(7) 
R54 
N 
X( T 4k - T4o)(T5k - T5 0 ) 
k=l 
N 
' T 4o) 2 
k=l 
then Eq.( 6 ) reduces to 
^ = R54 ® 
where X4 and X5, are the total atmospheric transmittances in Channels 4 and 5 of the AVHRR/2 and where the 
numerator and denominator on the right-hand side of Eqn. (7) represent, respectively, the covariance and the 
variance of brightness temperatures directly measured by the satellite in channels 4 and 5, with T 4 o and T 5 0 
being two temperatures of reference, this could be the mean temperature of the pixels considered in each channel 
or the temperature of a single pixel. 
2.1. Evaluation of Total Transmittance 
Another significant application of this technique consists in obtaining the atmospheric transmittance. Thus, 
assuming that the total transmittance Xk (k=4, 5) for channel k can be expressed as (Harris and Mason, 1992): 
^k = tkWater * ^kGas (?) 
where ikWater and tkGas are respectively the total water transmittance and the total transmittance due to the 
other gases (for exemple, O 3 , CO 2 , N 2 , N 20 » CH 4 etc.). They are given by 
Xk Water = Exp(-Ak W Water / COS 0) (10a) 
XkGas = Exp(-Gk W Gas / cos 0) (10b) 
in which 0 is the angle of observation; Ak and Gk are the band-average absorption coefficents in channel k, 
assumed to be independent of atmospheric temperature, for water vapor and other gases respectively; and W wa ter 
and W(}as are respectively the total effective contents of water vapor and other gases. 
Now, inserting Eq. (9) with Eqs.(lOa) and (10b) into Eq. ( 8 ), one gets: 
R 54 = Exp 
(G 5 - G 4 )*W Ga s * c -(A 5 - A 4 )*W W ater 
COS0 
Exp 
COS0 
(ID 
and 
X4 = A*R54® 
( 12 a) 
x 5 = A*R 54 ( b+ 1) 
( 12 b) 
The importance of Eqs. (12a) and (12b) lies in that they give a method to obtain the actual 
atmospheric transmittance with only the brightness temperatures measured by the satellite, through R 54 . 
22. Evaluation of Total Water Content W 
Water vapor in the atmosphere is an important constituent because it plays a significante role in the absorption 
and emission of radiative energy. Measurements of this constituent is important to increase the understanding of 
the biosphere-atmosphere interactions, the energy budget, and for monitoring climate change due to the 
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