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Hilbert Transform from Wavelet Analysis to Extract the Envelope of an Atmospheric Mode: Examples

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  • 1 Laboratoire de Météorologie Dynamique du CNRS, Ecole Polytechnique, Palaiseau, France
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Abstract

During the last few years a great number of papers have been devoted to a versatile tool: continuous wavelet analysis and its application. Thus, this tool has become widespread for analyzing meteorological and oceanographic data. Nevertheless, there is a topic that deserves to be further developed: obtaining the Hilbert transform from the continuous wavelet analysis to extract the envelope, sometimes called modulation law of an atmospheric mode. This is the purpose of this paper. It is discussed through the analysis of two types of time series, which represent, respectively, a simulated amplitude modulation and observational data related to the Indian summer monsoon. It is shown that continuous wavelet analysis and synthesis is a tool that is well adapted to detecting an envelope. Thus, a meteorological pattern associated with a given mode can be explored in more depth.

Corresponding author address: Dr. A. Ouergli, Laboratoire de Météorologie Dynamique du CNRS, Ecole Polytechnique, Palaiseau Cedex 91128, France. Email: ouergli@lmd.merlin.polytechnique.fr

Abstract

During the last few years a great number of papers have been devoted to a versatile tool: continuous wavelet analysis and its application. Thus, this tool has become widespread for analyzing meteorological and oceanographic data. Nevertheless, there is a topic that deserves to be further developed: obtaining the Hilbert transform from the continuous wavelet analysis to extract the envelope, sometimes called modulation law of an atmospheric mode. This is the purpose of this paper. It is discussed through the analysis of two types of time series, which represent, respectively, a simulated amplitude modulation and observational data related to the Indian summer monsoon. It is shown that continuous wavelet analysis and synthesis is a tool that is well adapted to detecting an envelope. Thus, a meteorological pattern associated with a given mode can be explored in more depth.

Corresponding author address: Dr. A. Ouergli, Laboratoire de Météorologie Dynamique du CNRS, Ecole Polytechnique, Palaiseau Cedex 91128, France. Email: ouergli@lmd.merlin.polytechnique.fr

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