Cyclogeostrophic inversion for estimating Sea Surface Currents from SWOT altimeter data

The spatial resolution of the Sea Surface Height (SSH) observations provided by the SWOT mission opens unprecedented perspectives for estimating ocean near surface circulation at scales <100km. The geostrophic balance, which relates the pressure gradient, the current velocity, and the Coriolis force, is commonly employed to estimate Sea Surface Currents (SSC) from SSH. This equation represents a drastic approximation of the Navier-Stokes equations adapted to mesoscales and larger scales ocean dynamics, which neglects in particular the velocity advection term. However, it is known that at the scales allowed by SWOT's observations, the advection term can no longer be neglected in the leading order balance, especially in highly energetic regions.But solving the cyclogeostrophic balance equation, which includes the advection term, can not be achieved analytically, and requires the use of numerical methods. Still, (1) existing iterative approaches are known to diverge, and ad-hoc procedures are required to avoid local discontinuities; (2) publicly available implementations are missing. To overcome these limitations, we propose a new Python package, named jaxparrow. jaxparrow formulates the cyclogeostrophic balance as a variational problem and solves this problem using state-of-the-art optimization procedures. Its implementation heavily relies on JAX, a Python library which brings together automatic differentiation and just-in-time compilation. In this presentation, we will describe the variational formulation of the cyclogeostrophic balance inversion and demonstrate the performance of this approach with high resolution ocean model data.We will then illustrate how global estimates of cyclogeostrophic SSC can be obtained from altimeter data by combining jaxparrow with existing SSH mapping techniques, and  describe how cyclogeostrophic corrections may improve our ability to estimate SSC from SWOT ocean data.