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\title{Lagrangian characterization of surface transport from the
Equatorial Atlantic to the Caribbean Sea using climatological Lagrangian
Coherent Structures and Self-Organizing Maps}



\author[1]{Ma. Eugenia Allende-Arandía}%
\author[1]{Rodrigo Duran}%
\author[1]{Laura Sanvicente-Añorve}%
\author[1]{Christian M. Appendini}%
\affil[1]{Affiliation not available}%


\vspace{-1em}



  
  \date{May 26, 2024}


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Ma. Eugenia Allende-Arand\selectlanguage{ngerman}ía\textsuperscript{1}, Rodrigo
Duran\textsuperscript{2,3}, Laura Sanvicente-Añorve\textsuperscript{4},
Christian M. Appendini\textsuperscript{1,*}

\textsuperscript{1}Laboratorio de Ingeniería y Procesos Costeros,
Instituto de Ingeniería, Universidad Nacional Autónoma de México, Puerto
de abrigo s/n, Sisal, Yucatán 97356, México

\textsuperscript{2}National Energy Technology Laboratory, United States
Department of Energy, Albany OR, United States.

\textsuperscript{3}Theiss Research, La Jolla, CA, United States

\textsuperscript{4}Instituto de Ciencias del Mar y Limnología,
Universidad Nacional Autónoma de México, Ciudad de México, C.P. 04510.

Corresponding author: Christian M. Appendini
(\emph{cappendinia@iingen.unam.mx} )

\textbf{Key Points:}

\begin{itemize}
\tightlist
\item
  Current transport routes and barriers are characterized from the
  Equatorial Atlantic to the Caribbean Sea.
\item
  Wind forcing is a significant factor in transporting suspended
  material by surface ocean currents.
\item
  Different areas in the Caribbean Sea require distinct wind conditions
  for floating material to arrive.
\item
  Transport routes and barriers over large regions can be characterized
  using tools from dynamical systems and unsupervised neural networks.
\end{itemize}



\textbf{Abstract}

This study presents an assessment of the transport of suspended material
by surface ocean currents, which have a critical role in determining the
connectivity and distribution of living and non-living material.
Lagrangian experiments reveal pathways from the Equatorial Atlantic to
ten strategic regions within the Caribbean Sea, determined by
considering the space-time variability of climatological Lagrangian
Coherent Structures, which act as recurrent attracting pathways and
transport barriers. Due to windage or Stokes drift, wind forcing is a
significant factor in determining the spatial locations where particles
cluster and the time needed to reach the Caribbean from the Equatorial
Atlantic. Pathways shift westward within the Caribbean and take less
time to arrive with increasing wind influence. Depending on the wind
effect, the particles show higher confluence in different areas of the
Caribbean. A case study is presented for the Mexican Caribbean nearshore
area, isolated from ocean-current trajectories. Here, wind weakens the
transport barrier responsible for this isolation and causes particle
confluence towards that region. Spatial patterns of the Eulerian
velocity identified through Self-Organizing Maps, with time dependence
given by their best matching units, can reproduce the characteristic
Lagrangian patterns of surface current climate variability. Our study
demonstrates the application of tools from dynamical systems and
unsupervised neural networks to understand Lagrangian patterns and
identify the processes that drive them. These findings improve our
understanding of transport mechanisms of suspended material by surface
ocean currents in the Western Atlantic and the Caribbean Sea, which is
essential for managing and conserving marine ecosystems.

\textbf{Plain Language Summary}

Ocean currents' movement of suspended material is important for
ecosystems as it affects the connection of marine populations and the
distribution of suspended material such as plastics and sargassum. This
research studies the transport routes from the Equatorial Atlantic to
the Yucatan Peninsula by identifying the distribution of particles in
different Caribbean Sea areas. We used different analysis methods to
determine the transport pathways and natural barriers. When barriers are
present, particles cannot reach certain areas without the influence of
wind. We found that particles released during the autumn-winter months
with a 1\% windage reached the Yucatan Peninsula in the following year's
spring, while particles released in the spring months with a 2\% windage
reached the area in the summer months of the same year. Understanding
the effect of wind forcing over suspended particles moving over surface
ocean currents allows for better managing and conserving marine
ecosystems.

\textbf{1 Introduction}

Ocean currents are a major factor in the movement of suspended material
over large distances along ocean basins. The conveyance of suspended
material by currents as a main transport mechanism is critical for
ecosystems as they determine the connectivity of some marine populations
inhabiting the benthic or pelagic environments (e.g., Bryan-Brown et
al., 2017; Sanvicente-Añorve et al., 2014, 2018). Ocean currents also
transport contaminant materials derived from anthropogenic activities
(Dow, 1999; Pohl et al., 2020; Zaborska et al., 2017), eventually
reaching the coast, accumulating in remote places, or sinking to the
ocean bottom. Considering the importance of currents in transporting
living and non-living suspended material, it is crucial to understand
their kinematics. For the Tropical Atlantic, different authors have
described the surface currents (Johns et al., 2014; Lumpkin \& Garzoli,
2005; Müller-Karger et al., 1989), while others have characterized the
climatological surface currents from the western tropical Atlantic to
the Gulf of Mexico (GoM) (Andrade \& Barton, 2000; Gordon, 1967; Johns
et al., 2002; Muller-Karger et al., 1988, 1995; Romanou et al., 2004;
Zavala-Hidalgo et al., 2014). Recently, studies have focused on
understanding the sargassum transport routes from the Equatorial
Atlantic through the Caribbean Sea (CS) and into the GoM (Athié et al.,
2020; Beron-Vera et al., 2022; Orfila et al., 2021; Ortiz-Royero et al.,
2013; Otero et al., 2016; Putman et al., 2018, 2020). This is due to the
emergence of a new sargassum generation area in the tropical Atlantic
(Gower et al., 2013; Wang \& Hu, 2017), resulting in substantial
environmental, social, and economic effects across the Caribbean region.
Besides sargassum, understanding the currents system from Equatorial
Atlantic to the GoM is relevant for plastics (Law et al., 2010),
nutrients (Williams \& Follows, 2003), and organisms (Sanvicente-Añorve
et al., 2019), as the results indicate the fundamental role of the North
Brazil and Guyana currents (Johns et al., 2014), establishing the
connectivity between the western Atlantic and the Caribbean
(Andrade-Canto \& Beron-Vera, 2022; Muller-Karger et al., 1988, 1995).

The Equatorial Atlantic to the GoM currents system has a clear seasonal
variability. During the summer and fall, a significant part of the North
Brazil Current (NBC) retroflects and merges into the eastward-flowing
North Equatorial Countercurrent (NEC), which then intensifies. In
spring, the NEC weakens and superficially reverses. In some cases, the
NBC and the western boundary current to the north intensify
simultaneously, forming part of the North Atlantic large-scale gyre
moving northwestward to the CS (Garzoli et al., 2003; Johns et al.,
2003). The current dynamics in the CS are dominated by a primary jet
that forms the Caribbean Current (CC) as water is transported through
the southern region of the Lesser Antilles by a boundary current along
the South American coasts (Rhein et al., 2005), continuing to flow
northwestward through the CS on to the Yucatan Channel. The southern CS
has small recirculation gyres off Panama and south of the Yucatan
Channel interacting with the bathymetry, while the slower northern jet
is dominated by mesoscale anticyclones (Chérubin \& Richardson, 2007).
In addition to ocean currents, atmospheric forcing influences surface
transport, partly determining the trajectory of near-surface material
(Johns et al., 2020; Müller-Karger et al., 1989; Putman et al., 2018).
The atmospheric variability in the region is dominated mainly by the
easterly winds, which in turn are modulated by the Intertropical
Convergence Zone (ITCZ) migration, cold fronts' arrival, and the
Caribbean Low-Level Jet (CLLJ) variability. This atmospheric dynamic
results in two climatic seasons, a windier and drier season from
December to March and the wet season from August to November, regulated
by the location of the ITCZ. May-June and September-October are
considered a transition period between seasons since easterlies tend to
weaken, coinciding with the intensification and bi-modal variability of
the CLLJ (García-Martínez \& Bollasina, 2020; Hidalgo et al., 2015;
Orfila et al., 2021).

While the mentioned studies characterize the ocean currents system or
the atmospheric variability in the region, the interaction of wind,
waves, and surface currents dictate transport routes of floating matter
in the ocean's surface layer. As such, this study aims to characterize
sea-surface current patterns and assess the effect of surface currents
and wind interaction on the displacement of floating particles. We
utilized Self-Organizing Maps (SOMs) and climatological Lagrangian
Coherent Structures (cLCS) to identify the primary transport routes and
transport barriers in the region stretching from the western tropical
Atlantic to the Central Subtropical Atlantic, including the entrance to
the GoM and the Yucatan Peninsula (YP). We used synthetic surface
drifters to compute the probability of arrival at select locations
within the CS with an emphasis on the eastern coast of the YP, where we
also included the effect of wind over the drifters. The results show how
the windage plays a key role in advecting particles to some areas along
the CS but also provide insight into using SOMs to represent
climatological conditions for particle dispersal. This paper is
organized as follows: section two describes the data and methods;
section three presents the results, describing preferential routes for
different combinations of wind and currents, persistent attraction zones
and transport barriers, and the modulation of transport barriers by the
wind. We summarize our main findings in section four.

