Minnesota Mathematics of Climate Seminar

Glacial Abrupt Climate Change as a Multiscale Phenomenon Resulting from Monostable Excitable Dynamics

Georg Gottwald

School of Mathematics and Statistics, The University of Sydney

6:00 pm CST, Tuesday, April 22, 2025

570 Vincent Hall (also streamed via Zoom)

Paleoclimate proxies reveal abrupt transitions of the North Atlantic climate during past glacial intervals known as Dansgaard-Oeschger (DO) events. A central feature of DO events is a sudden warming of about 10C in Greenland marking the beginning of relatively mild phases termed interstadials. These exhibit gradual cooling over several hundred to a few thousand years until a final abrupt decline brings the temperatures back to cold stadial levels. As of now, the exact mechanism behind this millennial-scale variability remains inconclusive. We aim at providing a dynamically consistent mechanism which gives rise to such abrupt climate changes without invoking any external drivers such as freshwater hosing.

Using the framework of statistical limit laws of deterministic slow-fast chaotic systems, we propose a multiscale setting which deterministically generates alpha-stable noise. This is possible if either a fast process is intermittent with long laminar durations or sporadically exhibits unconstrained large peaks. We illustrate the rigorous theory behind these statistical limit laws in simple examples and then use them to develop conceptual models for DO events.

In the first model abrupt climate changes emerge in a dynamic self-consistent way through complex interactions of a slow ocean, a fast atmosphere and an intermittent process sea-ice process on an intermediate timescale. The abrupt climate changes are caused in our model by intermittencies in the sea-ice cover. The ocean is represented by a Stommel two-box model, the atmosphere by a Lorenz-84 model and the sea-ice cover by a deterministic approximation of correlated additive and multiplicative noise (CAM) process. The key dynamical ingredients of the model are given by stochastic limits of deterministic multi-scale systems and recent results in deterministic homogenisation theory. The deterministic model reproduces statistical features of actual ice-core data such as non-Gaussian $\alpha$-stable behaviour. The proposed mechanism for abrupt millenial-scale climate change only relies on the existence of a quantity, which exhibits intermittent dynamics on an intermediate time scale. We consider as a particular mechanism intermittent sea-ice cover where the intermittency is generated by emergent atmospheric noise. However, other mechanisms such as freshwater influxes may also be formulated within the proposed framework.

Whereas this simple model reproduces many statistical features of DO events it fails to reproduce the slow relaxation to the stadia state. We then set out to describe a refined model which better models the heat exchange between the ocean and the atmosphere which is impeded by the presence of an isolating seance cover. In particular, we propose an excitable model to explain Dansgaard-Oeschger cycles, where interstadials occur as noise-induced state space excursions. Our model comprises the mutual multi-scale interactions between four dynamical variables representing Arctic atmospheric temperatures, Nordic Seas' temperatures and sea ice cover, and the Atlantic Meridional Overturning Circulation. The model's atmosphere-ocean heat flux is moderated by the sea ice, which in turn is subject to large perturbations dynamically generated by fast evolving intermittent noise. If supercritical, perturbations trigger interstadial-like state space excursions during which all four model variables undergo qualitative changes that consistently resemble the signature of interstadials in corresponding proxy records. As a physical intermittent process generating the noise we propose convective events in the ocean or atmospheric blocking events. Our model accurately reproduces the DO cycle shape, return times and the dependence of the interstadial and stadial durations on the background conditions. In contrast to the prevailing understanding that DO variability is based on bistability in the underlying dynamics, we show that multi-scale, monostable excitable dynamics provides a promising alternative to explain millennial-scale climate variability associated with DO events.

We discuss how the occurrence of intermittency and/or sporadic large events in a multi-scale setting can serve as a generic dynamical mechanism to generate jump-like behaviour.

This is joint work with Keno Riechers and Niklas Boers.