# 4DVarNet-SSH: end-to-end learning of variational interpolation schemes for nadir and wide-swath satellite altimetry

arXiv: https://arxiv.org/abs/2211.05904 · HTML: https://mlsanity.com/paper/2211.05904/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2022.

## Built on by (most cited first, 10 of 10)

- [LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2411.19305/) (2024)
- [Training neural mapping schemes for satellite altimetry with simulation data](https://mlsanity.com/paper/2309.14350/) (2023)
- [OceanBench: The Sea Surface Height Edition](https://mlsanity.com/paper/2309.15599/) (2023)
- [Scale-aware neural calibration for wide swath altimetry observations](https://mlsanity.com/paper/2302.04497/) (2023)
- [ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiability](https://mlsanity.com/paper/2608.23297/) (2026)
- [Multi-Modal Learning-based Reconstruction of High-Resolution Spatial Wind Speed Fields](https://mlsanity.com/paper/2312.08933/) (2023)
- [Simulation-informed deep learning for enhanced SWOT observations of fine-scale ocean dynamics](https://mlsanity.com/paper/2503.21303/) (2025)
- [Taking a Second Look: Correcting Sea Ice Forecasts with Sparse Observations](https://mlsanity.com/paper/2609.24591/) (2026)
- [PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilation](https://mlsanity.com/paper/2609.26890/) (2026)
- [REACT: Physically and Chemically Consistent Reconstruction of Marine Active Tracers](https://mlsanity.com/paper/2610.03888/) (2026)

## Abstract (arXiv)

The reconstruction of sea surface currents from satellite altimeter data is a key challenge in spatial oceanography, especially with the upcoming wide-swath SWOT (Surface Ocean and Water Topography) altimeter mission. Operational systems however generally fail to retrieve mesoscale dynamics for horizontal scales below 100km and time-scale below 10 days. Here, we address this challenge through the 4DVarnet framework, an end-to-end neural scheme backed on a variational data assimilation formulation. We introduce a parametrization of the 4DVarNet scheme dedicated to the space-time interpolation of satellite altimeter data. Within an observing system simulation experiment (NATL60), we demonstrate the relevance of the proposed approach both for nadir and nadir+swot altimeter configurations for two contrasted case-study regions in terms of upper ocean dynamics. We report relative improvement with respect to the operational optimal interpolation between 30% and 60% in terms of reconstruction error. Interestingly, for the nadir+swot altimeter configuration, we reach resolved space-time scales below 70km and 7days. The code is open-source to enable reproductibility and future collaborative developments. Beyond its applicability to large-scale domains, we also address uncertainty quantification issues and generalization properties of the proposed learning setting. We discuss further future research avenues and extensions to other ocean data assimilation and space oceanography challenges.