Ocean scale dispersion of Amazon river plume by chaotic advection

Abstract

Dispersion of physical and biogeochemical tracers of the Amazon River plume is an intriguing topic, investigated since the 90s, due to its large impact on the North tropical Atlantic Ocean. Here we quantitatively depict the nonlinear behavior of the Amazon River plume by means of Lagrangian simulations, analyzed through dynamical systems techniques. The interaction between the North Brazil Current, flowing northward along the coast, and its retroflection that diverts part of the coastal waters eastward is mostly responsible for the observed spreading of freshwater at ocean basin scale. By means of the finite scale Lyapunov exponents, we characterize this behavior and provide a quantitative tool that allows us to relate nonlinear dynamics of the Amazon River plume to hydrologic and seasonal variability. Single trajectory analysis identifies three main direct transport patterns, and their related target areas, of Amazon River’s nutrient-rich waters; trajectory pair analysis, on the other hand, is consistent with a general scenario of chaotic advection, due to the presence of nonlinear, large-scale dynamical features. In perspective, our findings provide the basis for a quantitative assessment of fate, distribution, and large-scale dispersion of riverine tracers, in relation to specific river discharge and ocean dynamics.

Introduction

The Amazon River (AR) is the longest river in the southern hemisphere and the largest river in the world for water discharge¹. Every second, it releases an average of about 200 thousand cubic meters of fresh water into the ocean, with a minimum discharge in December and a peak during the summer season^2,3. The Amazon River runoff, along with the coastal dynamics of the region, fosters the formation of the Amazon River Plume (ARP; Fig. 1), i.e., a complex fresh water pattern that spreads along and off the coasts of Brazil, French Guiana, Suriname, Guyana, and Venezuela and that largely impacts the North-West Tropical Atlantic Ocean (NWTAO) dynamics^2,4–8. Moreover, the nutrient-rich nature of this fresh water and the subsequent, intense biogeochemical activity hugely affects the biology of the ocean^9,10, also contributing to sargassum bloom formation¹¹. The dynamics and characterization of ARP are also used to study the effects of water depletion, anthropogenic effects, and climate change on the biogeochemical balance of the ocean¹².

Fig. 1.

(a) NBC retroflection (21 August 2019) and NBC ring (3 September 2020) as observed from Sentinel3 OLCI Chlorophyll-a product at 300 m resolution, superimposed to streamlines of the Globcurrent geostrophic currents derived from Sea Surface Height and in situ data (images from ESA SeaSHOT); the right panel shows a zoom-in of the 3 September 2020 NBC rigs, where the hyperbolic (i.e., saddle) point is highlighted at about 50W and 5N. (b) Sample trajectories of drifters following the along shore path of the NBC (black) and the countercurrent/ring path (red) with sea surface salinity map showing the freshwater patch closing around the new ring that is forming; the transects used for the computation of the arrival times are highlighted in white; map is generated by using MATLAB 7.1 (http://uk.mathworks.com/products/matlab). (c) Monthly histograms of the arrival times at north-west (blue) and east (red) barriers, highlighting the behavior of the circulation pattern. (d) Monthly total mass transports across the NW transect (blue) and the E transect (red), computed as the number of particles that have crossed the relative transect after 120 days.

Understanding, tracking, and assessing the impacts of the dispersion of ARP are important issues in the context of the climate and carbon cycle of the Earth: 20% of the total freshwater input into the ocean comes from the Amazon River, which contributes to a large sink of in the NWTAO^2,13. However, these tasks are highly nontrivial. During winter, after entering the Atlantic, Amazon waters turn north, towards the Lesser Antilles (Fig. 1). As it travels along-shore, the ARP is then subject to anticyclonic phenomena and forms large, elongating filaments that are visible from satellite-based sea surface salinity and/or chlorophyll concentration². However, as summer approaches, ARP begins to spread widely off-shore (Fig. 1), reaching a maximum extension of 1.3 million km¹⁴ and covering up to 15% of NWTAO⁶. However, the Amazon river’s size and discharge alone are not enough to justify such an extensive dispersion.

