Early warning signals for topological tipping points
- 1Centro de investigaciones del mar y la atmósfera, Universidad de Buenos Aires, Buenos Aires, Argentina (gcharo@fi.uba.ar)
- 2Geosciences Department and Laboratoire de Météorologie Dynamique, École Normale Supérieure and PSL University
- 3Department of Atmospheric and Oceanic Sciences, University of California
- 4Institut Franco-Argentin d'études sur le climat et ses impacts
The topology of the branched manifold associated with the Lorenz model’s random attractor (LORA) evolves in time. LORA’s time-evolving branched manifold robustly supports the point cloud associated with the system’s invariant measure at each instant in time.
This manifold undergoes not only continuous deformations — with branches that bend, stretch or compress — but also discontinuous deformations, with branches that intersect at discrete times. These discontinuities in the system's invariant measure manifest themselves in the decrease or increase of the number of 1-holes, thus producing abrupt changes in the branched manifold’s topology.
Topological tipping points (TTPs) are defined as abrupt changes in the topology of a random attractor’s branched manifold. Branched Manifold Analysis through Homologies
(BraMAH) is a robust method that allows one to detect these fundamental changes.
The existence of such TTPs is being confirmed by careful statistical analysis of LORA’s time-evolving branched manifold, following up on Charó et al. (Chaos, 2021, doi:10.1063/5.0059461). Research is being pursued on early warning signals for these TTPs, concentrating on local fluctuations in the system’s invariant measure.
How to cite: Charó, G. D., Ghil, M., and Sciamarella, D.: Early warning signals for topological tipping points, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-12686, https://doi.org/10.5194/egusphere-egu22-12686, 2022.
