Persistent meanders and eddies lead to a quasi-steady Lagrangian transport pattern in a weak western boundary current
Mainara Biazati Gouveia, Rodrigo Duran, Joao Antonio Lorenzzetti, Arcilan Trevenzoli Assireu, Raquel Toste, Luiz Paulo de Freitas Assad, Douglas Francisco Marcolino Gherardi
PPersistent meanders and eddies lead to aquasi-steady Lagrangian transport pattern in a weakwestern boundary current
M. B. Gouveia , R. Duran , J. A. Lorenzzetti , A. T. Assireu , R. Toste , L. P. de F.Assad , and D. F. M. Gherardi Division of Remote Sensing, Brazilian National Institute for Space Research, S ˜ao Jos ´e dos Campos, 12227-010,Brazil National Energy Technology Laboratory, Albany, OR 97321, USA Theiss Research, La Jolla, CA, 92037, USA Institute of Natural Resources, Federal University of Itajub ´a, Itajub ´a, 37500-015, Brazil Laboratory for Computational Methods in Engineering, COPPE/UFRJ, Rio de Janeiro, 21941-907, Brazil * [email protected] ABSTRACT
The Brazil Current (BC) is a weak western boundary current flowing along the Southwestern Atlantic Ocean. It is frequentlydescribed as a flow with intense mesoscale activity and relatively low volume transport between 5.0 to 10.0 Sv. We use a13-year eddy-resolving primitive-equation simulation to show that the presence of persistent meanders and eddies leadsto characteristic quasi-steady Lagrangian transport patterns, aptly extracted through climatological Lagrangian CoherentStructures (cLCSs). The cLCSs position the surface expression of the BC core along the 2000 m isobath, in excellentagreement with high resolution satellite sea-surface temperature and the model Eulerian mean velocity. The cLCSs deformationpattern also responds to zonally persistent cross-shelf SSH transition from positive (high) values near coastline to low (negative)values between 200 and 2000 m and back to positive (high) offshore from the 2000 m isobath. Zonally-paired cyclonic andanticyclonic structures are embedded in this transition, also causing the cLCSs to deform into chevrons. An efficient transportbarrier is identified close to the 200 m isobath confirmed by limited inshore movement of drogued buoys and accuratelyindicated by an along slope maxima of climatological strength of attraction. We also show that the persistent cyclonic andanticyclonic structures may induce localized cross-shelf transport. Regions of low climatological strength of attraction coincidewith large shelves and with stagnant synthetic trajectories. We also show that cLCSs accurately depict trajectories initiated atthe location of Chevron’s spill (November 2011) as compared to synthetic and satellite trajectories, and the outline of the oilfrom that accident. There is also an agreement between the large-scale oil slicks reaching the Brazilian beaches (from August2019 to February 2020) and the strength of climatological attraction at the coast. The identification and quantitative descriptionof climatological Lagrangian coherent structures is expected to improve the effectiveness of future emergency response tooil spills, contingency planning, rescue operations, larval and fish connectivity assessment, drifter launch strategies, wastepollutant dispersion and destination. Our work also clarifies the influence of persistent mesoscale structures on the regionalcirculation. Introduction
Subtropical western boundary currents (WBC) are one of the main contributors to the meridional ocean transport of heat andsalt . They are generally depicted as continuous surface flows and their intensity and persistence are considered as a dynamicbarrier for cross-flow transport , influencing the pathway of pollutants and fish larvae . However, the Brazil Current (BC) isconsidered a weak WBC in the Southwestern Atlantic Ocean (SWA) . The BC transports a relatively small volume (valuesranging 4–6.5 Sv) of water southward in the upper 520 m . Strong mesoscale activity develops in the vicinity of the BC,mainly near 22S, with large frontal meanders and eddies . Despite being weak relative to other western boundary currents, theBC has been found to exert significant control over Lagrangian transport , in this paper we examine persistent Lagrangiantransport patterns in a WBC with persistent meanders and eddies.The baroclinically unstable nature of the BC is caused by the presence of the Intermediate Western Boundary Currentflowing to the north between 800 and 1000 m depth, below the BC, which in the upper 500 m transports the Tropical Water(TW) and the South Atlantic Central Water to the south . The formation of meanders and eddies can also locally reverse the a r X i v : . [ phy s i c s . a o - ph ] A ug urrent flow offshore of the 1000 m isobath and cause changes in current transport . The intense mesoscale activity along theBC, from its origin in the bifurcation of the South Equatorial Current down to the Brazil-Malvinas confluence region, includesrecurrent or semi-permanent meanders, cyclonic and anticyclonic structures, and eddies .The method to compute climatological Lagrangian Coherent Structures (cLCSs) was developed recently and has been usedto extract important Lagrangian transport patterns from large velocity time series . Pattern identification include 1) isolatedregions where trajectories are unlikely to leave or enter; 2) regions that attract nearby parcels of water and therefore are moresusceptible to pollution impacts; and 3) recurrent transport patterns. Some recent studies have shown the relevance of cLCSs. showed the efficacy of some of the cLCSs as transport barriers by using synthetic drifters advected by the instantaneous modelvelocities and by using 3207 satellite-tracked drifter trajectories spanning over two decades (1994–2016). showed that cLCSswere efficient in identifying predominant transport patterns in the deep ( ≈ m ) Gulf of Mexico, as determined by RAFOSfloats and synthetic drifter trajectories.To compute cLCSs, and used a free-run simulation performed with NEMO (Nucleus for European Modelling of theOcean) and ROMS (Regional Ocean Modeling System), respectively, while used an operational HYCOM (Hybrid CoordinateOcean Model) simulation. Thus, in combination, these three papers show that cLCSs are robust in bypassing the variabilityinherent to geophysical flows, while accurately identifying predominant transport patterns. Searching for structures that wereable to bypass the chaotic nature of transport while extracting predominant, and important, transport patterns from long velocitytime series was the motivation behind the development of cLCSs .In this paper we show that cLCSs are also efficient in extracting the predominant circulation from another free-runningnumerical simulation, in the distinct setting of a WBC, characterized by the presence of persistent and recurrent eddies andmeandering. In this paper we offer new insights on the interpretation of cLCSs by relating them to the time-mean structureof Eulerian fields such as satellite sea-surface temperature (SST), model sea-surface height (SSH), and eddy-, mean-, andtotal-kinetic energies (EKE, MKE, and TKE, respectively). Further interpretation of cLCSs is based on comparisons withsatellite-tracked drifters and synthetic drifter trajectories. The transport patterns associated with persistent Eulerian structuresinclude regions with increased Lagrangian variability and offshore transport. We identify a cross-shelf transport barrier,separating distinct dynamical regimes, and persistent recirculation patterns in the transition region between them. We also showthat cLCSs highlight the transport patterns that help explain the observed drift of the Chevron’s oil spill (November of 2011)and the recent large-scale oil slicks observed at Brazilian beaches (from August 2019 to February 2020). Here, cLCSs arecomputed from daily-mean surface velocities from a 13 year (2003–2015) ROMS simulation with an eddy-resolving grid of1 /
36° ( ≈ km ) and 40 vertical levels. Following the method described in , we compute 7-day sliding window Cauchy-GreenTensors (CGT) in reverse time, from the daily climatological velocity. From these CGT we calculate the monthly and yearlyaverage CGT. Results
The underlying causes of quasi-steady attracting Lagrangian structures may differ. It is therefore important that the physicalinterpretation of monthly climatological attraction strength ( c ρ ) and cLCSs are supported by the combined use of complementarydata. In this study we use satellite data, in situ observations and numerical model outputs. The mean structure of the BC
