An Ensemble-Based Eddy and Spectral Analysis, With Application to the Gulf Stream

The "eddying" ocean, recognized for several decades, has been the focus of much observational and theoretical research. We here describe a generalization for the analysis of eddy energy, based on the use of ensembles, that addresses two key related issues: the definition of an "eddy" and the general computation of energy spectra. An ensemble identifies eddies as the unpredictable component of the flow, and permits the scale decomposition of their energy in inhomogeneous and non-stationary settings. We present two distinct, but equally valid, spectral estimates: one is similar to classical Fourier spectra, the other reminiscent of classical empirical orthogonal function analysis. Both satisfy Parseval's equality and thus can be interpreted as length-scale dependent energy decompositions. The issue of "tapering" or "windowing" of the data, used in traditional approaches, is also discussed. We apply the analyses to a mesoscale "resolving" (1/12 degrees) ensemble of the separated North Atlantic Gulf Stream. Our results reveal highly anisotropic spectra in the Gulf Stream and zones of both agreement and disagreement with theoretically expected spectral shapes. In general, we find spectral slopes that fall off faster than the steepest slope expected from quasi-geostrophic theory.