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The Discontinuity Circa 1885 in the Group Sunspot Number

  • Sunspot Number Recalibration
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Abstract

On average, the international sunspot number (\(R_{\mathrm{I}}\)) is 44 % higher than the group sunspot number (\(R_{\mathrm{G}}\)) from 1885 to the beginning of the \(R_{\mathrm{I}}\) series in 1700. This is the principal difference between \(R_{\mathrm{I}}\) and \(R_{\mathrm{G}}\). Here we show that this difference is primarily due to an inhomogeneity in the Royal Greenwich Observatory (RGO) record of sunspot groups (1874 – 1976) used to derive observer normalization factors (called \(k\)-factors) for \(R_{\mathrm{G}}\). Specifically, annual RGO group counts increase relative to those of Wolfer and other long-term observers from 1876 – 1915. A secondary contributing cause is that the \(k\)-factors for observers who began observing before 1884 and overlapped with RGO for any years during 1874 – 1883 were not based on direct comparison with RGO but were calculated using one or more intermediary or additional observers. We introduce \(R_{\mathrm{GC}}\) by rectifying the RGO group counts from 1874 – 1915 and basing \(k\)-factors on direct comparison with RGO across the 1885 discontinuity, which brings the \(R_{\mathrm{G}}\) and \(R_{\mathrm{I}}\) series into reasonable agreement for the 1841 – 1885 interval (after correcting \(R_{\mathrm{I}}\) for an inhomogeneity from 1849 – 1867 (to give \(R_{\mathrm{IC}}\))). Comparison with an independently derived backbone-based reconstruction of \(R_{\mathrm{G}}\) (\(R_{\mathrm{BB}}\)) indicates that \(R_{\mathrm{GC}}\) over-corrects \(R_{\mathrm{BB}}\) by 4 % on average from 1841 – 1925. Our analysis suggests that the maxima of Cycles 10 (in 1860), 12 (1883/1884), and 13 (1893) in the \(R_{\mathrm{IC}}\) series are too low by ≈ 10 %.

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Notes

  1. Also occasionally referred to as the Wolf, Zürich, or Brussels sunspot number.

  2. Available at: http://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-indices/sunspot-numbers/group/archive/ . Recently Vaquero et al. (2015) have extensively revised the group number data base by incorporating additional observers, correcting others, and eliminating questionable data. For an example of each type of change, see Carrasco et al. (2013) for Hadden, Aparicio et al. (2014) replacing Aguilar and Merino with Ventosa, and Vaquero and Gallego (2014) for solar meridian observations made at the Basilica of San Petronio in Bologna, respectively.

  3. The annual \(R_{\mathrm{G}}\) values on the NGDC website that we use in this study do not agree exactly with those published in Appendix 2 of Hoyt and Schatten (1998a). Contributing reasons for this difference include: a) possible use of slightly different data bases, and b) use of daily averaging in Appendix 2 vs. monthly averaging for online values. As an example of a), the difference between the annual GSN value of 72.0 for 1610 given in Hoyt and Schatten (1998a) and the corresponding online value of 36.0 appears to result from an additional daily value of zero (albeit on 29 February) in the yearly (month × day) “filldata” matrix of Harriot in the calculation of the NGDC value. The year 1790 provides a marked example of the effect of monthly vs. daily averaging of the Hoyt and Schatten interpolated filldata files, with an \(R_{\mathrm{G}}\) value of 90.5 in Hoyt and Schatten (1998a) vs. 65.1 in the online version.

  4. In Figure 3 in Cliver et al. (2015), the observers Tacchini, Winkler, Catania, Quimby, and Guillaume are first scaled to Wolfer before the plotted ratios are calculated (see Willis et al. (2015) and slide 14 in http://www.leif.org/research/SSN/Svalgaard11.pdf ).

  5. We detected two other problems for the Hoyt and Schatten reconstruction for earlier years. In certain cases, they treated strings of zeroes in month × day observer filldata matrices as if they were days with no observations, i.e., days which should have been represented by −99 entries. Examples of this can be found in 1842, for which only Schwabe (No. 279) and Schmidt (No. 292) observed. The Schmidt filldata matrix shows zeroes from 5 – 19 May, which were treated as −99s in the determination of the daily \(R_{\mathrm{G}}\) values (see 17 – 23 December for a similar occurrence). Also in 1842, both Schwabe and Schmidt have −99 entries in their filldata files for 1 – 2 January and 30 – 31 December, while the daily \(R_{\mathrm{G}}\) matrix for this year shows values of 9 and 4 (29 and 29) for 1 – 2 January (30 – 31 December).

