Probabilistic Measures for Fair AI and NWP Model Comparison

Probabilistic measures afford fair comparisons of AIWP and NWP model output (Tilmann Gneiting, Tobias Biegert, Kristof Kraus, Eva-Maria Walz, Alexander I. Jordan, Sebastian Lerch, June 10, 2025)Introduction of a New Fair Comparison Metric: The paper introduces the Potential Continuous Ranked Probability Score (PC), a new measure designed to allow fair and meaningful comparisons between single-valued output from data-driven Artificial Intelligence based Weather Prediction (AIWP) models and physics-based Numerical Weather Prediction (NWP) models. This approach addresses concerns that traditional loss functions (like RMSE) may unfairly favor AIWP models, which often optimize their training using these metrics. Methodology Based on Probabilistic Postprocessing: PC is calculated by applying the same statistical postprocessing technique—specifically Isotonic Distributional Regression (IDR), also known as Easy Uncertainty Quantification (EasyUQ)—to the deterministic output of both AIWP and NWP models. PC is then defined as the mean Continuous Ranked Probability Score (CRPS) of these newly generated probabilistic forecasts. Measure of Potential Skill and Invariance: PC quantifies potential predictive performance. A key property of PC is that it is invariant under strictly increasing transformations of the model output, treating both forecasts equally and facilitating comparisons where the pre-specification of a loss function might otherwise place competitors on unequal footings. AIWP Outperformance and Operational Proxy: When applied to WeatherBench 2 data, the PC measure demonstrated that the data-driven GraphCast model outperforms the leading physics-based ECMWF high-resolution (HRES) model. Furthermore, the PC measure for the HRES model was found to align exceptionally well with the mean CRPS of the operational ECMWF ensemble, confirming that PC serves as a reliable proxy for the performance of real-time operational probabilistic products.