\textbf{2 Data and Methods}

Our study uses daily sea-surface velocity data from a 25-year
climatology (1994-2018) based on the HYbrid Coordinate Ocean Model
(HYCOM) reanalysis, encompassing from the Equatorial Atlantic Ocean to
the coast of North Carolina, USA, including the Gulf of Mexico, as
delimited by coordinates -100\textsuperscript{o}W to
-20\textsuperscript{o}W and -7\textsuperscript{o}S to
35\textsuperscript{o}N (Figure 1 and Figure S1 in Supplementary
Information). To gain a deeper understanding of the primary current
pathways and transport barriers, we computed climatological Lagrangian
Coherent Structures (cLCS) and identified the main current patterns
using Self-Organized Maps (SOMs). The cLCS provided insights into the
transport barriers and primary current pathways, while the SOMs allowed
us to efficiently characterize the system by synthesizing spatial and
temporal variability into limited current patterns. To further identify
transport routes, the effect of wind, and the probability of particle
arrival in the CS region, we conducted Lagrangian experiments under
three different scenarios: (i) currents without additional wind, (ii)
currents with an additional 1\% of wind, and (iii) currents with an
additional 2\% of wind. For each scenario, we integrated trajectories
using time-dependent velocities from a HYCOM climatology, wind
climatology, and SOMs patterns. We further illustrate the implications
of our findings by analyzing a case study for the YP. Our approach
allowed us to understand the region's ocean currents system,
characteristics, and response to varying wind conditions in Lagrangian
terms. Following is a description of the data and methods employed in
the study.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1. Study area denoting the region for the Caribbean Sea particle
analysis (red box). Surface currents time-averaged from the HYCOM
climatology; the colors indicate the current's magnitude, the arrows'
current direction, and the red asterisks the location from which the
particles were released. The acronyms shown are referred to in the text
and correspond to the following: Gulf of Mexico (GoM), Yucatan Peninsula
(YP), Florida Current (FC), Gulf Stream (GC), Loop Current (LC),
Caribbean Current (CC), Guyana Current (GC), North Brazil Current (NBC),
North Equatorial Atlantic (NEA), North Equatorial Current (NEC), North
Equatorial Recirculation Region (NERR).

\textbf{2.1 Data}

\textbf{2.1.1 Currents}

To characterize ocean currents, we used the horizontal surface velocity
components from HYCOM (CDAM, 2015). HYCOM is a primitive equation ocean
general circulation model that remains isopycnic in the open stratified
ocean, smoothly reverting to a terrain-following coordinate near the
bottom and z-level coordinates in the mixed layer and/or unstratified
seas (Bleck, 2002). HYCOM provides different vertical mixing schemes for
the surface mixed layer and the interior diapycnal mixing,
parameterizing the contribution of background internal wave breaking,
shear instability mixing, and double diffusion. Processes are
parameterized in the surface boundary layer, including wind-driven
mixing, surface buoyancy fluxes, and convective instability (Chassignet
et al., 2003; Halliwell, 2004; Large et al., 1997). HYCOM simulations
include the Navy Coupled Ocean Data Assimilation data (NCODA) (Cummings,
2006; Cummings \& Smedstad, 2013). We used the eastward (\emph{u}
-component) and northward (\emph{v} -component) surface current velocity
from the HYCOM + NCODA GOFS 3.1 reanalysis from 1994 to 2015, and
analysis GLBv0.08 experiment from 2016 to 2018, which has a temporal
resolution of 3 hours and a spatial resolution of
1/12\textsuperscript{o}. In the rest of the article, we refer to this
velocity time series as HYCOM. HYCOM is forced by the National Centers
for Environmental Prediction (NCEP) Climate Forecast System Reanalysis
(CFSR), described in the next section. We calculated daily means for the
current data to create the 25-year climatology. A critically important
aspect to this study which is based on climatological currents: Duran et
al. (2018) showed that climatological ocean currents preserve the
ensemble-mean Lagrangian transport patterns of the instantaneous
velocity, thus using a climatological velocity to study instantaneous
Lagrangian patterns produces meaningful results; more details are
presented in section 2.2.1.

.

\textbf{2.1.2 Wind}

The wind used for this study is a climatology computed from the CFSR,
the same wind used to force the HyCOM simulations described in 2.1.1.
This reanalysis is a fully coupled model representing the interaction
between the atmosphere, oceans, land, and sea ice, described by Saha et
al. (2010). The CFSR assimilates \emph{in situ} and satellite
observations using sigma--pressure hybrid vertical coordinates, a
simplified Arakawa--Schubert convection scheme with momentum mixing
(Hong \& Pan, 1996, 1998; Pan \& Wu, 1995), and orographic gravity wave
drag (Alpert et al., 1988, 1996; Young-Joon Kim \& Arakawa, 1995). The
land surface model is based on the two-layer OSU land model (H. L. Pan
\& Mahrt, 1987), the SW radiation is parameterized following the NASA
approach (Chou et al., 1998; Hou et al., 2002), and the LW radiation
following the GFDL approach (Fels \& Schwarzkopf, 1975; Schwarzkopf \&
Fels, 1991), based on the RRTM developed at AER (Taubman et al., 1997).
CFSR is coupled to a four-layer Noah land surface model (Ek et al.,
2003) and a two-layer sea ice model (Wu et al., 2005). The temporal data
resolution is 1 hour, with a spatial resolution of 0.5\selectlanguage{ngerman}°. We used the
zonal (\emph{u} -component) and meridional (\emph{v} -component) wind 10
m above the surface from the CFSRv1 and CFSRv2 reanalysis data. To
ensure consistency, we also calculated daily means for the wind data and
interpolated them onto the current data grid to create the 25-year
climatology. For interpolation, we employed the Modified Akima cubic
Hermite interpolation method. This approach utilizes a piecewise
function of polynomials, with a maximum degree of three, to interpolate
the values of neighboring grid points in each dimension. Specifically,
the method employs local data information to generate a continuous curve
that passes through the given data points while minimizing the curvature
in the resulting interpolated function.

\textbf{2.1.3 Drifters}

To validate particle model parameterizations and particle displacement
in the Lagrangian experiments, we used the Global Drifter Program (GDP)
data (\emph{National Oceanic and Atmospheric Administration, Atlantic
Oceanographic and Meteorological Laboratory} , 2019). The GDP is a
branch of NOAA's Global Ocean Observing System and a scientific project
of the Data Buoy Cooperation Panel (\emph{Data Buoy Cooperation Panel} ,
1885). The GDP maintains a global 5° x 5° gridded array of
\textasciitilde{}1,300 satellite-tracked surface drifters to meet the
need for an accurate and globally dense set of \emph{in
situ}observations of mixed layer currents, sea surface temperature,
atmospheric pressure, winds, waves, and salinity (Lumpkin \& Pazos,
2009). Elipot et al. (2016) describe the interpolation methods for
drifter trajectories. We used surface drifter trajectory data from 2017
and 2018 with an hourly resolution.

\textbf{2.2 Analysis}

\textbf{2.2.1 Climatological Lagrangian Coherent Structures}

In recent decades, the theory of nonlinear dynamics has been applied to
vector fields with arbitrary time dependence, such as geophysical
datasets. Thorough reviews can be found in Samelson (2013) and Haller
(2015). The result of this research---often termed Lagrangian Coherent
Structures (LCS)---has been shown in many studies to accurately
identify, and even predict, ocean kinematics (e.g., Beron-Vera et al.,
2008, 2019; Duran et al., 2021; Filippi et al., 2021; Olascoaga et al.,
2006, 2008, 2013; Olascoaga \& Haller, 2012). LCS have proven an ideal
tool to search for persistent and recurrent pathways in the ocean,
enabling the detection of low-frequency structures that tend to modulate
parcel's movements, and that cannot be reliably found using Eulerian
methods (Duran et al., 2018). Termed climatological LCS (cLCS), these
structures provide a generic yet accurate and detailed Lagrangian
climatology without the need to know trajectories' initial location,
initial time, or when the trajectory ends. Of particular interest to our
study, cLCS have been shown to be effective in identifying transport
barriers and dominant pathways. Comparisons with a variety of observed
and synthetic drifter data have shown that strongly attracting cLCS can
act as efficient transport barriers, considerably reducing cross-cLCS
transport, other strongly attracting cLCS indicate recurrent pathways,
including possibly when cLCS are deformed as chevrons (Duran et al.,
2018; Gough et al., 2019; Gouveia et al., 2021). In regions where
currents are less energetic, cLCS are less attracting and are more often
deformed as chevrons, thus indicating recurrent pathways as well
(Kurczyn et al., 2021). These Lagrangian transport patterns can be
efficiently and accurately extracted from large time series of Eulerian
velocity data with the proper tools from nonlinear dynamics (Duran et
al., 2018), but cannot be identified with commonly used Eulerian
methods, such as streamlines of a time-averaged velocity (e.g.,
supplemental information of Duran et al., 2018). While cLCS have proven
very efficient in identifying predominant and recurrent Lagrangian
patterns, we note that they cannot always explain instantaneous
patterns, similar to how the climate is useful but cannot always explain
the weather. Additional evidence of the adequacy of the climatological
velocity for our study is provided in Text S1, where we show that the
climatological currents have very similar patterns to the instantaneous
1994--2018 time series using Self-Organizing Maps.

cLCS are based on the concept of hyperbolic LCS, material lines that
maximize the normal attraction of nearby trajectories; thus, LCS
delineate and shape Lagrangian transport. cLCS differ from LCS in two
crucial ways. Firstly, cLCS are computed from a climatological velocity
instead of an instantaneous one. Secondly, the Cauchy-Green tensor,
needed to solve the normal-attraction maximization problem, is averaged
over different initial times while LCS are computed from the
Cauchy-Green tensor of one initial time. In Duran et al. (2018), these
two averaging steps are shown to efficiently preserve and extract the
main Lagrangian transport patterns from large time series of
instantaneous velocities. Because of the latter averaging step, cLCS are
not material lines but rather result in an Eulerian field representing
recurring or persistent trajectory patterns. Interested readers can
refer to Duran et al. (2018) for further details and mathematical
explanation, while detailed information regarding the numerical
implementation is found in Duran et al. (2019).