The typical mean structure of the BC between 22 and 31S is easily extracted by time averaging Eulerian fields. The monthly-mean model Eulerian surface flow aligns well with the advection patterns of monthly-mean satellite SST from Multi-scaleUltra-high Resolution (MUR) dataset, suggesting a continuous surface poleward flow along the 2000 m isobath (Fig. 1).In the austral summer (Fig. 1a), between 17–20S and 38–29W cLCSs suggest Lagrangian transport from east to west, inagreement with the Eulerian mean. Between 20–22S meandering is more common by Vitória-Trindade seamount chain (20Sand 39–34W), including over the shelf near 20S where the mean Eulerian flow and cLCSs clearly show a meander (March) oran eddy (August). South of about 22S, the BC main axis of the flow is usually oriented poleward along the 2000 m isobath,with climatological squeezelines deforming as chevrons, similar to SST chevrons.Similar chevrons by climatological squeezelines can also be found in a coastal upwelling region, indicated by low SST nearthe shore in the austral summer (Fig. 1a), when there is an intensification of upwelling, although coastal circulation inshore ofthe 200 m isobath is equatorward. In the austral winter the chevron shape is observed only near the upwelling Cabo Frio (23Sand 42W; Fig. 1b).The advection of TW by the BC causes a zonal front with the cold and low salinity coastal water, between 21S and 31S inboth seasons. We observed the presence of stronger thermal fronts in the austral summer, due the intensification of upwelling atCabo Frio (23S) and Cabo de Santa Marta (28S). In March the TW, between 21 and 30S, is characterized by surface water withtemperatures above 26 . C (Fig. 1a) and in August by temperatures above 21° C (Fig. 1b). igure 1. March (a) and August (b) monthly mean SST from the MUR dataset (color shading), with spatial resolution of 0 . m are indicated in black lines. Note that color bars are different for each month.Persistent offshore advection can be seen through satellite SST, cLCSs and monthly Eulerian velocity in austral summerand winter (Fig. 1a and 1b). In the winter, the Eulerian mean surface velocity shows persistent offshore flow at 19.5S and 39W,around 23S and 39W, between 25–26.5S and 42W (Fig.1a). In the summer offshore transport is similarly located but can alsobe seen around 30S and 47W (Fig. 1b). Often these Eulerian offshore patterns coincide with cLCSs deforming as chevrons, andin the summer they coincide with satellite SST advection. In the austral summer, SST is consistent with offshore advection (e.g.26S and 42W), and chevron-like cLCSs (Fig. 1a), while in the austral winter offshore advection (e.g. 26S and 42W) does notcoincide with offshore SSH advection, yet cLCSs do conform to the offshore Eulerian flow (Fig 1b).Variability in the BC is evident in austral summer and winter through an intensification of eddy kinetic energy (EKE),between the 200 m and 2000 m isobaths south of about 23S (Fig. 2a and 2b). This alongshore EKE maxima is collocated to theEulerian mean peak BC velocity which is closely aligned with the 2000 m isobath, the mean peak velocity being in agreementwith chevron-shaped cLCSs (Fig. 2c and 2d). The alongshore EKE maxima south of about 22S, between the 200 and 2000 m isobaths, is about 0.1 m / s and slightly more energetic in the Summer (March). The alongshore MKE maxima is centeredalong the 2000 m isobath south of about 22S is about 0.1 m / s in the summer and about 0.05 m / s in the winter.In the summer, EKE maxima offshore of the 2000 m isobath, are located between 17 and 20S, offshore of the AbrolhosBank and between 21 and 26S, the latter is adjacent to the alongshore EKE maxima, between the 200 and 2000 m isobaths(Fig. 2a). In the winter, EKE maxima just offshore from the 2000 m isobath can be located between 17–18S, and near 22.5S,25.5S and 30S (Fig. 2b).In winter and summer, maxima MKE structures that are just offshore to the mean BC can also be seen, but are morelocalized near 22.5 and near 25S (Fig. 2c and 2d). These locations coincide with offshore flow in Eulerian-mean velocity(Fig. 1a and 1b).The low SST associated with intermittent coastal upwelling off Cabo Frio during austral summer (23S and 41–46W; Fig. 1a)coincides with a coastal jet in the Eulerian-mean velocity which deforms cLCSs as chevrons, and can be seen as an MKEmaxima (Fig. 2c).High stretching values ( c ρ > > . c ρ > 0.7, or > 2 in linear units) are found adjacent to the BC core between 200 to 2000 m isobaths, and between 23–31Swith regions of strong attraction interspersed by weakly-attracting regions (Fig. 3). Along the slope, climatological attractionstrength extrema coincides with EKE extrema, including a minimum near region 1 (Fig. 2 and 3).The climatological attraction strength, c ρ shown in Fig. 4, has some variability over the slope (200 to 2000 m isobaths)between 23S and 31S. This variation in c ρ suggests low-frequency variability of Lagrangian transport patterns with a tendencyfor some cross-slope transport where low c ρ predominates (see Supplementary Fig. S1 and S2). In general, the low frequencytime variability suggested by c ρ over the slope, near the latitudes 23.5–24.5S and between 26–27S, is largest from December toFebruary. In March, June, July, August and September high values of c ρ can be seen along most of the slope south of 23–25S,in contrast with other months where minima are interspersed with maxima. Continuous high values of c ρ over the slope areobserved in April, May, October and November months. The coastline and shallow shelf between 24 and 27S has a c ρ minimain all months, sometimes contrasting with a strong maxima along the coastline north of 24S (e.g. January through May). The c ρ minima in the nearshore environment and coastline between 24 and 27S identifies a stagnant region through the year, a igure 2. Monthly average maps of EKE (a and b), MKE (c and d) and TKE (e and f) (color shading) for March (left frames)and August (right frames), from 2003 to 2015. Units are m / s in log scale. Monthly cLCSs are represented by white lines.The 200 and 2000 m depth contours are represented by black lines. igure 3. Climatological attraction c ρ (colors, logarithmic scale), computed by yearly averaging 7-day CG tensors from the2003–2015 climatology, showing (a) locations with high values of annual mean c ρ ( > , . m isobath (colored dots).The 200 and 2000 m depth contours are represented by blacklines.region that should be relatively safe from spills originating outside the c ρ minima (Supplementary Fig. S3, middle panel).However, any pollution originating within this region including the coastline is unlikely to disperse, thus possibly causing agreater impact due to a higher concentration of contaminants (Supplementary Fig.S3, right panel).An intensification of c ρ near Cabo Frio upwelling region (Region 7 in Fig. 3a) is observed from January to May due to anincrease in speed associated with a coastal jet (Fig. S4) between São Sebastião Island to Cabo Frio (Region 8 to 7 in Fig. 3a). Apeculiar c ρ maxima with "U" shape can be seen in the months of April and May when the surface speed bends cyclonicallybetween 23 to 24S and 44 and 41.5W (Fig. 4, see also Fig. S4).A description of the mean structure BC is organized in four different regions based on structures from the model-meanSSH to illustrate upwelling process and persistent mesoscale activity and their association with persistent Lagrangian transportpatterns as seen through cLCSs (Fig. 5).The first region (Fig. 5c) comprises a group of zonally oriented topographic features near 20S starting at the Abrolhos shelfon the west (location 1 in Fig. 3a), the Vitória-Trindade Seamount chain (location 2 in Fig. 3a), and the oceanic island complexof Trindade Martin Vaz (location 3 in Fig. 3a) on the east. An important persistent oceanic feature captured by cLCSs in thisregion is the Vitória cyclonic eddy to the south of Abrolhos shelf in addition to the Abrolhos anticyclonic eddy on the eastcentered around 34.4W (Fig. 5c). The Abrolhos anticyclonic eddy translates from east to west near Vitória-Trindade seamountchain (Region 2 in Fig. 3a) between the latitudes 18 and 20S and longitudes of 38 and 32W (see Fig. S5). The second region(Fig. 5d) is characterized by the presence of a coastal upwelling near the Cabo de São Tomé (location 6 in Fig. 3a), identifiedby low SST values in austral summer (Fig. 1a), just offshore from the upwelling there is a cyclonic structure centered around22S and 40.2W. Further offshore there is an anticyclonic structure centered at 23S and 38W. Both of these structures inducepersistent Lagrangian transport seen through the deformation of cLCSs. This region also coincides with EKE and MKE maxima(Fig. 2) protruding offshore from the 2000 m isobath, and with an Eulerian mean velocity (Fig. 5d) all of which suggest offshoretransport. A synthetic drifter experiment confirms that the persistent mesoscale structures are likely to cause considerablecross-shelf transport (see Supplementary Fig. S2a–b). A third region (Fig. 5e) is located in front of the east-west oriented coastof Rio de Janeiro (location 7 in Fig. 3a) with a coastal upwelling jet near Cabo Frio