A new framework for climate sensitivity and prediction: a modelling perspective

The sensitivity of climate models to increasing CO2 concentration and the climate response at decadal time-scales are still major factors of uncertainty for the assessment of the long and short term effects of anthropogenic climate change. While the relative slow progress on these issues is partly due to the inherent inaccuracies of numerical climate models, this also hints at the need for stronger theoretical foundations to the problem of studying climate sensitivity and performing climate change predictions with numerical models. Here we demonstrate that it is possible to use Ruelle's response theory to predict the impact of an arbitrary CO2 forcing scenario on the global surface temperature of a general circulation model. Response theory puts the concept of climate sensitivity on firm theoretical grounds, and addresses rigorously the problem of predictability at different time-scales. Conceptually, these results show that performing climate change experiments with general circulation models is a well defined problem from a physical and mathematical point of view. Practically, these results show that considering one single CO2 forcing scenario is enough to construct operators able to predict the response of climatic observables to any other CO2 forcing scenario, without the need to perform additional numerical simulations. We also introduce a general relationship between climate sensitivity and climate response at different time scales, thus providing an explicit definition of the inertia of the system at different time scales. This technique allows also for studying systematically, for a large variety of forcing scenarios, the time horizon at which the climate change signal (in an ensemble sense) becomes statistically significant. While what we report here refers to the linear response, the general theory allows for treating nonlinear effects as well. These results pave the way for redesigning and interpreting climate change experiments from a radically new perspective.