# What is Wrong with the Group Sunspot Number and How to Fix it

код для вставкиWhat is Wrong with the Group Sunspot Number and How to Fix it Leif Svalgaard Stanford University (with help from many people) 2 March, 2012 1 The Problem: Two Sunspot Series Sunspot Number Series 200 Disagree 180 160 140 ~1882 Agree Wolf Group Eddy 120 100 80 60 40 20 0 1600 1625 1650 1675 1700 1725 1750 1775 1800 1825 1850 1875 1900 1925 1950 1975 2000 Researchers tend to cherry-pick the one that supports their pet theory the best вЂ“ this is not a sensible situation. We should do better. 2 The Ratio Group/Zurich SSN has Two Significant Discontinuities At ~1946 (After Max Waldmeier took over) and at ~1882 3 Weighting of sunspot count 223 227 228 231 232 233 234 235 3 4 13 4 4 6 9 3 1 1 1 1 1 1 1 1 8 46 11 223 227 228 231 232 233 234 235 3 4 13 4 4 6 9 3 1 1 6 1 2 4 4 1 8 46 20 126 100 26% inflated Unweighted count red 4 Removing the Recent one [+20%] by Multiplying Rz before 1946 by 1.20, Yields Leaving one significant discrepancy ~1882 5 The [Wolf] Sunspot Number J. Rudolf Wolf (1816-1893) devised his Relative Sunspot Number ~1856 as RWolf = k (10 G + S) [also RZ, RI, WSN] The k-factor serving the dual purpose of putting the counts on WolfвЂ™s scale and compensating for observer differences The Group Sunspot Number Douglas Hoyt and Ken Schatten devised the Group Sunspot Number ~1995 as RGroup = 12 G using only the number, G, of Groups normalized [the 12] to RWolf 6 But Groups have K-factors too Schaefer (ApJ, 411, 909, 1993) noted that with RGroup = Norm-factor G S Alas, as H&S quickly realized, different observers do not see the same groups, so a correction factor, K, had to be introduced into the Group Sunspot Number as well: RGroup = 12 K G [averaged over observers] And therein lies the rub: it comes down to determination of a K-value for each observer [and with respect to what?] 7 With respect to what? H&S compared with the number of groups per day reported by RGO in the вЂ�Greenwich Photographic ResultsвЂ™. The plates, from different instruments on varying emulsions, were measured by several [many] observers over the 100-year span of the data. H&S вЂ“ having little direct evidence to the contrary - assumed that the data was homogenous [having the same calibration] over the whole time interval. WeвЂ™ll not make any such assumption. But shall compare sunspot groups between different overlapping observers, assuming only that each observer is homogenous within his own data (this assumption can be tested as we shall see) 8 Reminding you of some Primary Actors 1849-1863 Johann Rudolf Wolf in Berne The directors of ZГјrich Observatory were: 1864-1893 Johann Rudolf Wolf (1816-1893) 1894-1926 Alfred Wolfer (1854-1931) 1926-1945 William Otto Brunner (1878-1958) 1945-1979 Max Waldmeier (1912-2000) Wolfer was WolfвЂ™s assistant 1876-1893 so we have lots of overlapping data 9 WolferвЂ™s Change to WolfвЂ™s Counting Method вЂў Wolf only counted spots that were вЂ�blackвЂ™ and would have been clearly visible even with moderate seeing вЂў His successor Wolfer disagreed, and pointed out that the above criterion was much too vague and instead advocating counting every spot that could be seen вЂў This, of course, introduces a discontinuity in the sunspot number, which was corrected by using a much smaller k value [~0.6 instead of WolfвЂ™s 1.0] вЂў All subsequent observers have