We obtained cLCS from the daily HYCOM climatology described above, which
allows us to characterize the Lagrangian kinematics of the currents in
the study area, identifying transport routes and barriers. The code to
compute cLCS is freely available (Duran et al., 2019).

\textbf{2.2.2 Self-Organizing Maps}

SOMs are a non-linear technique of artificial neural networks based on
an unsupervised training process that allows multivariate analysis. The
results obtained using SOMs retain the original data's topology while
projecting into a two-dimensional scheme for simplification. This allows
for visualizing, classifying, grouping, and detecting complex patterns
of any set of variables used in training simultaneously (Liu et al.,
2006). SOMs have been used for long-term currents characterization and
to study the possible hydrodynamic conditions in specific regions, such
as in Liu \& Weisberg (2005, 2007), who obtained the current patterns on
the west Florida platform and established a relationship between local
winds and coastal up/downwelling processes, or as in Vilibi\selectlanguage{polish}ć \selectlanguage{english}et al.
(2016), who used the SOMs method for forecasting system of surface
currents. More recently, Orfila et al. (2021) used SOMs to establish the
patterns and seasonal dynamics of the southern CS. These examples show
the versatility and capacity of the method as a useful and robust
technique for pattern recognition and feature extraction in variables
where non-linearity is important, as may be the case in oceanographic
processes. Further details of the SOMs method are in Liu \& Weisberg
(2011).

In this study, we determined the current patterns by applying SOMs over
the HYCOM 25-year climatology. The method uses a neighborhood function,
a unit search radius, and a linear initialization process. The training
algorithm employed a group series approach, carefully analyzing
parameters to ensure the lowest quantization and topological errors,
following best practices outlined by Meza-Padilla et al. (2019) and Liu
et al. (2006). Before the training process, each variable was spatially
and temporally normalized to prevent any single component from
dominating the map organization in cases where its magnitude is
disproportionately higher than that of the other components. This
normalization ensured that all variables contributed equally to the
SOMs, leading to a more balanced and accurate data representation. After
the training process, the components were denormalized and further
analyzed under the terms of each variable. The determination of each map
size (cluster) is a subjective and empirical process that depends on the
desired detail for the analysis (Liu, Weisberg, Lenes, et al., 2016;
Liu, Weisberg, Vignudelli, et al., 2016; Meza-Padilla et al., 2019;
Weisberg \& Liu, 2017; Zeng et al., 2015). After a series of sensitivity
tests, we choose the map sizes to obtain the minimum number without
losing essential pattern variation. The sensitivity tests were based on
the quantization error (QE), measuring how much detail is being learned
by the SOMs, and on the topological error (TE), measuring the properties
of the preserved space and the variation percentage of each pattern.
This empirical procedure depends intrinsically on the study (Polzlbauer,
2004). We determined the optimal number of patterns by quantifying the
associated QE and TE errors through various tests using different
cluster arrangements, including 2x2, 2x3, 3x3, 3x4, and 4x4. The results
showed that the QE decreases using the 3x3 cluster, and although the TE
increases when increasing the number of patterns, it remains an
acceptable and small value in terms of space preservation. As a result,
the spatial characterization was done for a cluster of nine patterns
(3x3 cluster). An additional recommendation when using SOMs to integrate
trajectories is to maximize the number of spatial patterns so that the
temporal variability given by BMUs, will correctly approximate the data
temporal variability. At some point, the method will detect that further
spatial patterns do not provide any additional information, e.g., in our
case with the 3x3 cluster, there is one pattern with 0\% frequency; this
means that eight spatial patterns are enough to extract the dominant
patterns and therefore additional patterns will not improve the spatial
or temporal representation of the data. We use the SOMs MATLAB Toolbox
developed by Vesanto \& Alhoniemi (2000) from the Laboratory of Computer
and Information at the Helsinki University of Technology
(\emph{Laboratory of Computer and Information Science, Adaptative and
Informatics Research Center} , 2015).

\textbf{2.2.3 Lagrangian experiments}

To identify transport routes and confluence zones in the study region,
we conducted several numerical experiments using a particle advection
model developed by the Ocean-Atmosphere Interaction working group at the
Institute of Atmospheric Sciences and Climate Change of UNAM. This model
has already been used to successfully model connectivity between coral
reefs in the southern GoM (Sanvicente-A\selectlanguage{ngerman}ñorve et al., 2018, 2019). The
Lagrangian model is implemented in MATLAB and operates offline with
archived ocean velocity data from HYCOM, integrating with a second-order
Runge-Kutta method. To simulate horizontal diffusion, we applied a
random walk scheme (Fabbroni, 2009; Lynch et al., 2015; Majda \& Kramer,
1999; Okubo \& Levin, 2001), determining a diffusion coefficient of 13,
by doing sensitivity tests with values in the range of 0 to 14
m\textsuperscript{2}s\textsuperscript{-1} (Döös et al., 2011; Döös \&
Jönsson, 2013; LaCasce \& Ohlmann, 2003; Lara-Hernández et al., 2019).
To calibrate the model, we used 21 GDP surface drifters released between
2017 and 2018 and optimized the diffusion coefficient to minimize the
daily distance between the drifters and the corresponding numerical
particles' positions after a 45-day advection. After 45 days, we
calculated the daily distance between the drifter and the synthetic
drifter positions. The optimal value of the diffusion coefficient
resulted from finding the minimum distance between the numerical
particles and the drifters in more than 50\% of the particles. After
calibrating the model, we conducted Lagrangian experiments by releasing
1,866,600 numerical particles (100 particles for each initial trajectory
position) during a climatological year, every third day, starting
January 1\textsuperscript{st}. The release polygon covered the Central
West Atlantic, between -45\textsuperscript{o}W and
-29\textsuperscript{o}W longitude and 0\textsuperscript{o} and
8\textsuperscript{o}N latitude, and consisted of a 17 x 9 node grid with
a spatial resolution of 1\textsuperscript{o}. The Lagrangian model was
integrated forward in time during a climatological year comprised of 365
days, starting when the particles were released. To complete a year of
Lagrangian simulations, the field of climatological velocities was
repeated consecutively. We used the HYCOM climatological daily data and
the spatial patterns obtained from the SOMs analysis to drive the
particle model with currents. The SOMs patterns were chronologically
ordered according to the Best Match Units (BMUs), thus identifying the
corresponding pattern for each day of the year. With this approach, we
will demonstrate that the patterns obtained from SOMs are comparable, in
Lagrangian terms, to the HYCOM data climatology. Besides forcing the
Lagrangian experiments with currents from the HyCOM climatology and the
SOMs patterns, we also forced them with these currents plus 1\% or 2\%
of wind from the CFSR climatological daily data. To analyze the
relationship between particle advection and the cLCS, we conducted a
case study on the east coast of the YP. For this area, we delimited an
irregular polygon to identify particles approaching the coastal region
and calculated the yearly and monthly accumulated sum of particles.

\textbf{3 Results and discussion}

\textbf{3.1 Hydrodynamic characterization}

The hydrodynamic characterization from the Equatorial Atlantic to the
GoM was done by characterizing the transport routes and barriers using
the cLCS and identifying the main current patterns using the SOMs. As
the cLCS denotes areas of maximum attraction (warm colors in Figure 2,
where red indicates the highest attraction strength of nearby water
parcels), they can be used to identify the likely displacement of the
released particles in the Lagrangian experiments, presented in section
3.2. From the cLCS results, we identified four regions of persistent
trajectories in the study area: (i) near the coast of Brazil, Suriname,
and the French Guiana coasts (associated with the Guiana Current (GC)
and the North Brazil Current (NBC), (ii) the Lesser Antilles, (iii) the
channel between Honduras and Jamaica, and (iv) the region from the
Yucatan Channel to the Florida Peninsula (associated with the Loop
Current (LC), the Florida Current (FC), and the Gulf Stream (GS)).
Besides being related to the intensification of currents, these regions
constitute paths that maximize the normal attraction of nearby
trajectories. This implies that any floating, suspended material or, as
in this case, numerical particles, are attracted by the cLCS and can
flow along them without crossing strongly-attracting cLCS, thus acting
as transport barriers (Duran et al., 2018; Gough et al., 2019; Gouveia
et al., 2021). These persistent trajectories organize and characterize
Lagrangian transport, where the cLCS are critical to interpreting the
Lagrangian expression of surface currents driving the transport of
drifting material.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Figure 2. Annual climatological Lagrangian Coherent Structures. The
colors indicate the strength of attraction, where red is the strongest,
and white indicates low persistent stirring and isolated regions behind
a transport barrier.

