A Developed VMD-DMD Algorithm with Machine Learning Models for Improving Sea Level Predictions: A Case Study of the Mediterranean Coastlines

Accurate prediction of sea level change in the Mediterranean Sea is essential for coastal risk management; however, the nonstationary behavior of sea level makes this difficult. This study presents a hybrid framework that integrates variational mode decomposition (VMD) and dynamic mode decomposition (DMD) with long short-term memory (LSTM) and extreme gradient boosting (XGBoost) to forecast monthly sea level anomaly (SLA). Thirty years of records from sixteen Mediterranean tide gauge stations (1993–2022) were used. The proposed VMD-DMD algorithm decomposed SLA signals into distinct multi-scale temporal components. It improved reconstructed signal accuracy compared to VMD-only decomposition, reducing average RMSE from 24.22 to 7.38 mm. For prediction, we compared our models against multiple baselines: the mean annual cycle with anomaly persistence (MAC_AP) and three-layer MLP. The proposed VMD-DMD-LSTM achieved the best overall performance (mean R2 = 0.92, RMSE = 20.37 mm, and MAE = 15.31 mm) with an 18% error reduction compared to three-layer MLP. VMD-DMD-XGBoost achieved RMSE = 24.90 mm and R2 = 0.88. Furthermore, in a direct comparison on identical data, our VMD-DMD-LSTM outperformed the benchmark VMD-EEMD-LSTM model, achieving about 12% lower errors. Thus, the proposed framework effectively isolates multi-scale dynamics and reduces residual noise, providing more reliable sea level forecasts for coastal operational planning.