File:Fig 4 Early indicators before a tipping point.png

English: Early indicators before a tipping point. (Top row) The time-series of the state of a system (‘X’) that is being slowly forced towards a tipping point (blue, purple, red), exhibits slowing recovery from fluctuations. (Middle row) This ‘critical slowing down’ can be seen as an increase in correlation between the state of the system from one time point, X(t), to the next, X(t+1). (Bottom row) This property (lag-1 temporal autocorrelation; AR(1)) can be measured on a ‘window’ of data (e.g. the blue interval) and plotted at the end of that window (the blue dot). The window can then be moved along the time-series, recalculating the indicator at each time step (e.g. purple and red intervals and dots). The resulting overall increase in autocorrelation (AR(1)) provides an early indicator that a tipping point is being approached.