THEROADSOFTHESEA-CANWEPREDICT THE MOTION OF PARTICLES CARRIED BY OCEAN …doglioli/griffa_CNR... · 2010-01-26 · ing the predictability of particles in ocean ﬂows. We focus on

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THE ROADS OF THE SEA - CAN WE PREDICTTHE MOTION OF PARTICLES CARRIED BYOCEAN CURRENTS?Annalisa Griffa, K. Schroeder (Scienze Marine - Sede Pozzuolo di Lerici),S. Aliani (Scienze Marine - Sede Pozzuolo di Lerici), A. Doglioli (Uni-versita of Marseille, France), A. Molcard (Universita of Toulon, France),V. Taillandier (CNRS- LOV, Villefranche sur Mer, France), T. Ozgokmen(RSMAS, Miami, USA), A. Haza (RSMAS, Miami, USA)ISMAR - [email protected]

Abstract

Ocean currents play a fundamental role in the transport of substances and species.Being able to monitor and predict their effects is of great relevance for a number ofapplications, such as correct management of the coastal ecosystem, manage con-trol in case of discharges of pollutants and understanding of pathways of invasivespecies. While transport by ocean currents is under many aspects very complex anddominated by turbulent and chaotic processes, it has been shown in recent worksthat it is often possible to find a hidden structure, at least for mesoscale motion, thatguides the movement of the avected quantities. Barriers of motion exist in the ocean,related to the main “Lagrangian coherent structures”, i.e. to structures such as gyres,jets and eddies. In this paper, we provide examples of methods to identify such bar-riers and applications in the Mediterrean Sea . The limits of these methods, that arebased on the assumption that the velocity field is well known, are also discussed, andpossible remedies in terms of Lagrangian assimilation are discussed.

1 Introduction

Currents are the roads of the sea. Theytransport physical properties such as tem-perature and salinity (T,S), chemical prop-erties, pollutants, particulate and sedimentsas well as biological quantities such as phy-

toplankton, zooplankton, larvae and jellyfish. Being able to understand and pre-dict transport by ocean currents is thereforecrucial for a number of applications. Theyinclude climatic applications, for instanceunderstanding heat transport or pathwaysof species invasions, as well as applications

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for a correct management of the coastalocean ecosystem and for damage control incase of accidents at sea such as dischargesof pollutants.

Transport predictions is very challeng-ing for a number of reasons (Piterbarg etal., 2007). To understand it, consider thebasic equation of Lagrangian transport, i.e.the equation that describes particles ad-vected by the current,

dx/dt= u(x,t),where x is the position of a particle and

u is the velocity. The equation shows thatthe trajectory of a particle, x(t), is the inte-gral of the velocity u(x,t). This implies thateven small errors in the prediction of u tendto accumulate and grow in the predictionof x(t). Since in practice small errors in uare unavoidable, due to incomplete knowl-edge of forcing, topography, coastline andto the influence of small scale unresolvedprocesses, we can expect that this will re-sult in significantly amplified errors in tra-jectories. Also, the equation is inherentlynonlinear, since u depends on the positionx, and it has the property of being veryoften chaotic. This implies that even forvery simple Eulerian flows u (in presenceof time dependence) trajectories are highlysensitive to initial conditions. Predictingthem is therefore very difficult, since evena slight difference in initial conditions inspace and time can result in significantlydifferent behaviours.

