| Summary: | The accuracy of global tidal models degrades significantly in coastal and estuarine regions. These models are important for correcting measurements from satellite altimetry and are used in numerous scientific and engineering applications. The new Surface Water Ocean Topography (SWOT) mission is providing measurements at unprecedented horizontal resolution in these regions. These data present both the opportunity and the necessity to quantify and correct the spatial variability in the model inaccuracies specific to these regions. We develop a variational Bayesian framework for tidal harmonic analysis which can be applied to SWOT, and is especially useful for exploting the data from the Cal/Val phase. The approach demonstrates superior robustness to different types of noise contamination in comparison to conventional least-squares approaches while providing full uncertainty estimation. By imposing a spatially coherent inductive bias on the model, we achieve superior harmonic constituent inference from temporally-sparse but spatially-dense data. Bayesian uncertainty estimation gives rise to statistical methods for outlier removal and constituent selection. Using our approach, we estimate a lower bound for the residual tidal variability for two SWOT Cal/Val passes (003 and 016) around the European Shelf to be 7% on average. We also show similar estimates cannot be produced using standard least-squares approaches. Tide gauge validation in the same region confirms the superiority of our empirical approach in coastal environments. Empirical corrections for the SWOT data products are provided alongside an open-source Python package, VTide.
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