Minnesota Mathematics of Climate Seminar

January 28, 2025

Modeling Permafrost Thaw Dynamics: A Conceptual and Energy-Based Approach, Maria Sanchez-Muniz, School of Mathematics

Permafrost, a critical carbon reservoir, is thawing rapidly under climate change, threatening to amplify global warming through potent carbon feedback. Traditional temperature-driven models overlook energy dynamics during phase transitions—key to thaw mechanisms. This talk introduces an energy-centric framework that prioritizes energy conservation, phase changes, and variable thermal properties. By shifting focus to energy density over temperature, the model naturally integrates phase transitions. Simulations highlight geothermal heat flux and soil water content as critical thaw drivers, revealing that low-ice permafrost degrades orders of magnitude faster than ice-rich systems. Energy of fusion emerges as a pivotal control, exposing non-linear water content-thaw relationships. Coupled with empirical data, this framework equips policymakers with insights into regional risks, emphasizing water content—not just warming—as a key determinant of resilience. The energy-driven approach advances permafrost modeling, refines climate projections, and underscores the urgency of integrating thaw dynamics into mitigation strategies.

February 4, 2025

Dynamics on Boundaries: A Study of a Climate Model and Theoretical Directions, Rodrigo Donizete Euzébio, Federal University of Goiás, Brazil

This talk addresses two topics: first, the study of a model of glacial cycles where trajectories are confined within a box-like boundary. Second, the development of a sufficiently general theory that allows us to treat boundary problems as classical, boundaryless equations. We employ a projection strategy to analyze the climate model and utilize discontinuities, regularizations, and time-scale systems to propose a theoretical approach for boundary systems.

February 25, 2025

Taking Care of the Land: Indigenous Natural Resources Management, Governance and Climate Adaptation, Florencia Pech Cardenas, Postdoctoral Fellow, Institute on the Environment, University of Minnesota

Indigenous peoples have been adapting to and managing their lands under changing socio-ecological contexts for millenia. Indigenous epistemologies and practices related to the environment allowed Indigenous communities to have a sustainable management of their natural resources and environments before sustainability and environmentalism existed in Western thought. In this talk, I will share my research which centers Indigenous relationships to natural resources and climate adaptation in Mexico and the Midwest. As an Indigenous interdisciplinary scholar and scientist, I engage in theories and methods from the humanities, social and natural sciences to build bridges between Indigenous and Western ways of thinking.

April 22, 2025

Glacial Abrupt Climate Change as a Multiscale Phenomenon Resulting from Monostable Excitable Dynamics, Georg Gottwald, School of Mathematics and Statistics, The University of Sydney

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.