Even though Lagrangian prediction ishighly challenging, a number of methodshave been put forth in the past decade thathave helped increasing our skills in this di-rection. Different methods have been sug-gested for different applications. Methodsbased on statistical approaches are partic-ularly suited for climatic problems. Theyconsist in separating the mean componentof the currents from the turbulent and fluc-

tuating component and parameterizing theturbulent part for instance using stochas-tic methods (Aliani and Molcard, 2003 ;Veneziani et al., 2005 ; Doglioli et al.,2006). Other methods are more suited forthe prediction of specific events, and theyare typically based on dynamical systemtheories. The basic concept here is thateven though the motion of a single parti-cle is extremely challenging to reproducebecause of the high dependence on initialconditions and on the details of the flow,the description of the general pattern oftransport is much more approachable. Ithas been suggested that ocean transport isdominated by main “coherent structures”(Hadden et al., 2005), such as vortices, ed-dies and jets, that are separated by invisi-ble barriers, i.e. regions that particle trajec-tories cannot cross. Methods from nonlin-ear dynamical system have been proposedto locate such barriers, that can be used toprovide information on the general fate of aparticle launched in a certain area. Detailson the specific trajectory might be difficultto determine, but its general behaviour isexpected to be determined by such barri-ers. A special relevance is given to the con-cept of hyperbolicity and in particular tothe presence of hyperbolic points that sep-arate different structures. Various methodscan be used to identify such points, rang-ing from direct identification in terms offlow invariants to methods based on localdispersion properties, such as Finite Time(FTLE) or Finite Size (FSLE) LyapunovExponents (Shadden et al., 2005 ; Artaleet al., 1997).

Dynamical system methods appear tohave a great potential for practical oceanapplications. Nevertheless it is importantto point out that they are “diagnostic” tools,in the sense that they can be used with great

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results only as long as the velocity fieldu is known with a certain degree of accu-racy. This is the case for instance for ve-locity fields from extensive HF (High Fre-quency) radar measurements, or from ac-curate ocean circulation models. In manycases, though, predictions from circula-tion models are still incomplete and thestructures can be considered known onlywith some approximation. In order to in-crease our knowledge of such structuresand our prediction capability, assimilationmethods can be used, that combine infor-mation from real time data with model re-sults. In particular, since we are interestedin Lagrangian predictability, we can expectthat assimilation of Lagrangian data will beespecially fruitful. For Lagrangian data wemean data from floating instruments thatfollow the current with good approxima-tion, either at the ocean surface (drifters)or in the ocean interior (SOFAR, RAFOSand Argo floats) communicating their po-sition via satellite or acoustically. In thelast few years, new methods for Lagrangiandata assimilation have been proposed in theliterature and tested using simplified mod-els (Molcard et al., 2003 ; Taillandier et al.,2006 ; Kutsnetsov et al., 2003). Some ofthese methods have been recently appliedto in situ data and the results appear verypromising in terms of flow correction andincreasing transport prediction skills.

In this paper we provide a brief sum-mary of results that have been obtained inthe last few years at CNR-ISMAR in col-laborations with a number of national andinternational laboratories aimed at increas-ing the predictability of particles in oceanflows. We focus on two main issues. InSection 2, we review the development andimplementation of methods from dynam-ical system theory focusing especially onthe FSLE tool (Haza et al., 2007) to high-

light flow feautures and barriers. We pro-vide some examples of applications in theAdriatic and Ligurian Sea, testing the resultusing independent Lagrangian data. Thepresented results are among the very firstexamples of application of the theory toreal ocean flows. In Section 3, we pro-vide a summary of work aimed at improv-ing flow prediction using Lagrangian dataassimilation. The development of a methodbased on a variational approach is brieflyreviewed and examples in coastal flows areshown, using different types of Lagrangiandata from Argo floats moving at 350 m todrifters at the surface. These results are thefirst successful applications of Lagrangiandata assimilation using in-situ data, andthe method is now transitioned toward op-erational systems. The potential of thesefindings for practical applications and thestrategies for further development are dis-cussed in Section 4.

