  The impact of the El Ni\~no-Southern Oscillation (ENSO) on the extratropics
is investigated in an idealized, reduced-order model that has a tropical and an
extratropical module. Unidirectional ENSO forcing is used to mimick the
atmospheric bridge between the tropics and the extratropics. The variability of
the coupled ocean-atmosphere extratropical module is then investigated through
the analysis of its pullback attractors (PBAs). This analysis focuses on two
types of ENSO forcing generated by the tropical module, one periodic and the
other aperiodic.
  For a substantial range of the ENSO forcing, two chaotic PBAs are found to
coexist for the same set of parameter values. Different types of extratropical
low-frequency variability are associated with either PBA over the parameter
ranges explored. For periodic ENSO forcing, the coexisting PBAs exhibit only
weak nonlinear instability. For chaotic forcing, though, they are quite
unstable and certain extratropical perturbations induce transitions between the
two PBAs. These distinct stability properties may have profound consequences
for extratropical climate predictions: in particular, ensemble averaging may no
longer help isolate the low-frequency variability signal.
