# Impact of Tidal Forcing on Surface Particle Transport Properties: Insights From Twin Ocean Simulations

Laura Gómez-Navarro, Erik van Sebille, Verónica Morales-Márquez, Ismael

Hernández-Carrasco, Aurelie Albert, Clement Ubelmann, Julien Le Sommer,

Jean-Marc Molines, Laurent Brodeau

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► To cite this version:

Laura Gómez-Navarro, Erik van Sebille, Verónica Morales-Márquez, Ismael Hernández-Carrasco, Aurelie Albert, et al.. Impact of Tidal Forcing on Surface Particle Transport Properties: Insights From Twin Ocean Simulations. Journal of Advances in Modeling Earth Systems, 2026, 18 (2), pp.e2024MS004805. 10.1029/2024MS004805. hal-05513225

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RESEARCH ARTICLE

10.1029/2024MS004805

**Key Points:**

* Twin ocean simulations reveal distinct ocean surface transport patterns, highlighting tides' role in Lagrangian dynamics

* Absolute distances decrease, but cumulative distances increase with tidal forcing, enhancing dispersion via complex pathways

* Tides add variability to surface particle accumulation patterns, optimizing simulations of pollution dispersal and marine connectivity

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

L. Gómez-Navarro,
*laura.gomez@icm.csic.es*

**Citation:**

Gómez-Navarro, L., van Sebille, E., Morales-Márquez, V., Hernández-Carrasco, I., Albert, A., Ubelmann, C., et al. (2026). Impact of tidal forcing on surface particle transport properties: Insights from twin ocean simulations. *Journal of Advances in Modeling Earth Systems*, 18, e2024MS004805. https://doi.org/10.1029/2024MS004805

Received 13 DEC 2024

Accepted 8 JAN 2026

**Author Contributions:**

**Conceptualization:** Laura Gómez-Navarro, Erik van Sebille, Verónica Morales-Márquez, Ismael Hernández-Carrasco, Clement Ubelmann

**Data curation:** Laura Gómez-Navarro, Aurelie Albert, Julien Le Sommer, Jean-Marc Molines, Laurent Brodeau

**Formal analysis:** Laura Gómez-Navarro, Verónica Morales-Márquez, Ismael Hernández-Carrasco

© 2026 The Author(s). Journal of Advances in Modeling Earth Systems published by Wiley Periodicals LLC on behalf of American Geophysical Union. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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# Impact of Tidal Forcing on Surface Particle Transport Properties: Insights From Twin Ocean Simulations

Laura Gómez-Navarro¹,² ID, Erik van Sebille² ID, Verónica Morales-Márquez³ ID,

Ismael Hernández-Carrasco⁴,⁵ ID, Aurelie Albert⁶ ID, Clement Ubelmann⁷ ID, Julien Le Sommer⁶ ID,

Jean-Marc Molines⁶,⁸ ID and Laurent Brodeau⁶ ID

¹Institut de Ciències del Mar (ICM, CSIC), Barcelona, Spain, ²Department of Physics, IMAU, Utrecht University, Utrecht, The Netherlands, ³Puertos del Estado, Madrid, Spain, ⁴Institut Mediterrani d'Estudis Avançats (IMEDEA, UIB-CSIC), Esporles, Spain, ⁵Instituto de Ciencias Marinas de Andalucía (ICMAN, CSIC), Puerto Real, Spain, ⁶Institut des Géosciences de l'Environnement (IGE), UGA-CNRS-IRD-INP, Grenoble, France, ⁷Datlas, Grenoble, France, ⁸Retired

**Abstract** Understanding the transport pathways of floating material at the ocean surface is important to improve our knowledge on surface circulation and assessing its environmental impacts. Numerical experiments through Lagrangian particle simulations are widely used to investigate the dispersion of floating material, typically relying on velocity fields from ocean circulation models. However, the contribution of different ocean dynamics (at different temporal and spatial scales) to the net Lagrangian transport remains unclear. Here we focus on tidal forcing, only included in recent ocean models, to explore its effect on particle dispersion at the ocean surface. By comparing a twin simulation with and without tidal forcing, we conclude that tide-induced dynamics play an important role in horizontal Lagrangian pathways. We focus on the Azores Islands region and find that surface particles travel a longer cumulative distance and a lower total distance with than without tidal forcing. Additionally, tidal forcing leads to higher variability in surface particle accumulation patterns. The differences found in the surface particle accumulation patterns can be greater than 40%. These findings have important implications for virtual particle simulations, suggesting that considering tidal currents alone may not capture the full range of tide-induced effects. A deeper understanding of the underlying dynamics is essential for accurately analyzing transport properties. Our outcomes can already help improve Lagrangian simulations made to understand the connectivity of marine species and for marine pollution applications, for example, ocean clean-up strategies for plastics or oil spills, in the Azores Islands and regions with similar dynamics.

**Plain Language Summary** At the surface of the Ocean we can find a variety of floating material for example, algae, larvae, plastics and oil spills. Accurately modeling their trajectories helps us understand ocean surface dynamics and their ecological, environmental and economic impacts. To simulate these trajectories, ocean currents derived from ocean models are typically used. These ocean models aim to represent different oceanic processes, and recent ones include the effect of tides. In this study, we investigate how tides affect surface particle trajectories in a region south of the Azores Islands. We examine both the distance traveled by the particles and their accumulation patterns. Our results show that tidal forcing influences both transport properties, and that its impact on accumulation patterns depends on the size of the ocean features, for example, whether the eddies are smaller or larger. We conclude that tides play an important role in shaping ocean surface trajectories. This has key applications for studying marine biodiversity and marine pollution forecasts.

## 1. Introduction

Understanding the pathways of floating material (e.g., larvae, plastics, oil spills, and drifters) at the surface ocean is important not only due to its ecological and environmental repercussions (e.g., Sala et al., 2016), but also to improve our knowledge on the ocean dynamics (e.g., Chamecki et al., 2019; van Sebille et al., 2020). Indeed, insights into 3D dynamics can be inferred identifying strong surface flow convergence and divergence regions, which have significant associated vertical dynamics (e.g., d'Asaro et al., 2018; Hernández-Carrasco et al., 2018; McWilliams et al., 2019; Tarry et al., 2021), with large biological implications (e.g., Lévy et al., 2001; Lévy et al., 2012; Mahadevan, 2016). Furthermore, understanding surface dispersion is useful to expand our knowledge on operational issues, such as the distribution of marine plastic (e.g., Onink et al., 2019), oil spills (e.g., Ainsworth et al., 2021), algae such as *Sargassum* (e.g., Miron et al., 2020; van Sebille et al., 2021) and larvae (e.g., Díaz-Barroso et al., 2022; Hidalgo et al., 2019; Largier, 2003). Additionally, identifying hotspots where pollutants or
**Funding acquisition:** Erik van Sebille

**Investigation:** Laura Gómez-Navarro, Verónica Morales-Márquez, Ismael Hernández-Carrasco

**Methodology:** Laura Gómez-Navarro, Erik van Sebille, Verónica Morales-Márquez, Ismael Hernández-Carrasco, Aurelie Albert, Clement Ubelmann, Julien Le Sommer, Jean-Marc Molines, Laurent Brodeau

**Resources:** Laura Gómez-Navarro, Erik van Sebille, Verónica Morales-Márquez, Ismael Hernández-Carrasco, Aurelie Albert, Julien Le Sommer, Jean-Marc Molines, Laurent Brodeau

**Software:** Laura Gómez-Navarro, Erik van Sebille, Verónica Morales-Márquez, Ismael Hernández-Carrasco

**Supervision:** Erik van Sebille

**Validation:** Laura Gómez-Navarro

**Visualization:** Laura Gómez-Navarro

**Writing – original draft:** Laura Gómez-Navarro

**Writing – review & editing:** Laura Gómez-Navarro, Erik van Sebille, Verónica Morales-Márquez, Ismael Hernández-Carrasco, Aurelie Albert

fish larvae accumulate can support ocean clean-up strategies and marine protected areas management, respectively (e.g., Krüger et al., 2017; Poje et al., 2014).

Simulating accurate trajectories of floating material in the ocean is complex as many processes are involved at different spatio-temporal scales (van Sebille et al., 2020). In this regard, the growing development of different sources of ocean velocity data has helped to analyze the impact of different dynamical scales on the transport processes: Ocean General Circulation Models (OGCMs) (e.g., Brunner et al., 2015; Sala et al., 2016), drifters (e.g., Maximenko et al., 2012; van Sebille et al., 2012), High-Frequency (HF) radar (e.g., Hernández-Carrasco et al., 2018; Révelard et al., 2021), altimetric satellite data (e.g., Beron-Vera et al., 2010; Liu et al., 2014) and other products like GlobCurrent (e.g., Onink et al., 2019) or a combination of them (e.g., Morales-Márquez et al., 2023). Nevertheless, limitations exist for these datasets because of their low spatial and/or temporal coverage or low spatial resolution. Among them, altimetric products are particularly relevant since they provide global coverage of geostrophic currents and are widely used for surface trajectory simulations. However, current nadir altimetric products do not capture all surface transport mechanisms (Bôas et al., 2019), especially those due to high-frequency motions such as internal tides and waves. Alternatively, OGCMs are not as limited by coverage and resolution, but to date they cannot resolve and represent all the different processes, like Langmuir circulation, and would need to be coupled to other models, like wave and biogeochemical models, to represent processes such as Stokes drift and bio-fouling, respectively (Tsiaras et al., 2021; van Sebille et al., 2020). Focusing on the open ocean, some of the processes that have received a great attention to improve the understanding of the surface transport properties from observations and numerical simulations, have been Ekman transport, Stokes drift and windage (e.g., Iwasaki et al., 2017; Morales-Márquez et al., 2021, 2023; Putman et al., 2020; Wenegrat & McPhaden, 2016); especially in the context of marine debris (e.g., Dobler et al., 2019; Higgins et al., 2020; Maximenko et al., 2018; Onink et al., 2019).

However, tidal effects, particularly those of internal waves on the eddy field, have received little attention regarding their impact on Lagrangian dynamics. A few studies have analyzed the role of tides in the transport of floating material, but these have not considered the impact of tide-induced dynamics (e.g., internal waves) and have only focused on the effect of tidal currents. For instance, Sterl et al. (2020) found that the impact of barotropic tidal currents on microplastic surface transport and accumulation was very small. Tidal currents have also been considered using the Surface and Merged Ocean Currents (SMOC) data set (Drillet et al., 2019) to understand the trajectories of *Sargassum* in the tropical Atlantic by van Sebille et al. (2021). Moreover, Lagrangian transport due to internal tides has been studied by Sutherland and Yassin (2022), but they found it to be negligible when averaged over an inertial period. Recent technological advances have allowed OGCMs to include tidal forcing, improving the representation of internal wave fields (Le Sommer et al., 2018). Tidally forced OGCMs allow not only the representation of tidal currents, but also the influence of tides on flow structures, for example eddies, filaments, or fronts. Only a few studies have employed twin simulations with and without tidal forcing to study ocean dynamics: Sánchez-Garrido et al. (2015); Staalstrøm and Røed (2016); Stanev and Ricker (2020); Masunaga et al. (2022); Lin et al. (2023), focusing on processes such as phytoplankton productivity, internal variability, and regional circulation. These works highlight the value of comparing tidally and non-tidally forced simulations, but their scope has mostly remained regional and process-specific. By contrast, our study applies this framework within an OGCM to assess the impact of tide-induced dynamics on Lagrangian dynamics, in particular surface accumulation patterns.

