Hybrid Variational Modal Decomposition-Extreme Learning Machine-Adaptive Boosting Model for Monthly Runoff Prediction

Monthly runoff prediction plays a crucial role in water resource management, flood prevention, and disaster reduction. This study proposed a novel hybrid model for predicting monthly runoff by combining variational modal decomposition (VMD) with an extreme learning machine (ELM) and adaptive boosting (AdaBoost) algorithm. First, VMD is used to decompose the monthly runoff data, simplifying it and addressing its non-stationarity by extracting subsequences at different frequency scales. Next, the ELM model is applied to each subsequence within the AdaBoost algorithm to enhance prediction accuracy and stability. To contextualise its performance, the proposed model was systematically compared with four representative comparable models (VMD-ELM, ELM-AdaBoost, LSTM, and VMD-TPE-LSTM) using the same training/validation datasets (80% for training and 20% for validation) and evaluation metrics (root mean square error, RMSE; mean absolute percentage error, MAPE). The results indicate that the VMD-ELM-AdaBoost model outperforms all comparative models: at Yanshan Station, it achieves an RMSE of 2.521 mm and MAPE of 8.56% (34.8–45.1% lower RMSE than VMD-ELM, ELM-AdaBoost, and LSTM); at Baiguishan Station, it yields an RMSE of 2.906 mm and MAPE of 9.02% (22.3–42.6% lower RMSE than VMD-TPE-LSTM and other alternatives). This study demonstrates that the VMD-ELM-AdaBoost model balances accuracy, efficiency, and data adaptability, providing a practical tool for monthly runoff prediction in data-limited basins.