Extracting statistically significant eddy signals from large Lagrangian datasets using wavelet ridge analysis, with application to the Gulf of Mexico

Abstract

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 3761 surface drifters from the Gulf of Mexico. The method, wavelet ridge analysis, is modified to exclude the possibility of features changing from rotating in the cyclonic sense to rotating in the anticyclonic sense or vice-versa, transitions that would be physically unrealistic for a coherent eddy. 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 in a two-dimensional parameter space by 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 massive 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 use in future research.

Quasi-Objective Coherent Structure Diagnostics from Single Trajectories

“…A further non-objective, single-particle diagnostics for LCS identification is the Lagrangian spin parameter [43], which relies on the calibration of an additional stochastic model for the velocity field. Yet another approach adapts the wavelet ridge analysis method of [7] to Lagrangian trajectory analysis [29,30]. While physically insightful, this technique is non-objective either, as it fits a time-varying ellipse model to identify signatures of coherent eddies based on the looping characteristics of trajectories.…”

“…Answering this question would enable, for instance, a mathematically justifiable and physically self-consistent extraction of Lagrangian jets, fronts and eddies from NOAA's Global Drifter Program, which comprises more than 20,000 trajectories [32]. Such an extraction should then lead to a systematic assessment of the performance of promising nonobjective trajectory-based methods, such as [30], in avoiding false positives and negatives in elliptic LCS detection.…”