paula agudelo turbulence, intermittency and chaos in high-resolution data, collected at the amazon...
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Paula Agudelo
Turbulence, Intermittency and Chaos in High-Resolution Data,
Collected At The Amazon Forest.
The data used consists of the wind velocity components along the three orthogonal directions and the temperature, all obtained using fast response sonic instruments.
60m tower built in the Rebio Jaru reserve in (10º04'S 61º56'W), Brazilian state of Rondonia.
(The Large Scale Biosphere-Atmosphere Experiment in the Amazon)
Data were collected as part of a LBA project
frequency of 60 Hz. (60 Samples/second) (9min)
DATA
Data at 21m and 66m
SERIES
6th
7thMarch/1999
12pm
3pm
6pm
9pm12am U V
W T
Histograms
Examples
Examples
Profiles
Fourier Vs WaveletsFourier transform Decompose a time series in sines and cosines
of different frequencies.
Wavelet transform Decompose a time series in different functions
Since sines and cosines are infinite functions,It only gives information of frequency
The wavelet function goes to zero, giving information of frequency and localization in time
7 March, 12pm at 66m
Kolmogorov law of -5/3 (n=2)
33nrn
nn
i Ku
2
2
i
j
j
i
xu
xu
8 March, 12pm at 66m
Kolmogorov law of 5/3
)2ln(2
)(
2)(
dyiWTKE
m
m
21
22)(4)(
)2ln(2)(
iWTiWTdyKSD mm
mE
)()(
)(m
mEmE KE
KSDKCV
nm
nm
n
dy
iWTxrx
22
)(~)()(
22
4
)(iWT
iWTRFF
m
m
m
Removing intermittencyWT:Wavelet Coefficients (Result of the transform) Sum over all WT = Series Variance
Km=Wave NumberSpectral density function
Standard deviation
Coefficient of energy variation
Structure Function
Flatness Factor (Similar to Kurtosis)
Results
Results
Chaotic BehaviorPhase Space reconstruction
how to go from scalar observations to multivariate phase space
to apply the embedding theorem
to say that what time lag (time delay) to use and what dimension to use are the central
issues of this reconstruction.
Average Mutual Information
)()(
),(log),( 2
, iBiA
iiAB
baiiABAB bPaP
baPbaPI
ii
Embedding dimension dE.
Global False Nearest Neighbors
7 March, 12pm at 21m
7 March, 12pm at 66m
Mutual Information
False Nearest Neigbors, 12pm 09/07 21m
0
20
40
60
80
100
1 2 3 4 5 6 7
Dimension
Perc
enta
ge o
f FN
N
False Nearest Neigbors, 12pm 09/07 66m
0
20
40
60
80
100
1 2 3 4 5 6 7
Dimension
Perc
enta
ge o
f FN
N
False Nearest Neigbors, 9pm 09/08 21m
0
20
40
60
80
100
1 2 3 4 5 6 7
Dimension
Perc
enta
ge o
f FN
N
Embedding dimension
False Nearest Neigbors, 9pm 09/08 21m
0
20
40
60
80
100
1 2 3 4 5 6 7
Dimension
Perc
enta
ge o
f FN
N
Lorenz Attractor
U Component12am
U Component12pm
T Component5pm
T Component5pm
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