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Abstract The decomposition of oceanic flow into its geostrophically balanced and unbalanced motions carries theoretical and practical significance for the oceanographic community. These two motions have distinct dynamical characteristics and affect the transport of tracers differently from one another. The launch of the Surface Water and Ocean Topography (SWOT) satellite provides a prime opportunity to diagnose the surface balanced and unbalanced motions on a global scale at an unprecedented spatial resolution. Here, we apply dynamic‐mode decomposition (DMD), a linear‐algebraic data‐driven method, to tidally‐forced idealized and realistic numerical simulations at submesoscale‐permitting resolution and one‐day‐repeat SWOT observations of sea‐surface height (SSH) in the Gulf Stream downstream of Cape Hatteras, a region commonly referred to as the separated Gulf Stream. DMD is able to separate out the spatial modes associated with sub‐inertial periods from super‐inertial periods. The sub‐inertial modes of DMD can be used to extract geostrophically balanced motions from SSH fields, which have an imprint of internal gravity waves, so long as the data extends long enough in time. We utilize the statistical relation between relative vorticity and strain rate as the metric to gauge the extraction of geostrophy.
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Wave and Turbulence Separation Using Dynamic Mode Decomposition
Abstract Separating the effects of waves and turbulence in oceanographic time series is an ongoing challenge because surface wave motion and turbulence fluctuations can occur at overlapping frequencies. Therefore, simple bandpass filters cannot effectively separate their dynamics. While more advanced decomposition techniques have been developed, they often entail restrictive assumptions about the wave and turbulence interactions, require synchronized measurements, and/or only decompose the signal spectrally without a time series reconstruction. We present our new wave–turbulence decomposition technique which uses dynamic mode decomposition (DMD). The technique is signal agnostic so it can be applied to any time series, and our only assumptions are that the waves and turbulence can be separated and that the waves are the most coherent features in the signal. Our approach requires minimal tuning, where the main user input is the wave frequency range of interest. To demonstrate the method, we apply it to synthetic, field, and laboratory data and compare the results to other modal decomposition methods. A sensitivity analysis on the synthetic data shows that the most sensitive parameter to the accuracy is the rank truncation in the DMD, and that the decomposition performs the best when the wave energy in the signal is of equal or greater magnitude than that of the turbulence. Given the accuracy of our decomposition, we are able to analyze the velocity autocorrelation of the separated turbulence time series with minimal wave contamination. Overall, our decomposition method outperforms the other decomposition methods and provides for robust separation of the waves and turbulence, demonstrating wide applicability to ocean signal processing. Significance StatementWhen measuring physical, chemical, and biological quantities in the ocean, the measurements are often influenced by both waves and turbulence. Isolating the individual effects of waves and turbulence on those variables is important to a wide range of analyses, such as estimating how momentum, heat, and nutrients are mixed throughout the water column. In this work, we propose a new method to separate the wave and turbulence components in ocean-data time series. When tested on laboratory, field, and synthetic data, our method was able to separate the wave and turbulence components of a signal more effectively than previously proposed algorithms.
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- PAR ID:
- 10661749
- Publisher / Repository:
- Journal of Atmospheric and Oceanic Technology
- Date Published:
- Journal Name:
- Journal of Atmospheric and Oceanic Technology
- Volume:
- 42
- Issue:
- 5
- ISSN:
- 0739-0572
- Page Range / eLocation ID:
- 509 to 526
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1175/JTECH-D-24-0039.1
