Dynamical Stability Indicator based on Autoregressive Moving-Average Models: Critical Transitions and the Atlantic Meridional Overturning Circulation

TL;DR

This paper introduces the $ ext{Upsilon}$ indicator, based on ARMA models, to detect early signs of critical transitions in the Atlantic Meridional Overturning Circulation using both simplified and complex climate models.

Contribution

The paper develops and tests a novel ARMA-based stability indicator for identifying approaching tipping points in climate system models.

Findings

The $ ext{Upsilon}$ indicator detects different types of tipping points effectively.

The indicator shows increased memory properties before instability in model simulations.

Applied to CESM2 data, it reveals stronger instability under quadrupling CO2 scenarios.

Abstract

A statistical indicator for dynamic stability known as the $\Upsilon$ indicator is used to gauge the stability and hence detect approaching tipping points of simulation data from a reduced 5-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 $\Upsilon$ indicator is designed to detect changes in the memory properties of the dynamics, and is based on fitting ARMA (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 show 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.