Tipping points in the climate system
The first step in exploring the properties of dynamical systems like the Earth climate is to identify the different phase-space regions where trajectories asymptotically evolve, called attractors or steady-states. In a given system, multiple attractors can exist under the effect of the same forcing. At the boundaries of their basins of attraction, the dynamics is highly nonlinear, small perturbations giving rise to abrupt and potentially irreversible changes called tipping points that correspond to the passage from one attractor to the other.
In a recent paper  we proved the existence of up to five attractors in a simplified climate system where the planet is entirely covered by the ocean (aquaplanet) under the same forcing, represented by fixed values of solar irradiation and atmospheric CO2 content. These attractors range from a snowball to a hot state without sea ice. Their exact number depends on the details of the coupled atmosphere–ocean–sea ice configuration. By changing the forcing, we have constructed the full bifurcation diagram for the aquaplanet , which is critical to obtain the range of stability for each attractor, the position of tipping points and the regions of multi-stability.
Our research currently aims at applying the same approach to other simplified configurations, to paleoclimates [3,4] and to the present-day climate. We investigate how the climate system responds to internal variability, self-reinforcing feedbacks or external forcing (of astronomical or anthropic origin), especially near tipping points. We are also interested in developing early warning methods for detecting the approach to such critical points.
 M. Brunetti, J. Kasparian, C. Vérard, Co-existing climate attractors in a coupled aquaplanet, Climate Dynamics 53, 6293 (2019), https://doi.org/10.1007/s00382-019-04926-7 ; SPOTLIGHT on the MITgcm blog
 M. Brunetti, C. Vérard, P. O. Baumgartner, Modeling the Middle Jurassic ocean circulation, Journal of Palaeogeography 4, 373-386 (2015); SPOTLIGHT on the MITgcm blog with two additional animations of the Jurassic surface currents
 M. Brunetti, C. Vérard, How to reduce long-term drift in present-day and deep-time simulations?, Climate Dynamics 50, 4425 (2018), https://doi.org/10.1007/s00382-017-3883-7