
corresponds to the grid size of the coarse-resolution velocity field. A
total of 100 000 particles were deployed at each site. Such a large number
of particles and the wide size of each site reduces the sensitivity of the
results to the exact location of the initial position and provides
statistically more robust estimates. We used 1 600 000 particles for each
Lagrangian experiment. Based on the Lagrangian tool, ARIANE, particles
reaching domain boundaries continue their movement along the model closed
boundaries. The frequency of particle release was specified with random
initial times, while the minimum duration of trajectory tracking was 1 year
(the maximum integration time was 5 years). Particles were released every
1 m from the surface to the base of the mixed layer, yielding a total of 150
release locations over this depth (667 particles per meter) (Fig. 2).
We analyzed and compared the properties of three sets of Lagrangian
experiments (with the same integration time), one performed using the full
resolution of the velocity field in 3D (HR-3D), one performed using the
filtered velocity field (CR-3D), and one using the full-resolution
surface-only velocity field (HR-SL).
Site specification
Sites were distributed in key regions of the flow in order to examine and
contrast connectivity properties between the two gyres, along the main jets,
and across the jets. The exact location of the sites is arbitrary, but in
order to have reliable results, we choose more than one site to represent
each key region of the domain. More precisely, three sites were located
along the main jet (-85 to -68∘ W and
27 to 32∘ N) on the western side of the
basin (sites 10, 11, and 12, Fig. 3b), and two sites were located upstream
of the secondary jet (-81 to -60∘ W and
33 to 35∘ N) at locations with lower
kinetic energy (sites 5 and 6) in order to study connectivity between
different parts of each jet, for example from the tails (ends) of the jets
to their heads and back (see Fig. 3). In addition, other sites between the
jets were selected to calculate connectivity properties between gyres (sites
1 to 4 in the subpolar gyre, sites 7 to 9 in the inter-jet region, sites 13
to 15 in the subpolar gyre). Also, five sites (1, 3, 8, 15, and 16) were
aligned along the model diagonal to determine the transfer time from north
to south and vice versa (Fig. 3b), but three other sites (2, 7, 13) can be
used for the same purpose.
Lagrangian indices
Different approaches, all based on the tracking of passive Lagrangian
particles, have been used to quantitatively measure connectivity between
different marine sites, e.g., Lagrangian probability density functions
(PDFs) (Mitarai et al., 2009; Froyland et al., 2009; Ser-Giacomi et al.,
2021), transport networks (Rossi et al., 2014), and characteristic timescales (Jönsson and Watson, 2016). Some of these methods rely on the general
definition of “connectivity time”, which depends on oceanographic
distances and is often estimated as the mean time required for particles to
move from one location to another (Cowen et al., 2007; Mitarai et al.,
2009). However, in the global ocean, mean and median transit times are not
well defined because each particle deployed at a given location will
eventually reach all other areas of a defined domain over a sufficiently
long time (Jönsson and Watson, 2016). To address this, Jönsson and Watson (2016) proposed using the “minimum connectivity time” (Min-T), defined as
the fastest travel time from source to destination for numerical particles,
inferred from a Dijkstra algorithm (1959). This minimum connection time
shows good correspondence with genetic dispersal in marine connectivity
(Alberto et al., 2011). The benefit of using the minimum connection time
rather than the average transit time has been shown in previous empirical
work (e.g., Mora et al., 2012; Mitarai et al., 2009; Döös, 1995;
Cowen et al., 2007). Following up on these previous advances, in this study,
we focus on mean and median values of minimum connectivity time for all
particles traveling from one given site to another in order to obtain a
clear picture of transit times. Furthermore, dispersion patterns of the
numerical trajectories show the main effects of the particle release
position and ocean circulation on the strength and persistence of
connections between site pairs. Specifically, we will provide a
comprehensive matrix containing analyses of the mean, median, and most
frequent values of the minimum connection time between each selected area
seeded with numerical particles.
Lagrangian PDF
The Lagrangian PDF approach is useful to examine the dispersion of particles
by turbulent phenomena. It has been widely used in fluid mechanics (e.g.,
Pope, 1994; Mitarai et al., 2009; Froyland et al., 2009; Ser-Giacomi et al.,
2021b). This method relies on the probability that particles have moved from
one location to another during a given time interval. Since the PDF values
provide an estimate of the mean dispersion properties of the numerical
particles, a correct estimation of the PDF values requires a large number of
trajectories (Mitarai et al., 2009); for the purpose of our study, 100 000
particles were assigned to each site. This number was set to have a
significant number of particles for the connectivity estimates but was,
however, limited to remain computationally manageable. The Lagrangian PDF
for each site is obtained by Mitarai et al. (2009):
LagrangianPDFξ,t=nξtN×Sξ,
where ξ is the sample space related to the discretion
of the Lagrangian PDF (here, a sample space of ∼ 1 km2 is applied
for the calculation of the PDF fields), Sξ is the area of the sample
space ξ, N is the total number of Lagrangian
particles, and nξt is the number of particles residing
in the sample space ξ at the simulation time
t.
ResultsTransit times
A quantitative assessment requires some degree of simplification due to the
multiple spatial and temporal scales involved. In this framework, it is
useful to determine the probability distribution of the numerical particles
deployed from the different sites for different integration times (see Fig. 4 for the results obtained for site 1). After the first week of deployment,
the concentration of numerical particles is larger around the starting
positions, as expected. After 6 months, the particles move a short
distance from their initial positions and spread over 5–10∘ of longitude, depending on the flow velocity. When particles are
close to strong jets, they disperse very rapidly (2–6 months), whereas in other parts of the basin, due to slower and less
energetic velocities, the dispersion occurs over a longer period (1.5–2 years).
PDF fields of the position of particles after increasing time
intervals in HR-3D. After 7 d (a), after 180 d (b), after 540 d
(c), and after 910 d (d).
At 1.5 years after their release, the particles deployed from the
subpolar gyre (site 1) are dispersed in the entire subpolar gyre and have
also penetrated the subtropical gyre along its eastern edge. Regardless
of the initial deployment position, 3.5 years after deployment, almost all
particles are concentrated along the two intense jets that separate the two
gyres (Supplement Figs. S1–S5). For particles leaving site 1, the
probability that they will reach sites 2, 3, and 4 after 2 years along the basin
diagonal is between 0.2 % and 0.8 %, and for sites 5, 6, and 14, it is
about 0.5 %. This means that connectivity between these sites and site 1
is achieved in less than 2 years. A uniform PDF distribution after 2.5 years
for the particles from site 1 shows that in less than 900 d they have
spread across more than 75 % of the basin. We also note that with longer
particle lifetimes, the PDFs show similar behavior compared with the other
sites (Fig. 4). After 1.5 years, particles are mostly on the eastern side of
the basin, moving slowly southward due to less energetic flow in these areas
(Fig. 4c, d).
