Lagrangian study of surface transport in the Kuroshio Extension area based on simulation of propagation of Fukushima-derived radionuclides

Lagrangian approach is applied to study near-surface large-scale transport in the Kuroshio Extension area using a simulation with synthetic particles advected by AVISO altimetric velocity field. A material line technique is applied to find the origin of water masses in cold-core cyclonic rings pinched off from the jet in summer 2011. Tracking and Lagrangian maps provide the evidence of cross-jet transport. Fukushima derived caesium isotopes are used as Lagrangian tracers to study transport and mixing in the area a few months after the March of 2011 tsunami that caused a heavy damage of the Fukushima nuclear power plant (FNPP). Tracking maps are computed to trace the origin of water parcels with measured levels of Cs-134 and Cs-137 concentrations collected in two R/V cruises in June and July 2011 in the large area of the Northwest Pacific. It is shown that Lagrangian simulation is useful to finding the surface areas that are potentially dangerous due to the risk of radioactive contamination. The results of simulation are supported by tracks of the surface drifters which were deployed in the area.


Introduction
The Kuroshio Extension (KE) prolongs the Kuroshio Current, a western boundary current in the Northwest Pacific, when the latter separates from the continental shelf of the Japanese island Honshu at Cape Inubo about 35 • 42 ′ N. It flows eastward from this point as a strong unstable meandering jet constituting a front separating the warm subtropical and cold subpolar waters of the North Pacific Ocean. There are cyclonic and anticyclonic recirculation gyres on the northern and southern flanks of the jet. The main features of the KE are described in (Qiu and Chen, 2005;Itoh and Yasuda, 2010). The Kuroshio and the KE transport a large amount of heat and release that to the atmosphere strongly affecting climate. It is a region with one of the most intense air-sea heat exchange and the highest eddy kinetic energy level. It is also a region with commercial fishing grounds Email address: prants@poi.dvo.ru (S.V. Prants) URL: www.dynalab.poi.dvo.ru (S.V. Prants) of Pacific saury, tuna, squid, Japanese sardine and other species.
The Kuroshio-Oyashio frontal zone contains various types of mesoscale and submesoscale eddies that transfer heat, salt, nutrients, carbon, pollutants and other tracers across the ocean. They originate, besides from the KE, from the Tsugaru Warm Current, flowing between the Honshu and Hokkaido islands, and from the cold Oyashio Current flowing out of the Arctic along the Kamchatka Peninsula and the Kuril Islands. Those eddies may persist for the periods ranging from a few weeks to a couple of years and have a strong influence on the local climate, hydrography and fishery.
A study of the role of the KE rings and their interaction with the mean flow is important by many reasons. They act to transfer energy to the mean currents, influent on the KE jet dynamics and drive the recirculation gyres. They transport for a long distance water masses with biophysical properties different from ambient waters that may have a great impact on living organisms. The strongest mesoscale eddies of both polarities are generated along the KE. The warm-core anticyclonic rings (ACR) are pinched off from the meandering KE mainly to the north whereas the cold-core cyclonic ones (CR) -to the south of it. The occurrence, distribution and behavior of the anticyclonic and cyclonic KE rings, moving generally westward due to the planetary β-effect, have been studied in a number of papers via hydrographic observations, infrared imaging and altimetry data (Tomosada, 1986;Ebuchi and Hanawa, 2001;Waseda, 2003;Itoh and Yasuda, 2010). However, the process of their separation from the parent jet is not fully understood.
Lagrangian tools have been successfully used to obtain a detailed description of different advective transport phenomena in the ocean and atmosphere. There is a vast literature on this topic (for a review see (Mancho et al., 2004;Wiggins, 2005;Koshel' and Prants, 2006;Prants, 2013) and references therein). As to the problem of eddy separation from strong jet currents and a cross-jet transport, there are papers on Lagrangian approach to the Loop Current eddy separation in the Gulf of Mexico (Kuznetsov et al., 2002;Andrade-Canto et al., 2013) and on Lagrangian description of cross-jet transport in the Kuroshio Current (Mendoza et al., 2010;Mendoza and Mancho, 2012).
In Refs. (Kuznetsov et al., 2002;Andrade-Canto et al., 2013) near-surface velocity fields from numerical models of circulation in the Gulf of Mexico have been used to study the eddy separation process by computing effective invariant manifolds (Kuznetsov et al., 2002) and finite-time Lyapunov exponents (Andrade-Canto et al., 2013). It has been shown there that the Lagrangian methods are a useful supplement to traditional approaches as they reveal flow details not easily extracted from Eulerian point of view.
