Effective detection of early warning signal with power spectrum in climate change system

The development of early warning signals (EWS) before abrupt changes can help prevent system collapse. Current EWS, such as increasing autocorrelation (AC) and variance, provide general indicators of impending tipping points by detecting the slowing down of dynamics near transitions. However, these conventional EWS often fail to distinguish between oscillatory behavior (e.g., Hopf bifurcation) and shifts to a distant attractor (e.g., Fold bifurcation). Additionally, traditional EWS are less reliable in systems affected by density-dependent noise. To address these limitations, alternative EWS based on power spectrum analysis, known as spectral EWS, have been proposed. In this study, we apply analytical approximations for EWS as systems approach different types of local bifurcations. This novel method allows us to use spectral EWS that offer enhanced sensitivity to approaching transitions and increased robustness to density-dependent noise. We demonstrate the application of spectral EWS as robust indicators across three general models with different bifurcations. Our analysis also reveals distinct signals preceding transitions in data from sea ice loss. This combined approach underscores the advantages of incorporating spectral EWS into existing methodologies, providing a more comprehensive toolkit for anticipating critical transitions in real-world systems.