Uncertainty quantification for overshoots of tipping thresholds

Abstract. Many subsystems of the Earth system, which are currently closely following a stable state, are at risk of undergoing abrupt transitions 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. Forcing a nonlinear system beyond a critical threshold that signifies the onset of self-amplifying feedbacks constitutes a possible mechanism for tipping. However, previous work has shown that it could be possible to briefly overshoot a critical threshold without tipping. For some cases, the peak overshoot distance and the time a system can spend beyond a threshold are governed by an inverse-square law relationship (Ritchie et al., 2019). However, in the real world or in complex models, critical thresholds and other system features, such as inherent timescales and the system's linear restoring force after perturbations, are highly uncertain. In this work, we explore how such uncertainties propagate to uncertainties in the probability of tipping in response to a temporary overshoot from the perspective of uncertainty quantification. We show the importance of constraining uncertainty in the location of the tipping threshold and the linear restoring force to the system’s stable state to better constrain the uncertainty in the tipping behaviour for overshoot trajectories. We first prototypically analyse effects of an uncertain critical threshold location separately from effects due to an uncertain linear restoring force. We then perform an analysis of joint effects of uncertain system characteristics within a conceptual model for the Atlantic Meridional Overturning Circulation (AMOC). The simple box model for the AMOC shows that these uncertainties have the potential to reverse conclusions for mitigation pathways. A pathway previously associated with a low risk of tipping may become highly dangerous if the tipping threshold were to be closer than previously assumed. In this conceptual model, we illustrate how constraining the highly uncertain diffusive timescale (representative of wind-driven fluxes) within this box model reduces the tipping uncertainty of the AMOC in response to overshoot scenarios.