Precipitation nowcasting, a critical spatiotemporal sequence prediction task, has significant applications in meteorological domains such as agriculture and transportation. While radar echo extrapolation based on deep learning is a commonly used nowcasting method, existing methods have limitations in capturing the complex spatiotemporal patterns of radar echoes. The performance of these methods degrades significantly over time, making it difficult to accurately predict the spatiotemporal evolution of precipitation. This study proposes GloCal-Net, a model that integrates global modes and local variations. The model is based on a U-Net architecture with hybrid Mamba-Transformer experts, designed to enhance the ability to capture complex patterns in radar echo sequences by optimizing the feature extraction mechanism. To validate the proposed model, comparative and ablation experiments are conducted on a real radar dataset from Jiujiang. Compared with mainstream deep learning models, in the 2-hour extrapolation task, the proposed model achieves a comparable Heidke skill score and a 4.19% higher critical success index, reaching 0.36 and 0.29 respectively. The learned perceptual image patch similarity decreases by 3.70%, reaching 0.31. The structural similarity increases by 2.07%, reaching 72.37%. These experimental results show that GloCal-Net improves several key performance indicators and simultaneously verifies the effectiveness of each component.