Coherency in the solar spectral irradiance

Coherency in the solar spectral irradiance (a blind source separation approach)

Thierry Dudok de Wit1, Gaël Cessateur1,2, Saïd Moussaoui3, Matthieu Kretzschmar1,4, Jean Lilensten2, Luis Vieira1 1

2 IPAG, Grenoble LPC2E, Orléans 3 IRCCYN, Nantes, 4 ROB, Brussels This work was supported by the FP7 SOTERIA and ATMOP projects

Dignity ?

T.
Dudok
de
Wit
(SORCE,
9/2011)

2

Coherency !

T.
Dudok
de
Wit
(SORCE,
9/2011)

Coherency ! 6
years
of
observaHons
(SORCE
&
TIMED)

sunspot
nr

relative flux

XUV
(1‐10
nm) EUV
(10‐120
nm) Lyα
(120.5
nm) FUV
(120‐200
nm) MUV
(200‐300
nm) NUV
(300‐400
nm) VIS
(400‐700
nm) NIR
(700‐1000
nm)

2004

2005

2006

2007

2008 year

T.
Dudok
de
Wit
(SORCE,
9/2011)

2009

2010

2011

especially at short timescales 3
months

sunspot
nr

relative flux

XUV
(1‐10
nm) EUV
(10‐120
nm) Lyα
(120.5
nm) FUV
(120‐200
nm) MUV
(200‐300
nm) NUV
(300‐400
nm) VIS
(400‐700
nm) NIR
(700‐1000
nm)

Jun04

Jul04

Aug04 year

T.
Dudok
de
Wit
(SORCE,
9/2011)

Sep04

Motivation Commonali>es
 =
likely
same
physical
drivers =
gives
deeper
insight
into
the
physics

Departure
from
this
coherency =
most
likely
due
to
instrumental
noise
or
to
par>cular
 processes

T.
Dudok
de
Wit
(SORCE,
9/2011)

6

Model assumption Decompose
the
SSI













into
elementary
contribu>ons I(λ, t) I(λ, t) = A1 (t) · S1 (λ) + A2 (t) · S2 (λ) + . . . amplitude source (mixing
coefficient)

Assume
 linear
decomposi>on instantaneous
decomposi>on This
is
“blind
source
separa>on”
because
neither
the
sources
 nor
their
mixing
coefficients
are
known
beforehand T.
Dudok
de
Wit
(SORCE,
9/2011)

7

0

2

4

6 time [s]

8

amplitude [a.u.]

amplitude [a.u.]

Example from ECG

0 T.
Dudok
de
Wit
(SORCE,
9/2011)

2

4

6 time [s]

8

8

Key questions How
many
sources
?
 3
? 42
? ...

Are
they
unique
? Ill‐posed
problem:
what
physical
constraints
can
we
use?

T.
Dudok
de
Wit
(SORCE,
9/2011)

9

Various approaches

I(λ, t) = A1 (t) · S1 (λ) + A2 (t) · S2 (λ) + . . .

1)
Sources
and
mixing
coefficients
are
orthogonal ! !Sk (λ)Sl (λ)" = 0 if k #= l !Ak (t)Al (t)" = 0 The
solu>on
is
given
by
the
Singular
Value
 Decomposi>on
(SVD) Similar
to
principal
component
analysis Simple,
unique
solu>on,
but
not
very
realis>c T.
Dudok
de
Wit
(SORCE,
9/2011)

10

Various approaches 2)
Sources
and
mixing
coefficients
are
independent P(Sk , Sl ) P(Ak , Al )

= =

P(Sk )P(Sl ) P(Ak )P(Al )

The
solu>on
is
given
by
Independent
Component
 Analysis
(ICA) Computa>onally
most
costly,
but
also
more
realis>c Very
popular
in
acous>cs
&
image
processing

T.
Dudok
de
Wit
(SORCE,
9/2011)

11

Various approaches 3)
Sources
and
mixing
coefficients
are
independent
and
 posi/ve Sk (λ) ≥ 0

