Master Thesis Defense by Jakob Stubkjær Harteg

Title: Assessing the Stability of Glacial-Interglacial Cycles: A Stochastic Model Analysis of Earth System Resilience

In this thesis, we study the stability of the glacial-interglacial cycle using a reduced complexity ice age model by Talento & Ganopolski (2021) with an added stochastic component to represent internal ice volume variability. The analysis of an ensemble of trajectories reveals different periods of significant divergence and convergence, in- dicating that the model’s sensitivity to noise varies in time. We assess the stability by applying a number of time-dependent resilience indicators to the ensemble. These indicators include convergence/divergence rate, stochastic/deterministic overlap, finite- time Lyapunov exponent and return time, and find that the model exhibits higher re- silience to perturbation during interglacials than during glacials. This suggests that the interglacial state could be represented as a more narrow valley in the Earth system stability landscape, compared to a wider glacial state. This may however be due to two key features of the model: a constraint keeping ice volume above pre-industrial levels and a memory term that makes the model more sensitive to noise at high ice volume levels. Repeating the analysing with a model of higher complexity would be necessary to better assess the robustness of the results. Furthermore, we explore the feasibil- ity of applying transfer operators to identify stable and decaying states and measure the temporal evolution of the system’s global stability using the spectral gap of the operator applied in a sliding time window. This approach is however complicated by our model being both non-autonomous and Markovian, two properties that transfer operator theory currently does not support, and we have yet to identify a meaningful approach. 

In light of approaching tipping points, there is an urgent need to delineate the Earth system stability landscape and better predict possible future trajectories. This thesis provides a tentative contribution to this effort by investigating the glacial-interglacial cycle—the region of the landscape which Earth has been in for the past 2.6 million years.

Supervisor: Jens Hesselbjerg Christensen
Censor: Peter Langen (AU)