Mathematics – Dynamical Systems
Scientific paper
2011-03-15
Phil. Trans. R. Soc. A 370 (1962) 1012-1040, 2012
Mathematics
Dynamical Systems
22 pages, 11 figures, changed title back, corrected smaller mistakes, updated references
Scientific paper
10.1098/rsta.2011.0316
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.
Sieber Jan
Thompson Michael J. T.
No associations
LandOfFree
Nonlinear softening as a predictive precursor to climate tipping does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nonlinear softening as a predictive precursor to climate tipping, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonlinear softening as a predictive precursor to climate tipping will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-261719