Accurate significant wave height (SWH) prediction is essential for the development and utilization of wave energy. Deep learning methods such as recurrent and convolutional neural networks have achieved good results in SWH forecasting. However, these methods do not adapt well to dynamic seasonal variations in wave data. In this study, we propose a novel method—the spatiotemporal dynamic graph (STDG) neural network. This method predicts the SWH of multiple nodes based on dynamic graph modeling and multi-characteristic fusion. First, considering the dynamic seasonal variations in the wave direction over time, the network models wave dynamic spatial dependencies from long- and short-term pattern perspectives. Second, to correlate multiple characteristics with SWH, the network introduces a cross-characteristic transformer to effectively fuse multiple characteristics. Finally, we conducted experiments on two datasets from the South China Sea and East China Sea to validate the proposed method and compared it with five prediction methods in the three categories. The experimental results show that the proposed method achieves the best performance at all predictive scales and has greater advantages for extreme value prediction. Furthermore, an analysis of the dynamic graph shows that the proposed method captures the seasonal variation mechanism of the waves.
Figure 1. Mean wave direction in the South China Sea for the 2020 monthly average; the data comes from the ERA5 monthly averaged data on single levels. The color bar represents monthly average significant wave heights (SWHs), and each arrow represents the mean wave direction at the longitude and latitude coordinates in the data.
Figure 2. Detailed STDG structure. a. Main STDG architecture, where the primary and three auxiliary modules run in parallel. b. An example of the temporal convolution module, which uses two dilated temporal convolutions with different dilation rates to capture multi-scale temporal features. c. A graph convolution module with depth $ D=2 $, which contains two graph convolution layers that process the graph information of long- and short-term patterns, respectively. d. The detailed structure of the SDGC module, which fuses the dynamic input $ {X}^{\mathrm{d}\mathrm{r}\mathrm{i}\mathrm{v}\mathrm{e}} $ and the node embeddings of long-term patterns $ {E}_{1},{E}_{2} $, to obtain the final dynamic node embeddings $ D{E}_{1},D{E}_{2} $.
Figure 4. Cross-characteristic attention and transformer.
Figure 5. The sea area range of the two datasets.
Figure 6. The average MAE, RMSE, and R-square of the prediction methods in the South China Sea.
Figure 7. Predicted values, true values, and RMSE for three methods.
Figure 8. Coefficient of determination of three methods.
Figure 9. Significant wave height prediction effect of single node.
Figure 10. Predicted value, true value, and RMSE of STDG in different seasons and levels in the South China Sea.
Figure 11. Predicted value, true value, and RMSE of STDG in different seasons and levels in the East China Sea.
Figure 12. Distribution of the number of large wave classes at different nodes in the test data.
Figure 13. The MAE, RMSE, and R-square of STDG model for large wave prediction in the South China Sea (SCS) and East China Sea (ECS) test data.
Figure 14. presents a visual representation of the adjacency matrix, which was derived from the data collected in each month of 2022 on the South China Sea test set. The adjacency matrix is employed to describe the direction and intensity of information propagation among the 91 nodes in the South China Sea. Each value in the adjacency matrix represents the propagation of a specific piece of information from a node on the horizontal axis to a node on the vertical axis. The color of the value indicates the extent of wave information propagation between the two nodes. The darker the color, the greater the intensity of information spread.
Figure 15. Geographic visualization of the adjacency matrix for each month of 2022 on the South China Sea test set. The arrows represent the direction of wave propagation between nodes. The darker the color of the curve, the more information is transmitted between nodes.
Figure 16. Geographic visualization of the adjacency matrix for each month of 2022 on the East China Sea test set. The arrows represent the direction of wave propagation between nodes. The darker the color of the curve, the more information is transmitted between nodes.
Figure 17. Comparison of cosine similarity matrix results for each month in different years.
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