In contrast, particles deployed in the main jet (Supplement Fig. S4)
remain mostly close to or move slowly to the southern basin during all
simulation times. This pattern reveals the strong influence of the jets on
particle movement. For this case, the PDF has the highest values in the jet
area and in the subtropical gyre. After 5 years, the lowest PDF values for
particles reaching the jet and the subtropical gyre are associated with
particles initially deployed along the western boundary of the subpolar gyre
(e.g., site 2). In conclusion, the PDFs show that particles spend long
periods of time in the subtropical gyre, indicating that this regional
retention by highly energetic nonlinear ocean dynamics prevents rapid
dispersion in all other regions. This significantly increases the mean
particle transit times.
Comparison of connectivity properties between HR-3D and CR-3DPDF histogram for HR-3D and CR-3D
Figure 5 shows the PDFs of the transit times of particles traveling between
selected sites for HR-3D and CR-3D. The PDFs are not Gaussian and are skewed
with a long tail. Figure 5a shows the PDFs of the particles deployed at site
1 in the center of the subpolar gyre and arriving at site 15 in the center of
the subtropical gyre, whereas Fig. 5b shows the reverse connection, i.e.,
for the particles deployed at site 15 traveling to site 1. For HR-3D the
first particles reach site 15 after about 200 d, and most particles reach
this site after about 600 d. The latest particles continue to arrive
at site 15 after 1600 d. The CR-3D PDF is shifted in time with respect to
HR-3D, with particles only reaching site 15 after about 300 d. The width
of the CR-3D PDF is broader than that of the HR-3D, suggesting a larger but
slower spread of particles across the domain before reaching site 15. The
median transit time from site 1 to site 15 is 751 d, while the minimum
transit time in this direction is 201 d. The Lagrangian connections for
particles deployed at site 15 and reaching site 1 (i.e., connectivity in the
opposite direction as for the previous case) show a longer transit time and
a greater spread for both simulations (Fig. 5b). The CR-3D PDF shows an even
larger delay in arrival time compared to HR-3D.
Comparison of HR-3D (black) and CR-3D (gray) transit time
distributions (a) for particles initially deployed from site 1 to site 15,
(b) from site 15 to site 1, (c) from site 10 to site 12, and (d) from site 12
to site 10.
For HR-3D, the mean time required for particles to travel along the basin
diagonal from the subpolar gyre to the subtropical gyre (i.e., from site 1
to site 15) is about 796 d, and the modal time is 559 d compared to
989 and 1262 d, respectively, for the reverse connection (i.e., from
south to north, site 15 to site 1). This means that the northward movement
along the diagonal is faster than the southward movement. The PDF
distributions cover almost the same time range, although the general shape
is different. The same transit times (mean and most frequent values) for
CR-3D are 891 and 644 from north to south and 1162 d and 1315 from south
to north. The minimum time required for particles from south to north (site
15 to site 1) in the HR model is 153 d shorter than in the CR model (201
vs. 355 d).
To compare the Lagrangian connectivity between the most distant sites with
the sites closer to each other and within the main jet ([30∘ N,
-85∘ W], [30∘ N, -70∘ W], where the mean
energy and eddy kinetic energy show the highest values) we computed the
transit time statistics between sites 10 and 12. The results are shown in
Fig. 5c for the direct connection (site 10 to site 12) and in Fig. 5d for
the opposite direction (site 12 to site 10). They suggest that the
connection along the eastward jet is faster (as expected): the first particles and
largest number of particles arrive within 10 d in HR-3D, whereas for
CR-3D the arrival time of the first particles is longer (40 d) and the
PDF distribution is larger.
As foreseen, the intense and highly energetic eastward jet moves the
particles very rapidly eastward, although fine-scale circulation (mesoscale
eddies and filaments) generated at the edges of the jet disperses the
particles that reach site 12 almost continuously (albeit in decreasing
numbers) until about 1400 d. The minimum and median transit times for the
HR-3D simulation are 11 and 348 d, while these values are larger for
CR-3D (64 and 213 d, respectively). The CR-3D velocity field induces
slower connections because the peak velocity of the jet is lower and its
width larger. The connection time in the coarser velocity field is
relatively continuous until about 1300 d. This can be explained by the
particles traveling through the larger-scale recirculation cells of the
subpolar and subtropical gyres before reaching site 12.
In contrast, the HR-3D and CR-3D PDFs have a more similar shape and
distribution for the opposite (westward) connection, with the first
particles reaching site 10 from site 12 in less than 50 and 452 d on
average and 546 d in median time (Fig. 5d). The minimum and mean transit
times for particles from site 12 to site 10 are longer. The modal value is
260 d, and the median transit time is 398 d. The similarity in
connectivity behavior for the opposite (westward) connection for both
velocity fields suggests that the particles move through the mean
larger-scale recirculation cells and follow the common pathways.
The above PDF results for both simulations (HR-3D and CR-3D) clearly show
the impact of the ocean fine-scale dynamics, which increase the efficiency of
the current advection and accelerate the particle motion; in this case, for
the CR-3D simulation, the PDFs of transit times are wider with longer mean
and minimum transit times due to insufficiently resolved turbulent motions.
Minimum and median transit time as a function of geographical distance
Figure 6 shows the minimum and median values of transit time as a function of
distance computed in HR-3D for sites along the basin diagonal. The results
indicate that with increasing distances, the transit times (minimum and
median) increase linearly. For the particles initially deployed from site 1,
the results show almost the same behavior for median and minimum time,
except for connections between site 1 and sites 12 and 15. The shortest
minimum transit time in a diagonal direction is from site 8 to site 12 with
a value of 2 d. The fastest connection based on median transit times is
from site 8 to site 5, with a value of about 95 d. The minimum transit
times from south to north and north to south are almost identical (about 200 d). The longest minimum transit time is for the particles moving from
site 12 to site 1 at 240 d, with a median value of 1109 d. This suggests
that the intense fine-scale circulation facilitates connections between site
8 (which is located in the middle of the diagonal transect) and site 12 (at
the eastern end of the main jet) and slows those between sites 8 and 5 (a
median transit time of 225 d versus 95 d). In general, the Lagrangian
transit times (median and minimum) for a site pair located at the same
distance along the basin diagonals differ. Such a difference arises from the
complex trajectories, followed by the numerical particles, and is induced by the
small-scale simulated dynamics. On the other hand, for site pairs located
at a shorter distance (less than 6∘), the minimum transit time is less
than 55 d regardless of the site location.