adopted that same 0.6 factor to stay on the original Wolf scale for 1849-~1865 10 Wolf-Wolfer Groups Number of Groups: Wolfer vs. Wolf 9 Wolfer 8 Yearly Means 1876-1893 7 6 Wolfer = 1.653В±0.047 Wolf 5 R2 = 0.9868 Wolfer 4 3 2 80mm 64X 1 Wolf 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Number of Groups 12 10 Wolf*1.653 8 Wolfer Wolf 6 4 Wolf 37mm 40X 2 0 1865 1870 1875 1880 1885 1890 1895 11 The K-factor shows in daily values too 1883 Month 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 Average Day 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 Wolf G 3 3 3 3 2 2 2 2 2 2 4 3 4 4 6 6 5 3.29 Wolf S 4 6 6 5 3 3 4 4 4 4 8 9 12 10 12 16 15 7.35 To place on WolfвЂ™s scale with the Wolf R Wolfer G Wolfer S Wolfer R 34 7 29 99 36 11 29 139 36 7 31 101 35 8 30 110 23 7 18 88 23 7 40 110 24 7 41 111 24 5 37 87 24 6 35 95 24 5 32 82 48 4 55 95 39 4 60 100 52 5 91 141 50 5 62 112 72 7 82 152 76 6 88 148 65 8 81 161 40.29 6.41 49.47 113.59 x1.5 G Ratio S Ratio x0.6 80mm 60 1.95 6.73 68 12 Number of Groups: Wolfer vs. Winkler 9 Wolfer 8 Yearly Means 1882-1910 We can make the same type of comparison between observers Winkler and Wolfer 7 Wolfer = 1.311В±0.035 Winkler R2 = 0.9753 6 5 4 3 2 1 Winkler 0 0 1 2 3 4 5 6 7 Number of Groups 9 Again, we see a strong correlation indicating homogenous data 8 Winkler*1.311 7 Wolfer 6 5 4 3 Again, scaling by the slope yields a good fit Winkler 2 1 0 1880 1885 1890 1895 1900 1905 1910 13 Number of Groups: Wolfer vs. Quimby 9 Wolfer Yearly Means 1889-1921 8 And between Rev. A. Quimby [Philadelphia] and Wolfer 7 Wolfer = 1.284В±0.034 Quimby 2 R = 0.9771 6 5 4 3 2 Same good and stable fit 1 Quimby 0 0 1 2 3 4 5 6 7 Number of Groups 9 8 Quimby*1.284 7 6 Wolfer 5 The Rumrill data has been considered lost, but I have just recently found the person that has all the original data. 4 3 Quimby 2 1 0 1885 QuimbyвЂ™s friend H. B. Rumrill continued the series of observations until 1951, for a total length of 63 years. 1890 1895 1900 1905 1910 1915 1920 1925 14 Making a Composite Comparison Sunspot Groups and Greenwich Groups 10 Groups 9 8 7 6 Average Quimby* Wolfer Winkler* Wolf* 5 4 RGO* 3 Matched on this cycle 2 1 Year 0 1875 1880 1885 1890 1895 1900 1905 1910 1915 1920 Compare with group count from RGO [dashed line] and note its drift 15 Composite on Logarithmic scale Comparison Sunspot Groups and Greenwich Groups 10 Log Scale Groups 50% Average 1 1875 1880 1885 1890 1895 1900 1905 1910 1915 1920 Quimby* RGO* Wolfer Winkler* Wolf* Year 0 Note that the discrepancy between the composite and RGO approaches 50% 16 RGO Groups/Sunspot Groups Early on RGO count fewer groups the Sunspot Observers 17 Same trend seen in Group/Areas Spot Groups vs. Spot Areas 2500 0.060 RGO Groups/Areas^0.73 0.050 RGO Areas 2000 0.040 1500 0.030 1000 0.020 0.010 500 0.000 0 1875 1880 1885 1890 1895 1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 There can be several instrumental reasons for such a drift, but there is also a вЂ�proceduralвЂ™ reason: Early on, there was a significant fraction of days with no observations. H&S count these days as having a group count of zero. 18 Extending the Composite Comparing observers back in time [that overlap first our composite and then each other] one can extend the composite successively back to Schwabe: Comparison Composite Groups and Scaled Zurich SSN 14 Zurich 12 Composite 10 8 6 4 2 