deforming cLCSs. A couple of cyclonicand anticyclonic features between 23–25S, and the 200 and 2000 m isobaths cause an onshore-offshore-onshore-offshoresequence, although cross-shelf transport seems limited not passing the 2000 m isobath where the core of the BC can be seenexcept possibly near 23S. Further offshore near 41W and 25S, there is a SSH maxima associated with recurrent anticyclonicLagrangian flow depicted by cLCSs deformation (Fig. 5e, see also Fig. S5). Near Cabo de Santa Marta (location 9 in Fig. 3a) isthe fourth and southernmost region (Fig. 5f), where the surface flow is influenced by a distinctive coastal upwelling region in29S, and the presence of two dipole-like structures, suggesting cross-shelf variations over the 200 m isobath, restricted inshoreof the 2000 m isobath.The BC axis (see MKE in Fig. 2c and 2d, and SST and cLCSs chevrons in Fig. 1) is positioned between anticyclonic andcyclonic structures (Fig. 5e). As it flows from northeast to southwest, the eastern flank of the BC gains counterclockwise rotationoffshore of the 2000 m isobath. The alongshore flow in the east-west oriented shelf near region 7 (Fig.3), becomes offshore flowfrom Cabo Frio as it approaches the 200 m isobath, and is fed by a clockwise circulation over the 200 m isobath, connectingwith the counterclockwise circulation offshore. Thus, the monthly-mean Eulerian velocity suggests limited cross-shelf transport igure 4. Monthly climatological attraction strength ( c ρ ) in the SWA. Note the discontinuous meridional distribution of high(red) c ρ values between the 200 and 2000 m depth contour lines (thin black lines). igure 5. March (a) and August (b) monthly climatological squeezelines (white lines) over model monthly-mean SSH. Blackrectangles indicate regions shown in panels (c) to (f). (c) Abrolhos Bank region (location 1 in Fig. 3a), (d) Cabo de São Tomé(location 6 in Fig. 3a), (e) Cabo Frio (location 7 in Fig. 3a) and (f) Cabo de Santa Marta (Region 9 in Fig. 3a). The presence ofcyclonic and anticyclonic eddies features are highlighted by curved arrows. Straight arrows indicate the direction of coastal jetsat upwelling regions. Reference months are indicated at the top left of each map. The vector scale is on the top of each map.Depth contours of 200 and 2000 m are represented by thin black lines. igure 6. Schematic representation of persistent Lagrangian transport based on the annual averaged cLCSs, colored accordingto annual c ρ . The map to the left shows the full domain of the study and the map to the right is a zoom in to the dashed ellipse.The 200 and 2000 m depth contours are represented by thin black lines. Regions Drifters (%) *weak attraction region 01 10.51weak attraction region 02 29.54weak attraction region 03 16.47weak attraction region 04 10.51weak attraction region 05 17.04
Table 1.
Percentage of satellite-tracked drifters with 15 m drogues distributed by NOAA’S GDP, with trajectories interpolatedin 6 hour intervals, that crossed the 2000 m isobath along a region of weak attraction, as indicated in Fig. 3b. The same driftercan be counted more than once if it crossed more than one region of weak attraction. *The percentage is related to the total of352 drifters.between the 200 and 2000 m isobaths (Fig. 5e), that coincides with weak attraction c ρ (Fig. 3b and 5), and coincides also withthe Eulerian-mean anticyclonic and cyclonic structures (b and c in the Fig. 6) found on both sides of the BC axis.Based on this, we propose a schematic representation of the persistent meandering between 23 and 27S (Fig. 6). Thestrength of normal attraction along the cLCSs deformed as chevrons by the BC is indicative of the kinematics: along the BCcore between 25–26S, cLCSs are weak ( c ρ c ρ ( 0.6 in logarithmic scale) reflecting an increase innormal attraction that is associated with the cross-shelf circulation described above. Between 23–24S, cLCSs reach high c ρ values (>0.8 in logarithmic scale) reflecting the coastal tributary to the alongslope flow, that is related to the coastal upwellingjet off Cabo Frio (see a in the Fig. 6). There are similar dipoles adjacent to the BC at different latitudes (Fig. 5d, e, f), and thecLCSs and c ρ show a similar response (Fig. S4). Variability of surface flow assessed through drifters
From a total of 352 trajectories of satellite-tracked 15 m drogued drifters, distributed by NOAA’s Global Drifter Program(GDP), and iSPHERE, distributed by Prooceano, with consent of PetroRio, interpolated to 6-h intervals, a minority crossed atsome time the 2000 m isobath and less than 30% of drifters cross the 200 m isobath (Table 1). Some of these trajectories areplotted with the annual c ρ maps (Fig. 7) to highlight the quasi-steady Lagrangian transport patterns associated with the BCaround 2000 m isobath. The observed transport patterns show a region of flow with a number of drifters spending several daystrapped in eddies and meanders near the Vitória-Trindade Seamount Chain (Fig. 7a, see also Region 2 in Fig. 3a) and AlmiranteSaldanha seamount (Region 5 in Fig. 3a). Drifters may also spend some time confined in weakly attracting regions, representedby low c ρ values or confined inshore of the 200 m isobath which also has low c ρ values except at some locations near thecoastline (Fig. 7b).When drifters travel just inshore of the BC core, between the 200 and 2000 m isobaths, there is some meandering (Fig. 7c);drifters that move offshore of the 2000 m isobath do so where there are persistent cyclonic structures (Fig. 5e and 5f). Further xamples of cross-shore transport show that the persistent cyclonic structures between 23–25S, 26.5S and 29S (Fig. 5e and 5f)tend to influence where drifters will move onshore or offshore (Fig. 7c–f). Onshore transport is less likely to cross the 200 m isobath than the 2000 m isobath. The cross-shelf flow of drifters between 24S and 27S (Fig. 7c–e) is more likely over regions oflow c ρ than over regions of high c ρ .The effect of persistent meandering and eddy-like structures (Fig. 5a and5b) on satellite-tracked drifters can clearly be seenas high values of Probability Density Estimates (PDE, see Methods section) measuring the likelihood of drifters visiting aregion. In February and May, regions of high PDE tend to be confined within c ρ maxima that occur close to upwelling regionsand along steep bathymetric features (Fig. 3, regions 2 and 5).Between 24–30S, PDE values tend to be well aligned with the slope, with values diminishing considerably towards thecoast at any given latitude. Exceptions are localized near 25S in February, May and August, when medium values of PDE( ≈ − × − ) can be seen just inshore of the 200 m isobath. PDE maxima ( > × − ) are confined offshore of, andadjacent to the 2000 m isobath. All drifters can be seen in the supplemental information (see Supplementary Fig. S6). Thedrifter PDE suggests seasonal variability with PDE maxima ( > × − ) located only north of 24S in the summer and autumn(Fig. 8a and 8b), with winter being a transition as PDE maxima diminish north of 24S and increase south of 26S (Fig. 8c), andin spring PDE maxima ( > × − ) is limited to south of 26S.In all cases PDE maxima tends to be just offshore of the 2000 m isobath, the only exception being a maximum centerednear 22S and 34W, mainly found in summer, autumn and winter.The isolated region next to the coastline between 24 and 27S has a larger zero PDE region in autumn and winter when c ρ isalso negligible in this region (Fig. 8b and 8c) relative to c ρ in summer and spring (Fig. 8a and 8d). In all seasons this coastalregion is well isolated. Another region that tends to be isolated is the coastline north of 20S, especially in autumn, winter andspring (Fig. 8b–d). Oil spill at Frade’s Field
