Mathematical aspects of tipping points in climate studies

19.04.2023, 14:00  –  Golm campus, Building 9, Room 2.22 and online

Anna von der Heydt (Utrecht University) and Robbin Bastiaansen (Utrecht University)

14:00 Anna von der Heydt (Utrecht University): Dynamical systems approaches to climate response and climate tipping (via zoom)

14:45 Tea and Coffee Break

15:15 Robbin Bastiaansen (Utrecht University): Tipping in spatially extended systems

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Anna von der Heydt (Utrecht University): Dynamical systems approaches to climate response and climate tipping
Abstract: The currently ongoing climate change and the debate about possible measures to be taken to limit the consequences of climate change, requires to know and understand the future response of the climate system to greenhouse gas emissions. Classical measures of climate change such as the Equilibrium Climate Sensitivity (ECS) are inherently linear and unable to account for abrupt transitions due to (interacting) tipping elements. In this presentation I will discuss more general notions of climate sensitivity defined on a climate attractor that can be useful in understanding the response of a climate state to changes in radiative forcing.

For example, a climate state close to a tipping point will have a degenerate linear response to perturbations, which can be associated with extreme values of the ECS. While many identified tipping elements in the climate system are regional and may have no direct impact on the global mean temperature, cascades of tipping elements can potentially have an impact, initiated by the threshold of the leading tipping element in a cascade.


Robbin Bastiaansen (Utrecht University): Tipping in spatially extended systems
In the current Anthropocene, there is a need to better understand the catastrophic effects that climate and land-use change may have on ecosystems, earth system components and the whole Earth system. The concept of tipping points and critical transitions contributes to this understanding. Tipping occurs in a system when it is forced outside the basin of attraction of the original equilibrium, resulting in a critical transition to an alternative, often less-desirable, stable state. The general belief and intuition, based on simple conceptual models of tipping elements (i.e. ordinary differential equations), is that tipping leads to reorganization of the full (sub)system. In this talk, I will review and explore tipping in conceptual, but spatially extended, and potentially spatially heterogeneous, models (i.e. partial differential equations).

In these spatially explicit models, additional stable states can emerge that are not uniform in space, such as Turing patterns and coexistence states (part of the domain in one state, the rest in another state with a spatial interface or front between these regions), which can lead to a different tipping behaviour. In particular, in these systems a tipping point might lead only to a slight restructuring of the system or to a tipping event in which only part of the spatial domain undergoes reorganization, limiting the impact of these events on the system's functioning.

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