1

Objective Calibration of Sunspot Numbers

 Leif Svalgaard

Stanford University, Stanford, CA, USA.http://leif.org/research

leif@leif.org

AGU Fall 2009, SH13C-03

Relative Sunspot Number R = k (10 Groups + Spots)Rudolf Wolf, 1816-1893

2

Wolf’s Discovery: rD = a + b R

.

H

North X

D

Y = H sin(D)

rY = H cos(D) rD For small rD

rY

Morning

Evening

East Y

rD

A current system in the ionosphere is created and maintained by solar FUV radiation

Wolf realized that this relation can be used to check the sunspot calibration

3

10 Days of geomagnetic variations

rY

-10

-8

-6

-4

-2

0

2

4

6

8Diurnal Variation of Declination at Praha

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

dD' 1840-1849rD

-10

-8

-6

-4

-2

0

2

4

6

8Diurnal Variation of Declination at Praha (Pruhonice)

dD' 1957-1959

1964-1965

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

The regular diurnal variation of the ‘compass needle’

4

Using rY from nine ‘chains’ of stations

we find that the relationship

between F10.7 and rY is extremely

good (more than 98% of the variation is

accounted for)

0

50

100

150

200

250

1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020

F10.7 sfu

25+Residuals

F10.7 calc = 5.42 rY - 130

Solar Activity From Diurnal Variation of Geomagnetic East Component

Nine Station Chains

232221201918171615141312

y = 5.4187x - 129.93

R2 = 0.9815

y = 0.043085x2.060402

R2 = 0.975948

0

50

100

150

200

250

300

30 35 40 45 50 55 60 65 70

rY

F10.7

This establishes that Wolf’s procedure and calibration are physically sound

The F10.7 radio flux is a good proxy for solar UV and activity in general

5

trend in rD = 0.53'/century

R2 = 0.7697

0

2

4

6

8

10

12

14

1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000

rD'

Wolf's Einheitliche Deklination Updated with Modern Stations in Europe

Solar Cycle in Range of Diurnal Variation of Magnetic Declination

R = 27.147rD - 202.77

r2 = 0.9683

0

20

40

60

80

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140

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180

200

7 8 9 10 11 12 13 14 15

rD'

R

Sunspot Number vs. Declination Range

Yearly Means 1945-1999

Wolf used the equivalent relation between sunspot number and magnetic declination

It makes no real difference if one uses F10.7 or the Sunspot number

Note the large range in the 1780-90s

6

Rudolf Wolf over time published several versions of his sunspot series

Compare his 1861 list with the modern official list

7

Rudolf Wolf’s ‘Relative’ Sunspot Number values changed over time…

Wolf started his own observations in 1849

0

20

40

60

80

100

120

140

160

4 5 6 7 8 9 10 11 12 13

R

ΔD'

Wolf 1861 List

Wolf 1875 and later Lists

1836-1848Schwabe

1849-1860Wolf

Range in Declination at Milan 1836-1919

25%

1861-1873Wolf

Wolf 1861 List

White dot:1874-1919

25% difference

Wolf noted that the points before 1849 fell consistently below the regression line for values after that time; he therefore decided to adjust the early values upwards

8

Comparing Wolf’s various lists we can trace the evolution of the sunspot number calibration

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

1740 1750 1760 1770 1780 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880

Evolution of Wolf Sunspot Numbers

W1861 / Rnow

W1875 / Rnow W1880 / Rnow

W1857 / Rnow

Staudacher

2x

25%

0

20

40

60

80

100

120

140

160

180

1740 1750 1760 1770 1780 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890

1861 1874 1882 and Now

W

Evolution of the Wolf Number

1 2 3 4 5 6 7 8 9 10 11

1857

0

2

4

6

8

10

12

14

1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000

rD'

Wolf's Einheitliche Deklination Updated with Modern Stations in Europe

Solar Cycle in Range of Diurnal Variation of Magnetic Declination

Doubling of Staudacher values. Raising all value before 1861 by 25%

Remember?

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Hoyt & Schatten: Group Sunspot Number RG = 12 Groups

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200

1750 1760 1770 1780 1790 1800 1810 1820 1830 1840 1850 1860 1870

1 2 3 4 5 6 7 8 9 10 11

Group Sunspot Number and 'Official' [Zürich, International] Sunspot Number

Group Zürich

0

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40

60

80

100

120

140

160

180

200

1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

11 12 13 14 15 16 17 18 19 20 21 22 23 24

Group Sunspot Number and 'Official' [Zürich, International] Sunspot Number

Group Zürich

Decent match after ~1875 [by design]. RGroup much lower than RWolf before that.

10

Having established

that the calibration of

the Wolf number is sound, we

can check the Group

number against the

same standard and find that RG is

too low before ~1877

RG = 17.123 rD - 117.1

R2 = 0.9275

RZ = 22.276 rD - 154.01

R2 = 0.9202

0

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40

60

80

100

120

140

160

6 7 8 9 10 11 12 13

rD'

RYearly Means 1841-1876

RZ = 21.69±0.81)*rD= ===- (145.0±7.2)

rD = (6.45±0.32) + ==(0.046±0.002)*RZ

RG = 23.657 rD - 157.91

R2 = 0.8544

RZ = 23.165 rD - 154.34

R2 = 0.8922

0

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40

60

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6 7 8 9 10 11 12 13

R

rD'

