  The provision of accurate methods for predicting the climate response to
anthropogenic and natural forcings is a key contemporary scientific challenge.
Using a simplified and efficient open-source general circulation model of the
atmosphere featuring O($10^5$) degrees of freedom, we show how it is possible
to approach such a problem using nonequilibrium statistical mechanics. Response
theory allows one to practically compute the time-dependent measure supported
on the pullback attractor of the climate system, whose dynamics is
non-autonomous as a result of time-dependent forcings. We propose a simple yet
efficient method for predicting - at any lead time and in an ensemble sense -
the change in climate properties resulting from increase in the concentration
of CO$_2$ using test perturbation model runs. We assess strengths and
limitations of the response theory in predicting the changes in the globally
averaged values of surface temperature and of the yearly total precipitation,
as well as in their spatial patterns. The quality of the predictions obtained
for the surface temperature fields is rather good, while in the case of
precipitation a good skill is observed only for the global average. We also
show how it is possible to define accurately concepts like the the inertia of
the climate system or to predict when climate change is detectable given a
scenario of forcing. Our analysis can be extended for dealing with more complex
portfolios of forcings and can be adapted to treat, in principle, any climate
observable. Our conclusion is that climate change is indeed a problem that can
be effectively seen through a statistical mechanical lens, and that there is
great potential for optimizing the current coordinated modelling exercises run
for the preparation of the subsequent reports of the Intergovernmental Panel
for Climate Change.
