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
Also occasionally referred to as the Wolf, Zürich, or Brussels sunspot number.
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.
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.
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 ).
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).
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).
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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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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DOI: https://doi.org/10.1007/s11207-015-0841-6