HR-3D minimum (a) and median (b) transit time against geographical
distance. Blue: particles initially deployed from site 1; red: particles
initially deployed from site 3; yellow: particles initially deployed from
site 5; purple: particles initially deployed from site 8; green: particles
initially deployed from site 12; gray: particles initially deployed from
site 15.
To more quantitatively assess the differences in connectivity between HR-3D
and CR-3D, Fig. 7 shows the comparison of minimum and median transit times
computed for a subset of sites for the two Lagrangian simulations. The
results clearly indicate that the minimum and median transit times in HR-3D
are significantly lower than for the coarse-resolution configuration. In
HR-3D, the resolved nonlinear dynamics induce intense currents, and the
particles move much faster than in CR-3D, in particular for the sites
located along the two main jets. Figure 7 suggests that for distant sites,
CR-3D will not provide realistic information about the connection time
between sites. The lack of fine-scale motions in the coarse-resolution
simulation leads to significant delays in the advection of numerical
particles, especially in areas where mesoscale variability plays an
important role in particle displacement. The results obtained for particles
deployed from site 15, for short-range connections (distances less than 10∘), show a better match for the median transit time for both
configurations: HR-3D and CR-3D. Based on a minimum connection time of less
than 50 d, there is some convergence between HR-3D and CR-3D for
particles deployed from site 1, whereas large differences arise for
distances greater than 6∘ and for areas that include hotspots of high
eddy kinetic energy. In addition, in HR-3D, the particles disperse not only
faster but also more uniformly than in CR-3D, which reduces transit times
between sites. From south to north along the diagonal, the results of both
simulations (median values of transit times) are similar, showing that in
this direction particles follow pathways less affected by small-scale ocean
instabilities.
Comparison of HR-3D and CR-3D minimum and median transit times.
(a, b) Along the diagonal direction for particles initially deployed from site 1. (c, d) Along the front for particles initially deployed from site 10. (e, f)
Along the diagonal direction for particles initially deployed from site 15.
Examples of depth arrival PDF for HR-3D and CR-3D
Connectivity studies of marine ecosystems commonly integrate Lagrangian
trajectories using 2D surface velocity fields because the focus is on
passively drifting biological species (e.g., plankton, fish larvae, algae). We test the robustness of such a strong assumption by
integrating Lagrangian particles in a 3D framework: for each site at the
initial integration time step, particles are distributed over the water
column extending from the surface to the base of the mixed layer (which can
be as deep as 150 m). Then, the particles are advected by the 3D flow,
without any depth constraint. In this way, we can test whether particles in
the upper ocean remain at the same depth throughout their journey and thus
confirm or invalidate the soundness of using 2D and not 3D velocity fields
for marine ecosystem connectivity estimates.
Figure 8a and b show the PDFs of the mean arrival depth of particles
initially deployed from site 1 and arriving at site 15 (left panel), as well as in
the opposite direction from site 15 to site 1 (right panel). Our analysis
indicates that the majority of particles in both simulations remain in the
depth range below 165 m without moving much deeper, although the peak
is deeper in the south-to-north motion for HR-3D and CR-3D and is quite
noisy.
The HR-3D and CR-3D PDFs (Fig. 8a, b) indicate that the particles are
almost twice as deep in the south–north connection as in the north–south
connection. From south to north, a small percentage of the particles reach
the bottom layer (more than 450 m deep) where frictional processes
alter the dynamics and thus play an important role in the transit of the
numerical particles. These processes do not appear to play a role in the
north–south movement.
Comparison of HR-3D (black) and CR-3D (gray) arrival depth
distributions (a) for particles initially deployed from site 1 to site 15, (b) from site 15 to site 1, (c) from site 10 to site 12, and (d) from site 12
to site 10.
The PDF of the mean arrival depth of particles deployed from site 10 to site
12 (Fig. 8c) shows that for the trajectories simulated by the high-resolution
fields there is a tail that extends down to 175 m, with a slightly
higher percentage of particles in the subsurface layer compared to the CR
results, and the particles in the upper layer tend to travel faster than
those are at greater depths, as velocities decrease with depth.
On the other hand, although the mean PDF of arrival depth for particles
moving from site 10 to site 12 shows the same behavior in the HR and CR 3D
velocity fields, in the opposite direction (site 12 to site 10) the PDF
distributions for the two simulations are completely different, considering
that the distribution is overall flatter in CR-3D than in HR-3D with a long
tail extending to 380 m in depth.
A comparison of the mean arrival depth of the numerical particles deployed
from site 12 to site 10 (Fig. 8d) in the HR case shows that the majority of
the particles remain within 50 m of the surface layer, while in the
opposite direction, some particles move to greater depths up to 150 m.
Furthermore and as already mentioned, the numerical trajectories simulated
in CR are relatively uniform across the upper layer where they were
initially seeded. Indeed, in CR, more than 70 % of the particles deployed
from site 12 and arriving at site 10 remain close to the surface mixed layer
and the subsurface, where the effects of turbulence at different scales on
the numerical particle distribution are more detectable.
Mainly, for all cases examined, in HR-3D, the particles tend to remain in
the subsurface layer due to the larger effects of coherent vortices as well
as other structures such as filaments and eddies. The PDFs of arrival depth
indicate that the differences between HR-3D and CR-3D are not limited to the
arrival time, but are also detectable on different 3D pathways for each
case, resulting in significant changes in the arrival depth. Thus, we can
add that the depth results differ depending on the direction of motion.
Also, the peak for all HR-3D cases is at the depth of less than 10 m
except for the south–north motion, which shows that in this direction, the
particles move more in the vertical direction due to weaker stratification
at depth and less turbulence in the surface layer.
Mean connection time fields for sample sites
The mean connection times from three sites (north, west, and south of the
basin) are shown in Fig. 9. Figure 9a shows that the particles from site 1
follow pathways that require the longest time to connect to sites in the
subtropical gyre and western boundary current regions, such as sites 10, 11,
12, 13, 15, and 16. The particles reached a depth of 150 m from the
surface layer near the eastern side of the basin between (-60
to -55∘ W) and (37.5 to
42.5∘ N) near site 4, although the transit time from site 1 to
site 4 was less than 300 d (not shown). Particles deployed from site 1,
moving from south to north, take almost 500 d, while they take about 400 d to travel the same distance from north to south. The shortest mean
transit times are between sites 1 and 4 and between sites 1 and 3 (both
less than 350 d), while the longest connections (from site 1) are
associated with sites 10 and 11 (944 and 915 d, respectively). This was
expected since these sites are located along the strong jet. Note that the
mean arrival depth for the shortest transit time is about 35 m (not
shown), while for the longest transit time, the mean arrival depth is over
100 m below the surface layer. For site 1, the mean transit time is
1.25 times greater in CR-3D than in HR-3D. Figure 9a and d show similar
distributions, although the connection times between site 1 and sites
at 30–40∘ latitude and -72.5 to
-62.5∘ longitude differ significantly.
