An Old and New Version of a Series of Wolf Numbers: Consistency of the Reliable and Instrumental Parts of Rows

Abstract

The Zurich row of average monthly numbers of Wolf W (W = Wrest U Wtool) consisting of the average monthly values restored by Wolf on sketchy observations Wrest (the restored row from 1749 to 1849), and a number of the regular observations Wtool from 1849 to our days (a reliable row). The paper examines the statistical parameters of long fragments without detail their "complex" history and the characteristics of the allocated intervals are compared. Highlighting "long" and "short" cycles for Wtool allows you to parameterize some characteristics and approximate their empirical dependence. These dependencies are used to assess the parameters of the Wrest series and their contradictions have been noted. Options for correcting the length and "power" of the restored series are offered.

Correction of Mean Values of Re-Established Cycles With Respect to the Certain Part of Wolf Number Series (Version V.1)

“…For the group of re-established cycles G0, these parameters equal to 1209 (= ΣТ 0 , months), 56713.65 (= ΣSq 0 ), 46.91 (~w 0 ). The classification of cycles with respect to their duration ("long" cycles with Тc>133 months and "short" ones with Тс<133 months) allowed for parametrisation and approximation of characteristics of certain cycles groups [5]. While projecting the "rules" obtained for G1÷G6 groups onto the G0 one, the discordance between the duration and the "energetics" of the re-established series has been determined, and the necessity for the correction of the time structure of the Wrest series firstly (e.g., the relation between the "long" (N L L ) and "short" cycles) has been pointed out.…”

“…One shall rely upon the relation of w = ΣSq/ΣТc to the number of "long" cycles in the group N L L (Fig. 1), where the relationship between ΣТc(N L ), ΣSq(N L ) and N L for groups of 9 certain cycles each were taken from the paper [5]. This relationship shall be used for the correction of mean values of cycles of the G0 group.…”

“…Additionally, cycles 1, 5 and 7 have abnormally long growth branches -more than half of the cycle. Moreover, the series' interval estimations have demonstrated the inconsistency of parameters of the Wrest series [5].…”