I am trying to get a good view of light wavelength distribution as a function of viewing angle, with a specific interest as $z \approx 90^\circ$ near the horizon (sunrise/sunset). Air mass coefficient values by viewing angle are well known and reasonably approximated, but what I cannot find is how wavelengths attenuate by air mass (for example, sunsets are red because blue is mostly adsorbed at the horizon).

AM0 defines the spectral irradiance without atmosphere (ie, in space) and it looks like this:

Altermatt Lecture:  The Solar Spectrum

(image source: Altermatt Lecture: The Solar Spectrum)

Question: How can I calculate the graph at "AM20" which is near the horizon using known AM0 data?

Given the AM0 spectra irradiance by wavelength (ie, from the ASTM G173-03 Reference Spectra), how can you approximate the resulting relative irradiance (or attenuation) as a function of wavelength and air mass coefficient? Mathematically, I'm looking for something that approximates this:

$ P^\prime(\lambda) = f(P(\lambda), AM) $


  • $ f() $ calculates the net irradiance adjusted for a given air mass coefficient. (Different wavelengths are adsorbed differently.)
  • $ P(\lambda) $ is the irradiance in units of $ \frac{W}{m^2\cdot \lambda} $ (Wm-2nm-1) with an air mass coefficient of 0 (AM0) based on known values.
  • $ P^\prime(\lambda) $ is the irradiance in units of $ \frac{W}{m^2\cdot \lambda} $ (Wm-2nm-1) after attenuating based on an arbitrary air mass coefficient.
  • $ AM $ is the air mass coefficient for which we want to adjust.

(NB: I'm new to this topic, if this is the wrong place for such a question, then please point me at the right SE community so I can move the post. Thanks!)


1 Answer 1


This paper covers that topic in detail:


Here is a 6am vs noon graph from the paper:

morning vs noon sun irradiance by wavelength

"Fig. 8. Early morning (6 am) relative irradiance of the sun is higher in the visible and NIR spectrum compared to midday exposure (noon). Calculations were made using the Simple Model ofthe Atmospheric Radiative Transfer of Sunshine (SMARTS), 2.9.5 model, available from NREL (National Renewable Energy Laboratory) and obtained in July 2015 at http://www.nrel.gov/rredc/smarts/about.html ."

  • $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Commented Jan 12, 2023 at 22:48
  • $\begingroup$ @Community, I'm not sure what to add... the graph speaks for itself! $\endgroup$
    – KJ7LNW
    Commented Jan 13, 2023 at 0:55

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