Probabilistic Climate Forecasting: Methodological issues arising from analysis in climateprediction.net

One of the chief goals of climate research is to produce meaningful probabilistic forecasts that can be used in the formation of future policy and adaptation strategies. The current range of methodologies presented in the scientific literature show that this is not an easy task, especially with the various philosophical interpretations of how to combine the information contained in Perturbed-Physics and Multi-Model Ensembles (PPE & MME). The focus of this research is to present some of the methodological issues that have arisen in the statistical analysis of the latest climateprediciton.net experiment, a large PPE of transient simulations using HadCM3L. Firstly we consider model evaluation and propose a method for calculating the Likelihood of each ensemble member based on a transient constraint involving regional temperature changes. We argue that this approach is more meaningful for future climate change projections than climatology based constraints. A further question we consider is which observations to include in our Likelihood function; should we care how well a model performs simulating the climate of Europe if we are producing a forecast for South Africa? The second issue deals with how to combine multiple models from such an ensemble together into a probabilistic forecast. Much has been said about the Bayesian methodology given the sensitivity of forecasts to prior assumptions. For simple models of the climate, with inputs such as climate sensitivity, there may be strong prior information, but for complex climate models where parameters correspond to non-observable quantities this is not so straightforward, and so we may have no reason to believe that a parameter has a uniform distribution or an inverse uniform distribution. We therefore propose two competing methodologies for dealing with this problem, namely Likelihood profiling, and the Jeffreys' prior, which is an approach typically known as OBJECTIVE Bayesian Statistics, where the use of the word objective simply implies that the prior is generated using a rule, rather than from expert opinion. We present novel results using a simple climate model as an illustrative example, with a view to applying these techniques to the full climateprediction.net ensemble.