A framework for early-stage coastal and estuarine tidal and mean sea surface correction from the Surface Water Ocean Topography mission

The NASA Surface Water Ocean Topography mission (SWOT), launched on 16 December 2022, will provide the highest spatial and temporal altimetric measurements of coastal oceans to date. The mission is ideally suited to studying mesoscale and submesoscale processes and is expected to enhance our understanding of coastal tides greatly. Although improved tidal analysis and prediction is, of course, useful for studying tides, arguably more important is the accurate removal of tidal variability from SWOT observations. This is a consequence of the fact that the tidal signal often dominates other sub-mesoscale processes which are of high interest to SWOT researchers. While SWOT presents unprecedented spatial resolution, the temporal sparsity renders the applications of conventional tidal analysis methods difficult in the early stages of the mission. Despite significant improvements in global and regional barotropic tidal models in the past few decades, the complexity of coastal and estuarine tides as well as the relatively limited in-situ measurements available for assimilation can lead to significant errors when used for tidal corrections. Further complications are introduced by the uncertainty in mean sea surface (MSS) estimates from gridded MSS Products. These errors can account for large percentages of the global Sea Level Anomaly error and grow significantly over rough bathymetry. As such, the accurate assessment of the uncertainty for the released data products and corrections derived from primary SWOT data are critical to the early success of SWOT science teams. We develop a fully Bayesian variant of tidal harmonic analysis to achieve tidal super-resolution and MSS correction for early-stage (<1 year) SWOT data products. Our approach can be applied to any location, without prior knowledge of bathymetry or gauge constraints but provides a natural framework for integrating physical priors, historical altimetry measurements, gauge constraints, and even spatial coherence. By taking a variational approach, the method avoids the computational bottlenecks presented by standard Bayesian methods. Additionally, we model the MSS as an additional parameter within the model, which yields provably accurate mean sea surface corrections and uncertainty approximation. A new constituent selection criterion is developed and provides reliable tidal constituent super-resolution when compared to standard methods (e.g. Rayleigh, Munk-Hasselman). We apply our variational Bayesian tidal analysis to simultaneously correct the mean sea surface and tidal correction errors present in the Bristol Channel SWOT Cal/Val site. We develop several 2-D Sea Surface models to illustrate how the Bayesian approach can integrate varying degrees of prior information, and tackle the challenging problem of tidal deformation. Additionally, results on simulated data indicate that the variational Bayesian harmonic analysis can significantly reduce the global error in both the estimated M2, N2, and S2 constituents and MSS after only 1 year of SWOT science orbit. Thus, we present our variational Bayesian tidal analysis as both a standalone tidal analysis tool and a specialized tool for SWOT empirical tidal and MSS correction. Our approach (VTide) will be released as part of the open-source Python package OTide in spring 2024.