# Solar spectral irradiance at earth's TOA

1. Jul 11, 2010

### everetthitch

(just tried general astronomy board but no luck)

I'm trying to reproduce a plot of Sun's black-body behavior like this one:
http://en.wikipedia.org/wiki/File:Solar_Spectrum.png
Problem is, after I convert the black-body radiance to irradiance, its curve is way too high as compared with measurement. The measurement data is taken from:
http://rredc.nrel.gov/solar/spectra/.../ASTMG173.html [Broken]

The top of atmosphere (TOA) irradiance at Earth's distance is obtained in the following way:
where:
c=3e8 m/s (speed of light)
h=6.625e-34 Joul Second (Planck's)
kB=1.38e-23 Joul/Kelvin (Boltzman's)
omega=pi*r_sun^2/D_sun_earth^2 (Sun disk solid angle as seen from Earth)
D_sun_earth=1.496e11 m (1AU)
Finally irradiance is E=L*omega (W/m^2/nm) (and one needs to multiply 1e9 to be in nm)

My curve is roughly twice above the measurement, so if I do:
E=L*omege*cos(67-deg)
I can get something close to the picture in the wiki link. This 67-deg is roughly Earth's spin inclination. However I really doubt multiplying cos(67-deg) makes sense, as we are talking about TOA irradiance, not anywhere on Earth surface.

What I'm missing here?

Thanks!

Last edited by a moderator: May 4, 2017