temperature correction (AT), defined as the difference between the observed sur
face temperature (T) and the surface radiative temperature (T.) will be negati-
ve (positive) if T. » T; (Ts « T2). With increasing altitude," T? tends to an
asymptotic value (8 €, This ‘value and that one correspondifig to a vanishi-
ng atmosphere layer (T8 0)» which coincides with the atmospheric temperature | where I
at ground levél, define thee different surface temperature intervals with re- rologic
gards to the atmospheric correction : if T PS Tao AT can be negative or tensity
positive, depending on the altitude; if T. > Te (15 Td): AT will be ne-
gative (positive), whichever is the altitüde. |
2. ANALYSIS
The atmosphere is considered to be a one-dimensional plane layer of
thickness H, bounded at the bottom by the earth surface. The thermodynamic pa- the k a
rameters which describe the atmosphere are supposed to vary only with the al- spectru
titude. Although the radiation propagates in all directions of the three dimen- water v
sional space, the problems remains one-dimensional by means of the hypothesis coeffic
on the dependence of the thermodynamic parameters on altitude. tempera
The medium is considered radiatively absorbing and emitting. The earth ans
surface is assumed to be a lambertian one and is characterized only by the mono- ted to
chromatic emissivity e (p = 1 - e , in the hypothesis that the Kirchoff law li 1
is valid) y y y near
In order to solve the radiative field, the monochromatic intensity the ass
is divided in two components (5) : IT (z, u > 0), the upwelling component and lated i
I, (z, u <0), the downwelling one, bing z the altitude and y the cosine of the vely :
observation angle. s
The quasi-steady radiation transfer equation, omitting for sake of
simplicity the subscript v , is
a sn wiqatq* o] (1)
3 peo paramet
Mido, Jo= e I; 2^55 [591 (o? yt3u*^ q^* sorptio
S 0 path of
- 2 à > paramet
u di“ /%dz = kn ol" = 1") (2) can be |
I SH. ).220 jew pa
er of |
where I is the Planck function, k and n are the monochromatic absorption coef- measure:
ficient and the refraction index respectively (for gases n = 1). In the infra-
red spectrum, the incoming solar radiation at z = H, that is I^ (H, u), is con-
sidered negligible, so that only the IT field is coupled to the I~ one.
The formal solution of equations (1 - 2) is :
F ng determi:
1-9(0, u) = T I? (T (n )Jexp (-^m7 y) d'nt/ u (8) king th:
E 1 5 intensi!
157(95598^g I, +2 of, I ^(o,"u*) Aqu (4) rt (z*,
I* (07,74) &I* (0507) $47 I9 (T (8*)) exp (-^ (n -m)/u y da" /v/(8) =f ik
n (z)%= st k(z* ) dz 3 Ny = nH)"; “+{("n) = exp (="n/ 1) (6) ez
where n is the dimensionless optical path in the z-direction. Defining
written
If the atmosphere is isothermal, the relation (4) becomes :
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