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Identification of Low-Dimensional Energy Containing/Flux Transporting Eddy Motion in the Atmospheric Surface Layer Using Wavelet Thresholding Methods

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  • 1 School of the Environment, Duke University, Durham, North Carolina
  • | 2 Department of Statistics, Duke University, Durham, North Carolina
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Abstract

The partitioning of turbulent perturbations into a “low-dimensional” active part responsible for much of the turbulent energy and fluxes and a “high-dimensional” passive part that contributes little to turbulent energy and transport dynamics is investigated using atmospheric surface-layer (ASL) measurements. It is shown that such a partitioning scheme can be achieved by transforming the ASL measurements into a domain that concentrates the low-dimensional part into few coefficients and thus permits a global threshold of the remaining coefficients. In this transformation–thresholding approach, Fourier rank reduction and orthonormal wavelet and wavelet packet methods are considered. The efficiencies of these three thresholding methods to extract the events responsible for much of the heat and momentum turbulent fluxes are compared for a wide range of atmospheric stability conditions. The intercomparisons are performed in four ways: (i) compression ratios, (ii) energy conservation, (iii) turbulent flux conservation, and (iv) finescale filtering via departures from Kolmogorov’s K41 power laws. For orthonormal wavelet and wavelet packets analysis, wavelet functions with varying time–frequency localization properties are also considered. The study showed that wavelet and wavelet packet Lorentz thresholding can achieve high compression ratios (98%) with minimal loss in energy (3% loss) and fluxes (4%). However, these compression ratios and energy and flux conservation measures are comparable to the linear Fourier rank reduction method if a Lorentz threshold function is applied to the latter. Finally, it is demonstrated that orthonormal wavelet and wavelet packets thresholding are insensitive to the analyzing wavelet.

Corresponding author address: Dr. Gabriel G. Katul, School of the Environment, Duke University, Box 90328, Durham, NC 27708- 0328.

Email: gaby@duke.edu

Abstract

The partitioning of turbulent perturbations into a “low-dimensional” active part responsible for much of the turbulent energy and fluxes and a “high-dimensional” passive part that contributes little to turbulent energy and transport dynamics is investigated using atmospheric surface-layer (ASL) measurements. It is shown that such a partitioning scheme can be achieved by transforming the ASL measurements into a domain that concentrates the low-dimensional part into few coefficients and thus permits a global threshold of the remaining coefficients. In this transformation–thresholding approach, Fourier rank reduction and orthonormal wavelet and wavelet packet methods are considered. The efficiencies of these three thresholding methods to extract the events responsible for much of the heat and momentum turbulent fluxes are compared for a wide range of atmospheric stability conditions. The intercomparisons are performed in four ways: (i) compression ratios, (ii) energy conservation, (iii) turbulent flux conservation, and (iv) finescale filtering via departures from Kolmogorov’s K41 power laws. For orthonormal wavelet and wavelet packets analysis, wavelet functions with varying time–frequency localization properties are also considered. The study showed that wavelet and wavelet packet Lorentz thresholding can achieve high compression ratios (98%) with minimal loss in energy (3% loss) and fluxes (4%). However, these compression ratios and energy and flux conservation measures are comparable to the linear Fourier rank reduction method if a Lorentz threshold function is applied to the latter. Finally, it is demonstrated that orthonormal wavelet and wavelet packets thresholding are insensitive to the analyzing wavelet.

Corresponding author address: Dr. Gabriel G. Katul, School of the Environment, Duke University, Box 90328, Durham, NC 27708- 0328.

Email: gaby@duke.edu

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