The Southern Oscillation Index characterizing El Nino

1
The Southern Oscillation Index characterizing El
Nino ()

Marcel Ausloos (1) and Filippo Petroni (1,2)
(1) SUPRATECS, Univ. Liege, Euroland (2)
Univ. LAquila, Italy
() part of E2C2 european project
2
a complex signal adequately described through a
Beck-like turbulence Model and Tsallis
non-extensive statistics

3
q-WAIT ! and q-SEE!

• M. Ausloos R. Lambiotte
• Brownian particle having a fluctuating mass
• Phys. Rev. E 73, 11105 (2006)
• http//arXiv.org/abs/cond-mat/0508773
• initially for Stock Markets
• but also for
• Traffic (cars, crowds, internet, )
• Granular gases (agglomeration-desagregation
  ion-ion, electrodeposition,)
• Space/ galaxies

4
Table of Contents

• Introduction
• (not everything you wanted to know about SOI and
  elNino and were not going to ask anyway)
• Data analysis time lag effects?
• Spectral analysis
• Detrended fluctuation analysis
• Turbulence  Beck-Tsallis  Model
• Non extensive statistics
• Variance fluctuation behavior hypothesis
• Time delayed correlations
• Intermittency exponent
• Conclusions

5
To be seen

• Shape and tails of PDF of SOI fluctuations (gt
  exponents!)
• Tsallis non-extensive statistics
• Fokker-Planck equation
• Kramers-Moyal coefficients
• Large number of cascades in process

6
(No Transcript)
7
El Niño

• The warm phase of the ENSO, characterized by the
  warming of the central and eastern equatorial
  Pacific regions due to a weakening of the trade
  winds

8
El Niño Conditions

• Trade winds ?
• Sea level pressures ?
• Thermocline ?
• SSTs ?

• Weaken (low SOI)
• Unusually high in west, low in east
• Rises in west, depresses in east
• Warm water spreads to central and eastern Pacific

9
La Niña

• The cold phase of the ENSO, characterized by the
  spreading of the cold tongue into the central and
  parts of the western equatorial Pacific regions
  due to the strengthening of the trade winds

10
La Niña Conditions

• Trade winds ?
• Sea level pressures ?
• Thermocline ?
• SSTs ?

• Strengthen (high SOI)
• Unusually low in west, high in east
• Depresses in west, rises in east
• Cold tongue spreads further into central and
  western Pacific

11
(No Transcript)
12
Walker circulation

• 1923
• Sir Gilbert Walker
• When air pressure is high in Pacific, it is low
  in Indian Ocean, from Africa to Australia and
  vice versa
• 1960 Bjerknes
• Connection to el Nino

13
(No Transcript)
14
(No Transcript)
15
Warm Episodes

• Enhanced cloudiness and rainfall in central and
  eastern Pacific
• Rainfall is reduced over Indonesia, Malaysia and
  northern Australia
• The normal circulation becomes weaker than normal

Sourcehttp//www.cpc.ncep.noaa.gov/products/analy
sis_monitoring/impacts/warm_impacts.html
16
Warm Episodes (cont.)

• Abnormally dry conditions
• northern Australia
• Indonesia
• Philippines
• Wetter than normal conditions
• west coast of tropical South America
• North America Gulf Coast
• southern Brazil to central Argentina

Source http//www.cpc.ncep.noaa.gov/products/anal
ysis_monitoring/impacts/warm.gif
(El Niño 2002)
17
Cold Episodes

• Enhanced rainfall over Indonesia, Malaysia and
  northern Australia
• Suppressed cloudiness and rainfall in central and
  eastern Pacific
• Normal circulation enhanced
• (e.g. cold 2002)

Source http//www.cpc.ncep.noaa.gov/products/anal
ysis_monitoring/ensocycle/djfschem_lanina.gif
18
Cold Episodes Cont.

