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Maximal Overlap Wavelet Statistical Analysis With Application to Atmospheric Turbulence

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Abstract

Statistical tools based on the maximal overlap discrete wavelet transform (MODWT) are reviewed, and then applied to a dataset of aircraft observations of the atmospheric boundary layer from the tropical eastern Pacific, which includes quasi-stationary and non-stationary segments. The wavelet methods provide decompositions of variances and covariances, e.g. fluxes, between time scales that effectively describe a broadband process like atmospheric turbulence. Easily understood statistical confidence bounds are discussed and applied to these scale decompositions, and results are compared to Fourier methods for quasi-stationary turbulence. The least asymmetric LA(8) wavelet filter yields coefficients that exhibit better uncorrelatedness across scales than the Haar filter and is better suited for decomposition of broadband turbulent signals. An application to a non-stationary segment of our dataset, namely vertical profiles of the turbulent dissipation rate, highlights the flexibility of wavelet methods.

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Abbreviations

ANOVA:

Analysis of Variance

DWT:

Discrete Wavelet Transform

EDOF:

Equivalent Degrees Of Freedom

LA:

Least Asymmetric

MODWT:

Maximal Overlap Discrete Wavelet Transform

PSD:

Power Spectral Density

SST:

Sea Surface Temperature

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Authors and Affiliations

  1. Department of Atmospheric Science, University of Washington, Seattle, WA, 98195-1640, U.S.A

    Charles R. Cornish & Christopher S. Bretherton

  2. Applied Physics Laboratory, University of Washington, Seattle, WA, 98195-5640, U.S.A

    Donald B. Percival

Authors
  1. Charles R. Cornish
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  2. Christopher S. Bretherton
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  3. Donald B. Percival
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Correspondence to Charles R. Cornish.

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Cornish, C.R., Bretherton, C.S. & Percival, D.B. Maximal Overlap Wavelet Statistical Analysis With Application to Atmospheric Turbulence. Boundary-Layer Meteorol 119, 339–374 (2006). https://doi.org/10.1007/s10546-005-9011-y

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  • DOI: https://doi.org/10.1007/s10546-005-9011-y

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