A novel multistep point and interval prediction framework for accurate short-term wave height estimation incorporating the TCN-GRU-Attention model and error distribution analysis

Accurate short-term wave height prediction is essential for wave power and offshore activities. This study proposes an innovative multistep point and interval prediction framework integrating a temporal convolutional network (TCN), gated recurrent unit (GRU), attention mechanism, and forecasting error distribution. First, datasets are preprocessed, and feature selection is performed to remove redundant features. Second, the TCN-GRU-Attention (TGA) model is applied to predict wave height. The input data for this model consists of multivariate features positively correlated with wave height. Finally, the wave height prediction interval is generated by using prediction error distribution models to estimate the probability density distribution of the prediction errors. Experimental results show that the TGA model achieves higher accuracy, demonstrated by a higher coefficient of determination and lower root mean square error than recurrent neural network (RNN), GRU, TCN, RNN-GRU, and TCN-GRU models. Furthermore, when prediction intervals are constructed, the coverage width-based criterion highlights the extreme value distribution as a superior option among interval forecasting methods. This choice provides a higher level of reliability in terms of the accuracy of the prediction intervals. Notably, interval prediction offers practical advantages over point prediction by quantifying forecast uncertainty, supporting risk mitigation and more informed decision-making in offshore operations.