  We study the impact of Brownian noise on transitions between metastable
equilibrium states in a stochastic ice sheet model. Two methods to accomplish
different objectives are employed. The maximal likely trajectory by maximizing
the probability density function and numerically solving the Fokker-Planck
equation shows how the system will evolve over time. We have especially studied
the maximal likely trajectories starting near the ice-free metastable state,
and examined whether they evolve to or near the ice-covered metastable state
for certain parameters, in order to gain insights into how the ice sheet
formed. Furthermore, for the transition from ice-covered metastable state to
the ice-free metastable state, we study the most probable path for various
noise parameters via the Onsager-Machlup least action principle. This enables
us to predict and visualize the melting process of the ice sheet if such a rare
event ever does take place.