Although the NWTAO circulation pattern is well known, full understanding of the actual large-scale dispersion mechanism of the Amazon waters is still lacking. It is reasonable to believe that nonlinear dynamics play a major role, since chaotic advection is a very efficient mechanism of tracer mixing and diffusion (Fig. 1c), even in regular time-periodic (i.e. non turbulent) velocity fields¹⁵.

The NWTAO is dominated by the presence of the North Brazil Current (NBC; Fig. 1a,b,d), i.e. the western boundary current of the wind-driven gyre of the northern tropical Atlantic¹⁶, flowing from SE to NW along the South American coast. The annual migration of the atmospheric Intertropical Convergence Zone (ITCZ) forces the NBC to retroflect into the North Equatorial Countercurrent (Fig. 1a,b), closing the equatorial wind-driven gyre and thus creating a transport pathway eastward^16–18. At the same time, the south American coast forces the NBC retroflection to shed large coherent ring-shaped structures, known as the NBC rings (Fig. 1a,b), which separate from the main branch of the current and travel northward¹⁹.

The behavior of the ARP can be thus divided into three different transport regimes (Fig. 1), each occurring in specific months, according to the strength of the retroflection and river discharge^6,20. When the NBC is weak, from January to April, the ARP flows northward, along-shore, and it remains enclosed in the continental shelf; when the NBC is strong, from April to July, the same northward transport drives the ARP to the Carribean region, detaching from the coast and forming rings; when the NBC retroflects eastward, from August to December, the ARP extends into the Central Equatorial Atlantic Ocean, giving rise to a slow or strong zonal transport, depending on the intensity of the retroflection⁶. The temporal separation among different transport regimes is not sharp and two or more regimes can be present during the same period⁶. Moreover, the NBC-weak transport regime is linked to the presence of the NBC rings, which entangle dispersion of tracers and slow down their travel toward the Caribbean region^2,3. Quoting verbatim from⁶ (pg. 6903), the ARP is not a coherent structure but it is “sheared apart by interaction with different current structures and multiple pathways for plume water exist concurrently”. Such a complex pattern is likely at the base of the nonlinear, broad dispersion of coastal and riverine tracers.

The dynamics of both NBC and NBC rings have been thoroughly investigated, on their own, from the Eulerian (using satellite salinity imagery) and Lagrangian (using ad-hoc released drifters) points of view^{2,3,8,16–18,21–24}. These studies describe the interplay among the ARP, the NBC, and the retroflection co-existing in all seasons, where pathways are not mutually exclusive and the plume behavior has a strong spatial-temporal variability. However, the ARP dispersion process has never been analyzed in detail by means of massive Lagrangian simulations and dynamical system techniques.

The NBC system displays the typical phenomenology of chaotic advection. This system is indeed characterized by very large, energetic, and slow-varying structures, i.e., the NBC rings that form near the equator, off the Amazon River; all elements that, combined together, enhance dispersion of the ARP.

More precisely, due to the co-existence between retroflection and rings, there are time intervals during which a slowly detaching ring is nearly tangent to the retroflection (Fig. 1a,b), and the tangent point behaves like a saddle point for the Lagrangian trajectory dynamical system, i.e., a point where stable and unstable directions intersect. Indeed, both rings and retroflection rotate clockwise. The presence of hyperbolic saddle points (right panel of Fig. 1a) is normally associated with the existence of unstable manifolds along which trajectories are stretched and folded. With this in mind, we aim at investigating what drives the dispersion of ARP tracers through a Lagrangian numerical approach (see Methods).

In this regard, the Finite-Scale Lyapunov Exponent (FSLE) analysis (see Methods), a well-established dynamical systems technique, will be employed to identify relative dispersion regimes and to measure specific quantities that relate to the dispersion process over a wide range of spatial scales^25–28. While average basin-scale dispersion properties of NWTAO are known from previous FSLE-based analysis of observational data²⁹, here we focus on Lagrangian properties of freshwater runoff by considering numerical particles debouching from the Amazon River mouth. On one hand, our results prove that the large-scale ARP dispersion cannot be explained by the sole river discharge and its subsequent buoyant plume dynamics. On the other hand, we observe that the interaction of the NBC and its retroflection forms a very effcient mechanism of transport and diffusion of tracers over basin scales. It is well known that absolute dispersion - defined as the mean displacement of trajectories from their initial position - is primarily governed by the large-scale modes of the velocity field, whereas relative dispersion - describing the separation between initially nearby trajectories - is influenced by the full range of motion scales. Consequently, two velocity fields that share the same large-scale components but differ in their small-scale variability may exhibit comparable absolute dispersion yet markedly distinct relative dispersion behaviors.

Results and discussion

A large amount of 2D Lagrangian trajectories were simulated by seeding a number of numerical particle pairs

every ten day, from January 1 st, 2009 to December 31 st, 2018, on a sub-surface layer at a depth of 9 m (see Methods). The total integration time of every single trajectory was set to 120 days, i.e., the order of magnitude of the advective time scale in the ocean region of interest. To evaluate the role of river outflow on the freshwater dispersion, we considered two different numerical experiments: in one experiment, for every release, the initial conditions are uniformly distributed allover the domain; in the other experiment, the initial conditions are concentrated in proximity of the AR mouth (small box in Supplementary Figure S1c). We will refer to these two cases as SIM-A and SIM-B, respectively. The simulations, sampling a 10 year time span with 36 release dates per year, allow a very detailed study of the climatology of the indicators used to characterize the ARP transport and diffusion properties from small to large scales.

Direct transport properties

Single-particle analysis of the SIM-B numerical experiment, i.e., the simulation of tracer particles emitted by the ARP at a 10-day rate for a 10-year period (2009-2018) highlights main transport patterns of AR fresh waters in response to the seasonal variability of the ocean surface circulation. Probability distributions of arrival times at the two virtual transects (Fig. 1b) were computed for each month and averaged over the total simulation time (Fig. 1c).

The arrival times to the north-west barrier display a single, stable peak around 50 days from November to May (Fig. 1c), i.e. the period in which ARP particle trajectories are mainly advected by the NBC, when the retroflection is very weak or absent. The peak gradually decreases by the end of spring, in response to the activation of the NBC retroflection (Fig. 1c). Summer/early Fall period is, on the other hand, characterized by relatively low peaks of particles exiting the barriers, with a significant prevalence of the eastward channel (Fig. 1c). In late Fall/early Winter (November and December), the arrival times uni-modal distribution at the north-west barrier, characterizing the first months of the years, are replaced with a bi-modal distribution (Fig. 1c): two distinct and well-resolved peaks are present in the histograms, indicating the coexistence of two different transport regimes, each with its own time scale, due to the combined effects of NBC and NBC rings transport mechanism.

Average cumulative transport computed across the two virtual transects (Fig. 1c) clearly indicates that the advection properties of ARP particles are strongly modulated by seasonal effects. The activation of NBC retroflection, indeed, is responsible not only for the eastward, large-scale transport of AR fresh waters across the NWTAO, but also for long recirculation times of ARP particles “trapped” in the region between the two transects.

These transport properties agree with seasonal patterns of physical and biogeochemical tracers. There is, indeed, a clear correlation between the values of chlorophyll-a and salinity when observed near the mouth of the Amazon river and when sampled offshore (Supplementary Figure S1a,b). However, a lag of days is present between the two quantities due to transport time. This lag is consistent with the expected arrival time of the trajectories in proximity of the retroflection region when released during wintertime. However, during summer, riverine freshwater is not fed at the same rate in the basin, i.e., almost no freshwater reaches the retroflection region during July - October. Despite that, offshore chlorophyll-a does not decrease when the riverine input decreases, which is likely related to the nonlinear recirculation induced by the retroflection.

Relative dispersion properties

Particle pair simulations were analyzed for the two initial configurations, SIM-A and SIM-B. The measure of monthly averaged FSLE spectra (Fig. 2) allows us to evaluate: 1) a climatology of the relative dispersion characteristics; 2) the scale-dependent differences between the two cases. In all FSLE computations, we considered an initial particle separation of 7 km and a constant amplification factor (see also Supplementary Text).

