Algebraic topology, a valuable tool in predicting climate tipping

Climate change is not a new thing. In its 4.5-billion-year history, the Earth has most likely seen many sudden changes to its climate. So, are human activities pushing the planet’s climate to yet another tipping point? Unfortunately, today’s climate models are not equipped to tell us. However, a recent study supported by the EU-funded TiPES and CloudCT projects could point the way to an answer.

Published in the journal ‘Chaos’, the study combines two leading climate change theories with algebraic topology tools in a model that shows how Earth’s climate does in fact undergo abrupt transitions. The analysis could help determine whether our climate system as a whole is about to tip as a result of global warming.

Scientists are not yet certain how climate evolves. “It is one of the truly unsolved mysteries about the climate sciences, that we are trying to get at,” observes the study’s senior author Prof. Michael Ghil of the École Normale Supérieure in Paris, France, in a news release posted on ‘EurekAlert!’. The two foremost climate change theories mentioned are Edward Lorenz’s deterministic chaos theory and 2021 Nobel laureate Klaus Hasselmann’s stochastic model of climate variability. The former deals with the apparently random or unpredictable behaviour in systems governed by deterministic laws – we have all heard of the butterfly effect – while the latter is based on the premise that everything fluctuates but regresses to the mean.“We have earlier, in 2008, brought these two theories together and shown that things get a lot more interesting if you have both deterministic chaos and stochastic perturbations,” notes Prof. Ghil. This combination resulted in something called a random attractor that changes with time. The shape the random attractor takes at a specific point in time – called a snapshot – determines where the climate system will most probably be. However, scientists are not sure how to interpret the random attractor’s shifts in time and what its changing path implies for our understanding of climate. This is where algebraic topology comes in.

In the algebraic topological analysis conducted, the researchers studied the number of holes in the climate system based on a relatively simple concept: If two systems’ geometric shapes are similar, then they have the same number of holes. As reported in the news release, investigation of the climate’s random attractor revealed that holes appear and disappear over time. This implies that the climate system experiences what appear to be instantaneous shifts between different regimes, which in turn suggests that it is in the nature of Earth’s climate to undergo the abrupt transitions we call tipping points.

“This is a fairly robust method of establishing critical conditions in very complex situations,” states Prof. Ghil, referring to the use of algebraic topology tools to help predict a climate tipping point. “So I think that it should be possible to use these tools in order to really foreshadow transitions in a system that is as complex as the climate system.”

Coordinated by the University of Copenhagen, Denmark, the TiPES (Tipping Points in the Earth System) project runs until the end of August 2023. The 6-year CloudCT (Climate CT- Cloud Tomography by Satellites for Better Climate Prediction) project ends in July 2025.

For more information, please see:

TiPES project website

CloudCT project website