Exploring multiscale dynamical landscapes and hierarchies of tipping points in the Earth System

Supervisors:

Professor Valerio Lucarini v.lucarini@leicester.ac.uk

Dr Larissa Serdukova   ls563@leicester.ac.uk

Project:

The Earth is a complex system featuring variability on a vast range of spatial and temporal scales. One of its features is metastability, i.e. the existence of multiple competing states for given boundary conditions and of processes that allow for transitions between such states. These transitions are often associated with the so-called tipping points, whose understanding is one of the major challenges of contemporary research in the area of the climate crisis. Tipping phenomena typically occur as a result of the presence of parametric modulations in the system or of the presence of noise. Key dynamical components determining the properties of the tipping behaviour are the so-called edge or Melancholia states, which are unstable solutions of the system living on the boundaries between the basins of attraction of the noise-free system. Noise-induced transitions between competing stable states of the system typically pass through such edge states, which behaves like a mountain pass/saddles in an effective dynamical potential, where the stable solutions are, instead, local minima. When a system has multiple scales of motions, as in the case of coupled atmospheric/ocean/ice dynamics, the behaviour of the system performing noise-induced transitions between competing states departs in most cases from the classical scenario described above. Understanding the features of the tipping behaviour is then extremely challenging and at the same time extremely relevant in terms of defining the safe operating space of the system, i.e. constraining the class of perturbations that do not change qualitatively the properties of the system, because critical transitions are avoided. The student will perform theoretical work complemented by numerical modelling on climate models of different levels of complexity. Experience is needed in some among the following areas: dynamical systems theory, statistical physics, data-driven methods, climate science, computational methods. 

References: 

• V. Lucarini, M. D. Chekroun, Theoretical tools for understanding the climate crisis from Hasselmann’s programme and beyond, Nature Reviews Physics 5, 744–765 (2023). 
• V.M. Galfi, V. Lucarini, F. Ragone, J. Wouters, Applications of Large Deviation Theory in Climate Science and Geophysical Fluid Dynamics, Riv. Nuovo Cimento 44, 291–363 (2021)
• M. Ghil, V. Lucarini, The Physics of Climate Variability and Climate Change, Rev. Mod. Phys. 92, 035002 (2020)
• D. D. Rousseau, W. Bagniewski, and V. Lucarini, A punctuated equilibrium analysis of the climate evolution of Cenozoic exhibits a hierarchy of abrupt transitions. Sci. Rep. 13, 11290 (2023)
• V. Lucarini, L. Serdukova, L., G. Margazoglou, Lévy-noise versus Gaussian-noise-induced Transitions in the Ghil-Sellers Energy Balance Model, Non. Proc. Geophys.. 29, 183–205 (2022)
• G. Margazoglou, T. Grafke, A. Laio, V. Lucarini, Dynamical Landscape and Multistability of the Earth’s Climate, Proc. R. Soc. A 477, 20210019 (2021)
• V. Lucarini, T. Bodai, Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View, Phys. Rev. Lett. 122,158701 (2019)
• P. Ashwin, S. Wieczorek, R. Vitolo, P. Cox Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system Phil. Trans. R. Soc. A 370 1166–84 (2012)