The cLCSs and c ρ computations have been successfully used to estimate the likely trajectory of oil spills such as during theaccidents in the Gulf of Mexico in 1979 and in 2010 .We show that performing the same computations using a free-run eddy-resolving ocean model it is possible to achieve agood level of agreement between cLCSs and the behavior of a much smaller offshore oil spill that occurred at the Frade’s Field(Fig. 9a), located 120 km off the coast of Rio de Janeiro State (Brazil), on November 7, 2011. The spill reached 160 km in lessthan 15 days, being contained on December, 30 of the same year (Fig. 9b).The agreement with cLCSs can be qualitatively assessed by comparing the oil spill trajectory with the trajectories of 30synthetic drifters released in the same month of the accident and with six satellite-tracked iSphere drifters deployed betweenNovember and December, 2011 (Fig. 9c). The synthetic drifters were allowed to move for 60 days, which is the same periodthe real spill progressed before its final containment.Part of the synthetic drifters (purple trajectories to northwest in Fig. 9c) agree with the observed spill trajectory (red shape)and with one of the iSphere drifters deployed in November (magenta trajectory – ID 403 – in Fig. 9c), for the most part movingalong a cLCSs. The other part of the synthetic floats (purple trajectories to southwest in Fig. 9c) correspond with iSpheretrajectories (orange, blue, yellow, gray and cyan lines in Fig. 9c) deployed in December, and the only other cLCSs originatingwhere the oil spill originated and where synthetic and real drifters were released. Thus, synthetic drifters, iSphere trajectoriesand cLCSs are all in good agreement: there are two main transport patterns originating at the spill location. While the oil spreadalong one of the cLCSs (Fig. 9b), it did not follow the monthly mean surface currents for November (Fig. 9d). Indeed the meanEulerian velocity is often perpendicular to cLCSs originating at the location of the spill.Notice that cLCSs are accurate indicators of the first part of the drifter trajectories – they were designed to extract likelytransport patterns over periods of about one week. The oil spill started in November near an upwelling region (Region 6 inFig. 3b, see also Fig. 9d) and permeated the southeast near the mean position of a cyclonic feature (Fig. 9e and 9f, see also 5d).The oil spill final positions coincide with the persistent squeezelines deforming into chevrons in November (23S and 39W) andadvecting the oil spill away from the 2000 m isobath. We note how the cLCSs agree with the thermal fronts (Fig. 9d), as withthe low-frequency SSH (Fig. 9e) and EKE (Fig. 9f) distribution. A large-scale oil contamination in Northeast Brazil with unknown origin
In 2019, Brazil experienced an oil-related environmental emergency that impacted a large number of beaches as far south as thestate of Rio de Janeiro, reaching an extension of almost 4000 km .Since late August, when it was first detected, more than a thousand beaches have reported occurrences of oil patches,including 12 marine protected areas . By November, over 2000 metric tons of oil were removed from these beaches andthere is still no indication or evidence of its origin . Crude oil may drift as shallow subsurface patches, making it difficult touse satellite sensors for monitoring. igure 7. Selected trajectories of satellite-tracked drifters with drogues of 15 m depth, interpolated at 6 hour intervals,distributed by NOAA’S Global Drifter Program, and of iSPHERE, distributed by Prooceano with consent of PetroRio,superposed to the annual-mean c ρ .(a) drifters trapped in eddies and meanders near the Vitória-Trindade Seamount Chain andAlmirante Saldanha seamount; (b)drifters confined in weakly attracting regions or inshore of the 200 m isobath; (c) drifterstraveled inshore of the BC core, between the 200 and 2000 m isobaths; (d) drifters moved offshore of the 2000 m isobath; (e)drifters moved onshore-offshore-onshore; (f) drifters moved onshore-offshore-onshore. Depth contours of 200 and 2000 m arerepresented by thin black lines. The ID of each drifter is shown in the insert of each frame. igure 8. The PDE (coloured contours) of (a) all austral Summer trajectories (Jan-Feb-Mar) over the c ρ distribution forFebruary (color shading), (b) all austral Autumn trajectories (Apr-May-Jun) over the c ρ values for May (color shading), (c) allaustral Winter trajectories (Jul-Aug-Sep) over the c ρ values for August, and (d) all austral Spring trajectories (Oct-Nov-Dec)over the c ρ distribution for November. Depth contours of 200 and 2000 m are represented by black lines.One of the most important Marine Protected Areas, the Abrolhos Bank, was oiled in early November 2019. This areais internationally recognized as a marine biodiversity heritage and has been included in the 16th round of bidding forexploration and production of oil and natural gas, under the concession regime, opened in December 2018 (resolution CNPEn°17/2018 and CNPE n°03/2019; ).We show the location of known oiled beaches located within our study area as per November of 2019 (Fig. 10a–d),December of 2019 (Fig. 10e–h), January of 2020 (Fig. 10i–j), and February of 2020 (Fig. 10k–l) (IBAMA, 2020).In this area, the oil beached for the first time during the months of November (Fig. 10a–c) and December (Fig. 10 and 10 g ).The floating oil moved from north to south following the BC and, although most of the contaminated coastline is outside ourmodel domain, it is possible to note that regions of maximum values of c ρ ( > Discussion
We offer, for the first time, an integrated representation for the role of eddies and meanders in shaping the mean flow of theBC based on the calculation of cLCSs. The quasi-steady nature of these Lagrangian structures allows the identification ofthe pervasive and consistent influence of mesoscale features in this western boundary current. Climatological squeezelinesdeforming into chevron shapes can be seen along the axis of the mean BC coinciding well with chevron shapes from satelliteSST, as it is advected by the mean flow. These structures characterize the BC core at the surface positioned along the 2000 m isobath, with a good seasonal agreement between model and high resolution satellite data (Fig. 1). High resolution modeloutput indicates that cLCSs deformation also responds to zonally persistent cross-shelf SSH transition from positive (high)values near coastline to low (negative) values between 200 and 2000 m and back to positive (high) offshore from the 2000 m isobath (Fig. 5a and 5b). Zonally-paired cyclonic and anticyclonic structures are embedded in this transition, also causing thecLCSs to deform into chevrons. In a recent work, found similar chevrons straddling The Malvinas Current lagrangian axis,and showed it was a persistent structure by superimposing shearless-parabolic LCSs that behaves as as a cross-shelf transportbarrier. Indeed, we show that hyperbolic cLCSs can also identify the deformation of fluid as chevrons along the core of the BC,in close agreement with monthly-mean satellite SST chevron-like advection patterns (Fig. 1).A number of independent studies have discussed the presence of mesoscale features along the BC , frequentlyinvoking the interaction with sharp topographic gradients and surface-subsurface flow shear as inducing the formation of igure 9. (a) The Chevron oil spill as observed by a true-color MODIS satellite image composite (courtesy of Petrobras) from12th November, 2011 at 10:30 (UTC–3) in the Frade’s field. (b) The shape of Chevron’s oil spill (red polygon) over the cLCSsfor November coloured according to their strength of attraction c ρ . (c) The chevron’s oil spill (red filled polygon), the 60 daytrajectories of 30 ROMS synthetic-drifters launched in November 1st, 2011 (purple lines), and the trajectories of 06 iSpheredrifters (courtesy of Prooceano and PetroRio S.A.) launched between November and December of 2011 (magenta, orange, blue,yellow, gray and cyan lines) plotted over the annual climatological squeezelines (grey contours). The dates of deployment andID of each iSphere are identified in the figure insert. (d) Chevron oil spill (blue polygon) over the ROMS surface velocity(black arrows), MUR SST (color shading), and cLCSs (white lines), all averaged for November. (e) Chevron’s oil spill (redpolygon) over the mean ROMS SSH (color shading) and cLCSs (white lines) for November. (f) Chevron’s oil spill (bluepolygon) over the ROMS TKE (color shading, in log scale) and the November cLCSs (white lines). Depth contours of 200 and2000 m are represented by thin black lines. igure 10. Location of beaches along the Brazilian coast within the study area that were oiled for the first time (pink dots)and that were re-oiled (blue dots) in November (a-d) and December (e-h) of 2019, and January (i-j) and February (k-l) of 2020.Depth contours of 200 and 2000 m are represented by thin black lines. Oiled sites are superposed to monthly mean cLCSs(colored lines) and c ρ (color shading) to indicate transport patterns and particle attraction sites.cyclonic and anticyclonic meanders with consequent pinching off of eddies . During the summer, the cLCSs deformationrepresented by the chevrons covers a large area with seamounts and sharp change in coastline orientation, coincident with EKEmaxima (-2 m / s , in logarithmic scale, 0.13 m / s in linear units) extending offshore of the Abrolhos Bank and between 21Sand 26S (Fig. 2a). During the winter, EKE maxima is less organized (Fig. 2b), possibly as a result of the increase in the numberof northward-moving cold atmospheric fronts. The presence of persistent meanders and eddies along the BC axis is also evidentin the seasonal (monthly means for March and August) EKE and MKE maps (Fig. 2a–d), monthly-model SSH (Fig. 5), seasonalPDE of drifter trajectories (Fig. 8) and model monthly mean surface velocities (Fig. S5). The orientation and location of cLCSstend to follow these known features, with our model SSH indicating both cyclonic (Vitória Eddy, Fig. 5c) and anticyclonicrotation (Abrolhos Eddy, Fig. 5c), near the Abrolhos region and Vitória-Trindade chain respectively (locations 1, 4, and 2 inFig. 3a). Intense flow shear caused by the Abrolhos Bank eastward shelf projection and the Vitória-Trindade seamount chain areboth evident as high c ρ values ( >
