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This paper is due to appear as a chapter of the forthcoming Handbook ofApproximate Bayesian Computation (ABC) by S. Sisson, L. Fan, and M. Beaumont.We describe the challenge of calibrating climate simulators, and discuss thedifferences in emphasis in climate science compared to many of the moretraditional ABC application areas. The primary difficulty is how to doinference with a computationally expensive simulator which we can only affordto run a small number of times, and we describe how Gaussian process emulatorsare used as surrogate models in this case. We introduce the idea of historymatching, which is a non-probabilistic calibration method, which divides theparameter space into (not im)plausible and implausible regions. Historymatching can be shown to be a special case of ABC, but with a greater emphasison defining realistic simulator discrepancy bounds, and using these to definetolerances and metrics. We describe a design approach for choosing parametervalues at which to run the simulator, and illustrate the approach on a toyclimate model, showing that with careful design we can find the plausibleregion with a very small number of model evaluations. Finally, we describe howcalibrated GENIE-1 (an earth system model of intermediate complexity)predictions have been used, and why it is important to accurately characteriseparametric uncertainty.

ABC for climate: dealing with expensive simulators