AN ANALYTICAL MODEL TO CALCULATE THE ATMOSPHERIC CORRECTION 
' . ON INFRARED THERMAL SIGNALS (?) 
PIER GIORGIO BERARDI 
Istituto di Aerodinamica 
Università di Napoli 
P.le Tecchio 80125-Napoli 
ABSTRACT 
An analysis is presented to determine the radiative field in the atmosphe- 
re with its upwelling and downwelling components for an absorbing and emitting 
medium. The atmosphere behaviour in the infrared spectrum is modelled by means 
of Bignell formula. Being the radiative phenomena mainly restricted to the tro- 
posphere, the temperature and the volumetric absorption coefficient are assumed 
to depend on altitude linearly and exponentially respectively. The radiative 
field is obtained in closed form. It is possible, for a given atmosphere, to 
define an equivalent atmospheric temperature (T3), dependent on the altitude, 
which allows to compute the monochromatic inten§ity with the classical isother- 
mal model. The bounding values of the function T8 define three different surfa- 
ce temperature intervals with regards to the atmospheric correction. The model 
has been tested by using meteorological data. 
INTRODUCTION 
The knowledge of time-dependent temperature maps of earth surface is of 
significant importance in many scientific fields (1,2), often depending on the 
precision of the available data. 
In the thermal infrared window (10.5 - 12.5 um) the atmosphere, even un- 
der clear sky conditions, is not totally transparent for the infrared radiation: 
the atmosphere perturbations may change the observed surface temperature by se- 
veral degrees. The absorption and emission by the atmospheric costituents, main- 
ly by water vapor and carbon dioxide, does not only alter the radiative signal 
of earth surface, but it also causes a smoothing of the temperature field. 
Many atmospheric models, both numerical (LOWTRA-RADTRA) and/or analytical, 
have already been developed to predict the atmospheric temperature correction. 
In order to provide simple, but sufficiently accurate, correction formulas, ana- 
lytical models, such as those suggested by Prabhakara (3) and Becker (4), are 
based on the linearization of the radiative transfer equation, both for one 
channel method and for the two-channels method in two adjacent windows. These 
models, which to a certain extent are not related to the knowledge of the meteo- 
rological data, can become less accurate at high values of surface temperature; 
this happens for an example for the meteorological conditions considered in fig.l. 
Present work deals with prediction of the radiative field in the atmosphere 
considered as an absorbing and emitting medium and modelled by means of Bignell 
formula in the thermal infrared spectrum. Being the radiative phenomena mainly 
restricted to troposphere, the atmosphere is modelled by assuming the volumetric 
absorption coefficient and the temperature to depend on altitude exponentially 
and linearly respectively. The atmosphere is so described by four parameters : 
two can be easily measured at ground level, the others can be obtained by using 
real or estimated meteorological data. The radiative field, obtained in closed 
form, shows that it is possible, for a given atmosphere, to define an equivalent 
atmospheric temperature (TZ), dependent on altitude, which allows to compute the 
monochromatic intensity with the classical isothermal model. The atmospheric 
(°) under CNR Contracts 80.00788.88/SAS 800175. 
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