Bridging the Gap in Extended-Range Ensemble Forecasting: A Machine Learning Diffusion Framework for High-Resolution Downscaling and Probabilistic Calibration

Subseasonal-to-seasonal (S2S) ensemble forecasts are critical for sectoral risk management, yet they are frequently constrained by coarse spatial resolutions and systematic biases. While post-processing is essential, conventional statistical methods (such as Bias Correction Spatial Disaggregation, BCSD) and deterministic deep learning approaches often fail to preserve physical consistency or inadvertently collapse the ensemble dispersion essential for quantifying uncertainty. This suppression limits their utility in representing high-impact extreme weather events.

To address these challenges within the context of next-generation machine learning post-processing, we present MSSDiff, a member-wise super-resolution diffusion framework designed to bridge the gap between coarse global ensemble outputs and local impacts. Instead of injecting stochastic noise that disrupts ensemble consistency, MSSDiff processes individual ensemble members using a deterministic probability-flow ODE sampling strategy. This approach simultaneously corrects biases and enhances resolution without disrupting the inherent spatiotemporal coherence or aleatoric uncertainty of the original dynamical ensemble.

The architecture features a Wavelet-Coupled Upsampling Module (WCUM) to explicitly recover high-frequency textures, such as precipitation extremes, and a Latent Space Attention (LSA) mechanism to capture large-scale teleconnections vital at the extended range. By jointly modeling temperature and precipitation, the framework leverages thermodynamic constraints to further improve physical reliability.

Validated on a newly constructed multi-model S2S benchmark (S2S-SR), MSSDiff is compared extensively against both traditional statistical methods and cutting-edge deterministic AI models. MSSDiff significantly improves the Anomaly Correlation Coefficient (ACC) for precipitation by over 19% compared to operational BCSD baselines. Crucially for ensemble forecasting, MSSDiff achieves the lowest Continuous Ranked Probability Score (CRPS) and produces quasi-uniform rank histograms. This demonstrates superior probabilistic calibration and the successful preservation of a physically plausible ensemble spread, offering a robust machine learning alternative to traditional calibration methods for extended-range extreme event forecasting.