Global climate models are central tools for understanding past and future climate change. The assessment of model skill, in turn, can benefit from modern data science approaches. Here we apply causal discovery algorithms to sea level pressure data from a large set of climate model simulations and, as a proxy for observations, meteorological reanalyses. We demonstrate how the resulting causal networks (fingerprints) offer an objective pathway for process-oriented model evaluation. Models with fingerprints closer to observations better reproduce important precipitation patterns over highly populated areas such as the Indian subcontinent, Africa, East Asia, Europe and North America. We further identify expected model interdependencies due to shared development backgrounds. Finally, our network metrics provide stronger relationships for constraining precipitation projections under climate change as compared to traditional evaluation metrics for storm tracks or precipitation itself. Such emergent relationships highlight the potential of causal networks to constrain longstanding uncertainties in climate change projections.