Solar Physics

, Volume 280, Issue 1, pp 205–221 | Cite as

A Comparison of the 10.7-cm Radio Flux Values and the International Sunspot Numbers for Solar Activity Cycles 19, 20, and 21

  • Robert A. GreenkornEmail author


A nonlinear analysis of the daily 10.7-cm radio flux values for each of Solar Cycles 19, 20, and 21 is used to determine if the results match those of the International Sunspot Numbers for each of these cycles. Fractals and chaos are described and a brief review of utilizing fractals and chaos is given. The origin of the 10.7-cm radio flux is discussed and a short review of recent work discussing its measurement and its relation to the international sunspot number and other proxies for solar activity cycles given. The parameters used to describe chaos for the 10.7-cm radio flux are discussed. The length of the data sets for either statistical analysis or nonlinear analysis of the 10.7-cm radio flux values is considered. These results indicate that the 10.7-cm radio flux values appear to be stochastic for Cycle 19 and chaotic for Cycles 20 and 21. The International Sunspot Numbers show similar behavior for these three cycles. A day-by-day comparison of the dimensionless 10.7-cm radio flux values and the dimensionless International Sunspot Numbers differences shows a linear trend. The results remain consistent in that the 10.7-cm radio flux values indicate, as did the International Sunspot Numbers, that there is a transition from stochastic behavior for Cycle 19 to chaotic behavior in Cycles 20 and 21. The day-by-day comparison of the 10.7-cm radio flux values and the International Sunspot Numbers emphasizes that the 10.7 cm radio flux values are responding to the magnetic field associated with the sunspots.


Radio flux Sunspots Activity cycles Chaos 



The values of the International Sunspot number [R i] are from the Solar Influence Data Centre (SIDC). The values of the 10.7-cm radio flux are from the radio flux data in “Solar Variability Affecting Earth,” National Oceanic and Atmospheric Administration (NOAA) CD Rom “NGDC-05/1”. Cycle times are from the NOAA/National Geophysical Data Center. Calculation of Lyapunov exponents, optimum time lag, global embedding dimension, local dimension, correlation sum, and dimension D 2 were calculated using cspW a set of algorithms in “Tools For Dynamics” provided by H.D.I. Abarbanel.

Supplementary material

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11207_2012_43_MOESM2_ESM.xls (1.2 mb)
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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.School of Chemical EngineeringPurdue UniversityWest LafayetteUSA

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