2 Computing transport bar-riers using FSLEs

The Finite Size Lyapunov Exponents(FLSEs) are a diagnostic tool that can beused to identify the main transport barri-ers and flow structures such as eddies, jestsand boundary currents. They correspond tomaps of relative dispersion in the flow field,and are relatively simple to implement. Inorder to compute FSLEs the velocity fieldu has to be known, either from high res-olution measurements (HF radar) or frommodel. The computations of FSLEs is per-formed seeding particles in small clusters(typically of three particles each) through-out the flow domain and numerically ad-vecting them forward and backward. For-mally FSLEs are defined as the time that

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takes for particles initially separated of agiven distance d0 to reach a distance d1=ad0 where a is a specified factor. Forwardadvection highlights regions of high dis-persion characterized by small values ofFSLEs, while backward advction identifyconvergence regions.

An example of computation of FSLEsusing results from an NCOM NRL modelin the Adriatic Sea (Haza et al., 2007)is shown in Fig.1 (left panel). The red(blue) lines indicate concentration (disper-sion) lines. The superposition of lines indi-cate “ridges”, i.e. areas that act as transportbarriers between different flow regions andthat cannot be crossed by particle trajecto-ries. Hyperbolic points are indicated by thecrossing of blue and red lines, as indicatedby the circle in Fig.1 off the Gargano Cape.These points are central to understand La-grangian pathways, since they separate dif-ferent structures and are characterized bydirections in which stretching can causeparticles to diverge from the structures (un-stable manifolds) as well as to converge(stale manifolds). Particles located close toa hyperbolic point can easily separate, fol-lowing the different manifolds.

FSLEs cmputations have been per-formed and tested during two recent fieldexperiments in collaboration with NURC-NATO, NRL, Universita of Miami, Uni-versita of Toulone and OGS. The two ex-periments took place in the Adriatic Sea(DART06, Haza et al., 2007) and in theLigurian Sea (MREA07-POET, Schroederet al, 2010) respectively. During DART06,FSLEs have been computed using theNCOM-NRL circulation model with 1 kmresolution, and FSLE maps (Fig.1, leftpanel) were used in real time to guidedrifter launches from ship. The goal wasto identify regions of high hyperbolicityso that the launched drifters would tend

to quickly separate, inducing a maximumcoverage of the area. The presence ofan hyperbolic point in the area off theGargano Cape have been suggested beforeby the analysis of historical drifter data(Veneziani et al., 2007), but the hyperbolicpoint is known to be present only at cer-tain times, and to depend on the flow struc-ture. For this reason, model results areneeded to pinpoint the exact time and lo-cation of the point. During DART06 threelaunches of drifter pairs have been per-formed guided by model forecasts, and twoover three show the presence of an hyper-bolic point that induces drifter trajectoriesto quickly separate and diverge. An exam-ple is shown in Fig.1, right panel, wherethe observed drifter trajectories (green andpurple lines) appear to separate quickly,one going to the north and the other to thesouth, in agreement with the model results,as shown by the numerical trajectories inblack. During the third launch, instead,the drifters did not separate and moved to-gether toward the north. This launch actu-ally acted as an inadvertent “control” ex-periment in the sense that the circulationmodel was indeed predicting at the timethat the presence of the hyperbolic pointwas cancelled by a strong wind episode.The ship, though, due to logistic reasonsperformed the drifter launches in any case,and the observed and numerical trajectoriesdid not show separation. This clearly in-dicates that a) the hyperbolic point is notpresent at all time and b) the model fore-cast is able to correctly capture its time de-pendence.

The second experiment took place inthe Ligurian Sea and had two compo-nents: a large scale component with drifterlaunches in open ocean (Schroeder et al.,2010), and a more coastal component in

