EGU General Assembly 2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Early warning signals for topological tipping points

Gisela Daniela Charó1,4, Michael Ghil2,3, and Denisse Sciamarella1,4
Gisela Daniela Charó et al.
  • 1Centro de investigaciones del mar y la atmósfera, Universidad de Buenos Aires, Buenos Aires, Argentina (
  • 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,, 2022.