Inverse-square law between time and amplitude for crossing tipping thresholds

Investigating climate tipping points under various emission reduction and carbon capture scenarios with a stochastic climate model

We study the mitigation of climate tipping point transitions using an energy balance model. The evolution of the global mean surface temperature is coupled with the CO 2 concentration through the green-house effect. We model the CO 2 concentration with a stochastic delay differential equation (SDDE), accounting for various carbon emission and capture scenarios. The resulting coupled system of SDDEs exhibits a tipping point phenomena: if CO 2 concentration exceeds a critical threshold (around 478   ppm ), the temperature experiences an abrupt increase of about six degrees Celsius. We show that the CO 2 concentration exhibits a transient growth which may cause a climate tipping point, even if the concentration decays asymptotically. We derive a rigorous upper bound for the CO 2 evolution which quantifies its transient and asymptotic growths, and provides sufficient conditions for evading the climate tipping point. Combining this upper bound with Monte Carlo simulations of the stochastic climate model, we investigate the emission reduction and carbon capture scenarios that would avert the tipping point.

Basin bifurcations, oscillatory instability and rate-induced thresholds for Atlantic meridional overturning circulation in a global oceanic box model

The Atlantic meridional overturning circulation (AMOC) transports substantial amounts of heat into the North Atlantic sector, and hence is of very high importance in regional climate projections. The AMOC has been observed to show multi-stability across a range of models of different complexity. The simplest models find a bifurcation associated with the AMOC 'on' state losing stability that is a saddle node. Here, we study a physically derived global oceanic model of Wood et al. with five boxes, that is calibrated to runs of the FAMOUS coupled atmosphere-ocean general circulation model. We find the loss of stability of the 'on' state is due to a subcritical Hopf for parameters from both pre-industrial and doubled CO₂ atmospheres. This loss of stability via subcritical Hopf bifurcation has important consequences for the behaviour of the basin of attraction close to bifurcation. We consider various time-dependent profiles of freshwater forcing to the system, and find that rate-induced thresholds for tipping can appear, even for perturbations that do not cross the bifurcation. Understanding how such state transitions occur is important in determining allowable safe climate change mitigation pathways to avoid collapse of the AMOC.