While cLCS allow us to characterize transport routes and barriers, SOMs
enable identifying main patterns of surface velocity and their temporal
occurrence. Using SOMs, we identified eight dominating patterns in a 3x3
array (Figure 3). Patterns 8 and 9 are slightly more frequent than the
others. They occur from August-December when the North Equatorial
Recirculation Region (NERR) and the NBC are well-defined and reach their
maximum intensity. The cLCS showed the most extensive spatial coverage
during these months in the NERR area. From January to April, patterns 7
and 4 show a significant decrease in the intensity of the NERR and the
NBC, while there is an increase in the CC and LC magnitude. These four
surface current patterns (8, 9, 7, and 4) occur 54.79\% of the time,
showing that the most intense surface currents in the study area are
present about half the time. Of the four remaining patterns, pattern 3
stands out, as it shows an intensification of the currents from the
Equatorial Atlantic to Florida (NERR, NBC, GC, CC, LC, FC), while
pattern 2 shows the most well-defined LC, followed by pattern 4. Also,
pattern 6 is relevant, as it thickens the NERR before reaching its
maximum intensity. BMUs give the temporal evolution of the patterns: the
NBC intensifies in the summer months to give rise to the formation and
separation of the NERR, reaching its maximum latitudinal extension in
September, between 10\textsuperscript{o}N and -5\textsuperscript{o}S. In
this same period, the currents within the CS intensify, mainly in July
and August, while the LC weakens in late August. Between January and
March, the NERR weakens, the CS current intensifies, and the LC is
re-established. Each pattern's occurrence percentage was larger than
10\% in all cases. Thus the SOM analysis provides a clear overview of
the current variability observed in the HYCOM climatology and its
evolution over a year.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Figure 3. The maps denote the identified spatial patterns by the
Self-Organized Maps (a), while the time series (b) show the Best Match
Units (BMUs), indicating the dates each pattern dominates. Each map,
placed according to its occurrence, indicates a pattern (according to
the number in parenthesis) and its respective percentage of spatial
variability. The colors indicate the current magnitude, and the arrows
the current direction. The BMUs are a key output of the SOMs analysis.
These units provide information on the temporal evolution of each
pattern the analysis identifies. Specifically, the BMUs indicate the
duration or periodicity with which each pattern occurs. The red line
indicates each pattern's period throughout the year.

\textbf{3.2 Lagrangian experiments}

\textbf{3.2.1 North Equatorial Atlantic without wind}

To understand the surface currents' Lagrangian transport, we used
surface current velocity data to integrate the trajectories of particles
released each third day and looked at the annual accumulated density of
particles (Figure 4). When released between June and November, the
distribution of particles shows that they tend to remain outside the CS
and move towards the northeast. Notably, during this period, particles
released in June and July remain in the NERR, and there is no
significant increase in particle density in the North Equatorial
Atlantic (NEA) areas. For particles released in September to November,
the particles that can enter the CS leave to the North Atlantic by the
northern arc of the Lesser Antilles. In contrast, particles released
between December and May enter the CS, and while some leave to the North
Atlantic, those remaining lead to the maximum particle density within
the CS. This maximum density is located in the Lesser Antilles and the
southern region of the Great Antilles.

The displacement and distribution of particles are associated with the
ocean currents' seasonality (Athi\selectlanguage{ngerman}é et al., 2020; De Souza \& Robinson,
2004; Holt \& Proctor, 2008) and, therefore, with the cLCS location
(Figure 2). Analyzing the particle distribution, we found that particles
take approximately 8 to 10 months to reach Florida from the Equatorial
Atlantic. We also found that particles reach the Yucatan Peninsula (YP)
and the GoM in about 6-7 months when released between October and
January (Figure 4). Between May and August, the particles are spatially
limited about 150 km offshore from Brazil to the YP, corresponding with
the months the cLCS intensifies (Figures S2 in Supplementary Information
and 4). Considering that cLCS have been shown to identify critical
oceanic kinematics aptly, the cross-cLCS transport is often limited, and
particle attraction causes flow along cLCS (Duran et al., 2018), our
findings confirm that the cLCS act as transport routes and hydrodynamic
barriers, limiting the movement of particles towards the coast. This
highlights the influence of the continental shelf on ocean dynamics,
where the transport is constrained not only by bathymetry but also by
the Earth's rotation, leading currents to move along isobaths and
inhibiting flow from crossing isobaths (vorticity conservation) (Brink,
2016).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 4. Lagrangian experiments results. The maps show the annual
accumulated particle density using the HYCOM climatology, without wind,
and according to the release month. The annual accumulated particle
density refers to the number of steps the particles take during a year.
The black line is the coastline, and the gray line is the 200 m isobath.

The Lagrangian experiments were also performed using the spatial
patterns identified by the SOMs analysis with the temporal evolution
given by the BMUs (Figure 3) as the surface current velocity. The
results (Figure 5) show that the SOMs' pathways and distribution of
particles are similar to those from the HyCOM climatology. A difference
between both datasets is that the velocity from the spatial SOMs remains
stationary according to the BMUs time series (Figure 3). However, the
differences in the distribution of particles are not significant, as we
will describe in section 3.2.3. The SOMs Lagrangian results show that
when particles are released between May and September, their
accumulation in the CS is minimal (\textless{}300 particles). Starting
in June, the NERR intensifies, the NBC moves eastward (Condie, 1991),
and the cLCS intensifies at the coasts of Brazil, Suriname, the French
Guiana, and the Lesser Antilles region.

On the other hand, the particles released in October-December show the
effect of the NERR intensification and of the cLCS as transport
barriers, which cause the particles to drift northward along the NEC
toward the Sargasso Sea, and promote a large accumulation of particles
from the Equatorial Atlantic to the north of the Dominican Republic.
This could be associated with NBC rings that stall and decay east of the
Lesser Antilles (between 14\selectlanguage{ngerman}°N and 18°N) during these months, as
described by Chérubin \& Richardson (2007), and which could displace the
particles to the northern part of the eastern CS and merging with inflow
from the NEC. Between January and April, the NEA, the eastern CS, the
Greater Antilles, and the Bahamas show the largest accumulation of
particles. It should be noted that during this period, the cLCS in the
Lesser Antilles and the Yucatan Channel are intensified, acting as
transport channels that carry particles into the CS and the GoM,
respectively.

Regardless of using the HYCOM climatology or the SOMs-derived velocities
used in the Lagrangian experiments, the particle trajectories show paths
following the strongest currents and the spatial distribution of cLCS.
Those paths create specific accumulation regions, particularly the NEA
and the Lesser and Greater Antilles. However, these results do not
consider wind as an additional forcing (e.g., windage), despite being
one of the most critical factors determining the dynamics at the ocean
surface, as we will analyze in the following experiments.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

Figure
5. Lagrangian experiments results. The maps show the annual accumulated
particle density using SOMs, without wind, and according to the release
pattern. The color indicates the accumulated particle density, and the
gray line is the 200 m isobath.

\textbf{3.2.2 North Equatorial Atlantic with wind}

Previous studies have shown the importance of wind over surface currents
(Allshouse et al., 2017; Clarke \& Van Gorder, 2018) related to the
transport of particles (Johns et al., 2020; Kwon et al., 2019; Laxague
et al., 2018; Lodise et al., 2019), we proceeded to include wind in the
Lagrangian experiments. Lumpkin \& Pazos (2007) found that near-surface
drifters have a windage factor effect of \textasciitilde{}1\% in the
wind direction, while drifters at 15 m depth have a windage effect
factor one order of magnitude smaller. Later, Lumpkin et al. (2013)
showed that this difference could be attributed to the combination of
the surface wind drag, the vertical shear of wind-driven currents above
15 m depth, and the wave-induced Stokes drift, which was shown to be
important by Clarke \& Van Gorder (2018). Here we included the direct
wind momentum transfer to floating material as windage (Putman et al.,
2020) by adding 1\% of the wind. To incorporate the effect of Stokes
drift, as Clarke \& Van Gorder (2018) suggested from analyzing large
times series of observations, we included an additional 1\% of the wind
to the current velocity. As such, we study wind's influence at the
surface by adding 1\% of the wind and, in other experiments, by adding
2\% of the wind. The latter may represent the effect of strong windage
or the joint effect of windage and Stokes drift. Similar approximations
have been applied by Putman et al. (2020), Johns et al. (2020), and Kwon
et al. (2019).

Our results show that 1\% windage is enough for the particles to remain
in the CC and reach the GoM independently of the particle release month
(Figure 6a). The 1\% windage allows the particles to either approach the
strong cLCS or to cross them so that they are advected towards the CS
and follow their path into the GoM. The largest accumulation of
particles near the northern CS and YP coast occurs for particles
released between October and March, when the particles also reach the
Florida coast, including the US Atlantic coast. The results suggest that
the wind is a key factor for accumulating particles in coastal regions
and that cLCS act as transport paths that cause particles to travel
greater distances. Important to notice is that the particles released
from September to January start entering the region of Central America,
particularly the coastal zone of Costa Rica, Panama, and Colombia.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

Figure 6. Lagrangian experiments results. According to the release
month, the maps show the annual accumulated particle density using the
HYCOM climatology, (a) with 1\% and (b) 2\% windage. The color indicates
the accumulated particle density, and the gray line is the 200 m
isobath.