Including tidal forcing in OGCMs can impact the flow field in different ways. It increases the energy at the finescales (here defined between 10 and 100 km) as reported by Verron et al. (2020), who observed higher Sea Surface Height (SSH) energy levels with tidal forcing compared to without. This difference is more pronounced in the northern hemisphere summer (from hereafter seasons referring to northern hemisphere), when high stratification conditions promote the generation and propagation of internal tides (Verron et al., 2020). One of the physical features that are responsible for this increase at the finescales are internal waves, which are ignored when only considering tidal currents and/or barotropic tides. Although internal waves occur at the interface between ocean layers (Arbic et al., 2018), their signal can sometimes be observed at the ocean surface (e. g., Jackson et al., 2012). Not only can they transport floating material (Shanks, 2021), but can also affect the background flow, namely eddies, by altering their kinetic energy (Barkan et al., 2017; Bühler & McIntyre, 2005; Mtfller, 1976), as internal waves can lead to the extraction of mesoscale energy through dissipation (Barkan et al., 2017). Since mesoscale eddies can retain floating material for several days (e.g., d'Ovidio et al., 2013; Condie & Condie, 2016; Limer et al., 2020; Bello-Fuentes et al., 2021), this energy loss could imply a loss of the
coherence of their structure and thus of their capacity to accumulate/trap material. One of the main mechanisms that generate coherent eddy structures are baroclinic instabilities (Stammer, 1997; Volkov & Fu, 2011), and these can be modified by tidal forcing (Lin et al., 2023). While no specific research has been done on the impact of internal waves on the retention capacity of eddies, some studies have been done with surface waves. Dobler et al. (2019); Morales-Márquez et al. (2023) found that surface waves created by forcings such as the wind and waves can have a significant effect on mesoscale structures like eddies, modifying their shape and eventually reducing their retention capacity.

Our study region is located south of the Azores Islands, one of the areas in the North Atlantic with the highest internal wave signal (Ray & Zaron, 2016; Savage et al., 2017). These internal waves are generated by the interaction of the flow (tidal or current) with the bathymetry, especially during summer (June to September), when stratification is high (Jackson, 2004; Lahaye et al., 2019; Rocha et al., 2016; Torres et al., 2018; Verron et al., 2020). At larger spatial scales, the Azores region lies within the influence of the eastward-flowing Azores Current, a dynamic feature marked by pronounced oceanographic instability. Numerous cyclonic and anticyclonic eddies detach from this current (Barbosa Aguiar et al., 2011; Sangrà et al., 2009; Zhou et al., 2000), travel across the Azores region (Caldeira & Reis, 2017; Cardoso & Caldeira, 2021; Sala et al., 2016), and can persist for several months (Alves & Colin de Verdière, 1999; Alves et al., 2002; Gould, 1985). The Azores Current displays seasonal, meridional and interannual variability, affecting its position, strength, transport, and eddy energy (Cardoso & Caldeira, 2021; Klein & Siedler, 1989; Stramma & Siedler, 1988; Volkov & Fu, 2011). In addition, this area is significant in the context of marine pollution due to its high exposure to floating marine debris, which reaches the islands through filaments and eddies generated from the Gulf Stream, and its connectivity with the other islands of the Macaronesian Archipelago (specially Madeira and Canary Islands) (Cardoso & Caldeira, 2021; Pham et al., 2020; Sala et al., 2016).

Despite increasing attention to various drivers of surface transport, the influence of tidal forcing, on Lagrangian dynamics remains under-explored. Most previous studies have either excluded tidal effects altogether or considered only barotropic tidal currents, overlooking the potential of internal tides and waves to modulate fine-scale flow structures such as eddies and filaments. This lack of attention is particularly relevant in regions like the Azores, where internal wave activity is pronounced and mesoscale structures play a key role in the surface transport of floating material. In this study, we investigate how the inclusion of tidal forcing in OGCMs affects surface ocean transport properties and the underlying mesoscale structures. We adopt a twin simulation approach using daily velocity outputs from a high-resolution OGCM, comparing runs with and without tidal forcing. Through this approach, our objective is to investigate the effects of tide-induced dynamics on surface transport properties, providing new insights into the role of tides in shaping Lagrangian transport patterns in the open ocean. In Section 2 we describe the data set used and the methods to evaluate the data. Section 3 describes the results obtained, which are discussed in Section 4, and Section 5 presents the conclusions along with suggestions for future studies.

## 2. Data and Methods

### 2.1. The Extended North Atlantic Simulation at 1/60° (eNATL60)

eNATL60 is an extended version of the NATL60 run (see Ajayi et al., 2020; https://github.com/meom-configurations/NATL60-CJM165) in which a larger spatial domain is covered. The model domain includes the North Atlantic basin: from 6°N to 66°N and from 80°W to 9.5°E (Figure 1), together with the whole Mediterranean and Black Seas and the Gulf of Mexico (not shown). With a spatial resolution of 1/60° (~1 km) and a model time-step of 40 s, the simulation is submesoscale-permitting (Verron et al., 2020). Two simulations were produced with this configuration with and without tidal forcing (Brodeau et al., 2020a, 2020b). The tidal constituents used are M2, S2, N2, K1, O1 (Brodeau et al., 2020b), and the presence of tidal forcing allows the conversion of tidal energy into the internal wave field. This conversion occurs through the interaction of wave and unbalanced motions, and via flow-topography interactions (Arbic et al., 2018). The simulation timespan is from mid-June 2009 to October 2010 (simulation years, no data assimilation included).

Verron et al. (2020) compared the simulation outputs to the altimeter SARAL/Altika, focusing on a spectral comparison with the simulation's surface data. They found that, at the large scales (down to approximately 80 km), the model's SSH spatial spectra closely matched that of SARAL/Altika in both the non-tidal and tidal run. The high frequency motions of eNATL60 were compared with altimetry by Ansong et al. (2020), showing a slight
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Spatial domain of the eNATL60 simulation (except the Gulf of Mexico, Black Sea, and eastern Mediterranean Sea domains). Black box shows the region of this study where virtual surface particles are released. Red box shows the subregion used for some of the analyses.</figcaption></figure>

overestimation of the SSH variance in the tidally forced run due to no explicit wave drag in the simulation. Additionally, Bella et al. (2024) used eNATL60 to examine internal tide-mesoscale interactions, further demonstrating the model's capability to resolve both tidal and mesoscale dynamics.

For the scope of this study, we use the hourly model outputs and the 2D surface velocity fields. Although the model is 3D, we focus only on the surface layer to assess the impact of tidal forcing by analyzing the surface expression of tide-induced dynamics. This provides a first estimate while acknowledging that tidal effects occur throughout the water column. This also enables the investigation of the surface impact of internal waves (Shanks, 2021), which is relevant to understanding the accumulation and dispersion of floating material (e.g., marine plastic and *Sargassum*). Given the timespan limitation of the model run, we only use model outputs from 1 July 2009 to 30 June 2010, to have a complete year. The limited temporal coverage of the eNATL60 simulation prevents the full assessment of seasonal variability. However, the available period still allows us to contrast dynamic patterns between winter and summer in the study area. Accurately quantifying the seasonal variability of tidal effects is beyond the scope of this study, as this would require longer simulations. Instead, our aim is to illustrate that these effects differ between seasons, consistent with the known seasonal behavior of tidal dynamics. We therefore interpret part of the temporal variability in our results as seasonally driven. Accordingly, although we only analyze summer 2009 and winter 2010 (hereafter simply referred to as summer and winter), we present these as periods of analysis rather than as comprehensive representations of seasonal variability. This set of simulations provides a valuable framework, combining high spatial and temporal resolution, broad spatial coverage, and the twin simulation setup with and without tidal forcing.

## 2.2. Particle Trajectory Simulations

The OceanParcels Lagrangian framework v2.2.2 (Delandmeter & van Sebille, 2019) is used to simulate 2D trajectories of virtual particles at the sea surface. Particles are advected using the velocity fields obtained from the outputs of the two model simulations with and without tidal forcing (eNATL60). A fourth order Runge-Kutta particle advection scheme is used with a run-time time-step (dt) of 5 min. We consider infinitesimal passive and buoyant particles. We perform simulations with particles released monthly at the surface over the whole region (black box in Figure 1) with a 0.04° spacing, making it a total of 106,926 particles. We release them on the first day of every month, from July 2009 to June 2010. To ensure all simulations have the same length, which is limited by the month of February, we advect the particles for 28 days. This monthly window is long enough to perform Lagrangian computations, and infer accurate coherent patterns in the Lagrangian framework, especially for the temporal scale of the features we are interested in this study. Additionally, monthly simulations also
provide a useful compromise between the shorter timescales of internal waves (order of hours to days), the intermediate timescales of mesoscale eddies in the region (weeks to months), and the temporal coverage of the eNATL60 simulation, thereby helping us to better disentangle the role of different dynamical processes. We remove particles which leave the domain (black box in Figure 1). In addition to these monthly forward simulations, a specific Lagrangian setup is required to calculate one of the diagnostics (Backward Finite Time Lyapunov Exponents [bFTLEs]). This is described in the corresponding section on bFTLEs (Section 2.3.2.3).

## 2.3. Lagrangian Diagnostics

To evaluate the impact of tidal forcing on the surface particle trajectories, we use a set of complementary Lagrangian diagnostics that provide information about transport properties at different temporal and spatial scales. Each method involves the tuning of specific parameters (detailed in the corresponding subsections), and since no single diagnostic is free of uncertainty or optimal across all scales, we apply several methodologies in parallel. This allows us to compare their outcomes and obtain a more robust picture of particle dispersion. In practice, we evaluate the effect of tidal forcing on particle dispersion by analyzing two Lagrangian properties: the distances traveled by the particles and their surface accumulation. While our aim is to investigate the full study region, computational constraints and boundary effects sometimes require us to restrict the accumulation analysis to the red-box subregion (Figure 1).

### 2.3.1. Distance Traveled

We evaluate the absolute distance (AD) and the cumulative horizontal distance (CD) traveled by each particle at the sea surface in km. AD is the shortest distance between the initial ($\vec{r}(t=0)$) and final ($\vec{r}(t=T)$) position of a 2D particle's trajectory, with $\vec{r}(t) = (x(t), y(t))$, where $x(t)$ and $y(t)$ denote the horizontal coordinates at time, $t$. AD renders the absolute (or net) distance traveled by the particle in a period, $T$, relative to its initial position. CD is the sum of all the distances traveled during each time-step, providing an estimate of the total distance explored by the particle. They are defined as:

$$AD(x, y, t) = |\vec{r}(t=T) - \vec{r}(t=0)| \qquad (1)$$

$$CD(x, y, t) = \sum_{n=0}^{N-1} |\vec{r}_{n+1} - \vec{r}_n|; \qquad (2)$$

where $\vec{r}_{n+1} = \vec{r}(t + \Delta t)$, $\vec{r}_n = r(t)$ and $\vec{r}_N = \vec{r}(t = T)$, with $n$ the summation index and $N$ the number of terms.

### 2.3.2. Surface Accumulation Patterns

The analysis of surface particle accumulation is more complex and requires different statistical and diagnostic techniques. These diagnostics are sensitive to parameter choices and are therefore associated with higher uncertainty than the distance-based metrics. We also analyze the impact of tidal forcing on transport barriers by computing particle-pair metrics like the FTLEs. Consequently, we use a range of techniques, which are described below.

#### 2.3.2.1. Gaussian Kernel Density Estimation (GKDE)

One of the methods used to calculate particle density is a two-dimensional horizontal Gaussian Kernel Density Estimation (GKDE). This is a non-parametric method, meaning it does not assume a predefined particle distribution (e.g., Gaussian). Instead, it estimates the probability density function (PDF) directly from the data, making it applicable even when the data are not Gaussian-distributed.

Conceptually, the method works by placing a smooth, bell-shaped Gaussian function (kernel) centered on each particle location (the “Gaussian” here refers only to the smoothing function, not to the overall particle distribution). The contributions from all kernels are then summed to obtain a continuous density field across the domain. The width of each kernel, called the bandwidth, controls the level of smoothing: a small bandwidth produces a more detailed but noisier estimate, while a large bandwidth produces a smoother but less detailed estimate.
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Box plots of mean cumulative distance (km) (top) and mean absolute distance (km) (bottom) traveled by the virtual particles per month.</figcaption></figure>

We apply the GKDE monthly to the particle distribution on day 28 within the entire domain (black box in Figure 1). We use the Python SciPy (Virtanen et al., 2020) stats gaussian_kde algorithm with a default kernel size (bandwidth), determined by Scott's Rule (Scott, 1992). This bandwidth selector calculates the optimal bandwidth value that avoids both over-smoothing and under-smoothing.

#### 2.3.2.2. Particle Density Histogram Skewness

We also investigate surface particle accumulation using histograms. In particular, we analyze the skewness of the two-dimensional particle density histograms, as this provides information on the occurrence of localized accumulation hotspots. We calculate the two-dimensional histogram of particle positions with a bin size of 0.1° by 0.1° for the subregion shown by the red box in Figure 1. This subregion is selected to avoid areas without particles, which appear as white intrusions and are present in all months (e.g., the white zone to the west in the no tides September GKDE subplot of Figure 3). The GKDE is calculated on each particle, so the impact of the region's boundaries is smaller than for the 2D histogram. From the 2D histograms (i.e., map of particle counts per spatial bin), we obtain the probability distribution of particle counts, calculated as a 1D histogram (10 bins). This distribution describes how often different particle densities occur across the subregion. We then analyze the skewness of this probability distribution. High positive skewness indicates that a small number of spatial bins
contain unusually large particle densities, consistent with localized accumulation. We compute the skewness values using the scipy.stats.skew function in Python (Virtanen et al., 2020). This function calculates skewness by implementing the Fisher-Pearson coefficient of skewness, defined as the third central moment of the distribution normalized by the standard deviation cubed (Zwillinger & Kokoska, 2000). We apply the same approach to the bFTLE fields, as described in Section 2.3.2.3.

We analyze the skewness in two complementary ways, by evaluating: (i) the skewness at the final step of each monthly simulation (day 28), and (ii) the temporal variability of the skewness over the full simulation period. To this end, we compute histograms and skewness at every time step, which allows us to quantify the evolution and variance of skewness in time. For the monthly comparison, we focus on the final skewness value. Although skewness formally measures the asymmetry of a distribution, in our case the histograms are consistently positively skewed. Their right tails therefore correspond to rare, high-density bins, which indicate localized particle accumulation zones. Previous studies have linked kurtosis to the occurrence of rare extremes in geophysical distributions (e.g., Silva-Fernandes & Peliz, 2020; White, 1980). In our case, the consistently positive skewness provides an equivalent diagnostic, since the asymmetry of the distribution is driven by the same rare, high-density events that would also contribute to elevated kurtosis.

### 2.3.2.3. Backward Finite Time Lyapunov Exponents (bFTLEs)

Finite Time Lyapunov Exponents (FTLEs) is a Lagrangian diagnostic for describing relative dispersion properties of fluid flows, providing information on the position of oceanic transport barriers, the so-called Lagrangian Coherent Structures (LCS) (Boffetta et al., 2001; Haller, 2015). FTLEs are based on the Lagrangian separation rate of two infinitesimally close trajectories, which grows exponentially over time (Haller, 2001; Shadden et al., 2005). This separation rate can be characterized either by fixing the integration time (Shadden et al., 2005), yielding the FTLEs, or the final separation distance, yielding the Finite Size Lyapunov Exponents (FSLEs) (Hernández-Carrasco et al., 2011). We choose FTLE because we use time as the independent variable, consistent with the distance computations (AD and CD) and the other diagnostics evaluated here, whereas FSLE uses spatial scale as its independent variable. Using FTLE ensures that the analyses obtained from the different Lagrangian metrics have comparable time scales.

FTLEs can be calculated forward and backward in time. Ridges in forward-in-time FTLE fields characterize regions of locally high divergence of particle trajectories, corresponding to repelling LCS, whereas ridges in backward FTLEs (bFTLEs) identify regions of locally high convergence, commonly referred to as attracting LCS. In this study, we focus on attracting LCS, as tracers such as nutrients, temperature, microplastics, and other pollutants tend to accumulate and spread along them, forming filament-like structures with elevated tracer concentrations (e.g., Manral et al., 2025). This property provides a direct and physically intuitive interpretation of attracting LCS. Since particles cannot cross them, the LCS determine the flow motion, defining the main transport pathways (Haller & Yuan, 2000; Shadden et al., 2005). Recent studies have shown there is a relationship between attractive LCS and ridges of accumulated Lagrangian horizontal convergence derived from velocity fields, revealing regions of particle aggregation (Hernández-Carrasco et al., 2018; Huntley et al., 2015). bFTLEs provide more details at finer scales than GKDE and 2D histograms, as the method allows identifying subgrid dynamical structures (Hernández-Carrasco et al., 2011, 2020). Moreover, bFTLEs describe the surface particle accumulation patterns by outlining accumulation zones, whereas the GKDE and histogram diagnostics identify the area of the accumulation zone due to eddies or other LCS. Based on Shadden et al. (2005), FTLE is derived by considering the stretching of two neighboring particles, initially separated a distance $\delta(t_0)$, and advected in the flow for a fixed integration time ($\tau$), after which their separation is $\delta(t_0 + \tau)$. We obtain the following expression for the FTLE in two-dimensional flows, denoted as $\lambda(x, y, t)$, which depends on position and time,

$$ \lambda(x, y, t) = \frac{1}{\tau} * \ln \frac{\delta(t_0 + \tau)}{\delta(t_0)} \quad (3) $$

To obtain the FTLEs we then compute the maximum eigenvalues of the Cauchy-Green deformation tensor after the integration time ($\tau$) defined in Haller (2001).

We set the initial particle separation $\delta(t_0)$ to 0.004° (~0.44 km), and the integration time, $\tau$ to -14 days (negative to implement it backward in time as we use backward FTLEs). $\delta(t_0)$ is at a finer resolution than the eNATL60
velocity fields' grid (0.0167°, ~1.83 km), which allows a better identification of the subgrid structures generated by chaotic advection (see Hernández-Carrasco et al., 2011; Hernández-Carrasco et al., 2020). We calculate bFTLEs biweekly, on days 1 and 15 of each month. We use a 2-week integration time because with $\tau = 28$ days the bFTLE results show high uncertainty, and for 1 week of integration time the coherent structures are not fully identified.

Therefore, as mentioned before, a specific Lagrangian simulation is necessary for the computation of bFTLEs. To comply with these space-time bFTLE parameterizations, we use a dedicated simulation setup in which particles were released every 0.004° and advected for 14 days, consistent with the chosen biweekly integration window. We perform the simulations for the same period as the other diagnostics (July 2009 to June 2010). To reduce computational costs, we restrict them to a subregion of the study domain (red box in Figure 1). A sensitivity analysis confirms that restricting the domain does not affect the GKDE accumulation patterns (not shown), supporting the use of the subregion for bFTLE computations and ensuring comparability with the other Lagrangian diagnostics.

Lastly, we consider that for this region, the backward FTLE fields (see Figures S1 and S2 in Supporting Information S1) reflect high flow convergence values above 0.5 days⁻¹. We select this threshold based on the characteristics of the bFTLE PDF. For all months, this threshold generally corresponds to the smallest bFTLE value in the asymmetric tail of the PDF (see Figure A1) associated with intermittent dynamics and identified here with maximum bFTLE values organized in filament-like structures. Given these PDF characteristics, we also analyze the skewness of the bFTLE distributions, calculated in the same way as for the particle density histograms (Section 2.3.2.2). This allows us to quantify the asymmetry of the bFTLE fields and thus the relative occurrence of rare, high bFTLE values associated with strong localized convergence zones.

### 2.3.3. Percentage Change With Tides

In the final analysis, we quantify the effect of tidal forcing on the diagnostics by computing the relative difference between the tidal and non-tidal simulations,

$$ \% \text{ difference} = \frac{(X_T - X_N)}{X_N} \times 100, \qquad (4) $$

where $X_T$ and $X_N$ denote the values for each diagnostic (CD, AD, percentage of GKDE $\ge$ 0.008 and percentage of bFTLE $\ge$ 0.5) for the tidal and non-tidal simulations, respectively. The X values correspond to the temporal aggregates used for each diagnostic; monthly values for CD, AD, and GKDE, and biweekly values for bFTLE. We use this percentage difference to summarize the change due to tides.

