Metastability in Climate Models: From Escape Probabilities to Geometric Early Warning Indicators
Abstract: Abrupt transitions between competing climate states often arise from noise-induced metastability rather than deterministic bifurcations. This talk presents theoretical tools for analyzing such transitions in stochastic dynamical systems. We first discuss the Stochastic Basin of Attraction (SBA) framework, where stability is quantified via escape probabilities solving generator-based boundary value problems, with extensions to Lévy-driven systems. We then introduce a recently developed geometric early warning indicator derived from the stochastic separatrix defined by the committor function in a bistable temperature–phytoplankton model. In the weak-noise limit, we demonstrate an explicit affine relation between the logarithm of the mean first passage time and the inverse square of the geometric indicator, revealing a fundamental geometric–temporal coupling. Applications to Arctic under-ice blooms and the Ghil–Sellers energy balance model highlight how these tools provide mechanistic insight into tipping phenomena under stochastic forcing.