from Antarctic cryosphere
… to solar oscillations
Sylvie Roques – Laboratoire d’Astrophysique – Observatoire Midi-Pyrénées
Multiscale dissection of
some natural systems
For Alex and Yves
Yves et Louise
adorent jouer
à la poupée Barbie
dans notre
garage….
Préparation du Congrès Wavelets and Applications Toulouse 1992
Aujourd’hui elle est
prof de philo…
Anecdote pour rire
Plein de week-ends
Alex nous impressionne
par ses talents de
multilinguisme, et prend
sous son aile le petit
Frédéric
Congrès Wavelets and Applications Toulouse 1992
Aujourd’hui il est
ingénieur du son et
musicien…
Alex adorait plus les fruits
que le canard… mais surtout nous
parlait avec tant d’amour de ses
multiples vies.
Mémoire affectueuse
Thierry te souviens-tu
des fameux TP sur la
détermination de e/m
des particules
chargées ?
Un clin d’œil à Thierry Paul – dès 1979 –
Rapport masse sur charge
Et j’ai toujours ton
livre de musique…
C’est aussi toi qui as dit en 90 : marre de la bouillabaisse,
maintenant je veux du cassoulet et du magret de canard
dans les Congrès Ondelettes !… Et hop à Toulouse !
Souvenir de jeunesse
Universe Science
Observation Science
Laboratory = Nature (Earth, ocean, space, …)
Question of climatic reheating (forecast ?)
Strong spatio-temporal variability (from planetary scales to kilometer, from million year to hour)
Antarctic Circumpolar Wave (ACW) and solar oscillations have in common :
a part on climate evolution
modulated multi-scaled pseudo-periodic signals (non-stationary)
A talk around Antarctica and Sun
In quest of Antactic Circumpolar Wave :
why and how ?
(Coll. Frédérique Rémy – LEGOS OMP Toulouse)
The Empirical Mode Decomposition
An application to solar variability
(Coll. Sami Solanki – Max Planck Lindau)
More information
http://webast.ast.obs-mip.fr/people/roques/AO3_remy_roques.pdf
Antarctica : some data
14 million km²
30 million km³
If the icecap melts away,
the mean sea level would
change between 60 and
80 m
Each year 5 mm of the
mean ocean level (2200
km³ of snowfall) settles
on the ground
chemical & climatic caracteristics
of the present time
glacial archives of Earth evidence of climatic evolution of the present time
The cryosphere is the
portion of the Earth's
surface where water is
in a solid form, usually
snow or ice. This
includes sea ice,
freshwater ice, snow,
glaciers, and frozen
ground (or permafrost).
Large
scales
Icecaps :
Variations =>
- Temperature modifications
- climatic evolution
Cimatic variability in Antarctica
Cryosphere : impacts
across all continents
Coupling between
Antarctica, Southern
system & high
latitudes :
not known Study of global climatic
variation of Earth on the
long range
In quest of Antarctic
Circumpolar Wave One of the strongest
natural event of Southern variability
Strictly observed in atmosphere, ocean and freshwater ice of Southern system
Little-discernible on the continent
No model is able to accurately generate it
In quest of Antarctic
Circumpolar Wave
It revolves clockwise around Antarctica, in 8 to 10 years
two minima and two maxima : apparent periodicity of 4 years
It impacts freshwater ices, atmospheric pressure, temperature, salinity and winds of Southern ocean
What we only know :
How to observe ACW ?
Detected in 1996 by
White and Perston
Strictly observed in
atmosphere, ocean and
frehwater ice of Southern
system
never observed neither
studied on the
continent
ERS 1 launched in 1991
Problem : 13 yrs to search a faint wave of period 8 yrs …
Coastal weather stations Temperature data of a dozen of coastal stations and of South Pole
Uniformely split on the coast around the continent
Data since 1955
Very noisy & strong seasonal signal
Search a specific signal probably very faint, that is a feature of ACW
sophisticated processing methods
Longuest « ground » data that exist at the present time
Example of temperature data
Halley
Pôle Sud
Halley Station (UK)
Fourier
Statistic analyses
Covariance analysis
Principal Component Analysis
Wavelets (it depends on what we do before)
Matching Pursuit ? (Mallat)
The failure of traditional methods
The (relative) failure of Matching
Pursuit
The algorithm allows us to choose, in a
given redundant finite dictionary of time-
frequency wave forms, a set of atoms
that match best the signal
Dilation scale
Translation
w: Frequency
modulation
Index n = (a,b,w)
The (relative) failure of Matching
Pursuit Search the atom that
match best the signal
Decomposition with a
residual vector