Fig. 2.

Monthly averaged FSLE spectra in log-log scale for SIM-B (particles initialized in front of the river mouth) and SIM-A (particles initialized uniformly in the basin). The horizontal and vertical axes of each month are, respectively, the relative separation scale and the correspondent value of FSLE . A plateau in the FSLE spectrum corresponds to exponential separation between trajectories at constant rate, i.e. , while the scaling corresponds to turbulent dispersion (Richardson’s law).

The general behavior of SIM-A FSLEs consists in an exponential regime up to separation scales of order km followed by a turbulent diffusion regime up to scales of order km (Fig. 2). The FSLEs computed for SIM-B display significant differences with SIM-A in the small-scale range that gradually attenuate as particle separation reaches the intermediate-scale range. These differences consist in a second plateau, generally higher and shorter than the SIM-A plateau, due to the strong action of NBC on particle separation in the initial phase of dispersion after release (Fig. 2). Regarding SIM-B, we assign a (constant) Lagrangian Lyapunov Exponent (LLE) to each plateau so that we have one exponential separation rate for the small-scale range ( km) and another one for the intermediate-scale range (10 km km).

Within the intermediate-scale range, SIM-A and SIM-B FSLEs substantially overlap (Fig. 2). This means that, from a given separation scale upwards, the relative dispersion properties do not depend any longer on the initial conditions. We define the overlap scale, , as the separation scale beyond which SIM-A and SIM-B FSLEs do not differ by more than of their average value. For both cases, the large-scale separation regime ( km) is well approximated with a Richardson scaling corresponding to turbulent diffusion. The seasonal variability of these quantities, obtained from the climatology of the FSLE curve (i.e., level and extension of the plateaus, overlap scale, and turbulent dissipation rate), provides an insight about the relation between relative dispersion properties and major changes in the ocean circulation occurring during the year.

We compare the trends in maximum Lyapunov exponents, associated with the two distinct plateaus in the river mouth spectra, during the climatological year (Fig. 3a). The seasonality sported by the small-scale Lyapunov exponents is clearly correlated to the river discharge (Fig. 3b): this is natural and to be expected, as a higher river discharge implies a higher initial energy of the particles released at the mouth.

Fig. 3.

Data analysis from the climatological study through the whole simulation time span (January 2009-December 2018). Values of maximum Lyapunov exponents (a) evaluated from small-scale (, blue line) and large-scale (, red line) plateaus follow different trends through the climatological year. Small-scale dynamics pretty much follow the behavior of Amazon river discharge (b) (Data from Olbido station (https://hybam.obs-mip.fr/)), while intermediate scale plateaus exhibit a different seasonal behavior, similar to the one sported by the mean turbulent dissipation rate (c), evaluated from Richardson’s scaling . The variability in FSLE overlapping scale (d) clearly shows that, as long as the NBC retroflection is active, the details in the river dynamics do not influence the large-scale dispersion mechanism.

However, the presence and variability of small-scale dynamics do not influence in any way the ever-present intermediate-scale dynamics (Fig. 3a). This suggests that, despite its sheer size, the Amazon River runoff does not significantly influence the ARP dispersion mechanism. An additional signal of such independent intermediate-scale dynamics is given by the behavior of mean turbulent dissipation rate (Fig. 3c), estimated as the fitting parameter of Richardson’s scaling from the FSLE spectra.

While Lagrangian chaos is normally expected in the small-scale range, large-scale exponential separation is not as common to observe. Our hypothesis is that the NBC rings interaction with other features, in particular with the NBC retroflection, is the cause of this large-scale chaotic dynamic. This is also supported by the fact that NBC, NBC rings, and NBC retroflection are the major coherent structures identified in the region of interest.

An additional support for our hypothesis is that the seasonal trend followed by the overlap scale (Fig. 3d) is clearly correlated to the behavior of the NBC retroflection. In particular, lies above km in the absence of eastward transport, and suddenly drops between km and km as soon as the retroflection strengthens. This type of correlation suggests that the role of the NBC retroflection, on the one hand, is to enhance large-scale tracer dispersion and, on the other hand, to favor the homogenization of the mixing properties throughout the domain.