Comparison of HR-3D and CR-3D mean arrival (transit) time (a, d)
for particles initially deployed from site 1, (b, e) from site 10, and (c, f) from site 15.
Figure 9b shows the mean arrival time from site 10. As shown in the mean
transit time map, a large area connecting the southwestern region to the
northeastern region has the lowest values. This clearly shows the direct
connection of the particles seeded in the main jet, which travel fast and
reach these areas rapidly. For these regions, the mean arrival depth values
were less than 70 m (not presented here). The longest connection times
are associated with sites 1 and 16 for particles that initially started from
site 10. These particles took over 1200 d to arrive north of site 1 and
appear to be in a shadow dynamical region that is not directly connected to
the jet. The results are similar in CR-3D for site 10, although the transit
time is significantly higher in the coarser simulation than in the finer-resolution simulation (Fig. 9b, e).
Figure 9c and f show the mean transit time of particles initially deployed
from site 15 to other sites for HR-3D and CR-3D. The distribution is
remarkably different. In the CR-3D simulation, the connection is fast in the
southernmost region and does not allow some transit times to be modeled
acceptably, such as the motion from site 15 to the areas around site 16 and
from site 15 to the northern part of the basin (north of site 1). This
figure clearly indicates that the particles in CR-3D move in a less
dynamical velocity field, especially for trajectories moving from south to
north and from south to west. The shortest connection time from site 15 and
site 14 in HR-3D is less than 13 d, while it is 50 d for CR-3D.
In all simulated cases, we were able to differentiate the impacts of highly
energetic small scales on particle transit times between different sites. As
shown in the surface vorticity snapshots in Fig. 1, filamentary structures
and small eddies in the jets separating the two gyres and the subpolar
region act as transport barriers, for example for particles traveling from
site 15 to site 1.
Transit time matrices between site pairsComparison of transit time between site pairs for HR-3D and CR-3D
To complete the study, we compared the minimum and median transit times for
all defined sites in the basin. We evaluate the sensitivity of the transit
time matrix to the currents provided by two different cases: HR-3D and
CR-3D. Specifically, in this section, we provide a complete matrix
containing the analyses of the median and minimum connection time between
each selected area seeded with numerical particles.
Figure 10 provides an overview of the structure and time characteristics
of the connectivity between sites. It shows that the connectivity between
the northern and southern sites is the weakest (the connection is the
longest in terms of both the minimum and median times) and it is not
symmetric. The longest connection is between the northern and southern
sites. The fastest connection is along the main jet (site 10 to site 13).
This matrix also highlights the difference in the definition of connectivity
when applying the minimum or the median time. The latter is 3 to
4 times larger than the first. Moreover, the minimum time for CR is slightly
larger than for HR and varies between 10 d and 4 months. The difference
increases notably for the median time, including along the principal jet
(with a delay in arrival time ranging from 1 to 6 months).
Comparison of HR-3D and CR-3D minimum and median transit times
between site pairs, (a) minimum transit time for HR-3D, (b) difference between
minimum transit time for CR-3D and HR-3D (CR3D - HR3D), (c) median transit
time for HR-3D, and (d) median transit time for CR-3D.
The longest connection is for particles moving from the northern edge of the
subpolar gyre (site 1) to the easternmost region between the two zonal jets
separating the gyres (site 9), with minimum and median transit times of 516
and 1131 d, respectively, for HR. For CR and for the same sites, these
times increase by an additional 30 and 164.5 d, respectively. On the
other hand, the shortest connection is between sites 6 and 5, along the
northern zonal jet, where we obtained 1 and 13 d as minimum and
median transit times, respectively, for HR. Note that this result is related to an
increased efficiency of the particle advection due to the resolved
small-scale nonlinearities, which seem to be particularly active in this
part of the basin. The resolved small scales act as stirring structures that
accelerate the movement of particles around, for example, the peripheries of
mesoscale eddies and along filaments. In addition, areas with longer transit
times show larger differences between HR and CR (for example, departures
from sites 14, 15, and 16 and arrivals at sites 1, 2, and 3).
Comparison of transit time matrices for HR-3D and HR-SL
To determine whether the Lagrangian properties of oceanic flows can be
evaluated in 2D (limited to the surface layer of the ocean), rather than
by including the full 3D framework, we compare connectivity properties
between defined sites for 2D and 3D high-resolution simulations (Fig. 11 and
Supplement Fig. S6). The results show that the transit times for
numerical particles deployed in the surface layer are generally shorter than
those for particles that started in deeper layers (3D), although there are
some exceptions such as the motion from site 2 to sites 6 and 7: in this
direction, a high percentage of particles in the surface layer need a longer
transit time to reach the final destination than similar particles in deeper
layers. This is due to vertical fluxes associated with the displacement of
isopycnals by internal dynamics (e.g., eddy pumping or eddy–eddy
interaction). Therefore, areas with similar values of connectivity
properties in the 2D and 3D simulations suggest that vertical motions for
these regions are not strong enough to add complexity to trajectories.
Comparison of HR-3D and HR-SL minimum and median transit times
between site pairs, (a) minimum transit time for HR-3D, (b) difference between
minimum transit time for HR-SL and HR-3D (HRSL - HR3D), (c) median transit
time for HR-3D, and (d) median transit time for HR-SL.
Although there are many similarities between the median transit time
matrices for the HR-3D and HR-SL cases (Fig. 11), the distribution of the
minimum transit time values shows differences; the main reason is related to
vertical movements. In other words, the vertical dimension of the
trajectories that exists in HR-3D gives the possibility to establish more
pathways between the different areas. This result provides important insight
into connectivity properties in the ocean: while 2D simulations provide
useful information on transit times, it is necessary to understand the rate
of connections using 3D simulations.
In conclusion, both 2D ocean connectivity and 3D ocean connectivity are important tools for
understanding the movement of water and other properties within the ocean,
but 3D connectivity provides a more complete picture by taking into account
the full three-dimensional movement of water and thus life.
Discussion and conclusion
Lagrangian connectivity analysis utilizes sets of numerical particle
trajectories to identify connecting pathways, as well as timescales and
transport between oceanic regions. This is a powerful tool to coherently
study the connection between different areas in the ocean. The current study
is one of the first large-scale studies to use high-resolution ocean flow
data and particle tracking to describe connectivity patterns in a
large-scale (although idealized) basin.
