Abstract
Abstract. We introduce a framework of cascading tipping, i.e. a sequence of abrupt transitions occurring because a transition in one subsystem changes the background conditions for another subsystem. A mathematical framework of elementary deterministic cascading tipping points in autonomous dynamical systems is presented containing the double-fold, fold–Hopf, Hopf–fold and double-Hopf as the most generic cases. Statistical indicators which can be used as early warning indicators of cascading tipping events in stochastic, non-stationary systems are suggested. The concept of cascading tipping is illustrated through a conceptual model of the coupled North Atlantic Ocean – El Niño–Southern Oscillation (ENSO) system, demonstrating the possibility of such cascading events in the climate system.
Highlights
Earth’s climate system consists of several subsystems, e.g. the ocean, the atmosphere, ice and land, which are coupled through fluxes of momentum, mass and heat
In equatorial ocean–atmosphere dynamics associated with the El Niño–Southern Oscillation (ENSO) phenomenon, the global meridional overturning circulation can be considered a background state, as it evolves on a much larger timescale
We focus on bifurcation-induced tipping points, and consider two types of bifurcations that are thought to be relevant to mechanisms of abrupt changes in the climate system; the back-to-back saddle-node bifurcation is often used to explain transitions between two coexisting equilibria, while the Hopf bifurcation can explain the appearance of oscillatory behaviour (Thompson and Stewart, 2002)
Summary
Earth’s climate system consists of several subsystems, e.g. the ocean, the atmosphere, ice and land, which are coupled through fluxes of momentum, mass and heat Each of these subsystems is characterized by specific processes, on very different timescales, determining the evolution of its observables. In the ESSENCE project (Ensemble SimulationS of Extreme weather events under Nonlinear Climate changE) several simulations were performed using the ECHAM5/MPI-OM coupled climate model, including socalled “hosing” experiments Sterl et al (2008), where fresh water is added around Greenland to mimic ice sheet melting From these climate model simulations we used two ensembles; the first is the “standard” experiment, where greenhouse gases evolve according to observations and from the year 2000 onwards follow the SRES-A1b scenario (experiment name SRES-A1b). We use the maximum of the Atlantic meridional overturning stream function at 35◦ N as an AMOC index, and the NINO3.4 index as an ENSO index, which is the average SST over the region 170–120◦ W by 5◦ S–5◦ N
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