Statistical inversion of surface tracers to infer fine-scale near-surface ocean currents

Measuring sea surface currents (SSC) directly is challenging. Instead, SSC are often inferred from indirect measurements like altimetry. However, altimetry-based methods only provide large-scale (>100 km) geostrophically-balanced velocity estimates of SSC. Here, we present a statistical inversion model to predict fine-scale SSC using remotely sensed sea surface temperature (SST) data. Our approach employs Gaussian Process (GP) regression, where the GP is informed by a two-dimensional tracer transport equation. This method yields a predictive distribution of SSC, from which we can generate an ensemble of surface currents to derive both predictions and prediction uncertainties. Our approach incorporates prior knowledge of the SSC length scales and variances that appear in the covariance function of the GP, which are then estimated from the SST data. The framework naturally handles noisy and incomplete SST data (e.g., due to cloud cover), without the need for pre-filtering.  We validate the inversion model through an observing system simulation experiment (OSSE), which demonstrates that GP-based statistical inversion outperforms existing methods, especially when the measurement signal-to-noise ratio is low.  When applied to Himawari-9 satellite SST data over the Australian North-West Shelf, our method successfully resolves SSC down to the sub-mesoscale. We anticipate our framework being used to improve understanding of fine-scale ocean dynamics, and to facilitate the coherent propagation of uncertainty into downstream applications such as ocean particle tracking.