Yearly Means 1877-1919

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Resolving Difference Between H&S GSN and Wolf SSN

obs name lat long interval WDC Washington D.C. 38.9 283.0 1840-1842 DUB Dublin 53.4 353.7 1840-1843 MNH Munchen 48.2 11.6 1841-1842 PGC Philadelphia 40.0 284.8 1840-1845 SPE St. Peterburg 60.0 30.3 1841-1845 GRW Greenwich 51.5 0.0 1841-1847 PRA Praha 50.1 14.4 1840-1849 HBT Hobarton -42.9 147.5 1841-1848 MAK Makerstoun 55.6 357.5 1843-1846 KRE Kremsmunster 48.1 14.1 1839-1850 TOR Toronto 43.7 280.6 1842-1848 WLH Wilhelmshaven 53.7 7.8 1883-1883 GRW Greenwich 51.5 0.0 1883-1889 WDC Washington D.C. 38.9 283.0 1891-1891 PSM Parc Saint-Maur 48.8 0.2 1883-1899 POT Potsdam 52.4 13.1 1890-1899 COP Kobenhavn 55.7 12.6 1892-1898 UTR Utrecht 52.1 5.1 1893-1898 IRT Irkutsk 52.3 104.3 1899-1899

0

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1600 1650 1700 1750 1800 1850 1900 1950 2000

Sunspot Number Series

Wolf

Group

Eddy GSNSSN

0

10

20

30

40

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60

70

80

25 30 35 40 45 50 55

<rY > nT

<R>Rz

Rg before 1850

Rg after 1880

1.4*Rg before 1850

Sunspot Number as a Function of Diurnal Range

Multiplying GSN [Rg] by a factor 1.4 brings them up into good conformance with the SSN [Rz], open red diamonds

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0.7

0.9

1.1

1.3

1.5

1.7

1.9

1750 1770 1790 1810 1830 1850 1870 1890 1910 1930 1950 1970 1990 2010

Ratio RZ / RG for when RZ < 10

Wolf

Wolf's Reconstruction

Wolfer-Brunner

Mix

Waldmeier

SIDC

Hathaway

We can quantify the difference between RZ and RG for the different observers

17.5%

?

We now see clearly the factor 1.4 before ~1875. But there is another jump ~1945 when Max Waldmeier took over: the numbers since then are ~20% higher than the Wolfer-Brunner standard [pink]. Rz vs. rD also shows this.

>

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The ratio between the Zürich sunspot number and the sunspot area (Balmaceda et al.) also clearly

shows this ‘Waldmeier’ discontinuity:

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

RZ / SA0.732

Wolfer Brunner Waldmeier SIDC

Monthly Means

Histogram Ratios

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-20

0

20

40

60

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100

12010th Order Curve Fit10th Order Curve Fit

1874-1944

1945-2000

The jump in RZ is 21% in 1945 and was maintained by SIDC when they took over as they relied on the Swiss station Locarno as their reference observer. Lately, the influence of Locarno is diminishing because of the large number of contributing stations

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The pre-Waldmeier observers carefully documented the group count and spot count separately. This was lost with Waldmeier.

G.S

R=2*10+4=24Wolf’s last observation

X

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Wolf, Wolfer, and Brunner counted single spots as one, regardless of size

Wolfer

MWO

The large spot on 1920, Nov. 21 was counted as one spot by A. Wolfer

G.S

16

But Locarno counts larger spots with a higher weight

1

1

21

5

53 4553/45 = 1.18

Wolfer,Brunner

4

This increases the sunspot number

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After more than 20 years, Waldmeier reveals that he introduced a weighting scheme according to size

1968

Later the spots were weighted according to size: A pore was counted as one, a larger spot but still without penumbra got a statistical weight of 2, a small group-forming spot one of 3, and a larger of 5.

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Conclusions• It is possible to calibrate the sunspot number

using the diurnal variation of the geomagnetic field [as Wolf did himself]

• The group sunspot number should be increased by 40% before ~1875

• The Zurich sunspot number should be increased by 20% before 1945

• There has been no particularly Grand Maximum

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1750 1770 1790 1810 1830 1850 1870 1890 1910 1930 1950 1970 1990 2010

Wolf NumberGroup Number

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Comparison between SIDC and Keller/Friedli [with Wolf telescope]

0

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1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Keller, FriedliFraunhofer 64x

Weighting

SIDC, SIDC, SIDC

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0 20 40 60 80 100 120 140 160 180 200 220

R SIDC

R Keller

1996.0-2000.5

2000.6-Now

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The original telescope used by Wolf is still in use

Die Sonnenfleckenaktivität 1993.Keller, H. U., Mitt. Rudolf Wolf Ges., Jahrg. 2, Nr. 4, p. 3 - 13[…] In autumn 1993 a new series of sunspot counts with Wolf's portable telescopes has been commenced, aiming to verify the historical reduction factors k of these instruments compared with today's counting mode at the standard Fraunhofer telescope.

The sunspot-activity in the years 1976 - 1995.Keller, H. U.; Friedli, T. K.Mitt. Rudolf Wolf Ges., Jahrg. 3, Nr. 7, p. 1 - 46The paper contains the last twenty years of sunspot relative and group numbers as observed by the standard observers M. Waldmeier, A. Zelenka and H. U. Keller in Zurich. Starting with January 1996 a new series of sunspot countings called Swiss Wolf Numbers RS will be initiated using standard observations made by T. K. Friedli at the original Fraunhofer Refractor used by Wolf and an international network of professional and amateur astronomers.

The 80/1100 mm Fraunhofer Refractor (64x) used by Wolf, Wolfer, Brunner, Waldmeier, Keller, and (now) Friedli