Ak (t) ≥ 0

The
solu>on
is
given
by
Bayesian
Posi>ve
Source
 Separa>on Computa>onally
costly,
but
also
more
realis>c Recent
but
very
ac>ve
field
of
research
(chemometrics,
 image
processing,
astrophysics,
...) [Kuruoglu,
IEEE
signal
proc.
magazine
87
(2010)] T.
Dudok
de
Wit
(SORCE,
9/2011)

12

First example XUV to VIS (TIMED & SORCE)

T.
Dudok
de
Wit
(SORCE,
9/2011)

13

Example 1: SVD analysis

relative flux

7
years
of
daily
observa>ons
from
0.6
‐
600
nm
(TIMED/ SEE,
SORCE/XPS‐SOLSTICE‐SIM)

2004

2005

2006

2007

2008

2009

2010

2011

year

T.
Dudok
de
Wit
(SORCE,
9/2011)

14

Example 1: SVD analysis

different
)me
scales
=
different
physical
processes

 ➞


decompose
the
data
beforehand
into
different
 )me‐scales

we
focus
here
on
>me
scales
ons data
are
normalized
to
their
solar
cycle
variability

T.
Dudok
de
Wit
(SORCE,
9/2011)

15

Example 1: SVD analysis Distribu>ons
of
the
weights I(λ, t) = W1 A1 (t) S1 (λ) + W2 A2 (t) S2 (λ) + . . . weight spectrum

2

10

2
to
4
outstanding
sources

1

k

weight W2 [%]

10

0

10

−1

10

−2

10

0

10

T.
Dudok
de
Wit
(SORCE,
9/2011)

20 30 mode number

40

50

16

Mixing coefficients

W A (t) 39% 1 1

mixing coefficient A(t) [a.u.]

W A (t) 24% 2 2 W A (t) 6.4% 3 3 W4A4(t) 4.1% W A (t) 2.1% 5 5 W A (t) 1.6% 6 6

2004 T.
Dudok
de
Wit
(SORCE,
9/2011)

2005

2006

2007

2008 year

2009

2010

2011

2012 17

Mixing coefficients

W A (t) 1 1

mixing coefficient A(t) [a.u.]

W2A2(t) W A (t) 3 3 W4A4(t) W5A5(t) W A (t) 6 6

TSI Mg
II

Apr04 T.
Dudok
de
Wit
(SORCE,
9/2011)

Jul04

Oct04

Jan05 year

Apr05

Jul05 18

Sources XPS

SEE

SOLSTICE FUV

SOLSTICE
 MUV

SIM S (!) 1

source S(!) [a.u.]

S (!) 2 S3(!) S4(!) S5(!) S6(!)

0 T.
Dudok
de
Wit
(SORCE,
9/2011)

100

200

300 400 wavelength( [nm]

500

600 19

Similarity map Most
of
the
salient
features
are
captured
by
sources
1
&
 2
only

The
similarity
maps
provides
a

very

compact
 representa>on
of
the
spectral
variability W2
S2(λ)

W1
S1(λ) T.
Dudok
de
Wit
(SORCE,
9/2011)

20

Similarity map

W2 S2(!)

400 300 200

wavelength [nm]

500

100

W1 S1(!)

T.
Dudok
de
Wit
(SORCE,
9/2011)

0

21

Similarity map facular
brightening

W2 S2(!)

400 300 200

wavelength [nm]

500

100 0

W1 S1(!)

T.
Dudok
de
Wit
(SORCE,
9/2011)

sunspot
darkening

22

Similarity map with proxies

DSA MWSI

ISN f10.7

MPSI MgII

400

Lya

300

SEM

200

wavelength [nm]

W2 S2(!)

500

TSI

100

W1 S1(!)

T.
Dudok
de
Wit
(SORCE,
9/2011)

0

23

Conclusion 1 The
variability
is
very
coherent:
 2
sources
capture
the
salient
features other
ones
contain
a
significant
amount
of
instrumental
 artefacts

Guidance
for
the
choice
of
proxies
 Instrumental
effects
are
omnipresent be
*very*
careful
in
the
interpreta>on
of
sources
>
2

T.
Dudok
de
Wit
(SORCE,
9/2011)

24

Second example EUV & FUV (TIMED/SEE)

T.
Dudok
de
Wit
(SORCE,
9/2011)

25

Example 2 Homogeneous
data
set:

amplitude [a.u.]

