K-Coefficients For Sunspot Observations Vary On All Timescales By Up To A Factor Of Two

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The historical observations of sunspots are the primary data source for a wide variety of solar and solar-terrestrial studies where timescales of half a century to many centuries are important. All sunspot counts have the problem of how to normalize their counts and to prevent that normalization from drifting with time. The Zurich and International sunspot counts use a Standard Observer who is defined to be a constant for normalizing the counts from the many secondary observers. The observed counts from the secondary observers are all scaled individually to the Standard Observer with a scale factor called a K-coefficient that is calculated over various timescales from quarterly to yearly. I have collected massive amounts of data on K-coefficients from Brussels, Astronomische Mitteilungen Zurich, and the AAVSO. I find that all individual observers have their K values changing on all timescales from one month to 20 years, with the typical RMS for the variation being 10-20 percent yet with excursions of up to a factor of two. The K values for Standard Observers before they became 'standard' varied normally with many excursions of up to a factor of two in size. The Standard Observers receive no special training, so there is a strong expectation that their real K values will vary similarly even after they become the definition of 'standard'. Another realization is that the data reduction methods used for the International and Zurich counts force the published counts to faithfully follow the true K-coefficients of the lone Standard Observer. This point is proved by the K-coefficient data wherein the reported K values for all observers around the world systematically and simultaneously go up and down by 10-20 percent RMS with occasional large excursions. The unfortunate conclusion is that the normal variations of the K values for the Standard Observer will force the published counts to reflect these same variations which will then appear as errors in the sunspot record. The implication is that the Zurich and International sunspot counts has systematic errors on all timescales with a typical size of 10-20 percent and even up to a factor of two. These systematic errors can be removed from the Zurich and International counts by using the systematic variations of K-coefficients from the secondary observers to derive the true K-coefficient for the Standard Observer and then to repair all the published counts. [This research is funded by the National Science Foundation.]

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