Level 4 global topography mapping with 4DVarNet

The study of mesoscale oceanic eddy dynamics requires regular, high-resolution space-time grids of topography observations. However, most observations come from the constellation of altimetry satellites, which measure the topography along very fine and still very sparse tracks, and surface currents must therefore be calculated using level 4 topography maps. These level 4 maps used operationally are produced by methods based on objective analysis (OA, Le Traon et al., 1998), such as historically used in the DUACS production until end 2024, or variational resolution, such as MIOST (Ubelmann et al., 2022), but their spatial resolution limits the scales of dynamics that can be resolved. While OA and MIOST can capture mesoscale dynamics down to approximately 150–200 km, sub-mesoscale features remain inaccessible with these methods. 

Recent advancements in neural network-based mapping models have the potential to refine the resolution of mesoscale topography reconstruction. The NeurOST model developed by S. A. Martin (2024), for instance, improves the spatial resolution by 30% compared with existing conventional methods like OA, establishing itself as a state-of-the-art technique in level-4 topography mapping. While the 4DVarNet model developped by Febvre et al. (2024) has proven effective in Observing System Simulation Experiments (OSSE) over the Gulf Stream, it has not yet been applied on real altimetric observations or on a global scale. 

In this study, we leverage the 4DVarNet model to estimate global surface current maps from both conventional nadir altimetry and SWOT KaRIn swath data. The model was trained on GLORYS12V1 reanalysis data over the Gulf Stream and the Agulhas Current, and subsequently applied to global altimetric observations, including SWOT KaRIn.  

Our results show that 4DVarNet-derived topography maps from nadir altimetry improve the effective resolution OA and over NeurOST in regions of high variability and strong currents, such as the Gulf Stream, Kuroshio, Agulhas and Brazil currents. The inclusion of SWOT KaRIn data further enhances the effective resolution and significantly reduces mapping errors. 4DVarNet's reconstructions also reveal more small-scale vortex structures and deformations compared to NeurOST. The resulting maps seem to improve our ability to observe eddy dynamics and their impact on energy transfer between different scales. 

Nevertheless, the model still needs many improvements to provide satisfactory topography on a global scale. Ongoing and future work includes further investigation into the contribution of additional geophysical variables to the topography reconstruction performance of 4DVarNet, such as bathymetry, sea surface temperature, salinity and ocean color, and the exploration of an unsupervised learning scheme for better generalization to real altimetric data. These developments aim to improve the model's applicability to diverse oceanic regions and enhance its ability in capturing sub-mesoscale eddy dynamics.