In this paper, the focus was on analyzing the connectivity of different
sites in a double-gyre ocean model using a Lagrangian approach with
numerical particles. A total of 16 sites were specified and at each site 100 000
particles were used for the numerical analysis. Lagrangian properties such
as mean, median, and modal transit times were calculated to examine
connectivity properties in the North Atlantic. In addition, the
probability density functions (PDFs) of transit times and mean arrival
depths for different simulations were compared. The analysis used
high-resolution 3D velocity fields (HR-3D), HR surface velocity (HR-SL), or
velocity fields averaged over a coarser-resolution grid (CR-3D).
The Lagrangian PDF modeling approach was implemented for the sample sites
in all the simulations. The particles have different trajectories to reach
their final destinations due to the small-scale motions induced by the
resolution of the fine-scale dynamics. The results indicate that particles
that remain in the surface layer or near the subsurface layer move faster
due to intensified velocities resulting from simulating the fine-scale
circulation. In the deeper parts of the basin, particles need more time to
reach their final site, as at depth, the velocity intensity decreases due to
the effect of the nonlinear dynamics. This finding is confirmed by comparing
the PDF of the 2D surface layer simulation with other simulations.
Fine-scale movements, especially in the upper 50 m of the surface
layer, play an important role in particle motion. The numerical particles in
the two simulations (HR-3D and CR-3D) show significantly different PDF
distributions, especially for movement from the western part of the basin to
the eastern part (e.g., from site 10 to sites 4 and 2, see Supplement
Fig. S7). It was also found that the particles transported by the
high-resolution velocity fields tend to move to deeper parts of the basin
compared to the CR-3D simulation.
In the 5-year simulation based on HR-3D velocity fields, the longest route
was obtained for particles deployed from site 9 (in the eastern part of the
western boundary current extension) to site 1 (in the subpolar gyre), with
an average transit time of 1145 d. This is due to less energetic flow in
the areas close to these sites. In contrast, transit times along the principal
zonal jet (site 10 to site 11) represent the shortest and fastest routes,
with an average transit time of 179 d.
As expected, the numerical particles remain concentrated around their
starting position during the first week after their deployment. But 3 years
after their departure and independently of their initial deployment
positions, almost all particles were concentrated along the two zonal jets. These
jets act as attraction hubs that eventually capture most of the particles.
Based on the mean arrival depth at the sample sites, we can see that the
particles move toward deeper depths in the interior of the ocean due to the
strong nonlinear velocity fields that develop around these jets on the
western side of the basin, with a direct impact on the vertical motion of
the numerical particles.
Our results emphasize the fact that because ocean circulation is turbulent at
horizontal scales of 10–100 km, it is not relevant to assess connectivity
properties using climatologies or low-resolution (> 100 km)
velocity fields; moreover we show that connectivity in the ocean is not 2D
but 3D and that assessments based on 2D fields may significatively alter
the results.
Lagrangian trajectories simulated with the coarse-resolution velocity fields
do not sufficiently show the effect of mesoscale eddies on particle
dispersion, which results in unreliable Lagrangian indices (e.g., transit
time) compared to estimates based on HR model simulations. The CR ocean flow
simulation used in this study, with a spatial resolution of ∼ 100 km, is inadequate to describe the mesoscale circulation. Yet, this
fine-scale variability has been shown to significantly shape and change the
connectivity of the North Atlantic.
In this context, our results show that the use of high-resolution velocity
fields, as opposed to coarse-resolution fields, resulted in a reduction of
39 % in mean transit time (we divided the difference between the transit
time, i.e., “transit timeHR3D - transit timeCR3D” or “transit timeHR3D -
transit timeHR2D” by the transit timeHR3D). This suggests that the use of
high-resolution velocity fields allows for a more accurate representation of
the complex flow dynamics in the region and results in faster particle
transport. The CR is less smooth than the HR due to the dispersion process.
In the HR case, the simulated ocean dynamics disperse the particles more
than in the CR case, and the numerical particle concentration in the HR case
is smoother. In the HR case, the flow field is more turbulent and contains
more small-scale dynamical structures than in the CR case. These small-scale
features can trap and release particles in batches or form blocking
patterns, resulting in high particle concentrations in some regions.
However, due to the chaotic nature of the flow field, these concentrations
are not maintained and the particles are eventually dispersed throughout the
domain, resulting in a smoother concentration distribution. In contrast, the
CR simulation has a smoother and more predictable flow field, resulting in a
more uniform dispersion of particles and a less fluctuating concentration
distribution. This may result in a less smooth concentration distribution
than in the HR simulation.
Moreover, the study also found that taking into account the full
three-dimensional (3D) velocity instead of just surface fields resulted in
an increase of 8.4 % in the mean transit time. This suggests that the
vertical component of the velocity field significantly affects the transport
behavior of the particles and that accounting for this vertical component leads
to a more accurate representation of their transport patterns. Overall,
these findings highlight the importance of considering the resolution and
dimensionality of the velocity fields when studying the transport behavior
of particles in the study region.
In particular, in coarse-resolution simulations, the dispersion of particles
is degraded. This results in longer transit times. It also limits the
connection between water particles at different depths. A possible solution
to overcome this problem when integrating Lagrangian trajectories using the
velocity calculated in coarse-resolution simulations is to parameterize the
missing dispersion. Some methods have been proposed in the literature. The
simplest parameterization consists of adding a random walk to the successive
position of each particle, which is compatible with an advection–diffusion
equation and is equivalent to a stochastic “Markovian” parameterization
(Berloff and McWilliams, 2002). However, this stochastic parameterization
does not adequately reproduce the small-scale ocean dynamics that involve
consistency in advection (Klocker et al., 2012a, b; Veneziani et al., 2004).
Different Markov parameterizations of higher order have been proposed in an
attempt to better reproduce the effect of the small-scale ocean dynamics
(Berloff and McWilliams, 2002; Griffa, 1996; Rodean, 1996; Sawford, 1991).
Other improved parameterizations include particle looping due to eddy
coherence (Reynolds, 2002; Veneziani et al., 2004), as well as relative
dispersion between different particles (Piterbarg, 2002). While these
methods have been developed and applied to horizontal flows, recent
developments include an isopycnal Markov-0 (Spivakovskaya et al., 2007) or
shear-dependent formulation (Le Sommer, 2011) and, more recently, an
isoneutral Markov-1 formulation (Reijnders et al., 2022). The latter appears
to better mimic the coherent behavior of the 3D ocean dispersion at small
scales. It would be interesting in future work to evaluate how such methods,
applied in a Lagrangian framework, might improve the results we obtained
with a coarse-resolution field.