1, 2.7 in linear units, see Fig. 4) and chaotic trajectories of drogued drifters (Fig. 7a). As theBC moves southwards, it crosses a wind-induced upwelling region around 21S in the Cabo de São Tomé Region (location6 in Fig. 3a, see also Fig. 5d and S8a), characterized by persistent year-round high c ρ (Fig. 4). The cLCSs deformation in theSão Tomé eddies depicted in Fig. 5d has a similar shape to those found along the BC axis further south, but with the offshoreeddy displaying a cusp bent towards the direction of anticyclonic rotation. As these chevrons are formed distant from theBC axis, their shapes tend to conform to the eddy rotation. The onshore eddy is a semi permanent cyclonic feature (see Fig.S8a–c) originated from the detachment of a BC unstable meander likely induced by baroclinic instability . The persistentmeanders and the cyclonic eddies they generate are known to induce or enhance coastal upwelling , here we associate theupwelling with high attraction values ( >
1, 2.7 in linear units) of c ρ (Fig. 4). There is a Lagrangian confluence region just southof the upwelling of Cabo Frio (location 7 in Fig. 3a) associated with the presence of cyclonic-anticyclonic features on both sidesof the 2000 m isobath near 25S (Fig. 5e, Fig. S8a–c). Here, our computations of c ρ and cLCSs accurately captured the mainelements of surface circulation known as a current-eddy-upwelling region , offering a spatio-temporally Lagrangian integratedview of a dynamically complex system. Further south, Cabo de Santa Marta (location 9 in Fig. 3a) is dynamically similarto Cabo Frio with alternating anticyclonic (offshore) and cyclonic (inshore) flows (Fig. 5f) that coincide with satellite SSTadvection (see Fig. S8d) enhanced by baroclinic instability . The persistent shelf-break upwelling results from the interactionof the BC with coastline orientation and shelf topography . During the summer, wind forcing enhances upwelling and in thewinter a northward flow advects cold, low-salinity water from the Plata river (Fig. 1a). The zonally organized cLCSs around abo de Santa Marta have chevrons structures over the MKE maxima (Fig. 2c and 2d) along the axis of the mean BC flow.The cLCSs extracted quasi-steady Lagrangian transport patterns associated with persistent meanders and rotationalstructures, as indicated in different regions (Fig. 5c–f). When the BC axis is over the 2000 m isobath, south of about 22S, frontalmeanders develop as a response to baroclinic instability due to vertical shear associated with the BC and the IntermediateWestern Boundary Current flowing below 500 m depth . As these meanders grow they can cause a reversion in the surfaceflow in the inshore front of the BC. We have used the annual average cLCSs to propose an schematic representation, shownin Fig. 6, of the quasi-stationary persistent meander flow based on the example of Fig. 5e. A similar baroclinic flow wasobtained by with an ocean model experiment with an horizontal resolution of 13 km and 20 σ levels showing the existence ofa quasi-standing vorticity wave pattern in the region. The typical cyclonic meandering between 200 and 2000 m depth is alsoknown to induce shelf-break austral Summer upwelling . described the existence of pairs of eddies with opposite rotationssouth of Cabo Frio in the same way as our schematic representation, but were unable to offer an explanation for that. Thispersistent feature associated with high attraction c ρ values ( >
1, 2.7 in linear units) probably contributes for frequent revisit ofdrifters during the austral summer and winter (Fig. 8a and 8b).Interpreting cLCSs is not always a simple task so that the integration of different and independent data is needed. For thatpurpose, Lagrangian drifters and synthetic floats released at specific sites have been successfully used to assess the significanceof the computed cLCSs . Despite the seasonal variability observed in the satellite SST and model-derived EKE and cLCSs,the BC flow tends to act as a transport barrier for particles. The computed PDE for 352 satellite-tracked drifters shows thatthey mostly concentrate in large patches along the 2000 m isobath (Fig. 8, see also Supplementary Fig. S6 for a plot of alltrajectories). There is a clear spatio-temporal pattern in the distribution of trajectories, from February to May they concentrateat the northern section equatorward of 24S and to the south between August and November. The prevalence of high attraction c ρ values ( >
1, 2.7 in linear units) also follow a similar trend as depicted from the monthly climatological attraction strengthmaps in Fig. 4.The strong variability in this alongshelf current is suggested by the presence of intense eddy activity (Fig. 2a and 2b,Fig. 5d–f), with the magnitude of EKE maxima being comparable to the MKE maxima (Fig. 2c,d). However, MKE is centeredalong the 2000 m isobath, while EKE maxima is centered just inshore, between the 200 and 2000 m isobaths. The location ofTKE maxima is similar to the location EKE maxima with contributions from the MKE maxima, again suggesting the persistenceof eddy activity (Fig. 2e,f). The deformation of climatological squeezelines crossing regions with high and low mean modelSSH and aligning with surface Eulerian velocities (Fig. S5) show a consistent signature. This is most evident poleward ofabout 23S, where SSH gradient of low SSH between 200 and 2000 m isobaths, and high SSH offshore of the 2000 m isobath(Fig. 5a and 5b), seem to concentrate most of the flow horizontal shear. Nearly 30% of the 352 drogued drifters used in thisstudy (Table 1) managed to cross regions of weak attraction (Fig. 3b, see also Fig. 7c drifter 127065; 7e drifters 403, 78862,2720460; 7f drifters 62273, 2525260). In fact, the PDE of drogued drifter positions (Fig. 8) suggest that high c ρ over theslope behave as a transport barrier around 200 m isobath, the likelihood of a drifter crossing this threshold is about an order ofmagnitude smaller than the likelihood of not crossing. When drifters cross the 2000 m isobath towards the 200 m isobath, theytend to do so along a section with low c ρ . Similarly, drifters released inshore of the 200 m isobath tend to be confined to theshelf (Fig. 7b).Our study domain covers two of the most important oil-producing areas of the southwest Atlantic, the Santos and Camposbasins, that are responsible for 87% of total oil production in Brazil. Our results highlight the complex nature of surfacetransport along the BC and the challenges it poses to those involved in modeling oil spill trajectory as part of contingencyplanning and emergency response. Using examples of two different oil spill events, we show that cLCSs and c ρ computationsprovide new information that is relevant for a detailed assessment of surface transport organization. Our results for the Frade’sspill agree with offshore transport that can be seen with drifting buoys (Fig. 9c), monthly SST-satellite (Fig. 9d), and themaxima EKE (Fig. 9f) offshore from the 2000 m isobath. We can see from (Fig. 9c that only one iSphere drifter (ID 403) andsome of the synthetic drifters managed to reproduce the movement of the oil spill with the same accuracy as the transportdetermined by the cLCSs (Fig. 9b). The usefulness of cLCSs for oil spill planning and response is again demonstrated here. Atthe Frade’s field oil spill location, the synthetic drifters and iSphere trajectories show two different transport patterns, with theoil following one of them. The fact that both transport patterns are clearly depicted by the cLCSs that originate at the spill’sorigin further support the potential of using these Lagrangian structures to constrain the most likely oil trajectories during anemergency response. By comparing to transport patterns, it is shown here once again that the time-averaged Eulerian velocitycan be misleading the Eulerian velocity tends to be perpendicular to the simulated and observed Lagrangian transport patterns,which are accurately depicted by cLCSs (Fig. 9d, see additional examples in the supplementary information of ). In thisstudy, we show that interpreting cLCSs is not always straightforward. The interpretation, and consequently the identification ofdominant transport patterns, is supported by comparisons between cLCSs with time-mean Eulerian fields such as SST, SSH andTKE (Fig. 1, 2 and 5), and with drifters (e.g. Fig. 8 and 9).Recently, a large-scale accident oiled nearly 4.000 km of beaches in Brazil between November 2019 and February 2020, for hich the origin has not been determined so far. This gave us the unique opportunity to evaluate how the computed c ρ andcLCSs would have contributed to the observed oil beaching patterns, without consideration to the source of contamination.By construction, cLCSs were designed to work for generic oil spills. The sequence of reported oiled sites by locals and theBrazilian government suggest that the oil spill should have originated close to the South Equatorial Current bifurcation centeredaround 10S and 14S . Most of the oil dispersed as subsurface patches, yet we found good agreement between the regions ofmaximum values of c ρ and persistent cLCSs and the first and re-oiled areas in the beaches Brazilian spill (Fig. 10), suggestingwhich regions are most vulnerable. Comparing the sites impacted only once, and those that were re-oiled in Fig. 10 (pink andblue dots, respectively), clearly the latter tend to happen closer to c ρ maxima ( > c ρ and cLCSs with model and observational data (satellite imagery and drifting buoys) showed to be a promisingtool to indicate likely oil spill trajectories and beaching sites. Summary and Conclusions
