Quantifying Organization in Time Series: Applications in Atmospheric Turbulence

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Quantifying Organization in Time Series
Applications in Atmospheric Turbulence

• Gabriel Katul, Karen Wesson, and
• Brani Vidakovic

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Surface Layer and Canopy Turbulence
Canopy Sublayer
Surface Layer
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Surface Layer and Canopy Sublayer
Surface Layer
Blending Region
2h
Canopy Sublayer
h
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Degree of Organization
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Degree of Organization
THE FLOW FIELD IS A SUPERPOSITION OF THREE
CANONICAL STRUCTURES
Mixing Layer
Boundary Layer
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Techniques
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Shannon Entropy
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Wavelet Thresholding
Wavelets disbalance geophysical data because
they concentrate most of the energy in few
coefficients. The process of setting the
amplitude of wavelet coefficients to zero when a
certain threshold is exceeded is known as
thresholding. The number of coefficients
remaining after thresholding measures degree of
organization associated with energetic events
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Threshold Criterion
Frequency or Fourier Domain
Wavelet Domain
Time Domain
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Thresholding and Variance Recovery
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Threshold Selection
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Wavelet Papers - since 1990
(from Addison, 2002)
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Time-Frequency local transform
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Can reduce the effects of gaps on transformation
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(No Transcript)
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Forward Transform Time to Wavelet
Inverse Transform Wavelet to time
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Mutual Information
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Mutual Information
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Canopy Sublayer Experiments
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Shannon Entropy Results
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Wavelet Thresholding Results
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Mutual Information Results
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Conclusions
Tools from nonlinear time series permit
identification of organization using scalar
measures. In this case study, we showed that
the CSL eddy motion is more organized than the
ASL eddy motion. That is, it is more amenable
to a low-dimensional model. For some systems,
complexity, entropy, organization, and
predictability are connected.