The procedure is
repeated each time on
the following residue
The (relative) failure of Matching
Pursuit
Decomposition of the
signal
Hierarchy of
structures
Time-frequency
energy distribution
(for plots)
L’échec de la poursuite adaptée
1 year
6 month
8 years Atom # 97
Only Halley
The Empirical Mode Decomposition
Complete (Fourier, wavelets, PCA)
Orthogonal (Fourier, wavelets, PCA)
Local (wavelets)
Adaptive (PCA)
Hilbert-Huang transform (1998)
Non-stationary signals – distinction of empirical « modes » –
Frequency bands – Hilbert transform
Basic idea
principle : signal = fast oscillations
superimposed with slow oscillations
method (N.E. Huang, 1998) : Empirical
Mode Decomposition
– Locally identify the faster oscillation
– Remove it from the signal and make
iterations on residue
Local adaptation on multiple « natural » scales
Principle of the algorithm EMD
Identification of extrema of X(t)
Interpolation between min and max to obtain upper and lower envelopes emin(t) and emax(t)
Calculate the mean m(t) = ( emax(t) + emin(t) ) / 2
Extraction of detail d(t) = X(t) – m(t)
Iteration on residue m(t)
In practice, the procedure is refined to impose that d(t) be zero-mean
EMD
• identification of extrema of X(t) • Determination of upper and lower envelopes (e.g. cubic splines)
10 20 30 40 50 60 70 80 90 100 110 120
-2
-1
0
1
2
IMF 1; iteration 0
10 20 30 40 50 60 70 80 90 100 110 120
-2
-1
0
1
2
IMF 1; iteration 0
10 20 30 40 50 60 70 80 90 100 110 120
-2
-1
0
1
2
IMF 1; iteration 0
10 20 30 40 50 60 70 80 90 100 110 120
-2
-1
0
1
2
IMF 1; iteration 0
10 20 30 40 50 60 70 80 90 100 110 120
-2
-1
0
1
2
IMF 1; iteration 0
Flandrin
Magrin
1) conditions on the number of extrema and zeros
2) on each point, the mean value of the enveloppe defined by local maxima and local
minima has to be zero (this imposes a local symetry)
EMD suite
• détermination of local mean m (in pink)
10 20 30 40 50 60 70 80 90 100 110 120
-2
-1
0
1
2
IMF 1; iteration 0
Flandrin
Magrin
Station Halley
Monthly fluctuations Seasonal cycle Oceanic impacts ACW (cf. satellite) Residual tendencies
# 3
# 4
# 5
# 6
ocean
quasi-quadri
ACW
tendency
1 year (TF)
6 month (TF)
8 years
EMD
Instantaneous
frequencies
the mode is not
stationary
Instantaneous frequencies of HH
Frequency
at « 8 years »
Examination of modes (wavelets)
modes 5 & 4
Wavelet
transforms
spectra
All the stations
wave « at 8 years » wave « at 4 years »
Scott
Dumont
Casey Mirny
Mawson
Molo
Novo Pole
Halley
Belling Faraday
Modes « at 8 years » Can we identify a
« revolving wave » ?
Modes « at 8 years » Can we identify a
« revolving wave » ?
Instantaneous phases
Moving centre ?
Apparent
retrograde
motion
Cycloid
Gloersen & Huang
(1999)
Instantaneous phases
Moving centre ?
Apparent
retrograde
motion
Cycloid
Gloersen & Huang
(1999)
Conclusion: open problems
You are invited to download data
http://www.antarctica.ac.uk/met/gjma/
algorithm ?
– Intuitive but ad-hoc and not unique
– Parameters can be chosen by the user
interpretation ?
– Modes vs Fourier, wavelets, …?
– Which scales are « natural » ?
performances ?
– Difficult to evaluate (no analytic definition)
– Necessary do do a lot of numerical simulations
Conclusion ACW
ACW found on continent
Only EMD was able to extract it
The ACW centre is probably moving
Necessity of modelisation :
understand underlying mechanisms
that maintain it
The eruptive Sun
eruptions
ejections
sunspots
granulation
pulsations (11 years)
The solar cycle (« sunspots »)
500 atoms
zoom LF
atoms
with
long
lifetime
Atom # 2 Atom # 1
atoms
with
long
lifetime
&
the most
energetic
p=11.01 years p=10.67 years
EMD of solar cycle
Cycle at 11 years
Matching pursuit
of modes #5 & #6
0.093750
(10.67 years) vs 10.67
Mode # 6
0.084961
(11.77 years) vs 11.01
1946 1978
18
« Grand Daddy »
Comparison with mode #6 of ACW
t = 0.72
• phase opposition
• correlation only with
South Pole
• less sensitive to
atmospheric and
oceanic perturbations
• evidence of large-
scale temperature
variation
Conclusion
Ability of EMD to make
interpretations easier modes have
not constant amplitudes or constant
frequencies
Will make easier the sudy of coupling
ACW solar cycle You are invited to download data
http://web.ngdc.noaa.gov/stp/SOLAR/solar.html
If we still have time… 3C273…
Yves, Sylvie and François Bourzeix (awarded
by the « Ecole Polytechnique »)
« Images des Mathématiques » 2011
The applications of
mathematics are
extraordinary for our
planet and our universe