Solar spectral irradiance at earth's TOA

[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

The top of atmosphere (TOA) irradiance at Earth's distance is obtained in the following way:
radiance (W/m^2/nm/Sr) L=2*h*c^2/(lamda^5*exp(h*c/(kB*lamda*T)-1))
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!

 

[zmike]

It's possible that you are missing some important factors when calculating the TOA irradiance. Have you considered the effects of atmospheric absorption and scattering? Depending on the wavelength of your radiation, these two processes can significantly reduce the amount of radiation reaching the Earth's surface. Additionally, the angle of incidence of the radiation can also play a role in how much is absorbed or scattered. It might be worth looking into these factors to see if that is the cause of your discrepancies.

 

[Huyen401]

Hi there! Sorry to hear you didn't have any luck on the general astronomy board. I don't have expertise in this area, but I did some research and here are some suggestions that may help you figure out what you're missing:

1. Double check your calculations and make sure all the units are correct. It's easy to make a mistake with all those different units involved.

2. Check your assumptions. Are you assuming a perfect black body for the Sun? Are you taking into account any atmospheric effects or absorption?

3. Look for other sources of data or information. Maybe there are other measurements or studies that can help you validate your results.

4. Consider reaching out to experts in the field for their advice. You can try posting on other astronomy forums or even contacting a university or research institute for assistance.

I hope this helps and good luck with your project!