Maximal likely phase lines for a reduced ice growth model

Abstract

We study the impact of white 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.