# Using proper divergence functions to evaluate climate models

arXiv: https://arxiv.org/abs/1301.5927 · HTML: https://mlsanity.com/paper/1301.5927/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2013.

## Built on by (most cited first, 5 of 5)

- [Can AI be enabled to dynamical downscaling? A Latent Diffusion Model to mimic km-scale COSMO5.0CLM9 simulations](https://mlsanity.com/paper/2406.13627/) (2024)
- [Hinge-Wasserstein: Estimating Multimodal Aleatoric Uncertainty in Regression Tasks](https://mlsanity.com/paper/2306.00560/) (2023)
- [Learning low-dimensional representations of ensemble forecast fields using autoencoder-based methods](https://mlsanity.com/paper/2502.04409/) (2025)
- [FACT: Multinomial Misalignment Classification for Point Cloud Registration](https://mlsanity.com/paper/2504.06627/) (2025)
- [CAFE: Counterfactual Prediction via Fast Posterior Estimation](https://mlsanity.com/paper/2609.32167/) (2026)

## Abstract (arXiv)

It has been argued persuasively that, in order to evaluate climate models, the probability distributions of model output need to be compared to the corresponding empirical distributions of observed data. Distance measures between probability distributions, also called divergence functions, can be used for this purpose. We contend that divergence functions ought to be proper, in the sense that acting on modelers' true beliefs is an optimal strategy. Score divergences that derive from proper scoring rules are proper, with the integrated quadratic distance and the Kullback-Leibler divergence being particularly attractive choices. Other commonly used divergences fail to be proper. In an illustration, we evaluate and rank simulations from fifteen climate models for temperature extremes in a comparison to re-analysis data.