The standard terrestrial spectra of the previous pages are calculated from the AM0 standard spectrum using the
software SMARTS , 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
where ρ is the density of air and k is the extinction coefficient. Integrating over a considerable
length z we obtain
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:
where the air mass m and the optical thickness τ are:
SMARTS is a well-done parametrization of m and τ(λ), not only for absorption, but also for
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  or , 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.