On the high frequency ingredients of the secular variation

C. Demetrescu, V. Dobrica, I. Vaduva

Institute of Geodynamics, Bucharest, Romaniae-mail: crisan@geodin.ro

Acknowledgements: The study has been supported by the Institute of Geodynamics (Projects 2/2003-2007) and by the National Authority for Scientific Research (Projects 151/2007, 81-021/2007)   

Background from http://www.geomag.bgs.ac.uk/mercator.html

Outline

- have a look at time series of annual means from 22 observatories (15 with 100-150 years of activity) - discuss the ingredients of the main field and of its secular variation

- discuss the time-space evolution of the various main field ingredients

- comparison with main field models (IGRF, CM4) - conclusions

1840

1860

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2000

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

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20000

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H (

nT

)

C L F

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

17600

18000

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19600

H (

nT

)

H A D

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

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17600

H (

nT

)

B F E

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

16400

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17400

H (

nT

)

E S K

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

18500

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21000

H (

nT

)

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

21000

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23000

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26000

H (

nT

)

C O I

F R D

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

17600

18000

18400

18800

19200

19600

H (

nT

)

V A L

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

36500

37000

37500

38000

38500

39000

H (

nT

)

A B G

~80-year variation visible in the time series of annual means of geomagnetic elements

- the solar cycle signature has long been recognized (Chapman & Bartels, 1940; Alldredge, JGR, 1976; Courtillot&LeMouel, JGR, 1976)

- if not accounted for, the external contributions map into the modelled internal field when using observatory data

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

17600

18000

18400

18800

19200

19600

H (

nT

)

H A D

- correction limited to the 11-year solar cycle effects (Sabaka et al., GJI, 2004; Olsen & Mandea, EPSL, 2007, Verbanac et al., EPS, 2007 ) by parameterization with Dst (Est+Ist) and Ap

1940 1960 1980 2000

Y ea r

-20

-10

0

10

20

30

Su

nsp

ot-c

ycle

-rel

ated

var

iati

on (

nT

)

H

+ External contributions

Observatory data

Geomagnetic indices to quantify long-term external field variations

Geomagnetic activity- aa (Mayaud, 1972; 1980) BV2

- IHV (Svalgaard et al., 2004; Svalgaard&Cliver, 2007; Mursula et al., 2004) BV2

- IDV (Svalgaard&Cliver, 2004) B- Dst for storm-time variations

Good correlation with the solar activity (R) in terms of 11-year averages, but differences in each solar cycle

1 8 6 0 1 8 8 0 1 9 0 0 1 9 2 0 1 9 4 0 1 9 6 0 1 9 8 0 2 0 0 0

Y ea r

4

8

1 2

1 6

2 0

2 4

2 8

3 2

3 6

4 0

aa (

nT

)

a aa a 1 1

Solar quiet daily variation Sq- x, y, z, r (Le Mouel et al., EPSL, 2005) TSI

1 8 6 0 1 8 8 0 1 9 0 0 1 9 2 0 1 9 4 0 1 9 6 0 1 9 8 0 2 0 0 0

Y ea r

4

8

1 2

1 6

2 0

IDV

(n

T)

ID VID V 1 1

A common trend is present also at longer timescales:- 22-year magnetic cycle (MC)- “secular”, “80-90-year”, Gleissberg cycle (GC)

R 1 1

1 8 5 0 1 9 0 0 1 9 5 0 2 0 0 0

Y ea r

- 8- 40481 2

aa (nT

)

08

1 62 43 24 0

aa (

nT

)

G C

M C

S C

Successive extraction of the 11-, 22- and ~80-year variations (running averages)

1 8 5 0 1 9 0 0 1 9 5 0 2 0 0 0

Y ea r

- 4

- 2

0

2

4

a aI D VI H VRT S I

1 9 1 0 1 9 2 0 1 9 3 0 1 9 4 0 1 9 5 0

Y ea r

- 4

- 2

0

2

4

M C

G C

Sta

nd

ard

dev

iati

on(Demetrescu&Dobrica, JGR, 2008)