  6. Hoyt and Schatten (1998a, 1998b) used Horrebow as a primary observer in the 18th century and Galileo as a primary observer for the early years of the 17th century.

  7. The \(R_{\mathrm{I}}\), \(R_{\mathrm{IC}}\), and \(R_{\mathrm{BB}}\) (group count) series are available at: http://www.sidc.be/silso/datafiles . To compare \(R_{\mathrm{IC}}\) (\(S_{\mathrm{N}}\)) with the other time series, we multiplied it by 0.6 (Clette and Lefèvre 2015).

  8. Surprisingly, the ratio of \(k\)-factors we obtain for Wolf Small Telescope to Wolf Big Telescope (2.058) is only 1.01. This may reflect, at least in part, the mixing of Schwabe’s and Wolf’s observations (as well as observations from the big and small telescopes) from the 1850s by Wolf (Friedli 2015) that affect the Hoyt and Schatten data base. Because of this Svalgaard and Schatten (2015) did not use Wolf’s observations before 1860.

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Acknowledgements

Ed Cliver acknowledges helpful discussions with Leif Svalgaard, Frédéric Clette, and Laure Lefèvre. We thank David Willis and Matthew Wild and an unidentified referee for helpful comments. Alan Ling acknowledges support from AFRL contract FA9453-12-C-0231.

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Correspondence to E. W. Cliver.

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Sunspot Number Recalibration

Guest Editors: F. Clette, E.W. Cliver, L. Lefèvre, J.M. Vaquero, and L. Svalgaard

Appendix: Sunspot Number Time Series (1841 – 1980)

Appendix: Sunspot Number Time Series (1841 – 1980)

