Lagrangian transport across the upper Arctic waters in the Canada Basin
Francisco Balibrea-Iniesta
Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Madrid, Spain
Search for more papers by this authorJiping Xie
Nansen Environmental and Remote Sensing Center, Bergen, Norway
Search for more papers by this authorVíctor J. García-Garrido
Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Madrid, Spain
Unidad Docente de Matemáticas, Universidad de Alcalá, Alcalá de Henares, Spain
Search for more papers by this authorLaurent Bertino
Nansen Environmental and Remote Sensing Center, Bergen, Norway
Search for more papers by this authorCorresponding Author
Ana M. Mancho
Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Madrid, Spain
Correspondence
Ana M. Mancho, Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, 28049 Madrid, Spain.
Email: [email protected]
Search for more papers by this authorStephen Wiggins
School of Mathematics, University of Bristol, Bristol, UK
Search for more papers by this authorFrancisco Balibrea-Iniesta
Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Madrid, Spain
Search for more papers by this authorJiping Xie
Nansen Environmental and Remote Sensing Center, Bergen, Norway
Search for more papers by this authorVíctor J. García-Garrido
Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Madrid, Spain
Unidad Docente de Matemáticas, Universidad de Alcalá, Alcalá de Henares, Spain
Search for more papers by this authorLaurent Bertino
Nansen Environmental and Remote Sensing Center, Bergen, Norway
Search for more papers by this authorCorresponding Author
Ana M. Mancho
Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Madrid, Spain
Correspondence
Ana M. Mancho, Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, 28049 Madrid, Spain.
Email: [email protected]
Search for more papers by this authorStephen Wiggins
School of Mathematics, University of Bristol, Bristol, UK
Search for more papers by this authorAbstract
The goal of this paper is to study transport, from a Lagrangian perspective, across selected circulation patterns in the upper Arctic Ocean waters. To this end, we apply the methodology of Lagrangian descriptors, using the function M, to the velocity field dataset provided by the Copernicus Marine Environment Monitoring Service. We focus our analysis on the Arctic region in the halocline (top 30 m depth), which is based on particular events occurring over the 2012–2016 time period. The advantage of the Lagrangian descriptor is that it highlights large-scale persistent dynamical structures relating to mathematical objects known as invariant manifolds, which determine fluid transport and mixing processes. These geometric flow structures play a crucial role in the evolution of the salinity content observed over the Arctic Basin. In this work, we identify these dynamical structures in the Beaufort Sea and show how they mediate transport processes according to a clockwise circulating pattern related to the Beaufort Gyre. Additionally, this approach highlights the importance of the Transpolar Drift Stream (TDS) as a transport barrier which maintains the salinity gradient between the Canada Basin and the Atlantic waters. Our approach also illustrates the variability of the intensity of the TDS during the analysed period and identifies secondary currents that feed it.
Supporting Information
Filename | Description |
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qj3404-sup-0001-MovieS1.movQuickTime video, 65 MB | Movie S1. This movie shows the time evolution of the M function, calculated with Τ = 300 days, from March 1, 2013 to March 1, 2015 at a depth of 30 m in a large Arctic area. |
Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.