In Refs. (Mendoza et al., 2010;Mendoza and Mancho, 2012) a special lobe technique from dynamical systems theory (Wiggins, 1992) and a method of distinguished hyperbolic trajectories (Ide et al., 2002) have been applied to find a geometrical skeleton of some transport processes in an altimetric velocity field in the Kuroshio region including surface cross-jet transport. In Refs. (Samelson and Wiggins, 2006;Uleysky et al., 2007Uleysky et al., , 2010a an detailed analysis, revealing mechanisms of chaotic zonal and cross-jet transport, has been carried out for a few kinematic and dynamical analytic models of meandering jets. In this paper we study numerically the process of interaction of cold-core cyclonic rings with the KE main current, the events of their separation from the parent jet and their role in near-surface crossjet transport. The special aim is to know whether it was possible for Fukushima-derived radionuclides to cross the KE jet which is supposed to be an impenetrable barrier. Simulation is based on solving advection equations for synthetic particles in the AVISO velocity fields. The results are plotted as 1) backward-in-time Lagrangian latitudinal maps, where colors code the latitudes from which particles in a given region came to their final positions on the map and 2) tracking maps showing where they were walking and how frequently visited different places in the region for a given period of time. In Sec. 3.1 we compute both types of the maps to trace origin of water masses inside two CRs pinched off from the KE jet in summer 2011 and to document the surface cross-jet transport. The Fukushima derived Cs isotopes are used as Lagrangian tracers to study transport and mixing processes. We apply the material line technique in Sec. 3.2 to trace the origin of water parcels with measured levels of concentrations of Fukushima derived Cs isotopes collected in two R/V cruises in June and July 2011 in the large area of the Northwest Pacific (Kaeriyama et al., 2013;Buesseler et al., 2012). The results of the simulation are supported by tracks of the surface drifters which were deployed in the area.  polynomials in time are used to provide accurate numerical results. Lagrangian trajectories are computed by integrating the advection equations with a fourth-order Runge-Kutta scheme with a fixed time step of 0.001th part of a day.

Data and methodology
Satellite altimetry demonstrates clearly that the KE alternates between two dominant states: one with two quasistationary meanders and another one when the meanders are not especially prominent (Qiu and Chen, 2005;Sugimoto and Hanawa, 2012). During the meandering state steep troughs develop stimulating ring pinchoff events on the both flanks of the jet. In this paper we will focus on that state with increased eddy activity. A sketch of the meandering KE state in Fig. 1 shows the eastward jet current with two crests near x = 143 • E and x = 151 • E which are anticyclonic side of the jet and two troughs near x = 147 • E and x = 153 • E with cyclonic rotations. In reality the KE jet is highly unstable, the meander's amplitude may change in the course of time, and locations of the crests and troughs may fluctuate strongly both in meridional and zonal directions.
Motion of a fluid particle in a two-dimensional flow is the trajectory of a dynamical system with given initial conditions governed by the velocity field. The corresponding advection equations are written as follows: where the longitude, x, and the latitude, y, of a passive particle are in geographical minutes, u and v are angular zonal and meridional components of the velocity expressed in minutes per day. June to 11 March 2011 with "red" and "green" particles originated from the latitudes <31 • N and >37 • N, respectively. Nuances of the grey color in geographic degrees code the particles originated from the latitudes between 31 • N and 37 • N. b) Zoom of the area with the CR1 demonstrates transport across the KE jet ("green" particles). Tracks of two drifters to be trapped by the CR1 are shown as black squares.
The Lagrangian technique we use is based on calculation of particle motion in an altimetric velocity field forward and backward in time. When integrating advection equations (1) forward in time we compute particle trajectories to know their fate and when integrating them backward in time we know origin of particles and their history. A graphic view of transport and mixing in a studied area is provided by so-called Lagrangian synoptic maps which are plots of one of the Lagrangian indicators versus particle's initial positions (Prants et al., 2011a;Prants, 2013;Prants et al., 2013). The region under study is seeded by a large number of synthetic particles whose trajectories are computed forward or backward in time for a given period of time.