Year

RI

RIC

RG

RG*

RGCDU2

RGC

RBB

1841

36.7

38.0

26.6

24.2

24.0

34.4

33.6

1842

24.2

24.2

18.8

17.1

15.8

22.6

23.2

1843

10.7

10.9

8.2

7.5

6.4

9.2

9.1

1844

15.0

15.1

11.8

10.7

9.0

12.9

13.4

1845

40.1

39.5

29.8

27.1

26.8

38.4

37.9

1846

61.5

61.6

43.8

39.9

39.4

56.5

55.5

1847

98.5

99.8

58.0

52.8

54.2

77.7

85.3

1848

124.7

125.0

85.8

78.1

81.2

116.3

115.6

1849

96.1

109.5

83.7

76.2

82.9

118.7

107.7

1850

66.5

75.8

55.0

50.1

54.0

77.3

77.2

1851

64.2

73.2

58.1

52.9

58.7

84.1

77.9

1852

54.1

61.6

49.8

45.3

51.0

73.0

66.6

1853

39.0

44.5

35.6

32.4

36.6

52.5

50.1

1854

20.5

23.4

17.3

15.8

17.9

25.7

24.0

1855

6.7

7.6

4.5

4.1

4.6

6.6

9.3

1856

4.3

4.9

3.1

2.8

3.1

4.4

5.8

1857

22.8

26.0

17.4

15.8

18.0

25.8

32.0

1858

55.0

62.6

44.4

40.4

43.8

62.8

63.5

1859

93.9

107.0

75.6

68.8

79.4

113.5

107.2

1860

95.9

109.3

85.6

77.9

89.5

128.3

120.0

1861

77.2

88.0

70.7

64.4

75.1

105.4

97.8

1862

59.0

67.3

50.5

46.0

53.1

74.6

69.5

1863

44.0

50.1

40.9

37.2

43.4

60.9

59.9

1864

47.0

53.5

34.5

31.4

36.2

51.0

52.9

1865

30.4

34.7

22.6

20.6

22.7

32.5

32.2

1866

16.2

18.4

13.7

12.5

13.9

20.0

21.2

1867

7.3

8.3

6.2

5.6

6.1

8.9

9.9

1868

37.6

37.7

28.9

26.3

30.0

42.3

41.6

1869

74.1

74.2

62.3

56.7

64.4

90.9

85.2

1870

139.1

139.2

96.2

87.6

99.9

140.4

135.4

1871

111.1

111.2

86.9

79.1

84.7

119.7

123.7

1872

101.4

101.5

80.1

72.9

82.1

114.3

104.8

1873

66.0

66.1

51.7

47.1

50.4

71.8

72.3

1874

44.6

44.7

35.0

31.9

32.7

47.1

48.2

1875

17.0

17.0

15.5

14.1

14.4

21.2

22.1

1876

11.3

11.3

9.1

8.3

9.0

12.8

14.2

1877

12.4

12.4

8.5

7.7

8.2

11.6

11.9

1878

3.4

3.4

2.7

2.5

2.7

3.8

5.1

1879

6.0

6.0

4.4

4.0

4.4

6.2

9.2

1880

32.2

32.2

24.8

22.6

24.7

33.9

32.6

1881

54.3

54.3

45.2

41.2

44.9

61.1

55.8

1882

59.4

59.4

47.9

43.6

47.9

63.9

57.7

1883

63.7

63.7

54.7

49.8

54.5

71.9

64.1

1884

63.5

63.5

61.7

56.2

62.0

80.8

70.5

1885

51.8

51.8

47.3

43.1

47.4

61.1

56.0

1886

25.5

25.4

22.6

20.6

22.3

28.9

29.1

1887

13.1

13.1

12.7

11.6

12.5

15.9

16.3

1888

6.7

6.7

7.6

6.9

7.8

9.8

9.4

1889

6.2

6.2

5.8

5.3

5.6

6.9

7.2

1890

7.1

7.1

7.8

7.1

7.5

9.3

8.3

1891

35.7

35.7

38.9

35.4

38.0

46.6

43.0

1892

73.0

73.0

68.3

62.2

66.3

81.5

74.6

1893

85.2

85.2

87.9

80.0

84.8

102.4

93.3

1894

78.0

78.0

88.0

80.1

81.9

95.3

85.8

1895

63.9

64.0

69.2

63.0

64.0

74.6

66.3

1896

41.7

41.6

39.7

36.2

37.6

43.6

41.5

1897

26.2

26.3

30.6

27.9

29.0

33.1

31.5

1898

26.7

26.6

26.0

23.7

24.3

27.6

26.2

1899

12.1

12.1

12.3

11.2

11.7

13.2

13.2

1900

9.4

9.4

9.1

8.3

8.6

9.7

10.5

1901

2.7

2.8

2.5

2.3

2.3

2.6

3.3

1902

5.1

5.1

3.8

3.5

3.5

3.8

4.1

1903

24.4

24.5

24.1

21.9

22.4

24.3

22.2

1904

42.1

42.1

45.3

41.2

41.7

44.8

45.4

1905

63.3

63.3

61.0

55.5

55.9

60.3

54.6

1906

54.1

54.1

56.2

51.2

51.3

54.9

54.2

1907

61.7

61.7

61.4

55.9

56.3

59.9

57.3

1908

48.5

48.5

53.1

48.4

49.3

52.4

49.5

1909

43.9

43.9

46.4

42.3

42.5

44.9

42.1

1910

18.5

18.5

21.5

19.6

19.1

20.1

20.6

1911

5.7

5.7

8.5

7.7

7.3

7.6

8.0

1912

3.6

3.6

3.6

3.3

3.3

3.5

3.7

1913

1.4

1.4

1.6

1.5

1.3

1.3

