Solar spectral irradiance at earth's TOA

1. Jul 11, 2010

everetthitch

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/am1.5/ASTMG173/ASTMG173.html

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)
r_sun=6.96e8 m (Sun's radius)
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!

2. Jul 11, 2010

Chronos

try square root.

3. Jul 11, 2010

everetthitch

That doesn't work, making the spectrum broader, let alone w/o any physical meanings...