Albion Lawrence

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.

Upper-ocean flows are a multi-scale jigsaw puzzle of turbulence and waves. Characterizing these flows is essential for understanding their role in redistributing heat, carbon, and nutrients, yet power spectral analysis cannot always distinguish between types of motion. We show that the scattering transform (ST), a wavelet convolution method, can extract geometric information from flow fields, offering insights beyond the power spectrum. The ST distinguishes balanced dynamics, internal waves, and types of turbulence -- even when their power spectra are identical. Applied to sea surface height (SSH) fields from ocean models, the ST differentiates regions with distinct underlying dynamics. Our analysis offers a framework for interpreting SSH from satellite altimetry missions and for analyzing other spatial maps (e.g., from airborne and coastal radar). More generally, the ST is an appealing way to characterize complex fluid motion in a variety of geophysical contexts.