Curves are reduced to their means over the common time interval and scaled with their standard deviations about the mean as a unit

(Demetrescu&Dobrica, JGR, 2008)

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

17600

18000

18400

18800

19200

19600

H (

nT

)

1 1 -y ea r sm o o th in g2 2 -y ea r sm o o th in g7 8 -y ea r sm o o th in gm easu red v a lu es

Ingredients of the observed fieldExample of data treatment

Steady variation

The 11- (red), 22- (blue) and ~80-year (green) variations extracted from data.

Successively filtering out the sunspot cycle signature, a 22-year variation, and a ~80-year variation present in the time series of observatory annual means, by running averages with 11-, 22- and 78-year windows respectively, results in a so called “steady variation”.

1860 1880 1900 1920 1940 1960 1980 2000

Y e ar

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

H (

nT)

H A D

1 1

2 2

~ 8 0 -y ea r v a r ia tio n

(Demetrescu&Dobrica, RRG, 2005)

HAD

11-year variation ~80-year variation

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

-100

-80

-60

-40

-20

0

20

40

60S

un

spot

-cyc

le-r

elat

ed v

aria

tion

(n

T)

0

40

80

120

160

200

Su

nsp

ot nu

mb

er

H

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

-100

-80

-60

-40

-20

0

20

40

60

80

22-y

ear

vari

atio

n (

nT)

H

F R D

A B G

H O N K A K

E u ro p e

A P I

H E R

T R W

V S S

L N N

IR K

S S HO T TT F S

22-year variation

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

-100

-80

-60

-40

-20

0

20

40

60

80

100

Sun

spot

-cyc

le-r

elat

ed v

aria

tion

(n

T)

Z

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

22-y

ear

vari

atio

n (

nT

)

Z

K A K

A B GF R D

H O N

E u ro p e

A P I

L N N

O T T

S S H

IR K

H E R

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

-0 .1

-0.05

0

0.05

0.1

0.15

Sun

spot

-cyc

le-r

elat

ed v

aria

tion

(de

gree

) D

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

-0 .15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

22-y

ear

vari

atio

n (

deg

ree)

H E R

F R D

A B G

E u ro p e

D

A P I

O T T

S S H

IR KL N N

1860 1880 1900 1920 1940 1960 1980

Y ea r

-800

-400

0

400

800

80-y

ear

vari

atio

n (

nT

)

A B G

F R D

E u ro p e

S S H

H O N

L N N

A P I

O T T

K A KIR K

H

1860 1880 1900 1920 1940 1960 1980

Y ea r

-800

-400

0

400

800

80-y

ear

vari

atio

n (

nT

)

A B G

F R D

E u ro p eS S H

H O N

L N N

A P I

O T T

K A K

IR K

Z

1860 1880 1900 1920 1940 1960 1980

Y ea r

-0 .8

-0.4

0

0.4

0.8

80-y

ear

vari

atio

n (

deg

ree) A B G

F R D

E u ro p e

S S H

H O N

L N N

A P I

O T T

K A K

IR K

D

1860 1880 1900 1920 1940 1960 1980 2000

Y ea r

-80

-60

-40

-20

0

20

40

60

80

Sun

spot

-cyc

le-r

elat

ed v

aria

tion

(n

T)

1860 1880 1900 1920 1940 1960 1980

Y ea r

-800

-400

0

400

800

stea

dy

vari

atio

n (

nT

)

A B G

F R D

E u ro p e

S S H

H O N

L N N

A P IO T T

K A K

IR K

H

1860 1880 1900 1920 1940 1960 1980

Y ea r

-2000

-1000

0

1000

2000

stea

dy

vari

atio

n (

nT

)

A B G

F R D

E u ro p e

S S H

H O N

L N N

A P I

O T T

K A K

IR K

Z

Steady variation

- carries the largest part of the field

- in terms of variation relative to the mean for the time interval with data

- large lateral differences in the time variation

Jerk ingredients

1850 1900 1950 2000

Y ea r

-0 .05

0

0.05

0.1

0.15

0.2

0.25

dD/d

t (d

egre

e/ye

ar)

C L F- the long-term variation of the geomagnetic field, dominated by the presence of geomagnetic jerks separating intervals of a relative smooth variation of the field,

- is produced by the ~80-year variation combined with the 22-year variation, both of internal origin, on which the SC-related variation is superimposed.

