![]() In recent years, the rapid development of artificial intelligence and modern statistical methods has propelled their application in precipitation prediction. Scholars worldwide have made substantial efforts to enhance prediction accuracy and optimize prediction models, yielding fruitful results. The study of monthly precipitation is a complex problem involving multiple levels and orders ( Radhakrishnan & Dinesh 2006). Monthly precipitation series are influenced by diverse factors, such as the atmosphere, region, and environment, exhibiting substantial ambiguity, contingency, and uncertainty. Precipitation anomalies often result in destructive floods, highlighting the importance of precise precipitation prediction. Precipitation, a key source of recharge for regional water resources, significantly impacts various aspects of regional life and production. Accurate long-term precipitation prediction serves as a critical indicator for efficient water resource utilization. ![]() The occurrence of water and drought extremes has become increasingly frequent due to global climate change, leading to a severe water resources situation ( Mohammadi et al. Overall, the proposed quadratic decomposition model exhibits excellent applicability, stability, and superior predictive capabilities in monthly precipitation forecasting. 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. 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. 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. ![]() 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. However, precipitation series are influenced by multiple factors, exhibiting significant ambiguity, chance, and uncertainty. Accurate prediction of monthly precipitation is crucial for effective regional water resources management and utilization.
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