An eddy tracking algorithm based on dynamical systems theory

This work introduces a new method for ocean eddy detection that applies concepts from stationary dynamical systems theory. The method is composed of three steps: first, the centers of eddies are obtained from fixed points and their linear stability analysis; second, the size of the eddies is estimated from the vorticity between the eddy center and its neighboring fixed points, and, third, a tracking algorithm connects the different time frames. The tracking algorithm has been designed to avoid mismatching connections between eddies at different frames. Eddies are detected for the period between 1992 and 2012 using geostrophic velocities derived from AVISO altimetry and a new database is provided for the global ocean.

[1]  B. Qiu,et al.  Oceanic mass transport by mesoscale eddies , 2014, Science.

[2]  Carolina Mendoza,et al.  Hidden geometry of ocean flows. , 2010, Physical review letters.

[3]  W. Munk,et al.  Spirals on the sea , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[4]  Reto Knutti,et al.  Imprint of Southern Ocean eddies on winds, clouds and rainfall , 2013 .

[5]  D. Lathrop.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering , 2015 .

[6]  Oscar Pizarro,et al.  Eddy characteristics in the eastern South Pacific , 2005 .

[7]  G. Lapeyre,et al.  Characterization of finite-time Lyapunov exponents and vectors in two-dimensional turbulence. , 2002, Chaos.

[8]  Igor Kononenko,et al.  Dynamic fuzzy paths and cycles in multi-level directed graphs , 2015, Eng. Appl. Artif. Intell..

[9]  F. d’Ovidio,et al.  Surface coastal circulation patterns by in‐situ detection of Lagrangian coherent structures , 2011 .

[10]  D. Chelton,et al.  Global observations of nonlinear mesoscale eddies , 2011 .

[11]  Jorge Tam,et al.  Average circulation, seasonal cycle, and mesoscale dynamics of the Peru Current System: A modeling approach , 2005 .

[12]  G. Haller.  Lagrangian coherent structures from approximate velocity data , 2002 .

[13]  A. Turiel,et al.  How reliable are finite-size Lyapunov exponents for the assessment of ocean dynamics? , 2010, 1009.2419.

[14]  Walter Munk,et al.  Spirals on the Sea: A Manifestation of Upper-Ocean Stirring , 2001 .

[15]  C. M. Place,et al.  An Introduction to Dynamical Systems , 1990 .

[16]  B. Hamann,et al.  A three‐dimensional eddy census of a high‐resolution global ocean simulation , 2013 .

[17]  R. Robinson,et al.  An Introduction to Dynamical Systems: Continuous and Discrete , 2004 .

[18]  Stephen Wiggins,et al.  Lagrangian Transport through an Ocean Front in the Northwestern Mediterranean Sea , 2006, physics/0608105.

[19]  D. Chelton,et al.  Global observations of large oceanic eddies , 2007 .

[20]  Frits H. Post,et al.  Detection, quantification, and tracking of vortices using streamline geometry , 2000, Comput. Graph..

[21]  J. McWilliams,et al.  A New Sea Surface Height–Based Code for Oceanic Mesoscale Eddy Tracking , 2014 .

[22]  Gustavo Goni,et al.  Oceanic mesoscale eddies as revealed by Lagrangian coherent structures , 2008 .

[23]  Annalisa Griffa,et al.  On the Predictability of Lagrangian Trajectories in the Ocean , 2000 .

[24]  Jordi Font,et al.  Vortices of the Mediterranean Sea: An Altimetric Perspective , 2006 .

[25]  J. Weiss,et al.  Vortex cores, strain cells, and filaments in quasigeostrophic turbulence , 2006 .

[26]  X. Carton.  Hydrodynamical Modeling Of Oceanic Vortices , 2001 .

[27]  Fangxin Fang,et al.  Evolution, movement and decay of warm-core Leeuwin Current eddies , 2003 .

[28]  James H. Faghmous,et al.  A daily global mesoscale ocean eddy dataset from satellite altimetry , 2015, Scientific Data.

[29]  A. Crisanti,et al.  Predictability in the large: an extension of the concept of Lyapunov exponent , 1996, chao-dyn/9606014.

[30]  Andrew T. Wittenberg,et al.  Impacts on Ocean Heat from Transient Mesoscale Eddies in a Hierarchy of Climate Models , 2015 .

[31]  Sofia C. Olhede,et al.  Extracting waves and vortices from Lagrangian trajectories , 2011, 1110.0140.

[32]  G. Simarro,et al.  Sea surface transport in the Western Mediterranean Sea : A Lagrangian perspective , 2013 .

[33]  J. T. Stuart.  On finite amplitude oscillations in laminar mixing layers , 1967, Journal of Fluid Mechanics.