In order to close these knowledge gaps in this ITN, we will investigate the model behaviour through the model hierarchy moving from low to high dimensionality and from simple to complex dynamics. For this endeavour to be successful, new tools within applied mathematics need to be developed in conjunction with the development and exploitation of realistic models, guided by observations and theories of the physics involved in describing the climate system. There is thus also a need for advanced analysis of the available observational time series, calling for the strong interdisciplinary collaboration as proposed here.
CriticalEarth Scientific Goals
WP1: Mathematical basis for critical transitions and tipping points Explore stochastic multiscale models in climate science and develop the theory of fast-slow systems and the relationship to classical bifurcation theory. Provide the theoretical basis for cascading tipping points in high-dimensional complex systems.
WP2: Transitions and rare events in climate models: Dynamical analysis – Investigate and identify critical transitions in stochastic and deterministic dynamical models, such as state-of-the-art Earth System Models and compute safe operating spaces and transition probabilities. Develop the methodology and the mathematics of rare event algorithms with models of intermediate complexity.
WP3: Tipping Elements in the climate: Physical processes – Quantify the Tipping Elements (TEs) and the interaction between different TEs in the Earth system.
WP4: Tipping points in observations and paleo-records: Connect the paleoclimatic recordings of abrupt changes with the theories of critical transitions and identify useful early warning signals for future abrupt changes.
WP5: Bifurcations and the model hierarchy: Develop a self-consistent framework for abrupt changes from observations and the model-hierarchy from low order to high-dimensional complex climate models. Investigate the role of long chaotic transient behaviour in low- and high-dimensional dynamical models to identify the conditions for masking critical transitions.
WP6: Response theory: Develop a theory of climate response in the presence of tipping points that goes beyond linear and equilibrium concepts, and specifically beyond equilibrium climate sensitivity. This theory should deal with responses on distinct temporal and spatial scales, have predictive power regarding the time evolution of different observables in the presence of time-dependent external forcing, and anticipate the nearing
of critical transitions.