Global storm-resolving models (GSRMs) have gained widespread interest because of the unprecedented detail with which they resolve the global climate. However, it remains difficult to quantify objective differences in how GSRMs resolve complex atmospheric formations. This lack of comprehensive tools for comparing model similarities is a problem in many disparate fields that involve simulation tools for complex data. To address this challenge we develop methods to estimate distributional distances based on both nonlinear dimensionality reduction and vector quantization. Our approach automatically learns physically meaningful notions of similarity from low-dimensional latent data representations that the different models produce. This enables an intercomparison of nine GSRMs based on their high-dimensional simulation data (2D vertical velocity snapshots) and reveals that only six are similar in their representation of atmospheric dynamics. Furthermore, we uncover signatures of the convective response to global warming in a fully unsupervised way. Our study provides a path toward evaluating future high-resolution simulation data more objectively.

Projecting climate change is a generalization problem: We extrapolate the recent past using physical models across past, present, and future climates. Current climate models require representations of processes that occur at scales smaller than model grid size, which have been the main source of model projection uncertainty. Recent machine learning (ML) algorithms hold promise to improve such process representations but tend to extrapolate poorly to climate regimes that they were not trained on. To get the best of the physical and statistical worlds, we propose a framework, termed climate-invariant ML, incorporating knowledge of climate processes into ML algorithms, and show that it can maintain high offline accuracy across a wide range of climate conditions and configurations in three distinct atmospheric models. Our results suggest that explicitly incorporating physical knowledge into data-driven models of Earth system processes can improve their consistency, data efficiency, and generalizability across climate regimes.