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Detection of critical slowing down (CSD) is the dominant avenue foranticipating critical transitions from noisy time series data. Most commonly,changes in variance and lag-1 autocorrelation (AC(1)) are used as CSDindicators. However, these indicators will only produce reliable results if thenoise driving the system is white and stationary. In the more realistic case oftime-correlated red noise, increasing (decreasing) the correlation of the noisewill lead to spurious (masked) alarms for both variance and AC(1). Here, wepropose two new methods that can discriminate true CSD from possible changes inthe driving noise characteristics. We focus on estimating changes in the linearrestoring rate based on Langevin-type dynamics driven by either white or rednoise. We assess the capacity of our new estimators to anticipate criticaltransitions and show that they perform significantly better than other existingmethods both for continuous-time and discrete-time models. In addition toconceptual models, we apply our methods to climate model simulations of thetermination of the African humid period. The estimations rule out spurioussignals stemming from non-stationary noise characteristics and reveal adestabilisation of the African climate system as the dynamical mechanismunderlying this archetype of past abrupt climate change.

Detection of approaching critical transitions in natural systems driven by red noise