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

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.

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

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.

Wavelet and index methods for the identification of pool–riffle sequences

The accuracy of hydraulic models depends on the quality of the bathymetric data they are based on, whatever the scale at which they are applied (e.g., 2D or 3D reach-scale modeling for local flood studies or 1D modeling for network-scale flood routing). The along-stream (longitudinal) and cross-sectional geometry of natural rivers is known to vary at the scale of the hydrographic network (e.g., generally decreasing slope, increasing width, etc.), allowing parameterizations of main cross-sectional parameters with proxy such as drainage area or a reference discharge quantile (an approach coined downstream hydraulic geometry, DHG). However, higher-frequency morphological variability is known to occur for many stream types, associated with varying flow conditions along a given reach: alternate bars, pool-riffle sequences, meanders, etc. To better take this high-frequency variability in bedforms into account in hydraulic models, a first step is to design robust methods to characterize the scales at which it occurs. In this paper, we propose and benchmark several methods to identify bedform sequences in pool-riffle morphology, for six small French rivers: the first one called the index method, based on three morphological and hydraulic descriptors; the second one called wavelet ridge extraction, performed on the continuous wavelet transform (CWT) of bed elevation. Finally, these new methods are compared with the bedform differencing technique (BDT, O’Neill and Abrahams (1984)), compared by computing a score that gives a percentage of agreement along the total surveyed length and by calculating the number of bedforms and the pool spacings for each method. The three methods were found to give similar results on average for wavelength estimation, with agreement from 64% to 84% and a similar number of bedforms identified. The filter-like behavior of the wavelet ridge analysis tends to give more robust results for the estimation of mean bedform amplitude, which varies from 0.30 to 0.81 with an SNR (signal-to-noise ratio) from 2.68 to 7.91. Otherwise, BDT gives higher mean bedform amplitude but lower SNR values from 0.85 to 1.73.