  The destruction of a chaotic attractor leading to rough changes in the
dynamics of a dynamical system is studied. Local bifurcations are characterised
by a single or a pair of characteristic exponents crossing the imaginary axis.
The approach of such bifurcations in the presence of noise can be inferred from
the slowing down of the correlation decay. On the other hand, little is known
about global bifurcations involving high-dimensional attractors with positive
Lyapunov exponents.
  The global stability of chaotic attractors may be characterised by the
spectral properties of the Koopman or the transfer operators governing the
evolution of statistical ensembles. It has recently been shown that a boundary
crisis in the Lorenz flow coincides with the approach to the unit circle of the
eigenvalues of these operators associated with motions about the attractor, the
stable resonances. A second type of resonances, the unstable resonances, is
responsible for the decay of correlations and mixing on the attractor. In the
deterministic case, those cannot be expected to be affected by general boundary
crises.
  Here, however, we give an example of chaotic system in which slowing down of
the decay of correlations of some observables does occur at the approach of a
boundary crisis. The system considered is a high-dimensional, chaotic climate
model of physical relevance. Moreover, coarse-grained approximations of the
transfer operators on a reduced space, constructed from a long time series of
the system, give evidence that this behaviour is due to the approach of
unstable resonances to the unit circle. That the unstable resonances are
affected by the crisis can be physically understood from the fact that the
process responsible for the instability, the ice-albedo feedback, is also
active on the attractor. Implications regarding response theory and the design
of early-warning signals are discussed.
