The earth climate consists of several subdomains that have remained in a sensitive balance for millennia but is now under threat from climate change. Here Georgios Margazoglou, from the Centre for the Mathematics of Planet Earth, explains the latest research into the climate’s global stability properties. Using a combination of statistical mechanics and the methods of data science, the team has studied the competing states and the transition paths between these subdomains to provide a general framework for better understanding multi-stable complex systems. The hope is that further research will be able to quantify transition probabilities in local and multi-stable climatic elements and further assess the risk of the associated tipping points.

earth-data-2254769_1280. Image by Pete Linforth from Pixabay

Earth’s climate is an extremely complex system, composed of five interacting subdomains: a gaseous atmosphere, a hydrosphere (water in liquid form), a lithosphere (upper solid layer), a cryosphere (water in solid form) and a biosphere (ecosystems and living organisms). These components are driven by the incoming solar energy, in the form of radiation, which is partly reflected, partly re-emitted and partly absorbed in a non-homogeneous way due to the greenhouse effect. The latter determines the comfortable temperature for which humans and life have adapted, and its intensity depends on the amount of certain hydrocarbons, such as carbon dioxide and methane, in the atmosphere. The climate’s response to the increase of greenhouse gases in the atmosphere due to industralisation is the increase of global temperature, as more heat is trapped inside it.

The 2022 report of the Intergovernmental Panel for Climate Change (Working Group 2) warns that “Climate change is affecting nature, people’s lives and infrastructure everywhere. Its dangerous and pervasive impacts are increasingly evident in every region of our world. These impacts are hindering efforts to meet basic human needs and they threaten sustainable development across the globe”. Centuries of scientific knowledge combined with mathematical and physical principles has allowed scientists, during the past few decades, to construct climate models that can be run as simulations in supercomputers and provide approximate predictions of our climate’s future. Such simulations try to frame our changing world and help policymakers find the best mitigation strategies.

The climate’s subdomains are in a sensitive balance that has remained so for millennia, but climate change now threatens this stability. The climate has also elements that are geographically distributed, such as the Amazon rainforest, the thermohaline circulation of the Atlantic ocean, and the Indian monsoon, to name a few, that play a crucial role in local systems, but with global significance. Therefore one can view the climate system as a multi-stable one, where several competing potential or actual states co-exist. Transitions between such states occur at so-called ‘tipping points’, which are, broadly speaking, organised in a multi-scale fashion. They are present at different spatial and temporal scales, and can affect a geographically limited region (e.g. Amazon forest dieback, or permafrost thawing) or the entire climate system (e.g. an ice age). A potential catastrophe of such ‘tipping elements’ could cause irreversible damage to climate and assessing the risk of such critical transitions is vital.

My recent research paper starts by viewing the Earth’s climate system as a dynamical landscape, that is investigated via the introduction of noise to certain degrees of freedom. This allows the study of climate’s global stability properties. The competing states and the transition paths between them are studied by combining a top-down approach based on statistical mechanics and a bottom-up approach based on methods of data science. This allows us to reach an unprecedented understanding of the nonequilibrium nature of the climate system and to provide a general framework for studying multi-stable complex systems. A promising expectation for future directions would be to quantify transition probabilities in local and multi-stable climatic elements and further assess the risk of the associated tipping points.

Georgios Margazoglou is a Post-Doctoral Research Assistant in the Mathematics of Planet Earth. He was awarded the University’s Early Career Research Output prize for his paper: Margazoglou, G., Grafke, T., Laio, A., and Lucarini, V. (2021)’ Dynamical landscape and multistability of a climate model’, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477, 20210 019,, 2021.

Find out more

‘Exploring the multistable and multiscale climate system via noise’, blog of the Nonlinear Processes in Geosciences Division of the European Geosciences Union, 7 Dec 2021

View our animations of a critical transition using a simulation of the intermediate complexity climate model PlaSim to model climate changes. The first animation shows a critical transition from the present day ‘Warm’ climate to a globally frozen ‘Snowball’ climate. A second animation depicts the opposite transition, from a ‘Snowball’ to a ‘Warm’ climate.

New paper: Lucarini, V., Serdukova, L., and Margazoglou, G. (2022) ‘Lévy-noise versus Gaussian-noise-induced Transitions in the Ghil-Sellers Energy Balance Model’, Nonlin. Processes Geophys., 29, 183–205,, 2022.