A robust minimization-based framework for cyclogeostrophic ocean surface current retrieval

Overview

Surface current estimation at submesoscales (1–50 km) from satellite observations remains limited by the geostrophic approximation, which excludes nonlinear advection effects that gain significance at finer spatial resolutions. This work presents a minimization-based inversion framework for the cyclogeostrophic balance equation, implemented in the open-source jaxparrow library. The cyclogeostrophic approach incorporates nonlinear advection to improve current retrievals, particularly relevant for high-resolution Sea Surface Height (SSH) data analysis.

Methods and approach

The study reformulates cyclogeostrophic inversion as a constrained minimization problem rather than employing traditional fixed-point iteration. This reformulation provides numerical stability in regions where cyclogeostrophic solutions may not exist. The method is evaluated using submesoscale-permitting model simulations and two SSH datasets: the DUACS product and the high-resolution NeurOST product. Validation is conducted against drifter-derived velocity measurements to assess performance across different ocean regions and spatial scales.

Results

Cyclogeostrophic corrections demonstrate increasing relevance with decreasing spatial scale, showing systematic departures from pure geostrophic estimates at submesoscale resolutions. The minimization-based approach consistently improves current estimates in energetic regions, with error reductions up to 20 percent relative to geostrophic-only calculations when validated against drifter observations. The method maintains computational efficiency while providing robust estimates even in complex flow regimes where traditional approaches encounter numerical instability.

Implications

The results indicate that nonlinear advection effects warrant systematic inclusion in operational and research-oriented surface current analysis pipelines utilizing high-resolution SSH observations. The robustness of the minimization-based framework supports its integration into automated processing workflows for submesoscale current retrieval. These findings have direct relevance for operational oceanography applications, environmental monitoring, and validation of altimetric SSH products at fine spatial scales.