We show that by combining cLCSs and c ρ with SST-satellite data, model Eulerian surface velocities, mean SSH, TKE, MKEand EKE, Lagrangian drifters and synthetic drifters, it is possible to gain new insights on how surface ocean transport isorganized in a complex weak WBC setting. The quasi-steady Lagrangian transport patterns in this western boundary currentelegantly captured the role of persistent and recurrent eddies and meandering on the surface transport. This novel approachproduced consistent results, making it possible to create an integrated representation for the role of mesoscale activity in shapingthe mean flow of the BC. Accurate representation of surface flows in current systems dominated by instabilities and intensemesoscale activity is particularly challenging, e.g. reconciling Eulerian and Lagrangian views. So far, published results in theBC has provided evidences that the interaction of surface and pycnocline-level flows, together with complex bottom topographyand sharp changes in the coastline orientation produce a number of persistent mesoscale features . The time-meanEulerian flow may not be representative of material transport, making it difficult to accurately describe at material transportthe surface of the ocean. We overcome this limitation by describing the surface flow of the BC from a Lagrangian point ofview, and then connecting it to Eulerian fields such as SSH, MKE and EKE. The significance of the above proposed schemewas assessed using two different oil spill events and proved to generate consistent results when compared to the observed spilltrajectory and oil beaching. Data and Methods
Our domain is bounded to the north by the Abrolhos National Bank and Vitória-Trindade Seamounts and to the south by thesouthern limit of Cabo de Santa Marta, between 17–31S and 29–50W.
ROMS velocity data
We use daily averaged outputs from a ROMS simulation with a horizontal resolution of 1 /
36° ( ≈ km ) and 40 terrain-following vertical levels. The model simulation was forced every 6 h by the atmospheric fields obtained from the ClimateForecast System Reanalysis (CFSR) and Climate Forecast System (CFSv2) with ≈ km horizontal resolution and every 5days lateral open boundary conditions by Simple Ocean Data Assimilation (SODA, version 3.3.1) with horizontal resolutionof 0 .
25° and 50 vertical levels . The simulation included the inputs of two rivers (Doce and Paraíba do Sul), using themonthly runoff climatology estimated by Brazilian National Water Agency and river temperature by the Operational SeaSurface Temperature and Sea Ice Analysis (OSTIA) . Tidal forcing included 08 main tidal constituents, two long periodsconstituents and three nonlinear harmonic constituents, extracted from the Oregon State University TOPEX/Poseidon GlobalInverse Solution – TPXO version 8 . Our free-running simulation was integrated from January 1, 2000 to December 31, 2015,totalling 15 years of experiment, the first 3 years were discarded as spin-up, in order to use the period of model integration inwhich the surface energy oscillates almost periodically around a steady state . Lagrangian Simulations
The ROMS simulations contains a built-in float algorithm that allows online tracking of passive floats across the model domain.Particle trajectories are calculated from the Eulerian velocity fields at each baroclinic time step using the fourth-order Milnepredictor and the fourth-order Hamming corrector . Particle simulations were performed to cover two objectives: i) analyzethe variability behind the low-frequency Lagrangian transport patterns extracted through cLCSs, and also test the informationextracted through cLCSs, like locations of enhanced cross-shelf transport or isolated regions, and ii) reproduce the Lagrangiantransport pattern that occurred during the Frade’s Field oil spill.For the first objective, 30 floats were launched at 28 different points in the study domain. All 28 launches, with 30 floatseach, were carried out in the austral summer and winter at the surface and include a random walk component. In the australsummer, the floats were launched on the 1st of December 2013 and traveled freely, in the horizontal direction, until the 28th of ebruary 2014. While in austral winter, the floats were launched on the 1st of June 2006 and traveled freely, in the horizontaldirection, until the 30th of September 2006.For the second objective, we launched, at a single point and once, 30 floats at the sea surface and included a random walkcomponent on 1st of November until 31th of December of 2011. The simulation coincided with the months and locationof Chevron’s oil spill in the Frades Field , oil spill data was provided by Petrobras. During the oil spill six surface drifters(iSpheres) were released by Prooceano, with the permission of PetroRio SA. The iSpheres is a low cost, expendable,drifting tracking buoy developed by Metocean Data Systems. The launch of iSpheres was intended to track and monitor oilspill from Chevron. Climatological LCS and c ρ The computation of cLCSs, structures organizing Lagrangian transport, used here is as developed by . cLCSs are computedusing the code in . The sea-surface velocity data is obtained from daily outputs of a 13-year ROMS simulation. Theclimatology of the superficial velocity was obtained by averaging each day of the time series, defining a 365 day climatology,disregarding, therefore, the leap days. Further description of the method can be found in , a description of the computationsand the code, can be found in . Trajectories were integrated using a 4th/5th order Runge-Kutta method, with step adaptation,and cubic interpolations. The trajectory integration was over 7 days periods ( T = − x ) and in time ( t ). An adequate time-scale to extract recurring or persistent transport related to mesoscale structures . Thecomputations use a numerical grid of 1024 × km to the north, south, east andwest of each grid point. Observed surface trajectories and their Probability Density Estimate (PDE)
We used 352 satellite-tracked drifters with drogues at 15 m depth distributed by NOAA’S Global Drifter Program – GDP ,with trajectories interpolated every 6 hours and spanning 13 years of data to compute a Probability Density Estimate (PDE) ofdrifter trajectories. The PDE is calculated using a Probability Density Function, PDF ( ρ , t | ρ , t ) , with the initial positionsof each trajectory being ρ = ( x , y ) at time time t , and the final position ρ = ( x , y ) at time t . And regions with high incidenceof trajectories were obtained with a Kernel Density Estimation in smoothed, approximately, with 3° x 3° boxes at 900 points,equally spaced, calculated according to . We adopted a lagrangian time scale of 3-days for each trajectory, based onestimated diffusion coefficient between 6 × and 9 . × cm s − . Auxiliary data
The sea-surface temperature was obtained from the global daily-SST data of the Multi-scale Ultra-high Resolution (MUR)sensor . The MUR provides data with spatial resolution of 0 . km intervals.We estimate the distribution of kinetic energy per unit mass for the mean and eddy fields. The TKE represents the sum ofthe MKE, the energy of the mean circulation and the EKE, the fluctuating part of the absolute velocity . MKE, EKE andTKE were calculated as the Equations 1, 2 and 3: MKE = (cid:0) ¯ u + ¯ v (cid:1) (1) EKE = (cid:16) u (cid:48) + v (cid:48) (cid:17) (2) MKE = MKE + EKE (3)Where ¯ u and ¯ v are the monthly mean surface current velocities computed from the daily means, and u (cid:48) and v (cid:48) are thedepartures from the mean. MKE, EKE and TKE are all in m s − . eferences Wiggins, S. The dynamical systems approach to lagrangian transport in oceanic flows.
