Multi-scale sea level prediction in dynamic coastal environments by harmonizing spectral analysis with deep learning

The present study aimed to develop a hybrid Spectral-Convolutional neural network (Spectral-CNN) model for sea water level prediction in 1–90-day horizons. Three spectral identification methods, including the classic periodogram, the continuous wavelet transform, and Whittle’s autoregressive periodicity methods, were employed for identifying the spectral lags of the studied time series. Three governing cycles, namely, semi-monthly (20 days), weekly (6.6–9.9 days), and annual (354 days) were identified accordingly. The results revealed that the model performed promisingly, with a maximum global RMSE of 0.0060 m and MAE of 0.0045 m, and seasonal maxima of 0.0128 m and 0.0085 m, respectively. The minimum R² was 0.9617 over the seasonal tests and 0.9928 for the global test. A comparison was conducted between the hybrid model and traditional ARIMA and Akaike information-CNN (AIC CNN) models, which revealed the superiority of the developed hybrid model. Furthermore, the seasonal analysis revealed that the lowest error values corresponded to summer (RMSE: 0.0074 m; R²: 0.9913), while the higher values belonged to winter. The uncertainty analysis indicated narrower prediction intervals in annual data (0.0171 m at the 60-day horizon), and relatively stable variance, with annual variance ranging from 0.0000235 m² at 1-day to 0.0000252 m² at 60-day.These results, which were obtained for a single coastal station using HYCOM reanalysis-based sea level data, demonstrated the potential of the proposed Spectral-CNN framework for multi-scale coastal water level prediction.