Estimating the probability of rare climate events: inference from a large deterministic computer code

Anthropogenic emission of greenhouse gases means that it is vital that we can predict future climates. One aspect of such possible future climates are so called low probability high impact events. These include things like the collapse of ice sheets that we hope are unlikely but if they did happen would have very major impacts on the climate. The only way we can address these problems is through computer models, we do not have any data that is applicable. Such models are very large and complex and require huge amounts of computer time. Thus simple Monte Carlo methods of inference cannot be used. Instead we use statistical methods to investigate the properties of the model. These are based around the concept of an emulator. An emulator is a statistical approximation to the model output given the model inputs, and includes a measure of its own uncertainty. We use Gaussian processes for our emulators but in principle other functions could be used. Having built an emulator we can use it to perform our inference rather than the computer model itself. We will illustrate these methods to estimate the risk of the collapse of the thermohaline circulation in the North Atlantic and discuss future improvements.