Precipitation prediction based on CEEMDAN–VMD–BILSTM combined quadratic decomposition model

Accurate prediction of monthly precipitation is crucial for effective regional water resources management and utilization. However, precipitation series are influenced by multiple factors, exhibiting significant ambiguity, chance, and uncertainty. In this research, we propose a combined model that integrates adaptive noise-complete ensemble empirical mode decomposition (CEEMDAN), variational modal decomposition method (VMD), and bidirectional long- and short-term memory (BILSTM) to enhance precipitation prediction. We apply this model to forecast precipitation in Fuzhou City and compare its performance with existing models, including CEEMD–long and short-term memory (LSTM), CEEMD–BILSTM, and CEEMDAN–BILSTM. Our findings demonstrate that the combined CEEMDAN–VMD–BILSTM quadratic decomposition model yields more accurate predictions and captures the real variation in precipitation series with greater fidelity. The model achieves an average relative error of 1.69%, at a lower level, and an average absolute error of 1.32 m, with a Nash–Sutcliffe efficiency coefficient of 0.92. Overall, the proposed quadratic decomposition model exhibits excellent applicability, stability, and superior predictive capabilities in monthly precipitation forecasting.