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.
While balanced motions dominate at scales consistent with or larger than the ocean mesoscale, in cases with substantial curvature (e.g. due to eddies), cyclogeostrophic effects can be key contributors to overall oceanic motions. As the authors note, this topic has been explored extensively over the past ~80 years both in meteorological and oceanographic literature. In this study, the authors develop and text an open source utility to compute the cyclogeostrophic correction for gridded altimeter data. The results show that a variational approach is more successful than a more commonly used iterative approach, and that in high-energy regions, both improve on the more limited geostrophic correction. The software utility and discussion will be of interest to readers. However, the statistical diagnostics have some inconsistencies. Revisions will be needed prior to publication.
Minor points