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The earth 
the mono- 
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= 
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b. anc ee 5 59, 5 0505 55 0 o D LN i 
l'lo, v) eI, * pl? 1-2 Es (n 4) (7) 
where E, (x) is the n-th order exponential integral function. For typical meteo- 
rologichl data, it happens that ny >> 1 and E4* 0. Therefore the upwelling in- 
tensity is given by : 
Ply) eel a 1% C1; 3) (8) 
3. ATMOSPHERIC MODEL 
To solve the radiative field in the atmosphere, the knowledge of 
the k and T-profiles is needed. Focusing the attention on the thermal infrared 
spectrum, the radiative behaviour of the atmosphere depends essentially on the 
water vapor content. Assuming the Bignell formula to predict the absorption 
coefficient as a function of pressure and of water vapor partial pressure and 
temperature, the k-profiles can be obtained as functions of the altitude by the 
meteorological data. The k-profiles show that the absorption coefficient decrea- 
ses strongly with the altitude and that the radiative phenomena is mainly limi- 
ted to the troposphere; in this layer the temperature decreases slowly almost 
linearly, as the related intensity of the radiation emitted by the atmosphere. 
This experimental evidence suggests an atmospheric model based on 
the assumption that the absorption coefficient and the temperature, as the re- 
lated intensity , decrease with altitude exponentially and linearly, respecti- 
vely : 
k(z) = ko exp (- bz) (9) 
I? (2) - I$ (15 czj (10) 
TS(z) - r8 (4 -x2)t5 E 
0 
The radiative behaviour of the atmosphere is so described by four 
1/b and 1/c, a measure of the effective layer involved in the ab- 
sorption and emission phenomena, respectively; k_, a measure of the mean free 
path of radiation photons; T^, the atmospheric temperature at ground level. The 
parameters T2 and k_ can be €asily measured at ground level, while the others 
can be obtaiRed by Using real or estimated meteorological data. Two dimension- 
less parameters can be derived : o = (1/b)/ (1/k_.), which characterizes the num- 
ber of m.f.p. of photons in the absorption layer? and s= (1/b)/ (1/c), which 
measures the relative importance of the two layers. 
parameters : 
4. ATMOSPHERIC CORRECTION FORMULAS 
Having assigned the functions k(z) and 12(z), it is possible to 
determine the radiative field. Considering for simplicjty the case e= 1 and ma- 
king the altitude dimensionless with respect to l/b, z  - z/(l/b), the upwelling 
intensity is given by : 
I'3(25, uos It +15 (1-7 -6 (z" + exp ( aexp (-2*)))(Es (0) - 
- Ey («exp (- z*))) on 
t= exp ( - o(l - exp (- z'))) (12) 
Defining an equivalent atmospheric intensity I2, the radiative field can be 
written in the same form derived for the isoth&rmal mode (8) . 
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