cloud layer, can be written as

4

(3.11)

based on the original CIF (*Z *is the cloud base height). The total downwelling radiation

can also be written as

4

4

(3.12)

square fit to the data points. Calculations are based on a mid-latitude summer

atmosphere.

The term in parentheses is the atmospheric transmission below the cloud and *T*c (*K*) is

the cloud base temperature. The cloud emissivity is assumed to be one, implying the

cloud reflection and transmission are zero. Using a cloud emissivity of one and the cloud

base temperature (clouds radiate at a temperature slightly colder than the cloud base

temperature) will result in an overestimation of the emitted cloud radiance. This is offset

by the fact that the cloud reflection is assumed to be zero and therefore the cloud does not

reflect downward any of the earth-emitted radiance. Equating Equations (3.11) and

(3.12), we can re-derive the term in parentheses in Equation (3.11) by computing the

cloud contribution to the total downwelling radiation using either measured moisture and

atmospheric temperature profiles or the Geophysics Laboratory model atmospheres. The

atmospheric emissivity was calculated using the Geophysics Laboratory model

atmospheres and Equation (3.2) (and Equation [3.3] etc.). Next, the cloud radiance was

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