A Deep Learning–Based Approach for Empirical Modeling of Single-Point Wave Spectra in Open Oceans

Abstract Directional wave spectra are of importance for numerous practical applications such as seafaring and ocean engineering. The wave spectral densities at a certain point in the open ocean are significantly correlated to the local wind field and historical remote wind field. This feature can be used to predict the wave spectrum at that point using the wind field. In this study, a convolutional neural network (CNN) model was established to estimate wave spectra at a target point using the wind field from the ERA5 dataset. A geospatial range where the wind could impact the target point was selected, and then the historical wind field data within the range were analyzed to extract the nonlinear quantitative relationships between wind fields and wave spectra. For the spectral densities at a given direction, the wind data along the direction where waves come from were used as the input of the CNN. The model was trained to minimize the mean square error between the CNN-predicted and ERA5 reanalysis spectral density. The data structure of the wind input is reorganized into a polar grid centered on the target point to make the model applicable to different open-ocean locations worldwide. The results show that the model can predict well the wave spectrum shapes and integral wave parameters. The model allows for the prediction of single-point wave spectra in the open ocean with low computational cost and can be helpful for the study of spectral wave climate. Significance Statement The directional wave spectra (DWS) describe the distribution of wave energy among different frequencies and directions. They are useful for many marine practical applications. Usually, DWS are modeled using numerical wave models (NWMs) based on wave action balance differential equations. Although contemporary NWMs perform well after years of development, their computational costs are relatively high. The fast-developed artificial intelligence (AI) might provide an alternative solution to this task. In this study, convolutional neural networks are used to model the DWS at some selected points in the open ocean. By “learning” from NWM data, AI can effectively simulate single-point DWS in open oceans with low computational cost, which can serve as a faster data-driven surrogate model in related applications.