Seasonal variability during 2013

We now focus on two particular releases relative to the year 2013, simulating Lagrangian drifters initialized in front of the river mouth (SIM-B). Surface salinity and chlorophyll maps (Fig. 4) show that 2013 is particularly dynamic, with the ARP spreading extensively within the basin. Furthermore, both northward and eastward transport regimes are clearly observable, hence our choice of focusing on this particular year (see also Supplementary Fig. S2).

Fig. 4.

(a,b) FSLE spectra (log-log scale) for the 2013 releases covering March-July (a) and August-December (b) periods respectively. The horizontal axis represents the relative separation scale , the vertical axis is the correspondent value of FSLE . Both spectra display two different plateaus, corresponding to chaotic advection regimes , the first one being associated with LLE (dashed green lines), the second one with (dashed purple lines). Large-scale dispersion is compatible with turbulent dispersion, i.e. (solid red lines). Sea surface salinity (c,d) and chlorophyll (e,f) maps show Eulerian averages performed over the corresponding periods. Salinity data are taken from the Copernicus product “Multi Observation Global Ocean Sea Surface Salinity and Sea Surface Density”, resolution is (https://data.marine.copernicus.eu/product/MULTIOBS_GLO_PHY_S_SURFACE_MYNRT_015_013/description). Chl-a data are taken from the Copernicus product “Global Ocean Colour Plankton MY L4 monthly observations”, resolution is 4 km (https://data.marine.copernicus.eu/product/OCEANCOLOUR_GLO_BGC_L4_MY_009_108/description). Maps are generated by using MATLAB 7.1 http://uk.mathworks.com/products/matlab.

We consider a first release in March and a second release in August. For each release, we compute FSLE spectrum for the entire trajectories evolution, that is, 120 days. These FSLEs (Fig. 4) display a double plateau shape, on small and mesoscales, and a decay that is compatible with Richardson type of scaling , at larger scales.

From a dynamical system perspective, a flat FSLE over a given scale range corresponds to an exponential separation regime in that range. Similarly, when two plateaus appear in the FSLE behavior, this is typically associated with the presence of two distinct large-scale mechanisms, each responsible for exponential separation between the trajectories at an average rate corresponding to the plateau levels. Furthermore, the “knee” of the plateaus occurs at a scale related to the spatial extent of these structures.

During the March-July period, the first plateau extends up to , followed by a second plateau, after a transition range, that ends at , Fig. 4a. Looking at the salinity and chlorophyll maps, Fig. 4c-e, the freshwater pattern appears to be stretched by coastal currents, along the northwest direction, up to latitudes 8°N where the plume begins to widen due to the action of the rings. In line with the double plateau scenario, the first exponential regime is presumably related to structures of size comparable to the amplitude of the coastal current, while the second is presumably related to structures (rings) of the order of the Rossby radius. At larger separation scales, the FSLE decays according to a Richardson type of scaling. For the August-December period, Fig. 4b, the scenario remains qualitatively the same, except for the widths of the two plateaus which now extend up to km and km, respectively. Interestingly, these variations in the FSLE are consistent with the changing shape of the salinity and chlorophyll maps, Fig. 4d-f, which now appear somewhat wider than previously, along the coasts, and significantly elongated eastward. Again, at larger scales, the FSLE decay is consistent with the Richardson scaling. Our hypothesis is that the activation of the NBC retroflection expands the size of the structures driving the exponential separation and, in particular, opens a major eastward transport channel that ultimately contributes to the spread of the ARP at basin scales.

Conclusions

The dispersion of the Amazon River Plume (ARP) in the tropical Atlantic remains a complex and not fully understood phenomenon. While extensive spreading is especially evident during boreal summer, numerous studies have indicated that river discharge alone cannot account for the observed dispersion scale-even for a system as large as the Amazon. Instead, ARP dynamics result from a multifaceted interaction of surface currents, wind forcing, buoyancy, and tidal effects. Local wind patterns modulate the northwestward flow of the plume and influence its residence time near the river mouth³⁰. In addition, currents such as the North Brazil Current (NBC) and its associated mesoscale eddies entrain freshwater into low-salinity bands, further dispersing the plume offshore³¹. These processes, combined with the geography and meteorology of the region, shape the evolving structure of the plume^32,33.

