Slowing down - early warning sign of an approaching tipping point 1. Introduction The phrase “tipping point” means that “little things can make a big difference, or at a specific moment in time, a small change can bring large and significant, longstanding consequences for a particular system. The term tipping element includes subsystems of the Earth that can be switched into a different state by small disturbances. Some of the possible future tipping elements in the Earth’s climate system include the Arctic summer sea- ice, the Greenland ice sheet, the Atlantic thermohaline circulation, El Nino-Southern Oscillation and others. Predicting a tipping point is important because such an abrupt change, for example in the climate system, could occur within decades or even years which is not enough time to adapt. Probably one of the best ways to predict an approaching tipping point is slowing down. Usually, as a system becomes unstable, and it shifts to some other stable state, the system is likely to become slower as it responds to small disturbances. Figure 1 indicates that kind of system. The ball represents the state of the system. The well gets shallower as the tipping point as we get closer to the upcoming tipping point. As a result the system returns back to its original state slower and slower (it takes more time for it to recover from small perturbations) (Figure 1). The slowing down indicator has been tested in climate models and palaeoclimate data that approach tipping points. Eight ancient events of abrupt climate change were reconstructed from geological records. The change in autocorrelation in time series was analyzed, in order to determine whether the climate system slows down when a critical threshold is approached. The slowing down should be reflected as a decrease in the rates of change in a system, and therefore, as an increase in the short- term autocorrelation in the time series. In all examples, autocorrelation showed an increase in the period before the transition which is a good indicator that slowing down occurred before the sudden change (Figure 2). Some simulations had stronger and bigger autocorrelation trend than others. The records which has the most data (more than 450 points) had the largest increase in slowing down prior to the abrupt change compared to the others. 2. Tipping point prediction The same methods were used to analyze results from climate models that were slowly brought closer to a known tipping point. The models simulates three different shifts in the climate system: ice-house Earth transition, collapse of the thermohaline circulation and desertification of North America. The control parameter of the system is changed gradually and eventually all simulations cross a tipping point. In each model the shift is preceded by a significant slowing down which is indicated by the increase in the autocorrelation (Figure 3). Figure 2. Autocorrelation of climate shifts in the past In order to use slowing down as a warning signal for approaching a tipping point, there is a need for high quality long time series and sufficient resolution. A large limitation is that slowing down will only take place if the system slowly and steadily towards a bifurcation point. Therefore, transitions caused by an abrupt large event will not be accompanied by slowing down. Some people also think that slowing down, on its own, is not a sufficient indicator for an approaching tipping point. Ideally, it should be combined with other warning signs of an upcoming threshold, in order to make more robust predictions. 3. Tests of slowing down 4. Limitations and Future work Figure 1. (left) Slowing down of a system. Figure 3. (bottom) Three simulated abrupt shifts in the climate. Rositsa Stoyanova, F600, University of Liverpool In principle, early warning signs can be seen before a tipping point is reached. Palaeodata and climate model experiments show that it is possible to detect slowing down that occurs before an abrupt transition happens. There are some limitations of using the slowing down indicator but it still serves as a potential way of predicting any climatic changes in the future. It could also be used as an universal way to predict tipping points in other systems. 5. Conclusion Dakos, V., Scheffer, M., Nes, E.H., Brovkin, V., Petoukov, V., Held, H. (2008) Slowing down as an early warning signal for abrupt climate change, PNAS, vol.105, Lenton, M.T.(2011) Early warning of climate tipping points, Nature Climate Change, vol.1, Lenton, M. T., Held, H., Kriegler, E., Hall, J.W., Lucht, W., Rahmstorf, S., Schellnhuber, H.J. (2007) Tipping elements in the Earth’s climate system, PNAS, vol.105, Lenton, T.M., Livina, V.N., Dakos, V., Nes, E.H., Scheffer, M. (2012) Early warning of climate tipping points from critical slowing down: comparing methods to improve robustness, Phil. Trans. R. Soc., 370,