Isolating Balanced Ocean Dynamics in SWOT Data

TL;DR

This work tackles isolating balanced ocean dynamics in SWOT SSH maps, where the signal combines balanced meso- and submesoscale flows with unbalanced internal waves and noise. It introduces a Bayesian Gaussian-process framework that separates a balanced signal B(k) and noise N(k) by fitting their wavenumber spectra to KaRIn and nadir observations, then reconstructs swath-balanced SSH across the nadir gap with quantified uncertainty. Evaluation on synthetic SWOT data from a high-resolution North Atlantic simulation shows successful noise removal while preserving eddies, fronts, and filaments down to roughly 10 km, with the posterior uncertainty reliably reflecting reconstruction error. The method provides a principled pathway to study balanced turbulence with SWOT, offering extensibility to include internal-tide signals and non-Gaussian statistics as needed.

Abstract

The Surface Water and Ocean Topography (SWOT) mission provides two-dimensional sea surface height (SSH) maps at unprecedented resolution, but its signal is a combination of balanced meso- and submesoscale turbulence, unbalanced internal waves, and small-scale noise. Interpreting the meso- and submesoscale flow features captured by SWOT requires a careful isolation of the balanced signal. We present a statistical method to do so in regions where internal-wave signals are negligible, such as western boundary current regions and the Southern Ocean. Our method assumes Gaussian statistics for both the balanced flow and the noise, which we infer by fitting parametric models to the observed SSH wavenumber spectrum. Using these inferred parameters, we perform a Bayesian inversion to reconstruct swath-aligned SSH maps that fill the nadir gap. We evaluate the method using synthetic data from a high-resolution simulation with realistic SWOT-like noise added. Comparisons with the underlying model data show that our reconstruction successfully removes small-scale noise while preserving meso- and submesoscale eddies, fronts, and filaments down to a feature scale of 10km. The comparison also demonstrates that the posterior uncertainty is a reliable estimate of the error.

Figures (11)

• Figure 1: SWOT sea surface height anomalies (SSHA) and their statistics in the Northwest Atlantic. (a) SSHA from SWOT's KaRIn and nadir altimeters for pass 9, cycle 483 (7 April, 2023). (b) Along-track SSHA variance spectra from the two altimeters, with reference lines of $k^{-4.7}$ and $k^{-1.7}$ indicating the balanced and noise-dominated regimes in the KaRIn data. (c, d) Model fits to these spectra consisting of a balanced part and small-scale noise. For the KaRIn data, the onboard smoothing and aliasing are taken into account. The sum of the models (black dashed lines) tracks the observed spectra (dots). Vertical lines indicate the transition between the balanced and noise models: $\qty{39.5}{\kilo\meter}$ for KaRIn and $\qty{87.5}{\kilo\meter}$ for nadir.
• Figure 2: Location of the SWOT rapid-repeat sampling in the Northwest Atlantic, overlaid on a map of surface geostrophic speed from the numerical simulation. The section of pass 9 used in the analysis is between 29 and 35N and is highlighted in orange.
• Figure 3: Balanced extraction applied to the observed SWOT SSHA field on pass 9, cycle 483 (7 April, 2023). (a) Observed SSHA data from KaRIn (swaths) and nadir (central track). (b) Extracted balanced SSHA field estimated from the observed SSHA. (c) Geostrophic speed $|\boldsymbol{u}_g|$ of the extracted balanced SSHA field. (d) Geostrophic vorticity $\zeta_g$ derived from the extracted balanced SSHA and normalized by the planetary vorticity $f$. The orientation of these maps is such that the lower left corner corresponds to the southeast corner of the patch shown in Fig. \ref{['fig:na_swot_passes']}.
• Figure 4: Cross-track profiles of the pointwise posterior uncertainty. Shown are the standard deviations for SSHA, the along-track geostrophic velocity $u_g$, the across-track geostrophic velocity $v_g$, and the normalized geostrophic vorticity $\zeta_g/f$, derived from the posterior covariance matrix $\mathbf{C}$ for both the full extraction and an extraction in which the nadir data is withheld. The nadir measurements are located at 60 across-track distance.
• Figure 5: Along-track SSHA variance spectra for SWOT pass 9, cycle 483 (7 April, 2023). Shown are the spectra computed directly from KaRIn data (blue) and from the extracted balanced field (black). Also shown are the spectra computed from draws from the probability distributions of the posterior uncertainty (red) and the posterior mean \ref{['eqn:postmeancov']} (green). The wavelength at which these two spectra intersect, the effective resolution of the extracted signal, is marked.