Annu. Revis. on Fluid Mech. ,295–328, DOI: 10.1146/annurev.fluid.37.061903.175815 (2005). Assad, L. P. d. F., Torres Junior, A. R., Arruda, W. Z., Mascarenhas Junior, A. d. S. & Landau, L. Volume and heattransports in the world oceans from an ocean general circulation model.
Revista Brasileira de Geofisica , 181–194, DOI:10.1590/S0102-261X2009000200003 (2009). Imawaki, S., Bower, A. S., Beal, L. & Qiu, B. Western boundary currents. In
International Geophysics , vol. 103, 305–338,DOI: 10.1016/B978-0-12-391851-2.00013-1 (Elsevier, 2013). Stommel, H. A survey of ocean current theory.
Deep. Sea Res. (1953) , 149–184 (1957). de Oliveira, B. L. A., Netto, T. A. & de Freitas Assad, L. P. Three-dimensional oil dispersion model in the campos basin,brazil. Environ. technology , 277–287, DOI: 10.1080/09593330.2017.1298678 (2018). da Rocha Fragoso, M. et al. A 4d-variational ocean data assimilation application for santos basin, brazil.
Ocean. Dyn. ,419–434, DOI: 10.1007/s10236-016-0931-5 (2016). D’Agostini, A., Gherardi, D. F. M. & Pezzi, L. P. Connectivity of marine protected areas and its relation with total kineticenergy.
PloS one , e0139601, DOI: 10.1371/journal.pone.0139601 (2015). Marta-Almeida, M. et al.
Efficient tools for marine operational forecast and oil spill tracking.
Mar. pollution bulletin ,139–151, DOI: 10.1016/j.marpolbul.2013.03.022 (2013). Romero, A., Abessa, D., Fontes, R. & Silva, G. Integrated assessment for establishing an oil environmental vulnerabilitymap: Case study for the santos basin region, brazil.
Mar. Pollut. Bull. , 156–164, DOI: 10.1016/j.marpolbul.2013.07.012(2013). Peterson, R. G. & Stramma, L. Upper-level circulation in the south atlantic ocean.
Prog. oceanography , 1–73, DOI:10.1016/0079-6611(91)90006-8 (1991). Castro, B. d., Lorenzzetti, J., Silveira, I. d. & Miranda, L. d. Estrutura termohalina e circulação na região entre o cabo desão tomé (rj) eo chuí (rs).
O ambiente oceanográfico da plataforma continental e do talude na região sudeste-sul do Brasil , 11–120 (2006). Stramma, L. & England, M. On the water masses and mean circulation of the south atlantic ocean.
J. Geophys. Res. Ocean. , 20863–20883, DOI: 10.1029/1999JC900139 (1999).
Silveira, I. d. et al.
Is the meander growth in the brazil current system off southeast brazil due to baroclinic instability?
Dyn. Atmospheres Ocean. , 187–207, DOI: 10.1016/j.dynatmoce.2008.01.002 (2008). Gouveia, M. B., Gherardi, D. F., Lentini, C. A., Dias, D. F. & Campos, P. C. Do the brazilian sardine commercial landingsrespond to local ocean circulation?
PloS one , 1–19, DOI: 10.1371/journal.pone.0176808 (2017). Lima, M. O. et al.
An assessment of the brazil current baroclinic structure and variability near 22 s in distinct oceanforecasting and analysis systems.
Ocean. Dyn. , 893–916, DOI: 10.1007/s10236-016-0959-6 (2016). Campos, E. J., Gonçalves, J. & Ikeda, Y. Water mass characteristics and geostrophic circulation in the south brazil bight:Summer of 1991.
J. Geophys. Res. Ocean. , 18537–18550, DOI: 10.1029/95jc01724 (1995).
Campos, E. et al.
Experiment studies circulation in the western south atlantic.
Eos, Transactions Am. Geophys. Union ,253–259, DOI: 10.1029/96EO00177 (1996). Duran, R., Beron-Vera, F. J. & Olascoaga, M. J. Extracting quasi-steady lagrangian transport patterns from the oceancirculation: An application to the Gulf of Mexico.
Sci. reports , 1–10, DOI: 10.1038/s41598-018-23121-y (2018). Gough, M. K. et al.
Persistent lagrangian transport patterns in the northwestern gulf of mexico.
J. Phys. Oceanogr. ,353–367, DOI: 10.1175/JPO-D-17-0207.1 (2019). Maslo, A., Azevedo Correia de Souza, J. M., Andrade-Canto, F. & Rodríguez Outerelo, J. Connectivity of deep waters inthe Gulf of Mexico.
J. Mar. Syst. , DOI: 10.1016/j.jmarsys.2019.103267 (2020).
Shchepetkin, A. F. & McWilliams, J. C. The regional oceanic modeling system (roms): a split-explicit, free-surface,topography-following-coordinate oceanic model.
Ocean. modelling , 347–404, DOI: 10.1016/j.ocemod.2004.08.002(2005). Shchepetkin, A. F. & McWilliams, J. C. Correction and commentary for “ocean forecasting in terrain-following coordinates:Formulation and skill assessment of the regional ocean modeling system” by haidvogel et al., j. comp. phys. 227, pp.3595–3624.
J. Comput. Phys. , 8985–9000, DOI: 10.1016/j.jcp.2009.09.002 (2009). SAFETY4SEA. Brazil’s abrolhos park in danger due to possible oil explorations. Online (2019). https://safety4sea.com/brazils-abrolhos-park-in-danger-due-to-possible-oil-explorations/ Accessed: 25 Nov 2019.
Beron-Vera, F. J., Bodnariuk, N., Saraceno, M., Olascoaga, M. & Simionato, C. Stability of the malvinas current.
Chaos:An Interdiscip. J. Nonlinear Sci. , 013152, DOI: 10.1063/1.5129441 (2020). Schmid, C., Schäfer, H., Zenk, W. & Podestá, G. The vitória eddy and its relation to the brazil current.
J. physicaloceanography , 2532–2546, DOI: 10.1175/1520-0485(1995)025<2532:tveair>2.0.co;2 (1995). Da Silveira, I. et al.
On the baroclinic structure of the brazil current–intermediate western boundary current system at22–23 s.
Geophys. research letters , DOI: 10.1029/2004GL020036 (2004). Calado, L., Gangopadhyay, A. & Da Silveira, I. A parametric model for the brazil current meanders and eddies offsoutheastern brazil.
Geophys. research letters , DOI: 10.1029/2006GL026092 (2006). Chen, H.-H., Qi, Y., Wang, Y. & Chai, F. Seasonal variability of sst fronts and winds on the southeastern continental shelfof brazil.
Ocean. Dyn. , 1387–1399, DOI: 10.1007/s10236-019-01310-1 (2019). Arruda, W. Z., Campos, E. J., Zharkov, V., Soutelino, R. G. & da Silveira, I. C. Events of equatorward translation of thevitoria eddy.
Cont. Shelf Res. , 61–73, DOI: 10.1016/j.csr.2013.05.004 (2013). Soutelino, R., Gangopadhyay, A. & Da Silveira, I. The roles of vertical shear and topography on the eddy formation nearthe site of origin of the brazil current.
Cont. Shelf Res. , 46–60, DOI: 10.1016/j.csr.2013.10.001 (2013). Castelao, R. M. & Barth, J. A. "upwelling around cabo frio, brazil: The importance of wind stress curl".
Geophys. Res.Lett. , DOI: 10.1029/2005GL025182 (2006). Rodrigues, R. R. & Lorenzzetti, J. A. A numerical study of the effects of bottom topography and coastline geometry on thesoutheast brazilian coastal upwelling.
Cont. Shelf Res. , 371–394, DOI: 10.1016/S0278-4343(00)00094-7 (2001). Calado, L., Gangopadhyay, A. & Da Silveira, I. Feature-oriented regional modeling and simulations (forms) for the westernsouth atlantic: Southeastern brazil region.
Ocean. Model. , 48–64, DOI: 10.1016/j.ocemod.2008.06.007 (2008). Campos, E. J. Equatorward translation of the vitoria eddy in a numerical simulation.
Geophys. Res. Lett. , DOI:10.1029/2006GL026997 (2006). Calado, L., Da Silveira, I., Gangopadhyay, A. & De Castro, B. Eddy-induced upwelling off cape são tomé (22 s, brazil).
