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Multistability is a ubiquitous feature in systems of geophysical relevanceand provides key challenges for our ability to predict a system's response toperturbations. Near critical transitions small causes can lead to large effectsand - for all practical purposes - irreversible changes in the properties ofthe system. The Earth climate is multistable: present astronomical andastrophysical conditions support two stable regimes, the warm climate we livein, and a snowball climate, characterized by global glaciation. We firstprovide an overview of methods and ideas relevant for studying the climateresponse to forcings and focus on the properties of critical transitions.Following an idea developed by Eckhardt and co. for the investigation ofmultistable turbulent flows, we study the global instability giving rise to thesnowball/warm multistability in the climate system by identifying the climaticedge state, a saddle embedded in the boundary between the two basins ofattraction of the stable climates. The edge state attracts initial conditionsbelonging to such a boundary and is the gate facilitating noise-inducedtransitions between competing attractors. We use a simplified yet Earth-likeclimate model constructed by coupling a primitive equations model of theatmosphere with a simple diffusive ocean. We refer to the climatic edge statesas Melancholia states. We study their dynamics, their symmetry properties, andwe follow a complex set of bifurcations. We find situations where theMelancholia state has chaotic dynamics. In these cases, the basin boundarybetween the two basins of attraction is a strange geometric set with a nearlyzero codimension, and relate this feature to the time scale separation betweeninstabilities occurring on weather and climatic time scales. We also discover anew stable climatic state characterized by non-trivial symmetry properties.

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