A coupled rainfall prediction model based on Hybrid CNN-Differential Transformer

Accurate rainfall prediction is crucial for effective water resource management, particularly in arid regions with sparse weather stations. While rainfall forecasting models have achieved high accuracy in wet and rainy regions, the prediction accuracy remains limited in arid areas, especially where station data is sparse. This study proposed a new coupled rainfall prediction model based on a Hybrid CNN-Differential Transformer architecture, which integrates the signal decomposition technique CEEMDAN with deep learning models, including CNN and Differential Transformer. The Differential Transformer leverages its unique attention mechanism to enhance temporal modeling, addressing challenges in capturing long-term dependencies in sparse data scenarios. CEEMDAN is utilized to decompose raw precipitation data into Intrinsic Mode Functions (IMFs), while a CNN module assists in spatial feature extraction. The proposed model is evaluated using weekly precipitation data from six stations in Ningxia Province, a typical arid region with sparse weather stations in China, serving as a representative example for similar regions globally. Notably, the Hybrid CNN-Differential Transformer model demonstrates a unique shift in performance, with relatively higher RMSE and MAE during training but superior accuracy in the evaluation phase, reducing MAE by 3.88%–45.13%, RMSE by 3.37%–34.36%, and improving NSE by 4.71%–31.36% compared to traditional hybrid CNN models. This shift highlights the model's robustness and ability to generalize effectively to unseen data, making it a reliable solution for real-world precipitation forecasting. Bayesian optimization further refines hyperparameters, ensuring optimal model performance. This study highlights the potential of the Differential Transformer in capturing complex spatiotemporal dependencies and provides a robust and generalizable solution for precipitation forecasting, particularly in arid regions with sparse station coverage. Its global applicability offers valuable insights for addressing similar hydrological challenges in drought-prone and resource-scarce environments worldwide.