Theoretical and Applied Climatology

, Volume 119, Issue 3–4, pp 465–479 | Cite as

Estimating probability distributions of solar irradiance

  • A. Voskrebenzev
  • S. Riechelmann
  • A. Bais
  • H. Slaper
  • G. Seckmeyer
Original Paper


In the presence of clouds the ability to calculate instantaneous spectral irradiance values is limited by the ability to acquire appropriate input parameters for radiative transfer solvers. However, the knowledge of the statistical characteristics of spectral irradiance as a function of season and time of the day is relevant for solar energy and health applications. For this purpose a method to derive the wavelength dependent probability density functions (PDFs) and its seasonal site variability is presented. In contrast to the UVB range, the derived PDFS at three stations in Europe (Bilthoven, Garmisch-Partenkirchen and Thessaloniki) show only minor wavelength dependence above 315 nm. But there are major differences of the PDFs that are attributed to the site specific cloud climatology at these stations. Furthermore the results suggest that the previously described relationship between air mass and bimodality is the consequence of seasonal cloud variations. For Thessaloniki it is shown that the pyranometer sample spread around the cloudless value is proportional to the secant of the solar zenith angle and therefore scales according to air mass. Cloud amount observations are utilized to associate the local maxima of the multimodal PDFs with rough cloudiness states confirming the already established interpretation of broadband data for spectral data as well. As one application example the likelihood of irradiance enhancements over the clear sky case due to clouds is assessed.


Spectral solar irradiance Solar energy Cloud Probability Modification factor Kernel density estimation 



We appreciate the helpful suggestions and data regarding the aerosol parametrization contributed by Bernhard Mayer (Munich, Germany). Further we would like to thank Greg Bodeker of Bodeker Scientific for providing the combined total column ozone database.


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Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  • A. Voskrebenzev
    • 1
  • S. Riechelmann
    • 1
  • A. Bais
    • 2
  • H. Slaper
    • 3
  • G. Seckmeyer
    • 1
  1. 1.Institute of Meteorology and ClimatologyUniversity of HannoverHannoverGermany
  2. 2.Laboratory of Atmospheric PhysicsAristotle University of ThessalonikiThessalonikiGreece
  3. 3.Laboratory for Radiation ResearchNational Institute of Public Health and the EnvironmentBilthovenNetherlands

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