A Variationally Constrained Attention Model for Sea Surface Height Reconstruction With Multisource Observations

Abstract

Sea surface height (SSH) is a key variable for characterizing ocean dynamics, yet its high-resolution reconstruction remains challenging due to sparse satellite observations and the limited ability of conventional methods to represent multiscale nonlinear processes. This study proposes a physics-constrained SSH reconstruction model, 4-D variational (4DVar) Attention, built upon a 4DVar framework. The model approximates gradient-based updates using neural networks and jointly assimilates satellite altimeter and in situ pressure-recording inverted echo sounder (PIES) observations, while combining a dual-scale U-Net and a Vision Transformer to model cross-scale spatiotemporal dependencies. Experiments in the Gulf of Mexico demonstrate that 4DVarAttention outperforms several representative methods in terms of reconstruction accuracy and spatiotemporal continuity, and further confirm that incorporating PIES observations significantly enhances the resolution of the reconstructed SSH fields, providing a foundation for extending physics-constrained deep learning-based data assimilation frameworks to broader oceanic regions.