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

Abstract

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.,

Reconstruction of Surface Kinematics From Sea Surface Height Using Neural Networks

“… (a) True raw divergence from the region of the LLC4320 simulation analyzed by Jones et al. (2023), and (b) the Lagrangian filtered divergence from the same region. (c) Unet predicted divergence trained on true divergence, and (d) Unet predicted divergence trained on the Lagrangian filtered divergence.…”

“…In fact, this is a notoriously difficult and unsolved problem, though progress has been made on practical methods to do so. Here we use the Lagrangian-filtered flow computed in Jones et al (2023) as an approximation of the balanced flow, and train the CNN to extract it from the raw LLC data. In short, Lagrangian filtering avoids the effects of Doppler shifting by applying low-pass temporal filtering in the Lagrangian frame 4 (In practice, this requires particle trajectories originating at each grid point, running forward and backward in time for a few days, with filtered data then reprojected onto the Eulerian grid, just to generate one snapshot.…”

“…First, one must find a method to filter IGW signals from the data, and since the repeat cycle period is an order of magnitude longer than the inertial time of roughly 1 day, the method must work on individual snapshots of SSH. This unfortunately obviates the use of methods such as Eulerian spectral filtering (Torres et al., 2018) and Lagrangian filtering (Jones et al., 2023), since each requires high temporal resolution. Second, one needs a model through which to infer the nongeostrophic flow from the filtered SSH signal.…”

“…See Jones et al. (2023) for a more extensive discussion). The waves present an exceptionally vexing challenge, as SWOT's 21‐day repeat cycle during its main operational phase will prevent the use of averaging over inertial times to remove IGW signals.…”

“…Still, we need language to describe these non-wave, non-geostrophic flows, so in lieu of a widely-accepted term, we will sometimes refer to them as "balanced ageostrophic" motions. See Jones et al (2023) for a more extensive discussion). The waves present an exceptionally vexing challenge, as SWOT's 21-day repeat cycle during its main operational phase will prevent the use of averaging over inertial times to remove IGW signals.…”