Empirical Mode Decomposition Applied to Eddy Covariance Calculations

Current atmospheric data analysis techniques rely heavily on the use of Fourier methods to analyze and interpret periodic oscillations within the atmosphere. However, these methods require a stationary atmosphere-a highly simplified assumption. This assumption generates errors when modeling meteorological phenomena, such as small-scale energy exchange of greenhouse gases. To better understand the dynamics and energy exchange of atmospheric variables in a nonstationary atmosphere, a relatively new spectral analysis tool can be used. Empirical Mode Decomposition (EMD) is an algorithm which can separate any oscillatory signal, whether nonlinear and/or nonstationary, into its intrinsic periodic components. Rather than utilizing a predetermined set of basis functions, such as in Fourier or Wavelet analysis, EMD 'sifts' basis functions empirically from the data set itself, allowing for a more adaptive and local description of the intrinsic variability of the signal. The basis functions are time-domain functions whose instantaneous amplitudes and frequencies may vary; they are not required to be orthogonal. We demonstrate that the EMD method can be used to reformulate traditional Eddy Covariance methods for calculating the frequency contributions to atmospheric (co)variances. 20 Hz sonic anemometer data taken during the 2002 Soil Moisture EXperiment (SMEX02) is used to calculate (co)variances using the EMD method. The method is compared with traditional methods, including Fourier analysis. We show that the EMD method oftentimes exhibits nonorthogonal contributions to the overall (co)variance. In fact, the nonorthogonal contributions can be linked to the degree of nonstationarity within the signal. Therefore, we present a new tool, which is similar to the Ogive function, which quantifies the degree of nonstationarity within a signal, and determines the necessary sampling duration required to capture the entire (co)variance. For the calculation of latent and sensible heat fluxes, errors due to nonstationarity are quantified using the EMD method and compared to the near-surface energy budget deficit.