Uncovering temporal regularity in atmospheric dynamics through Hilbert phase analysis

Area of Science:

• Complex Systems Analysis
• Time Series Signal Processing
• Climate Science Data Analysis

Background:

• Identifying regularities in complex oscillatory signals is crucial across disciplines.
• Traditional methods like Fourier analysis struggle with highly irregular or noisy data.

Purpose of the Study:

• To develop a novel method for uncovering hidden temporal regularities in complex oscillatory signals.
• To apply and validate this method on global surface air temperature (SAT) datasets.

Main Methods:

• A new approach utilizing the Hilbert transform (HT) combined with a moving window averaging technique.
• Analysis of the mean rotation period of the Hilbert phase as a function of averaging window length (τ).
• Application of machine learning algorithms to features derived from the method for time series classification.

Main Results:

• The method successfully identified expected periodicities (e.g., 1-year solar cycle) and revealed non-trivial periodicities in irregular SAT data, correlating with phenomena like El Niño.
• The Hilbert transform approach detected periodicities missed by Fourier analysis in complex SAT dynamics.
• Features derived from the method proved informative for SAT time series classification, validated by synthetic data analysis.

Conclusions:

• Hilbert analysis with temporal averaging is a powerful tool for discovering hidden temporal regularity in complex signals.
• This method offers a significant advancement for analyzing climate data and other complex oscillatory systems.
• The approach provides a new avenue for time series classification and understanding underlying data-generating mechanisms.