Time-frequency analysis of currents data sampled at four stations in the Réunion island: application of EMD and wavelets

Kbaier Ben Ismail, Dhouha; Lazure, Pascal and Puillat, Ingrid (2015). Time-frequency analysis of currents data sampled at four stations in the Réunion island: application of EMD and wavelets. In: ITISE 2015: International work-conference on Time Series Analysis, 1-3 Jul 2015, Granada, Spain.

URL: https://www.researchgate.net/publication/280072401...

Abstract

We consider the statistical analysis of high frequency sampled time series in nearshore waters of the Réunion island, located in the Indian Ocean 700 km east of Madagascar. We focus particularly on automatic measurements of current data sets at four different stations in the island. As this entire dataset is characterized by non-linearity and non-stationarity, two time-frequency decomposition methods, namely wavelets and Hilbert-Huang Transformation (HHT), are applied for the analysis of the entire dataset. Using the Continuous Wavelet Transform (CWT), some properties of the currents time series are determined. Then, the inertial wave and several low-frequency tidal waves are identified by the application of the Empirical Mode Decomposition (EMD) and the associated Hilbert spectral analysis (resp. HHT). Both wavelet and HHT approaches provide very useful information about the characteristics of currents measurements, although a poor low-frequency resolution is discerned for the Morlet wavelet spectra. Furthermore, the authors investigate the cross-correlations between currents at the different stations. Wavelet coherence and EMD based Time Dependent Intrinsic Correlation (TDIC) analyses are applied to consider the correlation between two nonstationary time series. By TDIC analysis, it was concluded that the high frequency modes have small correlation; whereas the trends are perfectly correlated. The results obtained by wavelet coherence are very similar, thus confirming that both approaches could be used for identification of main properties of marine environmental time series. The methodologies presented in this paper are general and thus can be applied on other time series from the environmental and oceanic sciences, where time series are complex with fluctuations over a large range of different spatial and temporal scales, from seconds to thousands of years. Keywords: Continuous wavelet transform, cross-correlation, cross-wavelet, empirical mode decomposition, Hilbert-Huang transform, Hilbert spectral anal-ysis, Morlet wavelet, stationarity, time dependent intrinsic correlation, time series, wavelets, wavelet coherence.

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