Climate simulators and climate projections

We provide a statistical interpretation of current practice in climate modelling. This includes: definitions for weather and climate; clarifying the relationship between simulator output and simulator climate; distinguishing between a climate simulator and a statistical climate model; statistical interpretation of the ubiquitous practice of anomaly correction, and a substantial generalisation (the ‘best parameter’ approach); interpreting simulator/data comparisons as posterior predictive checking, and a simple adjustment to allow for double-counting. We also discuss statistical approaches to simulator tuning, assessing parametric uncertainty, and responding to unrealistic outputs. We finish with a more general discussion of larger themes.