Lang et al. (2026) A multi‐scale loss formulation for learning a probabilistic model with proper score optimisation

Identification

• Journal: Quarterly Journal of the Royal Meteorological Society
• Year: 2026
• Date: 2026-09-04
• Authors: Simon T. K. Lang, Martin Leutbecher, Pedro Maciel
• DOI: 10.1002/qj.70291

Research Groups

• ECMWF (European Centre for Medium-Range Weather Forecasts), Reading, UK

Short Summary

This study explores the impact of a multi-scale loss formulation on training probabilistic machine-learned weather forecasting models, specifically AIFS-CRPS, and finds that it improves the representation of variability without negatively impacting forecast skill.

Objective

• To assess the effect of adding a multi-scale component to the afCRPS training objective in improving spatial structures compared to the scale-unaware loss function.

Study Configuration

• Spatial Scale: Global weather prediction on a 2-sphere.
• Temporal Scale: Forecasting up to 72 hours ahead with progressively longer forecast windows.

Methodology and Data

• Models used: AIFS-CRPS, a machine-learned weather forecasting model developed at ECMWF.
• Data sources: Copernicus ERA5 re-analysis dataset produced by ECMWF.

Main Results

• The multi-scale loss formulation improves the representation of variability in forecast fields without negatively impacting forecast skill.
• The multi-scale experiment and the ERA5 analysis are in better agreement compared to the scale-unaware loss experiment.
• Spectra of forecast fields show that the multi-scale loss experiment constrains small-scale variability more effectively than the scale-unaware loss experiment.

Contributions

• This study introduces a new method for training probabilistic machine-learned weather forecasting models by incorporating a multi-scale loss formulation, which improves the representation of variability without negatively impacting forecast skill.
• The results demonstrate the potential of this approach in improving the accuracy and reliability of weather forecasts.

Funding

• EuroHPC Joint Undertaking for awarding access to the EuroHPC supercomputer MN5.

Citation

@article{Lang2026multiscale,
  author = {Lang, Simon T. K. and Leutbecher, Martin and Maciel, Pedro},
  title = {A multi‐scale loss formulation for learning a probabilistic model with proper score optimisation},
  journal = {Quarterly Journal of the Royal Meteorological Society},
  year = {2026},
  doi = {10.1002/qj.70291},
  url = {https://doi.org/10.1002/qj.70291}
}