Uncertainty quantification for overshoots of tipping thresholds

To tip or not to tip? Many subsystems of the Earth are at risk of undergoing abrupt transitions from their current stable state to a drastically different and often less desired state due to anthropogenic climate change. These so-called tipping events often present severe consequences for ecosystems and human livelihood that are difficult to reverse. One common mechanism for tipping to occur is via forcing and driving a nonlinear system beyond a critical threshold that signifies self-amplifying feedbacks inducing tipping. However, previous work has shown that it is possible to briefly overshoot a critical threshold and avoid tipping. Specifically, the peak distance of an overshoot and the time a system can spend beyond a threshold are governed by an inverse square law relationship. In the real world or complex models, critical thresholds and other system features determining the permitted overshoot are highly uncertain. In this presentation, we look at how such uncertainties affect the probability of tipping from the perspective of uncertainty quantification. We show the importance of constraining uncertainty in the location of the critical threshold and the linear restoring rate to the stable state to reduce the uncertainty in the probability of tipping. Using a simple box model for the Atlantic Meridional Overturning Circulation, we highlight the need to constrain the high uncertainty found in wind-driven fluxes represented by a diffusive time scale within the box model to reduce uncertainty in the tipping probability for overshoot scenarios.