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1. Introduction
The increase of the spatial resolution in both numerical models and remote sensing observations revealed the prevalence of mesoscale eddies throughout the oceans. These coherent structures are able to trap and transport heat, mass, and momentum from their regions of formation to remote areas. Their crucial role in the transport of heat fluxes has been shown in many studies (Jayne and Marotzke 2002; Colas et al. 2012). For instance, the mean trajectories of the long-lived Agulhas Rings control the global transport in the Southern Ocean (Dencausse et al. 2010; Laxenaire et al. 2017, manuscript submitted to Geophys. Res. Lett.). In the Mediterranean Sea, the mean cyclonic pathways of the Algerian eddies (Escudier et al. 2016) have an impact on the regional transport of Atlantic water and Levantine Intermediate Water in the Algerian Basin. Additionally, mesoscale eddies can have a profound influence on biological productivity and on the upper-ocean ecology and biogeochemical cycles (McGillicuddy et al. 1998; D’Ovidio et al. 2010; Lévy et al. 2014; Cotroneo et al. 2016) especially in an oligotrophic area. Even large pelagic species, such as whales, exhibited a preference for the periphery of eddies during the seasonal phytoplankton biomass minimum in summer (Cotté et al. 2011). Finally, eddies can also influence near-surface winds and clouds or rainfall within their vicinity (Chelton et al. 2004; Frenger et al. 2016). Therefore, the dynamics of mesoscale eddies have a significant impact on the surface circulation and oceanic biogeochemistry at both local and regional scales. To investigate a large number of coherent structures for long periods (several years), the development of automatic eddy-tracking algorithms has recently become an important research topic in oceanography.
Different methods have been developed that use either the velocity fields or the altimetric sea surface maps to identify and track eddies. One of the earliest works in automatic eddy detection was developed to quantify the number of coherent vortices that emerge in the numerical simulations of two-dimensional turbulence (McWilliams 1990). To identify the rotating core of vortices, the relative vorticity was used for eddy detection. Doglioli et al. (2007) improves this method by using a wavelet analysis of the vorticity field. However, parallel velocity shears or filaments could have a strong vorticity signature, and geometrical constraints are generally...