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Accurate precipitation nowcasting over extended horizons (0-3 hours) is essential for disaster mitigation and operational decision-making, yet remains a critical challenge in the field. Existing deterministic approaches are predominantly constrained to shorter prediction windows (0-2 hours), exhibiting severe performance degradation beyond 90 minutes owing to their inherent difficulty in capturing long-range spatiotemporal dependencies from radar-derived observations. To address these fundamental limitations, we propose MambaRain, a novel multi-scale encoder-decoder architecture that synergistically integrates Mamba's linear-complexity long-range temporal modeling with self-attention mechanisms for explicit spatial correlation capture. The core innovation lies in a hybrid design paradigm wherein Mamba blocks leverage selective state space mechanisms to model global temporal dynamics across extended sequences with computational efficiency, while self-attention modules explicitly characterize spatial correlations within precipitation fields - a capability inherently absent in Mamba's sequential processing paradigm. This complementary synergy enables comprehensive spatiotemporal representation learning, effectively extending the viable forecasting horizon to 2-3 hours with substantial accuracy improvements. Furthermore, we introduce a spectral loss formulation to mitigate blurring artifacts characteristic of chaotic precipitation systems, thereby preserving fine-scale motion details critical for nowcasting accuracy. Experimental validation demonstrates that MambaRain substantially outperforms existing deterministic methodologies in 0-3 hour nowcasting tasks, with particularly pronounced performance gains in the challenging 2-3 hour prediction range.