Altermatt Lecture:   The Solar Spectrum


6.1:  The SMARTS software

The standard terrestrial spectra of the previous pages are calculated from the AM0 standard spectrum using the software SMARTS [11][19], which stands for a 'Simple Model of the Atmospheric Radiative Transfer of Sunshine'. This software was developed by Christian A. Gueymard and is available for free and is indeed user friendly. It gives you the opportunity to quantify atmospheric changes to the solar spectrum yourself without big efforts.

The mathematical principles of the calculations are as follows. Due to absorption, the intensity of sunlight decreases exponentially on its way through the atmosphere, described by the Beer-Lambert (or also called Bouguer) law. It assumes that a monochromatic light beam I is weakened by the amount of dI along its path through an infinitesimal length of dz, according to

Eq Beer-Lambert

where ρ is the density of air and k is the extinction coefficient. Integrating over a considerable length z we obtain

Eq Beer-Lambert integrated

This equation can be solved in two main ways:

  • with the assumption that the atmosphere as made up of stacked layers (like an onion), i.e. by discretization of k(λ, z) and ρ(z) into ki(λ, z) and ρi(z); the contribution of all layers is then summed up. A well-known model that follow this rigorous procedure is Modtran;

    MODerate resolution atmospheric TRANsmission model originated from the LOW resolution model LOWTRAN in 1989 (A. Berk, L.S. Bernstein, D.C. Robertson) and can be purchased here.
  • by parameterizing the entire atmosphere as a single layer, i.e. by taking z through the whole atmosphere and rewriting the equation as dimensionless transmittance Tatm:
  • Eq atmospheric transmittance
    where the air mass m and the optical thickness τ are:
    Eq for air mass m
    Eq for optical transmittance
    SMARTS is a well-done parametrization of m and τ(λ), not only for absorption, but also for scattering.

To use SMARTS yourself, download it from the National Renewable Energy Laboratory (NREL) in Golden, CO.

First, you need to register. Then, an email containing your username and password is emailed to you so you can login and download it as a zip file.

Unpack this zip file. A new folder will be created, containing all the necessary files. Feel free to change the name of this directory. Because the software will not register in your registry, you do not need administrator privileges on your computer to unpack the zip file or to run the program.

There is a Excel file in this directory. Just double-click it and then click on "Click here to start".

A grey configuration sheet appears where you may press the buttons to change the input parameters and the output data.

By default, the spectrum is written into the *.ext.txt file You may open it with Excel if you like to plot the data or use them for other plotting software. The input parameters are written into the *.out.txt file.

While most of the input parameters are rather self-explanatory, you need a deeper knowledge to make a realistic choice. A good source of this knowledge is [11] or [19], and the subfolder "Documentation" of your smarts folder contains pdf files that explain how to run SMARTS from Excel or from a text input file.


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