Opinion: Why all emergent constraints are wrong but some are useful – a machine learning perspective

• Published in: Atmospheric chemistry and physics Vol. 25; no. 4; pp. 2365 - 2384
• Main Authors: Nowack, Peer, Watson-Parris, Duncan
• Format: Journal Article
• Language: English
• Published: Katlenburg-Lindau Copernicus GmbH 21.02.2025; Copernicus Publications
• Subjects: Aerosol-cloud interactions; Aerosols; Analysis; Atmospheric chemistry; Bayesian analysis; Climate change; Climate change scenarios; Climate feedback; Climate models; Climate science; Climatic changes; Constraints; Future climates; Global climate; Invariants; Learning algorithms; Machine learning; Physics; Precipitation; Probability theory; Qualitative analysis; Statistical models; Trends; Uncertainty; Water vapor; Water vapour; Weather forecasting; Europe
• ISSN: 1680-7324; 1680-7316; 1680-7324
• DOI: 10.5194/acp-25-2365-2025

Global climate change projections are subject to substantial modelling uncertainties. A variety of emergent constraints, as well as several other statistical model evaluation approaches, have been suggested to address these uncertainties. However, they remain heavily debated in the climate science community. Still, the central idea to relate future model projections to already observable quantities has no real substitute. Here, we highlight the validation perspective of predictive skill in the machine learning community as a promising alternative viewpoint. Specifically, we argue for quantitative approaches in which each suggested constraining relationship can be evaluated comprehensively based on out-of-sample test data – on top of qualitative physical plausibility arguments that are already commonplace in the justification of new emergent constraints. Building on this perspective, we review machine learning ideas for new types of controlling-factor analyses (CFAs). The principal idea behind these CFAs is to use machine learning to find climate-invariant relationships in historical data which hold approximately under strong climate change scenarios. On the basis of existing data archives, these climate-invariant relationships can be validated in perfect-climate-model frameworks. From a machine learning perspective, we argue that such approaches are promising for three reasons: (a) they can be objectively validated for both past data and future data, (b) they provide more direct – and, by design, physically plausible – links between historical observations and potential future climates, and (c) they can take high-dimensional and complex relationships into account in the functions learned to constrain the future response. We demonstrate these advantages for two recently published CFA examples in the form of constraints on climate feedback mechanisms (clouds, stratospheric water vapour) and discuss further challenges and opportunities using the example of a rapid adjustment mechanism (aerosol–cloud interactions). We highlight several avenues for future work, including strategies to address non-linearity, to tackle blind spots in climate model ensembles, to integrate helpful physical priors into Bayesian methods, to leverage physics-informed machine learning, and to enhance robustness through causal discovery and inference.