We included a 2\% windage to the Lagrangian experiments to approximate
either strong windage or a combination of windage and Stokes drift
(Clarke \& Van Gorder, 2018). The results are shown in Figure 6b. We
found that particles remain near the coastal zone from Brazil to the
Lesser Antilles, covering the CS and reaching the GoM regardless of the
release month. Under 1\% windage, a high concentration of particles
follows the LC between October to April. Still, under 2\% windage, this
stops occurring as the particles are advected further south before
entering the LC. Nevertheless, a large concentration of particles
reaches the northern coast of Mexico and Texas during March and April.
Particles released between June and August with 2\% windage remain in
the NERR and leave the domain eastward, while those released from
September to November enter the CS through the Lesser Antilles southern
area, reaching the coasts of Nicaragua and the coasts of Central
America. The particle's distribution and trajectories are associated
with seasonal atmospheric variability. The periods of maximum particle
accumulation coincide with the latitudinal displacement of the ITCZ
(Aliaga Nestares et al., 2022; Haffke et al., 2016; Henke et al., 2012;
Skliris et al., 2022), which gives rise to significant wind variability
in the study area. When the ITCZ is in its southernmost location
(\textasciitilde{}3\textsuperscript{o} N) from February to March, the
wind intensifies in the Caribbean area, causing the particles to move
towards the southern region of the Caribbean basin and on the NBC
between October and January. This period corresponds to a weakening of
the cCLS in the Caribbean (Figure S2 in Supplementary Information). On
the other hand, during the summer months (June to September), the
windage intensity decreases in the Caribbean due to a northern
displacement of the ITCZ (\textasciitilde{}11\textsuperscript{o} N),
allowing the particles to advect towards the center and north of the
Caribbean basin. This particle's distribution is expected due to the
change of direction of the trade winds (Orfila et al., 2021). During
these months, the cLCS intensified in the Yucatan Channel, Honduras,
Panama, Colombia, and Venezuela, as well as in the Lesser Antilles
region (Figure S2 in Supplementary Information). It should be noted that
with 2\% wind, in addition to the particles that enter the Caribbean,
the highest particle density is found in the NERR region.

When adding 1\% or 2\% windage in the Lagrangian experiments, we
obtained similar results whether the currents were from the HYCOM
climatology (Figure 6) or the SOMs patterns (Figure 7). These results
indicate that using the current patterns obtained with the SOMs are an
adequate approximation to the currents' climatology, thus validating
their use to calculate particle displacement, as suggested in
Meza-Padilla et al. (2021). Comparing the results using 1\% and 2\%
wind, we found that particles move from the Equatorial Atlantic to the
CS. Some particles enter the GoM and exit through the Straits of
Florida. It is observed that with 1\% windage, the easterly winds
displace the particles further south so that more particles enter the
CS, covering the CS basin with the largest accumulation of particles
near the Greater Antilles coast (Caribbean northern region). The 1\%
windage also allows particles to reach areas with intense cLCS, such as
the Yucatan Current, where particles follow the LC and exit through the
Florida Strait. When including 2\% windage, particles are distributed
further into the southern Caribbean region, where the cLCS lead to
previously unreached areas, such as the Central America region. Also,
including 2\% windage results in stranded particles at the coast or
allows them to leave areas with strong cLCS. This occurs in the western
Caribbean, where particles are stranded before entering the Yucatan
Current and into the LC, and those entering the LC are displaced into
the western GoM.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

Figure 7. Lagrangian experiments results. The maps show the annual
accumulated particle density using SOMs patterns, with (a) 1\% and (b)
2\% windage added to the Lagrangian experiments. The color indicates the
accumulated particle density, and the gray line denotes the 200 m
isobath.

\textbf{3.2.3 Particle confluence in the Caribbean Sea}

To quantify particle density within the CS, we strategically defined ten
irregular polygons, hereafter called zones (Figure 8). We found that the
spatial distribution of particle density over one year within these
polygons is similar when using the HYCOM climatology or SOMs patterns
(Table 1; Figure 8). We also found that the areas can be grouped
according to the wind effect on particle clustering, dividing the
Caribbean into three regions:

\begin{itemize}
\tightlist
\item
  Region I: Comprises zone 7 (Dominican Republic-Puerto Rico Channel)
  and zone 8 (Northern Lesser Antilles). This region has the most
  significant particle density in the absence of wind.
\item
  Region II: Comprises zone 1 (Yucatan Channel), zone 4
  (Honduras-Jamaica Central Channel), zone 5 (Honduras-Jamaica East
  Channel), and zone 6 (Jamaica-Haiti Channel). This region has the
  largest confluence when including 1\% windage.
\item
  Region III: Comprises zone 2 (Quintana Roo, Mexico), zone 3
  (Honduras-Jamaica West Channel), zone 9 (Southern Lesser Antilles),
  and zone 10 (Central America). This region has the largest particle
  confluence with a 2\% windage.
\end{itemize}

Table 1 shows a breakdown of the results by zone. We identified three
main routes for particles to enter the CS: (i) along the edge of the
continental shelf by the GC, (ii) through the NBC separation and
intensification, and (iii) through the NERR and NEC dynamic interaction.
Those same inflow areas were reported by Johns et al. (2014), Goni \&
Johns (2001), and Condie (1991). The resulting percentages suggest that
less than 10\% of the total particles moving from the Equatorial
Atlantic to the CS reach the Caribbean coastal regions, even with 2\%
windage (Table 1). The results suggest that particles enter the
Caribbean basin regardless of the windage; however, the density of
particles increases or decreases in different regions according to the
windage. We find that the effect of wind is crucial for particles to
cross transport barriers to reach the coastal zone in the western
Caribbean (zones 10, 3, and 2). Further discussion focusing on the
Mexican Caribbean (zone 2) can be found in section 3.2.3.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

Figure 8. Zones comprising different regions according to the effect of
wind on particle clustering. Red indicates zones with the largest
particle confluence without the influence of wind (Region I). Similarly,
green denotes the zones with the largest confluence with 1\% wind
(Region II) and blue with 2\% wind (Region III). Time series represent
particle density (number of particles per unit area) of the three
Lagrangian experiments derived from HYCOM and SOM patterns as a function
of release month (lower abscissa, HYCOM) and SOM pattern (upper
abscissa, SOMs). The left ordinate axis is particle density for HYCOM,
and the right is particle density for SOMs. The variation in the y-axes
is attributed to the difference in the temporal occurrence velocity
fields used in the Lagrangian experiments. The current velocity fields
obtained from HYCOM climatology have a daily occurrence, whereas the
velocity fields generated by SOMs are semi-stationary, with a pattern's
duration determined by the BMUs. The annual accumulated particle
density, regarding the released month or pattern, refers to the number
of steps taken by the particles within each area during a year. Acronyms
indicate (Z) zone identifier number, (*) HYCOM climatology, and (o) SOMs
Patterns.

Table 1. Lagrangian experiment results for each zone within the
Caribbean basin. Colors indicate the area according to the wind effect
(Figure 8); \textbf{\%} is the particle percentage that arrives at each
zone based on the total number of particles released, \textbf{H} YCOM
climatology, and SOMs \textbf{P} atterns. Percentage values
in\textbf{bold} indicate the zones with the largest confluence according
to windage.\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\textbf{Zone}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\textbf{Location}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\textbf{Only currents}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\textbf{Only currents}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\textbf{Currents} \textbf{+ 1\% windage}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\textbf{Currents} \textbf{+ 1\% windage}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\textbf{Currents} \textbf{+ 2\% windage}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\textbf{Currents} \textbf{+ 2\% windage}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{\%}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{\%}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{\%}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{\%}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{\%}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{\%}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{H}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{P}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{H}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{P}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{H}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{P}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Yucatan Channel\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{0.08}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{0.11}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.01\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Quintana Roo\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.42\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.39\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{1.23}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{1.66}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
3\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
H-J West Channel\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.08\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.12\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{0.37}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{0.93}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
4\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
H-J Central Channel\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.09\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.09\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{0.42}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{0.67}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.35\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.49\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
H-J East Channel\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.24\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.21\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{0.54}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{0.55}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.07\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.04\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
6\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
J-Haiti Channel\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.35\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.36\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{0.57}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{0.50}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.01\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
7\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
DR-PR Channel\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{0.24}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{0.28}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.04\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.03\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.00\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
8\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
N Lesser Antilles\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{1.81}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{1.75}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.71\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.58\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.12\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.11\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
9\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
S Lesser Antilles\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.63\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.30\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
3.64\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2.14\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{5.36}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{4.56}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
10\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Panama\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.11\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{1.87}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{0.80}\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Delving into the analysis for each zone, we observed certain
characteristics in the particles' spatial distribution associated with
the forcings and main currents as defined by cLCS (Table 1; Figure S2 in
Supplementary Information and 10):

