Early-warning indicator based on autoregressive moving-average models: Critical Transitions and the Atlantic Meridional Overturning Circulation

A statistical indicator for dynamic stability based on autoregressive moving-average, ARMA(p,q), models is used to gauge the stability and hence predict 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. We study the indicator's ability to assess the stability of a time series subject to different types of tipping, including bifurcation-induced and rate-induced tipping, and show that the indicator is indeed able to identify the different types of induced instability. In the process we extend the underlying models from an ARMA(p,q) process to an ARIMA(p,q) (autoregressive integrated moving-average) process, which through the proper application of differencing converts a formerly non-stationary process into a stationary one, further extending the regime of validity of the statistical method. In addition, we apply the indicator to simulation data from the Earth systems model CESM2, to assess how the indicator responds to more realistic time series data.