Risk of tipping the overturning circulation due to increasing rates of ice melt

Abstract

Central elements of the climate system are at risk for crossing critical thresholds (so-called tipping points) due to future greenhouse gas emissions, leading to an abrupt transition to a qualitatively different climate with potentially catastrophic consequences. Tipping points are often associated with bifurcations, where a previously stable system state loses stability when a system parameter is increased above a well-defined critical value. However, in some cases such transitions can occur even before a parameter threshold is crossed, given that the parameter change is fast enough. It is not known whether this is the case in high-dimensional, complex systems like a state-of-the-art climate model or the real climate system. Using a global ocean model subject to freshwater forcing, we show that a collapse of the Atlantic Meridional Overturning Circulation can indeed be induced even by small-amplitude changes in the forcing, if the rate of change is fast enough. Identifying the location of critical thresholds in climate subsystems by slowly changing system parameters has been a core focus in assessing risks of abrupt climate change. This study suggests that such thresholds might not be relevant in practice, if parameter changes are not slow. Furthermore, we show that due to the chaotic dynamics of complex systems there is no well-defined critical rate of parameter change, which severely limits the predictability of the qualitative long-term behavior. The results show that the safe operating space of elements of the Earth system with respect to future emissions might be smaller than previously thought.

Keywords: abrupt climate change; overturning circulation; rate-induced tipping; tipping points.

Fig. 1.

Tipping of the ocean circulation. (A) Observational evidence for accelerating Greenland meltwater runoff (Materials and Methods) in comparison to conceptual boundaries of the safe operating space of the ocean circulation. (B) Maximum value of the meridional stream function, zonally averaged over the Atlantic basin, in a continuous model simulation. The forcing is increased to $F_{max}=0.31$ in small increments within 300 y each (black curve) and subsequently decreased to zero again (orange curve). (C, Inset) Time series of the forcing parameter $F$ in a parameter shift experiment with ramping duration $T=160$ y. (C, full plot) Corresponding values of the AMOC maximum (time is color coded). The black circles are the values shown in B. (D) Same as C but for $T=140$ y.

Fig. 2.

Dynamical mechanism for rate-induced transitions in a conceptual model. For the forcing parameter $0<\beta <{\beta }_c$ there is bistability of a present-day AMOC limit cycle (gray surface) and a collapsed AMOC (black line), separated by the unstable edge state (red surface). While the AMOC collapses in a bifurcation at ${\beta }_c$, a rate-induced collapse is possible when shifting from ${\beta }_1$ to ${\beta }_2$, depending on the model parameter $\gamma$ (Materials and Methods). (A) For $\gamma =0$ the model tracks the limit cycle for any rate of parameter shift. The orange and blue lines are trajectories for a fast and a slow rate, respectively. (B) For $\gamma =3$, there exist states on the limit cycle at ${\beta }_1$ (purple arch) that lie across the basin boundary at ${\beta }_2$. These tip to the other attractor in an instant parameter shift. Indeed, the orange trajectory crosses the basin boundary and tips to the collapsed AMOC, while the blue trajectory tracks the limit cycle. The green trajectory is obtained for a critical rate and evolves to the edge state. (C) Time series corresponding to the trajectories in $x$-$y$-$\beta$ space shown in B. (D) Analogous time series of parameter shift simulations with the ocean model using three different ramping durations.

Fig. 3.

Dependence of tipping on rate and initial conditions. (A) (Top) Ensemble of model simulations where the freshwater forcing parameter is increased linearly to $F_2=0.193$ over different durations $T$ starting after a 600-y spin-up at constant forcing $F_1=0.219$. Shown are color-coded time series of the AMOC maxima of the ensemble members. (Bottom) The outcome of the parameter shift is given as a bar plot. (B and C) Dependence on initial conditions for a fixed ramping duration of $T=70$ y. (B) (Bottom) The time series of a spin-up realization, given as 2-y averages of the AMOC maximum. The ensemble simulations branched off at the corresponding time points are shown above as time series of the AMOC maximum. The black line indicates when the parameter shift starts in the individual simulations. (C) As in B, but for a refined ensemble based on a 2-monthly sampling of a 10-y segment of the spin-up.

Fig. 4.

Tipping for an instantaneous parameter shift. Different initial conditions are generated by branching off a realization from the spin-up simulation every week, 2 mo, and 2 y for the ensembles in A, B, and C, respectively. The outcome of the instantaneous parameter shift from $F_1=0.193$ to $F_2=0.219$ branched off at the respective times is given by the bar plots. The time series above show the average of the AMOC maximum in between successive branch-off times.