There are a number of Lagrangian indicators (or descriptors in terminology of (Mendoza and Mancho, 2012)) that may be used to characterize transport and mixing processes in the ocean and atmosphere. Among them are zonal and absolute displacements of water parcels, the number of their cyclonic and anticyclonic rotations, vorticity, their residence time in a given area, the number of times particles visit different places in the region and others. The so-called M-function, which measures the Euclidean arc-length of the curves outlined by trajectories for a finite-time interval (Madrid and Mancho, 2009), can be also used to plot the corresponding Lagrangian maps. Sometimes it is useful to compute composite maps with two or more Lagrangian indicators plotted together. To compute the Lagrangian maps we apply the methodology elaborated in our recent papers and applied to study transport and mixing processes in different basins, from marine bays  and seas (Prants et al., 2011a) to the ocean scale (Prants et al., 2011b;Prants, 2013).
The material line technique used here is a powerful tool to trace origin, history and fate of water masses. A large number of synthetic particles (markers) are placed on a meridional and/or zonal line, crossing a feature under study, and evolve forward or backward in time. This method is especially useful if one place material lines along the transects with in-situ measurements. In Sec. 3.2 we carry out such simulations with material lines placed along the transects in the Northwest Pacific where concentrations of radioactive Cs isotopes have been measured in surface seawater during two R/V cruises in 2011 after the FNPP accident. Our simulations are complimented by tracks of available surface drifters (http://www.aoml.noaa.gov/phod/dac/index.php).

Lagrangian study of origin of Kuroshio Exten-
sion rings and possibility of surface cross-jet transport Documenting separation of rings from jets, their merging with jets and tracking their propagation are longstanding problems in oceanography. Altimeter velocity field along with drifter observations may be used with these aims. Near surface velocity fields on fixed days are shown in Fig. 2 where crosses and open circles mark "instantaneous" hyperbolic and elliptic stagnation points, respectively. Color codes the value of the velocity U in cm/s. Tracks of some drifters for 3 days are plotted by black squares.
In Fig. 2 we illustrate the process of formation of a CR (which we denote as CR1) from the KE meander in June 2011 when the KE was in the state with two prominent quasistationary meanders. In the beginning of June the trough of the first meander starts to steepen with its edges becoming day by day closer and closer to each other ( Fig. 2a on 10 June). The edges merge eventually closing a volume of water with a cyclonic rotation to be connected with the parent jet by an arch (Fig. 2b on 17 June). An elliptic point in its center and a hyperbolic point in the neck of the meander appear. Approximately five days later, the velocity field bifurcates, the ring CR1 is separated from the jet and the meander amplitude decreases correspondingly ( Fig. 2c on 5 July). Tracks of two drifters, encircling partly the ring, are shown in Fig. 2c.
Transport of water masses across strong jet currents, like the Gulf Stream and the Kuroshio, is important because they separate waters with distinct bio-physico-chemical properties. It may cause heating and freshing of waters with a great impact on the weather and living organisms. As to transport across the KE, one should mention the paper (Mendoza et al., 2010) where a turnstile mechanism (Wiggins, 1992) has been supposed to provide KE cross-jet transport in altimetric data sets. (Mendoza et al., 2010) have computed stable and unstable manifolds of relevant distinguished hyperbolic trajectories and found a lobe transport across a Lagrangian barrier defined from pieces of those manifolds. It is a mechanism of chaotic advection well studied with analytical model flows (Wiggins, 1992;Koshel' and Prants, 2006). However, it is not a direct evidence of cross-jet transport because of difficulties and inevitable errors in computing the manifolds and relevant trajectories in altimetric data sets. Moreover, the cross-jet transport has been found by (Mendoza et al., 2010) in a far downstream region between 155 • E and 165 • E where the KE jet is highly unstable and may even bifurcate.
The question whether the much more stable upstream KE jet between 141 • E and 153 • E is an impenetrable barrier for cross-jet transport is still open. The new aspect of that problem arised suddenly after the Fukushima accident. By the common opinion (Buesseler et al., 2012), it is difficult to expect observation of Fukushima-derived radionuclides on the southern side of the KE jet. Could contaminant waters from the Fukushima area cross the KE jet and appear on the southern side of the jet or not?
