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Accurate precipitation nowcasting is crucial for applications such as flood prediction, disaster management, agriculture optimization, and transportation management. While many studies have approached this task using sequence-to-sequence models, most focus on single regions, ignoring correlations between disjoint areas. We reformulate precipitation nowcasting as a spatiotemporal graph sequence problem. Specifically, we propose Graph Dual-stream Convolutional Attention Fusion, a novel extension of the graph attention network. Our model's dual-stream design employs distinct attention mechanisms for spatial and temporal interactions, capturing their unique dynamics. A gated fusion module integrates both streams, leveraging spatial and temporal information for improved predictive accuracy. Additionally, our framework enhances graph attention by directly processing three-dimensional tensors within graph nodes, removing the need for reshaping. This capability enables handling complex, high-dimensional data and exploiting higher-order correlations between data dimensions. Depthwise-separable convolutions are also incorporated to refine local feature extraction and efficiently manage high-dimensional inputs. We evaluate our model using seven years of precipitation data from Copernicus Climate Change Services, covering Europe and neighboring regions. Experimental results demonstrate superior performance of our approach compared to other models. Moreover, visualizations of seasonal spatial and temporal attention scores provide insights into the most significant connections between regions and time steps.