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the Gulf of La Spezia with significantlysmaller scales of the order of 5-7 km(POET experiment, Molcard et al., 2009,Haza et al., 2010). During POET, clus-ters of five drifters were launched in theGulf. Results from two launches per-formed two days a part from the same ini-tial conditions are presented in Fig.2 (up-per panels), showing a dramatically differ-ent trajectory behaviour. During the firstlaunch (left) the drifters move coherentlyin a cyclonic way exiting the Gulf after 12-15 hours. During the second launch, in-stead, the drifters quickly separate and endup sampling the whole Gulf, exiting aftermore that 20 hours. During POET, a VHFcoastal radar was operated in the area pro-viding maps of velocity fields at resolu-tion of 250 m every 30 minutes. FSLEsmaps were computed from the radar ve-locity and used to understand and quan-tify the different type of dynamics actingduring the two launches. Snapshots ofFLSLEs during the two launches are shownin Fig.2 (lower panels). During the firstlaunch, a clear ridge is depicted that sep-arate the area of the Gulf in two differ-ent regions. The drifters move along theevolving ridge and do not cross it as theyflow through the Gulf . This can be par-tially seen by comparing the drifter trajec-tories and the FSLE snapshot in Fig.2 (leftpanels) but it is much more clear consider-ing the animation depicting drifter motionsuperimposed to the evolving FSLE maps(http://www.rsmas.miami.edu/personal/ahaza/radar/LaSpeziafsleclusters.gif).Duringthesecondlaunch(rightpanel), noclearridgesseparatingtheGulfaredetectedandthestructuresarelessmarked, eventhoughthepresenceofanhyperbolicpointveryclosetothelaunchingregionofthedrifterscanbedetected, indicatedbythecrossingofblueandredlines.Thisexplainstheinitialseparationoftheclusterwithdriftersmovingindifferentdirection.Theanimationofdrifter/FLSEsevolutionshowsthatthedriftersindeedfollowthemanifoldlinesstemmingfromthehyperbolicpoint.

The results show that even at smallcoastal scales, where the dynamics arecomplex and driven partially by the largescale boundary current intruding in theGulf and partially by local forcing, La-grangian transport can be interpreted interms of barriers between dominant struc-tures well captured by FLSEs.

3 Improving transport pre-diction using assimila-tion

The results in Section 2 provide positive in-dications on the feasibility of forecastingthe main transport properties, since theysuggest that particle motion is mostly dom-inated by barriers between the main coher-ent structures, rather than by smaller scaleflow feautures. As a consequence, whenthe main coherent structures are well rep-resented and forecasted by the models, wecan expect that also particle transport iswell represented at least in terms of gen-eral behaviour, even though the details ofsingle trajectories might be missing. Onthe other hand, the nature of these coher-ent structures is still only partially under-stood and in many cases circulation mod-els are only partially able to capture them.A common problem with models, for in-stance, is related to the propagation veloc-ity of the structures, so that there might bephase shift errors involving the exact loca-tion of the structures at a given time.

A very effective avenue to improvemodel performance is to use real time datato correct model results using methods ofdata assimilation. In particular, in ourcase, since we are interested in transportprediction, we can expect that Lagrangiandata from floating instruments that directlysample current advection will be especiallyuseful.

A new method to assimilate La-grangian data have been developed byCNR-ISMAR in collaboration with theUniversita of Miami. The method is basedon correcting the velocity field at the levelwhere the instruments are transported by

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the currents (i.e. in the interior ocean forArgo floats and at the surface for drifters)by requiring minimization of the distancebetween observed positions and positionsof numerical trajectories launched in themodel (Molcard et al, 2003 ; Taillandieret al., 2006a). Once the velocity field iscorrected, the other variables of the model,i.e. the mass variables T,S and the sea sur-face height (SSH), are adjusted using somesimplified dynamical requirements such asgeostrophy and mass conservation (Ozgok-men et al., 2003). The method has beenimplemented using a variational approachand it has been first applied to Argo floats(Taillandier et al., 2006b) in the Mediterra-nen Sea as part of the MFS (MediterraneanForecasting System) project. Mediter-ranean Argo floats (MedArgo) are pro-grammed to drift at a parking depth of 350m, resurfacing at approximately 5 day in-tervals, and providing information on theirposition and on TS profiles. Lagrangianassimilation uses the position informationto correct the drift at 350m. An exampleof results obtained assimilating MedArgofloats in the region close to the BalearicIslands is shown in Fig.3. Results with-out assimilation (left panel) can be com-pared with results with assimilation (rightpanel). The superimposed orange-brownlines indicate the observed drift of one floatduring 10 days, the arrows indicate veloc-ity vectors and the color indicate the salin-ity field S. As it can be seen, the assimi-lation of the Argo float data induces a jetalong the eastern coast of the island thatwas not present without assimilation, inkeeping with the observed float drift. No-tice also that there are differences in theS fields between the two panels, due tothe dynamical adjustment performed dur-ing the assimilation. The Lagrangian as-similation of MedArgo has been recently

