Timescale competition controls tipping behaviour under climate overshoot

Tipping elements of the Earth system are often framed as threshold phenomena governed by peak global warming. However, climate components operate on widely differing intrinsic timescales, so the outcome of overshoot warming may depend not only on temperature thresholds but also on the interaction between forcing duration and system inertia. Here we use a comprehensive Earth system model with interactive ocean circulation, Arctic sea ice and a fully coupled Greenland Ice Sheet to simulate multi-millennial trajectories under extended overshoot scenarios. We find that reversibility is strongly component-specific. Fast components, including the Atlantic Meridional Overturning Circulation (AMOC) and Arctic sea ice, weaken during peak forcing but recover as greenhouse-gas concentrations decline. In contrast, the Greenland Ice Sheet shows persistent mass loss and long-term commitment even under strong mitigation, consistent with its slow dynamical adjustment and geometry-dependent feedback. Despite freshwater fluxes exceeding 0.1~Sv, AMOC collapse does not occur, highlighting the importance of spatial meltwater routing and advective export. Our results demonstrate that Earth system reversibility cannot be inferred from peak warming alone. Instead, overshoot duration reorganizes the hierarchy of tipping elements according to intrinsic process timescales. Tipping is therefore a dynamical outcome emerging from timescale competition within a coupled system. These findings imply that even temporary overshoot can irreversibly commit slow structural components of the climate system, redefining how climate stabilization targets should be interpreted on millennial timescales.