BAKTRAK: backtracking drifting objects using an iterative algorithm with a forward trajectory model


The task of determining the origin of a drifting object after it has been located is highly complex due to the uncertainties in drift properties and environmental forcing (wind, waves, and surface currents). Usually, the origin is inferred by running a trajectory model (stochastic or deterministic) in reverse. However, this approach has some severe drawbacks, most notably the fact that many drifting objects go through nonlinear state changes underway (e.g., evaporating oil or a capsizing lifeboat). This makes it difficult to naively construct a reverse-time trajectory model which realistically predicts the earliest possible time the object may have started drifting. We propose instead a different approach where the original (forward) trajectory model is kept unaltered while an iterative seeding and selection process allows us to retain only those particles that end up within a certain time–space radius of the observation. An iterative refinement process named BAKTRAK is employed where those trajectories that do not make it to the goal are rejected, and new trajectories are spawned from successful trajectories. This allows the model to be run in the forward direction to determine the point of origin of a drifting object. The method is demonstrated using the leeway stochastic trajectory model for drifting objects due to its relative simplicity and the practical importance of being able to identify the origin of drifting objects. However, the methodology is general and even more applicable to oil drift trajectories, drifting ships, and hazardous material that exhibit nonlinear state changes such as evaporation, chemical weathering, capsizing, or swamping. The backtracking method is tested against the drift trajectory of a life raft and is shown to predict closely the initial release position of the raft and its subsequent trajectory.

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  1. Allen AA (2005) Leeway divergence, USCG R&D center technical report CG-D-05-05. Available through:, ref: ADA435435. Accessed 22 Sept 2011

  2. Allen AA, Plourde JV (1999) Review of leeway: field experiments and implementation. Report CG-D-08-99. US Coast Guard Research and Development Center, 1082 Shennecossett Road, Groton, CT, USA. Available through, ref: ADA366414. Accessed 22 Sept 2011

  3. Allen A, Roth JC, Maisondieu C, Breivik Ø, Forest B (2010) Field determination of the leeway of drifting objects, technical report 17/2010, Norwegian Meteorological Institute

  4. Ambjörn C (2008) Seatrack Web forecasts and backtracking of oil spills-an efficient tool to find illegal spills using AIS, US/EU-Baltic International Symposium. 2008 IEEE/OES, pp 1–9

  5. Brodtkorb AR, Dyken C, Hagen TR, Hjelmervik JM, Storaasli OO (2010) State-of-the-art in heterogeneous computing. Sci Program 18(1):1–33

    Google Scholar 

  6. Breivik Ø, Allen A (2008) An operational search and rescue model for the Norwegian Sea and the North Sea. J Marine Syst 69(1–2):99–113. doi:10.1016/j.jmarsys.2007.02.010, Special Issue on Maritime Rapid Environmental Assessment–New Trends in Operational Oceanography

    Article  Google Scholar 

  7. Breivik Ø, Allen A, Maisondieu C, Roth J-C (2011) Wind-induced drift of objects at sea: the leeway field method. Appl Ocean Res 33:100–109. doi:10.1016/j.apor.2011.01.005

    Article  Google Scholar 

  8. Breivik Ø, Sætra Ø (2001) Real time assimilation of HF radar currents into a coastal ocean model. J Marine Syst 28(3–4):161–182. doi:10.1016/S0924-7963(01)00002-1

    Article  Google Scholar 

  9. Broström G, Carrasco A, Daniel P, Hackett B, Paradis D (2008) Comparison of two oil drift models and different ocean forcing with observed drifter trajectories in the Mediterranean. Proceedings of the 5th International Conference on EuroGOOS, 20–22 May 2008, Exeter, UK.

  10. Callies U, Pluss A, Kappenberg J, Kapitza H (2011) Particle tracking in the vicinity of Helgoland, North Sea - a model comparison. To appear in Ocean Dynam, MREA10 special issue

  11. Christensen JH, Hansen AB, Tomasi G, Mortensen J, Andersen O (2004) Integrated methodology for forensic oil spill identification. Environ Sci Technol 38(10):2912–2918. doi:10.1021/es035261y

    Article  Google Scholar 

  12. Davidson FJM, Allen A, Brassington GB, Breivik Ø, Daniel P, Kamachi M, Sato S, King B, Lefevre F, Sutton M, Kaneko H (2009) Applications of GODAE ocean current forecasts to search and rescue and ship routing. Oceanography 22(3):176–181. doi:10.5670/oceanog.2009.76

    Article  Google Scholar 

  13. Doucet A, De Freitas N, Gordon NJ (2001) Sequential Monte Carlo methods in practice. Springer, Berlin

    Google Scholar 

  14. Eide MS, Endresen O, Breivik Ø, Brude OW, Ellingsen IH, Roang K, Hauge J, Brett PO (2007) Prevention of oil spill from shipping by modelling of dynamic risk. Mar Poll Bull 54(10):1619–1633. doi:10.1016/j.marpolbul.2007.06.013

    Article  Google Scholar 

  15. Essen H-H, Breivik Ø, Gunther H, Gurgel K-W, Johannessen J, Klein H, Schlick T, Stawarz M (2003) Comparison of remotely measured and modelled currents in coastal areas of Norway and Spain. Global Atmosphere-Ocean Syst 9(1–2):39–64. doi:10.1080/1023673031000151412

    Article  Google Scholar 

  16. Engedahl H (1995) Implementation of the Princeton Ocean Model (POM/ECOM3D) at the Norwegian Meteorological Institute (DNMI). Research Report 5. The Norwegian Meteorological Institute, Oslo, Norway

