  Using an intermediate complexity climate model (Planet Simulator), we
investigate the so-called Snowball Earth transition. For certain values of the
solar constant, the climate system allows two different stable states: one of
them is the Snowball Earth, covered by ice and snow, and the other one is
today's climate. In our setup, we consider the case when the climate system
starts from its warm attractor (the stable climate we experience today), and
the solar constant is decreased continuously in finite time, according to a
parameter drift scenario, to a state, where only the Snowball Earth's attractor
remains stable. This induces an inevitable transition, or climate tipping from
the warm climate. The reverse transition is also discussed. Increasing the
solar constant back to its original value on individual simulations, we find
that the system stays stuck in the Snowball state. However, using ensemble
methods i.e., using an ensemble of climate realizations differing only slightly
in their initial conditions we show that the transition from the Snowball Earth
to the warm climate is also possible with a certain probability. From the point
of view of dynamical systems theory, we can say that the system's snapshot
attractor splits between the warm climate's and the Snowball Earth's attractor.
