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{"Abstract":["This dataset uses trajectory data from a large set of drifters to extract and analyze displacement signals associated with coherent eddies in the Gulf of Mexico, using a multivariate wavelet ridge analysis as presented in Lilly and Pérez-Brunius (2021). The data includes eddy displacement signals for all ridges, as well as the time-varying ellipse parameters and estimated ellipse center location. The instantaneous frequency is also included, as is the instantaneous bias estimate derived by Lilly and Olhede (2012). The data are organized as appended trajectory data that can be readily separated through the use of the "ids" field.  The ridge length (\\(L\\)),and ridge-averaged circularity (\\(\\overline{\\xi}\\))  are also included, as is measure of statistical significance denoted by (\\(\\rho\\)). The dataset is available for download as a NetCDF file.<\/p>\n\nLilly, J. M. and P. Pérez-Brunius (2021).  Extracting statistically significant eddy signals from large Lagrangian datasets using wavelet ridge analysis, with application to the Gulf of Mexico. Nonlinear Processes in Geophysics<\/em>, 28: 181\u2013212. https://doi.org/10.5194/npg-28-181-2021. <\/p>\n\nLilly, J. M. and Olhede, S. C.: Analysis of modulated multivariate oscillations, IEEE T. Signal Proces., 60, 600\u2013612, 2012. 10.1109/TSP.2011.2173681<\/p>"],"Other":["The GOMED database is a product of the Gulf of Mexico Research Consortium (CIGoM) and was partially funded by the CONACYT-SENER-Hydrocarbons Sector Fund, Mexico, project 201441.See database webpage with additional information, as well as request for download form (https://giola.cicese.mx/database/GOMED)","{"references": ["Lilly, J. M. and Olhede, S. C.: Higher-order properties of analytic wavelets, IEEE T. Signal Proces., 57, 146\\u2013160,\\u00a0https://doi.org/10.1109/TSP.2008.2007607, 2009.", "Lilly, J. M. and Olhede, S. C.: Analysis of modulated multivariate oscillations, IEEE T. Signal Proces., 60, 600\\u2013612, 2012."]}"]} 

Abstract. A method for objectively extracting the displacement signals associated with coherent eddies from Lagrangian trajectories is presented, refined, and applied to a large dataset of 3770 surface drifters from the Gulf of Mexico. The method, wavelet ridge analysis, is a general method for the analysis of modulated oscillations, here modified to be more suitable to the eddy-detection problem. A means for formally assessing statistical significance is introduced, addressing the issue of false positives arising by chance from an unstructured turbulent background and opening the door to confident application of the method to very large datasets. Significance is measured through a frequency-dependent comparison with a stochastic dataset having statistical and spectral properties that match the original, but lacking organized oscillations due to eddies or waves. The application to the Gulf of Mexico reveals major asymmetries between cyclones and anticyclones, with anticyclones dominating at radii larger than about 50 km, but an unexpectedly rich population of highly nonlinear cyclones dominating at smaller radii. Both the method and the Gulf of Mexico eddy dataset are made freely available to the community for noncommercial use in future research.