Cont. Shelf Res. , 1181–1188, DOI: 10.1016/j.csr.2010.03.007 (2010). Palma, E. D. & Matano, R. P. Disentangling the upwelling mechanisms of the south brazil bight.
Cont. Shelf Res. ,1525–1534, DOI: 10.1016/j.csr.2009.04.002 (2009). Campos, P. C., Möller Jr, O. O., Piola, A. R. & Palma, E. D. Seasonal variability and coastal upwelling near cape santamarta (brazil).
J. Geophys. Res. Ocean. , 1420–1433, DOI: 10.1002/jgrc.20131 (2013).
Campos, E. J., Velhote, D. & da Silveira, I. C. Shelf break upwelling driven by brazil current cyclonic meanders.
Geophys.Res. Lett. , 751–754, DOI: 10.1029/1999GL010502 (2000). Rodrigues, R. R., Rothstein, L. M. & Wimbush, M. Seasonal variability of the south equatorial current bifurcation in theatlantic ocean: A numerical study.
J. Phys. Oceanogr. , 16–30, DOI: 10.1175/JPO2983.1 (2007). Saha, S. et al.
The ncep climate forecast system reanalysis.
Bull. Am. Meteorol. Soc. , 1015–1058, DOI: 10.1175/2010bams3001.1 (2010). Saha, S. et al.
Ncep climate forecast system version 2 (cfsv2) monthly products.
Res. Data Arch. at Natl. Cent. forAtmospheric Res.
DOI: 10.5065/D69021ZF (2012).
Saha, S. et al.
The ncep climate forecast system version 2.
J. climate , 2185–2208, DOI: 10.1175/JCLI-D-12-00823.1(2014). Carton, J. A., Chepurin, G. A. & Chen, L. "SODA3: A new ocean climate reanalysis".
J. Clim. , 6967–6983, DOI:10.1175/JCLI-D-17-0149.1 (2018). Agência Nacional de Águas (Brasil). Agência nacional de Águas. Online (2018). http://biblioteca.ana.gov.br/index.asp?codigo_sophia=76975.Accessedin:28Aug.2019.
Donlon, C. J. et al.
The operational sea surface temperature and sea ice analysis (ostia) system.
Remote. Sens. Environ. , 140–158, DOI: 10.1016/j.rse.2010.10.017 (2012).
Egbert, G. D. & Erofeeva, S. Y. Efficient inverse modeling of barotropic ocean tides.
J. Atmospheric Ocean. technology ,183–204, DOI: 10.1175/1520-0426(2002)019<0183:EIMOBO>2.0.CO;2 (2002). Marchesiello, P., McWilliams, J. C. & Shchepetkin, A. Equilibrium structure and dynamics of the california current system.
J. physical Oceanogr. , 753–783, DOI: 10.1175/1520-0485(2003)33<753:ESADOT>2.0.CO;2 (2003). Narváez, D. A. et al.
Modeling the dispersal of eastern oyster (crassostrea virginica) larvae in delaware bay.
J. Mar. Res. , 381–409, DOI: 10.1357/002224012802851940 (2012). Van Sebille, E. et al.
Lagrangian ocean analysis: Fundamentals and practices.
Ocean. Model. , 49–75, DOI:10.1016/j.ocemod.2017.11.008 (2018).
Röhrs, J. et al.
Observation-based evaluation of surface wave effects on currents and trajectory forecasts.
Ocean. Dyn. ,1519–1533, DOI: 10.1007/s10236-012-0576-y (2012). Röhrs, J. & Christensen, K. H. Drift in the uppermost part of the ocean.
Geophys. Res. Lett. , 10–349, DOI:10.1002/2015GL066733 (2015). Duran, R., Beron-Vera, F. J. & Olascoaga, M. J. CIAM Climatological Isolation and Attraction Model–ClimatologicalLagrangian Coherent Structures. National Energy Technology Laboratory-Energy Data eXchange; NETL, DOI: 10.18141/1558781 (2019). https://bitbucket.org/rodu/clcss/src/master/.
Elipot, S. et al.
A global surface drifter data set at hourly resolution.
J. Geophys. Res. Ocean. , 2937–2966, DOI:10.1002/2016JC011716 (2016).
Davis, R. A., Lii, K.-S. & Politis, D. N. Remarks on some nonparametric estimates of a density function. In
SelectedWorks of Murray Rosenblatt , 95–100, DOI: 10.1214/aoms/1177728190 (Springer, 2011).
Silverman, B. W.
Density estimation for statistics and data analysis , vol. 26 (CRC press, 1986).
Epanechnikov, V. A. Non-parametric estimation of a multivariate probability density.
Theory Probab. & Its Appl. ,153–158, DOI: doi:10.1137/1114019 (1969). Assireu, A. T., Stevenson, M. R. & Stech, J. L. Surface circulation and kinetic energy in the sw atlantic obtained by drifters.
Cont. Shelf Res. , 145–157, DOI: 10.1016/S0278-4343(02)00190-5 (2003). Chin, T. M., Vazquez-Cuervo, J. & Armstrong, E. M. A multi-scale high-resolution analysis of global sea surfacetemperature.
Remote. sensing environment , 154–169, DOI: 10.1016/j.rse.2017.07.029 (2017).
Acknowledgements
This work has been supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Fi-nance Code 001. The code for cLCS and it’s acknowledgments are available at https://bitbucket.org/rodu/clcss . We thank E. van Sebille for the initial help with float releases. We thank F. J. Beron-Vera for helpful discus-sions. We thank Giullian N. L. dos Reis for processing the satellite MODIS data. We thank C. L. G. Batista, A. S.Ipia for discussions and constructive comments on the text. We thank L. P. Pezzi of LOA ( ) for authorization to use the Kerana cluster. We thank PROCEANO ( http://prooceano.com.br/site/ ) and PetroRio-S.A ( https://petroriosa.com.br/ ) for the iSpheres data. We hank Petrobras ( ) for the shape and image of MODIS referring to the oil spilloccurred in November 2011. We thank IBAMA for the oil spill locations data ( ). We thankthe developers of Regional Ocean Modeling System ( ) and the Jet propulsion Laboratoryfor providing the Multi-scale Ultra-high Resolution (MUR) Sea Surface Temperature (SST) Analysis which is available at( https://podaac.jpl.nasa.gov/dataset/MUR-JPL-L4-GLOB-v4.1 ); the National Center for AtmosphericResearch Staff (Eds) for CFSR and CFSV2 are available at ( https://rda.ucar.edu/ ); the SODA 3.3.1 products produced by Department ofAtmospheric and Oceanic Science ( ); the Brazilian National Water Agencyfrom river flow data ( ); the Group for High Resolution SST (GHRSST) Regional/GlobalTask Sharing (R/GTS) framework from Operational SST and Sea Ice Analysis (OSTIA) system; the ETOPO1 Global ReliefModel products produced by NOAA ( ); the altimeter products wereproduced by SSALTO/DUCAS and distributed by Copernicus Marine Environment Monitoring Service ( http://marine.copernicus.eu/services-portfolio/access-to-products/?option=com_csw&view=details&product_id=SEALEVEL_GLO_PHY_L4_REP_OBSERVATIONS_008_047 ); the OSU Tidal Data Inversion from TPXO GlobalTidal Models ( ); the drifter data are available from the NOAA Global Drifter Program( ). The work of RD was performed in support of the USDepartment of Energy’s Fossil Energy, Oil and Natural Gas Research Program. It was executed by NETL’s Research and Inno-vation Center, including work performed by Leidos Research Support Team staff under the RSS contract 89243318CFE000003.This work was funded by the Department of Energy, National Energy Technology Laboratory, an agency of the United StatesGovernment, through a support contract with Leidos Research Support Team (LRST). Neither the United States Governmentnor any agency thereof, nor any of their employees, nor LRST, nor any of their employees, makes any warranty, expressedor implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information,apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein toany specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarilyconstitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. Theviews and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or anyagency thereof.
Author contributions statement
M.B.G produced the results; M.B.G and R.D conducted the experiments; M.B.G, R.D and D.F.M.G wrote the paper; R.D cededthe code and assisted in the implementation; R.T calculated EKE, MKE and TKE. All authors analysed the results and reviewedthe manuscript.
Competing interests