Climate Simulators and Climate Projections

We provide a statistical interpretation of current practice in climate modeling. In this review, we define weather and climate, clarify the relationship between simulator output and simulator climate, distinguish between a climate simulator and a statistical climate model, provide a statistical interpretation of the ubiquitous practice of anomaly correction along with a substantial generalization (the best-parameter approach), and interpret simulator/data comparisons as posterior predictive checking, including 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.