Predictability-Guided Multiscale Probabilistic Forecasting of Wind Direction under Extreme Shear

Abstract: Accurate multi-horizon wind direction forecasting is critical for turbine yaw control and grid security. Rapid directional shear (turning $\ge 90<sup>\circ$) challenges models via non-Euclidean geometry on $S<sup>1$, multiscale dynamics, and regime-dependent uncertainty. Conventional discrete models and foundation models suffer from mid-frequency phase lag and turning misalignments. We show that directional predictability decays at disparate rates across frequency subbands, rendering monolithic mechanisms suboptimal. We propose a predictability-guided paradigm: slow synoptic drift $\to$ deterministic regression; intermediate turning $\to$ continuous latent differential flows; unresolved turbulence $\to$ conditional residual diffusion; followed by causal recalibration. On a 10,000-sequence multi-year benchmark, our framework maintains calm-weather accuracy (Test MCE $38.48<sup>\circ$) while reducing extreme-turning error (Case 1 MCE $60.69<sup>\circ$ vs $70.42<sup>\circ$ for zero-shot foundation models). The circular CRPS reaches $22.36<sup>\circ$, with 93.88\% coverage at nominal 95\% (91.01\% out-of-distribution). Density estimation further reveals near-antipodal bimodal structure under severe shear (13.39\%--15.43\% tail mass $\ge 135<sup>\circ$), exposing a geometric bound where single-center calibration under-covers (81.56\%), motivating multimodal circular manifold learning.