Radiative transfer to space affected by atmosphere?

[Mapes]

I'm trying to model radiation losses from a flat surface facing the sky at night. If we ignore radiative absorption/emission in the atmosphere, the heat flux is the well-known

$$Q=\epsilon\sigma(T_s^4-T_\infty^4)$$

where we have the emissivity, the S-B constant, the temperature of the surface, and where I would think $T_\infty$ is the effective temperature of outer space, 3K.

How does the presence of the atmosphere affect this model? How have other researchers dealt with this complication?

 

[russ_watters]

The IR transparency of the atmosphere is dependent on humidity. It would be a significant complication. I suppose you could get a reasonable estimate based on the view of Earth down from the top: http://www.goes.noaa.gov/ECIR4.html

With a known surface temperature and a measured temperature through the atmosphere, you can estimate the effect of sky transparency.

 

[Andy Resnick]

It's pretty easy: the emissivity is a function of wavelength. Becasue of conservation of energy, the emissivity = absoprtion. The heat transfer equation simply turns into an integral over wavelength.

The atmospheric absoprtion depends on pretty much everything, there's good computational models (LOWTRAN/MODTRAN/HITRAN) out there, some of which are public domain.

 

[GT1]

I'm trying to model radiation losses from a flat surface facing the sky at night. If we ignore radiative absorption/emission in the atmosphere, the heat flux is the well-known

$$Q=\epsilon\sigma(T_s^4-T_\infty^4)$$

where we have the emissivity, the S-B constant, the temperature of the surface, and where I would think $T_\infty$ is the effective temperature of outer space, 3K.

How does the presence of the atmosphere affect this model? How have other researchers dealt with this complication?

On most of the heat transfer calculations I've seen the sky temperature on a clear night was taken as 230K.