Using Lagrangian diagnostics from numerical simulations, our study reveals that large-scale ARP dispersion is mostly independent of river discharge. The FSLE analysis shows that dispersion is primarily driven by large-scale structures involving the NBC, NBC rings, the Amazon bulge, and the NBC retroflection.

We measured and compared climatologic monthly FSLE spectra for different initial conditions: uniformly distributed throughout the domain (SIM-A) and concentrated in the Amazon River Plume in proximity of the river mouth (SIM-B). The basin averaged dispersion properties (SIM-A) display an exponential separation regime, i.e. a nearly flat FSLE up to scales comparable to the Rossby radius, km, followed by a turbulent dispersion regime (Richardson’s scaling) at scales larger than the Rossby radius, compatible with an inverse cascade scenario³⁴. On the other hand, trajectories released at the river mouth (SIM-B) display an enhanced exponential separation at small scales, related to river discharge variability and lateral extension of the coastal currents, followed by a large-scale regime in which the dispersion rates recover the basin averaged properties.

If we define an overlap scale () as the scale beyond which the FSLEs measured from SIM-A and SIM-B do not differ more than a few percent, we notice that, during boreal winter, as the NBC retroflection weakens, this overlap scale occurs in the range km, and the ARP dispersion is primarily driven by the northwestward NBC transport. In summer, as the retroflection intensifies, overlap occurs in the range km: ARP dispersion aligns more rapidly with basin-scale properties, due to enhanced mixing promoted by the activation of the NBC retroflection.

Results obtained for a specific year, 2013, emphasize the response of the seasonal FSLE measured on ARP trajectories (SIM-B) in relation to major changes occurring in the large-scale features of the ocean surface circulation: while the double plateau shape is substantially preserved, the width of the plateaus increases as the spatial extent of the mechanisms driving dispersal is amplified by the NBC retroflection and the appearance of an eastward transport channel for freshwater.

While numerical resolution and forcing biases may affect our results, comparison with observational studies²⁹ confirms the presence of highly dispersive regimes in the region. It thus remains to be established whether this highly dispersive dynamics is limited to the surface layer. Indeed, previous studies on submesoscale features (e.g., filaments) showed that in the ocean interior the dispersal is highly reduced³⁵. We postulate that the buoyant character of the plume and its limited vertical extent may favor that the large dispersal properties we identified characterize also the whole 3D plume dispersal.

Lagrangian chaos is known as a major mechanism of mixing and dispersal of nutrients and organic material^36–38; it facilitates nutrient redistribution, supports plankton diversity, and regulates biogeochemical cycles, with significant implications for local ecosystems and regional circulation patterns^39,40; the presence of saddle-point bifurcations, one of the signatures of chaotic advection^41,42, contributes to prolonged mixing and dispersal in natural flows^43,44. Although exponential separation between trajectories is commonly associated to chaos, in a dynamical system context, it is worth stressing that, in Geo-fluid-dynamics, there can be alternative to this scenario. Basically, a flat FSLE regime may be due either to large scale chaotic advection in a low (or zero) Reynolds number flow, or to a more complex fluid configuration with many interacting scales as, for example, a turbulent direct cascade^34,45,46, characterized by a “” spectrum. Actually, this type of spectrum was observed in numerical simulations related to the Atlantic Ocean⁴⁷. In absence of detailed information about the Eulerian characteristics of the velocity fields, we cannot rule out a priori this or other alternative scenarios. However, we think that our results are remarkably consistent with the hypothesis that, in the central Atlantic sector we have considered, the regimes of exponential separation between tracer trajectories are related, in terms of characteristic spatial and temporal scales, to the major large-scale features of the system and to their seasonal variations. Interestingly, all FSLE curves display a large-scale decay (i.e. above the Rossby radius) compatible with a Richardson type of scaling. In a classical double cascade scenario of two-dimensional turbulence⁴⁵, a “” spectrum is associated to energy inverse cascade, in the range above the forcing scale, while a “” spectrum is associated to enstrophy direct cascade, in the range below the forcing scale. However, in realistic Geophysical flows, the formation of energetic large-scale structures may easily mask the role of secondary small-scale dynamics, as far as Lagrangian properties are concerned.

