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Abstract:
Some studies show that when a dynamical system approaches its critical transition point, the changing spectral exponent can be used as an early warning signal. However, the performance of the spectral exponent may be influenced by different bifurcation types and spectral estimation techniques. We therefore test the performance of spectral exponents obtained from different spectral estimation algorithms in several prototypical stochastic dynamical models and find that the spectral exponent based on the Burg method outperforms other existing estimators, which helps to improve the spectral exponent's robustness in practical application. We also find that in most numerical experiments, the early warning ability of the Burg-method-based spectral exponent is obviously better than the lag-one autocorrelation (AC1) and variance for an upcoming tipping point. We then employ spectral exponents for early warning of the abrupt change of sea level pressure in the North Pacific Ocean in 1976–1977. The spectral exponents obtained by the Periodogram and Burg method show a decreasing trend since 1966, which we interpret as a warning signal hindcasting the transition. While the spectral exponent estimated by the Periodogram method is sensitive to the frequency band, the spectral exponent estimated via the Burg method exhibits a consistent trend across frequency bands. This further indicates the robustness of the spectral exponent obtained from the Burg method as an early warning signal of critical transition point.