## 3. Results

Firstly, we look at the impact of tidal forcing on the distance traveled by the particles. Figure 2 shows that the particles travel a large range of distances after 28 days, but if we focus on the median values shown in the box plot, we observe differences between the travel distances with and without tidal forcing. The median CD values are higher for the tidal than for the non-tidal simulation, up to 25% larger in August with respect to the non-tidal simulation. For the median AD values (Figure 2 (bottom)), the opposite is observed: larger ADs are traveled by the particles in the non-tidal than in the tidal simulation. For some months (February to June), the non-tidal simulation values of the median are only slightly higher than the tidal values, but the percentile 75 values of most months also reflect this pattern.

Next, we analyze the impact of the tide-induced dynamics on the surface particle accumulation using the GKDE. The results obtained here using the optimal kernel size (see Section 2.3.2.1), seem to reflect the surface particle accumulation at mesoscale spatial scales. This can be observed in the red and yellow eddy mesoscale-like structures observed in Figure 3. While a higher presence (spatial coverage) of very high-density regions (red color) is evident in winter compared to summer for the non-tidal simulation in Figure 3, this seasonal contrast is much less apparent in the tidal simulation. This is clearer when we quantify the surface accumulation patterns. Figure 4 shows the percentage of particles with a high GKDE value (GKDE > 0.008) per month, identified as the yellow and red regions in Figure 3. This threshold corresponds to a high particle density for all months and in both
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Gaussian Kernel Density Estimation (GKDE) comparison between non-tidal (top) and tidal (bottom) simulations. Maximum GKDE value (top) and percentage of particles with a high GKDE value (≥0.008) (bottom) are shown in the top left textbox.</figcaption></figure>

simulations. In the non-tidal simulation, the percentage of particles in high-density zones is generally higher in winter than in summer, confirming the seasonal contrast. This implies a higher surface particle accumulation in winter (December to March) than in summer (July–September 2009 and May and June 2010). However, with tidal forcing, the percentage increases in summer and decreases in winter, suppressing the seasonal signal. Thus, while both simulations show seasonal variability, tidal forcing appears to reduce this variability, with summer accumulation becoming more dominant when tides are included.

To study the surface particle accumulation from another perspective, 2D histograms of the particles' distribution in the final time-step (i.e., after 28 days) are also analyzed. Figure 5 shows the monthly 1D histograms of the 2D histogram bin (0.1° in latitude by 0.1° in longitude) counts. It shows that all the probability density functions (1D histograms) of the surface particle accumulation (2D histograms) are positively skewed. Qualitatively, no big differences are observed between the non-tidal and tidal histograms. The vertical, dashed line in Figure 5 shows the maximum value of the 2D histogram bin counts. The particle density maximum is greater for the tidal than the
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Comparison of the percentage of particles with a high Gaussian Kernel Density Estimation value (GKDE $\ge$ 0.008) per month. Non-tidal results are shown in blue and tidal in red.</figcaption></figure>

non-tidal in seven out of 12 months (August, December, January, February, March, April, and June), but no clear seasonal pattern is evident.

Deeper analysis of the positive skewness of the histograms gives us insight into the presence of rare extremes, which are linked to high surface particle accumulation (see Section 2.3.2.2). Figure 6 (top) shows the temporal evolution of the skewness of the particle density distribution. Here, two-dimensional histograms are computed at every time-step of the 28-day simulation, from which one-dimensional histograms of the bin counts are derived. Skewness is then calculated from these one-dimensional histograms (Figure 5), providing a time series of skewness values. Both the non-tidal and tidal skewness increase with time. The final skewness value, indicated by the vertical line in Figure 6 (top), is defined as the skewness at the time when any of the particles released at the boundary of the region (black box Figure 1) first enters the subregion (red box Figure 1). We used this criterion to minimize and homogenize the impact of the simulation boundary effects. The final, monthly skewness values are shown in Figure 6 (bottom). Except for September, all months have higher skewness values in the tidal than the non-tidal simulation. For most months, the skewness' temporal variability is highest for the tidal simulation. The temporal variance of the skewness (up to the vertical line) is shown in the text boxes in Figure 6 (top). For six out of the 12 months it is higher for the tidal simulation, in three of the months the values are very close (0.002 difference or less) and in the three other months it is higher for the non-tidal simulation.

The backward FTLEs give us information on the attracting LCS, identifying transport barriers and high-flow stretching filaments along which particles tend to align (see Section 2.3.2.3). Figures 7 and 8 show the attracting LCS on day 1 of each month for the non-tidal and tidal simulations, respectively. We can observe how eddy structures are much sharper in the non-tidal than tidal simulations, specially from September to January. This coincides with the GKDE results in winter, for both diagnostics the identified surface particle accumulation patterns decrease in winter.

Between July and January, attracting LCS cover a visibly smaller spatial extent with tidal forcing than without (Figures 7 and 8). This is quantified in Figure 9 (top), which gives the percentage of particles with bFTLE values greater than 0.5 days⁻¹, corresponding to the portion of the fields shown in Figures S1 and S2 in Supporting Information S1 above this threshold. For the summer, autumn, and beginning of winter (from July–December 2009 and, January and June 2010), non-tidal FTLEs exhibit higher values than the tidal values. The
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Probability density functions of the surface particle accumulation (from the 2D, 0.1° binned histograms) after 28 days of advection. Results of the non-tidal simulation are shown in blue and from the tidal in red. Vertical, dashed lines indicate the maximum value.</figcaption></figure>

percentage of particles with high bFTLE values decreases to ~40% of the non-tidal value, when tidal forcing is used. During the end of winter and spring, the opposite happens, and the percentage of particles increases to ~50% with tidal forcing. For both the non-tidal and tidal simulations, the highest percentage of particles with a high bFTLE (>0.5 days⁻¹) is obtained in April, and another smaller peak seems to be present in July. This observed seasonal variability in the bFTLE high values is larger for the tidal than for the non-tidal simulations.

Figure 9 (bottom) shows the skewness value of the bFTLE fields (computed as described in Sections 2.3.2.2 and 2.3.2.3). For most months, it is higher with than without tidal forcing, or they are very close (except from 15 March 2010 to 15 April 2010 (inclusive)). This is consistent with the higher skewness values of the 2D bin count histograms obtained for most months when tidal forcing is included.

Lastly, we assess the impact of including tidal forcing by examining the percentage increase (or decrease) with tides, as defined in Section 2.3.3. As observed above, the impact varies depending on the diagnostic. In Figure 10, we can observe that for the distances traveled, CD shows a larger impact of tidal forcing than AD. The increase in CD ranges from 3.75% to 24.77% and the decrease in AD from 0.76% to 4.99%. For GKDE, we specifically examine the change in the percentage of particles with high values (GKDE ≥ 0.008), which indicate high surface
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Skewness temporal evolution in time for each month for non-tidal (blue) and tidal (red) simulations. Values in the text box are the variance of the skewness from the beginning of the month until the vertical line. The vertical line indicates the moment in time when any of the particles released at the boundary of the region first enters the subregion (see Section 2.3.2.2). Bottom plot shows the skewness value at the vertical line.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Figure 7.** Comparison of attracting Lagrangian Coherent Structures (backward Finite Time Lyapunov Exponents) on day 1 of each month from July–December 2009, for the non-tidal (left) and the tidal simulation (right).</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Figure 8.** Comparison of attracting Lagrangian Coherent Structures (backward Finite Time Lyapunov Exponents) on day 1 of each month from January–June 2010, for the non-tidal (left) and the tidal simulation (right).</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure 9.** Top: Percentage of virtual particles with backward Finite Time Lyapunov Exponent (bFTLE) >0.5 days⁻¹. Bottom: Skewness values of the backward FTLE fields.</figcaption></figure>

particle accumulation. The highest percentage change is observed for this diagnostic, with values exceeding 40% in several months. The impact of tidal forcing is highest in August 2009, when the proportion of particles with GKDE ≥ 0.008 becomes 12 times higher (not shown in Figure 10). Although during most months tidal forcing causes GKDE to increase, for 4 months (October to January) the percentage of particles with GKDE ≥ 0.008 decreases by 30%–84%. In contrast, in July-September 2009 and May-June 2010, the percentage of particles with GKDE ≥ 0.008 increases by 23%–1,095% (Figure 4). For the remaining months, the GKDE changes are less than 10%. For bFTLE, we specifically examine the percentage of particles with high bFTLE values (≥ 0.5 days⁻¹). Tidal forcing causes this percentage change to increase between February and May, and to decrease during the other months, reaching changes of around 40% in both directions. During late autumn and winter (October to February), there is a decrease in high bFTLE values, in agreement with the negative impact also observed for high GKDE.

**4. Discussion**

Overall, our results demonstrate that tidal forcing is a critical factor in Lagrangian analyses, as it significantly impacts surface transport patterns across seasons and spatial scales. Such variability is especially important to account for in simulations supporting pollution mitigation operations and the management of marine protected areas (e.g., Krüger et al., 2017; Poje et al., 2014).

One of the clearest expressions of this influence is seen in the distance diagnostics. Tidal forcing induces small-scale oscillations that increase particle trajectory length (CD), but slightly decrease the AD traveled (AD), similar to the findings of Stanev and Ricker (2020). These effects are consistent with the elevated presence of high-frequency motions in the tidal simulation (Verron et al., 2020), inducing small and highly fluctuating perturbations in the particle motions. Consequently, particle trajectories explore more of the ocean surface due to tidal forcing, which has implications such as a higher particle exposure to nutrients or pollution. This effect is particularly relevant for simulations of drifting biological material, such as algae (e.g., *Sargassum*; Miron et al., 2020; van Sebille et al., 2021) and larvae (e.g., Díaz-Barroso et al., 2022; Hidalgo et al., 2019;
<figure><img src="image_13.png" /><figcaption>**Figure 10.** Percentage difference with tidal forcing per month for each diagnostic calculated. From top to bottom: Cumulative Distance (CD), Absolute Distance (AD), percentage of particles with high Gaussian Kernel Density Estimation (GKDE ≥ 0.008) and percentage of particles with high backward Finite Time Lyapunov Exponents (bFTLE ≥ 0.5 days⁻¹) backward Finite Time Lyapunov Exponents.</figcaption></figure>

Largier, 2003), where enhanced exposure and dispersal directly influence survival, transport pathways, and ecological connectivity (e.g., Manral et al., 2025). Moreover, when we quantify this with the percentage change caused by tidal forcing (Figure 10), we find that even the smallest observed change (a 0.76% decrease in AD) corresponds to a difference of over 100 km in travel distance. Such differences are far from negligible and could substantially influence the accuracy of particle transport forecasts, particularly for pollution mitigation operations, especially in or near marine protected areas.

