# An eddy tracking algorithm based on dynamical systems theory

## Abstract

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.

### Keywords

Coherent structures Global ocean Mesoscale eddies Dynamical systems theory Stability analysis of fixed points Tracking algorithm## Notes

### Acknowledgments

D. Conti is currently a PhD fellowship (FPI/1543/2013) granted by the Conselleria d’Educaci, Cultura i Universitats from the Government of the Balearic Islands co-financed by the European Social Fund. A. Orfila acknowledges support from ENAP-Colombian Army through different grants. E. Mason is supported by a post-doctoral grant from the Conselleria dEducacio, Cultura i Universitats del Govern de les Illes Balears (Mallorca, Spain) and the European Social Fund. J.M. Sayol is supported by the JAE-Pre scholarships co-funded by CSIC and ESF. G.Simarro is supported by the Spanish Government through the Ramon y Cajal program. This work has been done thanks to financial support from H2020-EU JERICO-NEXT project. Comments from Prof. D. Chelton are greatly appreciated. Comments from three anonymous referees are greatly acknowledged.

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