Ocean density is a key physical variable in marine science. Integrating satellite remote sensing data with in situ observations enables comprehensive three-dimensional ocean density reconstruction and prediction. However, this task remains challenging for traditional interpolation techniques. To address this issue, we propose a reduced-order model that combines Hankel dynamic mode decomposition (HDMD) with a bidirectional long short-term memory (BiLSTM) network, thereby integrating dynamical systems theory with deep learning. HDMD captures the vertical evolutionary patterns of ocean density anomalies, enabling physically consistent interpolation and extrapolation across unobserved depths. The BiLSTM then integrates sea surface observations with HDMD-reconstructed subsurface profiles to achieve continuous three-dimensional reconstruction and temporal forecasting. Furthermore, the reduced-order formulation substantially improves computational efficiency. The proposed method is evaluated using simulation data from the Max Planck Institute Ocean Model, and results demonstrate that it achieves high estimation accuracy and consistently outperforms baseline models such as multilayer perceptrons. Moreover, the method preserves physical plausibility in vertical structure predictions by combining dynamical modeling with deep learning, offering a robust and interpretable framework for ocean state reconstruction.
Zhang et al. (Thu,) studied this question.