\begin{itemize}
\tightlist
\item
  Zone 1: The largest particle density is found with 1\% windage. These
  particles follow the cLCS formed by LC to enter the GoM.
\item
  Zone 2: The particle's density increases by three orders of magnitude
  with 1\% windage compared to the particle density by only considering
  currents. However, maximum particle confluence occurs with 2\%
  windage.
\item
  Zone 3: The maximum particle density occurs with 2\% windage as the
  particles are advected to this area, crossing barriers imposed by the
  cCLS from the currents.
\item
  Zone 4: The maximum particle confluence occurs with 1\% windage,
  although the particle density is in the same order of magnitude
  without windage. In comparison, with 2\% windage, the particles
  cluster west of the cLCS (zone 3) and follow their northward
  trajectory over the continental platform (Sheng \& Tang, 2004), as
  currents follow the orientation of the isobaths over the continental
  shelf (Brink, 2016; Lago et al., 2019)
\item
  Zone 5: The maximum particle density occurs with 1\% windage, as
  particles are displaced south in the eastern CS, leading the particles
  in this area and zone 4. With increased windage (2\%), the particles
  are advected further south, increasing the particle's density in zone
  3.
\item
  Zone 6: The density of particles is larger with 1\% windage, followed
  by the case without windage. When considering 2\% windage, the
  particle density diminished considerably, as the particles coming from
  the east are advected further south.
\item
  Zones 7 and 8: The highest density of particles occurs in the absence
  of windage, showing these areas as being located in the main transport
  route by currents and without winds. This result denotes the wind's
  relevance for advecting the particles into the CS.
\item
  Zone 9: For particles to arrive into this area, windage is essential
  as it advects particles to the south, creating a transport route
  towards the coast of Venezuela.
\item
  Zone 10: The particles only reach this area when considering a 2\%
  windage, as a strong windage allows crossing into an isolated region
  delimited by the cyclonic gyre located off the coast of Central
  America (Andrade \& Barton, 2000).
\end{itemize}

The most important result of these experiments is the particles'
geographical distribution according to the effect of wind. Zones 1, 4,
5, and 6 are dominated by windage (1\% windage), while zones 2, 3, 10,
and 9 are dominated by windage and Stokes drift (2\% of wind). The
distribution of particles can be explained by the persistent presence of
the cLCS identifying transport barriers that prevent particles from
reaching the coast (Figure 2 and Figure 9). For the particles to cross
these barriers, it is necessary for the winds to weaken the cLCS.

The dynamics of surface transport are partially controlled by the inflow
into the CS, which according to Johns et al. (2002), can be divided into
three main groups of passages: the Greater Antilles (zones 6 and 7), the
Leeward Islands (zone 8), and the Windward Islands passages (zone 9),
which coincide with the main transport routes identified by the cLCS.
The seasonal cycle of the mean currents inflow distribution in the
passages connecting the Atlantic Ocean with the CS has an annual and
semiannual variability with a maximum in late spring and summer and a
minimum in fall, continuing to the Yucatan Channel (Johns et al., 2002).
Nevertheless, the NBC is the single largest inflow source (40\%) to the
Caribbean (Ch\selectlanguage{ngerman}érubin et al., 2005), which displays a strong mesoscale
variability in inter-island passage transports. Chérubin et al. (2005)
also found that the current's maximum velocity position is in phase with
the transport variations and independently of its extension. The
Lagrangian experiments show that identifying transport pathways and
barriers can explain particle displacement distribution, where the wind
is a crucial parameter explaining particle intrusion into the Caribbean.
Once in the CS, the three westward jets described by Chérubin \&
Richardson (2007) flow with their speeds decreasing with increasing
latitude. These jets and their relation to our results are described
below.

\begin{enumerate}
\tightlist
\item
  The southern and fastest jet is located at \textasciitilde{}11.5°N,
  coinciding with the passage of particles at zone 9 with 2\% windage.
  This southern jet is characterized by southern cyclones, which move
  northwestward as the anticyclonic CC circulation intensifies.
\item
  The center and second fastest jet, at \textasciitilde{}14°N, coincides
  with the particle's passage through zone 8 without wind or with 1\%
  windage. This center jet flows faster between August and December and
  is seasonally intensified by the NBC; this coincides with the larger
  particle density found in the zone during this period when considering
  low wind influence (1\% windage or less). It is important to note that
  the intensification of the center jet is due to an increase in the
  mean kinetic energy (negative potential vorticity anomaly) that
  increases the number of cyclones during the fall. This is observed in
  the particle's trajectory once they enter the CS.
\item
  The northern and slowest jet is found at \textasciitilde{}16.8°N,
  corresponding to zones 6 and 7. These zones show confluence only
  without windage (zone 7) and 1\% windage (zone 6). This area is
  dominated by mesoscale anticyclones, sustaining westward currents
  south of Puerto Rico and Hispañola (Baums et al., 2006), so particles
  remain in this area with low wind conditions and are displaced further
  south only with 2\% windage. Therefore, the wind effect in this region
  is decisive in the particle's trajectory.
\end{enumerate}

Besides the water inflow and current jets, the Caribbean basin is
influenced by atmospheric phenomena such as the easterly waves,
anticyclonic cold fronts (also known as Central American Cold Surges),
Caribbean Low-Level Jet (CLLJ), the trade winds, and the ITCZ. The
easterly waves are wave-type disturbances in the tropical easterly
current. These waves are associated with the hurricane season (summer),
characterized by a cyclonic circulation that deforms the pressure field,
causing the wind direction to change from northeast to the east
(Caviedes, 1991). As such, easterly waves could promote particle
displacement from the Equatorial Atlantic towards the CS by the windage
effect. The arrival of anticyclonic cold fronts typically occurs between
September and April and can extend as far south as
10\textsuperscript{o}N latitude (DiMego et al., 1976). These cold fronts
are associated with a significant increase in wind intensity, cloud
cover, atmospheric pressure, wave height, and a decrease in temperature
(Appendini et al., 2014, 2018; Cao et al., 2020; Ortiz-Royero et al.,
2013). Considering the strong northerly wind component during cold
fronts, they could influence the particle transport by displacing them
towards the south, impending them to reach areas such as the Yucatan
Peninsula. The Caribbean Low-Level Jet (CLLJ) is a near-surface branch
of the easterlies that intensifies seasonally and has a nearly east-west
direction (García-Martínez \& Bollasina, 2020; Hidalgo et al., 2015).
The Caribbean Counter Current (CCC) is controlled by the CLLJ, which
during relatively mild wind conditions, promotes the intensification of
the Panama-Colombia Gyre (Orfila et al., 2021). While the CLLJ can
promote windage displacing particles towards the west, during its
relaxation phase, the particle displacement into the CCC and the
Panama-Colombia Gyre could be expected. Finally, the trade winds'
seasonality and the ITCZ's consequent latitudinal displacement (Aliaga
Nestares et al., 2022; Haffke et al., 2016; Henke et al., 2012; Skliris
et al., 2022) likely influence the currents and particularly the windage
effect on particle transport.

\textbf{3.2.4 Case study: particle confluence near the Yucatan
Peninsula}

This section analyzes connectivity with the nearshore area in the
Mexican Caribbean defined by zone 2. Before reaching zone 2, the
released particles are strongly influenced by the persistent cLCS in
zone 4, off the coast of Honduras and Nicaragua (Figure 9). These
prominent cLCS tend to attract trajectories as seen by most particle
density maxima within the CS interior, yet effectively block onshore
transport keeping zone 3 isolated as seen through persistent particle
density minima (Figures 5 and 6). An exception occurs with 2\% windage
when particles are released in March and September (Figure 6b). SOMs
with 1\% and 2\% windage have more trajectories reaching the coast but
also have several instances where the cLCS redirect transport
northeastward (Figure 7). Thus, the cLCS in zone 4 effectively attracts
particles and redirects them northward. Further north, next to the coast
of Mexico (north of about 18.5N), the Yucatan Current creates a strong
transport barrier that persists year-round along the Mexican coast
between \textasciitilde{}18\textsuperscript{o}N to
21\textsuperscript{o}N (Figure 9). However, the maximum attraction has
variations in intensity and spatial coverage. During May and December,
the barrier may be less protective than in other months, and September
is the only month in which the cLCS from zone 2 connect with the cLCS
from zone 4, suggesting a direct path towards the GoM.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

Figure 9. Climatological Lagrangian Coherent Structures (cLCS) at the
western Caribbean Sea. Colors indicate the strength of attraction, with
red indicating the strongest attraction of nearby parcels; white
indicates isolated regions or low stirring activity. Panel (a) are the
annual and (b) the monthly cLCS for the Caribbean basin and the Yucatan
Peninsula region, respectively.

The persistence of strong cLCS throughout the year efficiently prevents
particles from reaching zone 2 without the influence of wind (Figure 8).
However, the isolation of region 2 changes with the wind: some particles
enter zone 2 with 1\% windage, and considerably more enter zone 2 with
2\% windage (Figure 8). The persistent Yucatan Current transport barrier
is debilitated when cLCS are computed with currents plus 1\% windage,
and it is completely erased when cLCS are computed with currents plus
2\% windage (Figure 10). Also notable is that with 2\% windage, the zone
4 cLCS tend to converge while directing towards the Mexican coast from
about 84\textsuperscript{o}W to 86\textsuperscript{o}W in the vicinity
of 18\textsuperscript{o}N, a feature absent in the cLCS computed from
only currents (Figure 10, cf. left and right panels). Independent
experiments using an instantaneous velocity from HYCOM by Lara-Hern\selectlanguage{ngerman}ández
et al. (2023) show that with 2\% windage, trajectories reaching the
Mexican Caribbean coast move along these strongly attracting cLCS while
approaching the coast and then spread along the coastline (Text S2 and
figure S6). This constitutes an additional independent confirmation that
cLCS identifies and extracts the predominant transport patterns from the
instantaneous velocity.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}

Figure 10. cLCS for July with only currents (left panel), currents plus
1\% windage (middle panel), and currents plus 2\% windage (right panel).

