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Uncovering temporal regularity in atmospheric dynamics through Hilbert phase analysis.

Dario A Zappalà1, Marcelo Barreiro2, Cristina Masoller1

  • 1Departament de Física, Universitat Politècnica de Catalunya, Rambla St. Nebridi 22, 08222 Terrassa, Barcelona, Spain.

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This study introduces a novel Hilbert transform method combined with temporal averaging to reveal hidden periodicities in complex signals, like surface air temperature data. The approach successfully identifies climate patterns, outperforming Fourier analysis in irregular regions.

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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.