Global Station Weather Forecasting (GSWF), a prominent meteorological research area, is pivotal in providing timely localized weather predictions. Despite the progress existing models have made in the overall accuracy of the GSWF, executing high-precision extreme event prediction still presents a substantial challenge. The recent emergence of state-space models, with their ability to efficiently capture continuous-time dynamics and latent states, offer potential solutions. However, early investigations indicated that Mamba underperforms in the context of GSWF, suggesting further adaptation and optimization. To tackle this problem, in this paper, we introduce Weather State-space Model (WSSM), a novel Mamba-based approach tailored for GSWF. Geographical knowledge is integrated in addition to the widely-used positional encoding to represent the absolute special-temporal position. The multi-scale time-frequency features are synthesized from coarse to fine to model the seasonal to extreme weather dynamic. Our method effectively improves the overall prediction accuracy and addresses the challenge of forecasting extreme weather events. The state-of-the-art results obtained on the Weather-5K subset underscore the efficacy of the WSSM