Tipping elements in the Earth's climate system

Method for estimating the proximity to a tipping point. (A) Schematic approach: The potential wells represent stable attractors, and the ball, the state of the system. Under gradual anthropogenic forcing (progressing from dark to light blue potential), the right potential well becomes shallower and finally vanishes (threshold), causing the ball to abruptly roll to the left. The curvature of the well is inversely proportional to the system's response time τ to small perturbations. “Degenerate fingerprinting” (102) extracts τ from the system's noisy, multivariate time series and forecasts the vanishing of local curvature. (B) Degenerate fingerprinting “in action”: Shown is an example for the Atlantic meridional overturning circulation. (Upper) Overturning strength under a 4-fold linear increase of atmospheric CO₂ over 50,000 years in the CLIMBER-2 model with weak, stochastic freshwater forcing. Eventually, the circulation collapses without early warning. (Lower) Overturning replaced by a proxy of the shape of the potential (as in A). Although the signal is noisier in Lower than it is in Upper, it allows forecasting of the location of the threshold (data taken from ref. 102). The solid green line is a linear fit, and the dashed green lines are 95% error bars.