- the 11-year variation is decisive though in establishing the very short time scale characterizing jerks, and to some extent also the amplitude and timing of the jerk.

1880 1900 1920 1940 1960 1980 2000

Y ea r

19200

19600

20000

20400

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21200

H (

nT

)

m easu red v a lu es

C M 4 m o d e l

IG R F m o d e l

C L F

Comparison of H geomagnetic component - annual means, IGRF and CM4 models -

1880 1900 1920 1940 1960 1980 2000

Y ea r

18200

18400

18600

18800

19000

H (

nT

)

m easu red v a lu es

IG R F m o d e l

C M 4 m o d e lN G K

11-year variation 22-year variation ~80-year variation

1880 1900 1920 1940 1960 1980 2000

Y ea r

-30

-20

-10

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H (

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)

m easu red v a lu es

C M 4 m o d e l

IG R F m o d e l

C L F

1880 1900 1920 1940 1960 1980 2000

Y ea r

-40

-20

0

20

40

H (

nT

)

m easu red v a lu es

C M 4 m o d e l

IG R F m o d e l

C L F

1880 1900 1920 1940 1960 1980 2000

Y ea r

-200

-160

-120

-80

-40

0

40

H (

nT

)

m easu red v a lu es

IG R F m o d e lC L F

1880 1900 1920 1940 1960 1980 2000

Y ea r

-30

-20

-10

0

10

20

30

H (

nT

)

m easu red v a lu es

C M 4 m o d e l

IG R F m o d e l

N G K

1880 1900 1920 1940 1960 1980 2000

Y ea r

-40

-20

0

20

40

60

H (

nT

)

m easu red v a lu es

C M 4 m o d e l

IG R F m o d e l

N G K

1880 1900 1920 1940 1960 1980 2000

Y ea r

-250

-200

-150

-100

-50

0

50

H (

nT

)

m easu red v a lu es

IG R F m o d e lN G K

Comparison of ingredients of H

1950.5 1960.5 1970.5 1980.5 1990.5 2000.5

Y e ar

-15

-10

-5

0

5

10

15

Hs

(nT

)

N G K

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

Y ea r

-80

-60

-40

-20

0

20

40

60

80

Su

nsp

ot-c

ycle

-rel

ated

var

iati

on (

nT

)

1880 1900 1920 1940 1960 1980 2000

Y ea r

-30

-20

-10

0

10

20

30

H (

nT

)

m easu red v a lu es

C M 4 m o d e l

IG R F m o d e l

C L F

1880 1900 1920 1940 1960 1980 2000

Y ea r

-30

-20

-10

0

10

20

30

H (

nT

)

m easu red v a lu es

C M 4 m o d e l

IG R F m o d e l

N G K

1960 1970 1980 1990 2000

Y ea r

-30

-20

-10

0

10

20

H (

nT

)

N G K

C L F

K A K

H E R

IGRF: - no provision for external variations; the SC-related variation maps in the modelled main field

CM4: - the external field is accounted for via the Dst index

11-year SC-related variation in main field models

Unaccounted for, this variation leaks into the main field models

IGRF: - sampling the field every 5 years results in a distorted SC variation

CM4: - partially successful: CLF, NGK – yes; KAK, HER - no

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

Y ea r

7.6e+024

7.8e+024

8e+024

8.2e+024

8.4e+024

M (

nT

m3 )

ca lcu la ted v a lu es

1 1 -y ea r sm o o th in g

2 2 -y ea r sm o o th in g

7 8 -y ea r sm o o th in g

Dipole moment, IGRF

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

Y ear

-6e+021

-4e+021

-2e+021

0

2e+021

4e+021

M (

nT

m3 ) 1 1

2 2

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

Y ea r

-2e+022

-1e+022

0

1e+022

2e+022

3e+022

M (

nT

m3 )

1 1

2 2

~ 8 0 -y ea r v a r ia tio n

211

211

201

3 )h()g()g(rM

The SC-related variation is even seen in the dipole part of the modelled main field!

