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<p>Rainfall accuracy is a critical aspect of climate modeling, agricultural design, disaster management, and urban water resource allocation. However, successful forecasting is a problematic issue due to the non-linear, non-stationary, and complex nature of rainfall time series. Classical statistical algorithms do not identify long-term correlations and time variance, whereas the individual machine learning (ML) and deep learning (DL) algorithms have certain weaknesses, including noise, vanishing gradient, and hyperparameter optimization. To overcome such weaknesses, this study introduces a hybrid architecture that integrates both Variational Mode Decomposition (VMD) and Particle Swarm Optimization (PSO) together with both ML and DL models in a systematic way. VMD breaks down raw rainfall signals into intrinsic mode functions (IMFs), improving the quality of temporal features by isolating short-term variations, seasonal cycles, and long-term trends and reducing noise. PSO optimizes the hyperparameters, including thresholds, learning rate, dropout, sequence window, and balances underfitting and overfitting. The model is tested using rainfall data of 34 cities of five Pakistani provinces that are varied in terms of climatic regimes, including arid deserts and highlands with monsoon. In experiments, a 3-fold TimeSeriesSplit with 3 random seeds (41, 42, 43) was used, resulting in 95% confidence intervals within folds and seeds to guarantee reproducibility and strength. SMOTE and adaptive class weights were used to deal with the issue of class balancing. Findings sustain that the PSO-optimized Gradient Boosting (ML baseline) obtained the highest classical performance (PR-AUC = 0.9954, F1 = 0.9659), whereas among the DL models, the VMD + PSO-enhanced GRU had the best overall outcome (PR-AUC = 0.9846 [0.9806–0.9886], F1 = 0.9321 [0.9215–0.9428]) and achieved statistically significant superiority over its BASE and PSO-only counterparts (Wilcoxon <i>p</i> = 0.001953). In LSTM, BiLSTM, and GRU, VMD + PSO hybrids constantly enhanced the balance between precision and recall and sensitivity to minority rainy-day classes. The proposed VMD + PSO hybrid framework has greater generalizability, strength, and reproducibility, which can enhance the state of rainfall forecasting today by providing a data-driven, scalable tool that can be tailored to different climatic zones to support early warning systems, agricultural planning, and urban flood control.</p>

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A VMD–PSO hybrid framework with machine and deep learning for Aaccurate spatial–temporal daily rainfall occurrence prediction in Pakistan’s diverse climatic regions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月13日

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  • Hira Farman,
  • Muhammad Arif Hussain,
  • Sarang Shaikh,
  • Saif Hassan

摘要

Rainfall accuracy is a critical aspect of climate modeling, agricultural design, disaster management, and urban water resource allocation. However, successful forecasting is a problematic issue due to the non-linear, non-stationary, and complex nature of rainfall time series. Classical statistical algorithms do not identify long-term correlations and time variance, whereas the individual machine learning (ML) and deep learning (DL) algorithms have certain weaknesses, including noise, vanishing gradient, and hyperparameter optimization. To overcome such weaknesses, this study introduces a hybrid architecture that integrates both Variational Mode Decomposition (VMD) and Particle Swarm Optimization (PSO) together with both ML and DL models in a systematic way. VMD breaks down raw rainfall signals into intrinsic mode functions (IMFs), improving the quality of temporal features by isolating short-term variations, seasonal cycles, and long-term trends and reducing noise. PSO optimizes the hyperparameters, including thresholds, learning rate, dropout, sequence window, and balances underfitting and overfitting. The model is tested using rainfall data of 34 cities of five Pakistani provinces that are varied in terms of climatic regimes, including arid deserts and highlands with monsoon. In experiments, a 3-fold TimeSeriesSplit with 3 random seeds (41, 42, 43) was used, resulting in 95% confidence intervals within folds and seeds to guarantee reproducibility and strength. SMOTE and adaptive class weights were used to deal with the issue of class balancing. Findings sustain that the PSO-optimized Gradient Boosting (ML baseline) obtained the highest classical performance (PR-AUC = 0.9954, F1 = 0.9659), whereas among the DL models, the VMD + PSO-enhanced GRU had the best overall outcome (PR-AUC = 0.9846 [0.9806–0.9886], F1 = 0.9321 [0.9215–0.9428]) and achieved statistically significant superiority over its BASE and PSO-only counterparts (Wilcoxon p = 0.001953). In LSTM, BiLSTM, and GRU, VMD + PSO hybrids constantly enhanced the balance between precision and recall and sensitivity to minority rainy-day classes. The proposed VMD + PSO hybrid framework has greater generalizability, strength, and reproducibility, which can enhance the state of rainfall forecasting today by providing a data-driven, scalable tool that can be tailored to different climatic zones to support early warning systems, agricultural planning, and urban flood control.