  17. Engedahl H (2001) Operational ocean models at Norwegian Meteorological Institute (DNMI). Research Note, vol. 59. The Norwegian Meteorological Institute, Oslo, Norway

  18. Hackett B, Breivik Ø, Wettre C (2006) Forecasting the drift of objects and substances in the oceans. In: Chassignet EP, Verron J (eds) Ocean weather forecasting: an integrated view of oceanography. Springer, Berlin, pp 507–524

    Chapter  Google Scholar 

  19. Hackett B, Comerma E, Daniel P, Ichikawa H (2009) Marine oil pollution prediction. Oceanography 22(3):168–175. doi:10.5670/oceanog.2009.75

    Article  Google Scholar 

  20. Havens H, Luther ME, Meyers SD (2009) A coastal prediction system as an event response tool: particle tracking simulation of an anhydrous ammonia spill in Tampa Bay. Mar Poll Bull 58(8):1202–1209. doi:10.1016/j.marpolbul.2009.03.012

    Article  Google Scholar 

  21. Rao KS (2007) Source estimation methods for atmospheric dispersion. Atmos Environ 41(33):6964–6973. doi:10.1016/j.atmosenv.2007.04.064

    Article  Google Scholar 

  22. Rixen M, Ferreira-Coelho E (2007) Operational surface drift prediction using linear and non-linear hyper-ensemble statistics on atmospheric and ocean models. J Marine Syst 65:105–121. doi:10.1016/j.jmarsys.2004.12.005

    Article  Google Scholar 

  23. Rixen M, Ferreira-Coelho E, Signell R (2008) Surface drift prediction in the Adriatic Sea using hyper-ensemble statistics on atmospheric, ocean and wave models: uncertainties and probability distribution areas. J Marine Syst 69:86–98. doi:10.1016/j.jmarsys.2007.02.015

    Article  Google Scholar 

  24. Stohl A (1996) Trajectory statistics—a new method to establish source-receptor relationships of air pollutants and its application to the transport of particulate sulfate in Europe. Atmos Env 30(4):579–587. doi:10.1016/1352-2310(95)00314-2

    Article  Google Scholar 

  25. Stohl A (2002) Computation, accuracy and applications of trajectories-a review and bibliography. Dev Environ Sci 1:615–654

    Google Scholar 

  26. Turner C, Waddington T, Morris J, Osychny V, Luey P (2006) Leeway of submarine escape rafts and submarine emergency positioning beacons, USCG R&D Center Technical Report CG-D-05-06, 99 pp. Available through, ref: ADA457525. Accessed 22 Sept 2011

  27. Undén P, Rontu L, Jarvinen H, Lynch P, Calvo J, Cats G, Cuaxart J, Eerola K, Fortelius C, Garcia-Moya JA, Jones C, Lenderlink G, McDonald A, McGrath R, Navascues B, Nielsen NW, Ødegaard V, Rodriguez E, Rummukainen M, Room R, Sattler K, Sass BH, Savijarvi H, Schreur BW, Sigg R, The H Tijm A (2002) HIRLAM-5 scientific documentation, HIRLAM-5 Project. Available from SMHI, S-601767, Norrkoping, Sweden

  28. Vandenbulcke L, Beckers J-M, Lenartz F, Barth A, Poulain P-M, Aidonidis M, Meyrat J, Ardhuin F, Tonani M, Fratianni C, Torrisi L, Pallela D, Chiggiato J, Tudor M, Book JW, Martin P, Peggion G, Rixen M (2009) Super-ensemble techniques: application to surface drift prediction. Prog Oceanog 82(3):149–167. doi:10.1016/j.pocean.2009.06.002

    Article  Google Scholar 

  29. van Leeuwen PJ (2009) Particle filtering in geophysical systems. Mon Wea Rev 137:4089–4114. doi:10.1175/2009MWR2835.1

    Article  Google Scholar 

  30. Wessel P, Smith WHF (1996) A global, selfconsistent, hierarchical, high-resolution shoreline database. J Geophys Res 101(B4):8,741–8,743

    Article  Google Scholar 

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This work was made possible by funding from the Norwegian Defence Research Establishment (FFI) through the BAKTRAK project. The field work was organized and partly funded by the project “Uncontrolled drift of ships and larger objects,” funded by the Research Council of Norway (NFR) under the MAROFF programme (grant no. 200862). The analysis has also benefited from the MAROFF project FARGE (grant no. 200843). The authors wish to thank the Joint Rescue Co-ordination Centres (JRCC) and the Norwegian Navy for their continued support of the development of operational trajectory models for search and rescue. This work builds on results from the SAR-DRIFT project under the French-Norwegian Foundation (Eureka grant E!3652) and the FOB project funded through the NFR MAROFF programme (grant no. 180175). This project has also benefited from the Norwegian National Supercomputing Facility (NOTUR). Finally, we wish to thank the two anonymous reviewers for their thorough scrutiny of the manuscript which made us include important new material.

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Correspondence to Øyvind Breivik.

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This article is part of the Topical Collection on Maritime Rapid Environmental Assessment

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Breivik, Ø., Bekkvik, T.C., Wettre, C. et al. BAKTRAK: backtracking drifting objects using an iterative algorithm with a forward trajectory model. Ocean Dynamics 62, 239–252 (2012).

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  • Trajectory modeling
  • Search and rescue
  • Operational oceanography
  • Backtracking drifting objects
  • Inverse methods