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Abstract

Many statistical indicators used to detect critical transitions in dynamic systems are subject to limitations arising from various factors, underscoring the necessity of evaluating their performance in different scenarios. This study quantitatively assesses the sensitivity of three such indicators in climate-dynamics scenarios—spectral exponent, skewness coefficient, and kurtosis coefficient—to key factors including perturbation magnitude, sliding window length, and temporal resolution, using Kendall τ values across several synthetic datasets. The results indicate that the spectral exponent exhibits lower sensitivity to perturbation magnitude than the other two indicators, maintaining consistent median Kendall τ values even as perturbation magnitude increases. In contrast, the median Kendall τ values of the skewness and kurtosis coefficients increases with heightened perturbation, thereby increasing the likehood of false positives. Longer sliding windows enhance Kendall τ values for all indicators, with the spectral exponent and skewness coefficient showing more pronounced improvements. Notably, the spectral exponent outperforms the other two indicators in terms of Kendall τ values when sufficient window lengths are available. However, in synthetic datasets with low temporal resolution, the Kendall τ values of the skewness and kurtosis coefficients surpasses that of the spectral exponent. These findings provide some insights for utilizing these indicators to provide early warning singals for the potential critical transitions in real applications.