In order to document directly the cross-jet transport of Fukushima-derived radionuclides, we compute a special kind of Lagrangian maps by integrating the advection equations (1) for a large number of particles in the study area backward in time from a fixed day till the day of the accident (11 March 2011) and calculating their meridional displacements D y . Colors on such maps code the latitudes from which the corresponding particles came to their final positions on the map. The latitudinal map on 30 June 2011 in Fig. 3a demonstrates that "red" waters crossed the latitude 31 • N from the south, "green" waters crossed the latitude of the FNPP (141 • 05 ′ E, 37 • 25 ′ N) from the north whereas nuances of the grey color code the particles originated from the latitudes between 31 • N and 37 • N. Zoom in Fig. 3b shows the CR1 with "green" water in its core (originated from the latitudes >37 • N) that may contain increased concentration of Fukushima-derived radionuclides.
The simulation results are confirmed by tracks of two surface drifters which were trapped by the CR1 (Fig. 3b).
The southern track belongs to the drifter released in the beginning of January 2011.
It was transported by the Kuroshio Current from the southwest. The northern track belongs to the drifter No. 36473 released on 11 June in the R/V "Ka'imikai-o-Kanaloa" cruise (Buesseler et al., 2012) at the point ∼144 • E and ∼36 • N. It crossed the KE jet and was trapped by the CR1. Its track is also visible at the periphery of the CR1 in Fig. 2c. It is a "green" drifter in Fig. 2 in Ref. (Buesseler et al., 2012). Some of "red" drifters in that Fig. 2, deployed in the cruise, have been trapped by the meander trough that formed the CR2 in July 2011. The map in Fig. 3b is a clear evidence of transport of water across the KE jet. To check that finding we initialized a material line crossing the CR1 core along 31 • 06 ′ N (the horizontal red line in Fig. 2c) and evolved it backward in time till the day of the accident. It has been shown that the fragments of that line, containing "green" particles, really came from the area nearby the location of the FNPP whereas the other particles have been advected to form the CR1 from the west, mainly along the KE jet. However, the amount of potentially dangerous Fukushima waters in the core of the CR1 is comparatively small. Now we apply the material line technique to trace the origin of water masses in the CR1 and in a large CR named as CR2 that was born after a separation of the trough of the second KE meander from the parent jet in July 2011. In June-July 2011 it was deforming strongly and eventually produced a ringlike structure with a diameter of about 300 km that has been detached to the south from the parent jet and then reabsorbed in a short time. That ringlike structure with the center near x = 34 • 30 ′ N and y = 152 • E is seen in Fig. 2d in the altimetric velocity field on 30 July 2011.
Starting on 30 June, we evolve backward in time two perpendicular material lines with a large number of markers, crossing the CR1 (Fig. 2c). The other two material lines were chosen to cross the CR2 on 30 July (Fig. 2d) when a hyperbolic point appeared between the ring and the KE jet. Coming back to the question, whether the KE jet is an impenetrable barrier for Fukushima-derived radionuclides, we compute backward-in-time tracking maps. The region under study is divided in a large number of small cells, and one fixes how many times markers visited each cell during the month after the accident when the maximal leakage directly into the ocean and atmospheric fallout on the ocean surface have been registered. The result for CR1 markers is shown in Fig. 4a where the density of marker's traces, ν, is in the logarithmic scale. First of all, the probability that the CR1 contains the contaminant water is comparatively small because the density of points in the region around the FNPP is small. This map confirms the result of direct calculation of the cross-jet transport in Fig. 3b where only a small amount of potentially contaminant "green" water, originated from the latitudes >37 • N, is visible. It is clear from Fig. 4a that the CR1 consists mainly of Kuroshio water.
As to CR2 markers, the density of their traces in the area, that is supposed to be contaminated, is much higher as compared to the CR1 case (Fig. 4b).
It means that the probability to observe higher concentrations of Fukushima-derived radionuclides in surface waters of the CR2 is expected to be comparatively large. The CR2 contains water parcels that have moved during the month after the accident around the mesoscale eddies to be present to the north and east from the FNPP location. To the day of the accident there was the eddy system with a large anticyclonic warm-core Kuroshio ring (ACR) with the center around 144 • E and 39 • N, a small anticyclonic eddy to the north of it and a medium cyclonic eddy at the traverse of the Tsugaru Strait. It has been shown in our paper (Prants et al., 2011b) that namely this eddy system has governed mixing and transport of radioactive water part of which has been trapped by the ACR and advected around the adjacent eddies to the north whereas the very ACR moved slowly to the south. The concentration of radionuclides around those eddies might be significantly greater than in other places because they are a kind of attractors (Prants et al., 2011b). The influence of the ACR is evident on both the tracking maps as a patch with increased density of traces at its place.
