Assessing submesoscale sea surface height signals from the SWOT mission

TL;DR

This study uses SWOT's KaRIn wide-swath SSH measurements during the rapid-repeat phase to globally characterize submesoscale SSH signals via along-track variance spectra. It employs a two-component spectral decomposition, yielding a balanced signal with high-wavenumber slopes $s_b$ in the range $4$ to $6$ and a small-scale signal with $s_s \approx 1.3$, the latter strongly modulated by surface gravity-wave height, suggesting aliasing rather than an internal-wave continuum. Maps of the balanced signal in the South Pacific reveal compact cyclones with geostrophic vorticities comparable to the planetary vorticity $f$, challenging purely geostrophic or quasi-geostrophic interpretations and motivating semi-geostrophic perspectives. The work demonstrates SWOT's potential to illuminate global submesoscale turbulence and highlights the need for extended science-phase data to robustly assess seasonality and energy transfer between scales.

Abstract

The sea surface height (SSH) field measured by Surface Water and Ocean Topography (SWOT) mission's wide-swath altimeter is analyzed with a focus on submesoscale features. Along-track wavenumber spectra of SSH variance are estimated for the global ocean using the 1-day repeat period from March 26 to July 10, 2023. In regions with an energetic mesoscale eddy field, the spectra have a mesoscale plateau, a steep drop-off due to balanced submesoscale turbulence, and a much flatter power-law tail at small scales. These spectra are characterized by fitting a spectral model. For the balanced signal, this fit yields a power law exponent between -4 and -6 for most regions, broadly consistent with expectations and previous observations. The amplitude of the distinct small-scale signal, which typically dominates at wavelengths less than 30 to 50 km, is strongly correlated in time and space with the height of surface gravity waves, suggesting aliased wave signals as the most likely source. A simple method is proposed to isolate the balanced signal in regions with negligible internal tides. Maps of the balanced signal in the Antarctic Circumpolar Current show compact cyclones with geostrophic relative vorticities frequently in excess of the local planetary vorticity, challenging the quasi-geostrophic framework commonly used to interpret altimetric data.

Figures (10)

• Figure 1: Overview of SSH variance spectra from SWOT's rapid-repeat phase. (a–d) Examples of SSH variance spectra for the full KaRIn signal, the time mean KaRIn signal, the KaRIn anomalies, and the nadir anomalies. The vertical black lines indicate the wavenumbers of the M$_2$ internal tide for baroclinic modes 1 and 2. The vertical gray lines indicate 95% confidence intervals assuming that an independent sample is obtained every 10 cycles (left), every cycle (middle), and at every cross-track position (right). (e) SWOT's rapid-repeat orbit and the locations of the five regions selected for the example spectra, among which a--d correspond to the respective panels here and region e is shown in Fig. \ref{['fiteg']}.
• Figure 2: KaRIn's SSH signal in the South Pacific region. (a) The time mean KaRIn signal (color shading) displaying small-scale geoid variations not removed by the prior geoid model. The variations line up with the independent ETOPO geoid model (gray shading). (b) KaRIn's SSH anomalies (in-swath shading) and the DUACS product from nadir altimetry (background shading) on 24-04-2023 (SWOT cycle 500).
• Figure 3: Tidal signatures and model fits to example SSH variance spectra. (a) Spectrum of SSH anomalies and the HRET estimate of the internal-tidal signal in the tropical Atlantic region. (b) Spectrum of SSH anomalies in the Kuroshio Extension region. (c) Spectrum of SSH anomalies for a subpolar North Atlantic segment (location e in Fig. \ref{['swotpass']}e, centered on 43N, 51W). The spectra in (b) and (c) have negligible tidal signals as estimated by HRET, and the fits of the model \ref{['slopefiteq']} to the balanced and small-scale components of the signal are shown. Panel (b) shows a typical fit, whereas (c) shows an outlier with an anomalously flat balanced spectrum.
• Figure 4: Spectral properties of the SSH signal. (a,b) Map and histogram of the tidal ratio, the maximum of the ratio between the variance spectra of the HRET estimate for internal tides and the full KaRIn anomalies. (c,d) Map and histogram of the slope $s_\mathrm{b}$ of the balanced signal estimated from KaRIn data. (e,f) Map and histogram of the slope $s_\mathrm{b}$ of the balanced signal estimated from nadir data. (g,h) Map and scatter plot of the difference between these two estimates of $s_\mathrm{b}$. (i,j) Map and histogram of the small-scale slope $s_\mathrm{s}$ in KaRIn data.
• Figure 5: Correlations between the amplitude of the small-scale signal in KaRIn data and the significant wave height in the South Pacific region. (a) Time series of the small-scale amplitude in the KaRIn data. (b) Time series of the significant wave heights from ERA5 and as estimated from SWOT data.