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

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.