The GKDE analysis shows that including tidal forcing significantly impacts surface particle accumulation patterns (Figures 3, 4, and 10). In the non-tidal simulation, accumulation is higher during winter compared to summer. When tidal forcing is added, this summer-winter difference is attenuated, reducing accumulation in winter but enhancing it in summer. This seasonal difference is not only influenced by eddy-driven variability but also by the temporal variability of internal wave fields, which is modulated both by the spring-neap cycle (~14 days; Bella et al., 2024) and by the seasonal cycle of stratification (Jackson, 2004; Lahaye et al., 2019; Rocha et al., 2016; Torres et al., 2018; Verron et al., 2020). Tidal forcing reduces accumulation during winter, when tide-induced dynamics interact with intensified mesoscale activity, and enhances it in summer, when circulation is comparatively weaker. The mechanisms behind this seasonal modulation differ between winter and summer and also vary across spatial scales, as discussed below.
Focusing first on the mechanisms underlying the winter patterns, the high accumulation observed in the non-tidal simulation (Figure 4, GKDE) is likely linked to intensified eddy activity. Ajayi et al. (2020) found a higher number of eddies during winter than summer in the NATL60 simulation, which closely resembles the eNATL60 non-tidal simulation. This increased winter eddy number could explain the higher non-tidal winter GKDE results, since more eddies imply greater capacity to accumulate floating material (e.g., Bello-Fuentes et al., 2021; d'Ovidio et al., 2013). The lower accumulation capacity during winter for the tidal simulation could be associated with a decrease in mesoscale energy due to dissipation by internal waves (Barkan et al., 2017). This could reduce the retention capacity of mesoscale eddies, similar to the effect of surface waves (Dobler et al., 2019; Morales-Márquez et al., 2023). On the other hand, internal wave presence in winter is lower than in summer (Jackson, 2004; Lahaye et al., 2019; Rocha et al., 2016; Torres et al., 2018; Verron et al., 2020). Therefore, winter reduction of accumulation zones with tidal forcing may reflect attenuation of mesoscale coherence by tide-induced small-scale dynamics. This is consistent with Verron et al. (2020), who showed that fine-scale energy levels of eNATL60 increase with tidal forcing. Moreover, Haza et al. (2016) found that submesoscale structures make mesoscale eddies more permeable. During late autumn and winter (October-February), tidal forcing leads to a noticeable decrease in the occurrence of high surface accumulation zones, as observed in both GKDE and bFTLE patterns (Figure 10). This likely reflects the impact of tidal forcing on the mechanisms behind eddy generation. In the Azores region, baroclinic instability is the main driver of eddy formation (Volkov & Fu, 2011), particularly during winter (Ajayi et al., 2020). However, Lin et al. (2023) found that tidal forcing enhances vertical mixing, modifying stratification and reducing baroclinic instabilities, and thus the formation of eddies and associated accumulation zones.

In summer, stronger stratification enhances internal wave activity, particularly in the tidal simulation. This is captured in eNATL60 (Ajayi et al., 2022; Bella et al., 2024; Verron et al., 2020) and has also been observed in the region (Jackson, 2004). These internal waves generate surface convergence zones (Shanks, 2021), promoting particle clustering which could explain the GKDE increase. Another possible mechanism is the formation of persistent larger-scale convergence patterns under tidal forcing, such as tidal fronts, which are typically more pronounced in summer (e.g., Graham et al., 2018) and create surface convergence (Ricker et al., 2021). Although internal wave dynamics induce fine-scale stirring and stretching that would typically enhance bFTLE values, we observe a decrease, suggesting that tidal forcing combined with strong summer stratification disrupts frontogenesis, thereby reducing LCS (i.e., lower bFTLE values). This is consistent with high summer internal wave activity, which enhances vertical stirring along density surfaces (e.g., Garwood et al., 2020) but can weaken horizontal convergence (e.g., Swart et al., 2020), reducing small-scale bFTLE values. The increase in vertical motions during summer could result from internal waves themselves (e.g., Staalstrøm & Røed, 2016), or from enhanced vertical mixing under tidal forcing (Stanev & Ricker, 2020), a process particularly intensified in summer (Masunaga et al., 2022). Therefore, at small scales, tidal oscillations and vertical mixing may weaken submesoscale fronts, reducing LCS. These submesoscale fronts are most intense in spring, when frontogenesis is typically enhanced (e.g., Garabato et al., 2022; Taylor & Thompson, 2023) and upper-ocean fronts are strained into finer structures by a winter-intensified mesoscale eddy field (Garabato et al., 2022). This could explain the peak in bFTLE values during spring (Figure 9). Taken together, the two diagnostics highlight complementary aspects of the flow. Gaussian Kernel Density Estimation primarily reflects mesoscale-driven accumulation, whereas bFTLE is more sensitive to fine-scale stirring and frontogenesis. Under tidal forcing, these scales respond differently: mesoscale accumulation is enhanced in summer (GKDE), while fine-scale convergence is weakened (bFTLE). This contrast reflects how tides redistribute energy from the mesoscale to the submesoscale (Barkan et al., 2021), complicating yet enriching the interpretation of Lagrangian transport under tidal versus non-tidal conditions.

In addition, insight on rare extremes was obtained from analyzing the skewness of the distribution of the surface accumulation patterns (2D histograms and bFTLEs). Skewness does not directly measure extreme values but reflects the asymmetry of the distribution. Since our histograms are consistently positively skewed, their right tails correspond to localized accumulation zones. With tidal forcing, skewness increases, indicating a greater occurrence of these localized hotspots of floating-material accumulation. Capturing such fine-scale hotspots remains a major challenge in surface clustering predictions (e.g., Kunz et al., 2024), yet is critical for improving Lagrangian simulations in both research and operational contexts.
5. Conclusions and Perspectives

In this study, we investigated the impact of tide-induced dynamics on ocean surface Lagrangian properties using a high-resolution twin simulation (eNATL60) with and without tidal forcing in the region south-southeast of the Azores Islands. Our findings underscore that tidal forcing plays a fundamental role in shaping surface transport dynamics, and that its impact varies across seasons and spatial scales. By quantifying its influence using multiple diagnostics, we show that tidal forcing affects the distances traveled by particle trajectories and the formation and intensity of accumulation zones across multiple scales. Recognizing the role of tidal forcing is thus crucial to improving Lagrangian simulations in both research and operational applications, as our findings suggest that considering tidal currents alone may not capture the full range of tide-induced effects. Accurately representing tidal dynamics is therefore essential in high-resolution ocean models used to simulate particle trajectories.

Tidal effects influence the accuracy of particle trajectory forecasts used for applications such as predicting plastic dispersion, oil spills, and the arrival of biological material like *Sargassum*. They also shape particle dispersion pathways that influence the exposure of marine organisms to nutrients, pollutants, or thermal stress-factors, critical for understanding survival, recruitment, and connectivity. Notably, even small percentage changes in particle displacement due to tidal forcing can result in trajectory deviations of over 100 km, which are non-negligible for operational ocean forecasting, for example, in pollution mitigation efforts. Accurately resolving the combined effects of tides and other high-frequency dynamics is especially important for short-term prediction and for understanding floating material pathways in coastal and open-ocean settings. As Lagrangian simulations are increasingly used to support marine decision-making, accounting for tide-induced variability becomes essential to deliver reliable and actionable forecasts to policy-makers and other operational stakeholders involved in marine protection and emergency response. Ultimately, this enhances the capacity of ocean modeling to inform marine spatial planning, ecosystem monitoring, and conservation efforts.

One limitation of this study is the timespan of the eNATL60 simulation, which restricted our analysis to only one year. It would be interesting to investigate the interannual variability of the tidal effects we observed, given the EKE interannual variability in this region (Martins et al., 2002; Volkov & Fu, 2011). When new model simulations allow it, it would be useful to reproduce this study over longer periods. Nevertheless, this twin simulation of an OGCM at high resolution with and without tidal forcing provides extensive spatial coverage, making it particularly valuable for exploring additional scenarios. Our results are relevant to other regions with similar ocean dynamics, namely with high internal waves signals. Future studies could apply the methods implemented here to other regions. Regions of interest include those with weaker internal wave signals (e. g., eastern part of the North Atlantic basin or the Gulf Stream region) and those with stronger tidal currents (e. g., the North Sea).

We found that including tides is necessary to better understand the global geometry of the oceanic flows, particularly in terms of LCS and transport barriers. This opens the door to further studies analyzing the tidal impacts not only on surface ocean transport, but also at depth and on ocean mixing properties. Furthermore, the impact of the fine-scales, and especially unbalanced motions like internal waves, on ocean surface dynamics is still under investigation (Gula et al., 2022; Shakespeare & Hogg, 2018; Thomas & Daniel, 2021). Future work could look further into this by analyzing the impact of the different temporal and spatial scales on Lagrangian dynamics. In particular, high-frequency motions due to tides are especially relevant for the analysis of novel ocean data from wide-swath satellite missions such as the Surface Water Ocean Topography mission (Morrow et al., 2019).

Focusing on Lagrangian trajectory studies around archipelagos and coastal regions, future work could investigate the impact of tidal forcing on the arrival (Sala et al., 2016) and beaching (e.g., Kaandorp et al., 2020; Yoon et al., 2010) of virtual particles, as well as on connectivity between islands (Vaz et al., 2013). It would also be interesting to study its impact on the surface-ocean connectivity timescales at a global scale (Jönsson & Watson, 2016). Such studies are important for understanding pollution pathways and
<figure><img src="image_14.png" /><figcaption>**Figure A1.** Probability density function of the backward Finite Time Lyapunov Exponent fields on day 1 of each month for the no tidal forcing (blue) and tidal forcing (red) simulations. The vertical black line shows the threshold used at $0.5 \text{ days}^{-1}$.</figcaption></figure>

the threats to biodiversity, particularly on islands, and for guiding strategies for their protection. Our results can therefore contribute to operational oceanography efforts aimed at strengthening marine ecosystem monitoring programmes.

## Appendix A: Backward FTLE Distribution

The PDFs of the bFTLE fields for day 1 of each month are shown in Figure A1. All PDFs are positively skewed, demonstrating that the threshold of $0.5 \text{ days}^{-1}$ is representative of the start of the tail for all months.

## Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

## Data Availability Statement

Details on the model data used in this study, eNATL60, and its availability can be found here https://github.com/ocean-next/eNATL60 (Brodeau et al., 2020a). The codes used to generate the Lagrangian simulations and analyze them are available on GitHub: https://github.com/Parcels-code/Azores_TidalForcing, and the version used for the manuscript is published on Zenodo: https://doi.org/10.5281/zenodo.18499198 (Gómez-Navarro, 2026).
Acknowledgments

LGN and EvS were partly funded by the European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme (grant agreement no. 715386) and the ESA World Ocean Circulation project, ESA Contract no. 4000130730/20/INB. LGN is also grateful for current funding under the Marie Skłodowska-Curie Actions programme, funded by the European Union (HORIZON-MSCA-2023-PF RELACS, grant agreement no. 101155713). EvS was also partly supported through the IMMERSE project of the European Union Horizon 2020 Research and Innovation Program (grant agreement no. 821926). IHC acknowledges financial support from the project COPLA (PID2023-153236NA-100) funded by MICIU/AEI/https://doi.org/10.13039/501100011033/FEDER, UE. We also acknowledge funding from the Spanish government through the "Severo Ochoa Centre of Excellence" accreditation (CEX2019-000928-S). Furthermore, we would like to thank JAMES editor Stephen Griffies and the two anonymous reviewers for their insightful comments that have greatly improved this paper.