We conclude this section by emphasizing that the material line technique may be useful to finding the surface areas in the North Pacific that are potentially dangerous due to the risk of radioactive contamination. Before choosing the track of a planed R/V cruise, it is instructive to make a simulation by initializing backward-in-time evolution of material lines, crossing eddies in the region visible in the velocity field and on Lagrangian maps. The tracking maps computed in such experiments would help to know where one could expect higher or lower concentrations of Fukushima-derived radionuclides in this or that eddy.

Fukushima-derived radionuclides as Lagrangian tracers
In this section we apply the material line technique to trace the origin of water parcels with measured levels of 134 Cs and 137 Cs concentrations collected in two R/V cruises in June and July 2011 (Kaeriyama et al., 2013;Buesseler et al., 2012). Starting from the dates of sampling, we evolve backward in time material lines placed along the transects, where stations with collected surface water samples were located. Results of direct observation of radioactive Cs in surface seawater collected from R/V "Kaiun maru" in a broad area in the western and central North Pacific in July, October 2011 and July 2012 have been reported in Ref. (Kaeriyama et al., 2013). In this study, we focus on the results of measurements to be carried out at the stations C43-C55 from 26 to 29 July 2011 along the 144 • E meridian from 35 • N to 41 • N. That transect is partly shown in Fig. 2d. Its southern edge crosses the crest of the first KE meander whereas the northern edge crosses partly the ACR which is visible in the altimetric velocity field in Fig. 2d with an elliptic point in its center near x = 144 • E and y = 38 • N. It is the same ACR that has moved to the south from March to August and was mentioned in the end of the preceding section. The measured 137 Cs concentrations at the stations C43-C55 have been varied from the background level of 1.9 ± 0.4 mBq kg −1 (station C52) to 153 ± 6.8 mBq kg −1 (station C47). The ratio 134 Cs/ 137 Cs was close to 1. The level of the concentration of the caesium isotopes in the sea surface waters in the North Pacific before the accident did not exceed 2-3 mBq kg −1 .
We placed a material line along that transect and divided it into the four segments: 1) the segment 1, 35 • -36 • 30 ′ N, crossing the first meander's crest with initialization on 26 July, 2) the segment 2, 36 • 30 ′ -38 • N, crossing the southern edge of the ACR with initialization on 27 July, 3) the segment 3, 38 • -39 • 30 ′ N, crossing the core of the ACR with initialization on 28 July and 4) the segment 4, 39 • 30 ′ -41 • N, crossing the northern edge of the ACR with initialization on 29 July (not shown in Fig. 2d).
The tracking maps in Fig. 5 shows where markers of the corresponding segments were walking from 11 March to 10 April 2011. Markers from the segment 1, as expected, were advected to their places in the end of July mainly by the Kuroshio Current from the southwest and did not cross the latitude of the segment's northern end, 36 • 30 ′ N, (Fig. 5a). The risk of their radioactive contamination is small. It is confirmed by the measured 137 Cs concentrations at the stations C52-C55 in that segment to be 2-5 mBq kg −1 (Kaeriyama et al., 2013) that is slightly higher than the background level. Markers from the second segment have been found walk- ing mainly in the area to the north from the latitude 36 • 30 ′ N (Fig. 5b). Part of the initial material line crossed the ACR. That is why we see increased density of points at the place of that ring in March and April. A comparatively high level of Fukushima-derived caesium isotopes is expected in the corresponding water samples. It is really the case. The 137 Cs concentrations at the stations C49 and C50 of that segment were measured to be 36 ± 3.3 and 50 ± 3.6 mBq kg −1 (Kaeriyama et al., 2013). The caesium concentration levels up to 153 ± 6.8 mBq kg −1 (Kaeriyama et al., 2013) have been measured at the stations C46, C47 and C48 (our third segment) and C43, C44 and C45 (our fourth segment). The tracking maps in Fig. 5c and d show clearly an increased density of traces of the corresponding markers in the area where the maximal leakage directly into the ocean and atmospheric fallout on the ocean surface have been registered from 11 March to 10 April 2011. Those maps also demonstrate strong mixing in the Kuroshio-Oyashio frontal zone. Markers, to be initialized at the material lines with the length of 1.5 • , left traces in the area 25 • × 25 • , including some parts of the Sea of Japan and the Okhotsk Sea.
