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Resampling hierarchical processes in the wavelet domain: A case study using atmospheric turbulence

Publication ,  Journal Article
Angelini, C; Cava, D; Katul, G; Vidakovic, B
Published in: Physica D: Nonlinear Phenomena
July 15, 2005

There is a growing need for statistical methods that generate an ensemble of plausible realizations of a hierarchical process from a single run or experiment. The main challenge is how to construct such an ensemble in a manner that preserves the internal dynamics (e.g. intermittency) and temporal persistency. A popular hierarchical process often used as a case study in such problems is atmospheric turbulent flow. Analogies to turbulence are often called upon when information flow from large to small scales, non Gaussian statistics, and intermittency are inherent attributes of the hierarchical process under consideration. These attributes are key defining syndromes of the turbulent cascade thereby making turbulence time series ideal for testing such ensemble generation schemes. In this study, we propose a wavelet based resampling scheme (WB) and compare it to the traditional Fourier based phase randomization bootstrap (FB) approach within the context of the turbulence energy cascade. The comparison between the two resampling methods and observed ensemble statistics constructed by clustering similar meteorological conditions demonstrate that the WB reproduces several features related to intermittency of the ensemble series when compared to FB. In particular, the WB exhibited an increase in wavelet energy activity and an increase in the wavelet flatness factor with increasing frequency consistent with the cluster of ensemble statistics. On the other hand, the FB yielded no increase in such energy activity with scale and resulted in near Gaussian wavelet coefficients at all frequencies within the inertial subrange. The scaling behavior of the longitudinal (u′) and vertical (w′) velocity structure functions of various order p>0 confirms that WB preserves the small scale intermittency, whereas FB completely destroys it. The extension of WB to the multivariate case is also demonstrated via the conservation of co-spectra between u′ and w′ time series. Because the resampling strategy proposed here is conducted in the wavelet domain, gap-infected and uneven sampled time series can be readily accommodated within the WB. Finally, recommendations about the filter and block sizes are discussed. © 2005 Elsevier B.V. All rights reserved.

Duke Scholars

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

July 15, 2005

Volume

207

Issue

1-2

Start / End Page

24 / 40

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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ICMJE
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Angelini, C., Cava, D., Katul, G., & Vidakovic, B. (2005). Resampling hierarchical processes in the wavelet domain: A case study using atmospheric turbulence. Physica D: Nonlinear Phenomena, 207(1–2), 24–40. https://doi.org/10.1016/j.physd.2005.05.015
Angelini, C., D. Cava, G. Katul, and B. Vidakovic. “Resampling hierarchical processes in the wavelet domain: A case study using atmospheric turbulence.” Physica D: Nonlinear Phenomena 207, no. 1–2 (July 15, 2005): 24–40. https://doi.org/10.1016/j.physd.2005.05.015.
Angelini C, Cava D, Katul G, Vidakovic B. Resampling hierarchical processes in the wavelet domain: A case study using atmospheric turbulence. Physica D: Nonlinear Phenomena. 2005 Jul 15;207(1–2):24–40.
Angelini, C., et al. “Resampling hierarchical processes in the wavelet domain: A case study using atmospheric turbulence.” Physica D: Nonlinear Phenomena, vol. 207, no. 1–2, July 2005, pp. 24–40. Scopus, doi:10.1016/j.physd.2005.05.015.
Angelini C, Cava D, Katul G, Vidakovic B. Resampling hierarchical processes in the wavelet domain: A case study using atmospheric turbulence. Physica D: Nonlinear Phenomena. 2005 Jul 15;207(1–2):24–40.
Journal cover image

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

July 15, 2005

Volume

207

Issue

1-2

Start / End Page

24 / 40

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics