QFSNet: A Quaternion Fourier Spectral Network for Deterministic Precipitation Nowcasting

Precipitation nowcasting requires capturing complex, multi-scale spatiotemporal dynamics under strict latency constraints. However, existing deep learning paradigms face two fundamental bottlenecks: standard spectral representations fail to explicitly disentangle scale and orientation, leading to trajectory underfitting, and a critical mismatch exists between continuous pixel-wise optimization and discrete structural boundaries, causing models to blur sharp intensity transitions to minimize aggregate errors. To address these challenges, we propose QFSNet, a highly efficient deterministic nowcasting architecture anchored by a Quaternion Fourier Neural Operator. To resolve the directional misalignment, we introduce a lossless wavelet-quaternion representation that maps multi-scale details into a quaternion field, leveraging the non-commutative Hamilton product and a two-sided Quaternion Fourier Transform (QFT) to jointly model directional kinematics, and decouple the forecasting process into three specialized branches for fine-scale dynamics, macroscopic trends, and local phase transport. Furthermore, standard continuous optimization inherently causes structural blurring and the loss of high-contrast edges in predictions. To resolve this, we introduce a mathematically rigorous normal–tangent decomposition mechanism. This strictly decouples the boundary-reshaping dynamics required to restore sharp structural discontinuities from the intra-region intensity calibration , explicitly preventing the over-smoothing of abrupt precipitation transitions without introducing artificial artifacts. Extensive experiments across four benchmark datasets demonstrate that QFSNet achieves state-of-the-art performance, particularly in extreme precipitation detection, while requiring the lowest parameter count and computational cost, and maintaining the fastest inference speed.