In conclusion, the present study highlights the importance of small-scale
variability in determining patterns of connectivity and provides detailed
information on Lagrangian connectivity in the North Atlantic. Our results
can guide the spatial scales at which future OGCMs should be run for
reliable connectivity analysis; moreover, for Lagrangian studies, we
advocate refining OGCMs to the appropriate resolution with sufficient
spatiotemporal accuracy.
Data availability
Major parts of the data and analytical codes utilized in this study can be
accessed through the following link: 10.5281/zenodo.8123776 (Hariri, 2023).
Should any inquiries or requests for additional details arise, please reach
out to the corresponding author at saeed.hariri@io-warnemuende.de. We
actively promote the utilization and dissemination of our data and code to
foster further research and scientific progress.
The supplement related to this article is available online at: https://doi.org/10.5194/os-19-1183-2023-supplement.
Author contributions
SH and SSP contributed to the data analysis and preparing the figures. SH,
SSP, BBL, and ML contributed to the paper writing and design of the
Lagrangian experiments. All authors reviewed and accepted the final version
of the paper.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
The authors would like to express their great appreciation to Daniele Iudicone and Laurent Bopp for their insightful discussions. The authors
also thank three anonymous reviewers for helpful comments that improved
earlier versions of this study. We also acknowledge the mesoscale
calculation server CICLAD (http://ciclad-web.ipsl.jussieu.fr, last access: 15 August 2021) dedicated to the
Institute Pierre Simon Laplace modeling effort for technical and
computational support.
Financial support
This research has been supported by the Agence Nationale de la Recherche (grant no. ANR-11-BTBR-0008).The publication of this article was funded by the Open Access Fund of the Leibniz Association.
Review statement
This paper was edited by Ismael Hernández-Carrasco and reviewed by three anonymous referees.
ReferencesAlberto, F., Raimondi, P. T., Reed, D. C., Watson, J. R., Siegel, D. A., Mitarai, S., Coelho, N.,
and Serrão, E. A.: Isolation by oceanographic distance explains genetic
structure for Macrocystis pyrifera in the Santa Barbara Channel, Mol Ecol.,
20, 2543–2554, 10.1111/j.1365-294X.2011.05117.x, 2011.Berloff, P. S. and McWilliams, J. C.: Material transport in oceanic Gyres,
Part II: Hierarchy of stochastic models, J. Phys. Oceanogr.,
32, 797–830, 10.1175/1520-0485(2002)032<0797:mtiogp>2.0.co;2, 2002.Bharti, D. K., Katell Guizien, M. T., and Aswathi-Das, P. N.: Vinayachandran,
Kartik Shanker, Connectivity networks and delineation of disconnected
coastal provinces along the Indian coastline using large-scale Lagrangian
transport simulations, Limnology and Oceanography, Assoc.
Sci. Limnol. Oceanogr., 67, 1416–1428,
10.1002/lno.12092, 2022.Blanke, B. and S. Raynaud.: Kinematics of the Pacific Equatorial
Undercurrent: An Eulerian and Lagrangian approach from GCM results, J. Phys. Oceanogr., 27, 1038–1053,
10.1175/1520-0485(1997)027<1038:KOTPEU>2.0.CO;2,
1997.Blanke, B., Speich, S., Madec, G., and Döös, K.: A global diagnostic
of interocean mass transfers, J. Phys. Oceanogr., 31,
1623–1642,
10.1175/1520-0485(2001)031<1623:AGDOIM>2.0.CO;2,
2001.Blanke, B., Bonhommeau, S., Grima, N., and Drillet, Y.: Sensitivity of
advective transfer times across the North Atlantic Ocean to the temporal and
spatial resolution of model velocity data: Implication for European eel
larval transport, Dynam. Atmos. Ocean., 55/56, 22–44,
10.1016/j.dynatmoce.2012.04.003, 2012.Cotroneo, Y., Celentano, P., Aulicino, G., Perilli, A., Olita, A., Falco,
P., Sorgente, R., Ribotti, A., Budillon, G., Fusco, G., and Pessini, F.:
Connectivity Analysis Applied to Mesoscale Eddies in the Western
Mediterranean Basin, Remote Sens., 13, 4228,
10.3390/rs13214228, 2021.
Cowen, R. K., Gawarkiewicz, G., Pineda, J., Thorrold, S., and Werner, F. E.:
Population connectivity in marine systems An Overview, Oceanography, 20,
14–21, 2007.Dever, E. P., Hendershott, M. C., and Winant, C. D.: Statistical aspects of
surface drifter observations of circulation in the Santa Barbara Channel, J.
Geophys. Res.-Ocean., 103, 24781–24797,
10.1029/98JC02403, 1998.Dijkstra, E. W.: A note on two problems in connexion with graphs, Numer.
Math., 1, 269–271, 10.1007/BF01386390, 1959.Döös, K.: Interocean exchange of water masses, J. Geophys. Res.-Ocean., 100, 13499–13514, 10.1029/95JC00337, 1995.Drouet, K., Jauzein, C., Herviot-Heath, D., Hariri, S., Laza-Martinez, A.,
Lecadet, C., Seoane, S., Sourisseau, M., Plus, M., Lemée, R., and Siano, R.:
Current distribution and potential expansion of the harmful benthic
dinoflagellate Ostreopsis cf. siamensis towards the warming waters of the
Bay of Biscay, North-East Atlantic, Environ. Microbiol., 23,
4956–4979, 10.1111/1462-2920.15406, 2021.Fischer, H. B., List, J. E., Koh, R. C., Imberger, J., and Brooks, N. H.:
Mixing in Inland and Coastal Waters, Academic Press, New York,
10.1016/C2009-0-22051-4, 1979.Froyland, G. and Padberg, K.: Almost-invariant sets and invariant
manifolds Connecting probabilistic and geometric descriptions of coherent
structures in flows, Physica D, 238, 1507–1523,
10.1016/j.physd.2009.03.002, 2009.Froyland, G., Stuart, R. M., and van Sebille, E.: How well-connected
is the surface of the global ocean?, Chaos, 24, 033126, 10.1063/1.4892530, 2014.Gaylord, B. and Gaines, S. D.: Temperature or transport? Range limits in marine
species mediated solely by flow, Am. Nat., 155, 769–789,
10.1086/303357, 2000.Grant, S. B., Kim, J. H., Jones, B. H., Jenkins, S. A., Wasyl, J., and
Cudaback, C.: Surf zone entrainment, along-shore transport, and human health
implications of pollution from tidal outlets, J. Geophys. Res., 110,
C10025, 10.1029/2004JC002401, 2005.Griffa, A.: Applications of stochastic particle models to oceanographic
problems, in: Stochastic modelling in physical oceanography, edited by: Adler, R. J., Müller, P., and Rozovskii, B. L., 113–140, Birkhäuser
Boston, 10.1007/978-1-4612-2430-3_5, 1996.Hariri, S.: Near-Surface Transport Properties and Lagrangian Statistics
during Two Contrasting Years in the Adriatic Sea, J. Mar. Sci.
