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<p>Rainfall uncertainty, influenced by multiple meteorological factors, poses significant challenges for accurate forecasting. Traditional prediction methods often fail to capture the nonlinear and nonstationary characteristics of rainfall time series. To address this issue, this study proposes a hybrid rainfall prediction framework integrating crested porcupine optimization–based variational mode decomposition (CPO-VMD), minimum information entropy (MIE), and a convolutional neural network–gated recurrent unit (CNN–GRU) model. The maximum information coefficient (MIC) is employed for feature selection to reduce redundancy and improve input relevance. CPO is used to optimize VMD parameters, enabling effective decomposition of rainfall series into intrinsic mode functions, which are subsequently predicted and reconstructed using the CNN–GRU model. The proposed method is evaluated using monthly and weekly rainfall data from two meteorological stations in China with distinct climatic characteristics. Experimental results demonstrate that the proposed model consistently outperforms 17 benchmark models in terms of prediction accuracy and robustness. Statistical significance tests and error distribution analysis further confirm the stability of the proposed framework, while computational efficiency analysis indicates millisecond-level inference latency, highlighting its practical applicability.</p>

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Hybrid crested porcupine optimizer decomposition method and deep neural network to predict long-term rainfall

  • 期刊论文

  • 发表日期：

    2026年3月18日

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  • Man-Hong Fan,
  • Xiao-Ying Ma,
  • Shi-Qi Xu,
  • Rui-Lin Fu

摘要

Rainfall uncertainty, influenced by multiple meteorological factors, poses significant challenges for accurate forecasting. Traditional prediction methods often fail to capture the nonlinear and nonstationary characteristics of rainfall time series. To address this issue, this study proposes a hybrid rainfall prediction framework integrating crested porcupine optimization–based variational mode decomposition (CPO-VMD), minimum information entropy (MIE), and a convolutional neural network–gated recurrent unit (CNN–GRU) model. The maximum information coefficient (MIC) is employed for feature selection to reduce redundancy and improve input relevance. CPO is used to optimize VMD parameters, enabling effective decomposition of rainfall series into intrinsic mode functions, which are subsequently predicted and reconstructed using the CNN–GRU model. The proposed method is evaluated using monthly and weekly rainfall data from two meteorological stations in China with distinct climatic characteristics. Experimental results demonstrate that the proposed model consistently outperforms 17 benchmark models in terms of prediction accuracy and robustness. Statistical significance tests and error distribution analysis further confirm the stability of the proposed framework, while computational efficiency analysis indicates millisecond-level inference latency, highlighting its practical applicability.