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CRPS-LAM: Regional ensemble weather forecasting from matching marginals

Erik Larsson, Joel Oskarsson, Tomas Landelius, Fredrik Lindsten

TL;DR

This work addresses probabilistic regional weather forecasting for Limited-Area Modeling (LAM) where diffusion-based sampling is computationally expensive. It introduces CRPS-LAM, a CRPS-based probabilistic LAM that samples an ensemble in a single forward pass by injecting a latent vector $z \,\sim\, \mathcal{N}(0,I)$ through conditional normalization, and uses autoregressive rollout to extend horizons. The method trains with the unbiased fair CRPS estimator to align both marginal and joint distributions, achieving fast sampling while preserving fine-scale detail. On the MEPS-lam dataset, CRPS-LAM delivers competitive RMSE and CRPS with ensemble calibration comparable to state-of-the-art methods, while being up to ~39x faster than diffusion-based approaches, supporting parallel ensemble sampling in operational settings. This work offers a practical, scalable path for probabilistic regional forecasts and points to future directions in latent-variable integration and training strategies.

Abstract

Machine learning for weather prediction increasingly relies on ensemble methods to provide probabilistic forecasts. Diffusion-based models have shown strong performance in Limited-Area Modeling (LAM) but remain computationally expensive at sampling time. Building on the success of global weather forecasting models trained based on Continuous Ranked Probability Score (CRPS), we introduce CRPS-LAM, a probabilistic LAM forecasting model trained with a CRPS-based objective. By sampling and injecting a single latent noise vector into the model, CRPS-LAM generates ensemble members in a single forward pass, achieving sampling speeds up to 39 times faster than a diffusion-based model. We evaluate the model on the MEPS regional dataset, where CRPS-LAM matches the low errors of diffusion models. By retaining also fine-scale forecast details, the method stands out as an effective approach for probabilistic regional weather forecasting

CRPS-LAM: Regional ensemble weather forecasting from matching marginals

TL;DR

This work addresses probabilistic regional weather forecasting for Limited-Area Modeling (LAM) where diffusion-based sampling is computationally expensive. It introduces CRPS-LAM, a CRPS-based probabilistic LAM that samples an ensemble in a single forward pass by injecting a latent vector through conditional normalization, and uses autoregressive rollout to extend horizons. The method trains with the unbiased fair CRPS estimator to align both marginal and joint distributions, achieving fast sampling while preserving fine-scale detail. On the MEPS-lam dataset, CRPS-LAM delivers competitive RMSE and CRPS with ensemble calibration comparable to state-of-the-art methods, while being up to ~39x faster than diffusion-based approaches, supporting parallel ensemble sampling in operational settings. This work offers a practical, scalable path for probabilistic regional forecasts and points to future directions in latent-variable integration and training strategies.

Abstract

Machine learning for weather prediction increasingly relies on ensemble methods to provide probabilistic forecasts. Diffusion-based models have shown strong performance in Limited-Area Modeling (LAM) but remain computationally expensive at sampling time. Building on the success of global weather forecasting models trained based on Continuous Ranked Probability Score (CRPS), we introduce CRPS-LAM, a probabilistic LAM forecasting model trained with a CRPS-based objective. By sampling and injecting a single latent noise vector into the model, CRPS-LAM generates ensemble members in a single forward pass, achieving sampling speeds up to 39 times faster than a diffusion-based model. We evaluate the model on the MEPS regional dataset, where CRPS-LAM matches the low errors of diffusion models. By retaining also fine-scale forecast details, the method stands out as an effective approach for probabilistic regional weather forecasting

Paper Structure

This paper contains 11 sections, 3 equations, 30 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem definition.
  3. Our main contributions are:
  4. Related Work.
  5. Method
  6. Training.
  7. Experiments
  8. Conclusion
  9. Table of notation
  10. Experiment Details
  11. Additional results

Figures (30)

  • Figure 1: An overview of the forecasting process showing the inputs and outputs of the model (adapted from larsson2025diffusionlam).
  • Figure 2: Forecasts at 57h lead time for r_2. The faded area constitutes the boundary region.
  • Figure 3: The mean of the normalized rmse, crps, and ssr for all variables.
  • Figure 4: Energy spectra of humidity at 57h
  • Figure 5: An overview of the backbone model.
  • ...and 25 more figures