+, + 
Pu la + 12 (1 aed ; 12 =. 19 (zo) (13) 
20 797 G* cexp (a exp (25) (E, (a) - E, (n enp(-2*)) — (M) 
The equivalent atmospheric intensity depends on the altitude, that is on the 
layer of atmosphere between the earth surface and the sensor. 
The Planck function can be linearized and the relation (13) can be rewritten 
to give an explicit formula for the temperature field : 
T (2 #dorodtotoside (dar Tu NES enr de 12) (15) 
Alstol pelo ola ul de agent? (16) 
where the equivalent atmospheric temperature (1%) is the value attained at alti- 
tude z, ; again T8 depends on the altitude of the sensor. For zt<< 1l, T8 reco- 
vers the mean arithmetic temperature of the layer . For zt >>1, Ta tends to 
an asymptotic value T2, ; this temperature is practically reached at altitudes 
typical of the upper Boundary of the troposphere, being so confirmed a posterio 
ri that the radiative phenomena are restricted to troposphere. 
The atmospheric temperature correction will be positive or negative according 
the sign of (72 - T.) : AT will be negative (positive), if T,» T8 (T,« 13). 
The function ^ T2 (2) is bounded by the values TE, and TA, ättaîned ât z°> » 
ayers- and z > 0, respectively, (ia. coincides with the ätmospheF{c temperature at the 
ground level). The values of°T8 and 12 , related to a given atmosphere, defi- 
ne three different surface temBerature intervals with regards to the atmosphe- 
ric correction ::if 12 < T Ta AT can be negative or positive, depending on 
the altitude; if T,- o (T= T )s AT will be negative (positive), which- 
6) ever is the altitude. 
A preliminary statistical analysis has been performed to control the 
k-profile hypothesis on the basis of meteorological data measured by Air Force 
Meteorological Service in Rome at midday from Ist May to 31st August 1977. For 
each day the deviations of the experimental data from the calculated exponen- 
tial profile have been obtained at ten different isobaric levels (from 1000 
mb to 300 mb). The results show that the deviations have a Gaussian distribu- 
tion at each level (the regression coefficient on probability paper is always 
greater than 0.96), with relatively small values of the means (near to zero) 
and of the standard deviations. The analysis seems to prove a aood adequacy 
of the proposed model. 
The model has been finally applied to the same meteorological conditions con- 
sidered in the work of Nieuwenhuis (6), corresponding to midday of July 31, 
1978 in Netherlands. The atmospheric temperature corrections obtained by the 
present method are reported in fig. 1 and compared with the numerical results 
of ref. 6. The behaviour and the values of the calculated data are essential- 
ly the same of the RADTRA numerical ones. Present data seem to be more accura- 
te, with respect to numerical results, than those calculated by Nieuwenhuis with 
Becker model, especially at high values of the surface temperature. Some devia- 
tions, that can be noticed in the first two kilometers of the atmosphere, are 
due to local perturbations that cannot be taken into account by the present 
simplified model. 
An improvement of accuracy can be obtained by simple applying the 
present method twice, to a first layer (0 + 2.000 m) and to a second one 
(2.000 - 11.000 m) (see curve "two layers" of fig. 1), but in this procedure 
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