Edge States in the Climate System: Exploring Global Instabilities and Critical Transitions

Abstract

Multistability is a ubiquitous feature in systems of geophysical relevance and provides key challenges for our ability to predict a system's response to perturbations. Near critical transitions small causes can lead to large effects and - for all practical purposes - irreversible changes in the properties of the system. The Earth climate is multistable: present astronomical and astrophysical conditions support two stable regimes, the warm climate we live in, and a snowball climate, characterized by global glaciation. We first provide an overview of methods and ideas relevant for studying the climate response to forcings and focus on the properties of critical transitions. Following an idea developed by Eckhardt and co. for the investigation of multistable turbulent flows, we study the global instability giving rise to the snowball/warm multistability in the climate system by identifying the climatic edge state, a saddle embedded in the boundary between the two basins of attraction of the stable climates. The edge state attracts initial conditions belonging to such a boundary and is the gate facilitating noise-induced transitions between competing attractors. We use a simplified yet Earth-like climate model constructed by coupling a primitive equations model of the atmosphere with a simple diffusive ocean. We refer to the climatic edge states as Melancholia states. We study their dynamics, their symmetry properties, and we follow a complex set of bifurcations. We find situations where the Melancholia state has chaotic dynamics. In these cases, the basin boundary between the two basins of attraction is a strange geometric set with a nearly zero codimension, and relate this feature to the time scale separation between instabilities occurring on weather and climatic time scales. We also discover a new stable climatic state characterized by non-trivial symmetry properties.

43 pages; 15 figures. Revised version with additional figures, extended discussion, and new results on the boundary between the basins of attraction

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• Global Stability Properties of the Climate: Melancholia States, Invariant Measures, and Phase Transitions
• Applications of large deviation theory in geophysical fluid dynamics and climate science
• Attractors and bifurcation diagrams in complex climate models
• Co-existing climate attractors in a coupled aquaplanet
• The tipping times in an Arctic sea ice system under influence of extreme events
• Resonances in a Chaotic Attractor Crisis of the Lorenz Flow
• Robustness of competing climatic states
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• Multistability and rare spontaneous transitions in barotropic $\beta$-plane turbulence
• Response Theory and Phase Transitions for the Thermodynamic Limit of Interacting Identical Systems
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• Finite-time Lyapunov exponents of deep neural networks
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• Reduction Methods in Climate Dynamics -- A Brief Review
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• Introduction to the Special Issue on the Statistical Mechanics of Climate
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