64 



EKDAHL AND KEELING 



> 

 Z 



LU 



Q 



_i 

 < 

 DC 

 h- 

 U 

 LU 

 Q. 

 ISl 



Q 

 LU 

 N 



DC 



o 



-z. 



PERIOD, years 



Fig. 9 Power spectrum of the sunspot record from 1700 to 1961, obtained 

 from a discrete Fourier transform of the data record via the transform 

 algorithm of Cooley and Tukey. 20 The transform terms were weighted to 

 correspond to the Hann data window 2 ' and converted to a power spectrum. 

 Two spectra, from the first and last 2 data, were averaged in order to make 

 use of all the data. 



where l// m - 85 years, l// - 11 years, and C { , C 2 , and C 3 are constants (or 

 vary only slightly over 85 years). Expanding this function gives 



S(t) = C] + C 2 + C 2 sin 27r/ t + C 3 sin 27r/ m t 



+ -C 3 [cos 27T(/o - f m )t - cos 27T(/ + / m )t] (2) 



Because the final term in Eq. 2 contains frequencies close to 1/11 years, the 

 long-period oscillation is well represented solely by the term C 3 sin 27r/ m t, as 

 would be the case if the 11-year cycle were ignored in Eq. 1. Thus in 

 contradiction to the conclusion of Lai and Venkatavaradan, " the long-period 

 cycle is properly treated as independent of the 11 -year cycle when considering 

 the attenuation of ' C variations. 



To determine whether or not these spectral components of the solar activity 

 can seriously affect the l C record, we will first consider the simplest possible 

 attenuating model, that of Grey and Damon, l ' in which a perturbation of 

 the C sources passes through a single atmospheric reservoir to a sink provided 



