Spectral Coherence and the Statistical Significance of Turbulent Flux Computations

Christopher A. Biltoft Adiabat Meteorological Services, Salt Lake City, Utah

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Eric R. Pardyjak Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah

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Abstract

The squared spectral coherence, a frequency-domain analog of the squared correlation coefficient, identifies the frequencies at which two variables most strongly covary. A simple coherence significance test designed to determine whether coherence peaks exceed critical values expected from chance random number correlations is described. This significance test determines the probability with which coherence peaks are likely to arise out of random turbulence. A statistically significant coherence peak also indicates the likely presence of a significant turbulent flux. The test is illustrated using sonic anemometer–thermometer data acquired in an urban setting and over a salt playa. Successful application of this coherence significance test requires selection of a properly sized data record and a Fourier transform with appropriate windowing. The sampling period should be sufficiently long to span major flux-generating scales of motion up to the cross-spectral gap but not so long that extraneous larger scale motions are included. A record length and transform size that yield equivalent degrees of freedom in the range between 10 and 100 produces the most consistent and reliable significance test results.

Corresponding author address: Christopher Biltoft, Adiabat Meteorological Services, 674 16th Ave., Salt Lake City, UT 84103. Email: biltoftc@yahoo.com

Abstract

The squared spectral coherence, a frequency-domain analog of the squared correlation coefficient, identifies the frequencies at which two variables most strongly covary. A simple coherence significance test designed to determine whether coherence peaks exceed critical values expected from chance random number correlations is described. This significance test determines the probability with which coherence peaks are likely to arise out of random turbulence. A statistically significant coherence peak also indicates the likely presence of a significant turbulent flux. The test is illustrated using sonic anemometer–thermometer data acquired in an urban setting and over a salt playa. Successful application of this coherence significance test requires selection of a properly sized data record and a Fourier transform with appropriate windowing. The sampling period should be sufficiently long to span major flux-generating scales of motion up to the cross-spectral gap but not so long that extraneous larger scale motions are included. A record length and transform size that yield equivalent degrees of freedom in the range between 10 and 100 produces the most consistent and reliable significance test results.

Corresponding author address: Christopher Biltoft, Adiabat Meteorological Services, 674 16th Ave., Salt Lake City, UT 84103. Email: biltoftc@yahoo.com

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