8
years
of
daily
observa>ons
by
TIMED/SEE
 28‐195
nm,
0.1
nm
resolu>on no
flares

25c) use
Bayesian
Posi>ve
Source
Separa>on 3
sources
are
sta>s>cally
significant T.
Dudok
de
Wit
(SORCE,
9/2011)

26

Example 2 Source
nr
4
contains
plain
instrumental
noise 8 mixing coeff 4 measured temperature

6 4

T [a.u.]

2 0 −2 −4 −6 −8 2002 T.
Dudok
de
Wit
(SORCE,
9/2011)

2003

2004

2005 year

2006

2007

2008 27

Mixing coefficients

A1

1 amplitude/max

A2 0.8

A3

0.6 0.4 0.2 0 2002

2003

T.
Dudok
de
Wit
(SORCE,
9/2011)

2004

2005

2006

2007

2008

2009

2010

2011 28

Mixing coefficients (excerpt) A1

1

amplitude/max

A2 0.8

A3

0.6 0.4 0.2 0 2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

A1 A2 amplitude [a.u.]

A3

Oct02 T.
Dudok
de
Wit
(SORCE,
9/2011)

MgII

Jan03

Apr03

Jul03 29

ave amplitude [a.u.]

Superposed
epoch
 analysis
of
mixing
 coefficients
 confirms
limb
 (XUV‐like)
 contribu>on
of
 source
3

ave amplitude [a.u.]

Mixing coefficients 1

A1 A2 A3

0.5

0

1

MgII SEM

0.5

0 −10

T.
Dudok
de
Wit
(SORCE,
9/2011)

0 10 delay [days]

20 30

spectrum [W/m2/nm] 10 −5

20 40

T.
Dudok
de
Wit
(SORCE,
9/2011)

60 80 100 120 140 wavelength ! [nm] Si II

He II

CSiIVIV

OI

0 C II Si IV

HI OOIIVIVI N HI

HCI III

O II HI

Mg X O IV

Si XII Si XII

Fe XV He II Fe XVI Fe XVI Mg IX Fe XV

amplitude / ave spectrum

amplitude amplitude / ave spectrum / ave spectrum

Sources

10

5

0 2

1

160 180

S1

Coronal
&
transiHon
 region
lines

S2

Quiet
Sun
only

0 10 S3

5

200

Ho\est
coronal
lines

spectrum

31

Conclusions 2 Posi>ve
source
separa>on
gives
physically
meaningful
 sources
[Amblard
et
al.,
A&A
487
(2008)] Given
the
instrumental
noise
level the
variability
in
the
EUV
&
FUV
has
3
degrees
of
freedom
 only


e.g.
[Lean
et
al.,
JGR
87
(1982)] they
correspond
to
different
temperature
layers
of
the
 solar
atmosphere

Perspec>ves
for
reconstruc>ng
the
EUV/FUV
from
proxy
 data T.
Dudok
de
Wit
(SORCE,
9/2011)

32

Perspectives The
remarkable
coherency
of
the
solar
spectral
 irradiance
also
provides
a
means
for elimina>ng
part
of
the
instrumental
noise filling
gaps/s>tching
together
records
(see
poster) 10

10 NIMBUS/SBUV NOAA/SBUV UARS/SUSIM MgII index

9

8.5

8

7.5

7 1975

9.5 intensity [mW/m2/nm]

intensity [mW/m2/nm]

9.5

NIMBUS/SBUV NOAA/SBUV UARS/SUSIM MgII index

9

8.5

8

7.5

1980

1985

1990

1995 year

T.
Dudok
de
Wit
(SORCE,
9/2011)

2000

2005

2010

7 1975

1980

1985

1990

1995 year

2000

2005

2010

33