Dynamical stability indicator based on autoregressive moving-average models: Critical transitions and the Atlantic meridional overturning circulation

• Published in: Chaos (Woodbury, N.Y.) Vol. 32; no. 11; pp. 113139 - 113156
• Main Authors: Rodal, Marie, Krumscheid, Sebastian, Madan, Gaurav, Henry LaCasce, Joseph, Vercauteren, Nikki
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 01.11.2022
• Subjects: Autoregressive moving-average models; Carbon dioxide; Dynamic stability; Fresh water; Ice sheets; Numerical analysis; Time dependence; Time series
• ISSN: 1054-1500; 1089-7682; 1527-2443; 1089-7682
• DOI: 10.1063/5.0089694

A statistical indicator for dynamic stability, known as the Υ indicator, is used to gauge the stability and, hence, detect approaching tipping points of simulation data from a reduced five-box model of the North Atlantic Meridional Overturning Circulation (AMOC) exposed to a time-dependent hosing function. The hosing function simulates the influx of fresh water due to the melting of the Greenland ice sheet and increased precipitation in the North Atlantic. The Υ indicator is designed to detect changes in the memory properties of the dynamics and is based on fitting auto-regressive moving-average models in a sliding window approach to time series data. An increase in memory properties is interpreted as a sign of dynamical instability. The performance of the indicator is tested on time series subject to different types of tipping, namely, bifurcation-induced, noise-induced, and rate-induced tipping. The numerical analysis shows that the indicator indeed responds to the different types of induced instabilities. Finally, the indicator is applied to two AMOC time series from a full complexity Earth systems model (CESM2). Compared with the doubling CO 2 scenario, the quadrupling CO 2 scenario results in stronger dynamical instability of the AMOC during its weakening phase.