References

Ainsworth, C. H., Chassignet, E. P., French-McCay, D., Beegle-Krause, C. J., Berenshtein, I., Englehardt, J., et al. (2021). Ten years of modeling the Deepwater Horizon oil spill. *Environmental Modelling & Software*, **142**, 105070. https://doi.org/10.1016/j.envsoft.2021.105070

Ajayi, A., Le Sommer, J., Chassignet, E., Molines, J.-M., Xu, X., Albert, A., & Cosme, E. (2020). Spatial and temporal variability of the north Atlantic eddy field from two kilometric-resolution Ocean models. *Journal of Geophysical Research: Oceans*, **125**(5), e2019JC015827. https://doi.org/10.1029/2019JC015827

Ajayi, A., Sommer, J. L., Brodeau, L., Arbic, B. K., Serazin, G., Albert, A., et al. (2022). On the modulation of kinetic energy transfer by internal gravity waves. *EarthArXiv*. https://doi.org/10.31223/X5204J

Alves, M. L. G. R., & Colin de Verdière, A. (1999). Instability dynamics of a subtropical jet and applications to the Azores Front Current System: Eddy-driven mean flow. *Journal of Physical Oceanography*, **29**(5), 837–864. https://doi.org/10.1175/1520-0485(1999)029<0837:idoasj>2.0. co;2

Alves, M. L. G. R., Gaillard, F., Sparrow, M., Knoll, M., & Giraud, S. (2002). Circulation patterns and transport of the Azores Front-Current system. *Deep Sea Research Part II: Topical Studies in Oceanography*, **49**(19), 3983–4002. https://doi.org/10.1016/s0967-0645(02)00138-8

Ansong, J. K., Arbic, B. K., Menemenlis, D., Wallcraft, A. J., Bourdalle-Badie, R., Chanut, J., et al. (2020). Importance of damping in comparison of internal tides in several global hydrodynamical models with altimetry. In *Ocean sciences meeting 2020*.

Arbic, B. K., Alford, M. H., Ansong, J. K., Buijsman, M. C., Ciotti, R. B., Farrar, J. T., et al. (2018). Primer on global internal tide and internal gravity wave continuum modeling in HYCOM and MITgcm. In *New frontiers in operational oceanography* (pp. 307–392).

Barbosa Aguiar, A. C., Peliz, A. J., Cordeiro Pires, A., & Le Cann, B. (2011). Zonal structure of the mean flow and eddies in the Azores Current system. *Journal of Geophysical Research*, **116**(C2), C02012. https://doi.org/10.1029/2010JC006538

Barkan, R., Srinivasan, K., Yang, L., McWilliams, J. C., Gula, J., & Vic, C. (2021). Oceanic mesoscale eddy depletion catalyzed by internal waves. *Geophysical Research Letters*, **48**(18), e2021GL094376. https://doi.org/10.1029/2021GL094376

Barkan, R., Winters, K. B., & McWilliams, J. C. (2017). Stimulated imbalance and the enhancement of eddy kinetic energy dissipation by internal waves. *Journal of Physical Oceanography*, **47**(1), 181–198. https://doi.org/10.1175/jpo-d-16-0117.1

Bella, A., Lahaye, N., & Tissot, G. (2024). Internal tide energy transfers induced by mesoscale circulation and topography across the North Atlantic. *Journal of Geophysical Research: Oceans*, **129**(8), e2024JC020914. https://doi.org/10.1029/2024JC020914

Bello-Fuentes, F. J., García-Nava, H., Andrade-Canto, F., Durazo, R., Castro, R., & Yarbuh, I. (2021). Tiempo de retención y capacidad de transporte de los remolinos del noroeste del golfo de México. *Ciencias Marinas*, **47**(2), 71–88. https://doi.org/10.7773/cm.v47i2.3116

Beron-Vera, F. J., Olascoaga, M. J., & Goni, G. J. (2010). Surface Ocean mixing inferred from different multisatellite altimetry measurements. *Journal of Physical Oceanography*, **40**(11), 2466–2480. https://doi.org/10.1175/2010JPO4458.1

Bôas, A. B., Arduuin, F., Ayet, A., Bourassa, M. A., Brandt, P., Chapron, B., & Sebille, E. v. (2019). Integrated observations of global surface winds, currents, and waves: Requirements and challenges for the next decade. *Frontiers in Marine Science*, **6**, 425. https://doi.org/10.3389/fma rs.2019.00425

Boffetta, G., Lacorata, G., Redaelli, G., & Vulpiani, A. (2001). Detecting barriers to transport: A review of different techniques. *Physica D: Nonlinear Phenomena*, **159**(1–2), 58–70. https://doi.org/10.1016/S0167-2789(01)00330-X

Brodeau, L., Le Sommer, J., & Albert, A. (2020a). eNATL60 dataset [Dataset]. Zenodo. https://doi.org/10.5281/zenodo.4032732

Brodeau, L., Le Sommer, J., & Albert, A. (2020b). eNATL60: Material describing the set-up and the assessment of NEMO-eNATL60 simulations [Software]. Zenodo. https://zenodo.org/records/4032732

Brunner, K., Kukulka, T., Proskurowski, G., & Law, K. L. (2015). Passive buoyant tracers in the ocean surface boundary layer: 2. Observations and simulations of microplastic marine debris. *Journal of Geophysical Research: Oceans*, **120**(11), 7559–7573. https://doi.org/10.1002/ 2015jc010840

Bühler, O., & McIntyre, M. E. (2005). Wave capture and wave-vortex duality. *Journal of Fluid Mechanics*, **534**, 67–95.

Caldeira, R. M., & Reis, J. C. (2017). The Azores confluence zone. *Frontiers in Marine Science*, **4**, 37. https://doi.org/10.3389/fmars.2017.00037

Cardoso, C., & Caldeira, R. M. A. (2021). Modeling the exposure of the Macaronesia Islands (NE Atlantic) to marine plastic pollution. *Frontiers in Marine Science*, **8**, 332. https://doi.org/10.3389/fmars.2021.653502

Chamecki, M., Chor, T., Yang, D., & Meneveau, C. (2019). Material transport in the ocean mixed layer: Recent developments enabled by large eddy simulations. *Reviews of Geophysics*, **57**(4), 1338–1371. https://doi.org/10.1029/2019RG000655

Condie, S. A., & Condie, R. (2016). Retention of plankton within ocean eddies. *Global Ecology and Biogeography*, **25**(10), 1264–1277. https:// doi.org/10.1111/geb.12485

d'Asaro, E. A., Shcherbina, A. Y., Klymak, J. M., Molemaker, J., Novelli, G., Guigand, C. M., et al. (2018). Ocean convergence and the dispersion of flotsam. *Proceedings of the National Academy of Sciences*, **115**(6), 1162–1167.

Delandmeter, P., & van Sebille, E. (2019). The Parcels v2.0 Lagrangian framework: New field interpolation schemes. *Geoscientific Model Development*, **12**(8), 3571–3584. https://doi.org/10.5194/gmd-12-3571-2019

Díaz-Barroso, L., Hernández-Carrasco, I., Orfila, A., Reglero, P., Balbín, R., Hidalgo, M., & Alvarez-Berastegui, D. (2022). Singularities of surface mixing activity in the Western Mediterranean influence bluefin tuna larval habitats. *Marine Ecology Progress Series*, **685**, 69–84. https://doi.org/10.3354/meps13979

Dobler, D., Huck, T., Maes, C., Grima, N., Blanke, B., Martinez, E., & Arduuin, F. (2019). Large impact of Stokes drift on the fate of surface floating debris in the South Indian Basin. *Marine Pollution Bulletin*, **148**, 202–209. https://doi.org/10.1016/j.marpolbul.2019.07.057

d'Ovidio, F., Monte, S. D., Penna, A. D., Cotté, C., & Guinet, C. (2013). Ecological implications of eddy retention in the open ocean: A Lagrangian approach. *Journal of Physics A: Mathematical and Theoretical*, **46**(25), 254023. https://doi.org/10.1088/1751-8113/46/25/254023

Drillet, Y., Chune, S. L., Levier, B., & Drevillon, M. (2019). SMOC: A new global surface current product containing the effect of the ocean general circulation, waves and tides. In *Geophysical research abstracts* (Vol. 21).

Garabato, A. C. N., Yu, X., Callies, J., Barkan, R., Polzin, K. L., Frajka-Williams, E. E., et al. (2022). Kinetic energy transfers between mesoscale and submesoscale motions in the open ocean's upper layers. *Journal of Physical Oceanography*, **52**(1), 75–97. https://doi.org/10.1175/JPO-D- 21-0099.1

Garwood, J. C., Musgrave, R. C., & Lucas, A. J. (2020). Life in internal waves. *Oceanography*, **33**(3), 38–49. https://doi.org/10.5670/oceanog. 2020.313

Gómez-Navarro, L. (2026). Parcels-code/Azores_TidalForcing (Version v1.0.0) [Software]. Zenodo. https://doi.org/10.5281/zenodo.18499198

Gould, W. (1985). Physical oceanography of the Azores Front. *Progress in Oceanography*, **14**, 167–190. https://doi.org/10.1016/0079-6611(85) 90010-2
Graham, J. A., O'Dea, E., Holt, J., Polton, J., Hewitt, H. T., Furner, R., et al. (2018). AMM15: A new high-resolution NEMO configuration for operational simulation of the European north-west shelf. *Geoscientific Model Development, 11*(2), 681–696. https://doi.org/10.5194/gmd-11-681-2018

Gula, J., Taylor, J., Shcherbina, A., & Mahadevan, A. (2022). Chapter 8—Submesoscale processes and mixing. In M. Meredith & A. Naveira Garabato (Eds.), *Ocean mixing* (pp. 181–214). Elsevier. https://doi.org/10.1016/B978-0-12-821512-8.00015-3

Haller, G. (2001). Distinguished material surfaces and coherent structures in three-dimensional fluid flows. *Physica D: Nonlinear Phenomena, 149*(4), 248–277. https://doi.org/10.1016/S0167-2789(00)00199-8

Haller, G. (2015). Lagrangian coherent structures. *Annual Review of Fluid Mechanics, 47*(1), 137–162. https://doi.org/10.1146/annurev-fluid-010313-141322

