Multivariate probabilistic projections using imperfect climate models part I: outline of methodology

We demonstrate a method for making probabilistic projections of climate change at global and regional scales, using examples consisting of the equilibrium response to doubled CO2 concentrations of global annual mean temperature and regional climate changes in summer and winter temperature and precipitation over Northern Europe and England-Wales. This method combines information from a perturbed physics ensemble, a set of international climate models, and observations. Our approach is based on a multivariate Bayesian framework which enables the prediction of a joint probability distribution for several variables constrained by more than one observational metric. This is important if different sets of impacts scientists are to use these probabilistic projections to make coherent forecasts for the impacts of climate change, by inputting several uncertain climate variables into their impacts models. Unlike a single metric, multiple metrics reduce the risk of rewarding a model variant which scores well due to a fortuitous compensation of errors rather than because it is providing a realistic simulation of the observed quantity. We provide some physical interpretation of how the key metrics constrain our probabilistic projections. The method also has a quantity, called discrepancy, which represents the degree of imperfection in the climate model i.e. it measures the extent to which missing processes, choices of parameterisation schemes and approximations in the climate model affect our ability to use outputs from climate models to make inferences about the real system. Other studies have, sometimes without realising it, treated the climate model as if it had no model error. We show that omission of discrepancy increases the risk of making over-confident predictions. Discrepancy also provides a transparent way of incorporating improvements in subsequent generations of climate models into probabilistic assessments. The set of international climate models is used to derive some numbers for the discrepancy term for the perturbed physics ensemble, and associated caveats with doing this are discussed.