Using the Hilbert-Huang cospectrum to determine fluxes in nonstationary conditions

In recent decades Multiresolution methods have been used to decompose nonstationary signals in their scales. For example, Fourier and wavelet methods implicitly assume that the signal is composed by the superposition of specific functional forms. A novel, data driven approach, called Empirical Mode Decomposition (EMD) has been introduced in recent years by N. Huang. It consists in obtaining Intrinsic Mode Functions (IMF) through an adaptive/iterative procedure based on envelope averages without apriori assuming any previously defined signal form. Huang's EMD has been successfully used in analyzing nonlinear and nonstationary data, and has the remarkable feature of identifying trends in the data. Furthermore, each IMF is defined in such a way that Hilbert transform can be used to obtain instantaneous frequencies. The combination of both Hilbert spectral analysis and Huang's method is now known as the Hilbert-Huang Transform.

The micrometeorological community has been extensively associating covariances to turbulent fluxes, an approach that requires stationarity to be exact. However, data to which these methods are applied, are often nonstationary. In this study we propose a new method based on the Hilbert-Huang Transform as a way to obtain instantaneous cospectra whose integration corresponds to genuine geophysical fluxes, even if the original series are nonstationary.

Examples of the proposed method are shown. In stationary situations, the results quantitatively agree with those obtained by other methods (Fourier, Haar MRA, etc). However, in nonstationary conditions, such as the morning or evening transition, they are appreaciably different. The technique allows using variable size windows for flux determination.