A Physics-Informed Neural Network for Sea Surface Height Prediction in the South China Sea

Sea surface height (SSH) derived from satellite altimetry is widely used in oceanographic research and marine environmental monitoring. However, numerical ocean models for SSH forecasting are computationally expensive, while purely data-driven methods often lack physical consistency. To address these limitations, we propose a Geostrophic-Constrained Neural Network (GCNN) for short-term SSH prediction in the South China Sea (SCS), utilizing satellite data. Based on the SimVPv2 architecture, the model incorporates several strategies to enhance both physical consistency and forecast performance: (1) using mask information as input to reduce artifacts caused by land contamination in oceanographic data; (2) augmenting the loss function with a physics-informed term that enforces geostrophic balance; and (3) applying latitude-based weighting to this constraint to account for the breakdown of geostrophic approximation near the equator. On the test dataset, the GCNN achieves a root mean squared error (RMSE) of 1.73 cm, representing an 11% improvement over the unconstrained baseline model. Furthermore, the model is computationally efficient, requiring only about 3 hours for training and 3.7 milliseconds per inference. The GCNN not only improves predictive accuracy but also enhances interpretability by adhering to ocean dynamical principles, offering a promising approach for the modeling and prediction of SSH.