  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, our 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, our 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. While what we report here refers to the linear response, the general
theory allows for treating nonlinear effects as well. Our results pave the way
for redesigning and interpreting climate change experiments from a radically
new perspective.