Maps of the 22- and ~80-year variations

-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

L o n g itu d e (d eg rees)

-60

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Lat

itude

(de

gree

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L o n g itu d e (d eg rees)

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Lat

itude

(de

gree

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L o n g itu d e (d eg ree s)

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Lat

itud

e (d

egre

es)

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-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

L o n g itu d e (d eg rees)

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-45

-30

-15

0

15

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45

60

Lat

itude

(de

gree

s)

-140-130-120-110-100-90-80-70-60-50-40-30-20-1001020304050607080

1940 1965

~80-year variation maps, IGRF

1940

1945

1955

1950

1960

1965

-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

L o n g itu d e (d eg rees)

-60

-45

-30

-15

0

15

30

45

60

Lat

itude

(de

gree

s)

-800

-700

-600

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0

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-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

L o n g itu d e (d eg rees)

-60

-45

-30

-15

0

15

30

45

60

Lat

itude

(de

gree

s)

-800

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-600

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0

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-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

L o n g itu d e (d eg rees)

-60

-45

-30

-15

0

15

30

45

60

Lat

itud

e (d

egre

es)

-700

-600

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-400

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-200

-100

0

100

200

300

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500

600

700

800

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1000

-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

L o n g itu d e (d eg rees)

-60

-45

-30

-15

0

15

30

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60

Lat

itud

e (d

egre

es)

-800

-700

-600

-500

-400

-300

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-100

0

100

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500

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-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

L o n g itu d e (d eg rees)

-60

-45

-30

-15

0

15

30

45

60

Lat

itude

(de

gree

s)

-800

-700

-600

-500

-400

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-100

0

100

200

300

400

500

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-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

L o n g itu d e (d eg ree s)

-60

-45

-30

-15

0

15

30

45

60

Lat

itude

(de

gree

s)

-800

-700

-600

-500

-400

-300

-200

-100

0

100

200

300

400

500

600

700

800

Time derivative of the steady radial field at Earth’s surface

-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

L o n g itu d e (d eg rees)

-60

-45

-30

-15

0

15

30

45

60

Lat

itud

e (d

egre

es)

-140-130-120-110-100-90-80-70-60-50-40-30-20-100102030405060708090100110120130

1940, IGRF

-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

L o n g itu d e (d eg ree s)

-60

-45

-30

-15

0

15

30

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60

Lat

itud

e (d

egre

es)

-160

-140

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

1965, IGRF

WMM 2005

westward displacement of main secular variation foci

Conclusions

- data (annual means) from 22 observatories with long activity (15 with 100-150 years) have been processed to show the existence and some of the characteristics of a 22-year variation and of a ~80-year variation, superimposed on a so-called steady variation;

- in terms of the present analysis, the jerks seem to be merely a result of the superposition of the 11-year solar-cycle-related on the 22-year and the ~80-year variations. The way the three combine makes the difference in timing, magnitude, and length of jerks as observed;

- the steady variation, which carries the largest part of the field is characterized by a westward movement of its secular variation foci;

- the ~80-year variation shows several maxima and minima with variable amplitudes, concentrated in two longitudinal bands;

- the 22-year variation shows a high temporal and spatial variability; - the external variation still present in data (annual means uncorrected or incompletely corrected for the 11-year SC-related variation) leaks into the main field models;

- in terms of secular variation, all ingredients presented contribute significantly;