References
- Aagaard, K. and Carmack, E.C. (1989) The role of sea ice and other fresh water in the Arctic circulation. Journal of Geophysical Research: Oceans, 94, 14485–14498
- Aref, H. (1984) Stirring by chaotic advection. Journal of Fluid Mechanics, 143, 1–21
- Aurell, E., Boffeta, G., Crisanti, A., Paladin, G. and Vulpiani, A. (1997) Predictability in the large: an extension of the concept of Lyapunov exponent. Journal of Physics A: Mathematical and General, 30, 1–26
- Bleck, R. (2002) An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates. Ocean Modelling, 37, 55–88
- Branicki, M. and Kirwan, A.D.Jr. (2010) Stirring: the Eckart paradigm revisited. International Journal of Engineering Science, 48, 1027–1042
- Branicki, M., Mancho, A.M. and Wiggins, S. (2011) A Lagrangian description of transport associated with a front–eddy interaction: application to data from the North-Western Mediterranean Sea. Physica D, 240, 282–304
- de la Cámara, A., Mechoso, C.R., Ide, K., Walterscheid, R. and Schubert, G. (2009) Polar night vortex breakdown and large-scale stirring in the southern stratosphere. Climate Dynamics, 35, 965–975
- de la Cámara, A., Mechoso, C.R., Serrano, E. and Ide, K. (2013) Quasi-horizontal transport within the Antarctic polar night vortex: Rossby wave breaking evidence and Lagrangian structures. Journal of Atmospheric Sciences, 70, 2982–3001
- Carmack, E.C., Yamamoto-Kawai, M., Haine, T.W., Bacon, S., Bluhm, B.A., Lique, C., Melling, H., Polyakov, I.V., Straneo, F., Timmermans, M.L. and Williams, W.J. (2016) Freshwater and its role in the Arctic Marine System: sources, disposition, storage, export, and physical and biogeochemical consequences in the Arctic and global oceans. Journal of Geophysical Research: Biogeosciences, 121, 675–717
- Cohen, J., Screen, J.A., Furtado, J.C., Barlow, M., Whittleston, D., Coumou, D., Francis, J., Dethloff, K., Entekhabi, D., Overland, J. and Jones, J. (2014) Recent Arctic amplification and extreme mid-latitude weather. Nature Geoscience, 7, 627–637
- Curbelo, J., García-Garrido, V.J., Mechoso, C.R., Mancho, A.M., Wiggins, S. and Niang, C. (2017) Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex. Nonlinear Processes in Geophysics, 24, 379–392
- Curbelo, J., Mechoso, C.R., Mancho, A.M. and Wiggins, S. (2018a) Lagrangian study of the final warming in the southern stratosphere during 2002: Part I. The vortex splitting at upper levels. Climate Dynamics
- Curbelo, J., Mechoso, C.R., Mancho, A.M. and Wiggins, S. (2018b) Lagrangian study of the final warming in the southern stratosphere during 2002: Part II. 3D structure. Climate Dynamics
- Dee, D.P., Uppala, S.M., Simmons, A.J., Berrisford, P., Poli, P., Kobayashi, S., Andrae, U., Balmaseda, M.A., Balsamo, G., Bauer, P., Bechtold, P., Beljaars, A.C.M., van de Berg, L., Bidlot, J., Bormann, N., Delsol, C., Dragani, R., Fuentes, M., Geer, A.J., Haimberger, L., Healy, S.B., Hersbach, H., Hólm, E.V., Isaksen, L., Kållberg, P., Köhler, M., Matricardi, M., McNally, A.P., Monge-Sanz, B.M., Morcrette, J.J., Park, B.K., Peubey, C., de Rosnay, P., Tavolato, C., Thépaut, J.N. and Vitart, F. (2011) The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Quarterly Journal of the Royal Meteorological Society, 137, 553–597
- Dmitrenko, I.A., Kirillov, S.A., Forest, A., Gratton, Y., Volkov, D.L., Williams, W.J., Lukovich, J.V., Belanger, C. and Barber, D.G. (2016) Shelfbreak current over the Canadian Beaufort Sea continental slope: wind-driven events in January 2005. Journal of Geophysical Research: Oceans, 121, 2447–2468
- Evensen, G. (2003) The Ensemble Kalman Filter: theoretical formulation and practical implementation. Ocean Dynamics, 53, 343–367
- García-Garrido, V.J., Ramos, A., Mancho, A.M., Coca, J. and Wiggins, S. (2016) A dynamical systems perspective for a real-time response to a marine oil spill. Marine Pollution Bulletin, 112, 201–210
- Garcia-Garrido, V.J., Curbelo J., Mancho A.M., Wiggins, S. and Mechoso C.R. (2018) The Application of Lagrangian Descriptors to 3D Vector Fields. Regular and Chaotic Dynamics, 23, 551–568
- Gearon, M.S., French McCay, D., Chaite, E., Zamorski, S., Reich, D., Rowe, J.