performed in the framework of a multivari-ate system, i.e. as part of the MFS ob-serving system including T,S profiles fromMedArgo and XBTs and satellite SSH andSST (Tallandier et al., 2010). Results arevery positive and the Lagrangian MedArgoassimilation is now in the process of beingtransitioned to the operative MFS system.

Further investigations are presently car-ried out on the assimilation of surfacedrifters. Assimilation of surface driftersis expected to be more challenging thanfor Argo floats mostly because they sam-ple the very surface of the ocean (from 15to 1 or 2 m), that is characterized by smallscales fluctuations and dynamics that sig-nificantly deviate from geostrophy. Thisposes two significant question. The firstone is related to which scales should be fil-tered and which ones retained in the modelcorrection, while the second one is relatedto the correction of the mass variables, thathas to be performed differently than in thecase of Argo floats. A simple geostrophicbalance in fact cannot be used since theupper meters are strongly influenced alsoby Ekmn dynamics, so that a more com-plex dynamical decomposition has to beadopted. So far, we have been working onthe first step of assimilation, i.e. the ve-locity correction at the surface using drifterdata, and we have not attacked the prob-lem of mass correction yet. Results on sur-face correction are very promising (Tail-landier et al., 2008), as shown in the ex-ample in Fig.4 for the Adriatic Sea. Theleft (central) panels show results from theROMS model without (with) correction,for a snapshot of velocity (top panels) andfor numerical trajectories (bottom panels)launched along a section. The small redlines in the top panels indicate two day tra-jectories of four drifters used for the cor-

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rection. As it can be seen, the velocity cor-rection appears small, but it has a signifi-cant impact on trajectories. The trajectoriesof the non corrected model in fact appearretained inside the boundary current, whilethey tend to exit from it in the case of cor-rection, more in keep with what suggestedby MODIS satellite data (left panel) indi-cating significant intrusion from the bound-ary current in the interior. Of course thisis not a quantitative test of results yet, andwork is in progress to quantify the im-provement using independent data

4 Summary and discus-sion

In this paper, we have discussed meth-ods to improve the prediction of particlestransported by ocean currents. Results arevery encouraging and they show that, eventhough the problem is extremely challeng-ing, significant improvements can be ob-tained using appropriate techniques. Onthe other hand, a number of questions arestill open as discussed in the following.

The results in Section 2 strongly sug-gest that the motion of particles is con-trolled by barriers between the main co-herent structures in the flow, such asmesoscale eddies, jets and boundary cur-rents. The size of these structures dependson the flow environment and in particularon the Rossby radius of deformation, rang-ing from tens of km in the open sea inthe Adriatic and Ligurian sea, to few kmin small coastal gulfs such as the Gulf ofLa Spezia. Flow feautures smaller thanthese mesoscale structures do not appear todirectly influence the main characteristicsof particle transport, even though they caninfluence the details of single trajectories.

