PhD Defense by Kolja Leon Kypke
Title: Tipping in the Greenland ice sheet: Noise, rate and chaos
Abstract:
The Greenland ice sheet is an important element of the Earth’s climate system and is a central climate component for studying the phenomenon of abrupt changes in its overall state due to small changes in external forcing, commonly known as tipping. The focus on ice sheets is partly because of evidence of abrupt changes in the paleoclimate record of Greenland, and partly because the global consequences of tipping the ice sheet being easily understood. However, due to the vast complexity of the climate the conceptual understanding of tipping in simple low-dimensional systems requires some translation to be applicable to any real-world system. This thesis analyzes three models along a hierarchy of dimension and number of processes to bridge that gap.
Firstly, the abrupt changes of the last glacial maximum, the Dansgaard-Oeschger events, are represented as noise-induced tipping in a one-dimensional conceptual model with multiplicative noise. This study discusses the different attributions to the deterministic and stochastic components in the Itô and Stratonovich interpretations of the stochastic integral. The discrepancy results in considerations with regards to the physical interpretation of the model, as well as the paradigms of bistability and monostability of the stadial and interstadial states.
Secondly, the contemporary Greenland ice sheet in a state-of-the-art model is demonstrated to exhibit a novel mode of variability, namely that of oscillating ice streams, under mild external atmospheric forcing. The result of increasing this external forcing at different rates is that the time before tipping occurs can vary by tens to hundreds of millennia. Using concepts from dynamical systems theory, specifically that of chaotic transients, it is determined that these long and seemingly random tipping times are due to crossing a bifurcation point rather than experiencing a non-monotonic rate-induced tipping. Furthermore, the delay of the tipping depends sensitively on the initial condition and the rate of forcing, implying chaotic variability.
Thirdly, a conceptual model of coupled oscillating ice streams is con- structed and analyzed to validate the chaotic nature of the variability seen in the comprehensive model. This model displays various transitions to chaos, including period doubling, intermittency, and attractor crises, as well as chaotic transients similar to those that are proposed to delay the tipping in the comprehensive model.
Committee: Aslak Grinsted (chair), Anne Munck Solgaard (GEUS), Poul G. Hjorth (DTU)
Supervisor: Peter Ditlevsen