Solar Physics

, Volume 277, Issue 2, pp 417–430

Correlation Between the Sunspot Number, the Total Solar Irradiance, and the Terrestrial Insolation


  • A. Hempelmann
    • Hamburger SternwarteUniversität Hamburg
    • Institut für PhysikTU Dortmund

DOI: 10.1007/s11207-011-9905-4

Cite this article as:
Hempelmann, A. & Weber, W. Sol Phys (2012) 277: 417. doi:10.1007/s11207-011-9905-4


Our study deals with the correlations between the solar activity on the one hand and the solar irradiance above the Earth’s atmosphere and at ground level on the other. We analyzed the combined ACRIM I+II time series of the total solar irradiance (TSI), the Mauna Loa time series of terrestrial insolation data, and data of terrestrial cosmic ray fluxes. We find that the correlation between the TSI and the sunspot number is strongly non-linear. We interpret this as the net balance between brightening by faculae and darkening by sunspots where faculae dominate at low activity and sunspots dominate at high activity. Such a behavior is hitherto known from stellar analogs of the Sun in a statistical manner. We perform the same analysis for the Mauna Loa data of terrestrial insolation. Here we find that the linear relation between sunspot number and insolation shows more than 1% rise in insolation by sunspot number variations which is much stronger than for the TSI. Our conclusion is that the Earth atmosphere acts as an amplifier between space and ground, and that the amplification is probably controlled by solar activity. We suspect the cosmic rays intensity as the link between solar activity and atmospheric transparency. A Fourier analysis of the time series of insolation shows three dominant peaks: 10.5, 20.4, and 14.0 years. As a matter of fact, the cosmic rays data show the same pattern of significant peaks: 10.7, 22.4, and 14.9 years. This analogy supports our idea that the cosmic rays variation has influence on the transparency of the Earth atmosphere.


Atmospheric extinctionCosmic raysIntegrated Sun observationsSolar cycle, observations

Copyright information

© Springer Science+Business Media B.V. 2011