P p

where transmission is measured upwards from lower altitudes and thus increases from zero for z very small to 1.0 at the top of the atmosphere. Thus, summing the thermal emission from all the layers the total spectral radiance reaching the top of the atmosphere at z1 (where the optical depth is zero and thus the transmission is one) is

I,i (M) = Iyo T, (M, zo, zi) + which can be written as

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