Fukushima-derived 134 Cs and 137 Cs were measured in surface and subsurface waters, as well as in zooplankton and fish, at 50 stations in 4-18 June 2011 during the R/V "Ka'imikai-o-Kanaloa" cruise (see ref. (Buesseler et al., 2012) and a supplement to that paper). We initialize a material line as shown in Fig. 2a where 137 Cs concentrations have been measured on 10 and 11 June at 25 stations in the range from 1.4 ± 0.2 mBq kg −1 (station 13) to 173.6 ± 9.9 mBq kg −1 (station 10). The ratio 134 Cs/ 137 Cs was close to 1. Some markers are placed on the southern segment, 35 • 30 ′ -36 • 30 ′ N, crossing the first meander's crest (11 June), and the other ones -on the northern segment, 37 • -38 • N, to the north from the meander's crest (10 June). Traces of the markers of the southern segment are found on the both sides of the KE jet, whereas traces of the markers of the northern one are on the northern side of the jet only. The lower part of the southern segment crosses the jet itself but its upper part is outside of it (Fig. 2a). That is why the tracking map in Fig. 6a consists of two disconnected domains, one is to the south of the jet and another one is to the north. The measured 137 Cs concentrations at the stations 13 and 14, situated in the southern segment, were at the background level, in the range 1.4-3.6 mBq kg −1 (Buesseler et al., 2012), because the corresponding markers were advected by the KE current (Fig. 6a).
Density of traces of the markers from the northern segment is comparatively high in the area around the FNPP (Fig. 6b). This finding is confirmed by measurements at stations 10, 11 and 12 (Buesseler et al., 2012) where the concentrations of Fukushima-derived 134 Cs and 137 Cs were in the range 21.9-173.6 mBq kg −1 . The northern segment crosses partly the ACR visible in Fig. 2a, and the traces of its markers are dense at the place of that ring. Some markers were advected to their places on the initial segment by the Tsushima Current from the Sea of Japan to the Pacific Ocean through the Tsugaru Strait.

Summary
In this research, we used numerical simulations to study near-surface large-scale transport in the KE area based on AVISO altimetric velocity field. After solving advection equations for passive markers backward in time, we have computed Lagrangian maps for their displacements and tracking maps for the number of times markers visited different places in the region.
Two KE cold-core cyclonic rings, CR1 and CR2, have been chosen to illustrate the process of pinching off from the main jet in summer 2011. The tracking and Lagrangian maps were computed to trace the origin of water masses in the cores of those rings. They revealed near-surface cross-jet transport. This conclusion is supported by tracks of the surface drifters which were deployed in the area. Water masses, constituting the CR1, have been advected mainly from the southwest by the Kuroshio and the KE, and only a small amount of its water was originated from the area to the north from the KE jet. Traces of the CR2 markers have been found in a large area to the south and the north from the jet, including the area around the FNPP location. It is interesting that through a year, in June 2012, we have found a cold-core CR to be separated from the jet approximately at the same place as the CR1 did in June 2011. It was confirmed by the track of a surface drifter circulating around that CR. Simulation showed that it contained Fukushima derived markers which were able to cross the KE jet.
We used Fukushima derived caesium isotopes as Lagrangian tracers comparing the results of our simulations with in-situ observations of 134 Cs and 137 Cs concentrations in water samples collected in two R/V cruises in June and July 2011 (Kaeriyama et al., 2013;Buesseler et al., 2012). Evolving backward in time material lines along the transects where measurements have been carried out in those cruises, we computed the corresponding tracking maps. It is shown that the water parcels with caesium concentration, exceeding greatly the background level, were walking during one month after the accident in the area where the maximal leakage directly into the ocean and atmospheric fallout on the ocean surface have been registered. The density of traces of markers with low caesium concentration in that area was found to be comparatively small.
We would like to emphasize that the tracking technique elaborated in this paper may be useful to planning R/V cruises in the ocean. Before choosing the track of a planed R/V cruise, it is instructive to make a simulation by initializing backward-in-time evolution of material lines, crossing potentially interesting coherent structures in the region visible in the velocity field and on Lagrangian maps. The corresponding tracking maps would help to know where one could expect higher or lower concentrations of radionuclides, pollutants or other Lagrangian tracers.