Global directional wave spectra prediction based on energy-conserving deep learning

Directional wave spectra (DWS) provide a comprehensive description of ocean wave energy across frequencies and directions, serving as the foundation of numerical wave modeling. This work promotes the current artificial intelligence forecasting of ocean waves from integrated parameters such as significant wave height (SWH) to DWS, which captures the comprehensive physical state of waves, enabling the derivation of numerous important dynamical variables such as Stokes drift. However, the massive data volume of DWS presents a significant barrier to direct spatiotemporal prediction using deep learning. To overcome this barrier, we present WaveSpecNet, an energy-conserving deep learning framework for global spatiotemporal DWS prediction. WaveSpecNet consists of a compression-reconstruction module and a prediction module. It first compresses the two-dimensional DWS into a low-dimensional latent space, known as the latent features, then predicts these latent features instead of the original DWS. The predicted DWS is then restored from the predicted latent features. WaveSpecNet achieves comparable accuracy to state-of-the-art numerical wave models when validated against buoy observations, while takeing only 15 s to generate a 5-day global DWS forecast at a 1° × 1° resolution with 6-h intervals. Furthermore, WaveSpecNet also demonstrated the capability to maintain stable, non-accumulating errors during 90-day iterative forecasts driven by wind, indicating its promising potential for coupling with the Earth System Models to reduce computational costs.