Empirical Mode Decomposition for Estimating Ocean Turbulent Diffusion Coefficient from One Lagrangian Drifter Trajectory

With the empirical mode decomposition (EMD) for the Hilbert–Huang transform (HHT), nonlinear and non-stationary signals from Lagragian drifters’ trajectories are adaptively decomposed into a series of intrinsic mode functions (IMFs) with corresponding specific scale for each IMF. At each step of the EMD, the low-frequency component is mainly determined by the average of the upper Envelope (consisting of local maxima) and the lower envelope (consisting of local minima). The high-frequency component (stochastic) is the deviation of the signal relative to the low-frequency component (deterministic). The stochastic component is diffusive, but not the deterministic. In this paper, a criterion is proposed to separate Lagrangian velocity into low-frequency (non-diffusive, i.e., deterministic) and high-frequency (diffusive) components. The diagonal diffusion coefficients are calculated using classical mixing length theory and general ideas of a theory of turbulent diffusion. Non-diagonal diffusion coefficients are calculated using the classical theory of the first passage boundary. The turbulent diffusion coefficients for the California coastal region are presented using the data from the RAFOS floats.

Reference

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Chu, P.C., C.W. Fan, and N. Huang, 2014: Derivative-optimized empirical mode decomposition for the Hilbert-Huang transform. Journal of Computational and Applied Mathematics, 259, 57-64.