Haller, G., & Yuan, G. (2000). Lagrangian coherent structures and mixing in two-dimensional turbulence. *Physica D: Nonlinear Phenomena, 147*(3–4), 352–370. https://doi.org/10.1016/s0167-2789(00)00142-1

Haza, A. C., Özgökmen, T. M., & Hogan, P. (2016). Impact of submesoscales on surface material distribution in a Gulf of Mexico mesoscale eddy. *Ocean Modelling, 107*, 28–47. https://doi.org/10.1016/j.ocemod.2016.10.002

Hernández-Carrasco, I., Alou-Font, E., Dumont, P.-A., Cabornero, A., Allen, J., & Orfila, A. (2020). Lagrangian flow effects on phytoplankton abundance and composition along filament-like structures. *Progress in Oceanography, 189*, 102469. https://doi.org/10.1016/j.pcean.2020.102469

Hernández-Carrasco, I., López, C., Hernández-García, E., & Turiel, A. (2011). How reliable are finite-size Lyapunov exponents for the assessment of ocean dynamics? *Ocean Modelling, 36*(3–4), 208–218. https://doi.org/10.1016/j.ocemod.2010.12.006

Hernández-Carrasco, I., Orfila, A., Rossi, V., & Garçon, V. (2018). Effect of small scale transport processes on phytoplankton distribution in coastal seas. *Scientific Reports, 8*(1), 8613. https://doi.org/10.1038/s41598-018-26857-9

Hidalgo, M., Rossi, V., Monroy, P., Ser-Giacomi, E., Hernández-García, E., Guijarro, B., et al. (2019). Accounting for ocean connectivity and hydroclimate in fish recruitment fluctuations within transboundary metapopulations. *Ecological Applications, 29*(5), e01913. https://doi.org/10.1002/eap.1913

Higgins, C., Vanneste, J., & Bremer, T. S. (2020). Unsteady Ekman–Stokes dynamics: Implications for surface wave–induced drift of floating marine litter. *Geophysical Research Letters, 47*(18), e2020GL089189. https://doi.org/10.1029/2020GL089189

Huntley, H. S., Lipphardt, B. L., Jr., Jacobs, G., & Kirwan, A. D., Jr. (2015). Clusters, deformation, and dilation: Diagnostics for material accumulation regions. *Journal of Geophysical Research: Oceans, 120*(10), 6622–6636. https://doi.org/10.1002/2015JC011036

Iwasaki, S., Isobe, A., Kako, S., Uchida, K., & Tokai, T. (2017). Fate of microplastics and mesoplastics carried by surface currents and wind waves: A numerical model approach in the Sea of Japan. *Marine Pollution Bulletin, 121*(1), 85–96. https://doi.org/10.1016/j.marpolbul.2017.05.057

Jackson, C. R. (2004). An atlas of internal solitary-like waves and their properties. Retrieved from http://www.internalwaveatlas.com/Atlas2_i Index.html

Jackson, C. R., da Silva, J., & Jeans, G. (2012). The generation of nonlinear internal waves. *Oceanography, 25*(2), 108–123. https://doi.org/10.5670/oceanog.2012.46

Jönsson, B. F., & Watson, J. R. (2016). The timescales of global surface-ocean connectivity. *Nature Communications, 7*(1), 11239. https://doi.org/10.1038/ncomms11239

Kaandorp, M. L., Dijkstra, H. A., & van Sebille, E. (2020). Closing the mediterranean marine floating plastic mass budget: Inverse modeling of sources and sinks. *Environmental Science and Technology, 54*(19), 11980–11989. https://doi.org/10.1021/acs.est.0c01984

Klein, B., & Siedler, G. (1989). On the origin of the Azores Current. *Journal of Geophysical Research, 94*(C5), 6159–6168. https://doi.org/10.1029/94JC094iC05p06159

Krüger, L., Ramos, J., Xavier, J., Grémillet, D., González-Solís, J., Kolbeinsson, Y., et al. (2017). Identification of candidate pelagic marine protected areas through a seabird seasonal-multispecific-and extinction risk-based approach. *Animal Conservation, 20*(5), 409–424.

Kunz, L., Griesel, A., Eden, C., Duran, R., & Sainte-Rose, B. (2024). Transient attracting profiles in the Great Pacific Garbage Patch. *Ocean Science, 20*(6), 1611–1630. https://doi.org/10.5194/os-20-1611-2024

Lahaye, N., Gula, J., & Roullet, G. (2019). Sea surface signature of internal tides. *Geophysical Research Letters, 46*(7), 3880–3890. https://doi.org/10.1029/2018GL081848

Largier, J. L. (2003). Considerations in estimating larval dispersal distances from oceanographic data. *Ecological Applications, 13*(sp1), 71–89. https://doi.org/10.1890/1051-0761(2003)013[0071:CIELDD]2.0.CO;2

Le Sommer, J., Chassignet, E. P., & Wallcraft, A. J. (2018). Ocean circulation modeling for operational oceanography: Current status and future challenges. In *New frontiers in operational oceanography* (pp. 289–306). https://doi.org/10.17125/gov2018.ch12.289

Lévy, M., Ferrari, R., Franks, P. J., Martin, A. P., & Rivière, P. (2012). Bringing physics to life at the submesoscale. *Geophysical Research Letters, 39*(14), L14602. https://doi.org/10.1029/2012GL052756

Lévy, M., Klein, P., & Treguier, A.-M. (2001). Impact of sub-mesoscale physics on production and subduction of phytoplankton in an oligotrophic regime. *Journal of Marine Research, 59*(4), 535–565.

Limer, B. D., Bloomberg, J., & Holstein, D. M. (2020). The influence of eddies on coral larval retention in the Flower Garden Banks. *Frontiers in Marine Science, 7*, 372. https://doi.org/10.3389/fmars.2020.00372

Lin, L., von Storch, H., Chen, X., Jiang, W., & Tang, S. (2023). Link between the internal variability and the baroclinic instability in the Bohai and Yellow Sea. *Ocean Dynamics, 73*(12), 1–14. https://doi.org/10.1007/s10236-023-01583-7

Liu, Y., Weisberg, R. H., Vignudelli, S., & Mitchum, G. T. (2014). Evaluation of altimetry-derived surface current products using Lagrangian drifter trajectories in the eastern Gulf of Mexico. *Journal of Geophysical Research: Oceans, 119*(5), 2827–2842. https://doi.org/10.1002/2013JC009710

Mahadevan, A. (2016). The impact of submesoscale physics on primary productivity of plankton. *Annual Review of Marine Science, 8*(1), 161–184. https://doi.org/10.1146/annurev-marine-010814-015912

Manral, D., Gómez-Navarro, L., Denes, M. C., Iovino, D., Fogli, P. G., Masina, S., et al. (2025). Separation timescales of vertically migrating zooplankton and other (a)biotic materials in the Benguela System. *Journal of Geophysical Research: Oceans, 130*(4), e2024JC021701. https://doi.org/10.1029/2024JC021701

Martins, C. S., Hamann, M., & Fiúza, A. F. G. (2002). Surface circulation in the eastern North Atlantic, from drifters and altimetry. *Journal of Geophysical Research, 107*(C12), 10–1–22. https://doi.org/10.1029/2000JC000345

Masunaga, E., Uchiyama, Y., Zhang, X., Kimura, W., & Kosako, T. (2022). Modulation of submesoscale motions due to tides and a shallow ridge along the Kuroshio. *Deep Sea Research Part I: Oceanographic Research Papers, 186*, 103828. https://doi.org/10.1016/j.dsr.2022.103828

Maximenko, N., Hafner, J., Kamachi, M., & MacFadyen, A. (2018). Numerical simulations of debris drift from the Great Japan Tsunami of 2011 and their verification with observational reports. *Marine Pollution Bulletin, 132*, 5–25. https://doi.org/10.1016/j.marpolbul.2018.03.056
Maximenko, N., Hafner, J., & Niiler, P. (2012). Pathways of marine debris derived from trajectories of Lagrangian drifters. *Marine Pollution Bulletin*, **65**(1–3), 51–62. https://doi.org/10.1016/j.marpolbul.2011.04.016

McWilliams, J. C., Gula, J., & Molemaker, M. J. (2019). The Gulf Stream north wall: Ageostrophic circulation and frontogenesis. *Journal of Physical Oceanography*, **49**(4), 893–916. https://doi.org/10.1175/jpo-d-18-0203.1

Miron, P., Olascoaga, M. J., Beron-Vera, F. J., Putman, N. F., Triñanes, J., Lumpkin, R., & Goni, G. J. (2020). Clustering of marine-debris- and sargassum-like drifters explained by inertial particle dynamics. *Geophysical Research Letters*, **47**(19), e2020GL089874. https://doi.org/10.1029/2020GL089874

Morales-Márquez, V., Hernández-Carrasco, I., Fox-Kemper, B., & Orfila, A. (2023). Ageostrophic contribution by the wind and waves induced flow to the lateral stirring in the Mediterranean Sea. *Journal of Geophysical Research: Oceans*, **128**(4), e2022JC019135. https://doi.org/10.1029/2022JC019135

Morales-Márquez, V., Hernández-Carrasco, I., Simarro, G., Rossi, V., & Orfila, A. (2021). Regionalizing the impacts of wind- and wave-induced currents on surface ocean dynamics: A long-term variability analysis in the Mediterranean Sea. *Journal of Geophysical Research: Oceans*, **126**(9), e2020JC017104. https://doi.org/10.1029/2020JC017104

Morrow, R., Fu, L.-L., Ardhuin, F., Benkiran, M., Chapron, B., Cosme, E., et al. (2019). Global observations of fine-scale ocean surface topography with the Surface Water and Ocean Topography (SWOT) mission. *Frontiers in Marine Science*, **6**, 232. https://doi.org/10.3389/fma rs.2019.00232

Mtfller, P. (1976). On the diffusion of momentum and mass by internal gravity waves. *Journal of Fluid Mechanics*, **77**(4), 789–823. https://doi. org/10.1017/S0022112076002899

Onink, V., Wichmann, D., Delandmeter, P., & van Sebille, E. (2019). The role of Ekman currents, geostrophy, and Stokes drift in the accumulation of floating microplastic. *Journal of Geophysical Research: Oceans*, **124**(3), 1474–1490. https://doi.org/10.1029/2018jc014547

Pham, C. K., Pereira, J. M., Frias, J. P. G. L., Ríos, N., Carriço, R., Juliano, M., & Rodríguez, Y. (2020). Beaches of the Azores Archipelago as transitory repositories for small plastic fragments floating in the North-East Atlantic. *Environmental Pollution*, **263**, 114494. https://doi.org/10.1016/j.envpol.2020.114494