As fnal remarks, we observe that tracer dispersion regimes provide, in principle, the physical framework within which biogeochemical and ecological processes develop. Quantifying how such dynamics influence productivity represents the next step beyond the scope of this study, though the Amazon plume is known to enhance marine productivity in the Western Tropical North Atlantic (WTNA) by nearly 10% - far beyond what nutrient input alone would suggest⁴⁸. Plume’s stratifying effect alters seasonal variability and enhances diazotroph associations, supporting the biological carbon pump^49,50. undersaturation linked to the plume contributes to carbon export⁵¹, though climate change and deforestation may alter these nutrient dynamics and promote harmful algal blooms^52,53. Given the scale and impact of the ARP, it can be considered a natural biogeochemical perturbation of the tropical Atlantic.

Our findings emphasize that nonlinear dispersal and biological responses might significantly impact both efficiency and predictability of carbon dioxide removal strategies. The interplay between transport and reaction rates is critical and remains insufficiently understood⁵⁴. Future studies must investigate the feedback among dispersion, biology, and chemistry to better anticipate the outcomes of human interventions in marine systems.

Methods

The velocity fields used in the Lagrangian simulations were provided by CMCC (Euro-Mediterranean Centre for Climate Change) for the AtlantEco Project (https://doi.org/10.25424/cmcc-x754-gh24). The ocean circulation model is the GLOB16 eddy-resolving configuration of the NEMOv3.6 ocean-sea ice modeling system⁵⁵, with a grid resolution of , forced using the JRA55-do v1.4.0 surface-atmospheric dataset⁵⁶.

The model is forced with river discharge data, provided as a monthly climatology from Dai and Trenberth (2002)⁵⁷, compiled by Bourdalle-Badie and Treguier (2006)⁵⁸, and it includes 99 major rivers and coastal run-offs. The fresh water is added to the surface, assumed to be fresh and at local sea surface temperature⁵⁹. The model assimilates in situ observations of temperature and salinity and satellite sea-level anomalies (SLAs) and sea surface temperature (SST), implementing a three-dimensional variational analysis system (3DVAR), originally formulated for the Mediterranean Sea⁶⁰ and adapted to the global ocean by Storto et al. (2011)⁵⁹. All the in situ observations from moorings, Argo floats, Expandable Bathy Termographs (XBTs) and Conductivity–Temperature–Depth (CTDs) are extracted from the ENSEMBLES EN3v2a dataset⁶¹. The dataset of SLAs is the Archiving, Validation and Interpretation of Satellite Oceanographic Data (AVISO) along-track delayed mode dataset, which includes observations from European Remote Sensing (ERS) satellites ERS-1 and −2, Envisat, Geodetic Satellite (GEOSAT) Follow-On (GFO), Jason-1 and −2, Topex/Poseidon and Cryosat-2. SST observations are from the NOAA high-resolution daily analyses⁶², which use Advanced Very High Resolution Radiometer (AVHRR) infrared radiances and Advanced Microwave Scanning Radiometer-EOS (AMSR-E) microwave radiances, the latter available from June 2002–October 2011. The observational sea surface salinity dataset consists of the EN3 monthly objective analyses⁶¹. Validation of the model is provided in Storto et al. (2016)⁵⁹.

The domain area considered for the simulations extends from to and from to . The model output consists of daily mean zonal and meridional velocities, as well as temperature and salinity fields. As the native tri-polar grid is a structured but non-uniform grid, the fields have been interpolated on regular grid using bi-linear interpolation.

