A strictly geostrophic product of sea-surface velocities from the SWOT fast-sampling phase

TL;DR

This work addresses how to reliably extract strictly geostrophic sea-surface velocities from SWOT SSHa observations, overcoming limitations of ad hoc spatial filtering. The authors apply a dynamic mode decomposition–based, multi-resolution method (mrCOSTS) with internal-tide corrections from HYCOM to isolate the geostrophic SSHa component $\eta^g$ from SWOT's fast-sampling data, producing a global geostrophic dataset. They show that $\eta^g$ concentrates power at spatial scales $\gtrsim 100$ km and times $\gtrsim 10$–$20$ days, with $\eta^a$ carrying higher-frequency content, and that the vorticity/strain statistics for $\eta^g$ imply small Rossby numbers ($\zeta^g/|f|, |\alpha^g|/|f| \lesssim \mathcal{O}(1)$). Validation against Mediterranean SVP drifters indicates that mrCOSTS yields geostrophic velocities that are as good as or better than the L3$_{\text{HRET}}$ product, supporting its use as a robust baseline for altimetric velocity retrieval and for studies of the geostrophic energy cascade and quasi-geostrophic dynamics. The dataset, once publicly distributed, provides a valuable resource for driving and validating geostrophic analyses from SWOT and related altimetry missions.

Abstract

While geostrophy remains the simplest and most practical balance to extract velocity information from sea-surface height anomaly (SSHa), confusions remain within the oceanographic community to what extent this balance can be applied to altimetric observations with the launch of the Surface Water and Ocean Topography (SWOT) satellite. Given the limited temporal resolution of SWOT, many studies have resorted to claiming that the spatially filtered SSHa fields correspond to the geostrophic component. This introduces the ambiguity of which spatial scale to choose. Here, we build upon the recent developments in internal tide (IT) corrections (Yadidya et al., 2025) and apply a dynamic mode decomposition (DMD)-based method introduced by Lapo et al. (2025) to robustly extract the geostrophic component associated with sub-inertial frequencies from the SWOT one-day-repeat orbit; we distribute the global dataset as a public good. We provide the joint probability density function (PDF) of vorticity and strain, and spectra of SSHa at a few cross-over regions.

Figures (4)

• Figure 1: A snapshot of $\eta^g$ on an arbitrary day from the global SWOT Cal/Val orbit and zoomed-in plots of $\eta^g$ and $\eta^a$ at four Xover regions. The four regions, Kx, GS, CC and AR, are indicated by the black arrows in panel (a).
• Figure 2: Variance preserving frequency and along-track wavenumber power spectra, $\omega k|\hat{\eta}(\omega,k)|^2~[\text{m}^2\,\text{cpm}^{-1} \text{cps}^{-1}]$, of $\eta^g$ and $\eta^a$ at four Xover regions. The units on the axes are in cycles per kilometer (cpkm) and cycles per day (cpd).
• Figure 3: Snapshots of geostrophic speed $|{\bf u}^g|$, relative vorticity $\zeta^g/|f|$ and strain rates $|\alpha^g|/|f|$ pre-processed through mrCOSTS, and joint PDFs of the latter two from four Xover regions. Geostrophic speed is shown in the navy-yellow colormap, relative vorticity in blue-red colormap and strain rates in violet-orange colormap. The joint PDFs were diagnosed over the three months of $\eta^g$ along with L3$_{\text{HYCOM}}$, i.e., the raw SWOT data de-tided by the HYCOM forecast.
• Figure 4: Rotary frequency spectra of the SVP drifter velocities and quantification of how velocity estimates from the L3$_{\text{HRET}}$ and mrCOSTS product agree with them. The unfiltered spectra are shown in solid curves whereas the spectra of velocities low passed with the Butterworth filter are in dashed curves (a,b). The vertical dotted lines correspond to the inertial, diurnal and filter-cutoff frequency. Polar histograms between the drifter velocities and L3$_{\text{HRET}}$ and mrCOSTS estimates (c--f). A perfect alignment would collapse the histograms onto the cyan cross and $0^\circ$ in angle.