Eng., 8, 681, 10.3390/jmse8090681, 2020.Hariri, S.: Analysis of Mixing Structures in the Adriatic Sea Using
Finite-Size Lyapunov Exponents, Geophys. Astrophys. Fluid
Dynam., 116, 20–37, 10.1080/03091929.2021.1962851,
2022.Hariri, S.: Ariane Lagrangian Simulation, Zenodo [code and data set], 10.5281/zenodo.8123776, 2023.Hariri, S., Besio, G., and Stocchino, A.: Comparison of Finite Time Lyapunov
Exponent and Mean Flow Energy During Two Contrasting Years in the Adriatic
Sea, OCEANS'15 MTS/IEEE, Genoa, Italy, 10.1109/OCEANS-Genova.2015.7271418, 19-21 May 2015.Hariri, S., Plus, M., Le Gac, M., Séchet, V., Revilla, M., and Sourisseau, M.:
Advection and Composition of Dinophysis spp. Populations Along the European
Atlantic Shelf, Front. Mar. Sci., 9, 914909, 10.3389/fmars.2022.914909,
2022.
James, M. K., Armsworth, P. R., Mason, L. B., and Bode, L.: The Structure
of Reef Fish Metapopulations: Modelling Larval Dispersal and Retention
Patterns, Proceedings: Biological Sciences, 269, 2079–2086,
2002.Jönsson, B. and Watson, J.: The timescales of global surface-ocean
connectivity, Nat. Commun., 7, 11239, 10.1038/ncomms1123,
2016.Klocker, A., Ferrari, R., and LaCasce, J. H.: Estimating suppression of
eddy mixing by mean flows, J. Phys. Oceanogr., 42,
1566–1576, 10.1175/JPO-D-11-0205.1, 2012a.Klocker, A., Ferrari, R., Lacasce, J. H., and Merrifield, S. T.:
Reconciling float-based and tracer-based estimates of lateral diffusivities,
J. Mar. Res., 70, 569–602,
10.1357/002224012805262743, 2012b.Kot, C. Y., Åkesson, S., Alfaro-Shigueto, J., Amorocho Llanos, D. F., Antonopoulou, M., Balazs, G. H., Baverstock, W. R., Blumenthal, J. M., Broderick, A. C., Bruno, I., Canbolat, A. F., Casale, P., Cejudo, D., Coyne, M. S., Curtice, C., DeLand, S., DiMatteo, A., Dodge, K., Dunn, D. C., and
Halpin, P. N.: Network analysis of sea turtle movements and connectivity: A tool for conservation prioritization, Divers. Distrib., 28, 810–829, 10.1111/ddi.13485, 2022.LaCasce, J. H.: Statistics from Lagrangian observations, Prog. Oceanogr.,
77, 1–29, 10.1016/j.pocean.2008.02.002, 2008.Le Sommer, J., d'Ovidio, F., and Madec, G.: Parameterization of subgrid
stirring in eddy resolving ocean models, Part 1: Theory and diagnostics,
Ocean Model., 39, 154–169,
10.1016/j.ocemod.2011.03.007, 2011.Levin, S. A.: The problem of pattern and scale in ecology: The Robert H.
MacArthur Award Lecture, Ecology, 73, 1943–1967,
10.2307/1941447, 1992.Lévy, M., Iovino, D., Resplandy, L., Klein, P., Madec, G., Tréguier, A.-M.,
Masson, S., and Takahashi, K.: Large-scale impacts of submesoscale dynamics on
phytoplankton: Local and remote effects, Ocean Model., 43/44,
77–93, 10.1016/j.ocemod.2011.12.003, 2012a.Lévy, M., Resplandy, L., Klein, P., Capet, X., Iovino, D., and Ethé, C.: Grid
degradation of submesoscale resolving ocean models: Benefits for offline
passive tracer transport, Ocean Model., 48, 1–9,
10.1016/j.ocemod.2012.02.004, 2012b.
Madec, G., Delecluse, P., Imbard, M., and Lévy, C.: OPA 8.1 Ocean General
Circulation Model Reference Manual, Note du Pole de Modelisation, Institut Pierre-Simon Laplace, 91 pp., 1998.Mitarai, S., Siegel, D. A., Watson, J. R., Dong, C., and McWilliams, J. C.:
Quantifying connectivity in the coastal ocean with application to the
Southern California Bight, J. Geophys. Res., 114, C10026,
10.1029/2008JC005166, 2009.Mora, C., Treml, E. A., Roberts, J., Crosby, K., Roy, D., and Tittensor, D. P.:
High connectivity among habitats precludes the relationship between
dispersal and range size in tropical reef fishes, Ecography, 35, 89–96,
10.1111/j.1600-0587.2011.06874.x, 2012.Novi, L., Bracco, A., and Falasca, F.: Uncovering marine connectivity through
sea surface temperature, Sci. Rep., 11, 8839,
10.1038/s41598-021-87711-z, 2021.Palumbi, S. R.: Population genetics, demographic connectivity, the design of
marine reserves, Ecol. Appl., 13, 146–158,
10.1890/1051-0761(2003)013[0146:PGDCAT]2.0.CO;2, 2003.Piterbarg, L. I.: The top Lyapunov exponent for a stochastic flow modeling
the upper ocean turbulence, SIAM J. Appl. Mathemat., 62,
777–800, 10.1137/S0036139999366401, 2002.Poulain, P.-M. and Niiler, P.: Statistical-analysis of the surface
circulation in the California Current System using satellite-tracked
drifters, J. Phys. Oceanogr., 19, 1588–1603,
10.1175/1520-0485(1989)019<1588:SAOTSC>2.0.CO;2,
1989.Poulain, P.-M. and Hariri, S.: Transit and residence times in the Adriatic
Sea surface as derived from drifter data and Lagrangian numerical
simulations, Ocean Sci., 9, 713–720, 10.5194/os-9-713-2013, 2013.Pope, S.: Lagrangian PDF methods for turbulent flows, Annu. Rev. Fluid
Mech., 26, 23–63,
10.1146/annurev.fl.26.010194.000323, 1994.Reijnders, D., Deleersnijder, E., and van Sebille, E.: Simulating
Lagrangian subgrid-scale dispersion on neutral surfaces in the ocean,
J. Adv. Model. Earth Syst., 14, e2021MS002850,
10.1029/2021MS002850, 2022.Reynolds, A.: On Lagrangian stochastic modelling of material transport in
oceanic gyres, Physica D, 172, 124–138,
