Changing climatic conditions often have the potential to produce an irreversible change in many ecosystems such as lakes, forests, etc. Previous studies contribute to the predictability of such events by capturing statistical signatures, known as Early Warning Signals (EWS), mostly by incorporating uncorrelated environmental noise. However, the correlation time of environmental noise may be small but is never strictly zero. In fact, paleoclimatic trends report the presence of temporal autocorrelation/colour in climatic variables, suggesting that climate has memory. The implications of the frequency spectrum of noise on biological populations’ persistence urge us to study the predictability of these events in coloured environments. Here in this work, we test the ability of leading EWS to anticipate the occurrence of different types of dynamical transitions, under autocorrelated environmental stochasticity. We capture the trends in statistical indicators using Kendall’s rank correlation. Furthermore, we analyse the robustness of our results using significance testing. Apart from the leading indicators, we also investigate multifractal and topological quantities of a transitioning system, by employing Multifractal Detrended Fluctuation Analysis (MF-DFA) and the visibility graph method.
Results/Conclusions
We find that the temporal autocorrelation of noise strongly influences the predictability of critical transitions. Elevated temporal autocorrelation often observed in environmental variables weakens the EWS in case of saddle-node bifurcation. However, pitchfork bifurcation is not preceded by characteristic fluctuations that may serve as EWS. We also observe that climate reddening may/may not increase the chance of critical transition depending upon the nature of a dynamical transition. Furthermore, MF-DFA and visibility graph method serve as an indicator for saddle-node bifurcation. Multifractal behaviour and various geometric properties in the time series is observed in the vicinity of saddle-node bifurcation, but no such significant behaviour is observed for pitchfork bifurcation. Consequently, coloured noise can alter local stability properties of the system depending upon its non-linearity. These findings have significant inference in the administration of biological populations. Thus, understanding the bifurcation mechanism for predictability and disintegration between false positives and true positive signals of critical transition in coloured environments is crucial.