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<front>
<journal-meta>
<journal-id journal-id-type="publisher">NPG</journal-id>
<journal-title-group>
<journal-title>Nonlinear Processes in Geophysics</journal-title>
<abbrev-journal-title abbrev-type="publisher">NPG</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Nonlin. Processes Geophys.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1607-7946</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/npg-21-677-2014</article-id>
<title-group>
<article-title>Lagrangian descriptors and the assessment of the predictive capacity of oceanic data sets</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Mendoza</surname>
<given-names>C.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Mancho</surname>
<given-names>A. M.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Wiggins</surname>
<given-names>S.</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>ETSI Navales, Universidad Politécnica de Madrid, Av. Arco de la Victoria 4, 28040 Madrid, Spain</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, C/ Nicolás Cabrera 15, Campus Cantoblanco UAM, 28049 Madrid, Spain</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>School of Mathematics, University of Bristol, Bristol BS8 1TW, UK</addr-line>
</aff>
<pub-date pub-type="epub">
<day>18</day>
<month>06</month>
<year>2014</year>
</pub-date>
<volume>21</volume>
<issue>3</issue>
<fpage>677</fpage>
<lpage>689</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2014 C. Mendoza et al.</copyright-statement>
<copyright-year>2014</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://npg.copernicus.org/articles/21/677/2014/npg-21-677-2014.html">This article is available from https://npg.copernicus.org/articles/21/677/2014/npg-21-677-2014.html</self-uri>
<self-uri xlink:href="https://npg.copernicus.org/articles/21/677/2014/npg-21-677-2014.pdf">The full text article is available as a PDF file from https://npg.copernicus.org/articles/21/677/2014/npg-21-677-2014.pdf</self-uri>
<abstract>
<p>We use a recently developed Lagrangian transport tool, &lt;i&gt;Lagrangian
descriptors&lt;/i&gt;, to compare the transport properties of data distributed by
AVISO and numerical simulations obtained from the HYCOM model in the
Yucatán–Florida current system. Our data correspond to the months from June
through August 2010. Structures obtained from HYCOM are noisier than those
from AVISO; however, both AVISO and HYCOM succeed in identifying Lagrangian
structures that influence the paths of drifters, such as eddies, currents,
lobes, etc. We find evidence in which AVISO gives the positions of important
hyperbolic trajectories in a manner that is inconsistent with the
trajectories of the drifters, while for the same examples HYCOM succeeds to
this end.</p>
</abstract>
<counts><page-count count="13"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple">Andrade-Canto, F., Sheinbaum, J., and Zavala Sansón, L.: A Lagrangian approach to the Loop Current eddy separation, Nonlin. Processes Geophys., 20, 85–96, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-20-85-2013&quot;&gt;https://doi.org/10.5194/npg-20-85-2013&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Beron-Vera, F. J., Olascoaga, M. J., and Goni, G. J.: Surface Ocean Mixing Inferred from Different Multisatellite Altimetry Measurements, J. Phys. Oceanogr., 40, 2466–2480, 2010.</mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Bettencort, J. H., López, C., and Hernández-Garc\&apos;ia, E.: Oceanic three-dimensional Lagrangian coherent structures: A study of a mesoscale eddy in the Benguela upwelling region, Ocean Modell., 51, 73–83, &lt;a href=&quot;http://dx.doi.org/10.1016/j.ocemod.2012.04.004&quot;&gt;https://doi.org/10.1016/j.ocemod.2012.04.004&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Bleck, R.: An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates, Ocean Modell., 4, 55–88, 2002.</mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Branicki, M. and Kirwan, A. D., Jr.: Stirring: The Eckart paradigm revisited, Int. J. Eng. Sci., 48, 1027–1042, 2010.</mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Branicki, M. and Wiggins, S.: An adaptive method for computing invariant manifolds in non-autonomous, three-dimensional dynamical systems, Physica D, 238, 1625–1657, 2009.</mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">Branicki, M. and Wiggins, S.: Finite-time Lagrangian transport analysis: stable and unstable manifolds of hyperbolic trajectories and finite-time Lyapunov exponents, Nonlin. Processes Geophys., 17, 1–36, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-17-1-2010&quot;&gt;https://doi.org/10.5194/npg-17-1-2010&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Branicki, M., Mancho, A. M., and Wiggins, S.: 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, &lt;a href=&quot;http://dx.doi.org/10.1016/j.physd.2010.09.003&quot;&gt;https://doi.org/10.1016/j.physd.2010.09.003&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">Chassignet, E. P., Hurlburt, H. E., Smedstad, O. M., Halliwell, G. R., Hogan, P. J., Wallcraft, A. J., Baraille, R., and Bleck, R.: The HYCOM (HYbrid Coordinate Ocean Model) data assimilative system, J. Mar. Syst.,65, 60–83, &lt;a href=&quot;http://dx.doi.org/10.1016/j.jmarsys.2005.09.016&quot;&gt;https://doi.org/10.1016/j.jmarsys.2005.09.016&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">de la Cámara, A., Mechoso, C. R., Ide, K., Walterscheid, R., and Schubert, G.: Polar night vortex breakdown and large-scale stirring in the southern stratosphere, Clim. Dynam., 35, 965–975, 2010.</mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">de la Cámara, A., Mancho, A. M., Ide, K., Serrano, E., and Mechoso, C.: Routes of transport across the Antarctic polar vortex in the southern spring., J. Atmos. Sci., 69, 753–767, &lt;a href=&quot;http://dx.doi.org/10.1175/JAS-D-11-0142.1&quot;&gt;https://doi.org/10.1175/JAS-D-11-0142.1&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">de la Cámara, A., Mechoso, R., Mancho, A. M., Serrano, E., and Ide., K.: Quasi-horizontal transport within the Antarctic polar night vortex: Rossby wave breaking evidence and Lagrangian structures., J. Atmos. Sci., 70, 2982–3001, &lt;a href=&quot;http://dx.doi.org/10.1175/JAS-D-12-0274.1&quot;&gt;https://doi.org/10.1175/JAS-D-12-0274.1&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">d&apos;Ovidio, F., Fernández, V., Hernández-García, E., and López, C.: Mixing structures in the Mediterranean sea from finite-size Lyapunov exponents, Geophys. Res. Lett., 31, L12203, &lt;a href=&quot;http://dx.doi.org/10.1029/2004GL020328&quot;&gt;https://doi.org/10.1029/2004GL020328&lt;/a&gt;, 2004.</mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Farazmand, M. and Haller, G.: Computing Lagrangian Coherent Structures from variational theory, Chaos, 22, 013128, &lt;a href=&quot;http://dx.doi.org/10.1063/1.3690153&quot;&gt;https://doi.org/10.1063/1.3690153&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Forristall, G. Z., Schaudt, K. J., and Cooper, C. K.: Evolution and Kinematics of a Loop Current Eddy in the Gulf of Mexico During 1985, J. Geophys. Res., 97, 2173–2184, 1992.</mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Froyland, G., Horenkamp, C., Rossi, V., Santitissadeekorn, N., and Gupta, A. S.: Three-dimensional characterization and tracking of an Agulhas Ring, Ocean Modell., 52–53, 69–75, 2012.</mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple">Griffa, A., Haza, A., Özgökmen, T. M., Molcard, A., Taillandier, V., Schroeder, K., Chang, Y., and Poulain, P. M.: Investigating transportpathwaysintheocean, Deep Sea Res. II, 85, 81–95, 2013.</mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Haller, G.: Finding finite-time invariant manifolds in two-dimensional velocity fields, Chaos, 10, 99–108, 2000.</mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Haller, G.: Distinguished material surfaces and coherent structure in three-dimensional fluid flows, Physica D, 149, 248–277, 2001a.</mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">Haller, G.: Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence, Phys. Fluids, 13, 3365–3385, 2001b.</mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple">Haller, G.: Lagrangian coherent structures from approximate velocity data, Phys. Fluids, 14, 1851–1861, 2002.</mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple">Haller, G. and Yuan, G.: Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D, 147, 352–370, 2000.</mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple">Haza, A. C., Griffa, A., Martin, P., Molcard, A., Özgökmen, T. M., Poje, A., Barbanti, R., Book, J., Poulain, P., Rixen, M., and Zanasca, P.: Model-based directed drifter launches in the Adriatic Sea: Results from the DART experiment, Geophys. Res. Lett., 34, L10605, &lt;a href=&quot;http://dx.doi.org/10.1029/2007GL029634&quot;&gt;https://doi.org/10.1029/2007GL029634&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Haza, A. C., Özgökmen, T. M., Griffa, A., Molcard, A., Poulain, P. M., and Peggion, G.: Transport properties in small-scale coastal flows: relative dispersion from VHF radar measurements in the Gulf of La Spezia, Ocean Dynam., 60, 861–882, 2010.</mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple">Hernández-Carrasco, I., López, C., Hernández-García, E., and Turiel, A.: How reliable are finite-size Lyapunov exponents for the assessment of ocean dynamics?, Ocean Modell., 36, 208–218, 2011.</mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple">Ide, K., Small, D., and Wiggins, S.: Distinguished hyperbolic trajectories in time-dependent fluid flows: analytical and computational approach for velocity fields defined as data sets, Nonlin. Processes Geophys., 9, 237–263, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-9-237-2002&quot;&gt;https://doi.org/10.5194/npg-9-237-2002&lt;/a&gt;, 2002.</mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Jones, C. K. R. T. and Winkler, S.: Invariant manifolds and Lagrangian dynamics in the ocean and atmosphere, in: Handbook of dynamical systems, 55–92, North-Holland, Amsterdam, 2002.</mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple">Kuznetsov, L., Toner, M., Kirwan Jr., A. D., Jones, C. K. R. T., Kantha, L. H., and Choi, J.: The Loop Current and adjacent rings delineated by Lagrangian analysis of the near-surface flow, J. Mar. Res., 60, 405–429 &lt;a href=&quot;http://dx.doi.org/10.1357/002224002762231151&quot;&gt;https://doi.org/10.1357/002224002762231151&lt;/a&gt;, 2002.</mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple">Lekien, F., Shadden, S., and Marsden, J. E.: Lagrangian coherent structures in n-dimensional systems, J. Math. Phys., 48, 065404, &lt;a href=&quot;http://dx.doi.org/10.1063/1.2740025&quot;&gt;https://doi.org/10.1063/1.2740025&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple">Madrid, J. A. J. and Mancho, A. M.: Distinguished trajectories in time dependent vector fields, Chaos, 19, 013111, &lt;a href=&quot;http://dx.doi.org/10.1063/1.3056050&quot;&gt;https://doi.org/10.1063/1.3056050&lt;/a&gt;, 2009.</mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple">Malhotra, N. and Wiggins, S.: Geometric Structures, Lobe Dynamics, and Lagrangian Transport in Flows with Aperiodic Time-Dependence, with Applications to Rossby Wave Flow, J. Nonlin. Sci., 8, 401–456, 1998.</mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple">Mancho, A. M., Small, D., Wiggins, S., and Ide, K.: Computation of Stable and Unstable Manifolds of Hyperbolic Trajectories in Two-Dimensional, Aperiodically Time-Dependent Vectors Fields, Physica D, 182, 188–222, &lt;a href=&quot;http://dx.doi.org/10.1016/S0167-2789(03)00152-0&quot;&gt;https://doi.org/10.1016/S0167-2789(03)00152-0&lt;/a&gt;, 2003.</mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple">Mancho, A. M., Small, D., and Wiggins, S.: Computation of hyperbolic trajectories and their stable and unstable manifolds for oceanographic flows represented as data sets, Nonlin. Processes Geophys., 11, 17–33, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-11-17-2004&quot;&gt;https://doi.org/10.5194/npg-11-17-2004&lt;/a&gt;, 2004.</mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple">Mancho, A. M., Small, D., and Wiggins, S.: A comparison of methods for interpolating chaotic flows from discrete velocity data, Comput. Fluids, 35, 416–428, &lt;a href=&quot;http://dx.doi.org/10.1016/j.compfluid.2005.02.003&quot;&gt;https://doi.org/10.1016/j.compfluid.2005.02.003&lt;/a&gt;, 2006a.</mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple">Mancho, A. M., Small, D., and Wiggins, S.: A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues, Phys. Rep., 437, 55–124, &lt;a href=&quot;http://dx.doi.org/10.1016/j.physrep.2006.09.005&quot;&gt;https://doi.org/10.1016/j.physrep.2006.09.005&lt;/a&gt;, 2006b.</mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple">Mancho, A. M., Hernández-García, E., Small, D., Wiggins, S., and Fernández, V.: Lagrangian transport through an ocean front in the North-Western Mediterranean Sea, J. Phys. Oceanogr., 38, 1222–1237, &lt;a href=&quot;http://dx.doi.org/10.1175/2007JPO3677.1&quot;&gt;https://doi.org/10.1175/2007JPO3677.1&lt;/a&gt;, 2008.</mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple">Mancho, A. M., Wiggins, S., Curbelo, J., and Mendoza, C.: Lagrangian descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems, Commun. Nonlinear Sci., 18, 3530–3557, &lt;a href=&quot;http://dx.doi.org/10.1016/j.cnsns.2013.05.002&quot;&gt;https://doi.org/10.1016/j.cnsns.2013.05.002&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple">Mendoza, C. and Mancho, A. M.: The hidden geometry of ocean flows, Phys. Rev. Lett., 105, 038501, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.105.038501&quot;&gt;https://doi.org/10.1103/PhysRevLett.105.038501&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple">Mendoza, C. and Mancho, A. M.: Review Article: &quot;The Lagrangian description of aperiodic flows: a case study of the Kuroshio Current&quot;, Nonlin. Processes Geophys., 19, 449–472, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-19-449-2012&quot;&gt;https://doi.org/10.5194/npg-19-449-2012&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple">Mendoza, C., Mancho, A. M., and Rio, M.-H.: The turnstile mechanism across the Kuroshio current: analysis of dynamics in altimeter velocity fields, Nonlin. Processes Geophys., 17, 103–111, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-17-103-2010&quot;&gt;https://doi.org/10.5194/npg-17-103-2010&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple">Mezic, I., Loire, S., Fonoberov, V. A., and Hogan, P. A.: A New Mixing Diagnostic and Gulf Oil Spill Movement, Science, 330, 486–489, 2010.</mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple">Miller, P. D., Jones, C. K. R. T., Rogerson, A. M., and Pratt, L. J.: Quantifying transport in numerically generated velocity fields, Physica D, 110, 105–122, 1997.</mixed-citation>
</ref>
<ref id="ref43">
<label>43</label><mixed-citation publication-type="other" xlink:type="simple">Molcard, A., Poje, A. C., and Özgökmen, T. M.: Directed drifter launch strategies for Lagrangian data assimilation using hyperbolic trajectories, Ocean Modell., 12, 268–289, 2006.</mixed-citation>
</ref>
<ref id="ref44">
<label>44</label><mixed-citation publication-type="other" xlink:type="simple">Nencioli, F., d&apos;Ovidio, F., Dogliogi, A. M., and Petrenko, A. A.: Surface coastal circulation patterns by in-situ detection of Lagrangian coherent structures, Geophys. Res. Lett., 38, L17604, &lt;a href=&quot;http://dx.doi.org/10.1029/2011GL048815&quot;&gt;https://doi.org/10.1029/2011GL048815&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref45">
<label>45</label><mixed-citation publication-type="other" xlink:type="simple">Nencioli, F., d&apos;Ovidio, F., Dogliogi, A. M., and Petrenko, A. A.: In situ estimates of submesoscale horizontal eddy diffusivity across an ocean front, J. Geophys. Res.-Oceans, 118, 7066–7080, &lt;a href=&quot;http://dx.doi.org/10.1002/2013JC009252&quot;&gt;https://doi.org/10.1002/2013JC009252&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref46">
<label>46</label><mixed-citation publication-type="other" xlink:type="simple">Olascoaga, M. J.: Isolation on the West Florida Shelf with implications for red tides and pollutant dispersal in the Gulf of Mexico, Nonlin. Processes Geophys., 17, 685–696, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-17-685-2010&quot;&gt;https://doi.org/10.5194/npg-17-685-2010&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref47">