10.1016/S0167-2789(02)00660-7, 2002.Richter, D. J., Watteaux, R., Vannier, T., Leconte, J., Frémont, P.,
Reygondeau, G., Maillet, N., Henry, N., Benoit, G., Da Silva, O., Delmont, T. O., Fernàndez-Guerra, A., Suweis, S., Narci, R., Berney, C., Eveillard, D., Gavory, F., Guidi, L., Labadie, K., Mahieu, E., Poulain, J., Romac, S.,
Roux, S., Dimier, C., Kandels, S., Picheral, M., Searson, S., Tara Oceans Coordinators,
Pesant, S., Aury, J.-M., Brum, J. R., Lemaitre, C., Pelletier, E., Bork, P.,
Sunagawa, S., Lombard, F., Karp-Boss, L., Bowler, C., Sullivan, M. B.,
Karsenti, E., Mariadassou, M., Probert, I., Peterlongo, P., Wincker, P., de
Vargas, C., Ribera d'Alcalà, M., Iudicone, D., and Jaillon, O.: Genomic evidence for global ocean plankton biogeography
shaped by large-scale current systems, eLife, 11, e78129,
10.7554/eLife.78129, 2022.Rodean, H. C.: Stochastic Lagrangian models of turbulent diffusion,
American Meteorological Society
Boston, MA, 84 pp., 10.1007/978-1-935704-11-9,
1996.Rossi, V., Ser-Giacomi, E., López, C., and Hernández-García,
E.: Hydrodynamic provinces and oceanic connectivity from a transport network
help designing marine reserves, Geophys. Res. Lett., 41,
2883–2891, 10.1002/2014GL059540, 2014.Roughgarden, J., Gaines, S., and Possingham, H.: Recruitment dynamics in
complex life-cycles, Science, 241, 1460–1466,
10.1126/science.11538249, 1988.Sawford, B. L.: Reynolds number effects in Lagrangian stochastic models of
turbulent dispersion, Phys. Fluid. A, 3, 1577–1586,
10.1063/1.857937, 1991.Ser-Giacomi, E., Baudena, A., Rossi, V., Follows, M., Clayton, S., Vasile, R., López, C., and
Hernández-García, E.: Lagrangian betweenness as a
measure of bottlenecks in dynamical systems with oceanographic examples, Nat.
Commun., 12, 4935, 10.1038/s41467-021-25155-9, 2021a.Ser-Giacomi, E., Legrand, T., Hernandez-Carrasco, I.,
and Rossi, V.: Explicit and implicit network connectivity: Analytical formulation
and application to transport processes, Phys. Rev. E, 103,
042309, 10.1103/physreve.103.042309, 2021b.Ser-Giacomi, E., Vasile, R., Hernández-García, E., and
López, C.: Most probable paths in temporal weighted networks:
An application to ocean transport, Phys. Rev. E, 92, 012818,
10.1103/PhysRevE.92.012818, 2015.Spivakovskaya, D., Heemink, A. W., and Deleersnijder, E.: Lagrangian
modelling of multi-dimensional advection-diffusion with space-varying
diffusivities: Theory and idealized test cases, Ocean Dynam., 57,
189–203, 10.1007/s10236-007-0102-9, 2007.Swenson, M. and Niiler, P.: Statistical analysis of the surface circulation
of the California Current, J. Geophys. Res., 101, 22631–22645,
10.1029/96JC02008, 1996.Treml, E. A., Halpin, P. N., Urban, D. L., and Pratson, L. F.: Modeling population
connectivity by ocean currents, a graph-theoretic approach for marine
conservation, Landscape Ecol., 23, 19–36,
10.1007/s10980-007-9138-y, 2008.Trakhtenbrot, A., Nathan, R., Perry, G., and Richardson. D. M.: The importance of
long-distance dispersal in biodiversity conservation, Divers Distrib.,
11, 173–181, 10.1111/j.1366-9516.2005.00156.x, 2005.Van Sebille, E., England, E. H., and Froyland, G.: Origin, dynamics and
evolution of ocean garbage patches from observed surface drifters, Environ.
Res. Lett., 7, 044040, 10.1088/1748-9326/7/4/044040,
2012.Van Sebille, E., Griffies, S. M., Abernathey, R., Adams, T. P., Berloff, P.,
Biastoch, A., Blanke, B., Chassignet, E. P., Cheng, Y., Cotter, C. J., Deleersnijder, E.,
Döös, K., Drake, H. F., Drijfhout, S., Gary, S. F., Heemink, A. W.,
Kjellsson, J., Koszalka, I. M., Lange, M., Lique, C., MacGilchrist, G. A.,
Marsh, R., Mayorga Adame, C. G., McAdam, R., Nencioli, F., Paris, C. B.,
Piggott, M. D., Polton, J. A., Rühs, S., Shah, S. H. A. M., Thomas, M. D.,
Wang, J., Wolfram, P. J., Zanna, L., and Zika, J. D.: Lagrangian ocean analysis: fundamentals and practices,
Ocean Model., 121, 49–75, 10.1016/j.ocemod.2017.11.008,
2018.Veneziani, M., Griffa, A., Reynolds, A. M., and Mariano, A. J.: Oceanic
turbulence and stochastic models from subsurface Lagrangian data for the
Northwest Atlantic ocean, J. Phys. Oceanogr., 34, 1884–1906,
10.1175/1520-0485(2004)034<1884:otasmf>2.0.co;2, 2004.
Warner, R. R.: Evolutionary ecology: how to reconcile pelagic dispersal with
local adaptation, Coral Reefs, 16, S115–S120, 1997.Wang, Y., Raitsos, D. E., Krokos, G., Gittings, J. A., Zhan, P., and Hoteit, I.: Physical connectivity simulations
reveal dynamic linkages between coral reefs in the southern Red Sea and the
Indian Ocean, Sci. Rep., 9, 16598, 10.1038/s41598-019-53126-0,
2019.
Ward, B. A., Cael, B. B., and Robert, Y. C.: Selective constraints on global
plankton dispersal, P. Natl. Acad. Sci. USA, 118, e2007388118, 10.1073/pnas.2007388118, 2021.
Watson, J. R., Hays, C. G., Raimondi, P. T., Mitarai, S., Dong, C.,
McWilliams, J. C., Blanchette, C. A., Caselle, J. E., and Siegel, D. A.:
Currents connecting communities: nearshore community similarity and ocean
circulation, Ecology, 92, 1193–1200, 2011.