Nonlinear softening as a predictive precursor to climate tipping

TL;DR

This paper introduces a method to detect early warning signs of climate tipping points by analyzing nonlinear softening in the potential, which can signal an imminent shift even when linear indicators are absent.

Contribution

It demonstrates that nonlinear softening analysis can serve as a crucial early warning indicator for climate tipping points, supplementing traditional linear methods.

Findings

Detected nonlinear softening before the last ice age ending.

Identified significant nonlinear softening in paleo-climate data.

Showed nonlinear analysis can warn of tipping when linear trends are absent.

Abstract

Approaching a dangerous bifurcation, from which a dynamical system such as the Earth's climate will jump (tip) to a different state, the current stable state lies within a shrinking basin of attraction. Persistence of the state becomes increasingly precarious in the presence of noisy disturbances. We consider an underlying potential, as defined theoretically for a saddle-node fold and (via averaging) for a Hopf bifurcation. Close to a stable state, this potential has a parabolic form; but approaching a jump it becomes increasingly dominated by softening nonlinearities. If we have already detected a decrease in the linear decay rate, nonlinear information allows us to estimate the propensity for early tipping due to noise. We argue that one needs to extract information about the nonlinear features (a "softening") of the underlying potential from the time series to judge the probability and timing of tipping. This analysis is the logical next step if one has detected a decrease of the linear decay rate. If there is no discernable trend in the linear analysis, nonlinear softening is even more important in showing the proximity to tipping. After extensive normal form calibration studies, we check two geological time series from paleo-climate tipping events for softening of the underlying well. For the ending of the last ice age, where we find no convincing linear precursor, we identify a statistically significant nonlinear softening towards increasing temperature. The analysis has thus successfully detected a warning of the imminent tipping event.