Advanced Spectral Analysis and Cross Correlation Based on the Empirical Mode Decomposition: Application to the Environmental Time Series

In marine sciences, time series are often nonlinear and nonstationary. Adequate and specific methods are needed to analyze such series. In this letter, an application of the empirical mode decomposition method (EMD) associated to the Hilbert spectral analysis (HSA) is presented. Furthermore, EMD-based time-dependent intrinsic correlation (TDIC) analysis is applied to consider the correlation between two nonstationary time series. Four temperature time series obtained from automatic measurements in nearshore waters of the Réunion island are considered, recorded every 10 min from July 2011 to January 2012. The application of the EMD on these series and the estimation of their power spectra using the HSA are illustrated. The authors identify low-frequency tidal waves and display the pattern of correlations at different scales and different locations. By TDIC analysis, it was concluded that the high-frequency modes have small correlation, whereas the trends are perfectly correlated