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.

我们研究了白噪声对随机冰盖模型中亚稳态平衡状态之间过渡的影响。采用两种方法来实现不同的目标。通过最大化概率密度函数并数值求解Fokker-Planck方程，可以得出最大可能的轨迹，从而表明系统将随着时间的推移而发展。我们特别研究了从无冰亚稳状态开始的最大可能轨迹，并研究了对于某些参数它们是否演化为或接近冰覆盖的亚稳状态，以便深入了解冰盖的形成方式。此外，对于从覆冰的亚稳态到无冰的亚稳态的转变，我们通过Onsager–Machlup最小作用原理研究了各种噪声参数的最可能路径。