On the realism of forecast extrema

We are interested in the ability of weather models to predict extreme events. Nowadays, weather forecasts are generated not only using theory‑driven (or physics‑based) models, but also data‑driven (or machine‑learning), and hybrid (nudging‑based) models. The rapid development of data‑driven models and their adoption in operational weather forecasting have triggered investigations and discussions into how well these models compare to theory‑driven models when it comes to extreme events. This work aims to contribute to this effort.

The idea followed here consists in focusing on the extrema (maximum and minimum) of weather forecast fields (e.g., temperature anomaly). The general framework described in [1] is used to assess three aspects of the forecast separately.

• First, the physical realism of the extrema is checked to answer the question: “Is the extremum consistent with our understanding of the physics of the Earth system?”
• Second, the structural realism is assessed in terms of block‑extrema represented as parametric distributions, addressing the question: “Do the characteristics of the forecast‑extrema distribution resemble those of the observations?”
• Finally, the functional realism is measured to summarise the ability of the model to produce forecasts close to the observations. Here again, the focus is on block-extrema, and we discuss how these results differ from focusing on block-averages instead.

The Weather Prediction Model Intercomparison Project (WP-MIP) offers a convenient framework for our investigations. The corresponding dataset resembles forecasts of a variety of weather parameters from different contributing institutions. We show results for a subset of deterministic forecasts from theory-driven, data-driven, and hybrid models. We also suggest an extension of our approach to ensemble forecasts.

[1] Zied Ben Bouallègue (2026), “What is a realistic forecast?" Assessing data-driven weather forecasts, a journey from verification to falsification. Preprint, https://doi.org/10.48550/arXiv.2602.00622