07 Jan 2022
07 Jan 2022
Status: this preprint is currently under review for the journal NPG.

The Empirical Adaptive Wavelet Decomposition (EAWD): An adaptive decomposition for the variability analysis of observation time series in atmospheric science

Olivier Delage1, Thierry Portafaix1, Hassan Bencherif1,2, Alain Bourdier3, and Emma Lagracie1,4 Olivier Delage et al.
  • 1Laboratoire de l’Atmosphère et des Cyclones, (LACy, UMR 8105 CNRS, Université de la Réunion, Météo-France), Université de La Réunion, 97400 Saint-Denis de La Réunion, France
  • 2School of Chemistry and Physics, University of KwaZulu-Natal, Westville, Durban 4041, South Africa
  • 3Department of Physics and Astronomy, The University of New Mexico, Albuquerque, NM, USA
  • 4École Nationale Supérieure des Techniques Avancées, Paris, France

Abstract. Most observational data sequences in geophysics can be interpreted as resulting from the interaction of several physical processes at several time and space scales. As a consequence, measurements time series have often characteristics of non-linearity and non-stationarity and thereby exhibit strong fluctuations at different time-scales. The variability analysis of a time series consists in decomposing it into several mode of variability, each mode representing the fluctuations of the original time series at a specific time-scale.

Such a decomposition enables to obtain a time-frequency representation of the original time series and turns out to be very useful to estimate the dimensionality of the underlying dynamics. Decomposition techniques very well suited to non-linear and non-stationary time series have recently been developed in the literature. Among the most widely used of these technics are the empirical mode decomposition (EMD) and the empirical wavelet transformation (EWT). The purpose of this paper is to present a new adaptive filtering method that combines the advantages of the EMD and EWT technics, while remaining close to the dynamics of the original signal made of atmospheric observations, which means reconstructing as close as possible to the original time series, while preserving its variability at different time scales.

Olivier Delage et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on npg-2021-37', Anonymous Referee #1, 15 Feb 2022
    • AC1: 'Reply on RC1', Olivier Delage, 10 May 2022
  • RC2: 'Comment on npg-2021-37', Anonymous Referee #2, 05 Apr 2022
    • AC2: 'Reply on RC2', Olivier Delage, 10 May 2022

Olivier Delage et al.

Olivier Delage et al.


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Short summary
The complexity of geophysics systems results in time series with fluctuations at all time scales. The analysis of their variability then consists in decomposing them in a set of basis signals. We developed in the present work a new adaptive filtering method called: Empirical Adaptive Wavelet Decomposition that optimize the Empirical Mode Decomposition existing technic by overcoming its drawbacks using the rigor of wavelets as defined in the recently published Empirical Wavelet Transform method.