Poje, A. C., Özgökmen, T. M., Lipphardt Jr, B. L., Haus, B. K., Ryan, E. H., Haza, A. C., et al. (2014). Submesoscale dispersion in the vicinity of the Deepwater Horizon spill. *Proceedings of the National Academy of Sciences*, **111**(35), 12693–12698. https://doi.org/10.1073/pnas. 1402452111

Putman, N. F., Lumpkin, R., Olascoaga, M. J., Trinanes, J., & Goni, G. J. (2020). Improving transport predictions of pelagic Sargassum. *Journal of Experimental Marine Biology and Ecology*, **529**, 151398. https://doi.org/10.1016/j.jembe.2020.151398

Ray, R. D., & Zaron, E. D. (2016). M2 internal tides and their observed wavenumber spectra from satellite altimetry. *Journal of Physical Oceanography*, **46**(1), 3–22. https://doi.org/10.1175/JPO-D-15-0065.1

Révelard, A., Reyes, E., Mourre, B., Hernández-Carrasco, I., Rubio, A., Lorente, P., et al. (2021). Sensitivity of skill score metric to validate Lagrangian simulations in coastal areas: Recommendations for search and rescue applications. *Frontiers in Marine Science*, **8**, 191. https://doi. org/10.3389/fmars.2021.630388

Ricker, M., Meyerjürgens, J., Badewien, T. H., & Stanev, E. V. (2021). Lagrangian methods for visualizing and assessing frontal dynamics of floating marine litter with a focus on tidal basins. In I. M. Belkin (Ed.), *Chemical oceanography of frontal zones. The handbook of environmental chemistry* (Vol. 116, pp. 407–442). Springer. https://doi.org/10.1007/698_2021_812

Rocha, C. B., Gille, S. T., Chereskin, T. K., & Menemenlis, D. (2016). Seasonality of submesoscale dynamics in the Kuroshio Extension. *Geophysical Research Letters*, **43**(21), 11–304. https://doi.org/10.1002/2016GL071349

Sala, I., Harrison, C. S., & Caldeira, R. M. (2016). The role of the Azores Archipelago in capturing and retaining incoming particles. *Journal of Marine Systems*, **154**, 146–156. https://doi.org/10.1016/j.jmarsys.2015.10.001

Sánchez-Garrido, J. C., Naranjo, C., Macías, D., García-Lafuente, J., & Oguz, T. (2015). Modeling the impact of tidal flows on the biological productivity of the. *Journal of Geophysical Research: Oceans*, **120**(11), 7329–7345. https://doi.org/10.1002/2015JC010885

Sangrà, P., Pascual, A., Rodríguez-Santana, Á., Machín, F., Mason, E., McWilliams, J. C., et al. (2009). The Canary Eddy Corridor: A major pathway for long-lived eddies in the subtropical North Atlantic. *Deep Sea Research Part I: Oceanographic Research Papers*, **56**(12), 2100–2114. https://doi.org/10.1016/j.dsr.2009.08.008

Savage, A. C., Arbic, B. K., Richman, J. G., Shriver, J. F., Alford, M. H., Buijsman, M. C., et al. (2017). Frequency content of sea surface height variability from internal gravity waves to mesoscale eddies. *Journal of Geophysical Research: Oceans*, **122**(3), 2519–2538. https://doi.org/10. 1002/2016jc012331

Scott, D. W. (1992). *Multivariate density estimation: Theory, practice, and visualization*. John Wiley & Sons Inc. https://doi.org/10.1002/ 9780470316849

Shadden, S. C., Lekien, F., & Marsden, J. E. (2005). Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. *Physica D: Nonlinear Phenomena*, **212**(3–4), 271–304. https://doi.org/10.1016/j.physd.2005. 10.007

Shakespeare, C. J., & Hogg, A. M. (2018). The life cycle of spontaneously generated internal waves. *Journal of Physical Oceanography*, **48**(2), 343. https://doi.org/10.1175/JPO-D-17-0153.1

Shanks, A. L. (2021). Observational evidence and open questions on the role of internal tidal waves on the concentration and transport of floating plastic debris. *Frontiers in Marine Science*, **8**, 633. https://doi.org/10.3389/fmars.2021.621062

Silva-Fernandes, S. M., & Peliz, A. J. (2020). The turbulent structure of the Azores Current System: A statistical analysis. *Journal of Geophysical Research: Oceans*, **125**(11), e2020JC016327. https://doi.org/10.1029/2020JC016327

Staalstrøm, A., & Røed, L. P. (2016). Vertical mixing and internal wave energy fluxes in a sill fjord. *Journal of Marine Systems*, **159**, 15–32. https://doi.org/10.1016/j.jmarsys.2016.02.005

Stammer, D. (1997). Global characteristics of ocean variability estimated from regional TOPEX/POSEIDON altimeter measurements. *Journal of Physical Oceanography*, **27**(8), 1743–1769. https://doi.org/10.1175/1520-0485(1997)027(1743:GCOOVE)2.0:CO2

Stanev, E. V., & Ricker, M. (2020). Interactions between barotropic tides and mesoscale processes in deep ocean and shelf regions. *Ocean Dynamics*, **70**(5), 713–728. https://doi.org/10.1007/s10236-020-01348-6

Sterl, M. F., Delandmeter, P., & van Sebille, E. (2020). Influence of barotropic tidal currents on transport and accumulation of floating micro-plastics in the global open ocean. *Journal of Geophysical Research: Oceans*, **125**(2), e2019JC015583. https://doi.org/10.1029/2019JC015583

Stramma, L., & Siedler, G. (1988). Seasonal changes in the North Atlantic subtropical gyre. *Journal of Geophysical Research*, **93**(C7), 8111–8118. https://doi.org/10.1029/JC093iC07p08111

Sutherland, B. R., & Yassin, H. (2022). The nonlinear evolution of internal tides. Part 2. Lagrangian transport by periodic and modulated waves. *Journal of Fluid Mechanics*, **948**, A22. https://doi.org/10.1017/jfm.2022.690
Swart, S., Du Plessis, M. D., Thompson, A. F., Biddle, L. C., Giddy, I., Linders, T., et al. (2020). Submesoscale fronts in the Antarctic marginal ice zone and their response to wind forcing. *Geophysical Research Letters*, **47**(6), e2019GL086649. https://doi.org/10.1029/2019GL086649

Tarry, D. R., Essink, S., Pascual, A., Ruiz, S., Poulain, P.-M., Özgökmen, T., et al. (2021). Frontal convergence and vertical velocity measured by drifters in the Alboran Sea. *Journal of Geophysical Research: Oceans*, **126**(4), e2020JC016614. https://doi.org/10.1029/2020jc016614

Taylor, J. R., & Thompson, A. F. (2023). Submesoscale dynamics in the upper ocean. *Annual Review of Fluid Mechanics*, **55**(1), 103–127. https://doi.org/10.1146/annurev-fluid-031422-095147

Thomas, J., & Daniel, D. (2021). Forward flux and enhanced dissipation of geostrophic balanced energy. *Journal of Fluid Mechanics*, **911**, A60. https://doi.org/10.1017/jfm.2020.1026

Torres, H. S., Klein, P., Menemenlis, D., Qiu, B., Su, Z., Wang, J., et al. (2018). Partitioning ocean motions into balanced motions and internal gravity waves: A modeling study in anticipation of future space missions. *Journal of Geophysical Research: Oceans*, **123**(11), 8084–8105. https://doi.org/10.1029/2018JC014438

Tsiaras, K., Hatzonikolakis, Y., Kalaroni, S., Pollani, A., & Triantafyllou, G. (2021). Modeling the pathways and accumulation patterns of micro- and macro-plastics in the Mediterranean. *Frontiers in Marine Science*, **8**, 1389. https://doi.org/10.3389/fmars.2021.743117

van Sebille, E., Aliani, S., Law, K. L., Maximenko, N., Alsina, J. M., Bagaev, A., et al. (2020). The physical oceanography of the transport of floating marine debris. *Environmental Research Letters*, **15**(2), 023003. https://doi.org/10.1088/1748-9326/ab6d7d

van Sebille, E., England, M. H., & Froyland, G. (2012). Origin, dynamics and evolution of ocean garbage patches from observed surface drifters. *Environmental Research Letters*, **7**(4), 044040. https://doi.org/10.1088/1748-9326/7/4/044040

van Sebille, E., Zettler, E., Wienders, N., Amaral-Zettler, L., Elipot, S., & Lumpkin, R. (2021). Dispersion of surface drifters in the Tropical Atlantic. *Frontiers in Marine Science*, **7**, 1243. https://doi.org/10.3389/fmars.2020.607426

Vaz, A. C., Richards, K. J., Jia, Y., & Paris, C. B. (2013). Mesoscale flow variability and its impact on connectivity for the island of Hawai'i. *Geophysical Research Letters*, **40**(2), 332–337. https://doi.org/10.1029/2012GL054519

Verron, J., Bonnefond, P., Andersen, O., Ardhuin, F., Bergé-Nguyen, M., Bhowmick, S., et al. (2020). The SARAL/AltiKa mission: A step forward to the future of altimetry. *Advances in Space Research*, **68**(2), 808–828. https://doi.org/10.1016/j.asr.2020.01.030

Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., et al. (2020). SciPy 1.0: Fundamental algorithms for scientific computing in Python. *Nature Methods*, **17**(3), 261–272. https://doi.org/10.1038/s41592-019-0686-2

Volkov, D. L., & Fu, L.-L. (2011). Interannual variability of the Azores Current strength and eddy energy in relation to atmospheric forcing. *Journal of Geophysical Research*, **116**(C11). https://doi.org/10.1029/2011JC007271

Wenegrat, J. O., & McPhaden, M. J. (2016). Wind, waves, and fronts: Frictional effects in a generalized Ekman model. *Journal of Physical Oceanography*, **46**(2), 371–394. https://doi.org/10.1175/JPO-D-15-0162.1

White, G. H. (1980). Skewness, kurtosis and extreme values of northern hemisphere geopotential heights. *Monthly Weather Review*, **108**(9), 1446–1455. https://doi.org/10.1175/1520-0493(1980)108(1446:SKAEVO)2.0.CO;2

Yoon, J.-H., Kawano, S., & Igawa, S. (2010). Modeling of marine litter drift and beaching in the Japan Sea. *Marine Pollution Bulletin*, **60**(3), 448–463. https://doi.org/10.1016/j.marpolbul.2009.09.033

Zhou, M., Paduan, J. D., & Niiler, P. P. (2000). Surface currents in the Canary Basin from drifter observations. *Journal of Geophysical Research*, **105**(C9), 21893–21911. https://doi.org/10.1029/2000JC900096

Zwillinger, D., & Kokoska, S. (2000). *CRC Standard probability and statistics tables and formulae (section 2.2.24.1)*. Chapman & Hall/CRC.