To characterize particle distribution in zone 2, we considered the
seasonal variability of both surface currents and cLCS. Therefore, we
divided the results according to the different wind-forcing conditions.

With 1\% windage, particles will reach zone 2 using the transport route
defined by the cCLS in zone 4, which can be considered the CC
continuance ending on the YP eastern coast. The cLCS continues towards
the Yucatan Channel, giving rise to the LC. This suggests that the cLCS
at zone 4 are a pathway for offshore particles (further from the
continental shelf) to move towards the Yucatan Channel. Considering the
cLCS seasonal variability, the particles are transported over the
regions of maximum attraction located in zones 4 and 5 and up to zone 1.
Regardless of the release month, it takes approximately 5 to 8 months
for particles to reach zone 2 (Figure 11). The highest particle density
for zone 2 occurs when particles are released between September and
December, reaching the YP the following year and starting to cluster in
April.

With 2\% windage, particles are directed towards zone 2 by the cLCS in
zone 4, moving over the continental shelf and into the coastal regions
of Honduras and Belize before clustering in zone 2. Regardless of the
release month, the particle's arrival to zone 2 is between 4 and 8
months (Figure 11). In this case, there is considerable clustering
independent of the release month. Nevertheless, when particles are
released between March and June, there are a high number of months
(\textgreater{} 5) with a very high confluence in zone 2. Particles
released between these months arrive at the YP as soon as July, showing
the highest density starting in September.

Notably, the arrival and distribution of particles in zone 2, observed
in both HYCOM climatology and SOMs patterns (Figure 11), and the
temporal variability of particle density are closely linked to seasonal
changes in surface currents. Coastal geostrophic currents act as
transport barriers, hindering transport perpendicular to the coast;
therefore, the impact of wind is significant. When the wind blows
perpendicular to the coast, it adds a cross-shelf component in the upper
centimeters of the ocean due to windage or Stokes drift, in contrast
with geostrophic currents that flow along isobaths (Brink, 2016). Thus
wind allows particles to move perpendicular to the coast and cross the
transport barriers caused by along-slope currents. Perhaps more
accurately, the cross-shelf component due to wind erases the transport
barriers imposed by the coastal Yucatan Current while forcing
trajectories towards the coast (Figure 10).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image11/image11}

\end{center}
\end{figure}

Figure 11. Accumulated particle density, according to the release month
(HYCOM) or pattern (SOMs) (y-axis; Equatorial Atlantic) and the arrival
month (HYCOM) or pattern (SOMs) in zone 2 (x-axis; east coast of the
Yucatan Peninsula). The two panels on the left side are the monthly
accumulated particle density with the HYCOM climatology, and the two
panels on the right side are the accumulated particle density obtained
from the SOMs patterns. The listed months in the SOMs panels correspond
to the months given by the BMUs corresponding to the release pattern.
For each dataset, the first panel is the experiment with 1\% windage,
followed by 2\% windage. The color of the bullets indicates the density
of particles accumulated in zone 2.

As shown, the confluence of particles in zone 2 depends on currents and
the effect of wind. As the wind conditions depend on atmospheric
phenomena with a well-defined seasonal variability in the region, we
expect an influence on particle transport by the passage of easterly
waves, cold fronts, and the ITCZ latitudinal migration, as described
previously. In general, this zone's regional atmospheric dynamics
dominate zonal westward winds, with maximum intensities during February
and July due to the strengthening of the North Atlantic easterlies,
intensifying the CLLJ, and weakening during May and October.

\textbf{5 Conclusions}

This work identified the transport routes from the Equatorial Atlantic
to the YP using Lagrangian experiments correlated to the cLCS. We used
climatological currents from HYCOM and the most recurrent surface
current patterns obtained from the climatological SOMs analysis for
those experiments. The cLCS were calculated for the entire domain, and
the transport barriers were determined, emphasizing the CS to interpret
the distribution of particles in that area. We delimited ten strategic
areas based on transport barriers, for which the area adjacent to the YP
east coast was studied in detail.

We found that the SOMs reproduce the characteristic patterns of surface
currents climate variability while the cLCS identified recurrent
trajectories and persistent transport barriers, as confirmed with
Lagrangian particle release experiments. The cLCS show a yearly
persistence indicating mesoscale patterns in surface transport and a
surface transport barrier isolating the continental shelf from
circulation beyond the shelf break. Integrating these results with the
Lagrangian experiments, we found that the cLCS determine particle
trajectories since they function as transport pathways and transport
barriers. When the cLCS act as transport barriers, particles are
restrained from reaching specific areas unless there is windage to
debilitate or completely erase the cLCS transport barriers due to
currents.

Our results show that wind is a needed condition for particle confluence
within different regions of the CS, either representative of the effect
of windage or Stokes drift. For the regions of the Yucatan Channel,
Honduras-Jamaica Central Channel, Honduras-Jamaica East Channel, and
Jamaica-Haiti Channel, the 1\% windage is necessary, while the 2\%
windage is needed for the particles to reach Quintana Roo, Mexico,
Honduras-Jamaica West Channel, Southern Lesser Antilles, and Central
America. From the Equatorial Atlantic region, the particles will take
approximately four to eight months to reach the YP and will be
influenced by the atmosphere phenomena and the space-time cLCS
variability, being the Honduras-Jamaica West Channel, the main passage
of particles transported towards the peninsula. The particles released
during the autumn-winter months with a 1\% windage are those that reach
Quintana Roo, Mexico coasts in the spring of the following year, while
the particles released in the spring months with a 2\% windage are those
that reach this zone in the summer months of the same year. The higher
arrival of sargassum to the Mexican Caribbean in the summer months
reaffirms the importance of the 2\% windage for particles to arrive in
this area.

This spatio-temporal particle distribution is similar whether using the
HYCOM climatological data or the current patterns obtained with the
SOMs. In addition to the hydrodynamics that determines the trajectory of
particulate matter in the ocean, another important result is the
representation of ocean climate by SOMs. The seasonality in the surface
circulation is clearly illustrated by the BMUs distribution. From a
numerical model perspective, the SOMs approach, together with the cLCS
and its interaction with the large-scale dynamical atmospheric
circulation features, can be applied to study and improve the
representation of physical processes and approximate particulate matter
transport and distribution on the sea surface. Atmospheric phenomena
such as the easterly waves, anticyclonic cold fronts, Caribbean
Low-Level Jet, the trade winds, and the ITCZ influence particle
distribution, confluence, and aggregation. A more detailed study is
required to determine the influence on windage of each of these
phenomena.

Forecasting particle matter trajectories on the ocean still requires
further studies to reproduce the transport accurately, incorporating
other processes, such as degradation, growth, mortality, etc..
Nevertheless, this study is an advance in implementing different
analysis methods of the interaction between different processes that
determine ocean surface dynamics and their effect on particle transport.

\textbf{Acknowledgments}

This study was funded by UNAM-DGAPA PAPIIT Projects TA100420 and
IA101122 and CONACYT Project 320563. Funding for the development of
HyCOM has been provided by the National Ocean Partnership Program and
the Office of Naval Research. Data assimilative products using HyCOM are
funded by the US Navy. We also thank the Ocean-Atmosphere Interaction
group of the Institute of Atmospheric Sciences and Climate Change of
UNAM for the particle transport model provided, particularly Dr. J.
Zavala-Hidalgo, as well as G.U. Mart\selectlanguage{ngerman}ín-Ruiz and A. Ramírez-Manguilar for
IT support. Computer time was made available by the DoD High-Performance
Computing Modernization Program. RD would like to thank Julio
Lara-Hernández for the trajectory data used in Text S2. This work was
conducted under the Advanced Offshore Research Portfolio, FWP Number
1022409 at National Energy Technology Laboratory, U.S. Dept. of Energy.

\textbf{Disclaimer}

This project was funded by the United States Department of Energy,
National Energy Technology Laboratory, in part, through a site support
contract. Neither the United States Government nor any agency thereof,
nor any of their employees, nor the support contractor, nor any of their
employees, makes any warranty, express or implied, or assumes any legal
liability or responsibility for the accuracy, completeness, or
usefulness of any information, apparatus, product, or process disclosed,
or represents that its use would not infringe privately owned rights.
Reference herein to any specific commercial product, process, or service
by trade name, trademark, manufacturer, or otherwise does not
necessarily constitute or imply its endorsement, recommendation, or
favoring by the United States Government or any agency thereof. The
views and opinions of authors expressed herein do not necessarily state
or reflect those of the United States Government or any agency thereof.