<label>47</label><mixed-citation publication-type="other" xlink:type="simple">Pascual, A., Faugère, Y., Larnicol, G., and Traon, P. Y. L.: Improved description of the ocean mesoscale variability by combining four satellites altimeters, Geophys. Res. Lett., 33, L02611, &lt;a href=&quot;http://dx.doi.org/10.1029/2005GL024633&quot;&gt;https://doi.org/10.1029/2005GL024633&lt;/a&gt;, 2006.</mixed-citation>
</ref>
<ref id="ref48">
<label>48</label><mixed-citation publication-type="other" xlink:type="simple">Pierrehumbert, R. T.: Large-scale horizontal mixing in planetary atmospheres, Phys. Fluids A, 3, 1250–1260, 1991.</mixed-citation>
</ref>
<ref id="ref49">
<label>49</label><mixed-citation publication-type="other" xlink:type="simple">Prants, S. V., Budyansky, M. V., and Uleysky, M. Yu.: Lagrangian study of surface transport in the Kuroshio Extension area based on simulation of propagation of Fukushima-derived radionuclides, Nonlin. Processes Geophys., 21, 279–289, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-21-279-2014&quot;&gt;https://doi.org/10.5194/npg-21-279-2014&lt;/a&gt;, 2014.</mixed-citation>
</ref>
<ref id="ref50">
<label>50</label><mixed-citation publication-type="other" xlink:type="simple">Press, W., Teukolsky, S., Vetterling, W., and Flannery, B.: Numerical Recipes in Fortran 77, The Art of Scientific Computing, Cambridge University Press, Cambdridge, 2 Edn., 1999.</mixed-citation>
</ref>
<ref id="ref51">
<label>51</label><mixed-citation publication-type="other" xlink:type="simple">Rempel, E. L., Chian, A. C.-L., Brandenburg, A., Munuz, P. R., and Shadden, S. C.: Coherent structures and the saturation of a nonlinear dynamo, J. Fluid Mechan., 729, 309–329, 2013.</mixed-citation>
</ref>
<ref id="ref52">
<label>52</label><mixed-citation publication-type="other" xlink:type="simple">Samelson, R. and Wiggins, S.: Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach, Springer-Verlag, New York, 2006.</mixed-citation>
</ref>
<ref id="ref53">
<label>53</label><mixed-citation publication-type="other" xlink:type="simple">Shadden, S. C., Lekien, F., and Marsden, J. E.: Definition and properties of Lagrangian Coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows, Physica D, 212, 271–304, 2005.</mixed-citation>
</ref>
<ref id="ref54">
<label>54</label><mixed-citation publication-type="other" xlink:type="simple">Shadden, S. C., Lekien, F., Paduan, J. D., Chavez, F. P., and Marsden, J. E.: TheThe correlation between surface drifters and coherent structures based on high-frequency radar data in Monterey Bay, Deep Sea Res. II, 56, 161–172, 2009.</mixed-citation>
</ref>
<ref id="ref55">
<label>55</label><mixed-citation publication-type="other" xlink:type="simple">Sulman, M. H. M., Huntley, H. S., Lipphardt Jr., B. L., Jacobs, G., Hogan, P., and Kirwan Jr., A. D.: Hyperbolicity in temperature and flow fields during the formation of a Loop Current ring, Nonlin. Processes Geophys., 20, 883–892, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-20-883-2013&quot;&gt;https://doi.org/10.5194/npg-20-883-2013&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref56">
<label>56</label><mixed-citation publication-type="other" xlink:type="simple">Tallapragada, P. and Ross, S. D.: Particle segregation by Stokes number for small neutrally buoyant spheres in a fluid, Phys. Rev. E, 78, 036 308, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.78.036308&quot;&gt;https://doi.org/10.1103/PhysRevE.78.036308&lt;/a&gt;, 2008.</mixed-citation>
</ref>
<ref id="ref57">
<label>57</label><mixed-citation publication-type="other" xlink:type="simple">Titaud, O., Brankart, J. M., and Verron, J.: On the use of Finite-Time Lyapunov Exponents and Vectors for direct assimilation of tracer images into ocean models, Tellus A, 63A, 1038–1051, 2011.</mixed-citation>
</ref>
<ref id="ref58">
<label>58</label><mixed-citation publication-type="other" xlink:type="simple">Wiggins, S.: The Dynamical Systems Approach to Lagrangian Transport in Oceanic Flows, Annu. Rev. Fluid Mech., 37, 295–328, 2005.</mixed-citation>
</ref>
</ref-list>
</back>
</article>