# Multimodal 4DVarNets for the reconstruction of sea surface dynamics from SST-SSH synergies

arXiv: https://arxiv.org/abs/2207.01372 · HTML: https://mlsanity.com/paper/2207.01372/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2022.

## Built on by (most cited first, 13 of 13)

- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Efficient deep data assimilation with sparse observations and time-varying sensors](https://mlsanity.com/paper/2310.16187/) (2023)
- [LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2411.19305/) (2024)
- [Inversion of sea surface currents from satellite-derived SST-SSH synergies with 4DVarNets](https://mlsanity.com/paper/2211.13059/) (2022)
- [OceanBench: The Sea Surface Height Edition](https://mlsanity.com/paper/2309.15599/) (2023)
- [Learning of Sea Surface Height Interpolation from Multi-variate Simulated Satellite Observations](https://mlsanity.com/paper/2310.07626/) (2023)
- [Tensor-Var: Efficient Four-Dimensional Variational Data Assimilation](https://mlsanity.com/paper/2501.13312/) (2025)
- [Benchmarking AI-based data assimilation to advance data-driven global weather forecasting](https://mlsanity.com/paper/2408.11438/) (2024)
- [Scale-aware neural calibration for wide swath altimetry observations](https://mlsanity.com/paper/2302.04497/) (2023)
- [Simulation-informed deep learning for enhanced SWOT observations of fine-scale ocean dynamics](https://mlsanity.com/paper/2503.21303/) (2025)
- [Neural ocean forecasting from sparse satellite-derived observations: a case-study for SSH dynamics and altimetry data](https://mlsanity.com/paper/2512.22152/) (2025)
- [Impact of geophysical fields on Deep Learning-based Lagrangian drift simulations](https://mlsanity.com/paper/2604.03292/) (2026)
- [Drift Field Net: Learning Ocean Lagrangian advection fields from in-situ and satellite observations](https://mlsanity.com/paper/2609.16288/) (2026)

## Abstract (arXiv)

Due to the irregular space-time sampling of sea surface observations, the reconstruction of sea surface dynamics is a challenging inverse problem. While satellite altimetry provides a direct observation of the sea surface height (SSH), which relates to the divergence-free component of sea surface currents, the associated sampling pattern prevents from retrieving fine-scale sea surface dynamics, typically below a 10-day time scale. By contrast, other satellite sensors provide higher-resolution observations of sea surface tracers such as sea surface temperature (SST). Multimodal inversion schemes then arise as an appealing strategy. Though theoretical evidence supports the existence of an explicit relationship between sea surface temperature and sea surface dynamics under specific dynamical regimes, the generalization to the variety of upper ocean dynamical regimes is complex. Here, we investigate this issue from a physics-informed learning perspective. We introduce a trainable multimodal inversion scheme for the reconstruction of sea surface dynamics from multi-source satellite-derived observations. The proposed 4DVarNet schemes combine a variational formulation involving trainable observation and a priori terms with a trainable gradient-based solver. We report an application to the reconstruction of the divergence-free component of sea surface dynamics from satellite-derived SSH and SST data. An observing system simulation experiment for a Gulf Stream region supports the relevance of our approach compared with state-of-the-art schemes. We report relative improvement greater than 50% compared with the operational altimetry product in terms of root mean square error and resolved space-time scales. We discuss further the application and extension of the proposed approach for the reconstruction and forecasting of geophysical dynamics from irregularly-sampled satellite observations.