from Antarctic cryosphere

… to solar oscillations

Sylvie Roques – Laboratoire d’Astrophysique – Observatoire Midi-Pyrénées

sylvie.roques@irap.omp.eu

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