and Schmidt-Etkin, D. (2014). SIMAP Modeling of Hypothetical Oil Spills in the Beaufort Sea for World Wildlife Fund (WWF). 311pp. Report for WWF-Canada by RPS ASA. Available at: http://awsassets.wwf.ca/downloads/wwf_beaufort_sea_oil_spill_modelling_full_report_rps_asa.pdf [Accessed 14th Nov 2018].
- Giles, K.A., Laxon, S.W., Ridout, A.L., Wingham, D.J. and Bacon, S. (2012) Western Arctic ocean freshwater storage increased by wind-driven spin-up of the Beaufort Gyre. Nature Geoscience, 5, 194–197
- Holloway, G., Nguyen, A. and Wang, Z. (2011) Oceans and ocean models as seen by current meters. Journal of Geophysical Research: Oceans, 116(C8), C00D08
- Hunke, E.C. and Dukowicz, J.K. (1997) An elastic–viscous–plastic model for sea ice dynamics. Journal of Physical Oceanography, 27, 1849–1867
- Ide, K., Small, D. and Wiggins, S. (2002) Distinguished hyperbolic trajectories in time dependent fluid flows: analytical and computational approach for velocity fields defined as data sets. Nonlinear Processes in Geophysics, 9, 237–263
- Jones, C.K.R.T. and Winkler, S. (2002). Invariant manifolds and Lagrangian dynamics in the ocean and atmosphere. In B. Hasselblatt and A. Katok (Eds.), Handbook of Dynamical Systems, pp. 55–92. Amsterdam: North-Holland.
- Ju, N., Small, D. and Wiggins, S. (2003) Existence and computation of hyperbolic trajectories of aperiodically time-dependent vector fields and their approximations. International Journal of Bifurcation and Chaos, 13, 1449–1457
- Krishfield, R.A., Proshutinsky, A., Tateyama, K., Williams, W.J., Carmack, E.C., McLaughlin, F.A. and Timmermans, M.-L. (2014) Deterioration of perennial sea ice in the Beaufort Gyre from 2003 to 2012 and its impact on the oceanic freshwater cycle. Journal of Geophysical Research: Oceans, 119, 1271–1305
- Large, W.G., McWilliams, J.C. and Doney, S.C. (1994) Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization. Reviews of Geophysics, 32, 363
- Lin, P., Pickart, R.S., Moore, G.W.K., Spall, M.A. and Jianyu, H. (2018) Characteristics and dynamics of wind-driven upwelling in the Alaskan Beaufort Sea based on six years of mooring data. Deep-Sea Research II: Topical Studies in Oceanography, in press.
- Lopesino, C., Balibrea-Iniesta, F., García-Garrido, V.J., Wiggins, S. and Mancho, A.M. (2017) A theoretical framework for Lagrangian descriptors. International Journal of Bifurcation and Chaos, 27, 1730001
- Madrid, J.A.J. and Mancho, A.M. (2009) Distinguished trajectories in time dependent vector fields. Chaos, 19, 013111
- Mancho, A.M., Small, D. and Wiggins, S. (2004) Computation of hyperbolic trajectories and their stable and unstable manifolds for oceanographic flows represented as data sets. Nonlinear Processes in Geophysics, 11, 17–33
- Mancho, A.M., Small, D. and Wiggins, S. (2006) A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: theoretical and computational issues. Physics Reports, 237, 55–124
- Mancho, A.M., Wiggins, S., Curbelo, J. and Mendoza, C. (2013) Lagrangian descriptors: a method for revealing phase space structures of general time dependent dynamical systems. Communications in Nonlinear Science and Numerical Simulation, 18, 3530–3557
- Melsom, A., Bertino, L. and Sutherland, G. (2015). Quality information document for Arctic ocean physical analysis and forecast product ARCTIC_ANALYSIS_FORECAST_PHYS_002_001_A.
