1. Gabriel Katul, Karen Wesson, and Brani Vidakovic
Quantifying Organization in Time Series: Applications in Atmospheric Turbulence
Gabriel Katul, Karen Wesson, and
Brani Vidakovic

2. Surface Layer and Canopy Turbulence
Canopy Sublayer
Surface Layer

3. Surface Layer and Canopy Sublayer
Blending Region 2h
Canopy
Sublayer h

4. Degree of Organization

5. Degree of Organization
THE FLOW FIELD IS A SUPERPOSITION OF THREE CANONICAL STRUCTURES
Mixing
Layer d
Displaced wall
Real wall
REGION I
REGION II
REGION III
Boundary
Layer

6. Techniques:

7. Shannon Entropy:

8. 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

9. Threshold Criterion: Frequency or Fourier Domain Wavelet Domain Time

10. Thresholding and Variance Recovery

11. Threshold Selection

12. Wavelet Papers - since 1990
(from Addison, 2002)

13. Time-Frequency
local transform

14. Can reduce the
effects of gaps on
transformation

16. Forward
Transform:
Time to
Wavelet
Inverse
Transform:
Wavelet to
time

17. Mutual Information:

18. Mutual Information:

19. Canopy Sublayer Experiments

20. Shannon Entropy Results:

21. Wavelet Thresholding Results

22. Mutual Information Results

23. 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.