radiation leaving surface = eoBl(To)

eo = surface emissivity (a number between 0 and 1)

Bl(T) = the Planck function

surface radiation reaching satellite = eoBl(To)to

to = atmospheric transmittance (a number between 0 and 1)


radiation leaving layer i = eiB l(Ti)

radiation from layer i reaching satellite = eiB l(Ti)ti

total from all atmospheric layers = S eiB l(Ti)ti

satellite-measured radiance = eoBl(To)to + S eiBl(Ti)ti

(This is one form of the Radiative Transfer Equation)

weighting function = W i º eiti

satellite-measured radiance = eoBl(To)to + S W iBl(Ti)


Note: Changing ei changes the vertical location but not the shape of W i

Window Channels

If eo » 1, then S W i » 1 - to

So in a "window" ( to > 0) ...

satellite-measured radiance » Bl(To)to + Bl(TA)(1 - to)