• Wetter than normal conditions
• Northern Australia
• Indonesia
• Malaysia
• Philippines
• Drier than normal conditions
• West coast of tropical South America
• Gulf Coast of North America
• Southern Brazil to central Argentina

Source http//www.cpc.ncep.noaa.gov/products/anal
ysis_monitoring/impacts/cold.gif
(El Niño 2002)
19
The Southern Oscillation
Source http//www.ucar.edu/communications/lasers/
elnino/Figure_1.html

• refers to a seesaw shift in surface air
  pressure
• at Darwin, Australia and (the South Pacific
  Island of) Tahiti (Henson, 1998)

20
The Southern Oscillation Index

• The normalized difference in sea-level pressure
  (SLP) between Tahiti and Darwin
• A measure of the strength of the trade winds
• low SOI (smaller pressure difference) El Niño
• high SOI (large pressure difference) La Niña

Source jpl.nasa.govimages-el-nino-la-nina-th.html
21
http//www.bom.gov.au/climate/current/soi2.shtml
Chart last updated Friday 2nd June 2006
22
Southern Oscillation Index
http//www.cpc.ncep.noaa.gov/data/indices/
P (Darwin) - P (Tahiti)
(normalized)
1886-2006 (1886-2000)
1672 (1612) data points
23
DEFINITIONS

• Variability
• Normalized variability

DDt y(t) y(tDt) - y(t)
Z(t,Dt) DDt y(t) - ltDDt ygt /sDt
Time lag effect ?
24
Probability distribution function
Empirical probability to observe fluctuations
with amplitude larger than
xyi1-yi Asymptotic power law scaling for
fluctuation amplitudes ? 1.5 , 2.8
Histogram of SOI fluctuations
25
PDF symmetry ! but !!
26
Time lag effect
27
i-variability diagram
28
Detrended Fluctuation Analysis
on SOI increments
Long Range Correlations ?
Non Brownian values
29
DFA (2/3)
30
DFA (3/3)
Shorter series
31
Spectral density (1/2)
32
Spectral density (2/2)
33
Beck turbulence model
a specific temperature fluctuation distribution
a usual evolution equation
dx/dt - g F(x) R(t)
with an ad hoc restoring force / potential
U(x) C x2a
34
Tsallis non-extensive statistics
where
such that
35
Beck-Tsallis connection

• Relationship of q with of degrees of freedom n
  and a exponent of potential

Variance of variability
36
Chi-square hypothesis !
not too bad
37
Fokker-Planck equation
with Kramers-Moyal coefficients
38
Kramers-Moyal coefficients

• Drift coefficients
• Diffusion coefficients

39
Kolmogorov connection (1)
energy cascades
40
Kolmogorov connection (2)
Shorter series
41
Conclusions

• Evolution equation (140 years) for SOI
• Tail regimes of SOI fluctuation PDF show non
  Brownian--like motion effects up to 3 to
  4 years
• Beck turbulence model is OK
• Intermittency exponent related to Tsallis q
• Should be so nice to have other averages than
  monthly ones !

42
(No Transcript)
43
(No Transcript)
44
Bibliography

• A.M. Kolmogorov, J. Fluid Mech.13, 82 (1962)
• C. Tsallis, J. Stat. Phys. 52, 479 (1988)
• H. Risken, The Fokker-Planck Equation Methods of
• Solution and Applications, 2nd Edn. ,
  (Springer-Verlag, Berlin, 1989)
• E. Koscielny-Bunde, A. Bunde, S. Havlin, H. E.
  Roman, Y. Goldreich and H.-J. Schellnhuber, Phys.
  Rev. Lett. 81, 729 (1998)
• B.D. Malamud, D.L. Turcotte, J. Stat. Plan.
  Infer. 80, 173 (1999)
• K. Ivanova and M. Ausloos, Physica A 274, 349
  (1999)
• K. Ivanova, M. Ausloos, E.E. Clothiaux and T.P.
  Ackerman, Europhys. Lett. 52, 40 (2000)
• C. Beck, G. S. Lewis, and H. L. Swinney, Phys.
  Rev. E 63, 035303 (2001)
• Ch. Renner, J. Peinke, and R. Friedrich,
  Physica A 298, 499 (2001)
• M. Ausloos and K. Ivanova , Phys. Rev. E 63,
  047201 (2001)
• M. Ausloos and F. Petroni, Physica A (in press)

45
First signs
46
(No Transcript)
47
(No Transcript)
48
(No Transcript)