Extreme Weather Nowcasting With Second-Order State Spaces

Nowcasting weather extremes poses significant challenges due to the complex evolution of their dynamical systems. State space models (SSMs) excel in sequence modeling, offering a promising avenue to address this issue. However, existing SSMs typically rely on first-order ordinary differential equations (ODEs), limiting their capacity to capture higher order dynamics. To eliminate these limitations, we propose a second-order state space (S3) architecture, where the weather motion is decomposed as position and momentum in latent spaces to find multiorder behaviors. For sequential weather observations, we provide a recurrent counterpart of S3, which can be further parallelized through fast Fourier transform (FFT) for computational efficiency. Building on these S3 blocks, we develop a unified framework, S3Cast, for spatiotemporal sequence extrapolation. Empirical results demonstrate that S3Cast matches or exceeds the performance of state-of-the-art methods in the prediction of weather extremes, such as lightning, hail, and heavy precipitation.