A Robust Variational Framework for Cyclogeostrophic Ocean Surface Current Retrieval

Abstract. Estimations of surface currents at submesoscales (1–50 km) are crucial for operational applications and environmental monitoring, yet accurately deriving them from satellite observations remains a challenge. While the geostrophic approximation has long been used to infer ocean surface currents from Sea Surface Height (SSH), it neglects nonlinear advection, which can become significant at submesoscales. To address this limitation, we present a robust and efficient variational method for inverting the cyclogeostrophic balance equation, implemented in the open-source Python library jaxparrow. Unlike the traditional iterative approaches, our method reformulates the inversion as an optimization problem, providing stable estimates even in regions where a cyclogeostrophic solution may not exist. Using both DUACS and the high-resolution NeurOST SSH products, we demonstrate that cyclogeostrophic corrections become increasingly relevant at finer spatial scales. Validation against drifter-derived velocities shows that our approach consistently improves current estimates in energetic regions, reducing errors by up to 20 % compared to geostrophy alone in energetic regions of the global ocean. These results support the systematic inclusion of cyclogeostrophic inversion in the analysis of high-resolution SSH fields.