# Radiative Transfer Equation (IR)

_{i,calc}=

*B*(

^{-1}_{}*R*)

_{i,calc}*R*=

_{i,calc}_{i}

*B*(

_{i}*T*) + '

_{s}_{i}

*H*'

_{i}_{i}(

*p*) cos(

_{s}_{0}) +

*B*(

_{i}*T*(

*p*)) (

*d*

^{u}

_{i}/

*d*ln

*p*) (

*d*ln

*p*) +

_{i}

^{u}

_{i}(

*p*)

_{s}*B*(

_{i}*T*(

*p*)) (

*d*

^{d}

_{i}/

*d*ln

*p*) (

*d*ln

*p*)

*B _{i}*(

*T*) is the Planck function evaluated at the effective channel wavenumber.

*H*is the channel averaged solar irradiance at the top of the atmosphere.

_{i}_{0}is the local zenith angle of the Sun.

'

_{i}is the channel averaged two path transmittance from the Sun to the surface to the satellite.

^{u}

_{i}(

*p*) is the atmospheric transmittance measured between

*p*and the top of the atmosphere for channel

*i*.

^{d}

_{i}(

*p*) is the atmospheric transmittance between

*p*and the surface for channel

*i*.

**Explicit retrieved parameters**

_{i} is the surface emissivity at _{i}.

*T _{s}* is the surface temperature.

*T*(

*p*) is the surface temperature profile.

_{i}is the surface spectral reflectivity at

_{i}.

'

_{i}is the surface spectral bidirectional reflectance of solar radiation at

_{i}.

**Implicit retrieved parameters** (* i.e.*, within
_{i} and '_{i}).

CO_{2}(*p*) is the carbon dioxide profile.

*q*(*p*) is the humidity (water) profile.

O_{3}(*p*) is the ozone profile.

CO(*p*) is the carbon monoxide profile.

CH_{4}(*p*) is the methane profile.

NO_{2}(*p*) is the nitrogen dioxide profile.