.diance may be 
(3) 
z ) is the atmo- 
le. Monochro- 
gained. When 
the monochro- 
with the filter 
ed is generally 
sible to use an 
lat are close to 
approximation 
hat is, define, 
(4) 
raging schemes 
action and the 
ed here and we 
(5) 
irelength A and 
describing the 
iometry. How- 
atures because 
tain a method- 
ust be applied. 
e. By making 
îese dependen- 
he précipitable 
(6) 
Taking values for &a= 0.12 cm 2 g -1 and 17=1.4 g cm -2 which are typical for 11 fi m radiation in 
a dry continental atmosphere, the variation of t, with view angle, 6 has been calculated and 
is shown in Figure 1. For comparison we also show on Figure 1 values of the transmittance 
calculated using the LOWTRAN-7 atmospheric radiance/transmittance code (Kneizys et al., 
1986) with measured radiosonde profiles. 
Figure 1: Variation of total atmospheric transmittance with view angle. 
The model Calculations with radiosonde profiles fit (7) quite well. A further approximation 
can be made, when the argument of (7) is small, 
kxU 
cos 6 
( 8 ) 
This approximation underestimates the transmittance and it is better to use ( 8 ) with a weighted 
absorber amount, U* such that, 
IT = aU, (9) 
where a is a constant and 0 < a < 1. Curves derived using ( 8 ) with the modifcation of (9) are 
also shown in Figure 1 for a=1.0 (dashed) and a=0.9 (dotted). 
2.2 Atmospheric radiance. 
Equation (3) shows how the upwelling atmospheric radiance contributes to the radiances re 
ceived at the sensor. When the atmosphere is horizontally homogeneous, the variation of I a 
with 6 should be predictable from a measurement of the zenith value of I a . LOWTRAN-7 
calculations were also performed to calculate I a from radiosonde data. Figure 2 shows the 
variation of I a with zenith angle for 11 /¿m and 12 /zm radiation. Since the atmospheres used in 
the calculation were not exactly the same, some variation is caused by differing water vapour 
amounts. The variation follows quite closely a relation of the form, 
/a(M) = /«(A,0)^- 
— exp {— b{U) sec 0}] 
[1 - exp {-b(U)}\ 
( 10 ) 
The parameter b(U) depends on the total précipitable water (U) and may have a small depen 
dence on wavelength. Curves derived from (10) are also shown on Figure 2.