Investigation of Physics-Informed Methods for Improving Sea Surface Height Prediction Based on Neural Networks

Sea surface height (SSH) derived from satellite altimetry is essential for oceanographic research and marine monitoring. To improve SSH prediction accuracy, we propose a set of physics-informed methods based on neural networks (NNs). The main strategies include: (1) integrating a geostrophic constraint (GC) into the loss function; (2) incorporating land mask information (MI) to mitigate artifacts introduced by the land points in ocean data.

Utilizing altimeter satellite gridded absolute dynamic topography data, we evaluate three mainstream spatiotemporal predictive NNs—SimVPv2 (SV), PredRNNv2 (PR), and PredFormer (PF)—each exhibiting distinct inductive biases inherent to their architectures, to assess their performance under the proposed strategies. The results indicate that both strategies can significantly improve SSH prediction, though their effects vary across architectures. While SV shows limited improvement from MI, PR benefits the most, which can likely be attributed to its gating mechanism and recurrent architecture. In contrast, GC enhances the performance of SV more effectively than that of PR. However, both strategies degrade the performance of PF, a Vision Transformer (ViT)-based model that differs fundamentally from SV and PR. To our knowledge, this study is the first to identify land-induced artifacts in spatiotemporal predictive NNs and to implement a land mask input strategy to mitigate their impact on ocean forecasting.

Building upon these findings, we further explored the potential of multivariable inputs. Contrary to expectations, our experiments of concatenating wind speed with SSH as inputs reveal that directly combining heterogeneous oceanic variables is suboptimal. This finding highlights a broader multimodal integration problem in applying NNs to oceanography, which remains an open challenge.