  We study the response of a simple quasi-geostrophic barotropic model of the
atmosphere to various classes of perturbations affecting its forcing and its
dissipation using the formalism of the Ruelle response theory. We investigate
the geometry of such perturbations by constructing the covariant Lyapunov
vectors of the unperturbed system and discover in one specific case -
orographic forcing - a substantial projection of the forcing onto the stable
directions of the flow. This results into a resonant response shaped as a
Rossby-like wave that has no resemblance to the unforced variability in the
same range of spatial and temporal scales. Such a climatic surprise corresponds
to a violation of the fluctuation-dissipation theorem, in agreement with the
basic tenets of nonequilibrium statistical mechanics. The resonance can be
attributed to a specific group of rarely visited unstable periodic orbits of
the unperturbed system. Our results reinforce the idea of using basic methods
of nonequilibrium statistical mechanics and high-dimensional chaotic dynamical
systems to approach the problem of understanding climate dynamics.