- Mendoza, C. and Mancho, A.M. (2010) The hidden geometry of ocean flows. Physical Review Letters, 105, 038501
- Mendoza, C. and Mancho, A.M. (2012) The Lagrangian description of ocean flows: a case study of the Kuroshio current. Nonlinear Processes in Geophysics, 19, 449–472
- Mendoza, C., Mancho, A.M. and Wiggins, S. (2014) Lagrangian descriptors and the assessment of the predictive capacity of oceanic data sets. Nonlinear Processes in Geophysics, 21, 677–689
- Mezic, I. and Wiggins, S. (1994) On the integrability and perturbation of three- dimensional fluid flows with symmetry. Journal of Nonlinear Science, 4, 157–194
- Mezić, I. and Wiggins, S. (1999) A method for visualization of invariant sets of dynamical systems based on the ergodic partition. Chaos, 9, 213–218
- Morison, J., Kwok, R., Peralta-Ferriz, C., Alkire, M., Rigor, I., Andersen, R. and Steele, M. (2012) Changing Arctic ocean freshwater pathways. Nature, 481, 66–70
- Mysak, L.A. (2001) Patterns of Arctic circulation. Science, 293, 1269–1270
- Nese, J.M. (1989) Quantifying local predictability in phase space. Physica D, 35, 237–250
- Oki, T. and Sud, Y.C. (1998) Design of Total Runoff Integrating Pathways (TRIP)—a global river channel network. Earth Interactions, 2(2-001), 1–37
- Ottino, J.M. (1989) The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge: Cambridge University Press.
- Ottino, J.M. (1990) Mixing, chaotic advection and turbulence. Annual Review of Fluid Mechanics, 22, 207–253
- d'Ovidio, F., Fernández, V., Hernández-García, E. and López, C. (2004) Mixing structures in the Mediterranean Sea from finite-size Lyapunov exponents. Geophysical Research Letters, 31(17), L17203
- Panteleev, G., Nechaev, D.A., Proshutinsky, A., Woodgate, R. and Zhang, J. (2010) Reconstruction and analysis of the Chukchi Sea circulation in 1990–1991. Journal of Geophysical Research: Oceans, 115(C8), C08023
- Peralta-Ferriz, C. and Woodgate, R.A. (2015) Seasonal and interannual variability of pan-Arctic surface mixed layer properties from 1979 to 2012 from hydrographic data, and the dominance of stratification for multiyear mixed layer depth shoaling. Progress in Oceanography, 134, 19–53
- Pickart, R.S., Nobre, C., Lin, P., Arrigo, K.R., Ashjian, C.J., Berchok, C., Cooper, L.W., Grebmeier, J.M., Hartwell, I., He, J., Itoh, M., Kikuchi, T., Nishino, S. and Vagle, S. (2017) Seasonal to mesoscale variability of water masses and atmospheric conditions in Barrow Canyon, Chukchi Sea. Deep-Sea Research II: Topical Studies in Oceanography, in press
- Polyakov, I.V., Pnyushkov, A.V., Alkire, M.B., Ashik, I.M., Baumann, T.M., Carmack, E.C., Goszczko, I., Guthrie, J., Ivanov, V.V., Kanzow, T., Krishfield, R., Kwok, R., Sundfjord, A., Morison, J., Rember, R. and Yulin, A. (2017) Greater role for Atlantic inflows on sea-ice loss in the Eurasian Basin of the Arctic Ocean. Science, 356, 285–291
- Proshutinsky, A., Krishfield, R., Timmermans, M.-L., Toole, J., Carmack, E., McLaughlin, F., Williams, W.J., Zimmermann, S., Itoh, M. and Shimada, K. (2009) Beaufort Gyre freshwater reservoir: state and variability from observations. Journal of Geophysical Research: Oceans, 114(C1), C00A10
- Rampal, P., Weiss, J., Dubois, C. and Campin, J.-M. (2011) IPCC climate models do not capture Arctic sea ice drift acceleration: consequences in terms of projected sea ice thinning and decline. Journal of Geophysical Research: Oceans, 116(C8), C00D07
- Sakov, P., Counillon, F., Bertino, L., Lisæter, K.A., Oke, P.R. and Korablev, A. (2012) TOPAZ4: an ocean-sea ice data assimilation system for the North Atlantic and Arctic. Ocean Science, 8, 633–656
- Samelson, R. and Wiggins, S. (2006) Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach. New York, NY: Springer-Verlag.
