The “switch-on” problem for linear time-invariant operators

Lilly, Jonathan M.; Lettvin, E.

doi:10.1016/j.sigpro.2003.12.011

Cited by 2 publications

(2 citation statements)

References 1 publication

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“…In our version of frequency filtering, we apply a convolution filter to the timeseries of velocity and steric SSH at each point in x , y , z . We choose to use a sinc function as the window function for this filter, because its Fourier transform is a top‐hat (see e.g., Lilly and Lettvin (2004)), so the field after ω ‐filtering, ϕ ω is given by

{\phi }_{\omega }(t)=\int \nolimits_{t-{t}_{w}}^{t+{t}_{w}}\phi (t)\,\text{sinc}\left(\frac{f(t-\tau )}{1.1\,\pi }\right)\,\mathrm{d}\tau ,

where ϕ is the unfiltered field and t w = 36 hr. The width of the sinc function is chosen to be f /1.1, where f is the local Coriolis parameter.…”

Section: Methodsmentioning

confidence: 99%

Using Lagrangian Filtering to Remove Waves From the Ocean Surface Velocity Field

Jones

Xiao

Abernathey

et al. 2023

J Adv Model Earth Syst

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Near-surface ocean currents are a critical component of the Earth system, mediating the transfer of heat, momentum, and trace gasses between ocean and atmosphere (Cronin et al., 2019;Elipot & Wenegrat, 2021). These currents regulate marine ecosystems by transporting nutrients and phytoplankton laterally within the eutrophic zone (Barton et al., 2010;Resplandy et al., 2011), and they transport marine debris and plastic pollution around the globe (Van Sebille et al., 2020). Observed ocean surface currents are also used to evaluate the accuracy and biases of numerical ocean models. As a result, the oceanographic community requires accurate and detailed knowledge of the state of ocean surface currents.Satellite-based observations of sea-surface height (SSH), which is directly proportional to surface pressure, can be used to infer surface velocities via geostrophic balance. Modern ocean altimetry products like Archiving, Validation, and Interpretation of Satellite Oceanographic data (Ducet et al., 2000) typically have grid resolution of around 0.25° and an effective resolution of approximately 200 km. At this scale, geostrophic balance holds well, and altimetry-derived near-surface geostrophic velocities are used in many studies of ocean currents (e.g.,

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{\phi }_{\omega }(t)=\int \nolimits_{t-{t}_{w}}^{t+{t}_{w}}\phi (t)\,\text{sinc}\left(\frac{f(t-\tau )}{1.1\,\pi }\right)\,\mathrm{d}\tau ,

where ϕ is the unfiltered field and t w = 36 hr. The width of the sinc function is chosen to be f /1.1, where f is the local Coriolis parameter.…”

Section: Methodsmentioning

confidence: 99%

Using Lagrangian Filtering to Remove Waves From the Ocean Surface Velocity Field

Jones

Xiao

Abernathey

et al. 2023

J Adv Model Earth Syst

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“…We choose to use a sinc function as the window function for this filter, because its fourier transform is a tophat (see e.g. Lilly and Lettvin (2004)), so the field after ω-filtering, ϕ ω is given by…”

Section: ω Filteringmentioning

confidence: 99%

Using Lagrangian filtering to remove waves from the ocean surface velocity field

Jones¹,

Xiao²,

Abernathey³

et al. 2023

Preprint

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The Surface Water and Ocean Topography (SWOT) satellite will measure altimetry on scales down to about 15km: at these scales, the sea-surface-height signature of inertia-gravity waves, including barotropic tides and internal tides, will be visible. However, inertia-gravity waves have little impact on tracer transport. This paper explores how to remove the portion of the surface velocity and sea surface height that is associated with inertia-gravity waves in the Agulhas region of a high-resolution ocean model (LLC4320). Various filtering methods are compared. Lagrangian filtering, a method that accounts for Doppler shifting of high-frequency motions by the low-frequency velocity field, is found to preserve flow that appears super-inertial in the reference frame of the Earth. Other methods do not preserve these motions as effectively. We show that the signal that is preserved by Lagrangian filtering is primarily associated with convergent fronts, suggesting that it is part of the balanced flow that has been Doppler shifted into the super-inertial range. Lagrangian filtering also removes some signal that appears sub-inertial in the reference frame of the Earth, but is really super-inertial motion that has been Doppler shifted into the sub-inertial range.

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The “switch-on” problem for linear time-invariant operators

Cited by 2 publications

References 1 publication

Using Lagrangian Filtering to Remove Waves From the Ocean Surface Velocity Field

Using Lagrangian Filtering to Remove Waves From the Ocean Surface Velocity Field

Using Lagrangian filtering to remove waves from the ocean surface velocity field

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