Variability Analysis of Observational Time Series: An Overview of the Decomposition Methods for Non-stationary and Noisy Signals

Abstract

The analysis of observational data sequences in Geophysics consists of characterizing the underlying dynamics. An important preliminary step aims to analyze the variability related to the observed dynamic. The specific objectives related to this step are to remove noise, to determine the overall trend of the observational time series and to identify the relevant components contributing significantly to the original time series variability knowing that their number determines the dimensionality of the observed dynamics. Most of the observational time series have characteristics of non-stationarity and present fluctuations at all-time scales. In this context, variability analysis consists in representing time series in the time-frequency space and requires the development of specific numerical signal decomposition methods. The most commonly used techniques are adaptive and data-driven and among the most cited in the literature are the empirical mode decomposition, the empirical wavelet transform, and singular spectrum analysis. In this work, we describe all of these techniques and evaluate their ability to remove noise and to identify components corresponding to the physical processes involved in the evolution of the observed system and deduce the dimensionality of the associated dynamics. Results obtained with all of these methods on experimental total ozone columns and rainfall time series will be discussed and compared.