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

Abstract

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°) 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.

Diagnosing the Thickness‐Weighted Averaged Eddy‐Mean Flow Interaction From an Eddying North Atlantic Ensemble: The Eliassen‐Palm Flux

“…(2020) and Uchida, Jamet, et al. (2021), which are an air‐sea partially coupled, 48‐member ensemble of the North Atlantic ocean at mesoscale‐permitting resolution (1/12°; or sometimes referred to as “eddy rich”) using the hydrostatic configuration of the Massachusetts Institute of Technology general circulation model (MITgcm; J. Marshall et al., 1997). We have 46 vertical levels increasing from 6 m near the surface to 250 m at depth.…”

“…We use the model outputs from the realistic runs described in Jamet et al (2019b), Jamet et al (2020) and Uchida, Jamet, et al (2021), which are an air-sea partially coupled, 48-member ensemble of the North Atlantic ocean at mesoscale-permitting resolution (1/12°; or sometimes referred to as "eddy rich") using the hydrostatic configuration of the Massachusetts Institute of Technology general circulation model (MITgcm; J. Marshall et al, 1997).…”

Wavelet-based wavenumber spectral estimate of eddy kinetic energy: Idealized quasi-geostrophic flow

“…Namely, the global two-point correlation function, stemming from the assumption of homogeneity in the Fourier approach, virtually acts as a spatial averaging operator (cf. Uchida, Jamet, et al, 2021). For this setting, this assumption is valid, hence the superior performance in flux estimation of the Fourier approach.…”

“…Hann windows (Arbic et al, 2013;Uchida et al, 2017;Uchida, Jamet, et al, 2021) makes it di cult to detect the k 5/3 power law due to the domain size being small; there are only two wavenumber points at scales larger than the Rossby radius (red curves in Fig. 7).…”

“…The standard Fourier approach has had great success in providing us with spectral estimates of energy partition and its straightforward mathematical formulation facilitates the spectral interpretation in the original context, namely statisti--2-manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES) cally homogeneous flows where Fourier decompositions are natural. Issues persist, however, in geophysical flows which are statistically inhomogeneous, anisotropic and nonstationary (Uchida, Jamet, et al, 2021). The assumption of homogeneity lies on the fact that a Fourier transform is a global operator over the entire space-time domain of interest.…”