Predictions of critical transitions with non-stationary reduced order models

Here we demonstrate the ability of stochastic reduced order models to predict the statistics of non-stationary systems undergoing critical transitions. First, we show that the reduced order models are able to accurately predict the autocorrelation function and probability density functions (PDF) of higher dimensional systems with time-dependent slow forcing of either the resolved or unresolved modes. Second, we demonstrate that whether the system tips early or repeatedly jumps between the two equilibrium points (flickering) depends on the strength of the coupling between the resolved and unresolved modes and the time scale separation. Both kinds of behaviour have been found to preceed critical transitions in earlier studies. Furthermore, we demonstrate that the reduced order models are also able to predict the timing of critical transitions. The skill of various proposed tipping indicators are discussed.