Rate-induced tipping in non-autonomous random dynamical systems

The concept of a tipping point (or critical transition) describes a phenomena where the behaviour of a physical system changes drastically, and often irreversibly, compared to a small change in its external environment. Relevant examples in climate science are the possible collapse of the Atlantic Meridional Overturning Circulation (AMOC) due to increasing freshwater input, or the sudden release of carbon in peatlands due to an external temperature increase. The aim of this project is to develop the mathematical framework for tipping points and therefore contribute to a deeper understanding of them.
A number of generic mechanisms have been identified which can cause a system to tip. One such mechanism is rate-induced tipping, where the transition is caused by a parameter changing too quickly - rather than it moving past some critical value. The traditional mathematical bifurcation theory fails to address this phenomena. The goal of this project is to use and develop the theory of non-autonomous and random dynamical systems to understand rate-induced tipping in the presence of noise. A question of particular practical importance is whether it is possible to develop meaningful early-warning indicators for rate-induced tipping using observation data. We will investigate this question from a theoretical viewpoint and apply it to more realistic models.

Supervisors: Martin Rasmussen (Imperial College London, Department of Mathematics), Jochen Broeker (University of Reading, Department of Mathematics and Statistics), Pavel Berloff (Imperial College London, Department of Mathematics)

Impact will be realized in two ways: by research done as part of the training, and by the student cohort itself.

RESEARCH: The Centre will bring together two traditionally separate domains of mathematics: the "data driven" domain, represented by statistics (including time series analysis and data assimilation), and the "model driven" domain, represented
by analysis (including fluid dynamics and dynamical systems). By connecting with and through weather, oceans and climate research into application areas, the research will have a strong interdisciplinary component. Because most impacts of climate variability and change occur through extreme weather events and spells, our approach of studying weather and climate together, with a seamless transition from one to the other, will bring fundamental new insights. Through our international academic partnerships these advances will be spread globally. Weather, oceans and climate is not the only application area grossly under-constrained by data, so the novel mathematics developed here will have downstream implications, with multidisciplinary benefit.

COHORT: Those trained in the Centre will represent a "new breed" of mathematical scientist able to work across the above traditional disciplinary divide and possessing transferable skills such as team-building, management, leadership, and communication. They will take up positions in academia, research centres, government departments and the private sector and will apply their skills to pressing societal needs. Their influence will extend beyond the weather, oceans and climate area into the wider arena, both in the UK and worldwide.

ACADEMIA will benefit from overall advancement of an inter-disciplinary area of research. On the near term, this will occur through the new partnerships developed within the Centre. In addition, our summer schools and other training activities will be open to outside students. On the longer term, the research will inspire follow-on projects and some of the students will take up positions within academia, strengthening the research base through their enhanced skills. Moreover the entire cohort will continue their collaboration across institutional and national borders.

The PUBLIC SECTOR will benefit on both the near- and longer-term from improved tools for operational services and evidence-based policy-making and decision-making, ranging from weather forecasting to projections of climate variability
and change, and including impacts on energy and the environment. To this end, key partners in weather, oceans and climate services are engaged both within the UK (Met Office) and Europe (ECMWF and DWD). A broader network of public-sector beneficiaries (e.g. DEFRA and DECC), especially for risk assessment, will be served through the Grantham Institute for Climate Change at Imperial College and other intermediaries such as the Walker Institute at Reading. The researchers trained by the Centre will possess highly relevant skills for these public sector bodies.

The COMMERCIAL PRIVATE SECTOR will benefit from improved quantitative knowledge of environmental uncertainty and risk in a number of economically and societally important areas, such as energy, reinsurance, water resources, civil
engineering, retail, and agriculture. Specific examples are included in the Case of Support. This benefit will occur in the near-term and will provide a competitive advantage to the UK. The researchers trained by the Centre will possess highly relevant skills for the private sector in the general area of data-model fusion, in addition to areas relating specifically to weather, oceans and climate.

The GENERAL PUBLIC will benefit from improved public services and economic well-being. The detrimental effects of severe weather and climate change pose a major societal threat with significant economic impacts.