- Shadden, S.C., Lekien, F. and Marsden, J.E. (2005) Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D, 212, 271–304
- Smale, S. (1967) Differentiable dynamical systems. Bulletin of the American Mathematical Society, 73, 39–44
- Smale, S. (1980) The Mathematics of Time: Essays on Dynamical Systems, Economic Processes and Related Topics. New York, NY: Springer-Verlag.
- Smith, M.L. and McDonald, A.J. (2014) A quantitative measure of polar vortex strength using the function M. Journal of Geophysical Research: Atmospheres, 119, 5966–5985
- Spall, M.A. (2007) Circulation and water mass transformation in a model of the Chukchi Sea. Journal of Geophysical Research: Oceans, 112(C5), C05025
- Timmermans, M.L., Proshutinsky, A., Krishfield, R.A., Perovich, D.K., Richter-Menge, J.A., Stanton, T.P.
and Toole, J.M. (2011) Surface freshening in the Arctic Ocean's Eurasian Basin: an apparent consequence of recent change in the wind-driven circulation. Journal of Geophysical Research: Oceans, 116(C8), C00D03
- Tsubouchi, T., Bacon, S., Aksenov, Y., Garabato, A.C.N., Curry, B. and Lee, C.M. (2017) The Arctic Ocean seasonal cycles of heat and freshwater fluxes: observation-based inverse estimates. Journal of Physical Oceanography, 48, 2029–2055
- Uotila, P., Goosse, H., Haines, K., Chevallier, M., Barthélemy, A., Bricaud, C., Carton, J., Fučkar, N., Garric, G., Iovino, D., Kauker, F., Korhonen, M., Lien, V.S., Marnela, M., Massonnet, F., Mignac, D., Peterson, K.A., Sadikni, R., Shi, L., Tietsche, S., Toyoda, T., Xie, J. and Zhang, Z. (2018) An assessment of ten ocean reanalyses in the polar regions. Climate Dynamics, 1–38
- Watanabe, E. (2011) Beaufort shelf break eddies and shelf-basin exchange of Pacific summer water in the western Arctic Ocean detected by satellite and modeling analyses. Journal of Geophysical Research: Oceans, 116(C8), C08034
- Wiggins, S. (1994) Normally Hyperbolic Invariant Manifolds in Dynamical Systems. New York, NY: Springer. Applied Mathematical Sciences.
- Wiggins, S. (2005) The dynamical systems approach to Lagrangian transport in oceanic flows. Annual Review of Fluid Mechanics, 37, 295–328
- Wiggins, S. and Ottino, J. (2004) Foundations of chaotic mixing. Philosophical Transactions of the Royal Society, 362, 937–970
- Woodgate, R.A., Aagaard, K. and Weingartner, T.J. (2005) Monthly temperature, salinity, and transport variability of the Bering Strait through flow. Geophysical Research Letters, 32(4), L04601
- Xie, J., Bertino, L., Counillon, F., Lisæter, K.A. and Sakov, P. (2017) Quality assessment of the TOPAZ4 reanalysis in the Arctic over the period 1991–2013. Ocean Science, 13, 123–144