Eigen-ensemble-transformer model: An exceptionally accurate approach to spatiotemporal sea water level prediction

Accurate sea water level (SWL) prediction is essential for various applications, including wave energy potential assessment, marine operations optimization, ocean engineering advancements, and coastal management strategies. Traditional forecasting models often face challenges due to the complex, irregular, and dynamic nature of SWL variations. For the first time this study introduces an innovative predictive modeling approach that combines eigen time series analysis with a stacking ensemble framework to enhance spatiotemporal SWL forecasting across coastal monitoring networks. Unlike conventional methods that rely on multiple inputs, the proposed novel ensemble model utilizes a single eigen time series, significantly improving computational efficiency while maintaining high predictive accuracy. The model is validated using daily SWL data from 16 coastal monitoring stations along the Turkish coastline, demonstrating exceptional performance based on established performance evaluation criteria. Furthermore, the Eigen-Ensemble model is benchmarked against the Eigen-Transformer model, a state-of-the-art deep learning approach, and is found to be significantly superior in predictive accuracy, computational efficiency, and robustness. These results confirm the model's effectiveness in capturing spatiotemporal SWL variations with computational efficiency, offering a scalable, cost-effective forecasting framework for coastal monitoring, engineering, oceanography, and environmental management.