The numerical code that generates Lagrangian simulations from ocean surface current data was introduced and discussed in detail in recent papers^27,63. The Lagrangian model interpolates velocity data in space (cubic splines) and time (linear) in order to carry out the numerical integration of the trajectories. For the scopes of the present work, it was not necessary to consider an additional sub-grid dynamic parametrization of the velocity components not resolved by the large-scale fields. Possibly, this and other aspects regarding specific small-scale issues, e.g. the analysis of local instabilities by means of FSLE-based mixing maps, could be addressed in future studies. The numerical trajectories were analyzed in terms of single-particle (direct transport) and particle-pair (relative dispersion) statistics.

As far as single-particle dispersion is concerned, we computed the arrival times of trajectories released in proximity of the Amazon River mouth at two virtual transects (Fig. 1): the first one is perpendicular to the coast at a latitude of , to measure northward transport of the ARP, the second one is a vertical barrier at a longitude of , to measure eastward transport of the ARP due to the action of the retroflection mechanism.

Relative dispersion of initially close particles was studied by means of the established FSLE analysis technique^25,26,28,29. With respect to other indicators, the FSLE (Finite-Scale Lyapunov Exponent), , is proved to be the most reliable measure of relative dispersion over all available scales of motion²⁵. The major advantage of using a scale-dependent statistics is to avoid scale interference issues that typically affect the statistics of the mean square particle separation as function of time. The FSLE can be considered, in other terms, as the spectrum of the relative dispersion rate, function of the spatial scale, i.e. it is inversely proportional to the mean time taken by two particles to amplify their relative separation from a scale to a scale , where is a constant factor ().

It is worth stressing the meaning of the scaling laws typically observed in the FSLEs and how to relate them to the ocean surface circulation features. Generally speaking, a plateau in the FSLE, i.e. constant, in a given range of scales means that two trajectories separate exponentially over time, as long as their relative distance falls in that range. An exponential regime is expected to be observed, at least, in the range below the size of the smallest coherent structure of the system, where Lagrangian dynamics is generally chaotic¹⁵. In model simulations, the size of the actual smallest coherent structure depends, of course, on the resolution of the velocity field data.

In some cases, the FSLE can display more than one plateau, depending on the shape of the energy spectrum of the system. Each plateau level corresponds to a constant exponential separation rate in a particular range of scales²⁹. Normally, the upper bound (the “knee” scale) of the range where the FSLE has a plateau corresponds to the characteristic length scale of the coherent structure responsible of chaotic advection in that range.

In presence of a Kolmogorov type of energy spectrum, the expected scaling of the FSLE is of the type , in correspondence of the inertial sub-range where the mean square particle separation evolves according to the t Richardson’s law, with defined as the mean turbulent dissipation rate⁶⁴. In the ocean, this kind of super-diffusive regime is normally observed in the upper mesoscale range due to inverse cascade from the Rossby radius scale upwards²⁹. From the FSLE-based analysis, one can obtain information not only about scaling exponents but also about important physical parameters like Maximum Lyapunov Exponent, turbulent dissipation rate, diffusion coefficient, etc., that characterize the evolution of relative dispersion from small to large scales (see Supplementary Text, Table S1).

Author contributions

D.I. conceived the research. G.L., F.F., and D.I. designed the analyses. R.I., L.D.C. and J.B. analyzed both observational and numerical data and performed the Lagrangian analysis. All the authors contributed to other aspects of the paper and the writing of the manuscript.

Funding

This publication has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No 862923 (project AtlantECO).The work was also supported by MITHO (Multi-stressors impact on Ocean Health) project, funded by the European Space Agency via the contract Grant No. 4000142100/23/I-DT, and by the Horizon-Europe project FOCCUS (Forecasting and observing the open-to-coastal ocean for Copernicus users, Grant Agreement 10113391).

Data availability

The velocity felds used in the Lagrangian simulations were provided by CMCC (Euro-Mediterranean Centre for Climate Change) for the AtlantEco Project (https://doi.org/10.25424/cmcc-x754-gh24). The ocean circulation model is the GLOB16 eddy-resolving configuration of the NEMOv3.6 ocean-sea ice modeling system.

Declarations

Competing interests

The authors declare no competing interests.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-45016-z.