Forecast the Envelope, Reconstruct the Details: Learning Dynamic Spectral Priors for Precipitation Nowcasting

Precipitation nowcasting supports timely flood warnings and emergency response by forecasting the location and intensity of imminent rainfall. However, rapidly evolving echo details remain difficult to predict, and deterministic models often smooth intense local structures as lead time increases. Our analysis reveals that spectral envelopes formed by locally averaging wavelet detail magnitudes exhibit higher temporal coherence than signed coefficients averaged over the same regions. These envelopes summarise the spatial distribution and strength of local variations at multiple scales. Motivated by this observation, we propose DySP (Dynamic Spectral Prior), a deterministic framework that forecasts spectral envelopes to guide the reconstruction of future radar fields. A spectral pathway models multiscale envelope dynamics and produces latent spectral priors and envelope predictions for each forecast lead time. Our prior-guided spatiotemporal block (PGSTB) conditions spatial attention queries and keys on the latent priors and gates the attention output using envelope embeddings. To recover local structures not retained by the pooled envelopes, temporal-difference skip connections enrich the decoder with high-resolution observation features and their recent changes. Experiments on Shanghai, CIKM, and SEVIR demonstrate that DySP achieves state-of-the-art forecasting skill, improving the prediction of intense precipitation and the preservation of local echo structures.