# Inversion of sea surface currents from satellite-derived SST-SSH synergies with 4DVarNets

arXiv: https://arxiv.org/abs/2211.13059 · HTML: https://mlsanity.com/paper/2211.13059/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 84 references that are in the map.
- First posted on arXiv 23 Nov 2022.

## Builds on (most cited first, 7 of 7)

- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization](https://mlsanity.com/paper/2001.06270/) (2020)
- [Learning Variational Data Assimilation Models and Solvers](https://mlsanity.com/paper/2007.12941/) (2020)
- [Multimodal 4DVarNets for the reconstruction of sea surface dynamics from SST-SSH synergies](https://mlsanity.com/paper/2207.01372/) (2022)
- [Super-resolution data assimilation](https://mlsanity.com/paper/2109.08017/) (2021)
- [Joint calibration and mapping of satellite altimetry data using trainable variational models](https://mlsanity.com/paper/2110.03405/) (2021)

## Built on by (most cited first, 4 of 4)

- [OceanBench: The Sea Surface Height Edition](https://mlsanity.com/paper/2309.15599/) (2023)
- [ORCAst: Operational High-Resolution Current Forecasts](https://mlsanity.com/paper/2501.12054/) (2025)
- [ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiability](https://mlsanity.com/paper/2608.23297/) (2026)
- [Generative data assimilation highlights fronts as key regulators of ocean energy cascade](https://mlsanity.com/paper/2608.14955/) (2026)

## Abstract (arXiv)

Satellite altimetry is a unique way for direct observations of sea surface dynamics. This is however limited to the surface-constrained geostrophic component of sea surface velocities. Ageostrophic dynamics are however expected to be significant for horizontal scales below 100~km and time scale below 10~days. The assimilation of ocean general circulation models likely reveals only a fraction of this ageostrophic component. Here, we explore a learning-based scheme to better exploit the synergies between the observed sea surface tracers, especially sea surface height (SSH) and sea surface temperature (SST), to better inform sea surface currents. More specifically, we develop a 4DVarNet scheme which exploits a variational data assimilation formulation with trainable observations and em a priori terms. An Observing System Simulation Experiment (OSSE) in a region of the Gulf Stream suggests that SST-SSH synergies could reveal sea surface velocities for time scales of 2.5-3.0 days and horizontal scales of 0.5^circ-0.7^circ, including a significant fraction of the ageostrophic dynamics (≈ 47%). The analysis of the contribution of different observation data, namely nadir along-track altimetry, wide-swath SWOT altimetry and SST data, emphasizes the role of SST features for the reconstruction at horizontal spatial scales ranging from nicefrac120^circ to nicefrac14^circ.