A templex-based study of the Atlantic Meridional Overturning Circulation dynamics in idealized chaotic models

Abstract

Significant changes in a system’s dynamics can be understood through modifications in the topological struc-ture of its flow in phase space. In the Earth’s climate system, such changes are often referred to as tippingpoints. One of the large-scale components that may pass a tipping point is the Atlantic Meridional Overturn-ing Circulation (AMOC). Our understanding of tipping points can be enhanced using a recently proposedmathematical concept—the templex—which enables the identification of dynamics of different classes. Un-like traditional topological invariants, templex properties describe not only the topology of the underlyingstructure of a set of points in phase space associated with a finite time series but also the non-equivalentpathways allowed by the flow around that structure. In this study, we investigate the dynamics produced byan idealized autonomous model and its nonautonomous counterpart to consider long-term climate changesand reproduce phenomena occurring during different epochs, such as glacial and interglacial intervals. In thenonautonomous system, the trajectory visits two distinct domains in phase space, one of which shares certainproperties with those found in the autonomous case. A dissection of the templex and the definition of activetemplex properties improve our understanding of how the system tips from one regime to another. We alsodiscuss the relationship between our results and the nonautonomous model’s pullback attractor.