\textbf{Open Research}

Data from HyCOM and CFSR were used for this study (CDAM, 2015) and are
publicly available at
https://www.hycom.org/dataserver/gofs-3pt1/analysis,
https://www.hycom.org/dataserver/gofs-3pt1/reanalysis, and
https://www.hycom.org/dataserver/ncep-cfsr. cLCS computation code (Duran
et el. 2019) is freely available at
https://bitbucket.org/rodu/clcss/src. The code to compute SOMs (Vatanen
et al. 2015) is freely available at
http://research.ics.aalto.fi/software/somtoolbox/.

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\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image12/image12}

\end{center}
\end{figure}

\emph{Journal of Geophysical Research}

Supporting Information for

\textbf{Lagrangian characterization of surface transport from the
Equatorial Atlantic to the Caribbean Sea using climatological Lagrangian
Coherent Structures and Self-Organizing Maps}

\selectlanguage{ngerman}\section*{\texorpdfstring{Ma. Eugenia Allende-Arandía\textsuperscript{1},
Rodrigo Duran\textsuperscript{2}, Laura
Sanvicente-Añorve\textsuperscript{3}, Christian M.
Appendini\textsuperscript{1,*}}{Ma. Eugenia Allende-Arandía1, Rodrigo Duran2, Laura Sanvicente-Añorve3, Christian M. Appendini1,*}}

{\label{ma.-eugenia-allende-aranduxeda1-rodrigo-duran2-laura-sanvicente-auxf1orve3-christian-m.-appendini1}}

\textsuperscript{1} Laboratorio de Ingeniería y Procesos Costeros,
Instituto de Ingeniería, Universidad Nacional Autónoma de México, Puerto
de abrigo s/n, Sisal, Yucatán 97356, México

\textsuperscript{2} National Energy Technology Laboratory, United States
Department of Energy, Albany OR, United States. Theiss Research, La
Jolla, CA, United States

\textsuperscript{3} Instituto de Ciencias del Mar y Limnología,
Universidad Nacional Autónoma de México, Ciudad de México, C.P. 04510.

\textbf{Contents of this file}

Introduction

Figures S1 to S2

Text S1 to S2

Figures S4 to S6

Table S1



\textbf{Additional Supporting Information}

\textbf{Captions for Figures S1 to S6}

Figure S1. Surface currents monthly average from the HYCOM climatology.
The colors indicate the current's magnitude, and the arrows' the current
direction.

Figure S2. Monthly climatological Lagrangian Coherent Structures. The
colors indicate the strength of attraction, where red is the strongest,
and white indicates low persistent stirring and isolated regions behind
a transport barrier.

Figure S3. Correlation matrix of the magnitude between each of the 8
SOMs spatial patterns from the HYCOM climatology (HC) and the 8 SOMs
spatial patterns from the HYCOM instantaneous time series (HI). Only
significant correlations are shown as different from zero.

Figure S4. Correlation matrix of the vector angle from each of the 8
SOMs spatial patterns from the HYCOM climatology (HC) and the 8 SOMs
spatial patterns from the HYCOM instantaneous time series (HI). Only
significant correlations are shown as different from zero.

Figure S5. Top panel is the BMUs for the climatological velocity (red
line), repeated each year of the time series for comparison, and the
BMUs for the instantaneous velocity (blue line) over 1994--2018. The
middle panel is a histogram of the difference between the two BMUs in
the top panel. The bottom panel is each year's sum of differences other
than zero, the sum of the histogram in the second panel; the green line
is the 1994--2018 average.

Figure S6. The color contours are the density of trajectories points
that were initiated along the coastline of the Mexican Caribbean and
integrated back in time to find their provenance using HYCOM Global
instantaneous velocity of August 2018. Only the most attracting August
cLCS (black lines) are plotted (i.e. when their attraction strength is
above 1.2).

\textbf{Captions for Table S1}

Table S1. Correspondence between the HYCOM climatology (HC) SOMs spatial
patterns and the HYCOM instantaneous (HI) SOMs spatial patterns based on
the highest correlation between the directions (angle) of each spatial
pattern with another (see Figure S4).

\textbf{Introduction}

The text, figures, and table in this file complement the information in
the manuscript by presenting additional figures and providing
information on the HYCOM climatology, in particular the match between
climatology and instantaneous SOM patterns (Text S1), and the
correspondence of cLCS with trajectories from an instantaneous velocity
near the Yucatan Peninsula (Text S2).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image13/image13}

\end{center}
\end{figure}

\textbf{Figure S1.} Surface currents monthly average from the HYCOM
climatology. The colors indicate the current's magnitude, and the
arrows' indicate the current direction.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image14/image14}

\end{center}
\end{figure}

\textbf{Figure S2.} Monthly climatological Lagrangian Coherent
Structures. The colors indicate the strength of attraction, where red is
the strongest, and white indicates low persistent stirring and isolated
regions behind a transport barrier.

\textbf{Text S1.}

The spatial SOMs of the 1994--2018 time series of sea-surface velocity
(SSV) were computed from the HYCOM + NCODA GOFS 3.1 reanalysis and
analysis (described in the main document). The resulting spatial
patterns from this HYCOM instantaneous (HI) SSV time series were
compared to the spatial patterns from the HYCOM 1994--2018 climatology
(HC) by correlating both the SSV angle and the SSV magnitude at each
grid cell. The magnitude correlation was always above 0.7 (Figure S3);
thus, the angle correlation between SSV vectors was used to identify the
spatial pattern of the climatology that corresponded most closely to the
instantaneous time series SOMs (Figure S4). The climatological pattern
number 5 has a null frequency, i.e., it rarely happens; thus, it was
ignored. Except for HC 5, each climatological spatial pattern has one
clear maximum correlation with one of the instantaneous spatial
patterns. The correspondence between HC and HI patterns according to the
highest angle correlation is shown in Table S1. Using the correspondence
in Table S1 to rename the HI spatial patterns so that the names of the
two patterns that correlate the highest match, we can compare the
temporal evolution of matching spatial patterns according to BMUs
(Figure S5). Each year between 1994 and 2018, the period over which we
have a temporal evolution of instantaneous spatial patterns, the HI BMUs
are similar to the temporal evolution of the climatological spatial
patterns, i.e., the HC BMUs. Starting in 2016, and especially in 2017,
HI and HC BMUs differ more than in most previous years. It is unclear if
the ocean dynamics were different these years, or if the different model
setup may be partly responsible; data from 1994 to 2015 is from the
HYCOM GOFS 3.1 reanalysis, while the velocity starting in 2016 comes
from HYCOM GOFS 3.1 analysis.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image15/image15}

\end{center}
\end{figure}

\textbf{Figure S3.} Correlation matrix of the magnitude between each of
the 8 SOMs spatial patterns from the HYCOM climatology (HC) and the 8
SOMs spatial patterns from the HYCOM instantaneous time series (HI).
Only significant correlations are shown as different from zero.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image16/image16}

\end{center}
\end{figure}

\textbf{Figure S4.} Correlation matrix of the vector angle from each of
the 8 SOMs spatial patterns from the HYCOM climatology (HC) and the 8
SOMs spatial patterns from the HYCOM instantaneous time series (HI).
Only significant correlations are shown as different from zero.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image17/image17}

\end{center}
\end{figure}

\textbf{Figure S5.} Top panel is the BMUs for the climatological
velocity (red line), repeated each year of the time series for
comparison, and the BMUs for the instantaneous velocity (blue line) over
1994--2018. The middle panel is a histogram of the difference between
the two BMUs in the top panel. The bottom panel is each year's sum of
differences other than zero, the sum of the histogram in the second
panel; the green line is the 1994--2018 average.

\textbf{Table S1.} Correspondence between the HYCOM climatology (HC)
SOMs spatial patterns and the HYCOM instantaneous (HI) SOMs spatial
patterns based on the highest correlation between the directions (angle)
of each spatial pattern with another (see Figure S4).\selectlanguage{english}
\begin{longtable}[]{@{}lllllllll@{}}
\toprule
& SOMs Patterns & SOMs Patterns & SOMs Patterns & SOMs Patterns & SOMs
Patterns & SOMs Patterns & SOMs Patterns & SOMs Patterns\tabularnewline
HC & 1 & 2 & 3 & 4 & 6 & 7 & 8 & 9\tabularnewline
HI & 5 & 2 & 1 & 6 & 4 & 9 & 8 & 7\tabularnewline
\bottomrule
\end{longtable}

\textbf{Text S2.}

The ocean currents plus 2\% windage cLCS pointing towards the coast
discussed in section 3.2.3, are shown here to direct pathways of
particles toward the Mexican coast in August 2018 (Figure S6). As
trajectories get closer to the coast, another strong cLCS parallel to
the coast redirects trajectories along the coast toward the north.
Trajectory data was produced by Lara-Hern\selectlanguage{ngerman}ández et al. (2023) using
instantaneous velocity (not the same velocity as the cLCS) plus 2\%
windage. Similar results hold for other months (not shown).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image18/image18}

\end{center}
\end{figure}

\textbf{Figure S6.} The color contours are the density of trajectories
points initiated along the Mexican Caribbean coastline and integrated
back in time to find their provenance using HYCOM Global instantaneous
velocity of August 2018. Only the most attracting August cLCS (black
lines) are plotted (i.e. when their attraction strength is above 1.2).

\selectlanguage{english}
\FloatBarrier
\end{document}