1.6

1914

9.6

9.7

12.4

11.3

10.8

11.2

11.2

1915

47.4

47.4

50.5

46.0

45.0

46.4

42.2

1916

57.0

57.0

67.1

61.1

58.6

60.6

58.2

1917

104.2

104.2

110.1

100.3

102.4

104.6

95.4

1918

80.8

80.8

89.2

81.2

82.3

83.9

79.2

1919

63.5

63.4

71.6

65.2

66.2

67.9

65.8

1920

37.6

37.6

43.5

39.6

39.5

40.4

39.3

1921

26.1

26.1

28.7

26.1

26.6

27.2

26.6

1922

14.2

14.2

15.8

14.4

14.5

14.7

15.1

1923

5.8

5.8

6.9

6.3

6.3

6.4

7.0

1924

16.7

16.7

18.2

16.6

16.8

17.0

16.5

1925

44.4

44.4

51.2

46.6

46.8

47.1

46.5

1926

63.9

63.9

70.8

64.5

64.4

65.5

63.6

1927

68.8

68.8

77.6

70.7

70.5

71.3

71.8

1928

77.8

77.8

82.3

74.9

74.7

75.1

73.0

1929

64.9

64.9

74.4

67.7

67.5

66.7

65.1

1930

35.6

35.6

44.2

40.2

40.3

39.8

40.0

1931

21.1

21.1

26.0

23.7

23.8

23.6

24.6

1932

11.1

11.2

13.5

12.3

12.5

12.4

13.6

1933

5.5

5.5

5.9

5.4

5.5

5.5

6.8

1934

8.7

8.7

10.4

9.5

9.7

9.6

10.5

1935

36.1

36.1

42.8

39.0

39.1

38.6

40.0

1936

79.7

79.7

88.8

80.9

80.6

79.4

82.0

1937

114.4

114.4

120.6

109.8

109.1

107.5

113.1

1938

109.6

109.6

113.6

103.4

102.8

101.3

104.4

1939

88.8

88.8

97.3

88.6

88.2

86.8

93.5

1940

67.8

67.8

71.7

65.3

65.0

64.1

65.5

1941

47.5

47.5

49.9

45.5

45.4

44.7

44.7

1942

30.4

30.4

32.8

29.9

30.0

29.5

30.5

1943

16.3

16.3

15.5

14.1

14.4

14.2

14.6

1944

9.7

9.7

10.7

9.7

9.9

9.8

10.0

1945

33.2

33.2

37.3

34.0

34.0

33.5

33.6

1946

92.6

92.6

95.3

86.8

86.3

85.0

83.2

1947

151.6

128.8

144.9

131.9

131.0

129.0

122.3

1948

136.3

115.8

127.5

116.1

115.3

113.6

112.9

1949

134.7

114.4

129.3

117.7

116.9

115.2

112.4

1950

83.9

71.3

76.0

69.2

69.1

68.0

68.0

1951

69.4

59.0

58.3

53.1

53.0

52.2

51.4

1952

31.5

27.0

29.6

27.0

27.1

26.7

29.3

1953

13.9

12.1

13.6

12.4

12.5

12.3

13.6

1954

4.4

4.0

4.4

4.0

4.1

4.1

6.0

1955

38.0

32.5

38.1

34.7

34.7

34.2

34.9

1956

141.7

120.4

126.1

114.8

114.1

112.4

113.0

1957

190.2

161.6

165.9

151.1

150.0

147.7

147.6

1958

184.8

157.0

175.1

159.4

158.2

155.8

156.3

1959

159.0

135.1

149.5

136.1

135.2

133.2

131.2

1960

112.3

95.4

103.8

94.5

94.0

92.6

95.7

1961

53.9

45.8

49.1

44.7

44.8

44.1

47.4

1962

37.5

32.0

31.4

28.6

28.8

28.4

30.7

1963

27.9

23.9

24.5

22.3

22.5

22.1

23.8

1964

10.2

9.0

10.2

9.3

9.5

9.3

10.6

1965

15.1

13.2

14.6

13.3

13.5

13.3

14.6

1966

47.0

40.1

43.8

39.9

39.5

38.9

40.1

1967

93.8

79.7

95.8

87.2

86.3

85.0

85.3

1968

105.9

90.0

98.2

89.4

88.6

87.2

86.2

1969

105.5

89.6

96.0

87.4

87.0

85.7

87.7

1970

104.5

88.8

108.5

98.8

98.5

97.0

97.0

1971

66.6

56.6

73.5

66.9

66.8

65.8

66.3

1972

68.9

58.6

72.0

65.6

65.8

64.8

64.3

1973

38.0

32.5

39.3

35.8

36.0

35.4

35.6

1974

34.5

29.5

34.0

31.0

31.2

30.8

32.5

1975

15.5

13.5

15.1

13.7

14.0

13.8

14.4

1976

12.6

11.0

13.5

12.3

12.7

12.5

13.0

1977

27.5

23.6

    

27.9

1978

92.5

78.6

    

88.8

1979

155.4

132.1

    

137.1

1980

154.6

131.3

    

126.7

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Cliver, E.W., Ling, A.G. The Discontinuity Circa 1885 in the Group Sunspot Number. Sol Phys 291, 2763–2784 (2016). https://doi.org/10.1007/s11207-015-0841-6

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