Maximal Likely Phase Lines for a Reduced Ice Growth Model

TL;DR

This paper investigates the most probable transition paths between metastable states in a stochastic ice sheet model, using maximal likelihood trajectories and the Onsager-Machlup principle to understand ice formation and melting processes.

Contribution

It introduces a combined approach using maximal likelihood trajectories and the Onsager-Machlup principle to analyze rare transitions in a stochastic ice sheet model, providing new insights into ice sheet dynamics.

Findings

Maximal likely trajectories reveal potential ice sheet formation pathways.

The Onsager-Machlup approach predicts melting processes under stochastic influences.

Insights into transition probabilities between ice-covered and ice-free states.

Abstract

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.