Hybrid signal detection approach for hydro-meteorological variables combining EMD and cross-wavelet analysis

Abstract

The aim of this article is to present a methodology that describes the relationship between two time series according to their oscillatory modes. Cross-wavelet analysis is used to analyse the connection between the outputs of the empirical mode decomposition (EMD). The combined EMD and cross-wavelet methodology is used for the description of the connection between the annual mean streamflow of Quebec rivers and the North Atlantic Oscillation index (NAO). The relationship between the two time series is analysed by cross-wavelet analysis at the level of the mode of oscillation extracted from the EMD algorithm. The resulting cross-spectra are obtained individually for 18 stations and show intermittent intensity in these relationships between 1970 and 1990 for different oscillation modes. To highlight its particularity, the present methodology is compared with the results of a similar combination of multiresolution analysis (MRA) and cross-wavelet analysis. It shows that EMD isolates clearer bands of frequencies than MRA. Finally, a multi-site analysis is proposed, which performs a principal component analysis of the cross-spectra. This analysis illustrates the evolution of the relationships according to the geographic location. Finally, the advantages and limitations of the proposed methodology are discussed.