Calibration of HRRRCast ensemble spread

Develop and validate a method to calibrate the ensemble spread of HRRRCast’s diffusion-based probabilistic forecasts so that the spread realistically represents forecast uncertainty (e.g., achieving a spread-error ratio near unity) across variables and lead times.

Background

HRRRCast generates ensembles via DDIM-based diffusion, currently perturbed only by initial Gaussian noise. In Appendix A, the authors report an average spread-error ratio of about 0.6, indicating under-dispersion.

The conclusions explicitly note ensemble spread calibration as an open challenge and suggest potential improvements, such as incorporating GEFS-based initial condition perturbations and adding stochastic noise during sampling.

References

Additionally, ensemble spread calibration remains an open challenge, which we aim to improve via more diverse noise perturbations and initial condition perturbations using external systems like GEFS.

— HRRRCast: a data-driven emulator for regional weather forecasting at convection allowing scales  (2507.05658 - Abdi et al., 8 Jul 2025) in Conclusions; see also Appendix A (Ensemble calibration)

Finally, the spread of the $K$ samples is not yet a calibrated uncertainty, because it does not contain the mismatch between the prior and the actual distribution.

— Diffusion prior for KSTAR equilibrium reconstruction under sensor dropout  (2609.36536 - Nam et al., 29 Sep 2026) in Section 5.3, Uncertainty; Section 6, Conclusion; Appendix D, Calibration of the sample spread