Analysis of daily river flow fluctuations using Empirical Mode Decomposition and arbitrary order Hilbert spectral analysis
Résumé
In this paper we presented the analysis of two long time series of daily river flow data, 32 years recorded in the Seine river (France), and 25 years recorded in the Wimereux river (Wimereux, France). We applied a scale based decomposition method, namely Empirical Mode Decomposition (EMD), on these time series. The data were decomposed into several Intrinsic Mode Functions (IMF). The mean frequency of each IMF mode indicated that the EMD method acts as a filter bank. Furthermore, the cross-correlation between these IMF modes from Seine river and Wimereux river demonstrated correlation among the large scale IMF modes, which indicates that both rivers are likely to be influenced by the same events maritime climate event of Northern France. As a confirmation we found that the large scale parts have the same evolution trend. We finally applied arbitrary order Hilbert spectral analysis, a new technique coming from turbulence studies and time series analysis, on the flow discharge of Seine river. This new method provides an amplitude-frequency representation of the original time series, giving a joint pdf $p(\omega,\mathcal{A})$. When marginal moments of the amplitude are computed, one obtains an intermittency study in the frequency space. Applied to river flow discharge data from the Seine river, this shows the scaling range and characterizes the intermittent fluctuations over the range of scales from 4.5 to 60 days, between synoptic and intraseasonal scales.
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