Improving long-term wave forecasting through seasonal adjustment based on STL and CNN-GRU network

Most numerical models used to forecast wave parameters are time-consuming and computationally expensive. Currently, advanced machine learning techniques, such as artificial neural networks (ANN), provide a better alternative as they are substantially faster, more cost-efficient and more effective in handling non-linearity. In recent years, many ANN models have been developed to achieve satisfactory wave forecasting results. However, most of the research is limited to wave height forecasting and rarely any method that highlights the issue of seasonal fluctuation, which exists in time series data, is proposed. Keeping this in mind, this study proposes a hybrid convolutional neural network-gated recurrent network (CNN-GRU) model with a combination of seasonal adjustment based on seasonal-trend decomposition loess (STL) for wave parameters forecasting, including wave height and period. To evaluate model performance, error criteria methods, such as index of agreement (d), correlation coefficient (R) and root mean square error, were used. The results indicate that the proposed method outperformed every forecast horizon when compared with the model without seasonal adjustment with a degree of improvement ranging between 4 to 16 for wave height and 8 to 24 for wave period. Furthermore, the add-and-repeat prediction method is proposed in the study, where, after each prediction, the output of the model is added to the training set to produce a further prediction. The results from the proposed method indicate that predicted values follow the general trend to a great extent and there is a very small loss of accuracy between the first and final predictions with the R value reducing from 0.73 to 0.69 for wave height, and 0.63 to 0.61 for wave period.