0 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 There is now no systematic difference between the Zurich SSN and a Group SSN constructed by not involving RGO. 1940 19 Why are these so different? Observer Wolfer, A., Zurich 2% diff. Wolf, R., Zurich Schmidt, Athens Weber, Peckeloh Spoerer, G., Anclam Tacchini, Rome Moncalieri Leppig, Leibzig Bernaerts, G. L., England Dawson, W. M., Spiceland, Ind. Ricco, Palermo Winkler, Jena Merino, Madrid Konkoly, Ogylla Quimby, Philadelphia Catania Broger, M, Zurich Woinoff, Moscow Guillaume, Lyon Mt Holyoke College K-Factors H&S RGO to Wolfer 1.094 1.117 1.135 0.978 1.094 1.059 1.227 1.111 1.027 1.01 0.896 1.148 0.997 1.604 1.44 1.248 1.21 1.39 1.251 1.603 1 1.6532 1.3129 1.5103 1.4163 1.1756 1.5113 1.2644 0.9115 1.1405 0.9541 1.3112 0.9883 1.5608 1.2844 1.1132 1.0163 1.123 1.042 1.2952 Begin End 1876 1876 1876 1876 1876 1876 1876 1876 1876 1879 1880 1882 1883 1885 1889 1893 1897 1898 1902 1907 1928 1893 1883 1883 1893 1900 1893 1881 1878 1890 1892 1910 1896 1905 1921 1918 1928 1919 1925 1925 K-factors 1.8 This analysis 1.6 1.4 1.2 1 H&S 0.8 0.8 1 1.2 1.4 1.6 1.8 2 No correlation Number of Groups 12 10 Wolf*1.653 8 Wolfer 6 4 Wolf 2 0 1865 1870 1875 1880 1885 1890 20 1895 Why the large difference between Wolf and Wolfer? Because Wolf either could not see groups of Zurich classes A and B [with his small telescope] or deliberately omitted them when using the standard 80mm telescope. The A and B groups make up almost half of all groups 21 The H&S K-factor Problem вЂў H&S calculated their K-factor for an observer to RGO using only days when there was at least one spot seen by the observer вЂў This systematically removes about the lower half of the distribution for times of low solar activity вЂў Thus skews the K-factors вЂў This is the main reason for the discrepancy between the two sunspot number series вЂў And can be fixed simply by using all the data as we have done here 22 Who Cares about This? http://lasp.colorado.edu/sorce/data/tsi_data.htm 23 Removing the discrepancy between the Group Number and the Wolf Number removes the вЂ�backgroundвЂ™ rise in reconstructed TSI I expect a strong reaction against вЂ�fixingвЂ™ the GSN from people that вЂ�explainвЂ™ climate change as a secular rise of TSI and other related solar variables 24 This is what I suggest TSI should look like 25 Following closely a recent re-evaluation of the SunвЂ™s open magnetic flux The minimal solar activity in 2008вЂ“2009 and its implications for longterm climate modeling C. J. Schrijver, W. C. Livingston, T. N. Woods, and R. A. Mewaldt GEOPHYSICAL RESEARCH LETTERS, VOL. 38, L06701, doi:10.1029/2011GL046658, 2011 26 What to do about this? A plug for our Sunspot Workshop: http://ssnworkshop.wikia.com/wiki/Home 27 Abstract We have identified the flaw in Hoyt & Schatten's construction of the Group Sunspot Number (GSN). We demonstrate how a correct GSN can be constructed using only the Hoyt & Schatten raw data without recourse to other proxies. The new GSN agrees substantially with the Wolf Sunspot number, resolving the long-standing discrepancy between the two series. Modeling based on the old GSN of solar activity and derived TSI and open flux values are thus invalidated. This will have significant impact on the Sun-climate debate and on solar cycle prediction and statistics. 28

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