This result, if confirmed in other regionsof the world ocean and shown to be gen-eral, is expected to be extremely importantfor what concerns practical applications.The result in fact implies that the resolu-tion of circulation models can be limited tocorrectly reproduce mesoscale structures,while capturing submesoscale or smallerprocesses is not crucial for the problemof Lagrangian transport, that is central tomany practical applications of operationalprediction systems. Looking at the exis-tent literature, results in other parts of theworld show similar and compatible results,for instance the studies of relative disper-sion in the Gulf of Mexico and in the Nor-wegian Sea (LaCasce and Ohlman, 2003).On the other hand, other results in the Cal-ifonia Current seem to suggest that subme-soscale and smaller scales might be rele-vant for flow advection properties (Capetet al., 2008). This might be related to thefact that the California Current is character-ized by supwelling and significant verticalmotion, that is often dominated by subme-soscale structures. Overall, the central is-sue of the role of submesocale and smallerfeatures is still open and it requires signif-icant further investigations. Different re-gions of the ocean might have to be treateddifferently (Griffa et al., 2008), and it iscrucial to understand what are the physicalreasons for these differences and the con-sequences for the transport of biogeochem-ical properties and their modeling and pre-diction.

For what concerns assimilation meth-ods, the results in Section 3 show thatthey can be extremely useful to correctmodel forecasts, for instance reposition-ing and shaping coherent structures thatare not correctly reproduced by the mod-els. Assimilation has been successfully im-plemented in the case of Argo subsurface

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floats, and it is now in the process of beingtransitioned to operational systems. Workis in progress for surface drifters and themain questions to be addressed are concep-tually related to the ones discussed above.We have to decide weather or not the sig-nature of small scale processes present inthe data have to be maintained and usedin the assimilation or filtered away, andwhich type of dynamics have to be used,beyond geostrophy. In order to do that, anincreased knowledge of air sea interactionprocesses is necessary, as well as an im-proved understanding of the role played byvertical motion in the mixed layer. Finally,it should be pointed out that while La-grangian data are certainly a natural choiceto improve transport prediction, other typesof data can also be used, and fusion be-tween models and various data is expectedto be very important in the future. As anexample, work has already started to usesatellite data (SAR and visible) to improvetransport prediction in case of accidents atsea such as oils spill events (Mercatini etal., 2010).

5 Acknowledgements

The authors wish to acknowledge collab-orations with G. Gasparini, P.Poulain, M.Rixen, A. Poje,L. Piterbarg, N. Pinardi andS. Dobricic. The work was supported bythe EU projects MFSTEP and ECOOP andby ONR (Ofice of Naval Research).

Figure 1: Figure 1. (left) Forecastedsurface velocity from NCOM modelduring DART06 experiment.Superimposed are the 2-day model basedFSLE field and the location of ahyperbolic point (green circle). (right) 2day trajectories for real drifters (green andpurple) and numerical drifters (black lines)

Figure 2: Figure 2 Top panels show thetrajectories of two drifter clusters launchedfrom the same location two days apart inthe Gulf of La Spezia during the POETexperiment (June 2007). Bottom panelsshow FSLE maps computed from VHFradar at the time of the launches

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Figure 3: Fig 3 Left (right) panel shows anexample of OPA model results in theBalearic Sea without (with) assimilationof Argo float trajectories. Arrows indicatevector velocities, color the salinity fieldand the superimposed brown-orange linesindicate the observed 10 day drift of theassimilated float

Figure 4: Fig.4 Left (central) panels showan example of ROMS model results in theAdriatic Sea without (with) velocitycorrection from surface drifters. Toppanels depict the velocity field, withsuperimposed the 2 day trajectories (redlines) of the drifters used in the correction,while the bottom panels depict numericaltrajectories launched along a section. Leftpanel shows a Modis satellite image takenat the same time as the model results.

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[21] L. Piterbarg; T.M. Ozgokmen; A. Griffa; ; A.J. Mariano;. Predictability of la-grangian motion in the upper ocean. 2007.

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THEROADSOFTHESEA-CANWEPREDICT THE MOTION OF PARTICLES CARRIED BY OCEAN …doglioli/griffa_CNR... · 2010-01-26 · ing the predictability of particles in ocean ﬂows. We focus on

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