Sub-100 km ocean processes revealed by structure functions of SWOT sea surface height and in situ observing network

The Surface Water and Ocean Topography (SWOT) mission, equipped with a Ka-band Radar Interferometer (KaRIn), provides unprecedented sea surface height anomaly (SSHA) observations at kilometer-scale resolution over a wide swath. While regional studies have showcased SWOT’s capabilities, its SSHA wavenumber spectra at wavelengths below $\sim$70 km exhibit shallower slopes ($\sim k^{-2}$, where $k$ is the along-track wavenumber) than predicted by geostrophic turbulence theory. We analyzed SWOT SSHA data alongside \textit{in situ} measurements collected by the mission oceanographic campaign from the California Current System during the April–July 2023 calibration and validation (Cal/Val) period. We analyzed steric height from hourly CTD measurements on 11 moorings and 2 gliders and SWOT SSHA using structure functions, revealing that the shallow SWOT SSHA spectra at sub-70 km scales primarily result from KaRIn instrument noise, with a notable cross-track dependence (shallowest at the swath edges). Additionally, high-frequency internal gravity waves also contribute to the shallow spectral slope. Due to limitations in \textit{in situ} and SWOT observations, we could not quantitatively partition each individual process's contribution. Nevertheless, our results revealed, for the first time, the impact of instrument noise and high-frequency internal waves on the SSHA spectrum at sub-70 km that was previously unknown from conventional nadir altimeters, highlighting the complexity of small-scale SSHA signals and the need for further research.