Patrick Heimbach (Oden Institute, University of Texas at Austin, United States)

The Surface Water and Ocean Topography (SWOT) mission offers unprecedented spatial resolution capable of resolving fine-scale ocean features such as internal tides and mesoscale eddies. However, its 21-day repeat cycle introduces significant spatiotemporal gaps, limiting its ability to capture the rapid evolution of these small-scale processes. To fully exploit SWOT’s high-resolution measurements and reconstruct the evolving ocean state, data assimilation is essential. Sequential, filter-based methods often introduce abrupt adjustments to the model state, violating the equations of motion and conservation laws. In contrast, adjoint-based methods enforce dynamical consistency. This work aims to advance eddy and tide-admitting baroclinic four-dimensional variational (4DVar) data assimilation to the global scale in order to produce an ocean state estimate constrained by SWOT observations. Resolving internal tides and mesoscale eddies seen in SWOT data requires a high-resolution global model, but the nonlinearities and computational cost of global 4DVar at these scales are prohibitive. To address this challenge, this work introduces a multi-grid adjoint approach for ocean state estimation. The forward model runs at high resolution to resolve the fine-scale features observed by SWOT, while the adjoint model runs on a coarser grid to approximate sensitivities more efficiently. Preliminary results show that this coarse-grid adjoint improves numerical stability, reduces computational cost, and retains the essential dynamics needed to constrain the model trajectory to observations. Developed within an automatic differentiation framework, this method enables dynamically consistent assimilation of SWOT and other high-resolution datasets in global ocean models. Additionally, to account for the high spatial resolution but temporally sparse nature of SWOT data, a new model-data misfit operator is developed for efficient comparison with irregularly sampled observations. SWOT’s high-resolution observations offer a new window into small-scale ocean dynamics, which are vital for understanding the ocean’s kinetic energy balance and vertical transport. While we have not yet applied the framework to SWOT data, the assimilation of sea surface height observations from SWOT is expected to tightly constrain initial and surface boundary conditions, shedding light on mesoscale eddy activity and its role in energy exchange. A global state estimate that assimilates SWOT observations at eddy- and internal wave-permitting scales will mark a significant step forward in ocean modeling, enabling deeper insight into the dynamics operating at scales newly accessible through SWOT.